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Homework_10.html
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WZWHK5LZgl9279229we2OBUX50kuVjv5QDo7PBwnsvrhWJF%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%2B3DnRfV7nXGOc5zjHOc4xznOcY5znOMc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A7%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%2BEZ9JjlY4AhRhjjb1TWsI4NbGKCIzjJlCmcxhmcxTmcxwVcxCVcx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<section class="page-header">
<h1 class="title toc-ignore project-name">Homework_10.rmd</h1>
<h4 class="author project-author">Isaac Racine</h4>
<h4 class="date project-date">3/24/2021</h4>
</section>
<section class="main-content">
<div id="question-1" class="section level2">
<h2>Question 1</h2>
<p>Using a for loop, write a function to calculate the number of zeroes in a numeric vector. Before entering the loop, set up a counter variable counter <- 0. Inside the loop, add 1 to counter each time you have a zero in the matrix. Finally, use return(counter) for the output.</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="co">#---------------------------------------</span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="co"># FUNCTION zero_loop_counter</span></span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="co"># description: will count all of the zeros in a vector using a for loop</span></span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="co"># inputs: a numeric vector or matrix</span></span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="co"># outputs: the number of elements that are euqal to 0</span></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="do">########################################</span></span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a>zero_loop_counter <span class="ot"><-</span> <span class="cf">function</span>(<span class="at">x =</span> <span class="cn">NULL</span>) {</span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span>(<span class="fu">is.null</span>(x)){</span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a> x <span class="ot"><-</span> <span class="fu">c</span>(<span class="fu">rep</span>(<span class="dv">0</span><span class="sc">:</span><span class="dv">9</span>, <span class="dv">3</span>))}</span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a> counter <span class="ot"><-</span> <span class="dv">0</span></span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span>(i <span class="cf">in</span> x){</span>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span>(i <span class="sc">==</span> <span class="dv">0</span>){</span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a> counter <span class="ot">=</span> counter <span class="sc">+</span> <span class="dv">1</span>}</span>
<span id="cb1-16"><a href="#cb1-16" aria-hidden="true" tabindex="-1"></a> }</span>
<span id="cb1-17"><a href="#cb1-17" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb1-18"><a href="#cb1-18" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb1-19"><a href="#cb1-19" aria-hidden="true" tabindex="-1"></a><span class="co"># function body</span></span>
<span id="cb1-20"><a href="#cb1-20" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-21"><a href="#cb1-21" aria-hidden="true" tabindex="-1"></a><span class="fu">return</span>(counter)</span>
<span id="cb1-22"><a href="#cb1-22" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-23"><a href="#cb1-23" aria-hidden="true" tabindex="-1"></a>} <span class="co"># end of zero_loop_counter</span></span>
<span id="cb1-24"><a href="#cb1-24" aria-hidden="true" tabindex="-1"></a><span class="co">#---------------------------------------</span></span>
<span id="cb1-25"><a href="#cb1-25" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-26"><a href="#cb1-26" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(<span class="fu">zero_loop_counter</span>())</span></code></pre></div>
<pre><code>## [1] 3</code></pre>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="fu">zero_loop_counter</span>(<span class="fu">c</span>(<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">4</span>,<span class="dv">5</span>))</span></code></pre></div>
<pre><code>## [1] 5</code></pre>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>m <span class="ot"><-</span> <span class="fu">matrix</span>(<span class="fu">rep</span>(<span class="dv">0</span><span class="sc">:</span><span class="dv">2</span>, <span class="dv">4</span>), <span class="at">nrow =</span> <span class="dv">4</span>)</span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a><span class="fu">zero_loop_counter</span>(m)</span></code></pre></div>
<pre><code>## [1] 4</code></pre>
</div>
<div id="question-2" class="section level2">
<h2>Question 2</h2>
<p>Use subsetting instead of a loop to rewrite the function as a single line of code.</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="co">#Use this format: length(vec[vec == 0])</span></span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>z <span class="ot"><-</span> <span class="fu">c</span>(<span class="dv">0</span><span class="sc">:</span><span class="dv">3</span>, <span class="dv">3</span><span class="sc">:</span><span class="dv">0</span>)</span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>counter <span class="ot"><-</span> <span class="fu">length</span>(z[z<span class="sc">==</span><span class="dv">0</span>])</span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(counter)</span></code></pre></div>
<pre><code>## [1] 2</code></pre>
</div>
<div id="question-3" class="section level2">
<h2>Question 3</h2>
<p>Write a function that takes as input two integers representing the number of rows and columns in a matrix. The output is a matrix of these dimensions in which each element is the product of the row number x the column number.</p>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="co">#---------------------------------------</span></span>
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a><span class="co"># FUNCTION matrix_maker</span></span>
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a><span class="co"># description: will make a matrix of passed dimensions, and each element of the matrix will be the product of the col and row num</span></span>
<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a><span class="co"># inputs: two integers representing the col and row number</span></span>
<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a><span class="co"># outputs: matrix with elements as the product of the row and col</span></span>
<span id="cb9-6"><a href="#cb9-6" aria-hidden="true" tabindex="-1"></a><span class="do">########################################</span></span>
<span id="cb9-7"><a href="#cb9-7" aria-hidden="true" tabindex="-1"></a>matrix_maker <span class="ot"><-</span> <span class="cf">function</span>(<span class="at">row =</span> <span class="cn">NULL</span>, <span class="at">col =</span> <span class="cn">NULL</span>) {</span>
<span id="cb9-8"><a href="#cb9-8" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span>(<span class="fu">is.null</span>(row) <span class="sc">&&</span> <span class="fu">is.null</span>(col)){</span>
<span id="cb9-9"><a href="#cb9-9" aria-hidden="true" tabindex="-1"></a> row <span class="ot">=</span> <span class="dv">2</span></span>
<span id="cb9-10"><a href="#cb9-10" aria-hidden="true" tabindex="-1"></a> col <span class="ot">=</span> <span class="dv">2</span></span>
<span id="cb9-11"><a href="#cb9-11" aria-hidden="true" tabindex="-1"></a> m <span class="ot"><-</span> <span class="fu">matrix</span>(<span class="at">nrow =</span> <span class="dv">2</span>, <span class="at">ncol =</span> <span class="dv">2</span>)</span>
<span id="cb9-12"><a href="#cb9-12" aria-hidden="true" tabindex="-1"></a> } <span class="cf">else</span> {</span>
<span id="cb9-13"><a href="#cb9-13" aria-hidden="true" tabindex="-1"></a> m <span class="ot"><-</span> <span class="fu">matrix</span>(<span class="at">nrow =</span> row, <span class="at">ncol =</span> col)}</span>
<span id="cb9-14"><a href="#cb9-14" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb9-15"><a href="#cb9-15" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(m)){</span>
<span id="cb9-16"><a href="#cb9-16" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span>(j <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">ncol</span>(m)){</span>
<span id="cb9-17"><a href="#cb9-17" aria-hidden="true" tabindex="-1"></a> m[i,j] <span class="ot"><-</span> i <span class="sc">*</span> j}}</span>
<span id="cb9-18"><a href="#cb9-18" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-19"><a href="#cb9-19" aria-hidden="true" tabindex="-1"></a><span class="fu">return</span>(m)</span>
<span id="cb9-20"><a href="#cb9-20" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-21"><a href="#cb9-21" aria-hidden="true" tabindex="-1"></a>} <span class="co"># end of matrix_maker</span></span>
<span id="cb9-22"><a href="#cb9-22" aria-hidden="true" tabindex="-1"></a><span class="co">#---------------------------------------</span></span>
<span id="cb9-23"><a href="#cb9-23" aria-hidden="true" tabindex="-1"></a><span class="fu">matrix_maker</span>()</span></code></pre></div>
<pre><code>## [,1] [,2]
## [1,] 1 2
## [2,] 2 4</code></pre>
<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="fu">matrix_maker</span>(<span class="dv">6</span>,<span class="dv">4</span>)</span></code></pre></div>
<pre><code>## [,1] [,2] [,3] [,4]
## [1,] 1 2 3 4
## [2,] 2 4 6 8
## [3,] 3 6 9 12
## [4,] 4 8 12 16
## [5,] 5 10 15 20
## [6,] 6 12 18 24</code></pre>
<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="fu">matrix_maker</span>(<span class="dv">4</span>,<span class="dv">8</span>)</span></code></pre></div>
<pre><code>## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 1 2 3 4 5 6 7 8
## [2,] 2 4 6 8 10 12 14 16
## [3,] 3 6 9 12 15 18 21 24
## [4,] 4 8 12 16 20 24 28 32</code></pre>
</div>
<div id="question-4" class="section level2">
<h2>Question 4</h2>
<p>Use the code from the April 8th lecture (Randomization Tests) to design and conduct a randomization test for some of your own data. You will need to modify the functions that read in the data, calculate the metric, and randomize the data. Once those are set up, the program should run correctly calling your new functions. Also, to make your analysis fully repeatable, make sure you set the random number seed at the beginning (use either set.seed() in base R, or char2seed in the TeachingDemos package</p>
<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="co">#---------------------------------------</span></span>
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a><span class="co"># FUNCTION read_data</span></span>
<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a><span class="co"># description: read in (or generate) data set for analysis</span></span>
<span id="cb15-4"><a href="#cb15-4" aria-hidden="true" tabindex="-1"></a><span class="co"># inputs: file anem (or nothing as in this demo)</span></span>
<span id="cb15-5"><a href="#cb15-5" aria-hidden="true" tabindex="-1"></a><span class="co"># outputs: 3 col data frame of obs data (ID, x, y)</span></span>
<span id="cb15-6"><a href="#cb15-6" aria-hidden="true" tabindex="-1"></a><span class="do">########################################</span></span>
<span id="cb15-7"><a href="#cb15-7" aria-hidden="true" tabindex="-1"></a>read_data <span class="ot"><-</span> <span class="cf">function</span>(<span class="at">z =</span> <span class="cn">NULL</span>) {</span>
<span id="cb15-8"><a href="#cb15-8" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span>(<span class="fu">is.null</span>(z)){</span>
<span id="cb15-9"><a href="#cb15-9" aria-hidden="true" tabindex="-1"></a> x_obs <span class="ot"><-</span> <span class="dv">1</span><span class="sc">:</span><span class="dv">20</span></span>
<span id="cb15-10"><a href="#cb15-10" aria-hidden="true" tabindex="-1"></a> y_obs <span class="ot"><-</span> x_obs <span class="sc">+</span> <span class="dv">10</span> <span class="sc">*</span> <span class="fu">rnorm</span>(<span class="dv">20</span>)</span>
<span id="cb15-11"><a href="#cb15-11" aria-hidden="true" tabindex="-1"></a> df <span class="ot"><-</span> <span class="fu">data.frame</span>(<span class="at">ID =</span> <span class="fu">seq_along</span>(x_obs),</span>
<span id="cb15-12"><a href="#cb15-12" aria-hidden="true" tabindex="-1"></a> x_obs,</span>
<span id="cb15-13"><a href="#cb15-13" aria-hidden="true" tabindex="-1"></a> y_obs)</span>
<span id="cb15-14"><a href="#cb15-14" aria-hidden="true" tabindex="-1"></a> } <span class="cf">else</span> {</span>
<span id="cb15-15"><a href="#cb15-15" aria-hidden="true" tabindex="-1"></a> df <span class="ot"><-</span> <span class="fu">read.table</span>(<span class="at">file =</span> z,</span>
<span id="cb15-16"><a href="#cb15-16" aria-hidden="true" tabindex="-1"></a> <span class="at">header =</span> <span class="cn">TRUE</span>,</span>
<span id="cb15-17"><a href="#cb15-17" aria-hidden="true" tabindex="-1"></a> <span class="at">sep =</span> <span class="st">","</span>,</span>
<span id="cb15-18"><a href="#cb15-18" aria-hidden="true" tabindex="-1"></a> <span class="at">stringsAsFactors =</span> <span class="cn">FALSE</span>)}</span>
<span id="cb15-19"><a href="#cb15-19" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb15-20"><a href="#cb15-20" aria-hidden="true" tabindex="-1"></a> <span class="fu">return</span>(df)</span>
<span id="cb15-21"><a href="#cb15-21" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb15-22"><a href="#cb15-22" aria-hidden="true" tabindex="-1"></a>} <span class="co"># end of read_data</span></span>
<span id="cb15-23"><a href="#cb15-23" aria-hidden="true" tabindex="-1"></a><span class="co">#---------------------------------------</span></span>
<span id="cb15-24"><a href="#cb15-24" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-25"><a href="#cb15-25" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-26"><a href="#cb15-26" aria-hidden="true" tabindex="-1"></a><span class="co">#---------------------------------------</span></span>
<span id="cb15-27"><a href="#cb15-27" aria-hidden="true" tabindex="-1"></a><span class="co"># FUNCTION get_metric</span></span>
<span id="cb15-28"><a href="#cb15-28" aria-hidden="true" tabindex="-1"></a><span class="co"># description: calculate metric for randomization test</span></span>
<span id="cb15-29"><a href="#cb15-29" aria-hidden="true" tabindex="-1"></a><span class="co"># inputs: 2-col data frame for regression</span></span>
<span id="cb15-30"><a href="#cb15-30" aria-hidden="true" tabindex="-1"></a><span class="co"># outputs: regression slope</span></span>
<span id="cb15-31"><a href="#cb15-31" aria-hidden="true" tabindex="-1"></a><span class="do">########################################</span></span>
<span id="cb15-32"><a href="#cb15-32" aria-hidden="true" tabindex="-1"></a>get_metric <span class="ot"><-</span> <span class="cf">function</span>(<span class="at">z =</span> <span class="cn">NULL</span>) {</span>
<span id="cb15-33"><a href="#cb15-33" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span>(<span class="fu">is.null</span>(z)){</span>
<span id="cb15-34"><a href="#cb15-34" aria-hidden="true" tabindex="-1"></a> x_obs <span class="ot"><-</span> <span class="dv">1</span><span class="sc">:</span><span class="dv">20</span></span>
<span id="cb15-35"><a href="#cb15-35" aria-hidden="true" tabindex="-1"></a> y_obs <span class="ot"><-</span> x_obs <span class="sc">+</span> <span class="dv">10</span> <span class="sc">*</span> <span class="fu">rnorm</span>(<span class="dv">20</span>)</span>
<span id="cb15-36"><a href="#cb15-36" aria-hidden="true" tabindex="-1"></a> z <span class="ot"><-</span> <span class="fu">data.frame</span>(<span class="at">ID =</span> <span class="fu">seq_along</span>(x_obs), </span>
<span id="cb15-37"><a href="#cb15-37" aria-hidden="true" tabindex="-1"></a> x_obs,</span>
<span id="cb15-38"><a href="#cb15-38" aria-hidden="true" tabindex="-1"></a> y_obs)}</span>
<span id="cb15-39"><a href="#cb15-39" aria-hidden="true" tabindex="-1"></a> . <span class="ot"><-</span> <span class="fu">lm</span>(z[,<span class="dv">3</span>]<span class="sc">~</span>z[,<span class="dv">2</span>]) <span class="co">#3 col is y var, 2 is xvar</span></span>
<span id="cb15-40"><a href="#cb15-40" aria-hidden="true" tabindex="-1"></a> . <span class="ot"><-</span> <span class="fu">summary</span>(.)</span>
<span id="cb15-41"><a href="#cb15-41" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb15-42"><a href="#cb15-42" aria-hidden="true" tabindex="-1"></a> . <span class="ot"><-</span> .<span class="sc">$</span>coefficients[<span class="dv">2</span>,<span class="dv">1</span>] <span class="co"># grabbing matrix and getting slope</span></span>
<span id="cb15-43"><a href="#cb15-43" aria-hidden="true" tabindex="-1"></a> slope <span class="ot"><-</span> .</span>
<span id="cb15-44"><a href="#cb15-44" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb15-45"><a href="#cb15-45" aria-hidden="true" tabindex="-1"></a> <span class="fu">return</span>(slope)</span>
<span id="cb15-46"><a href="#cb15-46" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb15-47"><a href="#cb15-47" aria-hidden="true" tabindex="-1"></a>} <span class="co"># end of get_metric</span></span>
<span id="cb15-48"><a href="#cb15-48" aria-hidden="true" tabindex="-1"></a><span class="co">#---------------------------------------</span></span>
<span id="cb15-49"><a href="#cb15-49" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-50"><a href="#cb15-50" aria-hidden="true" tabindex="-1"></a><span class="co">#---------------------------------------</span></span>
<span id="cb15-51"><a href="#cb15-51" aria-hidden="true" tabindex="-1"></a><span class="co"># FUNCTION shuffle_data</span></span>
<span id="cb15-52"><a href="#cb15-52" aria-hidden="true" tabindex="-1"></a><span class="co"># description: randomize data for a regression analysis</span></span>
<span id="cb15-53"><a href="#cb15-53" aria-hidden="true" tabindex="-1"></a><span class="co"># inputs: 3 col data frame (ID, xvar, yvar)</span></span>
<span id="cb15-54"><a href="#cb15-54" aria-hidden="true" tabindex="-1"></a><span class="co"># outputs: 3 col data frame (ID, xvar, yvar)</span></span>
<span id="cb15-55"><a href="#cb15-55" aria-hidden="true" tabindex="-1"></a><span class="do">########################################</span></span>
<span id="cb15-56"><a href="#cb15-56" aria-hidden="true" tabindex="-1"></a>shuffle_data <span class="ot"><-</span> <span class="cf">function</span>(<span class="at">z =</span> <span class="cn">NULL</span>) {</span>
<span id="cb15-57"><a href="#cb15-57" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span>(<span class="fu">is.null</span>(z)){</span>
<span id="cb15-58"><a href="#cb15-58" aria-hidden="true" tabindex="-1"></a> x_obs <span class="ot"><-</span> <span class="dv">1</span><span class="sc">:</span><span class="dv">20</span></span>
<span id="cb15-59"><a href="#cb15-59" aria-hidden="true" tabindex="-1"></a> y_obs <span class="ot"><-</span> x_obs <span class="sc">+</span> <span class="dv">10</span> <span class="sc">*</span> <span class="fu">rnorm</span>(<span class="dv">20</span>)</span>
<span id="cb15-60"><a href="#cb15-60" aria-hidden="true" tabindex="-1"></a> z <span class="ot"><-</span> <span class="fu">data.frame</span>(<span class="at">ID =</span> <span class="fu">seq_along</span>(x_obs),</span>
<span id="cb15-61"><a href="#cb15-61" aria-hidden="true" tabindex="-1"></a> x_obs,</span>
<span id="cb15-62"><a href="#cb15-62" aria-hidden="true" tabindex="-1"></a> y_obs)}</span>
<span id="cb15-63"><a href="#cb15-63" aria-hidden="true" tabindex="-1"></a> z[,<span class="dv">3</span>] <span class="ot"><-</span> <span class="fu">sample</span>(z[,<span class="dv">3</span>])</span>
<span id="cb15-64"><a href="#cb15-64" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb15-65"><a href="#cb15-65" aria-hidden="true" tabindex="-1"></a> <span class="fu">return</span>(z)</span>
<span id="cb15-66"><a href="#cb15-66" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb15-67"><a href="#cb15-67" aria-hidden="true" tabindex="-1"></a>} <span class="co"># end of shuffle_data</span></span>
<span id="cb15-68"><a href="#cb15-68" aria-hidden="true" tabindex="-1"></a><span class="co">#---------------------------------------</span></span>
<span id="cb15-69"><a href="#cb15-69" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-70"><a href="#cb15-70" aria-hidden="true" tabindex="-1"></a><span class="co">#---------------------------------------</span></span>
<span id="cb15-71"><a href="#cb15-71" aria-hidden="true" tabindex="-1"></a><span class="co"># FUNCTION get_pval</span></span>
<span id="cb15-72"><a href="#cb15-72" aria-hidden="true" tabindex="-1"></a><span class="co"># description: calculate p-val from simulation</span></span>
<span id="cb15-73"><a href="#cb15-73" aria-hidden="true" tabindex="-1"></a><span class="co"># inputs: list of observed metric and vector of simulated metrics</span></span>
<span id="cb15-74"><a href="#cb15-74" aria-hidden="true" tabindex="-1"></a><span class="co"># outputs: lower and upper tail probability</span></span>
<span id="cb15-75"><a href="#cb15-75" aria-hidden="true" tabindex="-1"></a><span class="do">########################################</span></span>
<span id="cb15-76"><a href="#cb15-76" aria-hidden="true" tabindex="-1"></a>get_pval <span class="ot"><-</span> <span class="cf">function</span>(<span class="at">z =</span> <span class="cn">NULL</span>) {</span>
<span id="cb15-77"><a href="#cb15-77" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span>(<span class="fu">is.null</span>(z)){</span>
<span id="cb15-78"><a href="#cb15-78" aria-hidden="true" tabindex="-1"></a> z <span class="ot"><-</span> <span class="fu">list</span>(<span class="fu">rnorm</span>(<span class="dv">1</span>), <span class="fu">rnorm</span>(<span class="dv">1000</span>))}</span>
<span id="cb15-79"><a href="#cb15-79" aria-hidden="true" tabindex="-1"></a> p_lower <span class="ot"><-</span> <span class="fu">mean</span>(z[[<span class="dv">2</span>]] <span class="sc"><=</span> z [[<span class="dv">1</span>]])</span>
<span id="cb15-80"><a href="#cb15-80" aria-hidden="true" tabindex="-1"></a> <span class="co">#what is the proportion of the simulated values less than the obs values</span></span>
<span id="cb15-81"><a href="#cb15-81" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb15-82"><a href="#cb15-82" aria-hidden="true" tabindex="-1"></a> p_upper <span class="ot"><-</span> <span class="fu">mean</span>(z[[<span class="dv">2</span>]] <span class="sc">>=</span> z[[<span class="dv">1</span>]])</span>
<span id="cb15-83"><a href="#cb15-83" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb15-84"><a href="#cb15-84" aria-hidden="true" tabindex="-1"></a> <span class="fu">return</span>(<span class="fu">c</span>(<span class="at">pL =</span> p_lower,<span class="at">pU =</span> p_upper))</span>
<span id="cb15-85"><a href="#cb15-85" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb15-86"><a href="#cb15-86" aria-hidden="true" tabindex="-1"></a>} <span class="co"># end of get_pval</span></span>
<span id="cb15-87"><a href="#cb15-87" aria-hidden="true" tabindex="-1"></a><span class="co">#---------------------------------------</span></span>
<span id="cb15-88"><a href="#cb15-88" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-89"><a href="#cb15-89" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-90"><a href="#cb15-90" aria-hidden="true" tabindex="-1"></a><span class="co">#---------------------------------------</span></span>
<span id="cb15-91"><a href="#cb15-91" aria-hidden="true" tabindex="-1"></a><span class="co"># FUNCTION plot_ran_test</span></span>
<span id="cb15-92"><a href="#cb15-92" aria-hidden="true" tabindex="-1"></a><span class="co"># description: create a ggplot of histogram of simulated values</span></span>
<span id="cb15-93"><a href="#cb15-93" aria-hidden="true" tabindex="-1"></a><span class="co"># inputs: list of obs metric and vector simulated metrics</span></span>
<span id="cb15-94"><a href="#cb15-94" aria-hidden="true" tabindex="-1"></a><span class="co"># outputs: saved ggplot graph</span></span>
<span id="cb15-95"><a href="#cb15-95" aria-hidden="true" tabindex="-1"></a><span class="do">########################################</span></span>
<span id="cb15-96"><a href="#cb15-96" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggplot2)</span>
<span id="cb15-97"><a href="#cb15-97" aria-hidden="true" tabindex="-1"></a>plot_ran_test <span class="ot"><-</span> <span class="cf">function</span>(<span class="at">z =</span> <span class="cn">NULL</span>) {</span>
<span id="cb15-98"><a href="#cb15-98" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span>(<span class="fu">is.null</span>(z)){</span>
<span id="cb15-99"><a href="#cb15-99" aria-hidden="true" tabindex="-1"></a> z <span class="ot"><-</span> <span class="fu">list</span>(<span class="fu">rnorm</span>(<span class="dv">1</span>), <span class="fu">rnorm</span>(<span class="dv">1000</span>))}</span>
<span id="cb15-100"><a href="#cb15-100" aria-hidden="true" tabindex="-1"></a> df <span class="ot"><-</span> <span class="fu">data.frame</span>(<span class="at">ID =</span> <span class="fu">seq_along</span>(z[[<span class="dv">2</span>]]), <span class="at">sim_x =</span> z [[<span class="dv">2</span>]])</span>
<span id="cb15-101"><a href="#cb15-101" aria-hidden="true" tabindex="-1"></a> p1 <span class="ot"><-</span> <span class="fu">ggplot</span>(<span class="at">data =</span> df, <span class="at">mapping =</span> <span class="fu">aes</span>(<span class="at">x =</span> sim_x))</span>
<span id="cb15-102"><a href="#cb15-102" aria-hidden="true" tabindex="-1"></a> p1 <span class="sc">+</span> <span class="fu">geom_histogram</span>(<span class="at">mapping =</span> <span class="fu">aes</span>(<span class="at">fill =</span> <span class="fu">I</span>(<span class="st">"goldenrod"</span>),</span>
<span id="cb15-103"><a href="#cb15-103" aria-hidden="true" tabindex="-1"></a> <span class="at">color =</span> <span class="fu">I</span>(<span class="st">"black"</span>))) <span class="sc">+</span></span>
<span id="cb15-104"><a href="#cb15-104" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_vline</span>(<span class="fu">aes</span>(<span class="at">xintercept =</span> z [[<span class="dv">1</span>]], <span class="at">col =</span> <span class="st">"blue"</span>))</span>
<span id="cb15-105"><a href="#cb15-105" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb15-106"><a href="#cb15-106" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb15-107"><a href="#cb15-107" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb15-108"><a href="#cb15-108" aria-hidden="true" tabindex="-1"></a>} <span class="co"># end of plot_ran_test</span></span>
<span id="cb15-109"><a href="#cb15-109" aria-hidden="true" tabindex="-1"></a><span class="co">#---------------------------------------</span></span>
<span id="cb15-110"><a href="#cb15-110" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-111"><a href="#cb15-111" aria-hidden="true" tabindex="-1"></a><span class="co">#set seed</span></span>
<span id="cb15-112"><a href="#cb15-112" aria-hidden="true" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">81</span>)</span>
<span id="cb15-113"><a href="#cb15-113" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-114"><a href="#cb15-114" aria-hidden="true" tabindex="-1"></a><span class="co">#read data in</span></span>
<span id="cb15-115"><a href="#cb15-115" aria-hidden="true" tabindex="-1"></a>data <span class="ot"><-</span> <span class="fu">read_data</span>(<span class="st">"CleanedAbovegroundData.csv"</span>)</span>
<span id="cb15-116"><a href="#cb15-116" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-117"><a href="#cb15-117" aria-hidden="true" tabindex="-1"></a><span class="co"># Remove one of the ID columns because now there are two</span></span>
<span id="cb15-118"><a href="#cb15-118" aria-hidden="true" tabindex="-1"></a>data <span class="ot"><-</span> data[<span class="sc">-</span><span class="fu">c</span>(<span class="dv">1</span>)] </span>
<span id="cb15-119"><a href="#cb15-119" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-120"><a href="#cb15-120" aria-hidden="true" tabindex="-1"></a><span class="co"># get the slope for regression</span></span>
<span id="cb15-121"><a href="#cb15-121" aria-hidden="true" tabindex="-1"></a>x_obs <span class="ot"><-</span> <span class="fu">get_metric</span>(data)</span>
<span id="cb15-122"><a href="#cb15-122" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-123"><a href="#cb15-123" aria-hidden="true" tabindex="-1"></a><span class="co"># declare number of samples</span></span>
<span id="cb15-124"><a href="#cb15-124" aria-hidden="true" tabindex="-1"></a>n_samples <span class="ot"><-</span> <span class="dv">1000</span></span>
<span id="cb15-125"><a href="#cb15-125" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-126"><a href="#cb15-126" aria-hidden="true" tabindex="-1"></a><span class="co"># set up empty vector for simulated slopes</span></span>
<span id="cb15-127"><a href="#cb15-127" aria-hidden="true" tabindex="-1"></a>x_sim <span class="ot"><-</span> <span class="fu">rep</span>(<span class="cn">NA</span>, n_samples)</span>
<span id="cb15-128"><a href="#cb15-128" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-129"><a href="#cb15-129" aria-hidden="true" tabindex="-1"></a><span class="co">#loop through to calculate several simulated means</span></span>
<span id="cb15-130"><a href="#cb15-130" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span>(i <span class="cf">in</span> <span class="fu">seq_len</span>(n_samples)){</span>
<span id="cb15-131"><a href="#cb15-131" aria-hidden="true" tabindex="-1"></a> x_sim[i] <span class="ot"><-</span> <span class="fu">get_metric</span>(<span class="fu">shuffle_data</span>(data))} </span>
<span id="cb15-132"><a href="#cb15-132" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-133"><a href="#cb15-133" aria-hidden="true" tabindex="-1"></a><span class="co">#make list of slopes</span></span>
<span id="cb15-134"><a href="#cb15-134" aria-hidden="true" tabindex="-1"></a>slopes <span class="ot"><-</span> <span class="fu">list</span>(x_obs, x_sim)</span>
<span id="cb15-135"><a href="#cb15-135" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-136"><a href="#cb15-136" aria-hidden="true" tabindex="-1"></a><span class="co">#get upper and lower tails</span></span>
<span id="cb15-137"><a href="#cb15-137" aria-hidden="true" tabindex="-1"></a><span class="fu">get_pval</span>(slopes)</span></code></pre></div>
<pre><code>## pL pU
## 1 0</code></pre>
<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a><span class="co">#plot the simulated slopes</span></span>
<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a><span class="fu">plot_ran_test</span>(slopes)</span></code></pre></div>
<pre><code>## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.</code></pre>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>Clearly there is an association, likely that older forest age is associated with a higher amount of above ground biomass! This can be infered given that even when different seeds were set all the results were very singificant with the regression slops of the actual data being so far above that of any simulated data.</p>
</div>
<div id="question-5" class="section level2">
<h2>Question 5</h2>
<p>For comparison, calculate in R the standard statistical analysis you would use with these data. How does the p-value compare for the standard test versus the p value you estimated from your randomization test? If the p values seem very different, run the program again with a different starting seed (and/or increase the number of replications in your randomization test). If there are persistent differences in the p value of the standard test versus your randomization, what do you think is responsible for this difference?</p>
<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a>reg <span class="ot"><-</span> <span class="fu">lm</span>(data<span class="sc">$</span>Biomass<span class="sc">~</span>data<span class="sc">$</span>Age)</span>
<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb19-3"><a href="#cb19-3" aria-hidden="true" tabindex="-1"></a><span class="co"># here is the p-value</span></span>
<span id="cb19-4"><a href="#cb19-4" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(reg)<span class="sc">$</span>coefficients[<span class="dv">2</span>,<span class="dv">4</span>]</span></code></pre></div>
<pre><code>## [1] 2.413401e-40</code></pre>
<p>The p-value calculated from a standard statistical analysis using linear regression found a p-value of basically 0. This p-value matches the p-values estimated from the randomization test! There are no differences, both p-values are 0. This just means there is basically no chance, or a very tiny one, of all of the observed data happening by chance! There likely is an association between a forest plot’s age and aboveground biomass.</p>
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