diff --git a/Wald_Friedman.ipynb b/Wald_Friedman.ipynb index 650a28f..6854ce1 100644 --- a/Wald_Friedman.ipynb +++ b/Wald_Friedman.ipynb @@ -20,7 +20,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": { "collapsed": false }, @@ -41,7 +41,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": { "collapsed": false }, @@ -50,7 +50,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Fetching file: Wald_Friedman_utils.py\n" + "A file named Wald_Friedman_utils.py already exists in the specified directory ... skipping download.\n" ] } ], @@ -79,7 +79,13 @@ " * a type II error is when you accept a null hypothesis that is false \n", " \n", "\n", - " * $\\ldots$ \n" + " * Abraham Wald's **sequential probability ratio test**\n", + " \n", + " * The **power** of a statistical test\n", + " \n", + " * The **critical region** of a statistical test\n", + " \n", + " * A **uniformly most powerful test**\n" ] }, { @@ -105,7 +111,8 @@ " \"When Allen Wallis was discussing such a problem with (Navy) Captain Garret L. Schyler, the captain objected that such a test, to quote from Allen's account, may prove wasteful. If a wise and seasoned ordnance officer like Schyler were on the premises, he would see after the first few thousand or even few hundred [rounds] that the experiment need not be completed either because he new method is obviously inferior or because it is obviously superior beyond what was hoped for $\\ldots$ \"\n", " \n", " Friedman and Wallis struggled with the problem but after realizing that they were not able to solve it themselves told Abraham Wald it. That started Wald on the path that led *Sequential Analysis*. We'll formulate the problem using dynamic programming.\n", - " " + "\n", + "This started Wald on the path that led him to _Sequential Analysis_" ] }, { @@ -180,7 +187,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": { "collapsed": false }, @@ -197,7 +204,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": { "collapsed": false }, @@ -206,7 +213,7 @@ "data": { "image/png": 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Av7cUkbCy/PBKTtWeZny3G0lP7Oh0HIkQt/e8hcTYBBYfXMa5em37JiKXd8UC\n2RjT2f+xa/DjiEg0u7CtW0p8MpO63+x0HIkgKfHJ3NZjItUNNSw+uNzpOCIS5pozgrzQGNMG3x7I\nLmOMu+mfYAcUkeix8MAS6jz1TO91GwmxCU7HkQgzrusoMhLT+KRkHceqypyOIyJhrDkF7gGgChgH\nNAINTf7UBy+aiESTQ2cO89mxzXRL7szI7CFOx5EIFOuO5c68qXi8Ht4qWuR0HBEJY7FXusBaezeA\nMeY5a+1jwY8kItHG6/Uyb69vW7e78qdpWzcJmgHpfTGpeeyqtOys3EO/tAKnI4lIGLpigdzEN40x\nDwLDAC+wzlo7J9AGjTFPAiMBD/B9a+3GJucm4rs7XwPwvrX2iSbnEoAdwP+x1r4UaLsiEr42lW/j\n4JliBmUMID811+k4EsEubPv275/9mrf3LaIgNZ8Yd4zTsUQkzAQyTPMbYDpg8d1y+h5jzG8CacwY\nMxbIs9aOAh4FnvqCNmYCY4BbjTFNf7T/Z6AykPZEJPzVNdYzv2gxsa4YZuZpWzcJvi7J2YzuPJxj\n1eV8Urre6TgiEoYCKZD7W2tnW2t/Z639rbV2JhDo/V8n4L89tbV2D9DBGJMMYIzpCVRaa0uttV5g\nsf96/IVyAfBegO2JSJj78PAqTtae4uZuN5KemOZ0HIkSU3tNIiEmgcUHllFVX+10HBEJM4EUyPFN\nd60wxsQQ2BQNgCygosnj4/5jX3SuHMj2f/6fwA8BV4DtiUgYO1V7mqXFK0iJS2ZSj/FOx5EokhKf\nzG09J1DVUM372vZNRC4SSIH8HrDBGPOkfx7xRvyjwdfgcgWvC8A/73mttba4Gc8RkVZk4X7ftm7T\ncieRqG3dJMRu6jqajMQ0Vpas5VhVudNxRCSMNHsE2Fr7hDFmOTAC3yK9r1trPwuwvVL+OmIM0Bk4\n2uRcdpNzXfzHpgC9jDHTgK7AeWPMEWvtiss1lJGREmA0iTTqA+Ft/4liPj22ie4dujJ9wHjc7uDs\nXKF+IJfrA18eMptfrX6G9w4v4R/GPh7CVBJKeh+QQAU0RcJaux64lhUNS4GfAc8ZYwYDJdbaKv9r\nFxtjUowxOfgK46nAfdba3194sjHmp8DBKxXHABUVZ68hprR2GRkp6gNhzOv18txm3yY4M3pOobIy\nOLf+VT+QK/WB7nE96Z2ax+ajO1i5ZyN900wI00ko6H1AIPAfkkK62ai1dh2wyRizBvg18Lgx5mFj\nzB3+S77uo7GxAAAgAElEQVQJzAFWAq9ba4tCmU9EQmNz+XYOnD7EdRn96Z2a53QciWIul4tZ+dNw\n4eKtokU0ehqdjiQiYSDQRXbXzFr7k4sOFTY5txoYdZnn/muwcolIaNQ11jN//2JiXDHMzL3d6Tgi\ndEnOZlTn4awp/ZTVpZ8yruslvw2JSJRo9giyMWZyMIOISHRYceQTTpw/yc3dxpCRpG3dJDxM6zWJ\nhJg2vHdgKdXa9k0k6gUyxeK7xpgiY8y/GmO6By2RiESs07Vn+KB4BclxbZmsbd0kjKTEJzO5h2/b\nt8Xa9k0k6jW7QLbWTsF3m+li4GljzGJjzGz/fsgiIle0cP8S6hrrmNZrEomxiU7HEfkbN3UbQ7q2\nfRMRAlykZ609iW8R3WtAB+DHwDZjzMggZBORCFJ85gjrj238y3xPkXAT547lzrzb8Xg9vFX0rtNx\nRMRBgcxBHmuMeQHYhe8W01+11o7Atx3b00HKJyIRwOv1Mm/fQgBm5U/H7QrpBjoizTYwvR+9U/PY\nVWnZWbnH6Tgi4pBAvkv9AlgBGGvtD621u40xidbaQ8CbQUknIhFhU9lWDpwuZlDGAHqn5jodR+SS\n/mbbt33vats3kSgVSIF8zlr7srW2tsmxVQDW2n9v2VgiEilqG+t4Z/9iYt2xzMzTtm4S/rokZzOm\ny0jKqitYWbLW6Tgi4oAr7oNsjLkf+BeguzHmMODCd6vpeOBYcOOJSGu3vPhjTtWeZlL38aQndnQ6\njkizTO15KxvLtrL44HKGdxpMcnxbpyOJSAhdcQTZWvsq0Bff4rwx/j834tvRYnBQ04lIq3bi/EmW\nHV5J+/gUbu1+s9NxRJotOb4tt/e8hZqGGhYdXOp0HBEJsSsWyMaY31hrG4Fc4BXgZf+fV4GPg5pO\nRFq1+UWLqffUMz33NhJi2zgdRyQgY7vcQKekTFaXrKfk3FGn44hICDXnVtPP+z/+UzCDiEhk2X/q\nEJvKt9E9pRvDs/TLJml9Ytwx3JU/ld9ve555+97lu4Mew+VyOR1LRELgigWytXab/+PK4McRkUjg\n8XqYt28BALN6a1s3ab36pRXQL62AnZV72H58J9dl9Hc6koiEQHMW6X2Cb1HeF7LWjm3RRCLS6n16\ndBOHz5YwtNMgerXXnemldbsrbyq7T+zl7X2L6JtWQJy7Ob98FZHWrDn/yy83teKShbOIRKfzDedZ\neGAJ8e44ZuROcTqOyDXr1DaTcV1H8dGR1Xx05BMtOBWJAs0pkO+01n7vC0aSL2z3phFkEfmLD4o/\n4kzdWW7veQupCR2cjiPSIqb0mMiGY1tYcuhDRmQNpX2bFKcjiUgQaZGeiLSYiupKVhxeRWqbDkzM\nGed0HJEWkxSXxNRetzLHvsPCA+/zYJ+7nY4kIkHUnH2Qt/k/3Qj0A+4GZgMFwIbgRROR1uad/e/R\n4G1kZt4U4mPinY4j0qJGZQ+nc9ss3xz7M587HUdEgiiQpeXzgJFAIbAT381C3ghGKBFpfeyJIrZV\n7CC3fQ8GZ17ndByRFhfjjmFW/nS8eJm7byFer5bhiESqQJbitrPW3tbk8dPGmFUtHUhEWp9GTyPz\n9i3EhYtZ+dO1V6xELNMxj+sy+rOtYgebyrcxtNMgpyOJSBAEMoK8zxiTfeGBMSYL2NfykUSktVl7\n9DNKq44xMnsoOe26Oh1HJKjuzLudWFcM84sWU9dY53QcEQmCQPZBTgD2G2P2AB6gD7ApuPFEJNxV\n11fz7oEPSIhpw7Rek52OIxJ06YlpjM8Zy9Lij1h+eCVTet7idCQRaWHXug+y9nASiXKLDy2nqr6a\nGblTtPWVRI1J3W9m/dGNLC3+mBuyh2lLQ5EI05xdLFZe+ANU4BtN9gLxwP8Ncj4RCWPHqspZ+fla\n0hPTuKnbGKfjiIRMQmwC03tNpt5Tz/z9i52OIyItrNmL9IwxvwYmAVlAEZAL/GegDRpjnsS3G4YH\n+L61dmOTcxOBnwMNwPvW2ieMMYnAn4FOQBvgCWvte4G2KyIt7+2iRXi8Hu7Mu12335WoMyJ7CKtK\n1rKxbCvjuo6iV/seTkcSkRYSyCK9EdbaPsBWa+0w4BYgKZDGjDFjgTxr7SjgUeCpiy75DTATGAPc\nYowpAKYBG6y1NwH3AE8G0qaIBEfh8V3srNxD79Q8Bqb3czqOSMi5XW5m5d8BwJt2Ph6vx+FEItJS\nAimQa/0f2xhjXNbaTcDoANubAMwHsNbuAToYY5IBjDE9gUprbam11gu8D0yw1r5prb0wUp0DHAmw\nTRFpYXWNdby5dwFul5u7e9+hbd0kauV26MHwrMEcOVfKqpJ1TscRkRYSSIFsjTHfAlYBy4wxvyPw\nRXpZ+OYxX3Dcf+yLzpUDTbeVWwO8Anw/wDZFpIUtObSCE+dPMjFnHNltOzkdR8RRM/NuJzE2kXf3\nf8Dp2rNOxxGRFhBIgfwNYA7wE+B5fPOQp11j+5cbdvqbc9ba0cAdwKvX2KaIXINjVWUsP7yS1DYd\nmNxjgtNxRBzXLj6F6b0mc77xPG8Xvet0HBFpAYGsqkkC7gX64dvFohA4EWB7pfx1xBigM3C0ybns\nJue6AKXGmMFAubX2c2vtNmNMrDEm3Vp7/HINZWRou6lopz7Q8rxeL7/f8UcavY08OuxeumalOR3p\nitQPJBR9YGbaRDZWbGZj2Vam9BlH/04FQW9Tmk/vAxKoQArkefimQKzFN7p7IzCVwEaRlwI/A57z\nF74l1toqAGttsTEmxRiTg69Yngrc5//YHfiBMaYT0PZKxTFARYV+zRXNMjJS1AeCYMOxLews38uA\n9D70iO8V9n/H6gcSyj4wK/cOfrnxf/jDZ6/xk+E/IFY7u4QFvQ8IBP5DUiD/e9tZa29r8vhpY8yq\nQBqz1q4zxmzyzyduBB43xjwMnLLWLgC+iW8ahxd43VpbZIx5BviTv60E4FuBtCkiLaO6voa3it4l\nzh33l5X7IvJXOe26cmOXG1hVspblh1cxucd4pyOJyFUKpEDeZ4zJttYeBTDGZAH7Am3QWvuTiw4V\nNjm3Ghh10fXngfsDbUdEWtaigx9wtu4c03pNJj2xo9NxRMLStF6T2FKxnSWHljO00yD9XxFppa64\nSM8Y84l/9LYvsN8Ys9kYswnYD+QHO6CIOO/wmc9Z9fk6OiVlMjFnrNNxRMJWUlwid+ZNpd7TwLx9\nC5yOIyJXqTkjyP8U9BQiErY8Xg9z7Dt48XJP7xmaVylyBcM6Xc/a0s8oPL6bbRU7uS5DN9IRaW2u\nOIJsrV1prV0JrMZ3o467gDuBzv7jIhLB1pR+SvHZIwztNAjTMc/pOCJhz+Vyca+ZSYwrhrl7F1Db\nWOd0JBEJUCD7ID8FTAcsvrnHdxtjfhOUVCISFs7WnWPB/iUkxCRwZ961bnsuEj2y2nZiQs5YTtae\nYsmhD52OIyIBCuR3pf2tteOaPP6tMeaTlg4kIuHjnaL3qGmoYXbvO2jfRvuIigTith4T2Fi2leWH\nVzI8a7DuOinSigQyghxvjPnL9caYGAIrsEWkFdl38gCfHttEt+TOjO1yg9NxRFqd+Jh4ZudPx+P1\n8IZ9B6/X63QkEWmmQArc94ANxpgL845vxrdnsYhEmEZPI3P2voMLF/cW3InbFcjP0iJywcCMfgxI\n70Ph8d1sKNvC8KzBTkcSkWZo9nc9a+0TwONAMXAI+Lq19j+ClEtEHLTiyCccqypjdJcR9GiX43Qc\nkVZtdv4dxLnjeHvfIqrra5yOIyLN0OwRZGPMV6y1LwDrg5hHRBx24vxJFh9cRnJcW+7oNdnpOCKt\nXlpiR27rMYGFB5bw7oEl3GNmOh1JRK4gkN+b3mmMaR+0JCISFubte5c6Tz0z824nKS7J6TgiEWFC\nzlg6JWXyScl6is8ccTqOiFxBIAVyInDIGLPeGLPqwp9gBROR0NtxfDfbKnaQ274nI7KGOB1HJGLE\numO518zAi5c59h08Xo/TkUTkMgJZpPdvQUshIo6ra6zjzb0LcLvc3Gtm4nK5nI4kElF6p+YxrNP1\nbCjbwuqS9YztOsrpSCJyCVcskI0x7fDdbroA+AT4b2ttQ7CDiUhofVD8EZXnTzAxZxydk7OcjiMS\nkWbmTWVH5W4WHljCoMwBtIvX/uIi4ag5Uyx+7//4LNAH+Gnw4oiIE0rOHWV58cektunAbT0mOh1H\nJGK1b5PCtF6TqWk4z9y9C5yOIyKX0JwCuYe19u+ttYuAx4Abg5xJREKowdPAy7veoMHbyD1mBgmx\nbZyOJBLRbuwykp7turO5fDubyrY6HUdEvkBzCuT6C59YaxsB3QpIJIIsObSCI+dKuSF7GAPS+zod\nRyTiuV1uHup7N3HuON6w8zlde9bpSCJykeYUyBcXxCqQRSJE8ZkjfFC8gtQ2Hbgrf5rTcUSiRmZS\nBjPyplDVUM1re+bpNtQiYaY5u1iMMsYcbvI40//YBXittbrNlkgrVN9Yz0u73sDj9fBgn7tJjE1w\nOpJIVBnb5Qa2VexkR+Vu1h/bxA3ZQ52OJCJ+zSmQTdBTiEjIvXvwA45VlzOu62hMxzyn44hEHbfL\nzQMFs/nFZ08yb+9CTGouHRNSnY4lIjSjQLbWFociiIiETtGpg6w4/AmZienMyL3N6TgiUSstMZW7\n8qfz6p65vLp7Ho8P+ipuVyD38BKRYND/QpEoc76hlpd3vQHAg33vJj4m3uFEItHthuyh9E8rYM/J\nfawuWe90HBFBBbJI1FmwfzHH/TcE6dW+h9NxRKKey+XivoJZJMUm8k7Re5RXH3c6kkjUU4EsEkV2\nn9jLqpJ1ZLftxO29bnU6joj4tW/TjnvMTOo89by8+008Xo/TkUSiWnMW6bUoY8yTwEjAA3zfWrux\nybmJwM+BBuB9a+0T/uO/BMYAMcD/tda+E+rcIq1dTUMNr+ye69+D9R7i3CH/7y8ilzEk8zq2Vuxg\nS/l2Vhz5hIk545yOJBK1QjqCbIwZC+RZa0cBjwJPXXTJb4CZ+IrhW40xBcaYm4C+/ufcBvw6hJFF\nIsa8ve9yqvY0t/WYQE5KV6fjiMhFXC4X9/aeSUpcMu/uX0LpuWNORxKJWqGeYjEBmA9grd0DdDDG\nJAMYY3oCldbaUmutF1jsv34lMNv//FNAkjHGFeLcIq3a9oqdrD+2kZyULkzqPt7pOCJyCcnxbbmv\n4C4avI28vPsNGj2NTkcSiUqhLpCzgIomj4/7j33RuXIg21rrtdbW+I89Ciz2F9Ai0gzn6qp4zb5F\nrDuWB/vcQ4w7xulIInIZAzP6MSJrCIfPlvBB8Qqn44hEJacnIV5uJPhvzhlj7gC+AlxxZdFXn1hK\nY6Nq6GgWE+NSH/Cr7byBxnbniCvvx3+/dAA44HSkkFE/kNbaB7zuLFw9E3nvwHI+XFGPu7aD05Fa\nrdbaB+TShhVkcvf44N7gKtQFcil/HTEG6AwcbXIuu8m5Lv5jGGMmAf8ITLLWnm1OQzExmoUR7dQH\noD75cxrblRBT05E2p/NxReHfifqBtM4+EE9C2WBquq6hrvMmko7cjMur3/5crdbZB+RSEpPiychI\nCWobLq83dD9VGWNuAH5mrZ1kjBkM/NpaO7bJ+ULgdnyF8VrgPnxTLT4BJlhrm7s5pLeioll1tESo\njIwUor0PnK49w88/fZJ6Tz3/OPwHZCalOx0p5NQPpLX3gTfsO6wqWcctOTcxI2+K03FapdbeB6Rl\nZGSkBPRTUkjnIFtr1wGbjDFr8O1G8bgx5mH/9AmAbwJz8C3Me91aWwTcA6QBbxpjPjLGrDDGaAm+\nyGV4vV5e2/MWVQ3VzMy7PSqLY5FIcEfuFNIT01h+eCUHTh9yOo5I1AjpCHIIaQQ5ykX7iMG60g28\nsmcuBan5PD7oq7hd0XlPoGjvBxIZfaDo1EF+vfkZ0hM78o/Df0Ab3R4+IJHQB+TahfUIsogE37Gq\ncubtW0hCTAL395kVtcWxSKTI69CT8Tk3UlFTydy9C4jQgS2RsKLvnCIRpKbhPM8WvsT5xlq+VHAn\nHRNSnY4kIi1gWs9J5KR0Yd3RDawu/dTpOCIRTwWySITweD28vOsNyqrLGd/tRoZ2GuR0JBFpIXEx\ncTza/yGS49oyd+8CDpwudjqSSERTgSwSIZYWf8S24zvp3SGXGbla7S4SadISU3mk3/14vB7+WPgS\np2vPOB1JJGKpQBaJADsr97DowFJS23Tgkf736255IhHKdMxjRt4UTted5Y87XqHB0+B0JJGIpAJZ\npJWrqK7khZ2vE+OO4WsDHiIlPtnpSCISRBO6jWVI5nUcOH2It/YtcjqOSERSgSzSitU21vFs4YvU\nNNRwr7mTnHbaIlwk0rlcLu7vM5vObbNYVbKW9Uc3Oh1JJOKoQBZppbxeL6/unktp1THGdrmBG7KH\nOh1JREKkTUw8XxvwMImxibxu3+bwmc+djiQSUVQgi7RSHx5ZxabybfRq34O78qc5HUdEQiwjKY2v\n9PsSjZ5Gni18ibN155yOJBIxVCCLtEL2RBHzixbTPj6FR/s/QKw71ulIIuKAfmkF3N7zVk7WnuL5\nna/R6Gl0OpJIRFCBLNLKVNac5E87X8HtcvPogIdo36ad05FExEGTetzMwPR+7D1ZxIL97zsdRyQi\nqEAWaUXqGut5bsdLVNVXM7v3dHq17+50JBFxmNvl5qG+99ApKYMPj6xiY9lWpyOJtHoqkEVaCa/X\nyxz7NkfOlnBD9jDGdB7pdCQRCROJsQl8bcBDtImJ55Xdcyk5d9TpSCKtmgpkkVZiZclaPj22ie4p\n3bin9wxcLpfTkUQkjGS17cRDfe+l3lPPs9tfpKq+2ulIIq2WCmSRVqDo1EHe2vcuyXFteWzAg8TF\nxDkdSUTC0KCM/kzuPp7j50/w552v4/F6nI4k0iqpQBYJc6dqT/PHHS8D8Gj/B0hN6OBwIhEJZ7f3\nupW+HQ27TljeO7DU6TgirZIKZJEwdr7h/F/2N52Zdzv5qblORxKRMOd2uflKvy+RntCRJcUr2Hhs\ni9ORRFodFcgiYaq2sY6nt79A8ZkjjMgaws1dxzgdSURaiaS4JL428GESYhJ4cfcbbC0vdDqSSKui\nAlkkDNU11vOH7X+m6NRBrs8YwP0Fs7QoT0QC0iU5m8cHPUKsO5bnd75G4fFdTkcSaTVUIIuEmXpP\nA88VvoQ9WcSA9L58pd99xLhjnI4lIq1Qr/Y9+NbAR3C73Pyx8GV2VVqnI4m0CiqQRcJIg6eBP+14\nhV0nLH3TDF/t/4CKYxG5JvmpvfjGwC/jcrl4tvBF7IkipyOJhD0VyCJhotHTyAs7X6fw+C4KUvP5\nWv+HiHPHOh1LRCJAQcd8HhvwMF6vl2e2v0DRqYNORxIJayqQRcKAx+vhpd1vsLWikPwOvfj6wIe1\n17GItKh+aYZHBzxIg7eR32/7EwdOFzsdSSRshbxANsY8aYxZa4xZbYwZetG5icaYT40xa4wx/9Tk\neH9jTJEx5luhzisSbB6vh1d3z2Nj2VZ6te/ONwZ+hfiYeKdjiUgEGpDel0f63U+9p4Hfbf0TxWeO\nOB1JJCyFtEA2xowF8qy1o4BHgacuuuQ3wExgDHCrMabAGJPkv255KLOKhILX62WOfYf1xzbSPaUb\n37ruERJi2zgdS0Qi2PWZA3i4773UNtby261/5MjZUqcjiYSdUI8gTwDmA1hr9wAdjDHJAMaYnkCl\ntbbUWusFFvuvPw/cBhwNcVaRoPJ6vczdt4A1pZ/SLbkz3x70VRJjE52OJSJRYGinQTzY525qGs7z\n263PUXrumNORRMJKqAvkLKCiyePj/mNfdK4cyLbWeqy1tSHKJxISXq+Xt4sWsfLztXRum8W3r3+M\npLgkp2OJSBQZkT2ELxXcybn6Kp7a+ixlVeVORxIJG04v0rvcnQ90VwSJSF6vl4UHlrDiyCdkJWXy\n3eu/RnJcW6djiUgUGt15BPf0nsHZunP8ZsuzlFcfdzqSSFgI9R5Spfx1xBigM3+dOlEKZDc518V/\n7KpkZKRc7VMlQoRrH5i7YxFLiz8iOzmTn43/IamJ7Z2OFNHCtR9I6KgPXN5dGZNISIrlxa3z+O32\n5/jX8T8is22a07FalPqABCrUBfJS4GfAc8aYwUCJtbYKwFpbbIxJMcbk4CuMpwL3XfT8Zo8qV1Sc\nbZnE0iplZKSEXR/wer0sObSCRQc/ID2hI48PfJSGc24qzoVXzkgSjv1AQkt9oHmGdxzOqdwqFux/\nn58u/y++e/3XSE+MjCJZfUAg8B+SXF6vN0hRvpgx5hfAOKAReBwYDJyy1i4wxowBfgl4gXnW2v/2\nF9L/BXQH6oES4E5r7anLNOPVf4boFm5viLWNdby6ey6byreR2qYDPxj8TdISU52OFfHCrR9I6KkP\nBOb9g8tZdHApSbGJPNLvfvqk9XY60jVTHxCAjIyUgKbuhrxADhEVyFEunN4Qj9dU8mzhS5ScO0qv\n9t15tP+DtG/TzulYUSGc+oE4Q30gcGtLN/CGfZtGr4fpvSZzS/ebcLla77Ig9QGBwAtk3cdWJIh2\nVVpe2Pka1Q01jO1yA3flTyNWt48WkTA2qvMwOid34rnCl1lw4H0On/2cB/rMJiE2weloIiHj9C4W\nIhHJ6/XywaEV/H7b89R56nmgYDb3mJkqjkWkVejRLod/GPY98jv0YktFIb/a9DvKqyuu/ESRCKEC\nWaSFnW84zx93vMLCA0to36YdPxz8TW7oPMzpWCIiAUmJT+Y7gx7j5q5jOFZVxi83/g+Fx3c5HUsk\nJFQgi7SgsuoKfrXpd2ytKCS/Qy/+Ydj36N6um9OxRESuSow7hlm9p/Nw33tp8DTwzPY/897BZXi8\nHqejiQSVft8r0kIKj+/izzvncL7xPDd3G8PM3NuJccc4HUtE5JoNzxpMdttOPFv4EosPLuPI2c95\nuO+9JMYmOh1NJCg0gixyjTxeD+8dWMoz2/9Mo7eRh/vey6z86SqORSSidEvpwv839LsUpOZTeHw3\nv9z4PxytKnM6lkhQqEAWuQY1DTX8YfuLLD60nLSEVH405HGGZw12OpaISFAkx7flW9c9wi05N1Fe\nfZxfbfwftpYXOh1LpMWpQBa5SqXnjvHLDf/DjsrdFKTm8/fDvku3lM5OxxIRCaoYdwwz8qbwSL/7\n8Xq9PLfjZRbsf59GT6PT0URajOYgiwSopqGG9w9+yEefr8bj9XBLzk1Mz52M26WfN0UkegzpdB1Z\nbTN5tvAllhZ/ROHxXczKn05Bx3yno4lcM91JTyJSMO6c5PF6WH90Iwv3L+Fs/TnSEjoyu/d0BqT3\nbdF2pOXoDlqiPhB81fXVzN+/mLWlG/Di5br0ftyZP5X0xDSnowHqA+KjO+mJBMGB04eYu3cBh8+W\nEO+OY1qvSUzoNpa4mDino4mIOCopLon7CmYxpstI5u5dyLbjO9l5wjKh21hu7X4zCbFtnI4oEjCN\nIEtEaqkRg1O1p5lftJgNZVsAGNppEDNyp5Ca0OGaX1uCTyNHoj4QWl6vl01lW3ln/2JO1Z6mfXw7\nZuRNYVin63G5AhrAazHqAwIaQRZpEfWN9Xx4ZBUfHFpBnaeenJQuzMq/g9wOPZyOJiIStlwuF0Oz\nrmdARj+WFX/EssMreXHXHFZ9vo7ZvafrxknSamgEWSLS1Y4YeL1eth3fydv7FlF5/gQpcclMz53M\nyOyhWoTXCmnkSNQHnFVZc4K3i95ja0UhLlyMzB7K9NzJtItPCVkG9QEBjSCLXLXSc8eYt28h9mQR\nbpeb8d1uZErPibpTlIjIVUpL7MhjAx5k78ki5u5dyLqjG9hSvp3bek7kpq6jiXWrDJHwpBFkiUjN\nHTHwer0cOnOE1SXr+axsMx6vh75phll50+jUNjMESSWYNHIk6gPho9HTyJrST1l0YClVDdVkJqYz\nrttohncaTFJc8AYi1AcEAh9BVoEsEelKb4jV9TVsKNvCmtJPKTl3FIDMpHTuyptG//Q+oYopQaZv\njKI+EH6q6qtZdGApq0vX4/F6iHPHMSTzOkZ3GUHPdjktvphPfUBABfIFKpCj3Be9IXq9Xg6eOcya\nkk/ZVL6Nek89bpeb69L7MbrLCExqnuYZRxh9YxT1gfB1pu4s649uZE3pZxyvqQSgc9ssRncewfCs\n60mKS2qRdtQHBFQgX6ACOco1fUOsrq/ms2O+0eLSqmMApCd0ZHSXEYzMHhrSxSISWvrGKOoD4c/j\n9bD35H7WlH7KtoqdNHobiXPHMjjzOkZ3HkGv9t2vaVRZfUBAi/REAN9o8f5Th1hT+imby7dR72kg\nxhXD4MyBjP5/7N13fFRV+vjxz0x6IwlJgNAhhCf0rihNERdFBLuiotjrqqvud1d/X/vuurtfe2VX\nBdEV6yoKoiKKVEUIhp4DgSR0SCOVtJn5/XEnOCAlCZOZlOf9esWZueXcZ5jjnWfOPfec9qfTMzZJ\nW4uVUqoRsNvspLROJqV1MsWVJe5W5ZWs3JfKyn2ptItoy8j2p3Nau8FEeKlVWamT0RZk1WxUO6vJ\nKtrJloIM1uVtYGeR1bc4ISyOEe2t1uKo4Eg/R6l8SVuOlNaBpsnpcrK1YDvL96wkLWcDDpeDQHsg\nAxP60ru10DM2qdYTNmkdUKAtyKoFcTgd7CjehSnYxtaCbWwrzKLKWQVAgD3Auumj/ekkx3bX1mKl\nlGpC7DY70roH0roHxZUlrNyXyvLdK1m9P43V+9MAiA+Lo2dMEj1jrb/okFZ+jlo1J9qCrJoMp8vJ\nzuLdbCnYxpaD29h2MJMKR+Xh9YkRba0TZUwSZ/QYwKEipx+jVY2BthwprQPNh8vlYlfJXrYWZLDl\n4Da2FmRS7ig/vL5teJvDyXJyTPfDVwy1DihoAjfpichzwHDACdxnjFntsW4c8FegGvjKGPOXk+1z\nHJogN3Eul4uiyhIOlB2wkuKD28g4mMmhas+TYQLJ7oS4Z2zSEd0n9ISoQOuB0jrQnDmcDnaV7LEa\nTYYvEHsAACAASURBVAq2kVGYSaVHo0n7iHYkxyYxuHMvwqtbkRAWR1BAkB8jVv7UqLtYiMhooIcx\n5kwRSQFmAGd6bPIicC6wF1gsIp8AbU6yj2rCDlWXk1OWy/6yHA6U5XDgUK71WJZLuaPiiG3jw+IY\nlNDfah2I7U5MSLSfolZKKeVvAfYAurTqRJdWnTi3y1k4nA6yi3exxaPb3Z7SfSzetRwAGzZiQ2No\nG55Am/B42oS5H8MTaB0ao13x1BF83Qf5HGAOgDEmXURiRCTSGFMiIt2APGPMHgAR+RIYByQcbx8f\nx67qwOVyUemsoqSylNKqUkrcf4UVRRwoy+XAISsJLqr8bctOoD2QNmHxh09c7cLbkBzbndahsX54\nJ0oppZqCAHsA3aO70D26C+d1HUuVs5rsop3kOPaTmbPL+u4py2Fz/hY25285Yt9AeyAJYXG0CU+g\nTVg88WGtiQyOJDIogsigcCKCIogICtckugXxdYLcDvDsHpHrXpbhfszxWJcDJAFxJ9hHeZnT5aTS\nUUWV0/3nqKLS/bxmec1jhaPSnfyWWY+VvybCpVWlVDmrj3scGzZah8bSq3VP64QUHm/9qg9LIDY0\nWk9CSimlTkmQPZAeMd04I6E/OXG/NsaUV5e7r1b+esXygPtK5t7S/cctz4aN8MAwIoLDiQyKICIo\nwp1ARxAZHEFYYChB9iCCA4KtR3vg4edB9iCCAgIJtgcTFBBEoC3A6zMGKu/y9ygWJ6odx1t30hr1\nzPJ/UVlx/OTMX37T2/sY/b+PXuLCZf3X5fHK5XI/s57XrPFc7nQ5cbqcOFxOXO5Hp8uJEydOpxMn\nLvd6By6XC4fLQZWjimqX45TeY0hAMJFBEbSPSDx8Evn1RBJOVHAUbcLjiQ9trX3BlFJK+VxoYCid\nozrSOarjEctdLhfFVSUcKMslv7zAauw53PBTdsTV0NxD+Thd9b8R3IaNoIAggmyB2Gw2Amx27LYA\n7DYb9qOeB9js2GoesWO32bBhA5sNm7ssANvh5dYyW82RbL++OjKGoxfYTry+kQiwBXBul7PpFNW+\nQY/j6wR5D1brb432WP2Na9YleqzrAOwGKk6wzzE9OOK2xvq5Kh9KSNAZ8pTWA6V1QNW+DrShFUk0\nbOKlmgZfX8deAFwGICKDgd3GmFIAY0w2ECUinUUkEJjo3v7b4+2jlFJKKaWUt/ljmLe/AWMAB3AX\nMBg4aIz5XERGAv/E6mnwiTHm+WPtY4xZ79OglVJKKaVUi9FcJwpRSimllFKqXnSoAKWUUkoppTxo\ngqyUUkoppZQHTZCVUkoppZTy4O9xkL1KRJ4DhgNO4D5jzOqT7KKaCRHpizXj4nPGmNdEpCPwLtaP\nwL3AVGNMlT9jVA1LRP4JjAQCgL8Dq9A60KKISBjwNtAWCAH+AqxF60GLIyKhwAbgSeB7tA60GCIy\nBvgY6/O3AeuA/6OOdaDZtCCLyGighzHmTOBm4CU/h6R8RETCsT7vhR6LnwReNsaMAbYBN/ojNuUb\nInIW0Nv9///5wAtYdeAVrQMtyoXAKmPMWcCVwHNoPWipHgHy3M/1+6Dl+cEYM9YYc7Yx5l7qUQea\nTYIMnIPVgogxJh2IEZFI/4akfKQcKynynEDmLGCu+/lcYJyPY1K+tRi43P38IBCBNTTkF+5lWgda\nAGPMR8aYZ9wvOwM70XrQ4oiIACnAl1gtiGPQ74OW5ugJ486ijnWgOXWxaAd4dqnIdS/L8E84yleM\nMU6gwjonHhbhcfnkAEfO0qiaGWOMCzjkfnkT1hfjeK0DLZOILMeajfVC4FutBy3Os1jzLExzv9bv\ng5ant4jMAVpjtR6H17UONKcW5KPpdNOqhtaFFkJEJmNdOrubIz93rQMtiDFmBDAJeA+tBy2KiEwF\nVrhn5z0WrQPN31bgcWPMRVg/kt7iyAbhWtWB5pQg78FqMa7RniMvuauWpVhEQtzPO2DVD9WMich4\n4CHgPGNMMVoHWhwRGey+QRdjzDqsGza1HrQsFwCTReRHrKtJjwAlWgdaDmPMHmPMx+7n24F9QGxd\n60BzSpAXAJeBdZIEdhtjSv0bkvKjhcCl7ueXAl/7MRbVwESkFdY09RONMYXuxVoHWp7RwAMAItIW\niMSqB5e512s9aOaMMVcZY043xpwBvIl1eV3rQAsiIleLSM15oB3WqDYzqWMdaFZTTYvI37A64zuA\nu4wx6/0ckvIB9w+iZ4EuQBWwG7gGmIU11FM2cIMxxuG3IFWDEpFbgMeALViXz1zA9ViX1rQOtBDu\nob3eAjoBocDjQCrW8E5aD1oYEXkMyAS+QetAi+EeoGE2EAMEYZ0H1gLvUIc60KwSZKWUUkoppU5V\nc+pioZRSSiml1CnTBFkppZRSSikPmiArpZRSSinlQRNkpZRSSimlPGiCrJRSSimllAdNkJVSSiml\nlPKgCbJSSimllFIeNEFWSimllFLKgybISimllFJKedAEWSmlGgkRGSYi20Sk6zHWLRaRC49aFioi\n+SLS4QRljhGRpQ0QrlJKNVuaICulVCNhjFkF7DbGZB1j9VvAtKOWXQz8aIzZfZKiXacenVJKtRyB\n/g5AKaWUxd1yvO04qz8G/k9EYo0xBe5l1wFvuPe1AdMBAUKAlcaY+zzKHgP8xRgzyv16JrDUGDND\nRO4GLsf6TkgH7gRaA++5dw8D/mWMedtLb1UppRo1bUFWSqnGYzSwSERGiMiLIvLHmhXGmEPAp8AU\nABFJBAYAX7g3iQXWGmPOMsacAYwXkd5Hlf+blmQRGQZcbIwZY4wZARQCtwBXApuNMWOBMUC4N9+o\nUko1ZtqCrJRSjcdoIBP4Erj/GOtnAK8CrwHXALONMdXudQeBziKyAqgA2gHxtTjmWUCSiHwP2LAS\n4Ur3seaKyAxgPvDver4npZRqcjRBVkqpxqMbMBd40Rhz7dErjTGrRCRERFKAqcBVHquvAoYCI4wx\nLhFZddTuR7ceB7sfK4AvjDH3HH08dwv0GOAK4D5gZD3ek1JKNTnaxUIppRoBEWkH7DfGfA50FZEg\nETn/GJu+BTwClBpjNnssbwsYd3I8BEjC6otcowjo6D5WOHC6e/ly4HwRiXCvu0NEhovIFOA0Y8z3\nWH2SO4mIfmcopVoEPdkppVTjMBj4zv18MVaL8KJjbPcecAnw5lHLPwbOFJFFWKNbPAO8BMQAGGPS\ngHUikgrMxEqMMcakYnXb+EFElmC1GKcBm4Dn3OV9D/zdGOP0zltVSqnGzeZy6eg/SimllFJK1dAW\nZKWUUkoppTxogqyUUkoppZQHTZCVUkoppZTyoAmyUkoppZRSHjRBVkoppZRSyoMmyEoppZRSSnnQ\nBFkppZRSSikPmiArpZRSSinlQRNkpZRSSimlPGiCrJRSSimllAdNkJVSjYKIOEXko2Msf1NEnO7n\nw0Tkq5OU00ZELmyoOOtDRCaJyB4RefU4668RkVQR2SQiRkTeE5GuJyhvlohccJJj3iUiT5xCzNeL\nyLfHWN7F/VnVxJotIu+LSEod47tCRCKPs+5vInKr+7lTRNrXMfaeIjLK/fwiEXmzLvsrpVSgvwNQ\nSikP/UUk0hhTAiAiQcBQwAVgjFkFnH+SMsYC5wBzGzLQOpoEvGGMeezoFe5E8AFgsjEm3b3s98By\nERlojMk5eh9jzPUnO6Ax5pjJeB25jrO82hjTG0BEbMBtwBIRGWGM2Vqb+IAngOVAydErjDEP1yKG\nE7kY6/ttqTFmDjCnHmUopVowTZCVUo3JIuAS4B336/HAKqAfgIicBbwBCLAaeNIYM0dEugMrgIuA\nl4EAEYkA/gW8aYxJdu8/pua1iDwGdAAGAO8ZY14SkUeBq4EQrKTqfmOMS0QuBx4FAoBK4B5jzBLP\nwN2J4l/c8buAn4C7gZuBy4AKEWlnjLntqH2eAK6uSY4BjDEvi8ho4F7gf0VkEVYyeTFwE/A0VsI9\nW0SmuV/vA14AZhpj7DXvzxhzq3v/L9yxdQOWGGOudscwyR13MFAM3GSMWVfLzwtjjAuYLiIdgMeA\na93Hq4nvL+73bwN2AlPdxxNgkTv+W4B8rB82TwETga3GmL+597taRK4DWgH/MMa8LiLXA9caY851\nv4/rgWuBF4GH3P/eMcCGmu1EJBaYjvWZVwPvGGP+6d7fCVwH3A+0Bf7PGPOCux69C6S4/42+A+40\nxjhq+2+klGp6tIuFUqox+QgrQa0xxb2shgtwGWOcWEnVP0QkBHgGeNQY8xPwCvBJTQLIb1sgPV+f\nD5znTo6nYiVyQ4Ek998d7u1eBc53t5reidUifLQrsRL6QUAfIBa4zxjzEvAZ8KJncuyWArQyxiw6\nRnlzgTEerwcbY/q43yMA7oTvVWCsMWaQ+/jHa3GdiJWA9gTGisgZIhIAzMRKilOwkuhnjrP/yXwB\nnO25QER6A5cDvY0xgvXvcI4x5ib3JmOMMSvcz8cCw4wx/z1G2Z2NMf3d7+9ZEYlzL//NZ2uMmcev\n/95/PGq7p4F893sdBdwpImd67N/bGDMYmAz8zf0D5nqgwP3Z98RKrPvU5h9EKdV0aYKslGosXMAP\nQB8RiReRMOAM4HusVsQjGGNSgXnAx0CCMebf9TjmSmNMgfv5RGCGMabEnYC/hdXiCrAfuENEOhtj\nVhhjHjxGWROAWcaYcner6kzgdyc5fmsg9zjr9rvX15h/jG1OB4wxZrP79esnONYnxphKY0wZsAUr\n6XQAbdxdVwCWAd1PEvPxFAHRRy07CMQDU0UkxhjzqjHmPx7rPT/X74wxVccpexZYbxTYDAypZ4wT\ngNfcZRUAn3LkZ/Su+3EN1lWENsAB4AwRORcINMbcVZcWdqVU06QJslKq0XAnlp9itcZOBL45yaXs\n193bvVXPQ+Z7PI8BHnTffLYZ+D8g1L1uEpAIpLpvpht9jLISgAKP1wVYCdaJ5GJdzj+WtljJ2bFi\nrRF71PLdJzhWocdzB1Z3EYD7RGSt+z3PpP7fC105Ml6MMXuwfmRcDuwQkbnurhjHcqz3V8PzR0QR\n1vuuj5N9RoUA7h9INiDAGPMJ8DxW14/9IvKyu2+8UqoZ0wRZKdXYfIDV1eEy93M4freBp7GSl4fd\nLc5H80wE4cgW2aPtAf5mjOltjOlljOlpjBkJYIzJNMbcaIxJAF4CZh9j//1AnMfrOPeyE9mClThO\nPMa6C4GFJ9m/CIjyeF3X0R7OAP4HmGiM6YXVX7q+LgO+OXqhMWaxMWYiVsK/E/h7Pcr2/NxqfhQc\n/dnWJmmuz2eEMeYNY8xwoDdWF5zranEspVQTpgmyUqqxsAEYY37Eaq3ta4xZ7LnOk3sYsfbGmAeA\nr7Fa+ACqsFqDAfYCie4uGwEc2b/5aJ9jdQUIc5d/q4hMde+7QERqEtGVgPMY+8/DukEtTEQCsW6m\nm3eiN+xuMX8YeFlEBnq8t7uBwVj9i08kFegnIt3d/WVvOsn2R2uDlSDuEpFwrP62EbXY7/DnISJ2\nEbkTqyX/r54bici5IvKKiNiMMYeAtfz6Y6eaXz+nk6m5oTAFq2/4KqzPVkQk2B37ZR7be9YBT/OA\nmuHj4rFat0/4GYnI/4rIDQDGmL1AJvUbWUMp1YRogqyUaiw8k45PObL19IiExJ0QvQjc5V70KDDF\nnWQuAM4RkZXGmG1Y3QbSgCWcoEXWPRzYXGCNiGzCasH9xhiTC3wFrBKRDVitxzceY/9PsPoJpwLr\ngB1YI2r8Jv5j7Pc/wFsisllEDFbf6zHGmIPH2b9m2Lt9WAn2D1ijZizh2I53o+LXWInmNvfz54FC\nEfn4RDEDdo+uKLuAc4HRxphdR5W/GAgHtojIeuAKrM8KrJsvV4jIZSc5lgvIEpFfsD6H37v/XRZh\n/VjZAnzJkUO5zQVuF2tcbc+y/xdo7Y77B6wrBqlHxcxRr9/F+uG02V0vKvi1r7JSqpmyuVy+/SEs\nIs8Bw7FaYO4zxqz2WDcOqwWiGvjKGPMX9/JrgD9itQo8aow54UQBSinVErlHjVhqjIk76cZKKaWO\ny6fjILtvbOlhjDnTfalsBuA5xM6LWC0Re4HFIvIJ1k0fj2INnRSFNWaoJshKqRbP3W1kB3CxMeZn\n4CrgR/9GpZRSTZ+vJwo5B/dlMGNMuojE1MyaJSLdgDz3Xc+IyHz39jnAt+6hicqA230cs1JKNUrG\nGIe7/+8sdx/kvdS9H7JSSqmj+DpBboc1+1WNXPeyDPej55SqB7BuxogAIkTkc6ybLp4wxnzvm3CV\nUqpxM8Z8jnWDoVJKKS/x91TTv7kz/ah1Lvdja6wpZLth3ZjRpeFDU0oppZRSLZGvE+Q9WC3FNdpj\nXRKsWZfosa6De1kpsMI9HNJ2ESkWkXj3neXH5HK5XDbbiXJvpZRSSinVgtQpMfR1grwAeBx4Q0QG\nA7uNMaUAxphsEYkSkc5YifFErLEvy4CZIvJPrJbkiBMlxwA2m42cnOIGfBuqsUtIiNI6oLQeKK0D\nSuuAAqx6UBc+TZCNMT+6p2ldjjUL0l0icj1w0N2P7g6smbNcwPvGmAwA92gWP7mX3+3LmJVSSiml\nVMvi83GQfcSlvxZbNm0xUKD1QGkdUFoHlCUhIapOXSx0Jj2llFJKKaU8aIKslFJKKaWUB02QlVJK\nKaWU8qAJslJKKaWUUh40QVZKKaWUUsqDJshKKaWUUkp50ARZKaWUUkopD76eSU8ppZRSSrVgL7/8\nHBs3bsBms3HvvQ+QktL7iPWvvfYi69atxeFwcO2102jVqhWPPPJnundPwuVykZSUzH33PdigMWqC\nrJRSSimlfCItbQ27du1k+vQZZGdn8fTTTzJ9+ozD69esWU1WVibTp8+gqKiQG264hkceeZJBg4bw\n1FN/91mcmiArpZRSSqlTNm/e53zzzXxsNhsulwubzca0aTczePDQw9ukpq5i1KizAOjSpSslJcWU\nlZURHh4OwKBBQ+jTpy8AkZFRVFSU43Q68fXMz5ogK6VUI+V0udiUlc+StXvZuusg1PH7ITIsiOF9\n2nJm30Rio0IaJkilVIP76PsMVqUf8GqZw1LacMXYHifcZsOGdSxdupikpGRCQoIpLCxk0qSLj7v9\nxImTmThx8gnLzMvLRaTX4dfR0THk5+cdTpBtNhshIaEAzJ07h+HDR2Cz2cjKyuShhx6gqKiIadNu\nZtiw02v7VutFE2SllGpk8ovKWbZuL0vX7SWvqByA2KgQgoMD6lROzsFD/Hfxdj5bkkn/pDhGDUik\nf1IcAXa9P1spdXIulwuHw0GXLl0RSeGee25n4sTJvP76y9x1171eO8axLF36A/Pnz+X551+hrKyM\nG2+8lbFjx7F79y7uued2PvxwDoGBDZfGaoKslFKNQLXDSdrWXJas28PG7fm4gJCgAEYPSGTUgPZ0\nT2yFzWarU5ll5dWs3LyfJWv3kJaRS1pGLtGRwYzsl8jI/om0jQ1vmDejlPKqK8b2OGlrb0Po128A\nb7/9FiIpFBUVUV1djd1uJyws7Jjb16aLRXx8Avn5eYdf5+bmEBcXf0Q5K1f+yLvvvs1zz71CeHgE\n4eERjB07DoAOHTrSunUcubk5tGuX2ADv2qIJslJK+dGe3FKWrtvDig37KC6rAiCpQytG9W/PsJQ2\nhIXU/zQdHhrI2YM6cPagDuzYX8zStXv5ceM+vvwxmy9/zCalcwyjBrRnSM8EgoPq1jqtlGr+qqqq\nqPldvnz5EsaPn0BpaQlVVVWkp29i//59jBkz9vD2telicdppw5kx499MmnQxxqSTkNDmiIS7tLSE\n1157iRdffJ3IyEgAFiz4mry8XKZMuZa8vFwOHiwgPj7B+2/YgybISinlYxWVDn5O38/StXvJ2F0I\nWP2FfzesE6MGtKdDfITXj9m5bRTX/C6Ky89OInVLDkvX7iF9x0HSdxzkvZBAhvdpy+gB7encNsrr\nx1ZKNU3p6ZsICgpi2bIl5ObmMnXqNJYtW0xUVBQVFZWMHDmmzmX27dsfkV7ccceN2O0B3H//n8jP\nz2PGjH/z4IMP8d1331JUVMijj/75cCv0//t/j/Pcc/9g2bLFVFdX8+CDDzVo9woAm6/vCvQRV05O\nsb9jUH6UkBCF1gHV2OqBy+ViwaqdfL4sk/JKBzagd7fWjB7QnoE94gkK9G3f4P0FZSxbt5dl6/dS\nWFIJQI+O0dx0Qa9m0/2isdUB5XtaB+pv9ux3SUnpdUQXidmz32XKlGuZNestxo49l86du/gxwtpL\nSIiqUx81TZBVs6QnRAWNqx6UHKpixpebScvIJSo8iLMHdWBk/0Tio4/dl8+XHE4n67fl80PabtZt\nyyM0OIAbJvRiWEobf4d2yhpTHVD+oXWgfnbv3sUjj/yJK664mvPOu8Df4ZwyTZAtmiC3cHpCVNB4\n6sG2PYVMn7ORvKJyenWJ5dZJfYiOCPZ3WMe0YsNe3vnGUFnlZOzgDlw5NtnnLdve1FjqgPIfrQMK\n6p4gax9kpZRqIC6Xi29X7eTjH7bhdLq4aGQ3Jp7ZFbu9bqNR+NKZfRPp2q4Vr8/ZwPdrdrNtdxF3\nXNSHNs2ky4VSStVG020WUEqpRqy0vIpXPl3PB99nEBEWxINXDWTSyG6NOjmu0T4+gv+9figj+yeS\nvb+YJ95exWovT1KglFKNmbYgK6WUl23fU8TrczaQV1ROSucYbpvUh+jIpjWTXUhQADdO6IV0iuHd\nBYbX5mxg3JCOXH52jybd5UIppWpDE2SllPISl8vFwtW7+GhRBk6ni0kjujJpRNNoNT6eEf0S6Zpo\ndblYmLqLjN2F3HFRXxJi/H9zoVJKNRRtBlBKKS+o6VLx/ndbiQgN5P6rBnLRqO5NOjmu0SE+gkeu\nG8qIfu3I2lfM4zNXkWpy/B2WUko1GG1BVkqpU5S51+pSkVtodam4dVIfYppYl4qTCQkO4KYLeiOd\nYvnPAsOrn61n3NCOXHF2DwIDtK1FKdW8aIKslFL15HK5+C51Fx9+b3WpuPDMrkxuIjfi1dfI/ol0\nS4zitTkbWLh6F9t2F3LH5L7Ea5cLpVQzoj/7lVKqHlwuF+8v3MrshVsJDw3k/isHcvHo5tGl4mQ6\nJETy6PXDOLNvOzL3FvPkrNXszi31d1hKKeU12oKslFL1MGdpJgtTd9EhPoL7rxxIbFTz6lJxMiHB\nAdw8sTfdElvx3rdbePaDX3jo2iF6855S6qRefvk5Nm7cgM1m4957HyAlpffhdb/8ksojj/yZ7t2T\ncLlcJCUlc999D/LSS8+yadPGY+7TEDRBVkqpOvp65Q7mrsiiTUwYD1w1sNn1N66Lc4Z0pNrh5MPv\nM3jmg1/48zVDWtyPBaVU7aWlrWHXrp1Mnz6D7Owsnn76SaZPn3HENoMGDeGpp/5+xD67d+864T7e\n5vMEWUSeA4YDTuA+Y8xqj3XjgL8C1cBXxpi/iMgY4GNgA2AD1hlj7vV13EopBbA4bTcfLcogNiqE\nB1t4clxj/GmdOVRRzRfLs3juwzT+dM1gIsOC/B2WUsrH5s37nG++mY/NZsPlcmGz2Zg27WYGDx56\neJvU1FWMGnUWAF26dKWkpJiysjLCw3+drdPlch1Rbm328TafJsgiMhroYYw5U0RSgBnAmR6bvAic\nC+wFFovIJ+7lPxhjrvBlrEopdbSVm/bzzteGSPfMeHpj2q8mj+xGWUU1C1fv4rkP0/jjlEGEhehF\nSqW84dOMefxyYL1XyxzUph+X9Jh4wm02bFjH0qWLSUpKJiQkmMLCQiZNuvi420+cOJmJEyefsMy8\nvFxEeh1+HR0dQ35+3hHJblZWJg899ABFRUVMm3ZzrfbxNl/fpHcOMAfAGJMOxIhIJICIdAPyjDF7\njDEuYL57e7BajpVSym/WZuTy5rxNhIYE8MCVA0mMi/B3SI2KzWbjqnOSGdkvkax9xbz0yToqqxz+\nDkspdQpcLhcOh4MuXboyZsxYFi78BqfTyauvvujVY3jq1KkzN954K08//SwPP/wYf//7UzidzhPu\n0xB8/fO+HbDa43Wue1mG+9Fz5PkDQHesrhW9RWQO0Bp40hiz0DfhKqUUmB0FvDZnAwF2G/deNoAu\n7aL8HVKjZLfZuP584VBlNakmh9fmbODuS/rpOMlKnaJLekw8aWtvQ+jXbwBvv/0WIikUFRVRXV2N\n3W4nLOzYV89q08UiPj6B/Py8w69zc3OIi4s/Yv3YseMA6NChI61bx+F0Ok+4T0Pw91nrRC3DNeu2\nAI8bYy4CpgFviYhet1NK+UTm3iJe+GQdTqeLuy/pR89OMf4OqVELsNu59cI+9O3WmnXb8nhz3iac\nzoZv7VFKeV9VVRU2dza2fPkSxo+fQGlpCVVVVaSnb2Lx4u+P2H7ixMm8/PK/eOml6YcfPZNjgNNO\nG84PP3wHgDHpJCS0OSLhXrDga95//z+A1R3j4MECLrhgMosWLTzuPg3B14nmHqyW4hrtsfob16xL\n9FjXAdhjjNmLdZMexpjtIrLPvS77RAdKSNAWnpZO64CCU6sH2XuLeOHjtVRVOfif64Yxon97L0bW\nvD126xk89u8f+XnzAWJahXH35QOw2fzTW07PBUrrQP2sWbOGiIgw1q9fRXl5Mbfeeivfffcd7drF\nExYWwMUXTyQgIKBOZZ599gh++WUlv//9LQQEBPDUU09gs1Xw8ssv88QTT3DRRRN44IEHuO++ZVRX\nV/PUU08yatQo1q1bdcQ+Df2Z2nzRj6OGiJyB1Ro8XkQGAy8YY0Z7rF8PXICVLK8ArgZOAxKNMc+K\nSDvgRyDZGFN9gkO5cnKKG+x9qMYvISEKrQPqVOrBgYIynv7PGgpLK7lhQgqjNDmus7Lyav75/hp2\n7C9h/GmduOLsHj5PkvVcoLQO1N/s2e+SktLriFbg2bPfZcqUa5k16y3Gjj2Xzp27+DHC2ktIiKrT\nycenXSyMMT8CqSKyHHgBuEtErheRmlse7wA+ABYD7xtjMoAvgDEisgT4DLj9JMmxUkqdkoLi1ffK\nxAAAIABJREFUCp75II3C0kqmnJOsyXE91cwwmBgXzjc/72Teiix/h6SUqqXdu3excOHXHDiw/4jl\nV1899XDf4qaSHNeHT1uQfUhbkFs4bTFQUL96UFRWyT/eW8PevDIuGtmNSSO7NVB0LUd+UTlP/2cN\neUXlTBmXzLlDO/ns2HouUFoHFDTyFmSllGrMysqref7DtezNK+N3wzpx4Yiu/g6pWWjdKpQHpwwk\nOiKY9xduZdm6vSffSSml/EgTZKWUAiqqHLz0yVqy9xczekAiV471fX/Z5qxtbDgPXDWQiNBAZn61\nmdXpB/wdklJKHZcmyEqpFs/lcjHr63S27CpkWEobrhufoslxA+iYEMkfrhhIcFAAb8zbxI79etlb\nKdU4aYKslGrxFqft4aeN++mW2IqbJ/bGbtfkuKF0b9+K2y7sQ1W1k9fmbKCsXO+5Vko1PpogK6Va\ntKx9RcxeuIWI0EDuvKgvQYF6WmxoA5PjmTC8CwcKDjFz/mafTBurlFJ1od8ESqkWq+RQFa99tgGH\nw8Wtk/oQFx3q75BajItHdyOlcwypW3JYsGqnv8NRSqkjaIKslGqRnC4Xb83bRG5hOReO6Eq/7nH+\nDqlFCbDbuW1SH6Ijgvl40Ta27Dzo75CUUuowTZCVUi3SVz9ls3ZbHr27xjJphI517A/RkSHcPrkP\nANM/30BRaaWfI1JKKUugvwNQSilfS88u4NMl24mNCuHWSX30pjw/ks6xXDqmOx//sI1/fbGRB64c\nqJ+HUs3cyy8/x8aNG7DZbNx77wOkpPQ+vG7evM/55pv52Gw2XC4XxqTzj388xyOP/Jnu3ZNwuVwk\nJSVz330PNmiMmiArpVqUgyUVTP9iI3abjTsm96VVeLC/Q2rxzju9M1t3FZKWkcucZZlcMrq7v0NS\nSjWQtLQ17Nq1k+nTZ5CdncXTTz/J9OkzDq+fOHEyEydOPrztokULARg0aAhPPfV3n8WpCbJSqsVw\nOJ1M/3wjRaWVXHVOMj06Rvs7JAXYbDZuntiLx2euYt6KLHp0iKZ/kvYJV6qpObr112azMW3azQwe\nPPTwNqmpqxg16iwAunTpSklJMWVlZYSHh/+mvJkz3+Txx/9CVlamz0e70QRZKdVifLp4O1t2HmSI\nJHDu0I7+Dkd5CA8N4q6L+/HXd1N5Y+5GHrthGPHRYf4OS6lGIefjDyhevcqrZUYNHUbC5VedcJsN\nG9axdOlikpKSCQkJprCwkEmTLj7u9p6tv8eTl5eLSK/Dr6OjY8jPz/tNgpyevom2bdsSG9uarKxM\nsrIyeeihBygqKmLatJsZNuz0WrzL+tOb9JRSLcIvW3L4auUO2saGceOEXjpTXiPUpV0U15ybTGl5\nNa/P2UBVtdPfISnVorlcLhwOB126dGXMmLEsXPgNTqeTV1990avHOJa5c+cwYcKFAHTq1Jkbb7yV\np59+locffoy///0pqqsbdpIhbUFWSjV7Bw4e4s0vNxMcaOfOi/sRFqKnvsZq9ID2bN1VyIoN+/jw\n+61c+zvxd0hK+V3C5VedtLW3IfTrN4C3334LkRSKioqorq7GbrcTFnbsqzu16WIRH59Afn7e4de5\nuTnExcX/pqxffknlD3/4n8P7jB07DoAOHTrSunUcubk5tGuX6M23ewT9llBKNWtV1Q5e+2w9hyqq\nuemCXnRqE+nvkNQJ2Gw2po4Xduwv5vs1u+nRMZrhvdv5OyylWqSqqipqLrYtX76E8eMnUFpaQlVV\nFenpm9i/fx9jxow9vH1tulicdtpwZsz4N5MmXYwx6SQktPlNwp2bm0t4eASBgVaaumDB1+Tl5TJl\nyrXk5eVy8GAB8fEJ3n2zR9EuFkqpZu29b7eyY38JowckMqJfw7U2KO8JCQrgzov7ERocwKyvDLtz\nS/0dklItUnr6JoKCgli2bAm5ublMnnwJv/ySSlRUFBUVlYwcOabOZfbt2x+RXtxxx4289NKz3H//\nn8jPz+OZZ54+vE1eXi6xsbGHX48cOZq0tFTuuusWHn74jzz44EOHk+eGYvP1XYE+4srJKfZ3DMqP\nEhKi0Dqg1mUV8MIHv9C5TSQPTx1CcFCAv0NSdbAq/QCvz9lAYlw4j1w/lNDgun8h6rlAaR2ov9mz\n3yUlpdcRXSRmz36XKVOuZdastxg79lw6d+7ixwhrLyEhqk43nmgLslKqWdp1oITX/ruOsJBA7ry4\nrybHTdCwlDaMG9qRvXllzPra+HyYJ6Vast27d7Fw4dccOLD/iOVXXz31cN/ippIc14f2QVZKNTuH\nKqp5dc4GKqsc/P6SfrSJ/e34mo1dhaOSbQcz2VKwDVOwlT2l+6GOCWJoYCg9YrojsT2Q2CTahCc0\nudE7rji7B5l7i1i5aT/JHaMZO1iH51PKFzp06MiMGe/5Owy/0QRZKdXsvP/dVvbnl3HxWT0Y1LNh\nb+TwlmpnNZmFO9hSkIEp2EZW0Q4cLgcAgbYAEiPbEWirWyv4wYoi0nLWk5azHoCYkGh6xia5E+Ye\nxIbGeP19eFtggJ07Jvfl8Zmr+OC7DFI6x9I+PsLfYSmlmjlNkJVSzUra1lyWrdtL57aRTD2/FwcL\nGucNXk6Xk53Fu90txBlsO5hJpbMKABs2Okd1tJLZ1j1Iiu5KcEDdp8R2uVzkHsrHFGw9fJyf963h\n531rAEgIi0Nie9Aztgc9Y5OICm6cI3y0bhXK9eel8Opn63lz3iYenjqEwADtIaiUajiaICulmo3i\nskre/jqdwAAbN0/sTVBg40qiXC4XG/PSWbHnZ7Yc3M6h6kOH1yVGtKWnu2U3OaY74UGnPouczWYj\nITyOhPA4RnYYjsvlYk/pPkxBBlsKMthakMmyPStZtmclAB0iE+kTl8LZnUbSKjjqlI/vTUMkgTP6\ntOPHjfuY/2M2k0Z283dISqlmTBNkpVSz4HK5eHfBFopKK7n8rCQ6JjSe1tCaxHh+5kKyi3cCEBfa\nmkEJfa2EOLYH0SENn5DabDY6RCbSITKRsZ1G4XA62FG8+3DCvL0wi90le1m0cxmjO5zBuC5jGlWi\nfM25yaTvKGDuiiz694ija7tW/g5JKdVM6TBvqlnSYX1anp827ePfX2yiR8do/nz1YOx2m9/rwbES\n40EJ/Tiv6zl0jGrvt7iOp9JRxU97V/NN9vccrCgkyB7E6I5ncG7nsxpN94uNmfk8+2Ea7eMjeGza\nUIICT9wv2991QPmf1gEFdR/mTVuQlVJNXkFxBe8t2EJwkJ2bLuiF3e7fkRpcLheb8g1fZn5LdtGv\nifH53cbRIbLxTlYSHGAlxGe0H8aPe37mm+xFfLdjCUt3/cioRpIo9+nWmrMHd2DRmt18tiSTK8b2\n8Gs8SqnmSRNkpVST5nK5mPnVZkrLq5k6XmjrxyHdmmpifLQgeyCjO57JGe1P+02iPLrjmYzrPMav\nifIVZ/VgY2Y+3/y8g4HJ8fTs1PhH41BKNS3axUI1S3pJreX4IW0373xt6NutNX+4YsAR4/z6qh5Y\nifEW5md+S1bRDgAGJvRjQhNLjI+nylHFir2rWJC9iIMVhQTbg/yeKGfsKuTp91KJjw7liRtPO+4s\ne3ouUFoHFGgXC6VUC3Lg4CE+/C6D8JBAbpjQy+eTYDT3xLhGUEAQYzqeyZmJw1ixdxXfZH3Pwh2L\nWbJrBWM6juCczqN9nij36BjNead35qufdvDR9xlcd16KT4+vlGreNEFWSjVJTqeLGfM2UVHl4JYL\nexMbFeLT45dUlTI7/b+szdkAwMCEvpzfdVyjvPnOWzwT5eV7f2ZB1iK+3fEDy/as5OqUSxncpr9P\n47loZHfWb8vjh7Q9DOqZQL/ucT49vlKq+fJ5FwsReQ4YDjiB+4wxqz3WjQP+ClQDXxlj/uKxLhTY\nADxpjHnnJIfRLhYtnF5Sa/6+XrmDjxZlMEQSuPOivsdsPW6oerA5fwvvbvqQwspikmO6c1nypGad\nGB9PlaOKpXt+Yu62r6l0VnF6uyFc3nMyYYGhPothx/5inpq1mqjwIJ66+XQiQoOOWK/nAqV1QEHd\nu1j4dBR9ERkN9DDGnAncDLx01CYvAhcDI4HfiYjnNbNHgDyfBKqUatR255Tw6ZLttAoPYup48VnX\niipHFZ9s/YJX0t6kpKqMyUnnc8+gW1tkcgxWi/LYTqP482n30TmqIyv3pfL0zy+wvTDbZzF0bhvF\npJHdOFhSyXsLtvjsuEqp5s3X00ydA8wBMMakAzEiEgkgIt2APGPMHmOMC5jv3h53opwCfOnjeJVS\njUy1w8mb8zZT7XBy/fkptAqv+xTM9bGnZB//XP0yi3Yuo214Ag8OvYvfdTkbu61xzdbnD23DE3hw\nyF2M7zKW/PICnl/zOl9uX4DD6fDJ8ScM70z39q34adN+Vqcf8MkxlVLNm6/P7O2AHI/Xue5lx1p3\nAKi5y+UZ4H7Av4ObKqX8bt6KLLL3FzOiXzsGJSc0+PFcLheLdi7jH6tfYk/pPkZ2GM6fh91L56iO\nDX7spiTAHsCkpPO4d9BtRAe3Yn7WQp5fM53cQw1/4S/Abo1/HRxo551vDIUlFQ1+TKVU8+bvpo8T\nJbw2ABGZCqwwxmR7LldKtTyZe4uYtyKbuFYhTDmnZ4Mfr7CimNfWzuCTrV8QGhDC7f2nMUUuITjA\nN63WTVFybHcePu0PDG07kMyibP728/P8uHc1DX2/S2JcBJeelUTJoSpmfW0a/HhKqebN16NY7OHX\nFmOA9sBej3We4yJ1cC+bAHQXkQuBjkC5iOw0xnx/ogMlJER5LWjVNGkdaF4qqhy8PfNnnC4Xf7h6\nCF06xdZqv/rWg9W71/L66v9QXFHCwHa9ufO064gJi65XWS1PFP/T/jaWZv3Mm2ve5z+bPyKjJINb\nh1xNZEhEgx31qvG92JhVQFpGLuuyChh3WhdAzwVK64Cqu3qNYiEi/zDG/ElEugBtjTE/13K/M4DH\njTHjRWQw8IIxZrTH+vXABViJ8QrgamNMhsf6x4BMHcVCnYzetdz8fPDdVhas2sk5Qzpyzbm1az2u\nTz2ocFTy6da5LNuzkkB7IBcnXcCYjmf6fIzl5iLvUD6zNn3AtsIsYkKiub73lfSMbbjpoXMLD/Ho\nW9ZX0pM3nUavHm30XNDC6feBggYcxUJE4kSklfvlXPeNc/cAo0+w2xGMMT8CqSKyHHgBuEtErheR\nye5N7gA+ABYD73smx0qplsvsKODbVTtp2zqcy85KarDj7CjaxT9WvciyPSvpEJnIn4bew1mdRmhy\nfAriwlpz3+DbubD7eIoqi3nplzf4LONLqpzVDXK8+OgwpoxLprzSwYwvN+N0alcLpVTd1boFWUSu\nBgQIBlzAYOAhYL0xpmHOdPWnLcgtnLYYNB+HKqp5bMbP5BWV8/C1Q0jqUPtuDnWpB8t3r+SDLZ/h\ndDkZ22kUk7qfR1BA0Ml3VLWWVbSDtze+T86hPLpEdeK2/tOIDvH+pW+Xy8XL/11PWkYut1zUlzNS\n2nj9GKrp0O8DBQ3YgmyMmQ381RjzkDHmYeB2IBl4oG4hKqVU7f138TZyC8uZMLxLnZLj2nK6nHy+\n7Stmm/8SHhjG3QNv5tLkCzU5bgBdW3Xmz8Pu4/R2Q8gu3skzqa+wp2Sf149js9m4/jwhMiyId+Zv\n5sDBQ14/hlKqeavrKBbvisgI9/P2QJYx5h9ejkkppQDYsvMg36/ZTfv4CCaN6Ob18qscVby98X0W\nZC+iTVg8Dwy5i16tG350jJYsNDCEqb2u4MLu48kvL+C5Na+xpcD7vemiI0O4elwyFZUOZn2VrqNa\nKKXqpK4J8lbgARG50BizAmtaaKWU8rrKKgcz52/GBtxwfgpBgd4dlbKkqpSX094g9cBaukd35YGh\nd9EmPN6rx1DHZrPZOK/rOVzf+yqqHFW8kvYWK/emev04p/duy7DebdmcXcCStXu8Xr5Sqvmq6zfO\n6cCVwHUicinuWfGUUsrbPl+Wyf6CQ5w7rJPXu1bkHsrj2dRX2VaYxeA2/bln4C1EBjXc8GPq2E5r\nN5i7B95McEAw72z+kPmZ33q1pddms3HXZQMICwngo0UZ5BeVe61spVTzVtcE+XljTBVwFXAuUKvh\n3ZRSqi4y9xbx9c87SIgJ5eLR3b1bdmE2/7f6FQ6U5XJu57O4oc/V2t/Yj5Jjk3hwyJ3EhcbyZea3\n/Gfzx1R7cYSLuOgwrji7B4cqHLz7jU4gopSqnTolyMaY+e5HhzHmdqDVSXZRSqk6qXY4mTl/My4X\nTDu/FyFBAV4rOy1nAy/+8i9Kq8q4Si7hoh4TsNv8PaGoahfRlgeH3k2XqE78tG81r6+dyaFq791Y\nN3pAe3p1iWXttjxWbtrvtXKVUs3XKX0zGGO+81YgSikFMP/HbHbllB5OarzB5XLx/Y4lvLn+XWw2\nO7f3n8aoDsO9UrbyjlbBUdw7+Db6x/chvWArz6a+Rn55gVfKttlsXH9+CsFBdmYv3EpRaaVXylVK\nNV/adKKUajR25ZQwd0UWsVEhXHG2d2Zbc7qcfLz1C/6bMY9WwZHcP/gO+sb38krZyrtCAoK5pd9U\nzuo4gr2l+3lm9SvsKN7llbLbxIRxyegkSg5VMXvhFq+UqZRqvk6aIItIe/djx4YPRynVUjmdLmbO\nT8fhdDF1vBAeGnjKZZZXV/Dv9e+weNdy2ke0449Df0+nqA5eiFY1FLvNzuU9J3Np8oUUVZbw/Jrp\nbMjd7JWyxw3pSFKHVvy8+QC/bMnxSplKqeapNi3IX4hICNYYyDYRsXv+NXSASqmWYcGqnWTuLWJ4\n77YM7HHqw60VVRbzxKLnWZ+7iZTYZO4fcgexoTFeiFT5wthOo7i531RcLifT173N0t0/nnKZdruN\nG87vRWCAjXcWGMrKq7wQqVKqOapNgrsdKAXGAA6g2uNPzy5KqVO2v6CMz5ZuJyo8iCnjkk+5vANl\nOTyz+hW25WczPHEodw64kbDAMC9EqnxpYEJf7h10OxFB4XxgPuPzbV+d8igU7eMjuHBENwpLKvng\ne+9PUKKUah5Oeg3TGHMFgIi8YYy5peFDUkq1JE6Xi7fnp1NV7eSmC3oRFR58SuXtK93PS7/8m8LK\nYq7oeyGjE0Zis9m8FK3ytW7Rnfnj0Lt5de1bLMheRKWjksuSJ53SZ3r+6Z1ZnX6AZev2cnrvtvTp\n2tqLESulmoO6dJG4Q0SmishLIvKiiFzVYFEppVqMJWl7MDsPMig5nmEpbU6prD0l+3hhzb8orCzm\n8uTJXNZngibHzUB8WBx/GHwHiRFt+WHXcj7Y8hlOl7Pe5QUG2LlxQi/sNhuzvkqnvNJ74y4rpZqH\nuiTILwKTAIM15fSVIvJig0SllGoR8ovK+WhRBmEhgVz7OzmlZHZn8R5e+GU6xVUlXCWXcFanEV6M\nVPlbq+Ao7h10Gx0iE1m2+ydmp//3lJLkLu2iOO/0zuQWlvPp4u1ejFQp1RzU5TbxvsaYMR6vXxGR\npd4OSCnVMrhcLt75xlBe6eCG81OIjQqpd1nZRTt5Je1NDlWXc03K5ZzZfpgXI1WNRVRwJPcOuo1X\n0t7gx72rcLgcXJtyOQH2+k0mM3lkV9ZsyeG71F0M69WG5I56E6dSylKXFuRgz1ErRCSAuiXYSil1\n2E8b97NuWx69u8Yysn9ivcvZXpjNS7+8waHqcq7rfaUmx81cRFA4vx94K11bdebnfWuYtekDHE5H\nvcoKCgzghgkpAMycn05Vdf3KUUo1P3VJkL8EVonIcyLyHLAamNMwYSmlmrPC0kpmL9xCcJCd689L\nqXfXioyDmbyS9gaVzkpu6DOF09oN9nKkqjEKDwrj7oE3kxTdldQDa5mx8T2qnfXrR5zcMYaxQzqy\nL7+ML5ZneTdQpVSTVesE2RjzF+AuIBvIAm4zxvyjgeJSSjVj7327hdLyai4dk0RCTP2GXzP5Gbya\n9iZVzmpu6nMNQ9oO9HKUqjELCwzlzgE3kRzTnbScDby54V2q6pkkXzqmO/HRoXz10w6y9xV7OVKl\nVFNUp4k+jDE/GWNeNMa8ZIz5uaGCUko1X6kmh9XpB+jRIZpzhtRvgs7NeVt4fd0MnC4nt/a7joFt\n+nk5StUUhAaGcOeAG0mJTWZ97mb+vW4WlY66D88fGhzI9eel4HS5mDl/M9WO+t/8p5RqHnQmPKWU\nz5SWV/GfBYbAADs3TEjBXo+uFRtyNzN93UxcwK39p9Evvrf3A1VNRnBAMLf3n0afuBQ25Rumr5tJ\nhaOyzuX06daakf0T2XGghK9W7miASJVSTYkmyEopn/lg4VYKSyuZPLIriXERdd5/bc4G/r3+HWw2\nO3f0v4E+cdIAUaqmJiggiFv6XUf/+D6YggxeW/sW5dXldS7nqrE9iI4MZu7yTHbnlDRApEqppqLW\nCbKInNeQgSilmrd12/JYvmHf4fFn62rNgXW8ueE/BNgDuGvAjaS0PvUpqVXzEWQP5Oa+1zIooR8Z\nBzN5de1bHKo+VKcywkODuG68UO1wMWN+Ok7nqU1rrZRquurSgnyPiGSIyBMi0qXBIlJKNTtl5dXM\n+jqdALuNGyf0IsBet4tXP+9bw4wN7xFsD+LuATeTHJvUQJGqpizAHsANfa5maNuBbC/M5uW0Nymp\nLK1TGYOSExjeuy2Ze4tYsGpnA0WqlGrs6jKKxQRgGNYoFq+LyHwRudw9HrJSSh3Xxz9kUFBcwQVn\ndKFTm8g67fvzvjW8s+lDQgND+P2gW0iK6dowQapmIcAewPW9r+L0dkPILtrJUz+8SFlV3VqSp4xL\nplV4EJ8t3c6+/LIGilQp1ZjVdRSLAuADYDYQAzwIrBWR4Q0Qm1KqGdiUlc/itD10TIhg4pld67Rv\n6v40d3Icyj3uySFaIpfLhbOios5/rur6DXvW1Nltdq7tdTlnJA4js2Anr6y1ZlmsrajwYK79nVBV\n7WTm/M04XdrVQqmWptYz4YnIaOAG4GzgU+AmY8xmEekKfAYMapAIlVJNVnllNW9/lY7dZuPGC3oR\nGFD73+S/HFjP25s+ICQghN8PvJnOreo3JFxT4ayooCo3h6qcHKpyc63nudbz6twcnOV1v+kMm43A\n2FiC4hMIio93PyYQlJBAYHwCgdHR2OrY3aWpsNvsXJ1yKUHBdpZkr+S1tW9x14CbCQ2s3ZTmQ1Pa\nMEQSSDU5LFqzu95DEiqlmqa6TBX9N+BfwO3GmAoAEQkzxmSJyEcNEp1Sqkn77+Lt5BaWc8EZXeja\nrlWt91uXs5EZG98jyB7IXQNvokurTg0Ype+4nE4q9+ymfPt2jwQ4h6qcXBzFRcfcxxYSSlB8PIEx\nMWCrWzLrqiinKi+XQ1u3cGiL+W3ZgYEExsUfkTwHJyYSltyTgIi6jzLS2Nhtdu487TrKyitYvT+N\n19fN4M4BNxESEFyr/a/9nZCeXcAnP2yjf1JcvSe1UUo1PXVJkEuMMe8etWwJMMwY87QXY1JKNQNb\ndh7ku9RdJMaFM2lE11rvtyF3M29u+A+BtgDuHHAT3aOb7j3BNQlxmUnnkEmnbIvBWXLU8GEBAQS1\njiOkU6cjW3oTrITVHhlZ76m4azirqqjOz/u1ZfroVur9+47cwWYjpFNnwiSFcElp0gmz3W7nul5X\nUu10kJaznunr3uaO/jcQHBB00n2jI4K5+tyevDF3E29/lc6DVw085c9CKdU0nDRBFpFrgEeBLiKy\nA7ABLiAY2HeifY9T3nPAcMAJ3GeMWe2xbhzwV6Aa+MoY8xcRCQPeBtrC/2fvvuOjus6Ej/+maka9\nIiEJ0YQuSIDo3RQDxqa627FjJ3ZsJ9nsrpPdd7PJ+yabTeLNZrO7MXa8ibudrOPYsRPjAtg0gzG9\ni3oRAiRQ73X63PePGQkJhJCERm2e7+dDZm6ZuWfiR+c+99xzzyEEeEZV1fVdPa4Qovc4XB5e33Aa\nHfDY8nGYjJ17lvd05VleOfG/6HV6vp39GOnRIwNb0B6meb04i4toOnO63YTYGBtL+Oy5WMaMwZyY\nhCk+AWNMTMC7OehNJsyJSZgTk9rd7rHZcFdU4Koow15QgE09g/18Ho6CfGo2f9aSMIcqY7EqY7Fm\nZGAIHTgJs0Fv4PGsh3j1xFvkVJzk5eO/55sTvoapE0nyrMxE9p8q5VheJV8cK2LBpJReKLEQoq/p\ntE48fOAfqeI1fIly8+WzFyhUVbXTc3L6+zH/H1VVVyuKMhZ4XVXVOa22nwSWAsXAduCbwEQgTVXV\n/1IUJQ3YrKrqjWYH0MrL6ztbLDEIJSREIDHQd/687Ryf7i/gtunDeHBx58YrVqvO8buc19GAb038\nOuNiM266HIGOA03T2rQQ21QVT8OV4xljYwlVxrW0xBrj4wdMC6TX6cR+Pq/lt9nP51156K91wjx2\nHNYMBYO1f3Y/aB0DLq+bV4//gROVZxgfN5YnJjyKSX/jG6nV9Q5+9Oo+NE3jmSdmEhtpCXSxRQ+S\n84EASEiI6FLl25kW5OdUVX1aUZTRwFvt7DK/C8dbDKwDUFX1jKIo0YqihKuq2qAoykigUlXVIv9x\nNwKLVVX9n1afTwNkYEoh+rG8olo+O1DAkBgrd80f1anP5Faf900frWk8NfFrPZIcB5KztIT6fXup\n27cHV2lpy3pjTCwRs+e0tLSa4hMGTEJ8Nb3ZTOjYcYSOHQe0nzA7CvKp3vwZOqORsAnZRMyaRdjE\nbPSmzvXx7W2+yUQe4aXjv+dE5RleP/FHnhj/VQz6ju9wxESE8OCt6byx8Qy//1Tlu/dNHLD/XYUQ\nndOZPsiv+19/1APHSwIOtlqu8K87538tb7WtDGg5uyqKsgtIAVb2QDmEEAHgcnt5ff1pNA0eu2Ms\nIaYbd604X3uR3+a8jlvz8NSER8mKG9sLJe06d20N9Qf2U7d3D46LFwDQmc2ET5tB2PjxAz4hvpHr\nJsxnTtNw+BANR3z/9FYr4VOmETlrNlZlbL8bJcNkMPHUhK/xu5w3yKk4yRsn3+axrIfe20qQAAAg\nAElEQVRumCTPmziU/adLOX6+kt0nSpg7YWgvlVgI0RdumCCrqnrM/7ojAMfv6EzSZpuqqnMVRckG\n/ghkB6AsQoib9PHuCxRXNnHrlBSUtJgb7n+xroD/Ofo6bq+bb2Q9zIT4zF4oZed5bDYaDh+ift8e\nmk6fAk0DvZ7QrPFEzppN+OQp6C39s2tBoLVOmOPW3IXz8mXq9u3xtazv2kndrp0YoqOJnD6TiJmz\nCRk+vN9cPJgNJr418ev89thrHCk/juH0u3wt80H0HYwSotPp+NodY/nxa/v505ZcskbGEh3euSHj\nhBADzw37ICuKshPfQ3ntUlW1010sFEX5CVCkquor/uU8YKKqqo3+6av/1NwnWVGUf8HXwrwXKFNV\n9bJ//UlggaqqFR0cSkZ1F6KXnbtcwz8+9wXxURZe+KdbsYZ0fP19vqqAn29fS5PbztOzHmdO2rRe\nKmnHvC4X1YePUL5jJ9UHDuJ1OgEIzxhDwoL5xM+bgzk6uo9L2X9pXi91p05T/sVOKnftwe1/SNGa\nkuz7/2/+LViHtv+wYG+zuez8YsdvUCvPM3/4TP5mxqPob9DivWH3BX73lxxmZiXx/x6b0W+SfiHE\nDXXpj7UzCfKCDjZrqqp+0dmDKYoyG/hXVVWXKYoyBVjbOsFWFOU4sAIoAnYDD+HrUjFcVdXvKYqS\nCOxTVXXEDQ4lD+kFOXkoo3e5PV5+9uZBLpc38I8PTiJrRGyH+1+uL+L5Iy/T5LbxaOYDzEiaEpBy\ndSUO7AX51O74nPoDB/A2NQJgSkoicuZsImbMwpyYGJAyDmZel4umE8ep27eHxmNH0VwuACyjRhM5\nZy6Rs+agtwT2gbcbxYDNbeeFo69ysa6AOUOn85Wx93TYkuzVNP7z7SOol2r41posZoyTuOjv5Hwg\noOsP6XUmQW5+SO/qlmQdvgS5Kw/poSjKL4AFgAf4DjAFqFFV9UNFUeYBv/If531VVZ9VFMWCbwSN\nYYAFX4K94QaHkQQ5yEmF2Ls++vIC6768wPzsoXz9jnEd7lvUUMJzR16i0dXEw+PuY/bQwLUc3ygO\nNK+XhiOHqdm6uWUiDUNUNJEz+l+3gIGuve4q+tBQom6ZT/StSzDFxQfkuJ2pC5pcNn5z9GUK6guZ\nlzKLBzPu6vC/e2l1Ez95bT9mk4FnnpxJZGj/fChR+Mj5QEBgEuRsVVWPXa8lOUB9k2+WJMhBTirE\n3nO5rIGfvnmAyDAzP//GTEIt1+9aUdJYxtrDL1LvauAh5R7mpswMaNmuFweepkZqd35BzbYtuCsr\nAQjNGk/04qWEjZ/Q7x4sG2zcNdXU7NhO7fbPfTMI6nSET55C9JLbsI7J6NGLks7WBY2uJp478hKF\nDcUsSJ3DfWPWdFiOTQcu8c7WXGaMG8K31ozvsfKKnifnAwEBGOat+SE9fKNPfA3IwtfCexy4emY9\nIUQQ8Xi9vL7hNB6vxqPLlA6T49LGMp478hL1rgYeyLgz4Mlxe5wlxVRv3Uzd7l1oDgc6s5moBYuI\nXryUkOTkXi9PsDJGxxC/5i5il6+k4cB+qrds8o2EcfgQIWnDiV68lIgZM9GbbjyRR08JM4Xy95Oe\n4rkjL7Hj8m70Oj33pK+6bpK8ZGoqB86Usv90GdPHljNVSei1sgohAq9TE4VAy7jE5fj6BuuAuUCU\nqqqrAle8bpMW5CAnLQa9Y8PefN7fnsfsrCSeXHX9ESjKmspZe/hFap313DdmDQuHze2V8iUkRFBW\nVkfTyRNUb9lE04njABhj44i+dTFRtywYsFMoDyaapmHLPUvN1s00HD4EmoYhIpKohYuIXrgIY1T3\nH4rsal1Q72xg7ZGXKGksZfGw+dyVvuK6SXJxZSM/ef0AoRYjzzwxk3Br7yX0ovPkfCAgAF0smimK\nsktV1blXrfuiq32Qe4kkyEFOKsTAK6xo5Kdv3Dg5KG+qZO2RF6lx1HJP+kpuTeudKsPrcOA9fpDL\n6z7BWVIMgHVMBtGLlxI+eQo6Q+emvxa9y1VZQc22LdTu/AJvUxMYDETMmEnM4tuwjBjR5e/rTl1Q\n56xn7eGXKG0qY2naQtaMvuO6SXLzReKsrESeWpXV5fKJwJPzgYAAdLFoJVdRlKGqqhYDKIqSBOR2\n5WBCiMHB7fHyykcncXu8fG2Zct3kuMJWxXNHXqLGUctd6St6JTn2NDRQvXUzNVs3X0mwZs/pdoIl\nepcpLp6E+x4kbvVd1O3eRc3WzdTv2U39nt1YMxRiV64mdFxmQB+ejDRH8PTkp1h75EU2F2xHr9Oz\natSydo+5bMYwDqnl7D1ZyqT0eBnVQohBoivjIFuA8cAZwAuMAw5JC7Loj6TFILDe357Hhr353DJx\nKI8tb3/UikpbFWuPvESVvZo1o+/gtuGLAlomd10d1Zs/o2bbVjSHHUN4BMkr78A0fc5N3aIXfUvz\nemk6dYLqzZtoOnkC8A0TF7tyFWETsm+YKN9MXVDjqGXt4Rcpt1Vyx4glrBx1W7v7lVY18ZM39mMy\n6PnZN2YSEyETiPQncj4QEJgW5I6mmJazjhBB5uylGjbuzSch2sKDi8e0u0+VvZrnjrxMlb2aVaOW\nBTQ5dtfUUPXZRmp3fI7mdGKIiiJ2zZ1ELVhEYmq8nBgHOJ1eT9j4iYSNn4j94kUq139E45HDFD2/\nlpC04cSuXE34pMkBGXkkOiSKpyd/k7WHX2TjxS3odTqWj1x6zX6JsaE8eOsY/vCZyuvrT/G9Byah\nl+EBhRjQOt0HGUBRlEygebDKEOB5VVU7HvS0b0gLcpCTFoPAsDnc/OT1/VTW2fnhw1NJT426Zp9q\new1rD79Ihb2KFSOXtptQ9ARXVSVVGzdQt3MHmtuNMSaWmDuWEzVvPnqzb1xaiYPByXHpEpXrP6bh\n0AHQNMwpqcStWEX4tOnXJMo9EQNV9mrWHn6JSnsVq0Yt4/YRi6/ZR9M0nns/h5y8Sr6yZAxLpw27\nqWOKniP1gIDAPqS3FlgGJAHngNHAf6mq+ouuFrIXSIIc5KRCDIzX1p9i1/ESVs4Zzt3zR1+zvbO3\npG+Gs7yMqg2fULd7F3g8mOITiFm+gsjZc68ZFkziYHBzFhdRueET6vftBa8XU1IScctXETFzVstD\nmD0VA5W2atYeebHDLkO1DQ5+/Np+HC4P//L16aTEywgp/YHUAwK6niB35Z7UTH9r8VFVVacDS4HQ\nrhxMCDFwHVLL2HW8hOFJEayeO/Ka7bWOOp478hLltkqWDb+VFT3ccuwsKabktVe4+P9+QN3OLzDF\nJ5D42BOMeObfiZ6/sFfHzBX9g3loMkO/8RQjnvklkfPm4yovp+T1V7j4ox9Q+4XvzkJPibPG8PTk\nbxITEs2HeRvZUnDtHFlR4SF8/Y6xuNxXHmIVQgxMXRnFwuF/DVEURaeq6iFFUf4rEIUSQvQvNQ0O\nfv+pismo58mVmRgNba+t65z1PHfkZcqaKliatvC6T/x3h6OoiKpPPqT+wH7f7fTkFGJXrCJi+gyZ\n8U4AYB4yhKSvP07cqtW+bjdffkHpH96g8pOP8Nx/N4ZJM9EZu3K6a1+8NdbXJ/nIi3xwbj16dNeM\nzDIlI4F5E4fyZU4xH355gXsWXHunRQjR/3Wli8VLwDEgDZgGqMAcVVUnB6543SZdLIKc3FLrOZqm\nsfa9HI6fr+ThpRksnpraZntXJlboCmdpKZUfr/PdPtc0Qoal+R7Imjyl04mxxEFwctdUU/XpRmq/\n2I7mdGKMiyNu5WoiZ8/tkUS5rKnCP/FNHfeOWc2iYfPabLc53PzrG/upqLXzzw9NIWOYPM/el6Qe\nEBDYPsg6IAaoAR4EEoH3VFW93NVC9gJJkIOcVIg95/PDl/nfTWcZPzKW793fdlitBmcjzx15iaLG\nEhYNm9fh1Lyd5aoop/KTj3x9jL1ezKnDiF9zF2GTJnf5uyUOgpu7thbb9s2UbPwUze3GlDCEuNVr\niJg5+6bvPpT6Z4esc9Zzf8adLEid02Z77uUafvnHw8RFWvjp4zOwhtx8Yi66R+oBAYGdKCQUX2Kc\nhW9c5ONAVVcOJoQYWIorG3l32znCLEYeWz6uTYJa72zgN0dfoaixhAWpc286OXZVVVK1/mNqv9wJ\nHg/mocnErbmT8CnTpCuF6BZjVBSjnngMy/zFVG34mNovdlDy2itUrv+YuNV3EjGt+910EkMTWrpb\n/PnsOnTA/FZJ8pjUaJbPGs76Pfn8aUsuj6/ojwM+CSGupysJ8vtAObAb0AG3ACuBVQEolxCij7k9\nXl795BROt5cnVma2mfygxlHLb468QklTGfNTZnPfmNXdTo7dNTVUbfjEdzvc7caUmOhLXqbPlMRY\n9AhTTAyJDz9K7O0rqFr/EbW7vqTk5RepWv8JcavvJHzK1G7Fb1LYEJ6e/E2eO/wS755dh9PrYkna\ngpbta+aN5MT5Kr48Xkx2ehxTlSE9+bOEEAHUlS4Wu1RVnXvVui9kJj3RH8kttZu3bud5Ptp1kdlZ\nSTy5KrNlfaWtiuePvEyFvYpbh93C3ekru5VcuOvrqN64gZrt29CcTkzxCcSuWk3krDktQ3TdLIkD\n0V4MOMvLqPr4Q+r27Pb1b08bTtyauwibeOOZ+dpT2ljG80dfocZRy/KRS1k+YknL9xRVNPLTNw8Q\nYjLws2/MIDpcZtnrbVIPCAjsMG+5iqIMbV5QFCUJyO3KwYQQA0NeYS2f7M4nLtLCw0szWtaXNpXz\nrH8SkDtGLOlWcuxpaKDir+9z4Qf/RPWmTzGEhzPkka8z4pl/J2ruLT2WHAtxPeaEISQ9/iQjfv4L\nImbMwnGpgKLfrOXSv/+cxpMn6MoEWgCJYUP43pRvE2eJZcOFzazL29DyHcnxYdy3cDQNNhdvbDjT\n5e8WQvSNG7YgK4qyE1+fYwswHjjjXx4LHJIWZNEfSYtB99mdbv71jQOUV9v4/kOTUdJiAChqKOH5\noy9T72zgztHLWTp8YZe+19PUSPXmTdRs2YTXZsMQFU3sipVE3bIgYGMYSxyIzsSAo/AylR+to+HQ\nQQCsYzKIW3MXoWO71m+4xlHL80deprSp3Nf1KGMNep0er6bx7J+PcfJCFY/clsGiKak3/jLRY6Qe\nEBCYh/R+1M2yCCEGoHe3naOs2sbtM9NakuOCusu8cPRVGt1N7T6x3xGPzUbNlk1Ub/rUlxhHRJBw\n/4NELby1ZUpoIfpSSEoqyd/+W+wF+VR+tI7Go0e4/F//gTVDIe7OuwnNUDr1PdEhUXx3yrd44eir\nfFG4B4fHycNj78WgN/D48nH8y2v7eHfbOcYOj2FonMyyJ0R/1pU+yAbgIWA6vhbkvaqq/imAZbsZ\n0oIc5KTFoHuOnqvg+fdzGDYknB89Og2TUU9ezUV+e+x1HB4HD4+7j9lDp3Xqu7x2G9Vbt1D92ad4\nmxrRh4cTe/tyohctRh/SO/0wJQ5Ed2LAfvEClR9+QOPxHABCx2USt/ourGPGdOrzja4m/ufoa+TX\nX2LykIl8PfNBjHojB86U8bt1Jxg5NIIffnXqNRPuiMCQekBAYId5ex4YAmzHN4rF/YqizFJV9emu\nHFAI0T/VNTp5c8NpjAYdT67KxGTUc6Yql5dy3sSteXgs6ytMTZx0w+/x2u3UfL6Vqs824m1oQB8a\nRvzd9xJ962L0Fmsv/BIhbo5lxEhSnv4HbOfzqPzwA5pOnqDp9ClCs8YTt/pOrKPTO/x8mCmUv5v8\nJL879gZHynJweVw8Mf6rTB87hKNZSew5WcInuy9y5y2jeukXCSG6qisJ8nhVVRe0Wn7B3z9ZCDHA\naZrGmxvPUNfk4oFb00lNCOd4xSlePfEWaBpPTXiUCfGZHX6H1+GgZvs2qj/dgKe+Hn1oKHF33k30\n4qUYrJIYi4HHOmo0qd/7P9hyc6n8yJ8onzxB6PiJxK+5E8vI6ye4VqOFv530DV4+/gdOVJ7mdzlv\n8M2JX+fhpRmcvVTNJ7vzGT8qjvSUqF78RUKIzurK/R2zoigt+/u7XMjUQEIMApsPXOLouQrGDY9h\n6fRhHC7L4eXjf0CPjm9nP95hcux1Oqne/BkXfvhPVLz3LprbTeyqNYz85X8St3K1JMdiwLOOGUPq\nP36f1O//EGuGQtOJHAr+7WcU/mYt9oL8637ObDDzzYlfZ2J8Fmr1OV44+io6o4snVmaiaRovfXiC\n+iZnL/4SIURndaUP8o+Au4Ad/lWLgHdUVf2PAJXtZkgf5CAnfc467+ylGn719hEiQk385LHpnKk/\nzlun3yPEYObb2Y+THj2y3c95nU5qd+6gasN6PLU16EIsxCxdSsySZRjCw3v5V7RP4kAEIgaazpym\n8sMPsOWeBSBs8hTiVq3Bkja83f09Xg+/P/UOh8qOkRaRwncmPcG2/WWs23mBrJGxfO++bPT6m5ui\nXVyf1AMCut4HudMJMoCiKLOAmVx5SG9/14rXayRBDnJSIXZOTYODn75xgPomF99/aDIlulO8e3Yd\nYcZQvjPpGwyPHHbNZzw2G7Xbt1G96TM89XXoQkKIvnUJsbfdjiEiog9+xfVJHIhAxYCmaTSdOknl\nhx9gP58HQNiEicQuX9Xuw3xezcvbZ/7CnuIDJIcl8Z3sJ3jz4wvk5FWyas4I7pov/ZEDReoBAQF8\nSE9RlMdUVX0D2NvlUgkh+h23x8uL605Q2+jkwVvTKdCO8UHueiJM4fzd5CdJCR/aZn9PQwPVWzZR\ns20L3qYm9FYrsctXEr3kNoyRkX30K4ToGzqdjrCs8YRmZtF08gRV6z+m8XgOjcdzsGYoxK5YRWhm\nVstEOnqdnofG3oPZYGbH5V08d+RFvnHbYxS93cjHuy8yKjmS7PT4Pv5VQohmXeli8THwVVVVawNb\npB4hLchBTloMbuydrblsOnCJqWPjGZJ5ge2XdxEdEsXfT36KxNCElv3cNdVUf/YpNV9sR3M4MIRH\nEL30NqIX3YohtH+P5SpxIHozBprOqlRtWE/TCd/wcCEjRhK7fCXhkyaj0/se4dE0jY/Of8qm/M+J\nMkeyJuV+Xnu/CLNRz788Np0h0dJnv6dJPSAggF0sFEXZAkwFVKDlqQKZSU/0R1Ihdqx5PNakeDPJ\nU89yuvoMyWFJfGviY8RZfZODOMvLqN64gbrdX6K53RhjYohZdodv5rteGsf4ZkkciL6IAXtBPlXr\nP6bh8CHQNMxDk4ldvoKI6TPRGX03brcWfMEH59Zj0huZGXYHm7Y6SRsSzv99ZCpmk0y33pOkHhAQ\n2AR5QXvrVVXd0d76PiYJcpCTCvH6iioa+fkfDoLRztBpJym1lzAuNoNvjH8Yq9GKo/AyVRvWU79/\nL2gapiGJxN6xnIhZcwI2JXSgSByIvowBZ3ERVRs3ULdvD3g8GOPjib19OZFz56E3mTlWfoI3Tv4J\nt9fNMPcM1MMxzJswlMeWj23pmiFuntQDAgKQICuKEolvuumxwE7gWVVV3d0uYe+QBDnISYXYPrvT\nzc9/f5ASWwmxE3No8jYwN3kmD2TcifNiPlUbP6HxyGEAzCmpxK5YScTU6egMA7NFS+JA9IcYcFVW\nUPXpRup27kBzuzFERRFz2+1EL1jIJWcFL+a8SZ2zHmt9OlWnR/G128exYFJKn5Z5MOkPMSD6XiAS\n5LeAIuAL4G6gUFXVH3e3gIqi/BqYBXiB76qqerDVtiXAvwFuYKOqqs/41/8KmAcYgF+qqvrBDQ4j\nCXKQkwrxWpqm8eKHJzlUfAJrRg6azsOdI5cxo9RKzedbseedA8AyahSxy1cRlj1pwLdiSRyI/hQD\n7toaqjdvonb7Nrx2O3qLhci5t6CbO52Xiz+hqLEE6obgysvmhw/NZORQefi1J/SnGBB9JxCjWIxQ\nVfWrAIqibAS2dqdg/s/PB9JVVZ2jKMpY4HVgTqtdngOWAsXADkVR3geSgEz/Z2KBI8CNEmQhxFU2\nH7zM4aoDhGScIdyp4+Ha0VjXf0RJbQ3odIRNzCZm6TKsY8cN+MRYiP7IGBVNwr33E3vHCmo+30rN\n9m3UbN0MWzfzyPjx7BqZwJcRpRgy9vLCx3p++sh8wq0Dq1uTEINFZxJkV/MbVVU9iqJ0fuDkay0G\n1vm/64yiKNGKooSrqtqgKMpIoFJV1SIARVE2+Pf/LbDP//kaIFRRFJ2qqjdTDiGCypmCKv567iNS\nI84xdZ+LjHwbeErQrFail9xG9KLFmBMT+7qYQgQFQ1gYcStXE3v7choOH6J662bsJ04w9QRkxYSx\nZ5SNU6nb+M0GHf981yKZRESIPtCZBPnqRPRmEtMk4GCr5Qr/unP+1/JW28qAUf5E2OZf9wSwQZJj\nITqvtKqazz55lgcLikmu8D0+YEpKImbxUiJnz0FvkWGlhOgLOqORiBkziZgxE/vFi9Rs24xu/z4W\nHXIz51gjp0a+zx/X1/PIqjV9XVQhgk5nEuQ5iqIUtFoe4l/WAZqqqmk3cfyOLovbbFMUZQ3wGHDb\nTRxPiKDhrq2lZNunlG3dzB12X2JsGT+euKW3Ezous2VcViFE37OMGEHS408Sf+8D1H6xnfItnzE5\ntxEt9wP2H91H1l1f8U08In+3QvSKziTISg8erwhfS3GzZHz9jZu3tZ66K8W/DkVRlgE/BJapqtqp\nnvYJCf1rylvR+4IxBjSPh9oTJynb9jnlX+4CtweTScfpMck88PT3iRh27dTRg10wxoFoa0DFQEIE\nQ0c/TMYjD7Dz/T9TtuljkvOLKFz731hSkklauoSEBfMxx8b0dUkHlAEVA6Jf6PQ4yD1BUZTZwL+q\nqrpMUZQpwNrWE40oinIcWIEvMd4NPISvq8VOYLGqqhWdPJSMYhHkgu2pZUdRIXV7dlO/dw/u6ioA\nqiOMHFUsXIicwr/c/QihluB72CfY4kBca6DHwMbDZ9h38n+ZVFDJ2HwHeq8GOh2hWeOJnD2X8EmT\nB8zEPX1loMeA6BkBmyikpyiK8gtgAeABvgNMAWpUVf1QUZR5wK/w9XN+X1XVZxVFeRL4CXAWf7cO\n4FFVVS93cBhJkINcMFSI7vo66vfvo27PbhwXLwCgt1ipGjuUzfFVFMaF4C2YxI9XryIlIbyPS9s3\ngiEORMcGQwy8suEYhxyfEmYpZ0qxkRmFJrT8SwDoLRbCp00ncvZcrGMypAtGOwZDDIib1+8T5F4i\nCXKQG6wVotflojHnKHV7dtN4PAc8HtDrCRs/Af20bN4xnOJcYwF6VyhNZ7N5avEcZmYG7+gUgzUO\nROcNhhhwujz821sHKDYfxjT0Ika9kfui56Gcb/LdNaqqBMAYF0fk7DlEzpqLOSnpBt8aPAZDDIib\nJwmyjyTIQW4wVYiapmE/n0fd7l3UH9iPt6kRgJC04UTOnkPEjFmcdF7irdPv0eS2YbUNo+pUBrdN\nGcWDi8f0cen71mCKA9E9gyUGymtsPPOHgzSZi4gcewq710Z2fBYPKfegv3DJVz8cOojmsANgGTWa\nyNlziZg+A0N4cN5BajZYYkDcHEmQfSRBDnIDvULU3G6azqo0HjtK47GjuCp8IyAaoqKInDWbyNlz\nCUkdhsvj4oO89ey4vBuT3khs/VQunoxmxrhEnlqdhT7IJ/wY6HEgbt5gioELxXX86u0jeAw2Rsw8\nR6GtgJiQaB7LeojR0SPwOhw0HDlE3Z7dNJ06CZqGzmjEqowlPHsSYdmTMMXF9/XP6HWDKQZE90mC\n7CMJcpAbiBWip76exuM5NBw7QtPJE3jtvpYgvcVCWPYkImfP9Q3PZjAAUNpYxusn3+ZyQxFDwxKJ\nq57NgaN2MkfE8PS92ZiM0hdxIMaB6FmDLQZOXqhi7XvHMJt0zFvSyK7yL9DpdKwYuZTbhi9Cr/P9\n3buqq6nft4f6fXtxXLoyUqs5JbUlWbaMHBUUfZYHWwyI7pEE2UcS5CA3ECpETdNwFhXReOwIDTnH\nsOedA//foykhgbDsSYRNnERohoLO2HZExn3Fh3jn7Ac4PU7mJs/EVDqejXsKGZ4Uwfe/MhlrSGdG\ncBz8BkIciMAajDGw91QJL390iqgwMw/fFc8H+X+hxlGLEpPO1zIfJCokss3+rqpKGo8do+HYUWxn\nTqG5feOiGyIiCJuQ7atrsrIG7aRBgzEGRNdJguwjCXKQ668VotflwtbcdSLnWEvXCXQ6rOljCJs4\nibDsbMxDk9G10z3C7rbz7tl17C85jMVg4aGx91B9KZa3t+QyJMbK//3qVCLDzL38q/qv/hoHovcM\n1hjYfOASf9qaS2KMlb9/YBwfFqzjeMUpwk1hPJr5IFlx7U9h4HU4aDp1koZjR2nMOYqnrg6gpStG\nWPYkwidmY4pP6M2fE1CDNQZE10iC7CMJcpDrLxWip7ERW14u9nPnsOWexX7xAprLBYDeaiU0a4Lv\nduf4CRgiOh7I/lJ9Ia+f+CNltgqGRw7j8ayHOX/RxUsfniQyzMwPH5nKkOjB2QLUXf0lDkTfGcwx\n8Jcdeazfk8+IpAj+z4OT2Fe+j3Xn1uPWPCxJW8CqUcsw6q9/N0nzenHkX/Qny8dwFOS3bDPGxWFN\nH4M1PQNr+hjMKSkDtjvGYI4B0XmSIPtIghzk+qJC1DQNV0U59nO52HJzsZ3LxVlUeGUHnY6Q1GEt\nD8xYx2Rc03Xiet+7/fKua058akEda/98DLNJzz8/NIW0RJkp6mpyYhSDOQY0TeONjWf4MqeYrBEx\nPH1fNkVNRbxx4u1WF9IPEW+N69T3uaqqaMw5SuOJ49jO5eJtaGjZprdasYxO9yfNY7CMHDVgJigZ\nzDEgOk8SZB9JkINcb1SImtuN4/IlbLlnsZ3zJcSe2tqW7TqzGcuo0VjH+FpgLKNGY7B2rYW30lbF\nn8+u40TlmTa3TvNL6vnl24fxeLz8w/2TGDtcpp1tj5wYxWCPAY/Xywt/Oc6xvEpmZiby5KpMnB4H\n76jrOFDq64p1d/oKZidPb3mArzM0TcNVUuyv285hO3cWV2nplR0MBkKGpfnrN9C3AQcAACAASURB\nVF/ibIyKDsAvvHmDPQZE50iC7CMJcpDryQpR83pxlZXhKLyMs6gQZ1EhjsJCnKUlvok6/AxR0VjH\njGlpYQlJHdapFuL2uDwuthTs4LP8bbi87jYP35RWN/Hv/3uI+iYX375zPNPGDumR3zkYyYlRBEMM\nOFwe/vvdo5y7XMuSaal8ZfEYdDod+4oP8e7ZD3B4nAyPHMYDGXcyPHJYt4/jrqvDdi7Xd5fsXC72\n/Itt68CICMzJKYSkpPhfUzEnp2AIC+uBX9l9wRAD4sYkQfaRBDnIdadC1LxeXJUVOAtbJcFFl3EW\nF7c89d1MF2IhJCXZ14Li76NnjI9v98G6rjpRcZr3cj+iwlZJpDmCu9JXMD1xMjqdjtoGB7946xDl\nNXYeWaawaHLKTR9vMJMTowiWGGiwufiPPx6msKKRexaMYsXsEQDUOGr54Nx6DpYeRYeOuckzWDX6\ndsJNN5+0ep1O7Bcv+BLm83k4Cy/jqqhoGY2nmSEq+krSnJyC2f++q3fUuitYYkB0TBJkH0mQg1x7\nFaLmduOurcFVWYm7qhJ3VRWuqircVZW4KitxlZehOZ1tPqMzmzEPTW5TqYekpGKMje2RZLi1ClsV\n7+d+xPGKU+h1ehamzmX5yKVYjRYAmuxu/uPtw1wqa2D13BHcecuoHj3+YCQnRhFMMVBVZ+cXbx2i\nqs7BY8vHcsvE5JZtZ6vP8e7ZDylpLCXMGMrq0bczJ3lGl7pddIbX4cBZXORvYChseW2eDrs1Y0ws\npvh4jLGxvvdxcRhj4zDFxmGMjUUfGtoj9WwwxYC4PkmQfSRBDiJehwNPYwOehga8jY14GhqweB3U\nFBT5kl9/EuyuqbmmZaOZLsSCKSHhmluDpvj4gD+57fS42Fywnc35n+PyukmPHskDGXeRHJ7Uso/L\n7eHZPx/jTEENCyen8MhtGT2eoA9GcmIUwRYDRRWN/Ptbh7A5PPzt3ROYNObKzHker4ftl3ex/sIm\nHB4naRGpPKjcdVPdLjrLY7P5uqgVFuLwd1VzFhfjrqnuuF6Oi22TNBtjYjCER2AID8cQFo4hPNyX\nSHdQTwdbDIj2SYLsIwnyAKB5vWhOJ16HA6/TgeZw4HU4rqxz+NfZbXgaGlqSYI8/Cfb6l5uHTbsu\ngwFjdLS/go3ztVLExGKMi73SUmHtmZaKrjpecYr3z35Ehb2KKHMEd6WvZFripDZl8Xo1XvzwBAfV\ncqZmJPDtO8ej10ty3BlyYhTBGAN5RbX855+OoGnwTw9OJj01qs32q7tdzEmezupRdxBu7v2+wprH\ng7umxt+Y0XxnrxJ3ZSXu6ipclVV4mxo7/hKdDn1oaJuk2RAWjj48HENYGFGJcTQ6NfQhIehDQtCF\nhKA3h6C3hKAzh1xZ381nRsTAIAkyUL5jp1ZXb+vrYlyrO/9fa9ddaLPY9r+j5t+m+Y6pgda8TvO2\n2aY1l0sDvF40zQteDTQvmtfr28frhavet7x6PGgeN5rbjeb2vafVe83j8W9zX9mvVSLcXXqrtU0F\naPC/6v2VY0xKIjZTKMbYOIxRUf1u/M4KWyXvnf2IE5Wn2+1O0cyrabz1mcr2o0Uow6L5hweyMRkN\nfVTqgScYkyPRVrDGQE5eJc+/n4PFbOD7D01udxjIs9V5/PnsOor93S5Wjb6duQHodnGzvHab/05g\nFe7qKjwNja0aTBrwXtWA0vrBwS4xGNCbzS0JtM5oQGcwojP6/mEwoDMYWpZ92wz+bUZ0Bj06nR70\netDpfOedq97rdDrfa/M2dKDXoQPQ6XzLurbvde2s8/8Pvo+1yvvapIDXW99J/fQupc5gIGz8hC7P\n/CgJMrBrzT2D70cNVM2VicHoq1hMRl/F03zFbg5BH2L2X9VbrlzJm80t7/UWS0viawjzJcI3utLv\nrydFp8fF5vzP2VSwHbfXzZjoUdyfcWeb7hTNXG4vr60/xf7TZQwbEs4/PzSFUIu0cHRFf40D0XuC\nOQZ2nyjm1U9OYw0x8Hd3T2x3OMjmbhcbLmzG7nGQFpHCA8pdjIhM64MS3zxN0/Da7f6k2ZdIhxm8\n1FbUXLkr2dJI0+q9w4nX2erOpdMJbRqA3N1r5BIBEX/P/cTesbxLn5EEGSj5bJNWX+/o62K0rxsX\nZLqOrgLbXOFdvZ/Od2XZfLWpv/qKtNU2Hb4rWp3edzXrf6/zX/22XPG2vhLW631XzUbjlSvtVlfX\nGAx91k+2v50U7W47u4r2s+3STmoctUSZI7g7fSVTr+pO0czmcPPCX49zOr+aMalR/N09Ewm3mvqg\n5ANbf4sD0fuCPQb2nSrl1U9OodPBU6uyrjssZK2jjg/OredA6REAsuOzWDp8ISOjhvdmcQOip2JA\n83qvJMvt3D3VPB7/HVbfXVjfXVmtzV3XNndi/dta7vpq2pW7va3uADdv9+VrzetaStXqrdb+6qvv\nPnfqx3b9I71FZzAQPmkyhvDwLn1OEmQf6YMc5PrLSbHOWc/2S7v4onAPNrcNs8HMgpQ53D7iVixX\ndadoVtvg4Nk/H6OgrIHJY+L55uoszCbpVtEd/SUORN+RGIBTF6t44a/HcTg9PLQ0g8VTU6+7b251\nHh/kbSC/7hIA6dEjWZq2kKy4sQP2wWCJAQGSIDeTBDnI9XWFWNZUwdaCHewtOYTb6ybcFMbC1LnM\nT51DmCn0up8rqWri1+8epaLWzoJJyXz1tgwM/az/9EDS13Eg+p7EgE9+ST3PvneMukYnK2YP5+75\no66b8GqaRm7NeTbnb+dUlQpAclgSS9IWMC1xEgb9wLpglxgQIAlyM0mQg1xfVYgFdZfZVLCdo2XH\n0dCIs8SyJG0+s4ZOw2wwd/jZ80V1rH3vGA02F3fOG8mquSMGbItNfyEnRiExcEVZjY1n3z1KabWN\nuROS+NrtYzEaOr4AL2woZnP+dg6VHcOreYkJiebWtFuYM3QGFmNIL5X85kgMCJAEuZkkyEGuNytE\nTdM4U5XLpoLtnK0+B8Cw8GSWDF/I5IQJnWptycmr5LfrjuNye3l0mcKCSTJDXk+QE6OQGGirrsnJ\nc+8d40JxPRNGxfE3d44nxHzjOqrSVsW2SzvZXbQfp9dFqNHKgtQ5LEidS4S5a31Be5vEgABJkJtJ\nghzkeqNC9Hg9HCnLYXPBDi43FAGgxKSzdPhCxsaM6XTr767jxbyx4QwGg45vrcli8piEQBY7qMiJ\nUUgMXMvudPO7dSc5fr6SkUMjefq+iUSGdnyHq1mDs5EdhbvZcXkXja4mTHojs4dOZ3HafOKtcQEu\nefdIDAiQBLmZJMhBLlAVolfzcqG2gENlxzhSlkOdsx4dOiYPmcDStIWkRV7/4ZeraZrGhr35/GXH\necIsRv7+3omMSY3u8TIHMzkxComB9rk9Xn6/8Qy7TpSQGGPlHx6YREJ058eVdXic7Ck+wLaCL6i0\nV6NDR3r0SKYmZjMpYUK/alWWGBAgCXIzSZCDXE9WiJqmcbHuEofLjnG4LIcaRy0AYcZQpiZms2jY\nLQwJjb/Bt7Tl9Wr8aWsuWw9dJjYyhO/dP4mU+N6fxWqwkxOjkBi4Pk3T+MuO82zYm09UmJnv3pfN\n8KRrJxTpiMfr4XBZDl8U7uF87UUA9Do9GdGjmZqYTXbC+A4fTO4NEgMCJEFuJglykLvZClHTNC7V\nF3LInxRX2asBsBqtZCdkMXVINkpMeree5na5PbzyyWkOnikjJSGM792XTWxk+0O+iZsjJ0YhMXBj\nmw9e4p0tuYSYDfzt3RPIHBHbre+pttdwuCyHQ2XHWoaJ0+v0jI0dw9Qh2WQnZGE1dm32s54gMSBA\nEuRmkiAHue5UiJqmUdhQ3FLBV9gqAbAYQpgQn8XUxImMi83AqO/+bHZNdjcv/DWHMwU1ZKRG8Xf3\nTiTMIhOABIqcGIXEQOfsP+2bUETT4ImVmczMTLyp76u0VbXUpZfqCwEw6gyMi8tgypBsJsZnXncs\n+J4mMSBAEuRmkiAHuc5WiPXOBs7XXiSv9iInKk5T2lQOgNlgZkLcOKYmZpMZq2Ay3HwSm19Sz8sf\nn6S4sompGQk8tToTk3FgjSc60MiJUUgMdN7p/Gpe+GsONoeH5bOGc+ctI284DFxnlDWVc7gsh8Nl\nORQ2FANg0hvJjFUYEzOa0dEjSAkbGrDxlSUGBEiC3EwS5CDXXoWoaRpltgrO1/gS4rzaC5Q1VbRs\nN+mNjI8bx5TEbMbHjb3huMWd5fVqbNyXz7qdF/B4NW6bPoz7F6Wj18sYx4EmJ0YhMdA1BaX1vPDX\n41TU2kkbEs6TqzJJSei5B+5KGks5VJbD4dJjlDSVtawPMZgZGTmcUVHDGR09khGRw3qshVliQIAk\nyM0kQQ5yCQkRFJdWc6m+kLzaiy1JcYOrsWUfiyGEkVHDGR01glFRIxgRlUZIDyXFzcpqbLz6ySnO\nXa4lKtzMN5aPY/yo/jkU0mAkJ0YhMdB1Noebd7bmsjOnGKNBz70LR7NkWir6Hpy4SNM0KmxV/jt4\nF8irudgmYdahIzUiuaV+Hh09guiQqG4dS2JAwABIkBVF+TUwC/AC31VV9WCrbUuAfwPcwEZVVZ/x\nrx8PrAN+rarqbztxGEmQg4hX81LjqKWsqYKypnLKmioodZSSW3kBl9fdsl90SBSjo0YwOnoko6JG\nkBKehF4XmGmcNU1jZ04xf9qai8PpYdrYITy6TCHcKv2Ne5OcGIXEQPcdOVvOm5+eob7JxbjhMXxj\nxbiAPlDc4GrkQm0+ef4GjYK6S7g1T8v2OEsMI6OGkxQ6hCGh8QwJTSDBGn/DGf0kBgR0PUHu/tNG\n3aAoynwgXVXVOYqijAVeB+a02uU5YClQDOxQFOV9oAB4HtjSm2UV/YumaTS6miizlVPaKhEuayqn\n3FbRJhEGX+tDcnhSm9aHWEtMr5S1rtHJ7z89w5HcCqwhRp5clcmszESZNloIMaBMzkhgVEoUb244\nzbG8Sn782n4euS2DWVlJATleuCmMCfGZTIjPBMDlcVFQX9jSwnyhNp+DpUev+VyUObIlYR4SGk9i\naAJDrPHEWWNv6qFqEdx6tQVZUZSfAvmqqr7uXz4FzFBVtUFRlJHA71VVne/f9gOgHvgdYAJ+AJRL\nC/LgomkaNredemc99a5G6p0N/n9Xln2tw+U0uW3XfD7EYPZVitb4NhVkVtooGmvc7RwxsI7mVvDm\nxtPUNbkYmxbNN1ZkEhclQ7j1FWk5EhIDN6/ljtiWXBwuDzPGDeGRZUqvj8Dj1bxU2qops7VtJCmz\nVVBtr0GjbT6j1+mJs8SQHDUEC6GEm8OIMIUTYQ4nwhxBhH853ByOSRLpQa9ftyADScDBVssV/nXn\n/K/lrbaVAaNUVfUCDkVReq2Q4sY0TcOteXB6nDg8DhweZ5v3jmvW+5ZtbjsNzsY2CbCn1S209hh0\nBuKtcYyOHulrHbAmtCTDkeaIdltmQ01WGum9k6Ld6eadref44lgRRoOeB29NZ8n0YT3aZ08IIfqC\nTqdjfnYySlo0r35yiv2ny8i9XMvjK8aR1c0xk7tDr9OTEBpHQmgcWXFtcwKnx0WFrfJKNzub77W8\nqYJjJadv+N1Wo7UlYY4wRxBmCiXEYCbEEOJ/9b03X+d9iMGM2WAKWLc90fv6+pKpo+yh25nFKwff\nxmZ3dffjndONlveOP9H+1iuHuXJt3PJOo80Vc/N7TQMNL5qmoaG1vHo1rWW9t3l9y3svHs2Dx+t7\ndWsevF7fq8fr8W3zv3drHryat8u/vzWzwUyEKZxhESm+q/mWq/rwa5bDTKH9utI5d7mWVz45SXmN\nnWH+p75Te/CpbyGE6A8SY0L5wcNT2LC3gI++vMB/v3OUJVNTuXfhaMymvh2y0mwwkRyeRHL4td0/\nImLMXCwqoc7ZQIOrodWdygbqr1oub6q8piW6K3ToMOgNGHR6jDojer3v1aDT+9cbMOgNGHUG9Drf\nfjqdDr1Ojw4dOp2u5VWPDl3z9lbbQIdOh//9leP637Qst9naYUbV/sZuJWG90Chk0BlYkDqHxNCE\ngB6ntxPkInwtxc2S8fU3bt42tNW2FP+6Ltuct7NbhQt2ev8fsNH/x+t7b8RkDLlmXfN+FmNIy7+Q\nVu+v/hdiNGMxhmA1Woi0RNzwoYqekJDQtSlTu8rl9vLOZpX3t55FA+69dQwPLVNkbON+JtBxIPo/\niYGe9fiaCcyfMoz/fvsQWw5dRr1cwz88NJX01Oi+Ltp1jU0b3qn9vF6v/y5nI3a3A4fbgb3lnxO7\n296y7HA7W7333TH1eD24vf7GJK+7pZHJ7fXg8rj867wt20X3jExIZvzwUQE9Rm/3QZ4N/KuqqssU\nRZkCrG3uc+zffhxYgS8x3g08pKrqOf+2nwAVqqr+z42Oc7muWKuuarzRbj2g61dKHV/E3egq7so1\n4ZVd279K7PBqFB36VutbtvfjVtquCmS/Q6+mcUgtZ93O8xRXNhEfZeGJlZlkDOu/J4dgJf1PhcRA\n4DhdHt7fnseWQ5cx6HXckp3MytnDAzrSRXf01xhofZfX2+pur6Z5/Xd8278D7Fvf8i1t7iP7vrfd\ne87XK0T7q7v3i7r1qa7S6wwkWOO6/OD7QBjm7RfAAsADfAeYAtSoqvqhoijzgF/h+3/5fVVVn/Un\n0v8NDAdcQCFwt6qqNR0cRh7SC3KBqBA1TePw2Qo+/PI8l8sb0et0zM8eyn2L0rGG9HVvJdGe/npi\nFL1HYiDwTl6o4q1NKqXVNowGHQuyU1g+ezgxEYG/U9gZEgMCBkCC3EskQQ5yPVkhaprGsbxK1u08\nT0FpAzodzMpMYvXcESTGhvbIMURgyIlRSAz0Do/Xy54TpXy06wIVtXZMRj0LJ/kS5aiwnp2Aqask\nBgT0/1EshBgwNE3jxIUq1u08z4XienTAzMxEVs8dwdC4sL4unhBC9BsGvZ55E4cyKyuR3SdK+HjX\nBTYfvMSOo4XcOjWV22emERnat4myEF0hCbIQV9E0jVP51azbeZ68wjoApikJrJk3khQZnUIIIa7L\naNAzPzuZOeOT2JlTzCe7L/LpvgI+P1zIkmmpLJuRJjOKigFBEmQhWlELqvlg5wXOXvJ1cZ88Jp41\n80aSlihPwQshRGcZDXoWTU5h3oQkdhwtYv2efNbvyWfrocssnTaMZTOGEdrLE40I0RWSIIug5/F6\nOX2xmo37CjidXw1A9ug41twykhFJkX1cOiGEGLhMRgNLpg1jfnYy248UsmFvPh/vvsiWQ5e5bfow\nbpk4tN+NeiEEyEN6YpC60UMZmqaRV1jH3lMlHDxTRl2Tb2KZ8SNjWXPLSEYnR/VWUUUAycM5QmKg\nf3E4PWw7cpmNewtosPnq3Yxh0czMTGSakkBEAPopSwwIkFEsmkmCHOTaqxA1TeNSWQP7Tpey/1QZ\nlXV2AMKtJqaPG8Kc8UmSGA8ycmIUEgP9k83hZu+pUvadKm3p0mbQ68gcEcuszEQmjYnvseEzJQYE\nyCgWQlyjrLqJfadK2Xe6jKIK3wQyFrOBOeOTmJmZyLjhMRgNg2eSFCGE6O+sIUYWTU5h0eQUqurs\n7D9dxr5TpRw/X8nx85WYjXqy0+OZmZnIhFFxmIxSR4veJS3IYlAyhJjY+OV59p0q5UKxbyQKo0FP\n9ug4ZmYmMnF0HGaTTAk92EnLkZAYGFiKKxtbGjRKq5oAXzI9VUnwNWikxaDXd3kGNYkBIV0s/CRB\nDiKaplFRayevsJa8wjrOFdVSUFqPpvmm5M4cEcvMcYlMyUgg1CI3TYKJnBiFxMDApGkaBaUN7D1V\nwv7TZVTXOwBfl7gxqVGMTolidHIkI4ZGEnKDxg6JAQGSIDeTBHkQc7o8XCypJ6+wlnOFteQV1VHX\n6GzZbtDrUIbHMDk9nmljh/T5LE6i78iJUUgMDHxeTSP3Ug37TpVyLK+yJVkGX32fOiSc9OQoRqdE\nMjolivgoCzrdlVxIYkCA9EEWg4ymaVTW2jlX5Gsdzius5VJZAx7vlQu76HAzU5UERidHkZ4SxfCk\ncJKHRkuFKIQQg4Bep0NJi0FJiwGgqs5OXlGd/65hLfml9eSX1LP1sG//yDAzo5MjSU/xtTRHRFn7\nsPRioJIEWfQ5h9NDea2N8hobFTV232utvWWd0+Vt2deg1zE8KYLRza0FyVHERoa0aS0QQggxeMVG\nWoiNtDB97BAAXG4P+aUNLQlzXlEdR3IrOJJb0fKZ6HAzCdFW4qOsJERbSIi2+pctREeEoJdziLiK\nJMgiYFxuD412N402l+/V7qK+yUV5je1KElxjo94/BvHVrCEGEmNCSYyxMqpV67DJKA/XCSGE8DEZ\nDaSn+M4Rzarq7L4ueIV1lFTbKCpv4FxhLbmXa6/5vNGgIy7KSkKUhfhoXwIdG2Eh3Goi1GIkzGoi\nzGLEGmKURDqISIIcpLyahtfr/+d/7/JouFweXB4vLrfvn9N95b3L47ny3u3F6fK0JL5NzYmww/fa\nZHfjdHs7LINBryMuykJaYkSrisl3RZ8QbSXMYpSWYSGEEF0WG2lhRqSFGeMSW/oguz1equrslNfa\nqaixUV5jp8J/p7K8xt4yasb16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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -237,17 +244,17 @@ "Associated with these three actions, the decision maker suffers three kinds of losses:\n", "\n", " \n", - "* A loss $L_0$ if he decides $x = x_1$ when actually $x=x_0$\n", + "* A loss $L_0$ if he decides $x = x_0$ when actually $x=x_1$\n", "\n", - "* A loss $L_1$ if he decides $x = x_0$ when actually $x=x_1$\n", + "* A loss $L_1$ if he decides $x = x_1$ when actually $x=x_0$\n", "\n", "* A cost $c$ if he postpones deciding and chooses instead to draw another $z$ \n", "\n", "For example, suppose that we regard $x=x_0$ as a null hypothesis. Then \n", "\n", - "* We can think of $L_0$ as the loss associated with a type I error\n", + "* We can think of $L_1$ as the loss associated with a type I error\n", "\n", - "* We can think of $L_1$ as the loss associated with a type II error" + "* We can think of $L_0$ as the loss associated with a type II error" ] }, { @@ -262,7 +269,7 @@ "\n", "$$ J_k(p_k) = \\min \\left[ (1-p_k) L_0, p_k L_1, c + E_{z_{k+1}} \\left\\{ J_{k+1} (p_{k+1} \\right\\} \\right] $$\n", "\n", - "where $E_{z_{k+1}}$ denotes a mathematical expectation over the distribution of $z_{k+1}$ and the minimization is over the three actions, accept $x_1$, accept $x_0$, and postpone deciding and draw \n", + "where $E_{z_{k+1}}$ denotes a mathematical expectation over the distribution of $z_{k+1}$ and the minimization is over the three actions, accept $x_0$, accept $x_1$, and postpone deciding and draw \n", "a $z_{k+1}$. \n", "\n", "Let \n", @@ -337,7 +344,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": { "collapsed": true }, @@ -388,7 +395,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": { "collapsed": false }, @@ -399,9 +406,9 @@ "text": [ "Iteration Distance Elapsed (seconds)\n", "---------------------------------------------\n", - "5 8.042e-02 6.637e-02 \n", - "10 6.418e-04 1.121e-01 \n", - "15 4.482e-06 1.545e-01 \n" + "5 8.042e-02 4.618e-02 \n", + "10 6.418e-04 7.645e-02 \n", + "15 4.482e-06 1.071e-01 \n" ] } ], @@ -451,17 +458,33 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ - "# %load -r 22-260 Wald_Friedman_utils.py\n", + "# %load -r 22-276 dependencies/Wald_Friedman_utils.py\n", "\n", "class WaldFriedman(object):\n", " \"\"\"\n", - " Insert relevant docstrings here\n", + " This class is used to solve the problem presented in the \"Wald Friedman\"\n", + " notebook presented on the QuantEcon website.\n", + "\n", + " Parameters\n", + " ----------\n", + " c : scalar(Float64)\n", + " Cost of postponing decision\n", + " L0 : scalar(Float64)\n", + " Cost of choosing model 0 when the truth is model 1\n", + " L1 : scalar(Float64)\n", + " Cost of choosing model 1 when the truth is model 0\n", + " f0 : array_like(Float64)\n", + " A finite state probability distribution\n", + " f1 : array_like(Float64)\n", + " A finite state probability distribution\n", + " m : scalar(Int)\n", + " Number of points to use in function approximation\n", " \"\"\"\n", " def __init__(self, c, L0, L1, f0, f1, m=25):\n", " self.c = c\n", @@ -562,7 +585,7 @@ " Evaluates the value function for a given continuation value\n", " function; that is, evaluates\n", "\n", - " J(p) = min(pL0, (1-p)L1, c + E[J(p')])\n", + " J(p) = min( (1-p)L0, pL1, c + E[J(p')])\n", "\n", " Uses linear interpolation between points\n", " \"\"\"\n", @@ -585,9 +608,9 @@ "\n", " return J_out\n", "\n", - " def solve_model(self):\n", + " def solve_model(self, tol=1e-7):\n", " J = qe.compute_fixed_point(self.bellman_operator, np.zeros(self.m),\n", - " error_tol=1e-7, verbose=False)\n", + " error_tol=tol, verbose=False)\n", "\n", " self.J = J\n", " return J\n", @@ -707,7 +730,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 8, "metadata": { "collapsed": false }, @@ -718,9 +741,9 @@ "text": [ "Iteration Distance Elapsed (seconds)\n", "---------------------------------------------\n", - "5 8.042e-02 6.659e-02 \n", - "10 6.418e-04 1.144e-01 \n", - "15 4.482e-06 1.587e-01 \n", + "5 8.042e-02 4.080e-02 \n", + "10 6.418e-04 7.262e-02 \n", + "15 4.482e-06 1.044e-01 \n", "\n", "If this is true then both approaches gave same answer\n", "True\n" @@ -759,7 +782,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 9, "metadata": { "collapsed": false }, @@ -781,7 +804,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 10, "metadata": { "collapsed": false }, @@ -793,7 +816,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 11, "metadata": { "collapsed": false }, @@ -804,15 +827,15 @@ "text": [ "Iteration Distance Elapsed (seconds)\n", "---------------------------------------------\n", - "5 9.200e-01 7.225e-02 \n", - "10 4.523e-01 1.270e-01 \n", - "15 1.223e-01 1.811e-01 \n", - "20 2.126e-02 2.363e-01 \n", - "25 3.316e-03 2.913e-01 \n", - "30 4.752e-04 3.450e-01 \n", - "35 6.826e-05 3.993e-01 \n", - "40 9.806e-06 4.536e-01 \n", - "45 1.409e-06 5.071e-01 \n" + "5 9.200e-01 5.442e-02 \n", + "10 4.523e-01 1.026e-01 \n", + "15 1.223e-01 1.468e-01 \n", + "20 2.126e-02 1.917e-01 \n", + "25 3.316e-03 2.690e-01 \n", + "30 4.752e-04 3.602e-01 \n", + "35 6.826e-05 4.373e-01 \n", + "40 9.806e-06 4.816e-01 \n", + "45 1.409e-06 5.392e-01 \n" ] } ], @@ -826,15 +849,15 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The value function equals $ p L_1$ for $p \\leq \\rho_1$, and $(1-p )L_0$ for $ p \\geq \\rho_2$.\n", + "The value function equals $ p L_1$ for $p \\leq \\alpha$, and $(1-p )L_0$ for $ p \\geq \\beta$.\n", "Thus, the slopes of the two linear pieces of the value function are determined by $L_1$ and \n", "$- L_0$. \n", "\n", - "The value function is smooth in the interior region in which the probability assigned to distribution $f_0$ is in the indecisive region $p \\in (\\rho_1, \\rho_2)$.\n", + "The value function is smooth in the interior region in which the probability assigned to distribution $f_0$ is in the indecisive region $p \\in (\\alpha, \\beta)$.\n", "\n", - "The decision maker continues to sample until the probability that he attaches to model $f_0$ falls below $\\rho_1$ or above $\\rho_2$.\n", + "The decision maker continues to sample until the probability that he attaches to model $f_0$ falls below $\\alpha$ or above $\\beta$.\n", "\n", - "The value function is smooth in the interior region in which the probability assigned to distribution $f_0$ is in the indecisive region $p \\in (\\rho_1, \\rho_2)$.\n", + "The value function is smooth in the interior region in which the probability assigned to distribution $f_0$ is in the indecisive region $p \\in (\\alpha, \\beta)$.\n", "\n" ] }, @@ -848,14 +871,12 @@ "\n", "The slider let's you choose the cost parameters $L_0, L_1, c$, the parameters of two beta distributions $f_0$ and $f_1$, and the number of points and linear functions $m$ to use in our piece-wise continuous approximation to the value function.\n", "\n", - "It then draws a number of simulations from $f_0$, computes a distribution of waiting times to making a decision, and displays a histogram of correct and incorrect decisions. (Here the correct decision occurs when $p_k$ eventually exceeds $\\rho_1$. \n", - "\n", - " " + "It then draws a number of simulations from $f_0$, computes a distribution of waiting times to making a decision, and displays a histogram of correct and incorrect decisions. (Here the correct decision occurs when $p_k$ eventually exceeds $\\beta$.\n" ] }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 12, "metadata": { "collapsed": false, "scrolled": true @@ -863,19 +884,9 @@ "outputs": [ { "data": { + "image/png": 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QSJIkSZIkSZKkojNAIUmSJEmSJEmSis4AhSRJkiRJkiRJKjoDFJIkSZIkSZIk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x1lp40vGceI4uD6XUpVbW0tv5v+GpXvvM+Y4Xtx2lGD044kSZKknRBKenPhKYF1G7fyi6nlrNu4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\noJCkHMmsA/HfIYQBwFUk6w9sr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"text/plain": [ - "" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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SKs4AhSRJkiRJkiRJqjgDFJIkSZIkSZIkqeIMUEiSJEmSJEmSpIozQCFJkiRJ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\ncP4UFs6fQvsLHdz60Bpue3gNv1yykl8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z/Nw9uYCVGyt54o11vFmyhU/X7GTKeSM4Y3xf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\nnUuStkSh7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- "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -902,11 +913,7 @@ " value=133, description=\"m\")\n", "\n", "interact(all_param_interact, c=cslide, L0=L0slide, L1=L1slide, a0=a0slide,\n", - " b0=b0slide, a1=a1slide, b1=b1slide, m=mslide)\n", - "\n", - "# sbox= HBox(children=(VBox(children=(cslide, L0slide, L1slide, nslide)),\n", - "# VBox(children=(a0slide, b0slide, a1slide, b1slide))))\n", - "# interact(all_param_interact, sbox)" + " b0=b0slide, a1=a1slide, b1=b1slide, m=mslide)\n" ] }, { @@ -930,7 +937,7 @@ "\n", " * The sample size $n$ is not fixed but rather an object to be chosen; technically $n$ is a random variable. \n", " \n", - " * The parameters $\\rho_1$ and $\\rho_2$ characterize cut-off rules used to determine $n$ as a random variable.\n", + " * The parameters $\\alpha$ and $\\beta$ characterize cut-off rules used to determine $n$ as a random variable.\n", " \n", " * Laws of large numbers make no appearances in the sequential construction.\n", "\n", @@ -991,10 +998,11 @@ } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { - "display_name": "Python 3", + "display_name": "Python [Root]", "language": "python", - "name": "python3" + "name": "Python [Root]" }, "language_info": { "codemirror_mode": { @@ -1006,7 +1014,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.1" + "version": "3.5.2" } }, "nbformat": 4, diff --git a/dependencies/Wald_Friedman_utils.py b/dependencies/Wald_Friedman_utils.py index 71d4e8b..90b5efc 100644 --- a/dependencies/Wald_Friedman_utils.py +++ b/dependencies/Wald_Friedman_utils.py @@ -22,7 +22,23 @@ class WaldFriedman(object): """ - Insert relevant docstrings here + This class is used to solve the problem presented in the "Wald Friedman" + notebook presented on the QuantEcon website. + + Parameters + ---------- + c : scalar(Float64) + Cost of postponing decision + L0 : scalar(Float64) + Cost of choosing model 0 when the truth is model 1 + L1 : scalar(Float64) + Cost of choosing model 1 when the truth is model 0 + f0 : array_like(Float64) + A finite state probability distribution + f1 : array_like(Float64) + A finite state probability distribution + m : scalar(Int) + Number of points to use in function approximation """ def __init__(self, c, L0, L1, f0, f1, m=25): self.c = c @@ -123,7 +139,7 @@ def bellman_operator(self, J): Evaluates the value function for a given continuation value function; that is, evaluates - J(p) = min(pL0, (1-p)L1, c + E[J(p')]) + J(p) = min( (1-p)L0, pL1, c + E[J(p')]) Uses linear interpolation between points """ @@ -146,9 +162,9 @@ def bellman_operator(self, J): return J_out - def solve_model(self): + def solve_model(self, tol=1e-7): J = qe.compute_fixed_point(self.bellman_operator, np.zeros(self.m), - error_tol=1e-7, verbose=False) + error_tol=tol, verbose=False) self.J = J return J @@ -321,8 +337,8 @@ def WaldFriedman_Interactive(m): ax.set_ylim(0, 0.5 * max(L0, L1)) ax.plot(wf.pgrid, J) - ax.annotate(r"$\rho_2$", xy=(ub+0.025, 0.5), size=14) - ax.annotate(r"$\rho_1$", xy=(lb+0.025, 0.5), size=14) + ax.annotate(r"$\beta$", xy=(ub+0.025, 0.5), size=14) + ax.annotate(r"$\alpha$", xy=(lb+0.025, 0.5), size=14) ax.vlines(lb, 0.0, wf.payoff_choose_f1(lb), linestyle="--") ax.vlines(ub, 0.0, wf.payoff_choose_f0(ub), linestyle="--") @@ -355,15 +371,15 @@ def all_param_interact(c, L0, L1, a0, b0, a1, b1, m): ax[0, 0].set_title("Distributions over Outcomes", size=24) ax[0, 1].plot(wf.pgrid, J) - ax[0, 1].annotate(r"$\rho_1$", xy=(lb+0.025, 0.5), size=14) - ax[0, 1].annotate(r"$\rho_2$", xy=(ub+0.025, 0.5), size=14) + ax[0, 1].annotate(r"$\alpha$", xy=(lb+0.025, 0.5), size=14) + ax[0, 1].annotate(r"$\beta$", xy=(ub+0.025, 0.5), size=14) ax[0, 1].vlines(lb, 0.0, wf.payoff_choose_f1(lb), linestyle="--") ax[0, 1].vlines(ub, 0.0, wf.payoff_choose_f0(ub), linestyle="--") ax[0, 1].set_ylim(0, 0.5*max(L0, L1)) ax[0, 1].set_ylabel("Value of Bellman") ax[0, 1].set_xlabel(r"$p_k$") ax[0, 1].set_title("Bellman Equation", size=24) - + ax[1, 0].hist(tdist, bins=np.max(tdist)) ax[1, 0].set_title("Stopping Times", size=24) ax[1, 0].set_xlabel("Time")