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  1. {
  2.  "cells": [
  3.   {
  4.    "cell_type": "code",
  5.    "execution_count": 1,
  6.    "metadata": {},
  7.    "outputs": [],
  8.    "source": [
  9.     "import numpy as np\n",
  10.     "import matplotlib.pyplot as plt\n",
  11.     "#importing numbers and visual libraries"
  12.    ]
  13.   },
  14.   {
  15.    "cell_type": "code",
  16.    "execution_count": 45,
  17.    "metadata": {},
  18.    "outputs": [
  19.     {
  20.      "data": {
  21.       "image/png": 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\n",
  22.       "text/plain": [
  23.        "<Figure size 432x288 with 2 Axes>"
  24.       ]
  25.      },
  26.      "metadata": {
  27.       "needs_background": "light"
  28.      },
  29.      "output_type": "display_data"
  30.     }
  31.    ],
  32.    "source": [
  33.     "#creating figure and axes\n",
  34.     "#1,1 = single plot area ; 1,2 = side by side two plots ; 2,1 = one below other subplots... \n",
  35.     "\n",
  36.     "# Create the figure and two axes (two rows, one column)\n",
  37.     "fig, ax1 = plt.subplots(1, 1)\n",
  38.     "\n",
  39.     "# Share the x-axis for both the axes (ax1, ax2)\n",
  40.     "ax2 = ax1.twinx()\n",
  41.     "\n",
  42.     "# Create a plot of y = sin(x) on the first row\n",
  43.     "x1 = np.linspace(0, 5 * np.pi, 100)\n",
  44.     "y1 = np.sin(x1)\n",
  45.     "ax1.plot(x1, y1)\n",
  46.     "\n",
  47.     "# Create a plot of y = cos(x) on the second row\n",
  48.     "x2 = np.linspace(0, 5 * np.pi, 100)\n",
  49.     "y2 = np.cos(x2)\n",
  50.     "ax2.plot(x2, y2)\n",
  51.     "\n",
  52.     "# Save the figure\n",
  53.     "plt.savefig('sin_cos_2.png')\n"
  54.    ]
  55.   },
  56.   {
  57.    "cell_type": "code",
  58.    "execution_count": 46,
  59.    "metadata": {},
  60.    "outputs": [
  61.     {
  62.      "data": {
  63.       "image/png": 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\n",
  64.       "text/plain": [
  65.        "<Figure size 432x288 with 2 Axes>"
  66.       ]
  67.      },
  68.      "metadata": {
  69.       "needs_background": "light"
  70.      },
  71.      "output_type": "display_data"
  72.     }
  73.    ],
  74.    "source": [
  75.     "# Create the figure and two axes (two rows, one column)\n",
  76.     "fig, ax1 = plt.subplots(1, 1)\n",
  77.     "\n",
  78.     "# Share the x-axis for both the axes (ax1, ax2)\n",
  79.     "ax2 = ax1.twinx()\n",
  80.     "\n",
  81.     "# Create a plot of y = sin(x) on the first row\n",
  82.     "x1 = np.linspace(0, 4 * np.pi, 100)\n",
  83.     "y1 = np.sin(x1)\n",
  84.     "function1 = ax1.plot(x1, y1, label='Sine')\n",
  85.     "\n",
  86.     "# Create a plot of y = cos(x) on the second row\n",
  87.     "x2 = np.linspace(0, 4 * np.pi, 100)\n",
  88.     "y2 = np.cos(x2)\n",
  89.     "function2 = ax2.plot(x2, y2, label='Cosine')\n",
  90.     "\n",
  91.     "# Create the legend by first fetching the labels from the functions\n",
  92.     "functions = function1 + function2\n",
  93.     "labels = [f.get_label() for f in functions]\n",
  94.     "plt.legend(functions, labels, loc=2)\n",
  95.     "\n",
  96.     "# Save the figure\n",
  97.     "plt.savefig('sin_cos_3.png')\n"
  98.    ]
  99.   },
  100.   {
  101.    "cell_type": "code",
  102.    "execution_count": 56,
  103.    "metadata": {},
  104.    "outputs": [
  105.     {
  106.      "data": {
  107.       "image/png": 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\n",
  108.       "text/plain": [
  109.        "<Figure size 432x288 with 2 Axes>"
  110.       ]
  111.      },
  112.      "metadata": {
  113.       "needs_background": "light"
  114.      },
  115.      "output_type": "display_data"
  116.     }
  117.    ],
  118.    "source": [
  119.     "#Adding colors or icons - x, o are for icons where as r=red, b=blue, y=yellow\n",
  120.     "\n",
  121.     "# Create the figure and two axes (two rows, one column)\n",
  122.     "fig, ax1 = plt.subplots(1, 1)\n",
  123.     "\n",
  124.     "# Share the x-axis for both the axes (ax1, ax2)\n",
  125.     "ax2 = ax1.twinx()\n",
  126.     "\n",
  127.     "# Create a plot of y = sin(x) on the first row\n",
  128.     "x1 = np.linspace(0, 4 * np.pi, 100)\n",
  129.     "y1 = np.sin(x1)\n",
  130.     "function1 = ax1.plot(x1, y1,'m', label='Sine')\n",
  131.     "\n",
  132.     "# Create a plot of y = cos(x) on the second row\n",
  133.     "x2 = np.linspace(0, 4 * np.pi, 100)\n",
  134.     "y2 = np.cos(x2)\n",
  135.     "function2 = ax2.plot(x2, y2, 'c',label='Cosine')\n",
  136.     "\n",
  137.     "# Create the legend by first fetching the labels from the functions\n",
  138.     "functions = function1 + function2\n",
  139.     "labels = [f.get_label() for f in functions]\n",
  140.     "plt.legend(functions, labels, loc=2)\n",
  141.     "\n",
  142.     "# Save the figure\n",
  143.     "plt.savefig('sin_cos_4.png')\n"
  144.    ]
  145.   },
  146.   {
  147.    "cell_type": "code",
  148.    "execution_count": 66,
  149.    "metadata": {},
  150.    "outputs": [
  151.     {
  152.      "data": {
  153.       "image/png": 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\n",
  154.       "text/plain": [
  155.        "<Figure size 432x288 with 2 Axes>"
  156.       ]
  157.      },
  158.      "metadata": {
  159.       "needs_background": "light"
  160.      },
  161.      "output_type": "display_data"
  162.     }
  163.    ],
  164.    "source": [
  165.     "#Adding Title to a graph\n",
  166.     "\n",
  167.     "\n",
  168.     "# Create the figure and two axes (two rows, one column)\n",
  169.     "fig, ax1 = plt.subplots(1, 1)\n",
  170.     "\n",
  171.     "# Share the x-axis for both the axes (ax1, ax2)\n",
  172.     "ax2 = ax1.twinx()\n",
  173.     "\n",
  174.     "# Create a plot of y = sin(x) on the first row\n",
  175.     "x1 = np.linspace(0, 4 * np.pi, 100)\n",
  176.     "y1 = np.sin(x1)\n",
  177.     "function1 = ax1.plot(x1, y1,'m', label='Sine')\n",
  178.     "\n",
  179.     "# Create a plot of y = cos(x) on the second row\n",
  180.     "x2 = np.linspace(0, 4 * np.pi, 100)\n",
  181.     "y2 = np.cos(x2)\n",
  182.     "function2 = ax2.plot(x2, y2, 'c',label='Cosine')\n",
  183.     "\n",
  184.     "# Create the legend by first fetching the labels from the functions\n",
  185.     "functions = function1 + function2\n",
  186.     "labels = [f.get_label() for f in functions]\n",
  187.     "plt.legend(functions, labels, loc=3)\n",
  188.     "\n",
  189.     "#adding X and Y axes names\n",
  190.     "ax1.set_xlabel('$X$')\n",
  191.     "ax1.set_ylabel('$Y1$')\n",
  192.     "ax2.set_ylabel('$Y2$')\n",
  193.     "\n",
  194.     "# Add the title\n",
  195.     "plt.title('Sine and Cosine Chart')\n",
  196.     "\n",
  197.     "# Adjust the figure such that all rendering components fit inside the figure\n",
  198.     "plt.tight_layout()\n",
  199.     "\n",
  200.     "# Save the figure\n",
  201.     "plt.savefig('sin_cos_5.png')\n",
  202.     "\n"
  203.    ]
  204.   },
  205.   {
  206.    "cell_type": "code",
  207.    "execution_count": 67,
  208.    "metadata": {},
  209.    "outputs": [],
  210.    "source": []
  211.   },
  212.   {
  213.    "cell_type": "code",
  214.    "execution_count": 70,
  215.    "metadata": {},
  216.    "outputs": [
  217.     {
  218.      "data": {
  219.       "image/png": 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1a8soyhAGb78NVKsGjBqlWpKYxBgot0hNleqqAXrHGzcC2dnignO743XnnVIfbd48d68TU4wbJ5VxU1Lcvc6tt4o7eNw4v7vHjxcv4IMPuitG9erA7bdLMcwDwQqGG85x+LB0QEeOBOrUUS1NTGIMlFsQyShq2TK/veNx4+SQO+90X5Rhw4CLLhKPoyEECgulCuro0e73HmrXli/os8+AoqILdn/8sYyCvZjeGDtWRDDPSYh89plMJN9/v2pJYhZjoNxk5EiJ/vrss/PeLi0FPvxQqoE3a+a+GNWri4voyy+lJLihHMaNAypVkiGFF4weLcOW778/7+3t24G5c+Ux8mJ6o3NnoHt34L333L9WTPDppxIc0bWrakliFmOg3KROHWDIEGDChPMmgGbPFpfb3Xd7J8qoUcCRI8Dkyd5dMyo5c0aGEIMGAZde6s01BwyQa5WJ854wQbzDI0d6IwYgI/rVq4E1a7y7ZlSybRswf753vYc4RQsDRUSDiaiQiDYQ0dN+9r9GRMut7SciOuSz74zPPv3U74gR0hXOyTn71rhxYruGDfNOjN69gSZNjPumXObMEeUzerR310xMBO64Q0ZQe/eeffvTT4GrrwauvNI7UW66SfTtF194d82oZMIEeR0xQq0cfogpfap6pTCASpDywy0BVAGwAkD7IMf/BsD7Pv8fC/earmaSKMvRo8zVqjE/8AAzS8LPWrWY77nHOxFsnnxS0tqYirtBuPNOyQoQTplaJ7ATMr7xBjMz//ST/PvKK96Kwczcu7ckbjflWoLQvTvz1Vd7flmUX/Ldc33q5qbDCKo7gA3MvJGZTwMYD2BokONHAvgsyH69uOgi4PrrZQKopASzZomr7aabvBdl1CjxYNmdP0MZTp8WH+jw4UBSkrfX7tABSE4GvvoKgETvEQG33eatGIAEFq5bZ9x8Adm4UdY+qfhyyiem9KkOBqoJgK0+/2+z3rsAIrocQAsAs33eTiKiAiLKJ6KATjMiGmsdV1BSUuKE3KEzYgSwZw+QnY2JE4FatYB+/bwVARAd2L79WR1oKEt2tsR0Dx+u5vo33gjMmwfesxeffgpkZQFNm6oRIyHBdGQC8vnn8nrrrSqunmjrMWsrm+bEE33qFToYKH8zjIGW1d8G4EtmPuPz3mXM3BXArwC8TkSt/J3IzO8wc1dm7pqYmBiZxOEyZAhQsyZKP/sckybJgKpqVW9FsBk2TNZD7d+v5vpa8/XXktpowAA11x8+HCgtxba3vsWPPwK/+pUaMRo2lDlLO0jDUIbPP5fcUJdfruLqJbYes7ayS6s90adeoYOB2gbAN9i6KYAdAY69DWWGo8y8w3rdCCAbwFXOixgh1aoBQ4fizBcTcXh/sRL3ns2wYeLmKxPRbDhzRgzUkCHyfakgJQVo3hwnP/kKROoGcoAMDgoLgVWr1MmgJT/+KEmENQyOsIgpfaqDgVoMoDURtSCiKpCbdkH0CBFdCaAugDyf9+oSUVXr7wYAMgCs9UTqcLn5ZlQ+ehADqs7HoEHqxOjaVaL5vvlGnQxakp8P7N4t/i1VEAE33ojmG2agX7cjuOQSdaIYN18AJk2SV5W9zODElD5VbqCYuQTAQwCmAVgHYAIzryGiPxORb3GBkQDGW5EsNu0AFBDRCgBzALzEzFoaqNK+/XEKVfFAs29Rvbo6OYhkFPXDD5LnzWDx9deyqPraa5WKsSdjOKrwaTzUaqpSOS6+GOjVy6ybu4BvvwWuukrN5GAIxJo+JY5DJ3ONGjX4+PHjnl5zwQLgcNa16NmwEDV3rle6uG/mTJlm+eYbYGiw+J54gVnqM7VtC0yZolSU//z7DIY+2ATVB/dCramfK5Xl738HnngC2LRJ1XSLZuzbJxN0f/gD8PzzSkQgohPMXEPJxRWgfAQVL0yaBExNuA41d/8szn2F9OolC4WNm89i5Urgl1/UuvcsJn1XCXNqDUPNBVOkiqBCrrtOXs18pcXUqZIRxr4xBtcxBsojpk4F9qdZD/a33yqVpXJl+Y19+y3gdcS9lnzzjYxo3ShXGwbHjgGzZgFH+w8HHTsmObEU0qaNlIMxBsriu+8kJVWXLqoliRuMgfKALVtk0WO3G5tJpJZiAwXIPNT+/edlYIpffvgB6NYNSqMSAEyfLmuF2/66l2T4/eEHpfIQyZTcrFmStDuuOX1avo/rrpPoEYMnmDvtAVOt+e4hQyAPeE6O8oVIAwZICjjFOlA9+/dLaY0hQ1RLgsmTpXhvet8koE+fcw+OQq67TkpwKB7MqWf+fEkBY9x7nmIMlAdMmQI0by5z8Lj+evFjK7YMtWoB6enAtGlKxVDPjBkSJDF4sFIx7LVp11wjHQcMHgxs2CCbQnr2lGxdce/m++47WV3fv79qSeIKY6BcpqhIXCTXXGMF7nXtKn5sDdx8gwdLPcVdu1RLopCpU4F69cTFp5AlSyRI7GyUuz2iU9yRqVIFGDhQ9HMcBvwKzPJ77ddPMo0YPMMYKJeZP1/892c9SAkJYq2mTZNus0LsQcP06UrFUEdpqXwPAwdKgUKFTJ8uHZizWZZatZIIBQ3cfNdeKxVjVqxQLYkiNmwAfv5Z+Rq5eMQYKJeZOlU8A336+Lw5YIAkJV2yRJlcgFRQveSSOHbzLV8u2SM0mH+aPl1qPzVo4PPmkCFSn0pxuPk118ir4iVi6pgxQ14HDlQrRxxiDJTLTJki647O8wzYqcztB18RCQlSOFaDwZwa7NGJytxTAI4eBfLy/OSoHTwYOHlSsvsq5NJLpTMzc6ZSMdQxY4ZMIrdSmjc1LjEGykU2bZLcknYP9CwXXyzpUjTwrQ0eLIFsS5eqlkQBP/wgw5aGDZWKkZ0t69Eu6KD37i3Dbw3cfP37S/Bp3KXHKimREMYBA0xpdwUYA+Ui9gDJbwd9wADpNh875qlM/sQgikM336FDcv81ce9Vry5RledRvboYKU0M1OnTkrIrrli0SMLLVZVgiXOMgXKRWbOAxo2BK6/0s3PAAKC4GJg713O5fLn4YlkYH3froebMEb+mYvceIAbKHixdwKBBkhpryxavxTqPrCyJ6FPslfaeGTOkB9e3r2pJ4hJjoFyitFQ8A/36BfAMZGZKWXENfvGDBslg4vBh1ZJ4yKxZMkLp0UOpGJs2AT/9FGT+3Z6vVLxStkYNGeHF3TzUjBnSg6tfX7UkcYkxUC6xejWwd2+Q0u5JSdIt1cBA9e8vBnX+fNWSeMjs2bIKtUoVpWKUGyDWoYMMczVI5TBggAQ+7t2rWhKPOHJE6oQZ954yjIFyiVmz5DWggQJEK61dK4tMFJKaKu4lDXSgN+zcCaxbp4XbZvp0KS3Utm2AAxISZI3C7NnKV8raSRTi5jnJzhY3sAkvV4YxUC4xa5Zkgw5a18zumSkeRSUlARkZcaR45syRV8UGynYD9+9fToBY377SiVm/3jPZ/NGli5Rp0WDQ7w129EpammpJ4hYtDBQRDSaiQiLaQERP+9l/FxHtJaLl1navz77RRLTe2kZ7K7l/7NiHoKMnAOjYUVbKauDY79tXMgUozmHrDbNnS1bWlBSlYqxaBRw4UGYRtz80mYeqVEmeEzt9Ycwza5a4gf1Gr+hLLOlT5QaKiCoB+BeAIQDaAxhJRO39HPo5M6dY23vWufUA/AlADwDdAfyJiOp6JHpAFi+W6PFyDVRCgoRvzZ2r/BdvK8nsbKVieMOsWXLfFac3su91797lHNiqFdCs2Tm/sUL695eAQsU5bN1n1y5ZxKiBGzgcYk2fKjdQkBuxgZk3MvNpAOMBhFqIfBCAGcx8gJkPApgBQG1aaogeIQqhZwyIdtq2Ddi40W2xgtKtm0Rqxbyb75dfJHROA8WTnQ20bAlcdlk5B9phznPmiF9QIfZti/mOjL38o9zeg3bElD7VwUA1AbDV5/9t1ntluYmIVhLRl0TULMxzQURjiaiAiApKXC4jO2uWJIqoVy+Eg+0fgOJffOXK4s2IeQNlf8Byh7fuUloqOjCkTgwg8u7fL35BhbRpI6mPFC/fc5/sbKBmTfkh60WircesbWyZ/Z7oU6/QwUD5mx4u6+/6FkBzZu4EYCaAcWGcK28yv8PMXZm5a2JiYoWFLY8TJ2RNUcgd9LZtZR5Kgy5pnz7i1di5U7UkLjJ7tmjYgGFz3rByJXDwYBgddNuSKe5BEEluyexs5V5pd8nOlmUgLuqKClJi6zFre6fMfk/0qVfoYKC2AWjm839TADt8D2Dm/cxcZP37LoAuoZ7rNQsXSkqYkHvGRKKlNPjF20bVDnKLOZhFwfftqzyvmn2PQzZQTZvK8EWDeahevSSoULFX2j3s+afoc+8BMaZPdTBQiwG0JqIWRFQFwG0AJvseQESNfP69AcA66+9pAAYSUV1rMm+g9Z4y5s0T3ZeREcZJmsxDpaRIGHHMuvl++kmUjwaKJztbyj0FXYZQlj59ZDW14tTzmnil3SN655+AGNOnyg0UM5cAeAhyI9YBmMDMa4joz0R0g3XYw0S0hohWAHgYwF3WuQcA/F/Il7IYwJ+t95Qxd64o+tq1wzhJk198pUrSO47ZEZRdtqJXL6VinDkT5vyTTc+ekt1g5UpX5AoV2ysds/NQ+s4/lUus6VMwc9xt1atXZzcoKmJOSmL+7W/DPLG0lPmSS5hHjXJFrnD4+9+ZAebt21VL4gJ33MHcsKHcb4UsWSL3+JNPwjxxyxY58fXXXZErHG6+mfmyy5TfSndo1475mmtUS+EXAMdZAx3q1aZ8BBVLFBRI8dOePcM8UaOZ56wseY3JvHzz5smXE23zTzbNmgEtWigvYAiI7Fu2SMR+TLF7t6TBUjzKNgjGQDmI7fKwlXxY9O4NbN0q63QUctVVsh5KAx3oLJs3i0YNu/fgPHPnAq1bSymWsOnZU3oPijsytv6OOTdfdM8/xRzGQDnIvHlAcjLQoEEFTtZkHioxUcoqxNwIyra4ig1UaakU/atQJwYQ+ffulRpRCmnfXipQxFygRHY2cNFFUmnZoBxjoByipERKYldY/7VrJ794DUqW9ux5Lk9czDBvnoQoduigVIx162T9U0QGClA+xE1IEFFibgS1YIGE4Oq3/ikuMQbKIZYvB44ejcB1TSRFDDUYutjKMydHrRyOMm+efLAEtY+8/fVW2EC1agU0aqTcQAHyrG/aJJ7pmODgQSnklpmpWhKDhTFQDmHriworHkB+GBs2yFodhXTvLnX8NLCVzrBrl6yB0mD+acECSWTRsmUFGyA6N3RRPA9l6/GY6cjk5so9NQZKG4yBcoh582ThZYUmvm00GbpUqybJYzXopDuDbWk1MFDz58vXHFEgYc+esrB782bH5KoInTtLQI0GXmlnWLBAklJ2765aEoOFMVAOwBzhxLfNVVeJddBg6NKzJ7BkCXD8uGpJHGDePCk8p3jh5ZYtskX8nNgNKO5BJCZKLb+YMVDz50tVxurVVUtisDAGygEKCyXRdMSegSpVgB49tPjFZ2VJ4Ed+vmpJHGD+fNGklSsrFcP+WiN+TpKTpeCiBkPczExJbHH4sGpJIuTUKSnkZtx7WmEMlAPYiies/HuByMwEli2TiAuFpKdLPIEGOjAyDh8WDaqB4pk/H6hVC+jUKcKGEhLkC9Jg8iczUzwIeXmqJYmQggLJ8qzBc2I4hzFQDpCTI2uf2rRxoLGsLFkss3ChA41VnNq1RZFqoAMjIz9fNKgjvYfImD9f7IojhXwzMiTj9v79DjRWcXr0kM+jwaA/MhztZRqcwhgoB8jJkefakQw6qanSQ9ZgHiojQ/S7y/Ud3SUnR+5naqpSMQ4cANascbCDbivS3FyHGqwYF10kU3tRb6Dmz5e1iBVaZW9wC2OgImTPHmD9egc7XrVqSXiUBr/49HQJklBcxDUycnJkKFizpnIxAAcCJGy6dZM5NQ2GuJmZ5+qgRSWlpXIfjXtPO4yBihBbPzjqGcjMlKFLcbGDjYaP/Zk00IEVo6RENKcGbpucHLEn3bo51GC1apKOR4MvJzNTYgyWLlUtSQVZs0bmKo2B0g5joCIkJweoWlWiUx0jK0tqxy9b5mCj4XPZZUCTJlrowIqxYoUMATUwULm5Yk+qVXOw0YwMiTwrKir/WBfEUS+jAAAgAElEQVSxb68Gg/6K4Vh4pcFpjIGKkJwc6RVXrepgo2lp8qo4NMquDBy1BsqV4W34nD4tdiQ93eGGMzLEOCkeulx6qSxSj1oDlZsrH6JFC9WSGMqghYEiosFEVEhEG4joaT/7HyOitUS0kohmEdHlPvvOENFya5tc9lw3OXlSFrM6rv+aNpXhi+IJcECU6tatUZpvLSfn3L1UyPLl4gJzxUABWvQgMjPPZQqKOnJz5ctRXCfMKaJVn/pDuYEiokoA/gVgCID2AEYSUfsyhy0D0JWZOwH4EsDffPadZOYUa7sBHrJ4sUwTudJBT0/XwkBpEiwWPsznwisVY9sPxw1Uw4aSPFYDA5WWJlVAfv5ZtSRhsmsXsHGjC1+OGqJZn/pDuYEC0B3ABmbeyMynAYwHMNT3AGaew8wnrH/zATT1WEa/uKZ47Ea3bVM+dOncWTK/aKADw2PrVmD7di0MVG4u0Lx5hHkaA5GRocXQxf4NRF1Hxnajx4iBQhTrU3/oYKCaAPDVwtus9wIxBsBUn/+TiKiAiPKJaFigk4horHVcQYlDC3tyc4G2baWMk+No8ou3c2dGneLRZP6J+ZwHyRUyMmStg+KhS/v2skIi6jJK5OZKirHoKVCYaOsxaxtbZr8n+tQrdKjK5c/x67c7SER3AOgKwLfq0mXMvIOIWgKYTUSrmPmCXyszvwPgHQCoUaNGxN1NO73L0KHlH1shOnWSoUtuLjBihEsXCY2MDOCll4Bjx2RhZlSQkyOptiPOKxQZW7YAO3a4bKAA+bxXXOHSRcrHXgsddR2Z3Fyga1eHo5xcpYSZuwbZ74k+9QodRlDbADTz+b8pgB1lDyKi/gCeBXADM5+Nq2XmHdbrRgDZADxJWb1+vWSZsQPuHEejoUtGBnDmDLBokWpJwiAvT/LwKK6Man99rhmodu0kL5UGQ5f0dFnUfeSIaklCpKhIcvDFjnsPiFJ9GggdDNRiAK2JqAURVQFwG4DzokeI6CoA/4HczD0+79cloqrW3w0AZABY64XQtj5wzUAB8sNZtkx5zQs7S5AGtjI0jh+XNVCufjmhYQ/kOnZ06QIaDV3S08WzoDiNZOgsXSprAGLLQEWlPg2EcgPFzCUAHgIwDcA6ABOYeQ0R/ZmI7CiSVwBcBOCLMuGP7QAUENEKAHMAvMTMntzQ3FzpuLZr5+JF0tNl6FJQ4OJFyqduXfmcGnTSQ2PxYrlvGhio3FyxH64O5NLSpFS54qFLjx4Sqa2BrQwNW1ANnhOniFZ9Gggd5qDAzFMATCnz3h99/u4f4LxcAG71TYOSl3cur6tr2EOXvDygV6/gx7pMWhrwzTfSQ9Z+uYhtSRUniD12TAZyzz7r8oXS0uSLWbQI6O/3p+IJtWoBHTpEUUcmLw9o2VIW6cYQ0ahPA6F8BBWNHDkiHVbXO1716wNXXqlFlzQtTTJy//STaklCIC9P7psr4ZWhs2iR5CF1/Tmxhy4aWIb0dBGjtFS1JOVgr5OLLfdezGEMVAVYuFCeb0+ebXvBruJ1LppkXyofO7xSA7eNZwO52rUlzluDLyc9XTpwa5U6hkJg82ZZpKvBc2IIjDFQFSAvTzqsPXp4cLG0NAkXXL/eg4sFRqNgseD8/DOwb58WiicvT9bJ1a3rwcU0GbrYt12DQX9wXA+vNDiBMVAVIC8PSE4Wn7vr2L/4/HwPLhaYhAQxyNobKE/CK8uHWb4yz8RISwMOHQIKCz26oH+uuEJq/mn/nOTnS3hlhw6qJTEEwRioMCktlR+fZx0vjZbop6drESwWnLw8uV/ty6Yf85YNG1xeJ1cWTXywRCKKBo9rcPLyZJ2h4nVyhuAYAxUmP/4otc08UzwJCfJD0uAX7xsspi32At1KlZSLAXj4nLRpI75EDZ6T1FQZyB04oFqSAJw8KSnmFUd5GsrHGKgwUeJBSkuTJfrHjnl40QvRKFjMP0ePAitXKnfvAXKPatZ0eZ2cL/aCXQ2+HPv2a7tgd8kSqbaswXNiCI4xUGGSlycd1TZtPLxoWpr4Fhcv9vCiF6JRsJh/Fi/2KK67fJQM5NLSpHz5oUMeXvRCunUTe6ntc2IL5kmUkyESjIEKk/x86ah6uljV/iFp8ItPS5N7oOU6FzuQRLHiOXZMBrye20n7gop9sBddJKmdFMf1BCYvT+poXXKJakkM5WAMVBgcPizrOzxXPPXqycJTDX7xaWnAwYOaLtjNyxOfmidx3YFRNpDr3l0bH2xamrj4tOvIaLROzlA+xkCFwaJF8nwrmVu1Q6M0WbCrga08HzuuW4OJb2UepFq1ZP2DBl9OaqpEe65bp1qSMmzZIgt0NXhODOVjDFQY2At0u3dXcPG0NFmAqrgw3ZVXarpgd+NGuT8aKB4701K9egoursnQRZOo9wvRZJ2cITSMgQqD/HwJEqhdW8HFbcWryYJdDTrp56OJ4vF8gW5ZUlO18MG2bi0GWjsDlZ8PVKumvJClITSMgQoR5YonOVniljX4xdvVHY4eVS2JD/n5MjuveIGu8kxLmvhgicRWatmR6dbNLNCNEoyBCpGffpKOqTIPUqVK2izYTU3VIur9fOzMAIoX6NoKWdlzopEPNi1NgooUR72f49QpKQCqgRvYEBrGQIWIrXiUepBSU2UhquIKu/bkvza94xMntKmgaw/kkpMVCaCRD9a2A9os2F26FCgu1uI5MYRGhQ0UET3llBBENJiIColoAxE97Wd/VSL63Nq/kIia++x7xnq/kIgGOSVTWfLypGPatq1bVwiBtDSpFLtkiUIhJIq7bVstdKCwZIncFw16xvn5GgzkNPHB2lHv2jwnyoe33qCbPiWiAUT0LhGlWP+PDfXckA0UEU3w2b4AcG8FZPXXbiUA/wIwBEB7ACOJqOxEwhgAB5n5CgCvAXjZOrc9gNsAJAMYDODfVnuOk58vHVNXK+iWh0YLdu2sOoqj3gVNMgPYAznl+k8TH6xGUe9CXh7QvHnMVdD1RVN9+gCA3wG4g4j6AkgJ9cRw1O0RZr7V2m4BMDNMIQPRHcAGZt7IzKcBjAcwtMwxQwGMs/7+EkA/IiLr/fHMXMTMvwDYYLXnKEePSmYA5YqnQQMJj9LgF5+aKsEAGzeqlgRyP664Arj4YqVi2CnelD8nGvlgNYl6F5RGOZ3jk0+A++4Tb6ML6KhP9zLzIWZ+AsBAAN1CPTEcA/VCmf+fDePcYDQBsNXn/23We36PYeYSAIcB1A/xXAAyrCSiAiIqKCkpCUvA7dvFLmjwbJ8LjTILdgU7M4Byq6CRB8n2wWoy0j54UHm9TWDbNtmUfznApEnAjBlA5coVOj3R1mPWVtZd5ok+DZPv7T+Y+WkAH4V6YrkGiohmElFny6KehZmdSqbvL6tdWe0b6JhQzpU3md9h5q7M3DUxzBDTtm2lzMbgwWGd5g6pqbISfvNmpWIkJ0u9N+UGSqPMAPn5kuJN8UBO0KQjY38tym2lNr2HiAdyJbYes7Z3yuz3RJ+Ggo/tmHReg8xvhtpGKCOoJwG8RkQfEFGjcIUMgW0Amvn83xTAjkDHEFEigNoADoR4bmyhydBFm6h3jRboajKQEzTJPNK2rQQXKe/I5OcDVasCKSFPf7jC9u3A1q2uPic66dOIbUe5BoqZlzJzXwDfAfiBiP5ERNUqcrEALAbQmohaEFEVyCTd5DLHTAYw2vr7ZgCzmZmt92+zolJaAGgNQOdyepHTsaOshFduGUQHrlghwQHKsDMDdOyoUAhROjt3KreT5zCZR84nLw/o0gWoUkWpGB4M5LTRp07YjpDmoKwJtEIAbwH4DYD1RDQqXIH9YflAHwIwDcA6ABOYeQ0R/ZmIbrAO+y+A+kS0AcBjAJ62zl0DYAKAtQB+APAgM59xQi5tSUyUlfDKf/HyIyspURz1bmcGqKBD3yk08iAJycmyIEuT52TVKoVR76dPy0OqwZeTlycDuauucqd93fRppLaj3MkYIloAoCWANQDyAdwF4EcAjxBRFjOHHNMeCGaeAmBKmff+6PP3KQC3BDj3BVwYwBHbpKUB/+//ycr4pCRlYvjOL2RlKRDAzgzw6KMKLn4+eXmapXjTxgd7Luq9oADo00eBACtWAEVFWgxv8/OBq692dyCniz51wnaEEi1wP4A11hDQl98QkW7J9OOD1FSJUV26FEhPVybGxRdLUICyTrpGmQHy88WDpHggdz5pacBLL4kPtnp1ZWL4Rr0rMVC2kVY8grIHcg88oFQML4nYdoQyB7XazwVsrg3lIgaH0SY0SnGZKk38akVFYis1sJPnk5oqGTYKCpSKYdfbVPa45ucDTZoATZsqEkBYsUIG/Rp4Gj3BCdsRUV4EZtZhmWb8cemlsiJek/mFXbsk2ttzNMkMsHSp9I61NFCANs+Jsqh3TSroapHPUxNCtR0mWWy0YucaUozSwnSaVdDVQJTzadBAMmxo8pzs3asg88iuXcCmTVpYhbw8LQZyUYUxUNFKWtq5RRUK6dRJUdS7nRlAE8Vz+eVAIzdWCUZKWlp8L9jVqPegSX8qqjAGKlrRZMGusqh3jfwlmqR4809amhaZRzp0kKh3zw1Ufr5Erlx9tccXPp/du4FfftH4OdEUY6Cilc6dJcRcE/fNsmUyAewZeXny+Tt39vCiF6LRQM4/msxDKYt6z8sT46RwOQagTTxP1GEMVLRSpQrQtasWBsqOevd0wa4d1604M4AmmZYC07GjhJhrECiRluZxvc3iYolg1ODLyc2VgVyXLqoliS6MgYpm0tIkhKyoSLkYgIc6sKhIq8wAGgzkAmP7YHNzVUtytt6mZ2WqVqwATp7UwkBpMpCLOoyBimZSUyW+eelSpWI0bAi0aOHhYG7ZMjFSChcp22iS4i046elyz06eVCqG54ESmgxvi4vFKGtgJ6MOY6CiGaUx3ufj6YJdTRSPtgt0y5KWpkHSRKB+fY8X7Npx3c2alX+siyxfLvOz2j8nGmIMVDTTqJHEN2tgoNLTgR07PFqwm5srC3QVx3UvW6bpAt2y2AJq4ubztCOjwZdj/zw1GPBHHcZARTv2OhcNxAA80IHMchGNFI8GogSnQQMpCa2JgfKkTJVmC3SbNjULdCuCMVDRTlrauVhnhXTqJMFirg/mtm6VoZoG3dHcXI0X6JYlPV1h0sRzeOaV1midnCYDuajEGKhoRxP3TWKiZK12XQxNhi32QC4jQ6kYoZOWBuzZoyDX0Pm0bw/UrOmBgcrLk8gVxQt0d+yQNdIa9KeiEmOgop2UFG0q7Kany4Swq+tccnNlqKa48NKWLdoM5ELDFlTxc1KpkkcdmZwcCa+sWtXlCwVHk/5U1KLUQBFRPSKaQUTrrde6fo5JIaI8IlpDRCuJaITPvg+J6BciWm5tKd5+Ag2oXFnWueTkqJbk7DoXV6s75OVJSgLFhZdsBRs1Bqp9e6BWLeUjbUDumasVdouK5CHU4Mtxu4JuOESjvlU9gnoawCxmbg1glvV/WU4AuJOZkwEMBvA6EdXx2f87Zk6xtuXui6whGRkSUnbihFIx7HUurunAkyflc2rQHc3NBWrUkEQNUYFnQ5fySU+XCrsLF7p0AXvxugb+19xcSfiiyTq5qNO3qg3UUADjrL/HARhW9gBm/omZ11t/7wCwB8DFnkkYDaSnyzoXz5bo+6d+faBtWxd1YEGBfE4Nesa5uaLvE0OpSa0Lrg9dQiM1FSBycdCvyfDWTniiQX/KJur0rWoD1ZCZdwKA9XpJsIOJqDuAKgB8g1RfsIairxFRQIczEY0logIiKigpKXFCdn3QJFACcDlYzP58ilMcHTsmWXQ06KCHR1qaDF0WLVIqRu3aMvJ0zUDl5ACtWkmKE4XYhSwdtpOJth6ztrFhnOuZvnUK1w0UEc0kotV+tqFhttMIwMcA7mbmUuvtZwC0BdANQD0ATwU6n5nfYeauzNw1Maq6vSHg+tAldNLTgf37gfXrXWg8N1fW8zRo4ELjobNokcy1aTCQC48ePWTooslzkp8v99FR7PBKDb6cBQvk1WFRSmw9Zm3v+O7URd86heuampn7B9pHRLuJqBEz77RuyJ4Ax9UC8D2APzDz2VWpdm8AQBERfQDgCQdFjy7S04FvvpEecoK6gbHvYK5NGwcbZpae8Q03ONhoxdBkIBc+depIYSYNAmoyMoC33wZWr3Y40e7GjVJ8SQMDlZMj/SkvB3Kxpm9Vu/gmAxht/T0awKSyBxBRFQBfA/iImb8os6+R9UoQf+pqV6XVmYwM4MAB4KeflIrRti1Qt+653qNjFBbK0EwDv1puLpCcLPo+6sjIkA/g+NAlfDEAF2yl3XtQ/JzY/SkNHldfok7fqjZQLwEYQETrAQyw/gcRdSWi96xjbgXQE8BdfsIbPyGiVQBWAWgA4C/eiq8Rdo9Rce84IUFEcVwMu8HMTIcbDo/SUplj06CDXjEyMyVIYrXavlzz5sCll7rgbczNlXD69u0dbjg8fvpJUjppZqCiTt8qnYxh5v0A+vl5vwDAvdbf/wPwvwDn93VVwGjiyiuBevXkBzpmjFJRMjOB77+XH6hj00ULFkhjjvoNw2fdOuDQIe0UT+jYgi9YoLSIFZGI4kpHJi1NwuoVYn8unZ6TaNS3qkdQBqcgcmnoEj72IMfR3rHtLyFysNGKiQFoFTocHpdfLiUoNHhOMjIkn+uOHQ41ePiwjAw1GN4uWHAudslQcYyBiiUyMmSuZt8+pWLYCxMdm4favVvCAjXojs6fD1xyiUx+RyX20MXxScLwsb9Oxzoy+fky+aOBgcrJETEU96eiHmOgYgnXZp7DIylJsi85pgNtDaZ4/gmQz5SVFeWKJzNTssJ7UrwrMCkp8qw49rjOny+uPcXhlXv3yhyUBv2pqMcYqFiiWzdJ/DV/vmpJkJkpiR8cqTK+YIFoMsWZqbdtE5dUVpZSMSLHNvSKOzJVqsjSLMc6MvPnS9K7iy5yqMGKoUk8T0xgDFQskZQkiVQ1MVDFxQ5lX1qw4JzxVYh9W6Ne8XTsKEpcAzdfVpakV4w4+1JRkST306D3kJMjxrdLF9WSRD/GQMUaWVmSY8XVmhflY08DRKwDT5yQz6OBVViwQPS6wuA3Z0hMlCgPDQIlsrJkSVbEVUAKCsRIaWKgunaV/qIhMoyBijWysiShquIy8PXqyWLWiA3UokXyeTRw6M+fL4Y3JjJlZWQAK1dK5JtC7IjwiAf9mgxvT5wQW6lBfyomMAYq1khPl9Wymrj5Ik5a4FJCs3A5eFAimGNG8WRmSsSb4gKGNWvKtNG8eRE2NH8+0K4dcLHaQgf5+eLa7tlTqRgxgzFQsUatWuKD0sRA2UtTKszcuVI9t+4FtdU8JTdX9LkGHiRnSE2VoeDcuaolQc+eMn1UVFTBBs6cEb+aBl/OvHkS4RkzHRnFGAMVi2RlSc/49GmlYtg/0grbyuJisQwadEfnz5civt27q5bEIWrUkImSiIcukZOVJcapwgE1q1dLT0gTA5WSIiVFDJFjDFQskpUl8d1LlyoVo3lz4LLLIuikL1kiTv1evZwUq0LMny9RWdWrq5bEQXr1EquguBJzxB0Z28gqNlBFRdIv1OBxjRmMgYpF7B+qBm6+3r3FQFWogKFt2RSPoE6elIlvDTroztKrl4xSFc9DNWgguV0rPJibPx9o1kzSOCmkoAA4dUr54xpTGAMVizRsKElVNTBQvXrJyvp16ypw8ty5MvF9SdDCn66Tny/e0phTPBkZElCjyTxUTk4FAmqY5TnXoPegyUAupjAGKlbJypIIuNLS8o91EdvdEbYOLCkR+TXwl2Rnix6POcVTq5Zk59DAQGVlyWLdFSvCPHHDBmDXLi2+nLlzZWmF4oLPMYUxULFK794SGx32L95ZWrYEmjYVJR8Wy5eLxtLAQM2ZI3o8Jie+e/WSELpTp5SKYduXsN18c+bIa+/eTooTNiUlMgKMuVG2YoyBilX69JFX+wesCCLRgWHPQ9maSvEv/sQJ0d/27Yw5evaU2f1Fi5SK0ayZdGbC7sjMmSOVD6+80g2xQmbZMuDYMeWPa8yh1EARUT0imkFE661Xv4tdiOiMT3XHyT7vtyCihdb5n1vlig2A1Pxp3Vq5gQKkc7t7t1QCCZm5c4ErrgAaN3ZLrJCw558Ud9Ddw07NroGbr29fMVAhz0Mxy/Pdp4/y9PKa9KeCEo36VvUI6mkAs5i5NYBZ1v/+OMnMKdZ2g8/7LwN4zTr/IAC1pWR1o08f+eWUlCgVI+x5qNJSmfjWxL1XqVIML7ysW1cWQmtioA4fltFISPz4o/R8NBjeatKfKo+o07eqDdRQAOOsv8cBGBbqiUREAPoC+LIi58cFffoAR46E8Yt3hyuuABo1CkMHrlol82caGKjsbFn/VKuWaklcpFcvWRCteGG3PUoNedBvH6jYQJWUyLOtgZ0sj6jTt6oNVENm3gkA1mugeOIkIiogonwism9KfQCHmNkeHmwD0CTQhYhorNVGQYniEYVnhP2LdwciESU7O8R5qNmz5VWxXy3m559seveWxV4LFyoVo1EjWVVgf/3lkp0tETitWrkpVrkUFEg/sF8/Ty6XaOsxaxsbxrme6VuncD0vMxHNBHCpn13PhtHMZcy8g4haAphNRKsAHPFzXED1x8zvAHgHAGrUqFGRZaPRx6WXyi9+zhzgySeVitK7N/DZZ1JptNz57JkzZR1Xs2ZeiBaQ3FxZxxqz8082vXtLHP3MmcrDtfv2BT78UO575cpBDmQWAzV4sPL5p1mz5LVvX08uV8LMXQPt1EXfOoXrIyhm7s/MHfxskwDsJqJGAGC97gnQxg7rdSOAbABXAdgHoA4R2Ua2KYAdLn+c6KNPH5nPKS5WKobdu5w5s5wDi4vFX9K/v+sylUfMzz/Z1K0reflsTauQPn2klFm5efnWrJEV4BoMb2fNkmk8xYnUAcSevlXt4psMYLT192gAk8oeQER1iaiq9XcDABkA1jIzA5gD4OZg58c99i++oECpGK1aAS1aADNmlHPgwoUirwYGKjtbCvkqriDuDf37S8jiEX8dZe+wR6vluvk0mX86eVJG2h659yIl6vStagP1EoABRLQewADrfxBRVyJ6zzqmHYACIloBuUEvMfNaa99TAB4jog0QH+l/PZU+GtBkHgoQHThnTjlBhTNnirtJsV/tyBGxlR65bdTTr5/EdyvObl6/vmQDD8lANW8um0Jyc2UZWZQYqOjTt8wcd1v16tU5rujUiblvX9VS8IQJzABzbm6QgzIzmbt180ymQHzzjciana1aEo84eZI5KYn5t79VLQk/9hhz1aoikl9KSpjr1mW+5x5P5fLHM88wJyYyHznizfUAHGcNdKhXm+oRlMELBg6UvHbHjysVw15PGXAe6uhRcTNp4N6bPl1KJqWlqZbEI5KSJECi3ElC9+nTR0YlubkBDli8WJYhDBzoqVz+mDVLaoTVrKlaktjEGKh4YNAgWeMSdh4ZZ2nQQMp7B9SB9qJiDfwl06eLoqwST7lJ+vWT4n+7dikVo1cvieCbNi3AAdOmSU9HcUfm0CGZ2tXgcY1ZjIGKBzIzgWrVgvzivWPAACk/dOyYn52zZklPPiPDc7l82bhRkmRr0EH3Flvhh7wQyR1q1pRHIKiB6tpVJqwUMneuJD0xBso9jIGKB5KSpFs6fbpqSdC/v0SS+52LnzlTjGlSkudy+WJHGsadgUpJAerV08LNN3iwJOLfUTaQ+dAhiV4ZNEiJXL5Mny4VllNTVUsSuxgDFS8MGiTZWjdvViqGbX8uCDffuVNSHGnQHZ0+XUrVt2mjWhKPqVRJwhZnzKhgCWTnGDxYXi/oU82aJcMWxQaKGZgyRTpcVasqFSWmMQYqXrB/0IrdfElJYqQuMFBTp8rrkCGey+RLSYnowIEDlScoUMPgwcC2bdJZUEinTpII5YLHddo0SYzYo4cSuWwKC4FNm5Q/rjGPMVDxQtu2krdMg3mowYMlEcB5g7kpU6RESKdOyuQCJEDs8OE4dO/Z2Bp3yhSlYhBJn2r6dJ/yG8zy/PbtW04eJPfRpD8V8xgDFS/Yv/hZs5SX37juOnn9/nvrjdOnRRNdc43yYcv06SKCBp5GNTRuLKGWZ78cdQweDBw44JMEpbAQ2LJFuXsPEPvdvj1w+eWqJYltjIGKJwYNkuGB4qzVbdpI6qPvvrPeyMmRNVDXXqtULkAUT/fuEisQt1x7rSxCOnhQqRgDBkhn4eyg3/5DsYE6dkyCfK65RqkYcYExUPFE//6SRsj2TyiCSEZRs2dba4e//14WHCketuzcKZXPr79eqRjqueYaCURQ7A6uX19yIf7wg/XG1KlSJbpFC6VyzZ4tg37j3nMfY6Diibp1JUJhkvqcutdeK9kCZs+GDFt69VKeldUe0d1wQ/DjYp7u3cU6KJ6HAsTNt3AhcGDTEXlYNOg9TJ0qj2rMZ7nXAGOg4o1hwyRbwMaNSsXo2VN+5Pmf/QKsW6eFv+TbbyX3aIcOqiVRTKVKYhmmTvWJUFDD9dfLYG7lKz/IArphaotm+4aXx1WWEUUYAxVvDB0qr4pHUVWryhzD2V664vmnEyck9P2GG5THaejBtdcC+/YpL9PSpYsEn9LkSZIrKz1dqTxr10qchgb9qbjAGKh4o2VLGSJMnqxaElx3HZBx+HsUNbtC5hYUMnMmcOqUFh4kPRg0SOYrFUfzEQE3Xl+MTtumoGTwdTK6U8jXX8urMVDeYAxUPDJ0qFTZPXBAqRjXZh5GP8zCsmbqrcLkybL+s2dP1ZJoQr16khDP1sgKGd1yPuriEJY0HapaFEycKBnumzRRLUl8YAxUPDJ0qMwtKO4dN1z8HariNN7Zf3P5B7tIaakESAwZYuYVzuPmm2W+8scflYrRefMknEQS/rtlgFI5Nm4Eli8HbrpJqRhxBbHCnFtEVA/A5wCaA9gE4FZmPljmmIQmfS8AABcpSURBVD4AXvN5qy2A25j5GyL6EEAvAIetfXcx8/LyrlujRg0+rrg2klJKS4FmzaQr+OWX6uQYPhxH5yxG7cNbsH5DAlq1qnhTxcXF2LZtG06dOhX2uUVFUmGiQQOpARULJCUloWnTpqgcScaFbdvkOfnLX4Bnn3VOuHBgBlq0wNIznTDgxGTs3g0kJqoR5ZVXgCefFEOlKtKdiE4wc4WeUlX6NiJUVksE8DcAT1t/Pw3g5XKOrwfgAIDq1v8fArg53OvGXUVdf9x/P3ONGkHKlrrMkSPMVavy4bseZoD5xRcja27jxo28d+9eLi0tDfvcrVuZCwqYi4sjk0EXSktLee/evbxx48bIG0tPZ+7cOfJ2Ksry5cwAF/yf9xhgnjNHnSg9ejBffbW66zNHVlFXlb6NZFPt4hsKYJz19zgA5cWQ3gxgKjOfcFWqeGDYMFklq6oEx/ffA0VFqHXPzejRA5gwIbLmTp06hfr164PCDMFjlqm4WrXU9cydhohQv379Co0mL+Dmm6Xuxfr1kbdVESZOBBIS0PaJ65CUBHzzjRoxtm2T9VhR7t6LOn2r2kA1ZOadAGC9XlLO8bcB+KzMey8Q0Uoieo2IAia+J6KxRFRARAUlinPRaUHfvuLT+uQTNdf/4gugUSMgIwMjRgDLlkWuA8M1ToCkrTl9OvZSG1XkXvjF1sgqXMHM8nz27YsaLRti4ECxV6Wl3ovy1VfyqoGBSrT1mLWNDeNcz/StU7huoIhoJhGt9rOFFZJDRI0AdATgm3/lGYiPtBtkOPpUoPOZ+R1m7srMXRNjpascCZUrAyNGSPjakSPeXvvYMVn/dOONQEICbrZiJL74wlsxABk9JSQAdep4f+2o4LLLpLSFCgO1cKFM+Nx+OwDgV7+Skczcud6LMnEikJwMXHml99cuQ4mtx6ztHd+duuhbp3DdQDFzf2bu4GebBGC3dSPsG7InSFO3AviamYt92t5puWaLAHwAoLubnyXmuP12WfzjdSjxlClyXcsyNWsm6y8jdfOFS2mp5EOtXduZ5TUvvPACkpOT0alTJ6SkpGDhwoW49957sXbt2sgbV8nNNwNLl3qffeSTT6SA2I03ApBF1LVqAR9/7K0Y27fLqgwNRk/lEmv6VrWLbzKA0dbfowEES28wEmWGmz43myD+1NUuyBi7pKbKwl2v3XzjxwOXXAJkZZ1969ZbZaqjsNA7MY4elcoj9etH3lZeXh6+++47LF26FCtXrsTMmTPRrFkzvPfee2jfvn3kF1CJPcT9rKy3x0WKi4HPP5eV07VqAQCqVRNRvvxSMn94xUcfibdx1CjvrukSUadvVfu6XgIwgYjGANgC4BYAIKKuAO5n5nut/5sDaAag7OD+EyK6GAABWA7gfm/EjhGIxG/y179KnPWll7p/zd27JendI4+cN2y5+Wbg0UfFVv75z5Fd4re/lfUq5XHqlBioUHLUpqQAr78eeP/OnTvRoEEDVLXqfzdo0AAA0Lt3b7z66qvo2rUrLrroIjzyyCP47rvvUK1aNUyaNAkNGzbE3r17cf/992PLli0AgNdffx0ZGRnlC+UVzZtLMt8PPgCeeUZ8om4zcyawd+9Z957NqFHA+++LZ/q229wXg1k+dlYWcMUV7l/PZaJO3yodQTHzfmbux8ytrdcD1vsF9s2y/t/EzE2YubTM+X2ZuaM1hL2DmY95/RminttvF1/X+PHeXO/jj8UqjBlz3ttNmkh2nfff966eYkmJc5F7AwcOxNatW9GmTRs88MADmOtnouT48eNITU3FihUr0LNnT7z77rsAgEceeQSPPvooFi9ejIkTJ+Lee++94FzljBkD/PyzFELygv/9T7Lvl6lp0bOnTIt55ebLzZXgnbvv9uZ6bhKV+tbLmHZdNrMOqgxXX83ctav71yktZW7bljktze/ur75iBpi//Tb8pteuXRvW8fv2MS9ezHz4cPjXCkRJSQnPmTOH//jHP3LDhg35gw8+4F69evHixYuZmblKlSpn12mNHz+ex4wZw8zMF198MXfu3Pns1rhxYz5y5EjE8oR7T4Jy/DhzrVrMd9zhXJuBOHqUuXp15rFj/e5+5hnmSpWYd+1yX5QxY2S54NGj7l8rFBDBOqho3FTPQRl0YNQoyVq9YoW718nNlbQ5AUYI110HNGwIvPOO392OsmePzL/XrOlcm5UqVULv3r3x/PPP45///CcmTpx43v7KlSufDf+uVKkS7OUOpaWlyMvLw/Lly7F8+XJs374dNZ0UzAmqV5fR9pdfAocOuXut8eNlkinApM+oUZKpy+0psePHZRrslluUlyqLW4yBMgCjR4sCevNNd6/z3//KL/3WW/3urlwZuOceWcO7fbt7Yhw/LtvFFztXWqOwsBDrfRZyLV++HJdffnlI5w4cOBD//Oc/zztXS8aMkYm7Tz917xrM8hx26iTJav3Qrp3UVHz7bXfXRE2cKCsiYsG9F60YA2UQX/+dd0qEwr597lzj6FGJIx8xImh3dMwYUTrvv++OGIDMvSckOBO9Z3Ps2DGMHj0a7du3R6dOnbB27Vo899xzIZ37xhtvoKCgAJ06dUL79u3x9ttvOyeYk1x9NdC5s3Q03GLePGDlSuDhh4P2Hh55RCI+z5aDd4H//hdo1eq8YFOD16j2MarYzByUH1avZkeS4gXirbek/by8cg/t35/58suZS0pCbz7U+ZbiYsm798svobcdrTg6B2Xz5pvyPS5a5HzbzMw33cRcrx7ziRNBDzt9mrlxY3lW3GDRIvmYr77qTvsVBWYOyhCXJCcD/foB//6382F0JSXA3/4GdOsmWQnKYexYYPNmd2oq7tsnXqRLykvyYvDPnXfKyuaXXnK+7S1bZNH4fffJoqcgVK4MPPSQRKOvdmE1zssvS3aRseEkEjI4jjFQhnM8/DCwdavz5eDHjwd++UVKNoQw6TN8uKw5+fOfxZg4BbO49y66SKbcDBWgVi3gN7+R5HROZ8h46y15feCBkA4fO1bsWLD1aRWhsFA+3gMPOBtEYwgfY6AM57j2Wil08/e/O2cZSkuBF1+UMvMh1lNPTAT+8AdZbPvtt86IAQD790vtJzN6ipBHHhEL/+KLzrV59KiEbw4fLgudQqB+fRnQ/e9/EpXpFK++ClStKv01g1qMgTKco1Il4KmngLw85/xr33wjPe3f/z6sDAS33y4T1M8/74ytLC0FduwQvVq3buTtxTUNGgD33y9x3k7l5/vb3yRz71Ph5R/97W8lG/2rrzojxo4dktro7rtlyYNBLcZAGc5nzBigbVtRFJHORTEDL7wg/roAoeWBSEwUj+DSpc5Upt+7VxRZ06bOhZbHNY8/Lh2al1+OvK0dO2TUftttMk8ZBm3byiqJf/xDEl1EyiuvyGP/xBORt2WIHGOgDOeTmChKp7AQeO+9yNqaMEEszNNPVyhd+B13iMfxueciW+9y5gywc6fMJ5g5BYdo3Fg6Mx98EPlc1B//KFbhr3+t0OkvvCBBE08+GZkYq1bJEqx77pEcygYNUB1GqGIzYeblUFrKnJXFfMklUpq9Iuzbx3zxxczduoUXL16Gjz6ScN833gh+XLCQ6u3bJa2R2+lqdu7cySNGjOCWLVtyu3bteMiQIVxYWBhWG0OGDOGDBw86Io8rYea+7NnDXL++pK6q6He8ahVzQgLzo49GJMpf/sIRlYQ/c0aq2zdoII+uriDOwsyVC6BiMwYqBBYulMfjd7+r2PmjRzMnJjKvWBGRGKWlzEOGMFerxrx+feDjAinj48dl3dOGDRGJUS6lpaWcmprKb7311tn3li1bxvPmzXP3wkFw3UAxn+tBvPlm+OeeOcPcrx9znTrM+/dHJMaJE8yXXcacklIxW/nuu/IxPvwwIjFcJ94MFMlnji9q1KjBx48fVy2G/owdC7z7roSd33BD6OdNny6pyZ99FvjLXyIWY/t2CQJMTpZqqv68hevWrUO7du3kH6veBrOkdGMGqtcAEiKZeyqn3sbs2bPx3HPPYV6ZbN/MjCeffBJTp04FEeEPf/gDRowYgZ07d2LEiBE4cuQISkpK8NZbbyErKwvNmzdHQUEBjh07hiFDhiAzMxO5ublo0qQJJk2ahGrVquHnn3/Ggw8+iL1796J69ep499130bZt2+D3xC2YJeN4Tg6wZk3IEXgAxHf7/PPAf/7jyIIjO1HJU0+Ft0xrzx6Zy+rUCZgzR+85SiI6wcw1VMvhFWYOyhCYN94AunSR7Jw+eeaCsn27LLS88kqJFXeAJk1ElJwcmUsPBQZwqkjmrpKqRWicQmD16tXo0qXLBe9/9dVXWL58OVasWIGZM2fid7/7HXbu3IlPP/0UgwYNOrsvJSXlgnPXr1+PBx98EGvWrEGdOnXOJp8dO3Ys3nzzTSxZsgSvvvoqHghx3ZArEElSPGaJ+T55MrTzvv9ejNPo0fK8OMAtt0hw4csvS+h5KBw7BgwdKrkZ//1vvY1TPKK6YKFBZ5KSJHt1ly5SdjsvL3ha5+3bgd69pY76xIlyvkPccYdErD/1lDQbbI0Kv/Y69uyRNceNGwM1GzsmRtgsWLAAI0eORKVKldCwYUP06tULixcvRrdu3XDPPfeguLgYw4YN82ugWrRocfb9Ll26YNOmTTh27Bhyc3Nxyy23nD2uqKjIs8/jl+bNZRQ0ahQwbJh8UcEyQfz8s3yhKSmyONchq0AkHRk7YX7r1sETlxQVyWO9aJE85tFe+DgWUTqCIqJbiGgNEZVaVR0DHTeYiAqJaAMRPe3zfgsiWkhE64nocyKq4o3kcUTz5pK9eu1aCQEOVJLDNk67dwPTpgFdA36dFYJIxBg+XNaJBlofVVoqaZK2bpVUNY0aOSpGQJKTk7FkyZIL3g/kQu/ZsyfmzZuHJk2aYNSoUfjoo48uOMauzgucK89RWlqKOnXqnC3NsXz5cqxbt865D1JRbr9dsqvOmCFGKtBIavJksRpE0okpJ6VRuFSuLMamSRNZd/755/6fkyNHpJj0jBmSmHj4cEfF0JJo1LeqXXyrAdwIIGCZTiKqBOBfAIYAaA9gJBHZfZ2XAbzGzK0BHAQwxn8rhogYNEiMzuHDUufgb3+TjNMnTshCzUcfle6nbZzS0lwRo2pVmWe46y6ZvujXDxg3TpRNcbFkivjxR8m316iRLPT1ymXTt29fFBUVna2SCwCLFy9G3bp18fnnn+PMmTPYu3cv5s2bh+7du2Pz5s245JJLcN9992HMmDFYunRpSNepVasWWrRogS+++AKAGMAVbtfxCpW77z5npNq0kYmg/fulftTixZI7aOhQmafKzXUtlrt+fcly3rKlLK0aOlRGSZs3y3zTiy/K8oWvvpJpxdGjXRFDR6JP36qO0rB6mNkAugbYlwZgms//z1gbAdgHINHfccE2E8VXQfbsYb7+egl3sjciidYbOVJChj3gzBnmV15hbtHinAhTp67lxYuZly1jdihKO2y2b9/Ot9xyC7ds2ZLbt2/P11xzDf/000/8xBNPcHJyMnfo0IHHjx/PzMwffvghJycnc0pKCmdmZvLGjRuZmfnyyy/nvXv38i+//MLJycln237llVf4T3/6EzMzb9y4kQcNGsSdOnXidu3a8fPPP+9XHk+i+PwxfbpE5wESQu77vDz+OPOpU56IUVLC/Pe/SwSorwgA8zXXuJeQ3U3gQBSf1/o2kk2LKD4iygbwBDMX+Nl3M4DBzHyv9f8oAD0APAcgn5mvsN5vBmAqM3cIcI2xAMYCQJUqVboo99tHK8wyevrxRwmcSEiQLmiTJkpEycsDpkwBbrhhHTp0aIdq1cxEt40nUXzBWL1a0iHVqSMTQh07yrDWY7Ztk4LR9mAuK0scAdEIEZ0GsMrnrXeYOawa1F7oW6dwPUiCiGYCuNTPrmeZOZS02f7UDQd53y/Wl/gOIGHmIVzX4A8iKVrXubNqSUAEpKfLtm6dyVCuHR06SJoHxTRtKluMUMLMweaPtNC3TuG6gWLm/hE2sQ1AM5//mwLYARlu1iGiRGYu8XnfYDAY4pJY07eqgyRCYTGA1lYESRUAtwGYbPlj5wC42TpuNACHCxkZogkd3NW6YO6FoYJopW9Vh5kPJ6JtkAm374lomvV+YyKaAgCWtX4IwDQA6wBMYOY1VhNPAXiMiDYAqA/gv15/BoMeJCUlYf/+/UYxQ4zT/v37keTgOjRD9BON+laLIAmvMamOYo/i4mJs27YNp06dUi2KFiQlJaFp06aoXLmyalEMDhJvqY6MgTIYDIYoId4MVDTMQRkMBoMhDjEGymAwGAxaYgyUwWAwGLQkLuegiKgUQIh1Ac4jEUCJw+K4RTTJChh53cbI6y5eyVuNmeNmYBGXBqqiEFFBsFXcOhFNsgJGXrcx8rpLtMkbLcSNJTYYDAZDdGEMlMFgMBi0xBio8Agra7BioklWwMjrNkZed4k2eaMCMwdlMBgMBi0xIyiDwWAwaIkxUAaDwWDQEmOgQoCIBhNRIRFtIKKnVcsTDCJqRkRziGgdEa0hokdUyxQKRFSJiJYR0XeqZSkPIqpDRF8S0Y/WfU5TLVMwiOhR61lYTUSfEZFWac6J6H0i2kNEq33eq0dEM4hovfVaV6WMvgSQ9xXreVhJRF8TUR2VMsYKxkCVw/9v725C6yjDKI7/D42Csbqs1ERohVItflVEigURa7BqSdyKSkCXfkJBLS4UFXEhoqLoomALBkVqwW7Ulgq6URGLKFpQUWmvRFsQP6hgFY+LmUCMTSaS0PfN5fwgZGZWh0vmnjvv3MwjaRnwPHAdsA64SdK6sqnm9Bew1fb5wAbgjsrzTrmH5vH+S8EzwFu2zwMupuLckoaAu4HL2vHcy2hm/NRkB7B5xrEHgP221wD72/1a7OC/efcBF9i+CPgS2HayQ/WjFFS3y4GvbX9j+zjwKjBWONOsbE/aPtBu/0bz5jlUNtXcJA0DNwDbS2fpIulM4EraWTi2j9v+uWyqTgPAaZIGgEEqmzxt+z3gpxmHx4Cd7fZO4MaTGmoOJ8pre287SwngA5qJs7FAKahuQ8Dhafs9Kn/DnyJpFbAe+LBskk5PA/cBf5cOMg/nAkeBl9olye2Sqh1/YPt74EngEDAJ/GJ7b9lU83KW7UloPnQBKwrn+T9uA94sHaIfpKC66QTHqv9uvqTlwOvAvbZ/LZ1nNpK2AEdsf1w6yzwNAJcCL9heDxyjruWnf2nv3YwBq4GzgdMl3VI2Vf+S9CDNMvtE6Sz9IAXVrQecM21/mMqWSGaSdApNOU3Y3l06T4eNwKik72iWT6+W9HLZSHPqAT3bU1elu2gKq1bXAN/aPmr7T2A3cEXhTPPxo6SVAO3vI4XzdJI0DmwBbnb+wXRRpKC6fQSskbRa0qk0N5j3FM40K0miuT9y0PZTpfN0sb3N9rDtVTSv7Tu2q/2Eb/sH4LCkte2hTcAXBSN1OQRskDTY/m1souIvdUyzBxhvt8eBNwpm6SRpM3A/MGr799J5+kUKqkN74/NO4G2aE/s125+XTTWnjcCtNFcin7Q/15cO1WfuAiYkfQpcAjxeOM+s2iu9XcAB4DOac76qx/JIegV4H1grqSfpduAJYETSV8BIu1+FWfI+B5wB7GvPuReLhuwTedRRRERUKVdQERFRpRRURERUKQUVERFVSkFFRESVUlAREVGlFFRERFQpBRUREVVKQUUsgnYG10i7/ZikZ0tniljqBkoHiOgTDwGPSFpB8wT50cJ5Ipa8PEkiYpFIehdYDlzVzuKKiAXIEl/EIpB0IbAS+CPlFLE4UlARC9SOg5igmbt0TNK1hSNF9IUUVMQCSBqkmbG01fZB4FHg4aKhIvpE7kFFRESVcgUVERFVSkFFRESVUlAREVGlFFRERFQpBRUREVVKQUVERJVSUBERUaV/AA6BwGM2o4haAAAAAElFTkSuQmCC\n",
  220.       "text/plain": [
  221.        "<Figure size 432x288 with 2 Axes>"
  222.       ]
  223.      },
  224.      "metadata": {
  225.       "needs_background": "light"
  226.      },
  227.      "output_type": "display_data"
  228.     }
  229.    ],
  230.    "source": [
  231.     "import numpy as np\n",
  232.     "import matplotlib.pyplot as plt\n",
  233.     "# Import another rendering engine\n",
  234.     "import seaborn as sns\n",
  235.     "\n",
  236.     "# Create the figure and two axes (two rows, one column)\n",
  237.     "fig, ax1 = plt.subplots(1, 1)\n",
  238.     "\n",
  239.     "# Share the x-axis for both the axes (ax1, ax2)\n",
  240.     "ax2 = ax1.twinx()\n",
  241.     "\n",
  242.     "# Create a plot of y = sin(x) on the first row\n",
  243.     "x1 = np.linspace(0, 4 * np.pi, 100)\n",
  244.     "y1 = np.sin(x1)\n",
  245.     "# Add a label for the legend and make it blue\n",
  246.     "function1 = ax1.plot(x1, y1, 'b', label='Sine')\n",
  247.     "\n",
  248.     "# Create a plot of y = cos(x) on the second row\n",
  249.     "x2 = np.linspace(0, 4 * np.pi, 100)\n",
  250.     "y2 = np.cos(x2)\n",
  251.     "# Add a label for the legend and make it red\n",
  252.     "function2 = ax2.plot(x2, y2, 'r', label='Cosine')\n",
  253.     "\n",
  254.     "# Create the legend by first fetching the labels from the functions\n",
  255.     "functions = function1 + function2\n",
  256.     "labels = [f.get_label() for f in functions]\n",
  257.     "plt.legend(functions, labels, loc=0)\n",
  258.     "\n",
  259.     "# Add x-label (only one, since it is shared) and the y-labels\n",
  260.     "ax1.set_xlabel('$x$')\n",
  261.     "ax1.set_ylabel('$y_1$')\n",
  262.     "ax2.set_ylabel('$y_2$')\n",
  263.     "\n",
  264.     "# Add the title\n",
  265.     "plt.title('Sine and Cosine')\n",
  266.     "\n",
  267.     "# Adjust the figure such that all rendering components fit inside the figure\n",
  268.     "plt.tight_layout()\n",
  269.     "\n",
  270.     "# Save the figure\n",
  271.     "plt.savefig('sin_cos_6.png')"
  272.    ]
  273.   },
  274.   {
  275.    "cell_type": "code",
  276.    "execution_count": null,
  277.    "metadata": {},
  278.    "outputs": [],
  279.    "source": []
  280.   }
  281.  ],
  282.  "metadata": {
  283.   "kernelspec": {
  284.    "display_name": "Python 3",
  285.    "language": "python",
  286.    "name": "python3"
  287.   },
  288.   "language_info": {
  289.    "codemirror_mode": {
  290.     "name": "ipython",
  291.     "version": 3
  292.    },
  293.    "file_extension": ".py",
  294.    "mimetype": "text/x-python",
  295.    "name": "python",
  296.    "nbconvert_exporter": "python",
  297.    "pygments_lexer": "ipython3",
  298.    "version": "3.6.8"
  299.   }
  300.  },
  301.  "nbformat": 4,
  302.  "nbformat_minor": 2
  303. }
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