Hopfield Networks.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "pointed-clinton",
   "metadata": {},
   "source": [
    "# Hopfield networks"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "portable-alignment",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fundamental-oklahoma",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import os, sys\n",
    "import itertools"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "scenic-draft",
   "metadata": {},
   "source": [
    "## Hopfield Network class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "descending-climate",
   "metadata": {},
   "outputs": [],
   "source": [
    "class HopfieldNetwork():\n",
    "    \"\"\" Class for Hopfield Network.\n",
    "    \n",
    "    Attributes\n",
    "    ----------\n",
    "    units : int\n",
    "        The number of neurons in the network.\n",
    "    weights : numpy.ndarray\n",
    "        Weight matrix of shape (units, units).\n",
    "    sparse : bool\n",
    "        If patterns are sparse, then a modified update rule is used in recall.\n",
    "        \n",
    "    Methods\n",
    "    -------\n",
    "    init_weights(patterns, self_connections=False, norm=False)\n",
    "        Initalizes the weights of the network.\n",
    "    recall(pattern)\n",
    "        Recall a pattern, i.e.: a single data vector.\n",
    "    recall_until_convergence(pattern, exit=100)\n",
    "        Recall a single pattern until it converges. If does not converge, \n",
    "        exit after exit numbers of iterations.\n",
    "    get_attractors(verbose=False)\n",
    "        Return a 2D array of the attractors where each attractor is a row in the\n",
    "        array. The array is of shape (n_attractors, units).\n",
    "    if_attractor(attractor)\n",
    "        Check if the pattern called attractor is an attractor of the energy landscape\n",
    "        of the network.\n",
    "\n",
    "    \"\"\"\n",
    "    def __init__(self, sparse=False):\n",
    "        self.units = None\n",
    "        self.weights = None\n",
    "        self.sparse = sparse\n",
    "    \n",
    "    def init_weights(self, patterns, self_connections=False, norm=False, bias=0):\n",
    "        \"\"\" Initalizes the weights of the network.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        patterns : numpy.ndarray\n",
    "            Patterns of shape (n_patterns, n_features). n_features is equal to self.units.\n",
    "        self_connections : bool\n",
    "            Whether to allow the self-connections of neurons.\n",
    "        norm : bool\n",
    "            Whether to normalize the weight matrix. Important when bias is used.\n",
    "        bias : float\n",
    "            Bias term in sparse pattern update rule.\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        None\n",
    "        \n",
    "        \"\"\"\n",
    "        self.units = patterns.shape[1]\n",
    "        self.weights = np.zeros((patterns.shape[1], patterns.shape[1]))\n",
    "        \n",
    "        average_activity = np.sum(patterns) * (self.units * patterns.shape[0])**(-1)\n",
    "        \n",
    "        for idx, pattern in enumerate(patterns):\n",
    "            if self.sparse:\n",
    "                vec = pattern - average_activity\n",
    "                self.bias = bias\n",
    "            else:\n",
    "                vec = pattern.copy()\n",
    "            \n",
    "            self.weights += np.outer(vec, vec)\n",
    "        \n",
    "        if not self_connections:\n",
    "            np.fill_diagonal(self.weights, 0)\n",
    "        \n",
    "        if norm:\n",
    "            self.weights /= self.units\n",
    "        \n",
    "        assert np.all(np.abs(self.weights - self.weights.T) < 10e-8), \"non-symmetric weight matrix\"\n",
    "        \n",
    "    def set_weights(self, **rule_dict):\n",
    "        \"\"\" Set the weights of the network.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        rule_dict : dict\n",
    "            The rule of setting the weights. Could be gaussian (then has loc and scale), or\n",
    "            symmetrize.\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        None\n",
    "        \n",
    "        \"\"\"\n",
    "        if rule_dict[\"rule\"] == \"gaussian\":\n",
    "            self.weights = np.random.normal(loc=rule_dict[\"loc\"], scale=rule_dict[\"scale\"], \n",
    "                                            size=(self.units, self.units))\n",
    "        elif rule_dict[\"rule\"] == \"symmetrize\":\n",
    "            self.weights = 0.5 * (self.weights + self.weights.T)\n",
    "            assert np.all(self.weights == self.weights.T), \"not symmetric weight matrix\"\n",
    "            \n",
    "        else:\n",
    "            raise Exception(f\"Incorrect rule in {rule_dict}\")\n",
    "        \n",
    "    def recall(self, pattern, if_sequential):\n",
    "        \"\"\" Recall a pattern, i.e.: a single data vector.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        pattern : numpy.ndarray\n",
    "            Pattern of shape (self.units, 1)\n",
    "        \n",
    "        if_sequential : bool\n",
    "            Do sequential instead of batch update to recall.\n",
    "    \n",
    "        Returns\n",
    "        -------\n",
    "        pattern : numpy.ndarray\n",
    "            Recalled pattern of shape (self.units, 1)\n",
    "        \n",
    "        \"\"\"\n",
    "        if self.sparse:\n",
    "            if not if_sequential:\n",
    "                pattern = np.dot(self.weights, pattern) - self.bias\n",
    "            else:\n",
    "                raise NotImplementedError\n",
    "            \n",
    "            mask = pattern < 0\n",
    "            pattern[mask] = -1.0\n",
    "            pattern[np.invert(mask)] = 1.0\n",
    "            \n",
    "            pattern = 0.5 + 0.5*pattern\n",
    "            \n",
    "        else:\n",
    "            if not if_sequential:\n",
    "                pattern = np.dot(self.weights, pattern)\n",
    "            else:\n",
    "                idx = np.random.randint(pattern.shape[0])\n",
    "                pattern[idx] = float(np.dot(self.weights[idx,:].reshape(1,-1), pattern))\n",
    "\n",
    "            mask = pattern < 0\n",
    "            pattern[mask] = -1.0\n",
    "            pattern[np.invert(mask)] = 1.0\n",
    "            \n",
    "        return pattern\n",
    "    \n",
    "    def recall_until_convergence(self, pattern, if_sequential, with_energy, exit=100, **viz_recall_dict):\n",
    "        \"\"\" Recall a single pattern until it converges. If does not converge, \n",
    "        exit after exit numbers of iterations.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        pattern : numpy.ndarray\n",
    "            Pattern of shape (self.units, 1)\n",
    "        \n",
    "        if_sequential : bool\n",
    "            Do sequential instead of batch update to recall.\n",
    "        \n",
    "        with_energy : bool\n",
    "            Return the energy of the recalls after each iteration as list for plotting.\n",
    "        \n",
    "        exit : int\n",
    "            Exit loop after this many iterations (means that within exit number\n",
    "            of iterations the pattern did not converge to any attractors).\n",
    "            If if_sequential is False (i.e.: batch update), then exit loop either at\n",
    "            convergence or after exit number of iterations.\n",
    "            If if_sequential is True, force the loop to go up to exit number of iterations.\n",
    "            (This is a temproaray solution the problem is that when selecting an element in\n",
    "            pattern at random, the recall could look exactly like in the previous itertaion, and \n",
    "            so convergence woul be reached, which actually would not be the case. So just\n",
    "            force the loop until exit no. of iterations when if_sequential is True)\n",
    "            \n",
    "        viz_recall_dict : dict\n",
    "            Rules for visualizing recall per iteration.\n",
    "    \n",
    "        Returns\n",
    "        -------\n",
    "        patternr : numpy.ndarray\n",
    "            Recalled pattern of shape (self.units, 1)\n",
    "        \n",
    "        i : int\n",
    "            Convergence after i iterations.\n",
    "        \n",
    "        energies : list\n",
    "            List of energy values per iteration.\n",
    "        \n",
    "        \"\"\"\n",
    "        patternr_prev = np.zeros(pattern.shape)\n",
    "        patternr = pattern.copy()\n",
    "        i = 0\n",
    "        exit_condition = False\n",
    "        energies = []\n",
    "        \n",
    "        while not exit_condition:\n",
    "            patternr_prev = patternr.copy()\n",
    "            patternr = self.recall(patternr_prev, if_sequential)\n",
    "            \n",
    "            i += 1\n",
    "            \n",
    "            if with_energy:\n",
    "                energies.append(self.energy(patternr))\n",
    "            \n",
    "            if viz_recall_dict:\n",
    "                if i % viz_recall_dict[\"i\"] == 0:\n",
    "                    self.viz_recall(patternr, i, shape=viz_recall_dict[\"shape\"])\n",
    "            \n",
    "            if not if_sequential:\n",
    "                exit_condition = np.all(patternr == patternr_prev)\n",
    "            else:\n",
    "                # if not sequential, do until exit iterations pass (temporary solution)\n",
    "                exit_condition = False\n",
    "            \n",
    "            if i == exit:\n",
    "                #patternr = None\n",
    "                break\n",
    "                \n",
    "        return patternr, i, energies\n",
    "    \n",
    "    def viz_recall(self, pattern, i, shape):\n",
    "        \"\"\" Recall a pattern, i.e.: a single data vector.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        pattern : numpy.ndarray\n",
    "            Pattern of shape (self.units, 1)\n",
    "        \n",
    "        i : int\n",
    "            Iteration number\n",
    "        \n",
    "        shape : tuple\n",
    "            Shape of recall to be visualized, e.g.: (32,32) for the pict data. \n",
    "    \n",
    "        Returns\n",
    "        -------\n",
    "        None\n",
    "        \n",
    "        \"\"\"\n",
    "        plt.imshow(pattern.reshape(shape).T)\n",
    "        plt.axis(\"off\")\n",
    "        plt.title(f\"Recall at iteration {i}\")\n",
    "        plt.show()\n",
    "    \n",
    "    def get_attractors(self, if_sequential, verbose=False):\n",
    "        \"\"\" Return a 2D array of the attractors where each attractor is a row in the\n",
    "        array. The array is of shape (n_attractors, units).\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        if_sequential : bool\n",
    "            Do sequential instead of batch update to recall.\n",
    "            \n",
    "        verbose : bool\n",
    "            Whether to print info about which pattern (of all possible patterns)\n",
    "            is being processed (recalled until convergence).\n",
    "        \n",
    "        Returns\n",
    "        -------\n",
    "        unique_attractors : numpy.ndarray\n",
    "            The array of all attractors of the network's energy landscape.\n",
    "            Of shape (n_attractors, units).\n",
    "        \"\"\"\n",
    "        with_energy = False\n",
    "        patterns_all = np.array(list(itertools.product([-1, 1], repeat=self.units))).astype(float)\n",
    "        attractors = []\n",
    "        \n",
    "        for pattern in patterns_all:\n",
    "            if verbose:\n",
    "                print(f\"processing {idx+1}/{patterns_all.shape[0]}\")\n",
    "            patternr, _, _ = self.recall_until_convergence(pattern, with_energy, if_sequential, exit=100)\n",
    "            attractors.append(patternr)\n",
    "           \n",
    "        attractors = np.array(attractors)\n",
    "        unique_attractors = np.unique(attractors, axis=0)\n",
    "        \n",
    "        return unique_attractors\n",
    "    \n",
    "    def if_attractor(self, attractor, if_sequential):\n",
    "        \"\"\" Check if the pattern called attractor is an attractor of the energy landscape\n",
    "        of the network.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        attractor : numpy.ndarray\n",
    "            Whether to print info about which pattern (of all possible patterns)\n",
    "            is being processed (recalled until convergence). Of shape (self.units,).\n",
    "        \n",
    "        if_sequential : bool\n",
    "            Do sequential instead of batch update to recall.\n",
    "        \n",
    "        Returns\n",
    "        -------\n",
    "        idx : int or None\n",
    "            If the pattern is an attractor of the network, then return its index in\n",
    "            the attractor array (generated by self.get_attractors(verbose=False)).\n",
    "            If not attractor, return None.\n",
    "        \"\"\"\n",
    "        assert attractor.ndim == 1, \"attractor should be 1d instead of 2d\"\n",
    "        unique_attractors = self.get_attractors(if_sequential)\n",
    "        \n",
    "        for idx, unique_attractor in enumerate(unique_attractors):\n",
    "            if np.all(unique_attractor == attractor):\n",
    "                return idx\n",
    "\n",
    "        return None\n",
    "  \n",
    "    def energy(self, pattern):\n",
    "        \"\"\" Compute energy of pattern in the energy landscape defined by the weights.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        pattern : numpy.ndarray\n",
    "            Pattern of shape (self.units, ), NEEDS to be 1D\n",
    "        \n",
    "        Returns\n",
    "        -------\n",
    "        float\n",
    "            Energy.\n",
    "        \"\"\"\n",
    "        assert pattern.ndim == 1, \"pattern needs to be 1D, got 2D\"\n",
    "        return - np.linalg.multi_dot([pattern, self.weights, pattern])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "referenced-biodiversity",
   "metadata": {},
   "source": [
    "## Testing content addresable memory"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "developmental-conservation",
   "metadata": {},
   "source": [
    "If the network has succeeded in storing the patterns x1, x2, and x3, they should all be fixed points upon applying the update rule (i.e: applying the update rule to these patterns you retrieves the same pattern back (content addresable memory)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "occupational-district",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "weights are\n",
      "[[ 3.  1. -1.  3.  1. -1.  3. -1.]\n",
      " [ 1.  3.  1.  1. -1.  1.  1.  1.]\n",
      " [-1.  1.  3. -1.  1. -1. -1.  3.]\n",
      " [ 3.  1. -1.  3.  1. -1.  3. -1.]\n",
      " [ 1. -1.  1.  1.  3. -3.  1.  1.]\n",
      " [-1.  1. -1. -1. -3.  3. -1. -1.]\n",
      " [ 3.  1. -1.  3.  1. -1.  3. -1.]\n",
      " [-1.  1.  3. -1.  1. -1. -1.  3.]]\n",
      "Recalling x1\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "get\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Random patterns for testing content addresable memory\n",
    "x1 = np.array([-1, -1, 1, -1, 1, -1, -1, 1]).reshape(-1,1)\n",
    "x2 = np.array([-1, -1, -1, -1, -1, 1, -1, -1]).reshape(-1,1)\n",
    "x3 = np.array([-1, 1, 1, -1, -1, 1, -1, 1]).reshape(-1,1)\n",
    "\n",
    "patterns = np.vstack([x1.T, x2.T, x3.T])\n",
    "\n",
    "\n",
    "hn = HopfieldNetwork()\n",
    "hn.init_weights(patterns, self_connections=True)\n",
    "\n",
    "print(\"weights are\")\n",
    "print(hn.weights)\n",
    "\n",
    "rx1 = hn.recall(x1, if_sequential=False)\n",
    "rx2 = hn.recall(x2, if_sequential=False)\n",
    "rx3 = hn.recall(x3, if_sequential=False)\n",
    "\n",
    "assert np.all(x1 == rx1), \"x1 cannot be addressed\"\n",
    "assert np.all(x2 == rx2), \"x2 cannot be addressed\"\n",
    "assert np.all(x3 == rx3), \"x3 cannot be addressed\"\n",
    "\n",
    "print(\"Recalling x1\")\n",
    "plt.imshow(rx1)\n",
    "plt.axis(\"off\")\n",
    "plt.show()\n",
    "\n",
    "print(\"get\")\n",
    "plt.imshow(x1)\n",
    "plt.axis(\"off\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "thorough-eclipse",
   "metadata": {},
   "source": [
    "All can be retrieved, content addressable memory works. x1, x2, and x3 will be attractors of the network."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "spatial-david",
   "metadata": {},
   "source": [
    "## Convergence and attractors"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "rotary-pencil",
   "metadata": {},
   "source": [
    "Recalling distorted patterns. x1d has a one bit error, x2d and x3d have two bit errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "practical-wednesday",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xd1 converged to x1 after 2 iterations\n",
      "xd1\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "it should have converged to x1\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xd2 did not converge to x2\n",
      "xd2\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "it should have converged to x2\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xd3 converged to x3 after 3 iterations\n",
      "xd3\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "it should have converged to x3\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1d = np.array([1, -1, 1, -1, 1, -1, -1, 1]).reshape(-1,1)\n",
    "x2d = np.array([1, 1, -1, -1, -1, 1, -1, -1]).reshape(-1,1)\n",
    "x3d = np.array([1, 1, 1, -1, 1, 1, -1, 1]).reshape(-1,1)\n",
    "\n",
    "patternsd = np.vstack([x1d.T, x2d.T, x3d.T])\n",
    "\n",
    "hn = HopfieldNetwork()\n",
    "hn.init_weights(patterns, self_connections=True)\n",
    "\n",
    "for idx, p, pd in zip(range(patterns.shape[0]), patterns, patternsd):\n",
    "    pr, it, _ = hn.recall_until_convergence(pd, with_energy=False, if_sequential=False)\n",
    "    if np.all(pr == p):\n",
    "        print(f\"xd{idx+1} converged to x{idx+1} after {it} iterations\")\n",
    "    else:\n",
    "        print(f\"xd{idx+1} did not converge to x{idx+1}\")\n",
    "    \n",
    "    print(f\"xd{idx+1}\")\n",
    "    plt.imshow(pd.reshape(-1,1))\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()\n",
    "    \n",
    "    print(f\"converged to\")\n",
    "    plt.imshow(pr.reshape(-1,1))\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "    print(f\"it should have converged to x{idx+1}\")\n",
    "    plt.imshow(p.reshape(-1,1))\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "interracial-privacy",
   "metadata": {},
   "source": [
    "With self_connections = False, only x1d converges to x1 in 2 iterations, the rest do not converge at all.\n",
    "With self_connections = True, all converge - x1d to x1 in 2 iterations, x2d to a 1-bit corrupted (at index 1) version of x2, and x3d to x3 in 3 iterations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "equal-consensus",
   "metadata": {},
   "source": [
    "Finding the number of attractors in the network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "enclosed-banks",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1. -1. -1. -1. -1.  1. -1. -1.]\n",
      " [-1. -1. -1. -1.  1. -1. -1. -1.]\n",
      " [-1. -1.  1. -1. -1.  1. -1.  1.]\n",
      " [-1. -1.  1. -1.  1. -1. -1.  1.]\n",
      " [-1. -1.  1. -1.  1.  1. -1.  1.]\n",
      " [-1.  1. -1. -1. -1.  1. -1. -1.]\n",
      " [-1.  1.  1. -1. -1.  1. -1.  1.]\n",
      " [-1.  1.  1. -1.  1. -1. -1.  1.]\n",
      " [ 1. -1. -1.  1.  1. -1.  1. -1.]\n",
      " [ 1.  1. -1.  1. -1.  1.  1. -1.]\n",
      " [ 1.  1. -1.  1.  1. -1.  1. -1.]\n",
      " [ 1.  1. -1.  1.  1.  1.  1. -1.]\n",
      " [ 1.  1.  1.  1. -1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1. -1.  1.  1.]]\n",
      "There are 14 attractors (each one is a row)\n",
      "x1 is an attractor at index 3\n",
      "x2 is an attractor at index 0\n",
      "x3 is an attractor at index 6\n"
     ]
    }
   ],
   "source": [
    "attractors = hn.get_attractors(if_sequential=False)\n",
    "print(attractors)\n",
    "print(f\"There are {attractors.shape[0]} attractors (each one is a row)\")\n",
    "\n",
    "for idx, pattern in enumerate(patterns):\n",
    "    idx_attractor = hn.if_attractor(pattern, if_sequential=False)\n",
    "    print(f\"x{idx+1} is an attractor at index {idx_attractor}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "canadian-saudi",
   "metadata": {},
   "source": [
    "When the starting pattern is made even more dissimilar to the stored ones (e.g. more than half is wrong), the distorted patterns do not converge to their correct attractor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "worst-librarian",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "patterns_for_x1 = np.array([[-1, 1, -1, 1, -1, -1, -1, 1], # last 3 same as x1\n",
    "                            [1, -1, 1, 1, -1, 1, 1, -1],# first 3 same\n",
    "                            [1, 1, -1, 1, -1, 1, 1, -1]]) # only 1st same\n",
    "\n",
    "plt.imshow(x1)\n",
    "plt.axis(\"off\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "breeding-lesbian",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "all should converge to x1\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "converged to x1: False\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "converged to x1: False\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "converged to x1: False\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"all should converge to x1\")\n",
    "plt.imshow(x1.reshape(-1,1))\n",
    "plt.axis(\"off\")\n",
    "plt.show()\n",
    "\n",
    "for pattern_for_x1 in patterns_for_x1:\n",
    "    x1r, it, _ = hn.recall_until_convergence(pattern_for_x1, with_energy=False, if_sequential=False)\n",
    "    print(f\"converged to x1: {np.all(pattern_for_x1 == x1)}\")\n",
    "    plt.imshow(x1r.reshape(-1,1))\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "individual-happiness",
   "metadata": {},
   "source": [
    "## Sequential / Asynchronous Update"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "international-router",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3, 1024)\n"
     ]
    }
   ],
   "source": [
    "def read_pict_data(path_2_data):\n",
    "    \"\"\" Read pict.dat data. 11 binary images of shape (32, 32). Last two are distorted \n",
    "    versions of previous ones.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    path_2_data : str\n",
    "        Path to data.\n",
    "    \n",
    "    Returns\n",
    "    ----------\n",
    "    numpy.ndarray\n",
    "        Data as array of shape (11, 1024)\n",
    "    \"\"\"\n",
    "    ndim = 1024\n",
    "    return np.loadtxt(path_2_data, delimiter=\",\", dtype=int).reshape(-1, ndim)\n",
    "    \n",
    "path_2_data='pict.dat'\n",
    "patterns_all = read_pict_data(path_2_data)\n",
    "\n",
    "# Get first 3 images.\n",
    "patterns = patterns_all[:3,:]\n",
    "print(patterns.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "limited-tracker",
   "metadata": {},
   "source": [
    "Check an example image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "suburban-mining",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_idx = 0\n",
    "plt.imshow(patterns[show_idx].reshape(32,-1).T)\n",
    "plt.axis(\"off\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cheap-ukraine",
   "metadata": {},
   "source": [
    "Add teh first 3 images to the network and test if they are stable with synchronous update."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "mature-sapphire",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 1 iterations this converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 1 iterations this converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 1 iterations this converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hn = HopfieldNetwork()\n",
    "hn.init_weights(patterns, self_connections=False, norm=False)\n",
    "\n",
    "for pattern in patterns:\n",
    "    patternr, it, _ = hn.recall_until_convergence(pattern, with_energy=False, if_sequential=False, exit=100)\n",
    "    print(f\"in {it} iterations this converged to\")\n",
    "    plt.imshow(pattern.reshape(32,-1).T)\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()\n",
    "    print(f\"this\")\n",
    "    plt.imshow(patternr.reshape(32,-1).T)\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fixed-coaching",
   "metadata": {},
   "source": [
    "Image at index 9 is the distorted version of image at index 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "entitled-finance",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p10 below\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "is a degraded version of p1 below\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"p10 below\")\n",
    "plt.imshow(patterns_all[9].reshape(32,-1).T)\n",
    "plt.axis(\"off\")\n",
    "plt.show()\n",
    "\n",
    "print(\"is a degraded version of p1 below\")\n",
    "plt.imshow(patterns_all[0].reshape(32,-1).T)\n",
    "plt.axis(\"off\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "august-regular",
   "metadata": {},
   "source": [
    "Let's try to recall it with synchronous update."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "august-break",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 2 iterations p10 converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOcAAADnCAYAAADl9EEgAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAEj0lEQVR4nO3dvY3jVhhAUWngIgznm7uJhSvYKqcCY5pwvrmxVYiOx5Zo+4k/l+I5oRSIQ+niAe8bktdpmi5Az9veBwDcJ06IEidEiROixAlRP829+fXtm61cWNnH7f1673UrJ0SJE6LECVHihChxQpQ4IWp2lLK03//8Y8uP43/47Zdf9z4E/sbKCVHihChxQpQ4IUqcECVOiNp0lDK3XT83ZrHNv75H59+534+VE6LECVHihChxQpQ4IWrT3do5dnL39eg8Ovf7sXJClDghSpwQJU6IEidEiROixAlR4oQocUKUOCFKnBAlTogSJ0RlrkqZ44qV/Tj3+7FyQpQ4IUqcECVOiBInRIkTosQJUeKEKHFClDghSpwQJU6IEidEHeKqlDkjV024YoIjsHJClDghSpwQJU6IEidEHX63lv24v9C6rJwQJU6IEidEiROixAlR4oQooxQ2NzdmGfGqoxkrJ0SJE6LECVHihChxQpQ4IeqlRymPtthdMdE1cv5HRzP179rKCVHihChxQpQ4IUqcECVOiMqMUpa+UuFy6W+V808jj9AY/Z7rIzUrJ0SJE6LECVHihChxQpQ4IWqVUcrIWGSNres1xjPsY40rT+rPerFyQpQ4IUqcECVOiBInRIkTooZHKYWt5n+z9M2iKn/XlirjqK3P/ciYZeljtHJClDghSpwQJU6IEidEze7WnnHncvSfodf4vC2PY8Sr/gYqrJwQJU6IEidEiROixAlR4oSo6zRND9+8/fjy8E3b6P/dlqMP38t+RkePH7f3673XrZwQJU6IEidEiROixAlR4oSozJOtX5nxBiOsnBAlTogSJ0SJE6LECVHihCijFE6rcqO0R6ycECVOiBInRIkTosQJUeKEKKMUDqHynJo5Sx+jlROixAlR4oQocUKUOCFqeLd2ZGfKvXTOY+mdyzP+dqycECVOiBInRIkTosQJUeKEqOFRysjW9uj2+hm30bdm9NFj5YQocUKUOCFKnBAlTogSJ0Rteg+h0e11I5jPjnA/HZ5n5YQocUKUOCFKnBAlTogSJ0Qd4nEMW45g1hgpuOLjeWccH1k5IUqcECVOiBInRIkTosQJUYcYpYza8iZkSx/H0R1hfFQ/RisnRIkTosQJUeKEKHFC1HWapodv3n58efjmGXcgX1l95/IIRs/h28/fr3dff+ZggPWIE6LECVHihChxQpQ4IWp2lPL17dvDNyv35zkj/5z/Wj5u70YpcCTihChxQpQ4IUqcECVOiBq+h9CW9+c54za/c4WVE6LECVHihChxQpQ4IUqcELXp4xi2fEL1M58HSxv5DVs5IUqcECVOiBInRIkTosQJUYd4svWWI5gjPEGZ9W357JiP2/3XrZwQJU6IEidEiROixAlR4oSoQ4xSRm15E7Klj2OUK3g+O/L5sHJClDghSpwQJU6IEidEvfRu7YjCLt0zXCTw2ZG/TysnRIkTosQJUeKEKHFClDghyiiFy+VyzosE6qycECVOiBInRIkTosQJUeKEqOs0TXsfA3CHlROixAlR4oQocUKUOCFKnBD1F9bY5I+6rEolAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "patternr, it, _ = hn.recall_until_convergence(patterns_all[9], \n",
    "                                              if_sequential=False, with_energy=False, exit=1000)\n",
    "print(f\"in {it} iterations p10 converged to\")\n",
    "plt.imshow(patternr.reshape(32,-1).T)\n",
    "plt.axis(\"off\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "returning-sailing",
   "metadata": {},
   "source": [
    "p10 converges to stable point p1 in 2 iterations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "controlling-infection",
   "metadata": {},
   "source": [
    "image at index 10 is a mixture of the images at indices 1 and 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "sufficient-drinking",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p11 below\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "is a mixture of version of p2 and p3 below (in this order)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"p11 below\")\n",
    "plt.imshow(patterns_all[10].reshape(32,-1).T)\n",
    "plt.axis(\"off\")\n",
    "plt.show()\n",
    "\n",
    "print(\"is a mixture of version of p2 and p3 below (in this order)\")\n",
    "plt.imshow(patterns_all[1].reshape(32,-1).T)\n",
    "plt.axis(\"off\")\n",
    "plt.show()\n",
    "\n",
    "plt.imshow(patterns_all[2].reshape(32,-1).T)\n",
    "plt.axis(\"off\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "coordinated-namibia",
   "metadata": {},
   "source": [
    "Let's try to recall it with synchronous update."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "developmental-emperor",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 3 iterations p11 converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "viz_recall_dict = {}\n",
    "patternr, it, _ = hn.recall_until_convergence(patterns_all[10], if_sequential=False, with_energy=False,\n",
    "                                           exit=10000, **viz_recall_dict)\n",
    "print(f\"in {it} iterations p11 converged to\")\n",
    "plt.imshow(patternr.reshape(32,-1).T)\n",
    "plt.axis(\"off\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "characteristic-rolling",
   "metadata": {},
   "source": [
    "p11 converges in 2-3 iterations to a spurious stable point (neither p2 or p3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "duplicate-player",
   "metadata": {},
   "source": [
    "However, p11 does converge to p3 when the asynchrnonous update rule is used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "moved-skill",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 8000 iterations p11 converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "viz_recall_dict = {\"i\": 1000, \"shape\": (32, 32)}\n",
    "patternr, it, _ = hn.recall_until_convergence(patterns_all[10], if_sequential=True, with_energy=False,\n",
    "                                           exit=8000, **viz_recall_dict)\n",
    "print(f\"in {it} iterations p11 converged to\")\n",
    "plt.imshow(patternr.reshape(32,-1).T)\n",
    "plt.axis(\"off\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "indian-significance",
   "metadata": {},
   "source": [
    "After around 8k iterations, we p11 converges to the stable point p3 with sequential update."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "corporate-vienna",
   "metadata": {},
   "source": [
    "## Energy in Hopfield Networks"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dangerous-slave",
   "metadata": {},
   "source": [
    "The energies of the image data points in the network that stores the first 3 images are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "desirable-pontiac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x1 e: -1470864.0\n",
      "x2 e: -1395344.0\n",
      "x3 e: -1494272.0\n",
      "x4 e: -734700.0\n",
      "x5 e: -535440.0\n",
      "x6 e: -696624.0\n",
      "x7 e: -699116.0\n",
      "x8 e: -172592.0\n",
      "x9 e: -270860.0\n",
      "x10 e: -422892.0\n",
      "x11 e: -174592.0\n"
     ]
    }
   ],
   "source": [
    "for idx, pattern in enumerate(patterns_all):\n",
    "    print(f\"x{idx+1} e: {hn.energy(pattern.flatten())}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "centered-prize",
   "metadata": {},
   "source": [
    "The distorted p10 and the mixed p11 have greater energy, which it makes sense as they are not attractors - p10 is a degraded version of p1, and p11 is a mix between p2 and p3."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "favorite-constraint",
   "metadata": {},
   "source": [
    "Asynchrnously recall p11 (mix) and observe the energy vs. iteration. The energy is minimized at the recalled pattern approaches the attractor - a local minimum in the energy landscape of the network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "judicial-height",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 8000 iterations p11 converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "viz_recall_dict = {\"i\": 1000, \"shape\": (32, 32)}\n",
    "patternr, it, energies = hn.recall_until_convergence(patterns_all[10], if_sequential=True, with_energy=True,\n",
    "                                           exit=8000, **viz_recall_dict)\n",
    "print(f\"in {it} iterations p11 converged to\")\n",
    "plt.imshow(patternr.reshape(32,-1).T)\n",
    "plt.axis(\"off\")\n",
    "plt.show()\n",
    "\n",
    "plt.plot(energies)\n",
    "plt.title(\"Energy vs. iter. (sequential update for p11)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "characteristic-replication",
   "metadata": {},
   "source": [
    "Setting (forcing) the weight matrix of the network to be drawn from a normal distribution (i.e.: not symmetric, should fail to recall), and iterating an arbitrary starting state (e.g.: p2) reults in the following: the recalled pattern is not drawn to any attractor, and the energy is fluctuating, even reaches postitive values - the recall is also Gaussian noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "previous-norfolk",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the weights are forced to by asymmetric Gaussian\n",
      "[[-1.4980634  -0.86355605  0.53675219 ...  0.57447774  0.6408322\n",
      "  -0.71132156]\n",
      " [ 0.08751037  0.08086753 -1.08115747 ... -0.85972068  1.03219596\n",
      "  -1.50016862]\n",
      " [ 0.56800074  2.38406788  0.45933858 ... -0.20351043 -0.07330078\n",
      "  -1.01857697]\n",
      " ...\n",
      " [ 0.66836657 -0.82942074 -1.24256111 ... -0.59896846  0.75530048\n",
      "   0.25108939]\n",
      " [-0.38514932  1.03115923  0.03718502 ... -0.03980832 -0.92732335\n",
      "  -1.77751229]\n",
      " [ 0.05891325  1.55241916 -0.34359252 ...  0.86810106  0.3677978\n",
      "  -0.6121712 ]]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOcAAAD3CAYAAADmIkO7AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAN6ElEQVR4nO3decwkRR3G8ed5YRWWRY4FhQVhBVEUSfBETFQSXRETgkbXK+EwosYEE+IR1EgkMZ5BOSSKIcplVMCgIkZxFUFRjNFE44WiHC7H4i6H7Hog8JZ/dL3YjjM98/Z21/569/tJ3uSdnp6u6u55pmequrucUhKAeOa2dAUAjEc4gaAIJxAU4QSCIpxAUIQTCGqrCqfta22flP8/0fb1LZfT+rXbAtvftn3CFq7DJtsHbMk69K23cNq+1fY/80ZcZ/tC28v6Km8obCfbT649PtL27VuyTnWzfDCllI5OKV006/wd1OnRD91aHZallG7uoaxNI3+P2P50fm5l3n/150/rug4L+j5yHpNSWibpMEnPlPS+nsvb5tjefkvXYXNEq38O/bL8vn2CpH9Kunxktl1r832or7oU+VqbUlon6WpVIZUk2X6+7Z/Yvt/2r2wfWXtud9sX2L7T9n22v56n72b7Ktvr8/SrbO87Sx1sH2x7je17bf/B9mtrzy23faXtB2z/TNKBDctZ+PR8a67fXbbfVXv+ebZvyOt1l+1zbT8mP/fDPNuv8qfuCZK+LWlF7ZN4he052++1/Wfb99i+zPbuI+W/2fZfJF2zcPSyfUbeLrfYPrphHRaWvdH272y/Kk9/mqTzJB2R63L/hNdfa/ukSfPbfmyuy19s3237PNs75ueOtH277VNtr5N0QdN+tf1hSS+UdG4u49w8/dFvILZ3sX1xfv1ttj9gey4/t6htM+I1kv4q6Uczzt+tlFIvf5JulfTS/P++kn4t6ez8eB9J90h6haoPiFX58Z75+W9JulTSbpKWSHpxnr5c0qslLZW0s6pPtK/XyrxW0kn5/xMlXZ//30nSWklvkrS9pGdJ2iDpkPz8VyRdlud7hqQ7Fl47Zr1WSkqSvpznP1TS+tq6PlvS83M5KyX9XtIptdcnSU+uPT5S0u0jZZwi6ad5uz1W0uckfXmk/Itz+TvmdX1I0lskbSfp7ZLulOQJ67Ba0oq87V8n6e+S9h7dbg37dux2rj1/lqQrJe2e99M3JX20tr4PS/p4XrcdF7Nfx23HvC2+kV+7UtIfJb25Vr+Zt81IGddIOn3Mvr9D0u2SLpC0R28Z6jmcmyRtzCv0fVVfByTpVEmXjMx/taQTJO0taV7SbjOUcZik+2YI5+sk/WjktZ+T9MG8wx6SdHDtuY9MeoPWdlB9/k9I+vyE+U+R9LVFhvP3kl5Se7x3ruP2tfIPqD1/oqQ/1R4vzfPsNeO++qWkYyeFbcz8Y7dzfmxVYT+wNu0ISbfU1vffknZos19Ht2Pefw9KenrtubdJunZzto2k/SQ9IulJtWnLJD0n74cnSPqqpKv7ylDf3/dfmVL6nu0XS/qSpD0k3S9pf0mrbR9Tm3eJpB9IeqKke1NK940uzPZSSWdKermqo6ok7Wx7u5TSIw312F/S4SNf07aXdImkPfP/a2vP3TbDuo3Of2iu41MkfUrVTlyal/2LGZY3Wt+v2Z6vTXtE1RtiXPmStG7hn5TSP2xL1Zvp/9g+XtI7VQV9Yb49FlnHSfZUtd6/yHWQqsBuV5tnfUrpX7X6tN2vUlXvx+h/99ltqr6dLZh529Qcr+pD55baazdJ+nl+eLftkyXdZftxKaUHpixv0Ur95rxO0oWSzsiT1qo6cu5a+9sppfSx/Nzutncds6h3SXqqpMNTSo+T9KI83WPmrVsr6bqR8pallN6u6ivpw6o+FBbsN8Nqjc5/Z/7/s5JulHRQruP7p9Rv3GVBayUdPVLfHVJKd0x53VS295d0vqSTJS1PKe0q6Te1Oi52uaPzb1DViHJIre67pKqBZdJrpu3XpjptUPWtYv/atP1UffXcHMdLumjKPAv1mvb+a6VkP+dZklbZPkzSFyUdY/so29vZ3iE3FOybUrpLVSPJZ3JDwRLbCztrZ1U7/v7cQPLBGcu+StJTbB+Xl7fE9nNtPy1/Ml8h6XTbS20/XdXX62lOy/Mfouq37KW1Oj4gaZPtg1X9xqm7W9IBI4+X296lNu08SR/OQZLtPW0fO+O6TrOTqjfV+rzsN6n6nV2vz74LjVgz+J/5U0rzqsJ/pu3H5zL2sX1UwzKm7dfRbfaovP8uU7W9ds7b7J2q3mOt2H6BqiPv5SPTD7f91Nxgt1zSOaq+Pv+tbVlNioUzpbRe1Q/301JKayUdq+qosl7VkeI9tfocp+rT8EZVrWWn5OlnqWpA2KCqweQ7M5a9UdLLJL1e1RFunf7bICFVR5FlefqFqn7oT3OdpD+p+i19Rkrpu3n6uyW9UdVv7fP139AuOF3SRa5ac1+bUrpRVePSzXnaCklnq2pQ+a7tjXldD59lXadJKf1O0icl3aDqTX+opB/XZrlG0m8lrbO9YYZFjpv/VFXb5qe2H5D0PVVHxknOUvN+PVvSa3Jr6zljXv8OVb9zb5Z0vaqfUF+Yoe6TnCDpivy+qTsg122jqm8bD0p6w2aU08j5hy5mZHulpFskLUkpPbyFq4Ot2FZ1+h6wNSGcQFB8rQWC4sgJBNV4EsKqudUTD6tX3/nLRRd21IrDFv2aaWW1WWabuk/TVI8o9W9Tx6Hvs7b7pe0y25Q1t9dNY/tJOXICQRFOICjCCQRFOIGgCCcQFOEEgurles5JTc19dGF03WTfh66b89sur2T3RtddMH2sc5OS22PN/PjpHDmBoAgnEBThBIIinEBQhBMIinACQfXSldJ1c3iUZvmSV2iUvnJmkrb1iNJt08d2LFUPjpxAUIQTCIpwAkERTiAowgkE1bq1tk3LVOkT37t8Telllm6BLHlPqDbaljXkFnaOnEBQhBMIinACQRFOICjCCQRFOIGgit5DqEkf974peX+etsssqeRJ4G33WckLAZpE2GccOYGgCCcQFOEEgiKcQFCEEwiKcAJBOaWJg1drft1Bk59sEGXk4ghlTVOyuyfKkAtdG0Idm6yZv5yRrYEhIZxAUIQTCIpwAkERTiAowgkE1diVsmpudauulCFfDVL66odJSg8Z0XVZUbqrorx3mke2pisFGBTCCQRFOIGgCCcQFOEEgiKcQFCtb/AVZcTgrVXpLp2SY720qUcf74HodeTICQRFOIGgCCcQFOEEgiKcQFC9DMcwSZSTudsawijJUVpdm5TcHiX3WdvlTcKREwiKcAJBEU4gKMIJBEU4gaAIJxBUY1dK6fvHtNF1s3yUpvcmJbs3+tiXUbZH1+vW/h5C46dz5ASCIpxAUIQTCIpwAkERTiAowgkEVXRk6yhXnkS6wqHrsrpWep+1uT9P6a6xNmU1LW9ur5sYjgEYEsIJBEU4gaAIJxAU4QSCIpxAUK1v8NWmibr0FR8lb+3fZMjdRKWvPoqyrSJcdcWREwiKcAJBEU4gKMIJBEU4gaAIJxBUL2OldH1lQdf6uCql5Nga22J3Qx/bo+vtyA2+gG0E4QSCIpxAUIQTCIpwAkERTiCo1l0pJbs+SjbZR7mxVmlD3p9Runu6LosjJxAU4QSCIpxAUIQTCIpwAkG1Ho6h65apKCdzNxnCie9dr1vpoSvaKH0vo67LYzgGYGAIJxAU4QSCIpxAUIQTCIpwAkE1nvg+hJPAS45A3EeTfZQTvaN0f0UZQiMCjpxAUIQTCIpwAkERTiAowgkERTiBoMJclTIEW/M6d33lTNf1KL19S3bdrJm/nKtSgCEhnEBQhBMIinACQRFOICjCCQTVuiula22brktelTKEKyOGfoOvklelRBmOgRt8AQNDOIGgCCcQFOEEgiKcQFCEEwiq9cjWXYtyhUPpbpY2XQdRRqFuq+v6R7lipfMxVDpdGoDOEE4gKMIJBEU4gaAIJxBU69baoY9c3KasIaxzlFbekifg99HCXvKk+DXz46dz5ASCIpxAUIQTCIpwAkERTiAowgkE1ctwDFGUvL9Q22W2MfRuljb1KHmPqc0prw2GYwAGhnACQRFOICjCCQRFOIGgCCcQVJiulCGMDF3yfjqluz221v3ZRxdM16OAMxwDMDCEEwiKcAJBEU4gKMIJBEU4gaAau1JWza1uNbJ1lKtBIpQ1rbzo9WhS8uZZQxiNvO0+oysFGBjCCQRFOIGgCCcQFOEEgiKcQFCtx0qJctVBk1IjEPdhCCNst9Vm3drus0ijmC8WR04gKMIJBEU4gaAIJxAU4QSC6mVk6yG0hrbRdp3btPyVbmWM0rLd9UUCQ36fcuQEgiKcQFCEEwiKcAJBEU4gKMIJBNX6HkJR7gMT4QTlafVoEqULo6QhdG8wsjWAiQgnEBThBIIinEBQhBMIinACQTVeldJ190aUZvI+ul9KNr33MVpzybJKDq/RJMr7cRKOnEBQhBMIinACQRFOICjCCQRFOIGgGrtSuu4eKHmDrGmva6Nk03vJrpkmXV9t07a80tsjwujsHDmBoAgnEBThBIIinEBQhBMIinACQTXe4Gt+3UGTn2wQZbyLIdzga5LSN8HqelsN/YZnJbf/3F43cYMvYEgIJxAU4QSCIpxAUIQTCIpwAkENYtj5KMuLcqVIH/UoeTVIlKudun4Pc1UKsI0gnEBQhBMIinACQRFOIKiiJ75HuRdQkz5u7V/yQoCS+qhjm1bj6MMqSM31Z2RrYGAIJxAU4QSCIpxAUIQTCIpwAkG1PvE9iign4Ec/ibrtMkueZN9UXun7JnVdR058B7YihBMIinACQRFOICjCCQRFOIGgGq9KAbDlcOQEgiKcQFCEEwiKcAJBEU4gKMIJBPUfvIVFb1Vbe/AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEICAYAAABbOlNNAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAABcnElEQVR4nO29eZQkV3ng+/tyr8zal65epW5Jra0lJKFGiNUGgSUWI9kDWNgM4phn2Tzw4IfnzMDg8eCZ0RvjBWPGgEcDHsRuPQwIsAEJCRBgba0FpG6pF6n3tbr2yn2574+IGxmZGblVZlZlZd/fOXUq60ZG5o2sjPvdbxelFAaDwWAwaHyrPQGDwWAwdBdGMBgMBoOhBCMYDAaDwVCCEQwGg8FgKMEIBoPBYDCUYASDwWAwGEowgsFgWIOIyG4R+dXVnoehNxGTx2BYK4jIIWASyLuGP6+Uev/qzKg7EJGPAhcppd652nMx9AaB1Z6AwdAkv66U+mEn30BEAkqpXCffo5s4167XUB9jSjL0BCLybhH5mYj8lYjMishBEXmD6/iQiHxORE6KyHER+e8i4ned+3MR+RsRmQE+KiJjIvIdEVkQkcfs5//Mfv6nROSvy97/OyLyRx7z+nsR+auysXtE5IP24/9oz2dRRPaKyA0NXu8hEXmdiNwE/Cfgt0RkSUR+sZzrbfRzNpwbGMFg6CVeCuwFxoG/AD4nImIfuwvIARcB1wC/BvxfZee+AKwD7gA+BcSB9cBt9g+u13qHiPgARGQcuAH4qsecvoK1aIv93BH7vb8mIpcA7wdeopQaAG4EDjVzwUqp7wP/L/CPSql+pdRVy7xeg8HBCAbDWuNbIjLn+vk917HDSqn/rZTKYy2MG4BJEZkE3gD8kVIqrpQ6A/wNcKvr3BNKqf9pm1QywL8B/otSKqGU2mO/HgBKqUeBeSxhgP06P1ZKnfaY708BBbzK/vutwENKqRNYvpIwcLmIBJVSh5RSz7fw2QDQ7PUqpZKtvqehtzA+BsNa45YaPoZT+oFSKmFv0vuBUSAInCwqEPiAo65z3Y8nsO6NasfBEhTvBO6zf/+t14SUUkpEvga8A3gQ+G3gS/axA7b56aPADhH5AfBBW2i0wvk0d70GQwlGYzCcCxwF0sC4UmrY/hlUSu1wPccdnjeFZYbZ7BrbUvaaXwJuFpGrgMuAb9V4/68CbxWR87FMOP/kvKlSX1FKvRJrMVfAx5q6ssq5Q/PXazCUYASDoedRSp0E7gX+WkQGRcQnIheKyK9UeX4e+AaWEzoqIpcC7yp7zjHgMeCLwD/VMscopZ7EEjafBX6glJoDEJFLROS1IhIGUkCS0lDcRjkNbNU+j2av12AoxwgGw1rjO3b0jf75ZoPnvQsIAXuAWeDrWD6IarwfGMIyT30Ra9efLnvOXcCV9vF6fBV4HZYzWhMG/hw4a7/POqwII0Tkd0RkdwOvC/D/2b+nReQJ+3HD19vkexnOAUyCm8HQACLyMWC9Uuo219irsUxKW5VShVWbnMHQZozGYDB4ICKXisiLxOI64D3AN13Hg8AHgM8aoWDoNYxgMBi8GcDyM8SBu4G/Bu4BEJHLgDks08wnVmd6BkPnMKYkg8FgMJRgNAaDwWAwlLDmE9zGx8fV1q1bV3saBoPBsKZ4/PHHzyqlJryOrXnBsHXrVnbt2rXa0zAYDIY1hYgcrnbMmJIMBoPBUIIRDAaDwWAowQgGg8FgMJRgBIPBYDAYSjCCwWAwGAwlGMFgMBgMhhKMYDAYDAZDCW0TDCLiF5EnReS79t+jInKfiOy3f4+4nvthETlgNz+/0TV+rYg8bR/7pKtfb1fz/WdOcWYhtdrTMBgMhrbQTo3hA8Czrr8/BNyvlNoO3G//jYhcjtV7dgdwE/BpEfHb53wGuB3Ybv/c1Mb5dYRMrsB7v/w4X3q4aq6IwWAwrCnaIhhEZDPwJqwOVZqbKTZQvwu4xTX+NaVUWil1EDgAXCciG4BBpdRDyqrs9wXXOV1LIpNDKTizWN7DxWAwGNYm7dIYPgH8B8Bdl37SbjGoWw2us8c3UdqI/Jg9tsl+XD5egYjcLiK7RGTX1NRUWy5gucQzVifGKSMYDAZDj9CyYBCRNwNnlFKPN3qKx5iqMV45qNSdSqmdSqmdExOeNaBWjGQmB8DUkhEMBoOhN2hHEb1XAG8RkTcCEWBQRL4EnBaRDUqpk7aZ6Iz9/GPAFtf5m4ET9vhmj/GuJmE0BoPB0GO0rDEopT6slNqslNqK5VR+QCn1TuDbgO6Pext29yt7/FYRCYvINiwn86O2uWlRRK63o5He5Tqna9GC4exSmkLBND0yGAxrn06W3f5z4G4ReQ9wBHgbgFJqt4jcDewBcsD7lFJ5+5z3Ap8H+oDv2T9dTcI2JWXzivlklpFYaJVnZDAYDK3RVsGglPox8GP78TRwQ5Xn3QHc4TG+C7iinXPqNFpjAMvPYASDwWBY65jM5xZxC4azxs9gMBh6ACMYWiRZpjEYDAbDWscIhhYpMSUZjcFgMPQAa77n82qTyOQQgaDfZwSDwWDoCYxgaJFEJk806Gc4GjKCwWAw9ATGlNQiiUyevlCAiYGw8TEYDIaewAiGFklmckRDfkswGI3BYDD0AEYwtEg8kzeCwWAw9BRGMLRIMpOnL+Rnoj/MTCJDLl+of5LBYDB0MUYwtEgikyNm+xiUgpl4ZrWnZDAYDC1hBEOLJLTGMBAGTMMeg8Gw9jGCoUUSto9hvN8SDCYyyWAwrHWMYGgRLRjW2RqDcUAbDIa1jhEMLWKFqwaKGoMRDAaDYY1jBEMLKKVIZC2NoS/kZyAcMILBYDCseYxgaIF0roBS0BfyA5jsZ4PB0BMYwdAC8bTVvS0atATDuElyMxgMPYARDC2gS25Hw1YtwomBMGeNxmAwGNY4RjC0QDJrCwZtSuo3GoPBYFj7GMHQAo7G4PIxLKZypLL5WqcZDAZDV9OyYBCRiIg8KiK/EJHdIvJn9vioiNwnIvvt3yOucz4sIgdEZK+I3Ogav1ZEnraPfVJEpNX5dZKE7WPoC9qmJBOyajAYeoB2aAxp4LVKqauAq4GbROR64EPA/Uqp7cD99t+IyOXArcAO4Cbg0yLit1/rM8DtwHb756Y2zK9jeGkMYLKfDQbD2qZlwaAsluw/g/aPAm4G7rLH7wJusR/fDHxNKZVWSh0EDgDXicgGYFAp9ZBSSgFfcJ3TlSRsk1EsXCYYjMZgMBjWMG3xMYiIX0SeAs4A9ymlHgEmlVInAezf6+ynbwKOuk4/Zo9tsh+Xj3ctyYxtSgoVo5LACAaDwbC2aYtgUErllVJXA5uxdv9X1Hi6l99A1RivfAGR20Vkl4jsmpqaanq+7SKetk1Jdh7DaCyEiBEMBoNhbdPWqCSl1BzwYyzfwGnbPIT9+4z9tGPAFtdpm4ET9vhmj3Gv97lTKbVTKbVzYmKinZfQFDpcVWc+B/0+BiNBZhOmJ4PB0KvMJ7Okc70dediOqKQJERm2H/cBrwOeA74N3GY/7TbgHvvxt4FbRSQsItuwnMyP2uamRRG53o5GepfrnK4kkcnh9wnhQPFj7A8HHKe0wWDoPX7j0z/n7x44sNrT6CiBNrzGBuAuO7LIB9ytlPquiDwE3C0i7wGOAG8DUErtFpG7gT1ADnifUkqvpO8FPg/0Ad+zf7qWRCZPNOjHHVXbF/KTsH0PBoOhtygUFIfOxjkxl1rtqXSUlgWDUuqXwDUe49PADVXOuQO4w2N8F1DLP9FV6H7PbmIhv+N7MBgMvcV8MktBQcqYkgzViNtNetxEQwGSxpRkMPQkM7b/MN3j1Q2MYGgB3aTHTTTkJ25MSQZDTzITtwRDKltY5Zl0FiMYWiDhpTEY57PB0LMUBUNv3+NGMLRAooqPwTifDYbeZFYLBuNjMFQjkclVaAx9IT8J43w2GHqSaWNKMtTDMiWV+hhioQDxTA6r3JPBYOglZo0pyVCPpKePwU9BWf2gDQZDb2Gcz4a6eDqf7bpJxgFtMPQeJlzVUJNCQZHM5p3Kqhrd/zmeNg5og6HXmDHOZ0Mtyvs9a2K2oEj2+I7CYDgX0YIhm1fkC73rRzSCYZloU1GsIvPZ+ttoDAZD7zEbz6BLo/WyA9oIhmWiy15UmJJCxsdgMPQiqWyeeCbv9HY3gsFQQSJraQQVpiTbx2AEg8HQW+g+KxuG+wBI9XDkoREMy0RXUC3PfO5zNAZjSjIYeonpJUswbByKAEZjMHigTUk6PFWjnc+m9LbB0FtojWGj1hiMYDCUozUCbTrSRMNGYzAYehEdkbTB0RiMKclQRnm/Z41JcDMYehMtGDbZGkMvJ7kZwbBMtKmo3Pkc8PsIBXymJ4PB0GPMxjP4BNYN2hpDDye5GcGwTLSpKBqs7I4aC/lNFzeDoYN88eHD/Nl3dq/oe07HMwxHQ85m0JiSDBUU8xj8FceioYBxPhsMHeSHe07zz788uaLvOZvIMBoLEQlqwdC797gRDMskkc0T9AuhQOVHGDXNegyGjjIdTzOXyK5oefvppQyj0RCRoHXPG42hBiKyRUR+JCLPishuEfmAPT4qIveJyH7794jrnA+LyAER2SsiN7rGrxWRp+1jnxTRyefdRzKTpy9YqS2Aae9pMHSas4sZMvkC8RW8z2YTGUZiQSIBozE0Qg74Y6XUZcD1wPtE5HLgQ8D9SqntwP3239jHbgV2ADcBnxYRvcJ+Brgd2G7/3NSG+XWEeDpX0aRHY9p7GgydQynFdDwNFBvnrAQz8SyjsXDRlGScz9VRSp1USj1hP14EngU2ATcDd9lPuwu4xX58M/A1pVRaKXUQOABcJyIbgEGl1EPK0g+/4Dqn60hk807OQjnRkN/4GAyGDrGQypHNWyakmRUSDIWCsn0MQcIBY0pqChHZClwDPAJMKqVOgiU8gHX20zYBR12nHbPHNtmPy8e93ud2EdklIrumpqbaeQkN49W9TRMNBYzGYDB0iOmltPNYZyN3msVUjnxBMRoL4/NZvkWTx9AAItIP/BPwR0qphVpP9RhTNcYrB5W6Uym1Uym1c2JiovnJtoFEJucZqgoQC/uNj8Fg6BDTLi1hpQSDNl2NxoIARAI+42Ooh4gEsYTCl5VS37CHT9vmIezfZ+zxY8AW1+mbgRP2+GaP8a4kkcl7hqoC9AWN89lg6BRujWEmnl2R99QCaCQaAiAS9BtTUi3syKHPAc8qpT7uOvRt4Db78W3APa7xW0UkLCLbsJzMj9rmpkURud5+zXe5zuk6vPo9a2JhP/FMbkVD6QyGc4WpJZfGsEI+Bl1ZdSxm9WKIBP097Xz2toU0xyuAfws8LSJP2WP/Cfhz4G4ReQ9wBHgbgFJqt4jcDezBimh6n1JKf8LvBT4P9AHfs3+6EsvH4P3xRUMBlIJ0ruBEMBgMhvagNYahviAzK2RKcjQGbUoK9rYpqWXBoJT6Gd7+AYAbqpxzB3CHx/gu4IpW57QSJDK5Gs7nYntPIxgMK0UuX+A9d+3iD197ETu3jq72dDrG9FKG4WiQ8f4wcyskGLTJqkRjMKYkQznxmlFJpsKqYeWZSWT4yb4p7ttzerWn0lGm42nGYiFGo6EVC1ediaeJBH2OXzES8Pe0xmAEwzLIFxSZXKGq89m09+xNcvkCt3zq5zzwXHcuvLp+1/NTS6s8k85ydinDWH+YkViQ2RVyPs/Es4zajmeAcNBnWnsaSnGa9FTxMWiBYUpv9xbzySxPHZ3jsUOzqz0VT3SPkANnelswTC+lGe8PMRoLrZiPYSaeZrS/KBgiQb/JYzCUondmkWoagy0wEib7uadYTFmC3h0u2U3o7+WRmURPmzmm4xnGYmGGoyFm45kVif6bSWSdUFXQPobe/YyNYFgGemdW3u9ZU/QxGI2hlygKhpWrz9MMWjAUFByeTqzybDpDNl9gLpFlvD/MaDRErqBYSnf+Ppux/RoaK8HNmJIMLqq19dQY53Nvspiy7NlnV7BwWzMkXTvYXjUnaWfzWH+IEXuh7rSfQSnFbDzrvB/0fh6DEQzLoFaTHig6n42PobdY6HZTkksw9KoD+qz92Vs+BiunoNN+hmdPLrKUznHhRL8z1ut5DEYwLANHMNQxJZn2nr2F1hi63ZQU8vsqNIZ/fOwIzxyfX41ptRUnA7k/7Nj8O539fM8vjhPwCW+8coMzpvMYerW6gREMy8AxJVUVDLbGYJzPPYW2ZSezeeIrYNduFv29vGT9QInGMJ/I8uFvPM1XHz2yWlNrG7qY3VgsVBQMHdQYCgXFd546wau2jzNaZkoCq7pBL2IEwzKo52Pw+4RwwGeczz2Gdj5Dd2oNWmO4YtMgz08tUShYu9mfP3+Wgio1Na1VSjQGe6HuZJLbY4dmODGf4pZrSjsA6J4M6R51QBvBsAzqmZLA8jMY53NvoU1JAGfj3edn0Av/jo1DpLIFTswnAXhwn9WzpBcWsamlNCG/j8FIgMFIAL9POqoxfOupE/QF/bz+8smS8V7v4mYEwzJI1dEYwBIaxvncW6wFjSES9LF9neUkPXBmCaUUP91/FuiNHsXTSxnG+kOICCLCSDTUsdLbmVyBf3n6JL+2Y7KiYKYjGHrgM/XCCIZlkGhIY/CbBLceYzGVc/7n3RiZlMzm6Qv6ucgWDM9PxXl+Ks7xOUtz6IXd7fRSmjFXBvJoLNgx5/NP9k0xn8xyy9WVjSQjwd5u79mOstvnHFplr1U5NRoKkOjR3cS5ykIqy/ljUZ47tVjSRaxbSGYswTAaCzEcDXLgzBI+u+7xeaPRnljEdNazZjga6pgp6VtPHWc0FuKV28crjkUCRmMwlJHM5gkFfPh91aqNWyGriS6MXDEsn8VUjomBMP3hgBNP300ks1ZXQRHhool+np9a4sF9U2wdi7J9XX9PLGLalKQZ7ZBgSGRy/HDPad505QaC/spl0piSDBWk7J1ZLaKhAHGX8/m/fmcPf3Pfvk5PzdBBltI5BiIBxvpDXetj0H6vCyf62Xd6kYdfmOHVF0/0RG0fpRRnl9KM9xc1hpFYZ3wMTxyeI50rcMNl6zyPO6YkE65q0CSz1XsxaGJhP0nb+ayU4ptPHuPuXUdXYnqGDrGYyjIQDjIWCznx9N2E9jEAXLSun7lElmQ2z6u2T1hlote4KSmeyZPOFUpqFo3Ggswl2l9I75GD0/h9UrXhkdEYDBUkGtIY/I7GcHYpw2wiy8n5FCdsR6Bh7bGYsjSG8f4wZxe7UGPI5p0FSzugAz7hZReOWWWi17jz+eyiLofh0hjsQnqLbTbbPvLCDFdsHKQ/7O2GLTqf1/ZnWg0jGJZBynUDViMaCjg+hn2nF53xXYe7s5b/uUKhoJhPNm96yOULJDJ5+iMBxvrD3akxuLoK6ro+Lz5/hP5wwO44trY1Bifr2eVj6ERZjFQ2z1NH57huW/X2qGHb+dwLuSFeGMGwDLSTrxaxkJ9ENo9Sir2nLMEQ9AtPGMGwqvxg9yle9j/uZyHVnHDQ5TAGIkHG+62WkvlCd9XJcZuSNo30sW08xs1XbwR6o+jbWduv49YYRlvMfi4UFPc8dbxEm3ryyByZfIGXbhurep5JcGsAEfkHETkjIs+4xkZF5D4R2W//HnEd+7CIHBCRvSJyo2v8WhF52j72SRGpHvaziiRr9HvW9IUCKGXFOe87vchoLMTO80d53AiGVeX4XJJEJs9Mk85jndw2EAkwFgtRUKxYI/pGcTuf/T7hR//+V/mdl54PWDk3uYIil1+7O9xiOQyXxhBrrV7Sk0dn+cDXnuKufz3kjD1ycBoReEkNjcGYkhrj88BNZWMfAu5XSm0H7rf/RkQuB24FdtjnfFpE9Cr7GeB2YLv9U/6aXUEyW6hrSoqFi+09955e5OLJfnZuHWHPyYWuLMB2rqBv5Gaz0rWGMWibkoCuy2WwNIZqNnG9w13LgsEyJbmL2ek+zMuNTDo2a/n87vrXw47QfOSFGS5bP8hQX7DqeUXn89r9PGvRFsGglHoQmCkbvhm4y358F3CLa/xrSqm0UuogcAC4TkQ2AINKqYeUFWLwBdc5XUUyk2soXBUgns6x79Qil64f5MXnj5AvKH5xbG4FZmnwQicnNlvHailVNCXpHWu35TJYGoP3Ld0LO9zpeIaBSMCx7wOM2D0Zlqu9nZpPAZYm+YPdp8nkCjxxZJaXXlBdWwAI+q08prX8edaikz6GSaXUSQD7tw4I3gS44zaP2WOb7Mfl4xWIyO0isktEdk1NTbV94vVw23KroU1N+08vEc/kuXhygBdvsaxpj3dpM/lzgWTG2uE12w7SbUrSNu5uymXI5gvkCqrq9zLcA+GVU0tpJlz+BYD+cICAT5btYzg5n6I/HOD8sSif+9kL/PKYlb9Qy7+g6eX2nqvhfPbyG6ga45WDSt2plNqplNo5MTHR1sk1gtuWWw0tGJ48agmBS9b3MxQNcvFkP48fMYJhtdDOwmbrWC2mLVPFQCToxNF3U72kemVaGjF9/OuBs/xg96n2T65NTC+lS8xIgFVIL7b87OdT8yk2DEV498u38sSROf7Xgy8A1IxI0vRye89OCobTtnkI+/cZe/wYsMX1vM3ACXt8s8d415HKFupHJdnxz08dnQNg++QAANeeP8ITh2edWvndzvRS2inC1gukbBNSs34erTH0hwMMR0P4pLt8DLoUfHkVUE0kUN+U9Ikf7uev793b8HtmcoUV7Qo3Ey8th6EZjYYcjeGrjx7hg3c/1fBrnlxIsX4owtt2bmEgHOC+Pae5ZHKgQgB50QvZ5NXopGD4NnCb/fg24B7X+K0iEhaRbVhO5kdtc9OiiFxvRyO9y3VO15DLF8jkCw2bkn5xdJ6NQxEGI5Yt9MXnjbCQynFgjfTk/W/f3cPb//6hNSPI6qF3eM06n92mJL9PGI2FusrHUOxDXs3HUN+UdHgmzlyicSfut546zlv+7mcr9jlYdZLCFeMjsSDTSxnu+Oc9fPgbT/ONJ443HEp8aj7JhqEI/eEAv/USa79az7+gCQd9Jo+hFiLyVeAh4BIROSYi7wH+HHi9iOwHXm//jVJqN3A3sAf4PvA+pZT+tr4X+CyWQ/p54HvtmF87qdfWU6N3bkvpHBevH3DGdYr9WglbPbWQ4vhckscOlccWrE2Sy9QYFlJZQn6fs8CO94eduPpuoN73sp4pKZXNc3oh3VTy35HpBAW1Mk74fEExk8iUlMPQjMZC7Do8y//+6UE2j/QBjflScvkCU4tp1g9Z57z7FVsZ7w9x4471Dc3JShrsTY2hLWW3lVLvqHLohirPvwO4w2N8F3BFO+bUKRxbbgMJbppLXIJh61iUsViIXYdmecd153Vmkm1E7yC//YsTvPSC+g65bifphKs2H5U0ECneLlYhvS7SGJzmUcsr4XB0JgFYPYwbyewHa9MAMNuhRjlurHpIeAqGdQMRROBP3nQ5Qb/wp/fsJpXNO+bcakwtpSko2DAUAWDzSJRdf/L6hucUCfqMj8FgkbKjWupqDK4v5SWTRcEgIlyxaYjnTi10ZoJtRu8g/+Xpk2TXcHKURu+Ymy2JvlguGGLhrvQx1NUYqixkh6cTzuNGzUmnbcEwn+z856A/ay9T0r+7YTvfef8rec8rtxX7JDSQr3HSDlVdbwuGZrF8DGv/nvDCCIYm0TuzupnPrhv0YpdgAGvX04wtdzWZS2S5cCLGbCLLz+wWkWsZvWNeajYqKZVlIFJMeOq20tt1BUOgtinp8IxLMDS40GvBsBLfZW2uqmZKumLTEGDZ/aExU5LOYdjQkmAwGoOBxn0Mfp8QCfrwSbHSpWY4Guq6cgpepLJ5ktk8v37VRob6gtzz1PHVnlLLpJwEt+Y1BnelzfH+MEvpXNcsDEVT0vIS3I5Mx53H8w1rDNZiPbsCgmGmhsbgpply2Fpj2DDYt6w59UL9qWoYwdAkekFpxAYbCwXYOhareO5INEg8kyfT5eUJFmwz0sRAmDdeuZ5795x2dqZrlaSjMbRqSrJzGbrEnFSMSvK2q9dLcDsykyDot1KJ5hpwQKeyecfM2KiG0QpedZK8aEYwnJpP0hf0M9i3PFdrL1SsrYYRDE2ScnZm9QXDUDTIZRsHK8aHo3Ya/wrcULX4o689WVI8rBy9QAz3hXjLVZtIZPL88NnTKzS7zqAX0GZLYlSaknT2c3c4oOtHJVm3errKZuTwTIJL11vf1UY0Bm1GavT5rTK9lEakWGa7GsV8jcZ8DBuGIiy3Vme4rMfFQirLYpNVe7sVIxiaRJdUqOdjAPj077yY//ymyyvGh+0v90rcULW4d89p/uHnB6t2v9K24+FokOu2jbJ+MMI9T3VlzmHDaKfkchLcyqOSoHvKYtQTDCG/DxHvnXS+oDg2k+RFmy07fSMhq9o+D8uvbNoM0/EMI9FQzT7r0KzGkFq249l6r9KSGO/78hO8/ytPLvv1ugkjGJqkUR8DwKXrBz2/eFpjWAnbbDVS2TyJTJ7D0wmePbno+RztBxnqC+L3Ca+5dIJdh9duPkO+oBzzXTMJboWCYimTY9AlGMZjlsYw1S0ag60BhQPet7SIVI27P7WQIpMvcNmGQfw+aUiTPW13UxuJBlfE+Ty95J3DUE4zVU9PtiwYSj/P3ScWeOTgdE9E7xnB0CT1atI0glaHV9MB7d7lfb9KfRzHlGQLsnUDEeaT2TVb09+t9pfXSpqNZ/h3X33SsxhbPJNDKSqikqC7NIa+oB9fjR11+Q5Xc8QOVd06FmOor7GF/oxtSrpk/cCyOuI1y0w802CZisaikgoFxemF1LIjksDyMegeF3OJDDPxDKlsgT0n1kYoei2MYGiSpL3TbMTHUA1d5301Q1b1ghbwCd9/5qTnc+YdU5J1Q47GQijVmKmhG9G76kjQV+F8fvzwLN/+xQnu9RCSTp0kl8YQCwcIB3wrYkZphEYKO/ZVCa88MmNFJJ0/FmW4L9iwKSkS9HHeaHRFPoOz8XRJ57ZqNNpZ7Ww8Ta6gnKzn5eAIoVyBF84Wo7p6oX2vEQxNkmwwwa0WuuvUajqf9c38azsm2Xd6iec9ajfNJTMEfOJkcbfaLWu10dreeH+YdK5QovnoxfDhF6YrznPXSXLTHw50TdOlRkrBW9VAKzWGw9MJAj5hw1CEwQYFw+nFNOsHI4xEVyYnZ3qpQY2hTr6GRvtI1g+2Zkqy3ivPC1OWYAgHfDy+hs2tGiMYmiSZzRMK+Oo6wWoRC/kJ+GRVfQzaZKLLcniVW55LZBmOBp2ojVa7Za02erHQEUXushhFwTBT4YzXkSZuUxJYWmOz0U2dohGNIVxFYzg8k2DTSB8Bv4/hBn0Gp+dTrBuMMBQNOmU0OkU2X2A+ma0bqgqNJ7idbDG5DUrNVgfPLhHwCa+7bJLHD89WDehYKxjB0CSpBnZm9RARO8lt9QXDjo1DXLVlmO8/4yEYklkGXe0Nta9huU1RVhu9WIzbO093kpsWDKcWUiXlIaC6xhALBZpOlOsUjWkM3glZR2cSnDcaBWjYlHR6McX6wQjDfc1pkU8dnSvx9TTCbIPJbWDt2EUgXUcwnGqxHAaUOrpfmIpz3miUl14wyumFtNMydK1iBEOTJBpo69kI1s5sFU1J8Qwilr/jph3r+eWx+Yq+C/OJLMMuwTC6xk1JelHU1+E2A7kXw3Jzkrvfs5touMs0hnqCoUpU0uHpomCwnM+1/79KKU7Np5gcDDMSbdxfdnQmwW98+udNhzzrKraNRCWJCOGAr26tpJPzKUJ+n6MFL4dwoGhKOng2zgUTMa493+7SuMb9DEYwNEmygSY9jbBSYX7VmEkU48Jv3DEJUKE1zCUzjuMZitFUa1Vj0D4Gx5TkikxaSGbZNNzHxECYh8oEg3ZUl5uSoiF/V/kY6lX89YpKmk9kmU9mOX/MFgzREAupXM1+BgvJHOlcgUnblASNCYbdJ+ZRCk402fjJKYfRgGCAxmoYnZpPMjkUrhnFVf99rOUzaQuGbeMxLl0/SCzk74hgUErxg92nVqRighEMTZLMNFaSuB5DfctvR9gOZuIZZ7d3wUQ/F4zHeOj50iJ5c2UaQ1/IT1/Q76j2zaCUYtehSvv9SqKjksZtW7U7l2EumWWoL8j1F4zx8AvTJfN0d29zEw0FukpjiDbifC5bMI/YxfPOG40BOP/vWhm8utz2pMuU1Ij2u8fOl6nXv+Hffu4R/vaH+52/p+N2Ab0GTEnQWJ+Ek/OpZddIct7H/rwPTsVJ5wpsG+/H7xOuOW+kI5FJ+88s8ftffHxFqg8YwdAkqWy+oazneoxEG7PldoryuPCt4zGOz6VKnjOfyDo7Qs1oLMTMMgTaU0fneOvfP8RP9k0tb8JtQJsXxj00hvmk5Wi/3rYRH3L5GRZTWfw+qfi/x7rJ+Zyt73z26lF82A5VdZuSoLYGcNolGEZiurxL/e/ycyet+P6zi7W/P08emeMn+844fzdjSoLq+RpuTi20ltxmvY/1ee+xr+uCCUu4Xnv+CHtPLbS9PMYZu2jhSpRhMYKhSRpx8jVCKw3M28FsPFsiGDYORzg5X1Txs/kCi+mcsyPUjMSWZwI7ajvjqmVZrwS637OObil3PmuNAUr9DLqyanlNnWh45ZzPe08tsvO//7Dkf+Qm2UBzHa8FUzvaz7NNScU6XvU1hvUlGkP978Szdg+SWhpDOpdnKZ1j76lFp53sTDyN3yeO0KpHPVOSUsqpk9QK2pT0rBYM45Zg2Ll1hIIq9ntvF3pDthIbSiMYmiTRNlNSkFS2s2F+tZgu0xg2DPUxl8g6C91CWdazZsTVeL0ZdKbs/tOrKBjs3fKYXc5iKV0pGC4YjzExEK4QDOURSQDRoL9E6+gkTx+f5+xSmgNnvHuFJzP1Ndmwh4nlyHSC8f6QYybT/+9ai4/+X64bDBMJ+ggFfHVNSYupLEdnLKFWSzDobnDxTN6J7NE5DI36A6rlazjvkciSyRVa1xgCRY2hPxxgYsD6Xl29ZRifwK5D7TUnaROuEQxdSKoBlb0RimUxVt6cpJRi1nY+azYOWzfJCducVF4OQzO6TE1nyq6ts7/KwrYSlPsYEmWmpKE+K2ej3M9QXllVEw0HSGbzzs62k+jPz0soK6UaTnArb15/ZCbBFtuMBG5TUvX/8emFNMPRIJGgHxFpKJBi7ylrQ3D+WLRmGRH39WkTzdkG6yRp6vVJ0FpX6xqD9XkvpnJsG485GuVAJMgl6wd54kh7BcOMEQzdSyNOvkYoFtJbeXOSjjop1xigeNPoG71cfV+uxqDt0gfOLK3IQuqFjkrSGdxaY0hlrd4YOmdD+xkO2mUOFqpoDDojPLkCWp8WDF4LcDavyBdUAz4GH5l8oSTiaCaeYcLl1B2yTUO1Fp9TCykmB4qL6nBfqG4Wvza3vGr7OIs1Ghy5v1u6/e1MPN1QcpvGEoA1BMOczmFo1flcXD61f8H9d3n4d6votWIlNpNdJxhE5CYR2SsiB0TkQ6s9n3IacfI1wnATYX7tRt98bsGwadgWDHOlfXyHy+K8R2MhFlO5pitInrEXtmQ2X3LD5PIFPvLNp9tuYsrlCxVNhVLZAiG/j6DfR1/Q75jN3OXFAV510QQi8OVHjgCwlMox4NFYXptumqnUuly0+cVLKDda2FEfdyeYzZclMeqNQK2S8GcWUqwbdAmTBjSGPScXGeoLcsXGoZLrKUfb0UN+H8/Z/ijL7NlYRBLUb6Bzwt78aC15ubg/723jpYJhIBxgKdXe78U5qzGIiB/4FPAG4HLgHSJS2dBgFWnEydcIzYT5tRv9BRtxCYbJwQgiOIu2s1iWawzLTHI7vZBinW2D3X+mKASePj7Plx85wgPPnal26rK486cv8Ia/fbBkLJXNO7u8WDjglMTQN5peFM8bi/L2a7fwhYcOcehsnMV01tvHYHdLa6Wr3Xwiy1/+4Dn+5FtP13ye1hi8Pnf9/vV8DF5NbBZS2RKtMBTwEQ356zqf3TWGGjElPXtygcs2DDgRYWermJNmbIFxzXnDjsbQaMltTSToq1lE7/hsklDA55ROXy7uEucXTJS27+0PB5ww53Yxew47n68DDiilXlBKZYCvATev8pwcdD3/9kQlNR7m125mPRKGQgEf4/3hClNShY/B1iBmm6yXdGYxzSsuGgdg/+min+GxQ1bBsYU2h/YdnUlweCZRYrZKuYR6LFxMTisXDAB//GsXE/T7+Nj3n7Odz5U+hljY1hiW4YBOZfN86kcHeNVfPMCnfvQ8X3r4SM1y5rrvg1d9rUZ7hJQ3scnmCyQy+Qpz4XCN0tv5gmJqMc3kYOOmpEJBsffUIpeuH2R8oHbnu5lEFhG4/oIxDs8kmI1nWErnHL9QI9SLSjo+l2TjUKSl5DYoZllDMSJJ0x+x/E/tLFGva5QtnIOCYRNw1PX3MXusBBG5XUR2iciuqamVi4uv13C9GZqtMdNOHI2hzEy0cSjiFBebS1o3aPmCqAVaM36GZCbPYirHRev6WTcQZp9LMDx60HLQLSTbu7uKp/MoBUsuM4/bDBgLBZwF3UswrBuM8PuvvpDvPXOKuYS3xqD7Ky8nZPXvHjjAX/5gLy/ZOso7rttivU6NxczRGLxMSZnmTEl60dTXXV7qYygaqrorPbuUpqBg0uW4rVd47/BMgmQ2z+UbBp0FvqopKZ5muC/Ijo2DKIWThd6UKSlY25R0fC7JppHW/Avu9wIrD8iNvm/aGbV2LkcleYnwCk+lUupOpdROpdTOiYmJtk7gwJlF/uCLj3vaWOs1XG+GvpCfcMC3Ku09tR23vIzxxuE+p1zBfCLDYCRYUUV2OfWSziza4Y0DYbZP9nPANiUVCsopUdzuL7terN3qfDKTd0IM62kMAL/36m2OycRTY7CFzHKS3A5NWyUUPvful/CizcPW61RZRNK5vDNHbx+DdR11TUll3c30zrM8iXGoL+D4mMpxktsGSn0M6VylT0ejHc+XbRisa0qajWcZiYW4bIPVf/pnB6xs/Gacz+E6UUnHZ5OOT61VIkEfk4Phiqx47ZNaTLfne62Ucu7beCbf8S5x3SYYjgFbXH9vBlasyXA6l+f9X3mS7+8+xQ/2VFYbTTWosjfKcDS4KhrDbDxD2LYlu9kw1MfJ+RRKKadERDmjy6iXpB3Pk4MRtq8bYP+ZJZRSPD+15JhG2m1K0js1t9qdyhWcekIxV3JaNcEQDQX49zde4nlMH4dKjaGRsh8LqZzj9K3nxNaLqN8nnj4pp0dIA1FJUMznqHbdw33VK//qqqSTJT6G2v1Fnj25gE9g+2Q/kaCfgXDA0YDKmY6nGYuF2DzSR384wM9twdCUKSngJ50reEa/pXN5ziym2dg2weCvcDxDsalTeUOo5ZLIWJFzG21NrdPmpG4TDI8B20Vkm4iEgFuBb6/Um3/8vn08d2qRaMjPjzycoc30e26ElWpyUo5ObivP5N04HCGRsXanuhdDOcOOj6FxwXDalRC1fbKfRMaKTHrMTgDaPNLXfo3B/l+5NYZUJk+fdj6HAs5NO5/IeJrNAH7zmk38xVtfxBuvXF9xrJqP4f1feZL/667Hau5a512CN6YFTBWNQS+iW8einuVIlutjKJqSygRDjXItutezOzlsuE4ZjWdPLnLBRL/z/mP9oaqmpNl4lpGo9d28dP2Ak5ndrCkJIO2R5KYFW7s0ht99xTbe/fJtFeNag2iXA1pvxLTJqtPmpK4SDEqpHPB+4AfAs8DdSqndK/HeD78wzZ0PvsBvv/Q8br56Ez/df7aiimEi0z4fA9Bwf912M1ulf67OZTgxl6qqMYQCPgbCgabqJekaL5MDlsYAVqLbY4dmGO8P86LNQ23fASXSpRncYO2U9aIRddU5mk9mGQgHPJsv+XzC23duqQjbheIOvdw38PTxeX747Bnec9djVc0rC8msY9uPhutoDPZifPHkAKlspcmm6XBVbUqyF63y//NQX5C5ZNZT83nu5AKxkL+kzeZQnZwcKyJp0Pl7vD9cNcltOp5xzEaXbhhwxpvLY6jerEdH3bVLMNz28q3cdEXlpkH7pNoVsqo/Wy0YOh200lWCAUAp9S9KqYuVUhcqpe5YifdcSGX547t/wfmjUT7yxsu44dJ1LKVzTsSMplEnX6OMROsnBnWCmYS3YNBx3Sfnk8wnMp6LIdh1npo0JYXs7mDb11lhfQdOL/HowRmu2zbCUF/QWaTahV703TZed8+CmKst53yyslhgIxR3+qVzn09muWAixr8+P83vfv4xT+e0p8ZQRTDoiKTtk9ZCWb4A6z7k9X0MpQtmNVPSUDRIJleocOAqpXhw/xQvu3CsRIhqU5KXv2w+meX4XJJL1xcX+fH+sKfGUJ6Rf+l6S5iE/D7PPJLq11m97/Nxu8xGu5zP1dCCYbFNpiStMVxwLmoMq8XH793HyfkkH/+tq4mFA7z8ojFCAR/3P1tqTtI3VLQNzmewInxWo72nVXLbSzDYGsO8pTGU5zBoRmIhZpqY95mFFBMDYat8QizEeH+YB/dPcXwuyc7zRxvuM9wMcafmU2lUUkm4aiaPUqpkkW4GLWTcLUILBcViKsubrtzAx99+FY8cnOY/f6tU6VVKseAWDHXCXrUpSQvVcv+OExTRQKMeKGoYWpsa9PAxQKXP4NB0gqMzSV59cWnAR63Ce7qi6uVujWHA25S0kCzNyL/M1hi8zJ61KArASlOS1hharZNUj/6w9Zm0XWMYswTDueZjWHGePbnAFx46xDuvP58Xn2d1X4qGArz8wjEeeK607nm7fQxDfSHmE94q+3J49uRCQ008yktua8b7wwR8wrHZhFOG2ovRaLBpjcGdKbt9XT8/3W85Fa/bNspgRO9QG4vu+dN7nuG/fXdPzedoe7279HEqW3AJhgD5giKdKyxbMPh8Ql/Q7+zYwRJIBWXZ7X/jms289tJ17D4xXzq3TJ5cQTnvWc2JrZlatGoTaYdvhcaQbdT5XBmVFAr4KjRgJ/u5bPH56X4rNPzV28sEQ43Qax2RdPnGomAYi4WZTWQrImvKo+UusTWGZsxIUBSAXt+nE3NJ1g2Ene5rnaLofG7PAq5zGM5JH8NKo5Tiv9yzm+FoiA++/uKSYzdcuo5D0wlemCrG3De6M2uUkWiQjJ1k1Cr7Ty/yhr/9Kbd86udOxqgX2XyBxVTOUzD4fcLkYIT9p5dQyjsSx5p3c/WS3FnPABdPWjvf/nCAS9cPODvWRiOT/vX5ab7yyJGqgiSTK5CxF50S57Or0Jw238TTOVs7Wl6LR615aLRJbLDPen2vooPzZTv14lyqawwT/WFGY9qWX/o5JTM5REozcb3wMiV5/Y+rlWt5cN8UW0b7nG5vmlqh13tOLjAWC5X8/3WSW/nmYsZuyKO/m/3hAOePRUv8GY1Q7mR3c3wu2baIpFpEg35E2ud8no1n8PuELaPW3Dsd5n5OC4Zv/+IEjx6a4T/ceEmFPf01l64DKCnVoJ2MkTY5nxupfd8oWkU+MLXEr//Pn/HpHx/wbM8461EOw82m4T5nl1fLx9BMKY8zZZmyF9m28mvOGybg9zmLU6Pq8VwiSzKbd7SOcpIlC7VbYygtiQHW7n2hrF5QM0RDgRIfg2OesSN9RqIhZsu0wnLbvuPEruFjmBgIO+a/8gVVV1atZ24pt70vpLIVyW3uebkFQyZX4KHnp3n19gnP96mW5LbHdjy7z5mwNYCpMnOS3hW7Ny1//bar+I83XVrzusoJ1zIlzbYvua0WPp+0tSyGbsUbDlhdFI3G0CGW0jnu+OdnuWrzEG/fuaXi+OaRKJdMDpT4GVKZ9voYlhP6WQ29K/3q772U1102yV98fy8/2F2Zi6HV9Wq1ZzYMF7Ofq/kYRmMh4pl8Q6afVNYKf3XvGLWt/Lqto0Ax83a+gexnpZQjlLyuD0qje/QOPpsvkCsol8Zg/V5K55ZtSgK777NbEJVpAyOxEJlcqVa4UCYYQgEfIb+v5HXcTC1agkE/v8LH0GDzqHBZraRq1+0lqJ84Mks8k6/wL2iGPVrVZvMF9p1eKjEjAVWT3GY9MvJ3bh2tOL8e1ZzPhYLixHyKzSugMYBdSK9dzueljKMxDnXAJ1fOOSsY7vzJ85xZTPNnN19RtWbKay9bx2OHZpxdpxMWWEdlb5ThKrbc5aB3WxdNDPDXb78KKHbnKn2edzkMzQZXKeJqPoZmeklox+k6l8Zw9ZZh3nbtZm65xqp20ozGELft8z6B+5897VmLxr3z1q+ZKgvpjNoaw/RShmxetSQYkl6mJEdjqAzl9IoGiob9FdFNmqnFtOX/sbWrcm0tmSk0FCmna/ukGzUluZzPD+6bwu8TXn7hmOdrD0eDFZrvC1NxMrmC40TWOIKhLMltWtfwatKnUI72MZSX3j4bT1tJYiskGPoj7auwOuOK1jKCoYO851UX8Ml3XMPVW4arPudXL54gV1A88oIVtprM5gn5fQT87fnYllup1AttgxyIBIiGAvQF/Z6FyrxKbrtxlyKu6nxuol6SuxyGJhL085dvu8ppEFPNx/Du//MoX330SMmY3lX+ysUTzCayPFoWUgyltnqtyjtC3dYU+u1IIF0CZLmCwarS6mFK6tMd0SqFqJdgiIUCnhpDPJ0jmc073cFGPSLCktlcw33I3QXmFpI5TxNav53T4Z7zg/unePF5w55JgNZ1Bivs3o7jecNQyfhYlXpJswkrI79VH161qCTdhKpdOQz16A8H2lYSw517ZARDBxnqC/KWqzbWfM4Vm4YQwYkqSWaKNup2oDWGeiGr88ks3/lF7cog1o4i6Gg/Y/0hZwfmZraeYHBpDENVHLKOrbsBgXbaTm5bN1A9PFDvrt0aQ76geHDfFI8dLF349Q1xyzWbCAd83Lu7NHIMiqak8f6QI2xSumyEk+BmLdzHWxQM0ZC/JGNZv5++Jv05u4WoV8axlXBXubvUGpdupjPiERGWzDTeI8Td97maxiAiJYvP9FKaZ44vVEQjufEyJe05uUAo4KtoYtMfDhAO+Cq+n7q8djOhqV5Ucz7rHIaV0hgGIsG2hqvqjWQnwrvLOWcFQyPEwgG2jcfYfcLa+TRzAzaCTqqar7PAfvpHB/jDrz7p7L69mC3LTRjrD3sKBm1yqqYNbHBpDNUWS6/Frhq6P/DkYPXIEr27dn/Zp+NWFc/ya9C72A1Dfbxq+wT37j5VEe6rF+rJwYijMWh7sxbsumSB1hiqfR71iIYCJLJujcF6rBOcvExJC07l2qKvKhoOeEYlaQet1hgsZ3alj6HRpEurH7LVjrS8F4Ob4b6iaehBHaZaxb8ARVOS+3/x7MkFLp7sJ1imYYuIleS2WKkxVAuKaIaqgmHOMq2uhPMZLFNSOxLcCgXFbCLr1CkzGkMXsGPjEHu0YMjm2+Z4Bqs5ezTkr6kxKKX47i9PAtTtleu+qcZioSqmpDSDkUDFzarRGkMs5CdUxZfSjAnszGKagE+q+jTA+hwiQV9J9nO1Hsf6PYejQW7cMcmJ+RRPHy/LE7AXhPWDEUcLKQ811qYX7Whvp8YQC/kdc6OXKWnB7gjn9m3F6mkMWjB4ZJ0ns4XGTUkBy5S0lMmhVGWdJM2QbRr6/jMn+c/f2s2m4T6u2DTk+Vx9ne5saaUUe04slCS2uRkfCFdEJU1Xya9plmKxwEpTUn844BmJ1Qna1cVt0W7Fq++7WrWs2oURDHXYsXGQ43NJZuOZtnVvc+MupDe1mK7IQXjiyJxj7qi1EM/EM86OArRg8NAYElnGasSFW03efTUXyuEq0TFenF5Is24gXLcpylBfqY1aR6yUv4fexQ5Hg7zuskn8PqmITtJO3PVDEdK5QknynDvBDTrjY3Db7b0+K68SHNFQFY2hTDBYPobKkhiN2uW1KUl/1tWue6gvyGOHZviDLz3Bhev6ufsPXuZZS0pT7rA+s5hmOp4pqZHkZqI/5BmV1BbBUCXB7ZhdbrtVU1Wj9LcpKqmY+FeMSkp0uPS2EQx10D1qd59YsBOk2vuR6SiTn+6f4sZPPMhb/u7nzmIF8N1fFn0LtaKAytXwsf4wM/FMhZnFMjlVXwRFhI3DfQzV2OHr6JhGwmzPLKaYGKxffmAwEixxPusFcTpeuqvUZrfhvhAjsRDXnjfCzw9MlzxHO3F1L4XFVLai0Fw44MPvE6f/73LzGPrspjA6Z8TKDSi+VsDvYzASKIkkmk9mK3bqsXB1jcHv0riGo8GKQnqNhqsChG3nc3mSXTnj/WHSuQLvetn53P3719d12Gq7/cN2Y509HqUw3IzFwhUabbWM/Gbx+YSQ3+fhfF6ZHAZNfyRgZbm3uICXRxJWy0xvJ0Yw1GGHHUO9+8R8230MYNVLeuTgDO/6h0etm0LB/3xgP2DZFv/l6ZNctdkSTtU0Bm2DHCszJWXyhQobZyPq+ku3jXL1lupmA/COjvHizEK6pKlLNQb7vAVDKlsoWTBnE9kSM9fG4UiFVqE1Bt1lbCGVq+ilISJEQ9aiLkJTRdrc6DpHSVcIqPaZaEZioRJzoZfTN1olKmlqMc1oLOTs1kc9HP/JTLHPRD36gn5SuULRSd7nfd0ffP3F3P37L+O/3nxFQ+UjXnXROFdsGuQvvr+XZCbvmF8vq5KDMD5gBUfongnpXJ6ldK5E620Fr2Y9VtZzZ2skuWlXF7fygBEjGLqAkViIjUMRdp9YIJFpfGfWKGOxMEvpHLdcvYlvv/8V/PZLz+PuXcc4dDbOY4dmOL2Q5neuPx+orjGU2yChGBJYbk5qRF3/H7/5Iv7Hb76o5nO8omO8OLOYKqmTVI1yh5o7lNG98Ft9IorzLxcoYGkMoYDPWWQWU1ln9+iOKtMO6MFIcNn9f6NlFVYXkrkKbaDcYbzgIRhiIe88hqmltBORBEX/jvszSWZyRJswJaWz+Yoku3I2Dvdx3bbRhl4TrF36n755ByfnU/yvB5/n2ZMLbB7pq+rDGO8Pky8oxzSoe4iPtpjDoOkL+km7Etx0IuOm4WiNs9pLu7q4aVOS0Ri6jMs3DvHMiXnLlNRG5zPAB163nc/dtpOPv/0qoqEA//drLiToFz7xw31895cniQR9vOnKDfQF/VUX4nIbJOD4EWZcphilVIWTermMxurXS0rn8swmskzWCFXVDEYCJZVQ3R2+SgVDpmQxG+oLspDMlnTrSmRyxEJ+J+pnIZlz9esuLqDaYbvciCT3a+jMZq9In5GyTn2eGkM4QCKbr+g6dtYuh1F8rVKNQSlV0su6HpEyU9JyfSteXLdtlDdduYG//8nzPHpwpqoZCdzZz6VBBu3SGMr7Pmvz7EpqDO3q4lauMQwawdAdXLFpkINn40zHM233MVw40c8Nl006DrF1AxHe/fJt3POLE3zryeO89tJ1xMIBe3Hx/iJ4ZTNrs5LbwTcdz5DJF0pyFZaLV9hkOcWs58Y0hnJTUsiO7HGHrM4ls4zESgVDQcGSu8Jp2ooe0zeQpTHorPXiAqo1hlYWR60xFMt8V9ZdGomGnB0xaHNTpcagVGUZB10OQ1NeSC+TL1BQjfcIsaKSCo4QXq5vpRofesOlFJTlfK7meIbKJDfnO9yGTQtoJ3vxs9Q5DJtX0scQbk+znplEhpCrFa+jMXSwkJ4RDA2wY+MQSlk3dLtNSV78wa9cQH/IioF+84usJLzhGguxV9KalympnQk+ozHLRlyrZLju9VwruU0zWLbzP7uUdhKjZpZKNQZ3JVSv5LhEJkcs7NIYXM7nUo2hdcGgfQyJjLXbX0znKsIhR1wVVlPZPOlcwVNjgFJ7dKGgqmsM9v9cJ+41nvnsI5WzNAafQH+bNeAto1F+71VWq8taNY4myuol1avh1SzuDG8otpedbCAQol1ojaHVQnqzdsSh3jwaU1KXsMP1BW/UydcKw9EQf3jDRawbCPOaS6wqr1ZTn9qmJLfGUExCK5pk2qlOrxuMkMkVakZKHTobt9+vviAajFg7f73znlpKc4nd9avSx1BcVL3U6nimXGPIOQUQ3aWpdchqK7vmYi8FV26AhykpkcmTzuVdTt9KjcF6neIiMp/Mks2rEh9DeSE9nVzXeLiqVdtJay3L9a3U4v2v2c5/vXmH8931QpuSdALkjK05tE1jCJSakoqCp7kS3q0w2EIXN3ck00w8W/K5GMHQJWwYijgLbTS4Mskxv/eqC3j4wzc4O1x3vkM5XhpDOGDtmN2mpHb2u904pNuAVs/GfuSFGYb6iu08a+H+smuBc8F4P0G/OKYkpSxnpVsweN0kibSlMfSHAojYUUm5ApGgrySGXe/2WzMl+Z33LC+5rXEnuVVz+moB47ZHl2c9AxWF9JrNwwgH/S01J2qEvpCfd71sa9UESbD8OhdOxPj648coFBQzCSsbvFpF32YJB32OlgjWPRIJ+toeVViL5XZxe/zwDFd+9F6esRM3ZxOZEv9hyK4nZQTDKiMijtbQ16ZeDI28p6+sr24tjcFtg9SMl5XFODGXIhryt2VBWD9U7A9djYcPTnPdttGGdqU6bHIhmXNyF3QPAq31LKbt6Kto5e5pwUNj0DXxF5LZkn7PGr0Yt7IYOU12MnmX3b508+AuIVKsk1T6HLdJSlOe3OZ+PR0q/L2nTxH0Cy+/aLyh+eqorKnFdNWIoZVARHj/ay/iuVOL3LvnNLNxK6igXQUqy01J0/HMimoLsPwubk8fmyeZzfNX9+4FKsvdQOezn1v6L4jI20Rkt4gURGRn2bEPi8gBEdkrIje6xq8VkaftY58UewsnImER+Ud7/BER2drK3NqNtpeuhI/BixH7i1Ct+Y7bBqkZLSuLccLuXtWOzE9tHqqmMZyYS3J4OsH1F3iXaS7H8RWksiULohX9ZN0AXtm6boGiSdpRSfp1F+08hnIHbX87NAadx5DJVRTQ0wy76iVViwaKujrKafTnUN7BbNgOFVZK8b1nTvGq7RMNX4N2vp9eTHVMY2iUX3/RRraNx/jk/fuZjqfbktymidiakWY2nikJWlgJdBe3ZjWGE/Y99eO9Uzx2aIaZRKbC99LpekmtiudngN8EHnQPisjlwK3ADuAm4NMiou/KzwC3A9vtn5vs8fcAs0qpi4C/AT7W4tzayg47A7rdJTEaZTgaQinvngXlNkjNWFlI6Yn59rU11P2hq2kMjxy0MmCvv6CxWHi3r6BSMFh/a1PasIfGUOFjsP0HA5GA43yupjG0w5QUz+QrmvRoRkpMSTnP9/TSGLS2N14W2z9qa4+/ODbP8bkkb7xyQ8Pz1d/fMwvpVRcMAb+P973mIvacXODHe6faFqoKVs8Ut8Ywk8jWrNfVCRyNtUnBcHzOKt0xMRDmY997jvlk5f3d6QqrLQkGpdSzSqm9HoduBr6mlEorpQ4CB4DrRGQDMKiUekhZ4SxfAG5xnXOX/fjrwA3Sjq1tm9h5/gjhgI/zx2L1n9wBRmLFXWc5M/F0iQ1SM9YfLvExnJhLsqlNcdy6P/TJOW+N4eHnLf/CZesb677lNgkVd8qhknyJWcfJXrzW/nAAn1T6GHTCl6UxZKtoDK0LhkjA2hUm0rmKJj0aL1NSZYJbpcYwE7fKYVQkzNmF9P7l6ZME/cLrL5tsfL62KWkpnaua9byS3HL1Rs4bjZLI5NuuMaTKfAztfP1GWU4XtxNzSbaNx/jD117ErsOzKFVZJl/n73SKThnMNwFHXX8fs8c22Y/Lx0vOUUrlgHmgMTvECrBxuI+nP3pjU9mg7WTYoxSCZjaRZdTDfjpmh0kWCopUNs/ZpUxbchg064ciVU1JDx+c5qUN+hegVGPQse3j/WGrGKAtGNwF9DQiUpL9XCgoEtkyjSGZI5UtVPTSiLbBlOTzCdGgv0xjKF1wnQJzLlNSuVZRnigHdsXcaGXkkC6k9y9Pn+QVF41XFOSrhVs4tjuHYTkE/D7e/5qLgOo9QpaDu+8EtK8OU7Msp4vb8VmrdMetLznPCRQp13asAIRVFAwi8kMRecbj5+Zap3mMqRrjtc7xmtPtIrJLRHZNTU3VvoA2UivKotMU49e9TEkZRj0Wh7H+EPmCYj6ZdRbwdjYp2TAU8TQlNetfAGtnpSOILMdogEjQz2gszGIqZ0cq6ZLb1e2tqVwepYrhn4N9QRbTWc/sYEdjaCHzGaAvZBVL08Kpv6zukru8+nwySzTkryh7rkNn3ZVap5e8FzNdSO/YbHNmJCgtCbLapiTNb7x4Ey+/cIyXNmh2bATdd0Ip1fY6TM3QbIXVdC7PmcU0G4f7CAV8/NHrtgPFYA9Np30MdXVJpdTrlvG6x4Atrr83Ayfs8c0e4+5zjolIABgCKvs2WnO6E7gTYOfOndUzrHoIr4YvYMU7e9kgoVgWYzqedjqptVsw3LfnNEqpEoe2rrDZjGBwRxBNLaUZ12Wm+4ua0lyVUtHum0QniJVrDIORfEX00WsvXcd/euOlDZu7qqEro84nffSHA56RNVb2s9V+1WtBDgd8+ISS3g7Vdrl6gQv4hF+7vHEzEpRmfq9mVJKboN/HV37v+ra+ZiRoZZJn8sVcm3blSDRDfyRYtxGXm9PzpffpW6/dzPbJAaeQpmaoL0gymyeTK3Rkw9qpLfC3gVvtSKNtWE7mR5VSJ4FFEbne9h+8C7jHdc5t9uO3Ag+oWmm15xj6S12uPmrzitcCMu4qi9HOHAbNhqE+0rlCRamOh1+YZqgvyKXrB6qc6Y22m55dzDhJXWMu+/xcIkt/uLLJ0GCkKBh0gpg7KmkpnbPaspZpDAORILe/+sKWk7x0LwVLAHnvtXSCYq12mlbfZ7ePwTvEUn8XXn7ReIX2VI+wy5TULRpDJ9CJjKlsoW6f804y0GQXt2N2l7nN9n0qIly9ZbgikrDTSW6thqv+hogcA14G/LOI/ABAKbUbuBvYA3wfeJ9SSm+F3gt8Fssh/TzwPXv8c8CYiBwAPgh8qJW59RoD4QABn1RoDDq5zSviQu+2Z+IZTswlEYHJofbFcm+oksvw8AszTfkXNLonw5SrDMRoiWDIeBa8czviHI0hVNQY8gVl17nqTERZLOQnmbXCVavZ7a08lKxnnSRNNFzaDa5aiXQdvvrGK9Y3PdduNCV1Au1LSWfzqysYmuzidmKuMZNvpwVDS2EJSqlvAt+scuwO4A6P8V3AFR7jKeBtrcynlxERK369bHde60uvd5vTS2lOzCWZ6A83VFu/UTboXIa5lBPOe3wuyZGZBO9++damX89a4C0fg1789HVNxzMVWc8aK3TPuvkcjcF2LOua+PPJbIXzuV30hfwspnLk8qqmYDgyk6Av6GfziHfpZ7fGoE2EXv/Xa7YM83e/fQ037mheMPR1mfO5UxT7Pq+uxtCsj0Fnspf7FMpx+sV3o8ZgWFmGo6GSTmDgDuGs/NKPRIOIWKakE3OptvoXwFtjeNTOX1iOI3GwL8DpxRRL6VylxrCUtrrUeVznYJ/lm1BKOc1utMbgjhDqnMYQIJGxwlWr2e11/wqvXgyaaNjvRCXpDcCYR38Cn09484s2Vu3bXYvIOWJKKvZ9zte8RzqN7uLmlZjqxfHZJOP94br5Ul4Z/+3ECIY1xEg0WNEDQWcFe+2GAn4fI9EQ0/G0ncPQXsFQTHIrhqw+dWSOaMjPpctw6A5GghydsWys2scwEg0hYucAJLwX1aG+IJl8gXSu4DS7KdcYoHPJiXpBX/Do3qYZjoZYSOWYKesnUfI6oYCTx9CpXe45IxhcfZ/1Z9lK343lor9/jZqTTsw31n60q30MhpVl2KOQ3myi9pfeKouR6UhbQyfJzS0Yjs1z5aahmo3jq6F7K0CxPpDfJwz3BWuaktw3idYYdMKY2xncMcEQ8jvhqtU0Br3Ap7KVJbc1sVBRY9D1otovGIq3/EAVR3kvUG5KGuoLLkvDapVmu7gdbzAJVX+Hyi0I7cIIhjVEeScwsHaWsZC/6qI3Fgux/8wS6Vyh7aYkKM1lyOQKPHtigau3DC/rtdw279LmNJZwm6tmSnL5EZK2jV4njK2ExhALWQ5GK5vYe9EvLRXuvSBHw0UfQ8c0BnsnHfPIpeglHFOSrTGshn8BmuvippSy6pk1kIQ6Gg3xy4/+Gu962dZWp+hJ734zepCRmKUxuKN4Z+OZmn1yx/vDPD+1BLQ3h0GzYbjP0RieO7VAJl/gqmUKBvdO2l04biwW5vBMgoLyNn94agzhlfMxREMBMvmC1YuhWriqR32ncqy+z9b8OyUYfD4hZJfu7mWKGkPe9k2tzvU208VtJp4hlS00ZEry2aVSOtFPA4xgWFOMRENk8oXSsgmJTM2MztGYVXwP2pvDoNlgl8VQSvGLo3MAyxYM7kXc7XQdjYU4eNYSbl4ag9sRl0jn8Ekxjt1t2ulUyXR3ufNqGoN7ga/pY7A1Bt15rxMO03DQ19MRSeB2PheYiXuXjFkJ+pto1tNoqOpKYATDGsIr+3kmnqmZ0eleYDtlSsrkLDvuU0fnGe8PO018mkUv4qOxUImZYyQWcureNOJjiIYCTkJQOOAj6LceR9oYqutG11xyX0M5Xs2FyonZTmylVEft4pGgv+cFQ7jE+exdZHIlGGyivWcnklCXixEMawh3JzDNTLy2xqDLYoQDvo6o0xtcndx+cWyOq7cMLbvfg14wy8tMu2vRV8tjAEswJDK5kh28SLE6aafassZcfZOr+Q8aMSVFQ1YyXjpX8KzB3y4iwXPHlJTO5pmtUpZ+JWimi9txp/WuEQyGJtCLiztkdbaOxqDLYmxqU4OecjbYjrJ9pxd5fmqJqzYPL/u19ALv1bFM41UCQu/K5pNZ4um841/Q6OibjmkMofoaQzTkd2raVNutx1wVVmeqFNBrB+986fn8xjWb6j9xDaMLJp5dypDJF1algB4018XtxFySvqB/1fwhbno3Xq0HKTclpbJ54nXq2OtjndqFaI3h3t2nUWr5/gUo7qQnyjqWuc1hXm04A36fXYAvV6ExQHEh7lS/36hLY6i2ExcRRqJBTtdokKML/8XTOWbiGc4f886QbpXf/5ULO/K63UTEFsI6Ym61opKa6eJ2wg4p74Y2NEZjWEOUm5KcqpENmJLancOg0UluP953BoAXlVWBbAa92y5vZdmI43YwEihqDCFvjaFjUUkN+BjA+j+FAr6qYbN63olM3upRXCPazFCbgN9HwCeOQ3e1BEMzXdyOz7Wvw2KrGMGwhhgu0xiKIY3VFyO9+9403Jndp89OcktlC2wbjzVd7dNNJOjj3S/fyhuuLK0BpG/qgYh3SWsotjpMZHIlCzUUF+tO1UpyC6L+GkljI9FQTdu+nvdSOstsYvVi73uFSNDv1B5aLR8DNN7F7cRcks0NhKquBMaUtIYI+n0MRAKOpnB01iofMdZfPRRvKBrkE791NS+/qHPN8DYORzg+l6yoGd8sIsJH37KjYlwvkLVKGgzZXdzimTybR1ZYY9DJdOFAzYzv80ajJF3tJsvRAubkfIp8Qa1aiGWvEAn6OKFNSavkY4DGurh1osNiKxjBsMYYsRvBA3zjiWOMxUJ1Hb63dNjRuH6oD5htyb9QCy0YapnMBvusOkuJdKWPQWc/hzssGOqFgP7Jmy8jm69eTE2/ztEZbRdffSfkWiYc8Ds9z2slgXaaRiqsnuiiiCQwpqQ1x4hdevvMYor7nz3DW6/dvKotRwEnb+FFLUQk1SIc8NMfDtQ0w+gubvFMZVTSuoEwoYCvc9VVnSzr2gv5QCRY0zyks2S1Jmg0htbQpsOAT5yaRatBfyRYN8Gtm5LbwGgMa47haIiZeIavP36MXEHxWy/ZUv+kDnPdtlF+sm+KHRtba5FZi80jfTUTf7RgyOVVhcbwzuvP51XbJzomQMMBHyLVy2E0ivYx6AqzncpjOFfQTv6RWGhVI30GIgGO2cK+Goem4wDGx2BYHiPRIAfOLPGPjx3lpdtGuWCif7WnxA2XTXLDZc31Hm6Wu373uppF8AYjQadUSLnGEAsHuLyDQku35Ww1m1j7GI7Prm6IZa+gvy+r6V8Aa9NSXhW5nAf3TbFxKNI1gsGYktYYw9EQx+eSHJ5OcOt1q68trBSTg5E6pqSiMCjXGFaCob5gywuQNnUdM4KhLWhT0mp/jhsGI3aBPO/Ag3Quz88OnOW1l63rihwGMBrDmkM7YAcjAd5wxYZVnk33MOSKWCrPY1gJPv07L2Z8oDWfgM8nTm+HWqXUDY2hM91XWzDoNp2nF1KcPxarOP7ICzMkMnluuLSzWnczGI1hjaEjVX7zxZvNwuHCrU10KsO5FldtGW5L8TOdRb2aUTS9QtHHsLrRXdqhrB3M5Tzw3BkiQR8vu7BzIeXNYgTDGmPreIygX3jHdeet9lS6CnfGcSy8dgWmnruJSGqdsGNKWt3PUmsMpxaSFceUUtz/3GleedF4V230WhIMIvKXIvKciPxSRL4pIsOuYx8WkQMisldEbnSNXysiT9vHPim2UU1EwiLyj/b4IyKytZW59SqvvGicXX/yei5ZP7DaU+kq3BpDdBVMSe1Cz91EJLVO0fm8uhqDrifmpTEcOLPE0Zkkr+0iMxK0rjHcB1yhlHoRsA/4MICIXA7cCuwAbgI+LSJaHH4GuB3Ybv/cZI+/B5hVSl0E/A3wsRbn1pOISM+XTF4O7s9kNXwM7UJXWO1Eg55zDe1jWM1yGGAJ+6G+IKfmKwXD/c9ZNcZec+nESk+rJi0JBqXUvUopnbnxMLDZfnwz8DWlVFopdRA4AFwnIhuAQaXUQ8rqT/kF4BbXOXfZj78O3CDd4qI3dD3uUNHyWklrCV1h1RTQa51uiUqC0t7obh549gyXbxh0ytd3C+30Mfwu8D378SbgqOvYMXtsk/24fLzkHFvYzAOe3hgRuV1EdonIrqmpqbZdgGHtEgkW+x30gsbQDYvZWscxJXXBZ6lb4LqZS2R4/MgsN1y2bpVmVZ26gkFEfigiz3j83Ox6zkeAHPBlPeTxUqrGeK1zKgeVulMptVMptXNiortUMMPqoc1Ja1pj0FFJXbCYrXW6SWNYP9RXIRh+sm+KfEHx2ku7TzDU3VoppV5X67iI3Aa8GbjBNg+BpQm4s682Ayfs8c0e4+5zjolIABgCZhq4BoMBsHI7phbTRLsouqNZdFSScT63zq9eso4jMwkmBzrTi6QZNg4Vk9y0JvPU0TmiIX/Haoy1QqtRSTcB/xF4i1LKXQzk28CtdqTRNiwn86NKqZPAoohcb/sP3gXc4zrnNvvxW4EHXILGYKjLUF+QcMBXtWfDWsBoDO3j4skB/vstV+KrUQp9pXBCVl1aw77Ti2yfHKhZqn21aPUO+jtgALhPRJ4Skb8HUErtBu4G9gDfB96nlNL54O8FPovlkH6eol/ic8CYiBwAPgh8qMW5Gc4xhvqCFXWS1hraxzBm8hh6Cp3k5jYn7T21xCWTq1/rzIuW7iI7tLTasTuAOzzGdwFXeIyngLe1Mh/Duc26gQgj0dpVLLudbRMxRqJB1g0awdBLaI1BRyZNL6U5u5Tm4snuzEda29srg8HFv7/xEhZStatYdjtvunIDN+1Yv6bNYYZKNjiCwdIY9p1eAjCCwWDoNBMDYSZaLGS32ogIAX/32ZwNraGT3LTGsP/MIkDXVjAw2xKDwWBYATYMRRzn895Tiwz1BVnXpRsZIxgMBoNhBdgwFHHqJe07vcglkwNd03+hHCMYDAaDYQXYMNzHqYUUSin2nlrk4vXdGZEERjAYDAbDiqA7uR2eTrCQynFJlzqewQgGg8FgWBE22LkMD+636rt1a0QSGMFgMBgMK4IOWf3xXiMYDAaDwUBRMDz0/DTrBsKr3ieiFkYwGAwGwwqgey4ks/muzV/QGMFgMBgMK0BfyM+w3Wa0m81IYASDwWAwrBjrBy1zUjdHJIERDAaDwbBi6CqrFxtTksFgMBigWGV1+7ruTW4DU0TPYDAYVox3vOQ8LhiPdX3fkO6encFgMPQQV24e4srNQ6s9jboYU5LBYDAYSjCCwWAwGAwlGMFgMBgMhhKMYDAYDAZDCS0JBhH5byLySxF5SkTuFZGNrmMfFpEDIrJXRG50jV8rIk/bxz4pdqcKEQmLyD/a44+IyNZW5mYwGAyG5dGqxvCXSqkXKaWuBr4L/CmAiFwO3ArsAG4CPi0ifvuczwC3A9vtn5vs8fcAs0qpi4C/AT7W4twMBoPBsAxaEgxKqQXXnzFA2Y9vBr6mlEorpQ4CB4DrRGQDMKiUekgppYAvALe4zrnLfvx14Abp1r53BoPB0MO0nMcgIncA7wLmgdfYw5uAh11PO2aPZe3H5eP6nKMASqmciMwDY8BZj/e8HUvr4Lzzzmv1EgwGg8Hgoq5gEJEfAus9Dn1EKXWPUuojwEdE5MPA+4H/Anjt9FWNceocKx1U6k7gTnt+UyJyuPZVVGUcD8FzDnAuXve5eM1wbl73uXjN0Px1n1/tQF3BoJR6XYNv8hXgn7EEwzFgi+vYZuCEPb7ZYxzXOcdEJAAMATMNzG+iwflVICK7lFI7l3v+WuVcvO5z8Zrh3Lzuc/Gaob3X3WpU0nbXn28BnrMffxu41Y402oblZH5UKXUSWBSR623/wbuAe1zn3GY/fivwgO2HMBgMBsMK0qqP4c9F5BKgABwG/gBAKbVbRO4G9gA54H1Kqbx9znuBzwN9wPfsH4DPAV8UkQNYmsKtLc7NYDAYDMugJcGglPo3NY7dAdzhMb4LuMJjPAW8rZX5LIM7V/j9uoVz8brPxWuGc/O6z8VrhjZetxhrjcFgMBjcmJIYBoPBYCjBCAaDwWAwlHDOCgYRucmu43RARD602vPpBCKyRUR+JCLPishuEfmAPT4qIveJyH7798hqz7XdiIhfRJ4Uke/af58L1zwsIl8Xkefs//nLev26ReT/sb/bz4jIV0Uk0ovXLCL/ICJnROQZ11jV66xWq65RzknBYNdt+hTwBuBy4B12fadeIwf8sVLqMuB64H32dX4IuF8ptR243/671/gA8Kzr73Phmv8W+L5S6lLgKqzr79nrFpFNwL8DdiqlrgD8WNGMvXjNn6dYV07jeZ11atU1xDkpGIDrgANKqReUUhnga1i1mnoKpdRJpdQT9uNFrIViE6V1qe6iWK+qJxCRzcCbgM+6hnv9mgeBV2OFfaOUyiil5ujx68aKrOyzk2KjWAmzPXfNSqkHqUz4rXadnrXqmnm/c1UwOHWZbNw1m3oSu4z5NcAjwKSdbIj9e90qTq0TfAL4D1j5NZpev+YLgCng/9gmtM+KSIwevm6l1HHgr4AjwElgXil1Lz18zWVUu86W17dzVTA0XJepFxCRfuCfgD8qq4jbc4jIm4EzSqnHV3suK0wAeDHwGaXUNUCc3jChVMW2qd8MbAM2AjEReefqzqoraHl9O1cFQ7VaTj2HiASxhMKXlVLfsIdP2yXQsX+fWa35dYBXAG8RkUNYJsLXisiX6O1rBus7fUwp9Yj999exBEUvX/frgINKqSmlVBb4BvByevua3VS7zpbXt3NVMDwGbBeRbSISwnLUfHuV59R27HpUnwOeVUp93HXIXZfqNor1qtY8SqkPK6U2K6W2Yv1fH1BKvZMevmYApdQp4KhdogbgBqySNL183UeA60Ukan/Xb8Dyo/XyNbupdp2eteqaemWl1Dn5A7wR2Ac8j1VCfNXn1IFrfCWWCvlL4Cn7541YfS7uB/bbv0dXe64duv5fBb5rP+75awauBnbZ/+9vASO9ft3An2EV73wG+CIQ7sVrBr6K5UfRPW3eU+s6gY/Ya9te4A3Nvp8piWEwGAyGEs5VU5LBYDAYqmAEg8FgMBhKMILBYDAYDCUYwWAwGAyGEoxgMBgMBkMJRjAYDAaDoQQjGAwGg8FQwv8PbpWPxvqhWYgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rule_dict = {\"rule\": \"gaussian\", \"loc\": 0.0, \"scale\": 1.0}\n",
    "#rule_dict = {\"rule\": \"symmetrize\"}\n",
    "hn.set_weights(**rule_dict)\n",
    "assert not np.all(hn.weights == hn.weights.T)\n",
    "\n",
    "print(\"the weights are forced to by asymmetric Gaussian\")\n",
    "print(hn.weights)\n",
    "\n",
    "es = []\n",
    "p_random = patterns_all[1]\n",
    "for i in range(100):\n",
    "    p_random = hn.recall(p_random, if_sequential=False)\n",
    "    es.append(hn.energy(p_random.flatten()))\n",
    "    if i % 25 == 0:\n",
    "        plt.imshow(p_random.reshape(32,32).T)\n",
    "        plt.title(f\"Recalled pattern at iteration {i}\")\n",
    "        plt.axis(\"off\")\n",
    "        plt.show()\n",
    "\n",
    "plt.plot(es)\n",
    "plt.title(\"Energy vs. iter.\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "casual-aquatic",
   "metadata": {},
   "source": [
    "Now, the weight matrix is forced to be symmetric (e.g. by setting w=0.5*(w+w')), but from the previous Gaussain. As a result, the weigts do not store the first 3 patterns.\n",
    "\n",
    "Iterating a pattern (e.g.: p2), the recalled pattern is now drawn to an attractor since the weights are symmetric. But, this attractor is a spurious attractor since the weights do not store the desired 3 patterns. The energy gets stuck in local minimum (not global)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "severe-swift",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the symmetric weigths are\n",
      "[[-1.4980634  -0.38802284  0.55237647 ...  0.62142215  0.12784144\n",
      "  -0.32620415]\n",
      " [-0.38802284  0.08086753  0.65145521 ... -0.84457071  1.0316776\n",
      "   0.02612527]\n",
      " [ 0.55237647  0.65145521  0.45933858 ... -0.72303577 -0.01805788\n",
      "  -0.68108474]\n",
      " ...\n",
      " [ 0.62142215 -0.84457071 -0.72303577 ... -0.59896846  0.35774608\n",
      "   0.55959523]\n",
      " [ 0.12784144  1.0316776  -0.01805788 ...  0.35774608 -0.92732335\n",
      "  -0.70485724]\n",
      " [-0.32620415  0.02612527 -0.68108474 ...  0.55959523 -0.70485724\n",
      "  -0.6121712 ]]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Symmetrize prev Gaussian.\n",
    "rule_dict = {\"rule\": \"symmetrize\"}\n",
    "hn.set_weights(**rule_dict)\n",
    "assert np.all(hn.weights == hn.weights.T)\n",
    "print(\"the symmetric weigths are\")\n",
    "print(hn.weights)\n",
    "\n",
    "es = []\n",
    "p_random = patterns_all[1]\n",
    "for i in range(100):\n",
    "    p_random = hn.recall(p_random, if_sequential=False)\n",
    "    es.append(hn.energy(p_random.flatten()))\n",
    "    if i % 25 == 0:\n",
    "        plt.imshow(p_random.reshape(32,32).T)\n",
    "        plt.title(f\"Recalled pattern at iteration {i}\")\n",
    "        plt.axis(\"off\")\n",
    "        plt.show()\n",
    "\n",
    "plt.plot(es)\n",
    "plt.title(\"Energy vs. iter.\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "minus-calcium",
   "metadata": {},
   "source": [
    "## 3.4 Distortion Resistance"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "purple-kruger",
   "metadata": {},
   "source": [
    "Here, the resistance of Hopfield network to noise and distortion is investigated. To study the network's robustness, noisy / distorted test patterns by randomly fipping a selected number of units in the patterns are generated. The aim is to see if the network can recover the original clean patterns that have been used for training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "cheap-southeast",
   "metadata": {},
   "outputs": [],
   "source": [
    "def add_noise_via_flip(pattern, ratio, seed=100):\n",
    "    \"\"\" Adds noise to a pattern via fliping a ratio of the pixels.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    pattern : numpy.ndarray\n",
    "        Pattern vector.\n",
    "    \n",
    "    ratio : float\n",
    "        The ratio of flips.\n",
    "        \n",
    "    seed : int\n",
    "        Random seed.\n",
    "    \n",
    "    Returns\n",
    "    ----------\n",
    "    pattern_noisy : numpy.ndarray\n",
    "        Noisy pattern.\n",
    "    \"\"\"\n",
    "    assert pattern.ndim == 1\n",
    "    assert 0 <= ratio <= 1.0\n",
    "    indices = np.arange(pattern.size)\n",
    "    n = int(ratio * pattern.size)\n",
    "    np.random.seed(seed)\n",
    "    indices_flip = np.random.choice(indices, n, replace=False)\n",
    "    pattern_noisy = pattern.copy()\n",
    "    pattern_noisy[indices_flip] = - pattern[indices_flip]\n",
    "    return pattern_noisy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "dutch-wholesale",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3, 1024)\n"
     ]
    }
   ],
   "source": [
    "patterns_all = read_pict_data(path_2_data)\n",
    "patterns = patterns_all[:3,:]\n",
    "print(patterns.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "peaceful-vampire",
   "metadata": {},
   "source": [
    "Example added noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "generous-biography",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = 0\n",
    "ratio = 0.1\n",
    "\n",
    "plt.imshow(patterns[idx].reshape(32,-1).T)\n",
    "plt.axis(\"off\")\n",
    "plt.show()\n",
    "\n",
    "pattern_noisy = add_noise_via_flip(patterns[idx], ratio)\n",
    "\n",
    "plt.imshow(pattern_noisy.reshape(32,-1).T)\n",
    "plt.axis(\"off\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "knowing-dealing",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 2 iterations p1 with 10.0% noise\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "converged to this\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEICAYAAABS0fM3AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAZ6klEQVR4nO3de7hcdX3v8fcHIqKSAJpwiRHiDS9Y9eiIIlpBgtWIRDhSqaJ4qdGeg0V9LBJjW3tsrVqt2GIP5iCPWhTqhYCSSAA5GDlKcUcIJIR4QdQYJBvFStHahnzOH2ttGCZ7MzNZe8929u/zep559sxav1nr+9sze31m/daavWSbiIgo127TXUBEREyvBEFEROESBBERhUsQREQULkEQEVG4BEFEROESBDF0JG2UdOQA1/e3kt7WQ7uzJf15n8u+StIf73JxU0TSrZIW9dBuoSRLmjXB/CdIuk7SXZL+dPIr7Z2kp0r65nTW8LsqQTAk6j/M30j697bbWdNd13SwfajtqwAkvVfSeVO1LknzgNcCn6gfHylpywR1vcX2+yZqN9W1/o46HbjK9mzb/zDVK5N0qqQRSb+V9Kn2ebZvAH4p6WVTXcewSRAMl5fZ3qvtdupkr2CiT3YzVQ/9fR2w2vZvBlDOTHQwsHFXnriL78WtwF8D504w/7PAm3elnpksQTADSHqdpKslfVjSnZJ+KOklbfP3lvRJSbdJ+qmkv5a0e9tz/5+kj0r6BfBeSY+Q9BVJv5L07br91XX7j0v6SMf6vzLe0Ek9VPLhjmkXS3pHff9ddT13Sdos6ege+3urpEWSXgy8G3hlvYe0flf622V1LwG+3mNdn6rX9TDgq8D8tr23V41X6zjLeIOkTfXruEbSwRO0GxuSeb2kn9Tt3yLpWZJukPTL9j1GSbtJeo+kH0naJukzkvZum/+aet7PJS3vWNduks6Q9IN6/uclPbyH38eVwFHAWXWfD6lfm89IGq3X9x5Ju9Xtu7429V7VFyX9S/2++Y6kp43Nt32h7YuAn09Q1lXA0ZIe3K3+kiQIZo5nA5uBucCHgE9KUj3v08B24HHAfwNeBPxxx3NvAfYD/gb4OHA3cABwSn2jbVl/1PbHOxc4Gjh/nJo+R7XhU91233rdF0h6AnAq8Czbs4E/AG7tp8O2LwXeD/xLvYc0tkHot78P5Peofq/91HU3VYBsbdt7+9wEtd5L0supwuIEYB7wDcb/vbZ7NvB44JXAmcByYBFwKPCHkl5Qt3tdfTsKeAywF3BWvd4nA/8beA0wH3gEsKBtHX8KvBx4QT3/Tqr3SLffwwvrPpxa9/m7wD8Ce9c1vIBq2O31Hf3p9tosAb4APJzqPXaRpAd1q6eu6afAfwFP6KV9KYY2CCSdW3+y2dBj+z+UdJOqA42fm+r6pshF9Se9sdub2ub9yPb/sX0P1YbwQGB/SftTbZTeZvtu29uAjwIntT13q+1/tL0d+E/gvwN/afvXtm+qlweA7WuBf6Pa+FMv5yrbt49T7zcAA8+vH78C+JbtrcA9wIOBJ0t6kO1bbf+gwe8GgH7728OQzz7AXU3r6tGbgb+1val+Ld4PPH2ivYLa+2z/h+3LqML7fNvb6g3eN6iCEODVwN/bvsX2vwPLgJNUDb+8ArjE9lrbvwX+HNjRUddy21vq+e8FXqE+h27qvbJXAsts32X7VuAjVAE0ppfXZp3tL9r+L+DvgT2B5/RRyl1Ur2vUhnk8+FNUn2g+062hpMdTvfGPsH2npP2muLap8nLbV0ww72djd2z/uv4QvhfVp6YHAbfdt4PAbsBP2p7bfn8e1ftiovlQBcPJwOX1z4+NV5BtS7oA+CNgLfAq4Lx63vfr4aT3AodKWgO8ow6JJg6mv/52cycwu2FNvToY+JjuP/Qm4JHAjyZ4TnsA/2acx3vV9+d3LONHVK/z/vW8e38ntu+W1D60cjCwUlJ7ONxTP7cfc4E9xqnjkW2Pe3lt2mvdoeqg/Pw+6pgN/LKP9jPe0O4R2F4L/KJ9mqTHSrpU0jpJ35D0xHrWm4CP276zfu62AZc7nX4C/BaYa3uf+jbH9qFtbdr/Be0o1bBK+9DAozqWeR6wpB6bfRJw0QOs/3yqT48HU+32f+neldqfs/08qg2NgQ/21bOda4f++9vNDcAhk1BXL+v9CfDmtrr3sf0Q25NxyuNWqt/zmIOoXufbgdtoe40lPZRqeKi9rpd01LVnvdfRjzuohmU662hfTi+vTXutu1G9V3v6ACFpPlUY9TXcN9MNbRBMYAXwVtvPBN4J/FM9/RDgkPpA1DWqDjIWwfZtwGXARyTNqQ/8PbZt7Liz/T3AhVQHjR9ah+lrO9psAb4N/DPwpQcaXrF9HVW4nAOssf1LuPf88hfWB+3+g+rT6z270MXbgYVjxyz67W8PVlONZd+PpD07bupocjvwiPYDsp21juNsYJmkQ+t17C3pxF2su9P5wNslPVrSXtx3vGI78EXgWEnPk7QH8L+4/7bhbOBvxoaoJM2TtKTfAur31ufrZc2ul/cO6r3EPjxT0gn10NTbqIL/mrq2WZL2BHYHdq9fm/aRjyOBK+shrqjNmCCo39zPBb4g6Xqq874PrGfPojqgdiTVMMU5kvYZfJWNfUX3/x7Byh6f91qqT0E3UQ11fJH7fjfjOZXqgN7PqDb251P9sbX7NNWB1H/uYf3nUx3AbD8282DgA1SfEn9GdXDw3QCSXi2p11MOv1D//Lmk79T3e+5vD+v6DLBY0kPapj2SKrjab49tf5Ltm6n6fUt9PGf+BLW2P2cl1V7RBZJ+BWygOt4xGc6leq3WAj+kCt+31uvdCPxPqtfnNqrfWft3ID4GfBm4TNJdVBvdZ+9iHW+lOpZxC3B1vc6JTvWcyMVUxxrupDq+cEJ9vADgPVSvxxlUw5a/qaeNeTVVsEUbDfOFaSQtpDrI9RRJc4DNtnf6g5d0NnCN7U/Vj78GnGH724Osd1hJ+iBwgO1T2qb9PtUnuYW2d0z45BlA0vuBbbbPnO5aSifpvcDjbJ+8C8/9PWCF7cMnvbAhN2P2CGz/Cvjh2K60KmOn6F1Eddrc2OmOh1B9IolxSHqiqq/jS9JhwBuBlW3zHwScBpwz00MAwPa7EwLDz/aNCYHxDW0QSDof+BbwBElbJL2Rarfvjaq+rLOR6nxjgDVUu+M3Af8X+DPbE33hJKqzKi6k2oX/PNUpfhcDSHoS1RkXB1Kdtx4RQ26oh4YiIqK5od0jiIiIyTGUXyibO3euFy5cON1lREQMlXXr1t1he17n9KEMgoULFzIyMjLdZUREDBVJ435DPUNDERGFSxBERBQuQRARUbgEQURE4RIEERGFaxQEkk5UdaGXHZJaXdruLuk6SZe0TXu4pMslfa/+uW+TeiIion9N9wg2UF1Wb20PbU8DNnVMOwP4mu3HA1+rH0dExAA1CoL6knpdL/AgaQHwUqr/Sd9uCfddBvHTVNdFjYiIARrUMYIzgdO5/3VQAfavLyQydkGRCS8hKWmppBFJI6Ojo1NWaEREaboGgaQrJG0Y59bTFYokHUv1v9zXNSnU9grbLdutefN2+oZ0RETsoq7/YsL2oobrOAI4TtJiYE9gjqTz6gtL3C7pQNu3SToQKOlawhERvxOmfGjI9jLbC2wvBE6iul7o2NWFvgyMXfXqFOr/eR8REYPT9PTR4yVtAQ4HVklaU0+fL2l1D4v4AHCMpO8Bx9SPIyJigIbywjStVsv576MREf2RtM72Tt/5yjeLIyIKlyCIiChcgiAionAJgoiIwiUIIiIKlyCIiChcgiAionAJgoiIwiUIIiIKlyCIiChcgiAionAJgoiIwiUIIiIKlyCIiChcgiAionAJgoiIwiUIIiIKlyCIiChc02sWnyhpo6Qdkna6/FlH290lXSfpkrZpfyfpZkk3SFopaZ8m9URERP+a7hFsAE4A1vbQ9jRgU8e0y4Gn2H4q8F1gWcN6IiKiT42CwPYm25u7tZO0AHgpcE7H8y+zvb1+eA2woEk9ERHRv0EdIzgTOB3Y8QBt3gB8daKZkpZKGpE0Mjo6OsnlRUSUq2sQSLpC0oZxbkt6WYGkY4Ftttc9QJvlwHbgsxO1sb3Cdst2a968eb2sOiIiejCrWwPbixqu4wjgOEmLgT2BOZLOs30ygKRTgGOBo2274boiIqJPUz40ZHuZ7QW2FwInAVe2hcCLgXcBx9n+9VTXEhERO2t6+ujxkrYAhwOrJK2pp8+XtLqHRZwFzAYul3S9pLOb1BMREf3TMI7GtFotj4yMTHcZERFDRdI62zt95yvfLI6IKFyCICKicAmCiIjCJQgiIgqXIIiIKFyCICKicAmCiIjCJQgiIgqXIIiIKFyCICKicAmCiIjCJQgiIgqXIIiIKFyCICKicAmCiIjCJQgiIgqXIIiIKFzTS1WeKGmjpB2SdrrqTUfb3SVdJ+mScea9U5IlzW1ST0RE9K/pHsEG4ARgbQ9tTwM2dU6U9CjgGODHDWuJiIhd0CgIbG+yvblbO0kLgJcC54wz+6PA6cDwXTw5ImIGGNQxgjOpNvY72idKOg74qe31A6ojIiI6zOrWQNIVwAHjzFpu++Ienn8ssM32OklHtk1/KLAceFEvhUpaCiwFOOigg3p5SkRE9KBrENhe1HAdRwDHSVoM7AnMkXQe8EHg0cB6SQALgO9IOsz2z8apYwWwAqDVamUYKSJiknQNgqZsLwOWAdR7BO+0fXI9e7+xdpJuBVq275jqmiIi4j5NTx89XtIW4HBglaQ19fT5klZPRoERETG1ZA/fKEur1fLIyMh0lxERMVQkrbO903e+8s3iiIjCJQgiIgqXIIiIKFyCICKicAmCiIjCJQgiIgqXIIiIKFyCICKicAmCiIjCJQgiIgqXIIiIKFyCICKicAmCiIjCJQgiIgqXIIiIKFyCICKicAmCiIjCJQgiIgrX9JrFJ0raKGmHpJ0uf9bRdndJ10m6pGP6WyVtrpfzoSb1RERE/2Y1fP4G4ATgEz20PQ3YBMwZmyDpKGAJ8FTbv5W0X8N6IiKiT432CGxvsr25WztJC4CXAud0zPoT4AO2f1svb1uTeiIion+DOkZwJnA6sKNj+iHA8yX9q6SvS3rWRAuQtFTSiKSR0dHRKSw1IqIsXYNA0hWSNoxzW9LLCiQdC2yzvW6c2bOAfYHnAH8GfF6SxluO7RW2W7Zb8+bN62XVERHRg67HCGwvariOI4DjJC0G9gTmSDrP9snAFuBC2waulbQDmAvkI39ExIBM+dCQ7WW2F9heCJwEXFmHAMBFwAsBJB0C7AHcMdU1RUTEfZqePnq8pC3A4cAqSWvq6fMlre5hEecCj5G0AbgAOKXeO4iIiAHRMG53W62WR0ZGpruMiIihImmd7Z2+85VvFkdEFC5BEBFRuARBREThEgQREYVLEEREFC5BEBFRuARBREThEgQREYVLEEREFC5BEBFRuARBREThEgQREYVres3iofJXX9nITVt/Nd1lRETssifPn8NfvuzQSV1m9ggiIgpX1B7BZKdoRMRMkD2CiIjCJQgiIgqXIIiIKFzTaxafKGmjpB2Sdrr8WUfb3SVdJ+mStmlPl3SNpOsljUg6rEk9ERHRv6Z7BBuAE4C1PbQ9DdjUMe1DwF/ZfjrwF/XjiIgYoEZBYHuT7c3d2klaALwUOKdzEcCc+v7ewNYm9URERP8GdfromcDpwOyO6W8D1kj6MFUoPXeiBUhaCiwFOOigg6akyIiIEnXdI5B0haQN49yW9LICSccC22yvG2f2nwBvt/0o4O3AJydaju0Vtlu2W/Pmzetl1RER0YOuewS2FzVcxxHAcZIWA3sCcySdZ/tk4BSqYwcAX2DnoaOIiJhiU376qO1lthfYXgicBFxZhwBUxwReUN9/IfC9qa4nIiLur+npo8dL2gIcDqyStKaePl/S6h4W8SbgI5LWA++nPgYQERGDI9vTXUPfWq2WR0ZGpruMiIihImmd7Z2+85VvFkdEFC5BEBFRuARBREThEgQREYVLEEREFC5BEBFRuARBREThEgQREYVLEEREFC5BEBFRuARBREThEgQREYVLEEREFC5BEBFRuARBREThEgQREYVLEEREFC5BEBFRuKbXLD5R0kZJOyTtdPmztna3SrpR0vWSRtqmP1zS5ZK+V//ct0k9ERHRv6Z7BBuAE4C1PbQ9yvbTO66XeQbwNduPB75WP46IiAFqFAS2N9ne3GARS4BP1/c/Dby8ST0REdG/QR0jMHCZpHWSlrZN39/2bQD1z/0mWoCkpZJGJI2Mjo5OcbkREeWY1a2BpCuAA8aZtdz2xT2u5wjbWyXtB1wu6WbbvQwn3cv2CmAFQKvVcj/PjYiIiXUNAtuLmq7E9tb65zZJK4HDqI4r3C7pQNu3SToQ2NZ0XRER0Z8pHxqS9DBJs8fuAy+iOsgM8GXglPr+KUCvexgRETFJmp4+erykLcDhwCpJa+rp8yWtrpvtD1wtaT1wLbDK9qX1vA8Ax0j6HnBM/TgiIgZI9vANt7daLY+MjHRvGBER95K0ruMUfiDfLI6IKF6CICKicAmCiIjCJQgiIgqXIIiIKFyCICKicAmCiIjCJQgiIgqXIIiIKFyCICKicAmCiIjCJQgiIgqXIIiIKFyCICKicAmCiIjCJQgiIgqXIIiIKFyCICKicE2vWXyipI2Sdkja6fJnbe1ulXSjpOsljbRN/ztJN0u6QdJKSfs0qSciIvrXdI9gA3ACsLaHtkfZfnrH9TIvB55i+6nAd4FlDeuJiIg+NQoC25tsb27w/Mtsb68fXgMsaFJPRET0b1DHCAxcJmmdpKUTtHkD8NWJFiBpqaQRSSOjo6NTUmRERIlmdWsg6QrggHFmLbd9cY/rOcL2Vkn7AZdLutn2vcNJkpYD24HPTrQA2yuAFQCtVss9rjciIrroGgS2FzVdie2t9c9tklYCh1EfV5B0CnAscLTtbOAjIgZsyoeGJD1M0uyx+8CLqA4yI+nFwLuA42z/eqpriYiInTU9ffR4SVuAw4FVktbU0+dLWl032x+4WtJ64Fpgle1L63lnAbOphouul3R2k3oiIqJ/XYeGHojtlcDKcaZvBRbX928BnjbB8x/XZP0REdFcvlkcEVG4BEFEROESBBERhUsQREQULkEQEVG4BEFEROESBBERhUsQREQULkEQEVG4BEFEROESBBERhUsQREQULkEQEVG4BEFEROESBBERhUsQREQULkEQEVG4BEFEROGaXrP4REkbJe2Q1HqAdrdKurG+LvHIOPPfKcmS5japJyIi+tfomsXABuAE4BM9tD3K9h2dEyU9CjgG+HHDWiIiYhc02iOwvcn25oY1fBQ4HXDD5URExC4Y1DECA5dJWidp6dhESccBP7W9vtsCJC2VNCJpZHR0dCprjYgoStehIUlXAAeMM2u57Yt7XM8RtrdK2g+4XNLNwAiwHHhRLwuwvQJYAdBqtbL3EBExSboGge1FTVdie2v9c5uklcBhwJ3Ao4H1kgAWAN+RdJjtnzVdZ0RE9GbKh4YkPUzS7LH7VHsAG2zfaHs/2wttLwS2AM9ICEREDFbT00ePl7QFOBxYJWlNPX2+pNV1s/2BqyWtB64FVtm+tMl6IyJi8jQ6fdT2SmDlONO3Aovr+7cAT+thWQub1BIREbsm3yyOiChcgiAionAJgoiIwiUIIiIKlyCIiChcgiAionAJgoiIwiUIIiIKlyCIiChcgiAionAJgoiIwiUIIiIKlyCIiChcgiAionCyh++qj5JGgR/t4tPnAndMYjnDIH0uQ/pchiZ9Ptj2vM6JQxkETUgasd2a7joGKX0uQ/pchqnoc4aGIiIKlyCIiChciUGwYroLmAbpcxnS5zJMep+LO0YQERH3V+IeQUREtEkQREQUbsYGgaQXS9os6fuSzhhnviT9Qz3/BknPmI46J1MPfX513dcbJH1T0tOmo87J1K3Pbe2eJekeSa8YZH2TrZf+SjpS0vWSNkr6+qBrnGw9vK/3lvQVSevrPr9+OuqcTJLOlbRN0oYJ5k/u9sv2jLsBuwM/AB4D7AGsB57c0WYx8FVAwHOAf53uugfQ5+cC+9b3X1JCn9vaXQmsBl4x3XVP8Wu8D3ATcFD9eL/prnsAfX438MH6/jzgF8Ae0117w37/PvAMYMME8yd1+zVT9wgOA75v+xbb/wlcACzpaLME+Iwr1wD7SDpw0IVOoq59tv1N23fWD68BFgy4xsnWy+sM8FbgS8C2QRY3BXrp76uAC23/GMB2CX02MFuSgL2ogmD7YMucXLbXUvVjIpO6/ZqpQfBI4Cdtj7fU0/ptM0z67c8bqT5RDLOufZb0SOB44OwB1jVVenmNDwH2lXSVpHWSXjuw6qZGL30+C3gSsBW4ETjN9o7BlDdtJnX7NatxOb+bNM60zvNke2kzTHruj6SjqILgeVNa0dTrpc9nAu+yfU/1gXGo9dLfWcAzgaOBhwDfknSN7e9OdXFTpJc+/wFwPfBC4LHA5ZK+YftXU1zbdJrU7ddMDYItwKPaHi+g+rTQb5th0lN/JD0VOAd4ie2fD6i2qdJLn1vABXUIzAUWS9pu+6KBVDi5en1f32H7buBuSWuBpwHDGgS99Pn1wAdcDZ5/X9IPgScC1w6mxGkxqduvmTo09G3g8ZIeLWkP4CTgyx1tvgy8tj76/hzg32zfNuhCJ1HXPks6CLgQeM0Qf0Js17XPth9te6HthcAXgf8xpCEAvb2vLwaeL2mWpIcCzwY2DbjOydRLn39MtQeEpP2BJwC3DLTKwZvU7deM3COwvV3SqcAaqrMOzrW9UdJb6vlnU51Bshj4PvBrqk8VQ6vHPv8F8Ajgn+pPyNs9xP+5scc+zxi99Nf2JkmXAjcAO4BzbI97CuIw6PE1fh/wKUk3Ug2ZvMv2UP9raknnA0cCcyVtAf4SeBBMzfYr/2IiIqJwM3VoKCIiepQgiIgoXIIgIqJwCYKIiMIlCCIiCpcgiIgoXIIgIqJw/x8gAmf1I/aGuQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 2 iterations p2 with 10.0% noise\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "converged to this\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 2 iterations p3 with 10.0% noise\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "converged to this\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ratio = 0.1\n",
    "#ratio = 0.4\n",
    "#ratio = 0.5\n",
    "#ratio = 0.6\n",
    "#ratio = 0.8\n",
    "\n",
    "hn = HopfieldNetwork()\n",
    "hn.init_weights(patterns, self_connections=True, norm=False)\n",
    "\n",
    "for idx, pattern in enumerate(patterns):\n",
    "    pattern_noisy = add_noise_via_flip(pattern, ratio)\n",
    "    \n",
    "    viz_recall_dict = {\"i\": 100, \"shape\": (32, 32)}\n",
    "    patternr, it, energies = hn.recall_until_convergence(pattern_noisy, if_sequential=False, with_energy=True,\n",
    "                                               exit=1000, **viz_recall_dict)\n",
    "    print(f\"in {it} iterations p{idx+1} with {ratio*100}% noise\")\n",
    "    plt.imshow(pattern_noisy.reshape(32,-1).T)\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()\n",
    "    \n",
    "    print(\"converged to this\")\n",
    "    \n",
    "    plt.imshow(patternr.reshape(32,-1).T)\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()\n",
    "\n",
    "    plt.plot(energies)\n",
    "    plt.title(f\"Energy vs. iter. (Little model for p{idx+1})\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "subject-taste",
   "metadata": {},
   "source": [
    "Up to 50 % of noise (randomly flip this many pixels) can be removed - noisy p1, p2, and p3 all converge to their own attractors, i.e.: themselves. \n",
    "At 50 %, noisy p1, p2, and p3 converges to p2, p1, and p1, respectively - incorrect attractors.\n",
    "At 60%, noisy p1 and p2 converge to the inverse of their attractors, and noisy p3 converges to a spurious attractor.\n",
    "Beyond around 70 %, they all converge to the inverse of their respective, correct attractors ."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "southwest-medicaid",
   "metadata": {},
   "source": [
    "## Memory Capacity in Hopfield Networks"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bibliographic-backing",
   "metadata": {},
   "source": [
    "Let's add more memories / patterns to the network to see where the limit is. \n",
    "\n",
    "Firstly, let's add p4 into the weight matrix and check if moderately distorted patters can still be recognized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "valued-reservoir",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4, 1024)\n"
     ]
    }
   ],
   "source": [
    "patterns_all = read_pict_data(path_2_data)\n",
    "n_patterns = 4\n",
    "patterns = patterns_all[:n_patterns,:]\n",
    "print(patterns.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tired-subdivision",
   "metadata": {},
   "source": [
    "Try batch mode (Little model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "racial-campbell",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 2 iterations this converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 3 iterations this converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 2 iterations this converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 3 iterations this converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "if_sequential = False\n",
    "hn = HopfieldNetwork()\n",
    "hn.init_weights(patterns, self_connections=True, norm=False)\n",
    "\n",
    "for pattern in patterns:\n",
    "    patternr, it, _ = hn.recall_until_convergence(pattern, with_energy=False, \n",
    "                                                     if_sequential=if_sequential, \n",
    "                                                     exit=10000)\n",
    "    print(f\"in {it} iterations this converged to\")\n",
    "    plt.imshow(pattern.reshape(32,-1).T)\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()\n",
    "    print(f\"this\")\n",
    "    plt.imshow(patternr.reshape(32,-1).T)\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "swiss-thriller",
   "metadata": {},
   "source": [
    "Try sequential mode."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "separate-friendly",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 10000 iterations this converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOcAAADnCAYAAADl9EEgAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAEbUlEQVR4nO3dQW7TQBiA0aTiFOzZc4mKE/SUPQHqJTgF4hQx64rYqow9/py+t0wk6qZ8Gmn+eHydpukC9DwdfQHAfeKEKHFClDghSpwQ9WXpzeenF1u5sLO32+v13utWTogSJ0SJE6LECVHihChxQtTiKIX9/fz96+7rP75+H3od9Fg5IUqcECVOiBInRIkTosQJUUYpBzMyYY6VE6LECVHihChxQpQ4IcpuLYvmvph/udhp3puVE6LECVHihChxQpQ4IUqcEHWKUYrtfD4jKydEiROixAlR4oQocUKUOCHqFKMU45LjLH32Rlz7snJClDghSpwQJU6IEidEiROixAlR4oQocUKUOCFKnBAlTogSJ0SJE6LECVHihChxQpQ4IUqcEHWKM4Rock7QvqycECVOiBInRIkTosQJUeKEqIcepcw9LsAIoGvpEQ9zHvXvaeWEKHFClDghSpwQJU6IEidEPfQoZW6L3ROZ97dmJHK5rPv8R/6skaycECVOiBInRIkTosQJUeKEqOs0TbNvPj+9zL+5sbXb4UvqW+UcqzJSe7u9Xu+9buWEKHFClDghSpwQJU6IEidEZe5K2WPr2mFRxxk5plj7s5beK4xZrJwQJU6IEidEiROixAlR4oSo1XelFLaa2d8ef+ez/9/Z+hk87kqBkxEnRIkTosQJUeKEqMXd2tufb7NvnmFXraLyBfytz2nyf2AbdmvhZMQJUeKEKHFClDghSpwQlTlDiPf2eFqz0ce5WDkhSpwQJU6IEidEiROixAlRRikDrDn2vzL2OPt5PyNt/VlZOSFKnBAlTogSJ0SJE6LECVFGKSwafdDYyPHM1geebc3KCVHihChxQpQ4IUqcECVOiDJKYbjK3SyV65hj5YQocUKUOCFKnBAlToha3K1dc/bN2n+Px+Ip2v/PyglR4oQocUKUOCFKnBAlToha/cX3rbe2K+fKjFb53Yw+eqycECVOiBInRIkTosQJUeKEqMwZQmvvgLFl/3E+x3OxckKUOCFKnBAlTogSJ0SJE6Iyo5Qlj3wHzNy17HEdladGj/x7LqmPj6ycECVOiBInRIkTosQJUeKEqOs0TbNvPj+9zL/5oB51W360MxwYVrnGt9vr9d7rVk6IEidEiROixAlR4oSoU3zxfaTPuuta2bkcqX6NVk6IEidEiROixAlR4oQocUKUUcrBth5hrFUfK3xGVk6IEidEiROixAlR4oQocULU0FGK83n+teZ3Kz1Ogv1YOSFKnBAlTogSJ0SJE6LECVFDRylrt/mNYN571N+L96ycECVOiBInRIkTosQJUeKEqFMc8LX16GD0XR3uImENKydEiROixAlR4oQocUKUOCHqFKOUrY0eXxiXHOfMYywrJ0SJE6LECVHihChxQtSn3K3l4yo3Caz9WfUd2SVWTogSJ0SJE6LECVHihChxQpRRCovcJHAcKydEiROixAlR4oQocUKUOCHqOk3T0dcA3GHlhChxQpQ4IUqcECVOiBInRP0FyxTPx2FOMCIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 10000 iterations this converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOcAAADnCAYAAADl9EEgAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAEbElEQVR4nO3d4W3TQBiA4SRiCqZgiYoJOmUnQF2CKRij5idCJFZl7Mt7yfP8TARcG16ddF9sn5dlOQE9l3svALhOnBAlTogSJ0SJE6K+rL35cnl1lAsHe/94O1973c4JUeKEKHFClDghSpwQJU6IWh2lcLwfv35eff37129D10GPnROixAlR4oQocUKUOCFKnBBllHJnRibcYueEKHFClDghSpwQJU6IclrLqltfzD+dnDQfzc4JUeKEKHFClDghSpwQJU6ImmKU4jifZ2TnhChxQpQ4IUqcECVOiBInRE0xSjEuuZ+1370R17HsnBAlTogSJ0SJE6LECVHihChxQpQ4IUqcECVOiBInRIkTosQJUUOvSnEVA3yenROixAlR4oQocUKUOCFq6Gnt7PejmWGNIz3jzzySnROixAlR4oQocUKUOCFKnBCVeRzDEWOWW39u6wjgiNHB3mvkcdg5IUqcECVOiBInRIkTosQJUedlWW6++XJ5vf3mxFxd8jxm+KzfP97O1163c0KUOCFKnBAlTogSJ0SJE6IyV6WsHXnvrXKEzvFmvqmcnROixAlR4oQocUKUOCFKnBD10FelbBnPFI7QH8HIMcUR/9bI9bsqBSYjTogSJ0SJE6LECVHihKjNo5T6N/rZx+xjiiPs/XwboxSYjDghSpwQJU6IEidErd5DaPZTtQpfwP/b7D/bqPXbOSFKnBAlTogSJ0SJE6LECVGZxzHwt62Pp5h9TMEfdk6IEidEiROixAlR4oQocUKUUcoAW56ubCQyn72v4rJzQpQ4IUqcECVOiBInRIkToqYfpbgJ2f1svXJmzcjP7Ij178nOCVHihChxQpQ4IUqcECVOiJp+lGJccj9H/O5HXqVT/79j54QocUKUOCFKnBAlTohaPa3dcu+brX8fj6X+pfIZ2DkhSpwQJU6IEidEiROixAlRm7/4vvdYxL2A5rP1M/NZf46dE6LECVHihChxQpQ4IUqcEJW5h9CzHr3PvP6Z1z4DOydEiROixAlR4oQocUKUOCEqM0pZ88hXwIx8/MAWW9dR+R1X1rGFnROixAlR4oQocUKUOCFKnBB1Xpbl5psvl9fbbz6orc/4qB/LH2Hk81BGPkV7q61rfP94O1973c4JUeKEKHFClDghSpwQNcUX30d6xlPX06lzcjlSfY12TogSJ0SJE6LECVHihChxQpRRyp2N/PL4mvpY4RnZOSFKnBAlTogSJ0SJE6LECVFDRynuz/OvR/7Z+D92TogSJ0SJE6LECVHihChxQtTQUcrsT0mGkeycECVOiBInRIkTosQJUeKEqClu8LX3uGT0aMYoiC3snBAlTogSJ0SJE6LECVHihKgpRil7Gz2+MC65n5nHWHZOiBInRIkTosQJUeKEqKc8reXzZj7tPJ3mWOMtdk6IEidEiROixAlR4oQocUKUUQqrZh5FzM7OCVHihChxQpQ4IUqcECVOiDovy3LvNQBX2DkhSpwQJU6IEidEiROixAlRvwGdu9PJWs17tgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 10000 iterations this converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOcAAADnCAYAAADl9EEgAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAD70lEQVR4nO3dMW7VQBRAUX7EIhA9PbtgzeyCnh6xCkyNlG99Ro7/fc45ZdI4jq5G8rNnbtu2fQB6Xp59AcDrxAlR4oQocUKUOCHq494v//z+4lEuvLGXTz9vr/787AsBHiNOiBInRIkTosQJUeKEKHFClDghSpwQJU6IEidEiROixAlR4oQocUKUOCFKnBAlTogSJ0SJE6LECVHihChxQpQ4IUqcECVOiNo9jmGCb5+/3v3d918/TrsOOJqVE6LECVHihChxQpQ4IUqcEHXbtvuHV08/2fremMWIhRInW8Mw4oQocUKUOCFKnBAlToi69CjlntUvWXwBw1swSoFhxAlR4oQocUKUOCFKnBB16gZflVHE6rgEzmTlhChxQpQ4IUqcECVOiDr1aW3lpXJPZJnAyglR4oQocUKUOCFKnBAlTogasYfQ0Xv+vMVL9m+xL9GZ7IH0PPYQgmHECVHihChxQpQ4IUqcEHXqVymrJowi9lT2Ttqzch8r135VVk6IEidEiROixAlR4oQocULUiFFKZVwyYSSyauX6r3w/CqycECVOiBInRIkTosQJUeKEqBEbfB1tdTRjPPA4Y5bH2eALhhEnRIkTosQJUeKEKHFC1IivUs5UOkelYPXaVzdlq9+PM1k5IUqcECVOiBInRIkTojytfTLHIHCPlROixAlR4oQocUKUOCFKnBB16VHKvTHF9FHE9BfHV16Kn/B3Hc3KCVHihChxQpQ4IUqcECVOiLr0KOU9ctTEdVg5IUqcECVOiBInRIkTosQJUcsnW68+sof3aG9U5WRrGEacECVOiBInRIkTosQJUcujlAkqm0VNGDvduydnbyZW+Z+dySgFhhEnRIkTosQJUeKEKHsIXcyVn2q+N1ZOiBInRIkTosQJUeKEKHFC1KVHKZWXuY824Rr3TL//Z7FyQpQ4IUqcECVOiBInRIkToi49SpnA6IB7rJwQJU6IEidEiROixAlR4oSoSx/HsMIXE8dwHx/nOAYYRpwQJU6IEidEiROixAlRRin/wXjgX+7HMYxSYBhxQpQ4IUqcECVOiPK09iB7Ty73VJ5qrlx/5dqn87QWhhEnRIkTosQJUeKEKHFClFHKk62OYI5mLPI8RikwjDghSpwQJU6IEidEiROijFLgyYxSYBhxQpQ4IUqcECVOiBInRIkTosQJUeKEKHFClDghSpwQJU6IEidEiROixAlR4oQocUKUOCFKnBAlTogSJ0SJE6LECVHihChxQpQ4IUqcECVOiBInRIkTosQJUeKEKHFClDghSpwQJU6IEidEiROixAlRt23bnn0NwCusnBAlTogSJ0SJE6LECVHihKi/6oHnvkh7G4YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in 10000 iterations this converged to\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "if_sequential = True\n",
    "hn = HopfieldNetwork()\n",
    "hn.init_weights(patterns, self_connections=True, norm=False)\n",
    "\n",
    "for pattern in patterns:\n",
    "    patternr, it, _ = hn.recall_until_convergence(pattern, with_energy=False, \n",
    "                                                     if_sequential=if_sequential, \n",
    "                                                     exit=10000)\n",
    "    print(f\"in {it} iterations this converged to\")\n",
    "    plt.imshow(pattern.reshape(32,-1).T)\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()\n",
    "    print(f\"this\")\n",
    "    plt.imshow(patternr.reshape(32,-1).T)\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "rocky-maker",
   "metadata": {},
   "source": [
    "3 patterns could be stored so far with stable recall of all - stable points. Adding p4 and beyond worsens the network, and the patterns are not stable anymore."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "suitable-vampire",
   "metadata": {},
   "source": [
    "Let's repeat this with learning a few random patterns instead of the pictures and let's see if the network can store more patterns - i.e.: have a greater memory.\n",
    "\n",
    "\n",
    "Let's create 300 random patterns and train a 100-unit network with them. After each new pattern has been added to the weight matrix, the number of stable patterns (a single iteration does not cause them to change) is calculated and an accuracy score (representative of the memory capacity) is visualized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "cardiovascular-ethernet",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_random_patterns(n, ndim, bias=0):\n",
    "    \"\"\" Generates random patterns of dimension ndim, optionally biased random patterns with bias. \n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    n : int\n",
    "        The number of pattern vectors.\n",
    "    \n",
    "    ndim : int\n",
    "        The number of units of the pattern vector, i.e.: number of units in the Hopfield\n",
    "        network trained on the patterns.\n",
    "        \n",
    "    bias : float\n",
    "        For biasing the  random patterns.\n",
    "    \n",
    "    Returns\n",
    "    ----------\n",
    "    patterns : numpy.ndarray\n",
    "        The patterns.\n",
    "    \"\"\"\n",
    "    patterns = np.random.normal(loc=0, scale=1, size=(n, ndim)) + bias\n",
    "    mask = patterns < 0\n",
    "    patterns[mask] = -1.0\n",
    "    patterns[np.invert(mask)] = 1.0\n",
    "    return patterns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "scenic-ordering",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 100)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "patterns_random = get_random_patterns(n=10, ndim=100)\n",
    "patterns_random.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "strategic-blanket",
   "metadata": {},
   "source": [
    "Run the experiment with allowing for self-connections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "interested-digit",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_patterns = 300\n",
    "ndim = 100\n",
    "ns_patterns = np.arange(1, n_patterns+1)\n",
    "accuracies_all = []\n",
    "print_me = False\n",
    "\n",
    "for n_pattern in ns_patterns:\n",
    "    \n",
    "    patterns_random = get_random_patterns(n=n_pattern, ndim=ndim)\n",
    "    hn = HopfieldNetwork()\n",
    "    hn.init_weights(patterns_random, self_connections=True, norm=False)\n",
    "    accuracies = []\n",
    "    \n",
    "    for pattern in patterns_random:\n",
    "        \n",
    "        patternr, it, energies = hn.recall_until_convergence(pattern, with_energy=False, if_sequential=False, \n",
    "                                                  exit=10000)\n",
    "        accuracies.append(np.all(pattern == patternr))\n",
    "    \n",
    "    accuracy = np.sum(np.array(accuracies)) / patterns_random.shape[0]\n",
    "    accuracies_all.append(accuracy)\n",
    "    \n",
    "    if print_me:\n",
    "        print(f\"n_pattern={n_pattern}, accuracy={accuracy}\")\n",
    "\n",
    "fig = plt.figure(figsize=(8,6))\n",
    "plt.plot(accuracies_all)\n",
    "plt.title(\"Accuracy of recall vs. number of patterns\")\n",
    "plt.ylabel(\"Accuracy (real number)\")\n",
    "plt.xlabel(\"Number of patterns\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "breathing-trauma",
   "metadata": {},
   "source": [
    "The more patterns we train the network on (i.e.: save in the weight matrix), the lesser its memory capacity for a given number of neurons in the network.\n",
    "\n",
    "It has been shown that the capacity of a Hopfield network is around 0.138N where N is the number of neurons in the network. In the case of the image data set before, the network could not live up to this standard. \n",
    "\n",
    "Nevertheless, in the case of random patterns here, the network memory capacity does show this tendency. For 100 units above, there is an abrupt drop in memory capacity at around 20 patterns in the plot, which is approximately 0.138x100 = 14\n",
    "\n",
    "The difference between random patterns and the pictures is that the pictures are likely to be correlated, whereas the random patters are not. Training Hopfield networks on corralated data results in poor weights, with rather low memory (since recall is inaccurate with correlated weights). "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "impressive-photographer",
   "metadata": {},
   "source": [
    "Let's do the same experiment, but with adding an increasing amount of noise to the patterns to be recalled.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "level-riding",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_patterns = 100\n",
    "ndim = 100\n",
    "ns_patterns = np.arange(1, n_patterns+1)\n",
    "\n",
    "accuracies_per_noise_ratio = {}\n",
    "\n",
    "noise_ratios = np.arange(0,6) / 10\n",
    "\n",
    "print_me = False\n",
    "\n",
    "for noise_ratio in noise_ratios:\n",
    "    accuracies_all = []\n",
    "    for n_pattern in ns_patterns:\n",
    "\n",
    "        patterns_random = get_random_patterns(n=n_pattern, ndim=ndim)\n",
    "        hn = HopfieldNetwork()\n",
    "        hn.init_weights(patterns_random, self_connections=True, norm=False)\n",
    "        accuracies = []\n",
    "        for pattern in patterns_random:\n",
    "            pattern_noisy = add_noise_via_flip(pattern, noise_ratio)\n",
    "            patternr, it, energies = hn.recall_until_convergence(pattern_noisy, \n",
    "                                                                 with_energy=False, if_sequential=False, \n",
    "                                                                 exit=10000)\n",
    "\n",
    "            accuracies.append(np.all(pattern == patternr))\n",
    "\n",
    "        accuracy = np.sum(np.array(accuracies)) / patterns_random.shape[0]\n",
    "        accuracies_all.append(accuracy)\n",
    "        \n",
    "        if print_me:\n",
    "            print(f\"noise_ratio={noise_ratio}, n_pattern={n_pattern}, accuracy={accuracy}\")\n",
    "    \n",
    "    accuracies_per_noise_ratio[str(noise_ratio)] = accuracies_all\n",
    "\n",
    "fig = plt.figure(figsize=(8,6))\n",
    "    \n",
    "for noise_ratio, accuracies in accuracies_per_noise_ratio.items():\n",
    "    plt.plot(accuracies, label=f\"noise_ratio={float(noise_ratio)*100}%\")\n",
    "    \n",
    "plt.xlabel('Number of patterns')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.title('Accuracy per number of patterns for different noise levels')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "seeing-melbourne",
   "metadata": {},
   "source": [
    "Increasing the noise in the patterns to be recalled also degrades the memory capacity of the Hopfield network."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "existing-castle",
   "metadata": {},
   "source": [
    "The self-connections in the network are always positive and quite strong; they always support units to remain at their current state. In general it is a good idea to remove self-connections, even though it seems that this step lowers the memory performance. In fact, self-connections promote the formation of spurious patterns and have negative effect on noise removal capabilities. So let's check the same experiment with the self-connections removed this time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "advanced-springfield",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This cell takes around 3-4 mins to run on Intel i7 CPU\n",
    "\n",
    "self_connections = False\n",
    "n_patterns = 50\n",
    "ndim = 100\n",
    "ns_patterns = np.arange(1, n_patterns+1)\n",
    "accuracies_all = []\n",
    "print_me = False\n",
    "\n",
    "for n_pattern in ns_patterns:\n",
    "    \n",
    "    patterns_random = get_random_patterns(n=n_pattern, ndim=ndim)\n",
    "    hn = HopfieldNetwork()\n",
    "    hn.init_weights(patterns_random, self_connections=self_connections, norm=False)\n",
    "    accuracies = []\n",
    "    \n",
    "    for pattern in patterns_random:\n",
    "        \n",
    "        patternr, it, energies = hn.recall_until_convergence(pattern, with_energy=False, if_sequential=False, \n",
    "                                                  exit=10000)\n",
    "        accuracies.append(np.all(pattern == patternr))\n",
    "    \n",
    "    accuracy = np.sum(np.array(accuracies)) / patterns_random.shape[0]\n",
    "    accuracies_all.append(accuracy)\n",
    "    \n",
    "    if print_me:\n",
    "        print(f\"n_pattern={n_pattern}, accuracy={accuracy}\")\n",
    "\n",
    "fig = plt.figure(figsize=(8,6))\n",
    "plt.plot(accuracies_all)\n",
    "plt.title(\"Accuracy of recall vs. number of patterns (no self-conn.)\")\n",
    "plt.xlabel(\"Accuracy (real number)\")\n",
    "plt.ylabel(\"Number of patterns\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "attractive-confusion",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This cell takes around 3-4 mins to run on Intel i7 CPU\n",
    "\n",
    "self_connections = False\n",
    "n_patterns = 50\n",
    "ndim = 100\n",
    "ns_patterns = np.arange(1, n_patterns+1)\n",
    "\n",
    "accuracies_per_noise_ratio = {}\n",
    "\n",
    "noise_ratios = np.arange(0,6) / 10\n",
    "\n",
    "print_me = False\n",
    "\n",
    "for noise_ratio in noise_ratios:\n",
    "    accuracies_all = []\n",
    "    for n_pattern in ns_patterns:\n",
    "\n",
    "        patterns_random = get_random_patterns(n=n_pattern, ndim=ndim)\n",
    "        hn = HopfieldNetwork()\n",
    "        hn.init_weights(patterns_random, self_connections=self_connections, norm=False)\n",
    "        accuracies = []\n",
    "        for pattern in patterns_random:\n",
    "            pattern_noisy = add_noise_via_flip(pattern, noise_ratio)\n",
    "            patternr, it, energies = hn.recall_until_convergence(pattern_noisy, \n",
    "                                                                 with_energy=False, if_sequential=False, \n",
    "                                                                 exit=10000)\n",
    "\n",
    "            accuracies.append(np.all(pattern == patternr))\n",
    "\n",
    "        accuracy = np.sum(np.array(accuracies)) / patterns_random.shape[0]\n",
    "        accuracies_all.append(accuracy)\n",
    "        \n",
    "        if print_me:\n",
    "            print(f\"noise_ratio={noise_ratio}, n_pattern={n_pattern}, accuracy={accuracy}\")\n",
    "    \n",
    "    accuracies_per_noise_ratio[str(noise_ratio)] = accuracies_all\n",
    "    \n",
    "fig = plt.figure(figsize=(8,6))\n",
    "    \n",
    "for noise_ratio, accuracies in accuracies_per_noise_ratio.items():\n",
    "    plt.plot(accuracies, label=f\"noise_ratio={float(noise_ratio)*100}%\")\n",
    "    \n",
    "plt.xlabel('Number of patterns')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.title('Accuracy per number of patterns for different noise levels (no self-conn.)')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "increasing-relay",
   "metadata": {},
   "source": [
    "Indeed, removing the self-connections, further degrades the memory of the network, but results in fewer spurious attractors."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "resident-faculty",
   "metadata": {},
   "source": [
    "Now, let's bias the patterns, and see the same experiment when the patterns contain more +1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "medium-antique",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bias = 0.5\n",
    "n_patterns = 30\n",
    "ndim = 100\n",
    "ns_patterns = np.arange(1, n_patterns+1)\n",
    "print_me = False\n",
    "\n",
    "accuracies_per_noise_ratio = {}\n",
    "\n",
    "noise_ratios = np.arange(0,6) / 10\n",
    "\n",
    "for noise_ratio in noise_ratios:\n",
    "    accuracies_all = []\n",
    "    for n_pattern in ns_patterns:\n",
    "\n",
    "        patterns_random = get_random_patterns(n=n_pattern, ndim=ndim, bias=bias)\n",
    "        hn = HopfieldNetwork()\n",
    "        hn.init_weights(patterns_random, self_connections=True, norm=False)\n",
    "        accuracies = []\n",
    "        for pattern in patterns_random:\n",
    "            pattern_noisy = add_noise_via_flip(pattern, noise_ratio)\n",
    "            patternr, it, energies = hn.recall_until_convergence(pattern_noisy, \n",
    "                                                                 with_energy=False, if_sequential=False, \n",
    "                                                                 exit=10000)\n",
    "\n",
    "            accuracies.append(np.all(pattern == patternr))\n",
    "\n",
    "        accuracy = np.sum(np.array(accuracies)) / patterns_random.shape[0]\n",
    "        accuracies_all.append(accuracy)\n",
    "        \n",
    "        if print_me:\n",
    "            print(f\"noise_ratio={noise_ratio}, n_pattern={n_pattern}, accuracy={accuracy}\")\n",
    "    \n",
    "    accuracies_per_noise_ratio[str(noise_ratio)] = accuracies_all\n",
    "\n",
    "fig = plt.figure(figsize=(8,6))\n",
    "    \n",
    "for noise_ratio, accuracies in accuracies_per_noise_ratio.items():\n",
    "    plt.plot(accuracies, label=f\"noise_ratio={float(noise_ratio)*100}%\")\n",
    "    \n",
    "plt.xlabel('Number of patterns')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.title('Accuracy per number of patterns for different noise levels')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "freelance-prospect",
   "metadata": {},
   "source": [
    "Biased patterns further degrade the memory capacity of the Hopfield network since the recall update rule cannot account for the sparse patterns without a bias term in the update rule."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "electronic-continuity",
   "metadata": {},
   "source": [
    "## 3.6 Sparse Patterns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "recorded-maria",
   "metadata": {},
   "source": [
    "The reduction in capacity because of bias is troublesome, since real data usually is not evenly balanced. Here the network is trained on sparse patterns but this time the weights are centered (i.e.: the mean activity in the patterns is removed from the weights) and a slightly modified update rule is used to account for the bias in the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "governing-patio",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_random_patterns_sparse(n, ndim, activity=0.7):\n",
    "    \"\"\" Generates random patterns of dimension ndim, optionally biased random patterns with bias. \n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    n : int\n",
    "        The number of pattern vectors.\n",
    "    \n",
    "    ndim : int\n",
    "        The number of units of the pattern vector, i.e.: number of units in the Hopfield\n",
    "        network trained on the patterns.\n",
    "        \n",
    "    activity : float\n",
    "        Defines the mean activity in the patterns (the lower, the sparser).\n",
    "    \n",
    "    Returns\n",
    "    ----------\n",
    "    patterns : numpy.ndarray\n",
    "        The patterns.\n",
    "    \"\"\"\n",
    "    patterns = np.zeros((n, ndim))\n",
    "    n_active = int(activity * patterns.shape[1])\n",
    "    \n",
    "    for pattern in patterns:\n",
    "        indices = np.arange(pattern.shape[0])\n",
    "        mask = np.random.choice(indices, n_active, replace=False)\n",
    "        pattern[mask] = 1.0\n",
    "    \n",
    "    average_activity = np.sum(patterns) * (patterns.shape[1] * patterns.shape[0])**(-1)\n",
    "    \n",
    "    return patterns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "devoted-baseline",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean activity level: 10.00%\n",
      "[[0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0.\n",
      "  0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 1. 0. 0. 0. 0. 1. 0.\n",
      "  0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0.\n",
      "  0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      "  0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 1. 1. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      "  1. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0.\n",
      "  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.\n",
      "  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      "  0. 1. 1. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      "  0. 0. 1. 0. 0. 1. 0. 0. 1. 1. 0. 0. 1. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0.\n",
      "  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0.\n",
      "  0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 1.\n",
      "  0. 0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "# Testing\n",
    "n_pattern = 3\n",
    "ndim = 100\n",
    "activity=0.1\n",
    "\n",
    "patterns_random_sparse = get_random_patterns_sparse(n=n_pattern, ndim=ndim, activity=activity)\n",
    "average_activity = \\\n",
    "    np.sum(patterns_random_sparse) * \\\n",
    "    (patterns_random_sparse.shape[1] * \\\n",
    "     patterns_random_sparse.shape[0])**(-1)\n",
    "print(f\"mean activity level: {average_activity * 100:.2f}%\")\n",
    "print(patterns_random_sparse)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abroad-exclusion",
   "metadata": {},
   "source": [
    "Let's test if a stable point can be recalled with the sparse/biased recall update rule, and no self-connections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "optimum-integer",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.    0.03  0.03 ... -0.07 -0.07  0.03]\n",
      " [ 0.03  0.    0.03 ... -0.07 -0.07  0.03]\n",
      " [ 0.03  0.03  0.   ... -0.07 -0.07  0.03]\n",
      " ...\n",
      " [-0.07 -0.07 -0.07 ...  0.    0.83 -0.07]\n",
      " [-0.07 -0.07 -0.07 ...  0.83  0.   -0.07]\n",
      " [ 0.03  0.03  0.03 ... -0.07 -0.07  0.  ]]\n",
      "True\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOcAAADnCAYAAADl9EEgAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAADRElEQVR4nO3c0WnCYBSA0Vg6RadwieIEnbIThC6RKTKG6VPfpFpo/D/lnMcI8SJ8XPDhHrZtm4Cel9EDAJeJE6LECVHihChxQtTrbx++v3z4K/fBzOsyeoQ/Ob0d//2de/0Ge8w6TdP0df48XHpuc0KUOCFKnBAlTogSJ0SJE6LECVHihChxQpQ4IUqcECVOiBInRIkTosQJUeKEKHFClDghSpwQJU6IEidE/Xp9j8ez14W4R/Isv4HNCVHihChxQpQ4IUqcECVOiBInRIkTosQJUeKEKHFClDghSpwQJU6IEidEiROixAlR4oQocUKUOCFKnBDl+t4g87rs8t5nuTyHzQlZ4oQocUKUOCFKnBAlTogSJ0SJE6LECVHihChxQpQ4IUqcECVOiBInRIkTosQJUeKEKHFClDghyoGvKxziYhSbE6LECVHihChxQpQ4IUqcECVOiBInRIkTosQJUeKEKHFClDghSpwQJU6IEidEiROixAlR4oQocUKUOCFKnBAlTogSJ0SJE6LECVHihChxQpQ4IUqcECVOiBInRIkTosQJUeKEKHFClDghSpwQJU6IEidEiROixAlR4oSo19ED1J3ejqNHIGJel7t+n80JUeKEKHFClDghSpwQJU6IEidEiROixAlR4oQocUKUOCFKnBAlTogSJ0SJE6LECVHihChxQpQ4IUqcEOX6Htxor0uMX+fLz21OiBInRIkTosQJUeKEKHFClDghSpwQJU6IEidEiROixAlR4oQocUKUOCFKnBAlTogSJ0SJE6LECVHihKgh1/fmddnlvXtdR4MRbE6IEidEiROixAlR4oQocUKUOCFKnBAlTogSJ0SJE6LECVHihChxQpQ4IUqcECVOiBInRIkTosQJUUMOfDnEBdfZnBAlTogSJ0SJE6LECVHihChxQpQ4IUqcECVOiBInRIkTosQJUeKEKHFClDghSpwQJU6IEidEiROixAlRQ67vwY95XUaPcLN7X420OSFKnBAlTogSJ0SJE6LECVHihChxQpQ4IUqcECVOiBInRIkTosQJUeKEKHFClDghSpwQJU6IEidEiROiDtu2jZ4BuMDmhChxQpQ4IUqcECVOiBInRH0Dpjok1heAYS8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Testing\n",
    "\n",
    "idx = 1\n",
    "sparse = True\n",
    "bias = 2\n",
    "hn = HopfieldNetwork(sparse=sparse)\n",
    "hn.init_weights(patterns_random_sparse, self_connections=False, norm=False, bias=bias)\n",
    "print(hn.weights)\n",
    "patternr, it, energies = hn.recall_until_convergence(patterns_random_sparse[idx], \n",
    "                                                     with_energy=False, if_sequential=False, \n",
    "                                                     exit=10000)\n",
    "print(np.all(patternr == patterns_random_sparse[idx]))\n",
    "\n",
    "plt.imshow(patterns_random_sparse[idx].reshape(10,10))\n",
    "plt.axis(\"off\")\n",
    "plt.show()\n",
    "\n",
    "plt.imshow(patternr.reshape(10,10))\n",
    "plt.axis(\"off\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "nonprofit-psychology",
   "metadata": {},
   "source": [
    "Similar experiment as before, but this time the memory capacity vs. number of patterns is investigated for different values of network bias in the recall update rule. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "federal-center",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_patterns = 35\n",
    "ndim = 100\n",
    "activity = 0.1\n",
    "sparse = True\n",
    "print_me = False\n",
    "\n",
    "ns_patterns = np.arange(1, n_patterns+1)\n",
    "\n",
    "accuracies_per_biases = {}\n",
    "\n",
    "biases = np.arange(-20,22,5) / 10\n",
    "\n",
    "for bias in biases:\n",
    "    accuracies_all = []\n",
    "    for n_pattern in ns_patterns:\n",
    "\n",
    "        patterns_random = get_random_patterns_sparse(n=n_pattern, ndim=ndim, activity=activity)\n",
    "        hn = HopfieldNetwork(sparse=sparse)\n",
    "        hn.init_weights(patterns_random, self_connections=True, norm=False, bias=bias)\n",
    "        accuracies = []\n",
    "        for pattern in patterns_random:\n",
    "            #pattern_noisy = add_noise_via_flip(pattern, noise_ratio)\n",
    "            patternr, it, energies = hn.recall_until_convergence(pattern, \n",
    "                                                                 with_energy=False, if_sequential=False, \n",
    "                                                                 exit=10000)\n",
    "\n",
    "            accuracies.append(np.all(pattern == patternr))\n",
    "\n",
    "        accuracy = np.sum(np.array(accuracies)) / patterns_random.shape[0]\n",
    "        accuracies_all.append(accuracy)\n",
    "        \n",
    "        if print_me:\n",
    "            print(f\"bias={bias}, n_pattern={n_pattern}, accuracy={accuracy}\")\n",
    "    \n",
    "    accuracies_per_biases[str(bias)] = accuracies_all\n",
    "    \n",
    "fig = plt.figure(figsize=(8,6))\n",
    "    \n",
    "for bias, accuracies in accuracies_per_biases.items():\n",
    "    plt.plot(accuracies, label=f\"bias={bias}\")\n",
    "    \n",
    "plt.xlabel('Number of patterns')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.title(f'Accuracy per number of patterns for different biases (activity={activity})')\n",
    "plt.legend(bbox_to_anchor=(1.22, 1), loc=\"upper right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "intellectual-shareware",
   "metadata": {},
   "source": [
    "So in the case of sparse patterns, the network memory capacity is better when the modified update rule that accounts for the bias is used and when the weights are centered according to the mean activity in the sparse patterns.\n",
    "\n",
    "In the case of an average of 10% activity in the patterns, the more positive of the bias among the values test (e.g.: bias = 2), the greater the memory capacity of the network. Nevertheless, negative biases in this case, almost fully eliminate the memory of the network. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "centered-willow",
   "metadata": {},
   "source": [
    "Let's further decrease the activity and run the same experiment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "designed-capital",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_patterns = 60\n",
    "ndim = 100\n",
    "activity = 0.05\n",
    "sparse = True\n",
    "\n",
    "ns_patterns = np.arange(1, n_patterns+1)\n",
    "\n",
    "accuracies_per_biases = {}\n",
    "\n",
    "biases = np.arange(-20,22,5) / 10\n",
    "\n",
    "print_me = False\n",
    "\n",
    "for bias in biases:\n",
    "    accuracies_all = []\n",
    "    for n_pattern in ns_patterns:\n",
    "\n",
    "        patterns_random = get_random_patterns_sparse(n=n_pattern, ndim=ndim, activity=activity)\n",
    "        hn = HopfieldNetwork(sparse=sparse)\n",
    "        hn.init_weights(patterns_random, self_connections=True, norm=False, bias=bias)\n",
    "        accuracies = []\n",
    "        for pattern in patterns_random:\n",
    "            #pattern_noisy = add_noise_via_flip(pattern, noise_ratio)\n",
    "            patternr, it, energies = hn.recall_until_convergence(pattern, \n",
    "                                                                 with_energy=False, if_sequential=False, \n",
    "                                                                 exit=10000)\n",
    "\n",
    "            accuracies.append(np.all(pattern == patternr))\n",
    "\n",
    "        accuracy = np.sum(np.array(accuracies)) / patterns_random.shape[0]\n",
    "        accuracies_all.append(accuracy)\n",
    "        \n",
    "        if print_me:\n",
    "            print(f\"bias={bias}, n_pattern={n_pattern}, accuracy={accuracy}\")\n",
    "    \n",
    "    accuracies_per_biases[str(bias)] = accuracies_all\n",
    "    \n",
    "fig = plt.figure(figsize=(8,6))\n",
    "    \n",
    "for bias, accuracies in accuracies_per_biases.items():\n",
    "    plt.plot(accuracies, label=f\"bias={bias}\")\n",
    "    \n",
    "plt.xlabel('Number of patterns')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.title(f'Accuracy per number of patterns for different biases (activity={activity})')\n",
    "plt.legend(bbox_to_anchor=(1.22, 1), loc=\"upper right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bottom-leather",
   "metadata": {},
   "source": [
    "It seems that the memory is even further expanded for the same bias values.\n",
    "\n",
    "Lastly, for an activity level of 1%, we get something unexplainably weird - the more patterns are stored, the greater the memory. This is most certainly untrue, so I guess this is the limit of my from-scratch implementation ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "manufactured-superior",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAk8AAAGDCAYAAAAyBfQ8AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAD3JklEQVR4nOz9eZxcdZ3vj78+59Re1Vv1mnTS+5J0moA0BhNlFTPRwOAQsTPGjOI4XI14BS4685u5M3fuHeb+dHAQAYHo3AB6ieQqyqCTOIKyCSSBYEL2rdOdpNPd6aW6uvaqc87n+8dZ+tTWXb13J+/n45FHus76qVPLedXr/f6834xzDoIgCIIgCCI3hLkeAEEQBEEQxEKCxBNBEARBEMQEIPFEEARBEAQxAUg8EQRBEARBTAASTwRBEARBEBOAxBNBEARBEMQEIPFELBgYY19kjP1hDs//VcZYH2MsyBgrnqtxzDZM5WnGmI8xtneGztHJGLtF+/tvGWP/Zlr3Z4yxc9p1/xBjrJkx9kfGWIAx9l9nYjxTwfxcMqy7jjF2fLbHlA3GWClj7DhjzDEDxw4yxupy2C7p9V7oMMYeZox9Za7HQcwsl714Yoy9pt0U7HM9FmL+whizAngYwFrOuYdzPjjNx+eMsQbT4xsZY+en8xxT4GMAPgFgCed81UyfjHP+vznnXzYt+i6Ae7Tr/kcA3wLwGuc8j3P+6EyPxwxj7B8ZY/93svtzzt/knDdP55imyN8AeJpzHp3KQbTvUfNrBu316hhvX/PrzRir0T4LlqmMJ8sYP84YO8YYCzPGXmWMVY+xrZcx9kvGWIgx1sUY+5xpnY0x9nNNJHPG2I0puz8E4O8YY7bpfg7E/OGyFk+MsRoA1wHgAP50ls897V8OM81CHHM2JvFcygE4AByegeFMO9P8WlUD6OSch+ZoHNVIvu6pj2d7PJcE2g/GLwCYtBhcKDDGSgD8AsDfA/ACeA/AjjF2+QGAONTP/SYATzLGVpjW/wHA5wH0pu7IOe8BcAyzfE8hZhnO+WX7D8A/AHgLqqPw65R1S6F+2PoBDAJ43LTurwAcBRAAcATA1dpyDqDBtN0zAB7U/r4RwHkAfw31A/cTAEUAfq2dw6f9vcS0vxfA0wAuaOtf1JYfAnCbaTsrgAEAV2V4jvp5/1bbphPAJtN6O9Rf9mcB9AF4CoAz25gzHP+LUL9IvquN8QyAT5rWdwK4xfT4HwH8X+3vGu2a3QXgnLb/VwB8GMAHAIZTrvsXtdfrMQB+qF9QHzetLwDwfwD0AOgG8CAAMWXf7wEY0l+XlOdiB/CIdr0vaH/bATQBCGljDQL4fYZ99edyt7ZvD4D/Zlq/CsA72nPqAfA4AJu27g1t35B2/C8AiABQtMdBAIuh/tj5GwCnob4n/x8Ab8r5/1J7Ld/I4bX5IoAOqO/jMzC9L0zb/CWAKABZG8f/NH0GTmnX8iUAi037cABfA3ASwJksn73NALq05/F3ML1PoL1HtGsfNF2b0wB+r40lqq1rwgTfwzlexy9oxxsA8HfaunVQb6gJ7dwHsjy3TgD/P6jfDT6on2GHeTymbfVx6N8lf2Za1wDgdajv9QEAO0zrlgF4Wbv+xwF81rTuU9qxAlA/Bw9kGef1AE6lLLsLo99tHQD+S8r62wHsBzCijXsdgH9OeU0eN38fAviIdu1F03H+DMAHGb4TzmL0cxYEcIP2HK8w7VsG9fNROoHv+rsBvG167NaOsSzDtm7tdW4yLfsJgG9n2PY8gBszLP87qI7enN/n6N/M/JvzAczpk1e//LcAaNO+EMu15SKAA1BvtG6ojsPHtHV3al9IHwbAtC+Ham3deOJJAvAdqF/2TgDFADYAcAHIA/AzaAJJ2+c/oP46KoIqkG7Qln8r5Yv0dgAHszxH/bwPa+e9AeqNqFlb/wjUm59XG8OvAPz/s405w/G/qF27v9Ku21ehigemre/E+OLpKe0ar4X6Bfyi9gVZCeCi6Xl/URvPfdr1aId6Y9FvfC8C2Kq9ZmUA9kL78jft+3UAlizP5X8B2K3tWwrgbQD/lDJWS5brrK//qXb+K6CKYl0QtEG9iVi0bY8CuNe0f+p750aYbrLasnu18S3RXo+tAH6acv4fa+d3jvXaaNuMYPR9sAjAiizP7YsA/mB6fDPUm/nV2jgeA/BGynN5Gep7KtN1boF6Y7xe2/9h7bVJEk9jXJvXAHzZ9PgRTOA9nON1/JG27ZUAYgCWZxpbluvVCfUHzlJtTG8h5UeUads7MSqM26F+Nhdp634K9SYsIPk7yA31x8ZdUN9PV2uvxwptfQ+A67S/i6D9uMswzq8B+I+UZesB1GvvkRsAhDH643AV1M/bJ7QxVUITH6mvSerrBlVofcK07mcA/maM7wSLadsnAHzH9PgbAH6l/V0F9QdJtn+f07b7PoAnU8Z3CMCGDNflQwAiKcse0M+ZsjybeLoDwPtjvU/o38L+N+cDmLMnruZxJACUaI+PAbhP+3s11Btf2o0SwH8C+EaWY44nnuLQfoFm2f8qAD7t70VQnYeiDNsthvrLMF97/HMA38pyzBuh3jzcpmX/D6p9zaB+Wdeb1q2G5hbkOOYvwvTrFaoQ5AAqtMedGF88VZrWDwJoNz1+AZrI0M5lCDNt2V6oLkY51Juc07TuzwG8atr37DjvidMAPmV6/CdQw1XmsY4nnpaZlv0LgP+TZft7AfxyjPfOjUgXT0eR7LQtgvoetpjOX5fLawP1BjwMVbynCZwMr7FZPP0fAP9ieuzRxlFjei43j3G8fwDwvOmx/kt/wuIJk3gP53gdzQ7wXgAbM40ty/PrBPAV0+NPATid7XVN2Xc/gNu1v38M4IfmsWjL2wG8mbJsK4D/of19FsB/gfb9MMa5/s78OmTZ5kVo33faOb6XZTvjNcn0ukF1gbdpf+dpr1l16jVFZvF0LVSxKGiP34PJacvln/ae/XbKsrcAfDHDttcB6E1Z9ldQ8+xSt80mnj4BoGMiY6R/C+vf5Zzz9AUAv+WcD2iPt2vLAPUXYxfnXMqw31KoN9nJ0M9NiZmMMRdjbKuWkDgCNdRSyBgTtfMMcc59qQfhnF+A+sHfwBgrBPBJAM+NcV4fT85X6YIqwEqh3lD3McaGGWPDAH6jLc845iwYcX/OeVj70zPOPmb6TH9HMjw2H6ubc/XbSUN/LtVQ3age03PZCtVF0jk3zjgWa8dLPfZEMJ/D2J8x1sQY+zVjrFd7rf83gJIJHrsawC9Nz+8o1HBJeZbzA1leG+390A41TNrDGPsPxtiyHMeRdJ0450GoordyjHGk7m+s18Yy2QT8ybyHc7mO5lyWMCb2fgayvA9SYYz9BWNsv2ksrRh9X3wLqjjcyxg7zBj7kmn81+r7aPttgiqKAVUQfwpAF2PsdcbY6ixj9EEVMubxfJIxtpsxNqQd91Om8Uzlu287gDu0PCvdlekaZx8AAOd8D1SxdYP2Hm2A6jROhCCA/JRl+VB/hE5l22zkQf1xQlyiXJbiiTHmBPBZqB/GXsZYL9RQ0JWMsSuhfvFVZUkuPQfV1s5EGOoXuU5Fynqe8vi/AWgGcC3nPB9qGANQvzDPAfBq4igTz0JNWLwTwDuc8+4s2wFAEWPMbXpcBdXBGYAqTlZwzgu1fwWcc/ONInXMEyWEsa/JRKlkjDHTY/25nIPqPJWYnks+59yc5Dnec7kA9caUeuyJsDTL/k9CdTcbtdf6b6G+ztnINNZzUHOWCk3/HCmvfc6vF+f8Pznnn4DqvByDGqrKhaTrpL23iqGGs3MZRw9M14kx5tL2nwyTeQ/nch2zkev1zfY+MNBme/0IwD0AijnnhVBDSQwAOOe9nPO/4pwvhuokPaHNyDwH4PWU8Xs451/V9nuXc3471B8OL0J1mjPxAdScMX08dqhO73ehpjAUAtiJ0ffpWN99Y14XzvkRqCLykwA+B1VMTeQ4+vfdZgA/18UwY6xKK4mQ7d8mbf/DUEOw+nN1a88l08SDEwAsjLFG07Irs2ybjeVQUz+IS5TLUjwB+DTUX5otUENlV0F9s78J4C+g2vQ9AL7NGHMzxhyMsY9q+/4bgAcYY21MpcE05XU/gM8xxkTG2DqoOQNjkQf1i3+YMeYF8D/0FVydsbEL6hdmEWPMyhi73rTvi1BzHb4B1d4fj/+pTbG9DsCtAH7GOVegfnl/jzFWBgCMsUrG2J/kcLxc2Q9gozb+awB8ZorHKwPwX7Xj3Qn1ddupXa/fAvhXxlg+Y0xgjNUzxsZ7Dcz8FMB/Z2rtmxKo4aWJzkT6e81RXAE1J0Wf0ZMHNccoqP16/mrKfn0A6lIeFzPGCkzLngLwz/r7TRvn7RMcH7R9yxljf6rdRGJQf23LOe6+HcBdjLGrtBvu/wawh3PemeP+PwdwK2PsY9p07v+FSX4XTfI9PJXr2AeghjE23ni/xhhbon2u/xaZZ3a5oYqFfm0cd0F1nqA9vpMxtkR76NO2laFOLGlijG3WPgdWxtiHGWPLtc/4JsZYAec8AfU9l+113QvV6dYdQxvUHLB+ABJj7JNQ8xB1/g/U1/3j2uer0uRWpr5/M7EdwH+F+iPxZ1m26YearpB6rJ9ATTL/PEzfd5zzs5pwzPZPd+R/CaCVMbaBqTWt/gFqwvqx1AFoTugvAPwv7fv/o1DzSn+ib8MYs7PR2lg27R5h/jF0A9Tvb+IS5XIVT1+AOhPirPbrrpdz3gt1BtQmqL+0boNqD5+FGtduBwDO+c+gzi7ZDtXGfRFqUiigCpnboNq1m7R1Y/EI1KTUAagJrL9JWb8Zai7GMaiJ0/fqKzjnEai/EmuhftDHohfql+8FqOG9r5i+NP4aauL8bqaGk16B6oZNF38P9ReeD8D/RPZfnLmyB0Aj1Gv2zwA+w0drLv0F1BuAPsvp51BdlVx5EGo+xQcADgJ4X1s2EV6Hej1/B+C7nPPfassfgPqLOwD1Zp96M/1HAM9qYZjPaq/PTwF0aMsWQ016fQnAbxljAajvmWsnOD4dAarzeQHqbKYboE6eGBfO+e+gvq4vQP2RUQ9gY64n5pwfhpqsvF3b3wf1MzZZJvoensp11G/6g4yx98fYbjtUMd+h/Ut7H2luzL9CnYXZB3WSwVumTT4MYA9jLKiN9xuc8zOc8wBUUbMR6uvXi9GEeED93ujUrsVXoAqONDjncah5mZ/XHgegipv/B/U1+RxM4THO+V6oPwi+BzVx/HWMOpDfB/AZptbMy1Z766dQc75+b0qXSB1TGOrn+i3tff8Rbfl5qJ9HDvVH7oTgnPdDDWf+s/bcroXpPcvUQp1msbMF6nfzRW3cX9XetzrHof7wrYSaBxuBdi0YY4ug/jB/caLjJBYO+owoYgHCGPsHqNNpM345atvcCDUZc0m2bYipw9SaYWcAWLPkyhHEvIMxVgpVjHxI+0E2b2GMbQNwgXP+3+d6LGPBGPtXqBMEnpjrsRAzBxWMW6Bo4YC/hPorkyAIYsJojkyuEwXmDO3HyR1QywjMazjn/22ux0DMPJdr2G5Bwxj7K6jJm7s452/M9XgIgiBmCsbYP0FNpH+Ic35mrsdDEACF7QiCIAiCICYEOU8EQRAEQRATgMQTQRAEQRDEBFhwCeMlJSW8pqZmrodBEARBELPGvn37BjjnpeNvScwGC0481dTU4L333pvrYRAEQRDErMEYy6mdDTE7UNiOIAiCIAhiApB4IgiCIAiCmAAkngiCIAiCICbAgst5IgiCIAgimX379pVZLJZ/g9pcmoyRqaEAOCRJ0pfb2touZtqAxBNBEARBLHAsFsu/VVRULC8tLfUJgkDVr6eAoiisv7+/pbe3998A/GmmbUidEgRBEMTCp7W0tHSEhNPUEQSBl5aW+qG6eJm3mcXxEARBEAQxMwgknKYP7Vpm1UgkngiCIAiCmDLHjx+3NTY2rkhd3t7eXr1v3z7HTJ//H//xH8vr6+tXNDU1taxevbrpxIkTtkzbvfnmm66mpqaWqqqq1i9+8YtLFUWZ8LlIPBEEQRAEMWPs2LGjq62tLTrT52lrawvv37//6IkTJ458+tOf9t13331LMm23ZcuW6ieeeKKrs7PzUEdHh+PnP/95/kTPNWPiiTG2jTF2kTF2KMt6xhh7lDF2ijH2AWPs6pkaC0EQBEEQM48kSbjjjjtqmpqaWtatW1cXCASEVatWNb/xxhsuANi0aVNVa2vr8oaGhhX33XffYn2/LVu2VOqu0d13351R9IzHbbfdFsjLy1MA4GMf+1iwp6cnzXnq6uqyBoNB4ZZbbgkJgoBNmzYNvvjii0UTPddMzrZ7BsDjAH6cZf0nATRq/64F8KT2P0EQBEEQk+SbPz+w9ERvwDWdx2yqyAs/9Jkrz423XWdnp2Pr1q2da9euDd155501Dz30UFI/vocffri7vLxcliQJa9asad6zZ4+zpqYmvnPnzqKOjo5DgiBgYGBABIAnn3zS+/3vf78i9Rw1NTXR3/zmNx1jjWPr1q2lt9xyiz91eVdXl3XRokUJ/XF1dXW8p6fHOt7zSmXGxBPn/A3GWM0Ym9wO4Meccw5gN2OskDG2iHPeM1NjSuXlHz2FCydPJS1zwYMwgrM1BIIgCGKBY7EKsNhGAzll1XW46Yt3z+GI5o6Kior42rVrQwCwefPmwUcffbTMvP7ZZ5/1PvPMMyWSJLH+/n7rgQMHHFdffXXEbrcrGzdurF6/fr2/vb3dDwBf/epXh7761a8OTXQMTzzxhPfAgQOurVu3Hk9dp0qOZBhjEz3FnNZ5qgRgVrHntWVp4okxdjeAuwGgqqpq2gYQCcYx2D0qlJyiCzcvuhlvDryK3uisaTiCIAhiASMIDIsaCuZ6GAa5OEQzRaoQMT8+duyY7fHHHy/ft2/f0dLSUnnDhg010WhUsFqt2L9//9GXXnop//nnny968skny3bv3n1iPOfp61//euXLL79coB37CAC8+OKLed/97ncXvfnmm8edTmeaUqqpqUmYnaauri5bRUVFInW78ZhL8ZRJ6mWcZsk5/yGAHwLANddcM21TMf/kK1uwqjc0ep7BCOSfn8SN7V+A0DjhEChBEARxmXHs7R4cfvMCPvPfb4Qo0hysnp4e2yuvvOK+5ZZbQtu3b/euWbMmuGvXrkIA8Pl8otPpVLxer3zu3DnLa6+9VnDDDTcE/H6/EAwGhfb2dv+NN94YbGpqugIY33l67LHHugF064/feust59e//vXqnTt3nqysrJQy7VNdXZ1wu93K7373O/dNN90Ueu6554q/9rWvZawiPhZzKZ7OA1hqerwEwIXZHIDdaUFF7eivhbhNxEUABcVOuGvnz68IgiAIYn7Sd2YEABCPSHB6Ms6Mv6yoq6uLbtu2rXjLli3VtbW1sQceeKBfF0+rV6+OtLa2hhsbG1dUVVXF2traggAwPDws3nrrrQ2xWIwBwIMPPjgp5+yb3/zm0nA4LN555531ALB48eL473//+1MAsGzZshbdnXriiSe6/vIv/7I2Go2ym266aeTOO+9My40aj7kUTy8BuIcx9jzURHH/bOY7ZUSPhSpUZ4wgCIIYH7tTvY3GIzKcnjkezBzT3NwcP3369OHU5Xv37jVyj1544YXOTPsePHjw6FTP//bbb5/Itk4XTgBw/fXXh0+ePJk2zokwY+KJMfZTADcCKGGMnQfwPwBYAYBz/hSAnQA+BeAUgDCAu2ZqLLnCNdGUKaGMIAiCIFKxGeIpY5SIuESZydl2fz7Oeg7gazN1/kmhkPNEEARB5I7NIQIg8XS5QdltZgzxNLfDIAiCIBYGuvMUI/F0WUHiyYQRtiPniSAIgsgBXTwloiSeLidIPJnRHScSTwRBEEQO2A3nSZ7jkRCzCYknE+Q8EQRBEBPB5qCE8csREk9mdNFEs+0IgiCIHBCtAkSLQOIJwPHjx22NjY0rUpe3t7dX79u3zzHT59+1a5enpaVlucViaXv66aezVrpetWpVc01NTeuyZctali1b1tLd3T3hyXNzWedp/qGLJ5nEE0EQBJEbNqeIOOU8ZWXHjh1ds3Geurq6+NNPP9357W9/u3y8bX/84x93XH/99eHJnoucJxN6fScyngiCIIhcsTkt5DxpSJKEO+64o6apqall3bp1dYFAQFi1alXzG2+84QKATZs2VbW2ti5vaGhYcd999y3W99uyZUtlfX39iqamppa77757yWTO3dzcHL/22msjgjDz0oacJzNU54kgCIKYIDaHZX4ljL/4taW4eMQ1rccsawnj0z8Yt21KZ2enY+vWrZ1r164N3XnnnTUPPfRQqXn9ww8/3F1eXi5LkoQ1a9Y079mzx1lTUxPfuXNnUUdHxyFBEDAwMCACwHiNgafydL785S/XCIKA2267zfed73ynZ6KCi8STGZptRxAEQUwQcp5GqaioiK9duzYEAJs3bx589NFHy8zrn332We8zzzxTIkkS6+/vtx44cMBx9dVXR+x2u7Jx48bq9evX+9vb2/3A+I2BJ8uOHTs6amtrEz6fT7j11lvrn3jiieJ77rlncCLHIPFkgmbbEQRBEBPF7rRgODDp9JnpJweHaKZgjGV9fOzYMdvjjz9evm/fvqOlpaXyhg0baqLRqGC1WrF///6jL730Uv7zzz9f9OSTT5bt3r37xHjO09e//vXKl19+uUA79pHU7bJRW1ubAICioiKlvb19aO/evW4AJJ4mDYXtCIIgiAlic4rkPGn09PTYXnnlFfctt9wS2r59u3fNmjXBXbt2FQKAz+cTnU6n4vV65XPnzllee+21ghtuuCHg9/uFYDAotLe3+2+88cZgU1PTFcD4ztNjjz3WDaB7IuNLJBIYGBiwLFq0SIrFYmznzp0FN998c2Ciz5MSxk2Q80QQBEFMFJuDwnY6dXV10W3bthU3NTW1+Hw+ywMPPNCvr1u9enWktbU13NjYuGLz5s01bW1tQQAYHh4W161b19jU1NRy3XXXNT/44IOTcs5ef/11V3l5+cqdO3cW3XfffdUNDQ1G2YRly5a1AEAkEhFuueWWxqamppYVK1a0LFq0KHH//ff3Zz9qZsh5MkPOE0EQBDFBbE4L4jEZXOFgAht/h0uU5ubm+OnTpw+nLt+7d+9x/e8XXnihM9O+Bw8ePDrV899www3hvr6+DzKt08N6+fn5yuHDh6d8LnKezBhFMud2GARBEMTCwea0ABxIxObRjDtiRiHxZIJrs+04FckkCIIgcmS0vx2F7i4XSDyZ4dSehSAIgpgYVocIgPrbXU6QeDJBCeMEQRDERNGdJxJPlw8knsxQwjhBEAQxQWy6eIpSztPlAoknMySeCIIgiAliI+fpsoPEk4nRsN0cD4QgCIJYMNgclDAOAMePH7c1NjauSF3e3t5evW/fPsdMn3/Xrl2elpaW5RaLpe3pp58uyrbdm2++6Wpqamqpqqpq/eIXv7hUUSZ+0yfxZIZ62xEEQRATxOakhPGx2LFjR1dbW1t0ps9TV1cXf/rppztvu+22MVutbNmypfqJJ57o6uzsPNTR0eH4+c9/nj/Rc5F4MsFpth1BEAQxQax2EYwB8SiJJ0mScMcdd9Q0NTW1rFu3ri4QCAirVq1qfuONN1wAsGnTpqrW1tblDQ0NK+67777F+n5btmyprK+vX9HU1NRy9913L5nMuZubm+PXXnttRBCyS5uuri5rMBgUbrnllpAgCNi0adPgiy++mNWlygZVGDcj02w7giAIYmIwxtQq45H5kTD+92/9/dJTvlOu6TxmQ1FD+J8++k/jtk3p7Ox0bN26tXPt2rWhO++8s+ahhx4qNa9/+OGHu8vLy2VJkrBmzZrmPXv2OGtqauI7d+4s6ujoOCQIAgYGBkQAGK8x8GSeR1dXl3XRokUJ/XF1dXW8p6fHOtHjkHgyo4smKpJJEARBTADqb6dSUVERX7t2bQgANm/ePPjoo4+Wmdc/++yz3meeeaZEkiTW399vPXDggOPqq6+O2O12ZePGjdXr16/3t7e3+4HxGwNPBp4hssTYxFvqkHgyoV/UTBeXIAiCILJhc1rmTcJ4Lg7RTJEqRMyPjx07Znv88cfL9+3bd7S0tFTesGFDTTQaFaxWK/bv33/0pZdeyn/++eeLnnzyybLdu3efGM95+vrXv1758ssvF2jHPpLL+GpqahJmp6mrq8tWUVGRGGufTJB4MmOUKpjbYRAEQRALC5tTRIJyntDT02N75ZVX3Lfcckto+/bt3jVr1gR37dpVCAA+n090Op2K1+uVz507Z3nttdcKbrjhhoDf7xeCwaDQ3t7uv/HGG4NNTU1XAOM7T4899lg3gO6JjK+6ujrhdruV3/3ud+6bbrop9NxzzxV/7WtfuzjR50kJ42Zoth1BEAQxCeaT8zSX1NXVRbdt21bc1NTU4vP5LA888EC/vm716tWR1tbWcGNj44rNmzfXtLW1BQFgeHhYXLduXWNTU1PLdddd1/zggw9Oyjl7/fXXXeXl5St37txZdN9991U3NDQYZROWLVvWov/9xBNPdH3lK1+pqa6ubq2pqYndeeed/omei5wnE9SehSAIgpgMNocFvkhorocxpzQ3N8dPnz59OHX53r17j+t/v/DCC52Z9j148ODRqZ7/hhtuCPf19X2QaZ05rHf99deHT548mTbOiUDOkxmqME4QBEFMAvs8mm1HzDwknkyQ80QQBEFMBpvTgnhUoglHlwkknsxQkUyCIAhiEticIhSZQ07QjKPLARJPZmSabUcQBEFMHOpvd3lB4smEYTxR2I4gCIKYADanKp6oUOblAYknM5QwThAEQUwCuy6eopQ0fjlA4skEJ/FEEARBTAKbUwRweTtPx48ftzU2Nq5IXd7e3l69b98+x0yfPxKJsPXr19dVVVW1rly5ctnx48dtmbZbtWpVc01NTeuyZctali1b1tLd3T3hsk1U58kMzbYjCIIgJgGF7bKzY8eOrtk4z/e///2SgoIC6ezZs4d++MMfFt1///1L/uM//iNjA+Ef//jHHddff314suci58kMOU8EQRDEJKCEcRVJknDHHXfUNDU1taxbt64uEAgIq1atan7jjTdcALBp06aq1tbW5Q0NDSvuu+++xfp+W7Zsqayvr1/R1NTUcvfddy+ZzLl//etfF37pS18aBIC77rrL9/bbb+cpyszMACPnycRonac5HghBEASxoNCdp8Q8yHm68Ld/tzR28qRrOo9pb2wML/7f/zxu25TOzk7H1q1bO9euXRu68847ax566KFS8/qHH364u7y8XJYkCWvWrGnes2ePs6amJr5z586ijo6OQ4IgYGBgQASA8RoDpy7v6+uz1dbWxgHAarXC4/HIfX19lkWLFqUp2i9/+cs1giDgtttu833nO9/pEYSJeUkknsyQ80QQBEFMAptDzXm63J2nioqK+Nq1a0MAsHnz5sFHH320zLz+2Wef9T7zzDMlkiSx/v5+64EDBxxXX311xG63Kxs3bqxev369v7293Q+M3xg4lUwFShljaQt37NjRUVtbm/D5fMKtt95a/8QTTxTfc889gxN5niSeTBjXnYpkEgRBEBNAEAVY7OK8yHnKxSGaKRhjWR8fO3bM9vjjj5fv27fvaGlpqbxhw4aaaDQqWK1W7N+//+hLL72U//zzzxc9+eSTZbt37z4xnvP09a9/vfLll18u0I59pKKiIn7mzBlbfX19IpFIIBgMimVlZWlWYG1tbQIAioqKlPb29qG9e/e6AZB4mjSUME4QBEFMErtjfoinuaSnp8f2yiuvuG+55ZbQ9u3bvWvWrAnu2rWrEAB8Pp/odDoVr9crnzt3zvLaa68V3HDDDQG/3y8Eg0Ghvb3df+ONNwabmpquAMZ3nh577LFuAN364/Xr1w9v27at+JZbbgk9/fTTRatXrw6khuMSiQQGBgYsixYtkmKxGNu5c2fBzTffHJjo8yTxZIbCdgRBEMQk0fvbXc7U1dVFt23bVrxly5bq2tra2AMPPNCvi6fVq1dHWltbw42NjSuqqqpibW1tQQAYHh4Wb7311oZYLMYA4MEHH5yUc/aNb3xjYMOGDbVVVVWtBQUF8o4dO07r65YtW9Zy7NixI5FIRLjlllsaE4kEUxSFXXfddSP3339//0TPReLJhOE4cTV2mmo/EgRBEEQ2bE7LZe08NTc3x0+fPn04dfnevXuP63+/8MILnZn2PXjw4NGpnt/lcvFdu3ZlLE1w7NixIwCQn5+vHD58eMrnolIFZsyOE824IwiCICaAzWlBLDL3s+2ImYfEk5kk8UShO4IgCCJ3bI7L23m6nCDxZMI8yS7TlEeCIAiCyIbdSQnjlwsknszI5DwRBEEQk8NKCeOXDSSeTJjdJi6TeCIIgiByx+60QIorkGVKmr3UIfFkRkmK283dOAiCIIgFh97fLkFJ45c8JJ7MKBwQ2OjfBEEQBJEjen+7y7VFy/Hjx22NjY0rUpe3t7dX79u3zzET53zssceKq6urW6urq1sfe+yx4kzbRCIRtn79+rqqqqrWlStXLjt+/LhtquedUfHEGFvHGDvOGDvFGPubDOsLGGO/YowdYIwdZozdNZPjGQ+ucDCLoP09lyMhCIIgFho2p9rfjvKektmxY0dXW1tbdLqP29fXJ37nO99ZvHfv3qPvvffe0e985zuL+/v7xdTtvv/975cUFBRIZ8+ePXTPPff03X///Uumeu4ZE0+MMRHADwB8EkALgD9njLWkbPY1AEc451cCuBHAvzLGpqwIJ43CwSzkPBEEQRATR3eeLucZd5Ik4Y477qhpampqWbduXV0gEBBWrVrV/MYbb7gAYNOmTVWtra3LGxoaVtx3332L9f22bNlSWV9fv6Kpqanl7rvvzkncvPjiiwXXX3/9SHl5uVxaWipff/31I7/4xS8KUrf79a9/XfilL31pEADuuusu39tvv52nKFNzSGaywvgqAKc45x0AwBh7HsDtAI6YtuEA8phaytsDYAjAnL3ruALDeSLxRBAEQUwE+zwRT7/78dGlQ91B13Qe01vpCX/8L5aP2zals7PTsXXr1s61a9eG7rzzzpqHHnqo1Lz+4Ycf7i4vL5clScKaNWua9+zZ46ypqYnv3LmzqKOj45AgCBgYGBABYLzGwN3d3dYlS5bE9eWVlZXx7u5ua+r2fX19ttra2jgAWK1WeDweua+vz7Jo0aJJv1AzKZ4qAZgv9HkA16Zs8ziAlwBcAJAHoJ3zOQyYJYXtSDwRBEEQuaMnjM+1eJpLKioq4mvXrg0BwObNmwcfffTRMvP6Z5991vvMM8+USJLE+vv7rQcOHHBcffXVEbvdrmzcuLF6/fr1/vb2dj8wfmPgTPUYM7VVy7LdlG7yMymeMjWGSx3snwDYD+BmAPUAXmaMvck5H0k6EGN3A7gbAKqqqqZ/pMboOJjIjL8JgiAIIleMsF10bmfb5eIQzRSp4sX8+NixY7bHH3+8fN++fUdLS0vlDRs21ESjUcFqtWL//v1HX3rppfznn3++6MknnyzbvXv3ifGcpyVLliRef/31PH15d3e37YYbbgikbl9RURE/c+aMrb6+PpFIJBAMBsWysrIpvUgzmTB+HsBS0+MlUB0mM3cB+AVXOQXgDIBlqQfinP+Qc34N5/ya0tLS1NXTAlc4wEfDdlTniSAIgpgIesL45TrbDgB6enpsr7zyihsAtm/f7l2zZk1QX+fz+USn06l4vV753Llzltdee60AAPx+vzA0NCS2t7f7n3rqqXNHjx51AarzdOzYsSOp/37zm990AMCnP/1p/+uvv57f398v9vf3i6+//nr+pz/9aX/qmNavXz+8bdu2YgB4+umni1avXh0QhKnJn5l0nt4F0MgYqwXQDWAjgM+lbHMWwMcBvMkYKwfQDCBjR+QZR3ea9Jwn0k4EQRDEBLBYRQgWdlmH7erq6qLbtm0r3rJlS3VtbW3sgQce6N+1a1chAKxevTrS2toabmxsXFFVVRVra2sLAsDw8LB46623NsRiMQYADz74YE7OWXl5ufzNb37zQltb23IA+Na3vnWhvLxcBoB777138Yc//OHQpk2b/N/4xjcGNmzYUFtVVdVaUFAg79ix4/RUnyebyR5ujLFPAXgEgAhgG+f8nxljXwEAzvlTjLHFAJ4BsAhqmO/bnPP/O9Yxr7nmGv7ee+9N+1h5Qkb3378NW00+4p0jKPvaVbAtzRt/R4IgCILQ2PbNN1F3VSlu3JQWRJkSjLF9nPNrsq0/cOBA55VXXjkwrSe9zDlw4EDJlVdeWZNp3Uw6T+Cc7wSwM2XZU6a/LwBYO5NjyBU9TZ0SxgmCIIjJYnVY5jzniZh5qMK4jiaWqFQBQRAEMVnsTstlHba7XCDxpKE7TfpsO3KeCIIgiIlic4okni4DSDzpKCkJ4ySeCIIgiAlic1gu69l2lwsknnQobEcQBEFMEZvTQr3tLgNIPGnosw713nZUI5MgCIKYKDanBfEIJYxf6pB40pFTnCcqkkkQBEFMELvmPF2OebPHjx+3NTY2rkhd3t7eXr1v3z7HTJzzscceK66urm6trq5ufeyxx4ozbfPoo48WFxUVXbls2bKWZcuWtTz88MMlUz3vjJYqWEgYTpNRJPPye+MTBEEQU8PmsAAcSMRko13L5c6OHTu6ZuK4fX194ne+853F+/btOyIIAj70oQ+1bNy4cbi0tDTN+rvtttt8P/7xj89O17nJedKh2XYEQRDEFKlq9eLjX1wOwZKpveuljyRJuOOOO2qamppa1q1bVxcIBIRVq1Y1v/HGGy4A2LRpU1Vra+vyhoaGFffdd99ifb8tW7ZU1tfXr2hqamq5++67l+RyrhdffLHg+uuvHykvL5dLS0vl66+/fuQXv/hFwUw9NzMki3UoYZwgCIKYIsWLPShe7JnTMfznk48sHTjX5ZrOY5YsrQ7/yVfvHbdtSmdnp2Pr1q2da9euDd155501Dz30UFJD2ocffri7vLxcliQJa9asad6zZ4+zpqYmvnPnzqKOjo5DgiBgYGBABIDxGgN3d3dblyxZEteXV1ZWxru7u62ZxrVr167CpqYmT11dXfTxxx8/19DQkJj4VRiFnCcNniKeyHkiCIIgiIlRUVERX7t2bQgANm/ePPj2228nKclnn33W29LSsrylpaXl5MmTjgMHDji8Xq9st9uVjRs3Vj/77LOFHo9HAcZvDJypvRxj6Y7fZz/72eGzZ88ePHHixJGbb7458PnPf752qs+TnCedlLAdlDkcC0EQBEFMklwcopkiVbyYHx87dsz2+OOPl+/bt+9oaWmpvGHDhppoNCpYrVbs37//6EsvvZT//PPPFz355JNlu3fvPjGe87RkyZLE66+/bjSh7e7utt1www2B1O0rKiqMHKj777+//5/+6Z8qp/o8yXnS4FQkkyAIgiCmRE9Pj+2VV15xA8D27du9a9asCerrfD6f6HQ6Fa/XK587d87y2muvFQCA3+8XhoaGxPb2dv9TTz117ujRoy5gfOfp05/+tP/111/P7+/vF/v7+8XXX389/9Of/rQ/dUxdXV1GKG/79u2FdXV10ak+T3KedDStZITtaLYdQRAEQUyIurq66LZt24q3bNlSXVtbG3vggQf6d+3aVQgAq1evjrS2toYbGxtXVFVVxdra2oIAMDw8LN56660NsViMAcCDDz6Yk3NWXl4uf/Ob37zQ1ta2HAC+9a1vXSgvL5cB4N5771384Q9/OLRp0yb/v/zLv5T953/+Z6EoirywsFB65plnOqf6PNlCEwnXXHMNf++996b9uLEOP/p/+AG8f96MoZ8eR+Ht9fCsXjz+jgRBEAQxwzDG9nHOr8m2/sCBA51XXnnlwGyO6VLnwIEDJVdeeWVNpnUUttMwKoyLmvNERTIJgiAIgsgAiSed1JynBebIEQRBEAQxO5B40hgtVaDPtiPxRBAEQRBEOiSedNLqPM3lYAiCIAiCmK+QeNKhCuMEQRAEQeQAiScNw2kSqcI4QRAEQRDZIfGkoztPAgAGcp4IgiAIYgIcP37c1tjYuCJ1eXt7e/W+ffscM3HO6667rjEvL++qm266qSHbNpFIhK1fv76uqqqqdeXKlcuOHz9um+p5STzp6LPrBKb+o9l2BEEQBDFlduzY0dXW1jblqt6ZeOCBB3q3bt16Zqxtvv/975cUFBRIZ8+ePXTPPff03X///Uumel4STxp6XScmMDCBUdiOIAiCICaIJEm44447apqamlrWrVtXFwgEhFWrVjW/8cYbLgDYtGlTVWtr6/KGhoYV9913n1GJesuWLZX19fUrmpqaWu6+++6cxc3tt98eyM/PH3OK169//evCL33pS4MAcNddd/nefvvtPEWZ2qwwas+ik+o80Ww7giAIYgEy9PMTSxO9Idd0HtNa4Q57P9M0btuUzs5Ox9atWzvXrl0buvPOO2seeuihUvP6hx9+uLu8vFyWJAlr1qxp3rNnj7Ompia+c+fOoo6OjkOCIGBgYEAEgPEaA+c69r6+PlttbW0cAKxWKzwej9zX12dZtGiRlOsxUiHxpGE4TQIDGKOcJ4IgiAWOEk6g75H3UXRnExyNRXM9nMuCioqK+Nq1a0MAsHnz5sFHH320zLz+2Wef9T7zzDMlkiSx/v5+64EDBxxXX311xG63Kxs3bqxev369v7293Q+ojYG/+tWvDk11TJna0DHGpnSTJ/GkozlNTGBgIs22Iwhi9lDiMkb+sxP5n6iG4KCv5ekifiEIeSSO4O6ey0o85eIQzRSMsayPjx07Znv88cfL9+3bd7S0tFTesGFDTTQaFaxWK/bv33/0pZdeyn/++eeLnnzyybLdu3efmC7nqaKiIn7mzBlbfX19IpFIIBgMimVlZfJUniflPOnoYomBnCeCIGaVeNcIgm9dQOy0f66Hckkh9UcAANHjQ1Aik47QEBOgp6fH9sorr7gBYPv27d41a9YE9XU+n090Op2K1+uVz507Z3nttdcKAMDv9wtDQ0Nie3u7/6mnnjp39OhRF6A6T8eOHTuS+m8iwgkA1q9fP7xt27ZiAHj66aeLVq9eHRCEqckfEk8aRnsWShgnCGKWkYMJAKoDRUwfUn9E/UEscUQOD8z1cC4L6urqotu2bStuampq8fl8lgceeKBfX7d69epIa2truLGxccXmzZtr2traggAwPDwsrlu3rrGpqanluuuua37wwQdzds7a2tqaN2/eXPfOO+/kl5eXr3zhhRfyAeDee+9d/NxzzxUAwDe+8Y0Bn89nqaqqan3ssccqvvvd756f6vMkf1hHSU0YJ/FEEMTsoIzEAQA8Su7IdJLoD8O62AMlKiG8vx/ua9IiQMQ00tzcHD99+vTh1OV79+49rv/9wgsvdGba9+DBg0cnc859+/Ydz7T8kUceuaD/7XK5+K5duybkVo0HOU8anMQTQRBzhBxQxZMSI+dpOpH6I7CUOuG6shSx08OQNZFKEFOFxJMOTwnbkXYiCGKW0MUTJ/E0bShxGfJwDNYSJ1xXlQEcCH/QP/6OBJEDJJ50ZLPzBHKeCIKYNRTdeaKwXRIXLlzA22+/Pal9pQE1WdxS5oK1zAXrYjfCB0g8EdMDiScNw2lioIRxgiBmFTlIzlMm9u3bh9/+9rdIJBIZ1ysxCcF3LmT8vjbEU4kTAOC6qgyJcwFjOUFMBRJPOgoHBK0mBZUqIAhiFpFHtNl2URJPZnw+HwBgeHg44/rwgX4M//tpxM6kl3jQyxTo4sl5ZSnAQO4TMS2QeNJRuBqyAwCRxBNBELMDTyjGLDseo7CdmfHEk9QbBgDEzwbS1iX6wxAL7RBsIgDAUmCHrSYf4f0XkypOnz9/HsFgMG1/ghgLEk8aXOFGJVTGKGxHEMTsoCeLAzTbzoyiKPD7VUdJF1GpJC7q4mkkbZ0+086M66oySP0RJC6EjGU/+clP8Oabb07XsC9rjh8/bmtsbFyRury9vb163759jpk453XXXdeYl5d31U033dSQbZtHH320uKio6Mply5a1LFu2rOXhhx8umep5qc6Tjtl5EhhA2okgiFlAz3diNpFynkyMjIxAUdS+Wdmcp0SvKoLiZ0fA+egPYM45pP4I3NeUJ23vbC3B8IunEDkyCFulB7FYDLFYLKs4I6aHHTt2dM3UsR944IHeUCgk/OhHPyoda7vbbrvN9+Mf//jsdJ2XnCcNniSeAC6TeiIIYubRZ9pZSp2U82TCLGgyiRs5lIASTKjXLSRBGowa65RAHDwupzlPotsK6yI34p2qo6WH63SHi5g6kiThjjvuqGlqampZt25dXSAQEFatWtX8xhtvuABg06ZNVa2trcsbGhpW3HfffYv1/bZs2VJZX1+/oqmpqeXuu+9ekuv5br/99kB+fr4yE89lLMh50uHqLDtAm21H4okgiFlAD9tZSpyQ+sNzPJr5g+42eb3ejM6T1Ke6Tu4PV8C/8wziXSOwasnhiYvJyeJmbNX5CO/rA5cVhELqMUZG0sN+5nFwzlFUlFtj4fPnz+P06dO49tpr4XDMSKRqXF588cWlFy9edE3nMcvKysKf/vSnx22b0tnZ6di6dWvn2rVrQ3feeWfNQw89lOQIPfzww93l5eWyJElYs2ZN8549e5w1NTXxnTt3FnV0dBwSBAEDAwMiAExXY2AA2LVrV2FTU5Onrq4u+vjjj59raGjIPIUzR8h50tFm2wGgCuMEQcwaciABMMBS7ACPK7OWb8llBUp4SvePGcXn84ExhpqamoziKdGnCk3nyhIwh5iU9yQNqOsspen6wV5TAB5XkOgJGc5TJBJBPJ65+vi///u/4/nnn8953KdOncKrr76KqTaeXahUVFTE165dGwKAzZs3D7799tse8/pnn33W29LSsrylpaXl5MmTjgMHDji8Xq9st9uVjRs3Vj/77LOFHo9HAaavMfBnP/vZ4bNnzx48ceLEkZtvvjnw+c9/vnaqz5OcJw2u8CTnSSHxRBDENBGPx9HT04Pq6uq0dUogDsFtheC0AlBrPTHnzH81B/9wAYE/nMeiv73WyBVKJZFIwGq1zvhYMuHz+ZCfn4/i4mJEIhFEo9EkJyfRFwazixAL7LBV5SPeNTrjTuqPgNkEiPm2tOPaavIBALHOEYTso4njfr8fpaXpaTODg4MYGRnB8PAwCgsLIflj4BEJ1gp3xnH39/ejqKgINlv6uWeLXByimSL1vWR+fOzYMdvjjz9evm/fvqOlpaXyhg0baqLRqGC1WrF///6jL730Uv7zzz9f9OSTT5bt3r37xHQ5TxUVFUY8/P777+//p3/6p8rJPbtRLk9pnAlzzhPVeSIIYhr54IMP8PTTT2ecEi8H4hDzbBDs6pT62Zpxl7gYhhJIgMczp4t0dnbi29/+9pghrZnE5/OhqKgIhYWFANKTxhN9IVgr3GCMwV6Vh0RfyKjQnuiPwFLiNH4Qm7EU2CEW2hHvGkl6PTI9T0mSjOWnTp0CAPhfOo2Bp9N63xr09/dnFGGXCz09PbZXXnnFDQDbt2/3rlmzxrjIPp9PdDqditfrlc+dO2d57bXXCgDA7/cLQ0NDYnt7u/+pp546d/ToURcwfc5TV1eX8Qtg+/bthXV1ddGxts8FEk8aPHW2HYkngiCmCT23JhBIr0ckB+IQ8mxgDlU8Zav1pChKUn2iqWI0Iw5lDt2dO3cOsixjaGho2s45EXSnR881MieNc84h9YVhLVfDcraqfIAD8XPq9ZX6wxlDdjq2mnzEOpPFU6akcfOyEydOgHOO2NkRyP4Y5AzXTZZlDA4OXtbiqa6uLrpt27bipqamFp/PZ3nggQeMqqSrV6+OtLa2hhsbG1ds3ry5pq2tLQgAw8PD4rp16xqbmpparrvuuuYHH3wwZ+esra2tefPmzXXvvPNOfnl5+coXXnghHwDuvffexc8991wBAPzLv/xLWUNDw4rm5uaWH/zgB2XPPPNM51SfJ4XtdMxhO5GBz3ruPkEQlyrRqPpDN5PzpATisJa7R52nDDPuZFnG9773PXz84x/Hhz70oWkZk9FPL5wAvOmJzYODgwCAcHj2k9jj8TiCwWBW50kJJqCEJVjKdPGUBzC1WKa9Jh/ycAyWq9OTxXXs1fmI7O9H0DcCr9eLoaGhjM6TLtjKy8tx5swZxIZUtw5QyySI9YVp28uyfNmKp+bm5vjp06fTbLm9e/ce1/9+4YUXOjPte/DgwaOTOee+ffuOZ1r+yCOPXND//sEPftANoHsyx88GOU86ClfDdQDAQM4TQRDTRiwWA5AunrjCIQcTEPOsYA71t2ymWk/hcBjBYBDd3dP3/a/Xl1LCmZ2uuRRPulAqKiqC0+mE3W5Pcp4S2kw7a4UqngSHBZYyF2JdI2rJAg5YS7OLJ1tNAQAg4BtBQUEBPB5PRudJH8eHP/xhJBIJnP7jsdEx9ITStu/vV02Wy1U8XU6QeNLgSkqpgmm0xwmCuLzJJp6UiATIHILHlPMUTRczuoCZrnpEXOFQglo/vSwz7uaDeCosLARjDIWFhUnOU0JrywKvDe+//z4457BX5yN+NmBUHR8rbGctd4HZRYRCIXg8HuTn52d1ngRBwMqVK2GxWHDy5ElAZBBcFqNApxldPJWUTLmANTHPIfGkk1qqgOo8EQQxTWQL2+mhMzHfnPOU7jzpOVPZKm1PFCWUMLooZMp5CofDhmiKRCLTcs6JoLtMer5TUVFRkvMkXQxDcFnwwanDeOmll9Dd3Q1bVT54VELkiCr6UgtkmmECg606H6F4BG63GwUFBVmdp8LCQthsNtTW1qJj4BwsFS5YF3uyiqeCggLY7fYpPX9i/kPiSYentmch8UQQxPSgO0+6CNLRk7ZFj81oYJtptp3ZeZoOV9zcT0/OELbTXSfzuWcTn88Hi8UCj0ctEaQ7T/pzT/SGYCl34dw5Na/44sWLsFXnAQAihwYhFoxez2ywJU5IkOG2O5Gfn5/x2uriCQAaGxoxIocQLuWwVrgh9YXTanJd7jPtLidIPGmk1nmixsAEQUwX2ZwnXcQIeVYwu5bzlCFsp4uueDw+aScoHo8bs/0UczPiDGE7XTzZ7fY5C9sVFRUZNYIKCwuRSCQQCoXAOUeiLwxruRtnz6qtyvr7+2EpcUJwWQBJGTNkp5MoU8WVPSKioKAAiUTCeJ109HIJAFBXrHYMOSsMwlrhBk8okAZHXwtFUTAwMEDi6TKBxJNOWqmCuR0OQRCXDllznrSZW2K+DUxkYFZhTOcJmHze08svv4yHH34Y//Ef/4HAgHYMkWVMGB8cHIQgCFi8ePGcOU+64wOMhu+Gh4ch++PgMRnRAsW4FhcvXgRjTC1ZgLFDdjpxdVPYR4CCAjWB3HxtY7EYwuGwMQ7nsIgixY1O/3lYF6kFMs2hu+HhYUiSROLpMoHEkwZPmW1HzhNBENPFWM4TswpgWoiJOcSss+10Jiueenp6YLfb8d577+Hffv9TfCB2QSi1Z3SeBgYGUFRUBI/HM6PiaXBwEAMDA0nLOOdJjg8AQ8D4fD6jp12vMgxATc7WE7X10J01Q0+7VMIxrf/dgIz8fFVJmZPGzUnrABA/H8BSVoqzPeehFIgAS55xRzPtgOPHj9saGxtXpC5vb2+v3rdv37Q3+nv77bedV1111bKGhoYVTU1NLT/60Y8yNiCMRCJs/fr1dVVVVa0rV65cdvz48SmXf59R8cQYW8cYO84YO8UY+5ss29zIGNvPGDvMGHt9JsczJopa3wnQZt2ReCIIYhqQZRmJRAKiKCIajUKSRp0eORCHkG8zwlOC3ZJxtl0oFILTqQqCySaNDw0NYcWKFdiyZQsWu0ux13oKvwy/ZZQsMDM4OIji4mK4XK4ZE08XL17ED3/4Qzz33HNJuUbhcBjxeDyjeBoeHjZ62l0IXYTVasUVV1yBkZERRKNR2LW6S9bKpHZqGdGFrKVXQr5bFV1mYWoulwCoBTjrSpdCURR0nD0DS6lzdNYfaKbdWOzYsaOrra1tylW9U/F4PMpPfvKTM6dOnTr829/+9uTf/u3fLtWbCpv5/ve/X1JQUCCdPXv20D333NN3//33L5nquWdMPDHGRAA/APBJAC0A/pwx1pKyTSGAJwD8Ked8BYA7Z2o846Jwtb4TQBXGCYKYNvSQndfrBZCcNK4E4hA9oz+CmT2781RaWgqLxTIp5ykSiSAcDsPr9aK0tBS3ln8MH7EvR398GEOh4aRtFUXB0NCQIZ5isRhkeXpbxgSDQTz33HOIx+Pw+Xzo6ekBoIrJgQ71b3PYzm63w+VyGeJJ8Fhx7sJ5LFmyBOXl5QBU8WKvykfFtz4Mu1bHabwxAIBTssA2AgiCkNV54gm1kXBVXQ3sdjtOnjwJa4U7KWzX39+PvLw8Q+RerkiShDvuuKOmqampZd26dXWBQEBYtWpV8xtvvOECgE2bNlW1trYub2hoWHHfffct1vfbsmVLZX19/YqmpqaWu+++Oydxs3LlytgVV1wRA4CampqE1+uVenp60op///rXvy780pe+NAgAd911l+/tt9/OU5Sp5ebMZIXxVQBOcc47AIAx9jyA2wEcMW3zOQC/4JyfBQDO+cUZHM+YcM4hUMI4QRDTjC6eiouL0d/fj2AwaOTYyIG40WIEAAS7mDHnKRQKoaSkJOuU+vHQW6zoAk4OxFGXvxS7+4/iQnQA5l+1IyMjkCQJxcXFhiMUDoeRl5c34fNmIpFI4Kc//SlCoRA2bdqE7du34/Dhw1i8eDGGf3UaXcePAgxJzhMwWq4gMRICL7Ohr6cP1113HcrKygCo4mXp0qWwZKiWnolQKASnwwkhKiDy3kXkpRTK9Pl8sFqtcLvdatsXhcNZVYCGUAOOHz+O66++EvIHA1BiEgS7xZhpFz3lQ2hPLwr/tB5i3tw0Bz5y9K+XhoInxs+anwBuT1O4Zfl3xm2b0tnZ6di6dWvn2rVrQ3feeWfNQw89lBTHfPjhh7vLy8tlSZKwZs2a5j179jhramriO3fuLOro6DgkCAJ092gijYFfffVVVyKRYC0tLbHU7fv6+my1tbVxALBarfB4PHJfX59l0aJFmSvE5sBMhu0qAZgv9HltmZkmAEWMsdcYY/sYY3+R6UCMsbsZY+8xxt7TrdFpR6ZSBQRBTD96vpMezjHnPcmBBATTDZY5LOAZ2rOEw2G4XC4UFBTkHLbzv9yF4V1nAIzOnisuLgagtjfxFhXBbXOih/vAE6O/wvUcpJKSErhcLuP804GiKPjlL3+J7u5ubNiwAQ0NDairq8Phw4ehKApiZ0YQkFQ3J1U86eUKpL4wBl1hcM5RVVWFwsJCWCwWTPTeEAwG4cnzwHllKcLv9cHhFzB4pg/SsHrv1csUMMaMnnm2pXlYuXIlwuEwznH1fIledSy6eAq904NYxzAE5+XZ/ayioiK+du3aEABs3rx58O23306KoT777LPelpaW5S0tLS0nT550HDhwwOH1emW73a5s3Lix+tlnny30eDwKkHtj4K6uLutdd91V96Mf/ahTFNNLVGQq78EYm9JNfiZf3fR21kZZtqTztwH4OAAngHcYY7s55yeSduL8hwB+CADXXHPNjKia9MbA6gXXcxEIgiAmg9l5AkbFE08o4FEpyZ0Q7CISKY2BFUUxxBPnHMePZ2zllQTnHKE9PWAWAYWfrDWcJ12QyCNxOJqLUOldhO6ebijhBMQCtbCjWWiZnafp4PXXX8eRI0fwiU98AsuXLwcArFixAv/+7/+Oc8c7IQbiCNiicMAKm5B8eyoqKsLRo0chJ2T0wA/GGJYsWQJBEFBSUoKLFycWuNCrixf/+TLEP1aJ/P93Er0j/ej9l3eR//GqpBl/iXMBCPk2iAV2NHga4Ha7cajnBK5HFRK9IUQKFCQSCRTnFSHy5iA8H6sEs8zdfKxcHKKZIvWeaX587Ngx2+OPP16+b9++o6WlpfKGDRtqotGoYLVasX///qMvvfRS/vPPP1/05JNPlu3evftELs7T0NCQ8MlPfrLhH/7hH7o//vGPp1cuhSrozpw5Y6uvr08kEgkEg0GxrKxsSrHomXx1zwNYanq8BMCFDNv8hnMe4pwPAHgDwJUzOKbscFOdJ/21JvOJIIgpojtPqeLJKJCZ5Dyl5zxFo1Fwzo1K2KFQCIlE5pYqOtJgFEowAdkfA08oGBwcREFBAaxWK5SYDB6XIeTZUFW+BCEWw1DfaFHMwcFB2Gw2eDyeKTtPciiR5Gq99957aG5uxpo1a4xly5YtgyAIOLTvgHquEiBPcSL0Xl/SsQoLC1UhiRh6wv0oKyuDw6GG6MrKyiblPLndaskB29I8lK1cirAYh2OFF/6XO+EbHJ3xFz8fhG2JGrYURRFXXnklTnWeRsQuIdETMs7t6RcABXCvWjShsVxK9PT02F555RU3AGzfvt27Zs0aw2r1+Xyi0+lUvF6vfO7cOctrr71WAAB+v18YGhoS29vb/U899dS5o0ePuoDxnadoNMrWr1/fsHHjxsEvfelLvkzjAYD169cPb9u2rRgAnn766aLVq1cHBGFq8mcmxdO7ABoZY7WMMRuAjQBeStnm3wFcxxizMMZcAK4FMKnOylNGwajzpM26o6RxgiCmiu48ud1uOBwOI2Fcn+UmJDlPFihROSnMoG+vh+2A8csVxM9o6zkg+aIYGhoy8p2U4KhoW7pE/X3b1dll7KvPtGOMTUk8KVEJfQ+/h57v7EXgjfMYGfIjFAqhtrY2yY1wOp1oaGjAsa6TgJUhwMPId+Yh8Pp5cHlUeBXmac18rVFcGOhFVVWVsa60tNSYcZcrwWDQqGAOAPn5+ZAVGfZblwJ1bsSlOPIUB5RwAtJABLalozlfV111FRRFwZn8QSR6R8WT81gc9vqCnEolXKrU1dVFt23bVtzU1NTi8/ksDzzwgKFqV69eHWltbQ03Njau2Lx5c01bW1sQAIaHh8V169Y1NjU1tVx33XXNDz74YE7O2bZt24reffddz/bt20uWLVvWsmzZspa3337bCQD33nvv4ueee64AAL7xjW8M+Hw+S1VVVetjjz1W8d3vfvf8VJ/njIXtOOcSY+weAP8JQASwjXN+mDH2FW39U5zzo4yx3wD4AKp8+TfO+aGZGtOY402pMG4sm4vBEEQWotEo7HY7hZMXELp4stvt8Hg8hvOkZHKe7KL6o03igFV9jXXh4na7oedz+P3+MafExzpHZ41JAxEMDg6itbUVQLLjVeGpgI1bcPbCOVyD1QDUnCddmOgzxyZT1Ty4uwdKSIKtOh/+nWfQ/dowAKCsOL0O0ooVK3DixAkMlsXh9/nR3FQHeX8M4QP9cF9drn4Xv60aC73NCcRPxdPEEzCaND4e8XgciUTCcJ6A0UKZI8ERCJ8oA54FhH0jCBdrNaSWjgqtsrIyVFZW4vjgObT0LEL/ogG47E5Y/Rzu9Zev69Tc3Bw/ffr04dTle/fuNWLNL7zwQmemfQ8ePDhh42TLli1DW7ZsGcq07pFHHjEiXS6Xi+/atasj03aTZUaDspzznZzzJs55Pef8n7VlT3HOnzJt8xDnvIVz3so5f2QmxzMm5lIFjJwnYv4RiUTwr//6rzh6dG7MWWJy6G6Iw+FIEk+ZwnaCQ+9vN5r3pIsns/M0XtJ4rNMPW41a+DHQ60M0Gk2aaQeojpfFY0e5UoDz/ep9JpFIwO/3GyFGi8UCm82W1XmS/LGMybhKXEbwzW7Ym4pQ9tUrUfrVKzGcp4nIPelpKc31jRC5gINKJxRFQUn9IljKXQi8dh5c4fD/5gwsx1UBd6znNAAkiSTzjLtc0F+DVOcJUGcb+iNqgngenBh+ST2fHrbT+dCHPoTBqB/98WH0915EEfNA8FjhbCnOaQzEwoYqjOukJozrywhinhAIBJBIJJKathLzn1gsBlEUYbFY4Ha7TeIpATBAcFuNbZldFU/mGXd62M7tdiM/Px+MsTHDdvJIHPJgFM6WYjCnBQM9qqAwZtrpLWHyrBBcFlQoRRgKDSMYDBqJ5fq2ALIWyoyfC6D323vh/48zaetCe3uhhBLIv0kVOPbqfASrGDxWF/ixkbRCoGwggSWKF6d8aq+6Im8R8m9cCuliGEM/PYbgG93IX12J/Px8hEIh5OfnJ9WBmuiMO/2amsWTOSTq86kuV3X7lYDAYCl1QnAkB2paW1thEUUcFy+gv78f+SEb3NeUz2miODF70KuskS1sRxDzBd3BmGxjWGJuiEajRmJzathOcFuNzgaAmvMEIKnWk9l5EkUReXl5Y4qnWKe6zl5bAEuxA0MDqthOcp4EQHBZwSwCFonq8rNnz6aVNNDPm0k8BV47B3Ag+IduRI6OCnouKQi+cR622nzYa0eLVfb29qKivByQOKJHkyMt8a4A6uRy43FRURGcK0sheh2IHByAY7kXhbfVG4LJHLIDMOEZd/prYA7buVwuWCwWjIyMYHh4GA6HAwXLKlDyhRUovL0+7RgOhwPLmpfhpNiDmBRHkeKG+8NpE8OISxQSTzo8g/NE2omYR+iiicTTwiIWi8FuV8sAeDwexONxxONxyIF4WhFFpoftTM5MKBSC3W6HxaIKq/FqPcXO+MFsAqyL3bCUODEUGAZjbLRMQSAOwWMzfiSWubywMBFdXV05i6fExTAiRwbhub4S1kVu+H52ArJfDcuF3u+DPBJH/k2jAieRSGBgYACLapZAzLch/EGyQxQ7O4LawiWwWCxgjKGgoABMZCj803q4riqF98+XgQmjzyFTXtNEZtxlcp4YY8jPzzecJ12oOZqK4GjI2DINV1/TBpmpSe2li8thKZ7TRHFFURRKhpwmtGuZtQz5uOKJMXYrY+ySF1lcHnWc9KtCzhMxn9BF01x0uScmj57kD4zerEOhkCpiUsSToIftUpwnfdYboIaoxnKe4p0jsFXlg4kCLMVO+GMBFBQUGOJLSRFtVrcd5TYvzp49i4GBAeTl5RnjBTKLp8Ab58EsAvKuXwLv55aBSwoGnz8OLikIvHYe1iUe2BsLje37+/vBOUfFogo4ryhB9ITPEIicc8TPjsBT7cWyZctQXFxsJMY7l3nh3bgMgtY4OZvzBExsxl0m5wmAIZ6Gh4fTinRmoqamBnkW9bVZem3juNvPMIf6+/sLSEBNHUVRWH9/fwGArBPYcplttxHA9xljLwB4mnN+aWarmpwnQ0TJJJ6I+QM5TzPH/v374fV6M96Up0osFksK2wHqzdsSiMNannzzZhnEUygUShJPBQUFRkXu1Fo1SkRCojeE/I+rz8NS7ICfheHNG3WS5GAiOUndZUFFxIv3e08YbVnMpIonyR9D+I8X4V5VAdFjg+ixofD2Bvh+dgL9PzoIeSiKwvUtSTNC+/rUmk3l5eVwemwIvnUBkSODcF9dDtkXgxJIwFadh9s+dBvi8fRGxTqtra1IJBJGPzszqW1axiIYDMLpdCK1GnVBQQE6OjoQiUTQ2Di+GBIEAR9u/BAOnTgM71WpDTRmF0mSvtzb2/tvvb29raCo0lRRABySJOnL2TYYVzxxzj/PGMsH8OcAntZKmj8N4Kec88C0DXWuUfjo203/0FOLFmIeQeJpZggGg3jxxRcBAG1tbbjlllumtblrNBo1BInudAQDQeQFExDzrEnb6knJqbPt9JlggHqDVxQFgUDASHLWiXWNABywablGYrEDIyyCKvvoTDF5JA7rolHRJritqOgvNFqMpApIl8uFeDwOSZJgsVgQ/EM3wDnyrhvt3epuK0fs1DDCf7wIS7kLjuXepGP09vbCarXC6/WCeRnEAjsiHwzAfXU54mfVsgq2qnzY7PYk1yuV0tJSrF27Nus6IFk8JRIJvP/++1i5cmXSa6pXF0+loKAAgYB6WzMnpI/F9e2fwPX4RE7bziRtbW0XAfzpXI/jciEndco5HwHwAoDnASwC8GcA3meMfX0GxzarJCWMi5QwTsw/Fqp4OnbsmHFDmo/09PQAAJqamvD+++/j8ccfx8GDBzNOwZ8MmZyngM8PyByCJyXnya7nPGV3nvSbeqbQXfyMHxCZUdAx7uKIMwkFgnpernAooeSwneiyojTqNlys1PpR5kKZSjiB0J5euFaWpjXgLfx0PZwrS1D4p/Wj7r1GX18fysrKIAgCmMDU0N1JH5SIhPjZgJqjleLCTRR9xp2eNK730du1axf27t2btK25urgZs0jNJWxHXL7kkvN0G2PslwB+D8AKYBXn/JNQ26g8MMPjmz3MpQqozhMxDzHPtpuuG/tMI8syduzYkXbzmk/o4umOO+7A3XffjYKCArzwwgvYvXv3tBzfnPOk37ADPtVtEfNTxJNVAITRsB3nHOFwOGMxx0xJ47HOEdgqPUaO0HBEPU9eQj2/Ek4ASvJ5BZcFlijDokVqccdMYTtAFU/Bd3rA4zLybkwPiwl2C4o/txyO+sKk5ZxzdaZdxehMNOfKEkDmiBwZROzsCGxL8pJmHU4GQRBQWlpqJI2//PLLOHLkCKxWK06dOpW07VjOk06uzhNxeZKL83QngO9xzldqBS0vAgDnPAzgSzM6ulmCc67OrGPJs+141jx7gph9dMdJluVxe5vNF2IxtYjiyMjI+BvPET09PfB6vXA4HFi0aBG+/OUvw+v14ty5qfdWVRQF8XjccJ5EUYTL5ULQrzpxYqrzxBiY3WIkU8fjcciynJbzBKQ7TzwhI34+AFvNqADQ6zblRdTzyCNagUzTefU6U1WL1DBcNvEUGgki+HY3HMu8sFZkdon0Pnxm9CRuc56SbWkexEI7wvv6kLgQgq06P/VQk0IXT7t378Y777yDVatWYfXq1Th//nxS3lYuzhOJJ2IschFP/wOA8bORMeZkjNUAAOf8dzM0rtlFE0mjdZ705Qvj1z1xeWAO1y2U0J3emmQ+h+0uXLhguC6A6mAUFhZOi+Azt2bR8Xg8CIxo4qkoPb9HsI82BzYXyNSx2+1wOp1p4il+LgDIHPaaUQEwODgIBganXwsHBkcLZBrnc6l5Vlc3r8SNN95o1IPS0XOFRjoGoIQkeD66OOtz/d73voc333wzaXlvby8AJDlPjDE4V5Yg1uEHFA5bVXL17smiz7j7zW9+g2XLlmHdunVobGwE5xwdHWp3Dr1UxFjOk9vths1mS1tPEDq5iKefIbnWgawtu3TQRRJVGCfmMZFIxJgdNF3iSQ7EEb8QHH/DSaKLB31q+HwjHA7D7/cniScAyMvLm1bxpDtPgHpjDgWCYHYRYmG6eGJ20SiSaS6QaSZTrafYGXW8ZvE0NDSEfIcHGI6DS0rmljAuVUjlWzy48cYb0/om6uceuTAEZhWSCl+aOXv2LGKxGN55552kGXPmmXZJx71itMedrWp6nCd9xt2SJUuwYcMGCIKAyspKOJ1OnDx5EkDmGk86DocDNpuN8p2IcclFPFk458YnQfv7kpLkus2cVmF8geSVEJcHkUjE+FKfLvE08koX+n/4QVL3+ulkvjtPer7T4sXJbkp+fj6CwSAUZWrXRc9TS3WeQrEwrBXujA2eBYdlTOcJyFzrKdbph6XcZYghQHWevHmFAAckXzSpr51xPm17JZw5FKyLp+BFP2zV+Vnbj5w5o7ZpiUQi+OMf/2gs7+3tRVFRUdosOusSD8QiOywlToju5FmHk6Wurg4333wzPve5z8FqVY8pCALq6+tx6tQpKIqStcaTzuLFi9PeDwSRSi7iqZ8xZkx/ZIzdDmBg5oY0BxjOk/aYnCdinqEoSlJz1+lznhLgURnx8zPjDOniKRKJZM3TihwaQPTU8Iycfzx08WQOKQGqeFIUxRAvkyWr8yRHYSnPXA6B2UUj52ks58nv9xs/8LjCET8bSHKdOOcYGhqCt0TNYZIGo1ACcTC7aCSUA4Dg1sojhJL7zemIogi73Y5wMAR7XWbXCVDFU01NDZYuXYp33nkHsqwKwL6+vox1mRhj8H62GYV/1pD1mBPFarXi+uuvT7teDQ0NCIVC6O3tHdN5AoDNmzdj3bp10zYm4tIkF/H0FQB/yxg7yxg7B+CvAfyXmR3WLENhO2KeE4/HwTmfdvGkRNQbZuykb1qOl4ouHoDsoTv/rjMIvHp2Rs4/Hj09PSgsLEy72eblqTk4Uw3dZcp5cluckKEApZkNfMGRnvOUSTzF43HjfZDoDYHHZNhNyeLBYBDxeBwli9TwmDQQydgSRnee5CzOEwA4LQ5EWSKreAqHw+jp6UFtbS0++tGPYnh4GEeOHEE8Hsfg4GCaONWx1xakzc6bCRoaVIF26tQp432YTTyJophWfJQgUhn3HcI5P805/wiAFgAtnPM1nPNT4+23kNDrORlhO0Z1noj5hX6TnG7xxCPqDXOmnB+zeMoUuuMKh+SPGbPAZpuenp60fCdgdNbVVMONetjO7Dw5EqrTE8ti4gh2i1HnKRwOw2KxpCUvp9Z6indqhSZT8p0AoGRRGZhdhDQY0VrCJIfImFUALAKUcGbnCQAc3IqoIMG2JHNid1dXFwCgtrYWTU1NKC4uxltvvWXUXMrkPM0mHo8HixYtwsmTJ8cN2xFELuQkrxlj6wFsAXAfY+wfGGP/MLPDmmX0tAbdcdLrjVCpAmKeoIulvLw8iKI47c5T/Gwgqar1dDGeeFJCCUDiExJPQ0NDOHDgwJTHFo1GMTQ0NKZ4mgnnyR5Rv3ZjzsxfMCxltp3L5UrLjTLXeuKc49SRk3jFdQi/fv03Rp0jc5NfS4lTC9sl0psRMwbRZVFfiyzY4gLiNnnMfCer1YrFixdDEAR89KMfRW9vL95++20Acy+eANV9On/+PAYHBzO2ZiGIiTBuexbG2FMAXABuAvBvAD4DU+mCSwHDedK/oFjycoKYa3Sx5HQ64XQ6cxZP8XNjV29WwhKsi9xI9IQQOzMC5zJvxu0my3jiSR5W1/OYDCUmQbCP327z3XffxTvvvIMVK1YYzW4ngz6FPpN4crlcEARhyuIpU8K4fUT9ggnFM7+GzC6Cx2VwJb1Apo7uPH3wwQd444030NPTA6doR/fhIezfvx+tra0A1GTpgoICDBc7EO8OQgkm4PCkzyQTXNasCeNyMA57TMCwK7u4PnPmDKqrq43XY+XKlfj973+PI0eOwGazzYuaSY2NjXjzzTdx7NixtLY2BDFRcnGe1nDO/wKAj3P+PwGsBjB218WFRkrOE6OcJ2KeMVnx5HvxFPw7z2RcxyUFPKGofcgsQsa8p46ODvzgBz+YdOJ0LBaD3W6HIAgZxZM0HDX+lv25uU/6FH1dmEwWPVk8k3gSBAF5eXlTDtvFYjEIgmDM/AIA26DqOGXLARMcWnPguJzWmkXH5XLBarXi6NGjiEdj+FhiGf7LjZtw77334qMf/SiOHz+OQ4cOoaioCKIowlLshDwUBY/JEPLTc60EtyVr2C52ZgR2bkNEjmVcHwgE0N/fj9raWmOZxWLBRz7yEQCq6zQfcogqKyvhcDiQSCSy5jsRRK7k8rNN/4YKM8YWAxgEUDvG9gsPmm1HzHN0oeB0OtO63I+FHpYba52Yb4O9Nj9j3tOJEyfQ39+PPXv24Oabb57wuHXx5HA4xnSeAEAeicFali4UUtHFUyQSmdJN8MKFC8jLy8t6DL3WE5c5Iof6YSlxwVY5sfPprVmMPEpJgTgog9lYVkGqu29KVEY4HE7rNQeoLvkdd9wBxhiWRorg23ECrjovbG43PvGJT2DNmjV49913jdIWlmKn2kUB6VXNAdV5SvRmHk+sYxhOwYaElEAikUgSggDQ2dkJAEniCQCuueYa/OEPf8CSJUswHxBFEfX19Th8+DCJJ2LK5PJz4FeMsUIADwF4H0AngJ/O4JhmnbSEcYESxon5xWSdJx6Vsuay6GEawWmBo6EIUl84LfdId2f27t2bFILLFV085eXlZXRaksTTBJ2nXAVkNnp6esas55Ofnw//gA99j+zD0E+Pw/+fnRM+h7kpMAAk+iMQFMBld2Z1npjuPMUkhMPhjM4TACxfvhzLli1DvCsAZheTWqa43W7ceOONuPLKKwEAlpLRMYh56TWVBJcla9gu1uGHu0TNAct0zc+cOQOHw5E2o87hcOBrX/sabrrppozHnQv0WXeULE5MlTHFE2NMAPA7zvkw5/wFANUAlnHOL62EcZ6lVAEVySTmCZFIBBaLBVarNWfxxDmHEpOz3hR150lwWmFvKAQARE+Nhu4URUFvby8WL16MaDSaVPgwV8ziKXPYLmZU2dYLOI53PP25TyVpPh6PY2BgIGPIDlBzxSxnYhgZCYBzDku5C7J/4uLR3BQYACTN3XF73NnDdnZVPMVDMcTj8aziyRhr5whsVWM31rUUj9aUEvIyhe2sUMJS2g9GORiH1BdG3iLVwcomnmpqajKG5vLy8uZVm5OGhgaj/Q5BTIUxxRPnXAHwr6bHMc65f4xdFiRcTnaeqDEwMd+IRCJGj7GcnSeJAzIHj6u5TanoOS6C0wLrIjcElwUxU+hueHgYsVgMbW1tqKqqSip8mCvjiSd5OAZLmQvMIeYkTswtSaYinsZKFgeAwZ8cgTNmgcRkFH61FY76wkmJpzTnqTcEiAx5hfnZnSdNPIX840+pV6ISEn0h2MdprCt4rGBaYczU2XaAVuuJq05l0vg71K/7/Gq10GbqNff5fPD5fGkhu/lKXl4evvKVr6CtrW2uh0IscHIJ2/2WMbaBZeojcKmg/9gy6jxpjylsR8wTIpGIcRN2Op2QJClrxW4dc+mBTO6T4Ty5LGACg72hENFTw0bVanNC9Uc/+lH4/X4cOnRoQuM2i6doNJo2Znk4BkuhHWK+PadyBdMlnsZKFldiMuSROIqb1XWBUABCvg08Kk+4nEOq85ToDcFa6oLH4xkjYVzNeQoG1PVjOU/xrhGAJ9d3ygRjDJZiB8BUlyntnFpzYDmcLp6YTURBlSqeUp2nbPlO85mysrJ55YYRC5NcxNP9UBsBxxhjI4yxAGNs6h0z5xOpFcZFShgn5hepzpO+bCz0WkFA+k0RMIft1Buno6EIykgcUr963J6eHgiCgLKyMjQ2NqK0tBRvvfXWhHo+6uJJT9A1u088IUMJJSAW2iEW2GZdPLndbqOSuBlZmwFYUFxojNlSoIUWc8zL0snkPFkrVPEUCoUyXkvdeQoHM/e1Szp+1wggALal4zfWtZQ6IebZRh12E7qgShXZsQ4/bDX5cHnUMaSKpzNnzsDtdqO0tBQEcTmRS4XxPM65wDm3cc7ztcfT0wJ7nkAJ48R8JxqNTlg86VWqAWRMGlciEsAApjkdRt6TVrKgp6cHZWVlsFgsRuHDixcvGt3pc8HsPAHJ4knSksVFzXlSRnIL21kslgnNOMyEXlk8k6GuJ7EXlKt5PiMjIxALVKdioqE7s/OkhBOQ/XFYF7nh8Xggy3LGcgt6zlO21ixm4p0jsC7yGPuMRcGf1MD7uWUZ14l6c2DT+0QOxCFdDMNRX2C858zXnHOOM2fOoLa2NuN1JIhLmXHFE2Ps+kz/ZmNws4YukvTPPyPniZhfTM55GidsF06AOSzGjwWL1wGx2IGYFrpLbV3S2tqK/Px8vPXWWzmNWVEUxOPxrOJJFymWQgfEfBvkQBxcUc/b19eX8Zh+vx8FeflwCLZJO0+JRAIXL17Mmu+ki7rCRWqJAFU8ac7TBCqhK4qS5DwlelXhYalwG07cwEB6j3WmlSrQhUo254nLCuLnkpsBj4Wl2JnU+86MHrYz13qKHlPbu9jrCiGKIhwOR5J4unDhAgKBwIIK2RHEdJFL2O6bpn9/D+BXAP5xBsc063BqDEzMcyYjnpKcpyw5T3rITsfRUIhYhx9+vx/hcDhJYOiFD7u6ujLe9FOJx1WhMZ54Up0nGxKKjF2/2omtW7fi5z//ecZjDg8PwxWywDLCER6ZXOHOgYEBcM6ztgyRh2OAANiLXHC5XAgEAhDz9bBd7s6Tnt+lO096HSVbhRt1dXVwOp34zW9+k5aEz0QGZhUQjoYhCEJS2C/p+BdC4All3HynXEgN23HOEXzrAqwVLliXqEIv1e175513YLfbsWLFiimfnyAWGrmE7W4z/fsEgFYAmX8WLlSyhu3mbEQEYaAnh08l50kJpec88YhkOA46Fq8TPCaj5/wFAOkJ1Xotn2zJzmbMfd30XmJpYTsGiAU2nI9exC9su7H3j+/C6/ViYGAgY0K8b3AI7rAFDm5FaHj8MRjnGowYP5J04ZctT0cejkHMt4OJzCiUyawCBLdlQuIptSlwojcE5rRAyLfB7XbjU5/6FLq7u/HOO++k7cvsIiKxqNHXjicU9D70Lvp/+AGiJ3zgnCPWqc6Es1dPvdUIs4uAwIz3Sey0H4neEDwfrTRCcmbxNDw8jMOHD6OtrS2ruCOIS5nJNIY6D1VAXTqkzLajOk/EfEIXSebZdubl2Rh3tl043XnSCzReOH8BjLE0d0Z3UXIpmKlvw3pikP2xtEKZ8nAMYp4Nb/zhTbz6+qvIhxOfu+kOJEpE/OxnP0urwxSLxhCJRZHvzANnYQyFx3e/ACDeE8LF778Pa4UbBetrDfHk9Wbu4ycNR43aU/n5+UZ/OzHfPqGE8dSmwGqyuNsQI62trThy5AheffVVNDc3J4k5wWFBOB4x8p1iZ/yQBqOQgwkMbDsE62I3wAHRq4Y8pwpjLKlQZvAP3RA8VriuKjO2cblcxrXYvXs3GGO49tprp3xugliI5JLz9Bhj7FHt3+MA3gQw9Zbm84j0hPHk5QQxl5hbswCAzWaDIAg5h+0EjzVj37JMYTv9cW9PD4qLi9OmdE9GPMXe7kPg9fNptZ7k4SiEAhveeecd1FfX4o74tVhsLzEEW2reU9+7ao++spVV8JQXICrHIQ2N398ucUEVbHIojoH/cwgX3u1AYX5BWpuR0XGp5RMAVTzpYxYL7IbzNDQ0hP7+/jHPa3aeuMKR6A3DWjGa/M0Yw/r162Gz2fDiiy8mhe+YXUQkETXEU/T4EGARsOhvVqFoQyN4XEGiJ5RzvlMu6M2BE/1hRI8NwX3tIjDr6C1Cd54ikQjef/99tLa2UoNd4rIll5yn9wDs0/69A+CvOeefn9FRzTbZcp5kEk/E3GNuzQKoN91cCmXymKyFxeyQM862S6jFEU3oNYZ6+/syJlRPRjxZuQXxs4EM4imGgDuBaDSKlitaYRFEyP44vF4vLBZLknjisoKeP5wGAJStXIq8JV5ITEbgg/EzCKT+CCAyVHzzwyj4VC2GwsPI81mMApBmuMIh++MQC1WXLy8vD6FQCJIkaeUU1Of0y1/+Es8//3xOz99ut0MejoHH5aQWKgDg8Xiwfv36tPCdYBcRkWJGsnj0uA+O+gIITgvcH65A+f1tKPnLVhR8cvqStQWXBXJIQvCtC4DI4PlI8uuvi6d9+/YhHo9j9erV03Zuglho5CKefg7g/3LOn+WcPwdgN2Ns/O6dC4lss+0obEfMA1LFk/53LuKJ2S1a641k8cQ5z+g8MYeICOIIhIMZxZPuRE1EPNlgQaInBI/bY4gnrnBI/hj6BTUMtGTpEogetdaTXlvKLJ5C7/bCH1S3LSwqhNurJqD7PugZdxyJ/jAsXgcEmwj3xxbDb4mgAC6jJIMZJRAHFJ4UtgNgJI0rIQnRYATnz5/H4OAgfL70Y+jozpPdbkeiR00Wty5Knzm3YsUKLF++HK+++ir27NmDeDwO5rAgosTgcrkgDUQgDUTgaCoy9mECg6OxKGO18MkiuK2Qh6II7+uD66qytGPrxVnfeecd1NbWZp2tSBCXA7mIp98BcJoeOwG8MjPDmRuMsJ1oShhnFLYj5gfZxNN4dY6UqATBIUJ0WdLCdjwmAwrSw3YOCwYFVeCMJZ70mXRjMeo8iYDC4ZKtiMXUfm1KKAFIHH2JIdhsNpSWlkIosBvOjlk8KXEZI787i0ihAlEU4fF4jGsR6vGNG7qT+iOwlKq/90ZGRiBJEryuQkgX06+fUXuqKIN40soVnDl2yihu2dHRMe7zt9vtCL7VDeawpDlPwGj4rrKyErt27cIjjzyCd0eOIsYTcLvdasgOgKM5c47WdCG6rJD9MfCEgrzrKtPW6yHEUCiENWvWzOhYCGK+k4t4cnDOjSxP7e9L03kyV95lDKDZdsQ8IJN4crlcOSSMy2B2UXWeUsJ25r52ZgSHBQNMFU/6zDozjDHY7facnCddYDnz1a8LR0Q9VyAQMMoU9AYHsHjxYgiCADFvtMp4eXk5QqEQgsEgQu/0QAkkEC1lKCgogCAIxrWIIoHIoeyJ41zhkAYjsJSq2+vJ4sXeEiT608WTXl1cz3nSSyyYC2V2nD4Di8UCj8eD06dPZz237jwpxwKIdfhR8MkaCLbMxSw9Hg/uuusu3HXXXaisrMSegYMA1Nc5esIHS4kTlhJnxn2nC33mpb2hMKPI08VTWVkZGhoaZnQsBDHfyUU8hRhjV+sPGGNtACbfF2EeYjhP5iq5AiPniZgX6CLJ3CMt17Cd4LBAcFnBYzK4NPprwNzXzozgFDEoBFDgyEsSa2ZyFU/6Nu4aL0SvA3atqVMgEIA0HIMEGReHB7BkyRIAaskCfTabOWk8cmwQ1koPRhIhFBYWAhi9kcslFoQPZhdPsi8KyBzWkmTxVLa4DNJAFFxO/oVk1J4qSHaezIUyO7u7sHTpUtTX1+PMmTNQlMy/smKxGBhjCP/mLGzV+XB/OF2MmmGMobq6Gps2bcLnr7gNV8o1WN7YjOhpPxzNRWPuOx3otZ48H0t3nQAYyeGrV6+miuLEZU8u4uleAD9jjL3JGHsTwA4A98zoqGYb/bvP5DwxAVQkk5gQr7zyStbijlMhGo3C4XBAEEY/rrmIJyUqac5TevVoJaI6UYIzZcaZRcCAEECZK3uIKFfxFA1HYeEC7OUe2JbmwX5RnU2mO0+DLACFK6PiKd8OHpWgxOVR8dTbh8T5IOzV+RgeHjbEky7slMV2JM4FIPkyh+4SWp8+S5kqtgYGBuBwOJBX6QUUDmkweT9pOAbmsBiJ8w6HAxaLRQvb2RBBHP0jg6itrUV9fT0ikYjRZDjt+UejsAlW8JiCoj9ryNhTLhtl3jJ8OFEPS3cCkJQZD9kBgPPKUhSsr0vKrTKzaNEi/NVf/RWuuuqqGR8LQcx3xq3zxDl/lzG2DEAz1JTqY5zzsdu5LzQyhe0ERuKJmBDnzp3D+fPnIUkSLJbJlFDLjLm6uI7T6UQikRjzXDwmQyhyGDPqlHDCqAmUzXmKRqMIsAiusBVmHU+u4iniD8EKCyxlLjCHCPsBAXCoBTblYRcuWtXwYGWl6nToY5NH4nCXqC1Meju7UZWoAFviROj9UJp4kkvUMFjk4ADyrl+SNga9ybHF5DyVlJTApompRF8Y1rLRLARzmQJAdYP0Wk+C3YJeuzpDr7a2FkVFqsjo6OhAficQfq8Pno8uhuuqMjCLgPBAANaEgLzrKzOGwcZC0OpthT/oB7MKsNfOfEkAS4E9Y66TDmPMeK0I4nInlzpPXwPg5pwf4pwfBOBhjG2Z+aHNHnryJ0tyntiEuscTRDgchizLWfuyTZZs4klflw0lquU8aeLJXK4gW85Tb28vAKDEUpj1uDabLaeE8WggDBu3wFrugm1pHmywwCKIRthuwBZEQUGBkVdkCDstaby8vBx9veq1jBSon0VdPOm1rmJMgrXSkzV0Jw2EIbgsELWQlC6edCcqNWlc9sWMZHEdc6HMHpsfVmbB4sWL4fF4UF5ejtOnTyNyoB+J3hB8Pz+J3ofeQ+CtbgTP+mAXbci7uWrca5UK0xr9Ro8OwV5fmFRviSCIuSeXT+Rfcc6H9Qeccx+Av5qxEc0FhvNkWkbOEzFB9Nlv3d3d03rcyYonI+fJ6FtmDtupf7MU8aSPvQR5WY+bc85TKKo6T8UO2BZ7wEQBbqvTCNtd5MNGyA5AWvPd8vJyDAR9gMeCgKJeWz3vRq91FQ6H4byiBIlzAWOmnpnExdGZdtFoFMFgECUlJRBsIsRCe1rSuDQcM8oU6JjrU3XzQSy2FkMUVXFTX1+Ps2fPInRhBJ41i1Fy1wqIRXb4f9WBWCIGV4kna5L4WAiaeOIJZVbynQiCmBi5iCeBmbIDGWMigOkrLjIPSK0wDkATT3M0IGLBwTk3hMx8EE9c4eBx1XkSXXrOk8l5ikiAhSU5Goqi4I9//CPKrEVwJDJX3wYmkPMUjcJutYKJAphFgK3SA5diRyAQQMA3goAcTgoDGWE7LWm8rKwMMpcRWcQwPDwMYNR5AkZnHDoa1GWZil5KA+GkkB0AlJSUAFDzoKS+UfGkRCXwqJQUtgNGnafh4WH4pSAWyaNipq6uDoqioFcZhG1pHhzNXpR95UqU3r0SSpEFziLPuNcpE8w+KmpnI9+JIIiJkYt4+k8A/48x9nHG2M0Afgpg18wOa5bJkPPEGM22I3InFosZs67Onz8/rceORCJpzVfHFU9xrTWLQ0zKeTLWa33tzLOmOjo6MDg4iCuLmqBE09u56OReqiAGu2nctqV5cMQsCIyMoC86CABJzpPgsIDZRMNBKs0rBgD48+Pw+/0QBMEI8enXIBKJwLrIA2YXETuTLJ6UqAQlkEgrU6CLJ2uZC4n+0YbBeuuVVOcpPz8fiqLg8OHDAIBFkXxjll51dTVEQUS3MATrktGx2esKEGfSpJvm6jlPllInLF5qvEsQ841cxNNfQy2U+VUAXwPwAZKLZi58Msy2g0hhOyJ39JCd1+vF4ODguDPhckVRFESj0Qk7T0ZfO7sFzCqA2QQooeTZdqkz7fbs2QO3243GkhrwyPjiaaycQC4piMkJ2F0m8VSVD5diQ2AkgIuCHwIT0gpxivmjtZ7yQzYwzjAkhjA8PGzUeDJfg0gkAiYy2Gvy08STnixuNYknQRCMRG9rmQuQFLWcAQDJp4unZLGiC7YPPvgATqsDXsUDOaAKUavVisWuUnRbfGkiJxaLJZWXmAh6zhO5TgQxPxlXPHHOFQC7AXQAuAbAxwEcneFxzSqZ6jwxqjBOTABdxDQ2NgIALly4kLbN7l+8hkf+50MIHx/M+bjxeByc84mH7WJaTpPmYOhNX3WUsJQ0025wcBAnT57ENddcA5vLboivTORSZVwaiCABCU7P6Ew2W1UeXNyOuJTABcGHMm9JWnNes3iSu8MogAuDEV9SmQLzNdCfv622ANLFCOTg6JgSA9pMu9LRMgVer9fIV7KUqddQL2eg13jKFLYD1JpTVRVLwMAMlwoAKhUvfAgiEBzt28c5N0pMTAaL1wHXNeVwp/SXIwhifpBVPDHGmhhj/8AYOwrgcQDnAIBzfhPn/PHZGuCsQKUKiCmiO0965eVMobt9R/ZjmIdw7pn3EXj9XE6zOTNVFwdU94cxBt/+bkRPD6ftN+o8aeIppcp4al+7d999F4Ig4JprroHgEMHjMniWxti6mzKWeIr3hRCHDEfBqHgSC+3wONTH/cIIllSmlxYQC+yGMIl3jaDEUYi+/osZxZPeqBaAMZU/dmbEWC/1hwEBhiM0ODhohOwAGCUK9Bl38nAMEBiElJ5uungCgNoatRGvPkYuKajwq3lN5lYtiUQCnPPJO0+iAO9nmozingRBzC/Gcp6OQXWZbuOcf4xz/hiA7D9HFzCcZtsRU8QctispKUlLGu/v6EG/NAwAiDfY4d/ViaHnjkKJZQ+PyYE4en6qtulIFU/6bLPAhWFEjw6l7ctj6keVacUehZT+dmbxFIvF8Mc//hEtLS3Iy8sz9uFZxqYLgrHynqK9AXDG4SwarW/EGENB2Wiy9ZLa9Cn8Yr4NciAOLilIdAdRVlyK4eFhBIPBjM6TJElIJBKwVXrArALiptCd1B+BxesEswiQZRmDg4MoLi421gsuKwSPFYk+XTxFIRbY0opZut1uw5Wub65Xt9XcsURvCMWyBy67M0k86a1ZJus8EQQxvxlLPG0A0AvgVcbYjxhjH4daJPPSQ+EASwnbUXsWYgLo4snpdKKyshLd3d1JztKBP+wz/lauKUDBp2oROTKIi08cgBLP/Jsk/H4fAud9xnFTcdodiLEElGC6A6SLMsN5clkhhzM7TwcOHEAsFsO1116rbquJp2yhu1zEU7hPdYAcruRxFy4ZdX6WLE13noR8GyBzRE8PgycUVFSPzsbTyxTomEOXzCLAVp2c9yT1j860Gx4ehqIoSc4ToLpPklauQC1TkC529GbE+fn5KF5cBmYVRt2x80EwMNTW1OL48eNGSQNzU2CCIC49soonzvkvOeftAJYBeA3AfQDKGWNPMsbWztL4ZgfOk0N2gPqYtBORI5FIBIwxOBwOLFmyBKFQyJheDwDHuk6iWFTDP8PDw8i7fgmKP7ccUl8YkQ/6Mx4z/MeLiEEVPJkcDIfNgRikpOKXOlwTPnrisei2GgnjXFbUGlAuKzjn2Lt3LxYvXmzMfBOc6j5KlqTxnMRTvyqe9PwonaL6MvUYzJrkAumI+eqxI1rRy8rl1ca6TM4TYOr9V1uARG8ISjgBrnAkBqJZZ9rpWMpcSPSFwTlPqy5uZtmyZWhra1MbGOfbTOIpAMFlwY233ARZlvHrX//ayHcCSDwRxKVKLgnjIc75c5zzWwEsAbAfwN/M9MBmE67w9L5T5DwREyAcDsPpdEIQBKN2kR66u3jqAgZkP1prl8Pj8RiiyrGiGJZSJ0J7e9OOF+8JIdEbRoypwiij82S1q85TBvGkxFJynlwW8KgELvOk1iwdHR0YGBjAtddeazivzHCeJieeuMwR8YWSttXx1BbDwgWUO4szNpcVC1SxFT0yCDHfBu/SUuMY44unfIADsc4RNX9JUsYVT9YyF3hMhuyPQx5JL5Cps379etxwww3aGO1GLapEdxDWJXkoLS3FzTffjOPHj+ODDz4wrg2F7Qji0mRCNf8550Oc862c85tnakBzgoI054kxUM4TkTPhcBgul5qAXF5eDovFYoinD956HwCw8rqrUVBQYIgnxhjcqxYhfjaARG8o+Xh/7AMEhpigCphM4skh2rSwXSbnSZttpxVbNKqMRxKj4slpwYEDB+B0OrFixQpjXz1sx7OIp/Fm20m+KOKKOqZU8STaLfhI3Yew+iMfybiv7jwpYQm26nwwxlBeXp5W4wmAcb31kKltaT4gMsTO+CFpM+2sJaMz7dxud9p11Nu0xE4NA0p6jaeMY9SS2nlCRqIvBFulmjD+kY98BEuXLsWuXbsMsUbOE0FcmlDDJEDLecoQtiPxROSI7jwBao7MokWLjBl3x86eQLnFi+LqchQWFiaF81xXlwEiS3KfuMIR3t8PR3MREnYOkYlpU/oBwC7YEEMCciiRNnNPiclqfSdRfV/rZQmUUMJIHGcOEWfOnEF9fX1Sc2G9QONkc56ki2EktLklmcTDLV+4DcuvvyrjvmKe1cistFWpYqmxsVEtRikmtzlJdZ6YVYBtaR5iZ/xG2xWz85TqOgGjM+6iJ9Ske0vR+E6RWKCWU4hfCAEKYNOKYwqCgNtvvx2SJOH3v/89AHKeCOJSZUbFE2NsHWPsOGPsFGMsa6iPMfZhxpjMGPvMTI4nG1zhYCntpyhh/NLH7/dPW/PnSCRiOCEAUFlZiZ6eHlw4fhYD8giW1zYBUENPfr/fqEYuuq1wXlGC0PsXjcTx2OlhKCNxuD5UhpgowSFkbpVihw0JJkORZWN2nQ6PyUaNJwCmKuOS4TwNJ4IIBAKoqalJ2neqYbvExTDikJK2zRUmCoZLZqtSc8Suu+46fOELX0jbNlOtK3tdARLdQSTOB8EcIgRPckPgVIQ8K5hDVJ0n5O48QeGIHlMFl23JaAuWkpIS3HzzzYYrR84TQVyazJh40nrg/QDAJwG0APhzxlhLlu2+A7UNzNxAztNlx+DgIL73ve+hs7NzWo5nDtsBqniSJAmvvqw6ECuvbwOgiidFUYxZWQDgWVUBHpWMJOnwHy+C2UU4l3sRZxLsWVpJ2rlWagBSWuhOiUoQTP3RDPEUGg3bnRtSC3mmiicjbJclYdxisUAQhDGdJ0mLjk1GPIgFdkBkRjgsG1arFaIoJoun2gKAA5FDA7CUusAYQygUQiQSySieGGOwlrkMN05vTjzm+PSk9iODEPKs6gxBE3r4ThTFtIR5giAuDWbSeVoF4BTnvINzHgfwPIDbM2z3dQAvALg4g2MZk6wJ43OgnSRJmrYbOpGdoSHVNTCLmPGInw8YfdfMcM6TwnbAaM+2kwOdqLB64V1aCmA06dnvH51Sb6stgKVETRxX4jIihwbhvKIEzCoixiTYMSqCzNgVTTyxRNqMuzTnyT3qPHGtZEFX73l4PJ60WW9MZGo7lyxhO8bYmP3tEhfDkD3q52ky4slW6YGjsQjMMvbXk17ryiyebNX56mc3ocBa4oTP58OOHTsAAIsXL854HD3vSXBZjAT7sdCT2qW+MGyVeWmJ74IgYOPGjdi8eXNSOxmCIC4dZvKTXQmtKrnGeW2ZAWOsEsCfAXhqrAMxxu5mjL3HGHuvvz/ztO4poaSXKmBz5DwdOXIEzzzzTFJeDDH9BINBAGol6FyInR3BxScPYOSVs2nr4vE4ZFlOcp4KCwvhcqhianltc9JyAEmvr5o4XoF41wgCr50Dj8twfUid0h/jcdjkzOLJJqk3+hjSk8aVmJwkBPScJzmsOk8cHF3nulBTU5Nx1htzWCbVHJgrXHWeHKqIMOdS5UrRHY0o/kKaSZ0Rc5VxABBsohFGO8kv4KmnnkJvby/+7M/+DNXV1RmPoec95RKyA5LdKXPIzozb7U5z9AiCuHSYSfGUqaBmqhp5BMBfc87HrFzOOf8h5/wazvk1paWl0zW+5FFlqvOUpT3FTKI7IaFQaJwtiamgX99cxJMciGPo/x4FZA45w8w23fkwiyfGGMpdJQAHVt7QZizPJJ4AwNVWDogMgVfPQSywGe1GokocdlnMmJtll1RhEs1QroBHZWOmHaCKCmYVoGjiacQRQzAYRG1tbcbnLDgsWWfbAeqMu0yz7eSRGHhcgWTnRguZyZDrfqnOEwAI1R68aj2EXcdeR1lZGb761a/iyiuvzHoMiyGeckvuFtxW4/vCuiRvnK0JgrgUmfjPwtw5D2Cp6fESAKndUq8B8Lz2RVkC4FOMMYlz/uIMjiuNTGE7xjBtycQTQf8VrRfZI2YG3Xkaqz8boNYsGvrpMchhCWKBLaOg0F8zs3gCgA95GlE+4kZRpamfmtUKt9udJp5EtxXO1hJEDvTDdVWZ8X6MyXHYuFULwyV/XG1x9bePWigz+XkoMQnWlBCU4LKohTIVjl6rH0ik5zsZ2zrEMZsDZ3OepIuqkElYlFlJlnY6nUYIVqfTMYDTYh+uu/ajuHHtzWmz9FLRnadsBTJTYQJTC2UOx8bNyyII4tJkJsXTuwAaGWO1ALoBbATwOfMGnHPjZy9j7BkAv55t4QRAC9ulLBPnJmxH4ml2yDVs5//NGcQ6/Cj6bBMiB/ozOk/m1ixmFsGL8sJ0ZyK1XIGO56OLETs9DNc15QDU/LeELMHO1b50Qop4skY1gWVJTxhPzXkC1KRx3aHqYT7k5eXB6/VmfN6C05KxcrmO3W5PCpfp6CUCEmz2xFOq83QhdBEOhwM3/cnHc8o5EgvtcDQXwd5cNO62xj4FdoADYh4lhBPE5ciMiSfOucQYuwfqLDoRwDbO+WHG2Fe09WPmOc0mPNNsO0bi6VImF/EU/qAfwTe74V69CO6ryxE97oMyEEnbLlPYDgCUcMKY5WamsLAQPT09acvtVflY/N9Hi0calbNhzdgqxRJRq4zvl87A3V2Ajym1EAQBnHMoUTlpth2ghpuUcAIcQLc0gIbmpqzhMeawgA9mfw/a7Xb4fL605VJ/BMxhQVyOz5p4CofV9ir6czl79iyWLFmSc7I2ExhK7mqd0HnzblwCnqUnIUEQlz4zOhWEc76Tc97EOa/nnP+ztuypTMKJc/5FzvnPZ3I8WckUtpujOk+6eEr9NT2fUcIJDP38hNESZCEwnnjiCofvF6dgq8pD4fo6AGooayJhOyUsQXRnFk96o9qxMMQTt0AJpzhLMgdiCj678lPwWvPx+9538cwzz+DixYuApKjv6TTnSXWwhoLDiCixMROaBYeYtbcdMEbYrj8Ma5kTsVhsVsSTy+WCLMvG6xgOhzEwMICqqqoZPa9zeTFcV5bN6DkIgpi/0DxaQHWYxEx1nmZ/KAvReYqeGkb4vT4kuoNzPZScGU88yYE4eFSCq63cmDIvOCxQonJaLpz+mqVWk1ZCCWOWmxm91pM+hmx0dXWp23N3mpDRZ8KVFpfgjsU34UbXVejv78dTTz2FQx8cUseblvOkOk/dUbUqyNjiafzZdpnyxRL9EVhKXbMmnlILZepV3ZcuXZp1H4IgiKlC4glawjibX87TQhJP8oh6E+XSHKjNSZBIJIzrm1U8+dT15nYdzGkBZA6eSH6e4XAYDocjKTGZSwp4TDbqK5nJNuMulYMHD6KkuARe7jGKOOroTpTgskLMs6FJWoR77rkHbrcbR48eVcfryBC2i0joTgzCY3NlzXcy9s3wXHX02XZm90yJSlBG4rCUzp7zlCqezp49m9ScmSAIYiYg8QRkKVUAzHaVTFmWjZvAwhJPaviGJxZG2M5cBiKbeJJ86nMSi0YFgN7zjafMQkttzQKYxM0kxdPw8DDOnj2LK1qvAAODEkmp46Q5UcxlgehWE8FdLlUQjWjlLtKdJws45+gRhrC0aPGY5QBG+9uN3aLF7D5J/Voz3jl0ns6dO4eKigqq7E0QxIxC4gla/kjqlZiDIplmwbSgxJNfc56yuBTzDXO4LKvzNKQ5T6baP0KWnm+prVkAQA6p22RKGC8oUGs4jSWeDh8+DAC44sortPpMKc6TJp4Ep0UVaDIHj8rIy8tDMKw+P5YinkS3FcMshChLoKpsbGdGcE68v50+044V2yBJ0qyKp3A4DEmS0N3dPeP5TgRBECSeAIDPj4Rx89TvBSWeDOdpYYknt9udtc6T5ItCyLOBWUc/Itka5mYST3pJgEw5TzabLWOtJzMHDx5EZWUlvF6vkehthodN4klrfiuHEpp4CoGDZ8x56hHUGXI1lWMLDOO5ZkkazySepP4IIDAoHiFpm5lEv+6RSAS9vb2QJInynQiCmHFIPAEZ27PMRakCc+LxwhJPC9N5KioqGjPnyVKUfPPPFrZL7WsHjIbtMs22A7LXegKA/v5+9Pb24oorrlDP60wvVZCU86T3rQvGkZeXB0mWkEB6UU3BZUGvMAw3t6OwJHu+01jPVSejeLoYhqXYgVginrTNTGIO2509q7bOIfFEEMRMQ+IJWRoDiwx8lrWALp68Xu+CEU+c8wUbtissLBwz50ksSp49ly1sN9GcJ/3c2cTTwYMHwRjDihUr1GO40ksVGGE7hwWCR83vUUIJeDxqxesQi2V0nkZYBEWKG2KGcGIuz1VHzykyO3fmmXbA7Ignq9UKi8WCSCSCc+fOobCwEPn5+TN+XoIgLm9IPAGqw5Q6224OnacFJZ4iklpXCAsnYTwYDMLlcsHhcGQUT1zhkIdj6BX9ScnlmcJ2iUQCiUQiQ9hOz3nKXIe2sLAQfr8/rdYT5xwHDx5EbW0t8vLU6uSC05LBeZLA7CKYyAyBJgcTxj5hFjPcIx3BbUWIxeDijoy5WGayhSi5rCByeCDNeeIyhzQYMWo8AbMjnoDRQplnz54l14kgiFmBxBOg1nPKNNtuDsWTJEk5Na2da/SQHbCwnCePxwOr1ZrxGssjMXBFwS+O/Ra7d+82lmcKZWUtkBlKgDlEMDHzR6ywsBCyLKfVerpw4QJ8Pp8RsgP0yuDpCeO6MDPCdiGTeBLigCX53LKgIMLi8HC7kRCeDcGZZWbhkSEM/uQo0K2Ke10oSb4oIPNZd54AVTxduHABoVCIksUJgpgVSDxBD9slL9PDeLOZNB4Oh2G1Wo0b4EJwnyT/aM7LQhVPqUUv5aEYJCiQFRkjIyPGcmYTAZbsxmTrayeHE1lDdkD2cgUHDx6EKIpYtmyZsUx1npLHqYon9fjMKoDZxSTxFLEm0koRGInyzAFmG/ujbzzXFMdLuqg+X6VDPZYhnrTleo0nYPbEk8vlUiurg/KdCIKYHUg8AWo9pzTnSXs8y+JJDycBC0M8KVq+E9jCKZJpFk+A2oDXjOSLIgF1WVLYTmBgdjHJjcna1y6Uua+dTibxpCgKDh06hMbGxiQxJrgsgJRcsFIJJ5LcI8FthRxMwG63w8osiAjpswj9fj8AIM/mHrPGE6CGrVmGKuOS1ttPPqHWkjLEU0qNJ2B2nSf9fGVl1DKFIIiZh8QTNHcpm3iaxUKZ+qythSSe9DIFYr59QTRK5ZwjGAzC7XYb4ik1dCf7opCY+lxSw2qpbUvG7GuXJd8JyFzr6eDBgwgGg0khO0Cdbacf0zh+REoST6LHapRHcFkcatguBd1Fy3N4so4r6bwOMS1slxiIAALAAhIsosVIGE/0hyHkWSE4LXMmnibSDJggCGIq0DcNAMiZ6zwBsx+2W2jOkzwSh+CxgjnEBRG2i8VikCQpyXlKFU+SLwbZrX40zM4TMNrfTidb2E4JjR22s9lscLlchng6f/48fvWrX6GqqiopZAeMJp2bZ9yZc54ALS8qqK53MwfCSG/aqztP5dfWZB1X0nlThCLnHFJ/BM4VJQADrMyS5DxZS1UBqS/Tr+9Mo197ynciCGK2IPEEZA7b6WGNWdQDC1I8+WMQ89VikjMZtoud8SNyeCDn7Yd7h/Dys79Km82mO0kejyfjdHtAdZ6UvFHxZD4Gc4hJeUDZnaexw3bAaLkCv9+P559/Hh6PB+3t7Uk98gCtpx5G848451DCkuFIAVrYTneeYEeYp793RkZG4HA44L2hZsxxjT7XZPGkhBLgUQm26nzYavJhVQTEYjFwzpG4GIalVBUxemuW2XKB9GtP+U4Lj6GhtzAw8OpcD4MgJgyJJ2Su86QnkJPzNDbySBxivl1tIRKfOfEUeP08/L/pzHn7Pb/9A946sw/dx7qSlpvFU1bnaShqOE+KoiS9DoLDAm4SFJFIBHa7PbkpcEIGjytjOk+AKp4GBwfx05/+FIlEAp/73OfgdrvTttNFmB6243EZUHiS86SH7TjncHE7QnI0LRHe7/cb4cJcEBwieGTUZdPznSwlTjiXF8MqiYgGI+p5IxIsJudptkJ2AFBdXY3a2losWbJk1s5JTA9nzjyG0x3/OtfDIIgJQ+IJyFKqYHYTxmVZRiwWW4DiKQaxwAZmFWfUeVKiEpRY7jlV5wd6AAC9Pb1Jy/UwXDbxxGUOeSQG2TX6fjDnPQkOMWkcGfva6a1T3GOXA9BrPfX19eEzn/lM1mRnI2ynNQdWTK1ZjG3cNkDh4BEJTtkKictJ1b8B1XmaSAFJwZnsPOniyVrihKOlGFaIiAyHTMniyc7TbLFkyRJ84QtfoGbAC5CENIxYrG+uh0EQE4bEEzR3KXXy0SyLJ/OsLavVClEU57144pICJSQZzhNmsEgmj8ngOYonSZLQE1CnrvddTP5iHs95kv0xQAEUR/o+gBrK4ikJ45nynQCMW8W7uLgYAPAnf/InaGxszLqd0aRXE00ZxZOpv51LUv8OBAJJx/H7/RMTT44M4klkEIscsJY4YbfaEA1GjIbAc+U8EQuXRGIYicQQZDk9R48g5jNj/zS+XMgYttMSxmdptl1q7ozT6Zz34kkvkCnm28D6hSkljIf29sJS6oS9NnNYSdHEU8ZWOin09PRA4jIYB/oGLyatCwaDEAQBTqczo3iSfOo1l0z3fnPSuC4oOOdgjI3dmmUc8bRy5UoUFxejurp6zO2YVQAszMh5MlqzmMN2eqHMQBxOyQrYVPFUWlpqPMdIJDKhsB1ziEnXXOqPwOJ1gInq9XcWuuEbCCB+NgBYBIiFo1XHdfeUILLBOUcioU5iiMf74HRSwj+xcCDnCcjcGFh/LM+NeHI4HIYbNV8xyhQU2MEsApRJiicucwz/6jSCe3qybxPT8n1ycLf0BrFVSgn6/YNJAlgvUyAIQmbnSRdPluR9dASnCCijBUEzhe2M1izjhO2sVitqampyqrkkOK3guvMUSRdnen6VNBSFi9vTxq2XKZio8wQOowRFYiACS8moy+YsyUMcEsL7+2EtdRqilpwnIhcUJQLO1R9g0WjvOFsTxPyCxBPUX0DZnafZGUMm8TTvnSf/qPMk2CZfqkDqD4MnlLSaQmb08gBjbaPT1dmFAu5CpVKMaCKWVCVcL5DJOYesVclOdp5iAAMkQVZFiyBk7G/HNfcno3gapynwZDA3B9bDdixD2E4aHBVP5rCdXqZgYgnjo/3tuKL2rtNn1AGA0+tBgsmApCQtj8fjJJ6IcUkkho2/YzEST8TCgsQTkMV5Mq2bBRakeDIKZNoA6+TDdvFuVcSkVrPW4ZJiOIDjJY0rioKzZ8+iXC6EV1GLQfb2jn4x6+Ip0RNC4BcdANKdJzHfjrikVut2u91pCeP6WCVJQjwez5rzZC4lMFXMzYGNsJ0zPWwnDUZghQiraEkST5Nxnpipv53sjwEST3Ke7A47ZChQoBj5TgA5T0RukHgiFjKXvXjinM+L2XYLUjz542pfNacFzCIAkjKp0g4JTTxlc5WSCjWOI54uXryIaCyKRUohvFwVT319o0njunhSAnFYoYqDJOdpKAqxyI54PA6bzQa3253ReVKictbWLHIooV4Tcexw3EQQXKPNgZWIBFiYmgulj8ui9reTBqNgYPA43RmdpwmH7bTzmWfa6egCKQ4Z1jL1GiiKQuKJyIlk8UQz7oiFxWUvnqDd61PTTvQ8lNmq8xQOh2Gz2WCxqDesBSGeRrQCmWz0Rj6ZcgXjOk8mwaTEMm+jo+c7VfBC2JgF+Ra34TwpijIqnsISBDAwDkRHRnPLZF8MliKHIZ48Hk+K86SF7aLSpFuzTAa9OTAAcK1AZmqulOCxQhpU3zMetyct50mfyZnzOU1hu9EaT6PPVRdIrk9VwblCnTmoC9HLvWxAT88vsffd22dtwslCJCGpgp4xEVFynogFBoknXRylugRz4DyZb8K6eJrPX77ySBxCvnoDFXTxNMHQHVc4Ehc08ZTFVTIvHy/nqaurC3kONzzcAUuxE8VigeE8RSIRcM7h8XgghxNgYLBARKRH/RLnkqIKQu9Y4kkP28ljVxefxnwnQM950ksVJDcF1hHdVqOMQl5eXprzNBHXCVBn2wHqNZf6I2A2EULe6PPSBZLYnKc6jxidmZgayrzcCAQOIRA4BEWZ35M+5pJEwgcAcDpryXkiFhyXvXgynKVU62mWe9tlEk+KoqRVv55PyCNxiAXqDZRZtRvtBMWTNBABTygQ823gMSmjWDQLprFynjjn6OrqQqW7HEwQYCl1opjlYXBwEPF4PKnGkxJKAAywCBZEL6rLZX8M4IAlQ9hOH5fZjRmzr904ZQomiuCyqEn1CSWtr52xjUmw6eJJH/fIyMiEksWB5OeaGFCTxc1ul+48mYtx6i5feXn5hM51qSHJqoiMx31zPJLZQ1EkvLP7E+jt+1VO20tamQKPpxmxWPaZtgQxH7nsxZPuLGWbbTeXzhMwf6uMc861sJ16AzXCdhMslKmH7Oz1hUklAMyYQ3Vj5TwNDQ0hGAxikbVYnQHossIrqe1OLl68mCyewhIEpwU2hw3xSAyJi2GjxpOYErZTFMXIb2KmsF22nCclJE2/86QlnysRSRVPmZwnz2ioLK8wH4lEwhA2E60uDqSH7czJ4kBm8dTT0wPGWNZq6ZcLsqTP5Bya45FMH4qSwNmz26AomQtaxuMXEQ53oL//tzkdLyENQxAccDmrEY/3g/OZK7JLENMNiSddHGWdbTc7w0gVT7qbMV/FkxKWAImrM+1gFk8Tu2CJ7iCYVYBtaZ66f4a8p+Scp+xfsEa+k1wAscAOwWlBUVy9pr29vSniSXWHbC47JMgI778I2afeFMw5T3qvOT0cxWwCIOQStpvmnCdTixYlLGV0tpKcp0JVKAWDQcRiMUSj0Qk7T0ZxzmACsi+ak3jq7e1FaWnphHKrLkUk+dITT8PD7+LkqX/G4ODrGddHNffI7/9jTsdLJPywWgtht1eAcxnxeO6NvwlirrnsxRMfx3may7AdgEkVyvz/2nvzaEnSs7zz90VkZkRud626dWvp6uqtpFa3ulut1tYgCS0jENZYrLY4smA8DFiALfABe1jm2B57GJthPB6bAWGGMWDAQmIzy4AlYGS0S93qfVEv6q7qrv1W3S3XWL/544svMjIz8t7MW3ep6vv9zunTlRGRkZFRtzKf+7zv97ydZ5YJ13Z23EG0pgMyB8TThA3j/tkGxcPVnjjI6WnKbpMbNIyfPn2aSqXCVNvBni5hlQvU/BKO43Dx4sVh56lSoOiUiCsWnUeXCJe7YKnQz6zzBL3ASSEEwimkZbtskz9A7EfIIN7+sl1mREvcye950llPomRTrysx2mg0thRTkJ7TLSh3UPavtIPRztPhw4cnfp1XGtp58oNXTtnO81Va/6jmbt235Hnnx2oAD4IVJZ7cxb7nGwzXA/tePOnVdiOjCnahYVvnBW1H2U5KyZXffIrWF89t6zUO0hvNMlC288cXT6pZvEXxaC0TAbCB81QQGzpPp0+f5vjx48TrPvaUg1UpIBAsHDiYOk/FYpFSqZT2JRWLReKqRXilS+fJy2pOny1GOk+gmsZl4jwN9TslTd2bzbWbFC3GooaP9OORDeOgGr2z4mkrAZnp67qFNEpilPPk+376Ws1m04gnss7TK0c8+f4SAF43vz8pK37W1x7Z9HxhsEahMI3jHEqeb1bcGa4f9r14Sp2lwTuxi85TXvlnyz1PYQyhTIMUd4ph5ylpGJ/AeQqvdJBeROloLV3FltfTFHshCNXTM2q13fr6OisrKxw/fEw1oCdlO4CF2YNcvHiRRqNBrVZDCNFznopF4hJgC8JLHexZFynlSOcJevPtcufa6YDMHSrb6SiCjRrGLWf7nCfh9pLjB8WTXm2nnafz59WXqhFPEIVKbAf+K6ds53tKPHVHNHd73fNYVgnLKrG29tCm5wvCVYrFGVxnMTmvEU+G64d9L55GNoyL3WsY307xpJ2ZSRygrRCt+0rQ1Ad7nsZv+tSORvFIDeFs4Dx1I4RjY7n2SOfp9OnTABydVV/cumwHsDA1j+/7nDlzJnWS0p6nUgk/DHBPzgJqpV0QBEgpKZVKlMtqhVlWPIlEPLVarV0ZzQJZ8dTpe9x3jC7buQUcx6FYLPY5T1pQTfS6yT20asUht0vPBxwUT4uLixO/ziuN69F5iuOARuOpkfu91HkaXbZznMPU63eytr5531MQrFIsTFMsziFE0ZTtDNcVRjxtElVwvYknLZo2G2NytURrHla1iLDVj9BWynb+uSYUBMVDlZ7zlNfz5EVYTgHhFHJ7nqSUPPDAA9RqNQ4UVGnKnnbSUteB6hwAq6uraq5dkPQlVZXzFAQBlXsOAlBIMp5AOSuWZQ2ljFuuTdwJWVpa4sCBA/3X2hoe2rsdiJINluiJp5zRL3bGeRJCUK/XaTabrK+vU6vV+nqzxkWvuBt0nTSO4/SJp/n5+X2fLi6lJNJRBdeReDp16hd54MFvGyn4fE/3POU7T13vAo6zyPTU65KMK3/ka0kpk4bxWYSwcJxDI0WZwXAtsu/FU9owPhCSqR/vVdnOtm2KxeJVOE87LJ7Wfezp3pfkVhrGgzNNiotVhG1hOb3wyUFkN0S4NsLJd56ee+45XnrpJd7+9rcjm0q82NNOOjh3vjSdOokqIDOZDZf0PAVBgHv7PO6rZnFOzvaJJ/2cwbLdanudIAiG8ox6ZbttFk9CYFUKvbJdXsO47nlK7mWtVkudp62U7LLnGlc8mZIdxHE3XXZ/vay2i+OAs+c+jpQRne7Z3GO8ZDWc511EyuF/5553EddZZHr6XuLYp9F8eoPX6yClT7GoftlxnEOm58lwXbHvxdNI50k/3IWoglFL3rcyokWLps1mwF0tcTKaRTNpSKaUEv9ck9JR1VO0UcN47EdYSdlu8H3Fccxf/uVfMjs7y7333ku0psuJvTJTwYe5OeU+pQGZ9Isnq2Rz4O/eiXN8akg8Dc+3s7nsq1LYoHiK2qo/K0/cXC1WuUCcNOrnle1EwUK4dipEdVDmVgIys68JUDw4Wjz5vk+73WZtbc2IJyAMe0L7einbXbnyafxkNd2o8pnvLyFECSkDfP9K3z4pZVK2O8TU9D0AG/Y96bl2heIMAI6zaHqeDNcVRjxtttpuF52nwZVbWxJPibjY8bLduj8gnibLeYqWu8huRFGLJ0sgSlau6NM9T6I07Dw9/vjjXLp0iXe+853Ytq3KifWScrMyg211H46OKQDShnHd46QZx3laTuZyHTx4sO969OiUwR667SBbChwlzma+9Waqb1ICJiuetuo8jVu2M/1OPaKk38m2K/jXScP42bMfo1BQPXF55bMo8gjDNeq1V6tjBkp3QbCMlD6Os4jrLOI4hzfMe9LiqViYAcB1FhNH69odRzWK1dUHOX363+/1ZRh2mX0vnmSkG8b7t+9mzlO73cZ1XWzb7tu+FfG0G2U7GURq+O1UprfFFiDGbxjXyeKlo70mZt2IPUjshVhuAcst9PVEhWHIpz/9aRYXF7njjjsA1Yuly4nCFqrU1wlTh0gHZILqEdJhjmHYe9088dQ3oqVcYFk0mZudGxqAuxOjWTSpYBI9p26Q6hsXcW5UQqlerxMEAb7vb915cjcu25VKpT7xZJynnvNUdm8gDFdzS1ybEUVtvvLA32RtjCX/V0unc4Yry5/l2LHvRYhC7qgUHWBZn7oLGO570iU3J1k5Nz39OtbHEU8Z5ymOO4Th+lW9l92m03mZRx/7QZ7/+v+Gl6xGNOwP9r14SnOc9th5GizZgXKiJg3JTMt2Oyie0oyn6YzzJASiaI3tPAVnm2CrZnFNXlkOMs6TYyP9KBW0Dz74IKurq7z73e/GstSPcrTmU8hcl1VWA3WPHz8OwPz8fG9FXKUnnrIzBPPKdlEUpUJWuDYrosXCfL/rBCrnabv7ndL3kpTqhDues6VjFmBrMQUA5TsPMPXNN1I4OPzzCT3n6cKFC0xPT+f+HO83dLO4W74BKSPCsLHJM4bpds/RaDzJ6toD2315Q5w793FAcPTIB3BKC7nlM13Sm5p6LTDsTulSn85smp6+l653bmQJMEic2554uv6ynqKoy+OP/whRpD6jV1a+uMdXZNhN9r14kiPHsyTO0y7YyHlhi3Dtlu2itf6ATM0k4sk/mzSLF3o/gpYzynlKep6SXh7pR3iex2c+8xluuukmbrnllsy1eX2N7Fa5QNwJOXHiBD/+4z/OwYMHiVv9ZTvYWDxpEaL7nqKCZE20OTgzP3ytrSC3H2k7SGMDxjx/Nppgq86TPe0w9Y7jI8VatmxnXCdF6jyVbwC21jSuBwt7yQq3nSKOA86d/13m59+O6x7BcRdzBYwOyKxVX4VllYacJy24dFr49NQ9ACOdszDteZrue971Ip6klDzz7D+l0XyS1975CxQK0yyvfGGvL8uwi+x78XQtDAYe5TxtqWynHadIjlz5tvapU6x/+qWJr1MTDgRkakTBHks8SSkJzjUpHan1bRdJcnffsbFEej3nCZRAfOCBB2i327zrXe9KV9LF3RDpRf3iqVJIA0O1mIjbAaJkIwpWKpA2c56gF5S57K2DgIP1uaH3FreCHXSekiiCMZvRs+Jpq87TZjiOQ7fb5cqVK0Y8JeiMp7KrxJO/BfGkx7vsdPbR5Sv/H76/xNGj3wOo8lmegNElKcdZyD1GPbYoFVV0R73+GoQosbae3zQ+2PPklPJHtEgpt1T2vBq+9sw/5aWXf23DY86d+zjnz/8eJ078CAcPvpvZ2Tezsvz567Jny7A1jHga5Tzt8mq7UeLJ8zzieIKRJxnHaVTprvv0Mp0nruTuG4fu15axKoWhPhjlPG3ueEVrPnE7pHik2rfdyul50udTPU9JnIEXcebMGQ4cOMCxY8d6580pJyrnKSCLKq0lq8gS50kLpuyfB50nLZ6WWurL8EClXzxJKYnaOymeEudpQvEkhOgr4W0njuOkXxhGPCl0unjqPPmTr7jT7pV2fHaKs2c/huMsMj/3dgBc5zDd7oUhEaCuQ1AszuM4h+l2B3ueLuI4C1hW8jNqOUzV7xjZNB6Eq1iWi22rPDvHOQiIoZLhyy//Gp//wltpNL+2De92c6SMOX/+9zl//vdGHrO+/hjPPPs/Mzf3Vm6+6UcBmJu9n653jk7n9K5cp2Hv2ffiKc15EvnO0240jOeN+QAlnvSokHHJiqdRpbvYi4jWtzY4OPYiuk9dofzaA2lApmbcsl1wQX25FA/3i6e8HCftRCnnSX0wSy9iZWWF2dnZvmN7I2OyZbvi0KganS4OjCzbCSHSfYPz7S6vX6EgLaYL/dcvAzUax97xst144sxxHAqFAvV6fWgxwnaRbZg34kmhnSc3LdtNLp70ir2ddJ46nZdZXv4cRw7/rVT0jGrc9vxLFItzWFYB1zk81FTudS+kfUua6el7aTQezw3LVAGZM+ljyypRKs0POVpnz/0OnneBhx/+0K4IqG73DHHcodl8ljBs5R7z4qlfpFic4o7X/B8Iof5dzc19A4Ap3e0j9r14Sp0le28axn3fVwnXI8QTTJYyHvubO0+yGxI3A2Q0ua3WffoKMoip3LMwtE8UrbFCMoPzyViWxZ74+MM//EM+ee4LtLvtvmO1mLIy+UVRJ2B5eTnNbtKk4inTiyWSsl32N+komWsHo8VTqVRKBXWlUukb0XJp5TKzsob0+t/rTqWLayYt2+mU8Z0q2UFvOHCtVtvS+JdXIqrkZuE6R4At9jxlnKedKgVduPCfAThy5LvTbaN6j3z/Mo6zkB4zGJTp+RfTlXaaqel7iGOfZo7oCYIVioX+PrzBcmCz9Rzt9tc5fsP3Y1klHn74QzSbz2zhnY5Ps/Vc8qeYRuOJof1SxqyuPsj8/DsolXqfP+XyCRxn0TSN7yP2vXhKnaXBfthdcp70arrtEk+bOU9SSrVdQtQIhvZvRvuRJexph9KNw1/IomiNNZ4lON/CnnPTDCGAp59+mmeWT/G74gs88VjvQ0uX8YRTSHueWutNgiDIcZ50I3t/2Y5Q9jli2b6kjcRTeo7MiBYpJZcuLzEb14ZKjDuVLt73Xhi/YRzg3nvv5Z577tmR64GeeDL5Tj3CqEmhUMO2K1iWs6URLXrFXhS1Uxdqu1lvPE61eiuueyTd1hvSO1iWu0SpdCA55jBShml8AUC3e37YeZp6HZAflhkGa2lApsZJsp40S5f+CwDHj38/977ut7GsEg89/Hd2VEC1ms+mf15ff2Rof7v9AmG4ysz06/u2CyGYm72flZUv7nqPlmFv2PfiadOG8R1uAByVLg5bFE9Z5ymvbBdKSLKtJi3dRa2A7rMrlO8+mLv6ShTtMZ2nVp/rpLOI7jh8G1OyzO/9we/xiU98QokV7TxlVtstr6gvozznyaoV+1fwJYJDZkp3cTvA3qRsN5jfVK1WaTabNJtN2p02c9SGmtvT8M1rpOcJ4K1vfSv33XffjlwP9MSTKdn1iMImBbuWlH5nt1S2y6aU71R+UKPxFLXa7X3btHs0WC70/SWc0sLAMRfSa42iZiq8NK57mFLpYO6w4SBc7SvbqfMeopuJQLi09Emmp+/FcQ5RqZzg3tf9ViKgPpTGA2w3rdZzOM5hyuXjrK0/OrR/dfVBAGZmhv9Nzc7eTxCs0NxgLI3hlYMRT5tEFWihsVNst3iKvSid6ZZXtoszg3X1qI9x6TxxGWKZDtEdJNsw3ul0cssNMogIL3f6+p10L9GxA0f4b/3X8477384zzzzDn/zJn6TiKbvabnVtFSC35ynb7wQ9oaH7nmQkkd1orLJdFh2UeemSWjp+oDg12nnaoZ4ne8alct8h3FcNr/LbK3Qj+g033LDHV3LtEEYt7KQfrlic25p4yrhNnr/9fU9BsILnnac+IJ5KJdW4nc1xkjLG9y9TctS/e9dVQlk3jfcynobdx0rlJtqdUzmvvzZUtnOdRcJwlSjq0m6fptl8moWD39J3rle/6l8QBFc2TC+/Gpqt56hVb2Nq6h7W88TT2oMUi3OUyyeG9s3N3Q+Yvqf9wr4XT/oLfshJ0cbTDpftNhJPOvtp0rKdXVdf/Lllu4xbonuExr7WRy5RWCgPNXprdNnuwoUL/PzP/zynTp0aOia42AbZ3++ke4mq9RoWFm957Ru54447OHv2bDooWCeMA6w0VgGYmZnpO3e05o8WT4krpFfebdYwPsp5unhRfVHMubND4inKJJfvBMIWzH3XSYoL104Q5cLCAh/+8Ie57bbb9vpSrhm08wRQKs5uaUSLWrGnPoT8HXCeGg3ljtTqr+nbbllFSqWDfb1HQbCKlCFOSYknx1HiSTeND6aLZ6mUT9Bun+rbJqUkCPKdJ3W+iywtqZLdwYPf3HfMzMwbAMHq6vaHh0oZ0W4/T7V6G9NTd+N5F4ZW/62tfZWZ6dcPLTDS11+p3MrKshFP+4F9L55GOU9CCHV3dnix3TjO0yQp49KPsOvF9M+DZL/wowmcp3DVw39xncrdC7kfHNBrGH/ooYeI45ilpeEP/eC8cplKOc5Tra6+cGQ3ZGFhgUajQbup9glH5TJhC1ZbalabFj699+MNZU8NOk+9viS1fVTOU57zpMVTrVajWqkMl+1awYajU16pLC4ujvyZ2I8o50n9LKuy3VZCMpu47lFgZ5wnXVrSs+qyuM5iX8+TjksoJeKpWJzFspz0mMF08SzlygmC4Epfynocd5DSzxFPvXLgpaVPUq/fSbl8rO+YQqFOvfaaLSevB8E6X/jCO7hw4Y+H9nU6LxHHPtXaSaaSkM/1tZ775HlLdDovMZ1TstPMzb2FldUHclcYGl5ZGPGkW3TyEpQtsWsN41ooZdH9JJOuttPOU17PU9aNmkQ8dR5TH6CVu/NLdqB6nsIg5PHHHweg0RgeSxGcbyFKFvZc7/1q8VSfnkqvUQ/cvbKi8qh0v5Pl2Kx21odKdrGfzNsbdJ4ShykVT+lQYLXdtm2EEEM5T3nOUxRFvPTSSxw6dAjLsYfLdskqvp0YCmy4fggzzlOxtLWepyhs4jiLWFZ5Z5yn5lM4pUNpE3iWwZRxT4unZLWdEEI1dyelvc2cJ6DPfQrSdPGZ/tdNnr+2/gjr64/2leyyTM/cx9rawyMFSrs9Omvp7Nn/RKf7EpeW/nxoX7OlmsVr1ZPU67cjRKmvaXxt7asAzExvIJ5m7yeOO7syk9Cwt+x78dTLeRreJ4TY8aiCbrdLqVTKzeGxLCtNcB4X6UWsFboEItywbCeK1kQN4+1HLlE8Vhs5IFaf83R4MRWEuhyXJbigmsWzAkOLp+pMz3nS4uny2jIUrLQJXDg2a93GcL9TGpA5qudJOUvZuXZAmueUdZ48z8t1ngBWVlY4dOgQwi0gB8VT09+xmALD9UMUNTPO0zxhuE4cT7ayVa/Yc5yDI7OeribCoNl4mlr99tx9g5EBfjIixskILSfjTnW9ixQKM2ngZZZK5QRAX99TECRz7ZJ08d45lXN19sxvAbCwkC+eZmfeSBx3aTSeHNq3vPJFvvild3L+/B8M7Ysij5fPqOTwlZWvDK2K0yvtqtVbsSyHev32vqbx1bUHk+39pc4sMzNvBixWTN/TK559L55ScTSY8wTKjdoF8ZTnOmkmGdEiY0nsR/zO03/GE6UzubEBumG8cLA8tvMUXGoTnGvlZjtlEQWLZ63z1Ot1FhcXh5wnKSX+wEo7UCKrVCrh1JQwi7sRMzMzFItFLjdXUtcJICpBO+pukPE0MDLGsUFky3Z6RVyvtDYonkaV7TQLCwtYrp32Y+n35r3UGHpvhv2Hcp7Uz0GpqES+HoQ72TlqOKVDqfMzyAMPfjtPP/1TE4uoKPJotb8+1CyuUY3bjaGU81Kp9+/fdQ+nAsvzLuDmlOwAymU1kLvT5zwpJ26wbKfiHWp0vXNUqyepVG7KPacum62ufmVo38WkHPf81/+3vhWLABcu/AG+f5nDi99BGK4ORR40W8/hujdg26qFYmrqLhqNx5EySl7vQaam7sGy+j8bshSLU0zV72R55fMjjzG8MthR8SSE+BYhxDNCiOeFED+Zs/+DQojHkv++IIS4eyevJ49RCePArpTttlU8BREhMV7k07L93LKd3lZYqKS5SJvReUqVzip3DVv8WdqyyxnrCnfd8VqmpqaGxFO07iM74VDDeavVolqtIvT4lW6IZVkcOHCAK+2VdDtAo6BE0qh08cKA8yQskQ4Hhl5Td9YhyoonneieV7bTHDp0SI2SycQfhBfbxOs+7sn+6zLsL6SURAM9TwDBhE3jUbJirzTCeQrDJo3G45w7/wlefPHfTXTuVvs5pAyHmsU1vYZw9bqev4RtVyhkEvUd53ASlBnheRfScM1BbLuM4yz2O0+JkBwUT9BbyTeqZAfKAatUbk5jAzRxHLB0+S+o1+7A95c4deqX0n1SRpx+6Vep1+/k5pv/IQArq1/qe34rWWmnmZq6hyhq02w9p/7ffGoo3ymP2blvYH39sSHxZnhlsWPiSajc+l8E3gu8BvgeIcTgv9YXgbdLKe8C/gXwKzt1PSMZFVVAsgLvehJPXoyPEgG+FfaljWu0W1I8WEH60VDfTh7hUgerXupL7s7j6aWvI4XkrlffSb1eHyrb6WbxPPFUq9UQRQusnsBbWFhg2Vvrc54alioJDjtPSghaU8O/FYpyobfarh1CQajXSsiKpzBUaeSjnCchBAcPHlRDjP0oFdfdZ9Vv044RT/uaKGoDMnWeUvE0YdN46jw5h3Ln27XbLwJQqdzMi6f+HefP//7Y5242dLP46LId9HqZfG8pbRbXZIMyPe8CTinfeQK94q7XhxSmPU/TQ8fq84wq2WlmZt7A6tqDfaW3ldUvEwQr3HTT3+fw4nfy0su/lvZaLS39BZ3OKW688e/hukcou8dZXfly+tw4Dmi3X6RaO5lum55Sv8uvrz3C2tojSBkxPbO5eDq08K3ceutPsuOrjQx7yk46T28EnpdSviCl9IHfAd6fPUBK+QUppe6m/BJwjN1mA/G0G6vttlM8xX6EJ5RI8EU4wnkKwRYUkobtcUp34ZUOhfn+axwsFUgpefLcsyzEU8xPzaW5SFHUu4a8sSygynbVahUhRN9w4IMHD9KKuvjF3gfkOmp14nDPk4coF7BKOb1jGedJz7XLOo1Z8TQ4FFijR7QcOHCAQqGgeqlkb0Vj99kVCocqQ86XYXe4VqbZ6zTw1HlKRnhMkjIuZUQcd7ALNZzSQaKoNeRiaPF05x3/ltnZt/D0136a5TGXyDeaT2HbFcrlG3P3uwMjWjx/WDxpp6nTeRnfv4Ljjg5JLVdO0OnreVoFhnueAKamXstU/S6q1ZND+7LMTL+BMFxPm7wBLl36M2y7ytzc27jllp/Asoo89/y/RErJ6dP/nnL5OAtJ9MHM7JtYWe31PbU7p5AyoJpxnsrlExQKM6yvP5o0iwump+7d8LoA6vXXcPyGv0uhYMYVvZLZSfF0FHg58/hMsm0U3w8ML4HYYfQvLrmJ2ZZA7nBI5qB46n59lbP/7ItpY/NkzlOUOk8eQW7DeNyN1Jy4xKEZp2k8XO5SmO81in/961/nZ3/2Z/nc5z5HHKsbeO7cOS43VjgZHUEGUTrnTDeDQzKWZdbpG8uij9FlMeHYaVO7bhpftXrnWI9alCikGViaaN0f6nfSWOVCmjAet3rp4ppxxJNlWdRqtXQMiX4PcVc5fN6La6Zkt0csLf0Fn/ns67e0qm270cNkszlPMNlw4Ow5Skkv0aD7pMSToFq9hdfe+UtUKjfx+BM/nJnNNppm42lqtVcjRP7Hfylxf3TGke8vpXPtNG5S2ltffwyQuTEFmkrlBEGwkjaKB+EqluXmNpjfcstPcN99v79p9MXMzBuBXt9THAcsLX2KAwfeiW27OM4CJ078CJcv/yUvvPCvWW88xvHjP5AO8p2dfTNhuJbO3Wsl962WEW1CCKan7mJt/RFW175KrfYqisWdmxNpuL7YSfGU99Ofq0SEEO9Aiaf/ccT+HxRCPCiEeDAvO+iqkBs4T0Ls+HiWQfEUXmghuyHhihI15XJ5IvGUOk8yzM15kt0Q4RbSVWmb9T3FfkS87vc5T6dPnyYMQ/7yL/+SX/u1X2N5eZlHHnmEgm1zU7SADOK0zJXtewrOtygervWdP4oi2u12enzWeVpYUB/Yy7L3W/da2GJKloc+XONNxFM2qmAwAXwc8QTwgQ98gHe/+90AaR+W7EZ4L6xBJK9J8fTSS/+Bc+d/b68vY0dZW3uIMFwb23nZSbTzVEh7nmaAyXqesufQwZSDfU/t9gu47jEsy6FYnOLuu/4fhCjywtf/9YbnllLSaD49NJYli207FItzmYbwS0ORBr1YAZX0PTiaJYuOK+h0VOkuCNZy+500o0RdlnL5KI5zOA3L1CW7hYX3psccv+G/o1w+zqnTH6VYnOfw4nek+2YT8bWyovqe1Eo7i0rllr7XmZq6h1brOdbWvsr0GP1Ohv3DToqnM0B2ZsMx4NzgQUKIu4BfBd4vpbySdyIp5a9IKe+TUt6n3YjtIm0Yz7sT9s42jMdxjOd5feIp/ZLv9Jwnz/NSh2fD8/kRPur5XpzfMB57EZZjp0Jjs7JdtKyEW1Y8LS8vMzMzw7d/+7dz6dIlPvrRj/Loo49y8tgtOBSRQZw6T1o8pWNZFvvDQHVIaNZ50n1Z09PTFLBZCdfT49f8JvW4PPT3opyn/JKZEk+9qILB2XOlUmks8XT06FGmp1WfRtZ58p5dQRQtnBPDPRx7zZkzv8m5c7+715exo7STL+VrYSyGDoO0E+fJshxsuzah85SU/uxqJnX7Ut8x7c6LVDOr0crlo8zN3k8jcVJG0e2eIYqaI/udNDrHKYo6RFEznWun0UGZ60meUV7GU3ptOq4g6T8Kg9Wh0SxbYXbmjayuPqCGdSclu/m5t6f7Lcvhtlt/BoAbbvi+PqfLdY9QLh9nZVX1PTVbz1Gp3Iht93+GTE3fDUiiqL1hvpNh/7GT4ukB4DYhxE1CiBLwAaAv1lUIcRz4A+BDUspnc86x82zUML7DOU++7yOl7BdP2cZmJptvl3WevDgg8oabweNuhHBUb5Bw7U3LduEV1aCdLdtduXKF+fl57r77bn74h3+YY8eO4fs+d7/6teo6MuJJN42nY1kGnKc04ykRT5ZbUH1ZqFLZjKyy7CvxFMcx616TKVnuH4AcS6LGBs5TpUjcUY3go5wnLZo2Ek9950zFU0T32RWcm6f7mtCvBaSUeP6FkTlBrxS0o3EtZOtEUVJyy6xMK0043y7rPOl4AM/viScpJe32KcoDS/mrtZN0uy+nZb88Gk01pHfUSjuNShm/MJQurtFBmV1P/T68oXhyjwMiXXEXBKtDAZlbYXrmPnx/iXb7BZaW/oID8+8YKgUePPhuXn/vx7nx+A8OPX925s2srn4ZKSNarWf7+p3S15jqLQDPGwZs2L/s2Ke9lDIE/j7wSeBp4BNSyieFEB8WQnw4OeyfAPPALwkhHhFCPDjidDuHFkcjogp2UjxpQZTvPG1BPPm9nieJ7EvNTo/xQqyk5GRPOZs6T+GVxHlKGsyllKl4AuUOfehDH+IjH/kINx1XH+YyiFMxpJ2njVbaAZmyXc95kmHMbFzhSncVgLW1NWIZU5flvn6uuB1ALDcs2xErcakbxrOMW7bLost2wdkm4eXONbnKLghWiGMf3794zTRUbzdKSJzGtmt0Oi/R6ZzZ0+vpuUa9XxKKpVn8nNV2o/5OtPix7SqFQh3LctOgSgDfv0QUtahWbu57nu7XabWfH3l9aqWd1dfbk4dOGdcZU44z7PjrvifLcikURvcC2baD6x5Js56CcHiu3VbQpbcXT/0CQbDMwsK35h43M3MfljUcXqv6nhqsrz9Kp3M6VzwVi7OUyzfiOIu47pGrvmbDK4cd/VVZSvlnUsqTUspbpJQ/m2z7ZSnlLyd//h+klLNSynuS/3Zd2stYqnlkoxrGN6+WbZntFk+xF+GLntvk+d7QB7Qu2wHY06UxxFMHq1JIBUer1cL3/VQ8gXKI5ubmUudFhhG2bafDdCEZy1K0UhGmGXSeRMZ5ir2ImbhGy+/Q6XRYWVG/vU/Jcl9JMk0Xr28gnlCN70i2RTxp56nzuPpyuRb7nbTjFMf+NdFMvRP4/hJx3GFx8duAvXefwtR5yoinnPl2q6sP8tefuSc/wyl1nurK4Skt9DlPrfYLAEMhknqFmk7KzqPRfJpK5WZse/SkAFBOUhAs003E6KDzBKQr7Bxn89mGlfKJjPO0ti1lu0rlForFOS5e/BNsu8L8/Ns3f1KGmdk3AXD27MeQMhopKG++6ce45eYfv+rrNbyyuLbqDHtBTL7rBOru7Lbz1Na9OUpA6FVl4wwHzpbtQK24k0G/+tMN46Ccp3hts7JdF3ugZAfDOUtATzwlyea1Wq3nPOWMZYFeWa9XtlPOk5QS6UXMSrX90qVLqXiqx+XcAcd5GU+QEU9JCTKbLg498aQDMmF88RRcaGPPOhuOrdkr+uaTvUJLd7rf6eCBd1IqLbC8vLfJzlGe81ScJfD7xevS0qeIombfzLfeObTzlKzYcxb6ep56GU/94qlcvgHLcvuW7w/SbDxFfcRYliy6AXy98UR6DaOO2WilXXptlRO026eQUhJuk/MkhEhLaQfm35m7em8jXGeRcvkEFy/9KUCu8wSwuPg3OXz4O3L3GfYv+148SSnzV9rBjieMb+Q86aX1WjzpxuqNiP1+58lnOOsp7macp6kSUdPf8D2Gy90+t0iLp6zzpOk5T0o81et1Go1GbyzLQMkOlPNk23Z6D4RTgEhCKIm7YSqelpaWWF5exrIsqrgDzpMezZLfMC60eLqs7nee8wQqIFOLJz2UeRSiaKUjfdyTs5v+5r0X9IunCxsceXUMzgjbTTpJ+GK5fIK52ftZXvnCnl5PGDURotg3wqNUnBvKedKrvHTmUf851C8cum/KcRbw/X7xZFnloT4jISyq1dtGOk9BsErXO7dps7h6zUQ8rT8GWGnkQt8xSRlLl+82olI+QRiu4XnniWN/W8QT9CILRpXsNmN29k3EsY8QhZHjYAyGPPa9eCKS+SvtSEp5O9grsmHZLnGgKhW1Om1c58m3wtQ18UV/XIEMY/V+U+epBDHEzfyhpTKMiVa6QyvtLMtKV51lEcVk+X7QE0/NZpO4FSA7IYWFytBz0tEsifiwMiNapBdRky7FQpGlpSVWVlaYqU9jIfrEU5yW7fKH8g45TzkN4wBBEKTiqVDoPwbgwoU/4uWXfz11AbT7dC2W7KDfbdop56nTOcN//es7ki/Z3afTOYUQBVz3KHNz9xMEyxs6LztNFLaw7epACOsscdwhitTPXxCspo3beeXUKLPaDlBlO68X0dJuv0ClciJ3SX+tenLk+280VbJ4rbZxszj0RrQ0Gk9SKh1I85GyTOI86QHBa+uPAGxLwzjA4cVv55abf5wDB96xpefPzrwZUC7eRjPrDIZBjHjaxHliB0MyB8WTXg0GPRGV5zxFzfw+JZkkjOv0bY+wv7E6KXVlG8ZhdFBmuKJ6hAZX2s3OzmLbwx+mvbKdes1arUaz2SRs5A/thV66eHqObPikFyEQHJiZT8t2s9Mzav9Az5NVKyLs/B9n7TSFl9WXV15IJvTEU6lUwrKGz/Xsc/8Lzz73L/jc5+/noYc+yOqxTxMXuzi3zOS+7l7T9S5QLKryarZnZjtpNp8ijv20vJNHEKwSx5uPAdoK7c5pXPcollVgdvZ+AFb2MO8pjBp9/U7QSxnXQkkFO8q+bf3naGFZTtrkXHIWiKJm2ozebr840iWp1k7i+5dyz6vHstTGKNtpQRTHnTRraviYw33HboROM9fRBnnp4luhWJzhxIkf3rLwmU36nkaV7AyGUex78SRjmdssDoAQO7pKSYsnXSKSfpz2WGnxpEtaWjyFq13O/69fpvv86tD54iRhfGZmBgBfBP3OUyI4RKZhHEYHZYY5GU/ZlXaDCEuobKxM2U5KSfOKihoYLJdBf7o4kJYUpRch9ZiW+QNp2W52Xn0RyYGep1HN4pDX8zSc8wT94mkQKSOCYIXDi9/JTSf+AZ5/kfM3/ipL9/32UGL6tYLnXcB1j1Iszu9Y2a7TPateqzsU4Qao5OcvfPFdnDn7mzvz+p3TVJIvZtc9TKVy857mPUVha0g8DaaMr6x8GctysSxnpPOU7ZnSGUuqOd6n2z0zUjzppudmczhpfL3xGKXSAs5A4GUehUI1HS9SyllpB1Ct3sqxY9/LwYP/zabnK5dvACzW1h8FoJgz124vcJxD3HDDf8/hw9+515diuM7Y9+KJeLTzJGyhGsp3iG63S6lUSl0cHeSI6DWMg3KfUvF0pQsxhJeHe6CkH+ERpuLJG5hvpyMALCdTtgOiRr7zFF3uz3iK45jl5eWR4gmU+6TLdjp+YH1FjWUYFC3QGwqssQacJ4CDCwdpNpt4nsfcAfXa2aHHUcNPE9Nzr6lkgSWIGwFYvZgBTZ7zNIjqTZHUp+7k5pt/lDe/6S84OPMeOvNfH/m6e43nXcB1FnGdxR0r23UT0dQdIZ487wJhuJqOwdhOdExBudKb0TY7ez+rq18hjvNL0TtNGDXTcptGu39+kjK+svolZqZfT7E4N6LnqV+A6dEonneJTuclpIyoDMQUaPRg29ZA6U7KmOXlzzM7++ax34vue8pbaQdgWUVedfKfjrWE37JKuO5RGo3Hgd7A5GuBk7f9DAfmv2mvL8NwnWHEU8zosp1gx1fb5QVk2rNuT0ih+p50z1PcSlbj5fQpRd2AQIaUy2WckoM/MN9Ol+20eLBqJbA2dp5EycKqKXHRaDQIwzB3pZ0mK57SlPHVJHV5QDxJKYecp+zYEy38FhZ7ZYG5+TnlbnX7G8ZHZTyBWpWj+5yscnGouVuLJ9/38TxvhHhaSY6dTc9Zn30Nnn+OKNq8mX8v8LyLOM4ijnNoB8XT2eT/+eKp01VL3bs7kL8UBMtEUbNvwO3c3P1EUYv1xOHYbcKwOVy2yzhPvr9Ms/k1ZmbflEQY5DtPhYzzVErF08V0pd1gxpPGKR2iUKgP9T01mk8RBMvMz7117PeixdOost2kVConiGP1i1rhGnGeDIatsu/Fk4zlyJVSYhdW2+WJp8Kci/TjtPxVqVRS50mLp6g1LJ66XfXB5LourusON4x72nlSAkVYArs2OuspvKIGAuv7s9FKO40o2sPiaV2Jp8FG7W63SxRF/WW7THJ33A1BwMLhnnianZ3FcuxUFMpIEjcDrA3KdtAr3Q3GFMB4zpN2DUrFnnDUfRI6d+daIorahOH6Loqns/n7O2p7Z8T+cbh48U957vl/NbRdJ4vr2WmgG4CtPSvdRVErx3nS4mk5HWQ7O/tmSiPEUxg1sbPOU6k3HLg9IuNJI4SgWj05tOJu+cpnAZibQDzpVXSjynaTkv172q6eJ4Nhr9j34olYpkvOh9jhhPFRc+10j1G2aVyLpyhxnOI88eT3GtBd1x1uGNc9T5keHWvaGd0wfqUzdkyBRhQsZNBrGAdoNhsIx0YU+n/cBtPFodePFXuq5ChKNjOzM6mgmZ2dTYI0o+R++CDzm9GzpOIpp+9qvLKdEk/FUu+9V6q3JO9jdKLzXqHFkuMcwnEOEQTL6W/924l2nDz/Ym5TeDdxnjzvPFIOz1rcjDgOeO75f8lLL/0qQbDWt6+dxhT0nKdicZqp+p171jQeDrhG+ppA4AcrrKx8CduuMFW/i0JxhiBcHTpHFLYoZASYShl38LyLtNovUiodSPuR8tAr7rL9mleWP0utdntuUvgoes7TcMbTVtDlVTXvb7JMJoPhWmPfiyflPI3YudvOU1KqS3uMEvE0btnO89WXY7lcplwuDztPA6vtQKVy55XtZCwJl7vYmfDH5eVlCoVC6ijlIUq9sl2hUKBcLtPstNLSX5bBgMzstclupDKpXBshBAcOHKBWq6mVcKWe85TGFOyweNLjNbJ5N5XyjQhh074GxVM3aRBX4kl9CWaXu28HUdQmCJZx3WNIGfVlEWk63ZcBkDLckvu1dPkvkmZ3yWoyxDU9d+c0YFEuH+3bPjt3P2vrD284422niKLWkLARwqZYnCEIVlhZ/RLT06/HsooUi7P4fp7z1OhznlTK+CE8f0mttCtvnEdUrZ0kDNfSv48wbLK29lXm59420XtxXN3ztHmD+Tho5+la6ncyGLbKvhdPG0UV7EbO06iynXrcy3ryfZ8wDDcs23XCTNmu7OKJAOn1Ot5jr79hHEaPaInWPIjk0Eq7ubm53GX8GuU89V6zVqvR9NpD8QAwPJoFQNgWomgp58mPUifqDW94A296k1pWLFw7FYKbBWRqeuJpa2W7ICnbZT/4LatEuXyCVvvaaxr3uko8ue7hdCn5dq+4067TzMwb+h73HdM5m2YEjeqL2ogzL/9HXPcYllUeKsWpmIIjWFb/3/3c7P1IGaYlst1Cyji3bAfq56bVeo5W6zlmZ98CKCEehmtDjlyYt2LPOZj0PL2waZhjuuKupVbcrax8ESlD5ubHL9kBzM+9lYWD76W+yRDhcdFZT9sxmsVg2GuMeIo2yXna4dV22SRr2QmhINKVY1nnCVTW06iynYxi/Ehtc103cZ4iYq9XSpHdSJUoC733a085yG7Yt3oNsgOB+zOeNirZQX/DOKi+p5bfGbnSDvrFE2hxpHqetNB73etex1vfqj78LcdOrzca03kSac/T1p0n264N5clUq7dcF2W77LbtQvc5bSSeOt0z1Ot3pn+ehEbjKVbXHuDYsQ8xM3NfmsqdnjsTU5Blevo+LMtheflzY7/W0tJf4PmXJ7q+QaKcuXaaYnGO1dUHANIVbyplWxKG6wPnGV6x5ziHaLe/ThAsU6nmN4tr0l68pO/pyvJnse0KM9Ovn+j9uO4RXvva/wvbHg633Qquewwh7G0LyDQY9pJ9L56kzB8KDDvbMC6lzCnbhVjlQuqSDM63a7fbvbJdO+i7NpkZCtzreQrSOXOg+ogsx+5rkE/jCgbcJ52JVDigri+KIlZWVjZcaQf9DeOgxFM72lg8aXGosdxCmjA+GCsAqi9Kr7aL1n2w8kVR3zkT58veqvMUrFAqDb/3auUWOp3TxPHGA5Z3G8+7QKEwhW1Xdkw86Sbwmel88RTHPp53MR2hMaqpfBQvn/mPWFaZI4e/m7nZt9BqPTeQtN0fU6CxbYeZmTdyZUzxFIYNHnv8h3juuZ8deUwQrG1aBtQhlnaOeFLlXolt16jX7gB6Lma2dBfHAXHsDfVNlUoH8RNxt1nZrlSap1Q6kK64W77yWWZn3rznCdqWVaRSuTmNXjAYrmf2vXjaKOdpJ6MKfN9HSjk0FNgqF9PS0qDz1Ol0lHgSqLEqnZ6rFPsxHkpYlctlXNclJCLs9r7UZTfqaxaHjHgaGBAcLneVC5aUw9bW1ojjeDznKewv27Wlh6gMi6Bms0mlUhlKKxeOnay2683hy2I5hbQEqQMyRwad6uds0PNUKBQQQtDtdonjeGTZrlgcfu/V6m1IGeUOeN1LPO9CKpoKhemk4Xj7y3ZqJtiNFIuzdL1+caReL6ZavZVicX6iuALfX+bixT/m8OK3USxOp6WulZUvAip3KwxX+5rFs8zPvZV2+3m63fObvpZa/i+5dOnPc92nOA554MHv4PEnfmTD84SREk+FEWU7UC6dZRX6tgVhTzxp98ouDDtPmlEZT1mq1ZO0Ws/Sbp+i031p4pLdTnHXa3+Z22796b2+DIPhqtn34kluJJ520HkaNdfOqhSUwBHD4qnVahG3g15PVKZ0J70QX4RYwqJYLKbn1fEFQFIG6xcjaYmw0e+cRJc7FGbdVJSMs9IOEvGUKQHWylViIfFLw/XPwYwnjeUWkN0Q6YVqUPDgazg2MilHRg0fa5N+J9hYPAkhKBaLaQP7qLJd3nDUdMXdNdb3pDOeIGk43oG4gm73LI6ziBA2rntkyHnqdFSzeNk9Rrl8bKKep3PnPkEcexw79iEA6vU7KBTqqXjqdF4CyC3bAczNfSMAy8uf3/S1tPCVMuDc2d8Z2n/x0p/S6ZxiefmzNJvPjDxPFGrhk1O2S1xLPQ4EdNmufziwdq8Kdn/Tuc5aEsKmXD62yTtSfU+t1nNcWf4MwET5TjtJpXLCOE+GVwT7XjyxwWo7sYNRBbniqa3KdsISCKcwNBy4vdpUs+YOKcGRXXEn/RiPELfkIIRIS336dYDcMljPeRos23X7ZtotL6uG6c3Ldv3OU7WgztGxhstag+niGp3jpFfbDb2GY6scrFgSrXkbjmZJz5ms9stb9QeqdKfLiKOiCoq5ZTvlAlxrK+663oVUPIFadr7d8+263bO4rlrp5jpHhspy+rHrHsN1j47d8xTHIWfO/hazM2+mVnsVoETDzMyb0r4nLXhGOU/V6klKpYMsL39209dTzpNgZuaNnD33sb7IBSljTp36KJXKzViWy8tnfmPkeXrOU17PkxLeehBtdlvgDztPg31T2nly3RvGKr9VayeJojbnzv4OrnsD5UzGksFguHqMeNrEedpV8ZT0PIFaFTY4HLi1rj6ciwtKTGVX3MVehC8CnJLTd96u1+07xnIKfO5zn+NLX1JfQpZbQJTsvqwnKSXhcmdopV2pVMoVO1kGe56qBXWOthgWT4NDgdNzuAVkp3+1XZY0zsCPiBv+ps3iAO6ts8x9z6soHc+PWdhIPEkpCYLlvoBMjW1XcN1j11TTeBwH+P5SX6lHOU/jle3GneeoxJMazeEkzlP2uZ3uGYSwcZxFXPdosn/zFRiXL/8VnneeG274vr7tc7P30+m+RKdzJg3ILJeP555DCMHc3DeyvPKFTV+z3XkR1z3G8Ru+H8+7wOXLf5nuW1r6FO3289x000dYXHw/Fy7859xgS9jYeTp06H3cdutPU6/fkW7LK9uFYZLGP1D60yNSNltpp+mtuHuG+fm3jgwCNhgMW2Pfi6eNBgOrhvGded2RzlNSVrIqSkCA6skplUq0G8lvpYeUeOov26m5duXkfKl4CjKiqBsiXJuHH36YRx/tja+wp/rjCuKmajTPOk96pd1mH8J6tZ3+Eq2gxFwr7g4dO7psZ6tVhbI/ViF9DR2k2QyI2+FY4knYgsrdCyOvv1i0mZ7+JK67PiSeoqhNHPsj82mq1VuuqbKd7y8BErfPeVJlu82E0dlzH+fzX/jGTRvg4zjA8y6lzlPZPUoUtdIvf1AxBY6ziGUVcN2jSOmnTc8bcf7C7+M4hzlw4F1923t9T1+i3TmN4yxuGLY4N/eNBMEyjeZTG75eu/0ilcoJDhx4B657lDNn1BBjKSWnTv0S5fIJDi18Kzcc+z7i2OPs2Y/nnieM1HvPc55cZ5Hjx78fIXofubZdRYhif9lOu1cjnKdRY1kGqVZvTf98rZTsDIZXEvtePF0rzpOMYqQf9ZyncqFvOHClUkmdkeLBJEQzK558tdrOHRBPOjgTlPMkShbr6+usr/eWR9tTJYILrVRApSvtMs7T8vLypiU7UOJJnUSpznKshEg76hdPemXbKOdJ3/e81XZaUAXJ4OJxxNNmVCotDi48yoGDp4fEUy9dPP/9Vyu30m6/sKUE7Z2gF1OQEU+lQ8SxRxiujXoaAOvrj+J5FzYd5KubwcuJeHISBypbuut0z+C6qj+nnPy/u0npTkrJ2tojzM3en+ZDaarV2ygW51lZ+SKdzumRJTvN3Ow3ALB8ZfSqOzVc+BSVyk0IYXP06AdZWf0SzeazXLnyX2k0n+TEjT+EEDa12quYnb2fM2d/M3fwcKT7lQrDP9N5qF67mTRDTJ0jca8GnKdCYYpbbv4JDh/57rHOXSjUcd2jCFFIRafBYNg+9r14kpINxJM+YPsZFE+6RNcbYFvoW01XLpfptBOxMO0g3IIaTZIQ+xEeAW6lnB4P4EWZY7ohflESBAGtVoswTMqCdx8kvNzh/M99hZU/eI7uc6vqdRLnKQxDVldXN20Wh5540qU72xMUpU3L61/mrZuzc3ueMoIpb7Wddp7CJTWyZrOAzHFwXHUux2kPiadeunj++69WbyWOPTo7MPx2K/TSxfudJ9g8rkCX9tbWHt74NZLm77TnSYsn71zmmDOpaNL7N5tx53nnCYIr1KfuHNonhGBu9i0sr3xBCZ5NxJPjHKRWu33Dviffv0wUNdNy2JHD341llThz9rc4deoXcZ0jLC6+Pz3+hhv+OzzvAktLnxo6VxjlC5+NKBZn+0a0jHKehBCcOPFD1JIMp3GYnX0L8/PftOEoF4PBsDX2vXhi07LdLomnxGXKrgrT41ogGQ7c7ST7Cti14lDZzhch5UQ8pc5T5CNjqZq4Q0mLTvqcRkOVGWpvOsziT9xH9b5DtL56kcZfvQQWFGaUKFlZWUFKuSXxFLcDKjg0u+2+40YFZEJ/qU5HK1y89Oc89fRPcuHinxAV1RdMuLR9zpNTUtfjOK1h5yknXTyLXnHXvkZKd15mNItm3JRxvbR/bX0z8aSbwY8k/z/atz2OPTzvIm75WP/+zsbiqdF4AoCp+rB4AiUIfP8SQbBMOUms3oi5uW9gde0hoqidu181i/eyk0qlORYW/gbnzn2ctfWHufHGD2NZvUUGB+bfQbl8nJfP/PrQuaKwiWWVJspTKhZn+8p22nnaDsHzmtt/jrte+8tXfR6DwTCMEU8b5jztbNmuWCymGUc95ynpeUrKdlq8VSoVun4XUS4gbAur2i+eom6oVtsl4qlYLGJbNl4y307nImV7j7Klu8J8mdlvv43D/+Mbqb39GPW3HksH+Y670g5UwzhArMVTK6BqualQ02wknrKlOquk/nzmzG9y/vzv8uSTP8aXT7+L02/4X7jo/Yk6ZozVdptRKilB5jjtvtR36JXt8kIyQZXt4NoZEOx5F7GsUp/Y682323jFnecl4mntkQ2P0yLJcZR4KhXnsKxS6kgpESbTsl6hUMvNghpkvfEEYFGr3Z67P1uC2sx5ApibeytS+qyMGNXS7iTiKdOIfcOx70XKkFJpgcOHv6vveCEsjh37XtbWHmJ9/bG+fWHUws7pd9oIPfOud44kaHObUr1No7jBsDPse/G02WBgJDviPuWliwN9PU9I0sykSqVCJ/SwkyTtQfEUdDykkGm5DsAplPAJkF6UzoJrRj3nKSueNPZUiZn33sT0e3tfJuNmPAFYA85T1AqoFMppmU6jxVN+2S7rPOm5aGc5tPA+7nv973Hjob9H5Kxx7sD/jSzkz6ublEJRibs850mX7UY5T8XiNKXSwWtIPF3AKS32fXHqbJ2NnKcwbBKGDUqlBbrdlzccV9LtnqNUOohtK6EphIXjHMmIp15MgcZ1j2walNloPEG1eiu2Xc7dXy4f7zWpjyGeZjYZ1dJuv4hllXDdw+m2qam7OHbsQ5y87WfS95flyOHvwrZrQ7EFUdjMHc2yEcp5ykQVhE1suzLU72UwGK4t9r14IpZq3lsOaTlvB/qehocCKyE0OMA2O6LFjwNkVX2o2rViOucOoNMZXr3nlhw8EarMpMR5aga98sXa2sbNw5qVlRVc1x0ao5JLKp7U68WtgFqpQqPR6FvppcXUps6TYxPHIZ53nnL5BqanX8dNJ36U2dPvQdo+zHW35bdr21b3olj0saz+ZuDAX0GI0oauQrVy7ay4UwGZh/q2KSdqbsOep27iOi0sfDMA62sPjT42k/GkyQZl6kynfvF0bMOeJykl6+tPjCzZgXJStPs0KqYgi227zEy/YUPxVC7fOCRWXnXyn3Ho0Ptyn1Mo1Fk4+B6uXPlM3890GDW34Dypsp0+T5gz185gMFx7GPEUS0ZaT1o87UBcwUjnKW0YL/Zt18LFd9XFWNVi33y7rqccpazz5DouPqpsp2fBNfwW9Xodx3Fynac8VlZWmJmZGetYXeqT2bJduUIYhn2Bna2Wcnj0XLks2SZx4RaSJfZR+kVsOTbFjsq9CWfzM3cmxbLWkFL9fft+v8Dwg2VKpbkNRVqleiut1vNjZyTtJF73Ao67OLTdcRY3FE9e0u908MB/gxDFDUt3nUzGk8Z1j+Bp56mjM54OZfYfpds9O/Ieed4F1Sy+gXgCOHHjD3H7q39u7FVtc/PfSKv1XNpIn0XFFIyXnZRleuY+gmCZTudUui3ckvM0g5QhUVKu28o5DAbD7rPvxdNmg4Fhl8p2icOkG6R7w4H7U8YDpyeeiEnLcXm5Ua7j4okgSetOynbdFlNTU0xNTU0knmZn80tWg+Q1jNcq6ksuW7oblS4O/WU7y7HT5e26+VgULIq+KkNFU1fGuq6NkFIixDKtpnqP2oHRBMHyyJKdplq9lShq4vnbOwJlUqSUeP6FIecJellPo9Dvu1w+Qb3+mpFN41LGeN65HPF0FM+/RBz7yeiWI+kcN1BZUHHcJQjy/87SZvGp1274HiuVExw58l0bHpNlLsk5Wr7Sv+oujkM6nZc2HbSbx/T0vQCsrn413RZtwTXSI3906S7aQt+UwWDYffa9eCLaKOcp+f8ulO1kJ0S4hVSwDQ4HLrtJ9EBROUi690mnjHc9leeUPWe5nDhPXoRMynbr7QbT09Nji6c4jlldXR1bPOkGbxmo8SlxO6ReVyuHsk3jo9LFoScgsQWiYKXiqZwpEzlSiYOgunno4maoYEeP9XXlZnkDM9gCPz9dPEu1kqy4a+1t6S4IVohjvy+mQOM4C7nui0Y5TwLHWWBq6h7W1x/LzTPy/SvEsT9ctnOOABLPu0Cn+3Lf3xdkV+Tlz7jbrFl8q9Sqr6JUWkjnvGmUCxZsyXmqVm6hUJhmba0nnsKwtaWeJ+jNtwvDZu5gYYPBcG2x78WTlKOjCrSoktHuNIxnG58HxZObLH/27KS8l8xo0/Ptun6O81QuZ1bbhUgk683GRM5Ts9kkiqLxnSddtgtjde0S6tNTADz77LNpn9WodHEAUbJA9PKeOgPL4gHsYhXbmyJwrn5em15h1mgcQMrecn2NP2KuXZZqkr+z103jeQGZGsdZJAiujEwP73rncUoLWFaR6enXEcddmq3hQbi9ZvBBcXQ42X+Obuds6hT29qvHo2bcbdYsvlWEEMzPv43l5c/3za3LW2k3/jktpqfvZTXTFxZFzdx08Y3Qw4H1ooQoauaOdzEYDNcW+148qaiC/F071TAupcxtGO8TT+X+hnFXKrHkWYl4SpwnveLOC9QXYrbnqVwp4xMSeSFxNyIgIgiCVDw1m800KHMUKyuqnDBx2c6P0mubnZ9lZmaGL33pS/ybf/Nv+IVf+AWWl5dHiyehBiOLJO+p2z2LUzqEZfVWPum+J8+++jJZ2uTcqRNFtS2V7UqlAxQKU7Taey2elLPkjijbASNHpHjd82mv1PSUKkvlhWWOFk/qcbv9Ip5/sa9ZPLt/cIAwqH8TjcbGzeJXw/zc2wjDNRqNXrxAmvE0Rl5UHjPT99JuP9/nGtlj9mFphp2n1sQCzGAw7D5GPG02nkUfs434vo+UcuRQYEjykgpWGpTpRImQkEokDZXtQlW2y2YUudUyUkj8dhfpRTRtdczU1BTT09MAQ/lLg2jxNHbDeKbnSYun0lSZj3zkI3z4wx/mPe95D3NzcxSLRY4dOzbyPJZrp43j3c4Z3HL/F7XQ4kmON+x2I7RY8rwKcTydNk6DmuEWho1Ny3ZCCLXibs+dp+F0cc1mQZld7zyOo9wj1z1CqXSQ9Q3E02BZTj93de3B3P3F4hSFQj03KNPzLuD7lzdtFt8qc3PfAFhcudIr3bXbpygU6hRHJMdvxvT06wElMOM4JI67W3CeBnuejPNkMFwPXH1AznXOhoOBhW4Y397XHDUUuDjTnyljVXrz7SwPbGml4il1npKynRf5lKxe6CZAuaqazLvtDpXQoVPyQSrx5PvqPOvr6xu6SpOLp6TnKeyJJ6tSxLIsFhcXWVxc5P7779/0PJZrp5EFne5Zpqdf17/fsSl2DtCIHiCOw77G5ElRYsnC98tIOdPnPOkvtWJp8y/YavU2li7/RdKAvjfhhKpsJyiVDg7t04Kq611kemCfckPPMz//dkD97E9Pvy63abzbPUehUB9KwbZth1LpAKurDwAMOU96W57zpJvF88aybAfF4gzTU3dzZfkz3HzzjwHQab9IpXzTlv+upqbuQogCq2tfTRvIJxU+hcIUYKU/Z1vpmzIYDLuPcZ7GiirYXucpVzx1wjRdPH35zHy7uOXjUqSTOEyiYCFcm7gVqBVWUYBT6A931KNa2h3lPLUKSszosh3kB2VmWVlZYWpqikJhTHFSECBU2S7S2VW14TiCzXBfPY97cjbNeBosEYk0riDadOTIZnS9c9j2POqfwxzd7rl0Of1mAZlZqrWTBMEK/ojVZIMsL3+ez3/hbQTBeKsex6HrXaBUOtg3UkTjbuA8heEacdzBdXphkdNTr6PTeWmozJeX8ZS+RhJHAFAu54mno7k9T7pZvF57zeg3d5XMzb+d9fXH8JNxO1uNKdDYdpl67TWsrX2VKJlrN6nzJISVpIyvEsceUvqmYdxguA7Y9+JJxowMyUzvzg6LJyklcSfoK9tBb0QLKIfJlUW6QS8rya4WVdkulPgEOMV+5yqdb9fpEHcjWpYSXvV6fWzxNMlKO0j6lQpWn/NkbyEBfPpbTjD1juP4/iWkDIdKQFa5QClQYqDTfXni82fpds9TLKroA8uaJ447hKFqbNdz7TYr2wHUqicBaDWfHet1r1z5a7rdszQaj499rZeWPpmsDszH8/JjCgAKhRksq5QbV5AOE84mbSdu32De04biKRnXIkQh9zpGZT3tVLN4lvn5twGS5eXPEUVdut65qxJPANMzr2d9/dHUOdpKyU2PaAnD5pbPYTAYdpd9L56IR5dYdirnaUg8eRHEDIunShGZOE9RK8C1HNqd3ngVPaIl9kI8EeKW8sVTx/OQ3ZCW5VGv17FtG9d1KZVKYzlPk4gnUH1PqucpRJSstJS3FTqd4aRqgNo3HOXgu94EsOnIj83wvPOUSqqkZVuq3KVX3AWTOE9aPLXGE0/N5tf6/r8Z7faLPP74D3P27MdGHuN5F3Bz+p1ACdtSKT/rSfd5ZZ2nqfprEaLA2vojfcfmBWRq0kHBzpHcESNl9xhR1ErFKex8s7hmqn4nxeIsV5Y/Q6dzGtjaSrss09OvJ469dHbeVlwjLZ567pVxngyGax0jnuTo1Xbs0Go7byCTaTBdPH35ciFtGI9bAW7Bod3ujVexqkXiZoD0Y3yGxZNeedf1PGIvoiW7qeMEbBpXEAQBjUZj7H4njShaSF85T7o3a6uMKgEVFypMv/Z2wLoq50lKmbg1SjRoB0rHF/ibDAXOolbczdBsPTfW6zaaTwPQaD411rWuryuHan2EU6VCH1/GLd8w8hyjgjJ1n1fWebJtl1rtdtYyy/GDYJ0oam5QtkvEU3l0WQ/64wo8/+KONotrhLCZm/tGlpc/m47SuVrxNJP0Ol258tcAW+pXKhbnCIJV4zwZDNcR+1o8yVjCOAnj25zzNOg8pU3hm5TtykW3TzzZtRJRyyf2IjwR9PVQZc/v+clqu7jTJ56mp6c3nG+3uroKjB9ToBFFGxnGRNsintSXrOMMOx2WVcR1D1+V86Rzj/SXfjFxoFLnyV8BBIXCzKbnEkJQq50cy3ny/UupqzWu86SbqvX/B2m1niOOu0zVRyd0VyonaLWeGyqbed1zqtQ20Gg+Pa3CMk+d+ihnz32cCxf+EBiOKdCk4imnWRx6oirbNN5Y39lm8Szzc2/D9y9z6eKfASpN/WpwnEO47jFWE+dpK3Pp0rLdFvumDAbD7rOvxVPqKI2KKhA72zCuYwW0u6Tn2WmsSkEldSdCpOy4dLtdokilhauyXYj0QuU8DYgnff5u4BF3Q1pheyLnadKMJ01atmsHQ03wk9LpnqVUWsidbg962OzWnSed8TQ9dYL77ruP2269FyEKdD213Q+WKRSmx17NV62epNl8dtMZd9p1mp6+l1br6yODK7OsJ6Kp03kpt8l8Pckw2mi8ydTU3QTBMt2Be6YDMgdLbQcPvAfLKvL1F/53vva1n+bZ5/45AJXKzbnn16JqsEdNo7dn4woau9AsrtGjWpYufwqndGjs+XgbMZOU7oChFYjjkJbtjPNkMFw37O+ogngT8aQbybc5YLzb7VIoFNIVbCPLdpmU8bgVUFmowKp6frVaTebbSYKVLoGIcMv9zbaWZVGyinRDH8/z8O1wSDzpBPFsxIFm686ThQxUSGbxYGWi5w7S7Z4Z+UUMUC7f0JfdM/H503luR3jf+5TocJ4/lPYABclQ4HGpVW9TM+68C2nidh7NhnKbFhe/nbW1h2i1vk69PnosiZQxjcaTlMs30umcptF8krnZt/Qds77+GIXC1IZuyvTUPYBqAi+Xj6fbu93zfSU7zdzc/bz9bQ8TRV2CYBnfv4yUMfXaq3PPX6ncRL3+Wmbn8uMoCoUZbLvKCy/+W86e+zjF4jSdzstUq7fsaLO4xnEOUq/dQaP5JOUthmMOMj19Lxcu/hHAlubSFYtzxLGH7y8BxnkyGK4H9rXzpPObRuc86eO233nKGwo83PPUSxGP20E6HFiX7nQEQGtJuRA6miCLa5fwAp9mqJ4zKJ5gdFDmysoKhUJh5ADfUYiClYZkXnXZrjN6ZReoBmTfv0QUdUcesxFpo3SmAdp1jqSiKvCXKY6x0k4zbtN4s/k0rnuU2Zk3po83otM5TRQ1OXLkbwP5pbvG+uNJk/fo3KJq9SSWVR5qAve887nBmhrbdnHdI0xN3cX09D0bHFfhjW/4z8wkAZKDCCF49av+BYcOvY9a9TYsq0SpdCB9X7vB3PzbgKvvd9JMZ96rbU/+y4Ie0dLpKDdw0pRyg8Gw+xjnCfYk52kw4wnye54AwuUuxFCp94snnTLevqzET554cgolvK5HS/TSxTXZuIK8pvCVlRVmZmYmDhEURYto1UP6MVZ16z9iUkZ0vXMslL915DG6ObrbPUu1esvEr9H1zmNZTp9ActzD6VgSP1imUr5x7PPVamrGXbP1bBo4mUej+TS12u2UyyewLIdG82lG+1S9kt383Fs5e+a30j4hTRR5NFvPcPz4D2x4fZZVYGrqtayvP5pu003zBw++Z5N3tz0sLr6fxcX378pr5TE/9zZOn/7olseyDFKrncS2a0gZbSmsVYsn3QdmnCeD4dpnnztPShSJTVbb7YrzVBhe0q+dqHBJxRNUp9WHaieJK9CuTms1EU/14d963aKDL0KaQjkzeiwLsGnW01ZiCgBEySZa9fqucSt4nsp42sx5gq1nPXW7ynHJCkTXOYznXUDKmCBY2XQocJZicZZS6SCt5ugVd1HUpd1+kVrt1VhWIemT2th5ajSeRIgS1eqt1Ouq7JSl2XwKKcMN+50001P30Gg8lfbppE3zzkby7ZXDzMzrueWWf8zioW/blvMJYTM9dc+W+6e0cFc/w2JL7pXBYNhd9rV42qznSeyS8yQ74VDJDnrOU7CknKbKtGpGHSzbddbUKp1ybfhD1yk6eASp85QtwWkhlbfiTkq5dfFUsFR2FWBfRcN4b4ba6Bl4Ze08bXHFndc9NyQaHPcwUgb4/hJBsDJWQGaWWvUkzQ3KdqqkF6cN0vXa7TSbX9uwybzReIJa7VVYVol6/U7a7Rf7wjLX15Nm8fpdm17f1NQ9SOnTaCjBplcW5vU8vRIRwubEjX8PxxkeYbNVbrrpH3DLzf9oS8/Nlu1su4oY+ducwWC4Vtjf/0o3axjfrbJdezhdHDJlu8vKaarN9YsnXbbrtNTjPPHkOsp5auFRdSt9Y1YcxxkZlNnpdPB9f2viqdj7sdrKaJb0Grr5AZlZ1CiS0tadJ2+4UVqLKbVqLpyo5wnUmJZW63nkiKGIeqVdLWm6rtVvJwhW8Pzh/CXQIZJPpiGSekl/o9HLh1pvPEaptLBh35JmavpugHRunc602i/O004wM3MfR45815aeqwNYfX/JzLUzGK4T9rV40r/pb5rztAOr7Ybm2uWIJ+EWQPTKdu50Bdu207KdKFgIx8aXqmdqMKoAwHVcPEJaostUbapvnxBiZFzBVmMKYEA8XY3zlKaL56dZg5oN5rrH0iTySVBz8y4NnV8/bjRUaWySsh2oAcFx3EkzqgZpNp/Gtqupa1arqVV2zUZ+6a7TeYkwXKdevwMgDZPMNo2vrz+eDKrdvD/NdRZxnMW076nnPI2+z4ado1joldK3khNlMBh2n30tnojGdJ62MSRTTa/PEU85IkNYQgVl6hlxtRKVSqU/ZbxWxEPtL5dzVtuVy4QioiE6TE0NZ9DsjHjq9W5dTc9Tt3uWUukgtj0sCrOU3WNDuUXj4PuXgHjIcdERA7qvqDTGaJYsesZdc8SMu2bja9Rqr0rLM3rZ/6iwTH0dWjQ5pQNK/CTiKQwbtNsvbBiOOcjU1D3pzLqudx4hShOXJw3bg2UV03wo4zwZDNcH+1o8aUdplPOEGDhwGwiCgDiOhxrG85wnAJFsF66NKFiUy+X+lPFqEV+EWAiKxWGh4pbV6yjxND20fzPxNOloFsg4T2J4BeEkdLpnNmwW17jlG7bkPOWNJAE9QNdNnZ2Jy3bVW4H8uAI9lqWWCYQsFOq47rGRY1oa608gRJFa7WS6rV6/M3XG1NgWydTU5v1Omunpe+h2X8b3r6Tz8Eyvzd5RLCiBblbaGQzXB/v70zLtecrfLeztX203OJoFVML4KJGht+v+piHnqVrEI6QkirklGx1fIAVMzeaLp0ajkaaWa1ZWVqhUKmlK+SRo8WRVCqOF6Rh0xxRPZfcYYbjW10A93vlVivig8ySEwHUP0+m8BECpND/ReQuFOq5zJHfGXbd7hihqDoVM1mqvHu08NZ6gVjuJZfX+LlTT+AuEYTOddTfOSjvNVBKWub7+6MiATMPuUSwp8WQyngyG6wMjnmBXx7MMiicZxioPKWe1HfR6hqyMeNI9T3q7LwIcq5T7/HK1V8qbzhFPesXdYFDm6urqlkp2kBVPWy/ZSRnT7Z7fcKWdRmc96ZDBcckLyEzPmZmlV5ywbAe6aXzYeWqmzeL9aeL12u2026eIok7fdikl640nqdfu6Ns+Vb8DUC7W+vpjlN3jE13nVP1OhLBZW3sYzztvmsX3GL3izjhPBsP1wb4WT2nO04gmW7EDOU9DQ4FHjGbRaOfJqilxNOg82TXlPLmFUeKptwIvm/GkGZX1tNWYAsiIp6vJePIvIWWAW95cPG0166nrnce2a7nzyLQTY1nlLY0NqVVP0mq9QByHfdsbza8Boq8EB2rFHcRDEQfd7lnCcJX6gKuUbRpvrD82tH8zbLtMrfpq1tYewvMu4ribr9Iz7By6bGecJ4Ph+mBfi6e9iCoYKZ7GLNuVy2U6nQ5xrJbBW0nPk2OPEE/13odxNl18cFtWPEVRtD3O09U0iyc9TBvNtdNsNevJ654fOX9OOzGTzLXLUq3ehpQ+nc7pvu3N5tNUKieGghDrI1bc6b4rHVOgcZwFSqUFrlz5a7reuYn6nTRT03ezuvagCiI1ztOeost2xnkyGK4P9rV4kmOLp+17zdHiKV9oaEcqW7bTK/b0do8At5jfm1Se6n1J1+v5q+2gXzytr68jpdxSszj0VtvZV7nSDjbOeNIUCtPYdm1LztMo0aCdp62U7ECV7YAhJ0mttBseAOy6x7Dt2lDf03rjCYQoUK2+aug59fodLC9/DhgvHHOQ6al7kEnMhel52luKhRlga4OFDQbD7rOj4kkI8S1CiGeEEM8LIX4yZ78QQvy7ZP9jQoh7d/J6hthktZ1efLSjZbu2ihkYXbYb7nmC3ogWvdrOKeWLp0riPJUtpy8gU+O6LsVisU88XU1MAWyP89QLyNzceRJCUN7Cirtu99xI0ZA6T1tcvl+t3AoIWpmm8TBs0Om+lLpMWYSwqNVeNbTirtF4gmr1Nmx7+O9XuVESsNIMqEnQTeNgAjL3Gi3STVSBwXB9sGPiSQhhA78IvBd4DfA9QojXDBz2XuC25L8fBD66U9eTS7TxarvUedrGqAItnvQqtrg9Ztmu1ivbQS9lXCSr7dwR4qlYLGJLi1ohf15WXlDm6uoqsA3i6SoDMkulA5tmPGlU1tP44imKPIJgua8xPItuIp80IFNj2y7l8nFamaynZvMZYLhZXFOr3U6z+UyaTK6TxesDJTuN3l6t3rqluWqVyk0UCsp5HFW+NOwOvdV2RjwZDNcDYqN5Wld1YiHeAvwzKeU3J49/CkBK+S8zx/x74L9KKT+WPH4G+CYp5flR573vvvvkgw8+uC3X+Ic/+Z0U33SeOA6QObU5AViWg2T77lGMRArJfKDEjhAFhFWg0zqVO87DLlRw3EW87nmisENkF+hUp7HiCKREIIhsm3IQY3dWcl+zXT9AQUKpeTl3f6cyRWwXELGKK5DCQloWtfUrW3qPll3CLR/D614iCptbOoeYl8hlQfAb+b1cg9jvCrHvi5Dnx4xGsME6LAn+pED8uD28vyhx/pFP+GWb6K+2llVV+M4A66YYeSm5pgpYcxLvF0rQGL5O656I4reGxOeEKhVbYB2RBP+lQPxQzjXWJM5HfKJHLcL/d2tCtfgBH3GDxP/5Er1gM8NuI26MKX0wIPjdAvFzOX/XhuuK5kKVv/WfHtjWcwohviqlvG9bT2rYMltPMNyco0C2CeUM8KYxjjkK9IknIcQPopwpjh8/vm0XKKOAOCgkzdfDXxwSwLLYToNOACUpEFHv1kdxB+nlN1ZFgUcUd4m6arCvRYRlRcikpigBOyoi2usQ5p6CUkdgRQH4+fsL0sd3Ckh6H9qF0B95/GbEhESyS+x12arulOcF0RPjf4nET1mIeYmwxn/B6BmL+NSIv9tAEH7OJn5u63/30cM2oiB7P1o+RC9YMCKOKn7eInrGQhR77yF6xhp9DU0Iv2ATP7v1awy/XMA6lf/zb9g95DlB9LBF/PK+bkM1GK4bdlI85X0aD36zjXMMUspfAX4FlPN09Zem+I6f/+PtOpXheuWH9uA1//GEx+/FNRr2hh/f6wswGAzjsJO/5pwBbsg8Pgac28IxBoPBYDAYDNcMOymeHgBuE0LcJIQoAR8ABq2ePwa+N1l192ZgbaN+J4PBYDAYDIa9ZsfKdlLKUAjx94FPAjbwH6SUTwohPpzs/2Xgz4BvBZ4H2sDf3anrMRgMBoPBYNgOdrLnCSnln6EEUnbbL2f+LIEf2clrMBgMBoPBYNhOzNIOg8FgMBgMhgkw4slgMBgMBoNhAox4MhgMBoPBYJgAI54MBoPBYDAYJsCIJ4PBYDAYDIYJMOLJYDAYDAaDYQKMeDIYDAaDwWCYACOeDAaDwWAwGCbAiCeDwWAwGAyGCRAq5Pv6QQixBJzexlMeAC5v4/n2K+Y+bg/mPm4P5j5uD+Y+bg/bcR9vlFIe3I6LMVw915142m6EEA9KKe/b6+u43jH3cXsw93F7MPdxezD3cXsw9/GVhynbGQwGg8FgMEyAEU8Gg8FgMBgME2DEE/zKXl/AKwRzH7cHcx+3B3MftwdzH7cHcx9fYez7nieDwWAwGAyGSTDOk8FgMBgMBsME7GvxJIT4FiHEM0KI54UQP7nX13O9IIS4QQjxaSHE00KIJ4UQP5psnxNC/IUQ4rnk/7N7fa3XA0IIWwjxsBDiT5PH5j5OiBBiRgjxe0KIryU/l28x93FyhBD/MPk3/YQQ4mNCCNfcx80RQvwHIcQlIcQTmW0j75sQ4qeS751nhBDfvDdXbbga9q14EkLYwC8C7wVeA3yPEOI1e3tV1w0h8ONSytuBNwM/kty7nwT+Skp5G/BXyWPD5vwo8HTmsbmPk/Nvgf8ipXw1cDfqfpr7OAFCiKPAR4D7pJR3AjbwAcx9HIdfB75lYFvufUs+Kz8A3JE855eS7yPDdcS+FU/AG4HnpZQvSCl94HeA9+/xNV0XSCnPSykfSv7cQH1RHUXdv99IDvsN4Nv25AKvI4QQx4C/AfxqZrO5jxMghJgC3gb8PwBSSl9KuYq5j1uhAJSFEAWgApzD3MdNkVJ+Blge2Dzqvr0f+B0ppSelfBF4HvV9ZLiO2M/i6SjwcubxmWSbYQKEECeA1wFfBg5JKc+DEljAwh5e2vXC/wn8YyDObDP3cTJuBpaAX0vKn78qhKhi7uNESCnPAv878BJwHliTUn4Kcx+3yqj7Zr57XgHsZ/EkcraZpYcTIISoAb8P/JiUcn2vr+d6QwjxPuCSlPKre30t1zkF4F7go1LK1wEtTGlpYpKenPcDNwFHgKoQ4u/s7VW9IjHfPa8A9rN4OgPckHl8DGVRG8ZACFFECaffllL+QbL5ohDicLL/MHBpr67vOuEbgL8phDiFKhu/UwjxW5j7OClngDNSyi8nj38PJabMfZyMdwMvSimXpJQB8AfA/Zj7uFVG3Tfz3fMKYD+LpweA24QQNwkhSqgGvj/e42u6LhBCCFR/ydNSyv8js+uPge9L/vx9wB/t9rVdT0gpf0pKeUxKeQL18/f/SSn/DuY+ToSU8gLwshDiVcmmdwFPYe7jpLwEvFkIUUn+jb8L1c9o7uPWGHXf/hj4gBDCEULcBNwGfGUPrs9wFezrkEwhxLeiek5s4D9IKX92b6/o+kAI8Y3AZ4HH6fXq/DSq7+kTwHHUB/F3SykHmygNOQghvgn4CSnl+4QQ85j7OBFCiHtQTfcl4AXg76J+OTT3cQKEEP8z8LdRK2ofBv4HoIa5jxsihPgY8E3AAeAi8E+B/8yI+yaE+Bngv0fd5x+TUv757l+14WrY1+LJYDAYDAaDYVL2c9nOYDAYDAaDYWKMeDIYDAaDwWCYACOeDAaDwWAwGCbAiCeDwWAwGAyGCTDiyWAwGAwGg2ECjHgyGHYRIYQUQvzrzOOfEEL8s206968LIb5rO861yet8txDiaSHEp7fhXD8mhKhkHv/01Z7TYDAYdhojngyG3cUDvkMIcWCvLyTLhFPdvx/4YSnlO7bhpX8MNYBWM7F4MhPpDQbDbmPEk8Gwu4TArwD/cHDHoHMkhGgm//8mIcRfCyE+IYR4Vgjxr4QQHxRCfEUI8bgQ4pbMad4thPhsctz7kufbQoifF0I8IIR4TAjx9zLn/bQQ4j+hAk8Hr+d7kvM/IYT4uWTbPwG+EfhlIcTPDxz/TUKIzwgh/lAI8ZQQ4peFEFay76NCiAeFEE8mQYwIIT6CmqH26eQ6/hVQFkI8IoT47eSYv5O8z0eEEP9eCyUhRFMI8c+FEF8G3pI8/lkhxKNCiC8JIQ4lx313cv2PCiE+M/lfl8FgMAxjxJPBsPv8IvBBIcT0BM+5G/hR4LXAh4CTUso3olK1/0HmuBPA24G/gRI4LsopWpNSvgF4A/ADyVgIgDcCPyOlfE32xYQQR4CfA94J3AO8QQjxbVLKfw48CHxQSvmPcq7zjcCPJ9d5C/AdyfafkVLeB9wFvF0IcZeU8t+hZnq9Q0r5DinlTwIdKeU9UsoPCiFuR6Vdf4OU8h4gAj6YnK8KPCGlfJOU8nPJ4y9JKe8GPgP8QHLcPwG+Odn+Nze5xwaDwTAWRjwZDLuMlHId+I/ARyZ42gNSyvNSSg/4OvCpZPvjKMGk+YSUMpZSPocaU/Jq4D3A9wohHkGN0JlHzdMC+IqU8sWc13sD8F+TIbEh8NvA28a4zq9IKV+QUkbAx1AuFcDfEkI8hBr5cQfwmlEnyPAu4PXAA8m1vwu4OdkXoQZTa3zgT5M/f5XePfk88OtCiB9AjWEyGAyGq6aw1xdgMOxT/k/gIeDXMttCkl9oksGspcw+L/PnOPM4pv/f8eC8JQkI4B9IKT+Z3ZHM02uNuD6xyfWPYuj1E5frJ4A3SClXhBC/DrhjnEsAvyGl/Kmcfd1EoGkC2Zs1FZHcEynlh4UQb0I5cY8IIe6RUl6Z4P0YDAbDEMZ5Mhj2gGRA6CdQJTXNKZTTAvB+oLiFU3+3EMJK+qBuBp4BPgn8kBCiCCCEOCmEqG5yni+jymsHkj6j7wH+eozXf6MQ4qak1+lvA58DplAibS3pRXpv5vgGUM88DvR1An8FfJcQYiG57jkhxI1jXEOKEOIWKeWXpZT/BLgM3DDJ8w0GgyEP4zwZDHvHvwb+fubx/w38kRDiKyjhMMoV2ohnUCLnEPBhKWVXCPGrqDLWQ4mjtQR820YnkVKeF0L8FPBplAP0Z1LKPxrj9b8I/CtUz9NngD+UUsZCiIeBJ1GlxM9njv8V4M+FEOeT1Xu/AjwmhHgo6Xv6n4BPJWIsAH4EOD3OjUj4eSHEbcl7+Cvg0QmeazAYDLmIntNtMBgMWycpA/6ElPJ9e3wpBoPBsKOYsp3BYDAYDAbDBBjnyWAwGAwGg2ECjPNkMBgMBoPBMAFGPBkMBoPBYDBMgBFPBoPBYDAYDBNgxJPBYDAYDAbDBBjxZDAYDAaDwTABRjwZDAaDwWAwTMD/Dxwts1IPj3ZAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_patterns = 100\n",
    "ndim = 100\n",
    "activity = 0.01\n",
    "sparse = True\n",
    "\n",
    "ns_patterns = np.arange(1, n_patterns+1)\n",
    "\n",
    "accuracies_per_biases = {}\n",
    "\n",
    "biases = np.arange(-20,22,5) / 10\n",
    "\n",
    "print_me = False\n",
    "\n",
    "for bias in biases:\n",
    "    accuracies_all = []\n",
    "    for n_pattern in ns_patterns:\n",
    "\n",
    "        patterns_random = get_random_patterns_sparse(n=n_pattern, ndim=ndim, activity=activity)\n",
    "        hn = HopfieldNetwork(sparse=sparse)\n",
    "        hn.init_weights(patterns_random, self_connections=True, norm=False, bias=bias)\n",
    "        accuracies = []\n",
    "        for pattern in patterns_random:\n",
    "            #pattern_noisy = add_noise_via_flip(pattern, noise_ratio)\n",
    "            patternr, it, energies = hn.recall_until_convergence(pattern, \n",
    "                                                                 with_energy=False, if_sequential=False, \n",
    "                                                                 exit=10000)\n",
    "\n",
    "            accuracies.append(np.all(pattern == patternr))\n",
    "\n",
    "        accuracy = np.sum(np.array(accuracies)) / patterns_random.shape[0]\n",
    "        accuracies_all.append(accuracy)\n",
    "        \n",
    "        if print_me:\n",
    "            print(f\"bias={bias}, n_pattern={n_pattern}, accuracy={accuracy}\")\n",
    "    \n",
    "    accuracies_per_biases[str(bias)] = accuracies_all\n",
    "    \n",
    "fig = plt.figure(figsize=(8,6))\n",
    "    \n",
    "for bias, accuracies in accuracies_per_biases.items():\n",
    "    plt.plot(accuracies, label=f\"bias={bias}\")\n",
    "    \n",
    "plt.xlabel('Number of patterns')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.title(f'Accuracy per number of patterns for different biases (activity={activity})')\n",
    "plt.legend(bbox_to_anchor=(1.22, 1), loc=\"upper right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ultimate-horizon",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "ann_lab_3",
   "language": "python",
   "name": "ann_lab_3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}