IsolationForestSpark.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "import copy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "import pandas as pd\n",
    "\n",
    "indextitle = pd.Series(np.array([\"Apples\", \"Oranges\", \"Puppies\", \"Ducks\"]), name=\"merge\") \n",
    "column = [1., 2., 3., 4.]\n",
    "df = pd.DataFrame(index=indextitle)\n",
    "df[\"column\"] = column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "df.index.rename(\"merge\", inplace=True)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "random.randint??"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "class Node(object):\n",
    "    def __init__(self, lefttree, righttree, splitattr, splitvalue, path, size=-1):\n",
    "        self.left = lefttree\n",
    "        self.right = righttree\n",
    "        self.splitattr = splitattr\n",
    "        self.splitvalue = splitvalue\n",
    "        self.size = size\n",
    "        self.path = path\n",
    "\n",
    "\n",
    "def itree(X, path=[], e=0, limit=10):\n",
    "    '''\n",
    "    X: data set to construct the tree\n",
    "    e: current tree height\n",
    "    l: limit of the height of the tree\n",
    "    '''\n",
    "    m, n = X.shape\n",
    "    print(path)\n",
    "    \n",
    "    if e > limit or m <= 1:\n",
    "        # let size = m, the number of samples in the matrix\n",
    "        # if the node is the leaf or vide,  0<= m <= 1\n",
    "        return Node([], [], None, None, path, m)\n",
    "    \n",
    "    rnd_attr = random.randint(0, n-1)  # choose one attribute by idx\n",
    "    maxvalue = np.max(X[:, rnd_attr])\n",
    "    minvalue = np.min(X[:, rnd_attr])\n",
    "    rnd_split = random.random()*(maxvalue - minvalue + 1e-10) + minvalue  # get a value [minvalue, maxvalue)\n",
    "    \n",
    "    X_left = X[X[:, rnd_attr] < rnd_split]\n",
    "    X_right = X[X[:, rnd_attr] >= rnd_split]\n",
    "    e = e+1\n",
    "    path_left = path.copy() + [0]\n",
    "    path_right = path.copy() + [1]\n",
    "    \n",
    "    print(\"at height\", e, \"X --> Xleft.length =\", X_left.shape[0], \"Xright.length =\", X_right.shape[0])\n",
    "    \n",
    "    return Node(itree(X_left, path_left, e, limit), itree(X_right, path_right, e, limit), rnd_attr, rnd_split, path)\n",
    "    \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rng = np.random.RandomState(42)\n",
    "\n",
    "# Generate train data\n",
    "X = 0.3 * rng.randn(100, 2)\n",
    "X_train = np.r_[X + 2, X - 2]\n",
    "# Generate some regular novel observations\n",
    "X = 0.3 * rng.randn(20, 2)\n",
    "X_test = np.r_[X + 2, X - 2]\n",
    "# Generate some abnormal novel observations\n",
    "X_outliers = rng.uniform(low=-4, high=4, size=(20, 2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "[]\n",
      "at height 1 X --> Xleft.length = 197 Xright.length = 3\n",
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      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 0, 1, 1, 0, 1, 0]\n",
      "[0, 0, 0, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 1, 1, 0, 1, 1, 0]\n",
      "[0, 0, 0, 1, 1, 0, 1, 1, 1]\n",
      "[0, 0, 0, 1, 1, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 5 Xright.length = 8\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 0, 1, 0]\n",
      "[0, 0, 1, 0, 1, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 4 Xright.length = 4\n",
      "[0, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 1, 0, 0, 1, 0]\n",
      "[0, 0, 1, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 1, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 141 Xright.length = 9\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 53 Xright.length = 88\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 41 Xright.length = 12\n",
      "[0, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 34 Xright.length = 7\n",
      "[0, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 33\n",
      "[0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 7 Xright.length = 26\n",
      "[0, 1, 0, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 6 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 0, 1, 0, 0]\n",
      "at height 10 X --> Xleft.length = 2 Xright.length = 4\n",
      "[0, 1, 0, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 11 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1, 0, 0, 1]\n",
      "at height 11 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0]\n",
      "[0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 8 Xright.length = 18\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 0]\n",
      "at height 10 X --> Xleft.length = 2 Xright.length = 6\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 0, 0]\n",
      "at height 11 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 0, 1]\n",
      "at height 11 X --> Xleft.length = 3 Xright.length = 3\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0]\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 1]\n",
      "at height 10 X --> Xleft.length = 13 Xright.length = 5\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 1, 0]\n",
      "at height 11 X --> Xleft.length = 7 Xright.length = 6\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 1, 1]\n",
      "at height 11 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0]\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1]\n",
      "[0, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 5\n",
      "[0, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 1, 0, 0]\n",
      "[0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 1, 0, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 1, 1, 0, 0]\n",
      "[0, 1, 0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 1, 0, 0, 0, 1, 1, 1, 0]\n",
      "[0, 1, 0, 0, 0, 1, 1, 1, 1]\n",
      "at height 10 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 1, 1, 1, 1, 0]\n",
      "[0, 1, 0, 0, 0, 1, 1, 1, 1, 1]\n",
      "[0, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 8 Xright.length = 4\n",
      "[0, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 2\n",
      "[0, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 4\n",
      "[0, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 1, 0, 0, 1, 0, 0, 1, 0]\n",
      "[0, 1, 0, 0, 1, 0, 0, 1, 1]\n",
      "at height 10 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 0, 0, 1, 1, 0]\n",
      "at height 11 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0]\n",
      "[0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 0, 1, 1, 1]\n",
      "[0, 1, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 0, 1, 0]\n",
      "[0, 1, 0, 0, 1, 0, 1, 1]\n",
      "[0, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 1, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 1, 0, 0]\n",
      "[0, 1, 0, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 1, 1, 0]\n",
      "[0, 1, 0, 0, 1, 1, 1, 1]\n",
      "[0, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 77 Xright.length = 11\n",
      "[0, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 72 Xright.length = 5\n",
      "[0, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 9 Xright.length = 63\n",
      "[0, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 5\n",
      "[0, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "at height 10 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 1, 0]\n",
      "at height 11 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0]\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 1, 1]\n",
      "[0, 1, 0, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 1, 0, 1, 0, 0, 0, 1, 0]\n",
      "at height 10 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 0, 0, 1, 0, 0]\n",
      "[0, 1, 0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 0, 1, 1]\n",
      "at height 10 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 1, 0, 1, 0, 0, 0, 1, 1, 0]\n",
      "[0, 1, 0, 1, 0, 0, 0, 1, 1, 1]\n",
      "at height 11 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0]\n",
      "[0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1]\n",
      "[0, 1, 0, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 9 Xright.length = 54\n",
      "[0, 1, 0, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 7 Xright.length = 2\n",
      "[0, 1, 0, 1, 0, 0, 1, 0, 0]\n",
      "at height 10 X --> Xleft.length = 2 Xright.length = 5\n",
      "[0, 1, 0, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 11 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 1, 0, 0, 1]\n",
      "at height 11 X --> Xleft.length = 4 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0]\n",
      "[0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1]\n",
      "[0, 1, 0, 1, 0, 0, 1, 0, 1]\n",
      "at height 10 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 0, 1, 0, 1, 0]\n",
      "[0, 1, 0, 1, 0, 0, 1, 0, 1, 1]\n",
      "[0, 1, 0, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 51 Xright.length = 3\n",
      "[0, 1, 0, 1, 0, 0, 1, 1, 0]\n",
      "at height 10 X --> Xleft.length = 48 Xright.length = 3\n",
      "[0, 1, 0, 1, 0, 0, 1, 1, 0, 0]\n",
      "at height 11 X --> Xleft.length = 31 Xright.length = 17\n",
      "[0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 1, 1, 0, 1]\n",
      "at height 11 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0]\n",
      "[0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1]\n",
      "[0, 1, 0, 1, 0, 0, 1, 1, 1]\n",
      "at height 10 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 1, 0, 1, 0, 0, 1, 1, 1, 0]\n",
      "[0, 1, 0, 1, 0, 0, 1, 1, 1, 1]\n",
      "at height 11 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0]\n",
      "[0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1]\n",
      "[0, 1, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 1, 0, 1, 0, 1, 0]\n",
      "[0, 1, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 1, 1, 0, 0]\n",
      "at height 10 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 1, 1, 0, 0, 0]\n",
      "[0, 1, 0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1, 1, 1]\n",
      "[0, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 9 Xright.length = 2\n",
      "[0, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 4\n",
      "[0, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 1, 0, 1, 1, 0, 0, 0]\n",
      "[0, 1, 0, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 1, 0, 1, 1, 0, 0, 1, 0]\n",
      "at height 10 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 1, 0, 1, 1, 0, 0, 1, 0, 0]\n",
      "at height 11 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0]\n",
      "[0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 0, 1, 1]\n",
      "[0, 1, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 1, 0, 1, 1, 0, 1, 0]\n",
      "[0, 1, 0, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 1, 0, 1, 1, 0, 1, 1, 0]\n",
      "at height 10 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 1, 1, 0, 1, 1, 0, 0]\n",
      "[0, 1, 0, 1, 1, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 1, 1, 1]\n",
      "[0, 1, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 1, 1, 1, 0]\n",
      "[0, 1, 0, 1, 1, 1, 1]\n",
      "[0, 1, 1]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 7\n",
      "[0, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 1, 0, 0]\n",
      "[0, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 6\n",
      "[0, 1, 1, 1, 0]\n",
      "[0, 1, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 1\n",
      "[0, 1, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 1, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 1, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 1, 1, 1, 0, 0, 0, 0]\n",
      "[0, 1, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 1, 1, 0, 0, 1]\n",
      "[0, 1, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 1, 1, 1, 0, 1, 0]\n",
      "[0, 1, 1, 1, 1, 0, 1, 1]\n",
      "[0, 1, 1, 1, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 0]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 0]\n",
      "[1, 1, 1]\n"
     ]
    }
   ],
   "source": [
    "root = itree(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# a path length\n",
    "def get_path(x, T, path=[], e=0):\n",
    "    if T.size >= 0:\n",
    "        return e\n",
    "    else:\n",
    "        e += 1\n",
    "        return get_path(x, T.left, path+[0], e) if x[T.splitattr] < T.splitvalue else get_path(x, T.right, path+[1], e)\n",
    "    \n",
    "x_evaluate = np.array([ 2.5,  1.68268672])\n",
    "\n",
    "get_path(x_evaluate, root)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9, 9, 2])"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randint(0, 10, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[]\n",
      "at height 1 X --> Xleft.length = 73 Xright.length = 183\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 64 Xright.length = 9\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 52 Xright.length = 12\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 21 Xright.length = 31\n",
      "[0, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 17 Xright.length = 4\n",
      "[0, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 13 Xright.length = 4\n",
      "[0, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 6\n",
      "[0, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 5\n",
      "[0, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 0, 0, 0, 0, 0, 1, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 1, 1]\n",
      "[0, 0, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 2\n",
      "[0, 0, 0, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 0, 0, 0, 0, 0, 1, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 0, 0, 0, 1, 1, 0]\n",
      "[0, 0, 0, 0, 0, 0, 1, 1, 1]\n",
      "[0, 0, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 0, 0, 1, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 0, 0, 0, 1, 0]\n",
      "[0, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1]\n",
      "[0, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 29 Xright.length = 2\n",
      "[0, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 8 Xright.length = 21\n",
      "[0, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 6\n",
      "[0, 0, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 4\n",
      "[0, 0, 0, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 1, 0, 0, 1, 0, 0]\n",
      "[0, 0, 0, 1, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0, 1, 1, 0]\n",
      "[0, 0, 0, 1, 0, 0, 1, 1, 1]\n",
      "[0, 0, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 14\n",
      "[0, 0, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 5\n",
      "[0, 0, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 1\n",
      "[0, 0, 0, 1, 0, 1, 0, 1, 0]\n",
      "[0, 0, 0, 1, 0, 1, 0, 1, 1]\n",
      "[0, 0, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 9\n",
      "[0, 0, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 0, 1, 0, 1, 1, 0, 0]\n",
      "[0, 0, 0, 1, 0, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 5\n",
      "[0, 0, 0, 1, 0, 1, 1, 1, 0]\n",
      "[0, 0, 0, 1, 0, 1, 1, 1, 1]\n",
      "[0, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 1, 1, 0]\n",
      "[0, 0, 0, 1, 1, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 3 Xright.length = 9\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 4 Xright.length = 5\n",
      "[0, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 0, 1, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 1, 0, 0]\n",
      "[0, 0, 1, 1, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 3 Xright.length = 6\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1]\n",
      "[0, 1, 1]\n",
      "at height 4 X --> Xleft.length = 5 Xright.length = 1\n",
      "[0, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 1, 1, 0, 1, 1]\n",
      "[0, 1, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 66 Xright.length = 117\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 64 Xright.length = 2\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 57 Xright.length = 7\n",
      "[1, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 50 Xright.length = 7\n",
      "[1, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 28 Xright.length = 22\n",
      "[1, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 24 Xright.length = 4\n",
      "[1, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 19 Xright.length = 5\n",
      "[1, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 7 Xright.length = 12\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 0, 0, 0, 0, 0, 0, 1, 0]\n",
      "[1, 0, 0, 0, 0, 0, 0, 1, 1]\n",
      "[1, 0, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 0, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 1, 0, 0]\n",
      "[1, 0, 0, 0, 0, 0, 1, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 1, 1, 0]\n",
      "[1, 0, 0, 0, 0, 0, 1, 1, 1]\n",
      "[1, 0, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 8 Xright.length = 14\n",
      "[1, 0, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 5\n",
      "[1, 0, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 0, 0, 0, 0, 1, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 2\n",
      "[1, 0, 0, 0, 0, 1, 0, 1, 0]\n",
      "[1, 0, 0, 0, 0, 1, 0, 1, 1]\n",
      "[1, 0, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 6 Xright.length = 8\n",
      "[1, 0, 0, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 2\n",
      "[1, 0, 0, 0, 0, 1, 1, 0, 0]\n",
      "[1, 0, 0, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 6 Xright.length = 2\n",
      "[1, 0, 0, 0, 0, 1, 1, 1, 0]\n",
      "[1, 0, 0, 0, 0, 1, 1, 1, 1]\n",
      "[1, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 4\n",
      "[1, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 0, 1, 1, 1]\n",
      "[1, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 6\n",
      "[1, 0, 0, 1, 0]\n",
      "[1, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 1\n",
      "[1, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 1, 0]\n",
      "[1, 0, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 92 Xright.length = 25\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 5 Xright.length = 87\n",
      "[1, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1]\n",
      "[1, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 47 Xright.length = 40\n",
      "[1, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 44 Xright.length = 3\n",
      "[1, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 42\n",
      "[1, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 37\n",
      "[1, 1, 0, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 4\n",
      "[1, 1, 0, 1, 0, 0, 1, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 23 Xright.length = 14\n",
      "[1, 1, 0, 1, 0, 0, 1, 1, 0]\n",
      "[1, 1, 0, 1, 0, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0, 1, 0, 1, 0]\n",
      "[1, 1, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 1, 0, 0]\n",
      "[1, 1, 0, 1, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 34 Xright.length = 6\n",
      "[1, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 29\n",
      "[1, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 1, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0, 0, 1, 0]\n",
      "[1, 1, 0, 1, 1, 0, 0, 1, 1]\n",
      "[1, 1, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 27\n",
      "[1, 1, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0, 1, 0, 0]\n",
      "[1, 1, 0, 1, 1, 0, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 22\n",
      "[1, 1, 0, 1, 1, 0, 1, 1, 0]\n",
      "[1, 1, 0, 1, 1, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 3\n",
      "[1, 1, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 0, 0, 0]\n",
      "[1, 1, 0, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 1, 0, 0]\n",
      "[1, 1, 0, 1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1, 1, 1]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 23 Xright.length = 2\n",
      "[1, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 16 Xright.length = 7\n",
      "[1, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 8 Xright.length = 8\n",
      "[1, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 5\n",
      "[1, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 1\n",
      "[1, 1, 1, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 1, 1, 0, 0, 0, 1, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 1, 1]\n",
      "[1, 1, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 5\n",
      "[1, 1, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 1, 0, 0, 1, 0, 0]\n",
      "[1, 1, 1, 0, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 1, 0, 1, 0]\n",
      "[1, 1, 1, 0, 0, 1, 0, 1, 1]\n",
      "[1, 1, 1, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 1\n",
      "[1, 1, 1, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 1, 1, 0, 0, 1, 1, 0, 0]\n",
      "[1, 1, 1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 1, 1, 0, 0, 1, 1, 1]\n",
      "[1, 1, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 2\n",
      "[1, 1, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 1\n",
      "[1, 1, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 1]\n",
      "[1, 1, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 1, 0, 1, 1, 0]\n",
      "[1, 1, 1, 0, 1, 1, 1]\n",
      "[1, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 1, 1, 0]\n",
      "[1, 1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 125 Xright.length = 131\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 27 Xright.length = 98\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 5 Xright.length = 22\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 4 Xright.length = 1\n",
      "[0, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 19 Xright.length = 3\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 4 Xright.length = 15\n",
      "[0, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 11 Xright.length = 4\n",
      "[0, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 9 Xright.length = 2\n",
      "[0, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 8\n",
      "[0, 0, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 1, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 6 Xright.length = 2\n",
      "[0, 0, 1, 0, 1, 0, 0, 1, 0]\n",
      "[0, 0, 1, 0, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 1, 0, 0]\n",
      "[0, 0, 1, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 1, 1]\n",
      "[0, 0, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 10 Xright.length = 88\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 5 Xright.length = 5\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 4 Xright.length = 1\n",
      "[0, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 1, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 1]\n",
      "[0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1, 1]\n",
      "[0, 1, 1]\n",
      "at height 4 X --> Xleft.length = 74 Xright.length = 14\n",
      "[0, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 72 Xright.length = 2\n",
      "[0, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 56 Xright.length = 16\n",
      "[0, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 33 Xright.length = 23\n",
      "[0, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 20 Xright.length = 13\n",
      "[0, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 7 Xright.length = 13\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 6 Xright.length = 7\n",
      "[0, 1, 1, 0, 0, 0, 0, 1, 0]\n",
      "[0, 1, 1, 0, 0, 0, 0, 1, 1]\n",
      "[0, 1, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 22 Xright.length = 1\n",
      "[0, 1, 1, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 19 Xright.length = 3\n",
      "[0, 1, 1, 0, 0, 0, 1, 0, 0]\n",
      "[0, 1, 1, 0, 0, 0, 1, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 1, 1]\n",
      "[0, 1, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 10\n",
      "[0, 1, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 2\n",
      "[0, 1, 1, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 1, 0, 0, 0]\n",
      "[0, 1, 1, 0, 0, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 1, 0, 1, 0]\n",
      "[0, 1, 1, 0, 0, 1, 0, 1, 1]\n",
      "[0, 1, 1, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 5\n",
      "[0, 1, 1, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 1, 1, 0, 0, 1, 1, 0, 0]\n",
      "[0, 1, 1, 0, 0, 1, 1, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 1, 1, 0, 0, 1, 1, 1, 0]\n",
      "[0, 1, 1, 0, 0, 1, 1, 1, 1]\n",
      "[0, 1, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 1, 1, 0, 1, 1]\n",
      "[0, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 12 Xright.length = 2\n",
      "[0, 1, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 8 Xright.length = 4\n",
      "[0, 1, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 4\n",
      "[0, 1, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[0, 1, 1, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 0, 0, 1, 0]\n",
      "[0, 1, 1, 1, 0, 0, 0, 1, 1]\n",
      "[0, 1, 1, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 1, 1, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 0, 1, 0, 0]\n",
      "[0, 1, 1, 1, 0, 0, 1, 0, 1]\n",
      "[0, 1, 1, 1, 0, 0, 1, 1]\n",
      "[0, 1, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 1, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 1, 0, 0, 0]\n",
      "[0, 1, 1, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 1, 1, 0, 1, 0, 1]\n",
      "[0, 1, 1, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 1, 1, 0, 0]\n",
      "[0, 1, 1, 1, 0, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1, 0, 1, 1, 1]\n",
      "[0, 1, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 1, 1, 1, 0]\n",
      "[0, 1, 1, 1, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 9 Xright.length = 122\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 5 Xright.length = 4\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 118 Xright.length = 4\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 31 Xright.length = 87\n",
      "[1, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 7 Xright.length = 24\n",
      "[1, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 4\n",
      "[1, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 0, 0, 0, 1, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 1, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 1, 1]\n",
      "[1, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 18 Xright.length = 6\n",
      "[1, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 12\n",
      "[1, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 4\n",
      "[1, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 1, 0, 0, 1, 0, 0, 1, 0]\n",
      "[1, 1, 0, 0, 1, 0, 0, 1, 1]\n",
      "[1, 1, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 7\n",
      "[1, 1, 0, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 2\n",
      "[1, 1, 0, 0, 1, 0, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 3\n",
      "[1, 1, 0, 0, 1, 0, 1, 1, 0]\n",
      "[1, 1, 0, 0, 1, 0, 1, 1, 1]\n",
      "[1, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 5\n",
      "[1, 1, 0, 0, 1, 1, 0]\n",
      "[1, 1, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 1, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 1, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 0, 0, 1, 1, 1, 1, 0]\n",
      "[1, 1, 0, 0, 1, 1, 1, 1, 1]\n",
      "[1, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 66 Xright.length = 21\n",
      "[1, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 6 Xright.length = 60\n",
      "[1, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 3\n",
      "[1, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 0, 0, 1, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 0, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 0, 1, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 1, 1]\n",
      "[1, 1, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 51 Xright.length = 9\n",
      "[1, 1, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 6 Xright.length = 45\n",
      "[1, 1, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 5\n",
      "[1, 1, 0, 1, 0, 1, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 10 Xright.length = 35\n",
      "[1, 1, 0, 1, 0, 1, 0, 1, 0]\n",
      "[1, 1, 0, 1, 0, 1, 0, 1, 1]\n",
      "[1, 1, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 6\n",
      "[1, 1, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 1, 0, 0]\n",
      "[1, 1, 0, 1, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 6 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 1, 1, 0]\n",
      "[1, 1, 0, 1, 0, 1, 1, 1, 1]\n",
      "[1, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 20 Xright.length = 1\n",
      "[1, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 10 Xright.length = 10\n",
      "[1, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 7\n",
      "[1, 1, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 5\n",
      "[1, 1, 0, 1, 1, 0, 0, 1, 0]\n",
      "[1, 1, 0, 1, 1, 0, 0, 1, 1]\n",
      "[1, 1, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 8 Xright.length = 2\n",
      "[1, 1, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 5\n",
      "[1, 1, 0, 1, 1, 0, 1, 0, 0]\n",
      "[1, 1, 0, 1, 1, 0, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0, 1, 1, 0]\n",
      "[1, 1, 0, 1, 1, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1, 1, 1]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 134 Xright.length = 122\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 132 Xright.length = 2\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 101 Xright.length = 31\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 3 Xright.length = 98\n",
      "[0, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1]\n",
      "[0, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 72 Xright.length = 26\n",
      "[0, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 67 Xright.length = 5\n",
      "[0, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 22 Xright.length = 45\n",
      "[0, 0, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 14 Xright.length = 8\n",
      "[0, 0, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 12\n",
      "[0, 0, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 3\n",
      "[0, 0, 0, 1, 0, 0, 0, 1, 0]\n",
      "[0, 0, 0, 1, 0, 0, 0, 1, 1]\n",
      "[0, 0, 0, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 41 Xright.length = 4\n",
      "[0, 0, 0, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 38\n",
      "[0, 0, 0, 1, 0, 0, 1, 0, 0]\n",
      "[0, 0, 0, 1, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 0, 1, 0, 0, 1, 1, 0]\n",
      "[0, 0, 0, 1, 0, 0, 1, 1, 1]\n",
      "[0, 0, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 1\n",
      "[0, 0, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 0, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1, 1]\n",
      "[0, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 14 Xright.length = 12\n",
      "[0, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 11\n",
      "[0, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 7\n",
      "[0, 0, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 0, 0, 1, 1, 0, 1, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 4\n",
      "[0, 0, 0, 1, 1, 0, 1, 1, 0]\n",
      "[0, 0, 0, 1, 1, 0, 1, 1, 1]\n",
      "[0, 0, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 10\n",
      "[0, 0, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 5\n",
      "[0, 0, 0, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 0, 1, 1, 1, 1, 0, 0]\n",
      "[0, 0, 0, 1, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 0, 0, 1, 1, 1, 1, 1, 0]\n",
      "[0, 0, 0, 1, 1, 1, 1, 1, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 29\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 0, 0]\n",
      "[0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 27\n",
      "[0, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 19 Xright.length = 8\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 13 Xright.length = 6\n",
      "[0, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 10 Xright.length = 3\n",
      "[0, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 7 Xright.length = 3\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 1, 1, 0, 0, 1, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 3\n",
      "[0, 0, 1, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 1, 1, 0, 1, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 0, 1, 1, 1]\n",
      "[0, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 6\n",
      "[0, 0, 1, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 1, 1, 1, 0, 0]\n",
      "[0, 0, 1, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 2\n",
      "[0, 0, 1, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 0, 1, 1, 1, 1, 1, 0, 0]\n",
      "[0, 0, 1, 1, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 1, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0]\n",
      "[0, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 2 Xright.length = 120\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1]\n",
      "[1, 0, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 110 Xright.length = 10\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 11 Xright.length = 99\n",
      "[1, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 4 Xright.length = 7\n",
      "[1, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 5\n",
      "[1, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 0, 0, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 1\n",
      "[1, 1, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 1, 0, 0, 0]\n",
      "[1, 1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 27 Xright.length = 72\n",
      "[1, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 24 Xright.length = 3\n",
      "[1, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 8 Xright.length = 16\n",
      "[1, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 7 Xright.length = 1\n",
      "[1, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 5\n",
      "[1, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 13 Xright.length = 3\n",
      "[1, 1, 0, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 12\n",
      "[1, 1, 0, 1, 0, 0, 1, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 0, 1, 1, 0]\n",
      "[1, 1, 0, 1, 0, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0, 1, 0, 1, 0]\n",
      "[1, 1, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 1, 0, 0]\n",
      "[1, 1, 0, 1, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 64 Xright.length = 8\n",
      "[1, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 55 Xright.length = 9\n",
      "[1, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 31 Xright.length = 24\n",
      "[1, 1, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 29\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 7 Xright.length = 17\n",
      "[1, 1, 0, 1, 1, 0, 0, 1, 0]\n",
      "[1, 1, 0, 1, 1, 0, 0, 1, 1]\n",
      "[1, 1, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 8 Xright.length = 1\n",
      "[1, 1, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 3\n",
      "[1, 1, 0, 1, 1, 0, 1, 0, 0]\n",
      "[1, 1, 0, 1, 1, 0, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 1, 1]\n",
      "[1, 1, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 2\n",
      "[1, 1, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 3\n",
      "[1, 1, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 0, 0, 0]\n",
      "[1, 1, 0, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 0, 1, 0]\n",
      "[1, 1, 0, 1, 1, 1, 0, 1, 1]\n",
      "[1, 1, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 1, 0, 0]\n",
      "[1, 1, 0, 1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1, 1, 1]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 4 Xright.length = 6\n",
      "[1, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 1, 0, 1, 0]\n",
      "[1, 1, 1, 0, 1, 1]\n",
      "[1, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 5 Xright.length = 1\n",
      "[1, 1, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 1\n",
      "[1, 1, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 131 Xright.length = 125\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 130 Xright.length = 1\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 92 Xright.length = 38\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 89 Xright.length = 3\n",
      "[0, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 42 Xright.length = 47\n",
      "[0, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 37\n",
      "[0, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 1\n",
      "[0, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 1, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 1, 1]\n",
      "[0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 12 Xright.length = 25\n",
      "[0, 0, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 7\n",
      "[0, 0, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 0, 0, 0, 0, 1, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 4\n",
      "[0, 0, 0, 0, 0, 1, 0, 1, 0]\n",
      "[0, 0, 0, 0, 0, 1, 0, 1, 1]\n",
      "[0, 0, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 23 Xright.length = 2\n",
      "[0, 0, 0, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 20 Xright.length = 3\n",
      "[0, 0, 0, 0, 0, 1, 1, 0, 0]\n",
      "[0, 0, 0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 0, 0, 1, 1, 1, 0]\n",
      "[0, 0, 0, 0, 0, 1, 1, 1, 1]\n",
      "[0, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 29 Xright.length = 18\n",
      "[0, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 27 Xright.length = 2\n",
      "[0, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 26\n",
      "[0, 0, 0, 0, 1, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 22\n",
      "[0, 0, 0, 0, 1, 0, 0, 1, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 1, 0, 0]\n",
      "[0, 0, 0, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 10 Xright.length = 8\n",
      "[0, 0, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 8 Xright.length = 2\n",
      "[0, 0, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 5\n",
      "[0, 0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 0, 1, 1, 0, 1, 0]\n",
      "[0, 0, 0, 0, 1, 1, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 4\n",
      "[0, 0, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 1, 1, 0]\n",
      "[0, 0, 0, 0, 1, 1, 1, 1, 1]\n",
      "[0, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 32 Xright.length = 6\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 17 Xright.length = 15\n",
      "[0, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 15\n",
      "[0, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 10\n",
      "[0, 0, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 1, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 1, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 1, 0, 1, 0]\n",
      "[0, 0, 1, 0, 0, 1, 0, 1, 1]\n",
      "[0, 0, 1, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 7 Xright.length = 3\n",
      "[0, 0, 1, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 2\n",
      "[0, 0, 1, 0, 0, 1, 1, 0, 0]\n",
      "[0, 0, 1, 0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 1, 1, 1, 0]\n",
      "[0, 0, 1, 0, 0, 1, 1, 1, 1]\n",
      "[0, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 14\n",
      "[0, 0, 1, 0, 1, 0]\n",
      "[0, 0, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 7\n",
      "[0, 0, 1, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 6\n",
      "[0, 0, 1, 0, 1, 1, 0, 0]\n",
      "[0, 0, 1, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 2\n",
      "[0, 0, 1, 0, 1, 1, 0, 1, 0]\n",
      "[0, 0, 1, 0, 1, 1, 0, 1, 1]\n",
      "[0, 0, 1, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 3\n",
      "[0, 0, 1, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 1, 1, 0, 0]\n",
      "[0, 0, 1, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 1, 1, 1, 0]\n",
      "[0, 0, 1, 0, 1, 1, 1, 1, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 5\n",
      "[0, 0, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 1, 0, 0]\n",
      "[0, 0, 1, 1, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1, 1, 1]\n",
      "[0, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 119 Xright.length = 6\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 4 Xright.length = 115\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 104 Xright.length = 11\n",
      "[1, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 97 Xright.length = 7\n",
      "[1, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 62 Xright.length = 35\n",
      "[1, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 27 Xright.length = 35\n",
      "[1, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 10 Xright.length = 17\n",
      "[1, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 8\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 11 Xright.length = 6\n",
      "[1, 0, 1, 0, 0, 0, 0, 1, 0]\n",
      "[1, 0, 1, 0, 0, 0, 0, 1, 1]\n",
      "[1, 0, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 22 Xright.length = 13\n",
      "[1, 0, 1, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 20 Xright.length = 2\n",
      "[1, 0, 1, 0, 0, 0, 1, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 11\n",
      "[1, 0, 1, 0, 0, 0, 1, 1, 0]\n",
      "[1, 0, 1, 0, 0, 0, 1, 1, 1]\n",
      "[1, 0, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 34\n",
      "[1, 0, 1, 0, 0, 1, 0]\n",
      "[1, 0, 1, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 23 Xright.length = 11\n",
      "[1, 0, 1, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 18\n",
      "[1, 0, 1, 0, 0, 1, 1, 0, 0]\n",
      "[1, 0, 1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 8\n",
      "[1, 0, 1, 0, 0, 1, 1, 1, 0]\n",
      "[1, 0, 1, 0, 0, 1, 1, 1, 1]\n",
      "[1, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 6\n",
      "[1, 0, 1, 0, 1, 0]\n",
      "[1, 0, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 4\n",
      "[1, 0, 1, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 1, 0, 0, 0]\n",
      "[1, 0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 1, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 0, 1, 0, 1, 1, 1, 0, 0]\n",
      "[1, 0, 1, 0, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1, 1, 1]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 9\n",
      "[1, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 6 Xright.length = 3\n",
      "[1, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 2\n",
      "[1, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 1, 0, 0]\n",
      "[1, 0, 1, 1, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 1, 1]\n",
      "[1, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 1, 0, 0, 0]\n",
      "[1, 0, 1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 3 Xright.length = 3\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 121 Xright.length = 135\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 95 Xright.length = 26\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 74 Xright.length = 21\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 18 Xright.length = 56\n",
      "[0, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 16\n",
      "[0, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 9 Xright.length = 7\n",
      "[0, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 5\n",
      "[0, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 0, 0, 0, 1, 0, 1, 0]\n",
      "[0, 0, 0, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 0, 0, 0, 1, 0, 1, 1, 0]\n",
      "[0, 0, 0, 0, 1, 0, 1, 1, 1]\n",
      "[0, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 3\n",
      "[0, 0, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1, 1]\n",
      "[0, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 6 Xright.length = 50\n",
      "[0, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 5\n",
      "[0, 0, 0, 1, 0, 0]\n",
      "[0, 0, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 1\n",
      "[0, 0, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1, 1]\n",
      "[0, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 10 Xright.length = 40\n",
      "[0, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 8 Xright.length = 2\n",
      "[0, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 6 Xright.length = 2\n",
      "[0, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 4\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0, 1, 0]\n",
      "[0, 0, 0, 1, 1, 0, 0, 1, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 1, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1, 1]\n",
      "[0, 0, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 19 Xright.length = 21\n",
      "[0, 0, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 16 Xright.length = 3\n",
      "[0, 0, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 13\n",
      "[0, 0, 0, 1, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 0, 1, 1, 1, 0, 1, 0]\n",
      "[0, 0, 0, 1, 1, 1, 0, 1, 1]\n",
      "[0, 0, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 19\n",
      "[0, 0, 0, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 1, 1, 0, 0]\n",
      "[0, 0, 0, 1, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 18 Xright.length = 1\n",
      "[0, 0, 0, 1, 1, 1, 1, 1, 0]\n",
      "[0, 0, 0, 1, 1, 1, 1, 1, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 20 Xright.length = 1\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 17 Xright.length = 3\n",
      "[0, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 8 Xright.length = 9\n",
      "[0, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 2\n",
      "[0, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 1\n",
      "[0, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 1, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 1, 1]\n",
      "[0, 0, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 2\n",
      "[0, 0, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 4\n",
      "[0, 0, 1, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 1, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 0, 1, 0, 0, 1, 0, 1, 0]\n",
      "[0, 0, 1, 0, 0, 1, 0, 1, 1]\n",
      "[0, 0, 1, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 0, 0, 1, 1, 0]\n",
      "[0, 0, 1, 0, 0, 1, 1, 1]\n",
      "[0, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1]\n",
      "[0, 0, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 24 Xright.length = 2\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 19 Xright.length = 5\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 4 Xright.length = 15\n",
      "[0, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 1, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 1]\n",
      "[0, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 8 Xright.length = 7\n",
      "[0, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 3\n",
      "[0, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 1, 0, 0]\n",
      "[0, 1, 0, 0, 1, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 1, 1]\n",
      "[0, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 1, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1, 1]\n",
      "[0, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 1, 0, 1, 0, 0]\n",
      "[0, 1, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 1, 0, 0, 0]\n",
      "[0, 1, 0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1, 1]\n",
      "[0, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 1, 1, 0]\n",
      "[0, 1, 0, 1, 1, 1]\n",
      "[0, 1, 1]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 11 Xright.length = 124\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 5 Xright.length = 6\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 1 Xright.length = 4\n",
      "[1, 0, 0, 0]\n",
      "[1, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 4\n",
      "[1, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 1, 0, 0]\n",
      "[1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 1, 1, 0, 0]\n",
      "[1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 105 Xright.length = 19\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 36 Xright.length = 69\n",
      "[1, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 33 Xright.length = 3\n",
      "[1, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 22 Xright.length = 11\n",
      "[1, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 21 Xright.length = 1\n",
      "[1, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 17 Xright.length = 4\n",
      "[1, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 10 Xright.length = 7\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 1, 0, 0, 0, 0, 0, 1, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 6\n",
      "[1, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 1\n",
      "[1, 1, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 1, 0, 0, 0, 1, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 4\n",
      "[1, 1, 0, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 1, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 1, 1, 0]\n",
      "[1, 1, 0, 0, 0, 1, 1, 1, 1]\n",
      "[1, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1]\n",
      "[1, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 68 Xright.length = 1\n",
      "[1, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 64 Xright.length = 4\n",
      "[1, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 58 Xright.length = 6\n",
      "[1, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 39 Xright.length = 19\n",
      "[1, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 6 Xright.length = 33\n",
      "[1, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 17 Xright.length = 2\n",
      "[1, 1, 0, 1, 0, 0, 0, 1, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 3\n",
      "[1, 1, 0, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 0, 1, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 0, 1, 1, 0]\n",
      "[1, 1, 0, 1, 0, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 1, 0, 1, 0, 1, 0]\n",
      "[1, 1, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 1, 0, 0]\n",
      "[1, 1, 0, 1, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1, 1]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 3 Xright.length = 16\n",
      "[1, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 14\n",
      "[1, 1, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 9\n",
      "[1, 1, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 1, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 0, 0, 0, 0]\n",
      "[1, 1, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 1, 1, 1, 0, 1, 0]\n",
      "[1, 1, 1, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
      "[1, 1, 1, 1, 1, 0, 1, 1, 1]\n",
      "[1, 1, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 8\n",
      "[1, 1, 1, 1, 1, 1, 0]\n",
      "[1, 1, 1, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 5\n",
      "[1, 1, 1, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 1, 1, 0, 0]\n",
      "[1, 1, 1, 1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 1, 1, 1, 0]\n",
      "[1, 1, 1, 1, 1, 1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 118 Xright.length = 138\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 117 Xright.length = 1\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 116 Xright.length = 1\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 111 Xright.length = 5\n",
      "[0, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 26 Xright.length = 85\n",
      "[0, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 12 Xright.length = 14\n",
      "[0, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 9\n",
      "[0, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 6\n",
      "[0, 0, 0, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 1, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 2\n",
      "[0, 0, 0, 0, 0, 0, 1, 1, 0]\n",
      "[0, 0, 0, 0, 0, 0, 1, 1, 1]\n",
      "[0, 0, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 10 Xright.length = 4\n",
      "[0, 0, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 6\n",
      "[0, 0, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 1, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 3\n",
      "[0, 0, 0, 0, 0, 1, 0, 1, 0]\n",
      "[0, 0, 0, 0, 0, 1, 0, 1, 1]\n",
      "[0, 0, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 0, 0, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 1, 1, 0, 0]\n",
      "[0, 0, 0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 0, 0, 1, 1, 1, 0]\n",
      "[0, 0, 0, 0, 0, 1, 1, 1, 1]\n",
      "[0, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 9 Xright.length = 76\n",
      "[0, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 6\n",
      "[0, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 0, 0, 1, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 0, 1, 0, 0, 1, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 2\n",
      "[0, 0, 0, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 0, 0, 0, 1, 0, 1, 0, 0]\n",
      "[0, 0, 0, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 1, 1, 0]\n",
      "[0, 0, 0, 0, 1, 0, 1, 1, 1]\n",
      "[0, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 41 Xright.length = 35\n",
      "[0, 0, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 13 Xright.length = 28\n",
      "[0, 0, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 8 Xright.length = 5\n",
      "[0, 0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 18 Xright.length = 10\n",
      "[0, 0, 0, 0, 1, 1, 0, 1, 0]\n",
      "[0, 0, 0, 0, 1, 1, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 33 Xright.length = 2\n",
      "[0, 0, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 15 Xright.length = 18\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 1, 1, 0]\n",
      "[0, 0, 0, 0, 1, 1, 1, 1, 1]\n",
      "[0, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 1, 0, 0]\n",
      "[0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1]\n",
      "[0, 0, 1]\n",
      "[0, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 135 Xright.length = 3\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 84 Xright.length = 51\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 79 Xright.length = 5\n",
      "[1, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 14 Xright.length = 65\n",
      "[1, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 11\n",
      "[1, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 4\n",
      "[1, 0, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 2\n",
      "[1, 0, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 0, 0, 0, 0, 1, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 0, 0, 0, 1, 0, 1, 0]\n",
      "[1, 0, 0, 0, 0, 1, 0, 1, 1]\n",
      "[1, 0, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 0, 0, 0, 1, 1, 0]\n",
      "[1, 0, 0, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 0, 0, 0, 1, 1, 1, 0]\n",
      "[1, 0, 0, 0, 0, 1, 1, 1, 1]\n",
      "[1, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 48 Xright.length = 17\n",
      "[1, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 21 Xright.length = 27\n",
      "[1, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 17 Xright.length = 4\n",
      "[1, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 13\n",
      "[1, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 0, 0, 1, 0, 0, 1, 0]\n",
      "[1, 0, 0, 0, 1, 0, 0, 1, 1]\n",
      "[1, 0, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 15 Xright.length = 12\n",
      "[1, 0, 0, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 14\n",
      "[1, 0, 0, 0, 1, 0, 1, 0, 0]\n",
      "[1, 0, 0, 0, 1, 0, 1, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 7 Xright.length = 5\n",
      "[1, 0, 0, 0, 1, 0, 1, 1, 0]\n",
      "[1, 0, 0, 0, 1, 0, 1, 1, 1]\n",
      "[1, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 13\n",
      "[1, 0, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 1, 0, 1, 0]\n",
      "[1, 0, 0, 0, 1, 1, 0, 1, 1]\n",
      "[1, 0, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 9\n",
      "[1, 0, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 0, 0, 1, 1, 1, 0, 0]\n",
      "[1, 0, 0, 0, 1, 1, 1, 0, 1]\n",
      "[1, 0, 0, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 6\n",
      "[1, 0, 0, 0, 1, 1, 1, 1, 0]\n",
      "[1, 0, 0, 0, 1, 1, 1, 1, 1]\n",
      "[1, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 4\n",
      "[1, 0, 0, 1, 0]\n",
      "[1, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 0, 1, 1, 1, 0]\n",
      "[1, 0, 0, 1, 1, 1, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 49 Xright.length = 2\n",
      "[1, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 6 Xright.length = 43\n",
      "[1, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 1\n",
      "[1, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 0, 1, 0, 0, 0, 1, 0]\n",
      "[1, 0, 1, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 1, 1, 0]\n",
      "[1, 0, 1, 0, 0, 0, 1, 1, 1]\n",
      "[1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 40\n",
      "[1, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 9 Xright.length = 31\n",
      "[1, 0, 1, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 5\n",
      "[1, 0, 1, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 1, 0, 1, 1, 0, 0, 0]\n",
      "[1, 0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 1, 0, 1, 0]\n",
      "[1, 0, 1, 0, 1, 1, 0, 1, 1]\n",
      "[1, 0, 1, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 29 Xright.length = 2\n",
      "[1, 0, 1, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 15 Xright.length = 14\n",
      "[1, 0, 1, 0, 1, 1, 1, 0, 0]\n",
      "[1, 0, 1, 0, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 1, 1, 1, 0]\n",
      "[1, 0, 1, 0, 1, 1, 1, 1, 1]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 127 Xright.length = 129\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 111 Xright.length = 16\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 26 Xright.length = 85\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 20 Xright.length = 6\n",
      "[0, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 17\n",
      "[0, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 14 Xright.length = 3\n",
      "[0, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 12 Xright.length = 2\n",
      "[0, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 7 Xright.length = 5\n",
      "[0, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 5\n",
      "[0, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 0, 0, 1, 0, 0, 1, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 1, 0, 0]\n",
      "[0, 0, 0, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 0, 0, 1, 1, 0]\n",
      "[0, 0, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1, 1]\n",
      "[0, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 4\n",
      "[0, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 83 Xright.length = 2\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 21 Xright.length = 62\n",
      "[0, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 17\n",
      "[0, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 1, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 1, 1]\n",
      "[0, 0, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 9 Xright.length = 8\n",
      "[0, 0, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 8\n",
      "[0, 0, 1, 0, 0, 1, 0, 0]\n",
      "[0, 0, 1, 0, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 3\n",
      "[0, 0, 1, 0, 0, 1, 0, 1, 0]\n",
      "[0, 0, 1, 0, 0, 1, 0, 1, 1]\n",
      "[0, 0, 1, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 7 Xright.length = 1\n",
      "[0, 0, 1, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 2\n",
      "[0, 0, 1, 0, 0, 1, 1, 0, 0]\n",
      "[0, 0, 1, 0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1, 1, 1]\n",
      "[0, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 32 Xright.length = 30\n",
      "[0, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 14 Xright.length = 18\n",
      "[0, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 11 Xright.length = 3\n",
      "[0, 0, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 9 Xright.length = 2\n",
      "[0, 0, 1, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 0, 1, 0, 0, 1, 0]\n",
      "[0, 0, 1, 0, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 15 Xright.length = 3\n",
      "[0, 0, 1, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 11\n",
      "[0, 0, 1, 0, 1, 0, 1, 0, 0]\n",
      "[0, 0, 1, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 1, 1, 0]\n",
      "[0, 0, 1, 0, 1, 0, 1, 1, 1]\n",
      "[0, 0, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 15 Xright.length = 15\n",
      "[0, 0, 1, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 14\n",
      "[0, 0, 1, 0, 1, 1, 0, 0]\n",
      "[0, 0, 1, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 13\n",
      "[0, 0, 1, 0, 1, 1, 0, 1, 0]\n",
      "[0, 0, 1, 0, 1, 1, 0, 1, 1]\n",
      "[0, 0, 1, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 13 Xright.length = 2\n",
      "[0, 0, 1, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 11 Xright.length = 2\n",
      "[0, 0, 1, 0, 1, 1, 1, 0, 0]\n",
      "[0, 0, 1, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 1, 1, 1, 0]\n",
      "[0, 0, 1, 0, 1, 1, 1, 1, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 3 Xright.length = 13\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1]\n",
      "[0, 1, 1]\n",
      "at height 4 X --> Xleft.length = 10 Xright.length = 3\n",
      "[0, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 7 Xright.length = 3\n",
      "[0, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 5\n",
      "[0, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 1, 1, 0, 0, 1, 0]\n",
      "[0, 1, 1, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 1, 1, 0, 0]\n",
      "[0, 1, 1, 0, 0, 1, 1, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1, 1, 1]\n",
      "[0, 1, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 1, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 1, 1, 0, 1, 1]\n",
      "[0, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 1, 1, 1, 0]\n",
      "[0, 1, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 1, 0, 0, 0, 0]\n",
      "[0, 1, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 1, 1, 0, 0, 1]\n",
      "[0, 1, 1, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 125 Xright.length = 4\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 47 Xright.length = 78\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 45\n",
      "[1, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 31 Xright.length = 14\n",
      "[1, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 12 Xright.length = 19\n",
      "[1, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 5\n",
      "[1, 0, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 2\n",
      "[1, 0, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 4\n",
      "[1, 0, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0, 1, 0]\n",
      "[1, 0, 0, 1, 0, 0, 0, 1, 1]\n",
      "[1, 0, 0, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 2\n",
      "[1, 0, 0, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 0, 1, 0, 0]\n",
      "[1, 0, 0, 1, 0, 0, 1, 0, 1]\n",
      "[1, 0, 0, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 1, 1, 0]\n",
      "[1, 0, 0, 1, 0, 0, 1, 1, 1]\n",
      "[1, 0, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 13 Xright.length = 6\n",
      "[1, 0, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 10 Xright.length = 3\n",
      "[1, 0, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 9\n",
      "[1, 0, 0, 1, 0, 1, 0, 0, 0]\n",
      "[1, 0, 0, 1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 1, 0, 1, 0]\n",
      "[1, 0, 0, 1, 0, 1, 0, 1, 1]\n",
      "[1, 0, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 2\n",
      "[1, 0, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 1, 1, 0, 0]\n",
      "[1, 0, 0, 1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 1, 1, 1, 0]\n",
      "[1, 0, 0, 1, 0, 1, 1, 1, 1]\n",
      "[1, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 11 Xright.length = 3\n",
      "[1, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 9 Xright.length = 2\n",
      "[1, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 8 Xright.length = 1\n",
      "[1, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 4\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 0, 1, 1, 0, 1, 0]\n",
      "[1, 0, 0, 1, 1, 0, 1, 1]\n",
      "[1, 0, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 1, 0, 0, 0]\n",
      "[1, 0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 11 Xright.length = 67\n",
      "[1, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 4 Xright.length = 7\n",
      "[1, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 1, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 1, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 1]\n",
      "[1, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 4\n",
      "[1, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 1, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 1, 0, 0, 0]\n",
      "[1, 0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 1, 1, 0, 0]\n",
      "[1, 0, 1, 0, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1, 1, 1]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 40 Xright.length = 27\n",
      "[1, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 36\n",
      "[1, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 1, 1, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 1, 0, 0]\n",
      "[1, 0, 1, 1, 0, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 1, 1]\n",
      "[1, 0, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 26 Xright.length = 10\n",
      "[1, 0, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 21\n",
      "[1, 0, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 0, 1, 1, 0, 1, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 14 Xright.length = 7\n",
      "[1, 0, 1, 1, 0, 1, 0, 1, 0]\n",
      "[1, 0, 1, 1, 0, 1, 0, 1, 1]\n",
      "[1, 0, 1, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 8 Xright.length = 2\n",
      "[1, 0, 1, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 6\n",
      "[1, 0, 1, 1, 0, 1, 1, 0, 0]\n",
      "[1, 0, 1, 1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 1, 1, 0]\n",
      "[1, 0, 1, 1, 0, 1, 1, 1, 1]\n",
      "[1, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 23 Xright.length = 4\n",
      "[1, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 13 Xright.length = 10\n",
      "[1, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 10 Xright.length = 3\n",
      "[1, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 7\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 0, 1, 0]\n",
      "[1, 0, 1, 1, 1, 0, 0, 1, 1]\n",
      "[1, 0, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 6\n",
      "[1, 0, 1, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 1, 1, 1, 0, 1, 0, 0]\n",
      "[1, 0, 1, 1, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 2\n",
      "[1, 0, 1, 1, 1, 0, 1, 1, 0]\n",
      "[1, 0, 1, 1, 1, 0, 1, 1, 1]\n",
      "[1, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 1, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 1, 0, 0, 0]\n",
      "[1, 0, 1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1]\n",
      "[1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 123 Xright.length = 133\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 34 Xright.length = 89\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 2 Xright.length = 32\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 0]\n",
      "[0, 0, 0, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 9 Xright.length = 23\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 8 Xright.length = 1\n",
      "[0, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 7\n",
      "[0, 0, 1, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 5\n",
      "[0, 0, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 0, 0, 1, 0, 0]\n",
      "[0, 0, 1, 0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 0, 1, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 0, 0, 1, 1, 0, 0]\n",
      "[0, 0, 1, 0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 1, 1, 1, 0]\n",
      "[0, 0, 1, 0, 0, 1, 1, 1, 1]\n",
      "[0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 21\n",
      "[0, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 11 Xright.length = 10\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 4\n",
      "[0, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 3\n",
      "[0, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0, 1, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 1, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 1, 1, 0, 1, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1, 1]\n",
      "[0, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 9\n",
      "[0, 0, 1, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 7 Xright.length = 2\n",
      "[0, 0, 1, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 2\n",
      "[0, 0, 1, 1, 1, 1, 1, 0, 0]\n",
      "[0, 0, 1, 1, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 1, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 82 Xright.length = 7\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 29 Xright.length = 53\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 23 Xright.length = 6\n",
      "[0, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 19\n",
      "[0, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 0, 1, 0]\n",
      "[0, 1, 0, 0, 0, 0, 1, 1]\n",
      "[0, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 15\n",
      "[0, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 1, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 10\n",
      "[0, 1, 0, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 1, 0, 0, 0, 1, 1, 0, 0]\n",
      "[0, 1, 0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 9 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 1, 1, 1, 0]\n",
      "[0, 1, 0, 0, 0, 1, 1, 1, 1]\n",
      "[0, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 2\n",
      "[0, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1, 1]\n",
      "[0, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 31 Xright.length = 22\n",
      "[0, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 14 Xright.length = 17\n",
      "[0, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 13 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 12 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 10 Xright.length = 2\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 16 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 6 Xright.length = 10\n",
      "[0, 1, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 4\n",
      "[0, 1, 0, 1, 0, 1, 0, 0, 0]\n",
      "[0, 1, 0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 6 Xright.length = 4\n",
      "[0, 1, 0, 1, 0, 1, 0, 1, 0]\n",
      "[0, 1, 0, 1, 0, 1, 0, 1, 1]\n",
      "[0, 1, 0, 1, 0, 1, 1]\n",
      "[0, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 13 Xright.length = 9\n",
      "[0, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 12\n",
      "[0, 1, 0, 1, 1, 0, 0]\n",
      "[0, 1, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 9\n",
      "[0, 1, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 1, 0, 0]\n",
      "[0, 1, 0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 6\n",
      "[0, 1, 0, 1, 1, 0, 1, 1, 0]\n",
      "[0, 1, 0, 1, 1, 0, 1, 1, 1]\n",
      "[0, 1, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 2\n",
      "[0, 1, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 5\n",
      "[0, 1, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 1, 1, 1, 0, 0, 0]\n",
      "[0, 1, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 1, 0, 1, 1, 1, 0, 1, 0]\n",
      "[0, 1, 0, 1, 1, 1, 0, 1, 1]\n",
      "[0, 1, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 1, 1, 0, 0]\n",
      "[0, 1, 0, 1, 1, 1, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1, 1, 1, 1]\n",
      "[0, 1, 1]\n",
      "at height 4 X --> Xleft.length = 4 Xright.length = 3\n",
      "[0, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 1, 1, 0, 0]\n",
      "[0, 1, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 1, 1, 0, 1, 1]\n",
      "[0, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 0, 0, 0, 0]\n",
      "[0, 1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 1, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 64 Xright.length = 69\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 25 Xright.length = 39\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 11 Xright.length = 14\n",
      "[1, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 8 Xright.length = 3\n",
      "[1, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 7 Xright.length = 1\n",
      "[1, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 2\n",
      "[1, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 1\n",
      "[1, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 1, 0, 0]\n",
      "[1, 0, 0, 0, 0, 0, 1, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 1, 1]\n",
      "[1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 0, 0, 0, 1, 1]\n",
      "[1, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 11 Xright.length = 3\n",
      "[1, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 6\n",
      "[1, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 3\n",
      "[1, 0, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 1, 0, 0, 0]\n",
      "[1, 0, 0, 1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 1, 0, 1]\n",
      "[1, 0, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 1, 1, 0, 0]\n",
      "[1, 0, 0, 1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 0, 1, 1, 1]\n",
      "[1, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 0, 0, 1, 1, 0]\n",
      "[1, 0, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 1, 0, 0, 0]\n",
      "[1, 0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 3 Xright.length = 36\n",
      "[1, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 5 Xright.length = 31\n",
      "[1, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 4\n",
      "[1, 0, 1, 1, 0, 0]\n",
      "[1, 0, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1, 1]\n",
      "[1, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 18 Xright.length = 13\n",
      "[1, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 11\n",
      "[1, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 6\n",
      "[1, 0, 1, 1, 1, 0, 0, 0]\n",
      "[1, 0, 1, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 4\n",
      "[1, 0, 1, 1, 1, 0, 0, 1, 0]\n",
      "[1, 0, 1, 1, 1, 0, 0, 1, 1]\n",
      "[1, 0, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 6 Xright.length = 5\n",
      "[1, 0, 1, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 4\n",
      "[1, 0, 1, 1, 1, 0, 1, 0, 0]\n",
      "[1, 0, 1, 1, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 2\n",
      "[1, 0, 1, 1, 1, 0, 1, 1, 0]\n",
      "[1, 0, 1, 1, 1, 0, 1, 1, 1]\n",
      "[1, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 9 Xright.length = 4\n",
      "[1, 0, 1, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 6 Xright.length = 3\n",
      "[1, 0, 1, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 2\n",
      "[1, 0, 1, 1, 1, 1, 0, 0, 0]\n",
      "[1, 0, 1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 1, 0, 1, 0]\n",
      "[1, 0, 1, 1, 1, 1, 0, 1, 1]\n",
      "[1, 0, 1, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 1, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 1, 1, 0, 0]\n",
      "[1, 0, 1, 1, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 1, 1, 1, 1, 1, 1, 0]\n",
      "[1, 0, 1, 1, 1, 1, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 45 Xright.length = 24\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 31 Xright.length = 14\n",
      "[1, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 16 Xright.length = 15\n",
      "[1, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 13 Xright.length = 3\n",
      "[1, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 12\n",
      "[1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 10\n",
      "[1, 1, 0, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 0, 0, 0, 0, 1, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 5\n",
      "[1, 1, 0, 0, 0, 0, 1, 1, 0]\n",
      "[1, 1, 0, 0, 0, 0, 1, 1, 1]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 10\n",
      "[1, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 4\n",
      "[1, 1, 0, 0, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 1, 1]\n",
      "[1, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 9\n",
      "[1, 1, 0, 0, 1, 1, 0]\n",
      "[1, 1, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 6 Xright.length = 3\n",
      "[1, 1, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 4\n",
      "[1, 1, 0, 0, 1, 1, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0, 0, 1, 1, 1, 1, 0]\n",
      "[1, 1, 0, 0, 1, 1, 1, 1, 1]\n",
      "[1, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 13\n",
      "[1, 1, 0, 1, 0]\n",
      "[1, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 11 Xright.length = 2\n",
      "[1, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 5\n",
      "[1, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 1\n",
      "[1, 1, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 1, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0, 1, 0, 0]\n",
      "[1, 1, 0, 1, 1, 0, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0, 1, 1, 0]\n",
      "[1, 1, 0, 1, 1, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 0, 0, 0]\n",
      "[1, 1, 0, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1, 1]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 20 Xright.length = 4\n",
      "[1, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 18 Xright.length = 2\n",
      "[1, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 13 Xright.length = 5\n",
      "[1, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 8 Xright.length = 5\n",
      "[1, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 4\n",
      "[1, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 1, 1, 0, 0, 0, 0, 1, 0]\n",
      "[1, 1, 1, 0, 0, 0, 0, 1, 1]\n",
      "[1, 1, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 2\n",
      "[1, 1, 1, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 1, 0, 0, 0, 1, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 1, 1, 0]\n",
      "[1, 1, 1, 0, 0, 0, 1, 1, 1]\n",
      "[1, 1, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 1, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 1, 0, 0, 1, 0, 0]\n",
      "[1, 1, 1, 0, 0, 1, 0, 1]\n",
      "[1, 1, 1, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 1, 1, 0, 0]\n",
      "[1, 1, 1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 1, 1, 0, 0, 1, 1, 1]\n",
      "[1, 1, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 1]\n",
      "[1, 1, 1, 0, 1, 1]\n",
      "[1, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 1, 1, 1, 0]\n",
      "[1, 1, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 0, 0, 0, 0]\n",
      "[1, 1, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 128 Xright.length = 128\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 72 Xright.length = 56\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 43 Xright.length = 29\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 4 Xright.length = 39\n",
      "[0, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 18 Xright.length = 21\n",
      "[0, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 17 Xright.length = 1\n",
      "[0, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 10 Xright.length = 7\n",
      "[0, 0, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 8\n",
      "[0, 0, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 7\n",
      "[0, 0, 0, 1, 0, 0, 0, 1, 0]\n",
      "[0, 0, 0, 1, 0, 0, 0, 1, 1]\n",
      "[0, 0, 0, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 5\n",
      "[0, 0, 0, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 1, 0, 0, 1, 0, 0]\n",
      "[0, 0, 0, 1, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 0, 1, 0, 0, 1, 1, 0]\n",
      "[0, 0, 0, 1, 0, 0, 1, 1, 1]\n",
      "[0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 19\n",
      "[0, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 17 Xright.length = 2\n",
      "[0, 0, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 14\n",
      "[0, 0, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 0, 1, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 9 Xright.length = 5\n",
      "[0, 0, 0, 1, 1, 1, 0, 1, 0]\n",
      "[0, 0, 0, 1, 1, 1, 0, 1, 1]\n",
      "[0, 0, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 1, 1, 0, 0]\n",
      "[0, 0, 0, 1, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 1, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 5 Xright.length = 24\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 4 Xright.length = 1\n",
      "[0, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 0, 0, 1, 0]\n",
      "[0, 0, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 5 Xright.length = 19\n",
      "[0, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 1, 0, 0, 1, 0]\n",
      "[0, 0, 1, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1, 1]\n",
      "[0, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 15 Xright.length = 4\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 12 Xright.length = 3\n",
      "[0, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 7\n",
      "[0, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 1\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 4\n",
      "[0, 0, 1, 1, 1, 0, 0, 1, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 1, 1, 0, 1, 0]\n",
      "[0, 0, 1, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 1, 1, 0, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 0, 1, 1, 1]\n",
      "[0, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 0, 1, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 1, 0, 0]\n",
      "[0, 0, 1, 1, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 53 Xright.length = 3\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 51 Xright.length = 2\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 24 Xright.length = 27\n",
      "[0, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 23 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 21\n",
      "[0, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 18 Xright.length = 3\n",
      "[0, 1, 0, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 13\n",
      "[0, 1, 0, 0, 0, 0, 1, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 0]\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 1]\n",
      "[0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 8 Xright.length = 19\n",
      "[0, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 2\n",
      "[0, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 0, 0, 1, 0]\n",
      "[0, 1, 0, 0, 1, 0, 0, 1, 1]\n",
      "[0, 1, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 14\n",
      "[0, 1, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 1, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 1, 0, 1, 0]\n",
      "[0, 1, 0, 0, 1, 1, 0, 1, 1]\n",
      "[0, 1, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 8 Xright.length = 6\n",
      "[0, 1, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 6 Xright.length = 2\n",
      "[0, 1, 0, 0, 1, 1, 1, 0, 0]\n",
      "[0, 1, 0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 2\n",
      "[0, 1, 0, 0, 1, 1, 1, 1, 0]\n",
      "[0, 1, 0, 0, 1, 1, 1, 1, 1]\n",
      "[0, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1]\n",
      "[0, 1, 1]\n",
      "at height 4 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 1, 1, 0]\n",
      "[0, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 0, 0, 0, 0]\n",
      "[0, 1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 1, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 126 Xright.length = 2\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 11 Xright.length = 115\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 9\n",
      "[1, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 6 Xright.length = 3\n",
      "[1, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 4\n",
      "[1, 0, 0, 1, 0, 0, 0]\n",
      "[1, 0, 0, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 0, 1, 0, 0, 1, 0]\n",
      "[1, 0, 0, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 1, 1, 0]\n",
      "[1, 0, 0, 1, 0, 0, 1, 1, 1]\n",
      "[1, 0, 0, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 61 Xright.length = 54\n",
      "[1, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 33 Xright.length = 28\n",
      "[1, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 9 Xright.length = 24\n",
      "[1, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 5\n",
      "[1, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 0, 1, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 1, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 1, 0, 0, 0, 1, 1, 0]\n",
      "[1, 0, 1, 0, 0, 0, 1, 1, 1]\n",
      "[1, 0, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 18 Xright.length = 6\n",
      "[1, 0, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 12 Xright.length = 6\n",
      "[1, 0, 1, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 8 Xright.length = 4\n",
      "[1, 0, 1, 0, 0, 1, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 3\n",
      "[1, 0, 1, 0, 0, 1, 0, 1, 0]\n",
      "[1, 0, 1, 0, 0, 1, 0, 1, 1]\n",
      "[1, 0, 1, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 3\n",
      "[1, 0, 1, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 0, 1, 0, 0, 1, 1, 0, 0]\n",
      "[1, 0, 1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 1, 0, 0, 1, 1, 1, 0]\n",
      "[1, 0, 1, 0, 0, 1, 1, 1, 1]\n",
      "[1, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 25\n",
      "[1, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 24\n",
      "[1, 0, 1, 0, 1, 1, 0]\n",
      "[1, 0, 1, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 19 Xright.length = 5\n",
      "[1, 0, 1, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 16\n",
      "[1, 0, 1, 0, 1, 1, 1, 0, 0]\n",
      "[1, 0, 1, 0, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 0, 1, 0, 1, 1, 1, 1, 0]\n",
      "[1, 0, 1, 0, 1, 1, 1, 1, 1]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 12 Xright.length = 42\n",
      "[1, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 9 Xright.length = 3\n",
      "[1, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 4\n",
      "[1, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 1\n",
      "[1, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 1, 1, 0, 0, 1, 0]\n",
      "[1, 0, 1, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 1, 1, 0]\n",
      "[1, 0, 1, 1, 0, 0, 1, 1, 1]\n",
      "[1, 0, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1, 1]\n",
      "[1, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 36 Xright.length = 6\n",
      "[1, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 32 Xright.length = 4\n",
      "[1, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 24 Xright.length = 8\n",
      "[1, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 22\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 5\n",
      "[1, 0, 1, 1, 1, 0, 0, 1, 0]\n",
      "[1, 0, 1, 1, 1, 0, 0, 1, 1]\n",
      "[1, 0, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 1, 1, 1, 0, 1, 0]\n",
      "[1, 0, 1, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 1, 1, 0]\n",
      "[1, 0, 1, 1, 1, 0, 1, 1, 1]\n",
      "[1, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 4\n",
      "[1, 0, 1, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 1, 0, 0, 0]\n",
      "[1, 0, 1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 1, 1, 1, 1, 1, 0]\n",
      "[1, 0, 1, 1, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 1, 1, 1, 0]\n",
      "[1, 0, 1, 1, 1, 1, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 0]\n",
      "[1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 118 Xright.length = 138\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 46 Xright.length = 72\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 8 Xright.length = 38\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 3 Xright.length = 5\n",
      "[0, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 0, 0, 1, 0]\n",
      "[0, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 0, 1, 1, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 1, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1, 1]\n",
      "[0, 0, 0, 1, 1, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 10 Xright.length = 28\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 9\n",
      "[0, 0, 1, 0, 0]\n",
      "[0, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 7 Xright.length = 2\n",
      "[0, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 5\n",
      "[0, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 0, 1, 0, 1, 0, 1, 0]\n",
      "[0, 0, 1, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 0, 1, 0, 1, 0, 1, 1, 0]\n",
      "[0, 0, 1, 0, 1, 0, 1, 1, 1]\n",
      "[0, 0, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 16 Xright.length = 12\n",
      "[0, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 6 Xright.length = 10\n",
      "[0, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 4\n",
      "[0, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 1, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 1, 1, 0, 0, 1, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 4\n",
      "[0, 0, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 3\n",
      "[0, 0, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 1, 1, 0, 1, 0, 1, 0]\n",
      "[0, 0, 1, 1, 0, 1, 0, 1, 1]\n",
      "[0, 0, 1, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 0, 1, 1, 0, 1, 1, 0]\n",
      "[0, 0, 1, 1, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 0, 1, 1, 1, 1]\n",
      "[0, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 6 Xright.length = 6\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 5\n",
      "[0, 0, 1, 1, 1, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 0, 1, 1, 1, 0, 1, 0]\n",
      "[0, 0, 1, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 0, 1, 1, 1]\n",
      "[0, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 4\n",
      "[0, 0, 1, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 0, 1, 1, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 1, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 8 Xright.length = 64\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 6 Xright.length = 2\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 5\n",
      "[0, 1, 0, 0, 0]\n",
      "[0, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1, 1]\n",
      "[0, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1]\n",
      "[0, 1, 1]\n",
      "at height 4 X --> Xleft.length = 15 Xright.length = 49\n",
      "[0, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 12 Xright.length = 3\n",
      "[0, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 8 Xright.length = 4\n",
      "[0, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 6\n",
      "[0, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 3\n",
      "[0, 1, 1, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 1, 1, 0, 0, 0, 1, 0, 0]\n",
      "[0, 1, 1, 0, 0, 0, 1, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 1, 1, 0, 0, 0, 1, 1, 0]\n",
      "[0, 1, 1, 0, 0, 0, 1, 1, 1]\n",
      "[0, 1, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 1, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 1, 0, 0, 0]\n",
      "[0, 1, 1, 0, 0, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1, 1]\n",
      "[0, 1, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 1, 1, 0, 1, 1]\n",
      "[0, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 20 Xright.length = 29\n",
      "[0, 1, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 19 Xright.length = 1\n",
      "[0, 1, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 13\n",
      "[0, 1, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 2\n",
      "[0, 1, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 0, 0, 0, 0]\n",
      "[0, 1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 0, 0, 1, 0]\n",
      "[0, 1, 1, 1, 0, 0, 0, 1, 1]\n",
      "[0, 1, 1, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 7 Xright.length = 6\n",
      "[0, 1, 1, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 5\n",
      "[0, 1, 1, 1, 0, 0, 1, 0, 0]\n",
      "[0, 1, 1, 1, 0, 0, 1, 0, 1]\n",
      "[0, 1, 1, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 4\n",
      "[0, 1, 1, 1, 0, 0, 1, 1, 0]\n",
      "[0, 1, 1, 1, 0, 0, 1, 1, 1]\n",
      "[0, 1, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 18 Xright.length = 11\n",
      "[0, 1, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 17\n",
      "[0, 1, 1, 1, 1, 0, 0]\n",
      "[0, 1, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 11 Xright.length = 6\n",
      "[0, 1, 1, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 8\n",
      "[0, 1, 1, 1, 1, 0, 1, 0, 0]\n",
      "[0, 1, 1, 1, 1, 0, 1, 0, 1]\n",
      "[0, 1, 1, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 3\n",
      "[0, 1, 1, 1, 1, 0, 1, 1, 0]\n",
      "[0, 1, 1, 1, 1, 0, 1, 1, 1]\n",
      "[0, 1, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 6\n",
      "[0, 1, 1, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 0\n",
      "[0, 1, 1, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 0\n",
      "[0, 1, 1, 1, 1, 1, 0, 0, 0]\n",
      "[0, 1, 1, 1, 1, 1, 0, 0, 1]\n",
      "[0, 1, 1, 1, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 4\n",
      "[0, 1, 1, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 1, 1, 1, 0, 0]\n",
      "[0, 1, 1, 1, 1, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 1, 1, 1, 1, 1, 1, 1, 0]\n",
      "[0, 1, 1, 1, 1, 1, 1, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 50 Xright.length = 88\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 8 Xright.length = 42\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 1 Xright.length = 7\n",
      "[1, 0, 0, 0]\n",
      "[1, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 5\n",
      "[1, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 1\n",
      "[1, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 0, 1, 1, 0, 0]\n",
      "[1, 0, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 1, 0, 0]\n",
      "[1, 0, 0, 1, 1, 0, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 1, 1]\n",
      "[1, 0, 0, 1, 1, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 35 Xright.length = 7\n",
      "[1, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 16 Xright.length = 19\n",
      "[1, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 6 Xright.length = 10\n",
      "[1, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 1\n",
      "[1, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 4\n",
      "[1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 1, 0, 0, 0, 0, 1, 0]\n",
      "[1, 0, 1, 0, 0, 0, 0, 1, 1]\n",
      "[1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 8\n",
      "[1, 0, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 1, 0, 0, 1, 0, 0]\n",
      "[1, 0, 1, 0, 0, 1, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 4\n",
      "[1, 0, 1, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 1, 0, 0, 1, 1, 0, 0]\n",
      "[1, 0, 1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 1, 0, 0, 1, 1, 1, 0]\n",
      "[1, 0, 1, 0, 0, 1, 1, 1, 1]\n",
      "[1, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 15\n",
      "[1, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 1, 0, 0]\n",
      "[1, 0, 1, 0, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 0, 1, 0, 1, 1]\n",
      "[1, 0, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 9\n",
      "[1, 0, 1, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 3\n",
      "[1, 0, 1, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 1, 0, 0, 0]\n",
      "[1, 0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 1, 0, 1, 0]\n",
      "[1, 0, 1, 0, 1, 1, 0, 1, 1]\n",
      "[1, 0, 1, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 6 Xright.length = 3\n",
      "[1, 0, 1, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 6 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 1, 1, 0, 0]\n",
      "[1, 0, 1, 0, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 1, 1, 1, 0]\n",
      "[1, 0, 1, 0, 1, 1, 1, 1, 1]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 5 Xright.length = 2\n",
      "[1, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 2\n",
      "[1, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1, 1]\n",
      "[1, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 39 Xright.length = 49\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 14 Xright.length = 25\n",
      "[1, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 12 Xright.length = 2\n",
      "[1, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 9 Xright.length = 3\n",
      "[1, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 6\n",
      "[1, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 2\n",
      "[1, 1, 0, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 1, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 1, 1, 0]\n",
      "[1, 1, 0, 0, 0, 0, 1, 1, 1]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1]\n",
      "[1, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 24 Xright.length = 1\n",
      "[1, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 21 Xright.length = 3\n",
      "[1, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 19\n",
      "[1, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 14\n",
      "[1, 1, 0, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 1, 0, 1, 0, 0, 1, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 7 Xright.length = 7\n",
      "[1, 1, 0, 1, 0, 0, 1, 1, 0]\n",
      "[1, 1, 0, 1, 0, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 1]\n",
      "[1, 1, 0, 1, 1]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 48 Xright.length = 1\n",
      "[1, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 37 Xright.length = 11\n",
      "[1, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 30 Xright.length = 7\n",
      "[1, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 21 Xright.length = 9\n",
      "[1, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 17 Xright.length = 4\n",
      "[1, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 14 Xright.length = 3\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 1, 1, 0, 0, 0, 0, 1, 0]\n",
      "[1, 1, 1, 0, 0, 0, 0, 1, 1]\n",
      "[1, 1, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 7\n",
      "[1, 1, 1, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 1, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 4\n",
      "[1, 1, 1, 0, 0, 0, 1, 1, 0]\n",
      "[1, 1, 1, 0, 0, 0, 1, 1, 1]\n",
      "[1, 1, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 6\n",
      "[1, 1, 1, 0, 0, 1, 0]\n",
      "[1, 1, 1, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 5\n",
      "[1, 1, 1, 0, 0, 1, 1, 0]\n",
      "[1, 1, 1, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 1\n",
      "[1, 1, 1, 0, 0, 1, 1, 1, 0]\n",
      "[1, 1, 1, 0, 0, 1, 1, 1, 1]\n",
      "[1, 1, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 9 Xright.length = 2\n",
      "[1, 1, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 7\n",
      "[1, 1, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 3\n",
      "[1, 1, 1, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 1, 1, 0, 1, 0, 1, 0, 0]\n",
      "[1, 1, 1, 0, 1, 0, 1, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 1, 1, 0]\n",
      "[1, 1, 1, 0, 1, 0, 1, 1, 1]\n",
      "[1, 1, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 1, 0, 1, 1, 0]\n",
      "[1, 1, 1, 0, 1, 1, 1]\n",
      "[1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 137 Xright.length = 119\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 121 Xright.length = 16\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 1 Xright.length = 120\n",
      "[0, 0, 0]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 7 Xright.length = 113\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 4\n",
      "[0, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 11 Xright.length = 102\n",
      "[0, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 9\n",
      "[0, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 2\n",
      "[0, 0, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 3\n",
      "[0, 0, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 1, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 0, 1, 0]\n",
      "[0, 0, 1, 1, 0, 1, 0, 1, 1]\n",
      "[0, 0, 1, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 1, 0, 1, 1, 0]\n",
      "[0, 0, 1, 1, 0, 1, 1, 1]\n",
      "[0, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 101 Xright.length = 1\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 84 Xright.length = 17\n",
      "[0, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 61 Xright.length = 23\n",
      "[0, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 58\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 17 Xright.length = 6\n",
      "[0, 0, 1, 1, 1, 0, 0, 1, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 7 Xright.length = 10\n",
      "[0, 0, 1, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 3\n",
      "[0, 0, 1, 1, 1, 0, 1, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 9 Xright.length = 1\n",
      "[0, 0, 1, 1, 1, 0, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 0, 1, 1, 1]\n",
      "[0, 0, 1, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 6 Xright.length = 10\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 4 Xright.length = 2\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 1, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 1]\n",
      "[0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 1, 0]\n",
      "[0, 1, 0, 1, 1]\n",
      "[0, 1, 1]\n",
      "at height 4 X --> Xleft.length = 9 Xright.length = 1\n",
      "[0, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 7\n",
      "[0, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 6 Xright.length = 1\n",
      "[0, 1, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 3\n",
      "[0, 1, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 1, 1, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 1, 0, 1, 0, 0]\n",
      "[0, 1, 1, 0, 1, 0, 1, 0, 1]\n",
      "[0, 1, 1, 0, 1, 0, 1, 1]\n",
      "[0, 1, 1, 0, 1, 1]\n",
      "[0, 1, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 68 Xright.length = 51\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 32 Xright.length = 36\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 30 Xright.length = 2\n",
      "[1, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 6 Xright.length = 24\n",
      "[1, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 5\n",
      "[1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 2\n",
      "[1, 0, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 1, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 1, 1, 0, 0]\n",
      "[1, 0, 0, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1, 1, 1]\n",
      "[1, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 17 Xright.length = 7\n",
      "[1, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 15\n",
      "[1, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 11\n",
      "[1, 0, 0, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 0, 0, 1, 0, 1, 0, 0]\n",
      "[1, 0, 0, 0, 1, 0, 1, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 6 Xright.length = 5\n",
      "[1, 0, 0, 0, 1, 0, 1, 1, 0]\n",
      "[1, 0, 0, 0, 1, 0, 1, 1, 1]\n",
      "[1, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 4\n",
      "[1, 0, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 0, 0, 1, 1, 1, 0]\n",
      "[1, 0, 0, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 1, 1, 1, 0]\n",
      "[1, 0, 0, 0, 1, 1, 1, 1, 1]\n",
      "[1, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 0, 1, 0]\n",
      "[1, 0, 0, 1, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 25 Xright.length = 11\n",
      "[1, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 9 Xright.length = 16\n",
      "[1, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 4\n",
      "[1, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 1, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 1, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 1, 1]\n",
      "[1, 0, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 1, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 1]\n",
      "[1, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 14\n",
      "[1, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 10 Xright.length = 4\n",
      "[1, 0, 1, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 7 Xright.length = 3\n",
      "[1, 0, 1, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 6 Xright.length = 1\n",
      "[1, 0, 1, 0, 1, 1, 0, 0, 0]\n",
      "[1, 0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 1, 0, 1, 0]\n",
      "[1, 0, 1, 0, 1, 1, 0, 1, 1]\n",
      "[1, 0, 1, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 1, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 1, 1, 0, 0]\n",
      "[1, 0, 1, 0, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 1, 0, 1, 1, 1, 1, 0]\n",
      "[1, 0, 1, 0, 1, 1, 1, 1, 1]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 8 Xright.length = 3\n",
      "[1, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 6 Xright.length = 2\n",
      "[1, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 3\n",
      "[1, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 1, 0, 0]\n",
      "[1, 0, 1, 1, 0, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 1, 1]\n",
      "[1, 0, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1, 1]\n",
      "[1, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 38 Xright.length = 13\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 32 Xright.length = 6\n",
      "[1, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 27 Xright.length = 5\n",
      "[1, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 9 Xright.length = 18\n",
      "[1, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 8 Xright.length = 1\n",
      "[1, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 6\n",
      "[1, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 2\n",
      "[1, 1, 0, 0, 0, 0, 0, 1, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 15\n",
      "[1, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0, 0, 0, 1, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0, 1, 0]\n",
      "[1, 1, 0, 0, 0, 1, 0, 1, 1]\n",
      "[1, 1, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 11 Xright.length = 4\n",
      "[1, 1, 0, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 7\n",
      "[1, 1, 0, 0, 0, 1, 1, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 1, 1, 0]\n",
      "[1, 1, 0, 0, 0, 1, 1, 1, 1]\n",
      "[1, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 0, 0, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0, 0, 1, 1, 0]\n",
      "[1, 1, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 1, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1, 1, 1]\n",
      "[1, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 5\n",
      "[1, 1, 0, 1, 0]\n",
      "[1, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 2\n",
      "[1, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 0, 0, 0]\n",
      "[1, 1, 0, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1, 1]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 5 Xright.length = 8\n",
      "[1, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 1]\n",
      "[1, 1, 1, 0, 1, 1]\n",
      "[1, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 5 Xright.length = 3\n",
      "[1, 1, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 1, 1, 1, 0]\n",
      "[1, 1, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 1, 0, 0, 0]\n",
      "[1, 1, 1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 146 Xright.length = 110\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 133 Xright.length = 13\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 3 Xright.length = 130\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 0, 0]\n",
      "[0, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 1, 0]\n",
      "[0, 0, 0, 1, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 111 Xright.length = 19\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 110\n",
      "[0, 0, 1, 0, 0]\n",
      "[0, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 105\n",
      "[0, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 0, 1, 0, 1, 0]\n",
      "[0, 0, 1, 0, 1, 0, 1, 1]\n",
      "[0, 0, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 12 Xright.length = 93\n",
      "[0, 0, 1, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 8\n",
      "[0, 0, 1, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 1, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 5\n",
      "[0, 0, 1, 0, 1, 1, 0, 1, 0]\n",
      "[0, 0, 1, 0, 1, 1, 0, 1, 1]\n",
      "[0, 0, 1, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 91\n",
      "[0, 0, 1, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 0, 1, 1, 1, 0, 0]\n",
      "[0, 0, 1, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 69 Xright.length = 22\n",
      "[0, 0, 1, 0, 1, 1, 1, 1, 0]\n",
      "[0, 0, 1, 0, 1, 1, 1, 1, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 18\n",
      "[0, 0, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 17 Xright.length = 1\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 10 Xright.length = 7\n",
      "[0, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 9 Xright.length = 1\n",
      "[0, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 7\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 2\n",
      "[0, 0, 1, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 0, 1, 1, 1, 0, 1, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 0, 1, 1, 1]\n",
      "[0, 0, 1, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 11 Xright.length = 2\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 9\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 8\n",
      "[0, 1, 0, 1, 0]\n",
      "[0, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 6 Xright.length = 2\n",
      "[0, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 1\n",
      "[0, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 1, 0, 0, 0]\n",
      "[0, 1, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1, 1, 1]\n",
      "[0, 1, 1]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 25 Xright.length = 85\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 21 Xright.length = 4\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 10 Xright.length = 11\n",
      "[1, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 4 Xright.length = 6\n",
      "[1, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 2\n",
      "[1, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 1, 0, 0]\n",
      "[1, 0, 0, 0, 1, 0, 1, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 1, 1]\n",
      "[1, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 0, 1, 1, 1]\n",
      "[1, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 10\n",
      "[1, 0, 0, 1, 0]\n",
      "[1, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 5\n",
      "[1, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 4\n",
      "[1, 0, 0, 1, 1, 0, 0]\n",
      "[1, 0, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 0, 1, 1, 0, 1, 0]\n",
      "[1, 0, 0, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 1, 1, 0]\n",
      "[1, 0, 0, 1, 1, 0, 1, 1, 1]\n",
      "[1, 0, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 4\n",
      "[1, 0, 0, 1, 1, 1, 0]\n",
      "[1, 0, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 1, 1, 0, 0]\n",
      "[1, 0, 0, 1, 1, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1, 1, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 1, 0]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 67 Xright.length = 18\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 24 Xright.length = 43\n",
      "[1, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 11 Xright.length = 13\n",
      "[1, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 7\n",
      "[1, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 6\n",
      "[1, 1, 0, 0, 0, 1, 0]\n",
      "[1, 1, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 4\n",
      "[1, 1, 0, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 0, 0, 0, 1, 1, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 1, 0, 0, 0, 1, 1, 1, 0]\n",
      "[1, 1, 0, 0, 0, 1, 1, 1, 1]\n",
      "[1, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 9\n",
      "[1, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 1, 1]\n",
      "[1, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 4\n",
      "[1, 1, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 4\n",
      "[1, 1, 0, 0, 1, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 1, 0, 0, 1, 1, 0, 1, 0]\n",
      "[1, 1, 0, 0, 1, 1, 0, 1, 1]\n",
      "[1, 1, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 1, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 0, 0, 1, 1, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 1, 1, 1, 0]\n",
      "[1, 1, 0, 0, 1, 1, 1, 1, 1]\n",
      "[1, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 32 Xright.length = 11\n",
      "[1, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 8 Xright.length = 24\n",
      "[1, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 1\n",
      "[1, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 3\n",
      "[1, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0, 1, 0, 0, 0, 1, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 22\n",
      "[1, 1, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 0, 1, 0, 1, 0, 0]\n",
      "[1, 1, 0, 1, 0, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 18 Xright.length = 4\n",
      "[1, 1, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 17 Xright.length = 1\n",
      "[1, 1, 0, 1, 0, 1, 1, 0, 0]\n",
      "[1, 1, 0, 1, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 1, 0, 1, 0, 1, 1, 1, 0]\n",
      "[1, 1, 0, 1, 0, 1, 1, 1, 1]\n",
      "[1, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 9\n",
      "[1, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 2\n",
      "[1, 1, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 6\n",
      "[1, 1, 0, 1, 1, 1, 0, 0]\n",
      "[1, 1, 0, 1, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 2\n",
      "[1, 1, 0, 1, 1, 1, 0, 1, 0]\n",
      "[1, 1, 0, 1, 1, 1, 0, 1, 1]\n",
      "[1, 1, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 1, 0, 0]\n",
      "[1, 1, 0, 1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1, 1, 1]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 15 Xright.length = 3\n",
      "[1, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 14\n",
      "[1, 1, 1, 0, 0]\n",
      "[1, 1, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 11 Xright.length = 3\n",
      "[1, 1, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 5\n",
      "[1, 1, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 6 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 6 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 2\n",
      "[1, 1, 1, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 1, 0, 1, 0, 1, 0, 0]\n",
      "[1, 1, 1, 0, 1, 0, 1, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 1, 1, 0]\n",
      "[1, 1, 1, 0, 1, 0, 1, 1, 1]\n",
      "[1, 1, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 1, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 1, 0, 0, 0]\n",
      "[1, 1, 1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1, 1, 0, 1]\n",
      "[1, 1, 1, 0, 1, 1, 1]\n",
      "[1, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 125 Xright.length = 131\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 104 Xright.length = 21\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 93 Xright.length = 11\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 17 Xright.length = 76\n",
      "[0, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 6 Xright.length = 11\n",
      "[0, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 5\n",
      "[0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 1\n",
      "[0, 0, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 1, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 8\n",
      "[0, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 5\n",
      "[0, 0, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 0, 0, 1, 1, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 0, 1, 0]\n",
      "[0, 0, 0, 0, 1, 1, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 1, 1, 0]\n",
      "[0, 0, 0, 0, 1, 1, 1, 1, 1]\n",
      "[0, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 35 Xright.length = 41\n",
      "[0, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 28 Xright.length = 7\n",
      "[0, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 11 Xright.length = 17\n",
      "[0, 0, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 10\n",
      "[0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 5\n",
      "[0, 0, 0, 1, 0, 0, 0, 1, 0]\n",
      "[0, 0, 0, 1, 0, 0, 0, 1, 1]\n",
      "[0, 0, 0, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 12 Xright.length = 5\n",
      "[0, 0, 0, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 7\n",
      "[0, 0, 0, 1, 0, 0, 1, 0, 0]\n",
      "[0, 0, 0, 1, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 0, 0, 1, 0, 0, 1, 1, 0]\n",
      "[0, 0, 0, 1, 0, 0, 1, 1, 1]\n",
      "[0, 0, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 4\n",
      "[0, 0, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 0, 1, 0, 1, 1, 0, 0]\n",
      "[0, 0, 0, 1, 0, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1, 1, 1]\n",
      "[0, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 11 Xright.length = 30\n",
      "[0, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 5\n",
      "[0, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 2\n",
      "[0, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0, 1, 0]\n",
      "[0, 0, 0, 1, 1, 0, 0, 1, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 0, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 1, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 1, 1, 0]\n",
      "[0, 0, 0, 1, 1, 0, 1, 1, 1]\n",
      "[0, 0, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 25 Xright.length = 5\n",
      "[0, 0, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 15 Xright.length = 10\n",
      "[0, 0, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 10 Xright.length = 5\n",
      "[0, 0, 0, 1, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 9\n",
      "[0, 0, 0, 1, 1, 1, 0, 1, 0]\n",
      "[0, 0, 0, 1, 1, 1, 0, 1, 1]\n",
      "[0, 0, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 0, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 1, 1, 0, 0]\n",
      "[0, 0, 0, 1, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 1, 1, 1, 0]\n",
      "[0, 0, 0, 1, 1, 1, 1, 1, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 6 Xright.length = 5\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 5\n",
      "[0, 0, 1, 0, 0]\n",
      "[0, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 1\n",
      "[0, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 1, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 0, 1, 0, 0, 1, 0]\n",
      "[0, 0, 1, 0, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 16 Xright.length = 5\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 4 Xright.length = 12\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 9 Xright.length = 3\n",
      "[0, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 8 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 4\n",
      "[0, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 1, 0, 1, 0, 0, 0, 1, 0]\n",
      "[0, 1, 0, 1, 0, 0, 0, 1, 1]\n",
      "[0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1, 1]\n",
      "[0, 1, 1]\n",
      "at height 4 X --> Xleft.length = 5 Xright.length = 0\n",
      "[0, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 5 Xright.length = 0\n",
      "[0, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 116 Xright.length = 15\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 111 Xright.length = 5\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 102 Xright.length = 9\n",
      "[1, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 4 Xright.length = 98\n",
      "[1, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 0, 0, 0, 1, 0]\n",
      "[1, 0, 0, 0, 0, 1, 1]\n",
      "[1, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 52 Xright.length = 46\n",
      "[1, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 27 Xright.length = 25\n",
      "[1, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 7 Xright.length = 20\n",
      "[1, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 6\n",
      "[1, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 19\n",
      "[1, 0, 0, 0, 1, 0, 0, 1, 0]\n",
      "[1, 0, 0, 0, 1, 0, 0, 1, 1]\n",
      "[1, 0, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 16 Xright.length = 9\n",
      "[1, 0, 0, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 12\n",
      "[1, 0, 0, 0, 1, 0, 1, 0, 0]\n",
      "[1, 0, 0, 0, 1, 0, 1, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 7\n",
      "[1, 0, 0, 0, 1, 0, 1, 1, 0]\n",
      "[1, 0, 0, 0, 1, 0, 1, 1, 1]\n",
      "[1, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 18 Xright.length = 28\n",
      "[1, 0, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 6 Xright.length = 12\n",
      "[1, 0, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 4\n",
      "[1, 0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 7 Xright.length = 5\n",
      "[1, 0, 0, 0, 1, 1, 0, 1, 0]\n",
      "[1, 0, 0, 0, 1, 1, 0, 1, 1]\n",
      "[1, 0, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 24 Xright.length = 4\n",
      "[1, 0, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 13 Xright.length = 11\n",
      "[1, 0, 0, 0, 1, 1, 1, 0, 0]\n",
      "[1, 0, 0, 0, 1, 1, 1, 0, 1]\n",
      "[1, 0, 0, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 0, 0, 1, 1, 1, 1, 0]\n",
      "[1, 0, 0, 0, 1, 1, 1, 1, 1]\n",
      "[1, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 6\n",
      "[1, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 3\n",
      "[1, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 0, 0, 1, 1, 1, 0]\n",
      "[1, 0, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 0, 1, 1, 1, 1, 0]\n",
      "[1, 0, 0, 1, 1, 1, 1, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 13 Xright.length = 2\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 11\n",
      "[1, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 9 Xright.length = 2\n",
      "[1, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 6\n",
      "[1, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 1\n",
      "[1, 1, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 1, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 0, 1, 0, 1, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 0, 1, 0]\n",
      "[1, 1, 0, 1, 0, 1, 0, 1, 1]\n",
      "[1, 1, 0, 1, 0, 1, 1]\n",
      "[1, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 137 Xright.length = 119\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 73 Xright.length = 64\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 9 Xright.length = 64\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 7\n",
      "[0, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 4 Xright.length = 3\n",
      "[0, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 3 Xright.length = 61\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 23 Xright.length = 38\n",
      "[0, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 7 Xright.length = 16\n",
      "[0, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 4\n",
      "[0, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0, 1, 0]\n",
      "[0, 0, 1, 1, 0, 0, 0, 1, 1]\n",
      "[0, 0, 1, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 0, 1, 1, 0, 0, 1, 0]\n",
      "[0, 0, 1, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 1, 1, 0]\n",
      "[0, 0, 1, 1, 0, 0, 1, 1, 1]\n",
      "[0, 0, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 11\n",
      "[0, 0, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 0, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 0, 1, 0]\n",
      "[0, 0, 1, 1, 0, 1, 0, 1, 1]\n",
      "[0, 0, 1, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 8 Xright.length = 3\n",
      "[0, 0, 1, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 3\n",
      "[0, 0, 1, 1, 0, 1, 1, 0, 0]\n",
      "[0, 0, 1, 1, 0, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 1, 0, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 0, 1, 1, 1, 1]\n",
      "[0, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 8 Xright.length = 30\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 3\n",
      "[0, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 1, 1, 0, 0, 1, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 1, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1, 1]\n",
      "[0, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 28 Xright.length = 2\n",
      "[0, 0, 1, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 22 Xright.length = 6\n",
      "[0, 0, 1, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 8 Xright.length = 14\n",
      "[0, 0, 1, 1, 1, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 4\n",
      "[0, 0, 1, 1, 1, 1, 0, 1, 0]\n",
      "[0, 0, 1, 1, 1, 1, 0, 1, 1]\n",
      "[0, 0, 1, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 1, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 62 Xright.length = 2\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 59 Xright.length = 3\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 50 Xright.length = 9\n",
      "[0, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 46\n",
      "[0, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 1, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1, 1]\n",
      "[0, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 42 Xright.length = 4\n",
      "[0, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 10 Xright.length = 32\n",
      "[0, 1, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 6 Xright.length = 4\n",
      "[0, 1, 0, 0, 0, 1, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 17 Xright.length = 15\n",
      "[0, 1, 0, 0, 0, 1, 0, 1, 0]\n",
      "[0, 1, 0, 0, 0, 1, 0, 1, 1]\n",
      "[0, 1, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 1, 0, 0, 0, 1, 1, 0]\n",
      "[0, 1, 0, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 1, 1, 1, 0]\n",
      "[0, 1, 0, 0, 0, 1, 1, 1, 1]\n",
      "[0, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 6 Xright.length = 3\n",
      "[0, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 2\n",
      "[0, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 0, 1, 0]\n",
      "[0, 1, 0, 0, 1, 0, 0, 1, 1]\n",
      "[0, 1, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 0, 1, 0]\n",
      "[0, 1, 0, 0, 1, 0, 1, 1]\n",
      "[0, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1, 1]\n",
      "[0, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 1, 0, 1, 0]\n",
      "[0, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1, 1]\n",
      "[0, 1, 1]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 28 Xright.length = 91\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 1 Xright.length = 27\n",
      "[1, 0, 0]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 4 Xright.length = 23\n",
      "[1, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 22\n",
      "[1, 0, 1, 1, 0]\n",
      "[1, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 17 Xright.length = 5\n",
      "[1, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 11\n",
      "[1, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 2\n",
      "[1, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 0, 1, 0]\n",
      "[1, 0, 1, 1, 1, 0, 0, 1, 1]\n",
      "[1, 0, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 9 Xright.length = 2\n",
      "[1, 0, 1, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 8 Xright.length = 1\n",
      "[1, 0, 1, 1, 1, 0, 1, 0, 0]\n",
      "[1, 0, 1, 1, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 1, 1, 1, 0, 1, 1, 0]\n",
      "[1, 0, 1, 1, 1, 0, 1, 1, 1]\n",
      "[1, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 0, 1, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 1, 0, 0, 0]\n",
      "[1, 0, 1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 1, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 1, 1, 0, 0]\n",
      "[1, 0, 1, 1, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 89 Xright.length = 2\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 77 Xright.length = 12\n",
      "[1, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 70 Xright.length = 7\n",
      "[1, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 62 Xright.length = 8\n",
      "[1, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 24 Xright.length = 38\n",
      "[1, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 10 Xright.length = 14\n",
      "[1, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 6 Xright.length = 4\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 10\n",
      "[1, 1, 0, 0, 0, 0, 0, 1, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 37\n",
      "[1, 1, 0, 0, 0, 0, 1, 0]\n",
      "[1, 1, 0, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 29 Xright.length = 8\n",
      "[1, 1, 0, 0, 0, 0, 1, 1, 0]\n",
      "[1, 1, 0, 0, 0, 0, 1, 1, 1]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 2\n",
      "[1, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 4\n",
      "[1, 1, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 0, 0, 0, 1, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0, 1, 0]\n",
      "[1, 1, 0, 0, 0, 1, 0, 1, 1]\n",
      "[1, 1, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 0, 0, 0, 1, 1, 0]\n",
      "[1, 1, 0, 0, 0, 1, 1, 1]\n",
      "[1, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 4\n",
      "[1, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 1, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 1, 0, 0, 0]\n",
      "[1, 1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 7 Xright.length = 5\n",
      "[1, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 2\n",
      "[1, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 1\n",
      "[1, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 0, 0, 1, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 1]\n",
      "[1, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 4\n",
      "[1, 1, 0, 1, 1, 0]\n",
      "[1, 1, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 1, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 0, 0, 0]\n",
      "[1, 1, 0, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 1, 0, 0]\n",
      "[1, 1, 0, 1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1, 1, 1]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 1, 0]\n",
      "[1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 124 Xright.length = 132\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 91 Xright.length = 33\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 52 Xright.length = 39\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 50 Xright.length = 2\n",
      "[0, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 17 Xright.length = 33\n",
      "[0, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 7 Xright.length = 10\n",
      "[0, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 4\n",
      "[0, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 1, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 1, 1]\n",
      "[0, 0, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 1, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 1, 1]\n",
      "[0, 0, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 7\n",
      "[0, 0, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 0, 0, 0, 1, 0, 0]\n",
      "[0, 0, 0, 0, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 0, 0, 1, 0, 1, 0]\n",
      "[0, 0, 0, 0, 0, 1, 0, 1, 1]\n",
      "[0, 0, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 5\n",
      "[0, 0, 0, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 1, 1, 0, 0]\n",
      "[0, 0, 0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 1\n",
      "[0, 0, 0, 0, 0, 1, 1, 1, 0]\n",
      "[0, 0, 0, 0, 0, 1, 1, 1, 1]\n",
      "[0, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 7 Xright.length = 26\n",
      "[0, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 1\n",
      "[0, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 3\n",
      "[0, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 0, 0, 1, 0, 0, 1, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 23 Xright.length = 3\n",
      "[0, 0, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 21 Xright.length = 2\n",
      "[0, 0, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 19 Xright.length = 2\n",
      "[0, 0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 0, 1, 1, 0, 1, 0]\n",
      "[0, 0, 0, 0, 1, 1, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1, 1]\n",
      "[0, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 1, 0]\n",
      "[0, 0, 0, 1, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 6 Xright.length = 33\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 4\n",
      "[0, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 0, 1, 1, 0]\n",
      "[0, 0, 1, 0, 1, 1, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 29 Xright.length = 4\n",
      "[0, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 10 Xright.length = 19\n",
      "[0, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 4\n",
      "[0, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 1\n",
      "[0, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 1, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 1, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 16\n",
      "[0, 0, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 12\n",
      "[0, 0, 1, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 0, 1, 1, 0, 1, 1, 0, 0]\n",
      "[0, 0, 1, 1, 0, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 10 Xright.length = 2\n",
      "[0, 0, 1, 1, 0, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 0, 1, 1, 1, 1]\n",
      "[0, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 32 Xright.length = 1\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 16 Xright.length = 16\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 11 Xright.length = 5\n",
      "[0, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 6 Xright.length = 5\n",
      "[0, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 4\n",
      "[0, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 1, 0, 0, 0, 0, 1, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1, 1]\n",
      "[0, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 1, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 1, 1, 0, 0]\n",
      "[0, 1, 0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 1, 1]\n",
      "[0, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1]\n",
      "[0, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 14\n",
      "[0, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 6 Xright.length = 8\n",
      "[0, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 2\n",
      "[0, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 1, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 1, 0, 0]\n",
      "[0, 1, 0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 1, 1]\n",
      "[0, 1, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 3\n",
      "[0, 1, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 1, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 1, 0, 0, 0]\n",
      "[0, 1, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 1, 0, 1, 1, 1, 0, 1, 0]\n",
      "[0, 1, 0, 1, 1, 1, 0, 1, 1]\n",
      "[0, 1, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 1, 0, 1, 1, 1, 1, 0]\n",
      "[0, 1, 0, 1, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 1, 1, 1, 0]\n",
      "[0, 1, 0, 1, 1, 1, 1, 1, 1]\n",
      "[0, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 8 Xright.length = 124\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 4 Xright.length = 4\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 1, 0]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 0, 1, 1, 0]\n",
      "[1, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 1, 1, 1, 0]\n",
      "[1, 0, 1, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 120 Xright.length = 4\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 90 Xright.length = 30\n",
      "[1, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 12 Xright.length = 78\n",
      "[1, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 9 Xright.length = 3\n",
      "[1, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 8 Xright.length = 1\n",
      "[1, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 3\n",
      "[1, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 0, 0, 0, 0, 0, 1, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 15 Xright.length = 63\n",
      "[1, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 13\n",
      "[1, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 10\n",
      "[1, 1, 0, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0, 0, 1, 0, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 8\n",
      "[1, 1, 0, 0, 1, 0, 1, 1, 0]\n",
      "[1, 1, 0, 0, 1, 0, 1, 1, 1]\n",
      "[1, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 51 Xright.length = 12\n",
      "[1, 1, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 10 Xright.length = 41\n",
      "[1, 1, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 8 Xright.length = 2\n",
      "[1, 1, 0, 0, 1, 1, 0, 0, 0]\n",
      "[1, 1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 14 Xright.length = 27\n",
      "[1, 1, 0, 0, 1, 1, 0, 1, 0]\n",
      "[1, 1, 0, 0, 1, 1, 0, 1, 1]\n",
      "[1, 1, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 7 Xright.length = 5\n",
      "[1, 1, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 7 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 1, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 1\n",
      "[1, 1, 0, 0, 1, 1, 1, 1, 0]\n",
      "[1, 1, 0, 0, 1, 1, 1, 1, 1]\n",
      "[1, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 11 Xright.length = 19\n",
      "[1, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 6 Xright.length = 5\n",
      "[1, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 1\n",
      "[1, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 2\n",
      "[1, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 0, 0, 1, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 1, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 1, 0, 0]\n",
      "[1, 1, 0, 1, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 15 Xright.length = 4\n",
      "[1, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 8\n",
      "[1, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 5\n",
      "[1, 1, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 2\n",
      "[1, 1, 0, 1, 1, 0, 0, 1, 0]\n",
      "[1, 1, 0, 1, 1, 0, 0, 1, 1]\n",
      "[1, 1, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 7\n",
      "[1, 1, 0, 1, 1, 0, 1, 0]\n",
      "[1, 1, 0, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 3\n",
      "[1, 1, 0, 1, 1, 0, 1, 1, 0]\n",
      "[1, 1, 0, 1, 1, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 1, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 0, 0, 0]\n",
      "[1, 1, 0, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1, 1]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 1, 1, 0]\n",
      "[1, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 141 Xright.length = 115\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 1 Xright.length = 140\n",
      "[0, 0]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 138 Xright.length = 2\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 41 Xright.length = 97\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 32 Xright.length = 9\n",
      "[0, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 14 Xright.length = 18\n",
      "[0, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 12\n",
      "[0, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 11\n",
      "[0, 1, 0, 0, 0, 0, 1, 0]\n",
      "[0, 1, 0, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 8\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 0]\n",
      "[0, 1, 0, 0, 0, 0, 1, 1, 1]\n",
      "[0, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 16\n",
      "[0, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 1, 0, 0, 0, 1, 0, 0]\n",
      "[0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 8 Xright.length = 8\n",
      "[0, 1, 0, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 5\n",
      "[0, 1, 0, 0, 0, 1, 1, 0, 0]\n",
      "[0, 1, 0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 7\n",
      "[0, 1, 0, 0, 0, 1, 1, 1, 0]\n",
      "[0, 1, 0, 0, 0, 1, 1, 1, 1]\n",
      "[0, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 6\n",
      "[0, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 2\n",
      "[0, 1, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 1, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 1, 1, 0, 0]\n",
      "[0, 1, 0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1, 1, 1]\n",
      "[0, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 8 Xright.length = 89\n",
      "[0, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 5\n",
      "[0, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 1, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 1, 0, 0, 0]\n",
      "[0, 1, 0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 1, 1, 0, 0]\n",
      "[0, 1, 0, 1, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1, 1, 1]\n",
      "[0, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 55 Xright.length = 34\n",
      "[0, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 8 Xright.length = 47\n",
      "[0, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 6 Xright.length = 2\n",
      "[0, 1, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 1\n",
      "[0, 1, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0, 1, 0]\n",
      "[0, 1, 0, 1, 1, 0, 0, 1, 1]\n",
      "[0, 1, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 46 Xright.length = 1\n",
      "[0, 1, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 45\n",
      "[0, 1, 0, 1, 1, 0, 1, 0, 0]\n",
      "[0, 1, 0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 1, 1]\n",
      "[0, 1, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 31 Xright.length = 3\n",
      "[0, 1, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 16 Xright.length = 15\n",
      "[0, 1, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 12\n",
      "[0, 1, 0, 1, 1, 1, 0, 0, 0]\n",
      "[0, 1, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 12\n",
      "[0, 1, 0, 1, 1, 1, 0, 1, 0]\n",
      "[0, 1, 0, 1, 1, 1, 0, 1, 1]\n",
      "[0, 1, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 1, 0, 1, 1, 1, 1, 0]\n",
      "[0, 1, 0, 1, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 1, 1, 1, 0]\n",
      "[0, 1, 0, 1, 1, 1, 1, 1, 1]\n",
      "[0, 1, 1]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 21 Xright.length = 94\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 7 Xright.length = 14\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 1 Xright.length = 6\n",
      "[1, 0, 0, 0]\n",
      "[1, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 4\n",
      "[1, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 0]\n",
      "[1, 0, 0, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 5 Xright.length = 9\n",
      "[1, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 4\n",
      "[1, 0, 1, 0, 0]\n",
      "[1, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 6\n",
      "[1, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 4\n",
      "[1, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 1, 1, 1, 1, 0, 0, 0]\n",
      "[1, 0, 1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 7 Xright.length = 87\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 5 Xright.length = 2\n",
      "[1, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0, 0, 1, 0]\n",
      "[1, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 1, 0, 0, 0]\n",
      "[1, 1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 83 Xright.length = 4\n",
      "[1, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 68 Xright.length = 15\n",
      "[1, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 66 Xright.length = 2\n",
      "[1, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 64 Xright.length = 2\n",
      "[1, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 13 Xright.length = 51\n",
      "[1, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 8 Xright.length = 5\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 42 Xright.length = 9\n",
      "[1, 1, 1, 0, 0, 0, 0, 1, 0]\n",
      "[1, 1, 1, 0, 0, 0, 0, 1, 1]\n",
      "[1, 1, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 1, 0, 0, 0, 1, 0]\n",
      "[1, 1, 1, 0, 0, 0, 1, 1]\n",
      "[1, 1, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 1, 0, 0, 1, 0]\n",
      "[1, 1, 1, 0, 0, 1, 1]\n",
      "[1, 1, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 14 Xright.length = 1\n",
      "[1, 1, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 11 Xright.length = 3\n",
      "[1, 1, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 9 Xright.length = 2\n",
      "[1, 1, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 7 Xright.length = 2\n",
      "[1, 1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 1, 0, 1, 0, 0, 1, 0]\n",
      "[1, 1, 1, 0, 1, 0, 0, 1, 1]\n",
      "[1, 1, 1, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 1, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 1, 0, 1, 0, 1, 0, 0]\n",
      "[1, 1, 1, 0, 1, 0, 1, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 1, 1]\n",
      "[1, 1, 1, 0, 1, 1]\n",
      "[1, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 1, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 0, 0, 0, 0]\n",
      "[1, 1, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 126 Xright.length = 130\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 122 Xright.length = 4\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 57 Xright.length = 65\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 49 Xright.length = 8\n",
      "[0, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 27 Xright.length = 22\n",
      "[0, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 11 Xright.length = 16\n",
      "[0, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 4\n",
      "[0, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 5\n",
      "[0, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 0, 0, 0, 0, 0, 0, 1, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 1, 1]\n",
      "[0, 0, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 0, 0, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 0, 0, 0, 1, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 0, 0, 0, 1, 1, 0]\n",
      "[0, 0, 0, 0, 0, 0, 1, 1, 1]\n",
      "[0, 0, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 12\n",
      "[0, 0, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 1, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 9\n",
      "[0, 0, 0, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 1, 1, 0, 0]\n",
      "[0, 0, 0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 4\n",
      "[0, 0, 0, 0, 0, 1, 1, 1, 0]\n",
      "[0, 0, 0, 0, 0, 1, 1, 1, 1]\n",
      "[0, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 13 Xright.length = 9\n",
      "[0, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 8 Xright.length = 5\n",
      "[0, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 6\n",
      "[0, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 1\n",
      "[0, 0, 0, 0, 1, 0, 0, 1, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 0, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 1, 0, 0]\n",
      "[0, 0, 0, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 1, 1, 0]\n",
      "[0, 0, 0, 0, 1, 0, 1, 1, 1]\n",
      "[0, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 7\n",
      "[0, 0, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 3\n",
      "[0, 0, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 1, 1, 0]\n",
      "[0, 0, 0, 0, 1, 1, 1, 1, 1]\n",
      "[0, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 4 Xright.length = 4\n",
      "[0, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 35 Xright.length = 30\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 30 Xright.length = 5\n",
      "[0, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 28 Xright.length = 2\n",
      "[0, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 14 Xright.length = 14\n",
      "[0, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 9\n",
      "[0, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 8\n",
      "[0, 0, 1, 0, 0, 0, 0, 1, 0]\n",
      "[0, 0, 1, 0, 0, 0, 0, 1, 1]\n",
      "[0, 0, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 10\n",
      "[0, 0, 1, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 0, 1, 0, 0, 0, 1, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 9 Xright.length = 1\n",
      "[0, 0, 1, 0, 0, 0, 1, 1, 0]\n",
      "[0, 0, 1, 0, 0, 0, 1, 1, 1]\n",
      "[0, 0, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 0, 0, 1, 0]\n",
      "[0, 0, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 0, 1, 0, 1, 0]\n",
      "[0, 0, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 0, 1, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 1, 1, 0, 0]\n",
      "[0, 0, 1, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1, 1, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 29 Xright.length = 1\n",
      "[0, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 22 Xright.length = 7\n",
      "[0, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 20 Xright.length = 2\n",
      "[0, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 15 Xright.length = 5\n",
      "[0, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 11 Xright.length = 4\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 1\n",
      "[0, 0, 1, 1, 0, 0, 0, 1, 0]\n",
      "[0, 0, 1, 1, 0, 0, 0, 1, 1]\n",
      "[0, 0, 1, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 1, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 5\n",
      "[0, 0, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 1, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 1, 0, 0]\n",
      "[0, 0, 1, 1, 0, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 0, 1, 1, 1, 1]\n",
      "[0, 0, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1]\n",
      "[0, 1, 1]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 43 Xright.length = 87\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 11 Xright.length = 32\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 10 Xright.length = 1\n",
      "[1, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 7 Xright.length = 3\n",
      "[1, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 2\n",
      "[1, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 0, 0, 0, 0, 0, 1, 0]\n",
      "[1, 0, 0, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 1, 1, 0]\n",
      "[1, 0, 0, 0, 0, 0, 1, 1, 1]\n",
      "[1, 0, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 1, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1, 1]\n",
      "[1, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 0, 0, 0, 1, 0]\n",
      "[1, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 0, 0, 1, 1, 0]\n",
      "[1, 0, 0, 0, 1, 1, 1]\n",
      "[1, 0, 0, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 21 Xright.length = 11\n",
      "[1, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 17 Xright.length = 4\n",
      "[1, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 12 Xright.length = 5\n",
      "[1, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 10\n",
      "[1, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 9\n",
      "[1, 0, 1, 0, 0, 0, 1, 0]\n",
      "[1, 0, 1, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 5\n",
      "[1, 0, 1, 0, 0, 0, 1, 1, 0]\n",
      "[1, 0, 1, 0, 0, 0, 1, 1, 1]\n",
      "[1, 0, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 0, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 1, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 1, 1, 0, 0]\n",
      "[1, 0, 1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 1, 1]\n",
      "[1, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 1, 0, 1, 0]\n",
      "[1, 0, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 1, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 1, 1, 0, 0, 0]\n",
      "[1, 0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 0, 1, 1, 1]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 8 Xright.length = 3\n",
      "[1, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 4\n",
      "[1, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 1, 0, 0]\n",
      "[1, 0, 1, 1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1, 1, 1]\n",
      "[1, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 1, 1, 1, 0, 0]\n",
      "[1, 0, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 78 Xright.length = 9\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 73 Xright.length = 5\n",
      "[1, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 40 Xright.length = 33\n",
      "[1, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 18 Xright.length = 22\n",
      "[1, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 13 Xright.length = 5\n",
      "[1, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 11\n",
      "[1, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 7\n",
      "[1, 1, 0, 0, 0, 0, 0, 1, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 1, 0, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 1, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 0, 0, 0, 0, 1, 1, 0]\n",
      "[1, 1, 0, 0, 0, 0, 1, 1, 1]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 19\n",
      "[1, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0, 0, 0, 1, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0, 1, 0]\n",
      "[1, 1, 0, 0, 0, 1, 0, 1, 1]\n",
      "[1, 1, 0, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 15\n",
      "[1, 1, 0, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 1, 0, 0, 0, 1, 1, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 7 Xright.length = 8\n",
      "[1, 1, 0, 0, 0, 1, 1, 1, 0]\n",
      "[1, 1, 0, 0, 0, 1, 1, 1, 1]\n",
      "[1, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 20 Xright.length = 13\n",
      "[1, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 16\n",
      "[1, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 1, 0, 0, 1, 0, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0, 1, 0]\n",
      "[1, 1, 0, 0, 1, 0, 0, 1, 1]\n",
      "[1, 1, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 13\n",
      "[1, 1, 0, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 0, 0, 1, 0, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 11\n",
      "[1, 1, 0, 0, 1, 0, 1, 1, 0]\n",
      "[1, 1, 0, 0, 1, 0, 1, 1, 1]\n",
      "[1, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 10 Xright.length = 3\n",
      "[1, 1, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 6\n",
      "[1, 1, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 1, 0, 0, 1, 1, 0, 0, 0]\n",
      "[1, 1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 5\n",
      "[1, 1, 0, 0, 1, 1, 0, 1, 0]\n",
      "[1, 1, 0, 0, 1, 1, 0, 1, 1]\n",
      "[1, 1, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 1, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1, 1, 1]\n",
      "[1, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 4 Xright.length = 1\n",
      "[1, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 1, 0, 1, 0, 0]\n",
      "[1, 1, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0, 1, 0, 1, 0]\n",
      "[1, 1, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 1, 0, 0]\n",
      "[1, 1, 0, 1, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1, 1]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 7 Xright.length = 2\n",
      "[1, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 4\n",
      "[1, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 1]\n",
      "[1, 1, 1, 0, 1, 1]\n",
      "[1, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 133 Xright.length = 123\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 130 Xright.length = 3\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 84 Xright.length = 46\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 58 Xright.length = 26\n",
      "[0, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 55\n",
      "[0, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 47 Xright.length = 8\n",
      "[0, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 41 Xright.length = 6\n",
      "[0, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 31 Xright.length = 10\n",
      "[0, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 14 Xright.length = 17\n",
      "[0, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 7\n",
      "[0, 0, 0, 0, 1, 0, 0, 1, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 4\n",
      "[0, 0, 0, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 0, 1, 0, 1, 0, 0]\n",
      "[0, 0, 0, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 0, 0, 1, 0, 1, 1, 0]\n",
      "[0, 0, 0, 0, 1, 0, 1, 1, 1]\n",
      "[0, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 3\n",
      "[0, 0, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 0, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 0, 1, 0]\n",
      "[0, 0, 0, 0, 1, 1, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1, 1]\n",
      "[0, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 5 Xright.length = 21\n",
      "[0, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 0, 0, 1, 0, 0]\n",
      "[0, 0, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 0, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 1, 1, 0, 0]\n",
      "[0, 0, 0, 1, 0, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1, 1, 1]\n",
      "[0, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 15 Xright.length = 6\n",
      "[0, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 12 Xright.length = 3\n",
      "[0, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 10\n",
      "[0, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 5\n",
      "[0, 0, 0, 1, 1, 0, 0, 1, 0]\n",
      "[0, 0, 0, 1, 1, 0, 0, 1, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 1, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1, 1]\n",
      "[0, 0, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 4\n",
      "[0, 0, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 0, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 1, 1, 0, 0]\n",
      "[0, 0, 0, 1, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 1, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 15 Xright.length = 31\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 6 Xright.length = 9\n",
      "[0, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 3\n",
      "[0, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 1, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 1, 1]\n",
      "[0, 0, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 1, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 8 Xright.length = 1\n",
      "[0, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 7 Xright.length = 1\n",
      "[0, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 6\n",
      "[0, 0, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 1, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 4\n",
      "[0, 0, 1, 0, 1, 0, 0, 1, 0]\n",
      "[0, 0, 1, 0, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 16 Xright.length = 15\n",
      "[0, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 6 Xright.length = 10\n",
      "[0, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 1\n",
      "[0, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0, 1, 0]\n",
      "[0, 0, 1, 1, 0, 0, 0, 1, 1]\n",
      "[0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 6\n",
      "[0, 0, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 5\n",
      "[0, 0, 1, 1, 0, 1, 1, 0]\n",
      "[0, 0, 1, 1, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 0, 1, 1, 1, 1]\n",
      "[0, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 13 Xright.length = 2\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 10 Xright.length = 3\n",
      "[0, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 9\n",
      "[0, 0, 1, 1, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 4\n",
      "[0, 0, 1, 1, 1, 0, 0, 1, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 1, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 1, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1, 1]\n",
      "[0, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1]\n",
      "[0, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 120 Xright.length = 3\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 11 Xright.length = 109\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 5 Xright.length = 6\n",
      "[1, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 4\n",
      "[1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 0, 1, 1, 1]\n",
      "[1, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 4 Xright.length = 2\n",
      "[1, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 0, 1, 0, 0]\n",
      "[1, 0, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 1, 0, 0]\n",
      "[1, 0, 0, 1, 0, 1, 0, 1]\n",
      "[1, 0, 0, 1, 0, 1, 1]\n",
      "[1, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 10 Xright.length = 99\n",
      "[1, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 8 Xright.length = 2\n",
      "[1, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 4\n",
      "[1, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 1, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 1, 1]\n",
      "[1, 0, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 1, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 1, 1, 0, 0]\n",
      "[1, 0, 1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 1, 1]\n",
      "[1, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 1, 0, 1, 0]\n",
      "[1, 0, 1, 0, 1, 1]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 18 Xright.length = 81\n",
      "[1, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 13 Xright.length = 5\n",
      "[1, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 9 Xright.length = 4\n",
      "[1, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 6\n",
      "[1, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 1\n",
      "[1, 0, 1, 1, 0, 0, 0, 1, 0]\n",
      "[1, 0, 1, 1, 0, 0, 0, 1, 1]\n",
      "[1, 0, 1, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 1, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 1, 0, 0]\n",
      "[1, 0, 1, 1, 0, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 1, 1, 0]\n",
      "[1, 0, 1, 1, 0, 0, 1, 1, 1]\n",
      "[1, 0, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 1\n",
      "[1, 0, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 1, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1, 1]\n",
      "[1, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 52 Xright.length = 29\n",
      "[1, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 46 Xright.length = 6\n",
      "[1, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 20 Xright.length = 26\n",
      "[1, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 17 Xright.length = 3\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 23 Xright.length = 3\n",
      "[1, 0, 1, 1, 1, 0, 0, 1, 0]\n",
      "[1, 0, 1, 1, 1, 0, 0, 1, 1]\n",
      "[1, 0, 1, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 4\n",
      "[1, 0, 1, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 1, 1, 1, 0, 1, 0, 0]\n",
      "[1, 0, 1, 1, 1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 1, 1, 1, 0, 1, 1, 0]\n",
      "[1, 0, 1, 1, 1, 0, 1, 1, 1]\n",
      "[1, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 8 Xright.length = 21\n",
      "[1, 0, 1, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 7\n",
      "[1, 0, 1, 1, 1, 1, 0, 0]\n",
      "[1, 0, 1, 1, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 6\n",
      "[1, 0, 1, 1, 1, 1, 0, 1, 0]\n",
      "[1, 0, 1, 1, 1, 1, 0, 1, 1]\n",
      "[1, 0, 1, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 10 Xright.length = 11\n",
      "[1, 0, 1, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 8 Xright.length = 2\n",
      "[1, 0, 1, 1, 1, 1, 1, 0, 0]\n",
      "[1, 0, 1, 1, 1, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 10\n",
      "[1, 0, 1, 1, 1, 1, 1, 1, 0]\n",
      "[1, 0, 1, 1, 1, 1, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 1, 0]\n",
      "[1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 120 Xright.length = 136\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 110 Xright.length = 10\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 47 Xright.length = 63\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 18 Xright.length = 29\n",
      "[0, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 5 Xright.length = 13\n",
      "[0, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 0, 1, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 0, 0, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 8 Xright.length = 5\n",
      "[0, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 4\n",
      "[0, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 0, 1, 0]\n",
      "[0, 0, 0, 0, 1, 0, 0, 1, 1]\n",
      "[0, 0, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 0, 0, 0, 1, 0, 1, 0]\n",
      "[0, 0, 0, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 0, 1, 1, 0]\n",
      "[0, 0, 0, 0, 1, 0, 1, 1, 1]\n",
      "[0, 0, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 0, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 0]\n",
      "[0, 0, 0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 0, 1, 1, 1, 1]\n",
      "[0, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 16 Xright.length = 13\n",
      "[0, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 15\n",
      "[0, 0, 0, 1, 0, 0]\n",
      "[0, 0, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 12 Xright.length = 3\n",
      "[0, 0, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 8 Xright.length = 4\n",
      "[0, 0, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 5\n",
      "[0, 0, 0, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 0, 1, 0, 1, 0, 1, 0]\n",
      "[0, 0, 0, 1, 0, 1, 0, 1, 1]\n",
      "[0, 0, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 0, 1, 0, 1, 1, 0]\n",
      "[0, 0, 0, 1, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 0, 1, 1, 1, 0]\n",
      "[0, 0, 0, 1, 0, 1, 1, 1, 1]\n",
      "[0, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 8 Xright.length = 5\n",
      "[0, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 5\n",
      "[0, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 0, 1, 0]\n",
      "[0, 0, 0, 1, 1, 0, 0, 1, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 1, 1, 0, 1, 0, 0]\n",
      "[0, 0, 0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 0, 1, 1, 0]\n",
      "[0, 0, 0, 1, 1, 0, 1, 1, 1]\n",
      "[0, 0, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 3\n",
      "[0, 0, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 1, 0, 0, 0]\n",
      "[0, 0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 0, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 0, 1, 1, 1, 1, 0, 0]\n",
      "[0, 0, 0, 1, 1, 1, 1, 0, 1]\n",
      "[0, 0, 0, 1, 1, 1, 1, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 56 Xright.length = 7\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 55\n",
      "[0, 0, 1, 0, 0]\n",
      "[0, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 28 Xright.length = 27\n",
      "[0, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 26\n",
      "[0, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 11 Xright.length = 15\n",
      "[0, 0, 1, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 9\n",
      "[0, 0, 1, 0, 1, 0, 1, 0, 0]\n",
      "[0, 0, 1, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 10 Xright.length = 5\n",
      "[0, 0, 1, 0, 1, 0, 1, 1, 0]\n",
      "[0, 0, 1, 0, 1, 0, 1, 1, 1]\n",
      "[0, 0, 1, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 12 Xright.length = 15\n",
      "[0, 0, 1, 0, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 9\n",
      "[0, 0, 1, 0, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 1, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 6\n",
      "[0, 0, 1, 0, 1, 1, 0, 1, 0]\n",
      "[0, 0, 1, 0, 1, 1, 0, 1, 1]\n",
      "[0, 0, 1, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 12 Xright.length = 3\n",
      "[0, 0, 1, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 10\n",
      "[0, 0, 1, 0, 1, 1, 1, 0, 0]\n",
      "[0, 0, 1, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 1, 0, 1, 1, 1, 1, 0]\n",
      "[0, 0, 1, 0, 1, 1, 1, 1, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 4\n",
      "[0, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 3\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 0, 1, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 6 Xright.length = 4\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 1 Xright.length = 5\n",
      "[0, 1, 0, 0]\n",
      "[0, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 2\n",
      "[0, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1, 1]\n",
      "[0, 1, 1]\n",
      "at height 4 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 90 Xright.length = 46\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 86 Xright.length = 4\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 5 Xright.length = 81\n",
      "[1, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 4\n",
      "[1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 0, 0, 0, 1, 1]\n",
      "[1, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 34 Xright.length = 47\n",
      "[1, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 31\n",
      "[1, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 27\n",
      "[1, 0, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 0, 0, 1, 0, 1, 0, 0]\n",
      "[1, 0, 0, 1, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 0, 0, 1, 0, 1, 0, 1, 0]\n",
      "[1, 0, 0, 1, 0, 1, 0, 1, 1]\n",
      "[1, 0, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 23\n",
      "[1, 0, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 1, 1, 0, 0]\n",
      "[1, 0, 0, 1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 21 Xright.length = 2\n",
      "[1, 0, 0, 1, 0, 1, 1, 1, 0]\n",
      "[1, 0, 0, 1, 0, 1, 1, 1, 1]\n",
      "[1, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 14 Xright.length = 33\n",
      "[1, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 12 Xright.length = 2\n",
      "[1, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 10 Xright.length = 2\n",
      "[1, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 6 Xright.length = 4\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0, 1, 0]\n",
      "[1, 0, 0, 1, 1, 0, 0, 1, 1]\n",
      "[1, 0, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 1, 0, 0]\n",
      "[1, 0, 0, 1, 1, 0, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 1, 1]\n",
      "[1, 0, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 27\n",
      "[1, 0, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 2\n",
      "[1, 0, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 0, 1, 1, 1, 0, 0, 0]\n",
      "[1, 0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 0, 1, 1, 1, 0, 1, 0]\n",
      "[1, 0, 0, 1, 1, 1, 0, 1, 1]\n",
      "[1, 0, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 21 Xright.length = 6\n",
      "[1, 0, 0, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 16\n",
      "[1, 0, 0, 1, 1, 1, 1, 0, 0]\n",
      "[1, 0, 0, 1, 1, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 2\n",
      "[1, 0, 0, 1, 1, 1, 1, 1, 0]\n",
      "[1, 0, 0, 1, 1, 1, 1, 1, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 1, 1, 0]\n",
      "[1, 0, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 37 Xright.length = 9\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 36 Xright.length = 1\n",
      "[1, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 11 Xright.length = 25\n",
      "[1, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 7 Xright.length = 4\n",
      "[1, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 6 Xright.length = 1\n",
      "[1, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 2\n",
      "[1, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 0, 0, 1, 0]\n",
      "[1, 1, 0, 0, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[1, 1, 0, 0, 0, 1, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 22 Xright.length = 3\n",
      "[1, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 18\n",
      "[1, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 1, 0, 0, 1, 0, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 0, 0, 1, 0]\n",
      "[1, 1, 0, 0, 1, 0, 0, 1, 1]\n",
      "[1, 1, 0, 0, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 14 Xright.length = 4\n",
      "[1, 1, 0, 0, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 13 Xright.length = 1\n",
      "[1, 1, 0, 0, 1, 0, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 0, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 1, 0, 0, 1, 0, 1, 1, 0]\n",
      "[1, 1, 0, 0, 1, 0, 1, 1, 1]\n",
      "[1, 1, 0, 0, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0, 0, 1, 1, 0]\n",
      "[1, 1, 0, 0, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 0, 0, 1, 1, 1, 0, 0]\n",
      "[1, 1, 0, 0, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 0, 1, 1, 1, 1]\n",
      "[1, 1, 0, 1]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 6 Xright.length = 3\n",
      "[1, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 3\n",
      "[1, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 0, 1, 0, 0, 0, 0]\n",
      "[1, 1, 1, 0, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 1, 0, 1, 0, 1]\n",
      "[1, 1, 1, 0, 1, 1]\n",
      "[1, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 1, 1, 0]\n",
      "[1, 1, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 1, 1, 1, 1, 0, 0, 0, 0]\n",
      "[1, 1, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1, 1, 1]\n",
      "[]\n",
      "at height 1 X --> Xleft.length = 93 Xright.length = 163\n",
      "[0]\n",
      "at height 2 X --> Xleft.length = 31 Xright.length = 62\n",
      "[0, 0]\n",
      "at height 3 X --> Xleft.length = 3 Xright.length = 28\n",
      "[0, 0, 0]\n",
      "at height 4 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 0, 0, 0]\n",
      "[0, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 0, 1, 0]\n",
      "[0, 0, 0, 1, 1]\n",
      "[0, 0, 1]\n",
      "at height 4 X --> Xleft.length = 17 Xright.length = 11\n",
      "[0, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 15 Xright.length = 2\n",
      "[0, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 10\n",
      "[0, 0, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 0, 1, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 0, 1, 0, 0, 0, 1, 0, 0]\n",
      "[0, 0, 1, 0, 0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 0, 0, 1, 1]\n",
      "[0, 0, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 8 Xright.length = 2\n",
      "[0, 0, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 7 Xright.length = 1\n",
      "[0, 0, 1, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 4\n",
      "[0, 0, 1, 0, 0, 1, 0, 0, 0]\n",
      "[0, 0, 1, 0, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 0, 0, 1, 1, 0]\n",
      "[0, 0, 1, 0, 0, 1, 1, 1]\n",
      "[0, 0, 1, 0, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 0, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 0, 1, 1]\n",
      "[0, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 7 Xright.length = 4\n",
      "[0, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 2\n",
      "[0, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 0, 1, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 0, 1, 0, 0]\n",
      "[0, 0, 1, 1, 0, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1, 0, 0, 1, 1]\n",
      "[0, 0, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 0, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 0, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 0, 1, 1, 0, 1, 1]\n",
      "[0, 0, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 0, 1, 1, 1, 0, 1]\n",
      "[0, 0, 1, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 1\n",
      "[0, 0, 1, 1, 1, 1, 0]\n",
      "[0, 0, 1, 1, 1, 1, 1]\n",
      "[0, 1]\n",
      "at height 3 X --> Xleft.length = 27 Xright.length = 35\n",
      "[0, 1, 0]\n",
      "at height 4 X --> Xleft.length = 4 Xright.length = 23\n",
      "[0, 1, 0, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 1, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 0]\n",
      "[0, 1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 0, 1, 0, 1]\n",
      "[0, 1, 0, 0, 1, 1]\n",
      "[0, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 4 Xright.length = 19\n",
      "[0, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[0, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 17 Xright.length = 2\n",
      "[0, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 14\n",
      "[0, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[0, 1, 0, 1, 1, 0, 0, 0]\n",
      "[0, 1, 0, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 0, 1, 0]\n",
      "[0, 1, 0, 1, 1, 0, 0, 1, 1]\n",
      "[0, 1, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 11\n",
      "[0, 1, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 0, 1, 0, 0]\n",
      "[0, 1, 0, 1, 1, 0, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 7 Xright.length = 4\n",
      "[0, 1, 0, 1, 1, 0, 1, 1, 0]\n",
      "[0, 1, 0, 1, 1, 0, 1, 1, 1]\n",
      "[0, 1, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 0, 1, 1, 1, 0, 0, 0]\n",
      "[0, 1, 0, 1, 1, 1, 0, 0, 1]\n",
      "[0, 1, 0, 1, 1, 1, 0, 1]\n",
      "[0, 1, 0, 1, 1, 1, 1]\n",
      "[0, 1, 1]\n",
      "at height 4 X --> Xleft.length = 18 Xright.length = 17\n",
      "[0, 1, 1, 0]\n",
      "at height 5 X --> Xleft.length = 17 Xright.length = 1\n",
      "[0, 1, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 10 Xright.length = 7\n",
      "[0, 1, 1, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 1 Xright.length = 9\n",
      "[0, 1, 1, 0, 0, 0, 0]\n",
      "[0, 1, 1, 0, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 4\n",
      "[0, 1, 1, 0, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 4\n",
      "[0, 1, 1, 0, 0, 0, 1, 0, 0]\n",
      "[0, 1, 1, 0, 0, 0, 1, 0, 1]\n",
      "[0, 1, 1, 0, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 0, 1, 1, 0]\n",
      "[0, 1, 1, 0, 0, 0, 1, 1, 1]\n",
      "[0, 1, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 3\n",
      "[0, 1, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 1, 1, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 1, 0, 0, 0]\n",
      "[0, 1, 1, 0, 0, 1, 0, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 1, 0, 1, 0]\n",
      "[0, 1, 1, 0, 0, 1, 0, 1, 1]\n",
      "[0, 1, 1, 0, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 0, 0, 1, 1, 0, 0]\n",
      "[0, 1, 1, 0, 0, 1, 1, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1, 1, 1]\n",
      "[0, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 15 Xright.length = 2\n",
      "[0, 1, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 12 Xright.length = 3\n",
      "[0, 1, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 4 Xright.length = 8\n",
      "[0, 1, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 1\n",
      "[0, 1, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 0, 0, 0, 0]\n",
      "[0, 1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[0, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 4\n",
      "[0, 1, 1, 1, 0, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 0, 1, 0, 0]\n",
      "[0, 1, 1, 1, 0, 0, 1, 0, 1]\n",
      "[0, 1, 1, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 2\n",
      "[0, 1, 1, 1, 0, 0, 1, 1, 0]\n",
      "[0, 1, 1, 1, 0, 0, 1, 1, 1]\n",
      "[0, 1, 1, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 1\n",
      "[0, 1, 1, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 0, 1, 0, 0, 0]\n",
      "[0, 1, 1, 1, 0, 1, 0, 0, 1]\n",
      "[0, 1, 1, 1, 0, 1, 0, 1]\n",
      "[0, 1, 1, 1, 0, 1, 1]\n",
      "[0, 1, 1, 1, 1]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[0, 1, 1, 1, 1, 0, 0, 0, 0]\n",
      "[0, 1, 1, 1, 1, 0, 0, 0, 1]\n",
      "[0, 1, 1, 1, 1, 0, 0, 1]\n",
      "[0, 1, 1, 1, 1, 0, 1]\n",
      "[0, 1, 1, 1, 1, 1]\n",
      "[1]\n",
      "at height 2 X --> Xleft.length = 36 Xright.length = 127\n",
      "[1, 0]\n",
      "at height 3 X --> Xleft.length = 27 Xright.length = 9\n",
      "[1, 0, 0]\n",
      "at height 4 X --> Xleft.length = 2 Xright.length = 25\n",
      "[1, 0, 0, 0]\n",
      "at height 5 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1]\n",
      "at height 5 X --> Xleft.length = 16 Xright.length = 9\n",
      "[1, 0, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 2 Xright.length = 14\n",
      "[1, 0, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 9 Xright.length = 5\n",
      "[1, 0, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 7\n",
      "[1, 0, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 1, 0, 0, 0]\n",
      "[1, 0, 0, 1, 0, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 6\n",
      "[1, 0, 0, 1, 0, 1, 0, 1, 0]\n",
      "[1, 0, 0, 1, 0, 1, 0, 1, 1]\n",
      "[1, 0, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 0, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 1, 1, 0, 0]\n",
      "[1, 0, 0, 1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 0, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 0, 1, 0, 1, 1, 1, 0]\n",
      "[1, 0, 0, 1, 0, 1, 1, 1, 1]\n",
      "[1, 0, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 6\n",
      "[1, 0, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 0, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 0, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 4\n",
      "[1, 0, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 1, 0, 0, 0]\n",
      "[1, 0, 0, 1, 1, 1, 0, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 2\n",
      "[1, 0, 0, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 1, 1, 0, 0]\n",
      "[1, 0, 0, 1, 1, 1, 1, 0, 1]\n",
      "[1, 0, 0, 1, 1, 1, 1, 1]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 0, 1, 1, 1, 1, 1, 0]\n",
      "[1, 0, 0, 1, 1, 1, 1, 1, 1]\n",
      "[1, 0, 1]\n",
      "at height 4 X --> Xleft.length = 4 Xright.length = 5\n",
      "[1, 0, 1, 0]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 1\n",
      "[1, 0, 1, 0, 0]\n",
      "at height 6 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 0, 1, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 1]\n",
      "at height 7 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 0\n",
      "[1, 0, 1, 0, 0, 1, 0, 0, 0]\n",
      "[1, 0, 1, 0, 0, 1, 0, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 0, 1]\n",
      "[1, 0, 1, 0, 0, 1, 1]\n",
      "[1, 0, 1, 0, 1]\n",
      "[1, 0, 1, 1]\n",
      "at height 5 X --> Xleft.length = 5 Xright.length = 0\n",
      "[1, 0, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 5 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 5 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 5 Xright.length = 0\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 0, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 0, 1]\n",
      "[1, 0, 1, 1, 0, 1]\n",
      "[1, 0, 1, 1, 1]\n",
      "[1, 1]\n",
      "at height 3 X --> Xleft.length = 123 Xright.length = 4\n",
      "[1, 1, 0]\n",
      "at height 4 X --> Xleft.length = 1 Xright.length = 122\n",
      "[1, 1, 0, 0]\n",
      "[1, 1, 0, 1]\n",
      "at height 5 X --> Xleft.length = 96 Xright.length = 26\n",
      "[1, 1, 0, 1, 0]\n",
      "at height 6 X --> Xleft.length = 75 Xright.length = 21\n",
      "[1, 1, 0, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 16 Xright.length = 59\n",
      "[1, 1, 0, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 13\n",
      "[1, 1, 0, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 1\n",
      "[1, 1, 0, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 6 Xright.length = 7\n",
      "[1, 1, 0, 1, 0, 0, 0, 1, 0]\n",
      "[1, 1, 0, 1, 0, 0, 0, 1, 1]\n",
      "[1, 1, 0, 1, 0, 0, 1]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 58\n",
      "[1, 1, 0, 1, 0, 0, 1, 0]\n",
      "[1, 1, 0, 1, 0, 0, 1, 1]\n",
      "at height 9 X --> Xleft.length = 38 Xright.length = 20\n",
      "[1, 1, 0, 1, 0, 0, 1, 1, 0]\n",
      "[1, 1, 0, 1, 0, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1, 0, 1]\n",
      "at height 7 X --> Xleft.length = 14 Xright.length = 7\n",
      "[1, 1, 0, 1, 0, 1, 0]\n",
      "at height 8 X --> Xleft.length = 4 Xright.length = 10\n",
      "[1, 1, 0, 1, 0, 1, 0, 0]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 1, 0, 1, 0, 1, 0, 0, 0]\n",
      "[1, 1, 0, 1, 0, 1, 0, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 4 Xright.length = 6\n",
      "[1, 1, 0, 1, 0, 1, 0, 1, 0]\n",
      "[1, 1, 0, 1, 0, 1, 0, 1, 1]\n",
      "[1, 1, 0, 1, 0, 1, 1]\n",
      "at height 8 X --> Xleft.length = 7 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 7 Xright.length = 0\n",
      "[1, 1, 0, 1, 0, 1, 1, 0, 0]\n",
      "[1, 1, 0, 1, 0, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 0, 1, 1, 1]\n",
      "[1, 1, 0, 1, 1]\n",
      "at height 6 X --> Xleft.length = 14 Xright.length = 12\n",
      "[1, 1, 0, 1, 1, 0]\n",
      "at height 7 X --> Xleft.length = 8 Xright.length = 6\n",
      "[1, 1, 0, 1, 1, 0, 0]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 3\n",
      "[1, 1, 0, 1, 1, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 2\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 0]\n",
      "[1, 1, 0, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 0, 1]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 0, 0, 1, 0]\n",
      "[1, 1, 0, 1, 1, 0, 0, 1, 1]\n",
      "[1, 1, 0, 1, 1, 0, 1]\n",
      "at height 8 X --> Xleft.length = 5 Xright.length = 1\n",
      "[1, 1, 0, 1, 1, 0, 1, 0]\n",
      "at height 9 X --> Xleft.length = 2 Xright.length = 3\n",
      "[1, 1, 0, 1, 1, 0, 1, 0, 0]\n",
      "[1, 1, 0, 1, 1, 0, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 0, 1, 1]\n",
      "[1, 1, 0, 1, 1, 1]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 9\n",
      "[1, 1, 0, 1, 1, 1, 0]\n",
      "at height 8 X --> Xleft.length = 1 Xright.length = 2\n",
      "[1, 1, 0, 1, 1, 1, 0, 0]\n",
      "[1, 1, 0, 1, 1, 1, 0, 1]\n",
      "at height 9 X --> Xleft.length = 1 Xright.length = 1\n",
      "[1, 1, 0, 1, 1, 1, 0, 1, 0]\n",
      "[1, 1, 0, 1, 1, 1, 0, 1, 1]\n",
      "[1, 1, 0, 1, 1, 1, 1]\n",
      "at height 8 X --> Xleft.length = 8 Xright.length = 1\n",
      "[1, 1, 0, 1, 1, 1, 1, 0]\n",
      "at height 9 X --> Xleft.length = 8 Xright.length = 0\n",
      "[1, 1, 0, 1, 1, 1, 1, 0, 0]\n",
      "[1, 1, 0, 1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 0, 1, 1, 1, 1, 1]\n",
      "[1, 1, 1]\n",
      "at height 4 X --> Xleft.length = 1 Xright.length = 3\n",
      "[1, 1, 1, 0]\n",
      "[1, 1, 1, 1]\n",
      "at height 5 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 0]\n",
      "at height 6 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0]\n",
      "at height 7 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0]\n",
      "at height 8 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0]\n",
      "at height 9 X --> Xleft.length = 3 Xright.length = 0\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 0]\n",
      "[1, 1, 1, 1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 0, 1]\n",
      "[1, 1, 1, 1, 0, 1]\n",
      "[1, 1, 1, 1, 1]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "\n",
    "def subsampling(X_train, sample_size=256):\n",
    "    m, n = X_train.shape\n",
    "    samples_no_replacement = np.random.randint(0, m-1, 256)\n",
    "    return X_train[samples_no_replacement]\n",
    "\n",
    "# create a forest\n",
    "def iforest(X_train, num_trees, subsample_size):\n",
    "    forest = []\n",
    "    height_limit = np.ceil(np.log2(subsample_size))\n",
    "    \n",
    "    for i in range(num_trees):\n",
    "        X_sub = subsampling(X_train, subsample_size)\n",
    "        forest.append(itree(X_sub, path=[], e=0, limit=height_limit))\n",
    "        \n",
    "    return forest\n",
    "    \n",
    "forest = iforest(X_train, 20, 256)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<__main__.Node at 0x9df0f60>,\n",
       " <__main__.Node at 0x9de5128>,\n",
       " <__main__.Node at 0x9e33ef0>,\n",
       " <__main__.Node at 0x9de56d8>,\n",
       " <__main__.Node at 0x97cc5f8>,\n",
       " <__main__.Node at 0x9e6f160>,\n",
       " <__main__.Node at 0x9e73d30>,\n",
       " <__main__.Node at 0x9e97be0>,\n",
       " <__main__.Node at 0x9e97198>,\n",
       " <__main__.Node at 0x9ec16a0>,\n",
       " <__main__.Node at 0x9f057b8>,\n",
       " <__main__.Node at 0x9ecbba8>,\n",
       " <__main__.Node at 0x9f37a90>,\n",
       " <__main__.Node at 0x9f4f7f0>,\n",
       " <__main__.Node at 0x9f62320>,\n",
       " <__main__.Node at 0x9f46128>,\n",
       " <__main__.Node at 0x9f62470>,\n",
       " <__main__.Node at 0x9fd18d0>,\n",
       " <__main__.Node at 0x9feeba8>,\n",
       " <__main__.Node at 0xa008cf8>]"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "forest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "average height for point idx = 0 is 8.95\n",
      "average height for point idx = 1 is 8.35\n",
      "average height for point idx = 2 is 7.95\n",
      "average height for point idx = 3 is 8.8\n",
      "average height for point idx = 4 is 6.45\n",
      "average height for point idx = 5 is 8.55\n",
      "average height for point idx = 6 is 8.4\n",
      "average height for point idx = 7 is 8.65\n",
      "average height for point idx = 8 is 8.75\n",
      "average height for point idx = 9 is 8.9\n",
      "average height for point idx = 10 is 5.75\n",
      "average height for point idx = 11 is 8.0\n",
      "average height for point idx = 12 is 8.65\n",
      "average height for point idx = 13 is 8.8\n",
      "average height for point idx = 14 is 8.65\n",
      "average height for point idx = 15 is 8.65\n",
      "average height for point idx = 16 is 8.9\n",
      "average height for point idx = 17 is 6.2\n",
      "average height for point idx = 18 is 7.6\n",
      "average height for point idx = 19 is 8.6\n",
      "average height for point idx = 20 is 8.5\n",
      "average height for point idx = 21 is 8.2\n",
      "average height for point idx = 22 is 8.35\n",
      "average height for point idx = 23 is 8.75\n",
      "average height for point idx = 24 is 5.8\n",
      "average height for point idx = 25 is 8.5\n",
      "average height for point idx = 26 is 8.7\n",
      "average height for point idx = 27 is 8.55\n",
      "average height for point idx = 28 is 8.8\n",
      "average height for point idx = 29 is 8.65\n",
      "average height for point idx = 30 is 6.4\n",
      "average height for point idx = 31 is 7.8\n",
      "average height for point idx = 32 is 8.55\n",
      "average height for point idx = 33 is 8.55\n",
      "average height for point idx = 34 is 8.55\n",
      "average height for point idx = 35 is 8.8\n",
      "average height for point idx = 36 is 8.9\n",
      "average height for point idx = 37 is 7.2\n",
      "average height for point idx = 38 is 7.8\n",
      "average height for point idx = 39 is 8.75\n"
     ]
    }
   ],
   "source": [
    "for idx, x in enumerate(X_test):\n",
    "    heights = []\n",
    "    for tree in forest:\n",
    "        #print(x)\n",
    "        heights.append(get_path(x, tree))\n",
    "    print(\"average height for point idx =\", idx, \"is\", np.mean(heights))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## version spark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using matplotlib backend: MacOSX\n",
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "\n",
    "%pylab\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <div>\n",
       "            <p><b>SparkContext</b></p>\n",
       "\n",
       "            <p><a href=\"http://10.255.140.110:4040\">Spark UI</a></p>\n",
       "\n",
       "            <dl>\n",
       "              <dt>Version</dt>\n",
       "                <dd><code>v2.2.1</code></dd>\n",
       "              <dt>Master</dt>\n",
       "                <dd><code>local[*]</code></dd>\n",
       "              <dt>AppName</dt>\n",
       "                <dd><code>PySparkShell</code></dd>\n",
       "            </dl>\n",
       "        </div>\n",
       "        "
      ],
      "text/plain": [
       "<SparkContext master=local[*] appName=PySparkShell>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "filename = './demo_fraud/Fraud-detection-using-deep-learning/data/creditcard.csv'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dist_data = sc.textFile(filename, use_unicode=\"utf-8\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[u'\"Time\",\"V1\",\"V2\",\"V3\",\"V4\",\"V5\",\"V6\",\"V7\",\"V8\",\"V9\",\"V10\",\"V11\",\"V12\",\"V13\",\"V14\",\"V15\",\"V16\",\"V17\",\"V18\",\"V19\",\"V20\",\"V21\",\"V22\",\"V23\",\"V24\",\"V25\",\"V26\",\"V27\",\"V28\",\"Amount\",\"Class\"',\n",
       " u'0,-1.3598071336738,-0.0727811733098497,2.53634673796914,1.37815522427443,-0.338320769942518,0.462387777762292,0.239598554061257,0.0986979012610507,0.363786969611213,0.0907941719789316,-0.551599533260813,-0.617800855762348,-0.991389847235408,-0.311169353699879,1.46817697209427,-0.470400525259478,0.207971241929242,0.0257905801985591,0.403992960255733,0.251412098239705,-0.018306777944153,0.277837575558899,-0.110473910188767,0.0669280749146731,0.128539358273528,-0.189114843888824,0.133558376740387,-0.0210530534538215,149.62,\"0\"']"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist_data.take(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[u'\"Time\"',\n",
       " u'\"V1\"',\n",
       " u'\"V2\"',\n",
       " u'\"V3\"',\n",
       " u'\"V4\"',\n",
       " u'\"V5\"',\n",
       " u'\"V6\"',\n",
       " u'\"V7\"',\n",
       " u'\"V8\"',\n",
       " u'\"V9\"',\n",
       " u'\"V10\"',\n",
       " u'\"V11\"',\n",
       " u'\"V12\"',\n",
       " u'\"V13\"',\n",
       " u'\"V14\"',\n",
       " u'\"V15\"',\n",
       " u'\"V16\"',\n",
       " u'\"V17\"',\n",
       " u'\"V18\"',\n",
       " u'\"V19\"',\n",
       " u'\"V20\"',\n",
       " u'\"V21\"',\n",
       " u'\"V22\"',\n",
       " u'\"V23\"',\n",
       " u'\"V24\"',\n",
       " u'\"V25\"',\n",
       " u'\"V26\"',\n",
       " u'\"V27\"',\n",
       " u'\"V28\"',\n",
       " u'\"Amount\"',\n",
       " u'\"Class\"']"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "header = dist_data.first().split(\",\")\n",
    "header"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# cleaning the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = dist_data.filter(lambda line:line[1:5] != \"Time\").map(lambda line:line.split(\",\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "284807"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[u'0',\n",
       "  u'-1.3598071336738',\n",
       "  u'-0.0727811733098497',\n",
       "  u'2.53634673796914',\n",
       "  u'1.37815522427443',\n",
       "  u'-0.338320769942518',\n",
       "  u'0.462387777762292',\n",
       "  u'0.239598554061257',\n",
       "  u'0.0986979012610507',\n",
       "  u'0.363786969611213',\n",
       "  u'0.0907941719789316',\n",
       "  u'-0.551599533260813',\n",
       "  u'-0.617800855762348',\n",
       "  u'-0.991389847235408',\n",
       "  u'-0.311169353699879',\n",
       "  u'1.46817697209427',\n",
       "  u'-0.470400525259478',\n",
       "  u'0.207971241929242',\n",
       "  u'0.0257905801985591',\n",
       "  u'0.403992960255733',\n",
       "  u'0.251412098239705',\n",
       "  u'-0.018306777944153',\n",
       "  u'0.277837575558899',\n",
       "  u'-0.110473910188767',\n",
       "  u'0.0669280749146731',\n",
       "  u'0.128539358273528',\n",
       "  u'-0.189114843888824',\n",
       "  u'0.133558376740387',\n",
       "  u'-0.0210530534538215',\n",
       "  u'149.62',\n",
       "  u'\"0\"']]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.take(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "u'0'"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u'\"0\"'.replace('\"', '')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = data.map(lambda line:np.array(list(map(lambda x:float(x.replace('\"', '')), line))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "31"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.take(1)[0].size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-72.7157275629303"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.map(lambda x:x[2]).min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit = 10\n",
    "m = 256\n",
    "limit = max(limit, int(np.log2(m)))\n",
    "np.log2(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# write a sample function for rdd data, refer to \n",
    "# https://spark.apache.org/docs/1.1.1/api/python/pyspark.rdd.RDD-class.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def subsamplingRDD(X_train, sample_ratio):\n",
    "    return X_train.sample(withReplacement=False,fraction=sample_ratio, seed=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "874"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sampledData = subsamplingRDD(data, 0.003)\n",
    "sampledData.count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# now write the function for create itree\n",
    "\n",
    "class Node(object):\n",
    "    def __init__(self, lefttree, righttree, splitattr, splitvalue, size=-1):\n",
    "        self.left = lefttree\n",
    "        self.right = righttree\n",
    "        self.splitattr = splitattr\n",
    "        self.splitvalue = splitvalue\n",
    "        self.size = size\n",
    "\n",
    "        \n",
    "def itreeRDD(X, e=0, limit=10):\n",
    "    '''\n",
    "    X: RDD sampled data set to construct the tree, header not included\n",
    "    e: current tree height\n",
    "    l: limit of the height of the tree\n",
    "    '''\n",
    "    # m : the number of samples in X, n: number of columns\n",
    "    m = X.count()\n",
    "    n = X.take(1)[0].size\n",
    "    \n",
    "    if e > limit or m <= 1:    \n",
    "        return Node([], [], None, None, m)\n",
    "    \n",
    "    rnd_attr = random.randint(0, n-1)  # choose one attribute by idx\n",
    "    column = X.map(lambda line:line[rnd_attr])\n",
    "    maxvalue = column.max()\n",
    "    minvalue = column.min()\n",
    "    rnd_split = random.random()*(maxvalue - minvalue + 1e-10) + minvalue  # get a value [minvalue, maxvalue)\n",
    "    \n",
    "    X_left = X.filter(lambda line:line[rnd_attr]<rnd_split).cache()\n",
    "    X_right = X.filter(lambda line:line[rnd_attr]>=rnd_split).cache()\n",
    "\n",
    "    #path_left = path.copy() + [0]\n",
    "    #path_right = path.copy() + [1]\n",
    "    \n",
    "    #print(\"at height\", e, \"X --> Xleft.length =\", X_left.shape[0], \"Xright.length =\", X_right.shape[0])\n",
    "    \n",
    "    return Node(itreeRDD(X_left, e+1, limit), itreeRDD(X_right, e+1, limit), rnd_attr, rnd_split, -1)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "#test itreeRDD\n",
    "m = data.count()\n",
    "subsample_size=256\n",
    "tree = itreeRDD(subsamplingRDD(data, float(subsample_size)/m), e=0, limit=8)\n",
    "\n",
    "t1 = tree\n",
    "l = 0\n",
    "while t1.size < 0:\n",
    "    print(t1.splitattr, t1.splitvalue)\n",
    "    t1 = t1.right\n",
    "    l += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create a forest RDD: seems pyspark doesn't support nested function， whether use itree or replace by forest.join(X_train)\n",
    "# https://stackoverflow.com/questions/42325496/how-to-use-spark-intersection-by-key-or-filter-with-two-rdd\n",
    "\n",
    "def iforestRDD(X_train, num_trees=150, subsample_size=265):\n",
    "    \"\"\"\n",
    "    X_train: RDD data set to construct the forest\n",
    "    \"\"\"\n",
    "    m = X_train.count()\n",
    "    n = X_train.take(1)[0].size\n",
    "    \n",
    "    lis = [None]*num_trees\n",
    "    forest = np.array(lis)\n",
    "    \n",
    "    # we can also allow the limit to be greater when the sample size is larger\n",
    "    height_limit = np.ceil(np.log2(subsample_size))\n",
    "    trainforest = list(map(lambda s:itreeRDD(subsamplingRDD(X_train, float(subsample_size)/m), \n",
    "                                                e=0, limit=height_limit), forest))\n",
    "\n",
    "    return trainforest\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "# test iforestRDD\n",
    "X_train = data\n",
    "m = X_train.count()\n",
    "n = X_train.take(1)[0].size\n",
    "\n",
    "lis = [None]*4\n",
    "forest = np.array(lis)\n",
    "\n",
    "# we can also allow the limit to be greater when the sample size is larger\n",
    "height_limit = np.ceil(np.log2(256))\n",
    "\n",
    "trainforest = np.array(map(lambda s:itreeRDD(subsamplingRDD(X_train, float(subsample_size)/m), \n",
    "                                    subsample_size, n, e=0, limit=height_limit), forest))\n",
    "trainforest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "forest = iforestRDD(data, 4, 256)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<__main__.Node at 0x1072444d0>,\n",
       " <__main__.Node at 0x1072c8510>,\n",
       " <__main__.Node at 0x107288390>,\n",
       " <__main__.Node at 0x10731d250>]"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "forest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    }
   ],
   "source": [
    "t1, t2, t3, t4 = forest\n",
    "\n",
    "T = t2\n",
    "l = 0\n",
    "while T.size < 0:\n",
    "    #print(T.splitattr, T.splitvalue)\n",
    "    T = T.right\n",
    "    l += 1\n",
    "print(l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# calculate the path length and add the cost indicated in the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cost(num_items):\n",
    "    #二叉搜索树的平均路径长度。0.5772156649:欧拉常数\n",
    "    return int(2*(np.log(num_items-1) + 0.5772156649)-(2*(num_items-1)/num_items))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test cost\n",
    "cost(11000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_path_RDD(x, T, e=0): \n",
    "    \"\"\"\n",
    "    x : a list or np.array, the row of RDD\n",
    "    T: a Node instance\n",
    "    e: recursive variable to record the length of a path\n",
    "    \"\"\"\n",
    "    if T.size == 1 or T.size == 0:  # if tree node is a leaf\n",
    "        return e\n",
    "    elif T.size > 1:\n",
    "        return e + cost(T.size)\n",
    "    else: # if tree has children\n",
    "        e += 1\n",
    "        return get_path_RDD(x, T.left, e) if x[T.splitattr] < T.splitvalue else get_path_RDD(x, T.right, e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# predict one line\n",
    "def predict_path(x, forest):\n",
    "    predictions = np.array(list(map(lambda T:get_path_RDD(x, T), forest)))\n",
    "    return predictions\n",
    "\n",
    "def predict_score(x, forest, num_samples):\n",
    "    predictions = np.array(list(map(lambda T:get_path_RDD(x, T), forest)))\n",
    "    return math.pow(2, -float(predictions.sum()/predictions.size)/cost(num_samples)) #Anomaly Score\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PythonRDD[28] at RDD at PythonRDD.scala:48"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "path_mat = X_train.map(lambda line: predict_path(line, forest))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "predictions = path_mat.take(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# test score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "num_samples = 256\n",
    "scores_mat = X_train.map(lambda line: predict_score(line, forest, num_samples))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "xx = scores_mat.take(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.34258774618003096, 0.7297400528407231)"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(xx), max(xx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost(256)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([246., 400., 129.,  79., 100.,  20.,  12.,   4.,   4.,   6.]),\n",
       " array([0.34258775, 0.38130298, 0.42001821, 0.45873344, 0.49744867,\n",
       "        0.5361639 , 0.57487913, 0.61359436, 0.65230959, 0.69102482,\n",
       "        0.72974005]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10717f090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(xx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}