{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "04ea618b-3abc-4ad5-bac2-b5f1aa01efc1",
   "metadata": {},
   "source": [
    "# **Norm of vectors**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "492c9f03-6420-4691-912b-6bd9404296e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# definition of norm of vectors\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "def norm1(x):\n",
    "   n=sum(np.abs(x))\n",
    "   return n\n",
    "\n",
    "def norm2(x):\n",
    "   n=0\n",
    "   for i in x:\n",
    "     n+=i**2\n",
    "   return np.sqrt(n)\n",
    "\n",
    "def norm2bis(x):\n",
    "   y=np.array(x)\n",
    "   n=np.sqrt(y@y)\n",
    "   return n\n",
    "\n",
    "def norminf(x):\n",
    "   n=max(np.abs(x))\n",
    "   return n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2b2673bb-a96e-4f46-8482-618b7d08942b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x= [-1, 2, -3, 4, -5]\n"
     ]
    }
   ],
   "source": [
    "# let's run the definitions on a simple example\n",
    "\n",
    "x=[-1,2,-3,4,-5]\n",
    "print('x=',x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "19d0406f-68b9-4b64-9d38-97615bf86787",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 norm: 15\n"
     ]
    }
   ],
   "source": [
    "print('1 norm:',norm1(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "975591a6-558b-47fe-aa01-56a9b0450df1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 norm: 7.416198487095663\n"
     ]
    }
   ],
   "source": [
    "print('2 norm:',norm2(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "892b2f56-a3b4-44c5-903a-3249781d25f9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 norm (alternate): 7.416198487095663\n"
     ]
    }
   ],
   "source": [
    "print('2 norm (alternate):',norm2bis(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "035a34d9-a06a-460f-83ae-d89210640743",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "inf norm: 5\n"
     ]
    }
   ],
   "source": [
    "print('inf norm:',norminf(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ad769938-e74f-4e79-9ed5-2dd0e4bb9d37",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numpy 1 norm: 15.0\n",
      "numpy 2 norm: 7.416198487095663\n",
      "numpy inf norm: 5.0\n"
     ]
    }
   ],
   "source": [
    "# built in commands from numpy.linalg\n",
    "\n",
    "from numpy import linalg as LA\n",
    "print('numpy 1 norm:',LA.norm(x,1))\n",
    "print('numpy 2 norm:',LA.norm(x))\n",
    "print('numpy inf norm:',LA.norm(x,np.inf))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9aeff587-b9bb-4616-90a0-64587c1a3e2e",
   "metadata": {},
   "source": [
    "# **Plotting**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1b72b8d0-5c56-4ada-80a3-52e329f4f8b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import necessary libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Generate data: Let's create a range of x values from -10 to 10\n",
    "x = np.linspace(-10, 10, 400)\n",
    "\n",
    "# Define a function to plot (for example, y = x^2)\n",
    "y = x**2\n",
    "\n",
    "# Plot the function\n",
    "plt.plot(x, y, label=\"y = x^2\", color='blue')\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.title(\"Plot of y = x^2\")\n",
    "plt.legend()\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "69aa17a8-e0ca-4c3a-9d6e-b8215ce2b597",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dYW1qDWNZei5FmgJv3r/By4SXuPf2Hm69voULLy7g/PPziJXH4mzMWZyNOQtLE0t0dOuIH2v+CA8njy/KzM9P9lgbzfJrfZKTk/H06VNYWlrCzCz9j5bElEQUn11cSJ64n+JQwKTAR9ezsrJC165dsW3bNvTo0QMAsHr1ari4uKB169bZNlwHDx7UuGfF3Nw8299p0dHRKF++PHx8fCCRSFC5cmX1cxl73jJen3FYbdSoUejUqRMAYNq0aahSpQqio6Ph5uaG169fQyaToXTp0pny+vv74+TJkxg8eDBMTExQq1YtjBo1KtM65cqVAwC8efMmU44MycnJMDc3R8OGDdXf1wzZNZL/ZdDNkoODA6KiojIti4qKgpWVFczNzSGTySCTybJcx8HBIdtxTU1NszwWa2xsnCv/sOTWuIYiN+ujVCmx9fpWzPhrBm68uqFeXt2hOnwr+aJN2TaoXLTyR//6MzY2hoWZBZxtnVHbubZ6eZoyDRdeXMDeO3vx540/cf/dfay/uh7rr65HfZf6GFtvLFqXzf4fu5zg5yd7rI1m+a0+aWlpkEgkkEql6pmnRc5A/e8cH9O/f3/UqlULL1++RLFixbB+/Xr06tVL44zVJUuW/OxsvXv3RvPmzVGhQgW0bNkSX331FVq0aAEAmQ5N/nsbqlevrv7/YsWKAQBev34NqVQKuVwOU1PTLPOuXbsW5cqVg1QqxY0bNz5Yp0CB9IYyOTk5y3pJpVJIJJIsP885/XwbdLPk5eWFgwcPZloWFBSkPkZqYmICd3d3HD9+XL3rUqlU4vjx4/Dz88vruKRDVCoV9tzZg/Enx+N69HUAgKWJJXpV64UfPX5E5aIf/vXyOWRSGeoUr4M6xetgetPpOPf0HH4P/x1br2/F2Sdn8dWTr9DApQFme8+Gl7OXVt6TiHLOwtgCCQEJmZYplUrExcfBqqBVrjZTFsY5P62jRo0aqFatGjZs2IAWLVrgxo0bOHDggMbXVKpUCY8fP872+QYNGuDQoUNZPlezZk08fPgQhw4dwrFjx/Ddd9/B29s728N2QObGJOMPwIzGqkiRIkhKSkJKSgpMTEwyve7KlStITEyEVCrFy5cvP7jH29u3bwEAdnZ2Grb2y+hVs5SQkIB79+6pHz98+BAREREoVKgQXFxcEBAQgOfPn6tPZhswYACWLl2KMWPG4IcffsCJEyfw559/ZvoA+fv7o2fPnvDw8EDt2rWxcOFCJCYmonfv3nm+faQbrkdfx4/7f0Tw02AAgLWpNUbXHQ2/2n6wNrPOtfeVSCSo71If9V3qY1azWVh4fiGWXliKv578hbpr6qKDWwcs8FkAVxvXXMtARJlJJJIPDoUplUqkGaehgEkB4fc++7e+ffti4cKFeP78Oby9veHs7Kxx/ZwchtPEysoKvr6+8PX1xbfffouWLVvi7du3sLGx+eTs1atXBwDcvHlT/f9AeiPUq1cv/PLLL3j58iW6deuGS5cuZcp2/fp1GBsbo1KlSp/8vjmlV83SxYsX0aRJE/XjjPOGevbsiXXr1uHly5d48uSJ+vmSJUviwIEDGDFiBBYtWoTixYtj1apV8PHxUa/j6+uLV69eYcKECYiMjET16tVx+PDhD076JsP3XvEeU89MxdzguUhVpsLC2ALDPYdjVN1RsDW3zdMsxayKYW6LuRhWZxgmnZqEtRFrsev2Lhy9fxQzm83E4NqDIZXozj/SRCRe165dMWrUKKxcuTJHV8C5un7+H17z58+Ho6MjatSoAalUiu3bt8PBweGzGiUgfa9QzZo1cfbs2UzN0oABA+Ds7Ixx48ZBLpejRo0aGDVqVKb5Fv/66y80aNDgo83dl9CrZqlx48bqE8eyktXs3I0bN8bly5c1juvn58fDbvnc+Wfn0X1nd9x/dx8A0N6tPZa0WoLiVmJO7MxQ3Ko4Vn29CiPqjMCP+3/EuafnMPTwUGy9sRVrvl6D8kXKC81HRLrD2toaHTt2xIEDB9SnluSWggULYs6cObh79y5kMhlq1aqFgwcPQiqVfvZ0Cn379sWGDRvUv483bNiAgwcP4vLlyzAyMoKRkRE2bdqE+vXr46uvvlJPerl161ZMmjRJW5uWJf5pSvmaUqXE7LOzUX9Nfdx/dx/FChbDLt9d2OW7S3ij9G+VilbCmd5nENg6EJYmlgh+Ggz3Fe7YfHWz6GhEpEOeP3+Obt26ffKEkJ+qX79+uHz5MhISEhAbG4tjx46hRo0a6uffvXunbthKlCgBlUqVaY+RjY0NVCoVGjdurF7Wq1cvPH/+XD3PYY8ePZCQkICyZcuq16lduzZSUlLUjdKhQ4cglUrx7bff5t7Ggs0S5WNRCVFotbkVxh4fizRVGnwr+eLGoBto79ZedLQsSSVSDKo1CDcG3UCTEk2QqEhE913d0X9ff7xXvBcdj4gEevfuHXbt2oVTp05h8ODBouN8FnNzc2zYsAGvX7/O8WsSExOxdu1aGBnl7oEyvToMR6QtVyKvoO0fbfE07inMjcyxpNUS/FDjhy+6RD+vuFi7IOj7IEw5PQVTz0zFyksrEfo8FPu67IOL9YcTshGR4atRowbevXuH2bNno3x5/T08/+89TTmR23uUMrBZonxn75296Pq/rkhUJKJc4XLY5bsLFe0qio71SWRSGSY3mYwGrg3QbWc3XI26itora2Nfl32oVayW6HhElMcePXokOoJB42E4yjdUKhXmnpuL9lvbI1GRCO9S3jjf57zeNUr/5l3KGxf6XUCVolUQlRiFRusaYeetnaJjEREZFDZLlC+oVCqMCRqDMcfGQAUVBnoMxMGuB/N8SoDc4GLtgrM/nEWrMq3wPvU9vv3zWywNWyo6FpHe0nTVNekfbXw/2SyRwUtTpuHH/T9iXsg8AMCvLX7Fb21+U9+3zRBYmVphb5e9GOQxCCqoMOTQEMwNmSs6FpFeyZhhOqc3VyX9kPH9/JJb9/CcJTJoijQFvt/1Pbbd2AapRIqVbVfihxo/iI6VK4ykRljaeikKWxTG1DNT8cvJX+Br74tWqlaioxHpBZlMBhsbG0RHRwMALCwssrzoQ6lUIiUlJdt7keV3ulIflUqFpKQkREdHw8bGRuN98j6GzRIZrFRlKrru7IodN3fAWGqMzd9sRqdKnUTHylUSiQRTmkyBhbEFAo4HYFvUNhQ7WQzzWszTiyv9iETLuIl6RsOUFZVKhffv38Pc3Jw/V1nQtfrY2Niov6+fi80SGaQ0ZRp67+mNHTd3wERmgl2+u9C6bGvRsfLM2PpjYSY1w4igEZh/fj6sTK0wsfFE0bGIdJ5EIoGjoyOKFi2a7X3TFAoFzpw5g4YNG37RoR1DpUv1MTY2/qI9ShnYLJHBUalUGLB/ADZd3QQjqRG2d9qerxqlDINrDcaNmzew6vkqTDo9CQVNC8Lfy190LCK9IJPJsv0lK5PJkJqaCjMzM+HNgC4yxPrwYCsZFJVKBf8j/lh1eRWkEik2ddiEr8t/LTqWMF/ZfYUpjaYAAEYeHYmV4SsFJyIi0j9slsigzA+Zj4WhCwEAa75eA9/KvmID6YCf6v6En+r9BAD4cf+PnIeJiOgTsVkig/HnjT8xKmgUAGBe83noWb2n4ES6QSKRYGazmRjgPgAqqNBtZzeEPgsVHYuISG+wWSKD8Nfjv/D9ru8BAENqD+G5Of8hkUiwpPUStCnbBsmpyWj7R1s8ePdAdCwiIr3AZon03t23d9FuazukpKWgvVt7LPBZoBOXq+oaI6kRtn67FTUcauBV0iu03twab9+/FR2LiEjnsVkivZaUloSO2zviXfI7eBbzxOZvNkMm/fLLRA2VpYkl9nfdD2crZ9x5cwedtndCqjJVdCwiIp3GZon0llKlxILHC3D7zW0UK1gMu3x3wcLYQnQsnedU0AkHuh5AAeMCOPHwBH4K+kl0JCIincZmifTWlDNTcCHuAkxlptjluwuOBR1FR9IbVeyrYH379QCA+efnY8u1LYITERHpLjZLpJd23tqJGedmAAB+a/0bahWrJTiR/ulYsSN+rv8zAKDP3j64/PKy4ERERLqJzRLpnXtv76HX7l4AgK/tvsb3Vb4XG0iPTWkyBa3KtEJyajI6bOvAE76JiLLAZon0SnJqMjpt74T4lHjUK14PPZ04l9KXkEll2PzNZpS2LY3HsY/Re09vqFQq0bGIiHQKmyXSKyMOj0BEZASKWBTBpg6bIJPwyrcvZWtuiz87/QkTmQn23tmLRaGLREciItIpbJZIb/xx7Q8sD18OCSTY/M1mFCtYTHQkg1HTsSZ+bfErAGBM0BhceH5BcCIiIt3BZon0woN3D9B/f38AwC8NfkGL0i0EJzI8g2sNxjcVvoFCqcB3O75DTHKM6EhERDqBzRLpvFRlKrrv7I6ElAQ0cGmASY0niY5kkCQSCVZ/vRolbErgUcwjDDowSHQkIiKdwGaJdN6Mv2Yg5FkIrE2tsbHDRs7QnYtszGzwR8c/IJPI8Mf1P/DHtT9ERyIiEo7NEum088/OY8rpKQCA39r8BlcbV8GJDF+d4nXwS4NfAACDDg7C09inghMREYnFZol0Vrw8Ht13dkeaKg1dq3RF1ypdRUfKN8Y1HIdaTrUQkxyDXnt6QalSio5ERCQMmyXSWWOCxuD+u/twsXZBYOtA0XHyFWOZMTZ9swkWxhY48fAEFp3ndAJElH+xWSKddOLhCSwPXw4AWNduHWzMbMQGyofKFS6nnk7g5xM/4+83fwtOREQkht41S4GBgShRogTMzMzg6emJsLCwbNdt3LgxJBLJB19t2rRRr9OrV68Pnm/ZsmVebAplIyElAX339gUADHAfgCYlmwhOlH/96P4jmpdqjuTUZPTd25eH44goX9KrZmnbtm3w9/fHxIkTcenSJVSrVg0+Pj6Ijo7Ocv2dO3fi5cuX6q/r169DJpOhU6dOmdZr2bJlpvX++INXAIn0y/Ff8DDmIVysXTCn+RzRcfI1iUSCFW1XoIBxAfz15C8sv7hcdCQiojynV83S/Pnz0a9fP/Tu3RsVK1bE8uXLYWFhgTVr1mS5fqFCheDg4KD+CgoKgoWFxQfNkqmpaab1bG1t82JzKAtnn5zFkrAlAICVbVeioGlBwYmohE0JzPKeBQD46dhPeBzzWHAiIqK8ZSQ6QE6lpKQgPDwcAQEB6mVSqRTe3t4ICQnJ0RirV69G586dUaBAgUzLT506haJFi8LW1hZNmzbFtGnTULhw4WzHkcvlkMvl6sdxcXEAAIVCAYVC8SmbpVHGWNocU5clKZLSb+QKFXpV64UmLk00bnt+q8+n0mZ9+lXvh63XtuLcs3Pot7cf9nfeD4lE8sXjisLPjmasj2asj2b6VJ+cZpSo9OQW4y9evECxYsUQHBwMLy8v9fIxY8bg9OnTCA0N1fj6sLAweHp6IjQ0FLVr11Yv37p1KywsLFCyZEncv38fP//8MywtLRESEgKZLOvJDydNmoTJkyd/sHzLli2wsLD4zC2ktc/XYs+rPShkXAiLyy+GpZGl6Ej0L8+Tn2PEnRFIUaVgiPMQNCvcTHQkIqIvkpSUhK5duyI2NhZWVlbZrqc3e5a+1OrVq1GlSpVMjRIAdO7cWf3/VapUQdWqVVG6dGmcOnUKzZpl/csgICAA/v7+6sdxcXFwdnZGixYtNBb7UykUCgQFBaF58+YwNjbW2ri66HLkZey7sg8AsLr9arQp2+Yjr8hf9fkcuVGf2JBY/HzyZ2x8tRGjOoyCo6WjVsbNa/zsaMb6aMb6aKZP9ck4MvQxetMsFSlSBDKZDFFRUZmWR0VFwcHBQeNrExMTsXXrVkyZMuWj71OqVCkUKVIE9+7dy7ZZMjU1hamp6QfLjY2Nc+WDkVvj6oo0ZRqGHBkCpUoJ30q+aF+x/Se93tDr86W0WZ/R9Udj552duPjiIn468RP+6KjfF0Pws6MZ66MZ66OZPtQnp/n05gRvExMTuLu74/jx4+plSqUSx48fz3RYLivbt2+HXC5H9+7dP/o+z549w5s3b+DoqJ9/MeujlZdWIux5GAqaFMR8n/mi45AGRlIj/P7V75BKpNh6fSuOPTgmOhIRUa7Tm2YJAPz9/bFy5UqsX78et27dwsCBA5GYmIjevXsDAHr06JHpBPAMq1evRvv27T84aTshIQGjR4/G+fPn8ejRIxw/fhzt2rVDmTJl4OPjkyfblN9FJURh7LGxAIDpTafDqaCT4ET0MTUda2JwrcEAgMEHB0OeKv/IK4iI9JveHIYDAF9fX7x69QoTJkxAZGQkqlevjsOHD8Pe3h4A8OTJE0ilmfu/O3fu4OzZszh69OgH48lkMly9ehXr169HTEwMnJyc0KJFC0ydOjXLw2ykfaOCRiFWHouajjUxqNYg0XEoh6Y2mYrtN7fj7zd/Y17wPPzS8BfRkYiIco1eNUsA4OfnBz8/vyyfO3Xq1AfLypcvj+wu+DM3N8eRI0e0GY8+wYmHJ7Dp6iZIIMHyNsshk2Z99SHpHmsza8xvMR9dd3bFtL+moUuVLihlW0p0LCKiXKFXh+HIcMhT5Rh0IH1P0kCPgahVrJbgRPSpOlfujKYlmyI5NRlDDg3J9o8SIiJ9x2aJhJgfMh933tyBfQF7TG82XXQc+gwSiQSBrQNhLDXGwbsHsefOHtGRiIhyBZslynMv4l9g+l/pDdK8FvNgY2YjNhB9NrcibhhddzQAYNjhYXiveC84ERGR9rFZojwXcDwAiYpEeBX3Qrcq3UTHoS/0S8Nf4GzljCexTzAveJ7oOEREWsdmifJU6LNQbLiyAQCwqOUivb6/GKWzMLbAnOZzAACzzs3C87jnghMREWkXmyXKM0qVEsMODwMA9Kreiyd1GxDfSr6o51wPSYokjD0+VnQcIiKtYrNEeWbT1U0IfR4KSxNLzGg6Q3Qc0iKJRIKFLRcCSP8+n392XmwgIiItYrNEeSJeHq+eqXt8w/FwLMjbyRgaDycP9KreCwAw/PBwKFVKsYGIiLSEzRLliZlnZ+JlwkuUti2NYZ7DRMehXDKj6QxYmlgi9HkoNl/dLDoOEZFWsFmiXPc45jHmh6TfIHe+z3yYGvFWMobKsaAjfq7/MwBg7PGxSEhJEJyIiOjLsVmiXDfu5DjI0+RoUqIJ2pZrKzoO5bIRXiNQ0qYkXsS/4FQCRGQQ2CxRrrr08hI2Xd0EAJjbfC6nCsgHzIzMMMt7FgBgXvA8RCZECk5ERPRl2CxRrlGpVBgdlD67c9cqXeHu5C44EeWVThU7oZZTLSQqEjHl9BTRcYiIvgibJco1R+4fwYmHJ2AiM8H0prz/W34ikUgwt/lcAMCK8BW48/qO4ERERJ+PzRLlijRlmnqv0pDaQ1DCpoTYQJTnGpVohK/KfYU0VRp+PvGz6DhERJ+NzRLlig1XNuB69HXYmNng5wb8RZlfzWo2C1KJFDtv7UTw02DRcYiIPgubJdK6JEUSxp8cDwD4pcEvKGReSHAiEqVS0UroXb03AGBM0BioVCrBiYiIPh2bJdK6xaGL8Tz+OVytXeFX2090HBJscuPJMDcyx7mn57D3zl7RcYiIPhmbJdKqmOQYzD43GwAwtclUmBmZCU5EohWzKoYRdUYASJ+oMlWZKjgREdGnYbNEWvVr8K+ISY5BRbuK6Fqlq+g4pCPG1BuDQuaFcPv1bWy5tkV0HCKiT8JmibTmVeIrLAxdCCB9r5JMKhMbiHSGtZk1fqr3EwBg0qlJSElLEZyIiCjn2CyR1sw6OwsJKQlwd3RHB7cOouOQjvGr7Qf7AvZ4GPMQay+vFR2HiCjH2CyRVjyPe47AC4EAgGlNp/G2JvQBC2ML/NLgFwDA1DNTkZyaLDgREVHOsFkirZh2ZhrkaXLUd6kPn9I+ouOQjurv3h/OVs54Hv8cyy8uFx2HiChH2CzRF3vw7gFWXV4FAJjedDr3KlG2TI1MMaHRBADAzLMzkZCSIDgREdHHsVmiLzbp1CSkKlPRonQLNHRtKDoO6bie1XqitG1pRCdGY0noEtFxiIg+is0SfZGbr25i09VNAIBpTaYJTkP6wFhmjMmNJwMA5gTPQUxyjNhAREQfwWaJvsiEkxOgggod3DqgVrFaouOQnuhcuTMq2lVETHIM5ofMFx2HiEgjNkv02SIiI/C/W/+DBBJMbTJVdBzSIzKpDFMaTwEALDi/AK+TXgtORESUPTZL9NmmnE7/Zedb2ReVilYSnIb0zTcVvkENhxpISEnA3HNzRcchIsoWmyX6LFejrmLX7V2QQILxDceLjkN6SCL5Z49k4IVA7l0iIp2ld81SYGAgSpQoATMzM3h6eiIsLCzbddetWweJRJLpy8ws841dVSoVJkyYAEdHR5ibm8Pb2xt3797N7c3Qe1PPpP+S61SpEyraVRSchvRV67KtUdOxJhIViVgQskB0HCKiLOlVs7Rt2zb4+/tj4sSJuHTpEqpVqwYfHx9ER0dn+xorKyu8fPlS/fX48eNMz8+ZMweLFy/G8uXLERoaigIFCsDHxwfJyZxdODvXo69jx80dAMC9SvRFJBIJJjRMn3dpSdgSvH3/VnAiIqIP6VWzNH/+fPTr1w+9e/dGxYoVsXz5clhYWGDNmjXZvkYikcDBwUH9ZW9vr35OpVJh4cKFGDduHNq1a4eqVatiw4YNePHiBXbv3p0HW6Sfpp1JnyKgY4WOqFy0suA0pO++Lv81qtlXQ3xKPBadXyQ6DhHRB4xEB8iplJQUhIeHIyAgQL1MKpXC29sbISEh2b4uISEBrq6uUCqVqFmzJmbMmIFKldJPRn748CEiIyPh7e2tXt/a2hqenp4ICQlB586dsxxTLpdDLperH8fFxQEAFAoFFArFF23nv2WMpc0xv9TNVzfx540/AQAB9QKEZtPF+ugSfapPQL0AdN7ZGYtCF8HPww82Zja5+n76VBsRWB/NWB/N9Kk+Oc2oN83S69evkZaWlmnPEADY29vj9u3bWb6mfPnyWLNmDapWrYrY2FjMmzcPdevWxY0bN1C8eHFERkaqx/jvmBnPZWXmzJmYPHnyB8uPHj0KCwuLT920jwoKCtL6mJ9r/uP5UEGFOtZ18OziMzzDM9GRdKo+ukgf6mOiMoGLmQueJD/BsC3D4Ovgmyfvqw+1EYn10Yz10Uwf6pOUlJSj9fSmWfocXl5e8PLyUj+uW7cuKlSogN9//x1Tp37+vEABAQHw9/dXP46Li4OzszNatGgBKyurL8r8bwqFAkFBQWjevDmMjY21Nu7nuvPmDs5eOQsAWNRxEWo41BCaR9fqo2v0rT5JJZPQfXd3HI45jCXdlsDKVHs/S/+lb7XJa6yPZqyPZvpUn4wjQx+jN81SkSJFIJPJEBUVlWl5VFQUHBwccjSGsbExatSogXv37gGA+nVRUVFwdHTMNGb16tWzHcfU1BSmpqZZjp8bH4zcGvdTzQmZA6VKia/Lf43azrVFx1HTlfroKn2pT+cqnTHt7DTcfn0bv1/+HT83+DnX31NfaiMK66MZ66OZPtQnp/n05gRvExMTuLu74/jx4+plSqUSx48fz7T3SJO0tDRcu3ZN3RiVLFkSDg4OmcaMi4tDaGhojsfML+6+uYvN1zYDgPrqJSJtkkllGNdgHADg15BfES+PF5yIiCid3jRLAODv74+VK1di/fr1uHXrFgYOHIjExET07t0bANCjR49MJ4BPmTIFR48exYMHD3Dp0iV0794djx8/Rt++fQGkXyk3fPhwTJs2DXv37sW1a9fQo0cPODk5oX379iI2UWfNODsDSpUSbcq2gbuTu+g4ZKB8K/uibKGyePv+LZZdXCY6DhERAD06DAcAvr6+ePXqFSZMmIDIyEhUr14dhw8fVp+g/eTJE0il//R/7969Q79+/RAZGQlbW1u4u7sjODgYFSv+M4nimDFjkJiYiP79+yMmJgb169fH4cOHP5i8Mj97HPMYm65uAgBMaMS9SpR7jKRG+KXBL+i1pxfmBc/D4FqDUcCkgOhYRJTP6VWzBAB+fn7w8/PL8rlTp05lerxgwQIsWKB5VmCJRIIpU6ZgypQp2opocOYFz0OqMhXepbxRu5junKtEhqlb1W6YcmYKHrx7gFWXVmFYnWGiIxFRPqdXh+Eo70UlRGHV5VUAgID6AR9Zm+jLGUmNMKbuGADAvJB5SElLEZyIiPI7Nkuk0aLQRUhOTUbtYrXRpEQT0XEon+hZvSccLB3wLO4ZNl/dLDoOEeVzbJYoW7HJsQi8EAgA+Ln+z5BIJIITUX5hZmQG/zrpc5nNPjcbaco0wYmIKD9js0TZ+u3Cb4iTx6GiXUW0Ld9WdBzKZwZ4DICNmQ3uvLmD3bd3i45DRPkYmyXKUpIiCQvOp58cH1A/AFIJPyqUtwqaFoRfrfSLOWaenQmVSiU4ERHlV/wNSFlac3kNXiW9QgmbEuhcOesbChPltqGeQ2FuZI7wl+E49uCY6DhElE+xWaIPKNIUmBs8FwAwuu5oGEn1boYJMhB2BezQr2Y/AMCsc7MEpyGi/IrNEn1gy7UteBL7BPYF7NG7em/RcSifG1l3JIykRjjx8ATCnoeJjkNE+RCbJcpEqVJi9rnZAIARdUbA3NhccCLK71ysXdCtSjcA6ecuERHlNTZLlMme23tw6/UtWJtaY2CtgaLjEAEAfqr3EySQYPft3bj56qboOESUz7BZIjWVSoU5wXMAAINrDYaVqZXgRETpKthVQHu39gCg3vNJRJRX2CyR2rmn53D+2XmYykwx1HOo6DhEmWTcbmfLtS14GvtUcBoiyk/YLJFaxhVwPar1gL2lveA0RJnVKlYLjUs0RqoyFYtCF4mOQ0T5CJslAgDcfn0be+/shQQSjPQaKToOUZZG1x0NAFgRvgKxybGC0xBRfsFmiQAAvwb/CgD4uvzXKF+kvOA0RFlrWaYlKtpVRHxKPFaErxAdh4jyCTZLhMiESGy4ugHAP3+5E+kiqUSKUV6jAACLQhchJS1FcCIiyg/YLBGWhC5BSloKvIp7oZ5LPdFxiDTqWqUrHC0d8Tz+ObZe3yo6DhHlA2yW8rmElAQsu7gMAPcqkX4wNfrnas15wfN4g10iynVslvK51ZdW413yO5QtVBZfl/9adByiHBngMQCWJpa4Fn0NR+8fFR2HiAwcm6V8LFWZigXnFwAARnqNhEwqE5yIKGdszGzQt0ZfAP9MeUFElFvYLOVj229sx+PYx7CzsEOPaj1ExyH6JMPrDIdMIsPxh8dx6eUl0XGIyICxWcqnVCqV+i/yIbWH8Ia5pHdcbVzxXaXvAAC/hvwqOA0RGTI2S/nUiYcncDnyMsyNzHnDXNJbGRclbLu+DY9jHgtOQ0SGis1SPpWxV+mHGj+giEURwWmIPk8NxxpoVrIZ0lRpWHh+oeg4RGSg2CzlQ9eiruHI/SOQSqTw9/IXHYfoi4yqmz5J5cpLK/Hu/TvBaYjIELFZyocy/gL/psI3KGVbSmwYoi/kU9oHlYtWRqIiEb+H/y46DhEZIDZL+UxUQhQ2XdsEAPCvw71KpP8kEon6FihLwpbwFihEpHVslvKZZReXISUtBZ7FPOHl7CU6DpFWdK7cGfYF7PEi/gW239guOg4RGRg2S/lIcmoyfrvwGwBgRJ0RgtMQaY+pkSkG1xoMAFhwfgFvgUJEWsVmKR/Zcm0LXiW9gou1CzpW7Cg6DpFWDfAYAFOZKcJfhuPsk7Oi4xCRAWGzlE+oVCrMD5kPIH0SSiOpkeBERNplV8AO31f9HgDUt/EhItIGvWuWAgMDUaJECZiZmcHT0xNhYWHZrrty5Uo0aNAAtra2sLW1hbe39wfr9+rVCxKJJNNXy5Ytc3sz8tyxB8dw49UNFDAugL41+4qOQ5QrhtcZDgDYfXs3Hrx7IDYMERkMvWqWtm3bBn9/f0ycOBGXLl1CtWrV4OPjg+jo6CzXP3XqFLp06YKTJ08iJCQEzs7OaNGiBZ4/f55pvZYtW+Lly5fqrz/++CMvNidPZfyl/UONH2BjZiM2DFEuqVS0ElqUbgEVVFgculh0HCIyEHrVLM2fPx/9+vVD7969UbFiRSxfvhwWFhZYs2ZNlutv3rwZgwYNQvXq1eHm5oZVq1ZBqVTi+PHjmdYzNTWFg4OD+svW1jYvNifP3Hp1C4fuHYIEEgzzHCY6DlGuyrh4Yc3lNYiTxwlOQ0SGQG9OXElJSUF4eDgCAgLUy6RSKby9vRESEpKjMZKSkqBQKFCoUKFMy0+dOoWiRYvC1tYWTZs2xbRp01C4cOFsx5HL5ZDL5erHcXHp/yArFAooFIpP2SyNMsb60jHnB6efq9S2XFu4FHTRakaRtFUfQ5Vf69PUpSncCrvh9pvbWHFxBYbV/vAPhPxam5xifTRjfTTTp/rkNKNEpSfX2L548QLFihVDcHAwvLz+mR9ozJgxOH36NEJDQz86xqBBg3DkyBHcuHEDZmZmAICtW7fCwsICJUuWxP379/Hzzz/D0tISISEhkMlkWY4zadIkTJ48+YPlW7ZsgYWFxWduYe6IS41D3xt9kaJKwfQy01HJspLoSES57sjrI1j2bBmKmhTFsgrLIJNk/bNMRPlbUlISunbtitjYWFhZWWW7nt7sWfpSs2bNwtatW3Hq1Cl1owQAnTt3Vv9/lSpVULVqVZQuXRqnTp1Cs2bNshwrICAA/v7/zH4dFxenPh9KU7E/lUKhQFBQEJo3bw5jY+PPGmPmuZlIUaWghkMNjOo0ChKJRGv5RNNGfQxZfq5PE0UT/Ln0T0S/j4aitAJt3dpmej4/1yYnWB/NWB/N9Kk+GUeGPkZvmqUiRYpAJpMhKioq0/KoqCg4ODhofO28efMwa9YsHDt2DFWrVtW4bqlSpVCkSBHcu3cv22bJ1NQUpqamHyw3NjbOlQ/G544rT5VjWfgyAIC/lz9MTEy0HU0n5FbdDUV+rI+xsTEGeAzA9L+mY8mFJfCt4pvtevmtNp+C9dGM9dFMH+qT03x6c4K3iYkJ3N3dM52cnXGy9r8Py/3XnDlzMHXqVBw+fBgeHh4ffZ9nz57hzZs3cHR01Epukbbd2IbIhEg4Wjriu0rfiY5DlKcG1xoMY6kxzj09hwvPL4iOQ0R6TG+aJQDw9/fHypUrsX79ety6dQsDBw5EYmIievfuDQDo0aNHphPAZ8+ejfHjx2PNmjUoUaIEIiMjERkZiYSEBABAQkICRo8ejfPnz+PRo0c4fvw42rVrhzJlysDHx0fINmqLSqVSTxcwpPYQmMgMc68SUXYcCzqic+X0w+ycpJKIvoReNUu+vr6YN28eJkyYgOrVqyMiIgKHDx+Gvb09AODJkyd4+fKlev1ly5YhJSUF3377LRwdHdVf8+bNAwDIZDJcvXoVX3/9NcqVK4c+ffrA3d0df/31V5aH2fTJ6cenEREZAXMjc/zo8aPoOERCZEwjsP3mdjyLeyY4DRHpK705ZymDn58f/Pz8snzu1KlTmR4/evRI41jm5uY4cuSIlpLploy/pHtW64lC5oU+sjaRYarhWAONXBvh9OPTWBq2FLO8Z4mORER6SK/2LFHO3Ht7D/vu7APwz+0fiPKrjL1LK8JXIDElUXAaItJHbJYM0NKwpVBBhVZlWqF8kfKi4xAJ9VW5r1DatjTeJb/D+ivrRcchIj3EZsnAxMvjseZy+u1feGsTIkAmlal/FhaHLoZSpRSciIj0DZslA7P+ynrEp8SjfOHyaF66ueg4RDqhV/VeKGhSEHfe3EHQ/SDRcYhIz7BZMiBKlRJLwpYASJ8uQCrht5cIAAqaFsQPNX4AACwOWyw4DRHpG/42NSBH7x/F32/+hpWpFXpU6yE6DpFO8avtBwkkOHj3IO6+vSs6DhHpETZLBmRR6CIAQJ8afVDQtKDgNES6pUyhMmhTrg0AYNnFZYLTEJE+YbNkIO68voPD9w5DAgkG1xosOg6RThpaeygAYP3V9UhKSxKchoj0BZslA7E0bCmA/79MulBpwWmIdJN3KW9UKFIB8SnxOPH2hOg4RKQn2CwZgNjkWKy7sg4AMNRzqNgwRDpMIpFgSO0hAIADrw5wGgEiyhE2SwZgXcQ6JKQkoEKRCmhWspnoOEQ67ftq38Pa1BovU17iyH3DvN0REWkXmyU99+/pAoZ6DoVEIhGciEi3WZpY4ofq6dMILL2wVHAaItIHbJb03KG7h3D/3X1Ym1rj+6rfi45DpBcGuA+ABBIEPQzCrVe3RMchIh3HZknPZUyw17dmXxQwKSA4DZF+KGlTErWsagH45+IIIqLssFnSY7de3cLR+0chlUjhV9tPdBwivfKV3VcA0m8RFJMcIzYMEek0Nkt6LONcpa/Lf40SNiXEhiHSM1Usq6CSXSUkKhLVN58mIsoKmyU9FZMcg/VX1gP4Z6I9Iso5iUQCP4/0PbJLw5YiTZkmOBER6So2S3pqzeU1SFIkoXLRymhcorHoOER6qUvlLrA1s8XDmIc4cPeA6DhEpKPYLOmhNGWa+qTUobU5XQDR57IwtkC/mv0AAItDFwtOQ0S6is2SHjpw9wAexjyErZktulXtJjoOkV4bXHswpBIpjj88juvR10XHISIdxGZJD2X8BdyvZj9YGFsITkOk31ysXdDBrQMAYEnoEsFpiEgXsVnSMzeib+D4w+OQSqQYXHuw6DhEBiHjnoobr27E2/dvBachIl3DZknPZEwX0MGtA1ysXQSnITIMDVwaoJp9NbxPfY/Vl1aLjkNEOobNkh55+/4tNlzZAOCfv4SJ6MtJJBIM8xwGIP1+canKVMGJiEiXsFnSI6svrcb71PeoZl8NDVwaiI5DZFC6VOmCIhZF8CT2Cfbe2Ss6DhHpEDZLeiJVmaq+Q/pQT04XQKRtZkZm6F+zPwBOI0BEmbFZ0hP77uzDk9gnKGxeGF0qdxEdh8ggDaw1EDKJDKcfn8aVyCui4xCRjmCzpCcWh6X/pdvfvT/Mjc0FpyEyTMWtiuPbit8C4N4lIvoHmyU9cDX6Kk49OgWZRIZBtQaJjkNk0DIunth8bTNeJ70WnIaIdAGbJT3w28XfAAAdK3ZEcavigtMQGTav4l5wd3SHPE2OleErRcchIh3AZknHxaXGYcv1LQDS7wNHRLlLIpGo9y79dvE3KNIUghMRkWh61ywFBgaiRIkSMDMzg6enJ8LCwjSuv337dri5ucHMzAxVqlTBwYMHMz2vUqkwYcIEODo6wtzcHN7e3rh7925ubsInCXoThOTUZNR0rIm6znVFxyHKF3wr+aJogaJ4FvcMu2/vFh2HiAT75GapZ8+eOHPmTG5k+aht27bB398fEydOxKVLl1CtWjX4+PggOjo6y/WDg4PRpUsX9OnTB5cvX0b79u3Rvn17XL/+z80y58yZg8WLF2P58uUIDQ1FgQIF4OPjg+Tk5LzarGylKlNx8HV6cze0NqcLIMorpkam+NH9RwD/XFxBRPnXJzdLsbGx8Pb2RtmyZTFjxgw8f/48N3Jlaf78+ejXrx969+6NihUrYvny5bCwsMCaNWuyXH/RokVo2bIlRo8ejQoVKmDq1KmoWbMmli5Nn69IpVJh4cKFGDduHNq1a4eqVatiw4YNePHiBXbv3p1n25WdPXf24I3iDews7OBb2Vd0HKJ8ZYDHABhJjXD2yVlcenlJdByifCv8Rbjwiy2MPvUFu3fvxqtXr7Bx40asX78eEydOhLe3N/r06YN27drB2Ng4N3IiJSUF4eHhCAgIUC+TSqXw9vZGSEhIlq8JCQmBv79/pmU+Pj7qRujhw4eIjIyEt7e3+nlra2t4enoiJCQEnTt3znJcuVwOuVyufhwXFwcAUCgUUCi0d35DxiSUP1T7ATKVTKtjG4KMerAuWWN9speT2tiZ2aGjW0dsu7kNi84vwqqvVuVVPOH42dGM9dFMm/VRqpTo+r+ueBz7GHu+24OmJZt+8Zj/ltOMn9wsAYCdnR38/f3h7++PS5cuYe3atfj+++9haWmJ7t27Y9CgQShbtuznDJ2t169fIy0tDfb29pmW29vb4/bt21m+JjIyMsv1IyMj1c9nLMtunazMnDkTkydP/mD50aNHYWFh8fGNyYHktGTEvIuBDDKUjyv/wblW9I+goCDREXQa65O9j9WmpqImtmEbtlzbgqZpTWFjbJM3wXQEPzuasT6aaaM+l+Mu4++3f8Ncao5319/h4C3t/i5MSkrK0Xqf1SxlePnyJYKCghAUFASZTIbWrVvj2rVrqFixIubMmYMRI0Z8yfA6KyAgINMeq7i4ODg7O6NFixawsrLS2vu0VbTFlgNb4NvaN9f22OkzhUKBoKAgNG/enPXJAuuTvZzWppWqFbav246LLy/icZHH6Fqvax6mFIefHc1YH820WZ8Vf64AAPR174uOzTtqI14mGUeGPuaTmyWFQoG9e/di7dq1OHr0KKpWrYrhw4eja9eu6kZh165d+OGHH7TaLBUpUgQymQxRUVGZlkdFRcHBwSHL1zg4OGhcP+O/UVFRcHR0zLRO9erVs81iamoKU1PTD5YbGxtr/QfHzsQuV8Y1JKyPZqxP9nJSm2F1huH7Xd/j90u/I6BBAIxl+aeW/Oxoxvpo9qX1uff2Hg7dOwQAGOI5JFdqndMxP/kEb0dHR/Tr1w+urq4ICwvDxYsXMWDAgEx7VJo0aQIbG5tPHVojExMTuLu74/jx4+plSqUSx48fh5eXV5av8fLyyrQ+kL5bMGP9kiVLwsHBIdM6cXFxCA0NzXZMIspfOlXsBPsC9ngR/wI7b+0UHYco3wgMC4QKKrQq0wplC2v31J5P9cnN0oIFC/DixQsEBgZmu/fFxsYGDx8+/NJsH/D398fKlSuxfv163Lp1CwMHDkRiYiJ69+4NAOjRo0emE8CHDRuGw4cP49dff8Xt27cxadIkXLx4EX5+fgDSJ58bPnw4pk2bhr179+LatWvo0aMHnJyc0L59e63nJyL9Y2pkioEeAwFwGgGivJKQkoC1EWsB/HMLIpE++TDc999/nxs5csTX1xevXr3ChAkTEBkZierVq+Pw4cPqE7SfPHkCqfSf/q9u3brYsmULxo0bh59//hlly5bF7t27UblyZfU6Y8aMQWJiIvr374+YmBjUr18fhw8fhpmZWZ5vHxHpph89fsT0v6Yj+GkwLr64CA8nD9GRiAzahisbECuPRdlCZdGidAvRcb7sBG8R/Pz81HuG/uvUqVMfLOvUqRM6deqU7XgSiQRTpkzBlClTtBWRiAyMg6UDfCv7YtPVTVgStgTr268XHYnIYClVSiwJWwIAGFJ7CKQS8TcbEZ+AiEgPZNybcev1rYhKiPrI2kT0uY49OIbbr2+joElB9KzeU3QcAGyWiIhypFaxWqhTvA5S0lKwInyF6DhEBmtxaPq5gT/U+AFWptqbjudLsFkiIsqhjL1Lyy4uQ0paiuA0RIbn7pu7OHD3ACSQwK921qfciMBmiYgohzpW7AhHS0e8THiJHTd3iI5DZHACLwQCAFqXbY0yhcoITvMPNktERDlkIjP5ZxqBUE4jQKRN8fJ4rLm8BoBuTBfwb2yWiIg+QX/3/jCRmSD0eShCn4WKjkNkMNZFrEN8SjzciriheanmouNkwmaJiOgT2Fvao3PlzgCgvryZiL7Mf6cLkEgkghNlxmaJiOgTZZzo/eeNP/Ey/qXgNET678i9I7j79i6sTa3Ro1oP0XE+wGaJiOgTuTu5o65zXSiUCvwe/rvoOER6L+NWQn1q9IGliaXgNB9is0RE9Bky9i4tv7gc8lS54DRE+uvO6zs4fO8wJJBgcO3BouNkic0SEdFn+KbCN3Aq6ISoxChsv7lddBwivbU0bCkAoG35tihlW0pwmqyxWSIi+gzGMmMM8hgEAFgUuggqlUpwIiL9E5sci3VX1gH4Z2+tLmKzRET0mfq794epzBQXX1xE6HNOI0D0qdZGrEVCSgIq2lVE05JNRcfJFpslIqLPZFfADl2qdAHASSqJPlWaMk09XcDQ2kN1brqAf2OzRET0BYbUHgIA2H5zO17EvxCchkh/HLp3CA/ePYCNmQ26V+0uOo5GbJaIiL5ATceaqO9SH6nKVCy/uFx0HCK9kbE3tl/NfihgUkBwGs3YLBERfSFOI0D0aW6+uomgB0GQSqQYVGuQ6DgfxWaJiOgLdajQAcWtiuNV0itsu7FNdBwinZcxXUC78u1QwqaE2DA5wGaJiOgLGUmNMLhW+mR6i0MXcxoBIg1ikmOw/sp6AMBQT92dLuDf2CwREWlB35p9YWZkhvCX4Qh5FiI6DpHOWn1pNZIUSahStAoauTYSHSdH2CwREWlBEYsi6FalGwBOI0CUnTRlGpZeSD8EN9RTt6cL+Dc2S0REWpIxjcCOmzvwLO6Z4DREumf/3/vxKOYRCpkXUv9xoQ/YLBERaUk1h2po5NoIaao0TiNAlIXFYel7XfvX7A9zY3PBaXKOzRIRkRZlnLD6e/jvSE5NFpyGSHdcj76OEw9PQCaRYWCtgaLjfBI2S0REWvR1+a/hYu2C10mv8ce1P0THIdIZi84vAgC0d2sPF2sXwWk+DZslIiItyjSNQBinESACgFeJr7Dx6kYAwPA6w8WG+QxsloiItKxvzb4wNzJHRGQEzj45KzoOkXC/h/8OeZocHk4eqOdcT3ScT8ZmiYhIywqZF1LfGHRR6CLBaYjEkqfKEXghEAAwos4IvZku4N/YLBER5YKMaQR23d6FxzGPBachEmfbjW2ITIiEU0EndKrYSXScz8JmiYgoF1Sxr4JmJZtBqVJiSdgS0XGIhFCpVFhwfgEAwK+WH4xlxoITfR42S0REucTfyx8AsPLSSsTL4wWnIcp7Zx6fQURkBMyNzPGjx4+i43w2vWmW3r59i27dusHKygo2Njbo06cPEhISNK4/ZMgQlC9fHubm5nBxccHQoUMRGxubaT2JRPLB19atW3N7c4goH2hZpiXKFy6POHkc1lxeIzoOUZ7L2KvUs1pPFDIvJDjN59ObZqlbt264ceMGgoKCsH//fpw5cwb9+/fPdv0XL17gxYsXmDdvHq5fv45169bh8OHD6NOnzwfrrl27Fi9fvlR/tW/fPhe3hIjyC6lEihF1RgBIP9E7TZkmOBFR3rn39h723tkLABhWZ5jgNF/GSHSAnLh16xYOHz6MCxcuwMPDAwCwZMkStG7dGvPmzYOTk9MHr6lcuTL+97//qR+XLl0a06dPR/fu3ZGamgojo3823cbGBg4ODrm/IUSU73xf7Xv8fOJnPIx5iD139uCbCt+IjkSUJwIvBkIFFVqVaQW3Im6i43wRvWiWQkJCYGNjo26UAMDb2xtSqRShoaHo0KFDjsaJjY2FlZVVpkYJAAYPHoy+ffuiVKlSGDBgAHr37q3x0ka5XA65XK5+HBcXBwBQKBRQKBSfsmkaZYylzTENCeujGeuTvbysjTGM0b9Gf8wKnoVfg39F2zJtc/09vxQ/O5qxPpopFAokpCZg3Y11AIAhtYbobK1ymksvmqXIyEgULVo00zIjIyMUKlQIkZGRORrj9evXmDp16geH7qZMmYKmTZvCwsICR48exaBBg5CQkIChQ4dmO9bMmTMxefLkD5YfPXoUFhYWOcrzKYKCgrQ+piFhfTRjfbKXV7UppygHI4kRgp8FY9GORShrUTZP3vdL8bOjGeuTvWNvjyFRkQgXMxfIb8px8NZB0ZGylJSUlKP1hDZLY8eOxezZszWuc+vWrS9+n7i4OLRp0wYVK1bEpEmTMj03fvx49f/XqFEDiYmJmDt3rsZmKSAgAP7+/pnGd3Z2RosWLWBlZfXFeTMoFAoEBQWhefPmMDbWz8stcxProxnrkz0RtTkhPYFN1zbhotFFDGut2+dv8LOjGeuj2Xv5e/Rb3A8A8HPTn9GmehvBibKXcWToY4Q2SyNHjkSvXr00rlOqVCk4ODggOjo60/LU1FS8ffv2o+caxcfHo2XLlihYsCB27dr10Q+2p6cnpk6dCrlcDlNT0yzXMTU1zfI5Y2PjXPnBya1xDQXroxnrk728rM3IuiOx6dom7Li1A3NbzIWztXOevO+X4GdHM9Ynaztu7cArxSsUMS+CHtV76HSNcppNaLNkZ2cHOzu7j67n5eWFmJgYhIeHw93dHQBw4sQJKJVKeHp6Zvu6uLg4+Pj4wNTUFHv37oWZmdlH3ysiIgK2trbZNkpERJ+jukN1NCnRBCcfncTSsKWY3VzzXnUifbXkQvokrP1r9oe5sbngNNqhF1MHVKhQAS1btkS/fv0QFhaGc+fOwc/PD507d1ZfCff8+XO4ubkhLCwMQHqj1KJFCyQmJmL16tWIi4tDZGQkIiMjkZaWfvnuvn37sGrVKly/fh337t3DsmXLMGPGDAwZMkTYthKR4cqYRuD38N+RkJL9PHFE+irseRhCnoXASGKEAe4DRMfRGr04wRsANm/eDD8/PzRr1gxSqRQdO3bE4sWL1c8rFArcuXNHfbLWpUuXEBoaCgAoU6ZMprEePnyIEiVKwNjYGIGBgRgxYgRUKhXKlCmD+fPno1+/fnm3YUSUb7Qp1wZlC5XF3bd3sS5iHfxq+4mORKRVGZNQNrBpAAdLw5mSR2+apUKFCmHLli3ZPl+iRAmoVCr148aNG2d6nJWWLVuiZcuWWstIRKSJVCLF8DrDMfjgYCw8vxADPQZCJpWJjkWkFU9jn2L7je0AgLZ2uj9FxqfQi8NwRESGome1nrA1s8X9d/ex/+/9ouMQac2SsCVIU6WhkUsjlLIoJTqOVrFZIiLKQwVMCuBH9/Qbis4/P19wGiLtiJPH4ffw3wEAwz2Hiw2TC9gsERHlMb/afjCSGuHM4zMIfxEuOg7RF1t1aRXi5HFwK+KGVmVaiY6jdWyWiIjyWDGrYvCt5AvgnxNiifSVIk2BhecXAgBGeY2CVGJ4rYXhbRERkR7ImEZg241teBr7VHAaos/3540/8TTuKewL2KNb1W6i4+QKNktERAK4O7mjSYkmSFWmqv8qJ9I3KpUK80LmAQCG1B4CM6OPT/6sj9gsEREJMrruaADAiksrEJMcIzYM0Wc4/vA4IiIjYGFsgQEehjMJ5X+xWSIiEqRlmZaoXLQyElISsPzictFxiD7ZvOD0vUp9avRBYYvCgtPkHjZLRESCSCQS9d6lRaGLIE+VC05ElHNXo67iyP0j6slWDRmbJSIigTpX7oxiBYshMiESm65uEh2HKMfmh6TPE9axQkeUsjWsSSj/i80SEZFAJjIT9ZVx80LmQalSCk5E9HHP455jy7X0W5Bl7B01ZGyWiIgE6+feD1amVrj9+jYO/H1AdByij1ocuhgKpQINXRuiVrFaouPkOjZLRESCWZlaYYB7+pVEc4LnCE5DpFmcPA7Lw9MvSBjlNUpwmrzBZomISAcMqzMMxlJjnH1yFuefnRcdhyhbqy+tVt/apE25NqLj5Ak2S0REOsCpoBO6V+0OAJgbPFdwGqKsKdIUWBi6EAAw0mukQd7aJCv5YyuJiPTAqLrphzR23dqFv9/8LTgN0Ye2Xt+KJ7FPULRAUXVznx+wWSIi0hEV7Sriq3JfQQWV+rJsIl2hVCkx+9xsAMBwz+EGe2uTrLBZIiLSIRmXYa+LWIeohCjBaYj+sf/v/bjx6gasTK0wqNYg0XHyFJslIiId0sClAWoXqw15mhxLwpaIjkMEIP2GuTPPzgQADPQYCGsza8GJ8habJSIiHSKRSDCm7hgAQOCFQMTJ4wQnIgLOPD6D88/Ow1RmavC3NskKmyUiIh3ToUIHuBVxQ0xyDG+wSzph1rlZAIDe1XvDwdJBcJq8x2aJiEjHSCVSjK03FkD6/bfeK94LTkT52eWXl3H43mFIJVKMrmf4tzbJCpslIiId1LVKV7hYuyAqMQprI9aKjkP5WMYVcL6VfA3+hrnZYbNERKSDjGXG6nOX5gbPhSJNITgR5Uf33t7D9pvbAQBj648VnEYcNktERDrqhxo/oGiBongU8whbr28VHYfyobnn5kKpUqJ12daoal9VdBxh2CwREekoc2NzjKgzAgAw8+xMKFVKwYkoP3kR/wLrrqwDAATUDxAbRjA2S0REOmygx0BYm1rj1utb2HN7j+g4lI8sPL8QKWkpqOdcD/Vd6ouOIxSbJSIiHWZtZg2/2n4AgBlnZ0ClUglORPnBm6Q3+O3CbwDy97lKGdgsERHpuGGew2BuZI6LLy7i2INjouNQPrDw/EIkKhJR3aE62pRtIzqOcGyWiIh0nF0BO/R37w8gfe8SUW6KSY7B4rDFAIDxDcdDIpEITiQemyUiIj0w0mskjKXGOPXoFIKfBouOQwZscehixMnjULloZbR3ay86jk7Qm2bp7du36NatG6ysrGBjY4M+ffogISFB42saN24MiUSS6WvAgAGZ1nny5AnatGkDCwsLFC1aFKNHj0ZqampubgoR0SdztnZGz2o9AQCTT08WnIYMVZw8DgvOLwAAjGswDlKJ3rQJuUpvqtCtWzfcuHEDQUFB2L9/P86cOYP+/ft/9HX9+vXDy5cv1V9z5sxRP5eWloY2bdogJSUFwcHBWL9+PdatW4cJEybk5qYQEX2WgAYBkElkOHr/KM4/Oy86DhmgwLBAxCTHoHzh8vi24rei4+gMvWiWbt26hcOHD2PVqlXw9PRE/fr1sWTJEmzduhUvXrzQ+FoLCws4ODiov6ysrNTPHT16FDdv3sSmTZtQvXp1tGrVClOnTkVgYCBSUlJye7OIiD5JKdtS6FGtBwDuXSLtS0hJwK8hvwIAxjUcB5lUJjiR7jASHSAnQkJCYGNjAw8PD/Uyb29vSKVShIaGokOHDtm+dvPmzdi0aRMcHBzQtm1bjB8/HhYWFupxq1SpAnt7e/X6Pj4+GDhwIG7cuIEaNWpkOaZcLodcLlc/jouLAwAoFAooFNq7JUHGWNoc05CwPpqxPtnT59qM8RqDDVc24PC9wwh+HIxaTrW0/h76XJ+8YKj1CQwNxJv3b1DatjQ6lu/42dunT/XJaUa9aJYiIyNRtGjRTMuMjIxQqFAhREZGZvu6rl27wtXVFU5OTrh69Sp++ukn3LlzBzt37lSP++9GCYD6saZxZ86cicmTP/yr7ujRo+pGTJuCgoK0PqYhYX00Y32yp6+1aWTbCCfensDQnUMxvtT4XHsffa1PXjGk+siVcsy8ORMA0NqyNY4ePvrFY+pDfZKSknK0ntBmaezYsZg9e7bGdW7duvXZ4//7nKYqVarA0dERzZo1w/3791G6dOnPHjcgIAD+/v7qx3FxcXB2dkaLFi0yHeb7UgqFAkFBQWjevDmMjY21Nq6hYH00Y32yp++1Kfe2HKr8XgXhceEoWr0oPJw8Pv6iT6Dv9clthlifJWFLEHs1FiWsS2BW11kwln3+dulTfTKODH2M0GZp5MiR6NWrl8Z1SpUqBQcHB0RHR2danpqairdv38LBwSHH7+fp6QkAuHfvHkqXLg0HBweEhYVlWicqKgoANI5ramoKU1PTD5YbGxvnygcjt8Y1FKyPZqxP9vS1NhXsK6Bb1W7YcGUDpp+bjv1d9+fK++hrffKKodQnOTUZ887PA5B+EYGFmXaOkOhDfXKaT2izZGdnBzs7u4+u5+XlhZiYGISHh8Pd3R0AcOLECSiVSnUDlBMREREAAEdHR/W406dPR3R0tPowX1BQEKysrFCxYsVP3BoiorwzrsE4bLq6CQfuHsDFFxe1vneJ8o/Vl1bjZcJLFLcqrp6egjLTi6vhKlSogJYtW6Jfv34ICwvDuXPn4Ofnh86dO8PJyQkA8Pz5c7i5uan3FN2/fx9Tp05FeHg4Hj16hL1796JHjx5o2LAhqlatCgBo0aIFKlasiO+//x5XrlzBkSNHMG7cOAwePDjLPUdERLqibOGy6FqlKwBgyukpgtOQvnqveI/pf00HAATUD4CpEX/3ZUUvmiUg/ao2Nzc3NGvWDK1bt0b9+vWxYsUK9fMKhQJ37txRn6xlYmKCY8eOoUWLFnBzc8PIkSPRsWNH7Nu3T/0amUyG/fv3QyaTwcvLC927d0ePHj0wZQr/4SEi3ZcxaeC+v/fh0stLouOQHlp2cRleJryEq7Ur+tToIzqOztKLq+EAoFChQtiyZUu2z5coUSLT3bidnZ1x+vTpj47r6uqKgwcPaiUjEVFeKl+kPLpU7oLN1zZj8unJ2NN5j+hIpEcSUhIw6+wsAOn3gONepezpzZ4lIiL60LiG6XuX9t7ZiwvPL4iOQ3pkSegSvEp6hTKFyqgnO6WssVkiItJjbkXc0L1qdwDALyd+EZyG9EVMcgzmBKff/mtSo0lfNFVAfsBmiYhIz01qNAnGUmMEPQjCqUenRMchPbAgZAFikmNQ0a4iOlfuLDqOzmOzRESk50ralkS/mv0ApO9d+vf5m0T/9SbpDRacXwAAmNx4Mu8BlwNsloiIDMC4huNgbmSO4KfBOHiXF61Q9uYGz0V8SjyqO1THNxW+ER1HL7BZIiIyAI4FHTGk9hAA6XuXlCql4ESki6ISorAkbAkAYErjKZBK2AbkBKtERGQgxtQbAytTK1yJuoLtN7aLjkM6aNbZWUhSJKF2sdr4qtxXouPoDTZLREQGorBFYYz0GgkAmHBqAlKVqYITkS55GvsUyy4uAwBMazINEolEcCL9wWaJiMiAjKgzAkUsiuDvN39jw5UNouOQDpl4aiLkaXI0dG0I71LeouPoFTZLREQGpKBpQQTUDwAATDo1CfJUueBEpAuuR1/H+ivrAQBzvOdwr9InYrNERGRgBnoMRLGCxfA07imWX1wuOg7pgLHHxkKpUqJjhY7wLO4pOo7eYbNERGRgzI3NMaHRBADA1DNTEZMcIzYQCXX60WkcuHsAMokMM5rNEB1HL7FZIiIyQD/U+AEVilTAm/dv1DdLpfxHpVLhp2M/AQD61eyHcoXLCU6kn9gsEREZICOpEeY0T7/318LzC/E45rHgRCTCzls7Efo8FAWMC2Bi44mi4+gtNktERAaqTdk2aFyiMeRpcow7OU50HMpjijQFAo6nn+w/0mskHCwdBCfSX2yWiIgMlEQiwbzm8wAAm65uwqWXlwQnory06tIq3H17F3YWdhhVd5ToOHqNzRIRkQFzd3JHtyrdAACjg0bzJrv5RGxyLCaeSj/sNqHRBBQ0LSg4kX5js0REZOCmN50OU5kpTjw8gUP3DomOQ3lg+l/T8SrpFcoXLo8f3X8UHUfvsVkiIjJwrjauGOY5DED63iXeBsWw3Xt7DwvPLwQAzPeZD2OZsdhABoDNEhFRPhDQIACFzQvj5qub+P3i76LjUC4aHTQaCqUCPqV90KpMK9FxDAKbJSKifMDGzAZTm0wFAIw/OR5vkt4ITkS54cTDE9h9ezdkEhl+bfErb2uiJWyWiIjyif7u/VHVvireJb/DhJMTRMchLUtTpmHEkREAgAEeA1CpaCXBiQwHmyUionxCJpVhccvFAIDl4ctxJfKK4ESkTWsur8HVqKuwMbPBpMaTRMcxKGyWiIjykUYlGqFTxU5QqpQYdngYpxIwELHJseqJRyc2mogiFkUEJzIsbJaIiPKZuc3nwszIDKcfn8aOmztExyEtmHByAqITo1GucDkMqjVIdByDw2aJiCifcbVxxU/10m+uOipoFJIUSYIT0ZeIiIzA0gtLAQBLWy2FicxEcCLDw2aJiCgfGlNvDJytnPEk9glmn50tOg59JqVKiUEHBkGpUqJTxU5oXrq56EgGic0SEVE+ZGFsgfk+8wEAs87Nwt9v/haciD7Huoh1CHkWggLGBdTfT9I+NktERPlUxwod0bJMS6SkpWDggYE82VvPvH3/Fj8dSz+cOqnxJBS3Ki44keFis0RElE9JJBIEtg6EmZEZTjw8gc3XNouORJ/g5+M/43XSa1Syq6S+nQ3lDjZLRET5WCnbUpjQMH2CSv8j/nj7/q3gRJQTF55fwIrwFQCAwNaBvP9bLtObZunt27fo1q0brKysYGNjgz59+iAhISHb9R89egSJRJLl1/bt29XrZfX81q1b82KTiIh0wsi6I1HRriJeJb1CwLEA0XHoIxRpCvy4/0eooEL3qt3RqEQj0ZEMnt40S926dcONGzcQFBSE/fv348yZM+jfv3+26zs7O+Ply5eZviZPngxLS0u0apX5xoJr167NtF779u1zeWuIiHSHicwEy9ssBwCsuLQCIc9CBCciTX4N+RWXIy/D1swW85rPEx0nX9CLZunWrVs4fPgwVq1aBU9PT9SvXx9LlizB1q1b8eLFiyxfI5PJ4ODgkOlr165d+O6772BpaZlpXRsbm0zrmZmZ5cVmERHpjAauDfBD9R8AAIMODYJCqRCciLLy95u/MenUJADAwpYLYW9pLzZQPmEkOkBOhISEwMbGBh4eHupl3t7ekEqlCA0NRYcOHT46Rnh4OCIiIhAYGPjBc4MHD0bfvn1RqlQpDBgwAL1799Z4p2a5XA65XK5+HBcXBwBQKBRQKLT3D0zGWNoc05CwPpqxPtljbbI2vfF07L2zFzde3cD/ZP9Da0Vr0ZF0kqjPj1KlRJ89fSBPk6N5yeboXKGzTn6G9ennK6cZ9aJZioyMRNGiRTMtMzIyQqFChRAZGZmjMVavXo0KFSqgbt26mZZPmTIFTZs2hYWFBY4ePYpBgwYhISEBQ4cOzXasmTNnYvLkyR8sP3r0KCwsLHKU51MEBQVpfUxDwvpoxvpkj7X5UK+ivTDv8Txsj9wOz72eKGleUnQknZXXn59Drw/h7LOzMJOa4Vuzb3Ho0KE8ff9PpQ8/X0lJOZu9XmizNHbsWMyerXnm2Fu3bn3x+7x//x5btmzB+PHjP3ju38tq1KiBxMREzJ07V2OzFBAQAH9/f/XjuLg4ODs7o0WLFrCysvrivBkUCgWCgoLQvHlzGBvzSof/Yn00Y32yx9pkr5WqFe7uuIs9d/dg7bu1CGkfwiut/kPE5+dp3FN0X9EdADCz2Uz0rtU7T973c+jTz1fGkaGPEdosjRw5Er169dK4TqlSpeDg4IDo6OhMy1NTU/H27Vs4ODh89H127NiBpKQk9OjR46Prenp6YurUqZDL5TA1Nc1yHVNT0yyfMzY2zpUPRm6NayhYH81Yn+yxNllb2mopTjw4gavRVzEvdB4mNJogOpJOyqvPj0qlwtAjQ5GQkoC6znUxpM4QyKSyXH/fL6UPP185zSe0WbKzs4Odnd1H1/Py8kJMTAzCw8Ph7u4OADhx4gSUSiU8PT0/+vrVq1fj66+/ztF7RUREwNbWNttGiYjI0Nlb2qN/8f749fGvmHpmKtqVb4dqDtVEx8q31l9ZjwN3D8BEZoJVbVfpRaNkaPTiargKFSqgZcuW6NevH8LCwnDu3Dn4+fmhc+fOcHJyAgA8f/4cbm5uCAsLy/Tae/fu4cyZM+jbt+8H4+7btw+rVq3C9evXce/ePSxbtgwzZszAkCFD8mS7iIh0VX2b+mhXrh1SlanotacXFGm6f7KuIXoU8whDD6WfFjK58WRUsKsgOFH+pBfNEgBs3rwZbm5uaNasGVq3bo369etjxYoV6ucVCgXu3Lnzwclaa9asQfHixdGiRYsPxjQ2NkZgYCC8vLxQvXp1/P7775g/fz4mTpyY69tDRKTLJBIJlrZcikLmhRARGYHpf00XHSnfSVOmoefunohPiUc953oYXXe06Ej5ll5cDQcAhQoVwpYtW7J9vkSJElneBHLGjBmYMWNGlq9p2bIlWrZsqbWMRESGxN7SHoGtA9Hlf10w7cw0+JT2gZezl+hY+caC8wtw5vEZWJpYYkOHDTz8JpDe7FkiIqK817lyZ3St0hVpqjR029kNcfKcXT1EX+Za1DX8cuIXAMACnwUoZVtKcKL8jc0SERFp9Fvr3+Bq7YqHMQ/hd9BPdByDl6RIQpf/dUFKWgralmuLPjX6iI6U77FZIiIijazNrLH5m82QSqTYeHUj/rj2h+hIBm344eG48eoGHCwdsLLtSo13lKC8wWaJiIg+qp5LPYxrMA4AMODAANx/e19wIsO07fo2rLy0EhJIsKnDJt77TUewWSIiohwZ32g86jrXRZw8Dp22d0JyarLoSAblwbsH6L+/PwDg5wY/o1mpZoITUQY2S0RElCNGUiNs+3YbilgUweXIyxh2aJjoSAZDniqH7w5fxMnjUM+5HiY1niQ6Ev0LmyUiIsqx4lbFsfmbzZBAghWXVmDjlY2iIxmEIYeG4OKLi7A1s8WWjltgJNWbmX3yBTZLRET0SVqUbqG+X9yAAwNwPfq64ET6bWX4SvV5Sn90/AMu1i6iI9F/sFkiIqJPNr7heDQv1RxJiiS029oOb5LeiI6kl0KfhcLvUPp0DNObTodPGR/BiSgrbJaIiOiTyaQybOm4BSVtSuLBuwfotL0T7x/3iaISotDxz45ISUtBB7cOGFt/rOhIlA02S0RE9FmKWBTB3i57YWliiZOPTmLEkRGiI+mN94r3aLe1HZ7HP4dbETesa7+O8ynpMDZLRET02SoXraw+4TvwQiCWX1wuOpLOU6qU6Lm7J0Kfh6KQeSHs6bwHVqZWomORBmyWiIjoi3xd/mtMazoNAOB30A8H/j4gOJFuG3diHLbf3A5jqTF2+e5CucLlREeij2CzREREXyygfgB6VuuJNFUavtvxHcKeh4mOpJPWXF6DmWdnAgBWfb0KDV0bCk5EOcFmiYiIvphEIsHKtivhU9oHSYoktNnSBnff3BUdS6fsvr0b/fb1A5B+NWGPaj0EJ6KcYrNERERaYSwzxo7vdsDd0R2vk16j5eaWeBn/UnQsnXD8wXH47vCFUqVE7+q9MbnxZNGR6BOwWSIiIq2xNLHEga4HUMq2FB68e4CmG5oiKiFKdCyhQp+Fot3WdkhJS8E3Fb7BirYreOWbnmGzREREWmVvaY9j3x9DcaviuP36Nrw3euN10mvRsYS4/PIyWm9pjURFIpqVbIYt3/BWJvqIzRIREWldSduSONnzJBwtHXE9+jqab2yOt+/fio6Vp8Keh6HphqZ4+/4tPIt5Ynfn3TA1MhUdiz4DmyUiIsoVZQqVwYmeJ2BfwB4RkRFovK5xvjmHKfhpMLw3eCMmOQZ1nevi6PdHYWliKToWfSY2S0RElGvcirjheI/jcLB0wLXoa6i/tj4evHsgOlauOvHwBFpsbIH4lHg0cm2EI92PcNJJPcdmiYiIclWlopVw7odz6pO+662ph6tRV0XHyhUbr2xEy00tkahIhHcpbxzsdpB7lAwAmyUiIsp1pWxL4Wzvs6hStAoiEyLRYG0DHLx7UHQsrVGpVJh6eip67O4BhVKB7yp9h31d9sHC2EJ0NNICNktERJQnHAs64nSv02jg0gBx8jh8teUrzAueB5VKJTraF3mveI/ee3pjwqkJAIAxdcfgj45/wMzITHAy0hY2S0RElGdszW1xrMcx9KnRByqoMDpoNHru7on3iveio32W+2/vo+6aulh/ZT2kEil+a/0bZjefDamEv14NCb+bRESUp0xkJljZdiUWt1wMmUSGjVc3wmOlh96dx7T3771wX+GOiMgIFLEogiPdj2BgrYGiY1EuYLNERER5TiKRYIjnEBzpfgT2Bexx89VN1F5ZG4vOL9L5w3Jx8jgse7oM3+74FrHyWNR1rovLP16Gdylv0dEol7BZIiIiYZqVaoZrA6/hq3JfQZ4mx/Ajw+G90Rt3Xt8RHS1LR+8fRY2VNXDkzREAwIg6I3Cq5ykUtyouOBnlJjZLREQklF0BO+ztvBdLWy2FmZEZTjw8garLq2L8ifE6cy7T09in+H7X9/DZ5IOncU9hb2KPoG5BmO8zH8YyY9HxKJexWSIiIuEkEgkG1x6M6wOvo1WZVkhJS8G0v6ahQmAFrL60Goo0hZBc8fJ4/HL8F5RbWg6brm4CAAz2GIyF5ReikWsjIZko77FZIiIinVG6UGkc6HoA//vufyhuVRyPYx+j776+cAt0w9rLa5GSlpInOd4kvcGU01NQanEpzDg7A8mpyWjg0gBhfcOwoMUCmMvM8yQH6Qa9aZamT5+OunXrwsLCAjY2Njl6jUqlwoQJE+Do6Ahzc3N4e3vj7t27mdZ5+/YtunXrBisrK9jY2KBPnz5ISEjIhS0gIqKckEgk+KbCN7jjdwfzms9D0QJF8eDdA/yw9we4LnTF+BPj8SjmkdbfV6VS4fyz8+izpw9cFrpg4qmJeJ30GmULlcUu31043es0ahWrpfX3Jd2nN81SSkoKOnXqhIEDc35Z5pw5c7B48WIsX74coaGhKFCgAHx8fJCcnKxep1u3brhx4waCgoKwf/9+nDlzBv3798+NTSAiok9gYWyBkXVH4sHQB5jXfB4cLB0QmRCJaX9NQ8lFJeG5yhNzz81FRGQElCrlZ71Hcmoyzjw+gzFBY1B2SVl4rfbCmog1SFIkoZp9NfzR8Q/cHHwT7d3aQyKRaHkLSV8YiQ6QU5MnTwYArFu3Lkfrq1QqLFy4EOPGjUO7du0AABs2bIC9vT12796Nzp0749atWzh8+DAuXLgADw8PAMCSJUvQunVrzJs3D05OTrmyLURElHMFTApgZN2RGOo5FLtv78bv4b/j5KOTCHsehrDnYcAxoJB5IXg4eaCGQw2Uti0NVxtXFDYvDEsTSxhJjSBPkyMxJREvE17iaexT3Hh1A1ejruLii4uQp8nV72VmZIZOFTuhX81+qO9Snw0SAdCjZulTPXz4EJGRkfD2/mfeC2tra3h6eiIkJASdO3dGSEgIbGxs1I0SAHh7e0MqlSI0NBQdOnTIcmy5XA65/J8frri4OACAQqGAQqG9kxAzxtLmmIaE9dGM9ckea6OZLtenfbn2aF+uPSITIrHr9i4ceXAEpx+fxtv3b3H0/lEcvX/0k8d0KOCAxiUao125dvAp7aO+8W1qamqW6+tyfXSBPtUnpxkNtlmKjIwEANjb22dabm9vr34uMjISRYsWzfS8kZERChUqpF4nKzNnzlTv6fq3o0ePwsJC+zdNDAoK0vqYhoT10Yz1yR5ro5mu18cVruhv2R+9K/TGo+RHeJD0AI+SHyE6JRqvUl4hMS0RycpkpKnSYCwxhonUBIWMC8HWyBbFzIrB1cwVZS3KwsnUKX0P0kPgzMMzOX5/Xa+PaPpQn6SkpBytJ7RZGjt2LGbPnq1xnVu3bsHNzS2PEuVMQEAA/P391Y/j4uLg7OyMFi1awMrKSmvvo1AoEBQUhObNm8PYmPN4/Bfroxnrkz3WRjPWRzPWRzN9qk/GkaGPEdosjRw5Er169dK4TqlSpT5rbAcHBwBAVFQUHB0d1cujoqJQvXp19TrR0dGZXpeamoq3b9+qX58VU1NTmJqafrDc2Ng4Vz4YuTWuoWB9NGN9ssfaaMb6aMb6aKYP9clpPqHNkp2dHezs7HJl7JIlS8LBwQHHjx9XN0dxcXEIDQ1VX1Hn5eWFmJgYhIeHw93dHQBw4sQJKJVKeHp65kouIiIi0i96M3XAkydPEBERgSdPniAtLQ0RERGIiIjINCeSm5sbdu3aBSB9no7hw4dj2rRp2Lt3L65du4YePXrAyckJ7du3BwBUqFABLVu2RL9+/RAWFoZz587Bz88PnTt35pVwREREBECPTvCeMGEC1q9fr35co0YNAMDJkyfRuHFjAMCdO3cQGxurXmfMmDFITExE//79ERMTg/r16+Pw4cMwMzNTr7N582b4+fmhWbNmkEql6NixIxYvXpw3G0VEREQ6T2+apXXr1n10jiWVSpXpsUQiwZQpUzBlypRsX1OoUCFs2bJFGxGJiIjIAOnNYTgiIiIiEdgsEREREWnAZomIiIhIAzZLRERERBqwWSIiIiLSgM0SERERkQZsloiIiIg0YLNEREREpAGbJSIiIiIN9GYGb12WMXN4XFycVsdVKBRISkpCXFyczt+5WQTWRzPWJ3usjWasj2asj2b6VJ+M39v/vQPIf7FZ0oL4+HgAgLOzs+AkRERE9Kni4+NhbW2d7fMS1cfaKfoopVKJFy9eoGDBgpBIJFobNy4uDs7Oznj69CmsrKy0Nq6hYH00Y32yx9poxvpoxvpopk/1UalUiI+Ph5OTE6TS7M9M4p4lLZBKpShevHiujW9lZaXzHziRWB/NWJ/ssTaasT6asT6a6Ut9NO1RysATvImIiIg0YLNEREREpAGbJR1mamqKiRMnwtTUVHQUncT6aMb6ZI+10Yz10Yz10cwQ68MTvImIiIg04J4lIiIiIg3YLBERERFpwGaJiIiISAM2S0REREQasFnSYYGBgShRogTMzMzg6emJsLAw0ZF0wpkzZ9C2bVs4OTlBIpFg9+7doiPpjJkzZ6JWrVooWLAgihYtivbt2+POnTuiY+mMZcuWoWrVqurJ8ry8vHDo0CHRsXTWrFmzIJFIMHz4cNFRdMKkSZMgkUgyfbm5uYmOpTOeP3+O7t27o3DhwjA3N0eVKlVw8eJF0bG0gs2Sjtq2bRv8/f0xceJEXLp0CdWqVYOPjw+io6NFRxMuMTER1apVQ2BgoOgoOuf06dMYPHgwzp8/j6CgICgUCrRo0QKJiYmio+mE4sWLY9asWQgPD8fFixfRtGlTtGvXDjdu3BAdTedcuHABv//+O6pWrSo6ik6pVKkSXr58qf46e/as6Eg64d27d6hXrx6MjY1x6NAh3Lx5E7/++itsbW1FR9MKTh2gozw9PVGrVi0sXboUQPr955ydnTFkyBCMHTtWcDrdIZFIsGvXLrRv3150FJ306tUrFC1aFKdPn0bDhg1Fx9FJhQoVwty5c9GnTx/RUXRGQkICatasid9++w3Tpk1D9erVsXDhQtGxhJs0aRJ2796NiIgI0VF0ztixY3Hu3Dn89ddfoqPkCu5Z0kEpKSkIDw+Ht7e3eplUKoW3tzdCQkIEJiN9ExsbCyC9IaDM0tLSsHXrViQmJsLLy0t0HJ0yePBgtGnTJtO/QZTu7t27cHJyQqlSpdCtWzc8efJEdCSdsHfvXnh4eKBTp04oWrQoatSogZUrV4qOpTVslnTQ69evkZaWBnt7+0zL7e3tERkZKSgV6RulUonhw4ejXr16qFy5sug4OuPatWuwtLSEqakpBgwYgF27dqFixYqiY+mMrVu34tKlS5g5c6boKDrH09MT69atw+HDh7Fs2TI8fPgQDRo0QHx8vOhowj148ADLli1D2bJlceTIEQwcOBBDhw7F+vXrRUfTCiPRAYgodwwePBjXr1/nORX/Ub58eURERCA2NhY7duxAz549cfr0aTZMAJ4+fYphw4YhKCgIZmZmouPonFatWqn/v2rVqvD09ISrqyv+/PPPfH8YV6lUwsPDAzNmzAAA1KhRA9evX8fy5cvRs2dPwem+HPcs6aAiRYpAJpMhKioq0/KoqCg4ODgISkX6xM/PD/v378fJkydRvHhx0XF0iomJCcqUKQN3d3fMnDkT1apVw6JFi0TH0gnh4eGIjo5GzZo1YWRkBCMjI5w+fRqLFy+GkZER0tLSREfUKTY2NihXrhzu3bsnOopwjo6OH/zBUaFCBYM5TMlmSQeZmJjA3d0dx48fVy9TKpU4fvw4z60gjVQqFfz8/LBr1y6cOHECJUuWFB1J5ymVSsjlctExdEKzZs1w7do1REREqL88PDzQrVs3REREQCaTiY6oUxISEnD//n04OjqKjiJcvXr1Ppim5O+//4arq6ugRNrFw3A6yt/fHz179oSHhwdq166NhQsXIjExEb179xYdTbiEhIRMf8k9fPgQERERKFSoEFxcXAQmE2/w4MHYsmUL9uzZg4IFC6rPcbO2toa5ubngdOIFBASgVatWcHFxQXx8PLZs2YJTp07hyJEjoqPphIIFC35wfluBAgVQuHBhnvcGYNSoUWjbti1cXV3x4sULTJw4ETKZDF26dBEdTbgRI0agbt26mDFjBr777juEhYVhxYoVWLFiheho2qEinbVkyRKVi4uLysTERFW7dm3V+fPnRUfSCSdPnlQB+OCrZ8+eoqMJl1VdAKjWrl0rOppO+OGHH1Surq4qExMTlZ2dnapZs2aqo0ePio6l0xo1aqQaNmyY6Bg6wdfXV+Xo6KgyMTFRFStWTOXr66u6d++e6Fg6Y9++farKlSurTE1NVW5ubqoVK1aIjqQ1nGeJiIiISAOes0RERESkAZslIiIiIg3YLBERERFpwGaJiIiISAM2S0REREQasFkiIiIi0oDNEhEREZEGbJaIiIiINGCzRERERKQBmyUiIiIiDdgsERH9x6tXr+Dg4IAZM2aolwUHB8PExATHjx8XmIyIROC94YiIsnDw4EG0b98ewcHBKF++PKpXr4527dph/vz5oqMRUR5js0RElI3Bgwfj2LFj8PDwwLVr13DhwgWYmpqKjkVEeYzNEhFRNt6/f4/KlSvj6dOnCA8PR5UqVURHIiIBeM4SEVE27t+/jxcvXkCpVOLRo0ei4xCRINyzRESUhZSUFNSuXRvVq1dH+fLlsXDhQly7dg1FixYVHY2I8hibJSKiLIwePRo7duzAlStXYGlpiUaNGsHa2hr79+8XHY2I8hgPwxER/cepU6ewcOFCbNy4EVZWVpBKpdi4cSP++usvLFu2THQ8Ispj3LNEREREpAH3LBERERFpwGaJiIiISAM2S0REREQasFkiIiIi0oDNEhEREZEGbJaIiIiINGCzRERERKQBmyUiIiIiDdgsEREREWnAZomIiIhIAzZLRERERBqwWSIiIiLS4P8AB5goo8qi5rYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate data for a sine wave\n",
    "x = np.linspace(0, 2 * np.pi, 400)  # x values from 0 to 2*pi\n",
    "y = np.sin(x)\n",
    "\n",
    "# Plot the sine wave\n",
    "plt.plot(x, y, label=\"y = sin(x)\", color='green')\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.title(\"Sine Wave\")\n",
    "plt.legend()\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b3b24dc7-c555-42f5-8428-ab7405ead4c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate data for both sine and cosine waves\n",
    "y_sin = np.sin(x)\n",
    "y_cos = np.cos(x)\n",
    "\n",
    "# Plot both functions on the same graph\n",
    "plt.plot(x, y_sin, label=\"y = sin(x)\", color='green')\n",
    "plt.plot(x, y_cos, label=\"y = cos(x)\", color='red')\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.title(\"Sine and Cosine Waves\")\n",
    "plt.legend()\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a8bc2c06-5aa4-43c0-a9eb-07c5363fcede",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'How to evaluate a 2D function using a python grid?')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pylab import figure, cm\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def f(x1,x2):\n",
    "    return (x1-x2) * np.exp(-(x1**2+x2**2))\n",
    "\n",
    "x1_min = -2.0\n",
    "x1_max = 2.0\n",
    "x2_min = -2.0\n",
    "x2_max = 2.0\n",
    "\n",
    "x1, x2 = np.meshgrid(np.arange(x1_min,x1_max, 0.1), np.arange(x2_min,x2_max, 0.1))\n",
    "\n",
    "y = f(x1,x2)\n",
    "\n",
    "plt.imshow(y,extent=[x1_min,x1_max,x2_min,x2_max], cmap=cm.jet, origin='lower')\n",
    "\n",
    "plt.colorbar()\n",
    "\n",
    "plt.title(\"How to evaluate a 2D function using a python grid?\" , fontsize=8)\n",
    "\n",
    "#plt.savefig(\"evaluate_2d_function_using_meshgrid_03.png\", bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "86701349-8884-4f5e-a73b-b9fec3663b5d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
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