{ "cells": [ { "cell_type": "markdown", "id": "8ef12ff3", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "# Correlation matrix\n", "\n", "In this example, we demonstrate how to apply correlations between random variables using a correlation matrix. When correlations are introduced, the variables no longer vary independently in the variable space but become related to each other. This affects all reliability, uncertainty, and sensitivity simulations.\n", "\n", "> Note: using the probabilistic library, two random variables can also be correlated using a copula function.\n", "\n", "First, let's import the necessary classes:" ] }, { "cell_type": "code", "execution_count": 14, "id": "b77e8141", "metadata": {}, "outputs": [], "source": [ "from probabilistic_library import UncertaintyProject, DistributionType, UncertaintyMethod\n", "import numpy as np" ] }, { "cell_type": "markdown", "id": "22f6f17f", "metadata": {}, "source": [ "We consider Hunt's model:" ] }, { "cell_type": "code", "execution_count": 15, "id": "4989b056", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [], "source": [ "from utils.models import hunt" ] }, { "cell_type": "markdown", "id": "54341fc6", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "We create an uncertainty project using the `UncertaintyProject()` class and refer to Hunt’s model:" ] }, { "cell_type": "code", "execution_count": 16, "id": "784295d2", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Model hunt:\n", "Input parameters:\n", " t_p\n", " tan_alpha\n", " h_s\n", " h_crest\n", " h\n", "Output parameters:\n", " Z\n" ] } ], "source": [ "project = UncertaintyProject()\n", "project.model = hunt\n", "\n", "project.model.print()" ] }, { "cell_type": "markdown", "id": "704602bf", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "We assume the following distributions for the variables:" ] }, { "cell_type": "code", "execution_count": 17, "id": "7a390139", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [], "source": [ "project.variables[\"t_p\"].distribution = DistributionType.uniform\n", "project.variables[\"t_p\"].minimum = 2\n", "project.variables[\"t_p\"].maximum = 4\n", "\n", "project.variables[\"tan_alpha\"].distribution = DistributionType.deterministic\n", "project.variables[\"tan_alpha\"].mean = 0.333333\n", "\n", "project.variables[\"h_s\"].distribution = DistributionType.uniform\n", "project.variables[\"h_s\"].minimum = 0\n", "project.variables[\"h_s\"].maximum = 1\n", "\n", "project.variables[\"h_crest\"].distribution = DistributionType.log_normal\n", "project.variables[\"h_crest\"].mean = 10\n", "project.variables[\"h_crest\"].deviation = 0.05\n", "\n", "project.variables[\"h\"].distribution = DistributionType.uniform\n", "project.variables[\"h\"].minimum = 0\n", "project.variables[\"h\"].maximum = 5" ] }, { "cell_type": "markdown", "id": "5f4751bd", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "### Uncorrelated variables\n", "\n", "We first run the uncertainty analysis without correlations (all variables are assumed to be independent). We use the `crude_monte_carlo` calculation technique and plot the realizations of variables $h_s$ and $t_p$." ] }, { "cell_type": "code", "execution_count": 18, "id": "51a2856e", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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uhOeSlZUltnj4hrh5U9w63kcfEX37rb3f8CRq/OnrriOqXDkqPCXS+/H3vJ+fqlA+xyNHrO+brCndvnd+2+jZxyDevycVLO/7fck6t7PfWO3fifo22tp9jLEw/lljwSdW+KlZ0//x0A14TLDS56pJGDu8nGeVFn7KlStHl156abHPOCy9cuXKRZ/37NmTatSoQaNHjxbv//rXv9L1119PTzzxhHCSZp+hTz/9lF544QXxvZEnaOTIkVS3bl0hDA0ePJiqV68uQuKDwo4d9n8TowgTD/Azz0SjGBLBNu4FC4g6dSJPtRsffhi9Hj6/qlWdXU+QMJwT7Rij2W7Pg3PTpl6emf7E9zduLz8nM6t9Nqh9W0WsjIUM76Ob4MNwH+exIdFCNyPEY4f0aK9kbN26lXbEzPSNGjUSfjgs7Fx22WU0e/ZsEcIeK0T179+f7rvvPurTpw9dffXVIpR+8eLFIiliULAzOHLnzssr2bk7dIiueJL9zsuIL1bH8nXERqf16pX8nAyC+rAmi8JLdp8YdpPTcXAOU4SVMREZ98zqs2o8g/zMIBGp+/ACb84c87GHP+PvvFwE+iHcMfH9LiPsYwc7PIPi7N+/n6cf8eoGBQUFkfnz54tXNzh+PBKpWTMSycjgaTL5xvvMmVPyGCtWpP4tb7yf2/TrZ+1vJ9rMrsertvYTq/ckdsvLS94eXqFTO3P7mD0r/Fmi58Prc4k/n0Tnwu/r1Im2dXZ2gdiXn30Z9zzo8Li6dGm0rYcMKYgsWxb9LAhwf+F+o8LY4fUYYnX+VlrzA+xL87HwKpJXi2arFqumMycmtmTMmpXaeZdXW5UqBW8V5lZbDxrEkYhEK1ZwbqvgtocbqJbTiu8VP5M1ahT/nDVC8c+qYQKND2xAbifvxtXrrz/1jDVvHhyNCPer77+PjhkYOxTI8wPSH0TjHWPPPJOoe/eoWSuZT4Mf/gfxPhaNGhHdc0/q37G/0bJl0f+zmp9p1iy6BWUwSqeteVDmtgCp4f6XzHGcBaAff4zu52Wbxj8LmzdzuZ7E/kephDbDLM3PeZCfCeAe3E8wbpwCwo/mAhAPfk6cOL12hDOLWKpSJZo80Qq7dxNxOiee6MPifAvnRPeRpeFM9Szws8Xa25iUZUoKbQAEFQg/IZXmDdMZq9VZ0IkVgNJ1hEsUsWRV8Al6xEuyydCre6JK1JPff1t2hFWiZ8EwXalmlgYgLMDnJ8TY8T/wMmIpHjbdBTGay0qdHcbte6JK1JOMv+00wkq2v5FsoQ2AoAPNT8hJx3TmRF1vheeeC6Yfg1U/DnZidvOepKuFcAM+9i23lPzc67/tpYYzFemYrmJNoGaEOT8LkM8JyTmz3ACaH1BkOmP/g3SditNVw/fr53+adb+wMxm6eU9kRz1xhF+XLubf+RFxxYLksGFEFSt6o01LRDqmK6/zs3BbczDBG28gdxDQL2eWG0D4Aa5iVQ3Ppq3492+9RTRuXHBviEw/DjuCl5vwgNi5c3LBxqu/bfx9HpiHDo1WTmc4jQLXMfY6TUC6pivDLF29urtCW1AmL6Ce2X6uRn0Iwg+Q4mPBD09szgme8M3MIkFCph+HDMHL0DZZxW2hL9FA/euvUU0Ql2+R+SwYQj+ngEgECzhGCUQuPplubqcgTV4g3Dmz0gXCD3AVq+r60qXdNevogEznWxmCl13/Lzf/tgoDtZVkpD//TFS7dnKhw3g2WDhJ51lRoU2AvnwoSXvsFRB+FCMItngvosiCgMw6OzIELzuanPi/ne5zoMpAnehZkKF1UaVNgJ7sCFj6BQg/CuHEFp9qkpAlTCGdulqCoQzBy44mJ/Zvu+GTotJAzfeUMzpzkk8z/NK6qNQmQD+qBSz9AoQfRXBii081Sch2bHQ7YikoyBIM/Ra8rPi8cJ/gaDDjb7vlk6LaQM2lLJIl+fRD66JamwC9aCrRbO8FEH4UwIktPtUk0b8/HBtVRpZg6KfgZcXnhTWSRmoDN31SVBuoVdC6qNYmYXEDCAqlJJrtvQDCjwLYtcVbmSSefFJ/x0YMfPoLXom0TRzlxH2QX41+6KZPimoDtQpaF9XaJBWyNdcg2P6cEH4UwO6q0MokYSWvCq+kVF1VYeALDrHaJkPg4SgnnmhjJzS3tSMqDdSqaF1UapNkICRfXTpJMtu7DcpbKIDdVaFbqnFOPmckfostrim7E8sswwC8gbUJ3Ne4fyW6r5x7x23tiNvlW3Qss6Fqm6RbBoavQZVzDhulHBbUVglofhTA7qrQLdV4rOCjSqIz5CIJJlbu64svRjUSbmtHVHG8V0nrokqbmIGQfOAHEH4UwK4t3oqw5GQwU8EfCANfMLFyX/n7Pn308UkJs8kg6M7hIPhA+FEEO6tCK8LSQw9F/58szFjFRGcY+IKJ1ftat6462pEwal1UQKZzuLHo476mmh8kcBcIP5quClMJS1wg1Oz7ypXVXlWpEBUD5N5XaEfCjSzncDb316sX/X/v3oguCzpweNbYkSyV46LZ97ySadFCXeHCGPjY/8jMP4QHPv5epVwkwP37GgSHSqCPc7gRZFGmjP9BFjwmq+p8rvO5pgLCj+akmiTiv+fOq7JwoVJUDHAP3Ndwke4kaWi22Uk+1leMxyZ+/t0URGRGl7HQZXaNKkTd6nyuVoDZK2QJ/nRIdKZSVAxwD9zXcOBWji6/zJ+ygix0ymU0V6NztQo0PwritYTt56oqqLlIgDNwX4ON2zm6/DB/ygiy0CmX0QmNztUOEH4Uw68EfzpMQvD7CCa4r8FE10lSRpCFHW2TbN+3DzU6VztA+Anx4IFJCAAQ9Ekylf9RrDO+GV74QeqU0mOHRudqB/j8KAQS/AEAdEXFSdKK/5EMP0idUnpU0+hc7QDhRyFUHDwAAEDHSdKOk67hB1m9uj9BFqoUug3audoBwo9CqDZ46BLBBgCQj0qTpJMagSzgbNwY/f+UKd6WHtEh6lbHc7UDhB+FUGnwUDX8FQCgJipNkk5dCIxzY82QW6VHEi36dEr90Emjc7UKhB+FUGnwCFqOCGidAAjPJKmKC0GqRZ9OpVw6aXSuygs/kyZNovr161P58uXF1rBhQ3rvvfcS7t+sWTPKyMgosbVt27Zon169epX4/sYbbyRdUGXwkKl+dhtonQAI1ySpgguB1UWfToVuSyU4Vx0Xl1JD3WvWrEljxoyhunXrUiQSoenTp1OHDh3oiy++oEsuuaTE/nPnzqWCgoKi93v37qXLLruMbrnllmL7sbAzderUovdZWVmkEzrk4NEl/NWvvEkAAHXSaMiuEahrzqMwlb2QKvy0a9eu2PtRo0YJbdC6detMhZ9KlSoVez9z5kzKyckpIfywsJObm0s6I3vwCIL6OUwDEABAnVpyshd9fjFX48WlMkkOT5w4QbNmzaJDhw4J85cVpkyZQl26dKGyZcsW+3zlypVUtWpVqlixIt1www00cuRIqly5csLjHDt2TGwGBw4cEK+FhYViSxfjGG4cSyYsTOTnE+3cScSyJd+mVIMH75ednfrYvJ8bzRPb1uvXs3Yw+d/fs4do9WqiJk3S/9thIih9WgfQ1s7gtTVPvgMGFE9gyFqJMWOi38d3X7famhdzVsY93k/XR+jEiWjblilj/j0LmQ8/TNSmjfk84VW/tnq8jAjbmySyceNGIewcPXqUzjjjDJoxYwa14dZKwccff0wNGjSg9evX0zXXXFNCG1SrVi3avHkzDRw4UBw3Pz+fSiWYqYcNG0bDhw8v8TmfCx8LAAAAAOpz+PBh6tatG+3fv1/4Eisr/LAPz9atW8WJzp49m1566SVatWoVXXzxxUl/d9dddwmBZsOGDUn3++6776h27dq0bNkyat68uWXNT15eHu3Zsydp49mRRJcuXUotW7akzMxM0o2FC4l69Cip2jTUx6++Gl1Fpfo9Y6Z+TvV7p229fn0mxfjCJ2TRImh+wtanw9bW/AzGa0A4qGLsWPeevSC1dblyLWnXrkzLGm4zrUi9ekTbtyf2OeL25+nLL5O7231g9myi3r1T78c5k9gE5tcYwvN3lSpVUgo/7GisFM2bN4/06dMn6T4HDx6MlC9fPvL0009bOmaVKlUikydPtnwO+/fv5+4qXt2goKAgMn/+fPGqG8ePRyI1a/Lja75lZEQieXnR/ZIxZ07J4/Dv+HM3iW1r49z5HNM5d5C8nZ3Abb5iRSQyY0b0FffAWp92Aj9jZs8Af8ab28+gzsyZE23r7OyConbiMcRJGxntHt/2Mtrdiz6wYkXieSF24/38nBetzt/K5fk5efJkMS2MGewbxPvcdtttKY+3bds2ERVWTde0yAGpNyYj/DWoeZN0B6kHwpVqQqd+aWio3chH5kbaEjdCyL3qA001T8orVfh55JFHaPXq1fT9998L3x9+z87K3bt3F9/37NlTfGbm6NyxY8cSTswHDx6kfv36iWgxPuby5ctF6HydOnWodevWvl1XkHAzWktGPoug5U3SHRUSXoYJFEuWKyCks+hza5HgVR8opfniUmq01+7du4WAs2PHDqpQoYJIeLhkyRJhA2TYF+i004rLZ5s2baI1a9bQ+++/X+J47NDMPkCcL2jfvn1UvXp1atWqFY0YMUK7XD+qoEKysHQJUt4knVE19QCfV1D7hiqZjlXHEBASRWilE5ruJG2JmyHkXvaBTv9dXJrl+WHBR+XFpVThhzU4yWAtUDwXXHCBSIhoRnZ2thCeQHCShblFUPIm6YyKuU90TdAWpsVL2IREtxcJbvaBEyYLBV0Xl8r5/AC10F21CdRBpQkmLCY4Hf0yZJRKUElIdNtM5VYfmJvEDKdTiQ4DCD8gJfCbAW5gdeKoWtX7yS8sjsC6LV5kOcOrJCS6vUhwow/MDeBCAcIP0KZYIdAbKxMMxzD06uX95Ke7I7Ad7YguixeZE2ysgBCP30KiF1qodPrAiYAuFJQpbwHUB34zwMt6S/yey5HE40WdINVMcFbgyeWjj4gWLCB67bVoaRarfkqq+2Wo4AyfqO38dt71ys/SaR/4UEFfPTeA8AMA8I1E0SG8Ij1yxFz48WLyU8nHwyqcMfjbb82/syIgurl4cTtCjrVXVibYZ58luu8+7wQgznT87rvRrO9cw1CGkOhlUVYnfWCHhgsFK8DsBQCQbkKdNs1c8PHKDKWSj4eVsgRMbFkCmeYHt/1y+HedO1vb98EH/fEB4kLHMp13VTJVVrO4ANi1y18n9XSB8AMA8J346JDdu/1dXVpxAr3jDqK33pI7mBuVs63gh5+S2345xvF++cX6b3R2stXRz7JpioWC8TyxYOqnk3q6QPgBAEhHhhkq0eq6UqXoNnSo/MGcBZlkGh8/zQ9uO74mO14ydHaytYsKIeSlkiwUDOLvgw4CKoQfAIB0ZJmh4lfXw4dHzW/xJjhZg7kTQcYrPyW3I+RSHS8ZqkfjBY1OCRYKiYQxHQRUCD8AAOkkCzU2BtMuXbxZ+Rqra/Y7efHFxH9fxmBuR5Dx2k/JbcdXNzRUujnZ6kynuIXCU08lfxZUF1Ah/AAAlBlc//a3xN9PmOCt5kXF3D8syMSvtpPhZS4at02TbmioVIrGCwOlYsxwZ52lt4AK4QcAoAS8iuRokWR4qXlRIaQ3PnkhM3Zs9DWZwylrfLyOAnLbNGnFkTYRKkXjhZVqGqaLiAXCDwBACWRrXmQP5olCyA2qVy++/5lnRoVBv6KA3C6VYeV4bv0t4D5NNUoXYQaEHwCAEsjWvMgczJOFkPfoEf3/xo3Fw565Hdjvws8oILfzzyQ73pw50U2FXDdA/7px8SDDs0K4nTUVqAPurfqaFy8z66YbQm6gQvkAt0tlpDqeymU5wk6ijO1+lwRxAoQfReCVn1kHSlavB+gB7q3cmkZOBvP77y+eX4e1D149i1bMfUx+ftQUFsQ6f8mOh5qCatNJ8bpxiYDZK+TVjIG34N7qqUZ34oTrFKtmPK41BYCKlFIgGaNdIPxIxu2sqUAdcG/1q2kkQ1i1asbLzXX/bwMQViD8aBLhYoS9An2QHb2kK7JqGskSVq04WjMNG7r7dwEIMxB+JGNV5c3ZZ2H+0gvZ0Us6I0ONLktYtRryrYMpAQBdgPAjGasqb656HFT/n/jEbkEx8cmOXtIRmX1BprCazNz36qvu/z0Awg6EH8nYzXJqqN2DIjAkSuwWBCFP9yRgYesLsoXVROa+du28+XsAhBkIP4oXdDRTu48aFQyBIeiRUCpFL7kJC9pr1kT/z69uCN4q9AUVhFUdo2aCCPdr3ReWIDkQfhTAUHlXqmRt/6FD9RcYwhIJJTt6ySvtTNu20ff8mq7grUpfCKqwChITr0GfP/9Uv9Z5YQlSA+FHEXgSfOst57/XTWDw2rlUplkw/m9zAjAZ0Utu45V2RqWouKAJq8CemfX220vup9vCElgDGZ4VgtXcyTLcpiJ2klAhDb5M59J69Yi+/db/bNlBzeacSjvDmhEWvFnQs6sZUS0qTteMtcC+IG9lnE23fwM1geZHIayGvAYhdNor59KFC6OvsaUJ/Fq9qeC34hVeamdkOxqbAd+b4JJMkE8EcnIFDwg/ipFM7T58eHBCp71wLuVBbcAAOWZBVfxWvMJL7YwKjsZAHbw2WacS5HVfWAJrQPhRkEQhr48+GpxJwgvnUh7U4jU+fq3eVPJb8QIvtTNeORoHJR1EmPAj3UE6AowOC0tgDQg/imKmdg9aNIrbzqUyfUdU81txG6+1M273Bdk5g4C6ZmMnAoxOC0tgDQg/mhG0aBQ36zjJ9B1R0W/FTY2IH4K3W30hyL5XQcVPs7HdxLI6LiyB4sLPpEmTqH79+lS+fHmxNWzYkN57772E+0+bNo0yMjKKbWXKlCm2TyQSoSFDhlC1atUoOzubWrRoQd988w0FCVmFH1V3LuVBLV4o9Gv1povfSjoaET8E73T7QtB9r4KKn2bjZIK8GbouLIHCwk/NmjVpzJgx9Nlnn9Gnn35KN9xwA3Xo0IG+/vrrhL9hIWnHjh1F2w8//FDs+3HjxtHEiRNp8uTJtH79eipbtiy1bt2ajh49SkEC0SjmbTJ2rByzoA4mSTc0IobgvWhR9D2/qiR4B933Kqj4bTZOJsgb/ToIC0ugqPDTrl07atOmDdWtW5fOP/98GjVqFJ1xxhm0bt26hL9hbU9ubm7RdtZZZxXT+jz99NM0aNAgIUSxVumVV16h7du303wjdScINEYdpOrV/V+9qWySdFMjwgJckybR//OrSqaAoPteeYlMB3EZZmMzDfqGDaf6NUqMBBtlkhyeOHGCZs2aRYcOHRLmr0QcPHiQzjnnHDp58iRdccUV9Pjjj9Mll1wivtuyZQvt3LlTmLoMKlSoQA0aNKD8/Hzq0qWL6TGPHTsmNoMDBw6I18LCQrGli3EMN44FrLX1F18U0iefEO3cSZSbS8Rdiidpr28BC19t2hDl5/v/t1PVKtq7lyg7O/E+e/YQrV59SrDRsU9zeye7xtj9FDt1qW3N+bE4TURstCQL8axJ9aOw6rXXEtWpQ7R9u7mAztpTPh/ez+1maNxY/X4dRAo9amurx8uIsLpEIhs3bhTCDpulWOszY8YMoQ0ygwUY9t9hjc7+/ftpwoQJtHr1amEmYxPa2rVrqXHjxkLTwz4/Bp07dxYaozfffNP0uMOGDaPhJkl0+FxycnJcvFoAAAAAeMXhw4epW7duQkZgNxllhZ+CggLaunWrONHZs2fTSy+9RKtWraKLL77YkoR30UUXUdeuXWnEiBGOhR8zzU9eXh7t2bMnaeNZhc9z6dKl1LJlS8rMzEz7eABt7UTzYxQjTQb7OljV/HjZp9PRRPBve/SI/j92dDN8r1591R9thlt42dZs2uJSMMnyY7HWMtYE5qVGyOy+s9l4zBh/7hnGav/wqq15/q5SpUpK4Ue62at06dJUh/WdRHTllVfSJ598Qs888ww9//zzKX/LDfb73/+evv1vESf2AWJ27dpVTPjh95dffnnC42RlZYnN7Phu3hS3jwfQ1la57jqiypUT141jwYAnGd7Pjg+PF306Ud2lzZujn6fynzK+i6+xxtF27HSuq/OqF2390UfFa+BZwep90LmuGsZq//BintUyzw/78sRqYVL5CbHZzBB0atWqJQSg5cuXF5MCOeormR8RAEFHh2g0Nx2zg5YOwiucOH57nTIAkazAD6Rqfh555BG66aab6Oyzz6bffvtN+NisXLmSlixZIr7v2bMn1ahRg0aPHi3eP/bYY3TttdcKTdG+ffto/PjxItT9jjvuEN+zaeuBBx6gkSNHiggyFoYGDx5M1atXp44dO8q8VACkY0SjmVWdV0UjYidUnfMAWZlEgfvRU3buAwAqIlX42b17txBwOF8PR2WxIzMLPmwDZNgX6LTTTimnfv31V7rzzjtFRFfFihWFmYz9fGL9g/r37y8ixvr06SMEpCZNmtDixYtLJEMEIB14xStbNa+zWSFROybzPYkFoeruJudMZA714j7o+uyAYCFV+JkyZUrS71kLFMtTTz0ltmSw9oc1RLwB4AXsk2KmPWGzkgrak1SoohExa8cqVfQpExIkcyj78LD5064AZPc+6P7sgOCgnM8PACqDulHetiPnGkqGKmVC/IK1JBypx/CrFz42iZJzJtPGOLkPeHaASkD4AcAiqBvlfTvGorJjtp912IwUBfzqVWV6MwdxzvTMbe7GfcCzA1QDwg8AFkHdKH/aMZEJTIUyIX4hQ0sSH2V1yy3ulWvBswNUQ3qeHwB0AXWj/G1Hdu/jiddPx1gVnHFTaUlY88Jh5uy47vW5ueUgj2cHqAaEHwAULr4YRKy2Dws+fjpmq+KM62a4vyoO8nh2gGrA7AWAzbDgeB+IsDrjBqkdVXLGDaKWRMV7DsINhB8AApYlWXVUa0fVnHGDqCVR7Z4DAOEHABfCgsPkjBu0dlTNGTeoWhKV7jkA8PkBQPMsybqiSjuqZmaKTzwYJC2JKvccAAg/AGicJVl3VGhHFc1MsXXY9u5Vsw6bzvccAAg/IBDEhijn5ETfZ2bKPisQhPpWrG3h7/02MxlaktWriQ4cIFq0iOi669TQkqiQEgCAdIDPDwhMJtw//IGod+/oZ/Xq+RuhA/RFZWdc/ptNmkT/z68qCBixz1u3btFXrzJPA+AVEH6A1iQKUd6+3f8QZaAvcMa1Bj9PN9+sRkoAANIBwg/QFtVClIHemNW32rJFb/8aN+HnqE8f8+/wvAHdgM8P0BbVMuEC/YEzbmJGjSrufB0PnjegExB+gLZ4HaIMp04ATj0Lhl+UV88bAH4C4Qdoi5chyqrUeQJABVh7+ssvwcs8DcILfH6AtniVCVelOk8A2NXQrFxJ9MYb0Ve3/N2sanMqVdIv8zQIJ9D8AOkY5iUWLn7+mejMM6Mp8FPlDonPhBvr+Ow0RDmVEzUfl52oOf+KCmHHAPihrbSqzeG/j+cC6AA0P0CZnCG33Ub04IPRV6u5QxKFKPN7J/WCVKvzBIKDV1oZP7SVqbSsTOXKRI8+mt7fAcAvIPwAaSQasA34cysDd2yI8pQp0c82bHC22lWtzhMIBl4mBvQj5UOyRJDGZy+8AK0P0AcIP0AKyQbsWPh7KwO3EaLMwpLxPih1noCa2hZVtDJ+aSsTaVnZrw5V2YFuQPgBUkg1YMfip5nJKydqEM4yDH5oZfzUViIRJAgKcHgGUrA7EPtlZvLCiRrI07bECx2GtsUvTYUfiTj91lYiESRwI2/atdeSVKD5AVKwOxD7aWZCnSe9UansiR9aGWgrgY5a2Hr15J4ThB8gBSvRIwYyzExQ7+uLShF7fmhlVK5KD8DcJMWnmYUL5bQRhB8ghdgBOxk8eMsauA31fteu0VdMHnqgUsSeX1oZaCuBrlrYhx+WE4gA4QdIwxiweXIwA1EkQPeIPT+1Msm0lSpEvYHw8aGFwBb+XkbeNDg8A6nwwMzZkp1keAYgmbaF+5PZipOFDv7eL1OqIeSbZV9mwcdNx2szZ2TUqQOy2KGQFjYeCD9AOogeAW73Jy/KnsRGqtgVzGOF/NhjMKyJcXpcXaLeQDipppAWNh6YvQAAgcNNHxi38gXF+5AtWOBtHiKVot5AOGlqIbDFTy2sMsLPpEmTqH79+lS+fHmxNWzYkN57772E+7/44ovUtGlTqlixothatGhBH3/8cbF9evXqRRkZGcW2G2+80YerAaoBP4dw40bEnlfZmb3O+qxa1BsIJ6Us+LyNGSPHvUGq8FOzZk0aM2YMffbZZ/Tpp5/SDTfcQB06dKCvv/7adP+VK1dS165dacWKFZSfn095eXnUqlUr+olHjBhY2NmxY0fR9gZ7+YFQweGTsrP7eg2EO28j9rzSnPilkVHZ3wKEh05Jik8z7dpJOS25wk+7du2oTZs2VLduXTr//PNp1KhRdMYZZ9C6detM93/99dfpnnvuocsvv5wuvPBCeumll+jkyZO0fPnyYvtlZWVRbm5u0cZaIhAuevTwdlUtGxVKNwQdrzQnfmlkVPa3AOGik4kWlotPy0QZh+cTJ07QrFmz6NChQ8L8ZYXDhw9TYWEhVapUqYSGqGrVqkLoYW3SyJEjqXLlygmPc+zYMbEZHDhwQLzysXlLF+MYbhwLJOfYsWgblylTmDDSh/NKtGmjbyQZa7VYuOPry84+9fkvv0Q/92M1FYY+zRqR2PZNtp+dZrB7XKdtzeUD6tSJJpNL9Czw6pv3C/BttEUY+rVMGjf2vq2tHi8jEklVV9tbNm7cKISdo0ePCq3PjBkzhDbICqwFWrJkiTCTlSlTRnw2c+ZMysnJoVq1atHmzZtp4MCB4rhsJiuVYLYbNmwYDR8+vMTnfC58LAAAAACoDytFunXrRvv37xe+xMoKPwUFBbR161ZxorNnzxamrFWrVtHFF1+c9HfsKzRu3Dih5WGn6UR89913VLt2bVq2bBk1b97csuaH/Yn27NmTtPHsSKJLly6lli1bUmZmZtrHA4mZPbuQcnKW0p//3JKOHEnc1lOmRE1gurFmDVHbtqn3W7SIqEkT784jDH2afW64/lAqzQmr7411FWvlBgyImlgNeJ+xY09p41atImrfPvXff/ttouuvT7+tzc6JI2zY0VSWv4WqhKFfB72tDxw4QFWqVEkp/Eg3e5UuXZrqsG6WiK688kr65JNP6JlnnqHnn38+4W8mTJgghB8WaJIJPsx5550nGuLbb79NKPywjxBv8fANcfOmuH08UJLcXO78JASfZMIP+znoeCt27uRrs7afH9cX5D7Nl8VCiyEkm+ULYgHiv0rnhDl1Nm8unlOHE3lauYe8X2zTOm3rRDmGdDX7+kGQ+7VqZHowz1pBuvATDzswx2ph4mFtDztGs7nrqquuSnm8bdu20d69e6kavPpCAbuLLVmSvJaSrLwSbiDTiTU20R8LmWHAanbmVBFc3O84gouFEBn3UPdEoukmmQRAKeHnkUceoZtuuonOPvts+u2334SPDZuxWLBhevbsSTVq1KDRo0eL92PHjqUhQ4aI/c4991zayctbIuHTw9vBgweF787NN98sorzY56d///5Cs9S6dWuZlwp8InZAdCu7r0rIKt0QXyKBHXY5gwSbVIKeIdiK5sROBJdq5TdUB+U5QOBC3Xfv3i0EnAsuuECYpNjkxYIP2wAZ9gXiPD2xSRHZR+iPf/yj0OQYG5vBGHZo3rBhA7Vv316Ezvfu3VuY0j788ENTsxYILq++6k52X9XwqlBmspxBiRLyMRxdFobw+lT5guzk1PGz2Knu+JEMEoQz95hUzc8U9jpNAmuBYvmeEwUkITs7u0hrBMINO3IG1c/B7UKZyVbW3IaJzDkGhjknCG3rFLumLD+LneqKHVNimPueKsxNMo6o2J+V8/kBwC1093Pww4k1VeHLYcOsm3OC2tZWcGLKgiNycuyYEsPc91RgroYFdCH8ABBS4c7Kytowz6Qi7CUSnFaSD7KAni4oz6EHJzTV0KGquwLoZCcF4VpZc9ZoK+gUTOnV8+ZmJXmA8hy68KGmBXSh+ZGMbnZSEL6VNVeP+fXXxOacvDx9IpO8eN7iw7A5r8/atcHzNfMbRMXpwQ5NC+hC8xPwSIYgapWCeE0ysKqtYWGBSZQ7SZfIJC+eN7MCs7VrRzVmTirJg1MgKk4PqmlaQBfCj6J2Ut7+8heuZO98gg9i5e8gXpPslXWyhJCs1Xn0UXNzjpFSQAcNZarnjWG/BDvPGcKwvYf9RNjpvmLF4p/DlKjfONJUMe0whB9F7aRGevvbbnM2wQdxYA7iNemysmYBhzNNrFjBBX+jtcMYXWpDue2X4IUwBcwXOkOHnvI9YxMs16DeskUPoTsMlNI0bxWEH0nYtX/ameCDODAH8ZpUwI6TbmyiPy+Lpurgl6Crk6fuCx32PWNN0IIFss4MBMXZHw7PkrBr/7QTMhjE/BhWryk/38+zCgZhyDfjtl+Crk6eOqBr6HTY6aTZOALhR9FIhnSEFlUGZifFCBP9xuq5crm3nBxXTj/lOQWJoOebcTtySFcnTx0I4uItLJTSaByB2UtBO2kqUgkCKgzMThyTk/3G6rm6XW0cDtbBwG2/BF2dPHVAlcUbCDYQfhS0k6YilSAge2B24pic6jfs/G3lmho2lHsdKoGUAN75Jejq5KkDKizeQPCB8COZ2Cia114jOvPM9IUWmQOzE8dkK7/5v/8jeuqp4tfg5TX57WDttqACjZU58VFr/Oo0ckhHJ08dkL14A+EAwo9CdtLu3YkmT3Zngpc1MDuJgrH6mypV/LsmP6N53BZUdNdYeU1s1JrTJISGsHrsGNG0aUTLlqUvTIFT9wdaNeA1EH4Uw02hxc1Vrpf2eju/8eua/PI7cFtQ0S0lgI6muXhhtUULol69iLKykNHZLaBVA16DaK+Ahwz67X3vxF5v9zd+XJMffgdehPTqFCmjY107Q1iNv2eGsApzV3hDp4FeQPhRFJ1CBmNxElKsYgFDP87JC0FFl0gZVYWIZGkNkH/Gf3QdB4H6wOwFpNvrVbTx+3FOXggqOkTK+Gmas2NWS+V7hazOwUNHsytwBwg/QAl7vYo2fq/PyQtBRYdIGb+ECDuO5FZ8r2Rp1YwJmfscJmj3MOsf9eq5+AeA0kD4AZ7gxDFZhoN2Krw8Jy8EFRW1aPH4IUTYcSS3qomqWtV/rRqfpzEh9+6dfiQgSN4/tm+Pvi5ciJYKOhB+gFIhxW6EIbuNV+fklaCiohbNT9OcXbOaVU0U46dWzZigWWCLBSkL0sNK/3j4YZjAgg6EHwAk4pWgoqIWzS/TnF2zmlUN0+7d/mnVdEtZoBOp+gfD37uRwwuoC6K9AAhoSK/fkTJWC8AaGi/WarDQEDvBuyFE2DWr2dFEcXuyUGoWos/n7JZw6XYkYBiK81q9Vl0iIoG3QPgBQAF0D+m1m7PH0Hh5IUTYNavZTWvgR/4ZNydoHfMpOcXKteoQEQm8B8IPAEBKzh6vhIhUwgzDNfQaNXKuifJaWHVrglY1n5IXWL1WK/3D77xiKnEiJFpC+PwA4CFBzyOSrm9KrDM5D7I86KbbVskcyQ1+/pmodu1TUVOqOYm74RcVJr8hO9dqJdBgzJhgTvipmOtynUGVgfADgEeEYSDJz3cnZ4/bbZVImEkWNaWSk7gbkYBhSspo91oT9Q/jfbt2FDrmhqwgsiOz14kTJ2jevHn0r3/9S7y/6KKLqGPHjnT66bCiAbWQpcINi7lh5870fVO8aiv+zf/8T1SDwpoeK/XTVPK9MiboAQOKf27VLypMjr1OrtXM7HrttURLloTPFHTCgzqDgdP8fP3113T++efT7bffLgQg3nr16kV169alr776ypuzBEAjzUuYzA25uen5pnjdVmvXmgs+umg/eILeuDH6/ylT7GmjwuTY6/RareTwCoMG98MQaQkdCz933HEHXXLJJbRt2zb6/PPPxfbjjz9S/fr1qU+fPt6cJdAev31fOEOrLBVumAaShg3T803xsq24jy1frr/2w5iQud/aSbKpQ6kTt/DqWsNiCtoRIi2hY+Hnyy+/pNGjR1PFihWLPuP/jxo1ir744gu3zw8EQOB58MGohsDPlRObCmRpXoI8kBj3lM0xBun4pnjVVsZqfeRIa/vv2hUMTZxupU5UvtYwaXCrhUhL6Fj4YZPXLh4p4ti9ezfVqVPH1rEmTZokNEbly5cXW8OGDem9995L+ptZs2bRhRdeSGXKlKF69erRu+++W+z7SCRCQ4YMoWrVqlF2dja1aNGCvvnmG1vnBdInVlXMg86ePf6unOJLAvipeQnqQBJ7T7nOFGPUnXIaKeVFWyVarSeDBfSgmTJUjGLT6VrDpMFtGiItoWPhh7U+999/P82ePVuYvnjj/z/wwAM0duxYOnDgQNGWipo1a9KYMWPos88+o08//ZRuuOEG6tChg/ArMmPt2rXUtWtX6t27t9AysZM1b7G+RuPGjaOJEyfS5MmTaf369VS2bFlq3bo1HT161O6lAodYmXxUWDl5pXkJ4kCSrBAkf844iZRyu62SrdZTETRThoFKUWw6XWuQNbhh1hIWEbFJRkZG0XbaaaeJzew9vzqhYsWKkZdeesn0u86dO0fatm1b7LMGDRpE7rrrLvH/kydPRnJzcyPjx48v+n7fvn2RrKysyBtvvGH5HPbv389Dp3h1g4KCgsj8+fPFa9A5fjwSqVmTpx7r24oV7v19o62zswt8/bvxzJnDz0p0i/2bxmf8vc73lNvXaGe+nry86H6y24rvqZ2+F7+ley1eEKbxQ6W2ttqXvBxH/GbOnJLPOj8PXoxXXvVrq/O37dj0FSxKewCHz7NJ69ChQ8L8ZUZ+fj499NBDxT5jrc78+fPF/7ds2UI7d+4Upi6DChUqUIMGDcRvu3TpYnrcY8eOic3A0FoVFhaKLV2MY7hxLNVZs4Zo716i7Gzrv+GVk1tNY7TxeecVihVfonIFrBrnsFavbgnnCTHClGNNcKzl4ARq/L0u3cHsnmZnFxZ7ZbPm6tVETZrIbSvuS3b6nhnpXIsXhGn8UKmteXxgTw7WbsoaR/ymXTuiNm2i+bs4jQX7avJ0zBoft6/Rq35t9XgZLAGRB9xzzz302GOPUZUqVZLut3HjRiHssFnqjDPOoBkzZlAbbn0TSpcuTdOnTxemL4PnnnuOhg8fLvyQ2CzWuHFj2r59u/D5MejcuTNlZGTQm2++aXrcYcOGiWPEw+eSk5Nj46oBAAAAIIvDhw9Tt27daP/+/cKXOBGeZSV87bXX6G9/+1tK4eeCCy4QEWR8ouw7xPmDVq1aRRdffDH5xSOPPFJMo8San7y8PGrVqlXSxrMjiS5dupRatmxJmZmZFGRYS9C2rbV9jZXThg3u2ZJj23rx4syk2gTg/J6yxufll5fSn//cko4cifbpRYvka0vY54edsBOt1q2iwrWEcfxQsa05bYZX4wj3VzMtSxgo9KhfW/E39lT4sapQYm2OESV25ZVX0ieffELPPPMMPf/88yX2zc3NLRFpxu/5c+N747NYzQ+/v/zyyxOeQ1ZWltji4Rvi5k1x+3gqct11RJUrJy8aGCv88ABSpoz758Ht3KlTpufVt8NAsnvKgs/Ro5liMuD9ZLctP15jx55ywjYrUlqpEtEvvySv4O72tbiRITgM44cqxLa1VwV4rVSgDwOZHsyzWtb2OnnyZDH/m1jYPLY8LmsZS46Gj1CtWrWEABS7D0uBHPWVyI8IuIuVopIMR/D4EWprJYMrCFYkSLK6Tfz5Cy/4ey1hyBAcdNweR8KSPFFlpAo/bG5avXo1ff/998L3h9+vXLmSunfvLr7v2bOn+Mzgr3/9Ky1evJieeOIJ+ve//y18dThE/t577xXfs18Ph9yPHDmS3n77bXFMPkb16tVFSDyQO/mceWY0tF3HUNugV2dPV6BQ8V7Ga3aM937mvsEkFyzcGAfClDxRZaRWIuXEiCyc7NixQ0RlccLDJUuWCBsgs3XrVjrttFPyWaNGjYQT8qBBg2jgwIGinhhHel166aVF+/Tv319EjHGpjX379lGTJk2EwMRJEYF/2FEVq140EOpp83vKsL+Wao9WokKpRk4iQ8Dx2iQaxmKRQcatccBO8kRViuy6Qfw4z1FyUrEbQ//DDz+IfDrx8Gf8ncEZZ5wR2bx5c0RHkOdHbl4Jfu80r4TbuSOMHDRm+WB0y9cThtwzqfJM+ZnHx608Maq2dRBJ1NZujgMzZljrF7yfbhw/Hu3PfO78ajxnZuN8nTpy8/zYNnuxX83PJmWSf/nlF/GdwW233eZKpBQILqqbBKCe1g+VShKEKUNwkHF7HAhD+ZtuMb5t/fsnzg5vRNPJ4DQnUVzsWxPPwYMHi5mWuG5XqjB3EF50ECxUmkiBfgJHUCe5sOH2OBCm8jc//UQ0fnzycf7hh+WM85Z9fow8OCz4DB48uFjyP87OzBFVycLJAdDN7q3SRAr0EziMSS5R2gcjrF6nSS6MuD0OGNGTLCxwHzBLx6BS9KQbC9lk8DwgY5y3LPxwIVFD88NRVJyfx4D/f9lll4mkhiB5sjhOZqWiU6/f6CBY+DWRqu7wrRMqCRxBm+TCihfjgBFxaOZAzX1CxehJpwtZVcf50+3W9PrTn/4kkhDCn8c6bNPkAY6z5B45Et5kVqqu0GVOpIgkC7bAEaRJLqx4NQ74EXHoBztcEFxkjPO2fX6mTp0Kwcfm5NajR8nPVXHqlYUdu7esHDteJ/dT3eFbV/zM42P1fL7/PprfasYMPfNchRkvx4EgJGGtlqbgIsv0q1yG5yChg1Ov6gPKggVys+N6NZGib4RL4AjCJBdmVBOodVrIJsLYn0scyXgeIPx4CKKF0htQGBU0I15MpOgb3gOBAwRZoNZlIZuRQdSvX3Rcj8UY92UVmZaa4Tno6ODUK5tEdm+GNTyqZMc1JlIDwxTn1FaPvgGAfsSPA8C6b9vo0SUzPC9ZQtKA8BNyp15VBxQWLFQNhXfDSRl9AwAQJDqlcOCOH+cLC0kqEH58sIX+8ov598jzoZ9mJFHdKMMUZ9X+r1JINgAAhE0zBp8fn2yh8SDPR0lio7p27ZKvNYuPMisocM+B3etIMgAAAImB5sdjEmkBkOcjtSmJJ/5EgoTXmhGz8znzTCKTsnYlTHHDhhE1b57aDwg5YPQHCSoB0BMIPz7A3uzvvku0aBEyPJsxaxZR584lP08m+HipGUlk2kom+MQycmR0s+IHFJREZ2EECSoB0BcIPz7SpAlRZqaff1F92EeGc58kI14D5KXWLFn+HbtY9QPSyU4O3PX9AgDIAcIPkDqB3HKLNYHkqaeIzjrLe82IG3VqZIbkA+/NVakSVOKeA6A+cHgGUjAmEKuw4ONHdly3o8diQ/KBOkJ3OlnDkaASAJJWdsgtoPkBUrCrYfErF5LVv1OlCtGePdaPG+ZElkEzV8lKw8CTy0cfeesbBgduEBZ/N2h+gBTsTAxGgVOVCq7yZMnp7QcNsnbcsCeyVGF16VY9NVkJKuvV87bGXboaMRAO5gakIDOEHyAFOxODn/lurObfKV06aoLjsHar1emB3MnYLXOVVQHZrXu+cOGpycWrySYoExrwlhMBKtYN4QcoWwmYBZG33vJfjWqngjOSFXqDF5OxW+YqP+85TyIDBph/59ZkE6QJDXjLhy4tIFQAwg+QYrpINoEYzJxpLRpMdgVnO8ISkDcZu2mu8uue8yQSr/Fxe7IJ0oQWBFR2JN6haNkhJ8DhGUh1jDOrBMwmA6/y+NiBBTTWUBkh0fyayMkUyQrdw85kbCc/ktv11Py4535MNkGa0FTCifO46o7E1QJUrBvCD5AeWaNqhmO7AxGSFbqDV5OxoW3kvseCTmy/dGqu8vqe+zHZBGlCUwUnQowOiTObBqggM8xeQLrpwphA/MjjYxU4gMrDy8lYNxMlTyLx5+q2c7XfDtxBNyc5GTt08bsqFaCCzBB+QMIK5ukMFDr7EegyEAUVrydjO/5csuFJZOxYbyebIE1ossP4nY4dOo2XnTRbQCQCwg8wHRhyctIbKHT2I9BpIAoifkzGKmobkxVGZqpX926yCcqEJluL63Ts0G287KTRAiIR8PkJOYnszPErE7t2Z539CHQbiIJIImd4L4vaqs7GjUTr1nnnG6ey/51T/K7D5nTs0HG8LKV5QWYIPyHGTgVzuwOFzo5xOg5EQSSIk7Hqk43uE5pfkYNujx06j5e6ArNXiLFbX8uOuccL04VfDothcQDVgXTMUyrnSwHB1OI6HTvC4HelGhB+QozTB97q79z0I/Cz7hAGIv1Bnapg4VSQ9VuLm87YEWS/KxWRKvyMHj2arr76aipXrhxVrVqVOnbsSJs2bUr6m2bNmlFGRkaJrW3btkX79OrVq8T3N954ow9XpBdOH3g7v3PDMU5G2DkGIn1BmoJgkY4gK0OLm87YEQRHYl2Q6vOzatUq6tu3rxCAjh8/TgMHDqRWrVrRP//5Typbtqzpb+bOnUsFHIf9X/bu3UuXXXYZ3RJXB4GFnalTpxa9z8rK8vBK9CSVndktu3M6fgR+OyzGAp8T/ZDZX4D7pJv4z4vEll6PHUHzu1IVqcLP4sWLi72fNm2a0AB99tlndN1115n+plKlSsXez5w5k3JyckoIPyzs5ObmenDWwSHZwBCPLLuz3w6L8WAg0gvZ/QWoJ8jKihzE2KE2SkV77d+/31TAScaUKVOoS5cuJTRFK1euFIJUxYoV6YYbbqCRI0dS5cqVTY9x7NgxsRkcOHBAvBYWFootXYxjuHEsL3KI8MDAlaNjCyjygxtrV+eBYsyY6P5+XgavmrKzre3H56VyWweJdNuZ+1Z+PtHOnUS8RmnY0L1QYzv9RQfC2qfXrGHNfvL7uWcP0erVRE2aJD8Wj1tt2pj3udhmDWtby8CrtrZ6vIxIxIrBw3tOnjxJ7du3p3379tEa7vUW+Pjjj6lBgwa0fv16uuaaa0pog2rVqkWbN28W5rQzzjiD8vPzqZTJCDts2DAaPnx4ic9nzJghjgMAAAAA9Tl8+DB169ZNKFPKly+vvvBz991303vvvScEn5qsZrDAXXfdJQSaDRs2JN3vu+++o9q1a9OyZcuoefPmljQ/eXl5tGfPnqSNZ0cSXbp0KbVs2ZIyMzPTPl5YYO0Ay8G3307066/m+7Dqmx0LuQtEV3Foaz9w2s4LFxL16FHSlGGYVV999VRGY6d9pl49ou3bE+dLie0vOhDWPs3PfkwcS0IWLUqt+bFKWNtaBl61Nc/fVapUSSn8KGH2uvfee+mdd96h1atXWxZ8Dh06JDQ8jz32WMp9zzvvPNEY3377ranww/5BZg7RfEPcvCluHy9sVZHjMSZMNseVKVP8O7S1P1hpZxZI2MeGzaoPPsgrM/P93HBG5lPhWljsx8aYObia9RcdCFufZrdP9lRIlfiP94vtL0Z/SycxZtjaWiZezLPKh7qz0okFn3nz5tEHH3wgzFRWmTVrltDW3HbbbSn33bZtm4gKq4aUvFqHKsfjR/4LJMpzL0yZH9Wff/a+ZlpQ0xSwJiSoCRvNnjMnOXOQ3wlYRarmh8Pc2a9mwYIFItfPTvZEI6IKFSpQ9n+93Hr27Ek1atQQOYHiHZ05L1C8E/PBgweF/87NN98sor3Y56d///5Up04dat26tY9XB7wqucG3/M03vS9IaaZ94gmUB2RdJ1AVwpT9yLYbpDQFbCrk82YT0JEjweuHqZ4zq5Fa6YbFg3AhVfiZNGlSUeLCWDg/DycqZLZu3UqnnVZcQcWJENk36P333y9xTHZoZh+g6dOnC+fp6tWri9xBI0aMQK6fgJTc4AgQngy8FnwwkPpTN87LbLu6h7NzP2QfKU54F8QJ3epzlkqQRX4noJXwY8XXmkPW47ngggsS/pY1RkuWLHHl/EA4K6pjIPW/bhyD4o3h6od2ry+ZIIv8TsAuqO0FlEKFiup2BlLgjnCK4o3h64dWr+/ZZ1P7OqmwaAJ6oUS0FwBWS274oR3AQJo+doVTr7Pt6kjQ+6HV8+YIQYNEvk4qLJpAamIj8WQXYIDmByiFChXVMZCmT6qCksyZZxK99pqexRv9iAJUtR+6de1OzjtRMWMZBUyBvf7CQizfc6NArZHDiR36ZQDhByiH7FBlDKTpk0qI5W3yZKLu3b2P2nN7MvcrnFrFfujmtVsRkOMxtMHsCxR7n1RYNIHk/YXb3yzVBTv0u/3sWAHCD1ASFnC+/z6qFeBIFz+1AxhIgyHEejGZJ8pBlUgj4VY/jEfGhO72tSd7zpKRyNdJh/4WJuZazNdmJsz6AXx+QoobWVC9RmaosqxK0EFD5Xw7dtMZyIi+StTP3O6HqcYDr6490XPm1GdI5f6m09jrZ6qLWGHWz/Eewk8IQfI+a+gwkOqAivl2Uk3mzJ13csLVU2Y5WeHUXOvs3XejNaw4D6zb/dDKeODltcc/Z7t2FXdytuszpGJ/C9vY+6GDVBd+O+5D+AkZOibvk7lSUnkgBd4Ozr/8QtSixanJKab2sZRBnIt3ul1uyup44HXkWexzxs/7E0/Ijfj0Ah3HXqc46Qd+O+7D5ydEWFntyrC9JgO1eoDswdmYnL75Jljh1HbGAy8jz+IdzpmgOS/rOPamg51+ICsSD8JPiNAtaZodB0tjAOXVk/EehJdUEVx2BmdjcnrxxagzrUrRV+m0CycPtDoeeBV5lmhxw/ztb0RxlY3Ee/5cNw2JbmNvutiN5JMhzEL4CRE6JU2zs1KKHUB7945+V6+enPBJoIe20O7gzH2OJ68+ffTVSMS3ixW/GmM88CICMtni5uabicaPLym08vsJE/R7tnUae93ATiTfq6/KEWYh/IQIVZOmpbNSGjXKfADdvt390GOgPla1hU7DrOvW1TOc2k7YcaLxwM1QciuLm2ToZiLSaex1i0T9hZOb8v1jB37DoV8GcHgOEXv2pN5HFbW91RUQT2CptEO6Fn7UGRlO6lYmVNbcGBFcTsKs+Vr4tzpFAdoJO07lWOxWBKSTaCDZodG6l+2RQack/aWwMBrFKAsIPyGBB0Aram6OslBhEK9a1dp+HJETpEEyCMgK57Uyoe7dWzyCyxic2Q+mc+fE/Sl+ctIpCtCJoJHMlOXGtbth3tHJRGRoGln7xm0bKwDpYDJNB1WfFZi9QlAjyM4AyCpJFSbPXr2S78MDRqVKwRskdcfPDMhuRHDx+fDg3Lx51KHZKL0Ri6qTk9Wxw0n/99qM54Z5RzcTETJQqwWEn5CEcevicGfFN8GYjFi7EMRBUldkh/M6ieCKPZ9kk9Nbb0WF7ddfjwpB/OrlYsXNscNquzz1lH+lZJzU9dIpqk7Fsj2gODB7hSThlQ4Od1Z9E3hyYhUymyt4tR42O7qqyMqAbNWvItn58G/5lRMZTpsW/X737ujzwMUY2WRsdm0ysvPaHTus+pvcd5+/yUOTmYGM90E0EalqBgob0PyEZIWsYoVop6Y5npx4cE8VscNt+eST+g6SuplfZWsXnUZwLVhQXIvCPkFsds3KivoA3Xpr4n7Jn/sZVehk7FC1UG8yTducOdFNt6g6oA8QfkKS8ErVAdDJpMgr8lQDqAGv2BHu7o/51Y520Stft1T9wQzu94l8lDg6TKXQa6djh6r+JsnMQDARAS+B2UsCslbIqlcqd2qa4/PmiYejdeIJYt0cVc2vVs0rbEZi4cqraDCrEVwMC/tmQotx/hwdlgpD4OCMyWed5W3oezpjh6qFepOZgWAiAl4BzY8EZPrfqLyacmqa48nroYfMfxPEujmqml+taBe7dDE3I7kdDWY1gsvNPsFaRq8DF9IdOwxhomvXU9XqAQgjEH4kINv/RtUB0KlpLmx1c9zCi3ZLFTHFZi4/fd2SnQ//La/wKrRf9tjhZ3oOALwEwo8EdPC/kYUT3wTZjra64lW7JdIuVqkiR0hNdD5sAvIKr4Q52WOHn+k5EgHhC7gBhB9JqOqAqAJ2TXM6hPGriJftZqZdlCmkmp2PFS1K5crO/6aXwpyMsUNmAkuVhC8QDODwLBFVHRBVwI6jY6yjrRnI95O63fzIk6SakGql5MALL0Rf7dT/8kOY83vsSOUfxu3ldR29dJzzZdSaA2oD4UcyiGZwfxKLJexmRJXqDalY3NFqBKQhaPC5c7Qal4Exkh/KEub8HDtkJ7BMR/iSVWsOqA3MXiAQGJNY9erFP4cZUR0Timx/lXTMrIag0b17dJLlV86ILNv52C9k+9U5dc5XwVQH1ASanxATNFUwT1Zt2hAtWUI0ZUowrskP/DShqJpryokWJR3NmW7PnmyTpRPhSwVTHVAXCD8hJaiqYGMQ4wkpM1P22eiDnyaUIPm6ORHmdHz2ZJssnQhfsk11QG0g/IQQv4uqAhBkXzc7wpyMZ88NLZPf/mFOitayH1ajRuqY6oDawOcnZMgoqgpA0LGSOFTGs+dmaLjM9BxWitayA3rt2qeuTbapTlWQJ0kB4Wf06NF09dVXU7ly5ahq1arUsWNH2rRpU9LfTJs2jTIyMoptZcqUKbZPJBKhIUOGULVq1Sg7O5tatGhB33zzjcdXowfIhhycgWv58uiGTLt64Pez54Wzr8zyOFaK1sZemwrZsFUDeZIUEX5WrVpFffv2pXXr1tHSpUupsLCQWrVqRYcOHUr6u/Lly9OOHTuKth9++KHY9+PGjaOJEyfS5MmTaf369VS2bFlq3bo1HT16lMIOVMHBGbhatIhuSPamB34+e15qmWSWx2EBaPPmqInLjNhrY1SMLpQFIt8UEn4WL15MvXr1oksuuYQuu+wyodXZunUrffbZZ0l/x9qe3Nzcou0sLqUco/V5+umnadCgQdShQweqX78+vfLKK7R9+3aaP38+hR2ogoM1cMWC8F218fPZC7KGd+3aqInLyrUhk34UuDso7vC8f/9+8VqpUqWk+x08eJDOOeccOnnyJF1xxRX0+OOPCwGK2bJlC+3cuVOYugwqVKhADRo0oPz8fOrCZaXjOHbsmNgMDhw4IF5ZE8VbuhjHcONY6XLttUR16hBt3544aoNz5Rw/HjWn5OYSNWyoz+pIpbZ2c+AaMIAozrprCt+/hx+Ohvx7ec+C2M4qPHts0uH9YpvVSVuz9ig729p+ut1Cu9fWrl30ecjPJ9q5s/iYFn/tQe3Xa9YQ7d2bvN327CFavZqoSRN/zsmrtrZ6vIwIq0oUgAWZ9u3b0759+2gN36kEsADD/jus0WFhacKECbR69Wr6+uuvqWbNmrR27Vpq3Lix0PSwz49B586dhcbozTffLHHMYcOG0fDhw0t8PmPGDMrJyXHxKgEAAADgFYcPH6Zu3boJ+YBdZJQXfu6++2567733hODDQowdKe+iiy6irl270ogRIxwJP2aan7y8PNqzZ0/SxrNzjuzT1LJlS8q0kHyGV/pmq5REnzth4cKoNiG2HhYr3H75peS+hn381VejqyiVsdvWOsBOnr172/sNJ3lkM5lXBLGd/YKfvfvvL/ms8fM3cWLJZ8xJW/NYUa9eai3Thg36aHX9uLag9mvWJ7Rtm3q/RYv81fx40dY8f1epUiWl8KOE2evee++ld955R2hw7Ag+DDfa73//e/r222/Fe/YBYnbt2lVM+OH3l19+uekxsrKyxGZ2bDdvipXjJUqAxs6FbIZyKzFafG6SqlWJbr+d6MgR8/11y4bq9r2TCXfjRPcl2W/8uPwgtbOfmE3c/FmyXD922pp3Gzv2lABslpdnzBhrplTV8OPagtavr7uOqHLl1Ekqr7vO//Hdi3lWeYdnVjqx4DNv3jz64IMPqFatWraPceLECdq4cWORoMPHYAFoOccAx0iCHPXVkFUlGjq18vvx492vTxMbtcH/T1QVXXcHSd1JFbIb9vBdnfDT8TQozr5meWmCcm1+oWpdPZlI1fxwmDv71SxYsEDk+mFHZcNBmfPzMD179qQaNWqInEDMY489Rtdeey3VqVNH+AeNHz9ehLrfcccd4ns2bT3wwAM0cuRIqlu3rhCGBg8eTNWrVxd5hHQcFBPhZn0ahMCrS7LsurGEdRDTCb9LLuheSiRVKRCdr81v/Kyrd0KD2nVShZ9JkyaJ12ZxT/nUqVNFCDzDoe+nnXZKQfXrr7/SnXfeKQSlihUr0pVXXin8fC6++OKiffr37y9yBfXp00cISE2aNBFh9fHJEHUaFL0eLBECr+fAFYvs4qBAzUWGrqVErJYC0fHaZOGHwDhXk9p1UoUfK77WK1nPGcNTTz0ltmSw9oc1RLzpQrqDXbq/l124EDjz02J271Z3dQWKg0WGNVCR3Tt4jGja9NQ4wq9ujR061Y1UwuEZpJ/YLN3fyy5cCIK9igdRsMiwBiqye4dXmpkTKfzZVAuaQWFTDZ1avXJwhRMhCHKBRRUKOsLx1BrwQdSvxMWHFv3Z+NnjjbVAjKwi2hB+FMFK1eJ4vNDIyCxcCMKD3wUWVSroqPMiwy8BEuZB/SINd1h0vejcOfr8GbnLOGeTjOcQwo9CJBoUWbPTr190cPRjsJRZuFDH1TxQu8CiigUddVxk+ClAoiK7+3hd762aRdeL+OSeRn4rv59DCD+KkWhQHDdOv8FSxmDMqwigLn4XWFS5oKNOiwy/BUiYB/UzJTZ16Loh6zmE8KMgiQZFnQZLWYMxryKMEgJAPfyuNh7k6uZ+IUuA1Nk8qCJemxJLOXDdkPkcQvgBgRyMubI5TGDq4bcjKxxn9RYgdTQPqoofpsROCQRWLq3hd36rVCDUXSN0yJqpSkJI/t6tLLlAX0dWOM7qL0AivYN77ehHOpNOJokUee5q0cK/594KEH40QZesmWEYjIE+eW6QVyd9IEAGB54r3nqL6J57iH7+2bvs8PECKws/qiXRhdlLA5IVPJUVrSITDMb64rcjKxxn0weRV8GB54oHHywu+FSpQvTEE94uolV8DiH8KE6qgqf8eZ8+4fJvsRJVgFIc6qYP8NuRNUiOszJSO6g4cQH3FtF79xLdeqv3i2g2hQ0bRlSxYvHP+bmU8RxC+AmAfwt33lGjKDRYGYzHjMFgrHIuF78dWYPgOMsRjLISNQZJgAwjslM+zP3vuDJ06Kk8P4YQtGGDnP4D4UdxrPqtsDAQJu1PosHYeN+unZTT0hoZuVz8TN2ge6qIHj3kJmoMggAZVmRG7M1NMK7s2xd9ffddkgKEH8WxkzUzbLlKzAZjXkUA/VaGIDFGm6twb3QXIMOKrCCREwqnJUG0lwb+LZUqlUwJbkYYo5viowoKC0kLVEtbgCra6pKfn/z72FW7jqkdVHsWgoisIJEPFU5LAs2P4vAgwJKzFfzMkRAUZDiQqlJkM/baly+39pswCtiy2bkzuPdGlWch6MiK2NuhcFoSaH404NFHiSZOjDo2myEjR0JQcyedeSZR9+7RyIRGjYjWrnV3RWrYv+PVwIbvhl/Oo2bXbgUI2P5rPHJziQ4cCN69UeVZCAN+JTjUKS0JND8awB3yhRfMv0OoqbtOeJz/ggcBXoHm5Li7IlXFrybRtSfDq5VhWLGj8WjYMPrq96rdS1R5FsKEjIi9pgqnJYHwowncMefMiXYUlUNNZZiR3M6dFLufm5E1KhTZtHrtsUDAlhtVF7saD0qeHRWehTDid8ReKYXTkkD40QjVQ011sd9bccIzI90VqVf2bzsCp5NrV03A1pl0NB6vvhqcPDsq+4IEHb8j9jol0Dj97nfR1zZtSAoQfoCWOWLSIZ0BNZ0VqRf2b7sCp9VrHzRITQFbd9LReHDuKpUXP0HxBQHeLdyHD49GLzO//hp9rVdPzvwA4UcjVNWs6Ga/d2NAdSJAuR1x4UTgtHrtzZsjl4uKGo+g5NlBvbDwsWBBtLxFfNqW7dvlLJAh/GiCypoV3ez3VpzwvBCg3KyR5FTgxKQjF2g8oqBeWLh8Lk8ouECG8KMBKnYcne33yQbeVKQbWeNWxIVTgROTjlwgfJ4C9cLCYRlQdYEM4UcDVOw4uq9mEw28yXArssYNx/V0BE4Zk46qK1Ivz9XsOBA+kz8Ly5YRTZ1KdOyY+v1EJVS2DKi6QEaSQw1QseOYrWb5QTPTTqmahJEHXk5myEIj26Nfe41oz55T3/NEFTv48jWw4OOGcBBflsNvgTP22r0uK2CWUJHbkrVvidpSVskDJ+fq5DgsZJp9b/Sv2OvnJIdBxngWuM169Uq/7cNGKssAj79sGeDnXZaPWDUVF8gRUIL9+/dzNxKvblBQUBCZP3++eHXCihXchVNvvJ8s5syJRDIyolvsORmf8fd+kE5bHz8ebcMZM6Kvx44Vf8/fqwKfS82aJds7tt3z8rw7Z6vtbPQLs/NL1C/4M7622P35vdd9yMm5pnOc+P5m3Kv468/Ojrb1nDnOxg8dcKvtZY/VMtBhfjhuMl4Z/Zpf3RyvrM7fEH7SaDy/HijZE51VzCYtPi+/Bi5dBy8dBU4r7Wz020SDsVm/TTQJGtvw4d70cyfn6sVxzK4/dpJ44AH1BPF0SbfNEgmRYRk/+LqtCD+8n0rjVfZ/+3VOToGr45XV+Rs+Pxqgi5+A6kkYg4bqDqN2fdWsZJ8eOpTonHPc92Fwy68uneNYuX6j9IoqjqxukE6bqezkG2qTko3xit/LGK/g86MJVvwEVCBdX5Yg4Ke/ip++O177qlnNPu1F4Uu3/OrSOY6d7NtBKv7ptM1QGFU/n8tOceMVs2EDUZky/p8LND8aAc2K+shYiaqa+M7uitSuw76b6R3cWj2ncxw7169Cigu3cNJmqqf/8BNdLAPx4xUL78Z7GUgVfkaPHk1XX301lStXjqpWrUodO3akTZs2Jf3Niy++SE2bNqWKFSuKrUWLFvTxxx8X26dXr16UkZFRbLvxxhspCKg60QH1w01Vz2ljRy3vdnoHt/LvpHMcu2YJ2Sku3MJJm6me/sPv1Aqqm8BVRKrws2rVKurbty+tW7eOli5dSoWFhdSqVSs6dOhQwt+sXLmSunbtSitWrKD8/HzKy8sTv/mJZ5gYWNjZsWNH0fYG9ywAPAIr0fRXpE4yb7tVBNat1XM6x3GaeVyV5KFOcdJmqqf/kKEphmXAJhGF2L17t/DSXrVqleXfHD9+PFKuXLnI9OnTiz67/fbbIx06dAhMtBdQv611CDeV1c52ogBTRXul055WQujdilh0ehyzCL7YaK8g9yk7bebV8+bn+KFKeL8svGprLaO99u/fL14rGWVfLXD48GGhMYr/DWuI2JR2wQUX0N1330179+51/XxB+LL/JiIoK1GrGPeIVeqp7pmdFamhvmcNSDK8KgLr1urZ6XHsZB5Pt9SKathpM93LhEBTLB9lor1OnjxJDzzwADVu3JguvfRSy78bMGAAVa9eXfj+xJq8OnXqRLVq1aLNmzfTwIED6aabbhJmslIm+uZjx46JzeDAgQPilYUq3tLFOIYbxwoaCxfyPYxOQgY88I8dS9SunT5tzVl4s7Ot7ad7N+B7NmRIIY0aRXTvvYV05Ii1e9a48an/nzwZ3czgY7RpQzRhAtHjj5f8PtYUkuw4sRMN97FEESV8vIcfjv5NY3iweq6pcHIc4/rz84kWLeJyD9EOk51d6LgNdMJqm7GprEeP6P9jHZ/TaRu/xo81a4h4PZ5szOBs86tXEzVpQoGk0KO2tnq8DFb/kAKwdua9996jNWvWUM1Uy77/MmbMGBo3bpzQ8tSvXz/hft999x3Vrl2bli1bRs2bNy/x/bBhw2j48OElPp8xYwbl5OTYvBIAAAAAyICtQd26dROWpPLly6st/Nx77720YMECWr16tdDWWGHChAk0cuRIIdBcddVVKfc/88wzxf533XWXJc0PO1Lv2bMnaePZkUTZobtly5aUmZmZ9vGCAK/G69UrrvGJhVdvrE3gHBB2ItqstrXbGifjmMlWoq++6vzYqt0z1kK8/PJS+vOfW9KRI5lp3TMrf5e1IDt3RjVnDRvaOz6bkXr3Tr3flCmnwm9VwujT5cq1pF27Mh21QZBJt3/IGKtZ89O2ber9WPMXZM3PUg/amufvKlWqpBR+pJq9WO667777aN68eUJ7Y1XwYW3PqFGjaMmSJZYEn23btgmfn2oJYkmzsrLEFg/fEDdvitvH05mPPiL69tvk+3zzDdG6dc6SJiZr60TJ0TZvTi9xnPGb+ESU7HugUiJKN+8ZCz6G8JPuPUsE30aOgnEKP/ZsmrOyn8qPZ9OmGD+86B/mxyzZ1m4mL73uOqLKlVMnJuT9gi7kZnowz1pBqsMzh7m/9tprwrzEuX527twptiMxI1XPnj3pkUceKXo/duxYGjx4ML388st07rnnFv3m4MGD4nt+7devnwif//7772n58uXUoUMHqlOnDrVu3VrKdQJ1HIS9djR06uiqg9O3rk7dujvHguAlL9UtMWEQkSr8TJo0SaimmjVrJrQyxvbmm28W7bN161aRpyf2NwUFBfTHP/6x2G/YDMawQ/OGDRuoffv2dP7551Pv3r3pyiuvpA8//NBUuwPCVY/Gj+RodhNR6lKfSJcaQulONDoIol4Qtuu2er1eJS9FYkK5SDd7pYLNYbGwNicZ2dnZwhwGUpNIjetHbSpZ9WhU017oVJ8o9p6ZoVINIae18fh+mO3DwpMq98ELwnbdya43dqxLpSnmPs+aYq5X5WSMVLk2X9BRKs8P8I9E2ob+/f3RQshS+6qkvdAt14fuqvpUJslEK3x+f/PNRA8+GEyNSNjKsiS7XiNgQWVNMXAHCD8hJNkgP368f4OgDLWvSv4fOtYnMu5Z9er61BCKNW9wW/K9jZ9okgmiBizYqWqSDIsA7sf1GvupqCkG7gHhJ2Q2dyuDvJ+DoN/1aFTSXug6sPK92bjxVHi41/csHaz6U6USRIOqEdFRAPf6ehkOnVdNUwzcBcKPIvjl9GpnkPdrEPRb7auKo6HOA6txj1gIcOOeeSH42zHn2BEwg6QR0VUAd4rV6+CcQappioG7QPgJmc093UEsKIOgChWQMbB6J/jbNefYFTCDohHRWQB3gtXr4GSJqmmKgbtA+AmZzT3dQSwog6AKjoYYWL0T/O2ac1IJokFdDIRNALdyvQxniVZNUwzcBcJPyGzuTgd5XQdBP3OXOPlbYR5YvRT87ZpzkgmiQV4MhE0At3K9xn6qaYqBu0D4CZnN3ckgr+sg6GfywHT+VlgHVi8FfyfmnESCqBeLAZUSCropgKt0XU6ul+vvqaopBu4C4SeENvdEDz8P5v36RQcB3bUQXGTULz8qN0w3YRxYvRT8nZpzYgVR1joZ+8b/lnnyyahgZneiVzGjtxsCuIrXZfd6dS48DGzCVd1Bcfbv389Kd/HqBgUFBZH58+eL13iOH49EataMRDIyeJ1bcuPP8/Ki+7kNH3PFikhkxozoq/E3En2uA0Zb16lTYNqebrepcf/8+FsqkaxPW4X7VqJ2i914PyfMmRNt//hny/iMv7dyjPj7y/ezX7+Sn/P7VMc0zsmsnyQ6Jzfa2mucXJeK6NDWQaHAo7a2On9D8xNim3sibUMQtBCJSjC47UcVtjwpOjnbumHOMdMQPPEEEZcStKvpC2pCQRWvSwfzG5ALhB8FCLPTq0zc8KMKW54U3QR/N8w5sYsBFsQeesjZRB9UQVm169LJ/AZCWtgUnAIF7vzHDT+qsOVJkVVwNBa7hXcN4cXviT7+bwZVUFbpunQqFAzkAuFHEokGcLcG6bDDWrTNm+1XjLc7scqqTh9WwV929fF0JvqgCsqqXJfXFdhBsIDZSwJQy3rP2LH2zSlO7kvY8qR4hRU/My8SItr1DUlnog9qQkGn1+W2X45q5jegNhB+AlzKIsxwyKodP6p07gt8tvR0qnUi7KYjwARVUHZyXV4sAFUyvwH1gfAT8qiIIGPV2TXVfeHtL38hev31xCvUsCYq9Au3V/VOhd10BZigCsp2rsurBaAq5jegB/D58ZH8fOfOksAZVvyorFS6//lnottuS+5jAp8t73C6qjfz4WLS8Q1x4qTt1MdJJ6xcl5d+OfC/A3aA8OMjO3da2w9qWX+x295Bixyx6+QtAyer+kTO0Xfemf4iJF0BJqiCcqrrSidazsrf5kUJP5ssRMUKWDqbFYE3wOzlI7m51vaDWtZf7LZ3kEyUujjf2/W1SWZaGTrUHaE4CMlA/cZrv5ygmhWB+0D48ZGGDYMZ7aE7TirdByFyRCfnezu+NlZ866yARYj7+OGXA/+7xCDz9Skg/Cg0gPPAfMcdRG+9hZTsqtyXoJooZTvfOxmEra7qrfhwJQOLEO/wK9wfWjl9tbx+AeHHZxIN4JUqEVWuHFXJo2Oqc1+Cqh2QmRMlnUHYyqrejkAapJBzHQhquL/qmhadtLx+AeFHAvED+PDhRL/8QrR3b/H9wtwxZd+X114jOvPM4JooZeVEcWMQTrWqtyqQ8nOnkm+IKhOl14TFL0cVTYtsLa+qINpLEsYAzh2OHwikZFcvWiU7O7iRIzJyovhVfsAwraQyfV18cVTYVSHSLVnZDk7YGbSIQr7HQQz3V7HGmJcRdjoDzY9kkJJd3RV1kFeoMkot+NXXeQJ98snU+3F1dkZ2xFYqbdjChRRIDciCBfLbXkVNi9saQGS+NgfCj2TQMf0feHmVycKLzpEj6Q6QMnwv/OzrbLJMhQrRelYmyocfJm0Jo69JOkK+F6YyZL42B8KPZNAx/R94OVvzLbcQ9e+vZ+SIWwOk35otP/u6LosKKxNlOpFrMgmrr4nTvueVoBjUgrrpAuFHMuiY/g+8BuPHE82aRVrh9gDpp2bLz76uy6JCtvDlJWE16Tvpe1brCxYU2D+fsEXYWQXCj2TQMeXUUTPo21efladXK2m/NFt+9nVdFhWyhS8v0UX75jZO+p7V+oJ8XCcaoCD7LzoFwo8CoGPKq6PGA4ouK88grKT96uu6LCqsTJT8vY7oon1zGyd9z6oAyOOVUxOYqv6LsoDwowjomHLqqOm08gzKStqvvq7DosLKRDlmDGmJLto3L7Db9+wKgE59pVTzXwyt8DN69Gi6+uqrqVy5clS1alXq2LEjbdq0KeXvZs2aRRdeeCGVKVOG6tWrR++++26x7yORCA0ZMoSqVatG2dnZ1KJFC/rmm29IddAx3a2jZiXih9GgawRuJe1XX9dhUZFqotQ1z48u2jevsNP37NQX1EHDqwNShZ9Vq1ZR3759ad26dbR06VIqLCykVq1a0aFDhxL+Zu3atdS1a1fq3bs3ffHFF0Jg4u2rr74q2mfcuHE0ceJEmjx5Mq1fv57Kli1LrVu3pqNHj/p0ZUA2PKA+95y1fV98UQ+/nzCvpIO+qNBBSAuq9k2FvhcrKFpFdQ2v8kQUYvfu3ey2GVm1alXCfTp37hxp27Ztsc8aNGgQueuuu8T/T548GcnNzY2MHz++6Pt9+/ZFsrKyIm+88Yal89i/f784D351g4KCgsj8+fPFK/CW+La+9VYjViL5tmKFHndmzpxIJCMjusWev/EZf+8H6NP+EYS2Pn48+ozNmBF95fcqIrut+fmtUiVYY5bfbW11/laqvMX+/fvFayWu8pmA/Px8eshIzfpfWKszf/588f8tW7bQzp07hanLoEKFCtSgQQPx2y5dupQ45rFjx8RmcODAAfHKmije0sU4hhvHAvbamlPov/22tVWUDreHTSC8Yh4wIBreHruSZt8Q/t6P60Cf9o+gtHXjxqf+f/JkdFMN2W3Nz2/r1kQXXUS0Z09iDS9r0q69Vo8xy++2tnq8DJaASAFOnjxJ7du3p3379tGaNWsS7le6dGmaPn26MH0ZPPfcczR8+HDatWuXMIs1btyYtm/fLnx+DDp37kwZGRn05ptvljjmsGHDxO/jmTFjBuXk5LhyfQAAAADwlsOHD1O3bt2EMqV8+fIJ91NG88O+P+y3k0zw8YpHHnmkmDaJNT95eXnC/yhZ49mRRNmnqWXLlpSZmZn28YD1tmZfnnr1iLZvN8+PY6yiNmxQ0xdEVdCn0dZBRKV+zTXdkml4dafQo7Y2LDepUEL4uffee+mdd96h1atXU80USS1yc3OFhicWfs+fG98bn8Vqfvj95ZdfbnrMrKwsscXDN8TNm+L28UDqtubmHjs2mhuDMavOzoNJmTJoTSegT/sH2jpcbc3O4Gy256guNsvzdMbBDEFbpGV6MM8qH+3FFjcWfObNm0cffPAB1apVK+VvGjZsSMuXLy/2GUuP/DnDx2ABKHYflgQ56svYB4SLsEecAAD0RIdIRV05Xbapi/1qFixYIHL9sKOy4aDM+XmYnj17Uo0aNUROIOavf/0rXX/99fTEE09Q27ZtaebMmfTpp5/SCy+8IL5nv54HHniARo4cSXXr1hXC0ODBg6l69eoiJB6Ek7CsogAAACgu/EyaNEm8NmORNoapU6dSr169xP+3bt1Kp512SkHVqFEjITANGjSIBg4cKAQcjvS69NJLi/bp37+/yBXUp08f4UDdpEkTWrx4sUiKCMKLsYoCAAAQbqQKP1YCzVauXFnis1tuuUVsiWDtz2OPPSY2AAAAAIBYUNsLAAAAAKECwg8AAAAAQgWEHwAAAACECgg/AAAAAAgVEH4AAAAAECog/AAAAAAgVED4AQAAAECogPADAAAAgFChRGFT1TCSL1qtDmuleu3hw4fF8WQXyws6aGu0c9BAn0ZbB5FCj+ZFY95OlUQZwo8Jv/32m3jNy8tz7YYAAAAAwL95nOuEJiIjYqXGRMg4efIkbd++XRRb5VIZbkiiLEj9+OOPVL58eVfOEaCtZYI+jbYOIujX+rc1izQs+HAx89i6oPFA82MCN1jNmjXJbfgGQ/jxB7Q12jlooE+jrYNIeQ/mxWQaHwM4PAMAAAAgVED4AQAAAECogPDjA1lZWTR06FDxCtDWQQB9Gm0dRNCvw9PWcHgGAAAAQKiA5gcAAAAAoQLCDwAAAABCBYQfAAAAAIQKCD8AAAAACBUQflziH//4B5177rlUpkwZatCgAX388cdJ9581axZdeOGFYv969erRu+++69apBB47bf3iiy9S06ZNqWLFimJr0aJFynsD7LdzLDNnzhSZ0Tt27Iim9KBPM/v27aO+fftStWrVRLTM+eefjzHEo7Z++umn6YILLqDs7GyRkfjBBx+ko0ePom8nYfXq1dSuXTuRZZnHgvnz51MqVq5cSVdccYXoz3Xq1KFp06aRp3B5C5AeM2fOjJQuXTry8ssvR77++uvInXfeGfnd734X2bVrl+n+H330UaRUqVKRcePGRf75z39GBg0aFMnMzIxs3LgRt8Lltu7WrVvkH//4R+SLL76I/Otf/4r06tUrUqFChci2bdvQ1i62s8GWLVsiNWrUiDRt2jTSoUMHtLEHbX3s2LHIVVddFWnTpk1kzZo1os1XrlwZ+fLLL9HeLrf166+/HsnKyhKv3M5LliyJVKtWLfLggw+irZPw7rvvRh599NHI3LlzuXxWZN68ecl2j3z33XeRnJycyEMPPSTmxGeffVbMkYsXL454BYQfF7jmmmsiffv2LXp/4sSJSPXq1SOjR4823b9z586Rtm3bFvusQYMGkbvuusuN0wk0dts6nuPHj0fKlSsXmT59uodnGc525rZt1KhR5KWXXorcfvvtEH48autJkyZFzjvvvEhBQYH1GwoctTXve8MNNxT7jCfoxo0bo0UtYkX46d+/f+SSSy4p9tmtt94aad26dcQrYPZKk4KCAvrss8+EOSW2Nhi/z8/PN/0Nfx67P9O6deuE+wPnbR3P4cOHqbCwkCpVqoRmdbFPM4899hhVrVqVevfujbb1sK3ffvttatiwoTB7nXXWWXTppZfS448/TidOnEC7u9zWjRo1Er8xTGPfffedMC+2adMGbe0iMuZEFDZNkz179ohBhwehWPj9v//9b9Pf7Ny503R//hy429bxDBgwQNih4x80kF47r1mzhqZMmUJffvklmtLjtuYJ+IMPPqDu3buLifjbb7+le+65Rwj1nDEXuNfW3bp1E79r0qSJqBZ+/Phx+stf/kIDBw5EM7tIojmRK78fOXJE+Fu5DTQ/IDSMGTNGOOPOmzdPODsCd/jtt9+oR48ewrm8SpUqaFaPOXnypNCwvfDCC3TllVfSrbfeSo8++ihNnjwZbe8y7ITLWrXnnnuOPv/8c5o7dy4tWrSIRowYgbbWHGh+0oQH+1KlStGuXbuKfc7vc3NzTX/Dn9vZHzhva4MJEyYI4WfZsmVUv359NKmLfXrz5s30/fffi+iO2AmaOf3002nTpk1Uu3ZttLkLbc1whFdmZqb4ncFFF10kVs9s2ildujTa2qW2Hjx4sBDs77jjDvGeI3MPHTpEffr0EQInm81A+iSaE8uXL++J1ofBnUsTHmh49bV8+fJiAz+/Z7u8Gfx57P7M0qVLE+4PnLc1M27cOLFSW7x4MV111VVoTpf7NKds2LhxozB5GVv79u3pD3/4g/g/hwcDd9qaady4sTB1GQIm85///EcIRRB83OvXho9gvIBjCJ1RX17gBlLmRM9cqUMWPsnhkNOmTRNhen369BHhkzt37hTf9+jRI/Lwww8XC3U//fTTIxMmTBDh10OHDkWou0dtPWbMGBHaOnv27MiOHTuKtt9++83dThDydo4H0V7etfXWrVtFxOK9994b2bRpU+Sdd96JVK1aNTJy5Mg07ng4sNvWPDZzW7/xxhsiHPv999+P1K5dW0TsgsTw+MrpRXhjMePJJ58U///hhx/E99zG3Nbxoe79+vUTcyKnJ0GouyZwXoKzzz5bTLQcTrlu3bqi766//noxGcTy1ltvRc4//3yxP4f4LVq0SMJZB7+tzznnHPHwxW88qAH32jkeCD/e9Wlm7dq1Ij0GT+Qc9j5q1CiRagC429aFhYWRYcOGCYGnTJkykby8vMg999wT+fXXX9HUSVixYoXpuGu0Lb9yW8f/5vLLLxf3hfv01KlTI16Swf94p1cCAAAAAFAL+PwAAAAAIFRA+AEAAABAqIDwAwAAAIBQAeEHAAAAAKECwg8AAAAAQgWEHwAAAACECgg/AAAAAAgVEH4AAIGhWbNm9MADD8g+DQCA4kD4AQAAAECogPADAAAAgFAB4QcAECi4Unf//v2pUqVKlJubS8OGDUv5G67yw/udffbZlJWVRdWrV6f777/fl/MFAPgPhB8AQKCYPn06lS1bltavX0/jxo2jxx57jJYuXZr0N3PmzKGnnnqKnn/+efrmm29o/vz5VK9ePd/OGQDgLyhsCgAIlMPziRMn6MMPPyz67JprrqEbbriBxowZk/B3Tz75pBB8vvrqK8rMzPTpbAEAsoDmBwAQKOrXr1/sfbVq1Wj37t1Jf3PLLbfQkSNH6LzzzqM777yT5s2bR8ePH/f4TAEAsoDwAwAIFPGam4yMDOEHlIy8vDzatGkTPffcc5SdnU333HMPXXfddVRYWOjx2QIAZADhBwAAiITQ065dO5o4cSKtXLmS8vPzaePGjWgbAALI6bJPAAAAZDNt2jThK9SgQQPKycmh1157TQhD55xzjuxTAwB4ADQ/AIDQ87vf/Y5efPFFaty4sfAZWrZsGS1cuJAqV64c+rYBIIgg2gsAAAAAoQKaHwAAAACECgg/AIDA8/rrr9MZZ5xhul1yySWyTw8A4DMwewEAAs9vv/1Gu3btShgaD8dmAMIFhB8AAAAAhAqYvQAAAAAQKiD8AAAAACBUQPgBAAAAQKiA8AMAAACAUAHhBwAAAAChAsIPAAAAAEIFhB8AAAAAhAoIPwAAAACgMPH/ASEtzX2p2b5zAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.settings.uncertainty_method = UncertaintyMethod.crude_monte_carlo\n", "project.settings.minimum_samples = 300\n", "project.settings.maximum_samples = 300\n", "project.settings.save_realizations = True\n", "\n", "project.run()\n", "\n", "plt = project.result.get_plot_realizations('h_s', 't_p')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "df15912b", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "### Correlation matrix (2 variables)\n", "\n", "Let's now correlate the variables $h_s$ and $t_p$ using a correlation matrix. We apply a positive correlation coefficient of $0.9$, which implies that higher values of $h_s$ are associated with higher values of $t_p$. The correlation coefficient must be a value in the interval $[-1.0, 1.0]$." ] }, { "cell_type": "code", "execution_count": 19, "id": "64531f1b-b8a6-4ce1-87aa-d98f8bd000b9", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "gallery", "statistics" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.correlation_matrix['h_s', 't_p'] = 0.9\n", "\n", "project.run()\n", "\n", "plt = project.result.get_plot_realizations('h_s', 't_p')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "f04bee5f", "metadata": {}, "source": [ "Let’s apply a negative correlation coefficient of $-0.9$, which means that when $h_s$ increases, $t_p$ tends to decrease:" ] }, { "cell_type": "code", "execution_count": 20, "id": "92d3f894", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.correlation_matrix['h_s', 't_p'] = -0.9\n", "\n", "project.run()\n", "\n", "plt = project.result.get_plot_realizations('h_s', 't_p')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "0a2dcf91", "metadata": {}, "source": [ "If the correlation coefficient is $0.0$, the variables are independent:" ] }, { "cell_type": "code", "execution_count": 21, "id": "ae4885a4", "metadata": {}, "outputs": [ { "data": { "image/png": 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uhOeSlZUltnj4hrh5U9w63kcfEX37rb3f8CRq/OnrriOqXDkqPCXS+/H3vJ+fqlA+xyNHrO+brCndvnd+2+jZxyDevycVLO/7fck6t7PfWO3fifo22tp9jLEw/lljwSdW+KlZ0//x0A14TLDS56pJGDu8nGeVFn7KlStHl156abHPOCy9cuXKRZ/37NmTatSoQaNHjxbv//rXv9L1119PTzzxhHCSZp+hTz/9lF544QXxvZEnaOTIkVS3bl0hDA0ePJiqV68uQuKDwo4d9n8TowgTD/Azz0SjGBLBNu4FC4g6dSJPtRsffhi9Hj6/qlWdXU+QMJwT7Rij2W7Pg3PTpl6emf7E9zduLz8nM6t9Nqh9W0WsjIUM76Ob4MNwH+exIdFCNyPEY4f0aK9kbN26lXbEzPSNGjUSfjgs7Fx22WU0e/ZsEcIeK0T179+f7rvvPurTpw9dffXVIpR+8eLFIiliULAzOHLnzssr2bk7dIiueJL9zsuIL1bH8nXERqf16pX8nAyC+rAmi8JLdp8YdpPTcXAOU4SVMREZ98zqs2o8g/zMIBGp+/ACb84c87GHP+PvvFwE+iHcMfH9LiPsYwc7PIPi7N+/n6cf8eoGBQUFkfnz54tXNzh+PBKpWTMSycjgaTL5xvvMmVPyGCtWpP4tb7yf2/TrZ+1vJ9rMrsertvYTq/ckdsvLS94eXqFTO3P7mD0r/Fmi58Prc4k/n0Tnwu/r1Im2dXZ2gdiXn30Z9zzo8Li6dGm0rYcMKYgsWxb9LAhwf+F+o8LY4fUYYnX+VlrzA+xL87HwKpJXi2arFqumMycmtmTMmpXaeZdXW5UqBW8V5lZbDxrEkYhEK1ZwbqvgtocbqJbTiu8VP5M1ahT/nDVC8c+qYQKND2xAbifvxtXrrz/1jDVvHhyNCPer77+PjhkYOxTI8wPSH0TjHWPPPJOoe/eoWSuZT4Mf/gfxPhaNGhHdc0/q37G/0bJl0f+zmp9p1iy6BWUwSqeteVDmtgCp4f6XzHGcBaAff4zu52Wbxj8LmzdzuZ7E/kephDbDLM3PeZCfCeAe3E8wbpwCwo/mAhAPfk6cOL12hDOLWKpSJZo80Qq7dxNxOiee6MPifAvnRPeRpeFM9Szws8Xa25iUZUoKbQAEFQg/IZXmDdMZq9VZ0IkVgNJ1hEsUsWRV8Al6xEuyydCre6JK1JPff1t2hFWiZ8EwXalmlgYgLMDnJ8TY8T/wMmIpHjbdBTGay0qdHcbte6JK1JOMv+00wkq2v5FsoQ2AoAPNT8hJx3TmRF1vheeeC6Yfg1U/DnZidvOepKuFcAM+9i23lPzc67/tpYYzFemYrmJNoGaEOT8LkM8JyTmz3ACaH1BkOmP/g3SditNVw/fr53+adb+wMxm6eU9kRz1xhF+XLubf+RFxxYLksGFEFSt6o01LRDqmK6/zs3BbczDBG28gdxDQL2eWG0D4Aa5iVQ3Ppq3492+9RTRuXHBviEw/DjuCl5vwgNi5c3LBxqu/bfx9HpiHDo1WTmc4jQLXMfY6TUC6pivDLF29urtCW1AmL6Ce2X6uRn0Iwg+Q4mPBD09szgme8M3MIkFCph+HDMHL0DZZxW2hL9FA/euvUU0Ql2+R+SwYQj+ngEgECzhGCUQuPplubqcgTV4g3Dmz0gXCD3AVq+r60qXdNevogEznWxmCl13/Lzf/tgoDtZVkpD//TFS7dnKhw3g2WDhJ51lRoU2AvnwoSXvsFRB+FCMItngvosiCgMw6OzIELzuanPi/ne5zoMpAnehZkKF1UaVNgJ7sCFj6BQg/CuHEFp9qkpAlTCGdulqCoQzBy44mJ/Zvu+GTotJAzfeUMzpzkk8z/NK6qNQmQD+qBSz9AoQfRXBii081Sch2bHQ7YikoyBIM/Ra8rPi8cJ/gaDDjb7vlk6LaQM2lLJIl+fRD66JamwC9aCrRbO8FEH4UwIktPtUk0b8/HBtVRpZg6KfgZcXnhTWSRmoDN31SVBuoVdC6qNYmYXEDCAqlJJrtvQDCjwLYtcVbmSSefFJ/x0YMfPoLXom0TRzlxH2QX41+6KZPimoDtQpaF9XaJBWyNdcg2P6cEH4UwO6q0MokYSWvCq+kVF1VYeALDrHaJkPg4SgnnmhjJzS3tSMqDdSqaF1UapNkICRfXTpJMtu7DcpbKIDdVaFbqnFOPmckfostrim7E8sswwC8gbUJ3Ne4fyW6r5x7x23tiNvlW3Qss6Fqm6RbBoavQZVzDhulHBbUVglofhTA7qrQLdV4rOCjSqIz5CIJJlbu64svRjUSbmtHVHG8V0nrokqbmIGQfOAHEH4UwK4t3oqw5GQwU8EfCANfMLFyX/n7Pn308UkJs8kg6M7hIPhA+FEEO6tCK8LSQw9F/58szFjFRGcY+IKJ1ftat6462pEwal1UQKZzuLHo476mmh8kcBcIP5quClMJS1wg1Oz7ypXVXlWpEBUD5N5XaEfCjSzncDb316sX/X/v3oguCzpweNbYkSyV46LZ97ySadFCXeHCGPjY/8jMP4QHPv5epVwkwP37GgSHSqCPc7gRZFGmjP9BFjwmq+p8rvO5pgLCj+akmiTiv+fOq7JwoVJUDHAP3Ndwke4kaWi22Uk+1leMxyZ+/t0URGRGl7HQZXaNKkTd6nyuVoDZK2QJ/nRIdKZSVAxwD9zXcOBWji6/zJ+ygix0ymU0V6NztQo0PwritYTt56oqqLlIgDNwX4ON2zm6/DB/ygiy0CmX0QmNztUOEH4Uw68EfzpMQvD7CCa4r8FE10lSRpCFHW2TbN+3DzU6VztA+Anx4IFJCAAQ9Ekylf9RrDO+GV74QeqU0mOHRudqB/j8KAQS/AEAdEXFSdKK/5EMP0idUnpU0+hc7QDhRyFUHDwAAEDHSdKOk67hB1m9uj9BFqoUug3audoBwo9CqDZ46BLBBgCQj0qTpJMagSzgbNwY/f+UKd6WHtEh6lbHc7UDhB+FUGnwUDX8FQCgJipNkk5dCIxzY82QW6VHEi36dEr90Emjc7UKhB+FUGnwCFqOCGidAAjPJKmKC0GqRZ9OpVw6aXSuygs/kyZNovr161P58uXF1rBhQ3rvvfcS7t+sWTPKyMgosbVt27Zon169epX4/sYbbyRdUGXwkKl+dhtonQAI1ySpgguB1UWfToVuSyU4Vx0Xl1JD3WvWrEljxoyhunXrUiQSoenTp1OHDh3oiy++oEsuuaTE/nPnzqWCgoKi93v37qXLLruMbrnllmL7sbAzderUovdZWVmkEzrk4NEl/NWvvEkAAHXSaMiuEahrzqMwlb2QKvy0a9eu2PtRo0YJbdC6detMhZ9KlSoVez9z5kzKyckpIfywsJObm0s6I3vwCIL6OUwDEABAnVpyshd9fjFX48WlMkkOT5w4QbNmzaJDhw4J85cVpkyZQl26dKGyZcsW+3zlypVUtWpVqlixIt1www00cuRIqly5csLjHDt2TGwGBw4cEK+FhYViSxfjGG4cSyYsTOTnE+3cScSyJd+mVIMH75ednfrYvJ8bzRPb1uvXs3Yw+d/fs4do9WqiJk3S/9thIih9WgfQ1s7gtTVPvgMGFE9gyFqJMWOi38d3X7famhdzVsY93k/XR+jEiWjblilj/j0LmQ8/TNSmjfk84VW/tnq8jAjbmySyceNGIewcPXqUzjjjDJoxYwa14dZKwccff0wNGjSg9evX0zXXXFNCG1SrVi3avHkzDRw4UBw3Pz+fSiWYqYcNG0bDhw8v8TmfCx8LAAAAAOpz+PBh6tatG+3fv1/4Eisr/LAPz9atW8WJzp49m1566SVatWoVXXzxxUl/d9dddwmBZsOGDUn3++6776h27dq0bNkyat68uWXNT15eHu3Zsydp49mRRJcuXUotW7akzMxM0o2FC4l69Cip2jTUx6++Gl1Fpfo9Y6Z+TvV7p229fn0mxfjCJ2TRImh+wtanw9bW/AzGa0A4qGLsWPeevSC1dblyLWnXrkzLGm4zrUi9ekTbtyf2OeL25+nLL5O7231g9myi3r1T78c5k9gE5tcYwvN3lSpVUgo/7GisFM2bN4/06dMn6T4HDx6MlC9fPvL0009bOmaVKlUikydPtnwO+/fv5+4qXt2goKAgMn/+fPGqG8ePRyI1a/Lja75lZEQieXnR/ZIxZ07J4/Dv+HM3iW1r49z5HNM5d5C8nZ3Abb5iRSQyY0b0FffAWp92Aj9jZs8Af8ab28+gzsyZE23r7OyConbiMcRJGxntHt/2Mtrdiz6wYkXieSF24/38nBetzt/K5fk5efJkMS2MGewbxPvcdtttKY+3bds2ERVWTde0yAGpNyYj/DWoeZN0B6kHwpVqQqd+aWio3chH5kbaEjdCyL3qA001T8orVfh55JFHaPXq1fT9998L3x9+z87K3bt3F9/37NlTfGbm6NyxY8cSTswHDx6kfv36iWgxPuby5ctF6HydOnWodevWvl1XkHAzWktGPoug5U3SHRUSXoYJFEuWKyCks+hza5HgVR8opfniUmq01+7du4WAs2PHDqpQoYJIeLhkyRJhA2TYF+i004rLZ5s2baI1a9bQ+++/X+J47NDMPkCcL2jfvn1UvXp1atWqFY0YMUK7XD+qoEKysHQJUt4knVE19QCfV1D7hiqZjlXHEBASRWilE5ruJG2JmyHkXvaBTv9dXJrl+WHBR+XFpVThhzU4yWAtUDwXXHCBSIhoRnZ2thCeQHCShblFUPIm6YyKuU90TdAWpsVL2IREtxcJbvaBEyYLBV0Xl8r5/AC10F21CdRBpQkmLCY4Hf0yZJRKUElIdNtM5VYfmJvEDKdTiQ4DCD8gJfCbAW5gdeKoWtX7yS8sjsC6LV5kOcOrJCS6vUhwow/MDeBCAcIP0KZYIdAbKxMMxzD06uX95Ke7I7Ad7YguixeZE2ysgBCP30KiF1qodPrAiYAuFJQpbwHUB34zwMt6S/yey5HE40WdINVMcFbgyeWjj4gWLCB67bVoaRarfkqq+2Wo4AyfqO38dt71ys/SaR/4UEFfPTeA8AMA8I1E0SG8Ij1yxFz48WLyU8nHwyqcMfjbb82/syIgurl4cTtCjrVXVibYZ58luu8+7wQgznT87rvRrO9cw1CGkOhlUVYnfWCHhgsFK8DsBQCQbkKdNs1c8PHKDKWSj4eVsgRMbFkCmeYHt/1y+HedO1vb98EH/fEB4kLHMp13VTJVVrO4ANi1y18n9XSB8AMA8J346JDdu/1dXVpxAr3jDqK33pI7mBuVs63gh5+S2345xvF++cX6b3R2stXRz7JpioWC8TyxYOqnk3q6QPgBAEhHhhkq0eq6UqXoNnSo/MGcBZlkGh8/zQ9uO74mO14ydHaytYsKIeSlkiwUDOLvgw4CKoQfAIB0ZJmh4lfXw4dHzW/xJjhZg7kTQcYrPyW3I+RSHS8ZqkfjBY1OCRYKiYQxHQRUCD8AAOkkCzU2BtMuXbxZ+Rqra/Y7efHFxH9fxmBuR5Dx2k/JbcdXNzRUujnZ6kynuIXCU08lfxZUF1Ah/AAAlBlc//a3xN9PmOCt5kXF3D8syMSvtpPhZS4at02TbmioVIrGCwOlYsxwZ52lt4AK4QcAoAS8iuRokWR4qXlRIaQ3PnkhM3Zs9DWZwylrfLyOAnLbNGnFkTYRKkXjhZVqGqaLiAXCDwBACWRrXmQP5olCyA2qVy++/5lnRoVBv6KA3C6VYeV4bv0t4D5NNUoXYQaEHwCAEsjWvMgczJOFkPfoEf3/xo3Fw565Hdjvws8oILfzzyQ73pw50U2FXDdA/7px8SDDs0K4nTUVqAPurfqaFy8z66YbQm6gQvkAt0tlpDqeymU5wk6ijO1+lwRxAoQfReCVn1kHSlavB+gB7q3cmkZOBvP77y+eX4e1D149i1bMfUx+ftQUFsQ6f8mOh5qCatNJ8bpxiYDZK+TVjIG34N7qqUZ34oTrFKtmPK41BYCKlFIgGaNdIPxIxu2sqUAdcG/1q2kkQ1i1asbLzXX/bwMQViD8aBLhYoS9An2QHb2kK7JqGskSVq04WjMNG7r7dwEIMxB+JGNV5c3ZZ2H+0gvZ0Us6I0ONLktYtRryrYMpAQBdgPAjGasqb656HFT/n/jEbkEx8cmOXtIRmX1BprCazNz36qvu/z0Awg6EH8nYzXJqqN2DIjAkSuwWBCFP9yRgYesLsoXVROa+du28+XsAhBkIP4oXdDRTu48aFQyBIeiRUCpFL7kJC9pr1kT/z69uCN4q9AUVhFUdo2aCCPdr3ReWIDkQfhTAUHlXqmRt/6FD9RcYwhIJJTt6ySvtTNu20ff8mq7grUpfCKqwChITr0GfP/9Uv9Z5YQlSA+FHEXgSfOst57/XTWDw2rlUplkw/m9zAjAZ0Utu45V2RqWouKAJq8CemfX220vup9vCElgDGZ4VgtXcyTLcpiJ2klAhDb5M59J69Yi+/db/bNlBzeacSjvDmhEWvFnQs6sZUS0qTteMtcC+IG9lnE23fwM1geZHIayGvAYhdNor59KFC6OvsaUJ/Fq9qeC34hVeamdkOxqbAd+b4JJMkE8EcnIFDwg/ipFM7T58eHBCp71wLuVBbcAAOWZBVfxWvMJL7YwKjsZAHbw2WacS5HVfWAJrQPhRkEQhr48+GpxJwgvnUh7U4jU+fq3eVPJb8QIvtTNeORoHJR1EmPAj3UE6AowOC0tgDQg/imKmdg9aNIrbzqUyfUdU81txG6+1M273Bdk5g4C6ZmMnAoxOC0tgDQg/mhG0aBQ36zjJ9B1R0W/FTY2IH4K3W30hyL5XQcVPs7HdxLI6LiyB4sLPpEmTqH79+lS+fHmxNWzYkN57772E+0+bNo0yMjKKbWXKlCm2TyQSoSFDhlC1atUoOzubWrRoQd988w0FCVmFH1V3LuVBLV4o9Gv1povfSjoaET8E73T7QtB9r4KKn2bjZIK8GbouLIHCwk/NmjVpzJgx9Nlnn9Gnn35KN9xwA3Xo0IG+/vrrhL9hIWnHjh1F2w8//FDs+3HjxtHEiRNp8uTJtH79eipbtiy1bt2ajh49SkEC0SjmbTJ2rByzoA4mSTc0IobgvWhR9D2/qiR4B933Kqj4bTZOJsgb/ToIC0ugqPDTrl07atOmDdWtW5fOP/98GjVqFJ1xxhm0bt26hL9hbU9ubm7RdtZZZxXT+jz99NM0aNAgIUSxVumVV16h7du303wjdScINEYdpOrV/V+9qWySdFMjwgJckybR//OrSqaAoPteeYlMB3EZZmMzDfqGDaf6NUqMBBtlkhyeOHGCZs2aRYcOHRLmr0QcPHiQzjnnHDp58iRdccUV9Pjjj9Mll1wivtuyZQvt3LlTmLoMKlSoQA0aNKD8/Hzq0qWL6TGPHTsmNoMDBw6I18LCQrGli3EMN44FrLX1F18U0iefEO3cSZSbS8Rdiidpr28BC19t2hDl5/v/t1PVKtq7lyg7O/E+e/YQrV59SrDRsU9zeye7xtj9FDt1qW3N+bE4TURstCQL8axJ9aOw6rXXEtWpQ7R9u7mAztpTPh/ez+1maNxY/X4dRAo9amurx8uIsLpEIhs3bhTCDpulWOszY8YMoQ0ygwUY9t9hjc7+/ftpwoQJtHr1amEmYxPa2rVrqXHjxkLTwz4/Bp07dxYaozfffNP0uMOGDaPhJkl0+FxycnJcvFoAAAAAeMXhw4epW7duQkZgNxllhZ+CggLaunWrONHZs2fTSy+9RKtWraKLL77YkoR30UUXUdeuXWnEiBGOhR8zzU9eXh7t2bMnaeNZhc9z6dKl1LJlS8rMzEz7eABt7UTzYxQjTQb7OljV/HjZp9PRRPBve/SI/j92dDN8r1591R9thlt42dZs2uJSMMnyY7HWMtYE5qVGyOy+s9l4zBh/7hnGav/wqq15/q5SpUpK4Ue62at06dJUh/WdRHTllVfSJ598Qs888ww9//zzKX/LDfb73/+evv1vESf2AWJ27dpVTPjh95dffnnC42RlZYnN7Phu3hS3jwfQ1la57jqiypUT141jwYAnGd7Pjg+PF306Ud2lzZujn6fynzK+i6+xxtF27HSuq/OqF2390UfFa+BZwep90LmuGsZq//BintUyzw/78sRqYVL5CbHZzBB0atWqJQSg5cuXF5MCOeormR8RAEFHh2g0Nx2zg5YOwiucOH57nTIAkazAD6Rqfh555BG66aab6Oyzz6bffvtN+NisXLmSlixZIr7v2bMn1ahRg0aPHi3eP/bYY3TttdcKTdG+ffto/PjxItT9jjvuEN+zaeuBBx6gkSNHiggyFoYGDx5M1atXp44dO8q8VACkY0SjmVWdV0UjYidUnfMAWZlEgfvRU3buAwAqIlX42b17txBwOF8PR2WxIzMLPmwDZNgX6LTTTimnfv31V7rzzjtFRFfFihWFmYz9fGL9g/r37y8ixvr06SMEpCZNmtDixYtLJEMEIB14xStbNa+zWSFROybzPYkFoeruJudMZA714j7o+uyAYCFV+JkyZUrS71kLFMtTTz0ltmSw9oc1RLwB4AXsk2KmPWGzkgrak1SoohExa8cqVfQpExIkcyj78LD5064AZPc+6P7sgOCgnM8PACqDulHetiPnGkqGKmVC/IK1JBypx/CrFz42iZJzJtPGOLkPeHaASkD4AcAiqBvlfTvGorJjtp912IwUBfzqVWV6MwdxzvTMbe7GfcCzA1QDwg8AFkHdKH/aMZEJTIUyIX4hQ0sSH2V1yy3ulWvBswNUQ3qeHwB0AXWj/G1Hdu/jiddPx1gVnHFTaUlY88Jh5uy47vW5ueUgj2cHqAaEHwAULr4YRKy2Dws+fjpmq+KM62a4vyoO8nh2gGrA7AWAzbDgeB+IsDrjBqkdVXLGDaKWRMV7DsINhB8AApYlWXVUa0fVnHGDqCVR7Z4DAOEHABfCgsPkjBu0dlTNGTeoWhKV7jkA8PkBQPMsybqiSjuqZmaKTzwYJC2JKvccAAg/AGicJVl3VGhHFc1MsXXY9u5Vsw6bzvccAAg/IBDEhijn5ETfZ2bKPisQhPpWrG3h7/02MxlaktWriQ4cIFq0iOi669TQkqiQEgCAdIDPDwhMJtw//IGod+/oZ/Xq+RuhA/RFZWdc/ptNmkT/z68qCBixz1u3btFXrzJPA+AVEH6A1iQKUd6+3f8QZaAvcMa1Bj9PN9+sRkoAANIBwg/QFtVClIHemNW32rJFb/8aN+HnqE8f8+/wvAHdgM8P0BbVMuEC/YEzbmJGjSrufB0PnjegExB+gLZ4HaIMp04ATj0Lhl+UV88bAH4C4Qdoi5chyqrUeQJABVh7+ssvwcs8DcILfH6AtniVCVelOk8A2NXQrFxJ9MYb0Ve3/N2sanMqVdIv8zQIJ9D8AOkY5iUWLn7+mejMM6Mp8FPlDonPhBvr+Ow0RDmVEzUfl52oOf+KCmHHAPihrbSqzeG/j+cC6AA0P0CZnCG33Ub04IPRV6u5QxKFKPN7J/WCVKvzBIKDV1oZP7SVqbSsTOXKRI8+mt7fAcAvIPwAaSQasA34cysDd2yI8pQp0c82bHC22lWtzhMIBl4mBvQj5UOyRJDGZy+8AK0P0AcIP0AKyQbsWPh7KwO3EaLMwpLxPih1noCa2hZVtDJ+aSsTaVnZrw5V2YFuQPgBUkg1YMfip5nJKydqEM4yDH5oZfzUViIRJAgKcHgGUrA7EPtlZvLCiRrI07bECx2GtsUvTYUfiTj91lYiESRwI2/atdeSVKD5AVKwOxD7aWZCnSe9UansiR9aGWgrgY5a2Hr15J4ThB8gBSvRIwYyzExQ7+uLShF7fmhlVK5KD8DcJMWnmYUL5bQRhB8ghdgBOxk8eMsauA31fteu0VdMHnqgUsSeX1oZaCuBrlrYhx+WE4gA4QdIwxiweXIwA1EkQPeIPT+1Msm0lSpEvYHw8aGFwBb+XkbeNDg8A6nwwMzZkp1keAYgmbaF+5PZipOFDv7eL1OqIeSbZV9mwcdNx2szZ2TUqQOy2KGQFjYeCD9AOogeAW73Jy/KnsRGqtgVzGOF/NhjMKyJcXpcXaLeQDipppAWNh6YvQAAgcNNHxi38gXF+5AtWOBtHiKVot5AOGlqIbDFTy2sMsLPpEmTqH79+lS+fHmxNWzYkN57772E+7/44ovUtGlTqlixothatGhBH3/8cbF9evXqRRkZGcW2G2+80YerAaoBP4dw40bEnlfZmb3O+qxa1BsIJ6Us+LyNGSPHvUGq8FOzZk0aM2YMffbZZ/Tpp5/SDTfcQB06dKCvv/7adP+VK1dS165dacWKFZSfn095eXnUqlUr+olHjBhY2NmxY0fR9gZ7+YFQweGTsrP7eg2EO28j9rzSnPilkVHZ3wKEh05Jik8z7dpJOS25wk+7du2oTZs2VLduXTr//PNp1KhRdMYZZ9C6detM93/99dfpnnvuocsvv5wuvPBCeumll+jkyZO0fPnyYvtlZWVRbm5u0cZaIhAuevTwdlUtGxVKNwQdrzQnfmlkVPa3AOGik4kWlotPy0QZh+cTJ07QrFmz6NChQ8L8ZYXDhw9TYWEhVapUqYSGqGrVqkLoYW3SyJEjqXLlygmPc+zYMbEZHDhwQLzysXlLF+MYbhwLJOfYsWgblylTmDDSh/NKtGmjbyQZa7VYuOPry84+9fkvv0Q/92M1FYY+zRqR2PZNtp+dZrB7XKdtzeUD6tSJJpNL9Czw6pv3C/BttEUY+rVMGjf2vq2tHi8jEklVV9tbNm7cKISdo0ePCq3PjBkzhDbICqwFWrJkiTCTlSlTRnw2c+ZMysnJoVq1atHmzZtp4MCB4rhsJiuVYLYbNmwYDR8+vMTnfC58LAAAAACoDytFunXrRvv37xe+xMoKPwUFBbR161ZxorNnzxamrFWrVtHFF1+c9HfsKzRu3Dih5WGn6UR89913VLt2bVq2bBk1b97csuaH/Yn27NmTtPHsSKJLly6lli1bUmZmZtrHA4mZPbuQcnKW0p//3JKOHEnc1lOmRE1gurFmDVHbtqn3W7SIqEkT784jDH2afW64/lAqzQmr7411FWvlBgyImlgNeJ+xY09p41atImrfPvXff/ttouuvT7+tzc6JI2zY0VSWv4WqhKFfB72tDxw4QFWqVEkp/Eg3e5UuXZrqsG6WiK688kr65JNP6JlnnqHnn38+4W8mTJgghB8WaJIJPsx5550nGuLbb79NKPywjxBv8fANcfOmuH08UJLcXO78JASfZMIP+znoeCt27uRrs7afH9cX5D7Nl8VCiyEkm+ULYgHiv0rnhDl1Nm8unlOHE3lauYe8X2zTOm3rRDmGdDX7+kGQ+7VqZHowz1pBuvATDzswx2ph4mFtDztGs7nrqquuSnm8bdu20d69e6kavPpCAbuLLVmSvJaSrLwSbiDTiTU20R8LmWHAanbmVBFc3O84gouFEBn3UPdEoukmmQRAKeHnkUceoZtuuonOPvts+u2334SPDZuxWLBhevbsSTVq1KDRo0eL92PHjqUhQ4aI/c4991zayctbIuHTw9vBgweF787NN98sorzY56d///5Cs9S6dWuZlwp8InZAdCu7r0rIKt0QXyKBHXY5gwSbVIKeIdiK5sROBJdq5TdUB+U5QOBC3Xfv3i0EnAsuuECYpNjkxYIP2wAZ9gXiPD2xSRHZR+iPf/yj0OQYG5vBGHZo3rBhA7Vv316Ezvfu3VuY0j788ENTsxYILq++6k52X9XwqlBmspxBiRLyMRxdFobw+lT5guzk1PGz2Knu+JEMEoQz95hUzc8U9jpNAmuBYvmeEwUkITs7u0hrBMINO3IG1c/B7UKZyVbW3IaJzDkGhjknCG3rFLumLD+LneqKHVNimPueKsxNMo6o2J+V8/kBwC1093Pww4k1VeHLYcOsm3OC2tZWcGLKgiNycuyYEsPc91RgroYFdCH8ABBS4c7Kytowz6Qi7CUSnFaSD7KAni4oz6EHJzTV0KGquwLoZCcF4VpZc9ZoK+gUTOnV8+ZmJXmA8hy68KGmBXSh+ZGMbnZSEL6VNVeP+fXXxOacvDx9IpO8eN7iw7A5r8/atcHzNfMbRMXpwQ5NC+hC8xPwSIYgapWCeE0ysKqtYWGBSZQ7SZfIJC+eN7MCs7VrRzVmTirJg1MgKk4PqmlaQBfCj6J2Ut7+8heuZO98gg9i5e8gXpPslXWyhJCs1Xn0UXNzjpFSQAcNZarnjWG/BDvPGcKwvYf9RNjpvmLF4p/DlKjfONJUMe0whB9F7aRGevvbbnM2wQdxYA7iNemysmYBhzNNrFjBBX+jtcMYXWpDue2X4IUwBcwXOkOHnvI9YxMs16DeskUPoTsMlNI0bxWEH0nYtX/ameCDODAH8ZpUwI6TbmyiPy+Lpurgl6Crk6fuCx32PWNN0IIFss4MBMXZHw7PkrBr/7QTMhjE/BhWryk/38+zCgZhyDfjtl+Crk6eOqBr6HTY6aTZOALhR9FIhnSEFlUGZifFCBP9xuq5crm3nBxXTj/lOQWJoOebcTtySFcnTx0I4uItLJTSaByB2UtBO2kqUgkCKgzMThyTk/3G6rm6XW0cDtbBwG2/BF2dPHVAlcUbCDYQfhS0k6YilSAge2B24pic6jfs/G3lmho2lHsdKoGUAN75Jejq5KkDKizeQPCB8COZ2Cia114jOvPM9IUWmQOzE8dkK7/5v/8jeuqp4tfg5TX57WDttqACjZU58VFr/Oo0ckhHJ08dkL14A+EAwo9CdtLu3YkmT3Zngpc1MDuJgrH6mypV/LsmP6N53BZUdNdYeU1s1JrTJISGsHrsGNG0aUTLlqUvTIFT9wdaNeA1EH4Uw02hxc1Vrpf2eju/8eua/PI7cFtQ0S0lgI6muXhhtUULol69iLKykNHZLaBVA16DaK+Ahwz67X3vxF5v9zd+XJMffgdehPTqFCmjY107Q1iNv2eGsApzV3hDp4FeQPhRFJ1CBmNxElKsYgFDP87JC0FFl0gZVYWIZGkNkH/Gf3QdB4H6wOwFpNvrVbTx+3FOXggqOkTK+Gmas2NWS+V7hazOwUNHsytwBwg/QAl7vYo2fq/PyQtBRYdIGb+ECDuO5FZ8r2Rp1YwJmfscJmj3MOsf9eq5+AeA0kD4AZ7gxDFZhoN2Krw8Jy8EFRW1aPH4IUTYcSS3qomqWtV/rRqfpzEh9+6dfiQgSN4/tm+Pvi5ciJYKOhB+gFIhxW6EIbuNV+fklaCiohbNT9OcXbOaVU0U46dWzZigWWCLBSkL0sNK/3j4YZjAgg6EHwAk4pWgoqIWzS/TnF2zmlUN0+7d/mnVdEtZoBOp+gfD37uRwwuoC6K9AAhoSK/fkTJWC8AaGi/WarDQEDvBuyFE2DWr2dFEcXuyUGoWos/n7JZw6XYkYBiK81q9Vl0iIoG3QPgBQAF0D+m1m7PH0Hh5IUTYNavZTWvgR/4ZNydoHfMpOcXKteoQEQm8B8IPAEBKzh6vhIhUwgzDNfQaNXKuifJaWHVrglY1n5IXWL1WK/3D77xiKnEiJFpC+PwA4CFBzyOSrm9KrDM5D7I86KbbVskcyQ1+/pmodu1TUVOqOYm74RcVJr8hO9dqJdBgzJhgTvipmOtynUGVgfADgEeEYSDJz3cnZ4/bbZVImEkWNaWSk7gbkYBhSspo91oT9Q/jfbt2FDrmhqwgsiOz14kTJ2jevHn0r3/9S7y/6KKLqGPHjnT66bCiAbWQpcINi7lh5870fVO8aiv+zf/8T1SDwpoeK/XTVPK9MiboAQOKf27VLypMjr1OrtXM7HrttURLloTPFHTCgzqDgdP8fP3113T++efT7bffLgQg3nr16kV169alr776ypuzBEAjzUuYzA25uen5pnjdVmvXmgs+umg/eILeuDH6/ylT7GmjwuTY6/RareTwCoMG98MQaQkdCz933HEHXXLJJbRt2zb6/PPPxfbjjz9S/fr1qU+fPt6cJdAev31fOEOrLBVumAaShg3T803xsq24jy1frr/2w5iQud/aSbKpQ6kTt/DqWsNiCtoRIi2hY+Hnyy+/pNGjR1PFihWLPuP/jxo1ir744gu3zw8EQOB58MGohsDPlRObCmRpXoI8kBj3lM0xBun4pnjVVsZqfeRIa/vv2hUMTZxupU5UvtYwaXCrhUhL6Fj4YZPXLh4p4ti9ezfVqVPH1rEmTZokNEbly5cXW8OGDem9995L+ptZs2bRhRdeSGXKlKF69erRu+++W+z7SCRCQ4YMoWrVqlF2dja1aNGCvvnmG1vnBdInVlXMg86ePf6unOJLAvipeQnqQBJ7T7nOFGPUnXIaKeVFWyVarSeDBfSgmTJUjGLT6VrDpMFtGiItoWPhh7U+999/P82ePVuYvnjj/z/wwAM0duxYOnDgQNGWipo1a9KYMWPos88+o08//ZRuuOEG6tChg/ArMmPt2rXUtWtX6t27t9AysZM1b7G+RuPGjaOJEyfS5MmTaf369VS2bFlq3bo1HT161O6lAodYmXxUWDl5pXkJ4kCSrBAkf844iZRyu62SrdZTETRThoFKUWw6XWuQNbhh1hIWEbFJRkZG0XbaaaeJzew9vzqhYsWKkZdeesn0u86dO0fatm1b7LMGDRpE7rrrLvH/kydPRnJzcyPjx48v+n7fvn2RrKysyBtvvGH5HPbv389Dp3h1g4KCgsj8+fPFa9A5fjwSqVmTpx7r24oV7v19o62zswt8/bvxzJnDz0p0i/2bxmf8vc73lNvXaGe+nry86H6y24rvqZ2+F7+ley1eEKbxQ6W2ttqXvBxH/GbOnJLPOj8PXoxXXvVrq/O37dj0FSxKewCHz7NJ69ChQ8L8ZUZ+fj499NBDxT5jrc78+fPF/7ds2UI7d+4Upi6DChUqUIMGDcRvu3TpYnrcY8eOic3A0FoVFhaKLV2MY7hxLNVZs4Zo716i7Gzrv+GVk1tNY7TxeecVihVfonIFrBrnsFavbgnnCTHClGNNcKzl4ARq/L0u3cHsnmZnFxZ7ZbPm6tVETZrIbSvuS3b6nhnpXIsXhGn8UKmteXxgTw7WbsoaR/ymXTuiNm2i+bs4jQX7avJ0zBoft6/Rq35t9XgZLAGRB9xzzz302GOPUZUqVZLut3HjRiHssFnqjDPOoBkzZlAbbn0TSpcuTdOnTxemL4PnnnuOhg8fLvyQ2CzWuHFj2r59u/D5MejcuTNlZGTQm2++aXrcYcOGiWPEw+eSk5Nj46oBAAAAIIvDhw9Tt27daP/+/cKXOBGeZSV87bXX6G9/+1tK4eeCCy4QEWR8ouw7xPmDVq1aRRdffDH5xSOPPFJMo8San7y8PGrVqlXSxrMjiS5dupRatmxJmZmZFGRYS9C2rbV9jZXThg3u2ZJj23rx4syk2gTg/J6yxufll5fSn//cko4cifbpRYvka0vY54edsBOt1q2iwrWEcfxQsa05bYZX4wj3VzMtSxgo9KhfW/E39lT4sapQYm2OESV25ZVX0ieffELPPPMMPf/88yX2zc3NLRFpxu/5c+N747NYzQ+/v/zyyxOeQ1ZWltji4Rvi5k1x+3gqct11RJUrJy8aGCv88ABSpoz758Ht3KlTpufVt8NAsnvKgs/Ro5liMuD9ZLctP15jx55ywjYrUlqpEtEvvySv4O72tbiRITgM44cqxLa1VwV4rVSgDwOZHsyzWtb2OnnyZDH/m1jYPLY8LmsZS46Gj1CtWrWEABS7D0uBHPWVyI8IuIuVopIMR/D4EWprJYMrCFYkSLK6Tfz5Cy/4ey1hyBAcdNweR8KSPFFlpAo/bG5avXo1ff/998L3h9+vXLmSunfvLr7v2bOn+Mzgr3/9Ky1evJieeOIJ+ve//y18dThE/t577xXfs18Ph9yPHDmS3n77bXFMPkb16tVFSDyQO/mceWY0tF3HUNugV2dPV6BQ8V7Ga3aM937mvsEkFyzcGAfClDxRZaRWIuXEiCyc7NixQ0RlccLDJUuWCBsgs3XrVjrttFPyWaNGjYQT8qBBg2jgwIGinhhHel166aVF+/Tv319EjHGpjX379lGTJk2EwMRJEYF/2FEVq140EOpp83vKsL+Wao9WokKpRk4iQ8Dx2iQaxmKRQcatccBO8kRViuy6Qfw4z1FyUrEbQ//DDz+IfDrx8Gf8ncEZZ5wR2bx5c0RHkOdHbl4Jfu80r4TbuSOMHDRm+WB0y9cThtwzqfJM+ZnHx608Maq2dRBJ1NZujgMzZljrF7yfbhw/Hu3PfO78ajxnZuN8nTpy8/zYNnuxX83PJmWSf/nlF/GdwW233eZKpBQILqqbBKCe1g+VShKEKUNwkHF7HAhD+ZtuMb5t/fsnzg5vRNPJ4DQnUVzsWxPPwYMHi5mWuG5XqjB3EF50ECxUmkiBfgJHUCe5sOH2OBCm8jc//UQ0fnzycf7hh+WM85Z9fow8OCz4DB48uFjyP87OzBFVycLJAdDN7q3SRAr0EziMSS5R2gcjrF6nSS6MuD0OGNGTLCxwHzBLx6BS9KQbC9lk8DwgY5y3LPxwIVFD88NRVJyfx4D/f9lll4mkhiB5sjhOZqWiU6/f6CBY+DWRqu7wrRMqCRxBm+TCihfjgBFxaOZAzX1CxehJpwtZVcf50+3W9PrTn/4kkhDCn8c6bNPkAY6z5B45Et5kVqqu0GVOpIgkC7bAEaRJLqx4NQ74EXHoBztcEFxkjPO2fX6mTp0Kwcfm5NajR8nPVXHqlYUdu7esHDteJ/dT3eFbV/zM42P1fL7/PprfasYMPfNchRkvx4EgJGGtlqbgIsv0q1yG5yChg1Ov6gPKggVys+N6NZGib4RL4AjCJBdmVBOodVrIJsLYn0scyXgeIPx4CKKF0htQGBU0I15MpOgb3gOBAwRZoNZlIZuRQdSvX3Rcj8UY92UVmZaa4Tno6ODUK5tEdm+GNTyqZMc1JlIDwxTn1FaPvgGAfsSPA8C6b9vo0SUzPC9ZQtKA8BNyp15VBxQWLFQNhXfDSRl9AwAQJDqlcOCOH+cLC0kqEH58sIX+8ov598jzoZ9mJFHdKMMUZ9X+r1JINgAAhE0zBp8fn2yh8SDPR0lio7p27ZKvNYuPMisocM+B3etIMgAAAImB5sdjEmkBkOcjtSmJJ/5EgoTXmhGz8znzTCKTsnYlTHHDhhE1b57aDwg5YPQHCSoB0BMIPz7A3uzvvku0aBEyPJsxaxZR584lP08m+HipGUlk2kom+MQycmR0s+IHFJREZ2EECSoB0BcIPz7SpAlRZqaff1F92EeGc58kI14D5KXWLFn+HbtY9QPSyU4O3PX9AgDIAcIPkDqB3HKLNYHkqaeIzjrLe82IG3VqZIbkA+/NVakSVOKeA6A+cHgGUjAmEKuw4ONHdly3o8diQ/KBOkJ3OlnDkaASAJJWdsgtoPkBUrCrYfErF5LVv1OlCtGePdaPG+ZElkEzV8lKw8CTy0cfeesbBgduEBZ/N2h+gBTsTAxGgVOVCq7yZMnp7QcNsnbcsCeyVGF16VY9NVkJKuvV87bGXboaMRAO5gakIDOEHyAFOxODn/lurObfKV06aoLjsHar1emB3MnYLXOVVQHZrXu+cOGpycWrySYoExrwlhMBKtYN4QcoWwmYBZG33vJfjWqngjOSFXqDF5OxW+YqP+85TyIDBph/59ZkE6QJDXjLhy4tIFQAwg+QYrpINoEYzJxpLRpMdgVnO8ISkDcZu2mu8uue8yQSr/Fxe7IJ0oQWBFR2JN6haNkhJ8DhGUh1jDOrBMwmA6/y+NiBBTTWUBkh0fyayMkUyQrdw85kbCc/ktv11Py4535MNkGa0FTCifO46o7E1QJUrBvCD5AeWaNqhmO7AxGSFbqDV5OxoW3kvseCTmy/dGqu8vqe+zHZBGlCUwUnQowOiTObBqggM8xeQLrpwphA/MjjYxU4gMrDy8lYNxMlTyLx5+q2c7XfDtxBNyc5GTt08bsqFaCCzBB+QMIK5ukMFDr7EegyEAUVrydjO/5csuFJZOxYbyebIE1ossP4nY4dOo2XnTRbQCQCwg8wHRhyctIbKHT2I9BpIAoifkzGKmobkxVGZqpX926yCcqEJluL63Ts0G287KTRAiIR8PkJOYnszPErE7t2Z539CHQbiIJIImd4L4vaqs7GjUTr1nnnG6ey/51T/K7D5nTs0HG8LKV5QWYIPyHGTgVzuwOFzo5xOg5EQSSIk7Hqk43uE5pfkYNujx06j5e6ArNXiLFbX8uOuccL04VfDothcQDVgXTMUyrnSwHB1OI6HTvC4HelGhB+QozTB97q79z0I/Cz7hAGIv1Bnapg4VSQ9VuLm87YEWS/KxWRKvyMHj2arr76aipXrhxVrVqVOnbsSJs2bUr6m2bNmlFGRkaJrW3btkX79OrVq8T3N954ow9XpBdOH3g7v3PDMU5G2DkGIn1BmoJgkY4gK0OLm87YEQRHYl2Q6vOzatUq6tu3rxCAjh8/TgMHDqRWrVrRP//5Typbtqzpb+bOnUsFHIf9X/bu3UuXXXYZ3RJXB4GFnalTpxa9z8rK8vBK9CSVndktu3M6fgR+OyzGAp8T/ZDZX4D7pJv4z4vEll6PHUHzu1IVqcLP4sWLi72fNm2a0AB99tlndN1115n+plKlSsXez5w5k3JyckoIPyzs5ObmenDWwSHZwBCPLLuz3w6L8WAg0gvZ/QWoJ8jKihzE2KE2SkV77d+/31TAScaUKVOoS5cuJTRFK1euFIJUxYoV6YYbbqCRI0dS5cqVTY9x7NgxsRkcOHBAvBYWFootXYxjuHEsL3KI8MDAlaNjCyjygxtrV+eBYsyY6P5+XgavmrKzre3H56VyWweJdNuZ+1Z+PtHOnUS8RmnY0L1QYzv9RQfC2qfXrGHNfvL7uWcP0erVRE2aJD8Wj1tt2pj3udhmDWtby8CrtrZ6vIxIxIrBw3tOnjxJ7du3p3379tEa7vUW+Pjjj6lBgwa0fv16uuaaa0pog2rVqkWbN28W5rQzzjiD8vPzqZTJCDts2DAaPnx4ic9nzJghjgMAAAAA9Tl8+DB169ZNKFPKly+vvvBz991303vvvScEn5qsZrDAXXfdJQSaDRs2JN3vu+++o9q1a9OyZcuoefPmljQ/eXl5tGfPnqSNZ0cSXbp0KbVs2ZIyMzPTPl5YYO0Ay8G3307066/m+7Dqmx0LuQtEV3Foaz9w2s4LFxL16FHSlGGYVV999VRGY6d9pl49ou3bE+dLie0vOhDWPs3PfkwcS0IWLUqt+bFKWNtaBl61Nc/fVapUSSn8KGH2uvfee+mdd96h1atXWxZ8Dh06JDQ8jz32WMp9zzvvPNEY3377ranww/5BZg7RfEPcvCluHy9sVZHjMSZMNseVKVP8O7S1P1hpZxZI2MeGzaoPPsgrM/P93HBG5lPhWljsx8aYObia9RcdCFufZrdP9lRIlfiP94vtL0Z/SycxZtjaWiZezLPKh7qz0okFn3nz5tEHH3wgzFRWmTVrltDW3HbbbSn33bZtm4gKq4aUvFqHKsfjR/4LJMpzL0yZH9Wff/a+ZlpQ0xSwJiSoCRvNnjMnOXOQ3wlYRarmh8Pc2a9mwYIFItfPTvZEI6IKFSpQ9n+93Hr27Ek1atQQOYHiHZ05L1C8E/PBgweF/87NN98sor3Y56d///5Up04dat26tY9XB7wqucG3/M03vS9IaaZ94gmUB2RdJ1AVwpT9yLYbpDQFbCrk82YT0JEjweuHqZ4zq5Fa6YbFg3AhVfiZNGlSUeLCWDg/DycqZLZu3UqnnVZcQcWJENk36P333y9xTHZoZh+g6dOnC+fp6tWri9xBI0aMQK6fgJTc4AgQngy8FnwwkPpTN87LbLu6h7NzP2QfKU54F8QJ3epzlkqQRX4noJXwY8XXmkPW47ngggsS/pY1RkuWLHHl/EA4K6pjIPW/bhyD4o3h6od2ry+ZIIv8TsAuqO0FlEKFiup2BlLgjnCK4o3h64dWr+/ZZ1P7OqmwaAJ6oUS0FwBWS274oR3AQJo+doVTr7Pt6kjQ+6HV8+YIQYNEvk4qLJpAamIj8WQXYIDmByiFChXVMZCmT6qCksyZZxK99pqexRv9iAJUtR+6de1OzjtRMWMZBUyBvf7CQizfc6NArZHDiR36ZQDhByiH7FBlDKTpk0qI5W3yZKLu3b2P2nN7MvcrnFrFfujmtVsRkOMxtMHsCxR7n1RYNIHk/YXb3yzVBTv0u/3sWAHCD1ASFnC+/z6qFeBIFz+1AxhIgyHEejGZJ8pBlUgj4VY/jEfGhO72tSd7zpKRyNdJh/4WJuZazNdmJsz6AXx+QoobWVC9RmaosqxK0EFD5Xw7dtMZyIi+StTP3O6HqcYDr6490XPm1GdI5f6m09jrZ6qLWGHWz/Eewk8IQfI+a+gwkOqAivl2Uk3mzJ13csLVU2Y5WeHUXOvs3XejNaw4D6zb/dDKeODltcc/Z7t2FXdytuszpGJ/C9vY+6GDVBd+O+5D+AkZOibvk7lSUnkgBd4Ozr/8QtSixanJKab2sZRBnIt3ul1uyup44HXkWexzxs/7E0/Ijfj0Ah3HXqc46Qd+O+7D5ydEWFntyrC9JgO1eoDswdmYnL75Jljh1HbGAy8jz+IdzpmgOS/rOPamg51+ICsSD8JPiNAtaZodB0tjAOXVk/EehJdUEVx2BmdjcnrxxagzrUrRV+m0CycPtDoeeBV5lmhxw/ztb0RxlY3Ee/5cNw2JbmNvutiN5JMhzEL4CRE6JU2zs1KKHUB7945+V6+enPBJoIe20O7gzH2OJ68+ffTVSMS3ixW/GmM88CICMtni5uabicaPLym08vsJE/R7tnUae93ATiTfq6/KEWYh/IQIVZOmpbNSGjXKfADdvt390GOgPla1hU7DrOvW1TOc2k7YcaLxwM1QciuLm2ToZiLSaex1i0T9hZOb8v1jB37DoV8GcHgOEXv2pN5HFbW91RUQT2CptEO6Fn7UGRlO6lYmVNbcGBFcTsKs+Vr4tzpFAdoJO07lWOxWBKSTaCDZodG6l+2RQack/aWwMBrFKAsIPyGBB0Aram6OslBhEK9a1dp+HJETpEEyCMgK57Uyoe7dWzyCyxic2Q+mc+fE/Sl+ctIpCtCJoJHMlOXGtbth3tHJRGRoGln7xm0bKwDpYDJNB1WfFZi9QlAjyM4AyCpJFSbPXr2S78MDRqVKwRskdcfPDMhuRHDx+fDg3Lx51KHZKL0Ri6qTk9Wxw0n/99qM54Z5RzcTETJQqwWEn5CEcevicGfFN8GYjFi7EMRBUldkh/M6ieCKPZ9kk9Nbb0WF7ddfjwpB/OrlYsXNscNquzz1lH+lZJzU9dIpqk7Fsj2gODB7hSThlQ4Od1Z9E3hyYhUymyt4tR42O7qqyMqAbNWvItn58G/5lRMZTpsW/X737ujzwMUY2WRsdm0ysvPaHTus+pvcd5+/yUOTmYGM90E0EalqBgob0PyEZIWsYoVop6Y5npx4cE8VscNt+eST+g6SuplfZWsXnUZwLVhQXIvCPkFsds3KivoA3Xpr4n7Jn/sZVehk7FC1UG8yTducOdFNt6g6oA8QfkKS8ErVAdDJpMgr8lQDqAGv2BHu7o/51Y520Stft1T9wQzu94l8lDg6TKXQa6djh6r+JsnMQDARAS+B2UsCslbIqlcqd2qa4/PmiYejdeIJYt0cVc2vVs0rbEZi4cqraDCrEVwMC/tmQotx/hwdlgpD4OCMyWed5W3oezpjh6qFepOZgWAiAl4BzY8EZPrfqLyacmqa48nroYfMfxPEujmqml+taBe7dDE3I7kdDWY1gsvNPsFaRq8DF9IdOwxhomvXU9XqAQgjEH4kINv/RtUB0KlpLmx1c9zCi3ZLFTHFZi4/fd2SnQ//La/wKrRf9tjhZ3oOALwEwo8EdPC/kYUT3wTZjra64lW7JdIuVqkiR0hNdD5sAvIKr4Q52WOHn+k5EgHhC7gBhB9JqOqAqAJ2TXM6hPGriJftZqZdlCmkmp2PFS1K5crO/6aXwpyMsUNmAkuVhC8QDODwLBFVHRBVwI6jY6yjrRnI95O63fzIk6SakGql5MALL0Rf7dT/8kOY83vsSOUfxu3ldR29dJzzZdSaA2oD4UcyiGZwfxKLJexmRJXqDalY3NFqBKQhaPC5c7Qal4Exkh/KEub8HDtkJ7BMR/iSVWsOqA3MXiAQGJNY9erFP4cZUR0Timx/lXTMrIag0b17dJLlV86ILNv52C9k+9U5dc5XwVQH1ASanxATNFUwT1Zt2hAtWUI0ZUowrskP/DShqJpryokWJR3NmW7PnmyTpRPhSwVTHVAXCD8hJaiqYGMQ4wkpM1P22eiDnyaUIPm6ORHmdHz2ZJssnQhfsk11QG0g/IQQv4uqAhBkXzc7wpyMZ88NLZPf/mFOitayH1ajRuqY6oDawOcnZMgoqgpA0LGSOFTGs+dmaLjM9BxWitayA3rt2qeuTbapTlWQJ0kB4Wf06NF09dVXU7ly5ahq1arUsWNH2rRpU9LfTJs2jTIyMoptZcqUKbZPJBKhIUOGULVq1Sg7O5tatGhB33zzjcdXowfIhhycgWv58uiGTLt64Pez54Wzr8zyOFaK1sZemwrZsFUDeZIUEX5WrVpFffv2pXXr1tHSpUupsLCQWrVqRYcOHUr6u/Lly9OOHTuKth9++KHY9+PGjaOJEyfS5MmTaf369VS2bFlq3bo1HT16lMIOVMHBGbhatIhuSPamB34+e15qmWSWx2EBaPPmqInLjNhrY1SMLpQFIt8UEn4WL15MvXr1oksuuYQuu+wyodXZunUrffbZZ0l/x9qe3Nzcou0sLqUco/V5+umnadCgQdShQweqX78+vfLKK7R9+3aaP38+hR2ogoM1cMWC8F218fPZC7KGd+3aqInLyrUhk34UuDso7vC8f/9+8VqpUqWk+x08eJDOOeccOnnyJF1xxRX0+OOPCwGK2bJlC+3cuVOYugwqVKhADRo0oPz8fOrCZaXjOHbsmNgMDhw4IF5ZE8VbuhjHcONY6XLttUR16hBt3544aoNz5Rw/HjWn5OYSNWyoz+pIpbZ2c+AaMIAozrprCt+/hx+Ohvx7ec+C2M4qPHts0uH9YpvVSVuz9ig729p+ut1Cu9fWrl30ecjPJ9q5s/iYFn/tQe3Xa9YQ7d2bvN327CFavZqoSRN/zsmrtrZ6vIwIq0oUgAWZ9u3b0759+2gN36kEsADD/jus0WFhacKECbR69Wr6+uuvqWbNmrR27Vpq3Lix0PSwz49B586dhcbozTffLHHMYcOG0fDhw0t8PmPGDMrJyXHxKgEAAADgFYcPH6Zu3boJ+YBdZJQXfu6++2567733hODDQowdKe+iiy6irl270ogRIxwJP2aan7y8PNqzZ0/SxrNzjuzT1LJlS8q0kHyGV/pmq5REnzth4cKoNiG2HhYr3H75peS+hn381VejqyiVsdvWOsBOnr172/sNJ3lkM5lXBLGd/YKfvfvvL/ms8fM3cWLJZ8xJW/NYUa9eai3Thg36aHX9uLag9mvWJ7Rtm3q/RYv81fx40dY8f1epUiWl8KOE2evee++ld955R2hw7Ag+DDfa73//e/r222/Fe/YBYnbt2lVM+OH3l19+uekxsrKyxGZ2bDdvipXjJUqAxs6FbIZyKzFafG6SqlWJbr+d6MgR8/11y4bq9r2TCXfjRPcl2W/8uPwgtbOfmE3c/FmyXD922pp3Gzv2lABslpdnzBhrplTV8OPagtavr7uOqHLl1Ekqr7vO//Hdi3lWeYdnVjqx4DNv3jz64IMPqFatWraPceLECdq4cWORoMPHYAFoOccAx0iCHPXVkFUlGjq18vvx492vTxMbtcH/T1QVXXcHSd1JFbIb9vBdnfDT8TQozr5meWmCcm1+oWpdPZlI1fxwmDv71SxYsEDk+mFHZcNBmfPzMD179qQaNWqInEDMY489Rtdeey3VqVNH+AeNHz9ehLrfcccd4ns2bT3wwAM0cuRIqlu3rhCGBg8eTNWrVxd5hHQcFBPhZn0ahMCrS7LsurGEdRDTCb9LLuheSiRVKRCdr81v/Kyrd0KD2nVShZ9JkyaJ12ZxT/nUqVNFCDzDoe+nnXZKQfXrr7/SnXfeKQSlihUr0pVXXin8fC6++OKiffr37y9yBfXp00cISE2aNBFh9fHJEHUaFL0eLBECr+fAFYvs4qBAzUWGrqVErJYC0fHaZOGHwDhXk9p1UoUfK77WK1nPGcNTTz0ltmSw9oc1RLzpQrqDXbq/l124EDjz02J271Z3dQWKg0WGNVCR3Tt4jGja9NQ4wq9ujR061Y1UwuEZpJ/YLN3fyy5cCIK9igdRsMiwBiqye4dXmpkTKfzZVAuaQWFTDZ1avXJwhRMhCHKBRRUKOsLx1BrwQdSvxMWHFv3Z+NnjjbVAjKwi2hB+FMFK1eJ4vNDIyCxcCMKD3wUWVSroqPMiwy8BEuZB/SINd1h0vejcOfr8GbnLOGeTjOcQwo9CJBoUWbPTr190cPRjsJRZuFDH1TxQu8CiigUddVxk+ClAoiK7+3hd762aRdeL+OSeRn4rv59DCD+KkWhQHDdOv8FSxmDMqwigLn4XWFS5oKNOiwy/BUiYB/UzJTZ16Loh6zmE8KMgiQZFnQZLWYMxryKMEgJAPfyuNh7k6uZ+IUuA1Nk8qCJemxJLOXDdkPkcQvgBgRyMubI5TGDq4bcjKxxn9RYgdTQPqoofpsROCQRWLq3hd36rVCDUXSN0yJqpSkJI/t6tLLlAX0dWOM7qL0AivYN77ehHOpNOJokUee5q0cK/594KEH40QZesmWEYjIE+eW6QVyd9IEAGB54r3nqL6J57iH7+2bvs8PECKws/qiXRhdlLA5IVPJUVrSITDMb64rcjKxxn0weRV8GB54oHHywu+FSpQvTEE94uolV8DiH8KE6qgqf8eZ8+4fJvsRJVgFIc6qYP8NuRNUiOszJSO6g4cQH3FtF79xLdeqv3i2g2hQ0bRlSxYvHP+bmU8RxC+AmAfwt33lGjKDRYGYzHjMFgrHIuF78dWYPgOMsRjLISNQZJgAwjslM+zP3vuDJ06Kk8P4YQtGGDnP4D4UdxrPqtsDAQJu1PosHYeN+unZTT0hoZuVz8TN2ge6qIHj3kJmoMggAZVmRG7M1NMK7s2xd9ffddkgKEH8WxkzUzbLlKzAZjXkUA/VaGIDFGm6twb3QXIMOKrCCREwqnJUG0lwb+LZUqlUwJbkYYo5viowoKC0kLVEtbgCra6pKfn/z72FW7jqkdVHsWgoisIJEPFU5LAs2P4vAgwJKzFfzMkRAUZDiQqlJkM/baly+39pswCtiy2bkzuPdGlWch6MiK2NuhcFoSaH404NFHiSZOjDo2myEjR0JQcyedeSZR9+7RyIRGjYjWrnV3RWrYv+PVwIbvhl/Oo2bXbgUI2P5rPHJziQ4cCN69UeVZCAN+JTjUKS0JND8awB3yhRfMv0OoqbtOeJz/ggcBXoHm5Li7IlXFrybRtSfDq5VhWLGj8WjYMPrq96rdS1R5FsKEjIi9pgqnJYHwowncMefMiXYUlUNNZZiR3M6dFLufm5E1KhTZtHrtsUDAlhtVF7saD0qeHRWehTDid8ReKYXTkkD40QjVQ011sd9bccIzI90VqVf2bzsCp5NrV03A1pl0NB6vvhqcPDsq+4IEHb8j9jol0Dj97nfR1zZtSAoQfoCWOWLSIZ0BNZ0VqRf2b7sCp9VrHzRITQFbd9LReHDuKpUXP0HxBQHeLdyHD49GLzO//hp9rVdPzvwA4UcjVNWs6Ga/d2NAdSJAuR1x4UTgtHrtzZsjl4uKGo+g5NlBvbDwsWBBtLxFfNqW7dvlLJAh/GiCypoV3ez3VpzwvBCg3KyR5FTgxKQjF2g8oqBeWLh8Lk8ouECG8KMBKnYcne33yQbeVKQbWeNWxIVTgROTjlwgfJ4C9cLCYRlQdYEM4UcDVOw4uq9mEw28yXArssYNx/V0BE4Zk46qK1Ivz9XsOBA+kz8Ly5YRTZ1KdOyY+v1EJVS2DKi6QEaSQw1QseOYrWb5QTPTTqmahJEHXk5myEIj26Nfe41oz55T3/NEFTv48jWw4OOGcBBflsNvgTP22r0uK2CWUJHbkrVvidpSVskDJ+fq5DgsZJp9b/Sv2OvnJIdBxngWuM169Uq/7cNGKssAj79sGeDnXZaPWDUVF8gRUIL9+/dzNxKvblBQUBCZP3++eHXCihXchVNvvJ8s5syJRDIyolvsORmf8fd+kE5bHz8ebcMZM6Kvx44Vf8/fqwKfS82aJds7tt3z8rw7Z6vtbPQLs/NL1C/4M7622P35vdd9yMm5pnOc+P5m3Kv468/Ojrb1nDnOxg8dcKvtZY/VMtBhfjhuMl4Z/Zpf3RyvrM7fEH7SaDy/HijZE51VzCYtPi+/Bi5dBy8dBU4r7Wz020SDsVm/TTQJGtvw4d70cyfn6sVxzK4/dpJ44AH1BPF0SbfNEgmRYRk/+LqtCD+8n0rjVfZ/+3VOToGr45XV+Rs+Pxqgi5+A6kkYg4bqDqN2fdWsZJ8eOpTonHPc92Fwy68uneNYuX6j9IoqjqxukE6bqezkG2qTko3xit/LGK/g86MJVvwEVCBdX5Yg4Ke/ip++O177qlnNPu1F4Uu3/OrSOY6d7NtBKv7ptM1QGFU/n8tOceMVs2EDUZky/p8LND8aAc2K+shYiaqa+M7uitSuw76b6R3cWj2ncxw7169Cigu3cNJmqqf/8BNdLAPx4xUL78Z7GUgVfkaPHk1XX301lStXjqpWrUodO3akTZs2Jf3Niy++SE2bNqWKFSuKrUWLFvTxxx8X26dXr16UkZFRbLvxxhspCKg60QH1w01Vz2ljRy3vdnoHt/LvpHMcu2YJ2Sku3MJJm6me/sPv1Aqqm8BVRKrws2rVKurbty+tW7eOli5dSoWFhdSqVSs6dOhQwt+sXLmSunbtSitWrKD8/HzKy8sTv/mJZ5gYWNjZsWNH0fYG9ywAPAIr0fRXpE4yb7tVBNat1XM6x3GaeVyV5KFOcdJmqqf/kKEphmXAJhGF2L17t/DSXrVqleXfHD9+PFKuXLnI9OnTiz67/fbbIx06dAhMtBdQv611CDeV1c52ogBTRXul055WQujdilh0ehyzCL7YaK8g9yk7bebV8+bn+KFKeL8svGprLaO99u/fL14rGWVfLXD48GGhMYr/DWuI2JR2wQUX0N1330179+51/XxB+LL/JiIoK1GrGPeIVeqp7pmdFamhvmcNSDK8KgLr1urZ6XHsZB5Pt9SKathpM93LhEBTLB9lor1OnjxJDzzwADVu3JguvfRSy78bMGAAVa9eXfj+xJq8OnXqRLVq1aLNmzfTwIED6aabbhJmslIm+uZjx46JzeDAgQPilYUq3tLFOIYbxwoaCxfyPYxOQgY88I8dS9SunT5tzVl4s7Ot7ad7N+B7NmRIIY0aRXTvvYV05Ii1e9a48an/nzwZ3czgY7RpQzRhAtHjj5f8PtYUkuw4sRMN97FEESV8vIcfjv5NY3iweq6pcHIc4/rz84kWLeJyD9EOk51d6LgNdMJqm7GprEeP6P9jHZ/TaRu/xo81a4h4PZ5szOBs86tXEzVpQoGk0KO2tnq8DFb/kAKwdua9996jNWvWUM1Uy77/MmbMGBo3bpzQ8tSvXz/hft999x3Vrl2bli1bRs2bNy/x/bBhw2j48OElPp8xYwbl5OTYvBIAAAAAyICtQd26dROWpPLly6st/Nx77720YMECWr16tdDWWGHChAk0cuRIIdBcddVVKfc/88wzxf533XWXJc0PO1Lv2bMnaePZkUTZobtly5aUmZmZ9vGCAK/G69UrrvGJhVdvrE3gHBB2ItqstrXbGifjmMlWoq++6vzYqt0z1kK8/PJS+vOfW9KRI5lp3TMrf5e1IDt3RjVnDRvaOz6bkXr3Tr3flCmnwm9VwujT5cq1pF27Mh21QZBJt3/IGKtZ89O2ber9WPMXZM3PUg/amufvKlWqpBR+pJq9WO667777aN68eUJ7Y1XwYW3PqFGjaMmSJZYEn23btgmfn2oJYkmzsrLEFg/fEDdvitvH05mPPiL69tvk+3zzDdG6dc6SJiZr60TJ0TZvTi9xnPGb+ESU7HugUiJKN+8ZCz6G8JPuPUsE30aOgnEKP/ZsmrOyn8qPZ9OmGD+86B/mxyzZ1m4mL73uOqLKlVMnJuT9gi7kZnowz1pBqsMzh7m/9tprwrzEuX527twptiMxI1XPnj3pkUceKXo/duxYGjx4ML388st07rnnFv3m4MGD4nt+7devnwif//7772n58uXUoUMHqlOnDrVu3VrKdQJ1HIS9djR06uiqg9O3rk7dujvHguAlL9UtMWEQkSr8TJo0SaimmjVrJrQyxvbmm28W7bN161aRpyf2NwUFBfTHP/6x2G/YDMawQ/OGDRuoffv2dP7551Pv3r3pyiuvpA8//NBUuwPCVY/Gj+RodhNR6lKfSJcaQulONDoIol4Qtuu2er1eJS9FYkK5SDd7pYLNYbGwNicZ2dnZwhwGUpNIjetHbSpZ9WhU017oVJ8o9p6ZoVINIae18fh+mO3DwpMq98ELwnbdya43dqxLpSnmPs+aYq5X5WSMVLk2X9BRKs8P8I9E2ob+/f3RQshS+6qkvdAt14fuqvpUJslEK3x+f/PNRA8+GEyNSNjKsiS7XiNgQWVNMXAHCD8hJNkgP368f4OgDLWvSv4fOtYnMu5Z9er61BCKNW9wW/K9jZ9okgmiBizYqWqSDIsA7sf1GvupqCkG7gHhJ2Q2dyuDvJ+DoN/1aFTSXug6sPK92bjxVHi41/csHaz6U6USRIOqEdFRAPf6ehkOnVdNUwzcBcKPIvjl9GpnkPdrEPRb7auKo6HOA6txj1gIcOOeeSH42zHn2BEwg6QR0VUAd4rV6+CcQappioG7QPgJmc093UEsKIOgChWQMbB6J/jbNefYFTCDohHRWQB3gtXr4GSJqmmKgbtA+AmZzT3dQSwog6AKjoYYWL0T/O2ac1IJokFdDIRNALdyvQxniVZNUwzcBcJPyGzuTgd5XQdBP3OXOPlbYR5YvRT87ZpzkgmiQV4MhE0At3K9xn6qaYqBu0D4CZnN3ckgr+sg6GfywHT+VlgHVi8FfyfmnESCqBeLAZUSCropgKt0XU6ul+vvqaopBu4C4SeENvdEDz8P5v36RQcB3bUQXGTULz8qN0w3YRxYvRT8nZpzYgVR1joZ+8b/lnnyyahgZneiVzGjtxsCuIrXZfd6dS48DGzCVd1Bcfbv389Kd/HqBgUFBZH58+eL13iOH49EataMRDIyeJ1bcuPP8/Ki+7kNH3PFikhkxozoq/E3En2uA0Zb16lTYNqebrepcf/8+FsqkaxPW4X7VqJ2i914PyfMmRNt//hny/iMv7dyjPj7y/ezX7+Sn/P7VMc0zsmsnyQ6Jzfa2mucXJeK6NDWQaHAo7a2On9D8xNim3sibUMQtBCJSjC47UcVtjwpOjnbumHOMdMQPPEEEZcStKvpC2pCQRWvSwfzG5ALhB8FCLPTq0zc8KMKW54U3QR/N8w5sYsBFsQeesjZRB9UQVm169LJ/AZCWtgUnAIF7vzHDT+qsOVJkVVwNBa7hXcN4cXviT7+bwZVUFbpunQqFAzkAuFHEokGcLcG6bDDWrTNm+1XjLc7scqqTh9WwV929fF0JvqgCsqqXJfXFdhBsIDZSwJQy3rP2LH2zSlO7kvY8qR4hRU/My8SItr1DUlnog9qQkGn1+W2X45q5jegNhB+AlzKIsxwyKodP6p07gt8tvR0qnUi7KYjwARVUHZyXV4sAFUyvwH1gfAT8qiIIGPV2TXVfeHtL38hev31xCvUsCYq9Au3V/VOhd10BZigCsp2rsurBaAq5jegB/D58ZH8fOfOksAZVvyorFS6//lnottuS+5jAp8t73C6qjfz4WLS8Q1x4qTt1MdJJ6xcl5d+OfC/A3aA8OMjO3da2w9qWX+x295Bixyx6+QtAyer+kTO0Xfemf4iJF0BJqiCcqrrSidazsrf5kUJP5ssRMUKWDqbFYE3wOzlI7m51vaDWtZf7LZ3kEyUujjf2/W1SWZaGTrUHaE4CMlA/cZrv5ygmhWB+0D48ZGGDYMZ7aE7TirdByFyRCfnezu+NlZ866yARYj7+OGXA/+7xCDz9Skg/Cg0gPPAfMcdRG+9hZTsqtyXoJooZTvfOxmEra7qrfhwJQOLEO/wK9wfWjl9tbx+AeHHZxIN4JUqEVWuHFXJo2Oqc1+Cqh2QmRMlnUHYyqrejkAapJBzHQhquL/qmhadtLx+AeFHAvED+PDhRL/8QrR3b/H9wtwxZd+X114jOvPM4JooZeVEcWMQTrWqtyqQ8nOnkm+IKhOl14TFL0cVTYtsLa+qINpLEsYAzh2OHwikZFcvWiU7O7iRIzJyovhVfsAwraQyfV18cVTYVSHSLVnZDk7YGbSIQr7HQQz3V7HGmJcRdjoDzY9kkJJd3RV1kFeoMkot+NXXeQJ98snU+3F1dkZ2xFYqbdjChRRIDciCBfLbXkVNi9saQGS+NgfCj2TQMf0feHmVycKLzpEj6Q6QMnwv/OzrbLJMhQrRelYmyocfJm0Jo69JOkK+F6YyZL42B8KPZNAx/R94OVvzLbcQ9e+vZ+SIWwOk35otP/u6LosKKxNlOpFrMgmrr4nTvueVoBjUgrrpAuFHMuiY/g+8BuPHE82aRVrh9gDpp2bLz76uy6JCtvDlJWE16Tvpe1brCxYU2D+fsEXYWQXCj2TQMeXUUTPo21efladXK2m/NFt+9nVdFhWyhS8v0UX75jZO+p7V+oJ8XCcaoCD7LzoFwo8CoGPKq6PGA4ouK88grKT96uu6LCqsTJT8vY7oon1zGyd9z6oAyOOVUxOYqv6LsoDwowjomHLqqOm08gzKStqvvq7DosLKRDlmDGmJLto3L7Db9+wKgE59pVTzXwyt8DN69Gi6+uqrqVy5clS1alXq2LEjbdq0KeXvZs2aRRdeeCGVKVOG6tWrR++++26x7yORCA0ZMoSqVatG2dnZ1KJFC/rmm29IddAx3a2jZiXih9GgawRuJe1XX9dhUZFqotQ1z48u2jevsNP37NQX1EHDqwNShZ9Vq1ZR3759ad26dbR06VIqLCykVq1a0aFDhxL+Zu3atdS1a1fq3bs3ffHFF0Jg4u2rr74q2mfcuHE0ceJEmjx5Mq1fv57Kli1LrVu3pqNHj/p0ZUA2PKA+95y1fV98UQ+/nzCvpIO+qNBBSAuq9k2FvhcrKFpFdQ2v8kQUYvfu3ey2GVm1alXCfTp37hxp27Ztsc8aNGgQueuuu8T/T548GcnNzY2MHz++6Pt9+/ZFsrKyIm+88Yal89i/f784D351g4KCgsj8+fPFK/CW+La+9VYjViL5tmKFHndmzpxIJCMjusWev/EZf+8H6NP+EYS2Pn48+ozNmBF95fcqIrut+fmtUiVYY5bfbW11/laqvMX+/fvFayWu8pmA/Px8eshIzfpfWKszf/588f8tW7bQzp07hanLoEKFCtSgQQPx2y5dupQ45rFjx8RmcODAAfHKmije0sU4hhvHAvbamlPov/22tVWUDreHTSC8Yh4wIBreHruSZt8Q/t6P60Cf9o+gtHXjxqf+f/JkdFMN2W3Nz2/r1kQXXUS0Z09iDS9r0q69Vo8xy++2tnq8DJaASAFOnjxJ7du3p3379tGaNWsS7le6dGmaPn26MH0ZPPfcczR8+HDatWuXMIs1btyYtm/fLnx+DDp37kwZGRn05ptvljjmsGHDxO/jmTFjBuXk5LhyfQAAAADwlsOHD1O3bt2EMqV8+fIJ91NG88O+P+y3k0zw8YpHHnmkmDaJNT95eXnC/yhZ49mRRNmnqWXLlpSZmZn28YD1tmZfnnr1iLZvN8+PY6yiNmxQ0xdEVdCn0dZBRKV+zTXdkml4dafQo7Y2LDepUEL4uffee+mdd96h1atXU80USS1yc3OFhicWfs+fG98bn8Vqfvj95ZdfbnrMrKwsscXDN8TNm+L28UDqtubmHjs2mhuDMavOzoNJmTJoTSegT/sH2jpcbc3O4Gy256guNsvzdMbBDEFbpGV6MM8qH+3FFjcWfObNm0cffPAB1apVK+VvGjZsSMuXLy/2GUuP/DnDx2ABKHYflgQ56svYB4SLsEecAAD0RIdIRV05Xbapi/1qFixYIHL9sKOy4aDM+XmYnj17Uo0aNUROIOavf/0rXX/99fTEE09Q27ZtaebMmfTpp5/SCy+8IL5nv54HHniARo4cSXXr1hXC0ODBg6l69eoiJB6Ek7CsogAAACgu/EyaNEm8NmORNoapU6dSr169xP+3bt1Kp512SkHVqFEjITANGjSIBg4cKAQcjvS69NJLi/bp37+/yBXUp08f4UDdpEkTWrx4sUiKCMKLsYoCAAAQbqQKP1YCzVauXFnis1tuuUVsiWDtz2OPPSY2AAAAAIBYUNsLAAAAAKECwg8AAAAAQgWEHwAAAACECgg/AAAAAAgVEH4AAAAAECog/AAAAAAgVED4AQAAAECogPADAAAAgFChRGFT1TCSL1qtDmuleu3hw4fF8WQXyws6aGu0c9BAn0ZbB5FCj+ZFY95OlUQZwo8Jv/32m3jNy8tz7YYAAAAAwL95nOuEJiIjYqXGRMg4efIkbd++XRRb5VIZbkiiLEj9+OOPVL58eVfOEaCtZYI+jbYOIujX+rc1izQs+HAx89i6oPFA82MCN1jNmjXJbfgGQ/jxB7Q12jlooE+jrYNIeQ/mxWQaHwM4PAMAAAAgVED4AQAAAECogPDjA1lZWTR06FDxCtDWQQB9Gm0dRNCvw9PWcHgGAAAAQKiA5gcAAAAAoQLCDwAAAABCBYQfAAAAAIQKCD8AAAAACBUQflziH//4B5177rlUpkwZatCgAX388cdJ9581axZdeOGFYv969erRu+++69apBB47bf3iiy9S06ZNqWLFimJr0aJFynsD7LdzLDNnzhSZ0Tt27Iim9KBPM/v27aO+fftStWrVRLTM+eefjzHEo7Z++umn6YILLqDs7GyRkfjBBx+ko0ePom8nYfXq1dSuXTuRZZnHgvnz51MqVq5cSVdccYXoz3Xq1KFp06aRp3B5C5AeM2fOjJQuXTry8ssvR77++uvInXfeGfnd734X2bVrl+n+H330UaRUqVKRcePGRf75z39GBg0aFMnMzIxs3LgRt8Lltu7WrVvkH//4R+SLL76I/Otf/4r06tUrUqFChci2bdvQ1i62s8GWLVsiNWrUiDRt2jTSoUMHtLEHbX3s2LHIVVddFWnTpk1kzZo1os1XrlwZ+fLLL9HeLrf166+/HsnKyhKv3M5LliyJVKtWLfLggw+irZPw7rvvRh599NHI3LlzuXxWZN68ecl2j3z33XeRnJycyEMPPSTmxGeffVbMkYsXL454BYQfF7jmmmsiffv2LXp/4sSJSPXq1SOjR4823b9z586Rtm3bFvusQYMGkbvuusuN0wk0dts6nuPHj0fKlSsXmT59uodnGc525rZt1KhR5KWXXorcfvvtEH48autJkyZFzjvvvEhBQYH1GwoctTXve8MNNxT7jCfoxo0bo0UtYkX46d+/f+SSSy4p9tmtt94aad26dcQrYPZKk4KCAvrss8+EOSW2Nhi/z8/PN/0Nfx67P9O6deuE+wPnbR3P4cOHqbCwkCpVqoRmdbFPM4899hhVrVqVevfujbb1sK3ffvttatiwoTB7nXXWWXTppZfS448/TidOnEC7u9zWjRo1Er8xTGPfffedMC+2adMGbe0iMuZEFDZNkz179ohBhwehWPj9v//9b9Pf7Ny503R//hy429bxDBgwQNih4x80kF47r1mzhqZMmUJffvklmtLjtuYJ+IMPPqDu3buLifjbb7+le+65Rwj1nDEXuNfW3bp1E79r0qSJqBZ+/Phx+stf/kIDBw5EM7tIojmRK78fOXJE+Fu5DTQ/IDSMGTNGOOPOmzdPODsCd/jtt9+oR48ewrm8SpUqaFaPOXnypNCwvfDCC3TllVfSrbfeSo8++ihNnjwZbe8y7ITLWrXnnnuOPv/8c5o7dy4tWrSIRowYgbbWHGh+0oQH+1KlStGuXbuKfc7vc3NzTX/Dn9vZHzhva4MJEyYI4WfZsmVUv359NKmLfXrz5s30/fffi+iO2AmaOf3002nTpk1Uu3ZttLkLbc1whFdmZqb4ncFFF10kVs9s2ildujTa2qW2Hjx4sBDs77jjDvGeI3MPHTpEffr0EQInm81A+iSaE8uXL++J1ofBnUsTHmh49bV8+fJiAz+/Z7u8Gfx57P7M0qVLE+4PnLc1M27cOLFSW7x4MV111VVoTpf7NKds2LhxozB5GVv79u3pD3/4g/g/hwcDd9qaady4sTB1GQIm85///EcIRRB83OvXho9gvIBjCJ1RX17gBlLmRM9cqUMWPsnhkNOmTRNhen369BHhkzt37hTf9+jRI/Lwww8XC3U//fTTIxMmTBDh10OHDkWou0dtPWbMGBHaOnv27MiOHTuKtt9++83dThDydo4H0V7etfXWrVtFxOK9994b2bRpU+Sdd96JVK1aNTJy5Mg07ng4sNvWPDZzW7/xxhsiHPv999+P1K5dW0TsgsTw+MrpRXhjMePJJ58U///hhx/E99zG3Nbxoe79+vUTcyKnJ0GouyZwXoKzzz5bTLQcTrlu3bqi766//noxGcTy1ltvRc4//3yxP4f4LVq0SMJZB7+tzznnHPHwxW88qAH32jkeCD/e9Wlm7dq1Ij0GT+Qc9j5q1CiRagC429aFhYWRYcOGCYGnTJkykby8vMg999wT+fXXX9HUSVixYoXpuGu0Lb9yW8f/5vLLLxf3hfv01KlTI16Swf94p1cCAAAAAFAL+PwAAAAAIFRA+AEAAABAqIDwAwAAAIBQAeEHAAAAAKECwg8AAAAAQgWEHwAAAACECgg/AAAAAAgVEH4AAIGhWbNm9MADD8g+DQCA4kD4AQAAAECogPADAAAAgFAB4QcAECi4Unf//v2pUqVKlJubS8OGDUv5G67yw/udffbZlJWVRdWrV6f777/fl/MFAPgPhB8AQKCYPn06lS1bltavX0/jxo2jxx57jJYuXZr0N3PmzKGnnnqKnn/+efrmm29o/vz5VK9ePd/OGQDgLyhsCgAIlMPziRMn6MMPPyz67JprrqEbbriBxowZk/B3Tz75pBB8vvrqK8rMzPTpbAEAsoDmBwAQKOrXr1/sfbVq1Wj37t1Jf3PLLbfQkSNH6LzzzqM777yT5s2bR8ePH/f4TAEAsoDwAwAIFPGam4yMDOEHlIy8vDzatGkTPffcc5SdnU333HMPXXfddVRYWOjx2QIAZADhBwAAiITQ065dO5o4cSKtXLmS8vPzaePGjWgbAALI6bJPAAAAZDNt2jThK9SgQQPKycmh1157TQhD55xzjuxTAwB4ADQ/AIDQ87vf/Y5efPFFaty4sfAZWrZsGS1cuJAqV64c+rYBIIgg2gsAAAAAoQKaHwAAAACECgg/AIDA8/rrr9MZZ5xhul1yySWyTw8A4DMwewEAAs9vv/1Gu3btShgaD8dmAMIFhB8AAAAAhAqYvQAAAAAQKiD8AAAAACBUQPgBAAAAQKiA8AMAAACAUAHhBwAAAAChAsIPAAAAAEIFhB8AAAAAhAoIPwAAAACgMPH/ASEtzX2p2b5zAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.correlation_matrix['h_s', 't_p'] = 0.0\n", "\n", "project.run()\n", "\n", "plt = project.result.get_plot_realizations('h_s', 't_p')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "ed355503-4514-4f75-a61b-782141b3ce2e", "metadata": {}, "source": [ "The correlation can only be set between variables that are present in the model. Otherwise, an error message is printed:" ] }, { "cell_type": "code", "execution_count": 22, "id": "4dc52b84-fe1a-46a1-b97e-bac02181e95b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Variable non_existing_variable is not available, value is not set.\n" ] } ], "source": [ "project.correlation_matrix['h_s', 'non_existing_variable'] = 0.8" ] }, { "cell_type": "markdown", "id": "ea7ca90f", "metadata": {}, "source": [ "### Correlation matrix (more variables)\n", "\n", "A correlation matrix must be positive definite. In the case of a correlation matrix of size 2, this is always the case.\n", "\n", "For a correlation matrix, the requirement can be checked by assessing the principal minors. A correlation matrix is positive definite when all the minors are positive.\n", "\n", "Let's consider a correlation matrix with three variables. We can check if the matrix is positive definite by checking if the determinant of the matrix is positive. This is done with the following method:" ] }, { "cell_type": "code", "execution_count": 23, "id": "b0fca87b", "metadata": {}, "outputs": [], "source": [ "def get_determinant_3d(rho_hs_tp, rho_hs_h, rho_tp_h):\n", "\n", " correlation_matrix = np.array([[1.0, rho_hs_tp, rho_hs_h], [rho_hs_tp, 1.0, rho_tp_h], [rho_hs_h, rho_tp_h, 1.0]])\n", "\n", " det = np.linalg.det(correlation_matrix)\n", "\n", " print(f'Determinant: {det}')" ] }, { "cell_type": "markdown", "id": "4afa2864", "metadata": {}, "source": [ "Let's now consider a correlation matrix which we know is positive definite; the corresponding determinant is positive:" ] }, { "cell_type": "code", "execution_count": 24, "id": "45fcef30", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Determinant: 0.1819999999999999\n", "ok\n" ] } ], "source": [ "project.correlation_matrix['h_s', 't_p'] = 0.8\n", "project.correlation_matrix['h_s', 'h'] = 0.6\n", "project.correlation_matrix['t_p', 'h'] = 0.7\n", "\n", "get_determinant_3d(project.correlation_matrix['h_s', 't_p'], \n", " project.correlation_matrix['h_s', 'h'], \n", " project.correlation_matrix['t_p', 'h'])\n", "\n", "\n", "project.validate()" ] }, { "cell_type": "markdown", "id": "c8f1e975", "metadata": {}, "source": [ "Given this correlation matrix, we run the Monte Carlo simulations:" ] }, { "cell_type": "code", "execution_count": 25, "id": "b6547b44", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.run()\n", "\n", "plt = project.result.get_plot_realizations('h_s', 't_p')\n", "plt.show()\n", "\n", "plt = project.result.get_plot_realizations('h_s', 'h')\n", "plt.show()\n", "\n", "plt = project.result.get_plot_realizations('t_p', 'h')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "13ff2b57", "metadata": {}, "source": [ "If a correlation matrix is not positive definite (the determinant is negative), an error message is printed indicating that the Cholesky decomposition is not possible:" ] }, { "cell_type": "code", "execution_count": null, "id": "5b4e02ec", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Determinant: -2.8880000000000003\n", "Error: Cholesky decomposition fails.\n" ] } ], "source": [ "project.correlation_matrix['h_s', 't_p'] = 0.9\n", "project.correlation_matrix['h_s', 'h'] = 0.9\n", "project.correlation_matrix['t_p', 'h'] = -0.9\n", "\n", "get_determinant_3d(project.correlation_matrix['h_s', 't_p'], \n", " project.correlation_matrix['h_s', 'h'], \n", " project.correlation_matrix['t_p', 'h'])\n", "\n", "project.validate()" ] } ], "metadata": { "kernelspec": { "display_name": "base", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.10" } }, "nbformat": 4, "nbformat_minor": 5 }