{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6cacfbb9-3694-4d95-a619-d6917688cbac",
   "metadata": {},
   "source": [
    "# Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6049f1ba-c721-4c30-840b-93294bc1333a",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "import itertools"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d659e10c-e325-48ce-8071-c4fbe0c15b2e",
   "metadata": {},
   "source": [
    "# Low pass filter"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32a640e5-bff4-466b-ba87-c3c6ed7fdcee",
   "metadata": {},
   "source": [
    "We want to analyse data from the stock market. To see the long term trends we want to \"smooth\" the day to day market oscillation, and keep the fluctuation which have a long period."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "229ef4b3-ec1a-494e-bbcd-35972d216d01",
   "metadata": {},
   "source": [
    "We will take the Fourier transform of the data and throw away the 90% and 98% modes with highest frequency, and antitrasform to get the smoothed data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "34bc9895-8c5c-4566-ab01-eae17ff59e25",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dow_data = np.loadtxt(\"dow.txt\")\n",
    "\n",
    "plt.plot(dow_data)\n",
    "plt.xlabel(\"day\")\n",
    "plt.ylabel(\"closing value\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "221df498-b932-4ac5-b23c-c420da980499",
   "metadata": {},
   "source": [
    "These are the Fourier coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0c61d66a-88dd-4297-9ad2-3ca6cad01897",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1024\n",
      "513\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cks = np.fft.rfft(dow_data)\n",
    "print(len(dow_data))\n",
    "print(len(cks))\n",
    "\n",
    "plt.plot(abs(cks)**2)\n",
    "plt.semilogy()\n",
    "plt.xlim(-1,200)\n",
    "plt.xlabel('k',size = 14)\n",
    "plt.ylabel('$|c(k)|^2$',size=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b51bd999-91c7-456b-9371-6f8057a08ccb",
   "metadata": {},
   "source": [
    "We set to 0 90% of them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ac2b96ae-146d-4228-b44b-83559b074eab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cks[len(cks)//10:] = 0\n",
    "\n",
    "plt.plot(abs(cks)**2)\n",
    "plt.semilogy()\n",
    "plt.xlim(-1,200)\n",
    "plt.xlabel('k',size = 14)\n",
    "plt.ylabel('$|c(k)|^2$',size=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b127511a-e613-47f5-8234-58bb13623385",
   "metadata": {},
   "source": [
    "We antitrasform to get the smoothed data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b4f98cfc-9478-4a1f-aee9-aafab838cb61",
   "metadata": {},
   "outputs": [],
   "source": [
    "dow_data_smooth0p1 = np.fft.irfft(cks)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38261246-4b21-4e92-be0a-84306bad242c",
   "metadata": {},
   "source": [
    "Same but setting to 0 98% of them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1968e9ac-ffe9-4b76-afe9-6665d499d6bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "cks[len(cks)//50:] = 0\n",
    "dow_data_smooth0p02 = np.fft.irfft(cks)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e716ee5-e489-499d-bd94-3d4cc18b294f",
   "metadata": {},
   "source": [
    "Now we can compare the data in real space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2b2f9455-2c3a-4ef8-9299-5132428185a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UviBXkFLxOcv5AXtoMAASbhRHIOO6DaJbYDckdzBzfsxksfwybdwuPu71NW9t0VaqvXXDpYT5m8/YJ/X4bgBtMrl/6BnbXj8wii+3ZPL3K3tjkA3c3vcOBvz2b56wlJNhtHFr0q28d9l7xAR713o6ETTdpkviWf18HNv1ZIa9DfgC4FbUU28lCIIgtDBiJqpwXt358WZmGz7AKLlZ4Y7nSdddTB4eR1lgD251Ps56n1EYJDdvGf5Fh8Cf8Ov6CmnupdgllU4OJ0MZQ9mhmVwZ8m/eGPUGf+n3FxKiJ2Av74nR2YZQRaHg8E7P/eq1J1xOCgAH6HDWps9f2ZvF/zeCm4fWtO0Y2INPjh0nxO5HYVUhf1nxF46WeddsKqty0l7K40n9Z8iSillyErFqBv5o86pOzM8SBEEQWi4RNAnnVXDuBgbL+7GrBp523gFI9I4MINhXmwg+y3UvSWpPZkX4U9j2NyRdFW2VAObl5PFypp7bRzzNhlk38I8pcZ5rmqoDjv2KVmrAz1ZTxsDprp3BUVWVzzamszW9CAApVwuaUqWOZ+2/2aCjX1Sg14o8V3A3QhWFu3LC6BrYlbzKPO5dfi8ljpo5TmV2F1fJv2OU3GxSYkhVIjE4S7lWp026qnS4a91LEARBaFlE0CScV/fpvgMgveM15BACQKdQP/zN2khxtiOTR6P0rLP4YFYU7imoYlHafkZVVvKx+3KC/UyEB5i99obzNWpB0z53ewBi5CzPsboyTasP5vPUIq2KN0D+fu2/WxzR5/RMakg37b7uHP4z9j9E+EaQVpLGM2ueQVW1oK20yskU3VoAFrhG85H7cgASdcsBlXKHq85rC4IgCC2HCJqE80Y5toNB6k6cqg7r2FlcFd+Om4dGE+xrxNekR2c5jKXDe2Cw4Uco/y1UuL8kF1/JySp3X752jyTYYqx1XYtRC7j2q1qmKUbK8ByrK2jafczm+T4nN5fO7jQAtijdz+m5pFAtaOrEMcIt4cwdNReDbOCXzF/4357/AWAuOUIXORu7amCZMpBF7otwYKCznEM36ShlVS5PgCUIgiC0TCJoEs4bx+aPAfhZGUhwZBfmXN/PM8yW59qFT9SHSDo7rvLOXBr4ChkXL+JR593c73iA6c6ZWExGgnxrB01GvYxRJ7Nf1TJN3aSjyGjBksNdEzQdOF7KT7uycbpqgpOS1HXoJJV0JYw8gs7pueQ2XQEIlUpwlRXQO7Q3jw16DIC52+ayN38//gXaPKtCay96dGhHBWaS9X0AGCtvw6Wo9dr0VxAEQWg+ImgSzovP1+7HmfwlAEnGBK9q2LvydrH42Gwk2YWrtAeVmbcTYPLH5BvI1+5RLFWG4ULP8hmXnLaKtsWkI0MNp0o1YJacRFdvvntypilhzmr+8tk2ftl33PPaoc3LANiidmfJ/Red07MZLQEcVbWhRleuVkvq+pjrGR01Gpfi4talMyB7GwAlwXH0bBsAwM8ubXuY0brtACzfc/zUSwuCIAgtiAiahCbncits+OET/NVystRQ6DzKc+yw7TD3rbwPh1KFq6wblVk3g2rApai0C/Lxuk5bqw+nU1zhREHmoNoOgBhJm9d0cqbphB1ZNcNznQu0idi5oUOJa289p+cz6mQOKdrWLUrefgAkSeKZoc8QYAygUsrgaLA2Ob0itI9n/tYKu1bZvJ+UigkHy0TQJAiC0KKJoElocj/syuZ63a8AfOO+hIRYLcCw2W3cv/J+iu3FdPDroQVM1aXDHC6F3pFWJvXV2p7479kc8MxrygTAWZ1pqqsOUjcpixg5C7uq53DwyHN9PPQ6mcOq1r/ijD0UlGk1otpY2nBLzEMALAlyka3T4YiIx99sACBdDSdXDcQouekrHaKk0nnOfRAEQRCangiahCb3wferGKHbjaJKfO0ayfjYCBRV4YnfnyCzNJNI30ge6/cKqCbPOc7qDNHc6/vxbuIAnpnYs1732qtoK+Bi5SNATaaptKp2QHKDbhUAvytx5DhMtY43RLqsZbj27NrCoNkrPK8bKwZiqmiLXZZ4KTgUfWgX/MwnaspKbFK0IpgD5f3kldr/UB8EQRCEpiWCJqFJldtdXOZYDsAaJZajtMGgk/nPjv/w+9HfMelMzB09l0CT9yTsK+LaAqCTJcb1jjhrVe8TtinaSrZ4+SCgeoKv4grvoKmflEqiTpvP9D93AkM6BZ/zMwKUWDoB0EU6hqJqm/AC/LznOENyOyCrKr/4mUirSCHAXFOIf7PSA4CB8gFyRdAkCILQoomgSWhSmw/nca1uNQBfukdrr+Vs5t0d7wLwt2F/o2dIT4JPWhW35P6LGNH1zNuZnMqk1/4o71Y7Ylf1tJFKiJZySTmqzV8qrh76MmPnr/ov+Nr4PEbJzXJ3f1Yrfbh9RKc/9JyRXbWVcNFSLkacHCuuArSilhc7c7mutAyAj/fNxWKsqTG1S9Hu21tOo6DcLrZTEQRBaMFE0CQ0qT1rv6OtVEiR6sdyZQDIFTzx+xOoqFzd7WomdZkEQPsgC3Ou78tHtw06pwnZ31evfLNjJEXVApGB0n7e//0Iafnl/PPHvXSQcvjB+CR/0S/BILn52T2QR5z3EeJrwtf0x7Zh9A1tT4nqg15S6CjlkFGobY9idyr0lQ/zQJENndtAWmkqe0pWe87bq0ajIhEuFROi2qh0isrggiAILZUImoQmU2Z30S5jCQDfu4fhQI85YjHHK44T7R/NXwf91av9VfHtGd0j7JzuFRPh7/l+U/WQ1yjdDgCO5JdjthfwuXE2XeRsstVg7nLM5B7nDMqwYDH98X3ffE16UqtX7nWTjnLcpmWaJGcF3aVMrIrCjZ2nArAk4yNAqwBeiRlXUBdAyzZViMrggiAILZYImoQmc+RoLmOlzQCMue5+enZNxWDdiU7S8dLFL2ExWBr1fjMv0yp6/+QeDECCfjtm7JRVVvFI8Yu0kwo4pLRlsv0fjJiQ6DnvdLWfGsLHqOegUl1cU87izV8OoqoqHZ2p6CQVpyWMB0Y8SIg5hOOVxzAEbqm5f7t+APSW0qiwi0yTIAhCSyWCJqHJOPYsxVeyk6OLwLd7HGV+CwG4t++9xLWJO8vZDffApd14dFwMO9XOFBgiMKtVXCFvJGb7P4hXUihTzdztnEEegQSdtB2L/qR97M6VxajjgCfTlEVWUSXrDhXQ3a3VZ7KHxWMxWLin7z0AGENXguRg+SOXQFttPlRv+YjYg04QBKEFE0GT0GSCDy0GYGdQAq9ueY1iezExQTHcGXdnk93zLyO78P39F2G9aDoAbxjfoXvGlyiqxEznXzhUHdicPIdJlhonaEqt3salu3QUgOMlVfRUtKDJFdEPgGu7XUukXySyoZRePXbRNcwPIqqDJimdSofINAmCILRUImgSmsSKbQdoX7gBgPVtY1h6eCkSEs8Nfw6DbGiy+8qyRJ/2geiH/x8ZllgA3KrEs67b+FkZ5GnnY6iZx3Ri5d0fYTHq2VNdI6qzdAxfKvEx6OiLtq2K2m4AAAadgfv63gdAuXklVe4qaNsXgI7ycSrLS/5wXwRBEISmIYImodEVVzhY9M18DJKbFDWSlY7vALip503Ehsaen04YfFjQ+11udDzFaMcbfOq+zOuw2SDTNyoQgPvHdPvDt7MYdeQRRJYaik5S6SMfxlWcSXspH5cqI7WvCdiu6HwF7fzaUVhVyMIDC8ESTLGs9UVXePAP90UQBEFoGiJoEhrd7wfzGVO9Ce2rgREUOXKI8I3g/vj7z2s/fC1m1iu9yVDDATCelFGSJIkPbh3I8kcu4bJe4X/4XhajlrlKVroCEC+lYsneBMAetQNG3wBPW4Ns8AxRfpTyEQ63g2yDlqVScvf/4b40liqnmy1phaJ2lCAIQrVmDZpWr17NpEmTiIyMRJIkFi9e7HX8ueeeo0ePHvj6+hIUFMTYsWPZuHGjVxu73c4DDzxAaGgovr6+TJ48maysLK82RUVFJCYmYrVasVqtJCYmUlxc7NUmIyODSZMm4evrS2hoKA8++CAOh6MpHvuCV1RexUh5B3uNBrYFFQDw9JCn8TX4ntd++J1Se+n3x0Z7vpclCPUz0S3c/9TTzonFqN1re3XQ1F8+QHC+tnJws9ID4ykr9K7sciXhlnByK3NZnLqY1OoNf5O3b2qU/jSGZxancO076/l0Q3pzd0UQBKFFaNagqby8nL59+/LWW2/Vebx79+689dZb7Nq1izVr1tCxY0cSEhLIy8vztHn44YdZtGgRCxYsYM2aNZSVlTFx4kTc7poJtdOmTSM5OZmkpCSSkpJITk4mMbFmybnb7WbChAmUl5ezZs0aFixYwMKFC5k5c2bTPfwFzHh8J4FSCc+GhoKkMq7jOEZGnfuGuOfq5MnevkYd4QE1W7FEWOu3LUt9+VdvjbKxukbUxXIKPfK0bVrWqXHoTwmajDojt8feDsCHKR9S6NsBgK7SsUbt1x/x9dYs2pHHb0vnU1quFeuct/Igw19cSWZ18U5BEIQ/kz9WBvkPGj9+POPHjz/t8WnTpnn9/MYbb/DBBx+wc+dOLr30Umw2Gx988AHz589n7NixAHz66adERUWxYsUKxo0bx969e0lKSmLDhg0MGTIEgPfff59hw4axf/9+YmJiWLZsGXv27CEzM5PISO0T/+uvv85tt93G7NmzCQgIoC52ux27vWa/sJISMYkXICh/M58H+LPPZMDf4M/jgx9vln6cnGnyqc4ELfzLcEqqnLS1+jTqvU4EaClqJ9KVMDrIuaA6KVD92arrW+c513S7hvd3vs/RsqO4eg2FddBNPtqo/TpXTrdCNymLxcZn8JXsHPlgI647FvL6cm1i+9dbs5hRXRdLEAThz6LVzGlyOBy89957WK1W+vbV3oS2bt2K0+kkISHB0y4yMpLY2FjWrVsHwPr167FarZ6ACWDo0KFYrVavNrGxsZ6ACWDcuHHY7Xa2bt162j69+OKLniE/q9VKVFRUoz5zq1W2nbeCtK1QZgycQahPw/aRaywnB00n5hwN6BDE6JhzqzpePxJvuK71/DTXdQ2S3lhnS7PezG29bwPgG9t63EA0x1FdzT8sbKt08pB+Ib6S9qGgU+HvfLngI8/xIEvTrYAUBEFoqVp80LR06VL8/Pwwm83MmTOH5cuXExqqvQnn5ORgNBoJCgryOic8PJycnBxPm7Cw2m+SYWFhXm3Cw70nAwcFBWE0Gj1t6vLEE09gs9k8X5mZmX/oWS8EH605zJfmI1TKMl0M0Vzd7epm64ufuXbQ1JQ+vn0Q/aICWWu5lGvtz3Kz4wnmuxNqDc2dbGrMVAJNgWRVHGOJJQCD5MaRd6jJ+3o25SXFjJW3ATVDjv3yl3iOi8nhgiD8GbX4oGn06NEkJyezbt06Lr/8cqZOnUpubu4Zz1FVFemkgoVSHcULz6XNqUwmEwEBAV5ff3bzVv+XzRY9BlXlpu6PI0vN90fMe3iu6YOmUTFhLP6/Ebx5Qz+2qD1Yo2hVz9UzxBcWg4Wbe94MwLuBgSiAM2dfk/f1bOSDP2GWnBxS2vIPp9a/PlVbMOIEoEIU4RQE4U+oxQdNvr6+dO3alaFDh/LBBx+g1+v54IMPAIiIiMDhcFBUVOR1Tm5uridzFBERwfHjx2tdNy8vz6vNqRmloqIinE5nrQyUcHrFVcWo4drk5ylFElfEDWvW/tQ1PHc+DO/qPRx5toLjN/a8ET+DH1kmWGXxQclv/lpNpozfAfhZGUSK2pFSQygWqhgi7wUQ270IgvCn1OKDplOpquqZfD1gwAAMBgPLly/3HM/OziYlJYXhw4cDMGzYMGw2G5s21Szl3rhxIzabzatNSkoK2dnZnjbLli3DZDIxYMCA8/FYF4RXt7yKS2+nq8PBEGdPr9VrzeHk4bnG2CrlXJ3tzgHGAG7scSMA7wUGoOYfaPpOncEby/ZTenAtAJuVGFRkNukHAjBaTgYQGwsLgvCn1KxBU1lZGcnJySQnJwNw5MgRkpOTycjIoLy8nCeffJINGzaQnp7Otm3buOuuu8jKyuK6664DwGq1cueddzJz5kxWrlzJ9u3bufnmm4mLi/OspuvZsyeXX34506dPZ8OGDWzYsIHp06czceJEYmJiAEhISKBXr14kJiayfft2Vq5cyaxZs5g+fboYcqundUfX8f2h75FU+Ft+Ib0GXNrcXcJy0lYpLnfzzcGpT8CW2CsRnaJjj8nEhuI9ZNsqz0PPvKmqit3l5n+/bKeLrH2AOFF3aqFNWyk3XN4NiEyTIAh/Ts0aNG3ZsoX4+Hji4+MBmDFjBvHx8Tz77LPodDr27dvHNddcQ/fu3Zk4cSJ5eXn8/vvv9O7d23ONOXPmMGXKFKZOncqIESOwWCwsWbIEna7mDfOzzz4jLi6OhIQEEhIS6NOnD/Pnz/cc1+l0/PDDD5jNZkaMGMHUqVOZMmUKr7322vn7ZbRiFc4KXtjwAgDXlVTQz+5APmnbkOYiyzXBit3VfJmR+iS5gsxBtKnoB8DHciHDXlxJaZWzaTt2ElVVuertdcQ8nUS8nApAqhJJMVrxz/VKLwB6yJmEYhOZJkEQ/pSadfxk1KhRqGeYJfvtt9+e9Rpms5l58+Yxb96807YJDg7m008/PeN1oqOjWbp06VnvJ9T27+R/c7TsKBHmEGamZVKi+uDTrldzdwuA2VfF8ux3u7lhcHSz9aG+A4OZ2aPx7bKFFLMBqyWFY8UjiYk4P0v7K51ukjOLARgga8OD25SaPfmKCGCP0oFecjpD5T3YHF3OS78EQRBaklY3p0loGvtzSsmxVTX4vOTcZD7dqwWkN9Ifi6qyU+1MgE/dtYnOt5uGdCDluXFMHdh8NbTOtALzZFWuUMaVasNe5tBfmrJLtZy8Gm6ApE1E36p2p1/1psYA66qzTcPl3WL1nCAIf0oiaBJISslh3NzVTHt/wxkzf6cqd5bzxO9PoKgKk7tMpuORDABKQ/qdsTbR+XY+yg2c6m+TGp5p69veyuCiYPSqSoVvNnct+KYJela3yuogSIebPrJWJ+r/Em/g63trVkCuVWIBGCbvptwu5jQJgvDn03Le2YTzT1Up/XUehi9vYLicwuH8co41INv0yuZXyCrLItI3kof6zaJ9xR4ABl88rql63GrcPqKT53u5nn/L/j4llmJnOyaXlQOQr//RK4h1KypJKdnkldpPd4lzdiJzFCNl4ivZcej9iO7eH4NOpkeENq9psxKDKunoJB/Hr+r0RV8FQRAuVCJo+jNLWYj/r09zqW47/zW8Tig2kjOK63XqLxm/8O3Bb5GQmH3RbI5ml3g2mw3pPrwJO916nJiHHh8VdOaG1XwMOg6rbbmzuARJBb3/Pnbm7fYc/3RDOvd+uo0b3lvf6H09sRruxCTwyjb9PNHeqOptZ4y+gVS20bYwinUkN3ofBEEQWjoRNP1ZqSqsrlkdaJHsXK9bxfaMojOcpDladpRn1z0LwG2xtzEwYiCFBzYgSyq5ugjwa9Nk3W5NfnroEu6+pDPPT+599sZow4iH1UiiXS4uLlMAmLe9ZoHD4mRtM99DeeV1nl9S5SSjoOKc+npieK6/rM1n8u0y1HPsoUu78ezEXiy+bwTO6Iu0dq6d53QfQRCE1kwETX8yiqKyNjWfqqwdkLcXp2Tg786bAEjQbfGsoDodu9vOjF9nYLPbiA2J5f5+9wNgPr4dgGz/+gUIfwYxEf48eUVPgnzrNyneYtRzWGkLwIyiXFRVZmPOOjZmbwTOvN9bYbmDS15ZxZjXfz2nCf0nhuf6SVqmSd+hJmjyMeq446JORIdYULuMAeBiaTtuZ/NvLCwIgnA+iaDpT+abbVnc9N+NfPLuKwAsd8WzxK0Np8VKRzh09DhOt1Lnuaqq8uLGF9lTsIdAUyBvjHoDo04LCEKKdwBQFNT3PDzFhcli1JFNMJWqkS5uBz7F2sTruVvnoqqqV4HOUyfsrz6QR3GFE5eicjC39Iz3OZJfzmcb072CsAqHiyBKPEUtaVd3JXxTpxHkqQEESWXYD/6CrfL81ZISBEFobiJo+pNwKyqKovLN1ixkFCbrtHkx37lHkEsQDt9IdJJKjJLKukMFdV7jf3v+x8KDC5GQeOnil2jrp2VFUFXalWlzbyrD48/L81yITHoZFZkjqvZ77VnQAbPOh5SCFJanL/cKck4NVvLL7HV+X5cb39vAU4tSeGrRLs9rlQ43o2Qt8CWsN1iC6zzXbDKQpAwBYO/P/6Xv88v4cM2R+j+kIAhCKyaCpj8Bh0shYc5v3PD+BkoqnQyR99JWKsSmWlil9ANAidQyC/2kVL7eklnrGj+n/cxrW7Q5UDMGzGBEuxE1B/MP4K/YqFSNyJH9mvpxLlgn6jkdrg6aYpQixkfdAMCb29+kylUTDBWUew+N5ZfV/JxfeuZhs5wSbfhuweZMT+D05sqDjNVt1Rr0uOKMffzKNRKAuOJfCKOIF5buYUdmMQ5X3RlKQRCEC4UImi5gJVVOtqQVsuuojUN55Ww6UsiB46Vco9N2sP/RPQQHWsVpY4fBAPSVD1F2Sg2edUfX8eTvTwJwY48bubX3rd43Sl8HQLLSlTaB/k35SH8Kh6qDps5SNmPaXkewOZj0knRsxpWeNqcGKAUnZ5rK61eSwJ8KNm5ax1eb0tE5yxgpV0/ujjl90ASwS+3MJiUGo+TmDn0SAFf+ey2PfbOjXvcVBEForUTQdAGb9cUmPn/vZRa99zxWygAIUEuZKGtDc1+5R3nayu37AxAnH/Ga0/R71u888MsDOBQHY6LG8NdBf/WqcL1qXy5JPy4CYLPanc6hvk39WBe8E5PBO8vZoJqYNXAWAK6AZUiGQqAmaDoxt8lreO4smaZuYX4Mk3ezzvQAK0yPEbd0ArOdr+InVeEM6gpt+53x/F5tA3jHNQmAW3TLCMEGwOLkYw18UkEQhNZFBE0XqOzCEhIPP8Ybxnf4h+EjlpseY4S8i9v1P2OWnBDRh2N+J610C9e+by/lo3doAVbSkSQeWvWQJ2B6beRr6OSa6tpF5Q7u+HgjA9zayrk9xj4EWlrG9imt1YoZlzDtiksB6Cwdo8rpZmLniQwMH4QkOzGHfw+oONwKf1+6h1Gv/YqtwklRRc0cpypn7S1OckuquOm/G/hpVzY6dxVzDG/jL1UC0FPO5BKdNkxXfsnTnvpMqqqSU57DxuyNrM5aTUp+ChXOCp6e0JNflHiSlc5YJDt368WejYIg/Dk064a9QuMqrnB4gpbipNlcrEuhUjWSp1qJlvP4zPhiTeOLHuHD4MFMe38j94zsDD5BVPlEYK7MIdxxmH8n/5t3drwDwGUdLuPlS17GIHtvHvtTSg79pEO0kUooUX3I8BMr5/6ormH+dA0YDCugjVSCu6IYSWrLzP6Pc8OPU9H770MfsAOHaygfVE/A/nJLhteQqt1VO2j6LvkYa1MLWJtawE0+64iQiig1hTPG9izX6VbTRz7MEvcwXuo5keyybL45+A0/Hv6RrLIsr+sYZSNxIYORfeKYa7+Wj42vcItuOf91TSCPwCb93QiCIDQ3ETRdID5ee4TnluzhvlFdeOyiELqkfgzAByEzmXcshr/p/8c0vbYJ7DK/KST0vorekkTys5d5htvKA2ModeSy2/IlP+3IBeDWXrfyyIBHvDJMJ3y49gjX6LYAsFrpi9Hkcx6e9E/AHECxLoRAdwGG4kNAT8LM0TjyR2NqswJzxCKyyyZ6mjvdqtdecFXO2hOynUrNa6Nc60EHpT1uIG9jEG+7rwQ3ILmI3fchH6S8j92tDffpJB1R/lFYDBZyK3LJr8xna94afDuuYUNxPOsKuzBcOsTd+qXMdt3cZL8SQRCElkAETa1cZmEFu47aWLlPC3Le/vUQMTtf5kqlimSlMz7xU7Ef28uTrruY57oKneTm9rGjoDpQOhEwqarKDwH+vG9oS7EuF6Ns5OmhT3NVt6s891JVlccX7qLC6eaVa/pwNK+QqcZfAfjBPYQgi3cmSjh3+aZoAisKcB7fD0zkx13ZOPJHo/c9iM6Szsep/wRpGqjaX+GyqjNnmirs2mu+VHJJ9YRvV49J3KH35cO1R9D5HsQc8R1v78gHoH9Yf27ocQMj24/EYrAA2v//1OJUPk6Zz3eHFmMI3M7DFn++z9Fxtfo7L7tuaMpfiSAIQrMTQVNrpSg4dnzFV98sZ5FyEVmqtj9YG4oYV74EJJjjuo4HowM9pzj92tK1bQBTB7b3ulRybjKvbn6VnY6doNPR0S4z57ov6RrU1avdD7uy+bK6HEGnEAs3yCsJkUqxGduyVhnCwit6Nu0z/5mE94Yj23Ef1VakPbdkD6Cj8tj1+Hb6F+nle4hu+1+m5lrpkjucCkcUJ6Yo2utY+n9i+G6QvA+T5CRNCUdq0xNTVgrmdp9hCNDmNIWYQ5g1aBYTOk3wmvAPWoDdLagb/7joeRasCscc+QWVRhs3tW3L/JxsRjh3A1c22a9EEAShuYmgqbVa+TzGtXOZaYC71B+Z7pjJJrUnj+m/xCw52ap04zelD6+H+LL8kUsod7jpFxXoOV1VVTbnbObDlA9Ze2wtACbZxN35x7nW5iI4sEutW76x7IDne/9dn/Cg/jMArGNnsn3gFehkqdY5wrkxdhgIRz6lk32f1+uqM5iqo9PwjfqIImsaimpj3N4lvK0fyAPOB3BgwF7H8NyJoGmgrP0/3KB0JzftC77Mfg9DQBWqKqEvu4glN76Mv/HMZSMkSWL9I3dytPQK7v/lXnI5xn3hbZiSua6Rnl4QBKFlEkFTa1SSjbpuHhKQrQbTVirkE+PLfOEew3X61QD8w3kzUcEWQnyNhPqZPKe6FTe/ZP7Ch7s+JKUgBQBZkpnSdQrjwm5i4PyhGCU32LIgMMrrtsdslUgovKD/mMTSFSDBz7qRjBt4hwiYGpkrQisB0V09DC7vEgL/V5VC+4ICXggN4f1AKxXoeLRoC4+qXzLbdXOdw3Mnhu8GSAfZZDbxr+ACyna/CYC7IpqqnClE+XU9a8B0Qpi/mTD/TlwT+QKfHn6AQ0b4PeIwtyoKkiwW5QqCcGES/7q1Rjs+R1LdbFa6M1l6kzXSAHwkh6fQ4EeucWxXu/HI2O6eIRa7287XB77myu+uZMavM0gpSMGkM3F9zPUsvWopzw9/nrCAthxSI7V7HN/tdUu7y02VU+Eh/bck6legqBIvOm/k7cBHoY5J4sIfI4d0waZaMOHk0O4Nntev6+zkPv13XFdaTkxuDwA+C/TjLxFtGG9cRm/pSK3huS82ZZC0OweD8Sjz2+ZzZ9twykxlBJoCmdL+ESrS70WxR+JjaPj/x85B7anMvAWjorLJV8en2978Yw8uCILQgomgqTXa8SUAX7pHE2y1MkOaxUvOG/jV3ZfSi5/lp8gHmHdjPFf3b4/dbeejlI8Y9804Xlj/Aukl6QQYA7i7z938fM3PPD30aaL8tYySQSezT43W7nE8xeuWpVUuOkvHeECnFbJ8zHU377onEeJvPn/P/SdiNurZosQAsPCr+YA2d/+WkvcwSS5SzP3ZUnArlUevR1UMrPfxYUpUBO0i5lOpO4DNbqPKVUV6STrPrPwQn+j/Yu4yj999zehUFUfhUL6Z+B0jwsdz4p8B8zkETWN6hlFp78R1BVqpi7l7PiajJKNxfgmCIAgtjBiea2WOZR0hMn8/KhLL3APpG2DiaHEl77gn8457MmmXTuCrS6tXwx3+gX9t+xfZ5drO9RG+EdzS6xau6XaNZ0XUyQw6mf1KFOiA3D1ex0oqnfyffjE6SWW5uz/fuLX9x0Z2b9Pkz/xnZNLLLFcGcKluO+N0W3jbPYVLpB3Ela3Fqep40zgdkHCVxFNRFUlg2y+xW46xPrACeJuLFrztuZZPdfIQFcZWVDA4vy1PVEwh1BKE2ZDnaednavg/BwFmA1/fO4y1/41jmN9a1vv48PcNf+e9y96rNZFcEAShtROZplYkq6iCV9/9EIDdSgdK8CU8wMyj47SMxLQhWpYotyKX+3+5n8d/f5zs8mzCLeG8MPwFfrz6RxJ7JdYZMIF3pkmtHp77dEM6b/1ykHJbAZOqt1+Z56opQ3DNgPa1LyT8YSaDzAr3ABRVoq98mF5SGi/oPwLgY/c4tpbXBKuKI5zC9Ad44KgvV5SV4+usKf1g1plxV0ZhzxvLo+lhzMnNJ8veE50soZMlryG5Tue4BY6/Wc9OpSvP5BdhUmFD9gZ+PPLjOT65IAhCyyUyTa3ImoP5DFC1YGajoi3v7xhiIXFoB/pFBdKjrT+rs1bzxO9PUOIowSAbuKfPPdza+1bM+rMPoxl1MvuU6snf+QexlZTx9GJtmG7I0MMYJTdpcjQ7VW1lXYcQyzllJ4SzM+l15GPlN6UPo3U7+NGkbZhcbIzgX1VXU1Y9OfzSHmHVNbokdpeN5l+Ot0lT9IQ8uQ1kFT+DH52e0AKYMabvQYJtajfcirZnXYeQmkApwnpuQ61GncxOpQtRLhd3FxUzLziQVze9waXRl9brz50gCEJrITJNrcjuYyX0l1MB2KTE8MjY7tw+ohOyLNGnvZXP9n3C/Svvp8RRQq+QXnw18Svu6XtPvd+4jHqZHIIpVn2RVDd7dm32HGuTrr3xbrSM5M6LOgHwz6viGvkJhRN0soRBJ/Giaxrlqrb6sUo1sLTr85RRkynsFl6z2i01eCTlqomO8nH0R3fib/T3DJG1oYj2Uj6KKrFT6ew5J8Jq5sbBUZgNMhPi2p5TXw06mXysZKmh3FpSgsFpocCey4J9C87peoIgCC2VCJpakawCG10lbS+wjrEjeGhsN3xNelRV5fUtrzNn6xxUVK7rfh2fjv+0VnHKszHoJEBiv6plm7ZtXgNAIKVEFW0E4EjE5Tx1RU82PXUpI7qGNt7DCbWY9DoOqFFc4XiRp5x3MN7xEnlB/b3aBFkMvJc4gNh2Abxx8wh+VgcD8M1Hr5OWX+5pdyLY3q+2pxzv7W5mT4kj5blxdDzH4TmTXvtnZJfSCZMK/Qq0Idv3d71PiaPknK4pCILQEomgqZVYtD2L46nJGCU3DoOVR6deCmgTvl/e/DKf7PkEgMcGPcazw57FoGv4liYnai3tVbR5TaZCrbDi5brN6HCTonQkKKonsiwRJlbNNTmzQfvrma5G8Jl7LEfUtkQGev/egyxGEnpHsPSBi4mJ8Kewk1aR+wrdRt5dtd/TLr46aNqudKt1H1mW0OvO/Z8CQ/W5J4LtcaV2ZGcEJY4S5u+Zf87XFQRBaGlE0NQKKIq251tvOQ0AV1hv9HptAu9/d/2Xz/Z+hoTEc8OeI7FX4jnf58RQzok3v+5qOgBXylql56XuoXRu43fO1xcaxqSvXQKgyym//+gQ70n9PYZPIl8NIEQqpWfVds/r8fJBALarWvYxOrjuxQDnwlCdadpXHWz3lLOQbeMA+Hzv55Q7y097riAIQmsigqZWIL/cjt2l0EvSghhDZF8Alh5eypvbtWKCfx38V67pfs0fvtdtwzuyV+kAQJx8hGjpOMN0e1BUie/cIwjzN53lCkJjOTHsdcJDl3arFTR1D/eu4D2wcxt+dA8BoH/JSgD8qaC/pAVNV02ZSmy7AN5NHNBo/bQYdEQEmGuCbSkLl60HHQM6UuIo4ZsD3zTavQRBEJqTCJpagRxbFQDdquczGSJjOVB0gOfXPQ/Abb1v46aeNzXKvZ6b3JvCgJ4Uq74ESWXMMWj1ftYpvcgmhFARNJ03ppPKAVzWK5wHL+1GkK+RR8Z297we7Gv0Osds0KHrcy0AnfJW8fWGg1wk78IguTmktGX4oEEsfeBierYNaLR+yrLEypkjSVfDqVINmCUnIc4cEnveBsAnuz/B4Xac+SKCIAitgAiaWoFjxZUA9DDkAFAWGM3MX2dS5a5iROQIHhnwSKPez+pnYYl7GAADqod1PnOPBSDklDdpoen4mWqCpkEdgzxzzh4a240vpg/ll5kj6zyvOLQ/R9UQfKlg05L3GKvbCsBKpX+d7RuDr0mPgsxBtR0AMVImg8MuI8wSRl5lHklpSU12b0EQhPNFBE0tnKqqfLEpE18qCVUKAHgt8yfSStKI8I3gxYtfRJYa939jsK+Rt11XkqdaAVjhjidJGQSc21Ybwrk5udjkqfObhnUJOe38MovJwCeuBAD+qf+Aa3TaKsgk96Am6mmN/dXFUXtImZRWqNzY40YAvtj7RZPfWxAEoamJoKmFK6l0UVjuIEavZZnWBUWw8MhSJCReuvglgsxBjX5Pq4+BbEIYZX+Da11/Z7pzJqr4o3LenTxf6cRKuvrwNer5nzuBXDUQg+QGYKPSg21q7ZVzje1EcdQYOZOCcjtXd7sag2wgpSCFXXm7mvz+giAITUm8E7ZwVouBb+8bzutjfCiTJJ6zajV2pvWcxoDwxpvMe7IQP20Irhwftrm7eAKmb+4d1iT3E+oWddIKt4Zk+CwmHVWYuNMxi21KV1a5+/KI4z5uHNyhKbrp5aCq1WjqIh1j1b5cgs3BjO80HoAv9olskyAIrVuzBk2rV69m0qRJREZGIkkSixcv9hxzOp389a9/JS4uDl9fXyIjI7nllls4duyY1zXsdjsPPPAAoaGh+Pr6MnnyZLKysrzaFBUVkZiYiNVqxWq1kpiYSHFxsVebjIwMJk2ahK+vL6GhoTz44IM4HC1j8qpBJ9NJPcabQYFkS27a+7XnwfgHm+x+bU6a7P2vG+Ix6mTemhbPwI7BTXZPobaT54+dupLuTCxGLcDapXbmascL3O78K8cI5bnJvRq9jyf7/K4hdO7RD4COUg6frj+My614huiS0pIoqCxo0j4IgiA0pWYNmsrLy+nbty9vvfVWrWMVFRVs27aNZ555hm3btvHtt99y4MABJk+e7NXu4YcfZtGiRSxYsIA1a9ZQVlbGxIkTcbvdnjbTpk0jOTmZpKQkkpKSSE5OJjGxpp6R2+1mwoQJlJeXs2bNGhYsWMDChQuZOXNm0z18Ax3M3cGXAdoclr8N/9tpN91tDFf20ybz9osKZFLfSFKeH8fEPpFNdj+hbkEnB00NyTQZ694P0CA37V/34V1D+dvN47BjxCS5aC/lUe5wExsaS1xoHE7FyaLURU3aB0EQhKbUrLutjh8/nvHjx9d5zGq1snz5cq/X5s2bx+DBg8nIyCA6OhqbzcYHH3zA/PnzGTtWW9316aefEhUVxYoVKxg3bhx79+4lKSmJDRs2MGSIVr/m/fffZ9iwYezfv5+YmBiWLVvGnj17yMzMJDJSCw5ef/11brvtNmbPnk1AQN3Ls+12O3a73fNzSUnTbBmhqiqvVBxE0UuMDe7D0LZDm+Q+J7QL9GHzU2PxN2t/PIwNyHIIjSfYUhM06aoLj9ZHgLnuavCyXP9rnDNZh8PaCZNtP12kY1Q63Fh9DFzX/Tp25e/iu9TvuDP2Tk8hVUEQhNakVb0b2mw2JEkiMDAQgK1bt+J0OklISPC0iYyMJDY2lnXrtCrW69evx2q1egImgKFDh2K1Wr3axMbGegImgHHjxmG329m6detp+/Piiy96hvysVitRUVGN+bgev6avZINewaiozGjCYbmTtfE3iZVyzSzApyb4qXS6z9DSm9XS8C10GpN/e20YsIt0jHKHC4CEjgn46H1IK0kjOS+5GXsnCIJw7lpN0FRVVcXjjz/OtGnTPJmfnJwcjEYjQUHeK8jCw8PJycnxtAkLC6t1vbCwMK824eHhXseDgoIwGo2eNnV54oknsNlsnq/MzMw/9Ix1cbgdvLr5ZQBuKasgKrLpl40LLYPupMyQn6n+SWGrT/MGTYRqxTdPZJoAfA2+JHTQPtwsTl3cXD0TBKEV+2DXB3y29zOqXFXN1odWETQ5nU5uuOEGFEXh7bffPmt7VVW90v91DQWcS5tTmUwmAgICvL4am6IqjA/qTTuni7v0baGJ56UILcvc6/tx9yWdGd4lpN7n+Brr2rPOt46WTaQ6aOosZ1Nud3lentJ1CgBJR5KocFacv/4IgtDqFVQW8O7Od3lp00tsztncbP1o8e/ATqeTqVOncuTIEZYvX+4VmEREROBwOCgqKvI6Jzc315M5ioiI4Pjx47Wum5eX59Xm1IxSUVERTqezVgbqfDPrzTzg05klWcfwDe1+9hOEC8qU+HY8eUXPBs0BOrXtrITufPuXEY3dtdML1epBdZGOUeGoGVYcED6AaP9oKlwVLE9ffrqzBUEQavlk9ydUuirpHdKbi9pd1Gz9aNFB04mA6eDBg6xYsYKQEO9P2wMGDMBgMHhNGM/OziYlJYXhw4cDMGzYMGw2G5s2bfK02bhxIzabzatNSkoK2dnZnjbLli3DZDIxYEDT1EJqkPwDGMDzCV4QGuL+Md3O7zynkK7af6RSnKX5npclSeLKrlcCYohOEIT6K6wqZMH+BQDc1+++Zl1I0qxBU1lZGcnJySQnJwNw5MgRkpOTycjIwOVyce2117JlyxY+++wz3G43OTk55OTkeOonWa1W7rzzTmbOnMnKlSvZvn07N998M3FxcZ7VdD179uTyyy9n+vTpbNiwgQ0bNjB9+nQmTpxITEwMAAkJCfTq1YvExES2b9/OypUrmTVrFtOnT2+SIbcGy9f2fzvxCV4QzuZ8LJQ7LaMv+TptHqGu6KDXocldJiMhseX4Fo6WHW2O3gmC0Mp8vPtjT5bp4nYXN2tfmjVo2rJlC/Hx8cTHxwMwY8YM4uPjefbZZ8nKyuL7778nKyuLfv360bZtW8/XiVVvAHPmzGHKlClMnTqVESNGYLFYWLJkCTpdzbyOzz77jLi4OBISEkhISKBPnz7Mnz/fc1yn0/HDDz9gNpsZMWIEU6dOZcqUKbz22mvn75dxJgUngiaRaRLqx6eZVz7mmrQ96PanbPN6PcI3gsERgwH46chP571fgiC0LoVVhSzYp2WZ7u17b7OXK2nWOk2jRo1CVdXTHj/TsRPMZjPz5s1j3rx5p20THBzMp59+esbrREdHs3Tp0rPer1k8tBMKUqFNTHP3RGglfIx6yh31L1PQ2Ep9O0LFFnSFB8mxVRFhNXuOje80no05G/nxyI/cFXdXs/VREISWb/6e+VS6KukZ3JORAd3B7QJd84UuLXpOk1DN5AeR/UBvOmtTQYCarVSaS994LZvURTrG7R97r3QZ22EselnPwaKDpBal1nm+oqj1+tAkCMKFq8JZwZf7vwTg7j53I300DmZHwNHT109saiJoEoQLUHMHTeaIHgB0lrJRFO/gx2qyela//Hjkx1rn2iqcXPTyL8z4akfTd1QQhBZrUeoiSh2lRPtHMzpiKBRnguKEwKbffPx0RNAkCBcgn2YOmk7Mv4uWcpGV2htfX9HpCkCb13RqRunzTRkcs1WxaLuYKC4If1Zuxc2ne7RpNYm9EtEVpQEqmAPBUv+6dY1NBE2CcAGKCDCfvVFT8o/AbfBDLymEOo/VOjyy/Uh89D5klWWxK3+X17G0/HLP90634nXs1J8FQbgw/ZL5C1llWVhNVq1USf4B7UBod/izlhwQBKFpPDupF33bW3n9ur7N0wFJwh7YBYD2roxahy0GC6OiRgG1V9GVOWqqiBdV1GSp1qbmE/u3n/l8Y+3rCYJwYflk9ycATO0+FR+9z0mld5p3FbkImgThAtTW6sN391/ENQPaN1sfXEFakcv27rr3ZJzQaQIASWlJuJWalX5OV002qajc6fn+/s+3YXcpPLnIOzMlCMKFZVfeLnbk7cAgG5jWc5r2YkHLqFcogiZBEJqEO0T7RNhBqTtoGh45nABjAPmV+WzL1eo5ldldLNtTs+3RjK+S2Z9TCtS9P6QgCBeerw58BcC4juMI9QnVXvQMz4mgSRCEC5AaqtUV60TdE7oNOgODwrTqvif2ont4wXavNruPlXDHx5vJtlV6ZaAEQbgwlThKSDqSBMDUmKnai4oCedVBU5sezdQzjQiaBEFoElJ1MdbOHENx1y606XQrLFnfBoBlaStQVIUVe3NrtTtaXMmwF3+h1O6qdUwQhAvL0kNLqXJX0TWwK/3a9NNeLE4DVyXozRDUsRl7J4ImQRCaiD60E3ZVj4/kwFmYXuv4xsOFuMu7orpNFFTlsWTfhtNeS4cbfyqasruCIDQzVVX5+sDXAFzb/dqaIfncvdp/Q7uB3LzlVETQJAhCkzAajRxR2wLgzt1X6/iRgnJQ9bjKegLw2E/za7UB6CDl8ItxJrvMd/G0vu42giC0fjvydpBanIpZZ2ZSl0k1B04ETW16Nk/HTiKCJkEQmoRRJ5OqRgKg5u6vdby4XCsn4CqNBaBtwFp+ND7OaLlmXpMON28Z3qSDrA3b3aX/iSHSXtyK2GJFEC40J7JM4zqOI8AYUHMgr/pDV1jzzmcCETQJgtBEJEkijeqSBydWvpykqEIrJ6CUdcOkQIFBRTXn8K7hDS6StbICd+h+Ik5Ow6ZaWO4eAECifjlXv71WBE6CcAGx2W21J4CfcCJTLTJNgiBcyNLkKAB0BbUzTUt2apXCR0m7GVmhVQH/2BKFUXLzb8O/uEr+nVl67ZPnbNdNzHNNAWC0vJ29WfkMmr2C3JKq8/AUgiA0te8PfY9DcRATFENcaFzNAbfL86Hryww/KhzNuyBEBE2CIDSZTJ2WaTIUpsJJe8xtTS8ir9QOwJW6dVxWUQnAj77+bFG6YpUqmGP8DybJyWp3HF+5R7FT7UyeGoCvZCdOOkxhuYMP16ad92cSBKFxnTwB/Lru13nXZCs6Am47FaqJx3+xccsHm2ptAn4+iaBJEIQmk61rj1uV0DlsUFZTTuD3g3nV36kMl3dzSUUlkqJDNhZyl3QLv7j7oUo6flP68oDzAUACJLYoWhmDQXLtzJUgCK1HldPtGWLfenwrR2xH8NH7MKHzBO+G1ZPAU9VIVGS2pBfx8+6c891dDxE0CYLQZGSjmQw1TPshvybQObEpbxfpGG0kG7Kix12uVfqt8D/MHc7HqHoij5nGZ7Dh5znv1KDpnd8OeSqGC4LQOqQctTF49gpufF8rM3Iiy3RFpyvwM/p5tVWrg6aDqpa1/vuVvbk8NuI89tabCJoEQWgyIX4mUtV22g95NUFTYfUk8It1ewDYqnTHXqJtLqwPSAHAqJfxNxu8rre5OmgaKO8HtE+p4+aubtZ0vSAIDfPxujRKqlxsOlLI7pxjnh0Brut+Xa22RYe1LZb2K+1Z+/gYEod1bNYtlUTQJAhCk2lzUtBUnLaDb7dloSgqVQ6tQvjFBu1T5DqlN66ynqiqDp0pl9dubItOlsgvs3tdL93QGbtqwCpV0FGqSdEn7c7hlaR9IngShFagylmzQ8CHO77GqTjpGdyT3qG9Pa/nllSxLjUfspMBCO0+lHaBPue7q7Xom7sDgiBcuNr4m9ijdADgcMp6ZmzbgaJChdOFhMIgdgOwXukFqhl3eRf0fgewyduB/pRWea+UuXdMT/as6kg8B+krHSKtunjmfZ9pn0Z7tA1gct/I8/eAgiA0WIXjRNCksjpnCeBdZkBRVG75cBM5OcdINmsfjvoMGnm+u1knkWkSBKHJtPE3sVvtCEBPKQMZha3phVQ63PSQMglQSylXTexUOwPgKtU+af6S+Uuta/3rhn7cO7IzO5UuAPSVD9dqc6y4someRBCExnKibIDOcogqjuOjt3BFpys8x3cetbEvp5Q4+QgA6WoEfbtGN0tfT3XOQVNqaio///wzlZXaP1KqKtLigiB46xsVyBE1gjLVjI/koLN0DINOptLhZpiszWfarPTAVZ30PrGlys68neRV5PHS1Vq9ltlXxXJlv3ZIksRO9UTQdKgZnkgQhD/qRKbJELQJgDjraCwGi+d4jk2LK+IkLWgK7zEEH2Pz7jl3QoODpoKCAsaOHUv37t254ooryM7OBuCuu+5i5syZjd5BQRBar5Hd2/B/o7uzV9U+JcZJRzDoZCqcbobJ2tDcOqWXp73qCsBdqRXEXJW5ihsGR7Ptmcu4aUgHT5vk6kxTbykNPd7Dd+KzmyC0fOV2F5KuDL2/9m9AB+OlXsdzq2u4jQ3U4gtz9MDz28EzaHDQ9Mgjj6DX68nIyMBiqYkMr7/+epKSkhq1c4IgtH592lvZUR3oDJQPYNDJOBwOhsjaJPD1Sm+v9qcO0QX7Gr2Op6lh2FQLZslJjJTV1N0XBKGRVdpdDAv6DElyE1llQrJZvI6fKHzb2VG94jay33nu4ek1OGhatmwZL7/8Mu3bt/d6vVu3bqSnpzdaxwRBuDD4mw1sqM4mDa0ekuvuPkSAVIliCvDMeQItQPrL4MkAbMzeSJmjrNb13KrsCcLEEJ0gtD43O76gKFDbGuXe0mNcl/pXUGpW1OWV2mkv5RHoPA6yHiL7N1dXa2lw0FReXu6VYTohPz8fk8nUKJ0SBOHC4W/Ws0mJQVElusjZLPxtC5fptgCgdhqFUv3PkL9Zz9anx/LIyIvpGNARl+JizbE1dV5zx4l5TZIImgShVUlfRz/zUrIMBiyqjovLXPSw74JN73maFFU4PMP3RPYHk99pLnb+NThouuSSS/jf//7n+VmSJBRF4dVXX2X06NGN2jlBEFo/s0FHCX7sUbV5SaN0O0iQtwIg9ZxU01DFU7RuTPQYAH7JqL2KDmCnoq2263NKpklFTGoSWp/8Mjuv/byfVftyz964NXPZUb5/kG8CtCBoePsrmeO8STu06kUWrt2FoqhUOhVPVppOFzdXb+vU4DpNr776KqNGjWLLli04HA4ee+wxdu/eTWFhIWvXrm2KPgqC0Ip1DLHQI8KfpLxBxMppvGrQPlE6VB3GmHGAlk1STprFPSZ6DB+mfMjvWb/jdDsx6Lwrg5+YDN5dzsJCFRWYz8/DCEITmLfyIJ+s16a3HHnximateN2kVr9KQfEhVkZpBW/v7DONySsOkKhbTg97JgU/vUjnJTehx8VcU7J2TqeWUZ/phAZnmnr16sXOnTsZPHgwl112GeXl5Vx99dVs376dLl26NEUfBUFoxfQ6mR8fvBi5fyJVak3ws0y+CMxWz88n54jiQuMI9QmlzFnG5pzNXte7ZVgH8gii3NIeHSoj5R011xCJJqEV2ptds3/iyFd/ZV9OSTP2pvEpisobn3yFa/XrLPLzQ5EkgnTdiQ2LQUHmJdeNANyq+5n2Ui6XyDsJlsqwm0Ohw4hm7r23c6rTFBERwfPPP8/SpUv58ccf+cc//kHbtm0bu2+CIFwgZFkiTwrmGdftlKg+JCud+Y/xNq82Jwc8siQzKmoUULvQ5TMTe7Fy5kh8468F4ErdOs+x5XuOc8N760kvKG+S5xCExlJa5eSWDzfx8ZIVdCxahwkHABmFFVw+93dybFXN3MM/Lr/MznXvrGPIk59x3aEnkVCY7x8CwPA2EwBtA95flb6scffGJLl4VP8V03QrASjsNBF0LWvjkgb3ZvXq1Wc8fskll5xzZwRBuHDdc0lnRm0axTfuS1CR6RboPbmza5j3z2OixvDNgW9YlbGKJ4c8iSxpn/EMOpkubfwg7jpYO5cx8ja6SEc5pLYjObMYgKcXpzD/ziHn5bkE4Vy89vN+AlMXk5j+NjpJ5XZjNNc7nqEEXwA2HC5gSny7Zu7lH/NK0j72pR3lS+MrRMl5fGVuS7HBjer2YXynywGqN+WWeNF1E0vkpzwfglyqjK3XLbS0dEyDg6ZRo0bVeu3k8Ve3213ruCAIQsdQXx68tBtvrjwI4Knw+/39I3j3t8M8dnmMV/shbYdg0VvIrcxld/5u4trEeV8wvDfbDfHEO7ez1PgUH7jHM8d1LW50lNm9i14KQkuTlZXBHMNH6CQtxdpTzuBx/Rc86boL0D4ctGYbDhewcEs6Hxvm0ktOJ0+18qJ/d+AI5qqhDOoYBmirZgF2qx151z2Rv+i1vehedt3AdWHdm6v7p9Xg/ytFRUVeX7m5uSQlJTFo0CCWLVvWFH0UBOEC0T6oZpdyH4MWNPVpH8i/b+pPhxBfr7ZGnZGL22srZ1Zlrqp9MUniLesstijd8ZEc3K//jrt1PwBg9THUbi8ILciU0i8IkCrYpXTkTp4D4Drdb3SQtA1q9brWPRn836tSman/mot1KZSrJj6I+RtuvzQAPr72ISxGLVjyM9Xkbl523chY+yuMtL/B++6Jnn8jWpIGB01Wq9XrKzQ0lMsuu4xXXnmFxx57rEHXWr16NZMmTSIyMhJJkli8eLHX8W+//ZZx48YRGhqKJEkkJyfXuobdbueBBx4gNDQUX19fJk+eTFaWd5XgoqIiEhMTPX1OTEykuLjYq01GRgaTJk3C19eX0NBQHnzwQRwOR4OeRxCEM4uPCvR8b9Sf/Z+fMVFnLj2Q5QzgWsff+Hv1suXb9UnocBMogiahJXNUMLpqBQCvuq4nO2ggq5W+GCQ3t+l+BqDK2bpHbXyK9nG3bikAjzrvYZcpAxWVoW2HEhtWs2jMz+w94JWqtiddjdCu0UL2mztZo+X/2rRpw/79+xt0Tnl5OX379uWtt9467fERI0bw0ksvnfYaDz/8MIsWLWLBggWsWbOGsrIyJk6c6DVMOG3aNJKTk0lKSiIpKYnk5GQSExM9x91uNxMmTKC8vJw1a9awYMECFi5cKPbSE4RG1qVNzbwlW6XzrO0vbn8xelnPIdsh0mxptY7vP14KSPzPPY5i1ZcwqZg46QiBFmOttoLQUqi7v8WPCtKVMH5X4vA36/nApc3xuUq3BhMOz6a2rZGqqlxf+gl6SeEn9yB+VAZysFKb3H19zPVebQPMp/+A0xIzTQ2e07Rz506vn1VVJTs7m5deeom+ffs26Frjx49n/Pjxpz1+IrBJS0ur87jNZuODDz5g/vz5jB07FoBPP/2UqKgoVqxYwbhx49i7dy9JSUls2LCBIUO0iaHvv/8+w4YNY//+/cTExLBs2TL27NlDZmYmkZGRALz++uvcdtttzJ49m4CAgAY9lyAIdZPlmiGH+gRN/kZ/BkcMZt2xdazKXMXt1tvrbOdEz2Ylhst02xgk78NsvrzR+iwIja1kzftYgQXuMajIxLWz8uGROLLUUNpL+YyVt1Hh6Nfc3Txnc75ewcNsA+A111T0AbupdNsI8wnzrIo9IdBy+qDJ3AKDpgZnmvr160d8fDz9+vXzfH/FFVfgcDj44IMPmqKPp7V161acTicJCQme1yIjI4mNjWXdOm0G/vr167FarZ6ACWDo0KFYrVavNrGxsZ6ACWDcuHHY7Xa2bt162vvb7XZKSkq8vgRBqJ/6BE1w9iG6E7YrXQHoJaeLek1Ci2SrcLJ14+9YC5JxqjpW+YzlugHtefiy7ijILHEPA2C8bhOVjta5mKHM7sJn5yfIkkq6dTCH1HYYAjcAcE33a9DL3rkaf7OBaUOiAfjwtoFsfkpLgIT4GtHJLW9eV4MzTUeOHPH6WZZl2rRpg9l8/ivy5uTkYDQaCQoK8no9PDycnJwcT5uwsLBa54aFhXm1CQ8P9zoeFBSE0Wj0tKnLiy++yPPPP/9HH0MQ/pTqGzSNihrFPzb+gx15O8ivzCfUJ7TOdgdVbRPxrtJRDoioSWiBnv4uhUG7/8UAPSxTBvD1rCnVS+7hnZv789Oy41CyhNHydt6pbJ21xi5/dRnf67SFGx0ufwj5i+PofY8go+OabtfUec7sKbE8PLYbYf5aHLHmr6Mx6VtelgnOIdPUoUMHr6+oqKhmCZjORFVVrzIIdZWkP5c2p3riiSew2Wyer8zMzD/Yc0G48M24TFtG/M+r4s7SUhPuG05sSCwqKr9l/nbadqmqVtOmq3QMxa388Y4KQiNSVZUVOw4zRadtG7TMfIUnYAK4PLYt/3rkdmymtvhKdtoVrDvdpVqsfTklDKn4jWCpjGxCofvlXHmJlmgZHT2KcN/wOs+TJMkTMAG0D7LQxt90XvrcUPXKNL355pv1vuCDDz54zp1pqIiICBwOB0VFRV7ZptzcXIYPH+5pc/z48Vrn5uXlebJLERERbNy40et4UVERTqezVgbqZCaTCZOpZf6PFYSW6oExXbl+UBThAfX/sDUmegwpBSmszFjJNd3r/rSapbZBUSV8JAdGR2FjdVcQGsXi5KMk6pYTIFVyRAknwzqwdiNJ4kibMfTL+owuBb8C953vbv4hh/PKSdRrpYeq+t5KsbOMNTlJANzU86bm7FqjqVfQNGfOnHpdTJKk8xo0DRgwAIPBwPLly5k6dSoA2dnZpKSk8MorrwAwbNgwbDYbmzZtYvDgwQBs3LgRm83mCayGDRvG7Nmzyc7O9mwHs2zZMkwmEwMGDDhvzyMIfwaSJDUoYAIYHTWaN7e/ycbsjVQ4K7AYLADcO7IL7/x2CNAmg+cSSARF+FdlN3q/BaGhFEVl3i+puBWFBb9sZrnpOwDecl1FdKhfnedUdBwLWZ/RtXQTr/+8j+93ZvPtX4YT4tfyP6Abc7bTTz6MEwOdEu7jvwe/ocpdRY/gHgwMryNIbIXqFTSdOo+psZSVlZGamup1n+TkZIKDg4mOjqawsJCMjAyOHTsG4ClpEBERQUREBFarlTvvvJOZM2cSEhJCcHAws2bNIi4uzrOarmfPnlx++eVMnz6dd999F4C7776biRMnEhOjVSBOSEigV69eJCYm8uqrr1JYWMisWbOYPn26WDknCC1Al8AuRPlHkVmayfpj67m0w6UAPDouxhM0ARxTQ4iQighwnH4uoiCcL8v3HmfOigMEUcLHxtexShWkKB1Z73sp31zeo85zQnpeTOXvRoKUIpb9uop0NZoP1x7h0XF1t29uiqKy9lA+Bp1Mh0OfAbDdfxTxPla+2PcFADf3vPmMU11ak2at075lyxbi4+OJj48HYMaMGcTHx/Pss88C8P333xMfH8+ECdrGfjfccAPx8fG88847nmvMmTOHKVOmMHXqVEaMGIHFYmHJkiXodDWTyD777DPi4uJISEggISGBPn36MH/+fM9xnU7HDz/8gNlsZsSIEUydOpUpU6bw2muvnY9fgyAIZyFJkmep8snVwU9dXXNM1SaJHziwn4yCivPWP0GoS26pnfZSLouNz9JXPkyR6secoKdY++RlRAb61HlOx/BgNio9AbhI3gVAWVXLXUm3ZOcxEj/YxIz3ltIx+ycANoVdy7K0ZeRW5BJiDmF8p9OXFmptzmn74KysLL7//nsyMjJqVc1+44036n2dUaNGoZ5hlcttt93GbbfddsZrmM1m5s2bx7x5807bJjg4mE8//fSM14mOjmbp0qVnbCMIQvMZHTWa+XvmszprNW7FjU6uvbomX9Uyw8FSCTe+v4G1j485390UBA+1vJDPDbOJlvPIUNrwjO+zPHb9uDNmXUx6HWvVWEaxg4vlFD5wT8CptNzVoMv3aHOGH9R/i0Fys87di8LAONbs+TsAN/S4AaPuwik22+CgaeXKlUyePJlOnTqxf/9+YmNjSUtLQ1VV+vfv3xR9FARBID4sngBjAEX2Inbk7aB/eO1/bwqrg6YQSjhaXHm+uygIXmL3zSVaziNdCaPi5h/4pHv9NqDdKPUDPmOwvA89LpyulrsatGOILyPlHdyg/xWAOa5r6cA+dhfsxigbua77dc3bwUbW4OG5J554gpkzZ5KSkoLZbGbhwoVkZmYycuRIrrvuwvrlCILQcuhlPZe0vwSAXzN/rXX8oq6hdO7YAYAQSRSaFZpX6r6d9MvVJn7vGDCbnvUMmAAydNHYVAsWyU6MlNmit1TRO228bHgPgI9c49is9mB76TcAXNXtKkJ8Qpqze42uwUHT3r17ufXWWwHQ6/VUVlbi5+fHCy+8wMsvv9zoHRQEQTihrnlNJ0gS+AVpJUKCpdLz2S1BqGXjN28gSyq/uvvi021kg841GPQkV1e47y8fpKiiZW4e/9z3u+m48W9ESEUc1bXjZdcNyOYMcp0p6CU9d8Te0dxdbHQNDpp8fX2x2+2AtmXJoUM1K1fy8/Mbr2eCIAinGBE5Ar2sJ60kjSO22qt6HaZgAIIRmSbh3BRXOPhxVzZ21x/I7rhdJDi1DWo/d49hQIegs5zgzaSX2aZ0A7SgqbQFTgRPLyjn8IbvmKJbh1uV2Nh3NlWYMIVqH2gmdplIpF/kWa7S+jQ4aBo6dChr164FYMKECcycOZPZs2dzxx13MHTo0EbvoCAIwgl+Rj8GR2j11k4dopMkCadZGwoQw3PCuUgvKKffC8u577NtvPVL6tlPOI3ig2tpI5VQrPpiibsMRS4hvzIfp7t+WwcZ9TLbVS3T1Fc6RElV/c77I0qqnOSV2uvdPr+0kif0WkmBj92XUx7Wnw/vbofefy+yJHNn7J1N1dVm1eCJ4G+88QZlZWUAPPfcc5SVlfHll1/StWvXehfBFARBOFejo0az7tg6fs38ldtjb/e8LgFOs5ZpskoVGGh5n86Flm3im2s833+5OZOZCTENOl9VVXYX7Ob7LXM5FBHGHqOFMse9rPyqpk0bnzbEBMcwKGIQI9uPpEtgl1rXMepkdisdAegoHcdR0XTDzSVVTrakFTL9f1uxGHWsmjWK0HoU0pTTVtNTzqBE9WGeawpP6CSWZvwPgHEdxtHR2rHJ+tycGhw0de7c2fO9xWLh7bffbtQOCYIgnMmoqFHM3jib5LxkCqtqtkuRJHAZA3GrEjpJJQgxr0mov59351Bqrwm0G1KLsdxZzsIDC/n24LccslVPWfExAzWr3iQkVFTyKvPIO5rHmqNrmLN1DrEhsUyNmcr4TuMx67VK+SaDjgKs5KlW2kg22jrSzroX6rkot7vo89wyz8+lVS7WHSpgct+zD6sFpy4CYIl7OMX4s69oD8uzlyMhMb3P9EbtZ0vS4KDp9ttv5+abb2bMmDEXTIVPQRBajwjfCHoG92Rv4V5WZ60GajY9lXU6ivAnlBIxRCfUm1pegGXBNew0HeIt1xTec09C4uzvb5WuSr7Y9wUfpXxEsb0YALPOxMUlRQypqCI3/m1uu3gMvgZfAErsJaSVpLG7YDdrjq5hQ/YGUgpSSFmXwlvb3+KevvdwVderMOm0mTN7lWja6HbRjQwqnW4sxnMqrXha6XUUgE3LLz/7iS47kdkrAPjWfRGgsqvicwAmdZlEt6BujdnNFqXBc5oKCgqYMGEC7du3Z+bMmSQnJzdBtwRBEE7vxCq6k+c1SYBelihU/QGtwKXSgosCCi1HxbcPcrEuhQCpkicNX9BfOoB8lphpddZqrvruKuZsnUOxvZiOAR15ZugzfBpyA2/k5tOppB3j48bgb/RHlmRkSSbQHEi/sH7c1PMm/jP2P6y8biWPDHiECN8Icitz+fuGv3P191fjMB4AYJ8aDUAPKYP/rU9v9Od2uGvXf8oqqkcl/awtGNwV5KkBWLoMZ9aVEvtt2zHIBv6v3/81ej9bkgYHTd9//z05OTn87W9/Y+vWrQwYMIBevXrxz3/+k7S0tCbooiAIgrfRUaMBWHdsHUjaJNl2QT7oZIkitKApiLI63xQE4WRVWTvxPbQURZU4qLQD4Db9z6dtX1xVzIxfZ/B/K/+Po2VHifCNYPZFs1l05SKmxkylPDkJgGNhI+ka5n/Gewebg7kj9g5+uOoHnhj8BMHmYNJK0jikew1z26/YhVZCo6ecwa4sWyM9cY3yKif36JawwPh3vui9CVCpctbj78yR1QCsV3oT296f3/I/BrTq3xfiirmTndPec4GBgdx99938+uuvpKenc/vttzN//ny6du3a2P0TBEGopUdwD8It4VS6Kpl1pcykvpE8mtADSZIoUS0A+EsV2FtwJWWh+bkVlXUfPgrAD8oQyq94C4Cx8jZUV+2VZLvydjF16VSWpy9HJ+m4vfftfHfld0zuMhmXW+L7zQfoXZUMQP9Lp9a7H0adkWk9p7HkqiVcH3M9IGEI3MbvHdez0Wyih5RBSWXj12pqs/MdnjB8wVB5L8MOzeVO3U9UOc9eaqH8gFZWYIPSCzlgA/sK9+Fv8Gd63IU7l+mEP7Rhr9PpZMuWLWzcuJG0tDTCw8Mbq1+CIAindfIGvgXqdubdGI/VYkBVVUqpDpqowCGCJuE0dmYV88an3zJG2YCiSnxuuoE+g0bhNgdjkex0dBz0tFVVlQX7FnBL0i1kl2cT7R/NFxO+YMbAGVgM2p+3T9al8f2iBZgkJ0cJIypmQIP7FGAM4OmhTzPQ8AyKPRS3oZzpEWF8GGxAKc1stGcHcJbk0mnPfwDYZ4wF4CH9t6j2M88FVN1O9Nnbte+79mdR2gcAPND/AYLMDatH1RqdU9C0atUqpk+fTnh4OLfeeiv+/v4sWbKEzMzG/Z8qCIJwOieG6H7L/A1F1YIjRVVPyjRViuE5oU6KonLfZ9vodfAdAH5UhvDSX6Yi62Tc7YcA0EfZi1tRqXBW8MSaJ5i9cTYuxcXY6LEsmLiAniE9va656UghY+RtADi7XIYkn3tOoo2xO+VHHsRRNBhVkvgoMIAjvv8ms6Rx3mMrHW6++s9zGNzl7FI6MrfdG5T5dSRAqqBf2ZoznrtpyyZMOChTzaQHbqbUWUrP4J5M7V7/zFpr1uD/q+3bt+eKK64gLy+Pd999l+PHj/PRRx8xduxY5D/wh0QQBKEhBkUMwtfgS15lHnsK9gCgqngyTQGUY6/HUIPw53Aor4yvNmeiqirJWcUEFu9mgm4TiirxpusqOoRoK9ykjsMBGCTvY29BKtN+mMYPh39AJ+mYNXAWb4x6A39j7blKMiqX6rQMTMdhV/+hvpr0OlCN2HOuZrbSHqvbTampgKlLp5KUlvSHrg2wat9xhpb/AsCHrvH4mE3kdrwSgKEVtbcoOllB6mYAvja3Y1fJL0hIPD30aXSy7g/3qzVo8PrFZ599luuuu46goAs/DScIQstl1BkZETmCZenL+CXjF2JDY3ErItMkaJxuhYIyBxFWrfbRpa//BoCPUUdReRXPGD4FYJEyggNqlOc8fXXQVOyfzpPLbqbSVUEbnza8OvJVBoSffsgtwraNcKkYl96CvsNFf6jvvqaat+ZLwwcyeOtGbmvThaOU8ehvj7IpexOPDXrMU9epoexZyXSRs6lSDSxTBnKVSYetw5WQ8i/6OZOhshh8Aus81794LzZZ5r/h2srUG3rcQJ82fc6pH61Rg1NDd999twiYBEFoETylB7J+BbwzTf5UUNmCd4cXmsbxkiqm/Hst3Z76ieEvreTn3TkczivzHF99II+jP7zCEHkf5aqJN5zXeZ3vCu3OP4ODeD7cj0pXBYMiBvHVpK/OGDABXFz6EwCFHSeB4dyCmRP8TDVZGzmsBxFuN88ckxnf/mYkJL4+8DXTfpzG4eLDXuftzymlwnH2SvhBx34F4DelL+X4YDHqkUK7cEhpiw4F0tfVeV5eqZ2g0n38IySIEp2LjgEdeWTAI+f+oK2QGE8TBKHVuqT9JegkHQeLDpJVmoWKSml1pilAqmiRG50KTWP9oQKeXrCO1a9cx/PH72eqbhWKCvfM38q+nJrq8I7tC3jCoO2ZNtt1M0dp4zmWU57Dbb/8hS+s2vDbdSEjee+y9wj1CT3zzW1ZjHRpe7La+0z7w8/ic1IRS7mNtpVLd+kYcb438O5l7xJiDuFg0UFu+OEGFqcuRlVVvt6Sybi5q5k4b81ZF0BEFm4C4HclDp0sMbBDEGaDzAall9Yg7fda53yyLo1Bs5ezzpBJkp8vMjL/vOif+Oh9/vDztiYiaBIEodWymqz0D+8PaIUuFRVKPHOaKrBVNv1Gp0LL8Mx3KfTfPZvr9KvpKx/mFcP73Kv7HoAj1VWur9et4g2DtmLsR98pJLeZAmhFUdcdW8fUJVPZmbcTH0ViXk4etxGFXq57FotbUSmr3nYld/FTmHCyUelBcPcRf/hZfI01mSZDuBY0tZFKqCzOY1jkML6Z/A1D2w6l0lXJM2uf4bHfnmD2T9p8qsN55ezPOcMWQs5KOlakAHDJuGvY9VwCCb0j8DHoWF8dNBXuXsmjX+/AedLw9t++302YZQdvh2h/vx7o8yBxbeL+8LO2NiJoEgShVRvVfhRwImiqyTT5SxXnZXd4ofll2ypx5qUyRdayPUvd2gq4xw0LuEv3A3N+3s0M/Ve8bHgfnaSywDWKPXGP8/bNA0jo1YabLz/AvcvvpcheRM/gniQWDGBUZSXG/L113i+/zM6o11Yx6tVVpCz9N2FHFqOoEu8Zb8PXbKjznIY4eU6TbPbHZtDK+fiXacNxoT6hvHvZuzwY/yA6SUdS+g84w+cgm44BnPnDQtYWjDjJUYPwa9vDszWL2aBjo6KtCAwsOUDS1gNsSSuq6YfpGI72C3FLEpeUw5397vjDz9kaiaBJEIRW7UTpgS3Ht1DhKqMUbbjAnwpKKsXw3J9Bjq2KyfI6ZEnlN3cf7nc+xFyXtoLtacNn7DbdwYP6xQD82zWZx13TiQrxxc+3EjXifRYe+QAVlWu6XcP8K+ZTpdfqFvkU76/zfj+l5JBZWElE+T66bf4bAHNc19Bz0JhGeZ4gi9Hr53yfjgBYy2rmMMmSzPQ+0/lw3IcY1CBkUz6Wjm9jCFpPcYV3IUxFUVmwKYM3Vx7EkaGtftumdCPMWjP3ymzQkUcgaUo4sqQSLx/0XOeI7Qg+0R/i1jmJr6riLnr/afeebfDque+//77O1yVJwmw207VrVzp16vSHOyYIglAfUQFRdA3sSmpxKuVyCiWqtnTcj0pKKmtXdRYuPMUVTi7R7QS0yt4Ac13X4FD1PKhfhFlykqcG8F/LdN4t0iZ0l7CXa79/kYKqAnz0Pjw15Cmu7Kotu8+1dIFi8CtJBbcLdN5vlVlFFehx8ZrhXUySk+Xu/mT0vo+5Cd0b5XmGdQlhXO9wOrfxA6DI0hFKNhJYcaRW2/7h/elY9TR7Xf9F778Xc8R3fJSax/CYFwk2BwOw4UgBj3+7C4BLI1bTG9ihdGGEf03Q5G/S42PQsVXtRkeOM0A+QHGlk+TcZO7/5X5kfRmRdj1vHc+jeMDARnnO1qjBQdOUKVOQJAlV9d4I88RrkiRx0UUXsXjxYrHKThCE82JU1ChSi1M56tjC41PuhiTQSSr28jNXNxYuDMUVlQyRtA1ttyndql+VeNs9hc/cY2kv5bFfjeKq2I6wNQNj6Erm7fkFFZWugV15beRrdAns4rlepaU95aoJX8UOBakQ1sPrfseKq5imW0kPOZNC1Y9HnfdwX/vARsu+6GSJdxNrAhObb2cAQirT6mxfZfehMvsWgttuxGFdwoGydUz8diL39L2HaT2mkV1c5WkbYtsNwF65KwHmk4YBZYlu4X5szY7hGt0aBkj7+eL497x+4GPsbjvuyihezzlAACrmmEGN8pytUYOH55YvX86gQYNYvnw5NpsNm83G8uXLGTx4MEuXLmX16tUUFBQwa9aspuivIAhCLSdKD6w5uobJAzvglrQ3A3dl429yKrQsiqJyaE8yFslOuWrisOq9YazLaGW32gkXekrdOVg6vIOpzUrPcNznEz73CpgAfEwG9p+o3ZS7myU7jrE3uyYAP1pYxu06rcjkHNe1FONPj4iAJnvGUn8taGpTlVbn8Uq7g2vk37nH6cSVdheSox2lzlJe2/IakxZP4recRSA5CMFGhJqLokpkW3rUCvJ6RPizRenOQYOBTyILWF34Lna3nYsiL0GXMY1Y8gAwtuvbZM/a0jU40/TQQw/x3nvvMXz4cM9rl156KWazmbvvvpvdu3czd+5c7rjjzzlJTBCE8y8uNI4QcwgFVQVsyd1KvMEfnaMIveMMq4iEC8L/1qdxdM96MMJxSzceuCgGSYKF27L497T+3PjeBkDBELSBzc6f0VnsGGULL4x4lgmdJ9R5TV+Tnn1KFP3lVI6nbuOBDdow1sHZ41FVCM5ZSyfdcUpUCwvdl/Di1XFc0r1NnddqDGXVQVOg8zg4KsBo8Tp+ddUiHjDOhzKIcA/noUP/x8u3Onln1zyOlh3laNl7+HUz418WwW+VZqyVweh8vIO8EkcJPbuksyRnFdf6RaBIEjI6Zg2aSS/fKyhepe0xpwZ2QDpN4cs/gwYHTYcOHSIgoHZEHRAQwOHD2iS1bt26kZ+f/8d7JwiCUA+yJDMqahQLDy7k18xfidX7YXYUoXOWnfVcoXV7bskentVrc32KA3vzyGXavKKHx2r/fWZKW/6x6Tkkn1QcCgyJGMLfR/ydtn5tT3tNi1HHPjUaADVnN6AlCbakFWE2yIxRNwDwIxdh8PFn6sCo012qUaiWUApVP4KlMj5ZupwVRRF0aePHwI5BTOxh5Rb3t1CdNLpSt465rmsYHj6Nyd3G833q98zZ/D7lHKfAmsb91jAA9MrTTF0SgSRJ2Ow2jpYd1V73BwWJy8or6KxOILFXIp9vzKCPpL2/S5H9mvRZW7oGD88NGDCARx99lLy8PM9reXl5PPbYYwwapI1zHjx4kPbt2zdeLwVBEM7ixBDdqsxVuAzaZHC9SwRNF7Kq6r0FY2UtaLKH1QwbqarKtwe/Ze6+e5B8UvHR+/DkkCd5L+G9MwZMUB00KVrQ5Mre5Xm9qMJBXkklY6v3mJt0w92sfXwMOrlpV5IZ9TKpajsAtm7ZxO8H8/l4XRrPL9mDuj8Jq1ROhtIGR4eRAIyXN2GrdOKj9+H6HtczRP8yFel3c3GxifZOrRyBSy5ib+Fe9hTs8QRM7f3ac1vv23jL9zLeyM2nd1EqAMWVDuKqf8dExjfps7Z0Dc40ffDBB1x55ZW0b9+eqKgoJEkiIyODzp0789133wFQVlbGM8880+idFQRBOJ0hbYdg1pnJLs/mgCmIIYDeVd7c3RKa0G8H8pBR6C2lAWCO0gqdZpdl89z651h3TNsOpF+bfvzjon/QIaBDva5rMerZVz2nqb2Ujz8VlGKhyukmsHAnYVIxlZIF324jQd/gt9EGM+plUpVIBsv76SIfheqak3mldmzJ3xMILFWGcWevUZD+Gwm6zRRX1NRqKih34a7oxAvu44QWlTDJ+SQBMR25Z0xbVFUlwBRAh4AOntV2RT4rIeUDejj3UuVwUeVwEytVB01t+zX587ZkDf6/HRMTw969e/n55585cOAAqqrSo0cPLrvsMmRZS1xNmTKlsfspCIJwRj56H4ZGDuXXzF9Za4QhgFEETRe0gjIHnaRsfKsngQdH92bhgYW8uuVVyp3lGGUj98ffzy29bkEn685+wWq+Jh0l+HFUDaGdVECMlMEWtQeVTjddjq4AYI/vYAbojWe5UuMw6nSkVGeaukpHPa9LKKiHVwHwq7sv9/aciPLTTPrJh1lRdAwIJbekig2HC2gv5RMqleBQdRxwd+ditT2XtK97FVxg1yG4kGkrFbLjwB505cV0lI+jIv3ph+fOKUSWJInLL7+cyy+/vLH7IwiCcM7GRI3RgiZ9FTMAo1LR3F0SmlCFw0VcdQZkh29nPkqexYbs9QD0bdOXF0a8QGdr5wZf1+HWSursU6Jppyugh5zJFncPKh1u2h/XgpQDQZdw5i18G49BJ3mG57pKxzyv95AyCVJtlKsmtqvdkAPCSTd2oYMjFfPRtUAfdmTZcCkqg43a72mfGo0dIxVn2MxaMvlx1NSNDvb95Oz6jbYVlQAc9+tBhM+fu5TQOQVNK1euZOXKleTm5qIo3hsDfvjhh43SMUEQhIa6uP3FSEgckCrJ0ekwuUWm6UJWZncRJx/hR18Lfw+3U5a9HpPOxAPxD3Bzz5sblF06WUKvcN5elcqe8g5cynbi5YN86r4Mgy2dkIrDuFSZY6F/fI+5+joxPAfQScpGhxs3Oi6StflWG5WerPrrZQCk+fenQ0EqVQd+pcp5NweOaytIL7VmQalW1BI4Y9AEUBTanw5H91O8ewUGyQU6OBYyjIimeshWosETwZ9//nkSEhJYuXIl+fn5FBUVeX0JgiA0l1CfUPq06QPAaouPyDRd4Gz2cjaH7+OvYaGUqS76tunLN5O+4dbet55zwAQQHmBm/ROXYuxyMQDD5D2AiiFVq820UemJyxTYCE9QP0a9zDFCqFBNGCU30VIuABfJ2sa7a5Q4Qv1MAAT2vhSAruXb+Xl3DofztA8OcRwCYKeqZd4qzxI05UVq17lK9zuTZW1uWG6b4Wc65U+hwZmmd955h48//pjExMSm6I8gCMIfMipqFDvydrDK4kNCuQiaLgRb0goprnByac8wT0HGw8WH+angMcoD3Miqyj3druPuYU+hlxtvYnZ52EAcaToipUKipVwGlmrzmZYpA8nNP39ZTJ0koSKzX40iXkolXjpIjhrEUFnbUHiNGsczei0H0nf4FbhXy3SUj7O1MIP8Mh0yCm0r9gGQrHQFYNqQ6DPe09F+GIc2tqWLnA1AuhJGadiftxL4CQ3ONDkcDq/CloIgCC3JmCht09SNPmYkRMmB1q7K6ebad9Zz1/+20OmJH9meUcTqrNVM+3Ea5WoOYS4X7x4v5r5hTzdqwATQISKUZFULMqbrfqC7OxWnqmOJe1iT12Y6WUV1aYX1Si8ARuh2M0LejUlykqm0IVMXXVPd2xxApo+27UtI3kYKyx10lY5icFdSrpo4pEby72n9uXnomVcSBvmaecp1JyWqD6WqD0+57sRkOj8T31uyBgdNd911F59//nmj3Hz16tVMmjSJyMhIJEli8eLFXsdVVeW5554jMjISHx8fRo0axe7du73a2O12HnjgAUJDQ/H19WXy5MlkZWV5tSkqKiIxMRGr1YrVaiUxMZHi4mKvNhkZGUyaNAlfX19CQ0N58MEHcTi8d4oWBKHl62TtRDu9FackkWYW26i0drd8uMnr578smcP9K++n3FlOO3cYXx/NoYu5C/yB4bjTiYnwJ8k9GIBEvZZlWqX0I7BNW0bFNF0F8FOd2CNurdIbgOHybsbKWwFYofTHbPB+9iN+WumF8IJNFJY7GCxrWSZd+wH8/MgoJvRpe9baUoEWIxuUXgyy/4eh9rdYo8ThY2j833Fr0+CgqaqqijfeeIORI0fywAMPMGPGDK+vhigvL6dv37689dZbdR5/5ZVXeOONN3jrrbfYvHkzERERXHbZZZSW1myN8PDDD7No0SIWLFjAmjVrKCsrY+LEibjdNeO106ZNIzk5maSkJJKSkkhOTvYaXnS73UyYMIHy8nLWrFnDggULWLhwITNnzmzgb0cQhOYmSRIjArRP2nstlc3cG+GPqHK62XSksPonFWObJMr9FqGicm33a7mvoB3BikJpUGyT3D+2nZWIkXdQIGn1i5yqjjddVxEdbGm0zXnro390ENMv7sQWJYYq1UBbqZAb9L8C2lDhqUFTZqA2jNaueDP5ZVWMlHcAYO4xlm7h/vW6Z7CvllWyY6QcHwARNHEOc5p27txJv379AEhJSfE61tA/ROPHj2f8+PF1HlNVlblz5/LUU09x9dVXA/DJJ58QHh7O559/zj333IPNZuODDz5g/vz5jB07FoBPP/2UqKgoVqxYwbhx49i7dy9JSUls2LCBIUOGAPD+++8zbNgw9u/fT0xMDMuWLWPPnj1kZmYSGamtUHj99de57bbbmD17dp3bxgiC0HJdHBLPV4Ub2Wlx4XQ7MegMzd0l4Rzs8WySq2AK/x5jsLZ9ySMDHmFazC3s+fkiAOxt4pqsD3cn9OcH43z2L/+INUosKWpnFo7p1mT3q4skSTw1oRfv/36Exe4RnoBpv9KeDUpPOp0SzOQF9sOu6glw5NLBncFwY/UITdex9b5neICp1ms+xgbnWS44DQ6aVq1a1RT9qOXIkSPk5OSQkJDgec1kMjFy5EjWrVvHPffcw9atW3E6nV5tIiMjiY2NZd26dYwbN47169djtVo9ARPA0KFDsVqtrFu3jpiYGNavX09sbKwnYAIYN24cdrudrVu3Mnr06Dr7aLfbsdvtnp9LSkrqbCcIwvnVLzQO6z43Np2Obcd3MCRyYHN3STgHObYqfKikV9v/cCAwF1RQ8q/mjtg72Hoom95qKkjQqe/IJu2HoU1X3nRf7fl5QIfmqVVkNsi87LyBaCkXP6mSR533oCJjOiVoMph92aj05BLdLv5leAtfyY7qG4YUXv/gUpIk/np5D15O0ob22vib6NLGr1GfpzVqsWFjTk4OAOHh4V6vh4eHe47l5ORgNBoJCgo6Y5uwsLBa1w8LC/Nqc+p9goKCMBqNnjZ1efHFFz3zpKxWK1FR529ioCAIp2e2BDGisgqA37J+a+beCOequMLJZeGvcSAwF0lVuSvXSEX+QP7y6Vb2bFuDWXJikwIwt+3RpP0YFVP7PaQ5DOoYTBEBTHM+zaygf7G/elNhs8H7rdzHoONLt/Zhv6ecCYAUfxPIDXvLH9e75n1x9aOjCbSIieD1yjRdffXVfPzxxwQEBHiGyk7n22+/bZSOnXDqkJ+qqmcdBjy1TV3tz6XNqZ544gmveVwlJSUicBKEFsBgCWBkRSU/+vmy5ujvPIaYn9gabc34N6uCtaX9zxYUcm1FOWnyWhalXEyUbiUYYL8plsFNPL/IqG8Z+YXXruvLM4tTuHV4R176aZ/ndf0pk7rNBpkflcFs0vVnsHsb6bSlw4iHGny/zm38WDVrFMEWIz5GMZ8J6hk0Wa1WT/BgtVqbtEMnRERodUdzcnJo27ZmR+rc3FxPVigiIgKHw0FRUZFXtik3N9dTFiEiIoLjx4/Xun5eXp7XdTZu3Oh1vKioCKfTWSsDdTKTyYTJVHvcVxCE5qUz+zOisgpZVTlScoijZUdp59euubslNMDqrNUsL/8RJLixMgT0CcB/edTwJT/ah3gKOx7x6cPg89Afo07G4VbO3rAJhQeYee8Wbaj55OzS5jTvwtJmgw4Vmfv5K23t+7H5d+PXc9z+pFOo77l3+AJUr6Dpo48+qvP7ptSpUyciIiJYvnw58fHxgFYj6rfffuPll18GYMCAARgMBpYvX87UqVMByM7OJiUlhVdeeQWAYcOGYbPZ2LRpE4MHa3+1Nm7ciM1m8wRWw4YNY/bs2WRnZ3sCtGXLlmEymRgw4HztLiQIQqMx+WNVFPrZ7Wwzm1mdtZobe9zY3L0S6im1KJXHVj+GKsF1JaUMCLmTcdfdS/Y/FhEpFTBT/zXDZW1y84HAi85LnwZ3CmZNaj6+LSTjYvU5/VDZidV0BZUKuWpXOhkt56tbF7wG5xwrKyupqKipspuens7cuXNZtmxZg29eVlZGcnIyycnJgDb5Ozk5mYyMDCRJ4uGHH+af//wnixYtIiUlhdtuuw2LxcK0adMALet15513MnPmTFauXMn27du5+eabiYuL86ym69mzJ5dffjnTp09nw4YNbNiwgenTpzNx4kRiYmIASEhIoFevXiQmJrJ9+3ZWrlzJrFmzmD59ulg5Jwitkc5AlWpgZPVGo6uzVjdzh4T6KnOU8eCqByl3ljOosoq/5heTG34xGMy84boGgLv1P6CXFLYo3anwP3ORxsby+tS+3Dg4im/+0jKKOxv1NUNyf73ce07XidIAbkXbePjUkgTCuWtw0HTllVfyv//9D4Di4mIGDx7M66+/zpVXXsl//vOfBl1ry5YtxMfHezJJM2bMID4+nmeffRaAxx57jIcffpj77ruPgQMHcvToUZYtW4a/f02diTlz5jBlyhSmTp3KiBEjsFgsLFmyBJ2u5g/JZ599RlxcHAkJCSQkJNCnTx/mz5/vOa7T6fjhhx8wm82MGDGCqVOnMmXKFF577bWG/noEQWghKiQfLqnQJoNvyt5EhVNsqdLSqarKCxteILM0E6tq4fXcfFLUrnTpoAVG3zGS5W6tcGOVamC28yZ8jY1bBfx0wgPMvHh1H3q2bRkfpCVqgqa/jOridcxi8g6STp0oLpy7Bv9p27ZtG3PmzAHgm2++ISIigu3bt7Nw4UKeffZZ/vKXv9T7WqNGjUJV1dMelySJ5557jueee+60bcxmM/PmzWPevHmnbRMcHMynn356xr5ER0ezdOnSs/ZZEITWoRwLXZwlhBuDOe4oZGP2RkZH110+RGg+n6xL4/klu3n+ylj8Qrbx05Gf0Ek6Hsi3EKQo5EeOJqFLCABvTRvIPfNn0N91gCy1DTmEcLHp/ARNLc4Z5r6H+Zu9fjbrRaapsTQ4/Kyo+P/27ju+qvr+4/jr3JmbdUMSsggjDAEJIJsgS0FEQRx1VCxixVVcqbOW/lqqFRDrqNCqRcSBirWKVasIWEUZAgJhL5lJSEgge971/f1xwk0uCRAgyb0kn+fjkQe553zvyfd8HyR553u+o8zb07N06VJuuOEGDAYDgwcP5tChQw1eQSGEOBdlmg0NGBB8EQDfZ8ojukDzn7RM/vTZdjwK/vjlt8xYOwOA+3vdy4RifcxSwoBrvRORLmkbgQcDP6luZKMHqVBrywwEHaJOPU4pzu4bmmTmW8M569DUuXNnPv30U9LT0/n666+9C0vm5OTI+B8hRMAo0/StH/pZ9GVAvk///rQ926JplTlcPLworeqVB1vCv6hwV9Ap9BIm2zpio5IjKpLoTn2972kVUnvwc6sWunbQb0Z25vo+bZg/ufbCraFWk8+AdXk813DOuiX/+Mc/8thjj9GhQwcGDhxISkoKoPc6nRibJIQQ/lah6X+J9zRGYjPZyCnPYVferjO8SzSVjPzqfQHNkasw2tJRbiubN11FxbavAPhB9SE23FZdzlj7V9aIJtw4N5CEWk28dMsljOpe97I4NXubZCB4wznr0HTjjTdy+PBhfvrpJ77++mvv8VGjRnnHOgkhhL+VV4Umi6OcwfGDAZlFF0hyiysZatjK40GvEdx6CQCVOVejXOG4d+mhaWfYEAwnLdxYcwuTQUmRtcbvCF2PhOo1FSU0NZxz6rOLi4ujT58+HDlyhMzMTAAGDhxIt26Nu5S9EELUV4VBD01aZQnDE4cDEpoCidr/PW+ZZ7Epbhceg5vosgicBQPpr+2mlTObEhVETvSgWu97767qYw+PbtqNcy8k/TtUh8tYCZYN5qxDk8fj4emnn8Zut9O+fXvatWtHREQEzzzzDB6Pf1dLFUKIEyqMVaHJWcywNsMA2HpsK8fLj/uzWqJK5+1/Y0mojbW2III8HuYf28kAbTc3GvVg+6V7EDcP6VrrfdYaW5pcHCDT/wNR33bVoalLrGy021DOeq7mtGnTmD9/PrNmzeLSSy9FKcWqVauYPn06FRUVPPvss41RTyGEOCuVVT1NBkcJsSGxdI/szs68nazMXMm1na/1c+1auMyNhBVt5oXEBABu09rQ0Z3BW5bnCNEqAfhYjeSDLrXHK2maxg9PXIbD7ZENZE+jW1z1eoYSLhvOWYemt99+mzfeeIMJEyZ4j/Xu3Zs2bdowdepUCU1CiIDgqBGaAIYnDmdn3k5WZKyQ0ORv2z5mXkQ4x0xGWpnjuWPcQna9cDndDOkAfO3uzz5bz1rjmU5oGynbgpyJyWjgiweHkl/moIPsH9dgzvrxXF5eXp1jl7p160ZeXl6DVEoIIc5XpUn/RWF0lgIwInEEAKuPrMbpdgLwr5/Sue7vq8gprvBPJVuozZs/4x273vsxudtDRNhjcE/+L++F3sFfnLfxkPMBIutYXkCcneQ2dobV0Vsnzt1Zh6bevXszd+7cWsfnzp1L7969G6RSQghxvpyGE6FJ72nqEd2DyKBISp2lbMzZCMAT/95CWnoBLy7d47d6tjjH9zEvrBynpkFJJ37Z40oAenRqz/E+D/CGexyVWCQ0iYB01o/nZs+ezbhx41i+fDkpKSlomsbq1atJT0/nyy+/bIw6CiHEWXOY9Ec4Rpfe02TQDAxrM4z/7PsPKzJWMCi+ehZWSaXLL3VsKf7+7c98tzuHN24fQNpP81gRbMOg4Lqkhwixmr3lgmssyBgVYvVHVYU4rbPuaRoxYgR79uzh+uuvp6CggLy8PG644QZ2797NsGHDGqOOQghx1lxGfcaQyVXiPTairf6I7uSlB4ynGDsjzl+ly83zX+9m/cF83llzgFePLAOga3Eb/nz15T5lQ2vsIyc9TSIQndNOhwkJCTLgWwgR0Jxm/fGcuaqnCSAlPgWTwcShokMcLDzoPW7UJDQ1lllfVa/Cvi7zf2w3OAjyeAj13FirbLCEJhHg6hWatmzZUu8L9urV65wrI4QQDcVlOhGayrzHQi2h9Ivtx9qstVW9Tfqmr6eapSXOz885xSxYdbDqlWJ/5QdggasLPZTE17VnWo3Hc6ESmkTgqVdouuSSS9A07YybXWqahtvtbpCKCSHE+XCZqh7PeSrA7QKj/uNuROKIGqHpekB6mhrLW6sPej83he6gyJKHzeMhNr8b7frba5WPDa9euTrYck4PQoRoVPX6X3ngwIHGrocQQjQot6XGKsiOYrDpKySPSBzB7PWz2XB0AxiuAk+Q9DQ1krxSBwAPXNaRdw6/ggJ+VVTMOmd/7kuoveDixfHh9E60szWzkL7tIpq2skLUQ71CU/v27Ru7HkII0aCMJjMVykyQ5oTK6tDULrwdHcI7cLDoIKaQvbiKe2I8p104xZkUleuzEiutW1CWI4R4PNxUUMnfPRfztzpWqdY0jUX3pJBX5qBNhK2pqyvEGZ31j4qZM2fy5ptv1jr+5ptv8txzzzVIpYQQ4nzZzEZKqPrFW1nic25Yoj7T1xSqD1I2yOO5RlFY7gQ8fJezEIBJhcX84BxEpD0cu81c53tsFqMEJhGwzjo0vf7663WuCN6jRw9ee+21BqmUEEKcrxCriVKlj5HZsPewz7kTq4MbQ3cDHglNDaik0sWUt9bz4Tc/El22F1v4RrLLDxLm9jCpqIhF7suItwed+UJCBKCzDk3Z2dnEx8fXOt66dWuysrIapFJCCHG+Qq0mb0/T377cyFdbq38+9Y3pS7ApBIOpBENQJpKZGsZ/t2Qx7sVvGL/vT9zyw5W8UZ5K59YfADC5qIg0ZzIbVRefAd9CXEjOOjS1bduWVatW1Tq+atUqEhISGqRSQghxvmqGplDK+TQt03vObDTTt7W+IrgpdCduz+lnBoszc7o93P/+Ru4q/SfXG1fhURr/DmnFQYsZu9vNqPJWPOa8D9AkNIkL1lnP6bzrrrtITU3F6XRy+eX6aq7ffPMNTzzxBI8++miDV1AIIc5FaJCJEqWHphCtgl0FvpvyJlj6Av/DFLobp9vjhxo2H0op/vVTOv21XUwyLcejNO5yprI24lsM5DGp8028HXEdOeuOAEhoEhessw5NTzzxBHl5eUydOhWHQ59OGhQUxJNPPslTTz3V4BUUQohzEWI1UYj+yzmMcjILyn3O79yfgDJoGG2ZFDvz/FHFZuOzzUeYtngr/7J8CMAi90i+D9OwWfLQ3KFMSnmSvy075C2fFB3ir6oKcV7O+vGcpmk899xz5Obm8uOPP7J582by8vL44x//2Bj1E0KIcxJqrdHTRDnFFU6fBXqDDBF4KhIBOOra5Jc6NhcLfzzEcMMWBhp2U6nMvOy6Dmv0NwDEcxXB5mDaR1UHpc4xEprEhemcVycJDQ1lwIABJCcnY7XKbtRCiMDiM6ZJK8fpVvR9Zhlr9h0HoKTChaukKwC57jR/VbNZKK10M8X4FQAL3aPJj9iPwZKPxxVG/8hxAIy+OAYAi9FAu0gJTeLCJEu6CSGapWCL0dvTFIo+nim/zMnkBesAKKpw4irprh9X23G4Hf6paDMQWnKAEcYteJTGAs/lWKL/B4Dj2EguitH394sJC+Lr1OF8+fAwLCb51SMuTPI/VwjRLJmNBkqrxjSFaNXjmRwufdB3cYULT0UCHmcYHir5Kfsnv9TzQqeUYlzFfwE4GDWU463SMZgL8TjDcRYM9Bm/1DUujM4xoae6lBABT0KTEKJZMhiguMaSAycrqnACGq4SfbHe7zO/b8rqNRtFJWVMMKwEIHr0b4hvry9J4zh+GSgzHaLkUZxoPiQ0CSGaJZPBQOmJx3Oa73IDHo+ipFLfF81dFZpWpK/wGSgu6qd4+xJaaSXk0IrP1HFyy3OxadE4CwYAEB8hywuI5kNCkxCiWTIaNO/juZN7mkocLm41fMMG673cWHEYTZnIKMngQNEBf1T1glay/n0AvrcN441t+r6k7Y3XgNJXtDHLbsiiGZH/zUKIZslk0CiuseRATSVFhTxtWkCUVsws07vYXJ0A+CHjhyav54XMXVFMx+P6Y82furTheMVx2oS2oXvoKD/XTIjGIaFJCNEs6T1N1UsO1OQ6sAqTVr0KeJeKcABWZKxougpe4Cqcbmb9459YcLBLxbCiXB/XdF/v+3h4VDfGXBzLG7f393MthWhYZ70iuBBCXAiMBq3G3nO+Y5rU4bU+rweUutkcBpuObqLIUUS4JbzJ6nmhenfNIdrnrQITvBKeSInrGO3C2jG+43hMBhP/lMAkmqGA72kqLi4mNTWV9u3bY7PZGDJkCOvXr/eeV0oxffp0EhISsNlsjBw5ku3bt/tco7KykgcffJDo6GhCQkKYMGECGRkZPmXy8/OZNGkSdrsdu93OpEmTKCgoaIpbFEI0AqOmUaL0MU02zYERt/fc9i36z5AMFQ1AX0cWSfYkXMrF6iOrm76yF6BP0zIZYdhCiaaxulURoPcymQzyt7hovgI+NN11110sW7aMd999l61btzJmzBhGjx5NZqa+Y/ns2bN58cUXmTt3LuvXrycuLo4rrriC4uJi7zVSU1NZvHgxixYtYuXKlZSUlDB+/Hjc7uofohMnTiQtLY0lS5awZMkS0tLSmDRpUpPfrxCiYRgMGuWazfu65rimTpq+cewStz7Dq43nCCMSRwBnP65JKcXDizbx/Ne7zrfKFxStKJO2hlzetdtxGx0k2ZO4Oulqf1dLiEYV0KGpvLycjz/+mNmzZzN8+HA6d+7M9OnTSUpK4tVXX0Upxcsvv8y0adO44YYbSE5O5u2336asrIz339dndBQWFjJ//nxeeOEFRo8eTZ8+fVi4cCFbt25l+fLlAOzcuZMlS5bwxhtvkJKSQkpKCvPmzeOLL75g9+7d/mwCIcR5UAYLlcoM6Jv2Ahhx00HLBuB7Ty8AYlUuw9sMA2Bl5krcHncdV6vb7qPF/CftCH//dh9Pf76jIasf0C5y7KTIoPFOhP4oc2rvqRgNRj/XSojGFdChyeVy4Xa7CQryXefDZrOxcuVKDhw4QHZ2NmPGjPGes1qtjBgxgtWr9S72DRs24HQ6fcokJCSQnJzsLbNmzRrsdjuDBg3ylhk8eDB2u91bpi6VlZUUFRX5fAghAkfNBS5DqtZqStRysWouKpSZ9R5977kQKrgkrANh5jDyKvLYdnzbOX29N1e1jCUL3B5FsmcX74SHU6JB54jOjOkw5sxvFOICF9ChKSwsjJSUFJ555hmOHDmC2+1m4cKFrF27lqysLLKz9b8WY2Njfd4XGxvrPZednY3FYqFVq1anLRMTE1Pr68fExHjL1GXmzJneMVB2u522bdue1/0KIRqWvsCl71pNJx7N7VcJXNWnE7lK7ykxF2cxpM0QAL7PqP/q4BVOz5kLNTOlDhedTXt41x4GwP2X3I9BC+hfJ0I0iID/X/7uu++ilKJNmzZYrVZeeeUVJk6ciNFY3Q2saZrPe5RStY6d7OQydZU/03WeeuopCgsLvR/p6en1vS0hRBMwaHhn0IVVLTuQpGUBsF/F8etLk8isGgy+bcc2hicOB2qHpqIKJ0u2ZVPpqv3YrtxR/0d5zUVpeQWrWhVQZjBwsb0To9rJukyiZQj40NSpUydWrFhBSUkJ6enprFu3DqfTSVJSEnFxcQC1eoNycnK8vU9xcXE4HA7y8/NPW+bo0aO1vnZubm6tXqyarFYr4eHhPh9CiMChaRr5St8gNgJ9ckg7LQeAwyqWILPBG5o+/t8ahrYZiobGrrxdHC2t/plw37sbuG/hBmYv2c0jH6Zx02urcbr1HqaKk4JUS9iKZc3mFfw7XN9T7sF+j5zxj1QhmouAD00nhISEEB8fT35+Pl9//TXXXnutNzgtW7bMW87hcLBixQqGDNG72fv164fZbPYpk5WVxbZt27xlUlJSKCwsZN26dd4ya9eupbCw0FtGCHHh0TTIR3+EFKX5hqZDKharyciRqtCUoB0nMiiSnq17AvBDZvUsutX7jgOwaN1hPtmUyfqD+aw/kAdAxUk9TQ53839c99rm13EYNC4q17g0cZi/qyNEkwn4BTW+/vprlFJ07dqVn3/+mccff5yuXbvy61//Gk3TSE1NZcaMGXTp0oUuXbowY8YMgoODmThxIgB2u50pU6bw6KOPEhUVRWRkJI899hg9e/Zk9OjRAHTv3p2xY8dy99138/rrrwNwzz33MH78eLp27eq3exdCnB8NOF41ZqmVdnJPU4xPT1OCdgy3RzEicQRbcrewImMFN150o8/13DV6kY6VOgAod/qGpnKHG6up+c4iSy9O56j9IAADjsVLL5NoUQI+NBUWFvLUU0+RkZFBZGQkv/jFL3j22Wcxm/VpxE888QTl5eVMnTqV/Px8Bg0axNKlSwkLC/Ne46WXXsJkMnHzzTdTXl7OqFGjeOutt3zGRb333ns89NBD3ll2EyZMYO7cuU17s0KIBqU/nqvqaaIIAx4StVwADntisJqMHFX6JJFYrYDc4kqGJw5nzqY5rM1aS6W7EqvR6r1ezUHfBWWnCE1ONxGNeVN+NmfjP/BocGlZOb3iUvxdHSGaVMCHpptvvpmbb775lOc1TWP69OlMnz79lGWCgoKYM2cOc+bMOWWZyMhIFi5ceD5VFUIEGA04TnVPUxx5WDUXDmUkiyisZoM3NMWQz+CZ3/Dp1CHEBMeQU5bDXR8u4hfdR9d57YIyJ1B7IHhZMx4Yvr9gP0sOfgnAg/mF9PjlZX6ukRBN64IZ0ySEEGdL0zTv47kYrYB2Bv3RXIZqjQcDZqOBnKp+oRitAFA88tFm7yy6dUdXkfphWp3Xzq/qaaqo4/HchWjl3mP8nFN82jIvbXwJhYfLSsvp4XBAVKcmqp0QgUFCkxCi2dI0yFaRAMRq+bTT9Blxh5U+K9agQa6KACBIcxJOKW6PYngbPTSZQncDdc+GK6vUw9HJj+dODlEXgh/25vKr+Wu57u+nXsx3ffZ6vkv/DgMGUvPzqdSsEJbQdJUUIgAE/OM5IYQ4H1knQhP5dPCGphg0Te+JqsRCgQohQislRiugwtOaQfGD0ZQJgyUPgyUHj6P20iNlVeHo5MdxRRXORr6jhrMru4hH/7WZ7Uf03QxKKl11lvMoD8+vfx6AgaZedHQe5Ii1HQkG+btbtCzyP14I0WwZNMglArfSMGtu+hr2AnBIxWCsMesrp6q3KVbLx+NRBJuDCXLrM2eNoXVvxFtWFTCOF1cywbCaXxmXYcXBd7tzG/GOGs7HGzIY+/IPbD9SxHjDGuaYX2GUYUOd60x9sf8LdubtJNQcypiyeACKQ9o3dZWF8DsJTUKIZktDw42RbPTepsGGnQAcUPEYDNWhqXoweEH1sgJl3QEwnSo0VfUwjTgyj1csc/mLeQEzzPPZmRX4e1CWVLp49KPNAAw27GCuZQ7XGH/kNfPLlGds9Slb7irnlY2vAHBXz7sIOpYBgIqU8Uyi5ZHQJIRotk50Ju31JPoc3+7p4NvTVDUYPFbL58TalO6SbgAYgw+BoYzLDRu53vADZvQepjKHCwoOc23Jh97rXGdYiaUko5HupuEcPl7m/fy3pn97PzdrbrQf/+5T9t0d73K07CgJIQlck3QLEWWHAEjs3LNpKitEAJHQJIRo9vao6tB0TIVzlFYYq3qaeiXayTnR06QV4KnqaXI5WuGuiEXTPIwO/5A3LX/lJcur/MP8MqAodbhh5UuYcLPS3YNj0QMwaoo+paceTB0oyhx68GurHWWQYRdoBp7kYQAs+5aCR0+OR0uPMn/rfAAe7vsw+SWKJIO+bVVovCz8K1oeCU1CiGbLUNWbtNpzsffYt+5LAI0TT+c++c0Q2rVPAiBGy/eGJofLg6tEf58tbIv3/VcYNzLZuJTIigzUxncAeMV1A67OVwLQz70p4PefO/Fo8WpD1dZRHYayxjqUEhWEsSIPjm4D4IWfXqDMVUbv1r25KukqjuYXkoC+pQxRnf1RdSH8SkKTEKLZ+8HTi9Xui/nZk8Df3dcCeHuaTEaDd+p8jFaA21MVmtweXMXJAKwNNnOYCJ52TgLg96b3mOl4Fs3j4jt3b9ap7oRdpO/Blqztp6g8sGfQnehp+oVtg37g4uuwBQXxo0cfx8X+b1mbtZavDn6FQTMwbdA0NE2jLGsvBk1RpgVDSLSfai+E/0hoEkI0WyeGLbkxMtH5B0Y7/spBpc/+MtYYCO4Iag3oyxKcCE1uj8JTkUCY00y5wcA7QZ150z2Wpe5+WDUXnchEGa3MdN2KxWQgJLEXbqXRWiuiODe9aW/0LJU53CRquVzk2gOaAbpfQ2iQiTWeHgA4D65ixtoZANzS9Ra6R+lhynNMn314PKhddeMK0YJIaBJCNFun+71uqHHSERwDnOhp8tQopTGsVO81WhFsATRSnffzpmss37p7s6L/39mt2hFmNYElmEMGfeyUIyOtge/k3OzMKmL+ygO43B6f46UON2NPPJprfymExtAq2MwWT0cAFhZuZ3/hfiKDInmgzwPe99mK9UHghba2TXMDQgQYWdxSCNFsmU+z+GLN0OSqCk02zUGIKvUeD6KSG8uO8mVELNmhxwA3ZQTxtOt2AIZntQZyCQ3Sf5QeMHemoyMdLTsN+EVD385Zu+pvPwBgNmrcntLBe7ys0sU441r9xcX648rWYVZ+VO04YjLyqk0/9Ui/Rwi3hHvfZ6+aOVcULGs0iZZJepqEEM1WmM3s/fyTqUN8ztXshTJYgilUwQBEq+pxTV20TPpWVhLh9oCxAmPwfv14TCgAmw7lAxBi0UNTlq0LAJZjOxvhbs5d2uECn9emonT6GH7GgwbdrwGgdaiVEmw8FRVPucHAJWEdOZrZgz1Hq/ejiyg/DEBJaIemqroQAUVCkxCi2bLXCE1927XyOefyVM9wMxsN3mUHosnz7ifXzXAYI5BcYgXg12NKODhrHL+/Wh/jU1y1KviJKxWG6gs+Bhfta/B7OVurfz7m/VwBPx3M8wagLlmfA3A4rC+ExQF6T5PJvpGNwQYsHsWVxzsw46vdjHnpewqqNieOqtTHapWHdWi6GxEigEhoEkI0WzVDE8CfJ/Twfu6sMc7HYjJ4t1KJoYDyqin53TQ9JESX6IPH/3f4f3iUh/ZRwT7XPbEKeLldD03hZYfB7d8ZdBPfWOv9/HipgxtfW8OYl76nvKKS5NwvANgZd623TGhwOUGx+vGpBQXEZB/wnnv0X5uhogi7Ow8Ahz2pKW5BiIAjoUkI0WzZbb7DNicP6eD93OWu7mmyGDWOovc0xWr5FFYtGdBN0x9HlZV2Q7mt5JbnsiV3CzHhQT7XHX6RPvtOsydSpqwYlQvyDhAovt9TvR/e0888RaQzmzwVSl77MdVl8uahGcsJrmjF5MJiOjh/9p77ZlcO5Om9Z7kqHFNIRJPVXYhAIqFJCNFsRYdaT3muZk+T/nguAtBn0K09cBxQdDPooWmPpwOuEv2R3DeHvyHU6hvGZv+iFwA92rRiX9WSBp7cuves8x/FAG0XT5j0bV9ecd1AVIQeFL868BXLDy/DpJlIqLgVE9BJO0IQldVvP66HpgMqHpvZ2NSVFyIgSGgSQjRbv740iS4xodx/We3NZU81pilWy+eP/9lOawqJ0opxK429qg2uYv3R3tKDS31W/B7YIZI4u97zNLJra/ZWbdlSmeW/weDf7s7xfq7h4Rbjtyyx/I6PrE/TSiths6cj77lHExNuJbs0m2d+fAaAu3vdjdHci1wVjlFT3seTnWNCq0OTJ54gCU2ihZLQJIRotuw2M8seGcHjV3ardc5dKzRFANC6alXwE71MB1UcFVhxlXQj2BTMkdIjbM7dTO9EO+D7yC/IbOQAbQBQuXsa6a7ObMGqg4AemF4xz+U58zy6GdKpUGY+cg3ndsfvcGKidZiFaSunUewopmd0T+7udTfBQWZ2eDoA0MOgX8dmNsJx/XHdQRUnoUm0WBKahBAtntGgcbSqpym+am+1E+OZdqmqhRyVmcvbXQ7Alwe+5M07BrBwyiCu7hnnc63DRr288bgemjYezmfqextIzytr9Ps4ITZMfyx5l/FLrjH+SKUy8axzIgMqX+Vx130Uoi+ZsCzjI9Zlr8NmsjFz2EzMBjOhViPbVQcA+ln0nqZShwuO66uBH1Bx8nhOtFgSmoQQLZ6mwWGlL3CZoB3HhMvb07TL0w6A2wa146qkqwD4+uDX2IONDO0SjXbSsuNZZj00mfP3gsfDDf9YzZdbs3nkX2lNdDdQ4fLQiiKeCPoUgOmuycxzj6eY6ll/Bms2c9NeAeCx/o/RPlxfsDLEYmJ7VU9TclVPk6OyEnV0B6CHSJtFQpNomSQ0CSFaPIMGOURQriyYNA9ttGP01PTZbztUe6JCLDx9bTIpCSlEWCPIq8hjXfa6Oq913NwGpzJicJVDUYb3+P7c0jrLN4ayShe/Ni3B7C4jM6gLH7gv9y2gOQhK+ACnx8mIxBHcdNFN3lMhVhPblR6gOngOYcRNSPF+NHclxcpGljGehAhbk92LEIFEQpMQosXTNA2FgUMqFoBe2n46a0cA2OzpTM9EO0aDhtlgZkzVNP2vDnxV57XMFisHVNUjuxrjmppyf9vSSic3GFcCsCxyIuD7xYPi/oMx6CjRtmj+POTPPr1lgztGckjFUqxsWJSDTtoRkrWDgB4gByZF15o9KERLIaFJCNHinYgMe6pmvt1s/A6DpshQ0RzDjtlY/aPyxCO65YeWU+mu5GTBFiM/K30weGV2zRl0GjnFFbzyzV4y8ht3fFNi2Q4StWO4TMF8VtHL55zJ/hPmiA2gNGYPn02ULcrn/JU94lAY2FHV29TH8DPJBr3XbZsniagQS6PWXYhAJqFJCNGiWE21f+wlttLH+myrGsszzLgNgDRPZ0Df8PaEvrF9iQ2OpcRZwg8ZP9S6ls1i5GeVAMCebRu8xw0aLFxziBeX7WHoc982zM2cwqCy7wEoSBzFL4d0ra6D5ShBcf8B4LaudzMgbkCt92qaxvJHhuNsq+/VN8SwnQGG3QBs8SR5NycWoiWS0CSEaFHqGsTcOszKJ1OHYGo/2Of4eo8eOGr2NBk0A1cnXQ3Af/b9p/b1zUZ+9ug9Taa83TXep7HtSJH3dc21nhqUx8Mw5yoASjpfw419E7l3REeCLC6SenyMZnDSM3IAjw+aespLdI4JY+iVtwBwrXG1d0D4Kk9PQq3mU75PiOZOQpMQokU51XT5vu1aceN1N5BdtfSAW2n8162HqJqhCeC6ztcB8EPGDxwrP4Yvzft4Ls5xmBPb+WqaHpxOcNRYkbxBZW4gjmOUqCDcHS/HYND43dhu/GLMOnIqDtPa1po5o5/HaDjDDLjEgWBv5325xn0xx7ATJj1NogWT0CSEaFFOt8aQ2WTifsdD/OBO5gHnQxxDX8Dy5NDUMaIjvVv3xq3cfLbvM59zlS43+1QCHqXRSishCr13ScN36xaHq3FCU8FP+jYpyz19CQsNA+CjPR/x2b7PMGgGnhv+XK1xTHUyGODKv6A0A5XKzF9d+gw7GQQuWjIJTUKIFuV0q1mbjQY2qK5Mcv6erzyDahyvPfXt+s7XA7B472KfR2039W9LJRYyVDSAdxaepmm4PNVByeluhMdzHg9laR8D8F/3YFqHWUnLSWPmupkAPNTnoTrHMZ3Sxdey86YVXF75VzYo/VGlhCbRkkloEkK0KH+65mIAHrisc61zdYUj/XjtH5VXdrgSm8nGwaKDbM7d7D0+oXcCv760g/cRXWdDJqA/nit3uL3lGqWnKWM9CVoexcrGkegh5Jbn8tvvfovL4+KK9ldwZ/KdZ33JsLjOZNLa+9rZWI8VhbgASGgSQrQogzpGsfPpsTx2Zdda58x1zKwDam2VAhBqCeWK9lcA8O89//Y5F2Q2svdEaNL00FTmcFPWCKHpo5/S6ffMMt5adQC2LwZgmacff/7FJTzy3SMcKz9G54jO/OXSv9Ravbw+2kYG84dx3b2vu8SGNUi9hbgQST+rEKLFOdU2IJaTepQ+vGcwEcEWusbVHRRuuugmPtv3GV8d+IpH+z9Kq6BW3uvsrVrzqZdhPwAdK7bzZ/Ueh8wRPOW8q8EGgj/+7y0ALFp7iMnqUzTgv+5BJKT/g825mwmzhPG3y/5GsDn49Bc6jbuGdWRschx7c0ro2y6iQeotxIVIQpMQQlQ5+TFcZIjltD0rvVv35uKoi9lxfAcf7/2Yu3reBejz5Va7e4AZLtF+Jlnbzxum2UR4SulhhHwVhsN11XnVdf3BPGZ9tcv7ul3pZjR3FkXKxupwJ6Z9n6KhMWvYLNqFtzvNleonsVWwdz0rIVqqgH4853K5+MMf/kBSUhI2m42OHTvy9NNP46kxmFIpxfTp00lISMBmszFy5Ei2b9/uc53KykoefPBBoqOjCQkJYcKECWRkZPiUyc/PZ9KkSdjtdux2O5MmTaKgoKApblMIESCMBg1DjSdYdY1lqknTNG7rfhsAi3YtwulxAvrPpSNEs8WThFFTfGH9AxFa9d5z1xtX4qw8v1XB/+/TbWw4lO99ParyfwDMM/XGGPc5APdfcj/DE4ef19cRQlQL6ND03HPP8dprrzF37lx27tzJ7Nmzef7555kzZ463zOzZs3nxxReZO3cu69evJy4ujiuuuILi4mJvmdTUVBYvXsyiRYtYuXIlJSUljB8/Hre7enzBxIkTSUtLY8mSJSxZsoS0tDQmTZrUpPcrhPC/mkHJdIqB4TWN7TCWyKBIjpYd5X+H9eByYjLda65rvOUKVAhDK/9GjoogWKvEkrWhrsudkyAqudq4lqNGIwvjC9A0N5e3vZy7e93dYF9DCBHgoWnNmjVce+21jBs3jg4dOnDjjTcyZswYfvrpJ0D/a+7ll19m2rRp3HDDDSQnJ/P2229TVlbG+++/D0BhYSHz58/nhRdeYPTo0fTp04eFCxeydetWli9fDsDOnTtZsmQJb7zxBikpKaSkpDBv3jy++OILdu/efcr6CSGan5qh6eQxTnWxGC3cdJG+htG7O95FKYWqWtDyS89guO41Fpuv5hbH/5GhWrPGo8/eC85ed071S88r4/K/fseu7Oo/DMca1mMyVHBfTDwucxmeyhieHfosBi2gf8QLccEJ6O+ooUOH8s0337Bnj75T+ObNm1m5ciVXX61vYXDgwAGys7MZM2aM9z1Wq5URI0awevVqADZs2IDT6fQpk5CQQHJysrfMmjVrsNvtDBpUvS7L4MGDsdvt3jJ1qayspKioyOdDCHFhO5vHcyfc0vUWLAYLm3M3sz57PT47pFxyK3Os97Jb6eOKtnqSALDl7azjSmc2a8ku9h8rrXFEMcX0BdNaR/FzkAGPK4RRkU8Ragk9p+sLIU4toEPTk08+ya233kq3bt0wm8306dOH1NRUbr31VgCys7MBiI2N9XlfbGys91x2djYWi4VWrVqdtkxMTEytrx8TE+MtU5eZM2d6x0DZ7Xbatm177jcrhAgINafln2oJgpO1Dm7N9V30xS5f3/I6npPWrQypsSDkzqrwFFJwbr3YGfnlPq+vNPzEishCloUEgzKQEvpb/vaLUed0bSHE6QV0aPrwww9ZuHAh77//Phs3buTtt9/mr3/9K2+//bZPuZPXHlFKnXE9kpPL1FX+TNd56qmnKCws9H6kp6fX57aEEBcIk6H+6xpNSZ6CyWBiXfY6chy+vUiRIRbv5wc88QBYSzPA4+ZsVdRY6ymSIkZELOT1Vvp2L+VZN9Azqu85rcckhDizgA5Njz/+OL/73e/45S9/Sc+ePZk0aRK//e1vmTlT3xIgLk5fcO7k3qCcnBxv71NcXBwOh4P8/PzTljl69Gitr5+bm1urF6smq9VKeHi4z4cQovmo7+M5gPjQeK7tdC0A2cZPAcU1vRMAGJgU6S2XTSQOZcSkXOz9eU+9rz/9s+08+MEmSipdAFykpfN/4c/yQusgANzHhuIq7E9iK1u9rymEODsBHZrKysowGHyraDQavUsOJCUlERcXx7Jly7znHQ4HK1asYMiQIQD069cPs9nsUyYrK4tt27Z5y6SkpFBYWMi6ddUDM9euXUthYaG3jBCiZajZSWM8i54mgPt634fVaGXr8Y28fm8Qr/zyEgDuHtaRe4Z35IO7B+PBQGbVvnQHf95+mqtVc7o9vLX6IJ9vPkJWQSkPGT/hlZA/8nycwmHQsBQnUZarj/XsEC1rKQnRWAJ6cctrrrmGZ599lnbt2tGjRw82bdrEiy++yJ136vsnaZpGamoqM2bMoEuXLnTp0oUZM2YQHBzMxIkTAbDb7UyZMoVHH32UqKgoIiMjeeyxx+jZsyejR48GoHv37owdO5a7776b119/HYB77rmH8ePH07Vr7a0WhBCiLnEhcdx+8e3M2zqPOWkvc3m7EZiNZiwmA7+/Wt+KxGjQSFcxJHEU57ED9bpuSYXL+/n/md7lKutyfhUfS7HRQLy5I3sy7+DE38Dto0Ia+raEEFUCuqdpzpw53HjjjUydOpXu3bvz2GOPce+99/LMM894yzzxxBOkpqYydepU+vfvT2ZmJkuXLiUsrHoV35deeonrrruOm2++mUsvvZTg4GA+//xzjMbqrRTee+89evbsyZgxYxgzZgy9evXi3XffbdL7FUJc+Kb0nEJUUBSHig7x9o63a51//65BpCt94omh8HC9rllcFZouNWzlessy7otrzVGTCXdlDC+Peg2UPmYqxGIkqsb4KSFEw9KUUurMxUR9FBUVYbfbKSwslPFNQlygLnl6KQVl+sreB2eNO6drfL7vc36/8veYDWY+uuYjOkV08jm//V9/pseOF/nBdhnDnvz0jNfbfqSQca+sZJ71Gea1yWen1YLHGU7ZwalseOom+j6jDz94d8pAhnVpfU51FqIlq+/v74DuaRJCiAvR+I7jGZ44HKfHyf+t+j/v9ionuO36sgNRztoTUOpSXOGig3G/NzBprmDKD09BuSIIDzLx0KgujOsZz6Wdohv8XoQQ1SQ0CSFEA9M0jT8O/iNh5jC2HtvKiz+96HNeheozfyM8eWe8llKK5Xv24m73HjutFsJcGiWH7sXj0Gf2mowGHrniIv5+W18MZzlwXQhxdiQ0CSFEI4gNieWZofr4y4U7F/Lxno+957QwPTRFevLgDCMkFqWt44OMxygIKiXS7SYlo583MD025qJGqr0Qoi4SmoQQopGMajeKe3vdC8Cf1/yZz/d9DoAhXF/gMggHVJ56+6Uv93/J7C0PYjAX0t7hZOGRbDZVDKFj6xA2/3EM91/WufFvQgjhFdBLDgghRFNr6Adc919yP3kVeXy05yN+v/L3pBenc1nsrRSpYMK1Mig+CkF2n/fkluXy4oYX+WL/FwAElcXzXu563O5g9qt4LgkyYw82N3BNhRBnIqFJCCEakaZp/GHwH7CZbLyz4x1e3fwqS8P/x022VtxSUYapJBta64/ZDhcd5uO9H/PBrg8od5WjodE/4iZi9hzHbl7L954kQMNuk8AkhD9IaBJCiEZm0Aw8PuBxukV2Y9a6Wewr2s2seCNzPIl0+mkG5t1vcqTkCFmlWd739IruxZMDn2Trfjua9jAA21QSgIQmIfxEQpMQQjSRazpdw5CEIczb/BaLd7xDqRG2lGVCWSYAJs3EgLgB3NLtFi5rexkGzcDmnw/S23AQgK0ePTSF2+RHtxD+IN95QgjRhKJsUaT2SyXii58YGbyMg93Go/rcQmtba7pHdSfE7LsNitPlpoumh6pdSl/fSXqahPAPCU1CCNHErCYDx1QrujmcdHBoBCVddeqy5dnYNAdOjKQrfbVvCU1C+IcsOSCEEE1M0zQKDRH6i5Kc05YNLTkEQJYWi6vq79zIEGtjVk8IcQoSmoQQwg8KDK0AcBWfPjSFlx4EINvUxnsswR7UaPUSQpyahCYhhKhhQIdIAMKsjTt6IdMVCoDnTKGpTO9pyrG08x5LiLA1XsWEEKckY5qEEKKGWb/oReeY/dzYL7FRv86lvbrDTgj1FILbBca6fxxHVIWmo+bq+sRJT5MQfiGhSQghaogMsfDE2G6N/nVG97sY9w4No6ag7DiExdYqk55Xhso/BAawxXZikC2SNq1sBJmNjV4/IURtEpqEEMIPYiNCyCOM1hShSo6i1RGabpv3I19rxwAoD07gw1tTmrqaQogaZEyTEEL4QZw9iGNK33OuLC+7zjIl+UexaQ4Aym3xTVY3IUTdJDQJIYQfBJmNFFQtO1B0PLPOMm2qeplyVASaWcYxCeFvEpqEEMJPys36TL2y/No9TR6PIqEqNGWqaMxGrUnrJoSoTUKTEEL4iSMoGgBn4dFa5wrKnSTWCE0mg/y4FsLf5LtQCCH8xBOsh6ZdP++j3OH2OVdc4fQ+nstUUZikp0kIv5PQJIQQfuIO1veSa6UKeG7JLp9zxRWuGqEpmrKTQpUQoulJaBJCCD9xVj2ei9YKWb7T9xHdyaGpqNzZ5PUTQviS0CSEEH7iCq4OTfmlDp9zJZWuGgPBW1NUIaFJCH+T0CSEEH6iqh7PRVFEmcM3FJWXFhKplQB6T1NMmCw5IIS/SWgSQgg/0UL10GTSPERQ4nNOFaQDUEQwEwZ1Y8rQpCavnxDCl4QmIYTwE6s1iHwVCkC0VoTL7fGeW/ztjwCUWON49vqehFhl1ysh/E1CkxBC+InNbPRupRKtFZJTXAlAYXn1cgNltgS/1U8I4UtCkxBC+InNYuQ44QBEU0hmQTkAO7OKvKGpfceufqufEMKXhCYhhPATg6b59DTlVvU07c8t9YYmc1QHf1VPCHESCU1CCOFHuTVC0/GqZQdKK10karl6gYh2/qqaEOIkEpqEEMJPTIYaPU0UcbxE72kqd7olNAkRgCQ0CSGEn/TvEElkbBtA72nKq+ppqqwoI1Yr0AtFtPdT7YQQJwv40NShQwc0Tav1cf/99wOglGL69OkkJCRgs9kYOXIk27dv97lGZWUlDz74INHR0YSEhDBhwgQyMjJ8yuTn5zNp0iTsdjt2u51JkyZRUFDQVLcphGiBjAaNKVcOAqoez5XooclakgmAw2CD4Ei/1U8I4SvgQ9P69evJysryfixbtgyAm266CYDZs2fz4osvMnfuXNavX09cXBxXXHEFxcXF3mukpqayePFiFi1axMqVKykpKWH8+PG43dUbYE6cOJG0tDSWLFnCkiVLSEtLY9KkSU17s0KIlicsDoA4Lc+7VYqtTA9NxUEJoGl+q5oQwlfAr5bWunVrn9ezZs2iU6dOjBgxAqUUL7/8MtOmTeOGG24A4O233yY2Npb333+fe++9l8LCQubPn8+7777L6NGjAVi4cCFt27Zl+fLlXHnllezcuZMlS5bw448/MmiQ/lffvHnzSElJYffu3XTtKlN+hRCNxK6PWYrVCnA59CUHQsqzACgLTiDKbxUTQpws4HuaanI4HCxcuJA777wTTdM4cOAA2dnZjBkzxlvGarUyYsQIVq9eDcCGDRtwOp0+ZRISEkhOTvaWWbNmDXa73RuYAAYPHozdbveWqUtlZSVFRUU+H0IIcVaCI3EbbQCEO3L0fyv10FQe0sZv1RJC1HZBhaZPP/2UgoIC7rjjDgCys7MBiI2N9SkXGxvrPZednY3FYqFVq1anLRMTE1Pr68XExHjL1GXmzJneMVB2u522bdue870JIVooTaMyRF/12+7Qf960cuihyRGa6LdqCSFqu6BC0/z587nqqqtISPDdVkA76Zm/UqrWsZOdXKau8me6zlNPPUVhYaH3Iz09vT63IYQQPpxheo9SlPMoAJFOPTy5w2W5ASECyQUTmg4dOsTy5cu56667vMfi4vQBlCf3BuXk5Hh7n+Li4nA4HOTn55+2zNGjR2t9zdzc3Fq9WDVZrVbCw8N9PoQQ4my5w/QepSjXUfJLKol16n+AeWS5ASECygUTmhYsWEBMTAzjxo3zHktKSiIuLs47ow70cU8rVqxgyJAhAPTr1w+z2exTJisri23btnnLpKSkUFhYyLp167xl1q5dS2FhobeMEEI0FmXXH+3HeHLYsXcvkVoJbqXRpnNvP9dMCFFTwM+eA/B4PCxYsIDJkydjMlVXWdM0UlNTmTFjBl26dKFLly7MmDGD4OBgJk6cCIDdbmfKlCk8+uijREVFERkZyWOPPUbPnj29s+m6d+/O2LFjufvuu3n99dcBuOeeexg/frzMnBNCNL6qHqU4Tzar1q7kUiDL1IbEqFanf58QokldEKFp+fLlHD58mDvvvLPWuSeeeILy8nKmTp1Kfn4+gwYNYunSpYSFhXnLvPTSS5hMJm6++WbKy8sZNWoUb731Fkaj0Vvmvffe46GHHvLOspswYQJz585t/JsTQrR4Wkw3AC7SMliavgXMkGnugAwDFyKwaEop5e9KNBdFRUXY7XYKCwtlfJMQot6KSooJeb4tRk3xvbsnw41bWWy/net/O8ffVROiRajv7+8LZkyTEEI0V9agYHYrfabccONWADKDuvizSkKIOkhoEkIIP7MYDazxXOx97VRGDoT28WONhBB1kdAkhBB+pmkaH7uHeV8v8QxAWcJO8w4hhD9cEAPBhRCiuduhOvBbx2/oYTjIq64JjDbK37RCBBoJTUIIESAWe4ax2KP3OFlMEpqECDTyXSmEEAFgwR0DfF5LaBIi8Mh3pRBCBIDLusXQt12E97WEJiECj3xXCiFEgAixVo+YMMuYJiECjnxXCiFEgLCajDU+lx/PQgQa+a4UQogAsXrfMe/nFulpEiLgyHelEEIEiJq9S+VOtx9rIoSoi4QmIYQIEHNu7ev9PKe4wo81EULURUKTEEIEiKFdor2fO1weP9ZECFEXCU1CCBFAnrm2B0nRITxwmWzYK0Sg0ZRSyt+VaC6Kioqw2+0UFhYSHh7u7+oIIYQQoh7q+/tbepqEEEIIIepBQpMQQgghRD1IaBJCCCGEqAcJTUIIIYQQ9SChSQghhBCiHiQ0CSGEEELUg4QmIYQQQoh6kNAkhBBCCFEPEpqEEEIIIepBQpMQQgghRD1IaBJCCCGEqAcJTUIIIYQQ9SChSQghhBCiHiQ0CSGEEELUg8nfFWhOlFIAFBUV+bkmQgghhKivE7+3T/wePxUJTQ2ouLgYgLZt2/q5JkIIIYQ4W8XFxdjt9lOe19SZYpWoN4/Hw5EjRwgLC0PTtAa7blFREW3btiU9PZ3w8PAGu67QSfs2PmnjxiXt27ikfRtXILSvUori4mISEhIwGE49ckl6mhqQwWAgMTGx0a4fHh4u37CNSNq38UkbNy5p38Yl7du4/N2+p+thOkEGggshhBBC1IOEJiGEEEKIepDQdAGwWq386U9/wmq1+rsqzZK0b+OTNm5c0r6NS9q3cV1I7SsDwYUQQggh6kF6moQQQggh6kFCkxBCCCFEPUhoEkIIIYSoBwlNQgghhBD1IKHpAvCPf/yDpKQkgoKC6NevHz/88IO/qxTwZs6cyYABAwgLCyMmJobrrruO3bt3+5RRSjF9+nQSEhKw2WyMHDmS7du3+5SprKzkwQcfJDo6mpCQECZMmEBGRkZT3soFYebMmWiaRmpqqveYtO/5yczM5Fe/+hVRUVEEBwdzySWXsGHDBu95ad/z43K5+MMf/kBSUhI2m42OHTvy9NNP4/F4vGWkjevv+++/55prriEhIQFN0/j00099zjdUW+bn5zNp0iTsdjt2u51JkyZRUFDQyHfneyMigC1atEiZzWY1b948tWPHDvXwww+rkJAQdejQIX9XLaBdeeWVasGCBWrbtm0qLS1NjRs3TrVr106VlJR4y8yaNUuFhYWpjz/+WG3dulXdcsstKj4+XhUVFXnL3HfffapNmzZq2bJlauPGjeqyyy5TvXv3Vi6Xyx+3FZDWrVunOnTooHr16qUefvhh73Fp33OXl5en2rdvr+644w61du1adeDAAbV8+XL1888/e8tI+56fv/zlLyoqKkp98cUX6sCBA+qjjz5SoaGh6uWXX/aWkTauvy+//FJNmzZNffzxxwpQixcv9jnfUG05duxYlZycrFavXq1Wr16tkpOT1fjx45vqNpWEpgA3cOBAdd999/kc69atm/rd737npxpdmHJychSgVqxYoZRSyuPxqLi4ODVr1ixvmYqKCmW329Vrr72mlFKqoKBAmc1mtWjRIm+ZzMxMZTAY1JIlS5r2BgJUcXGx6tKli1q2bJkaMWKENzRJ+56fJ598Ug0dOvSU56V9z9+4cePUnXfe6XPshhtuUL/61a+UUtLG5+Pk0NRQbbljxw4FqB9//NFbZs2aNQpQu3btauS70snjuQDmcDjYsGEDY8aM8Tk+ZswYVq9e7adaXZgKCwsBiIyMBODAgQNkZ2f7tK3VamXEiBHett2wYQNOp9OnTEJCAsnJydL+Ve6//37GjRvH6NGjfY5L+56fzz77jP79+3PTTTcRExNDnz59mDdvnve8tO/5Gzp0KN988w179uwBYPPmzaxcuZKrr74akDZuSA3VlmvWrMFutzNo0CBvmcGDB2O325usvWXD3gB27Ngx3G43sbGxPsdjY2PJzs72U60uPEopHnnkEYYOHUpycjKAt/3qattDhw55y1gsFlq1alWrjLQ/LFq0iI0bN7J+/fpa56R9z8/+/ft59dVXeeSRR/j973/PunXreOihh7Bardx+++3Svg3gySefpLCwkG7dumE0GnG73Tz77LPceuutgPwfbkgN1ZbZ2dnExMTUun5MTEyTtbeEpguApmk+r5VStY6JU3vggQfYsmULK1eurHXuXNpW2h/S09N5+OGHWbp0KUFBQacsJ+17bjweD/3792fGjBkA9OnTh+3bt/Pqq69y++23e8tJ+567Dz/8kIULF/L+++/To0cP0tLSSE1NJSEhgcmTJ3vLSRs3nIZoy7rKN2V7y+O5ABYdHY3RaKyVoHNycmoldlG3Bx98kM8++4xvv/2WxMRE7/G4uDiA07ZtXFwcDoeD/Pz8U5ZpqTZs2EBOTg79+vXDZDJhMplYsWIFr7zyCiaTyds+0r7nJj4+nosvvtjnWPfu3Tl8+DAg/38bwuOPP87vfvc7fvnLX9KzZ08mTZrEb3/7W2bOnAlIGzekhmrLuLg4jh49Wuv6ubm5TdbeEpoCmMVioV+/fixbtszn+LJlyxgyZIifanVhUErxwAMP8Mknn/C///2PpKQkn/NJSUnExcX5tK3D4WDFihXetu3Xrx9ms9mnTFZWFtu2bWvx7T9q1Ci2bt1KWlqa96N///7cdtttpKWl0bFjR2nf83DppZfWWiJjz549tG/fHpD/vw2hrKwMg8H3V6DRaPQuOSBt3HAaqi1TUlIoLCxk3bp13jJr166lsLCw6dq7SYabi3N2YsmB+fPnqx07dqjU1FQVEhKiDh486O+qBbTf/OY3ym63q++++05lZWV5P8rKyrxlZs2apex2u/rkk0/U1q1b1a233lrnFNjExES1fPlytXHjRnX55Ze3yOnE9VFz9pxS0r7nY926dcpkMqlnn31W7d27V7333nsqODhYLVy40FtG2vf8TJ48WbVp08a75MAnn3yioqOj1RNPPOEtI21cf8XFxWrTpk1q06ZNClAvvvii2rRpk3d5nIZqy7Fjx6pevXqpNWvWqDVr1qiePXvKkgPC19///nfVvn17ZbFYVN++fb3T5sWpAXV+LFiwwFvG4/GoP/3pTyouLk5ZrVY1fPhwtXXrVp/rlJeXqwceeEBFRkYqm82mxo8frw4fPtzEd3NhODk0Sfuen88//1wlJycrq9WqunXrpv75z3/6nJf2PT9FRUXq4YcfVu3atVNBQUGqY8eOatq0aaqystJbRtq4/r799ts6f+ZOnjxZKdVwbXn8+HF12223qbCwMBUWFqZuu+02lZ+f30R3qZSmlFJN06clhBBCCHHhkjFNQgghhBD1IKFJCCGEEKIeJDQJIYQQQtSDhCYhhBBCiHqQ0CSEEEIIUQ8SmoQQQggh6kFCkxBCCCFEPUhoEkIIIYSoBwlNQghxkpEjR5KamurvagghAoyEJiGEEEKIepDQJIQQQghRDxKahBAtWmlpKbfffjuhoaHEx8fzwgsv+JxfuHAh/fv3JywsjLi4OCZOnEhOTg4ASik6d+7MX//6V5/3bNu2DYPBwL59+5rsPoQQjU9CkxCiRXv88cf59ttvWbx4MUuXLuW7775jw4YN3vMOh4NnnnmGzZs38+mnn3LgwAHuuOMOADRN484772TBggU+13zzzTcZNmwYnTp1aspbEUI0Mk0ppfxdCSGE8IeSkhKioqJ45513uOWWWwDIy8sjMTGRe+65h5dffrnWe9avX8/AgQMpLi4mNDSUrKws2rZty+rVqxk4cCBOp5M2bdrw/PPPM3ny5Ca+IyFEY5KeJiFEi7Vv3z4cDgcpKSneY5GRkXTt2tX7etOmTVx77bW0b9+esLAwRo4cCcDhw4cBiI+PZ9y4cbz55psAfPHFF1RUVHDTTTc13Y0IIZqEhCYhRIt1po720tJSxowZQ2hoKAsXLmT9+vUsXrwY0B/bnXDXXXexaNEiysvLWbBgAbfccgvBwcGNWnchRNOT0CSEaLE6d+6M2Wzmxx9/9B7Lz89nz549AOzatYtjx44xa9Yshg0bRrdu3byDwGu6+uqrCQkJ4dVXX+Wrr77izjvvbLJ7EEI0HZO/KyCEEP4SGhrKlClTePzxx4mKiiI2NpZp06ZhMOh/T7Zr1w6LxcKcOXO477772LZtG88880yt6xiNRu644w6eeuopOnfu7PO4TwjRfEhPkxCiRXv++ecZPnw4EyZMYPTo0QwdOpR+/foB0Lp1a9566y0++ugjLr74YmbNmlVreYETpkyZgsPhkF4mIZoxmT0nhBANYNWqVYwcOZKMjAxiY2P9XR0hRCOQ0CSEEOehsrKS9PR07rnnHuLj43nvvff8XSUhRCORx3NCCHEePvjgA7p27UphYSGzZ8/2d3WEEI1IepqEEEIIIepBepqEEEIIIepBQpMQQgghRD1IaBJCCCGEqAcJTUIIIYQQ9SChSQghhBCiHiQ0CSGEEELUg4QmIYQQQoh6kNAkhBBCCFEP/w865BYeSeEAyAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(dow_data)\n",
    "plt.plot(dow_data_smooth0p1)\n",
    "plt.plot(dow_data_smooth0p02)\n",
    "plt.xlabel(\"day\")\n",
    "plt.ylabel(\"closing value\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5e5f852-a7c8-4c9b-9839-bfb7c2bcb723",
   "metadata": {},
   "source": [
    "# Ringing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9394abc8-09b2-4132-b066-5e71a4d15b5d",
   "metadata": {},
   "source": [
    "Pay attention when you apply a smoothing, or when you otherwise use Fourier coefficients to represent a signal with sharp features."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5567b6fa-341e-4e53-8fe0-373e11c0b73c",
   "metadata": {},
   "source": [
    "Consider a square wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "60c47980-4b94-4f88-bc7a-07fbbe190af7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def square_wave(x):\n",
    "    return np.sign(0.5-x%1.)\n",
    "\n",
    "xs = np.linspace(0,2,2000)\n",
    "wd = square_wave(xs)\n",
    "\n",
    "plt.plot(xs, wd)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4c25fb2-1e69-443f-a000-94dd06a07fa7",
   "metadata": {},
   "source": [
    "We can try to represent it with 5 or 20 Fourier coefficients and see what happens"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "dbe05195-f608-46b3-9abc-366fb094906d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.linspace(0,1,1000)\n",
    "plt.plot(xs, square_wave(xs))\n",
    "\n",
    "def smooth(N):\n",
    "    cks = np.fft.rfft(square_wave(xs))\n",
    "    cks[N:]=0\n",
    "    plt.plot(xs, np.fft.irfft(cks))\n",
    "\n",
    "smooth(5)\n",
    "smooth(20)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "296a3833-5e0a-4386-8d84-3fddb0aa747c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
