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factor_splines.html
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factor_splines.html
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<!DOCTYPE html>
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<head>
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<meta name="generator" content="pandoc" />
<meta name="viewport" content="width=device-width, initial-scale=1">
<meta name="author" content="Samuel Orso" />
<meta name="date" content="2017-09-20" />
<title>Factor splines</title>
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olOmNOjMKhUpWZWHK5LZgl9279229we2OBUX50kuVjv5QDo7PBwnsvrhWJF%2BYDIuVagZDxeFHOF1MEKbsBMEQS%2BKJjOVdXJ1BKw61EH%2BfeqSTzTz3I7ZA3Zuv%2Bwhshy3sDFL2TjctJR6n2SDsfFJ3A0I5ewXfAgugw7s%2B0XQG0SAfFVWHOEsr6TyphSHW5NHFc9J6Wa%2B7B3Dfp42HguHAUINniPlZCpQ%2Fl0CogDIrW%2F8u85iv7sGv8ZzGzYAxjwV%2FMCxTwobJQCTWU8HRPQeruaaXpRqestVdUOXso7dupeF7px4Z8%2Bed3arKFc44AIg51W9ch4kIIiUEocmSk4sBpCcj15oUDRJXYYExl37RmirrkIv55rLASYJJF%2BS3t0nopeptU%2BE%2BmLrLK%2BlPgQyid3mCBU6UP1rVz8R2n770zc%2FXf7x8s%2FNn9fvaFi3rmFHPfmMLWRP4lycho%2FjNPY4W82Os88wiJ34K4tdAIQjAOQkx8YArcM2PaAOjSZBL8uolzAJFFvGDXd8ej67P2AvKpUkOYghcnK7zl300RBcsExwzJ%2Fhbrd7GuYBwhgAIYtbTx%2F3%2Bd4klJ3gtKCQnGIz9InYZEzqG8EkjSzNavCB%2FcXYlcQshhyMsZrI6PYLWc3lOG%2FvlA4rHr%2F3uTFD3r38%2Fr%2B3fMKOke9W4oJ9G566u7au84CpOz%2Fct5R99wF7W6dIYjjnawrHIAh3hlungFOWgXoyzVKbHOr1eD19Il6vISsrrU8kSzbY%2B0QMGpdjgYh60zDTHJKHoyP4404pw27zB4o1o62gq%2BBLL299am8j%2Bzv774zj995%2FdgTOZsOfWr3rnTWPj2h8qGbo1%2FM%2F%2FkYYvmxfms7TtPrM54E7ns4vwBw0rFy%2FaNJjRRVTet31OgCBPABhongUDOCAzuE0h6gnxChToCJ1ulB0iH0jeqvscFBZotflk%2BhMQ5oJDqhrC%2Fl%2F%2FFxmAUlGYeK5Z6Jl5MDec2yJQdc%2Bl5ViNduL1avoZ805eGll04jy6COKheT8S%2BU6kQwdw%2BlW6nPpXF4qtEoBziwAye3mMnRLkqlPRLqZdQlsKxTcLghkqhzjrLL5M%2BWgUwldSkjbL1HPLrCf51d8MHbv66zu%2FmcGl5Kz0YNZ0%2Bmcf759kbEB29qGGrZiYWop2b2R9fYqnKnlWOVzqXqgNfQIB5LtRr8fQLLT7CyT0ZLaL2K0WFzU5e0TcfmojkckcgvcyhJ4pNlr8Bd63VyEhIbiGhfIBFGTq8R9lqcWB2Dl1G79Rn%2F9i8n08OU3L%2F760UX2E369YuvqVUPrI9VryFR8CXc5V%2FrYefbW7svv%2FYNdxUHv%2FOnFVQ1V8yse2Dde0UcAIY%2FzU4L0sA1FEQg3jJT0jVAJFBlqbOOrALk1dCOmkuHNF%2BmpaKOYunHhldNAlZhEyFGpz4R20C%2Bc47Vmu%2B6gqXo9lewuq5TfXrLnZORk9Ink5JjAlNwvYvJBoF8E5N8qd9nN3jrmj7mOx8OPLDXqolpgwv0zZkpuzaeTynf%2BvWjNvnr22b%2BbsfDJR7%2Be%2BcL6dQ1bXlu3CDvOWfHIMytnrhJPHt7x4L7eg%2F48%2B8C5U0euLuu%2Ff8ozr1xteHTRssdGru8V3kwfeHTMsN937%2FzksLEzFdlO5NQpNsMLWdAtnJlizzQYAAQu26AljUvWZbEQlyuJi1Ymcr8Iaal2jjKNg5qJ9Ctqx02jMyDFKHJw8TpUIvjHKhXZQlZ0%2FIwe1eO%2B%2B6%2FRVHpg2mv%2FuPbBuguPMtfKLU%2BtuXfjkIFraEVzg2tlMuZg6O57%2FvXBP1C3kZ3H9od2PPV81RMVE%2FaNAy3HEcaokRS34Ta%2BLAA8XotzQMRiizkRDVfN87X0JXae6NzkVR6Znehb6J8XL%2BY3IKovXMjn0oEDMrkmmc2iXu9yGm0DIkab6hgTZklwj%2FT6FDccpXsmn6Rjlxv%2BknyrTFMR8%2BU%2FcF9%2BDiRwh%2FUCiChwdeXD58cDhSwsRjeikNNcTo83%2F0AtP2DDKLywji1nhxSezMTjgo9eVHOy3LBbJgIQ0OsEsToiIFRHrIjI4wHOlfxEz6a4ZOTXTLq9eTjdTofW1bEH6up%2Bg5GIBDhGEr2BkRNVlMZTa%2FP3HKVyrMMKrF3H%2FKPYUAWjlGsXaRnXrxTIhrJwqp%2FbMtnphFYWIdgGoLWtddqASGuPzdA7YhNaqFZLvVJSEa48LZwUd4YSN4mJ%2Baq%2FctSSXgtmD6gf2emV91%2F9KNj38bHd9l3PX0tq19dMnzFw3OSsgsWjj%2BzqPXn0w4On3e9nZ%2BNJLYFZ1yqkQ2ITFEM5zzwyA%2B1KLJ1kVwpAjsvSTgx3S%2BrQQeiisxv5Ky%2B9kGbnqUmllmSFEhOP6%2FG4ug6C2nJQUPdSt0td36R1IFMgbsUalrqlQAbw4KK1v1BwIH%2FudKqm8NCQbeMHP2LUtVk3rv7Fb4712N3Tt%2FDeaWvZt3%2B8wA7swe6Y%2F5cvjv3I1rHJn%2BAyhLM44ODVn14%2F7bBUDpq%2Fhpxb8c388XfdM%2BrU3veu%2BTws17Pv7O79aFvzMnvxc3aaHRq8sAZX4jgUsP7CfvYntoNhGYquJiAAAKJNPAIyWLjk0ojFqENR0SwqyILNaiG9I0bRYhFECoKD518xh6iplZYz%2B5W8H0OIlBsz%2FtURB6IHmnaT7itJORvb6A94cnbjGZYvHrnSg0zENwfPGTGddQIKJwCEo9xyW8ALGdA7nO0UUg1Wn89iEGQLjwd01iRrUlXEarWAxVcVsTjAWxUBevt4QnM9%2FgxBMbluwe4SAjxpj%2FmcgN0ef3cCt2IAhVVLsR%2F7%2BTIjjZjU9PTeY1ew4I9%2FOvhn8cCeI%2FNf9BnK2Pk3%2FkZ7TF00%2B6HoquhndauXPAGAMIdb09Oqr8gOu6jFpbdQb5IDekccglHi%2FHK2DL%2B4emRymUNIE3%2BRo3WokKfbtNP37Cs0%2F7rxjQ0X2Cvs2Rex%2FNNLuysbxBB7lX3FPmdvl64rwyU44QusOVSzuj8AUTgmDuEc04FdsYcWQQ8COJyiuSoiUsFSFREct4ppwc9rSBlA%2BZuAPZTBx2Az2Uo2CY%2FhIHysic%2F1z59PI%2FdU5CtWz%2BaJB9gi9gKmYebVKZgHgMq89Bc%2Br1GJWSSDAQXQoWAyS%2FreEUlCQsTeEUKRr3B03DZmUZBwxy%2F6S%2FMZmh%2BdTYZHt5OF4oH1LKc%2BeilhJj0UhpMlAKQ6pAbjTRPxSW45Q0CbAac3asPzwaNfrY9LTuyi2ilOhUvnI8SSohNapUJK7wiAaDLZe0dMgujtHRGdt4%2B8%2FHaphRyV9%2Brq5lT1xe9nfPc0a2IrDuKQL%2F%2F9bve3DrL%2Fso%2FQj0kbVrGXCYuWZWXjUhzzD7xn%2F%2BD6GvYau8Q%2BZe8H8LUY7WK6yuVQ2KdHBJ0giCCaTTraO6LTiQaJoshJV81RgnG%2FQbydi5f%2FDYnpjc2ssZGSRrI3Ws1z7dXkYQC8NoLNxfFqVpwaNht1OotVT4GzFDJj9GrpGI15%2BJJiPpxLMg0v6dVv9AONx9jclFWuR6fyFGvI0TNxvRC%2BUjHmnkjBViRGg4Ix0Yn6RGzLWkgJZRVRDKHw1TvRrzc2NpL1J6JN5M0l0dc5snnk4%2BjCBF0QIT1soQCCJCMFzgtw3EBXxTekkO0%2B0aio0pV%2FbIp9V%2BKIgpPrUZJOFCUev%2FJSmsuNBjuVjDK1gKQgp2DnLbuZlRjwuJUAn2MY4nce4COtZjadZSsCntbhh6zRomMm0bbpo%2Bbh4oGrVQLPOume7Uev%2FBCXo1IDsUG7sFsvcaytVpDB7jBS2aqjKCdypaUI4xPzabNJKZdj%2BWvNn%2BtsW4%2FRVB2xkGeEk582NR%2FnE3ZMwaxy2guAqFp99FZ5bu%2BIXqDW3hHqvLVNiOltBiTmueJRtpW9oZgjHIE9sBOOujo9%2Bv1%2Ffvn5h%2F9Eeb77LHuYa%2B94HIt1bArbxs6yU1iIuRjEAnYqZp%2BE8erqdUBRONnA%2Bc75DE6XQaiKGAySLDuqIjKVEtavhpXmSgW%2FmlplYChutYXx7Ay7tLsRZ5PWUePGL949euKoYPr7t1HOh2jK6mdXrVC5wHaoXLBCCp%2BZp8MeAIEa%2BOqmZtns6x0xC7KTL2yZM%2BMtlRs3J6I2pViG8q258sX7OOxndrH0tpz5ki3rzuqxivyf%2FDnN%2BWMCN1SGs8yIxKS3y0aDQdYTwePVm8EMVRGzmVDK5UepkSi6cntnp2Ku8ktw20SOf5bGNm4BcRXyGdhfcfkJ9jQ7%2FVXTzl2vfEZGRLeJB94%2Fzf4%2BLjqZjFi9cuWqJwDVHIFw29ha4V6a0wSQ5BSFrGxTGvV4uH30CFSfoEoJiY4mt0CGlozy8D%2Bo5jgx%2B6jmBbwy4BEI%2B9d3rHnZ0I%2FGN%2B7usnL1ey%2BxM389WLx%2F1%2BINHRbWXfoDLjz%2B6Z07su%2BYN73vyIFFvd959sV3qtf2nfFA35F3FQw8AoDgABCGcv7JvJ7iABSRUp1epgK3CYLmFeJ5qGYSi7k3IEsbWYFQyQrE9PWqJzjM14yPj2OHrLDdhgYZZafDrqOCmQ8UpzGUuFzsLkUnVHMYs4uij%2F2F%2FcJfFxrfee3ld8QDzf2vsC8wo5nuaa44%2BMabh%2BghQAAA4XW1%2FpMcNqJgMuooCJQqiPLlrxWvQhjgF8%2F%2FSgXTwej3O6M%2FNmF1x8zWHdVaFh%2F5uU3bnwXkmg1yXz6aT6km%2BQwpyW6LRdQn2Q0U9TGTotqUGOKqNclWAjJldKcyenwSZ0h8cyc75y5CT3v2xU42u%2BnL9p6UYpSa0Nne7yy%2B1EQ%2F7PaW6%2Fdbm0N88llHNx18ic5qnrv59RXv0YUK93QAQr1q9QNhhyCJ3ORLiskXFJMvtDT5KhocAz63Yu7rj%2FPIY0oTXmKdjuAkfHg%2F60QWROeQZnI4%2Bgq5M9oX4lybrUY5GWGrIBJRpnoDiChTUeOcJmE%2BqKL%2BGCJdcNEhlrSb%2BQ6T8%2BR887zoCZJPFyv1ZQBBscZ6pWKmQyqDLKBgMIoCNwcUdUrMcuuKmVot8AvlzU6qi9roq82%2F0LSFwoaNC69OAIQGdoRMVnSRY2mRUFAYoxcJlTDIOdBSfeJRD5nMSvEEu4B%2BdkS6svyKX6HWC0A%2Bi1c2Kd5c2XRy3h0mgYbo%2F4spg%2FKNEDuCzdrMFFACSacHOUgFevPMXj5rMb9CfMoLfOrSA%2BKF5b9KyigFJCgExOMgQVJYD1TWiQQEwrO%2BG5rpVFUTC3DfaPxsA1vG9pEg3dQ8jnwV9QJea2Zv0k3XKtUKsJLHIlEqwBgjmU%2FLQUfRp9mbCwCxTjhHHZIf9OA8AILRID2BkJ%2Bs1ZoxwDW1OMStBHU83G1fm5MZ0%2B4QzhUdK3f33F8MRKk50lPCUEXzoVc4K1NnTEvz%2BRw6yqMpYkzrFSFGI7jd1ooIt4LJFRHRA24o%2F98LVH4tX7NllapJZ7zS6LZn8QVeLKsVKjrQrxv43GPPvUychyc%2FVveH0F3HR77xCrNs%2FmPDWy89tOWB3js3Y1%2Bb1GPe7Jq5dxTuORZ11TZuHC3LD00fOhwI7OVWtVZygRPSeVUt0%2BD1Wq2mVGqiGX4zmNwOu8HOhccRljzgqoiArYV5DSXF1SDB1sddEk825YBijeRQiVcrvHAqyJ5Pv%2F3%2Bk0l%2F7GwKzGzQ6Wa811i%2FqXFjfb0wlJ1jP%2FDXxwMGLpdcbNHcsTuWvv7ll29fOPPJXwAQpnMOLxWGxbIaK6VuPU3ySmaOmQ0cHDPPzVmNGM9qlJ1DHgNzu6hmOGTcZXYV9f8d8HTbUOn8QrbvuW11Tz3swiw0oRPvyPQu96Sywe9%2B2mlNGRBlVqGU88fB%2BdM97E%2BVvGCx2CV7ht%2FhtgIgmqhez9mjt1FnRYR6bscerSYTkLTqvTcUDPLPA6osi%2BJOiG7ST%2F%2Fn2W%2B%2F%2B%2BTCTLMsNCxmTzdu3Ny4evOmNS9gNlr5647tA%2Frh0V%2B%2Fmfny%2B4Gv3r54%2Bi%2BfxLF0cN44IRk6hdOTDF4jpdzqtkrxGit4uRskyaUyyqIw6paZQyiRZQ632%2B%2BJsUuivNbh53Kb%2Bx%2F2JYp%2Fe%2F%2B7qFl8eecf%2FzBk65bfb7WQLstc2AZl1GMH9v3fJxx%2Fp2pttp%2F%2Bc%2FeGrS8oUksFoBYpHVxK3cVlMjkJ4UaSuj0GvhQMgKIsVkScspUqq0GtY98IAxWmOZS1p2QNgeJSXkPW3DX3mE%2BzrxreeANH3lObN6LH8KHopW83l9G3%2B3TugmsDC9PnPNkLgEKQuYQCzplcKIVu8HC4a56vQ5YpvYtY4ESnSHIzW6Vn%2BQzd72xlLbYWV0R0nXpFDJm6XKvOqvPk5pJekVxrm%2FJekTY2T7teEU9KnHUa%2Bzj%2F8pXd%2BrzbxD1uragaVBdAqDC%2BjaAUkrJv%2FOXKcGMXmJOnbhQXF%2FF3QsHJVnf87VhB3sSqoa%2Fte5X9jf3r7FdPzMgtC%2FccNOnTtwb3ZPb6ZWdOPLzh7amPD50%2F4z8%2F1T4uVE5ICkzt9ewxXYdBbfPqVx54ddvqMauTndXFnYfmBnY%2B2PS66ypEhs2ZFOn5IO08%2FZFvfn4cEPYCCD24nnuUzM5i0nFz7dF7vEkWvcMhVEQcNgOA3q0Y7xjlCatesVT2mALbtRUfM1P06cfm%2F%2BGZhgadoWD%2FjBMnyJuLfn%2Fkk%2BjrfHXnDOow4N5XP4gWAxDYDoDjxAtAwcr9tZ3PJCDa7Ga5MmImVlQ04%2F3EwqZSIqAJJVQc3NDQ1CG3TceObXI7CJWYU1Zc0qFDaSkAubaKudSxTZAEd4Q9TqPRrNP5kj22yognrLcC1z6ISzW5xSTOhATTljhb3v2det7Zv%2FeNGZnLt9g16B6h%2BaqNHZHv0yaP8TSV89QGJTzetxgMRqNOEkSdYHeYAGw2nY7KRje1xiKGfD5zeUyFyuJsRTUiQi0bdclYkzcER73JeuD5E2zOnB07dKSgy2icydpGlxLpQTZOcjW%2FXTo9NjcO5nNT4GQCoiASQHfca2tMVBjHYVRo6SRfJQGoCAfcdruDiz%2BgdwRo66xWHrfb4RPMPm5p0302p1UPDkUPuCLEt534Igi1bHVIVIgEzfAqepHh1bRDypryyOa1DVNmblnVsDhFl79rIuIAXcHhmYdfJicWLNj3cnSLcv%2Fzx9HjQmV99dDDg8e8%2BheuMZq2cnxdUBBOApeiri69x23S22xcWW02g%2FV2ytpSV72Jmrp7m4JG6NDUt95RNPXwJ%2Bq8d0XUSWM2dhSfU9EknsU6wSyDnOwzeLgds1GbYvxvmcVylSHFilGFxE4PYRT74fKaf%2FwOTZcvobX5lZ3PPffii88%2F10Cy2I%2FswyeR%2FAFNmMfeZ1f%2F8rfzH545p1j5vdyW1apU%2B6E8nOEzCrKsS3foHJkBwQhWq7siYrXprboUaHXDzMdZ0GLBqpaeO2hPAhMUr62Y%2BgRHrThpU8Niry7c%2BPBf%2F%2Bf7yzvryabGFc8%2B6xowcMRg1kUqqh9azT5h%2F1GcNr14%2BGTWl29fevfUeYVXHNNSlVexqMKW6qHJyT6bL8OfnOK1pqalecxOp8wtv80MFRHz%2F%2BY2VT5yJ1l63Ul6r3vQ0njtQyL9GzaIW15cvXnjnI8uf%2FfJ57P0SQsajObpM%2Fd9mHXp3YunT59birloRDO2a6z%2F9T38eEzFCzE9okGOpw1ywy6zXm8wEF4DsZrB4FYtg03rc2nRkaE5IY15ZEfvjt4eRQtfaahz6rrsFoaZNlk%2FfTbaJFSenDQjlrnS6XyW1twOtIplrqLzeuZaEfHYJKq%2Frj%2F5t8pdueG5kbsG25Hfpq50%2Bj%2Fe%2F%2BtjA%2FbXzF82%2BdmN88r%2FevSPL3Z6ftEjj7Yds%2BJ13jSzsaHnpjbt7h4Uvrdr2aAH%2ByzaXLm4R1W3O7p2KO71FCCkX%2FuG7BQrwKPWJlwu3jPioEKS1%2BC0OXtFLGGbVeaCkj1xU3kqIVjV5ONWqo52xVGXhtxKNuHyEMcdA5NSJuSy17ZurRiBXdlrw2vN8lyzHQeQZdU9%2F83mRWePngiAsIOvrjKhElx8fh86ZZPJ4DS4PSaz2aZzWdVV7TFqEbMS%2F4daVmW0rJcrhBY127EvX9TPNNQl6UP7Z7zztlAZLeMO6GMSvnpozV2Dj54hp7RcjgiVau%2BHAQ0ms6hHK6jhiJZl%2BNX0NFTicIYQt7ER%2B76ptuiMte%2FtYyP4oI%2F8o0cx9iPtrx6K5UpSgI%2FWinsblz4lNc3rsZipYBZ0yQ7ubnTuxCyYK7c2A1U2Z2Rlk8LhUHSq1BmbsoRPKeSfcBbp2qSdPsY%2B3jNxsk5nLHCcaHqjg0snBF7dzc6QBZ3OvHR%2FdK5QyUaz6j5l%2B4tJbXTp7trW9eRvHClACAIIOpXGzLBdFiVAUWlxQZ3RLaD1pnQ4ngmjmhUfYgteQT9m%2FJktwFVH2Cn27hFSQLxsGO6IfhU9jUdYD0AgfL1LfHw3z%2FsVMqnHK5jB7OBLO0UHfIJCVam1GRJo46KKOdrSUrLvuwFOnfnuS%2FtYTsWfl%2FStKu2xq3cXzuCVn9wf%2Bpn87mrGy5vtC03HtkAsZ6YPCZW3yJl7RUQr6npF0P2%2F5cz0oeZ%2FksHR0%2BTL6D5y31Q6eN685sPxrixetlPl5%2FYlJxu9AFbZRbmnpqlpTq09K3F7TdV%2FbpXcPJZTfEtxCddDvj7d3EK4ZLfHjedrpx794PFH58%2F49MClCxdM44aRZaRxE%2BaPjywnw0Zg4ebdS6Xj7NzZoCl4FhAvMxuZrfluorSo0RSABN%2BtlHzx8nKeJv3cDAiV7Ijaw5Oq4OwWDQ4H8UFqqsXiE2laujso0QScEzYFFXSDxYr7U7DPVNCV5Dj2pcRw4eKhDx%2BZ%2F9jjp45OnvHwVFIePIvB49LSPRvZ%2ByPvJcsjvOq5cRenZNg4zJn2qEvdpyXVQg6tAS%2FXAzu1JvkcpuoIdVglCaojEuTngS3pjfw38rSkOlOZT8nQVNOmbD9lKoU5HFg8t2TMUz2mRrqPyi95omTcisrHK%2FsMJSfuLFn%2FUKvsVinhsvqH%2FRkZSeoOPFuKdcJwrcuYCALV8343AGpSu4xtNPOWXcZcCQNO1%2FXt0PNKk%2FGszp3Ly0IVZPfVC2Lfxb3C5ZVhQDjK7fd5dVemazjNozNTahCARxo62irVJxKnwUz4SzDKgg%2B07k9ljt9sw2apra1KOJCldLR6NAOuqD89OWHNwpPHcdniPisKChY%2BtHv7My8sX%2FFdifTO%2Bxlov4LNXXfvoH7vstCH5z462QkQypUYSDzBpV4Zzk5y6s3mZI%2BdGD1OMS3dlORL6h%2FR%2B3xOcNr6RpxJIPa5uRWkRdPQzZ6Nm29lf5Lfinl2ypuduEqQxqONXTatnD0HG9jQblU05erVU2%2B99f%2FEEzUL%2B%2F1uGTs397MxS%2B7YtDz%2FxwtzsfO%2BU4psZqMkeIVtnHNByAibW0GmBSxtctLd7iwZeNSYn1gJchaVBku9il8r9co82Ja9clCxDnKwNLs0IXQ6VLV4%2BOLx8%2BeOq7t%2FUVXVgmF14%2BYuGrN42MKqeVtnzHh627QZW8mHj01aNmxh794Lhz059ZEFD%2FCHvfj7JZN%2BN2XbM1Onbd8BiscDEJT9Fw8MDrdzWGSj0WYS9URPTS6LW%2FYmGSwW2So5HBScbqsz3UmsTqvThG7JlATlWg%2B33RHrzL7lpjuGUOGj1uaovjBEKnH2HjYCJfY6dmGv72BvYGd%2BARu7j1wgZ5vZ3Ma57Ec08RslQBKsgaxUVYkkUR726QUqUDlmFjgmiYqtbgjFLYRiI5p%2FYebmnxVpXPuF1kupUABdeGdcdiE4pdy0Dj5fmkmCgNS13E07lbRqK%2Fn1%2FmCviN%2Btt%2FWK6OGGznh%2Fs4t9I39VVFmLztSUlwuwZdCiRC2l%2FKk33lG0dHD%2FqprTbw5%2FZmTxqMV9Z8yYvelw%2FcCqjf%2F%2B6K9P9H9t4KLl7R%2BcvmJR99W%2Ff6Ggbs3LPQbRnMF1WW0mD5q1NDW4IJjSKdy5prTH%2BklDl%2BfctXrZxm5rs9r27dWuY8e8oqHTRvWb0MVZPfnuKWXOMUCwWLTQ8eKH6u5TWpiTanKAI8lnpW495N90QCAhzctKeI%2FFxVnZpaXZWcU4pzgrq7Q0K6tYnFrUrl1RYUFBYfwOQGEM7xzvEdt5hxKeSwWDXmrNT0936a1esbSDZAKH1ZRuIuCwOYjJYXKk5AWcoRQByhNPBdhblgFRMxHuG90bnN2obu8KDjc3eYHM1py5DiFU2NqhNXTQOXMWz10weE77sRWvffDZq0880vHB5vXv4PB3les1tv2D02z76xP2YNvdezD3pT3s7N497JOXhMCeTTu3t%2F2dq9X3n575qfMjIXZI%2FQ7b%2Fu6brOGD0zj0rT%2BwD%2F%2BwB3P2xr8GQKCCushU8W1OdzqUhlt5pRQDokeJazP8rQwGh88D1EYJNTvSOakf3feGku9qVGpqG4xTV8ojfbXWGSt18iYUtdZJXEnDlt0%2FedPztWvHjM%2BbtnB%2BHauecmLUlAeov2bk6HHjJkhCcGFoRIcJs1jnI2OaCgRBqd8NhFraSI%2BCBGbICTupxI21YNTrBbMkWKwmUYegHGS5WbPRiyhjVuw2EAfPVEriM1kjLsUhtexzTK9lO0kQ1%2Fdk29mzvXB9yo23qh9EHfeDXhAhJWwiKKAki0J1RCSQr20nattixUJOXfM71Bv9Hhc%2BCdeuaV3LRAIbAAjXdUoX16r7wqGgF3iOLui5Zpn1JodXKu1gsnFoi9Pi0DmtjnQHAR63E4fT4bythikCCP22ZKVVoUS%2Bhp0Bqm51Fnr%2BL2UjHz5YPXLwfRNx36B%2Bl3eeXrwWxYbNVy%2F8n%2BpGrtwd7tNtSfXsNFaLo9jTdPZ89ub%2FpXB47YrkEiRpzW3r%2BoJ09UfBJLnmAoG5dBi5LJ5U83Z%2F2GIGp7L7nGwzHPNQhS3J7yWaAKe27LkytvA6c%2FfPn39g4Oqa%2Bfun195VPX3qwLunC2vmH9i%2FoGZlTdOCgdOm3l0zdZoiv%2FGASic8yQYLAMhwBiA6Q93NqCLLub9OUmpcstOLaHGCwAsItnQvZqjyadHEUVx6cz%2B0JMt%2Bsjy645vIQH91edGont0XbPj9msiaPXiIVI2%2FNHhk35IePbMLh0yeP6V6%2FZPPA4KflKlzBqAsnGkVRaCONIPUOstxn%2FMhJ%2BnrRKMzxUmcTl2yP92s88eVhKvIfTe2KDHRmKtlyd%2F2PpPpA3vsPbRzw4w1sz%2F8snbmA6Or7%2Bw%2BpUPP8mXDl2wVvqx%2BwJu%2F%2FYmVHWb32L5q0oAeXXrkBYa2LZl5056LnkfvwhP6xD0X5YAIN3pyAOvaT85494494cnCD133dnN3O1oEqNZDegiV4IHicLJoMOhs4HS6dC6%2BLeC2ulLMRKks6LWkMWHX6XqfaELKyMnTOhsGs13PNCxJNkz%2BZ%2F0Qg6GhAeewK698pKaNLwyr2caOScrsU1mzMEJygRWCYYcgIoBopDa7TidSq4jaQa%2F8RJkG7MortqVTEvILI6Z9PL1rzacn%2F%2Fov0pY1S3t%2FraYhx5WrKDBA2ED6Yh0dqvitsEECMJuofkCEQsyAJOqq2jzatUOseZR82L1nz%2B7xMwlZzIVNAOBQIge7xQhgUfrILXa7jtog%2F71CzQq3qDNoZYbSkOzBpo31obZtOw24a8BDQx4ubWIXRk7UT9S1Kckrtu%2BbHgSEvqQKP1d3kPleHwFKDSZuX2mGBGlK3sc5EGO7FpnEzw8MXLlQ8pQsvpNv4K4ld9471NP2%2FhFAoDt1kaPi26q3zgo7lONnEnBvHfMfbr3iP964r4XTTjgzJSYsWHJ0V%2F3qF3eu3%2FB8lN07fsKwYRMeGCZM3nHw8LPP7T%2Bw%2FTH%2Bb%2FYjjwCBau4hdsY9BF%2BZRr1AgMrEoJdu5R%2F4fBhELEUxdqM72c5aTGef1%2BIQVnvjPTGxCb3wfhzek01IufGW24c%2BAOIZzq8gnCYLACAbHrsGKMNHNDV6EPR%2FosTBA8ziYuCw7Tjs%2BThseQz2CwV2Ou3PYeV9xMZBVchkAMkvnuAQM34FFf4CxEZ9KD5qXmxUIBBiM2mNMBxSoY3Sba1zpQWwlbVVwCXk5EIqmmhqKj93lzEgkm2zG3tH7IEWecP9w%2B9rGZ4ohslCYnXDUm9MGF2J0ihbnJBfkf59Rs7q4vv9Y9X1ozq9%2BdbRTwPhSMnYbk2zOnXtXqqkXKHH1tZM7NOvw5ip2e0XjzjcWDEhMjB%2FyIz70jFvcU%2FeGRvmVKrdoPJ0bltbq9R1v%2FYaDgTdn4hNzIa84ltA1MLCGETS7SCOQSAGkdoSIv86xGsg3HKMrOsQE6CUQxiaKGmtgtyAkWIwIMNxKIN5QK4xAIk3MIIVnNA%2FfAdPM%2BwIOhPaRNEtuvROycm7kHm7iMHM7wabASUqOtByowkglmHm5an5G8bOiYau9y%2FSAF7vYVQ2zqR5UUeUXdxLDtMT0SMkNXqR9Lhag0cfURpetbZG%2FAvZr2jRHOZSOkc5ztkqzrMIAf55rM9N5VmbON8PqhxBs8aRmyFqoTwG4b4dxLFrV2MQyS0hsq5DTACHylWC%2FhhXgUA%2BgFip9id54Z5wod3t1glmAKcgCUk%2BrogS11erXC6%2FJJ%2BWL8jcIsuyoNfbqiJ6Kri17tNEXW55EDWhHZV7uVhLarxnM5QhVqpNqbM3bcJ9eBf%2Bbn%2F07S9xNlt4lIyKtaWSunqyntWxHSQcba5nhhhNYrmqS%2B3jurSmJdWx7jiVLwUx3sKsmLb5bgdRi4YYhP92EMegKQaR3RIiX4PgeGy65RhZ1yEmwMdxnW4b5z7CQrQJJmEDGMEX1st6ino0mXXgy0%2B0x2rMHLeOu0ewbTh8BHua7RiLw9m2MThS2DCa%2F3fbaLyfPTsaR%2BCIsWwrAOXzv877434CJ6RAQFkZnnRvmsAPExtcAA6rqFMCF0%2Ba32f2945YHTpRoDazQHnjnES1lrm3%2BFq4%2BYgL%2Fygm0lglwc7fxSoM1BZEj3qKzovZ1zsLv1479tEH9ykddGe2jnx04rGmh6Mjpu%2F9zy%2FNwbFk68SdWpPhmOUDNr2FDyl9dMMXV699l61D26bmvgOVZjp2ZRN9qTc7xVdOrI9LlUxpXLoVMfk7Nb7fDFELp2MQKbeDOAZzYhAZLSGyrkNMgA3xlRNMtEfCbHWUTvF5CmKjOFSQeO%2FfrHjvH9%2BpMOtFUbKDBB6vWeALiC8fs96sl2LdkZoVarkRrHVH8v9lCDcaJGexM%2BzzQ42NZ9GHnuYrO3mL5LvvUdvFy4zXWq%2FB6ei%2FV%2B5Y9yQAqv0oW6R0aK94ppxcMTUAXpMJUu25YkGhw5Hbrl12RaQd5LrV3S5tj%2Bvm0xpaZCBL2vZIQjWCo6Q2%2F2lnOTKUqE%2F1UYJv5ZAOKb36Lxv32p%2BOTCrfUnn27ofnjujZq094yVz2TcPf%2Fv7%2B58IPi6dX3OnPyC0L3b917LZdPTcF8w%2F0mVQxcHZN%2BcTisqHF1YMuXO0r7Nv3562c52pXkOTnPL8TACXovgLUVWlXOH6L57V56vN2t3t%2B7FP1eajFc%2FGz689fe%2BUW3xc%2FvP58whegruiOKsCNGRZehzj%2BcwyiTQwCqAIhKbtXOVDENWdkOJQLre3tedlIaF%2BWlJTe3ghi5y4pbYNtKyK%2BAqGgV6RD66BdECyZQU%2BxzqKriLgsNtBaO9R97viBxZsNL1corarUot3Jy%2F%2BqHSkOv7bLFExMz5TiAMaaVIb%2Fwg7NmPnUc0VVb4%2Ba%2F3xO8a6Hj%2F0reqcOO967tWbwurHswpy73lz03Mt7Jg1ZtfPpwzvoK7OWGon8BOY%2F%2ByddrEUqp%2Fie%2B4eMYP%2F9%2ByRWGwjyVpav5k5sXH9%2F5MVNo2XdQ6Sw4ektO5V1zXc4lW4kzreeMU%2BJFaqnVDtxVIn1ikl8vyqRVppEbn5e21993vp2z4%2F9rD7PafGcS1R7PsEQk1d7TaLX%2FgqAo9URXolZHHYXKGOgqI3xIgApTICovZYRgzDHIa79iUMMSoA4xl6IQTg0iG84RDrHQ4OYwA4CqBbHZ9d89VRlx1zyq6euqsJ5fsnUqhXwYN5jsTttkj7YRp9eETFSj91nsfLIR0%2B9LqSttY3QmLJw6%2F3b430QyITiIlAqxdlBMcj%2FlHpUk%2B6gRVqnV4kwil39%2Be%2FsK5T%2F9sUYXdkp9n3vr4YN77ll3OW%2Bpzc8v7NpC3vppe0vPUtC7Ev2FzR%2FcQmlWcInr25%2BcGHXgtrefZ6cNHMlm8b%2BtaaRbXjh4Aku21jXgbraqmOrzaLyJC1RNqNUrt0Vk%2F1HquySb%2Fe8drD6PPN2z4%2Bp45Ngi%2Bd8fu35a9%2Ff4vtcJtrzCSkx3Wh3fS2Ph2YhR9gJVO1CD4WTPAaDTSACKjsZTifKZjMqJ%2FQQ8tX1yhOfG8nPjUN6iccXE96Pp8ejezqVFHXsFCrqot3J8iefZP%2Fq3KW8Y1m4nPwYfwOUY3tEGCUsjvv7PvxEa3orl8vQ6iZn76u47uxt1M%2Bb2Kjnf3P2ZWVxBdGcfXw7QXSpTl4Si1SnX6L2X2yaUjNt%2BDw0Xd40o6Z25NzmV4rxTJ9pvAljfYjl95r63Iuxboyetf0XbEBQGjL6zuy7cMOvu8aRRcWffLRjTHRO6DzXjNjutSq5e2KSf0PVDI8mmZuf107VNOfWz4851OeBFs%2B5ZLXnE%2FyxtZarrfrYDqw6wr2xGWIjpKsAWu%2BI2t%2BVyXex0jOkFJfNZpfsrQMOsKeYPHqqT%2BNdjB7q5euvRZPnb3oYUWsXUUomXo%2FW9JUVbx7J4HugOKR748Sz333%2Fyd8fMwk63mSElTs38OYRzF9LmyID2Efsvwpjn83sV86KdcDaFQ1NOXQi58u3ce%2FZMxo1nF6Nmgn7Y%2FTmxejV%2BpuEyuv9TaJArLfsb%2BIw6gkU6UvxFLggHe4Ot0uSrE5nKpjtqZKY4bc6eDxpBaOR51hGGj%2BVwg8UUAc4b5zk4det2ia1fWVJO2TlvZF9aafq7NnSl1EYN4y9zJ7BYRgeN5RaonxdR8%2BRfs09fmXXEH%2Becs89LqzDiTgeF3ljSZmwlZ1m55QTGn6hNi32qy1yujAU0iAXCmBQuG26zkI8nqx8t7tVlk4oDOW1Mbbh0RHvSCKixdiunWg32pIyxcyKCIieFj7YoVjVRAeseV9R9a0q5rdyvYktTFkxnyvWs%2FNzup6pu8B%2BROnrBae6djz2%2BInL0aAOq4Y%2Fe8%2BQDVf9G154buPm5xvWCb3mrjKRjN%2B7vp4xEwtQh3q8Y%2Ba0KbPYz19MYDO5tw1mkLIPz3985rOPP%2F10x9NP7wBEE68Q7pH8YFF6wGWwWXmN0KJs3CSfKkwsE%2FIgzx1QzhIE0DR3nLfB89CcmUMWLuFF2u%2BWPJGTu3C%2Bt3TBoiIAgpP5iG2lhdp%2BkEMyxSpMejflw753u9KSrHUfcfpp29njxj46a8zY3z3YPRTq3rmsqJu4b9TM2lGjps8c3qFLlw78AkQdn%2Bk78TN1N5wPn%2BSzg2gC%2FnKrZc73En4mKLYb3o4vKU6BwvQ0olRTQpJEXXkDB%2FTOLAxZRpmn39tucP%2FKjIL21tHmqcL5rLZZnbvMquO3Tl1n1aldEci5Ff%2FFEyCCePMvngykw%2BK%2FeMIh5f8VUtYgffQ49lB7%2BR0HUNTpQenhP6WBBkscHEs5y%2BQZ1WF29yx63DMUTVyicNM3RdTpRZly061Rq55Od5RisXIk%2FbGKDPGARzmLjqmfcouq%2Fe4LkcAKAEQZizSpY1khOWwS0KwXbHbQUZP2M1%2Bx3pUgbyrhA%2FvjeGG9tcNjs9M6maNnb2B4FnXTeR1Tw7TF6DZldL0ZRcHuMIs2WRn9LW10DWe%2Fei9JQJ4ELUkjOsxJ7m6%2BQYbnXvbTY2Ow6D6FHh%2F7lTTBZZSVLOtqB8g4iCCHzeZK%2BdC1Y38ymWJ3vb5SBnteXszG7cAfyXB6EYzgPBD%2FURrIP3Wr6u%2BOqQ9OmDF94qRp5JtZj%2F9u9sx5C%2Ficym8TiHvgB8gGOwAEwU4c%2FM4nELJA1RaoJelK5ZPTbBAIlYikk0WuCInpvPM3e2CJ%2B16ASv2UpGqjUBAIkMRRWhRNSeqtK6QAyGYBkJXxUyYgEkE7ZYLxAQJIVjbPWkkXx4%2BZIJRzr1gnnuT0TQ2Xp3rTPZ5kI5Hl5NZ2wZDslYJtjN4kb%2F%2BILklMTUvtHyFp1rT0tPw0qqdJaUlpzsxM6BvJlJ0W3iDhg5ZN3bwwdMsfKruRW2ZQbuRlt9evdcorVpPyolGwuJT%2FdUDsCHUKOz4AWfRHQvA065Z1snHLxtW7%2FoddaNewgZANO4LY%2Bn9OPN%2BrQSxmD80rC7ed1%2FRm9%2FpuaEacl3tH9TwUsfXIpYPVzprl6o4iBXdYT0AUtDAtYc3y%2BEuJtrjkUwGEVlI650ylKvE%2B5ABA%2FHNTwuf9lc%2BBgItUcf0%2FAgZwQedwuks0ypTyaYjSqY%2BiqLe60l3E5aIWOZ1mxPuV70toergeGwR4g0v8V2eKi0otVJZJ05xV7GHcsHQO%2B0ESk9LSjDup6913x%2FKzVKdeX9THFGzb1v5TDDfpQ45bECoJ9%2B43cBcf0nCXXr%2FF8%2F43notvxJ6rVEnqc1TWG05X9cp%2BAAQRKWiHl2Knck80KgqljCAC4Aq1QvJpPHP6XaxCImp1FiUv6pwAUXstt2Ud9NrbHGJCAsQx9ufEKktsFtJBzroOMYF9EK%2FV%2BGK1mv8PflNJUQAAAAABAAAAARmahXJJOF8PPPUACQgAAAAAAMk1MYsAAAAAyehMTPua%2FdUJoghiAAAACQACAAAAAAAAeAFjYGRg4Oj9u4KBgXPN71n%2FqjkXAUVQwU0Ap6sHhAB4AW2SA6wYQRRF786%2B2d3atm3b9ldQ27atsG6D2mFt2zaC2ra2d%2FYbSU7u6C3OG7mIowAgGQFlKIBldiXM1CVQQRZiurMEffRtDLVOYqbqhBBSS%2Fohgnt9rG%2BooxYiTOXDMvUBGbnWixwgPUgnUoLMJCOj5n1IP3Oe1ImajzZpD0YOtxzG6rSALoOzOiUm6ps4K8NJPs6vc%2F4cZ1UBv4u85FoRnHWr4azjkRqYKFej8hP3eqCfDER61uyT44DbBzlkBTwZD8h8%2FsMabOD3ZmFWkAiUs5f4f2SFNZfv6iTPscW%2BjOHynEzEcLULuaQbivCdW5SDNcrx50uFYLzFHYotZl1umvNM1tgNWX%2BV%2F3gdebi3ThTgVEMWKYci4kHZhxBie3TYx3rHbGr%2BPdo7x4dIHTKe5DFn%2BO%2Fj%2BW2VnE3ooW6isf0LIUENvZs1gf%2FLHojJwdpplCP5gn%2F5gi26FoYa19ZVFOJ6Sxuoz%2Fq2Ti20IKVJdnqvYJwnhfPH%2F2f6YHoQF30aZaK9J8T026RxH5fA%2FWPW%2F8IW4zkpnIfoFLifGB86v0ffm5nbyRs5iaHR3hNBD0HSfTzoPugRM%2BhdN0x052KoHLBS0tdgpidAiEesDsgWYO73RWQz2LWIwjqnMe%2FuYISQtlbyf2NlT9Q9PoBcBnrO6I5ELoMeyHkNnIXGdv809H%2FDXNOTeAEc0jWMJFcQxvFnto%2F5LjEvHrdbmh2Kji9aPL4839TcKPNAa6mlZUyOmZk6lzbPJ3bo56%2F%2FCz%2BVaqqrat5rY8x7xnzxl3nvo%2B27jFnz8c%2FmI9Nmh2XBdMsilrBitsnD9rI8aiN5DI%2FjSftC9mIf9pMfIB4kHiI%2BhWfQY5aPAYYYYYwpcyfpMMX0aZzBWZzDeVygchGXcBlX8ApexWt4HW%2FgLbzNbnfwLt7DJ%2Fp0TX4%2BUucji1hCnY%2FU%2BcijVB7D46jzkb3Yh%2F3kB4gHiYeIT%2BEZ9JjlY4AhRhhjytxJOkwxfRpncBbncB4XqFzEJVzGFbyCV%2FEaXscbeAtvs9sdvIv3cjmftWavuWs2mg6byt3ooIsFOyx77Kos2kiWsIK%2FUVPDOjawiQmO4CgdxnAcJzClz2PVbNKsy2ZzvoncjQ66qE2kNpHaRJawgr9RU8M6NrCJCY6gNpFjOI4TmNIn36TNfGSH5RrssKtyN%2B59b410iF0sUFO0l2UJtY%2F8jU9rWMcGNjHBEUypf0z8mm7vZLvZaC%2FLzdhmV2XBvpBF25IlLJOvEFfRI%2BNjgCFGGGNK5Rs6Z7Ij%2F45yNzro4m9Ywzo2sIkJjuBj2ZnvLDdjGxntLLWzLGGZfIW4ih4ZHwMMMcIYUyq1s8xkl97bH0y3JkZyM36j%2F%2B58rvTQxwBDjDDGNzyVyX35Ccjd6KCLv2EN69jAJiY4go%2Flfr05F%2BUa7CCzGx10sYA9tiWLxCWs2BfyN%2BIa1rGBTUxwBEfpMIbjOIEpfdjHvGaTd9LJb0duRp2S1O1I3Y4sYZl8hbiKHhkfAwwxwhhTKt%2FQOZPfmY3%2F%2FSs3Y5tNpTpL9ZQeGR8DDDHCGN%2FwbCbdfHO5GbW51OZSm8sSlslXiKvokfExwBAjjDGlUpvLTBY0K5KbiDcT672SbXZY6k7lbnTQxQI1h%2B1FeZTKY3gcT2KvTWUf9pMZIB4kHiI%2BxcQzxGfpfA7P4wW8yG4eT%2FkYYIgRxvgb9TWsYwObmOAITlI%2Fxf7TOIOzOIfzuEDlIi7hMq7gFbyK1%2FA63sBbeJtvdwfv4j28zyaP8QmVL%2FimL%2FENJ5PJHt3RqtyMbbYlPfQxwBAjjPEN9ZksqkMqN6PuV7bZy7LDtuRudNDFwzx1FI%2FhcTzJp73Yh%2F3kB4gHiYeIT%2BEZ9JjlY4AhRhjjb1TWsI4NbGKCIzjJlCmcxhmcxTmcxwVcxCVcxhW8glfxGl7HG3gLbzPxDt7Fe%2FgY%2F%2Begvq0YCAEoCNa1n%2BKVyTUl3Q0uIhoe%2B3DnRfV7nXGOc5zjHOc4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2F4nlj89Z9A7%2BtETl5RXdNNZGDm%2BvXYXWjgLDRzEhoLBAYv0%2F0NHAAAAAADBQ8CvAAFAAgFmgUzAAABHwWaBTMAAAPRAGYB%2FAgCAgsIBgMFBAICBOAAAu9AACBbAAAAKAAAAAAxQVNDACAAIP%2F9Bh%2F%2BFACECI0CWCAAAZ8AAAAABF4FtgAAACAAA3gBY2BgYGRgBmIGBh4GFoYDQFqHQYGBBcjzYPBkqGM4zXCe4T%2BjIWMw0zGmW0x3FEQUpBTkFJQU1BSsFFwUShTWKAn9%2Fw%2FUpQBU7cWwgOEMwwWg6iCoamEFCQUZsGpLhOr%2Fjxn6%2Fz%2F6f5CB9%2F%2Fe%2Fz3%2Fc%2F7%2B%2Bvv877MHGx6sfbDmwcoHyx5MedD9IOGByr39QHeRAABARzfieAFjE2EQZ2Bg3QYkS1m3sZ5lQAEscUDxagaG%2F29APAT5TwRIgnSJ%2Fpny%2F%2FW%2F%2Fv8P%2Fu0Bigj9C2MgC3BAqKcM3xgZGLUZLjNsYmQCsoGY4S3DfYZNDAyMIQAKyCHTAAAAeAGNVEd320YQ3oUaqwO66gUpi6wpN9K9V4QEYCquKnxvoTRA7VE5%2BZLemEvKyvkvA%2BtC%2BeRj6m9Iv0VH5%2BrMLEiml1XhzPdNn3n0rj6%2FEKn2%2FNzszO1bN29cv%2FbcdOtqGPjNxrPelcuXLl44f%2B7smdOnjh09crhe279vqrpXPuM%2BPbmzYj%2B2rVws5HMT42OjIxZnNQE8DmCkKiphIgOZtOo1EUx2%2FHotkGEMIhGAH6NTstUykExAxAKmEqSGMFl6aLn6J0svs%2FSGltwWF9lFSiEFfO1L0eMLMwrlT30ZCdgy8g2S0cMoZVRcFz1MVVStCCB8raOD2Md4abHQlM2VQr3G0kIRxSJKsF%2FeSfn%2By9wI1v7gfGqxXBmDUKdBsgy3Z1TgO64b1WvTsE36hmJNExLGmzBhQoo1Kp2ti7T2QN%2Ft2WwxPlRalsvJCwpGEvTVI4HWH0HlEByQPhx468dJ7HwFatIP4BBFvTY7zHPtt5Qcxqq2FPohw3bk1s9%2FRJI%2BMl61HzISwWoCn1UuPSfEWWsdShHqWCe9R91FKWyp01JJ3wlw3Oy2Ao74%2FXUHwrsR2HGHn4%2F6rYez12DHzPMKrGooOgki%2BHtFumcdtzK0uf1PNMOxwDhN2HVpDOs9jy2iAt0ZlemCLTr3mHfkUARWTMyDAbOrTUx3wAzdY%2BniaOaUhtHq9LIMcOLrCXQXQSSv0GKkDdt%2BcVypt1fEuSORsRUwgrZrAsamYJy8fu%2BAd0Mu2iYFhexjy9FIVLaLcxLDUJxABnH%2F97XOJAYQOOjWoewQ5hV4Pgpe0t9YkB49gh5JjAtb880y4Yi8AztlY7hdKitYm1PGpe8GO5vA4qW%2BFxwJfMosAk2X9n9X2cVVfnA36pzHNHJGbbITj75NTwpn4wQ7ySKfAu9u4kVOBVotr8LTsbMMIl4VynHBizBEJNVKBAfMNA9867j0InNX8%2BranLw2s6DOmqIHBIbDfQR%2FCiOVk4XBY4VcNSeU5YxEaGgjIEIUZOMi%2FoeJag4mEB3PUOweCaG4wwbWWAYcEMGKn9mR%2FsegY3R6zdYg2jipGKfZctzINQ%2FvxkJa9BOjR44W0OpTKAskcnjLTcKyuU%2FSVIWSKzKSHQHebYW9mfGYjfSHYfbT3%2Bv877XhsIwGzEUaleEwITyE2u%2F0q0Yfqq0%2F0dMDWuicvDanKbjsB2RY%2BTQwOnfvbMUhiNPFyDCRwhZhdjE69Ty6FjoOoeX0spZz6qKxxu%2Bed523KNd2do1fm2%2FUa6nFGqnkH8%2BkHv94bkFt2oyJj%2BfVPYtbzbgRpXuRU5uCMc%2BgFqEIGkWQQpFmUckZe2fTY6xr2FEDGH2px5nBcgOMs6WelWF2lmiKEiFjITOaMd7AehSxXIZ1DWZeymhkXmHMy3l5r2SVLSflBN1D5D5nLM%2FZRomXuZOi16yBe7yb5j0ns%2BiihRdlFbd%2FS91eUBslhm7mPyZq0MNzmezgspUUgVimQ3kn6ug48mntu3E1%2BMuBy8u4JnkZCxkvQUGuNKAoG4RfIfxKho8TPoEnyndzdO%2Fi7m8Dpwt4XrnSBvH45462t2hTEX4Bafun%2Bq8jIzK%2FAAEAAgAIAAr%2F%2FwAPeAF8egd8lFXW9zn3PmX6PNMnPZNJMRRDMkzmDYgZMRRDCEmMMUPJIgZEepHlRYyIiNhRUdYuS4ksy9reLDYsdOmLLC%2FLy7L2CgKrrCJkLt%2B9T2YyYPl%2BD8804J5zT%2Fn%2FzznPBQKbACSTvAEoqJAdtUhUJpQYjBJVAUrKSkIOJ1ZUOEKOUGkfV8ARiPB7E72m87WJZF58ibzhXPVE6QsAAnMufI4H9XXsUBh1UpOJSJLmQNWqNsasLkKhsrKnA%2FT1HCF9PQzSAPYtD5V5PW4lmFeIK86EcCRbObLp2lGjGxpH4%2Bf0wLkjjU3NDSNGxYSMxbSdDkzomhE1SypQalCISvniob1lDuTL7injC1O%2BMr%2FxmeJtxeRt%2FiJviJ8mmrjFOr0BJCZ3QAbkQFu0ypCZ45HcRqNJQkiT%2FLKsOO02s2Ryudze7CxVUnw%2Bv9%2BtmKTcgEEymzPRlgN2e5rHaeOXyeeiisnJFagMOSsqSkr45kL8Tr450SfM5%2Fy1V66pGvBwTV1BcYcDEX67QjQkbo8cigTplyVI2OHh%2F6zdXHO4%2BiR6SjoxMPzo8O21h2tPx7O2lmylNV%2FtY5Nwubj3fXUA%2F8BuFveBr74CoNB84V6pSnFCLhRCL7g7OijfR7Oy3FalR49AcXYRFBnsQUcgkAYO6H15j6wiAGu%2BI%2BAo6pleFDAWKJZMX%2BaImNunWOpiskIVH796ewAqEzvV9gqX9nQ4Qd8S%2F1V%2FScSM%2FrmsTP9FfNUNIvzuVlRPMFxY5PB6fY6iwsJw3%2FJIOOTx%2BlT%2BWzaR%2BxYWecrR7fWFFanqi%2F33nnn9%2Bv%2BMvXr7mk933%2Fv5Gy3PrN6yZjg7WFV1D5s2oGoh7nx%2Bk2vvTrkeDT0HKlieXvvakkfecj%2F5uKnhm6iNHRk27a6bevTL%2BclH3ulVkX3cBTJUXjip%2FCDvBiO4wQ95PB6qo%2Flen0%2BWTRpofo8nLa04mB3UgpeX5PbMLEzzKz4%2FtapOlXt5a1llpXhN7FF7r8zJ37o%2FiN15Q2XhvsE8RdajOqwFyrwFGETXr%2F0F9u9dNnZsWW9869X1azow9qe%2Fkpc7D52mPRf%2F%2FHcJFrR1npvf9sWX336EO7%2F9x7lqeUMn6frt8y%2B%2F%2FZD%2FJjzecOGEAnxvWdzjpTAzWtHbGjRhlhdMXqvLVZSWnl5kpSoChLJVtcwXSPea8vNLSrT0dEnTegyPaZIUqIlJLnSKhAV%2FpfBuhb9EbE53bYVIM%2F3S45hfiZ%2B7th8IFPHN5QuXcscms1vF8kiAZ2qBsEEEFQX7FnJDeNy%2B8nIF2JLZ7%2F77DPtk3rJhVV9vefPD%2B57CzCF98cr82%2Bs631s4%2FvbxrKPf1XjT0Iqrh%2F%2BuafTMxR%2B9e%2B%2BmxqZnxzzx5l8embstxo7PeX0Ju3DjoqYJA7C611hyd3hAtH%2FzpD5jAAVm4DM6Zjj5C5WIAIu9DuxCIB0kuvEBAKGBbSTz%2BL%2B3Qm7UZjaZqCSBqtrN%2BVQgmAMTua3joeaMhBTicTt9wULS8PSj5x58eNk9Z5c9RUrRiPte3MTKzvyHRd5Yh9vFygP4yq3JlfmyfHG%2Bso1LyP%2F5yqgRNVjuDPclRSGvk7Q%2B%2FejZJY89%2FOA5sTT7ifVb%2Bzru%2FOEM7tv0EisFhErSJGUpbrBBOOo3ms0ypVZUVc0umUyqilarYrDxpN1aJrKQuykJwvwz%2FyPMUOCTXSqlRa6CiEzJy8U4J8DWf%2FjpM%2FeeOMZeLMKpxYqbPTyx088Oz8MKtnMuFqefm4gzAKEZPpUqpG1g5qivGRSjkSKAxWo2giJRKOFCysqS4vjNhQXCAa4Bxz1HEI%2ByNlx0FBextqOk9SjezW49yhaIHbGzuBtOggKe1wgFWVapDCXbdSNt5ghfoNCgMxLA3X1v%2B%2BdV%2Beg%2FvIsdR9MJYWVcS5rISqDg%2BCuVQQLkSiTc7QoHPANIGq49dw6wi7GwgmvujZoUrrSRNsaMLqjsmfjnkYu4aU6SlJZ28xECNyqt0mMrM2pBricBidueiNS5iDcRA0ir4h%2By4yQgGJP%2FDwLVF05IQ%2BW9XLoPLou6LYoTFPCnGT0jYkaV2kfEaBok8y%2B1kkYCeeDQnIEyQI2nUrlDE3kkDT3PzsfZhXMoxZHGw2OmTRl7w%2BSpLeQoW8gexttwNi7C6ewO9hD7%2FusTaELr8eOAMA%2BA1nJtTNAj6jJKAAZEs8WgqihJRgX9wJHOkYoXkf8iwR2RiKKqRRiitWw3lYdnr30cDzNae%2F8Tw%2F1L3sS5gFALINXpKDQgmp1pQxW86M3O8aoqMTlNtTGnSjATM2tjXEgCYfS3hKyuCkFHkzBeScI6WKhFVxLuD%2BEQLt4TkOo6CU5f1drrhvrrVly%2FdspDayfe%2B8EtQx7fuJG0HcbZLyyc1r%2B5qXbojtE1xa0dt4x%2F5c31r9hA6MYtP5DrVgijoiV5Po6KKs3MBOCVStFlgez8bG57v8%2Fvq4tZ%2FGilfr8pX7VqJm1EzJQGeg3j5%2FxX8ruWMbrG4oduFyXxMEFyQlkpkMeJTvhKbCMY1j%2Fo2ykPlEmSr335KxvYPvbZydev29P65KNrX58%2Bc92zfxv6%2BKil76PnU1Sl6fe%2Bl694%2F%2FzIweMjUO1ZPnH2TU3fxqa09%2Bl%2F6OHXAQgEAaSZuhddMDiaZ1epkRAzpTKAxyVzrnGh7JLreGi7qF1VqO5WvoGQ0DwF584uo3cpz4sCBzc9T9SAQPKgoqI082X2QfxhshCzXmZ5Jmoo6MvOYAk7gCWH6cudN5%2B98oSroZZNBoRWbuEw1ygDmqI9OZ36aJrbbTPYqIFmZrldRpdFA27ONADF4%2FHXxjyKYhkRU9LgYsIJ6e%2BpgHAkGUjkgUhLSBg2N9w3IMwpylMaKScT%2Fn6efcC%2BPLN8xActmMGOhu%2B4bH6EpsV%2FyAgOoO0n9%2F%2BHnR2B5h7hr455LAPJ1%2Bwc%2B1i1AYGhXOs6eQf4IR%2BuigYUp8WSlweZTnAWFNpz6mJ2u4d60kbEPGnUwENEvUTbVJbqTCjIAQJlPo8IXEUNdQEJcCAhMvd%2Fgvy8Q3E6TmsbErv%2B%2BZ2tRuuN%2F7f1X%2BzsNyv%2FvYhoN066sbVlcRuZiq%2FiWvuP7rEb%2F7LuhyPfsFPLMffdxfMnz7%2B1fu5qEc0RPdM6QIHLo14FgCDKRFYNMiWU1MaoAsLfupYpQwobhpDby4OfkoJ4iZQWPyy9jNLm8wLSdEtUyzvBB3lwOVwbLXYqnl6U%2Bo3%2BQo%2FHnp1ttBtL%2BihOZyBQXGwBS0Z9zJIGwfoYXGwTYYlLnVeWdKFwoCSqAj0%2FLqoW8qk7kShFiku3kK9cfCPVHyDedt%2FqpeyLL06zk4uXtU1DyfXfE2fPmrng0Ccjbhg%2Bflxtq7zz3ZUzXhrU%2FO6sjqN73mrbXD2iY%2FKzm89vbBp7Y%2F3VcwaOI3vqq674XdnlYysH1Ym8GajvcgekQQFURnOzZJfFEgyCCwqLtNy6mKZRrzd9RMyrUkMdR%2BNfdbfu7DIBzCIaw0J5kS16edcXuNOdBXwbyU1J1ewxtvTOqxtHP%2F3%2BJIOl3xOz3v0nmr9Y%2Bf2d8VNjp4xrbbm7jQ5mdazJdtYzasufW2r%2B83%2FH0fEE%2B3DTXbdNum1%2BHfd4stOSZuvMURh1OXnyAPjtnsaYXeumMPAnaOwXTOb4NVYT72PqU%2BxG7xcf6mPNQAQX6%2FIUcHKmcllV1UUlBRXFZdIaYyZNUjgzJ6Rpm8u6mKrApzM0vUgYbrTrbF2SFHbS18Xa5GhSmF5P7JYqZODSiqKajIK%2FVYNEqQIEZRigFxShVFwJURhGD6JU0ZlDP443kvW7ccNSPH2abWFfCns140peoYDeNeZHHSqlRgkMcp00ViJSV30QKhkjagSue7JMQH4304%2FFkrTgKC9Tjh69VLueUScBrhFPNVAUJJTKEur6Ce0u1dCFuorNZH28UayJb2IaDjjNtKWsWmioXPicrpB365FYFc3LTU9PA%2BB2dlqdhUV2QCMFCAazGmNBl900ImaXkg7mVCR4KJVkyfpRJFR5F86oRckaXOFoe0m%2F7W6YevPVY5uWvzf1w3P7vm99YGyIHU4139VjH6ob1tLvqqpxR9u2r5m2onVI9RVXsHUX9eMTLkxQdnCc6AuVEIv2VCsq3G5XOGzt77rMZaWBtEDvNOgN0au8hkhEMg3QTPzqkVUq5feAklS7rOucMleiPU7ivc6kQtuiYCqrfNTdlVF8fxLxCKgtj3iUQC44%2BjrzOa06UfyDSESH3x2j106vnpWmTXnhlT1o%2BUfT%2Fqt9NdGau79%2FZhf73%2BexCP2T2Pz%2FZefZXez6I%2FgIyv%2FEkRs7Yf3IFpM1FG27n5x%2B%2BNQ9Q%2FotPPTGQSQBH%2FPd%2F9Yf%2Fvjjne1sx152gh0p6f3eKHwYW3%2FEZZ93sA627uCCpcfMzwj7AIC8WN4IKljh6miAWKkBQZHNZgqip6CSZLOSmpjVSs0yBZocIpTouZRiZWGortKL8gsDiITjI5Uik%2BLHJ7FXiYTziRJnywoMgWdwNFstbzxXRcbikdvy72CqiPvXAaQznI%2Ft4Idczsm9VLdbktKzzeY83vfZ7QGDlqalDY9ZNLRSTbODPb0mZneCvyYG9BLcSxY9KQVDSTe5ArmSp7voCQYwWfE4HPqnwOu4AyOYNn%2FC%2FfPZh2fjx7C84%2FaZ8xev2nXHraxT3vDKpkVrHaacdQ%2B%2B%2FxGdXTuy8Zr4NrZo3PgNgDCXI%2FUBnh9eKI36VZeLN%2BNWnxscUBNzSKpskmtiJleyNBOvSfVEKuQRD2%2B0Iw4l2BUdoTI%2BZiikBS%2B9h9OfOtrxL7aJvdiOkQOHDrc2tEs72U%2FHmW846xyGi3DSZ3j9azd1FvUDImwoz%2BE2NIBd1OtGAIdVkjTZUhOTqWTlLbMzaamUcEELnGVzAbVA0BHKleew8ew2Ng534wR8gL3Dxq5ZjO%2FxGuQP7A55A7ubrcHDnUMBdY8RLs0Mg6L5BgnAqphMiBbFWBOzKNxLAnII3zehaKqJofOXXkp5iCsitPAkbol0bqDV8RN4ijmIm4tl7zK2BLqkUsalGqFvNN1AqVkBQDQJoSl5QlZS0MVSLhaCX7P9dHD8OHKMEwKWxLu8KBdxL6ZDTbQo3e8nNquVEFemy2DIsGlmjQdbOr9BNkt%2Br%2BzlsmTu1FB3wd0z5VlnstgW8BBwKLpv9YJL5RlPdMKNOALkU1L14E93sr%2ByVfg43vTxgZtW%2FGXnd1vevKGVHafhuOnyAlyMU3AcPjDybB377rOT591Y2mUHeYJu%2FUg004jIzW%2BQJFm2GGhNrMaABoNsUijK3QmbMnfKFN2XPIHtjr%2FNdmE5uRrDZG78Xj5t2EIGAOCFiawBT%2BozgRw%2BbSAGXiPLwM0MRsr79e4NCw4Rxa5IJL6kRnJurq0bOKEZy79hDV4k7gVL5JHn1l4AdgYS%2BtfxVS0wMJpjIcRkNiOAzUBl2cq%2FUrNZoXwP3VtwpgBXF1eWAOXEQAdVfSMRDKBcx1awhYvEZm7FB7CZETKxJf4D39CN6%2FHf8XkJ6VIlly6LPUkqBVCQArccJKJUl6GXoPq6r3PD1MsbzldfSPxvRcyR3dAvmukGo9nI1bbxUPHKisdJjEQxq9QGilBcN36X0mUp6hA6Y9DpEYujXuXykscVRBpkK4wudhzbcaSC07GdfUgtRrZEms9Wzok3cw1WSi3nqklH6R3oPr8kYcedOm6WR9NMYETFagVwUFlRVM1MVW5RVLtHv11adI%2FEnAKwL1KEcM%2FJO9nv43fpSiwh81U7%2BqQGdrQtXseFv4FZvycdQPQ8%2BVKfDHgE0jgAfBZF8RpdNTGjRO01Mer6daQROSBexQQy16Hxpkj%2Bkj3BXubXE3gz1vNr%2FPlDb76Bs9nSNzaSY%2BxxdivejVP5tZCj0mP%2FOYvf4smfoAvtpHU62rkEFkhGowdsNrvdbQXBV3ZNM9TENGr%2FTSzoRn%2FZLXHoEyAo4ckJSx%2Bau%2BBBspEdYacX8yA6iCb0UGXmlKkTd504Fz8rb%2FgchAXYat0CdkjjEZynUFmSCDVIJg9AhmYypVOVEwBXRFK5UWSV22N7Ev4uHU92T9OQe%2BLX7PPaKziWzWZnfL9pJMZW1bO5OPS3LSUP1S3lg9poocvnk0ySppm8njQw8cTzu4wWMA6PAZgtFm40C%2FWaRcikzJbSWfPzuXKqQ0sxKLdfgl3BF0A82brsgaXLW7gB12EPzH7oTqxuZWvZKtp73M0Tm%2BPz4vvlDUeOLdxZwVwPk1KRVS2cQX0ce4s4n%2BRlpKcHICC7LeCGy4rdAbAELNlGX3ZNzCdRYyq%2BuhvwVHHWrRpn%2BIvGGoVFl%2FMhDadWMcJP9LZen9cr%2Bdin7JuOx%2FZeN2FqnzFL7767DtWvZu2f2TrnyermlsJrn977BC7f%2Flkz5g4srx3e8%2Borqypveeqmzf8qL%2F13n8KGgcUDKqrHbRP6FwNIYiqrimdLCgBFNBhVKlHOuxSdv3y2lARgcoLtYrOlOn53IGEMEF7k%2BdXC13JCQdThQHSbDQaX08hRhsdSYuuXVBAOtyLx4BHI6%2B6CYLnlEXbyLfYFex%2FD9zz7BAf0ztqVZ%2B7EwHn6YufCPz33%2FDraBqjXfyHBI2K%2BRonRKAOiVZYkC3BDJ%2Bq9VNpUJOaj%2BsXtVx6h57CC2dmLTMMKdPlKFXO0a4DY%2BdTwvZeN%2FqJLhrqRy8gSsx%2BT0e52yQh%2Bv2ynlszMrKwci9mcnemSzdRvt6NJiOSi%2BEtCbgo1UyM3WkiKOMKJUtMlGvCIi78nPihD2fPbzWFJ6WPdxqngfix9q9Sr9HQdwoJDth5mUy%2Fnm1hKoRixV%2FmpUJxwVT85trLi1EAa6twb%2BaS%2B9uuhNBsStmnSbVMVzTXLnPpUo6oYTYpJ0C2VLGYDkWXJqFCUkhDL9evG%2BooUZ3VpjZj8Izex59h6fnXg56wfNmF%2FDGMtC5Pi%2BGHyHdka%2F47Y4j27dJCYyF2B7wZVlZEQEERvNFFF4QqiSgVDdslOjEH5Z65AarLLowIDZAGWchEZbA%2FLwDo6mozsXBTfQUqoXleVJiZ0RugfzTJISFUVEExmlYuSRP1I0IAGUcZdOgxNpl1qFqqPbALSzPPvkbfjTVJ6vIrs30m%2FRXi%2F0ykkLWUbyWw9T7KjVgXRIIFRJlTBfN2EuvH0BNZX4iUpmc0y8bOPPmIblXMHz60Xa1gA6MDkVFt%2FZIKYnGpfnBa6sUmAHY9%2FmJhqI4S4fJ%2BQL55xoKIY%2BVYNoOZTiaaCvQtCfCFHMMy1CH34IX7GMmfKjQd%2FUoR8AzFIA%2BR3QIHeUTdBWVYkSTznFd6SVJko0DW%2BxLKLeyTRZYcwiGjADQ%2FjqVO8uP6KGOiGzmqyKN4maq1OtpHWXhja9SRIRonoRhEaJZ5K0NrOFyl%2F%2FvMAAGKNdIQ%2BqATAwK1gBjVKRVTIdwCUpB%2FrioP0XWLww7EvHPD6PGRL5ZkqbKpcLx3ptW2gZ%2Fz7GYIdmjju9pfm6E8Zq6OFTovBQvLy%2FP78LIMhaEkbFrNYZLfbPjjm5jWdnDM4JnvBk0Az%2Fy%2BZVYSeXlcUJWdMvMcN9%2B1u8h0omny9N6YT%2BhuGr1r0xzd%2BOr%2F5xbv%2FOn7T8Y9PswO%2FX3znY5MWPHHDsNfXvfono1K6rn7f%2BK3vx32E27h55MJbxwOBFVznDsUNTsjh7BvIojRg1Mw2n89szrWA2WPUFFDSh8QUL7iGxEC7mCz83SHi7H5mUeZ0aISzRVANCgTlw1AfH9d2D8WobftHX%2B7YNsMT%2BhpLLZbJM2ZOJJNvaZk%2BQ5rNdrPv2XH2t6XzFTdbPuiJ9jP3rwh0PPOXNWvWAMLoCyfoMWk2eDi6esRYymclxCubh8RkDexcM%2B%2BlZZJuOTk32SdwmnJoYkjgUBQyIf4DZqJx81Mjh9525cmTzcuHVf%2FBTQZgFvauOZFVwBH49ZIydr4kH4iQK81M2CcaDRi9Gi%2BobTZhqFy7xwIOIyi6fTTdPt5ft4%2BoT4Q%2BecShOXlPGioU%2FBLkji3iOnVPiAnZ9vHnOw9ON%2Fmw7Jv%2B1omT5kyVp7dNmDnLjWVoRx7zq9vG4YSfTjyy5vt7ViWNk9BynD61y%2BDMEKROSUpzOLKcJlOm3%2BOkzuoYFVUUVMesmuoZHFNTel5aloiry3bI3RbgrbNeR4XKwOMJ6AVAxMMtOP2GaQZcT2aVs%2B%2FY3zDt7LdoiJfID985vmNc3Qb61PyZM%2Bd3NmAPdGAahth3Jx%2B789Eel5%2B4rCjB7nSOkgMeuCKa7SZElSn1%2BqwAPhndyHVz283akJgZqJ4bgp8v7QVDiRwWFgxH9KfOeieocBWpiZ1l%2B9eu3bj%2Fufm1o2uv6ocGOq9zCZ23rKHh3ZdLPsoafsVgoKAwtzSV26sYyiEKd0SrzFlZAwZIfRwOUqzmSkGUpIHpPXr4fJFg8Kp0K1jRqlj7qv2GxYy5Eke5wr7FpDpWXFxYWDksVqi5e1fH3BkXz%2Bn4pxIOWz79gRHv0LneqJs2FQ76ewKfPao%2BpSsqEvmsj%2BykQFfCF6ZeRcGFyUQK8v26El%2F4WGzqS33OfxjpXbL2ndc3sTfYvm9%2BvP3WksHVg5tvOnmsZKGTFc2buvrNabOfa5w5%2Fdrrmura10otT%2FceNqZjJ5Xzew187smt%2F1i1bPw9We5Roeh1xYVrZ732vkM6L1UOHVlb2WcEHT5q0qRRuwBhBYC0lmeDB8LRdATw2Y0Wg8Fo9Nolp1MaEnNqJkCjR6D%2FJfU5336yUOPaKqJJEuCQeFQirWX7O%2B6YxfZjqapqE%2F61bQ958LsXt8S%2F40CwpeDekav%2Fvh0ILAPAD7lsA1jEZFcyGsFksprtJg9Rr4kR6DJ%2FZWoO7uobKtNnnyJUlrW3X3ttO14phMgLHn98yIjzPqkFgFxoY259XSt4oSTqd%2FL0JgaDT%2FNcE9PAaBctOk%2FsjOTEKYEwCRGJxwB6tajQpMDBcxoHXzN8CJbum6GLZe60066mRmnd%2BeJXN6mThXRIWPMH%2FUn%2BNdGgxLmTUKrIsmYzWa0Gg8lkN4P41WCzUcXkofbu2oTf3cjSZdpuokXRuGOyi1dx22KswGZWhYd5AffOIrF9jYxdh40sI74Et93MVivueDXr0gYPcG0ouF4DRIkAevQioLvExgPivyvuhO7qQJ5BQRgeLXS7XPrsKDMzI6PAajSaTPkuq9WRKzu46XwOzWzPRJNH7%2BG7krl7%2BOC8ePqbjJDCRIiEfKFykdziVfBd8q%2Bke9n%2B%2BuvnTGL7vy529F437Xwso%2FdL097ZwvbVXz9jOnlw3rz12%2BLfSS1Lh1%2B%2FurZpy%2BF4kfhtxYuQjGCut1tMFxHAq6vrscoOoatQFU0Xx29SyV%2FXLRG8TS0ierkyof%2BZtWWXEPbn7boC9dce3JHE5yf0pzhpostXLJYMcLnSvcYhMa9mp0Nidu8vu%2FxUrvPeVQMOCCQs6MzrxGVT5986ecr8W6dQmX3ELvzxh7swGyl%2FI6Xt6%2F70Qnv7mhfYKbbnQTS8jE7s8wA7B4LrOep1cC1ckMMn1Hl%2BRVFNlKpZmqrlcuQEq9U9hBOEwa5mQEaKzBKmSBWoSQVlTvPepDFCnPndRKFJtuemosq2GZrG9p%2FtaZv8wfaPbt58TGf7vePdSx%2Fwsv5K9SPtbB87%2FT%2Fs7H10mU722JDgM67pTN1euaIq8dIsyh%2BTpOUZ%2Bfg6PcNnz%2FZanE5V4I0FhsQsv8m6iSfIBUmS5S2dL8HBXl8ook%2BLIkFBaLdMkafPPzxZ2v7R5zsmPXeFIQMJ22e1lq48uri9oOMZ9uLa9lNYiho3Z9%2B6xqU%2FbcBDAybXN3ZFFJ3LddVEh0mcejw5BCxZZVnUS7wGFxqlMrTMRy%2BJIqpdWewrCD%2B6iu3%2Fsre97yvSbCP7xLR8SXyH1LKxZTYkqp%2F1XIZ4dpmjpLktAEU5bnchWNw5lhxTli9rcMynUdPgGPX%2BvJ2%2F2BgiqPTHK2HB5clePsGgXCkPt082oetPnbx1%2FbDrDtW395oycuG8yJd%2F3%2FXu6MZHa5Zcv2zRrf2wZn1HILfzsvKx%2Bb0rCstHz73%2B8VXN%2F8y%2F%2FJriK%2FqHR%2F%2B30LeE6xuRa8AjToRYDHa7y2UyEIfB4fWZnHbn4JjVYrfL3HVyQt3QpktOVnRhgnBcxKOXvoLpIyFPwCO6cjK3bsas9tdeeHRt8xasYDuu%2BTD4aeiNN0jGwgknTn4e%2F%2FyqK4UOT%2FGc4zM%2BcENZ1E8cDrfby3t%2Fj9NoJ7JNtumyPcmJ1sVDgItr7tQYgH%2BgrxdrpR2zt72PpSLjsXRp7XUHt5Mj8dki4Ynt%2FEpI9JkPcrlm6BV1m0GWiYgIK0G0GNEuC5llKWndDU1X%2Fx0SbTfiOtaElf%2FINyryZYexkjVJLfFF86aMXUzaumS4AZRtXEaWOMsoSyaOIVng81ETVTMyMjNzVEXJ9plMVLbbMxQ7yDqidR3RdPz2LIDSIO1WQ8wBsin%2FpGskRZpuUfew19lm7LMwJ1eRcrT7sG6R5NCsqBgvN92NPdk7uARPdt4vtTDH4m9q1lxH%2FPGvvE03jMkcer4XnuKKI5gApOW6bWqi%2BYoMaKSUSAQlGWWzQVWtfIZmMSoUAA1mj4T2S2cBqaROkYZeq3KlhdkClOu%2FmD2BI48cxZHsMWxja46fYO2kPwmyZ7A1fiy%2BDRewhcJLzK17ycs1KTC73ZrXK0koahm%2FJgob%2FpNT8no0p9XJMTHDAFyVskQJkKKvhBlTUzxHyokifvTqgNsSaw9mmBRz7n4cwoqu%2BvcfR9RErqqfl%2Bfkfr2%2FYcZNo8ic866XXnR8Z72xNZI450HXce2MIn%2BoKqkIYDYgmvQhAm8c7YR%2FMwyOoefSIULSSMJGySlCWEwR6LrOB4nC0uhAZiCmDrLp6%2B3xekDI4T38Id7D54ipCHUbcnIcfn%2BuNTMzIFGXy8qjKd9qSbTzYosp2hbbF7bnuBrm%2BREWRw08Coc18VTQ4xFQ6%2BEJhDmL2m6%2Fc%2FOZG4cpn31T3XpmM9quH32qucGAVz7Z9jEdXMUObcyzBF8xskNVg%2BknbU8BIO5gJWSlYgMK7tcIpZJMAaCyhONDYlbqCOKOo0cV29lA1ylOauB7yBN7yOHlOmgGQ75bkoI52TabW3Z7qCzl%2F3%2F2IIuHzuFynuSi2BZnlftyiBSnzxyCyzwcrImh4e0Xbhz2%2B9mfKtWtL7xTP39x26LeM2aFPyFVQ7CnuWmyw5K3EXsOrqIfh2dPY5tNjY2nGm7QTxGQIqmCtoEHIlG%2FAg4zmKnd7qNeu82mSJSaHQ5QoCRU1lYi9ElBdqqp5pwa1sv%2FRAMmELwQB0baym968pqFwxaOC99ePv7pgf89chFZcXX5l1NzcyPRii%2Bnphf8lzhBwpbiQanl0rP6Dg26zurbad4v56mukCugE0Wi7Vh7JsTasSV5lIO0dJbKBcljHAhLOdJqfN6cwad7QYchPV3OyCA%2Bn4mYMrPSXCNiBtuIGMiGNH4pGWmKygXqpwH4S8%2BePzvOII575nOCTh4R15lS69q26gmSEBt94OCr7YtF6z7vlm8b7mpdcN%2BrL%2FfHcyhjZk77c8arjmflv%2FBn9kZObzbAuFFEB4A0ST%2Bd2BztZXeaidFqTfd6iV%2FzO51ado7Fn%2BavjxnT0sDFqcleG3P6QR7xs%2BNNXUfUIJTSVqjbjT%2BpBpRfbpXXFSKawsFwiBuQbNyyZcyzs2sbcS679w9k3%2Fmvbhr%2B6qufy7sbvojGrt10dOm6WtZ5ttes1keObtl5BAjMBCYFpHXcnkW8R87TLC6j7EsnBrDZ8jIhM%2FOyYp9LSycWo2xQPZ4ctYBHz%2FYyHc11H2qb9S%2BiA4oURXyC3SM%2B0WGqPrVIoJJaFCmMXFRdbixfuGzBqEk3j1qwfGE43Pbogt%2BNn93Y9siC8v1T6%2BqnzxxRO50cnPC7BcsWhCMLly6MTZs8uu2RtlBo%2FiNtYyYOnz6ttm7aDBHpCoDEp%2BPghZnR%2F7I53U6Plce2UaYyMYkJqxeRED%2FHBp%2FidDkbYkCRuuwmm93WEFPtdgt6FMsl5xX9mtiW3kNfypcpEhAfkgPKkCfoEXdAGF7cGCBD0YAVbOGWH374gX38448%2FvsOW4BViZBv3vHrfq8eO8RdyHMhFiKNCMGoniiKGmUaJSlTVsUcEbCpFdAhyJGBIAFHnAbag8wAAgUm89lnw%2F0o5D7g2jvTvPzOzu9KCJNSFaAKEBMYHAokSuQpiY04OODjYsWxCcjbkNaluuPdyiXuaS0jHpPfeE0N68fVO%2FObSe%2B8uy39mVlqEzr76oeyi%2BbG7U3bK83yfkUZBGZwCMyKlaRaXRRTLC6E4JyfkAld4DKmpsbkrK0ttpSafxzc15nHqTVNjepQycUvmivi5NiuyMYtA0qyNo3NOVr9OFfZJmt75WUW7VMhOWtE4fsubj9zRP33SzuaW6LxFB3rWTJj4xSuvXdHyYsOAb%2Fbpj257c%2BOS5s4tvmrim7appHXPputbn8kPlVdURssit194%2FxklXdGr7p3261Hh7uKKUGH0uu2nzi8Pxya1V5qmAUYu4UfygiRwVi0%2FYrQaWIvIdGcQ4pBB7dzU9snCdpLZJF%2FSOXJNjdRPPa0uMhVd2TKurqk5Mq5FXFPXEB0%2F7ucNExvqGieOb6wDIIw7lSbR99oBPqhmvm9ikm0mm7%2Fc7yzPc%2BbV1IrpYEmnX1mlhbZglpActKMVbEo36zBrHWyifBGnSASrw44ZvIhr6bwgFCxiuH4R45HIul%2Bc91p4c3j55tf%2FfvilPddGFx5b8zJqf5X9DCi9v%2Fm10vvcrj6U09uHsg%2F0Ke%2F29invHSBfX7VJ%2BTAv99nwkcNvfNd82xjlI%2F4%2FSu%2BrLyi3%2FObXaPaLTJb0b6xlBfCX%2BDHKMLqgAOoieZk65HLlmXXU56PLK%2FRmGI2e9HQbys4GEGweShSEA0F1mAtak3BQbR1SPGxVVo3K6irbp3YM1ToJV3pGr452r7n58XnrWi6tr79h3tY9yqTy%2FKbYvMvxsYvGRLrPu%2FBCWegef0l%2BcNcmpeGP%2FqIz6oqkNPas06Fd6BEEkMAIbZHRaUaDTKd2RMKCgERqGDdkGNkrBpBGCE4XBIMoIpOMsR4lWko4kLBqJI%2BK5j8Faab66Q897w8yR4ALIR3yqYfpaPGg8hFyDSo70RG06A12%2FoayC49HL1E%2Fs9K3DL2QNXzKGb8fhTCZCCJkRZgzSkcQkogAAdYJoQTf6LXQWZQQHjx2hLz1I7pgEIaGErEHWAIzAAhaezTEW%2BS5kUqBYFHUgcViJEbamxB9uT%2FROLFE8QLBIegdsp5%2BnaSN8spKbara53ErgY4FlFnoIwadmhP5X7VaYcvuz5QHAu8h%2FcO3K%2Bs89eFTJuceP%2Bdft9utd0xUFqDpyj3kqh3K1%2BH6uhrlzX%2FZctHQEckuSNLhJG8MjPTGCNLRbwWDZH%2BFr%2F6Jm7D5hAmyIDMiQ0ZGTrbVkMkqRQ3FUq17vL06HSowmDyctbXd2N5201ln3XjW5a88G6uvnz2nLjJHWMg%2B7W0766bZL10emd02YWJ7G%2BNFAYSwiCGdcx%2BZGTqdRB35BoSomd9sMRrSZYQkAYOKeoYC8S5MM5WnxriwyfZwnAs9I2%2Fh3kG0RVlFY12UNylYiiCAo%2FgZTriVRKwOA5LAgiyuTNnkwQ4Hyucer4lJXb96j39EPHUF%2BJnjK%2F5%2BbriipGXeqiuf3np9%2B4YudA6O3jbYEQv6S2bt37Cle8be7rMBwVgcxo%2BIr4APJkRy7enY7QbIl%2FLTzVK65C8mdrvDIed4PSa5IIE5pbQ8dlABTRX6S6xu1DgHrezj3QjuuaN9%2Fn1P7N541ards5oXtJ3REgwFWsOdE%2Fb9v3W9wlu7a432i6at2N7wzOzzq6tvrAr76ePuDExYn%2BqLI0JEDyCnCdwXdyjui3uFjR%2FVNMjMIUk6ao6YiGZWHZ0i%2FDX75U5H1aEgAOK2LmrkhkxmMUmXJFnOsjrBQR%2FdrXNlOGl7yiCq4Y2Z%2BzTTkbYwT8qwtv73xo0CxS6XhZtDZ7WvpVaAD0ZnlC6fNWF%2Bvigy%2Byj67YoVdz%2FPrAF7Z8wo%2F9mM65SDUhQQLFSOCbslO2RAIOJINwsiAoTMFr0emUykKWYSWc8XiHtk4gMlbe5qgAb7UsMIa0IFwu6bbumd0PqX1%2F72IW5Tjkmn%2F3QfCVmPHEWCwiKd8Cj0e7KGEUURmUU6Ebk1RiCQCHSypSLhfEr%2F%2B2Eqe2hQsaNeALBCVcRlNjI7Fh1Y7Gaz0W60ySYW9pXNXt9QQI0EXB1%2F3PjAIiZPQYprQ3RWgnr3Xd88KXuOu%2FGW5v7s6Kwj6xc5btOZJpzh7hmf2cktXDiKGxPRSYI8MjopD%2BWfMDoJeePRSb4QbvyciNkVzReismdxFD2z4Oyi0vHr6MwOwnTUfEt8ic9KPBFjIvYqgzhkDw%2FxTGK3kxc9YlKPgt969IarH3%2FwwP4nFG9dY%2BPEiY2NdULbnf0v3Hr7wAu3dHR2dnTMm5cy6s2OlKZTy49OL2AW1Ib01FNiGh70BD7YIdHEB79%2FOej1B9UBL%2B6NL0aoFonqQehRdg4ip%2FLxIFqsSMPn2KuMXYbaUNsyJZw1fMrGrnIA6Qpa2n5Y%2BTuAYvg1fgUA6eAP5Nrjj4L8IMFW%2BuJUVye0D51Au5h8T7W6B7CZSZlyNlXeJ75ClUs8XEnM8as%2BEb9qmXpVwDBeWUH%2BLLTzNU5DpKiQug4YJk0jh0pMoyDbnI1lQp0JPk9rzJdhoRy8xZvKwaN4g9Cm5HHsnddbrUub3bCVWHLF4ldiF1wYPjM27aFzzp37w3lvHP3F7rOrUcnw6jY6d1dT86yJ4eiY0sOnTO6%2F%2FYLru%2Bj0cyyamXhHhoZU2lu3GPuhiOexHiQ0HfQPYqfoh9HVJ1B0w2%2F%2FheIgzFQV2SMV52iKgYTCOlIxU1N0cUXaQwR7uWRYkxbXSNDfPYvXhpfEa4MpdD7OPtrg4sg4yUbMNmIRLCjNZEJsvgbgEETRbiYUvqb4syENGQkj%2FJFkkzkxTAQrMmlscsKiQLvUAAeUNb8G7yQ062PCs0QKkEYsI9rR6nzH9imOvcoLeLew9%2FghbKIUT%2BhoLlq5jiPvcYqZDnXNrC6WKXZGjNP8%2BVlGYAXOBfY556p5%2BZaodTT0KC89ZE%2BUXqqiG9pSFPdShT1JcXDoO1XhHnmNmZqia%2BgnXgMYFag1wGbucZ7cAJnQGCmivUCW3ep0GlBamtthAIqVWwGovcRJi9eKLYy8TgmP0%2BBgddahWmkscQqUlpiPo4MhBwPPA1tV5FzFz7cKwm9%2Bd%2BCzzzahATIdd1Du%2FG5GoOPWnR9%2BofQoyl1qHsRXeDuriLez36eUA%2BdUeTlUxtt7N1fgvJMpulHDv1AchOdUhXek4hxNMZBQZI1UzNQUXVzB2vvoeGkj2IAMglnogXTIjaRLBGTZYORGZXcgqMUn8260FqnLBlSM7lL%2BuB%2BVocqr6Rhetkf5tfL7vfj3qKxH%2BSMavZf%2B%2BVuaSiUAhD7DLeIHkgA2yIZCCEdyXJ4cuz0tB9LAW%2BTMK3Ab3QxXJQWpdOWImbyK8arGGFaJqpEG2V2IO%2FyqihEFV1Wm94Xts3tnv8iA1RevaL1x1sDRP56CjrR2UWL1%2FZBiOG0%2BWqzyvXWXXHDpANrEwNWGNfM3DSi%2FfHYJ%2Frbsp%2B8e6j5uKR4aUmlIXgO18Vocrdaz1uOkKrqR6V8oDkKPqsgfqZipKbq4gr0RJcl9kqDwq4yNv3kb1KtYuCSJSmbrqZpIDiOjjbIoSpJTMDbFZEdTTJAFWdIRyZowKGrdjOZBjePIDroW0tZGwh2UUz1yNcPaH1CQ4fikjst3rbt0NcHv%2FagMUij5c2Vc18rz5%2FNZJM3JfMkD1dAaGU3tegXFxQDlWSZTbXkgUGPKKtBBcbEui2SWhkqnxEIQcFgyozFLwnGq7ZUx0g03TH%2FaTYLqcnOkuuX8iaFL8zhXsVAn4a3SSDRSWl1%2FRVfoo3fmXTau%2BubIbfnTo2vnNjQ0TVjXsWQjbb4%2BhL9FfuGvkV%2BcNqai1JldVTJn7srmu%2B7JLfy6KLhqVGhcaeOylsh5lbWnl49r6TrnKPVMv%2FLO%2FazH5ASbVEBr5VQ%2BUtQfAPb2jbbEazY1vfvCE6Xna%2BkHfxhi6RUj001a%2BkAasPTikemClt4lAX%2B3T%2BGCYcUDmqJ%2FlKrwqwogTCEpQjeUQBBOgS2RydU1JDM%2FP2g3GoNBuabG7%2FGMKZPlsC%2FfW50fjVVXsyDp7OxQNJZtNo6aSoF3p%2BS0NFDHPHgbYiBJgQZGv%2FERLZmZ0t5q6wkJKnqMhzBz8MufZG0ZXsZRzHYYrWJk1TDShwoZfiVWbn2rce4L19%2F03NdfPRtr2nHzvKc%2Femdx%2Fd3LDyM4XkaJq%2Bcfm%2FbY8bqFq1fv6FyOvX%2B1oHvwefbOru7Y0zcz5q91cn3Tq52bInXKZx9RCGvWp8UlOEsQzpxD6T%2F05acLVrNap952xtZhP0xWx0%2B0iY%2BfnCrjtT1FbQ2389oqStRWanr34n%2BeflDP00eNTBe09C6rWpeVidoeugYAvcGv8LTaXynTgF0DGRLXuBwA%2Fy5J0T00eaRi6JdU8UmS4qDyuqqwJBTvUMXlkqApuriC9Vdu9UkSBIfk5fPVpZGx4MYuV46oJ%2BkEY0tOTnr6qEKLpcQNmZh%2BSJ2ImdjppB56CnnSKS02%2BRpiJifBU2MEnYC8izsQ2clwI9I%2B1YYLf3Gtkw8SVgdtm4XAwyNdtX46hDAvXCL2GCmnN3ZetuitjjuuvUr5%2F0PfKX9DwuFDDfpT17zfga0rz19x8fIFq84TXdXF99Wdtr1n%2Fm5lz4fKh8pLyPrJR8gyV%2Bhdtuva4%2FMv2Lj1ih27%2Blg74MwMf2tPV9%2FaEPAZUHI97ucl3KK2k5t4PReeOJ319ZfAyRW8pRiS%2BgUt3aSlD6jpeSPTBS29y6C2pIDWK8yCw0JYeIl7wbKhNGJ1pqWZBQEIyYUcNwVKAXHz0vPBYdBQiw8WTxJRTWOGj2%2BK1tf%2FPFpXNzVaf2ojO%2BKOwcEvTpva%2FPOG6c1EmNrUMqWhpRkIfcaHKAN0OZ81eEfOGnzxWQOjb0jBFAZx%2FC%2BzhmCNsJ9hQWsvOLVn0n5GBm1eUrt%2FzK5jR21o%2FOiJKy9AhwzKa%2F6alefjSoYJlXV2dVyL7IwUqpp%2BQes1ytH2RjTouvnWlnFKMOP2oSGVpeD1c2ZST4ByefGmpvMavgVOruA1XMnTC0emC1p6V0B9A0u1np977PkV5qi9zXh%2BBQ8XJOgmziYWsLhqD%2B1vHQZzli2Dxi8VWsCcbXDIRM6dEpOdxEnL%2BCQocxLLTDtnDWdWTT4Wyh0nAU7ot8Herhf%2F%2FuZLf5xv0ulUfvGjOONEDrXMYEgzK%2BCtE9qVsXpQVixvbB7mnLQ8CVqeut5Qc%2F0zNdcJKk9oH6byMk5M5VGJGk2mO108BE7wQmekxuJwGFF%2Bvs6WAeDL0umKLHa6drMgI7HQX0YznaWSNBddcwhCLotpRQ5tBcd%2BThplmiAy%2BBMMx2M6XcOLuERnVGvx%2B3WnH9vn31Wm9Cv3oTPQhPGbvaRDW9Q9dstdd%2FXVrfR7t8jpaBvqQuejTSZZXeCR145%2B8%2B1PDivZbnPyN%2BhT3SphMXhgNARhQWRMoMKEHQ6%2FX19RkWu3V%2BXr9aEchzvgiMYCATCbfxaNmc3YJNDOmfLEZnDT4VwQvFNiQupwHj45Cp00iOdT56kG4bniI7dDo6KTeT2fSk%2BLtyhf7dl5pPfHLSgb4QUvT7nsi2%2BR%2BbhTt2fL%2BU90tDx99FwN5Pu4fbWMBnC3%2FZprdiD9%2FciByqY1XcvYaf26naXlbOCeHGf7BhavuJhFHD0h%2FFXwSAVgZP0Zi5ozAMh6jE0ZWF4vsh39sg5pyx2NKqQzEZ2XGU%2BdFNAgrdc1Ne977elTUafn6kbhr2ed0XJ29tMLqh5sYBENqFX4M4lKD8Q9ehmS1eqmkUWyR8ay7CDxvRTYHVKNZ7qk8YhEdy1YcOklCy%2B67Pqa0tKaiorSGvGlCzavv%2BiCDZu7ykKhsrKqKkDwa%2BHPgkEygQuqIm4KNEUEQjLdBhvobPTrYvM6MzavFyCQ9fpZmoNENQebXw6qkISXvbF5mNVHiE23yjF6xRM27knfvXTUtKZoET%2B%2FfAk7F%2Buray7vKyjOr%2BKHAr4bGHqI3IN7%2BG5S%2BAS7SU0nbeih999Xlbp%2FqtQllG7Sj%2Fp4jIw7kiaIOqTTySBou5KZB5gLq7jGWhvCumKTs7N6sN5L%2Bp1zkG2h8t3HkHQFCVwRmQhIknSCRC8wvD8WUrffQHtNwbWDkz3iI84XlPdRySFI3luLeVIwEfnuWhIEtNuffHstwOzeZBl%2F%2BgzwRczUIGsiggSSZNFlkHRtI0Z%2BoT8E%2BbOoWSnwxY%2FoUzVPdILhSZyRP8ezp2Vz%2BE4SGJn%2FndpNDXwrMFMaMYjsRi%2BqN9Luoz60qB5QH885cqO31JNM8Ua1DBJFgVlJkOt5SRihMGIaeQcIpN7Ap91gROGgt0eWkkvbi2wunXrfKIyCdLA9wszuRplAgHssUq3uc6%2FavnXvvku37cGf9hzou3r%2FLbcAELbTizQXhfm75mXsYF6m6kEvys4gbKuXAofMQuS5LUhtbJnmP9AJy8gdX3yp56m7v%2BAps89kZzPacGPqPmctKUf%2BVkA7vpHbtCsijrgDV9RLQAg9pa0JI9VZmsxW0W%2FVN5vqlE12xKZeO24nRzp2bfoHPRPEf7z2SBs4vvHEBm8ApCxj83oe25YVSSeAEcaCFtqW8B8j5EX48mN%2F%2FIKMjge2AeK7BW0S%2B6EYdkQaJaL3%2BXI8RW5ntmywWIrSafaLika5cnP12dklBpdLzpRy83Knx0heRt66PJxOMvMy82yFPiiEabFCndlkMzXHbNp2YiNNoxZenyxzKUghO%2FCtQOhvro%2FH5DgKdA420DrVfS4oWELdb%2F7qWvq7BuL7XXhXXu9CVyrtGKN5yj0hZNq9ecn93ynPj9q6VMBLtvjQpG%2Be6ps7ebnwys5f3ucNFDzwTXgIxqK0Tx5wFVff9zVyT%2F%2FQ4%2BXsWgfzjp%2B0n6MTYDbdHRriMbs%2FSh7wQyNfQ04lboD45x8nfd7MPgcMBhzF34tPQRpYGbthFXUmWnBEBixim90k62TJikTRaiW6PJLPDTwBLSYu4RpNwn%2B8DhpfWI1CfA%2BzWrZnHP5%2BzefKBrTh0zXKHkmuzliH39q3rwfXHT%2FUN3Nu1gWuZ9Wn05u0pyuGRuJWn14KAMTT4QTpzcPp0q6k3PF0dS8BvtMDAcsjIIiIQGKXQLYPAt8FgTU2uvZ8EQDruB3sL%2FEV7krVDmZIWNNupYoPkxTdQ3NGKoYYgS4mKQ4q76sKS0JxHADfqZupKbq4gq9wuaT6%2FwCVeR0IAAAAAQAAAAEZmiehT9dfDzz1AAkIAAAAAADJQhegAAAAAMnoSqH7DP2oCo0IjQABAAkAAgAAAAAAAHgBY2BkYODo%2FbuCgYGr9zfPv0quXqAIKrgJAJZXBsIAeAFtkQOsGEEQhv%2Fbnd272rZtG0Ft27ZtW1G9dYMiamrbZlgrqN17M89K8uVfTna%2FoRs4AwCUGVBCU0zQl7DAlEIZWoPOfhXUs0BbVQAL1CG0ZepQd9STPdUW9dQ61FGN%2BU5LpOW1pswUpmU0hZj%2BTGOmWnQ2lPNyV2rEoO%2FA%2BmUw0CwATG8cNjkwyXzEYZrG9Of5NUyy%2BXBY7Q4Hm9a8tgCH%2FWU4bOcwPfmsjc7GvDcYPWk7StjU2G8qAf5xwHQE6D%2BzHRXUbqzi96bmrEQNEeim4V965jWnB%2Bho0sNRHnTn7E5H0V3nQAlaAGsawqkxWKfGhDPoO2Ts%2FGdwsk5fIecd011vh9O%2FOaegHO9toBWAfYLM5JBSxvoNquliyEeDvUucbeXvMd55vIqRtTGMJTnzAkP5bdnsXvTX6VGOPkbfYe%2ByRgh%2F6xHoLms6QDmmlvyFPThTB2PEtbczfMbr3XUu1JD7fmqUjaYre68jzpPD3wJIH6QH0RyQ5L6Ui%2FGeGFqDOZLiPj7iXnpkDsKJ5%2BTwO3LmEe8JYecb2fcazoXMC%2FEd4z0J7EFS3MdH3EuPJJX07gom%2Bff4%2FDMcpS1ee85bBLQNGO84cgiqPerpVcghUBEeK%2FS1jzBBfUZbwUv5X%2F7bkOlslqCEwJ5TBw4lBFsBJdRuHA4vYk%2Fown8RLYvLrQAAeAEc0jWMJFcQxvFnto%2F5LjEvHrdbmh2Kji9aPL4839TcKPNAa6mlZUyOmZk6lzbPJ3bo56%2F%2FCz%2BVaqqrat5rY8x7xnzxl3nvo%2B27jFnz8c%2FmI9Nmh2XBdMsilrBitsnD9rI8aiN5DI%2FjSftC9mIf9pMfIB4kHiI%2BhWfQY5aPAYYYYYwpcyfpMMX0aZzBWZzDeVygchGXcBlX8ApexWt4HW%2FgLbzNbnfwLt7DJ%2Fp0TX4%2BUucji1hCnY%2FU%2BcijVB7D46jzkb3Yh%2F3kB4gHiYeIT%2BEZ9JjlY4AhRhhjytxJOkwxfRpncBbncB4XqFzEJVzGFbyCV%2FEaXscbeAtvs9sdvIv3cjmftWavuWs2mg6byt3ooIsFOyx77Kos2kiWsIK%2FUVPDOjawiQmO4CgdxnAcJzClz2PVbNKsy2ZzvoncjQ66qE2kNpHaRJawgr9RU8M6NrCJCY6gNpFjOI4TmNIn36TNfGSH5RrssKtyN%2B59b410iF0sUFO0l2UJtY%2F8jU9rWMcGNjHBEUypf0z8mm7vZLvZaC%2FLzdhmV2XBvpBF25IlLJOvEFfRI%2BNjgCFGGGNK5Rs6Z7Ij%2F45yNzro4m9Ywzo2sIkJjuBj2ZnvLDdjGxntLLWzLGGZfIW4ih4ZHwMMMcIYUyq1s8xkl97bH0y3JkZyM36j%2F%2B58rvTQxwBDjDDGNzyVyX35Ccjd6KCLv2EN69jAJiY4go%2Flfr05F%2BUa7CCzGx10sYA9tiWLxCWs2BfyN%2BIa1rGBTUxwBEfpMIbjOIEpfdjHvGaTd9LJb0duRp2S1O1I3Y4sYZl8hbiKHhkfAwwxwhhTKt%2FQOZPfmY3%2F%2FSs3Y5tNpTpL9ZQeGR8DDDHCGN%2FwbCbdfHO5GbW51OZSm8sSlslXiKvokfExwBAjjDGlUpvLTBY0K5KbiDcT672SbXZY6k7lbnTQxQI1h%2B1FeZTKY3gcT2KvTWUf9pMZIB4kHiI%2BxcQzxGfpfA7P4wW8yG4eT%2FkYYIgRxvgb9TWsYwObmOAITlI%2Fxf7TOIOzOIfzuEDlIi7hMq7gFbyK1%2FA63sBbeJtvdwfv4j28zyaP8QmVL%2FimL%2FENJ5PJHt3RqtyMbbYlPfQxwBAjjPEN9ZksqkMqN6PuV7bZy7LDtuRudNDFwzx1FI%2FhcTzJp73Yh%2F3kB4gHiYeIT%2BEZ9JjlY4AhRhjjb1TWsI4NbGKCIzjJlCmcxhmcxTmcxwVcxCVcxhW8glfxGl7HG3gLbzPxDt7Fe%2FgY%2F%2Begvq0YCAEoCNa1n%2BKVyTUl3Q0uIhoe%2B3DnRfV7nXGOc5zjHOc4xznOcY5znOMc5zjHOc5xjnOc4xznOMc5znGOc5zjHOc4xznOcY5znOMc5zjHOc5xjnOc4xznOMc5znGOc5zjHOc4xznOcY5znOM8XZouTZemS1OAKcAUYAowBZgCTAHm3x31O7p3vNf5c1iXeBkEAQDFcbsJX0IqFBwK7tyEgkPC3R0K7hrXzsIhePPK%2F7c77jPM1yxSPua0WmuDzNcuNmuLtmq7sbyfsUu7De%2Fxu9fvvvDNfN3ioN9j5pq0ximd1hmd1TmlX7iky7qiq7qmG3pgXYd6pMd6oqd6pud6oZd6pdd6p%2Ff6oI%2F6pC%2FKSxvf9F0%2F1LFl1naRcwwzrAu7AHNarbW6oEu6rCu6qmu6ob9Y7xu%2BkbfHH1ZopCk25RVrhXKn4LCO6KiOGfvpd%2BR3is15xXmVWKGRptgaysQKpUwc1hEdVcpEysTI7xTbKHMcKzTSFDtCmVihkab4z0FdI0QQBAEUbRz6XLh3Lc7VcI%2FWN54IuxXFS97oH58%2BMBoclE1usbHHW77wlW985wcHHHLEMSecsUuPXMNRqfzib3pcllj5xd%2B0lSVW5nNIL3nF6389h%2BY5NG3Thja0oQ1taEMb2tCGNrQn%2BQwjrcwxM93gJre4Y89mvsdb3vGeD3zkE5%2F5wle%2B8Z0fHHDIEceccMaOX67wNz3747gObCQAQhCKdjlRzBVD5be7rwAmfOMQsUvPLj279OzSYBks49Ibl97In%2FHCuNDGO%2BNOW6qlWqqlWqqlWqqlWqqYUkwpphTzifnEfII92IM92IM92IM92IM92IM92I%2FD4%2FA4PA6Pw%2BPwODwOj8M%2Ff7kaaDXQyt7K3mqglcCVwNVAq4FWA60GWglZCVkJWQlZCVkJWQlZDbQyqhpoNdAPh3NAwCAAwwDM%2B7b2sg8kCjIO4zAO4zAO4zAO4zAO4zAO4zAO4zAO4zAO4zAO4zAO47AO67AO67AO67AO67AO67AO67AO67AO67AO67AO67AO63AO53AO53AO53AO53AO53AO53AO53AO53AO53AO53AO5xCHOMQhDnGIQxziEIc4xCEOcYhDHOIQhzjEIQ5xiEMd6lCHOtShDnWoQx3qUIc61KEOdahDHepQhzrUoQ6%2Fh%2BP6RpIjiKEoyOPvCARUoK9LctP5ZqXTop7q%2F6H%2F0H%2B4P9yfPz82bdm2Y9ee%2FT355bS3%2FdivDW9reFtDb4beDL0ZejP0ZujN0JuhN0Nvht4MvRl6M%2FRm6M3w1of3PVnJSlaykpWsZCUrWclKVrKSlaxkJStZySpWsYpVrGIVq1jFKlaxilWsYhWrWMUqVrGa1axmNatZzWpWs5rVrGY1q1nNalazmtWsYQ1rWMMa1rCGNaxhDWtYwxrWsIY1rGENa1nLWtaylrWsZS1rWcta1rKWtaxlLWtZyzrWsY51rGMd61jHOtaxjnWsYx3rWMc61rEeTf1o6kdTP%2F84rpMqCKAYhmH8Cfy2JjuLCPiYPDH1Y%2BrH1I%2BpH1M%2Fpn5M%2FZh6FEZhFEZhFEZhFEZhFEZhFFZhFVZhFVZhFVZhFVZhFVbhFE7hFE7hFE7hFE7hFE7hFCKgCChPHQFlc7I52ZxsTgQUAUVAEVAEFAFFQBFQBBQBRUARUAQUAUVAEVAEFAFFQBFQti5bl63L1mXrsnXZuggoAoqAIqAIKAKKgCKgCCgCioAioAgoAoqAIqAIKAKKgCKgCCgCyt5GQBFQBPTlwD7OEIaBKAxSOrmJVZa2TsJcwJ6r0%2F%2B9sBOGnTDshOF%2BDndyXG7k7vfh9%2Bn35fft978Thp2wKuqqqKtarmq58cYbb7zzzjvvfPDBBx988sknn3zxxRdfPHnyVPip8FPhp8JPhZ8KP78czLdxBDAMAMFc%2FbdAk4AERoMS5CpQOW82uWyPHexkJzvZyU52spOd7GQnu9jFLnaxi13sYhe72MVudrOb3exmN7vZzW52s8EGG2ywwQYbbLDBBnvZy172spe97GUve9nLJptssskmm2yyySabbLHFFltsscUWW2yxxX6%2B7P%2BrH%2Fqtf6%2B2Z3u2Z3u2Z3u2Z3u2Z3s%2BO66jKoYBGASA%2FiUFeLO2tqfgvhIgVkOshvj%2F8f%2FjF8VqiL8dqyG%2Bd4klllhiiSWWWGKJJY444ogjjjjiiCOO%2BPua0gPv7paRAHgBLcEDlNxQAADArI3Ydv7Vtm3btm3btm3btm3bD7VvBoIgLXVVqCf0ztXT9dzd3j3cvcX90CN5Snmae%2Fp45np2e356gbeH94HP8Q3x3feH%2FX38NwJwoHigQ2Ba4GBQCK4NfgxVDE0OnQr7w1nCI8P7wi8jdqR4ZGzkRDQSLRmdH%2F0UqxTrEVsbux%2FPHe8b3xh%2FlgglzESJRJfE6MS6ZChZJzkj%2BRouCA9GJKQuMhI5hsZRHR2A7kZ%2FYZWxldhtPDPeFd%2BIPybyE0OIy2SIrEy2IneSX8mvFKB6UpfodPQYeiOTjmnK3GOzsCPYpexaLjdXiRvBHeJ%2B8BX5Lvxe%2FqOACmWEnsJ60SsyYjqxiLhE3CoeE6%2BLL8RvUlRqJXWThkszpJXSbjkq83JaOZ9cXm4gd5IXKZACK4qSSSmiVFWmq0lVUtOr%2BdXyagO1oxbRSM3UsmnFtOpaC62nNkqbo7M60HPppfXaemu9j77X4IwUI49RxqhrtDWOGzeM92Y985lFWWWtcdZia4d10%2FpiU3YZu6%2B91j7rME5xp5szGVAgDcgBioDhYDpYDjaDE%2BAmeAW%2Bp8R%2FA5ajfCcAAAABAAAA3QCKABYAWAAFAAIAEAAvAFwAAAEAAQsAAwABeAF9jgNuRAEYhL%2FaDGoc4DluVNtug5pr8xh7jj3jTpK18pszwBDP9NHTP0IPs1DOexlmtpz3sc9iOe9nmddyPsA8%2BXI%2BqI1COZ%2FkliIXhPkiyDo3vCnG2CaEn0%2B2lH%2BgmfIvotowZa3769ULZST4K%2BcujqTb%2Fj36S4w%2FQmgDF0tWvalemNWLX%2BKSMBvYkhQSLG2FZR%2BafmERIsqPpn7%2ByvxjfMlsTjlihz3OuZE38bTtlAAa%2FTAFAHgBbMEDjJYBAADQ9%2F3nu2zbtm3b5p9t17JdQ7Zt21zmvGXXvJrZe0LA37Cw%2F3lDEBISIVKUaDFixYmXIJHEkkgqmeRSSCmV1NJIK530Msgok8yyyCqb7HLIKZfc8sgrn%2FwKKKiwIooqprgSSiqltDLKKqe8CiqqpLIqqqqmuhpqqqW2Ouqqp74GGmqksSaaaqa5FlpqpbU22mqnvQ466qSzLrrqprs9NpthprNWeWeWReZba6ctQYR5QaTplvvhp4VWm%2BOyt75bZ5fffvljk71uum6fHnpaopfbervhlvfCHnngof36%2BGappx57oq%2BPPpurv34GGGSgwTYYYpihhhthlJFGG%2BODscYbZ4JJJjphoykmm2qaT7445ZkDDnrujRcOOeyY46444qirZtvtnPPOBFG%2BBtFBTBAbxAXxQYJC7rvjrnv%2FxpJXmpPDXpqXaWDg6MKZX5ZaVJycX5TK4lpalA8SdnMyMITSRjxp%2BaVFxaUFqUWZ%2BUVQQWMobcKUlgYAHQ14sAAAeAFFSzVCLEEQ7fpjH113V1ybGPd1KRyiibEhxt1vsj3ZngE9AIfgBmMR5fVk8qElsRjHOHAYW%2BQwyumxct4bKxXkWDEvx7JjdszQNAZcekzi9Zho8oV8NCbnIT%2FfEXNRJwqmlaemnQMbN8E1OE7Mzb%2FP%2F8xzKZrEMA2hl3rQATa0Uxs2bN%2B2f8M2AEpwj5yQBvklvJ3AqRcEaMKrWq%2F19eWakl7NsZbyJoNblqlZc7KywcRbRnBjc00FeF6%2Fenoi05EcG62tsXhkPcdk87BHVC%2BZXleUPrOsUHaUI2tb4y%2F8OwbsTEAJAA%3D%3D%29%20format%28%22woff%22%29%7Dhtml%7Bfont%2Dfamily%3Asans%2Dserif%3B%2Dwebkit%2Dtext%2Dsize%2Dadjust%3A100%25%3B%2Dms%2Dtext%2Dsize%2Dadjust%3A100%25%7Dbody%7Bmargin%3A0%7Darticle%2Caside%2Cdetails%2Cfigcaption%2Cfigure%2Cfooter%2Cheader%2Chgroup%2Cmain%2Cmenu%2Cnav%2Csection%2Csummary%7Bdisplay%3Ablock%7Daudio%2Ccanvas%2Cprogress%2Cvideo%7Bdisplay%3Ainline%2Dblock%3Bvertical%2Dalign%3Abaseline%7Daudio%3Anot%28%5Bcontrols%5D%29%7Bdisplay%3Anone%3Bheight%3A0%7D%5Bhidden%5D%2Ctemplate%7Bdisplay%3Anone%7Da%7Bbackground%2Dcolor%3Atransparent%7Da%3Aactive%2Ca%3Ahover%7Boutline%3A0%7Dabbr%5Btitle%5D%7Bborder%2Dbottom%3A1px%20dotted%7Db%2Cstrong%7Bfont%2Dweight%3A700%7Ddfn%7Bfont%2Dstyle%3Aitalic%7Dh1%7Bmargin%3A%2E67em%200%3Bfont%2Dsize%3A2em%7Dmark%7Bcolor%3A%23000%3Bbackground%3A%23ff0%7Dsmall%7Bfont%2Dsize%3A80%25%7Dsub%2Cs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O1awBnIgEdhcnWT1L1sp5SAmUCoHZ6PCwnIGB%2FkJO6l3NOBlhKaEHsLJqajmsZSV%2Bw2UubpUutlIBP5Dcq5qxBkmcgZH%2BS3JZ6MF2%2B0%2B7%2B4%2B07%2Brv6e2QkCFAlNJASXEoig6is%2FfzPqYrXzbL484BxQwsea0ywUFoaXfahYCFPiLnf61rK0ogrP0b8XU0IAAmHp5KFnpQC4pgjhn55qSkkSmDY7HagA%2FEDDUsh0Sk1iqy9GLq%2B4oRgufWMWUKXZ6qY5oMShLkKU880sscQbm1k%2FbRGgscUUopdPHNLMUUJmVP9ORQWAAlBCUNm5p2PEsIG4cafnVhK9SS7EbW9fNCSRERDm5VhxzSeKOKzUlPHIoDRTPqxJVr%2BfNRmwFQtEqR%2BmpZIUlkRLstqsIEyQfF1X48UIlVlZNLb1JhksLL%2BDPpSgMjEsGK6c1ZRfIlrcbURJWSAtfePFKUVWaJ%2BKb0Ix%2BUPjptutVUc1ilira8Gr1H1U%2BpXF%2F%2FwBfFVpSscAgNzc%2FlT1KOPuUP9eRxRERisWL%2FwCFPFQSsREsTZX88UorEHWyX48ULA%2F54htTr44pHGJis1HlDyOKGlQxy61B0R%2F3HimrqBI4n31G%2FwBKERIq02Sz7UFjIiI9nU6l7f4pwNqMpLP23GrPUgJFY%2B%2Fm%2B9GFIM5J89Q7804SspL8haz7Vnw4QZHFDPU78VoYUZFZe%2B%2B7PQsGEpZ9ayuQzu9Vwol8SvXchn%2BtRYtL4aMUO1qAHQLDUqCrW5pXCVJn6X8uFqycEXh6My3Z6EkKYfBAoZ6UXyeP%2FlNdqkEliBhuiLxUiQVmcF%2FrvQjAHLrOLKDqzmirrkMcT7bacHmtXaJxyVXIt5HmrKHrjFyxOnjmnPqUcQZueW581lRgYiUHP9OfNIwmOOBchxoOeakfVXJHrqOKEwTAKTrpwOaSxMQZueW580RUxTPrQm40581cU2FlibXH6TvV1QrISRkThmoQdAVipJ%2FT5qyiShmicW3qwsNFSYWXW25tVVgDJCqXCWpTeyoEAS7bVeJvfEIiqduKsxE5LOw2LWWhGK5wCi420NJjmDAwKA3DL54qBGIlqpFwePFBAIEIsQpOvA4pVJxJmxUakvccUJokGUGdjfmoAYkE4lFDKv8AqnCY45IWOLu1qjG9cQxR9X04qBOOU1Ba5%2FELpUV9HWe37jo6oRJ7OyUYwCj5SkgvzWfrVtantjdnf3dxl2dvfLsnIhZylKRLIFN6pMeSD%2FVuxnPJf5DZw98agkzkg%2F6FVuppws0mc1n%2FANCE5LOKMHLZSWIMzeyl3qwsj%2BSaH%2Fo%2B6nY1WRH%2BSQJTs0cEnarETfyTEB%2F0Lkup2qwmM5LM%2FwAhTZSz%2BKQ7%2FZ%2FefcfZ%2Fc9Xd09xEgYqMpASAkuMkRQUesfXzPqYw18%2FVl28oXF4ah35rYwUKtFUjdDdKLUCCIhIb71InIymMVVXfepMPlFYu2%2B%2Fmmph8fgzb81dTe2S46JrtapBCgGGpZ2tVkEiSy9FP4u4oODASy6%2FTUCx3opm0JEgqSXCtsvNOGSAMlUrjtx5pIOOIClCToOKESI5TWTuLc%2BaeBgIrByujDfzR6QBERKrcOl70o%2BuVz8Wb9tHEPTEexRTp%2BdVVJRZ3Ul258vUjERz61JVRpz5oXQ6OBcJatA%2ByiwCcbVESySPxv8Atom0o5ZTYapbfWrzAD5Qtovx3v8AjUQ%2BJRLj9NRZ1FkTjaqBvbG0bn9PDVKl1k44tvzUqYZZQsijZb0VTaFjiUW%2B978VocIxVg6bhwnihCRikWNzr%2BVU2eKOOU2OqvzTwAGOXWxuz6r4oLNiVDKNR9KkGUMVx%2FtjVEFhhrc6%2BOKVVMsmTd7v4oFMMc%2Btiqh154opmwssT7a8tWhCrvNWcPteoiRkkffU%2Fqo6lEyyn77pdnq4Apyh7bbu9RCnE%2B6FQ7%2FSospUe2ln2vVAyyx%2Bep3e1VVKvJJ%2F5Z%2BKqqYE5Q99Qz70HqUb4I7X5rTM0pJKPXS77WegpkCkf%2BetkP1qm0qQ9p%2Bm%2B7vVwBDlD0Tl2eosksT6q4Z6iEKj10u%2B1qoAhw%2BGpUPZqTVIVl6%2BLu9ApiDl1%2Bmod9%2BazVNoZC6u7eea2Jo%2Bq6qm3HmpCQjjFzc6D60TaUccp%2Bx105p9wgMcoOVbTnzQQkcTe40%2FOpMyhz8bJ%2B2qaTeuA9jco2rPelU%2Bqyvy3PJoopjjn1uVUMnNFM3A6OBcJatA%2ByiwCcbVESySPxv%2B2ibSjllNhqlt9avMAPlC2i%2FHe%2F41EPiUS4%2FTUWdRZE42qgb2xtG5%2FTw1SpdZOOLb81KmGWULIo2W9FU2hsSiorve%2FFbCvVbOm4slCEkxiUKKdfyokRIjlNjy%2FNPuEAAZQQHcP%2B7xQmYxLEuNfypwcxmEkIcR30xqiCDEMbnXxxUslgZsQl358UCunR1nt7%2Bjq64k9vZKMYBQFMpINqLq2tT2xuz7j7jtMuzt7pdkyRlOUpSkwRyXpkk1Bm3o%2Fknkv8hs4BO16sJMpzAH%2FUqTf2%2BlU2lGXYsv%2Bh11LPVjxZGc1h7qDyXepN%2FJNCf5Cqh1OtGImHZMH5sQ4U7U4Tfydgh%2F9HUgFTxUmzkTL3PhSgenIrv9n959x9p9x09%2FR2mMomKxWSSAkDjJEUFHrn9%2FM%2BpjDfz9WV5kb4I7X5roxNKSSj10u%2B1noKZApH%2FnrZD9aptKkPafpvu71cAQ5Q9E5dnqLJLE%2BquGeohCo9dLvtaqAIcPhqVD2ak1SFZevi7vQKYg5dfpqHffms1TaGQuru3nmtiaPquqptx5qQkI4xc3Og%2BtE2lHHKfsddOafcIDHKDlW0580EJHE3uNPzqTMoc%2FGyftqmk3rgPY3KNqz3pVPqsr8tzyaKKY459blVDJzRTNwOjgXCWrQPsosAnG1REskj8b%2Ftom0o5ZTYapbfWrzAD5Qtovx3v%2BNRD4lEuP01FnUWRONqoG9sbRuf08NUqXWTji2%2FNSphllCyKNlvRVNoWOJRb73vxWhwjFWDpuHCeKEJGKRY3Ov5VTZ4o45TY6q%2FNPAAY5dbG7Pqvigs2JUMo1H0qQZQxXH%2B2NUQWGGtzr44pVUyyZN3u%2FigUwxz62KqHXniimbSyF1d2881oTR9V1VNuPNSEhHGLm50H1om0o45T9jrpzT7hAY5Qcq2nPmghI4m9xp%2BdSZlDn42T9tU0m9cB7G5RtWe9Kp9VlflueTRRTHHPrcqoZOaKZuB0cC4S1aB9lFgE42qIlkkfjf9tE2lHLKbDVLb61eYAfKFtF%2BO9%2FxqIfEolx%2Bmos6iyJxtVA3tjaNz%2BnhqlS6yccW35qVMMsoWRRst6KptCxxKLfe9%2BK0OEYqwdNw4TxQhIxSLG51%2FKqbPFHHKbHVX5p4ADHLrY3Z9V8UFmxKhlGo%2BlSDKGK4%2F2xqiCww1udfHFKqmWTJu938UCmGOfWxVQ688UUzYWWJ9teWrQhV3mrOH2vURIySPvqf1UdSiZZT990uz1cAU5Q9tt3eohTifdCod%2FpUWUqPbSz7XqgZZY%2FPU7vaqqlXkk%2F8s%2FFVVMCcoe%2BoZ96D1AQxJEbEb881vDM0pXsLc7VlA%2FGJxCKd%2FrVCSmU%2FUa%2F5px4AHlBIjdfx80LLXiWBcb%2FAFpwstaSEBRH%2FwDmrBH%2FAI%2BOpZ%2BOalaSUMlAbzvQK6dMJdvf0dMICXZ2SjGAXWUkFzrRfJbWp7Zhuzv%2B57TLs7ezsn2SI9pylKRACOSVpkk0M2jLuyVZInKKlXi9TKXegeak81Ta9UZdqyeeqOd6vMLNGXasFMkN1XepZbPuQlZKoS680Yi9Ydnat5IQ7khUpxKm%2Fk7sLyuVuqNViJsu0mTyQ2DnWnIrv9n93939n9x09%2FTOUTExJCyEZASBxkhCgpXP7ksxW%2Fn6svjyshdXdvPNdGJo%2Bq6qm3HmpCQjjFzc6D60TaUccp%2Bx105p9wgMcoOVbTnzQQkcTe40%2FOpMyhz8bJ%2B2qaTeuA9jco2rPelU%2Bqyvy3PJoopjjn1uVUMnNFM3A6OBcJatA%2ByiwCcbVESySPxv%2B2ibSjllNhqlt9avMAPlC2i%2FHe%2F41EPiUS4%2FTUWdRZE42qgb2xtG5%2FTw1SpdZOOLb81KmGWULIo2W9FU2hY4lFvve%2FFaHCMVYOm4cJ4oQkYpFjc6%2FlVNnijjlNjqr808ABjl1sbs%2Bq%2BKCzYlQyjUfSpBlDFcf7Y1RBYYa3OvjilVTLJk3e7%2BKBTDHPrYqodeeKKZsLLE%2B2vLVoQq7zVnD7XqIkZJH31P6qOpRMsp%2B%2B6XZ6uAKcoe227vUQpxPuhUO%2F0qLKVHtpZ9r1QMssfnqd3tVVSrySf%2BWfiqqmBOUPfUM%2B9B6jEodHCOOa0zNKQqHFkuNqkmUSkXFzqKJsqMTlNg668058AETlCzXcb0EIcCF1GopWGQqC3xS%2F7aJpDE4aXOo4alVRBWTjhwNaBTCJy6y1xchb0UzaVjiUW%2B978VocIxVg6bhwnihCRikWNzr%2BVU2eKOOU2OqvzTwAGOXWxuz6r4oLNiVDKNR9KkGUMVx%2FtjVEFhhrc6%2BOKVVMsmTd7v4oFMMc%2Btiqh154opmwssT7a8tWhCrvNWcPteoiRkkffU%2Fqo6lEyyn77pdnq4Apyh7bbu9RCnE%2B6FQ7%2FSospUe2ln2vVAyyx%2Bep3e1VVKvJJ%2F5Z%2BKqqYE5Q99Qz70HqUb4I7X5rTM0pJKPXS77WegpkCkf%2BetkP1qm0qQ9p%2Bm%2B7vVwBDlD0Tl2eosksT6q4Z6iEKj10u%2B1qoAhw%2BGpUPZqTVIVl6%2BLu9ApiDl1%2Bmod9%2BazVNoQGJclwreea6Dikityqf680JMhHGJdFOg%2BtE2VEDKbnVW5p4AADKCElENhZfNCYAGJu5Gn50nxkAkhLiNvw80IIMbm5RtW5pXhIiDNV5ZdfNArp0dR7e%2Fo6utT2dkoxhFgplJA5NF8mWp7Y3Z3%2Fc9pl2dvZ2T7JEe05SlIgBHJK0ySaGbRl3ZKskTlFSrxeplLvQPNSeapteqMu1ZPPVHO9XmFmjLtWCmSG6rvUstn3ISslUJdeaMResOztW8kIdyQqU4lTfyd2F5XK3VGqxE2XaTJ5IbBzrTkV3%2Bz%2B7%2B7%2Bz%2B46e%2FpnKJiYkhZCMgJA4yQhQUrn9yWYrfz9WXx5WQuru3nmujE0fVdVTbjzUhIRxi5udB9aJtKOOU%2FY66c0%2B4QGOUHKtpz5oISOJvcafnUmZQ5%2BNk%2FbVNJvXAexuUbVnvSqfVZX5bnk0UUxxz63KqGTmimbgdHAuEtWgfZRYBONqiJZJH43%2FbRNpRyymw1S2%2BtXmAHyhbRfjvf8aiHxKJcfpqLOosicbVQN7Y2jc%2Fp4apUusnHFt%2BalTDLKFkUbLeiqbQscSi33vfitDhGKsHTcOE8UISMUixudfyqmzxRxymx1V%2BaeAAxy62N2fVfFBZsSoZRqPpUgyhiuP9saogsMNbnXxxSqplkybvd%2FFAphjn1sVUOvPFFM2FlifbXlq0IVd5qzh9r1ESMkj76n9VHUomWU%2FfdLs9XAFOUPbbd3qIU4n3QqHf6VFlKj20s%2B16oGWWPz1O72qqpV5JP%2FLPxVVTAnKHvqGfeg9RiUOjhHHNaZmlIVDiyXG1STKJSLi51FE2VGJymwddeac%2BACJyhZruN6CEOBC6jUUrDIVBb4pf9tE0hicNLnUcNSqogrJxw4GtAphE5dZa4uQt6KZtKxxKLfe9%2BK0OEYqwdNw4TxQhIxSLG51%2FKqbPFHHKbHVX5p4ADHLrY3Z9V8UFmxKhlGo%2BlSDKGK4%2F2xqiCww1udfHFKqmWTJu938UCmGOfWxVQ688UUzYWWJ9teWrQhV3mrOH2vURIySPvqf1UdSiZZT990uz1cAU5Q9tt3eohTifdCod%2FpUWUqPbSz7XqgZZY%2FPU7vaqqlXkk%2F8ALPxVVTAnKHvqGfeg9SjfBHa%2FNaZmlJJR66Xfaz0FMgUj%2FwA9bIfrVNpUh7T9N93ergCHKHonLs9RZJYn1Vwz1EIVHrpd9rVQBDh8NSoezUmqQrL18Xd6BTEHLr9NQ7781mqbQgMS5LhW8810HFJFblU%2F15oSZCOMS6KdB9aJsqIGU3OqtzTwAAGUEJKIbCy%2BaEwAMTdyNPzpPjIBJCXEbfh5oQQY3NyjatzSvCREGaryy6%2BaBXTo6j29%2FR1dans7JRjCLBTKSByaL5MtT2xuzv8Aue0y7O3s7J9kiPacpSkQAjklaZJNDNoy7slWSJyipV4vUyl3oHmpPNU2vVGXasnnqjnerzCzRl2rBTJDdV3qWWz7kJWSqEuvNGIvWHZ2reSEO5IVKcSpv5O7C8rlbqjVYibLtJk8kNg51pyK7%2FZ%2Fd%2Fd%2FZ%2FcdPf0zlExMSQshGQEgcZIQoKVz%2B5LMVv5%2BrL48rIXV3bzzXRiaPquqptx5qQkI4xc3Og%2BtE2lHHKfsddOafcIDHKDlW0580EJHE3uNPzqTMoc%2FGyftqmk3rgPY3KNqz3pVPqsr8tzyaKKY459blVDJzRTNwOjgXCWrQPsosAnG1REskj8b%2Ftom0o5ZTYapbfWrzAD5Qtovx3v%2BNRD4lEuP01FnUWRONqoG9sbRuf08NUqXWTji2%2FNSphllCyKNlvRVNoWOJRb73vxWhwjFWDpuHCeKEJGKRY3Ov5VTZ4o45TY6q%2FNPAAY5dbG7Pqvigs2JUMo1H0qQZQxXH%2B2NUQWGGtzr44pVUyyZN3u%2FigUwxz62KqHXniimbCyxPtry1aEKu81Zw%2B16iJGSR99T%2BqjqUTLKfvul2ergCnKHttu71EKcT7oVDv8ASospUe2ln2vVAyyx%2Bep3e1VVKvJJ%2FwCWfiqqmBOUPfUM%2B9B6jEodHCOOa0zNKQqHFkuNqkmUSkXFzqKJsqMTlNg668058AETlCzXcb0EIcCF1GopWGQqC3xS%2FwC2iaQxOGlzqOGpVUQVk44cDWgUwicustcXIW9FM2lY4lFvve%2FFaHCMVYOm4cJ4oQkYpFjc6%2FlVNnijjlNjqr808ABjl1sbs%2Bq%2BKCzYlQyjUfSpBlDFcf7Y1RBYYa3OvjilVTLJk3e7%2BKBTDHPrYqodeeKKZsLLE%2B2vLVoQq7zVnD7XqIkZJH31P6qOpRMsp%2B%2B6XZ6uAKcoe227vUQpxPuhUO%2F0qLKVHtpZ9r1QMssfnqd3tVVSrySf%2BWfiqqmBOUPfUM%2B9B6lG%2BCO1%2Ba0zNKSSj10u%2B1noKZApH%2FnrZD9aptKkPafpvu71cAQ5Q9E5dnqLJLE%2BquGeohCo9dLvtaqAIcPhqVD2ak1SFZevi7vQKYg5dfpqHffms1TaEBiXJcK3nmug4pIrcqn%2BvNCTIRxiXRToPrRNlRAym51VuaeAAAyghJRDYWXzQmABibuRp%2BdJ8ZAJIS4jb8PNCCDG5uUbVuaV4SIgzVeWXXzQK6dHUe3v6OrrU9nZKMYRYKZSQOTRfJlqe2N2d%2F3PaZdnb2dk%2ByRHtOUpSIARyStMkmhm0Zd2SrJE5RUq8XqZS70DzUnmqbXqjLtWTz1RzvV5hZoy7Vgpkhuq71LLZ9yErJVCXXmjEXrDs7VvJCHckKlOJU38ndheVyt1RqsRNl2kyeSGwc605Fd%2Fs%2Fu%2Fu%2Fs%2FuOnv6ZyiYmJIWQjICQOMkIUFK5%2FclmK38%2FVl8eVkLq7t55roxNH1XVU2481ISEcYubnQfWibSjjlP2OunNPuEBjlByrac%2BaCEjib3Gn51JmUOfjZP21TSb1wHsblG1Z70qn1WV%2BW55NFFMcc%2Btyqhk5opm4HRwLhLVoH2UWATjaoiWSR%2BN%2F20TaUcspsNUtvrV5gB8oW0X473%2FGoh8SiXH6aizqLInG1UDe2No3P6eGqVLrJxxbfmpUwyyhZFGy3oqm0LHEot9734rQ4RirB03DhPFCEjFIsbnX8qps8UccpsdVfmngAMcutjdn1XxQWbEqGUaj6VIMoYrj%2FAGxqiCww1udfHFKqmWTJu938UCmGOfWxVQ688UUzYWWJ9teWrQhV3mrOH2vURIySPvqf1UdSiZZT990uz1cAU5Q9tt3eohTifdCod%2FpUWUqPbSz7XqgZZY%2FPU7vaqqlXkk%2F8s%2FFVVMCcoe%2BoZ96D1GJQ6OEcc1pmaUhUOLJcbVJMolIuLnUUTZUYnKbB115pz4AInKFmu43oIQ4ELqNRSsMhUFvil%2F20TSGJw0udRw1KqiCsnHDga0CmETl1lri5C3opm0rHEot9734rQ4RirB03DhPFCEjFIsbnX8qps8UccpsdVfmngAMcutjdn1XxQWbEqGUaj6VIMoYrj%2FbGqILDDW518cUqqZZMm73fxQKYY59bFVDrzxRTNhZYn215atCFXeas4fa9REjJI%2B%2Bp%2FVR1KJllP33S7PVwBTlD223d6iFOJ90Kh3%2BlRZSo9tLPteqBllj89Tu9qqqVeST%2FAMs%2FFVVMCcoe%2BoZ96D1KN8Edr81pmaUklHrpd9rPQUyBSP8Az1sh%2BtU2lSHtP033d6uAIcoeicuz1FklifVXDPUQhUeul32tVAEOHw1Kh7NSapCsvXxd3oFMQcuv01DvvzWaptCAxLkuFbzzXQcUkVuVT%2FXmhJkI4xLop0H1omyogZTc6q3NPAAAZQQkohsLL5oTAAxN3I0%2FOk%2BMgEkJcRt%2BHmhBBjc3KNq3NK8JEQZqvLLr5oFdOjqPb39HV1qezslGMIsFMpIHJovky1PbG7O%2F7ntMuzt7OyfZIj2nKUpEAI5JWmSTQzaMu7JVkicoqVeL1Mpd6B5qTzVNr1Rl2rJ56o53q8ws0ZdqwUyQ3Vd6lls%2B5CVkqhLrzRiL1h2dq3khDuSFSnEqb%2BTuwvK5W6o1WImy7SZPJDYOdaciu%2F2f3f3f2f3HT39M5RMTEkLIRkBIHGSEKClc%2FuSzFb%2Bfqy%2BPKyF1d28810Ymj6rqqbceakJCOMXNzoPrRNpRxyn7HXTmn3CAxyg5VtOfNBCRxN7jT86kzKHPxsn7appN64D2Nyjas96VT6rK%2FLc8miimOOfW5VQyc0UzcDo4Fwlq0D7KLAJxtURLJI%2FG%2FwC2ibSjllNhqlt9avMAPlC2i%2FHe%2FwCNRD4lEuP01FnUWRONqoG9sbRuf08NUqXWTji2%2FNSphllCyKNlvRVNoWOJRb73vxWhwjFWDpuHCeKEJGKRY3Ov5VTZ4o45TY6q%2FNPAAY5dbG7Pqvigs2JUMo1H0qQZQxXH%2B2NUQWGGtzr44pVUyyZN3u%2FigUwxz62KqHXniimbCyxPtry1aEKu81Zw%2B16iJGSR99T%2BqjqUTLKfvul2ergCnKHttu71EKcT7oVDv9KiylR7aWfa9UDLLH56nd7VVUq8kn%2Fln4qqpgTlD31DPvQeoxKHRwjjmtMzSkKhxZLjapJlEpFxc6iibKjE5TYOuvNOfABE5Qs13G9BCHAhdRqKVhkKgt8Uv%2B2iaQxOGlzqOGpVUQVk44cDWgUwicus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<h1 class="title toc-ignore">Factor splines</h1>
<h3 class="author">Samuel Orso</h3>
<h3 class="date">2017-09-20</h3>
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<div id="TOC" class="toc">
<ul>
<li><a href="#general-formualtion-of-the-problem">General formualtion of the problem</a></li>
<li><a href="#problem-at-hand">Problem at hand</a></li>
<li><a href="#loading-packages">Loading packages</a></li>
<li><a href="#setup">Setup</a></li>
<li><a href="#b-spline-basis">B-spline basis</a></li>
<li><a href="#i-spline-basis">I-spline basis</a></li>
<li><a href="#some-remarks">Some remarks:</a></li>
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<section id="main-content">
<div id="general-formualtion-of-the-problem" class="section level2">
<h2>General formualtion of the problem</h2>
<p>Let the <span class="math inline">\(d\)</span>-dimensional random variable <span class="math inline">\((X_i)_{i=1}^d\)</span> be expressed as a non-linear factor model through its cumulative distribution function:<span class="math display">\[ F_i(X_i) = h(U,V_i),\quad i =1,\dots,d, \]</span> where <span class="math inline">\(U\sim\mathcal{U}(0,1)\)</span> and <span class="math inline">\(V_i\sim\mathcal{U}(0,1)\)</span> are independent The unknown function <span class="math inline">\(h(\cdot)\)</span> is believed to be well approximated by the tensor product spline <span class="math display">\[ \hat{h}(U,V_i) \equiv s(U,V_i) = \mathbf{B}(U)^T\mathbf{C}\mathbf{B}(V_i), \]</span> where <span class="math inline">\(\mathbf{B}(x)\)</span> is the spline basis for <span class="math inline">\(x\)</span> and <span class="math inline">\(\mathbf{C}\)</span> is a matrix of coefficients. Since <span class="math inline">\(U\)</span> and <span class="math inline">\(V_i\)</span> are not observed, we propose to estimate the unknown function via the simulated method of moments: <span class="math display">\[ \widehat{\mathbf{C}} = \arg\min_{\mathbf{C}}\lVert\widehat{\mathbf{m}}-\widetilde{\mathbf{m}}(\mathbf{C})\rVert^2_{\Omega}, \]</span> where <span class="math inline">\(\mathbf{m}\)</span> is a <span class="math inline">\(K\)</span>-vector of moments estimated on <span class="math inline">\(\{F_i(X_i)\}_{i=1}^d\)</span> and <span class="math inline">\(\Omega\)</span> is a suitable positive semi-definite matrix of weights. At the end of the procedure, we obtain an estimate of <span class="math inline">\(s(\cdot)\)</span>, <span class="math display">\[\hat{s}(U,V_i) = \mathbf{B}(U)^T\widehat{\mathbf{C}}\mathbf{B}(V_i)\]</span> Note that <span class="math inline">\(\widehat{\mathbf{m}}\)</span> is estimated on the observations where <span class="math inline">\(\widetilde{\mathbf{m}}\)</span> is estimated on pseudo-observations generated from <span class="math inline">\(\hat{s}\)</span>. In words, we try to obtain the best fit to the approximation <span class="math inline">\(s(\cdot)\)</span> of the unknown function <span class="math inline">\(h(\cdot)\)</span>.</p>
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<div id="problem-at-hand" class="section level2">
<h2>Problem at hand</h2>
<p>In this example we assume that the true function <span class="math inline">\(h(\cdot)\)</span> is parametric, it is the clayton generator: <span class="math display">\[h(U,V_i) = \left(1+\frac{-\log(V_i)}{F_{\alpha}^{-1}(U)}\right)^{-\alpha}, \alpha>0,\]</span> where <span class="math inline">\(F_{\alpha}(x)\)</span> is the cdf of a gamma distribution with parameter <span class="math inline">\((\alpha,1)\)</span>.</p>
</div>
<div id="loading-packages" class="section level2">
<h2>Loading packages</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">require</span>(splines2)
<span class="kw">require</span>(cosplines)
<span class="kw">require</span>(nnls)
<span class="kw">require</span>(plotly)</code></pre></div>
</div>
<div id="setup" class="section level2">
<h2>Setup</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">n <-<span class="st"> </span><span class="fl">1e3</span> <span class="co"># sample size for one dimension</span>
d <-<span class="st"> </span><span class="dv">3</span> <span class="co"># number of dimensions</span>
alpha <-<span class="st"> </span><span class="fl">2.5</span>
<span class="kw">set.seed</span>(123L)
z <-<span class="st"> </span><span class="kw">runif</span>(n) <span class="co"># latent factor</span>
eps <-<span class="st"> </span><span class="kw">matrix</span>(<span class="kw">runif</span>(n*d),<span class="dt">nc=</span>d) <span class="co"># latent error</span>
x <-<span class="st"> </span><span class="kw">clayton</span>(z,eps,alpha) <span class="co"># observations</span>
kn <-<span class="st"> </span><span class="kw">c</span>(.<span class="dv">03</span>,.<span class="dv">2</span>,.<span class="dv">5</span>,.<span class="dv">8</span>,.<span class="dv">97</span>) <span class="co"># knots</span>
df <-<span class="st"> </span><span class="dv">3</span> <span class="co"># degrees of the B-splines</span>
q <-<span class="st"> </span><span class="kw">seq.int</span>(.<span class="dv">02</span>,.<span class="dv">98</span>,.<span class="dv">01</span>) <span class="co"># theoritical quantiles for empirical moments</span>
m_hat <-<span class="st"> </span><span class="kw">average_moments</span>(x,q) <span class="co"># empirical moments (first is Spearmann, other are quantile dependences)</span>
B <-<span class="st"> </span><span class="dv">5</span> <span class="co"># number of bootstrap replicates</span></code></pre></div>
</div>
<div id="b-spline-basis" class="section level2">
<h2>B-spline basis</h2>
<p>We first try the B-spline basis approach.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Best approximation achievable given knots and degrees</span>
xx <-<span class="st"> </span>yy <-<span class="st"> </span><span class="kw">seq.int</span>(.<span class="dv">01</span>,.<span class="dv">99</span>,.<span class="dv">001</span>)
exp_grid <-<span class="st"> </span><span class="kw">expand.grid</span>(xx,yy)
zz_cl <-<span class="st"> </span><span class="kw">matrix</span>(<span class="kw">clayton</span>(exp_grid[,<span class="dv">1</span>],<span class="kw">as.matrix</span>(exp_grid),alpha)[,<span class="dv">2</span>],<span class="dt">nc=</span><span class="kw">length</span>(xx))
A <-<span class="st"> </span><span class="kw">bSpline</span>(xx,<span class="dt">knots=</span>kn,<span class="dt">degree=</span>df,<span class="dt">intercept=</span>F,<span class="dt">Boundary.knots=</span><span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>))
D <-<span class="st"> </span><span class="kw">qr.solve</span>(<span class="kw">crossprod</span>(A)) %*%<span class="st"> </span><span class="kw">t</span>(A)
coefs_hat <-<span class="st"> </span><span class="kw">apply</span>(zz_cl,<span class="dt">MARGIN=</span><span class="dv">2</span>,<span class="dt">FUN=</span>function(x,M)M%*%x,<span class="dt">M=</span>D)
coefs_hat_best <-<span class="st"> </span><span class="kw">apply</span>(<span class="kw">t</span>(coefs_hat),<span class="dt">MARGIN=</span><span class="dv">2</span>,<span class="dt">FUN=</span>function(x,M)M%*%x,<span class="dt">M=</span>D)
<span class="co"># Estimation</span>
<span class="co"># Use the independent copula as starting points</span>
zz <-<span class="st"> </span><span class="kw">outer</span>(xx,yy)
coefs_hat <-<span class="st"> </span><span class="kw">apply</span>(zz,<span class="dt">MARGIN=</span><span class="dv">2</span>,<span class="dt">FUN=</span>function(x,M)M%*%x,<span class="dt">M=</span>D)
coefs_hat2 <-<span class="st"> </span><span class="kw">apply</span>(<span class="kw">t</span>(coefs_hat),<span class="dt">MARGIN=</span><span class="dv">2</span>,<span class="dt">FUN=</span>function(x,M)M%*%x,<span class="dt">M=</span>D)
sv <-<span class="st"> </span><span class="kw">c</span>(coefs_hat2) <span class="co"># starting values</span></code></pre></div>
<p>We try two different starting values for the optimization: <code>sv</code> stands for starting values, it based on a independent copula, <code>coefs_hat_best</code> is the spline least squares estimator that uses <span class="math inline">\(Z\)</span> and <span class="math inline">\(\epsilon\)</span> directly as if they were observed. It represents the worse/best scenario cases.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt <-<span class="st"> </span><span class="kw">optim</span>(<span class="dt">par=</span><span class="kw">c</span>(sv),<span class="dt">fn=</span>of_smm,<span class="dt">method=</span><span class="st">"Nelder-Mead"</span>,<span class="dt">M=</span>A,<span class="dt">n=</span>n,<span class="dt">d=</span>d,<span class="dt">q=</span>q,
<span class="dt">m_hat=</span>m_hat,<span class="dt">B=</span>B,<span class="dt">control=</span><span class="kw">list</span>(<span class="dt">trace=</span><span class="dv">1</span>,<span class="dt">maxit=</span><span class="dv">200</span>*<span class="kw">length</span>(sv)))
opt1 <-<span class="st"> </span><span class="kw">optim</span>(<span class="dt">par=</span><span class="kw">c</span>(coefs_hat_best),<span class="dt">fn=</span>of_smm,<span class="dt">method=</span><span class="st">"Nelder-Mead"</span>,<span class="dt">M=</span>A,<span class="dt">n=</span>n,<span class="dt">d=</span>d,<span class="dt">q=</span>q,
<span class="dt">m_hat=</span>m_hat,<span class="dt">B=</span>B,<span class="dt">control=</span><span class="kw">list</span>(<span class="dt">trace=</span><span class="dv">1</span>,<span class="dt">maxit=</span><span class="dv">200</span>*<span class="kw">length</span>(sv)))</code></pre></div>
<p>Evaluate the value of the objective function (to minimize) at different estimates:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">C_hat <-<span class="st"> </span><span class="kw">matrix</span>(opt$par,<span class="dt">nc=</span><span class="kw">ncol</span>(A))
C_hat1 <-<span class="st"> </span><span class="kw">matrix</span>(opt1$par,<span class="dt">nc=</span><span class="kw">ncol</span>(A))
<span class="co"># Objective function at starting values and optimums</span>
d_f <-<span class="st"> </span><span class="kw">data.frame</span>(
<span class="st">"Starting value independent"</span> =<span class="st"> </span><span class="kw">of_smm</span>(sv,A,n,d,q,m_hat,B),
<span class="st">"Estimator independent"</span> =<span class="st"> </span><span class="kw">of_smm</span>(<span class="kw">c</span>(C_hat),A,n,d,q,m_hat,B),
<span class="st">"Starting value best"</span> =<span class="st"> </span><span class="kw">of_smm</span>(<span class="kw">c</span>(coefs_hat_best),A,n,d,q,m_hat,B),
<span class="st">"Estimator best"</span> =<span class="st"> </span><span class="kw">of_smm</span>(<span class="kw">c</span>(C_hat1),A,n,d,q,m_hat,B)
)
d_f</code></pre></div>
<div class="kable-table">
<table>
<thead>
<tr class="header">
<th align="right">Starting.value.independent</th>
<th align="right">Estimator.independent</th>
<th align="right">Starting.value.best</th>
<th align="right">Estimator.best</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="right">9.846859</td>
<td align="right">0.3834907</td>
<td align="right">0.224484</td>
<td align="right">0.0994666</td>
</tr>
</tbody>
</table>
</div>
<p>The <em>best</em> starting values use directly the <span class="math inline">\(Z\)</span> and <span class="math inline">\(\epsilon\)</span> as if they were observed, and estimate the usual least squares in such situation. The estimator based on the <em>best</em> starting values can be considered as the <em>oracle</em>. The <em>independent</em> starting values is based on an independent copula, it does not use any information from <span class="math inline">\(Z\)</span> nor <span class="math inline">\(\epsilon\)</span> and therefore more realistic.</p>
<p>Let’s illustrate the results.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Visualization</span>
xx <-<span class="st"> </span>yy <-<span class="st"> </span><span class="kw">seq.int</span>(.<span class="dv">01</span>,.<span class="dv">99</span>,.<span class="dv">03</span>)
exp_grid <-<span class="st"> </span><span class="kw">expand.grid</span>(xx,yy)
zz_cl <-<span class="st"> </span><span class="kw">matrix</span>(<span class="kw">clayton</span>(exp_grid[,<span class="dv">1</span>],<span class="kw">as.matrix</span>(exp_grid),alpha)[,<span class="dv">2</span>],<span class="dt">nc=</span><span class="kw">length</span>(xx))
P <-<span class="st"> </span><span class="kw">predict</span>(A,xx)
zz_best <-<span class="st"> </span><span class="kw">tcrossprod</span>(P%*%coefs_hat_best,P)
zz_hat <-<span class="st"> </span><span class="kw">tcrossprod</span>(P%*%C_hat,P)
zz_hat1 <-<span class="st"> </span><span class="kw">tcrossprod</span>(P%*%C_hat1,P)</code></pre></div>
<p>The plot of the true function <span class="math inline">\(h(\cdot)\)</span>.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_ly</span>(<span class="dt">x =</span> xx, <span class="dt">y =</span> yy, <span class="dt">z =</span> zz_cl) %>%<span class="st"> </span><span class="kw">add_surface</span>()</code></pre></div>
<iframe width="600" height="400" frameborder="0" scrolling="no" src="https://plot.ly/~orsosam/1.embed">
</iframe>
<p>The plot of <span class="math inline">\(\hat{s}(\cdot)\)</span> evaluated at the <em>oracle</em> (best starting values):</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_ly</span>(<span class="dt">x =</span> xx, <span class="dt">y =</span> yy, <span class="dt">z =</span> zz_best) %>%<span class="st"> </span><span class="kw">add_surface</span>() %>%<span class="st"> </span><span class="kw">layout</span>(<span class="dt">title =</span> <span class="st">"Oracle"</span>)</code></pre></div>
<iframe width="600" height="400" frameborder="0" scrolling="no" src="https://plot.ly/~orsosam/3.embed">
</iframe>
<p>The plot of <span class="math inline">\(\hat{s}(\cdot)\)</span> evaluated at the <em>best estimate</em> (using the best starting values):</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_ly</span>(<span class="dt">x =</span> xx, <span class="dt">y =</span> yy, <span class="dt">z =</span> zz_hat1) %>%<span class="st"> </span><span class="kw">add_surface</span>() %>%<span class="st"> </span><span class="kw">layout</span>(<span class="dt">title =</span> <span class="st">"Best estimate"</span>)</code></pre></div>
<iframe width="600" height="400" frameborder="0" scrolling="no" src="https://plot.ly/~orsosam/5.embed">
</iframe>
<p>Eventually the plot of <span class="math inline">\(\hat{s}(\cdot)\)</span> evaluated at the estimate based on the independent copula as starting values</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_ly</span>(<span class="dt">x =</span> xx, <span class="dt">y =</span> yy, <span class="dt">z =</span> zz_hat) %>%<span class="st"> </span><span class="kw">add_surface</span>() %>%<span class="st"> </span><span class="kw">layout</span>(<span class="dt">title =</span> <span class="st">"Estimate"</span>)</code></pre></div>
<iframe width="600" height="400" frameborder="0" scrolling="no" src="https://plot.ly/~orsosam/7.embed">
</iframe>
<p>It is hard to spot the difference between the best on the graphs. Clearly the estimator based on the independent copula is far from the true function. We can measure the performance of the estimators by the following comparison <span class="math display">\[ \frac{\lVert h - \hat{s} \rVert_{\infty}}{\lVert h\rVert_{\infty}} \]</span></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Max relative error</span>
d_f <-<span class="st"> </span><span class="kw">data.frame</span>(
<span class="st">"Starting value best"</span> =<span class="st"> </span><span class="kw">norm</span>(<span class="kw">t</span>(zz_best)-zz_cl,<span class="st">"I"</span>)/<span class="kw">norm</span>(<span class="kw">t</span>(zz_best),<span class="st">"I"</span>),
<span class="st">"Estimator independent"</span> =<span class="st"> </span><span class="kw">norm</span>(<span class="kw">t</span>(zz_hat)-zz_cl,<span class="st">"I"</span>)/<span class="kw">norm</span>(<span class="kw">t</span>(zz_hat),<span class="st">"I"</span>),
<span class="st">"Estimator best"</span> =<span class="st"> </span><span class="kw">norm</span>(<span class="kw">t</span>(zz_hat1)-zz_cl,<span class="st">"I"</span>)/<span class="kw">norm</span>(<span class="kw">t</span>(zz_hat1),<span class="st">"I"</span>)
)
d_f</code></pre></div>
<div class="kable-table">
<table>
<thead>
<tr class="header">
<th align="right">Starting.value.best</th>
<th align="right">Estimator.independent</th>
<th align="right">Estimator.best</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="right">0.0180413</td>
<td align="right">0.5190733</td>
<td align="right">0.0200325</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="i-spline-basis" class="section level2">
<h2>I-spline basis</h2>
<p>I-splines have the advantage over B-splines to constrain monotonicity on the function of interest.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Best approximation achievable given knots and degrees</span>
xx <-<span class="st"> </span>yy <-<span class="st"> </span><span class="kw">seq.int</span>(.<span class="dv">01</span>,.<span class="dv">99</span>,.<span class="dv">001</span>)
exp_grid <-<span class="st"> </span><span class="kw">expand.grid</span>(xx,yy)
zz <-<span class="st"> </span><span class="kw">matrix</span>(<span class="kw">clayton</span>(exp_grid[,<span class="dv">1</span>],<span class="kw">as.matrix</span>(exp_grid),alpha)[,<span class="dv">2</span>],<span class="dt">nc=</span><span class="kw">length</span>(xx))
A <-<span class="st"> </span><span class="kw">iSpline</span>(xx,<span class="dt">knots=</span>kn,<span class="dt">degree=</span>df,<span class="dt">intercept=</span>F,<span class="dt">Boundary.knots=</span><span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>))
D <-<span class="st"> </span><span class="kw">qr.solve</span>(<span class="kw">crossprod</span>(A)) %*%<span class="st"> </span><span class="kw">t</span>(A)
coefs_hat <-<span class="st"> </span><span class="kw">apply</span>(zz,<span class="dt">MARGIN=</span><span class="dv">2</span>,<span class="dt">FUN=</span>function(x,M)M%*%x,<span class="dt">M=</span>D)
coefs_hat_best <-<span class="st"> </span><span class="kw">apply</span>(<span class="kw">t</span>(coefs_hat),<span class="dt">MARGIN=</span><span class="dv">2</span>,<span class="dt">FUN=</span>function(x,M)M%*%x,<span class="dt">M=</span>D)
coefs_hat_best_p <-<span class="st"> </span><span class="kw">apply</span>(<span class="kw">t</span>(coefs_hat),<span class="dt">MARGIN=</span><span class="dv">2</span>,<span class="dt">FUN=</span>function(x,M)<span class="kw">nnls</span>(M,x)$x,<span class="dt">M=</span>A) <span class="co"># non-negative ls</span>
<span class="co"># Estimation</span>
<span class="co"># Use the independent copula as starting points</span>
zz <-<span class="st"> </span><span class="kw">outer</span>(xx,yy)
coefs_hat <-<span class="st"> </span><span class="kw">apply</span>(zz,<span class="dt">MARGIN=</span><span class="dv">2</span>,<span class="dt">FUN=</span>function(x,M)M%*%x,<span class="dt">M=</span>D)
coefs_hat2 <-<span class="st"> </span><span class="kw">apply</span>(<span class="kw">t</span>(coefs_hat),<span class="dt">MARGIN=</span><span class="dv">2</span>,<span class="dt">FUN=</span>function(x,M)M%*%x,<span class="dt">M=</span>D)
sv <-<span class="st"> </span><span class="kw">c</span>(coefs_hat2) <span class="co"># starting values</span></code></pre></div>
<p>We operate as with the B-splines. We add also two optimizations: first (see <code>opt4</code>) with a positive constraints on the coefficients, i.e. <span class="math inline">\(C = (c)_{ij} > 0; \forall i,j\)</span>, second (see <code>opt5</code>) with a unit constraint for the coefficients, i.e. <span class="math inline">\(C = (c)_{ij} \in[0,1]; \forall i,j\)</span>. Both additionnal optimizations use the <em>best</em> starting values <code>coefs_hat_best</code>.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Optimization</span>
opt2 <-<span class="st"> </span><span class="kw">optim</span>(<span class="dt">par=</span><span class="kw">c</span>(sv),<span class="dt">fn=</span>of_smm,<span class="dt">method=</span><span class="st">"Nelder-Mead"</span>,<span class="dt">M=</span>A,<span class="dt">n=</span>n,<span class="dt">d=</span>d,<span class="dt">q=</span>q,
<span class="dt">m_hat=</span>m_hat,<span class="dt">B=</span>B,<span class="dt">control=</span><span class="kw">list</span>(<span class="dt">trace=</span><span class="dv">1</span>,<span class="dt">maxit=</span><span class="dv">200</span>*<span class="kw">length</span>(sv)))
<span class="co"># Optimization using best estimates as starting values</span>
opt3 <-<span class="st"> </span><span class="kw">optim</span>(<span class="dt">par=</span><span class="kw">c</span>(coefs_hat_best),<span class="dt">fn=</span>of_smm,<span class="dt">method=</span><span class="st">"Nelder-Mead"</span>,<span class="dt">M=</span>A,<span class="dt">n=</span>n,<span class="dt">d=</span>d,<span class="dt">q=</span>q,
<span class="dt">m_hat=</span>m_hat,<span class="dt">B=</span>B,<span class="dt">control=</span><span class="kw">list</span>(<span class="dt">trace=</span><span class="dv">1</span>,<span class="dt">maxit=</span><span class="dv">200</span>*<span class="kw">length</span>(sv)))
<span class="co"># Optimization using best estimates as starting values under non-negative constrains</span>
coefs_hat_best_p[coefs_hat_best_p<=<span class="dv">0</span>] <-<span class="st"> </span><span class="fl">1e-3</span>
opt4 <-<span class="st"> </span><span class="kw">optim</span>(<span class="dt">par=</span><span class="kw">log</span>(<span class="kw">c</span>(coefs_hat_best_p)),<span class="dt">fn=</span>of_smm2,<span class="dt">method=</span><span class="st">"Nelder-Mead"</span>,<span class="dt">M=</span>A,<span class="dt">n=</span>n,<span class="dt">d=</span>d,<span class="dt">q=</span>q,
<span class="dt">m_hat=</span>m_hat,<span class="dt">B=</span>B,<span class="dt">control=</span><span class="kw">list</span>(<span class="dt">trace=</span><span class="dv">1</span>,<span class="dt">maxit=</span><span class="dv">200</span>*<span class="kw">length</span>(sv)))
<span class="co"># Optimization using best estimates as starting values under non-negative constrains</span>
coefs_hat_best_p[coefs_hat_best_p>=<span class="dv">1</span>] <-<span class="st"> </span><span class="dv">1</span><span class="fl">-1e-3</span>
opt5 <-<span class="st"> </span><span class="kw">optim</span>(<span class="dt">par=</span>boot::<span class="kw">logit</span>(<span class="kw">c</span>(coefs_hat_best_p)),<span class="dt">fn=</span>of_smm3,<span class="dt">method=</span><span class="st">"Nelder-Mead"</span>,<span class="dt">M=</span>A,<span class="dt">n=</span>n,<span class="dt">d=</span>d,<span class="dt">q=</span>q,
<span class="dt">m_hat=</span>m_hat,<span class="dt">B=</span>B,<span class="dt">control=</span><span class="kw">list</span>(<span class="dt">trace=</span><span class="dv">1</span>,<span class="dt">maxit=</span><span class="dv">200</span>*<span class="kw">length</span>(sv)))</code></pre></div>
<p>Evaluate the value of the objective function (to minimize) at different estimates:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">C_hat <-<span class="st"> </span><span class="kw">matrix</span>(opt2$par,<span class="dt">nc=</span><span class="kw">ncol</span>(A))
C_hat1 <-<span class="st"> </span><span class="kw">matrix</span>(opt3$par,<span class="dt">nc=</span><span class="kw">ncol</span>(A))
C_hat2 <-<span class="st"> </span><span class="kw">matrix</span>(<span class="kw">exp</span>(opt4$par),<span class="dt">nc=</span><span class="kw">ncol</span>(A))
C_hat3 <-<span class="st"> </span><span class="kw">matrix</span>(boot::<span class="kw">inv.logit</span>(opt5$par),<span class="dt">nc=</span><span class="kw">ncol</span>(A))
<span class="co"># Objective function at starting values and optimums</span>
d_f <-<span class="st"> </span><span class="kw">data.frame</span>(
<span class="st">"Starting value independent"</span> =<span class="st"> </span><span class="kw">of_smm</span>(sv,A,n,d,q,m_hat,B),
<span class="st">"Estimator independent"</span> =<span class="st"> </span><span class="kw">of_smm</span>(<span class="kw">c</span>(C_hat),A,n,d,q,m_hat,B),
<span class="st">"Starting value best"</span> =<span class="st"> </span><span class="kw">of_smm</span>(<span class="kw">c</span>(coefs_hat_best),A,n,d,q,m_hat,B),
<span class="st">"Estimator best"</span> =<span class="st"> </span><span class="kw">of_smm</span>(<span class="kw">c</span>(C_hat1),A,n,d,q,m_hat,B),
<span class="st">"Est best >0"</span> =<span class="st"> </span><span class="kw">of_smm</span>(<span class="kw">c</span>(C_hat2),A,n,d,q,m_hat,B),
<span class="st">"Est best [0,1]"</span> =<span class="st"> </span><span class="kw">of_smm</span>(<span class="kw">c</span>(C_hat3),A,n,d,q,m_hat,B)
)
d_f</code></pre></div>
<div class="kable-table">
<table>
<thead>
<tr class="header">
<th align="right">Starting.value.independent</th>
<th align="right">Estimator.independent</th>
<th align="right">Starting.value.best</th>
<th align="right">Estimator.best</th>
<th align="right">Est.best..0</th>
<th align="right">Est.best..0.1.</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="right">9.864652</td>
<td align="right">1.831215</td>
<td align="right">0.4325991</td>
<td align="right">1.934092</td>
<td align="right">0.397909</td>
<td align="right">0.3696951</td>
</tr>
</tbody>
</table>
</div>
<p>Let’s illustrates the results:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Visulaization</span>
xx <-<span class="st"> </span>yy <-<span class="st"> </span><span class="kw">seq.int</span>(.<span class="dv">01</span>,.<span class="dv">99</span>,.<span class="dv">03</span>)
exp_grid <-<span class="st"> </span><span class="kw">expand.grid</span>(xx,yy)
zz_cl <-<span class="st"> </span><span class="kw">matrix</span>(<span class="kw">clayton</span>(exp_grid[,<span class="dv">1</span>],<span class="kw">as.matrix</span>(exp_grid),alpha)[,<span class="dv">2</span>],<span class="dt">nc=</span><span class="kw">length</span>(xx))
P <-<span class="st"> </span><span class="kw">predict</span>(A,xx)
zz_best <-<span class="st"> </span><span class="kw">tcrossprod</span>(P%*%coefs_hat_best_p,P)
zz_hat <-<span class="st"> </span><span class="kw">tcrossprod</span>(P%*%C_hat,P)
zz_hat1 <-<span class="st"> </span><span class="kw">tcrossprod</span>(P%*%C_hat1,P)
zz_hat2 <-<span class="st"> </span><span class="kw">tcrossprod</span>(P%*%C_hat2,P)
zz_hat3 <-<span class="st"> </span><span class="kw">tcrossprod</span>(P%*%C_hat3,P)</code></pre></div>
<p>Recall the plot of the true function <span class="math inline">\(h(\cdot)\)</span>:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_ly</span>(<span class="dt">x =</span> xx, <span class="dt">y =</span> yy, <span class="dt">z =</span> zz_cl) %>%<span class="st"> </span><span class="kw">add_surface</span>()</code></pre></div>
<iframe width="600" height="400" frameborder="0" scrolling="no" src="https://plot.ly/~orsosam/1.embed">
</iframe>
<p>Plot of the estimate <span class="math inline">\(\hat{s}(\cdot)\)</span> based on the independent starting values:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_ly</span>(<span class="dt">x =</span> xx, <span class="dt">y =</span> yy, <span class="dt">z =</span> zz_hat) %>%<span class="st"> </span><span class="kw">add_surface</span>() %>%<span class="st"> </span><span class="kw">layout</span>(<span class="dt">title=</span><span class="st">"Estimate"</span>)</code></pre></div>
<iframe width="600" height="400" frameborder="0" scrolling="no" src="https://plot.ly/~orsosam/9.embed">
</iframe>
<p>Plot of <span class="math inline">\(\hat{s}(\cdot)\)</span> based on the best starting values:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_ly</span>(<span class="dt">x =</span> xx, <span class="dt">y =</span> yy, <span class="dt">z =</span> zz_best) %>%<span class="st"> </span><span class="kw">add_surface</span>() %>%<span class="st"> </span><span class="kw">layout</span>(<span class="dt">title=</span><span class="st">"Oracle"</span>)</code></pre></div>
<iframe width="600" height="400" frameborder="0" scrolling="no" src="https://plot.ly/~orsosam/11.embed">
</iframe>
<p>Plot of the estimate <span class="math inline">\(\hat{s}(\cdot)\)</span> based on the best starting values:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_ly</span>(<span class="dt">x =</span> xx, <span class="dt">y =</span> yy, <span class="dt">z =</span> zz_hat1) %>%<span class="st"> </span><span class="kw">add_surface</span>() %>%<span class="st"> </span><span class="kw">layout</span>(<span class="dt">title=</span><span class="st">"Best"</span>)</code></pre></div>
<iframe width="600" height="400" frameborder="0" scrolling="no" src="https://plot.ly/~orsosam/13.embed">
</iframe>
<p>Plot of the estimate <span class="math inline">\(\hat{s}(\cdot)\)</span> based on the best starting values under the positivity constraint:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_ly</span>(<span class="dt">x =</span> xx, <span class="dt">y =</span> yy, <span class="dt">z =</span> zz_hat2) %>%<span class="st"> </span><span class="kw">add_surface</span>() %>%<span class="st"> </span><span class="kw">layout</span>(<span class="dt">title=</span><span class="st">"Best under positivity"</span>)</code></pre></div>
<iframe width="600" height="400" frameborder="0" scrolling="no" src="https://plot.ly/~orsosam/15.embed">
</iframe>
<p>Plot of the estimate <span class="math inline">\(\hat{s}(\cdot)\)</span> based on the best starting values under the unity constraint:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_ly</span>(<span class="dt">x =</span> xx, <span class="dt">y =</span> yy, <span class="dt">z =</span> zz_hat3) %>%<span class="st"> </span><span class="kw">add_surface</span>() %>%<span class="st"> </span><span class="kw">layout</span>(<span class="dt">title=</span><span class="st">"Best under unity"</span>)</code></pre></div>
<iframe width="600" height="400" frameborder="0" scrolling="no" src="https://plot.ly/~orsosam/17.embed">
</iframe>
<p>Let’s measure the error:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Max relative error</span>
d_f <-<span class="st"> </span><span class="kw">data.frame</span>(
<span class="st">"Estimator independent"</span> =<span class="st"> </span><span class="kw">norm</span>(<span class="kw">t</span>(zz_hat)-zz_cl,<span class="st">"I"</span>)/<span class="kw">norm</span>(<span class="kw">t</span>(zz_hat),<span class="st">"I"</span>),
<span class="st">"Starting value best"</span> =<span class="st"> </span><span class="kw">norm</span>(<span class="kw">t</span>(zz_best)-zz_cl,<span class="st">"I"</span>)/<span class="kw">norm</span>(<span class="kw">t</span>(zz_best),<span class="st">"I"</span>),
<span class="st">"Estimator best"</span> =<span class="st"> </span><span class="kw">norm</span>(<span class="kw">t</span>(zz_hat1)-zz_cl,<span class="st">"I"</span>)/<span class="kw">norm</span>(<span class="kw">t</span>(zz_hat1),<span class="st">"I"</span>),
<span class="st">"Est best >0"</span> =<span class="st"> </span><span class="kw">norm</span>(<span class="kw">t</span>(zz_hat2)-zz_cl,<span class="st">"I"</span>)/<span class="kw">norm</span>(<span class="kw">t</span>(zz_hat2),<span class="st">"I"</span>),
<span class="st">"Est best [0,1]"</span> =<span class="st"> </span><span class="kw">norm</span>(<span class="kw">t</span>(zz_hat3)-zz_cl,<span class="st">"I"</span>)/<span class="kw">norm</span>(<span class="kw">t</span>(zz_hat3),<span class="st">"I"</span>)
)
d_f</code></pre></div>
<div class="kable-table">
<table>
<thead>
<tr class="header">
<th align="right">Estimator.independent</th>
<th align="right">Starting.value.best</th>
<th align="right">Estimator.best</th>
<th align="right">Est.best..0</th>
<th align="right">Est.best..0.1.</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="right">0.5807432</td>
<td align="right">0.4186104</td>
<td align="right">0.5006259</td>
<td align="right">0.1993607</td>
<td align="right">0.1780085</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="some-remarks" class="section level2">
<h2>Some remarks:</h2>
<ul>
<li>Here we propose to use the independent copula to obtain starting values for <span class="math inline">\(\mathbf{C}\)</span> since <span class="math inline">\(U\)</span> and <span class="math inline">\((V_i)_{i=1}^d\)</span> are not observed. Maybe a different strategy can be more optimal (closer to the ``ideal’’ starting values).<br />
</li>
<li>All the results depend on the knot sequences and the selected degree for the splines, those choices are totally arbitrary up to now.</li>
</ul>
</div>
</section>
</div>
</div>
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