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  {
   "source": [
    "## CartPole Skating\n",
    "\n",
    "> **Problem**: If Peter wants to escape from the wolf, he needs to be able to move faster than him. We will see how Peter can learn to skate, in particular, to keep balance, using Q-Learning.\n",
    "\n",
    "First, let's install the gym and import required libraries:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#code block 1"
   ]
  },
  {
   "source": [
    "## Create a cartpole environment"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "#code block 2"
   ],
   "cell_type": "code",
   "metadata": {},
   "execution_count": null,
   "outputs": []
  },
  {
   "source": [
    "To see how the environment works, let's run a short simulation for 100 steps."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "#code block 3"
   ],
   "cell_type": "code",
   "metadata": {},
   "execution_count": null,
   "outputs": []
  },
  {
   "source": [
    "During simulation, we need to get observations in order to decide how to act. In fact, `step` function returns us back current observations, reward function, and the `done` flag that indicates whether it makes sense to continue the simulation or not:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "#code block 4"
   ],
   "cell_type": "code",
   "metadata": {},
   "execution_count": null,
   "outputs": []
  },
  {
   "source": [
    "We can get min and max value of those numbers:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[-4.8000002e+00 -3.4028235e+38 -4.1887903e-01 -3.4028235e+38]\n[4.8000002e+00 3.4028235e+38 4.1887903e-01 3.4028235e+38]\n"
     ]
    }
   ],
   "source": [
    "#code block 5"
   ]
  },
  {
   "source": [
    "## State Discretization"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#code block 6"
   ]
  },
  {
   "source": [
    "Let's also explore other discretization method using bins:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Sample bins for interval (-5,5) with 10 bins\n [-5. -4. -3. -2. -1.  0.  1.  2.  3.  4.  5.]\n"
     ]
    }
   ],
   "source": [
    "#code block 7"
   ]
  },
  {
   "source": [
    "Let's now run a short simulation and observe those discrete environment values."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "(0, 0, -2, -2)\n(0, 1, -2, -5)\n(0, 2, -3, -8)\n(0, 3, -5, -11)\n(0, 3, -7, -14)\n(0, 4, -10, -17)\n(0, 3, -14, -15)\n(0, 3, -17, -12)\n(0, 3, -20, -16)\n(0, 4, -23, -19)\n"
     ]
    }
   ],
   "source": [
    "#code block 8"
   ]
  },
  {
   "source": [
    "## Q-Table Structure"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#code block 9"
   ]
  },
  {
   "source": [
    "## Let's Start Q-Learning!"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#code block 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0: 22.0, alpha=0.3, epsilon=0.9\n",
      "5000: 70.1384, alpha=0.3, epsilon=0.9\n",
      "10000: 121.8586, alpha=0.3, epsilon=0.9\n",
      "15000: 149.6368, alpha=0.3, epsilon=0.9\n",
      "20000: 168.2782, alpha=0.3, epsilon=0.9\n",
      "25000: 196.7356, alpha=0.3, epsilon=0.9\n",
      "30000: 220.7614, alpha=0.3, epsilon=0.9\n",
      "35000: 233.2138, alpha=0.3, epsilon=0.9\n",
      "40000: 248.22, alpha=0.3, epsilon=0.9\n",
      "45000: 264.636, alpha=0.3, epsilon=0.9\n",
      "50000: 276.926, alpha=0.3, epsilon=0.9\n",
      "55000: 277.9438, alpha=0.3, epsilon=0.9\n",
      "60000: 248.881, alpha=0.3, epsilon=0.9\n",
      "65000: 272.529, alpha=0.3, epsilon=0.9\n",
      "70000: 281.7972, alpha=0.3, epsilon=0.9\n",
      "75000: 284.2844, alpha=0.3, epsilon=0.9\n",
      "80000: 269.667, alpha=0.3, epsilon=0.9\n",
      "85000: 273.8652, alpha=0.3, epsilon=0.9\n",
      "90000: 278.2466, alpha=0.3, epsilon=0.9\n",
      "95000: 269.1736, alpha=0.3, epsilon=0.9\n"
     ]
    }
   ],
   "source": [
    "#code block 11"
   ]
  },
  {
   "source": [
    "## Plotting Training Progress"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
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     "output_type": "execute_result",
     "data": {
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     "execution_count": 20
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108.563315 90.206475 \r\nL 108.618101 199.087184 \r\nL 108.645494 123.955477 \r\nL 108.675931 111.098714 \r\nL 108.75811 203.90847 \r\nL 108.855507 101.456142 \r\nL 108.870725 152.883193 \r\nL 108.8829 201.096053 \r\nL 108.885944 102.25969 \r\nL 108.931599 110.69694 \r\nL 108.965079 67.70714 \r\nL 108.998559 209.533304 \r\nL 109.016821 157.302705 \r\nL 109.086826 203.104922 \r\nL 109.083782 85.786962 \r\nL 109.117262 140.829978 \r\nL 109.19031 17.083636 \r\nL 109.181179 201.096053 \r\nL 109.226834 167.347051 \r\nL 109.333363 211.542173 \r\nL 109.239009 110.69694 \r\nL 109.342494 210.738625 \r\nL 109.406411 121.946608 \r\nL 109.455109 139.222882 \r\nL 109.564681 208.729756 \r\nL 109.540332 117.527095 \r\nL 109.567725 166.141729 \r\nL 109.659035 74.537295 \r\nL 109.640773 211.542173 \r\nL 109.680341 152.883193 \r\nL 109.76252 211.140399 \r\nL 109.741214 110.69694 \r\nL 109.789913 152.883193 \r\nL 109.856874 212.747494 \r\nL 109.890354 91.81357 \r\nL 109.981664 210.336851 \r\nL 110.00297 190.649933 \r\nL 110.042537 102.25969 \r\nL 110.112542 169.35592 \r\nL 110.212983 195.872993 \r\nL 110.139935 103.465011 \r\nL 110.216026 145.651264 \r\nL 110.243419 95.831308 \r\nL 110.270812 211.542173 \r\nL 110.325598 112.705809 \r\nL 110.34386 197.881863 \r\nL 110.352991 107.080976 \r\nL 110.43517 127.973215 \r\nL 110.471694 116.723548 \r\nL 110.444301 191.453481 \r\nL 110.474738 148.061907 \r\nL 110.483869 212.345721 \r\nL 110.523437 66.903592 \r\nL 110.58431 125.562572 \r\nL 110.684751 208.327982 \r\nL 110.599528 113.911131 \r\nL 110.699969 168.552373 \r\nL 110.769974 93.822439 \r\nL 110.727362 196.274767 \r\nL 110.812585 133.999823 \r\nL 110.897808 212.345721 \r\nL 110.843022 55.653925 \r\nL 110.922157 129.982084 \r\nL 110.967812 109.893392 \r\nL 110.961725 176.989623 \r\nL 110.998249 119.937738 \r\nL 111.001292 209.13153 \r\nL 111.049991 109.491619 \r\nL 111.107821 112.705809 \r\nL 111.202174 206.319113 \r\nL 111.217393 162.927539 \r\nL 111.235655 100.25082 \r\nL 111.250873 191.855255 \r\nL 111.330008 138.821109 \r\nL 111.339139 143.642395 \r\nL 111.336096 115.518226 \r\nL 111.34827 139.222882 \r\nL 111.357401 98.241951 \r\nL 111.366532 197.881863 \r\nL 111.457842 138.017561 \r\nL 111.466973 212.747494 \r\nL 111.479148 95.027761 \r\nL 111.570458 170.159468 \r\nL 111.655681 98.241951 \r\nL 111.582633 182.212683 \r\nL 111.683074 159.713348 \r\nL 111.743947 107.080976 \r\nL 111.71351 191.051707 \r\nL 111.750034 176.989623 \r\nL 111.774384 195.069446 \r\nL 111.765253 126.36612 \r\nL 111.789602 135.205144 \r\nL 111.850475 102.25969 \r\nL 111.823082 210.336851 \r\nL 111.899174 123.955477 \r\nL 111.978309 195.47122 \r\nL 111.923523 103.465011 \r\nL 112.008746 119.535965 \r\nL 112.030052 207.122661 \r\nL 112.066576 56.457472 \r\nL 112.118318 171.364789 \r\nL 112.191366 76.947938 \r\nL 112.185279 197.881863 \r\nL 112.230934 115.92 \r\nL 112.276589 207.524435 \r\nL 112.337462 101.054368 \r\nL 112.349637 153.284967 \r\nL 112.370942 74.135521 \r\nL 112.367899 203.506696 \r\nL 112.459209 153.284967 \r\nL 112.489645 199.488958 \r\nL 112.556606 78.555033 \r\nL 112.562693 130.383858 \r\nL 112.599217 78.153259 \r\nL 112.571824 191.453481 \r\nL 112.666178 102.25969 \r\nL 112.772706 209.533304 \r\nL 112.769663 17.083636 \r\nL 112.778794 159.713348 \r\nL 112.812274 79.358581 \r\nL 112.803143 211.140399 \r\nL 112.894453 127.169667 \r\nL 112.976632 211.943947 \r\nL 112.912715 82.974545 \r\nL 113.004025 154.088514 \r\nL 113.070986 90.206475 \r\nL 113.067942 212.345721 \r\nL 113.110553 168.552373 \r\nL 113.171427 204.310244 \r\nL 113.159252 93.822439 \r\nL 113.210994 126.36612 \r\nL 113.226213 46.8149 \r\nL 113.256649 203.506696 \r\nL 113.311435 139.222882 \r\nL 113.408833 207.926208 \r\nL 113.390571 44.404257 \r\nL 113.421007 168.552373 \r\nL 113.436226 94.224213 \r\nL 113.497099 192.257029 \r\nL 113.530579 136.812239 \r\nL 113.603627 205.917339 \r\nL 113.588409 32.351042 \r\nL 113.634064 158.106253 \r\nL 113.637108 72.528426 \r\nL 113.734505 190.649933 \r\nL 113.743636 158.508027 \r\nL 113.801466 196.274767 \r\nL 113.758854 49.627317 \r\nL 113.850164 150.874324 \r\nL 113.862339 94.224213 \r\nL 113.898863 210.336851 \r\nL 113.956693 115.116452 \r\nL 113.984086 194.667672 \r\nL 114.002348 86.188736 \r\nL 114.069308 161.320443 \r\nL 114.102789 199.087184 \r\nL 114.139313 70.117783 \r\nL 114.163662 134.401596 \r\nL 114.215404 82.170998 \r\nL 114.251928 203.90847 \r\nL 114.273234 158.106253 \r\nL 114.32802 109.089845 \r\nL 114.358457 195.47122 \r\nL 114.382806 133.196275 \r\nL 114.422374 198.68541 \r\nL 114.449767 113.509357 \r\nL 114.486291 127.973215 \r\nL 114.56847 17.083636 \r\nL 114.538033 202.301375 \r\nL 114.592819 111.098714 \r\nL 114.620212 213.551042 \r\nL 114.611081 59.269889 \r\nL 114.702391 180.605588 \r\nL 114.711522 82.572772 \r\nL 114.708478 203.90847 \r\nL 114.815007 132.794501 \r\nL 114.827181 191.051707 \r\nL 114.903273 56.859246 \r\nL 114.921535 177.793171 \r\nL 114.982408 70.519557 \r\nL 114.930666 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117.676054 183.418004 \r\nL 117.779538 123.955477 \r\nL 117.785626 176.587849 \r\nL 117.803888 17.083636 \r\nL 117.870848 77.349712 \r\nL 117.873892 27.93153 \r\nL 117.943896 178.998492 \r\nL 117.974333 86.188736 \r\nL 117.977377 193.864124 \r\nL 117.989551 17.083636 \r\nL 118.086949 163.329313 \r\nL 118.120429 21.904922 \r\nL 118.175215 197.078315 \r\nL 118.190433 188.641064 \r\nL 118.233045 205.515565 \r\nL 118.223914 34.359911 \r\nL 118.284787 130.785632 \r\nL 118.318267 78.956807 \r\nL 118.324355 190.649933 \r\nL 118.394359 100.25082 \r\nL 118.497844 200.292506 \r\nL 118.415665 99.447273 \r\nL 118.503931 107.482749 \r\nL 118.506975 108.688071 \r\nL 118.531324 211.943947 \r\nL 118.589154 34.761685 \r\nL 118.616547 100.25082 \r\nL 118.680464 197.078315 \r\nL 118.665245 21.503149 \r\nL 118.726119 141.231752 \r\nL 118.796123 64.091175 \r\nL 118.805254 195.47122 \r\nL 118.835691 132.392727 \r\nL 118.939175 163.731086 \r\nL 118.89352 80.965676 \r\nL 118.945263 149.267228 \r\nL 118.966568 21.503149 \r\nL 119.033529 212.747494 \r\nL 119.051791 169.35592 \r\nL 119.143101 203.90847 \r\nL 119.127883 45.609579 \r\nL 119.155276 163.329313 \r\nL 119.252673 17.083636 \r\nL 119.161363 209.13153 \r\nL 119.270935 82.170998 \r\nL 119.307459 194.265898 \r\nL 119.334852 74.537295 \r\nL 119.383551 133.196275 \r\nL 119.392682 31.949268 \r\nL 119.435293 190.649933 \r\nL 119.487035 123.553703 \r\nL 119.59052 200.292506 \r\nL 119.55704 75.340843 \r\nL 119.596607 134.80337 \r\nL 119.630088 189.444612 \r\nL 119.605738 93.822439 \r\nL 119.703136 122.750155 \r\nL 119.706179 122.348381 \r\nL 119.71531 133.999823 \r\nL 119.748791 201.096053 \r\nL 119.727485 67.70714 \r\nL 119.824882 143.642395 \r\nL 119.919236 106.277428 \r\nL 119.858363 203.104922 \r\nL 119.934454 146.856585 \r\nL 120.034895 204.310244 \r\nL 119.958804 84.179867 \r\nL 120.037939 125.160798 \r\nL 120.089681 86.59051 \r\nL 120.044026 207.524435 \r\nL 120.114031 119.937738 \r\nL 120.153598 202.703149 \r\nL 120.168817 61.278758 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121.611515 180.203814 \r\nL 121.614558 68.108914 \r\nL 121.635864 80.563902 \r\nL 121.745436 203.90847 \r\nL 121.644995 74.537295 \r\nL 121.751523 181.810909 \r\nL 121.763698 44.404257 \r\nL 121.842833 190.24816 \r\nL 121.861095 138.419335 \r\nL 121.903707 206.319113 \r\nL 121.918925 34.359911 \r\nL 121.955449 107.482749 \r\nL 121.958493 37.975876 \r\nL 121.991973 208.729756 \r\nL 122.061977 119.535965 \r\nL 122.098501 185.0251 \r\nL 122.138069 28.735078 \r\nL 122.171549 153.284967 \r\nL 122.275034 76.14439 \r\nL 122.177637 195.069446 \r\nL 122.281121 150.070776 \r\nL 122.372431 95.831308 \r\nL 122.293296 201.497827 \r\nL 122.393737 98.241951 \r\nL 122.463741 206.720887 \r\nL 122.427217 86.992284 \r\nL 122.503309 94.224213 \r\nL 122.515484 198.283636 \r\nL 122.57027 44.002483 \r\nL 122.615925 167.748825 \r\nL 122.701147 69.314235 \r\nL 122.722453 194.667672 \r\nL 122.731584 77.751486 \r\nL 122.768108 199.890732 \r\nL 122.780283 54.448603 \r\nL 122.847243 161.722217 \r\nL 122.880724 50.430865 \r\nL 122.853331 187.837517 \r\nL 122.956815 72.528426 \r\nL 122.962903 205.917339 \r\nL 123.02682 64.492949 \r\nL 123.069431 175.784302 \r\nL 123.121173 73.733747 \r\nL 123.154654 209.935078 \r\nL 123.179003 150.47255 \r\nL 123.18509 200.694279 \r\nL 123.200309 60.073437 \r\nL 123.282488 151.677871 \r\nL 123.285531 57.26102 \r\nL 123.361623 207.524435 \r\nL 123.395103 101.054368 \r\nL 123.489457 197.480089 \r\nL 123.422496 71.323104 \r\nL 123.504675 163.329313 \r\nL 123.547287 90.206475 \r\nL 123.586854 193.060576 \r\nL 123.614247 133.999823 \r\nL 123.647728 75.742616 \r\nL 123.723819 203.104922 \r\nL 123.763387 81.36745 \r\nL 123.836435 114.714678 \r\nL 123.897308 197.480089 \r\nL 123.942963 17.083636 \r\nL 124.028186 198.68541 \r\nL 124.052535 136.410466 \r\nL 124.152976 65.296497 \r\nL 124.107321 200.292506 \r\nL 124.165151 95.429534 \r\nL 124.171238 110.69694 \r\nL 124.177326 78.956807 \r\nL 124.232112 211.140399 \r\nL 124.286898 166.543503 \r\nL 124.393426 94.625987 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125.656548 212.345721 \r\nL 125.738727 132.392727 \r\nL 125.811775 195.872993 \r\nL 125.805688 47.216674 \r\nL 125.817862 130.383858 \r\nL 125.820906 33.958137 \r\nL 125.924391 194.667672 \r\nL 125.991351 17.083636 \r\nL 125.970046 202.301375 \r\nL 126.046137 122.750155 \r\nL 126.137447 186.230421 \r\nL 126.122229 70.519557 \r\nL 126.155709 132.794501 \r\nL 126.16484 85.786962 \r\nL 126.177015 195.069446 \r\nL 126.259194 131.187406 \r\nL 126.271369 203.104922 \r\nL 126.353548 85.786962 \r\nL 126.37181 178.998492 \r\nL 126.453989 86.992284 \r\nL 126.472251 209.533304 \r\nL 126.55443 81.769224 \r\nL 126.584866 133.196275 \r\nL 126.633565 199.087184 \r\nL 126.603128 63.689401 \r\nL 126.694438 104.268559 \r\nL 126.706613 209.13153 \r\nL 126.7127 70.117783 \r\nL 126.807054 158.9098 \r\nL 126.886189 78.153259 \r\nL 126.840534 201.497827 \r\nL 126.916626 132.392727 \r\nL 127.001849 201.497827 \r\nL 126.931844 82.974545 \r\nL 127.023154 138.017561 \r\nL 127.074897 102.661463 \r\nL 127.111421 205.917339 \r\nL 127.13577 107.080976 \r\nL 127.150988 168.954146 \r\nL 127.199687 74.135521 \r\nL 127.248386 141.231752 \r\nL 127.26056 193.864124 \r\nL 127.312303 88.599379 \r\nL 127.354914 184.623326 \r\nL 127.370132 44.806031 \r\nL 127.418831 195.872993 \r\nL 127.464486 155.69561 \r\nL 127.50101 210.336851 \r\nL 127.546665 41.59184 \r\nL 127.567971 136.410466 \r\nL 127.589276 62.082306 \r\nL 127.59232 204.310244 \r\nL 127.677543 115.518226 \r\nL 127.695805 77.349712 \r\nL 127.74146 185.0251 \r\nL 127.759722 17.083636 \r\nL 127.851032 68.510687 \r\nL 127.878425 199.087184 \r\nL 127.887556 17.083636 \r\nL 127.963647 145.24949 \r\nL 128.061045 41.59184 \r\nL 128.064088 212.747494 \r\nL 128.073219 42.395388 \r\nL 128.109743 184.623326 \r\nL 128.1067 17.083636 \r\nL 128.185835 143.240621 \r\nL 128.201053 89.001153 \r\nL 128.252796 195.47122 \r\nL 128.295407 111.098714 \r\nL 128.3228 189.042838 \r\nL 128.383673 41.190067 \r\nL 128.404979 152.481419 \r\nL 128.462809 32.351042 \r\nL 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32.351042 \r\nL 136.601574 148.061907 \r\nL 136.616792 17.083636 \r\nL 136.653316 211.140399 \r\nL 136.711146 138.017561 \r\nL 136.772019 188.641064 \r\nL 136.74767 64.492949 \r\nL 136.817674 136.008692 \r\nL 136.90594 69.716009 \r\nL 136.881591 182.212683 \r\nL 136.924202 111.500488 \r\nL 136.978988 195.47122 \r\nL 137.009425 56.055698 \r\nL 137.033774 76.546164 \r\nL 137.097691 51.234412 \r\nL 137.106822 195.47122 \r\nL 137.152477 17.083636 \r\nL 137.219438 93.822439 \r\nL 137.2377 206.319113 \r\nL 137.286399 22.306696 \r\nL 137.325966 68.912461 \r\nL 137.395971 17.887184 \r\nL 137.347272 191.453481 \r\nL 137.435538 42.797162 \r\nL 137.459888 193.060576 \r\nL 137.548154 87.795831 \r\nL 137.599896 66.903592 \r\nL 137.581634 211.542173 \r\nL 137.621202 141.633525 \r\nL 137.721643 209.935078 \r\nL 137.691206 17.083636 \r\nL 137.72773 114.312905 \r\nL 137.809909 193.46235 \r\nL 137.840346 66.501818 \r\nL 137.898176 205.515565 \r\nL 137.952962 166.141729 \r\nL 138.004704 29.940399 \r\nL 137.974267 202.301375 \r\nL 138.065577 105.072106 \r\nL 138.141669 199.488958 \r\nL 138.102101 73.733747 \r\nL 138.147756 113.911131 \r\nL 138.196455 17.083636 \r\nL 138.214717 207.926208 \r\nL 138.257328 56.055698 \r\nL 138.327333 200.694279 \r\nL 138.269503 17.083636 \r\nL 138.3669 191.855255 \r\nL 138.369944 71.724878 \r\nL 138.439948 197.480089 \r\nL 138.479516 107.884523 \r\nL 138.48256 190.649933 \r\nL 138.500822 45.609579 \r\nL 138.592132 148.865455 \r\nL 138.598219 22.306696 \r\nL 138.601263 210.738625 \r\nL 138.704747 119.535965 \r\nL 138.723009 210.336851 \r\nL 138.786926 91.81357 \r\nL 138.814319 165.739956 \r\nL 138.875193 80.162129 \r\nL 138.844756 194.265898 \r\nL 138.923891 154.892062 \r\nL 138.987808 213.149268 \r\nL 138.993896 75.742616 \r\nL 139.036507 191.453481 \r\nL 139.060856 71.323104 \r\nL 139.146079 183.418004 \r\nL 139.173472 67.305366 \r\nL 139.152166 196.274767 \r\nL 139.276957 143.642395 \r\nL 139.359136 195.069446 \r\nL 139.286088 25.520887 \r\nL 139.383485 125.562572 \r\nL 139.416965 66.100044 \r\nL 139.39566 206.720887 \r\nL 139.477839 72.528426 \r\nL 139.569149 17.083636 \r\nL 139.590454 204.310244 \r\nL 139.593498 206.319113 \r\nL 139.596542 164.13286 \r\nL 139.64524 17.083636 \r\nL 139.706114 189.042838 \r\nL 139.709157 111.500488 \r\nL 139.773074 17.083636 \r\nL 139.721332 195.872993 \r\nL 139.800467 132.392727 \r\nL 139.897865 197.480089 \r\nL 139.82786 89.804701 \r\nL 139.906996 171.766563 \r\nL 139.910039 58.868115 \r\nL 139.937432 197.881863 \r\nL 140.019612 79.760355 \r\nL 140.113965 195.872993 \r\nL 140.110922 17.083636 \r\nL 140.138315 172.168337 \r\nL 140.141358 74.135521 \r\nL 140.241799 213.952816 \r\nL 140.247887 101.456142 \r\nL 140.263105 208.729756 \r\nL 140.323978 19.494279 \r\nL 140.357459 101.857916 \r\nL 140.360502 103.465011 \r\nL 140.363546 77.751486 \r\nL 140.467031 212.747494 \r\nL 140.372677 46.413126 \r\nL 140.473118 127.571441 \r\nL 140.537035 65.296497 \r\nL 140.488336 195.872993 \r\nL 140.576603 182.212683 \r\nL 140.649651 195.069446 \r\nL 140.613127 74.135521 \r\nL 140.652694 174.57898 \r\nL 140.704437 51.636186 \r\nL 140.674 201.096053 \r\nL 140.76531 133.598049 \r\nL 140.832271 195.872993 \r\nL 140.847489 76.14439 \r\nL 140.874882 188.23929 \r\nL 140.887057 55.252151 \r\nL 140.963148 203.90847 \r\nL 140.987498 135.205144 \r\nL 141.087939 206.720887 \r\nL 141.002716 22.70847 \r\nL 141.09707 189.042838 \r\nL 141.197511 62.885854 \r\nL 141.194467 194.265898 \r\nL 141.206642 74.537295 \r\nL 141.218816 183.819778 \r\nL 141.319257 136.812239 \r\nL 141.352738 17.083636 \r\nL 141.419698 199.087184 \r\nL 141.498834 17.083636 \r\nL 141.489703 211.140399 \r\nL 141.532314 80.965676 \r\nL 141.608406 199.890732 \r\nL 141.611449 17.887184 \r\nL 141.641886 78.956807 \r\nL 141.675366 210.336851 \r\nL 141.672323 17.083636 \r\nL 141.751458 115.92 \r\nL 141.787982 17.083636 \r\nL 141.839724 205.917339 \r\nL 141.864074 99.849047 \r\nL 141.964515 189.846386 \r\nL 141.897554 48.020222 \r\nL 141.973646 169.757694 \r\nL 141.98582 37.574102 \r\nL 142.064956 184.221552 \r\nL 142.089305 38.779424 \r\nL 142.159309 194.265898 \r\nL 142.119742 31.949268 \r\nL 142.201921 134.80337 \r\nL 142.241488 46.413126 \r\nL 142.232357 203.506696 \r\nL 142.265838 93.420665 \r\nL 142.320624 199.087184 \r\nL 142.332798 48.823769 \r\nL 142.37541 111.098714 \r\nL 142.478894 199.890732 \r\nL 142.396715 48.020222 \r\nL 142.484982 120.741286 \r\nL 142.488025 21.503149 \r\nL 142.503244 201.497827 \r\nL 142.59151 74.939069 \r\nL 142.597597 203.506696 \r\nL 142.701082 53.645055 \r\nL 142.704126 146.454812 \r\nL 142.743693 44.002483 \r\nL 142.801523 186.230421 \r\nL 142.813698 87.394058 \r\nL 142.868484 199.890732 \r\nL 142.850222 52.841508 \r\nL 142.926313 193.46235 \r\nL 142.944575 65.698271 \r\nL 142.965881 193.864124 \r\nL 143.035885 142.437073 \r\nL 143.066322 194.265898 \r\nL 143.072409 66.501818 \r\nL 143.142414 93.822439 \r\nL 143.215462 202.301375 \r\nL 143.233724 80.965676 \r\nL 143.255029 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163.440628 100.652594 \r\nL 163.468021 203.90847 \r\nL 163.519763 56.055698 \r\nL 163.5502 197.881863 \r\nL 163.574549 17.083636 \r\nL 163.604986 203.90847 \r\nL 163.662815 71.724878 \r\nL 163.690208 206.720887 \r\nL 163.684121 17.083636 \r\nL 163.772387 103.866785 \r\nL 163.854566 32.752816 \r\nL 163.805868 199.488958 \r\nL 163.878916 133.196275 \r\nL 163.979357 195.872993 \r\nL 163.976313 30.743947 \r\nL 163.988488 113.509357 \r\nL 164.09806 193.46235 \r\nL 164.031099 17.083636 \r\nL 164.101103 135.606918 \r\nL 164.201544 31.145721 \r\nL 164.113278 207.926208 \r\nL 164.210675 71.323104 \r\nL 164.31416 207.122661 \r\nL 164.216763 18.690732 \r\nL 164.323291 140.428204 \r\nL 164.390252 21.904922 \r\nL 164.344597 204.310244 \r\nL 164.423732 126.36612 \r\nL 164.499824 198.283636 \r\nL 164.472431 34.761685 \r\nL 164.533304 129.178537 \r\nL 164.606352 201.899601 \r\nL 164.591134 47.216674 \r\nL 164.609396 197.078315 \r\nL 164.694618 18.690732 \r\nL 164.655051 206.319113 \r\nL 164.718968 191.453481 \r\nL 164.725055 25.520887 \r\nL 164.764623 203.506696 \r\nL 164.822452 191.855255 \r\nL 164.82854 211.943947 \r\nL 164.871151 17.083636 \r\nL 164.913762 175.382528 \r\nL 165.020291 17.083636 \r\nL 164.980723 203.104922 \r\nL 165.023334 95.429534 \r\nL 165.07812 189.444612 \r\nL 165.126819 17.083636 \r\nL 165.132906 76.546164 \r\nL 165.199867 205.515565 \r\nL 165.166387 17.083636 \r\nL 165.239435 132.794501 \r\nL 165.263784 17.083636 \r\nL 165.291177 188.23929 \r\nL 165.349007 118.330643 \r\nL 165.419011 207.926208 \r\nL 165.358138 28.735078 \r\nL 165.458579 129.982084 \r\nL 165.476841 20.699601 \r\nL 165.470753 195.069446 \r\nL 165.571194 69.314235 \r\nL 165.671635 195.47122 \r\nL 165.629024 30.743947 \r\nL 165.680766 82.974545 \r\nL 165.756858 17.083636 \r\nL 165.711203 196.676541 \r\nL 165.769033 118.330643 \r\nL 165.772076 200.694279 \r\nL 165.842081 17.083636 \r\nL 165.878605 103.465011 \r\nL 165.963827 17.083636 \r\nL 165.933391 200.694279 \r\nL 165.988177 51.234412 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198.68541 \r\nL 167.330434 17.083636 \r\nL 167.406525 97.03663 \r\nL 167.479573 17.083636 \r\nL 167.513054 202.703149 \r\nL 167.516097 70.92133 \r\nL 167.549578 209.935078 \r\nL 167.625669 125.160798 \r\nL 167.689586 203.104922 \r\nL 167.637844 44.002483 \r\nL 167.735241 160.91867 \r\nL 167.850901 29.538625 \r\nL 167.771765 197.881863 \r\nL 167.853944 87.394058 \r\nL 167.860032 195.069446 \r\nL 167.863075 42.395388 \r\nL 167.963516 84.983415 \r\nL 167.972647 190.24816 \r\nL 168.030477 54.448603 \r\nL 168.070045 87.795831 \r\nL 168.076132 209.935078 \r\nL 168.179617 17.083636 \r\nL 168.210053 185.426874 \r\nL 168.292232 103.866785 \r\nL 168.316582 206.720887 \r\nL 168.347018 34.359911 \r\nL 168.410935 171.364789 \r\nL 168.496158 17.083636 \r\nL 168.490071 201.899601 \r\nL 168.532682 112.705809 \r\nL 168.544857 200.694279 \r\nL 168.623992 33.15459 \r\nL 168.63921 108.286297 \r\nL 168.733564 59.269889 \r\nL 168.721389 200.694279 \r\nL 168.748782 74.939069 \r\nL 168.815743 193.46235 \r\nL 168.764001 39.984745 \r\nL 168.861398 144.044169 \r\nL 168.940533 35.163459 \r\nL 168.964883 184.221552 \r\nL 168.97097 88.599379 \r\nL 169.037931 199.087184 \r\nL 169.010538 41.190067 \r\nL 169.083586 150.874324 \r\nL 169.092717 48.421996 \r\nL 169.174896 193.46235 \r\nL 169.199245 86.59051 \r\nL 169.284468 196.676541 \r\nL 169.2449 56.055698 \r\nL 169.308817 91.81357 \r\nL 169.366647 63.689401 \r\nL 169.397083 197.881863 \r\nL 169.409258 78.153259 \r\nL 169.506655 191.855255 \r\nL 169.439695 23.913792 \r\nL 169.521874 136.008692 \r\nL 169.534048 30.743947 \r\nL 169.57666 207.524435 \r\nL 169.634489 36.36878 \r\nL 169.710581 194.265898 \r\nL 169.646664 17.083636 \r\nL 169.747105 191.051707 \r\nL 169.847546 27.529756 \r\nL 169.862764 50.430865 \r\nL 169.877983 195.47122 \r\nL 169.957118 17.083636 \r\nL 169.972336 129.982084 \r\nL 170.027122 17.083636 \r\nL 170.036253 193.864124 \r\nL 170.084952 73.331973 \r\nL 170.151913 207.926208 \r\nL 170.121476 17.083636 \r\nL 170.194524 141.231752 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126.767894 \r\nL 171.515476 194.667672 \r\nL 171.491126 32.752816 \r\nL 171.536781 186.632195 \r\nL 171.573305 37.975876 \r\nL 171.555043 193.060576 \r\nL 171.649397 112.304035 \r\nL 171.743751 203.104922 \r\nL 171.737663 28.333304 \r\nL 171.752882 82.572772 \r\nL 171.755925 17.083636 \r\nL 171.853323 197.480089 \r\nL 171.862454 87.394058 \r\nL 171.956807 17.083636 \r\nL 171.938545 182.614457 \r\nL 171.962895 144.445942 \r\nL 171.981157 197.078315 \r\nL 172.038986 17.083636 \r\nL 172.063336 39.984745 \r\nL 172.069423 83.778093 \r\nL 172.072467 17.083636 \r\nL 172.084641 205.917339 \r\nL 172.185082 127.169667 \r\nL 172.197257 34.359911 \r\nL 172.248999 193.060576 \r\nL 172.294654 109.089845 \r\nL 172.297698 200.694279 \r\nL 172.328135 17.083636 \r\nL 172.401183 174.57898 \r\nL 172.504667 17.083636 \r\nL 172.462056 197.881863 \r\nL 172.513798 84.983415 \r\nL 172.516842 83.376319 \r\nL 172.599021 191.051707 \r\nL 172.58989 17.083636 \r\nL 172.62337 127.973215 \r\nL 172.644676 17.083636 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17.083636 \r\nL 174.148247 207.122661 \r\nL 174.178684 195.872993 \r\nL 174.23347 40.788293 \r\nL 174.19999 200.694279 \r\nL 174.303474 55.653925 \r\nL 174.306518 208.729756 \r\nL 174.364348 17.083636 \r\nL 174.413046 103.063237 \r\nL 174.443483 190.649933 \r\nL 174.431308 49.225543 \r\nL 174.525662 122.348381 \r\nL 174.574361 17.083636 \r\nL 174.562186 181.409135 \r\nL 174.63219 144.847716 \r\nL 174.711326 194.265898 \r\nL 174.708282 56.055698 \r\nL 174.7235 102.25969 \r\nL 174.753937 28.333304 \r\nL 174.763068 161.320443 \r\nL 174.833072 110.69694 \r\nL 174.912208 50.832639 \r\nL 174.857422 207.524435 \r\nL 174.936557 115.518226 \r\nL 174.988299 203.104922 \r\nL 175.024823 40.788293 \r\nL 175.043085 181.810909 \r\nL 175.046129 47.216674 \r\nL 175.155701 75.742616 \r\nL 175.240924 201.497827 \r\nL 175.189181 39.181197 \r\nL 175.268317 130.785632 \r\nL 175.36267 29.136851 \r\nL 175.280491 166.543503 \r\nL 175.377889 125.562572 \r\nL 175.426587 24.315565 \r\nL 175.396151 199.890732 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196.676541 \r\nL 176.921028 98.241951 \r\nL 177.009294 208.327982 \r\nL 176.933202 17.083636 \r\nL 177.027556 137.214013 \r\nL 177.033643 17.083636 \r\nL 177.036687 208.327982 \r\nL 177.137128 99.447273 \r\nL 177.191914 212.747494 \r\nL 177.167565 34.761685 \r\nL 177.249744 183.819778 \r\nL 177.350185 17.083636 \r\nL 177.316704 199.890732 \r\nL 177.362359 86.59051 \r\nL 177.417145 207.122661 \r\nL 177.411058 37.975876 \r\nL 177.444538 119.134191 \r\nL 177.535848 17.083636 \r\nL 177.481062 203.506696 \r\nL 177.55411 83.778093 \r\nL 177.602809 201.096053 \r\nL 177.566285 17.083636 \r\nL 177.663682 152.883193 \r\nL 177.691075 26.324435 \r\nL 177.748905 201.899601 \r\nL 177.776298 133.999823 \r\nL 177.79456 61.278758 \r\nL 177.800647 201.096053 \r\nL 177.873695 125.160798 \r\nL 177.876739 209.13153 \r\nL 177.971093 41.59184 \r\nL 177.986311 184.623326 \r\nL 178.065447 17.083636 \r\nL 178.016748 205.113792 \r\nL 178.095883 83.376319 \r\nL 178.114145 192.257029 \r\nL 178.168931 17.083636 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205.515565 \r\nL 179.581193 41.190067 \r\nL 179.599455 197.078315 \r\nL 179.608586 37.172328 \r\nL 179.693808 189.444612 \r\nL 179.699896 17.083636 \r\nL 179.775987 205.113792 \r\nL 179.80338 92.617118 \r\nL 179.903821 207.122661 \r\nL 179.845992 17.083636 \r\nL 179.912952 198.283636 \r\nL 179.992088 33.15459 \r\nL 179.943389 202.703149 \r\nL 180.022524 42.395388 \r\nL 180.083398 202.301375 \r\nL 180.049917 17.083636 \r\nL 180.13514 99.045499 \r\nL 180.211232 193.060576 \r\nL 180.162533 21.904922 \r\nL 180.22645 189.042838 \r\nL 180.28428 17.083636 \r\nL 180.244712 193.864124 \r\nL 180.339066 94.224213 \r\nL 180.418201 178.194945 \r\nL 180.402983 17.083636 \r\nL 180.451681 123.553703 \r\nL 180.527773 197.480089 \r\nL 180.53386 37.975876 \r\nL 180.576472 17.083636 \r\nL 180.564297 196.676541 \r\nL 180.628214 73.331973 \r\nL 180.661694 201.096053 \r\nL 180.734742 19.494279 \r\nL 180.74083 191.855255 \r\nL 180.819965 39.984745 \r\nL 180.853445 113.107583 \r\nL 180.862576 190.24816 \r\nL 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188.155202 17.083636 \r\nL 188.200857 196.676541 \r\nL 188.255643 188.641064 \r\nL 188.368259 17.083636 \r\nL 188.301298 209.935078 \r\nL 188.380433 20.297827 \r\nL 188.471743 189.444612 \r\nL 188.413914 17.083636 \r\nL 188.490005 88.599379 \r\nL 188.584359 17.083636 \r\nL 188.496093 198.283636 \r\nL 188.59349 167.347051 \r\nL 188.602621 189.444612 \r\nL 188.611752 103.465011 \r\nL 188.614796 17.083636 \r\nL 188.715237 199.890732 \r\nL 188.721324 58.868115 \r\nL 188.785241 192.658803 \r\nL 188.782197 42.797162 \r\nL 188.830896 120.339512 \r\nL 188.83394 25.119113 \r\nL 188.910031 194.265898 \r\nL 188.937424 188.641064 \r\nL 188.943512 190.24816 \r\nL 188.949599 153.686741 \r\nL 189.007429 74.135521 \r\nL 189.034822 198.283636 \r\nL 189.05004 124.759024 \r\nL 189.08352 197.881863 \r\nL 189.120044 17.083636 \r\nL 189.159612 155.293836 \r\nL 189.171787 17.083636 \r\nL 189.202223 193.060576 \r\nL 189.269184 156.900931 \r\nL 189.272228 192.257029 \r\nL 189.360494 49.627317 \r\nL 189.372669 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190.60231 187.435743 \r\nL 190.644921 26.726208 \r\nL 190.711882 169.35592 \r\nL 190.7271 19.896053 \r\nL 190.809279 190.24816 \r\nL 190.827541 91.411796 \r\nL 190.885371 17.887184 \r\nL 190.873196 205.917339 \r\nL 190.894502 157.704479 \r\nL 190.90972 190.649933 \r\nL 190.961463 27.127982 \r\nL 190.964506 119.535965 \r\nL 191.067991 17.083636 \r\nL 190.979725 201.497827 \r\nL 191.077122 31.547494 \r\nL 191.089297 17.083636 \r\nL 191.095384 157.302705 \r\nL 191.125821 89.804701 \r\nL 191.147126 185.0251 \r\nL 191.162345 17.083636 \r\nL 191.235393 78.956807 \r\nL 191.293222 17.083636 \r\nL 191.311484 210.738625 \r\nL 191.344965 26.726208 \r\nL 191.36627 186.230421 \r\nL 191.454537 22.306696 \r\nL 191.45758 89.001153 \r\nL 191.54889 17.083636 \r\nL 191.494104 206.319113 \r\nL 191.564109 160.115122 \r\nL 191.570196 198.68541 \r\nL 191.673681 17.083636 \r\nL 191.682812 89.804701 \r\nL 191.701074 202.703149 \r\nL 191.69803 17.083636 \r\nL 191.792384 109.089845 \r\nL 191.834995 17.083636 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17.083636 \r\nL 193.238126 211.542173 \r\nL 193.283781 119.535965 \r\nL 193.286824 194.265898 \r\nL 193.320305 17.083636 \r\nL 193.390309 174.57898 \r\nL 193.45727 39.582971 \r\nL 193.408571 197.881863 \r\nL 193.502925 56.859246 \r\nL 193.52423 188.641064 \r\nL 193.554667 17.083636 \r\nL 193.618584 144.847716 \r\nL 193.712938 17.083636 \r\nL 193.685545 192.257029 \r\nL 193.7312 62.082306 \r\nL 193.743374 19.494279 \r\nL 193.749462 138.821109 \r\nL 193.758593 25.119113 \r\nL 193.807291 205.113792 \r\nL 193.789029 17.083636 \r\nL 193.868165 46.8149 \r\nL 193.968606 178.194945 \r\nL 193.883383 17.083636 \r\nL 193.977737 59.269889 \r\nL 194.011217 191.051707 \r\nL 194.062959 34.359911 \r\nL 194.081221 120.741286 \r\nL 194.1634 17.083636 \r\nL 194.154269 162.123991 \r\nL 194.190793 129.178537 \r\nL 194.291234 184.623326 \r\nL 194.22123 17.083636 \r\nL 194.297322 178.596718 \r\nL 194.379501 17.083636 \r\nL 194.306453 209.533304 \r\nL 194.406894 111.500488 \r\nL 194.482985 184.221552 \r\nL 194.449505 24.315565 \r\nL 194.49516 102.661463 \r\nL 194.556033 17.083636 \r\nL 194.537771 203.506696 \r\nL 194.601688 176.989623 \r\nL 194.604732 185.0251 \r\nL 194.632125 17.083636 \r\nL 194.665605 116.723548 \r\nL 194.686911 17.083636 \r\nL 194.67778 207.122661 \r\nL 194.775177 41.190067 \r\nL 194.872575 181.409135 \r\nL 194.793439 17.083636 \r\nL 194.884749 123.955477 \r\nL 194.988234 48.823769 \r\nL 194.976059 196.274767 \r\nL 194.997365 75.742616 \r\nL 195.067369 209.935078 \r\nL 195.036933 17.083636 \r\nL 195.106937 208.729756 \r\nL 195.201291 23.110244 \r\nL 195.222596 60.475211 \r\nL 195.295644 17.083636 \r\nL 195.313906 192.658803 \r\nL 195.329125 80.563902 \r\nL 195.383911 198.283636 \r\nL 195.420435 17.083636 \r\nL 195.438697 140.02643 \r\nL 195.542181 17.083636 \r\nL 195.469133 193.060576 \r\nL 195.548269 133.999823 \r\nL 195.551312 202.301375 \r\nL 195.645666 17.083636 \r\nL 195.654797 62.48408 \r\nL 195.71567 17.083636 \r\nL 195.700452 192.257029 \r\nL 195.74002 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51.636186 \r\nL 330.930568 164.13286 \r\nL 330.994485 63.689401 \r\nL 330.970136 197.881863 \r\nL 331.043184 113.911131 \r\nL 331.101013 59.269889 \r\nL 331.13145 192.257029 \r\nL 331.143625 140.02643 \r\nL 331.213629 200.292506 \r\nL 331.22276 49.627317 \r\nL 331.234935 174.980754 \r\nL 331.317114 38.779424 \r\nL 331.262328 199.488958 \r\nL 331.344507 81.36745 \r\nL 331.435817 199.890732 \r\nL 331.444948 50.832639 \r\nL 331.454079 185.0251 \r\nL 331.551476 43.198936 \r\nL 331.536258 208.729756 \r\nL 331.566694 101.456142 \r\nL 331.578869 193.864124 \r\nL 331.633655 76.14439 \r\nL 331.64583 93.018891 \r\nL 331.648873 21.503149 \r\nL 331.664092 202.703149 \r\nL 331.755402 46.8149 \r\nL 331.816275 210.336851 \r\nL 331.831493 46.011353 \r\nL 331.868017 153.284967 \r\nL 331.962371 17.083636 \r\nL 331.910629 201.096053 \r\nL 331.977589 82.974545 \r\nL 332.059768 194.265898 \r\nL 331.989764 58.064568 \r\nL 332.090205 170.963016 \r\nL 332.117598 23.512018 \r\nL 332.141947 188.23929 \r\nL 332.202821 102.661463 \r\nL 332.236301 199.488958 \r\nL 332.306305 31.547494 \r\nL 332.358048 17.083636 \r\nL 332.415877 204.712018 \r\nL 332.522406 17.083636 \r\nL 332.491969 209.533304 \r\nL 332.531537 43.60071 \r\nL 332.635021 209.533304 \r\nL 332.543711 17.083636 \r\nL 332.644152 87.795831 \r\nL 332.711113 44.002483 \r\nL 332.662414 199.890732 \r\nL 332.735462 117.928869 \r\nL 332.738506 196.274767 \r\nL 332.750681 17.083636 \r\nL 332.841991 81.769224 \r\nL 332.863296 192.257029 \r\nL 332.930257 17.083636 \r\nL 332.954606 193.864124 \r\nL 333.039829 80.965676 \r\nL 333.042873 17.083636 \r\nL 333.061135 206.720887 \r\nL 333.149401 39.582971 \r\nL 333.161576 180.605588 \r\nL 333.240711 17.083636 \r\nL 333.258973 87.795831 \r\nL 333.262017 17.083636 \r\nL 333.344196 193.46235 \r\nL 333.365501 76.546164 \r\nL 333.462899 206.319113 \r\nL 333.371589 17.083636 \r\nL 333.475073 121.14306 \r\nL 333.578558 47.618448 \r\nL 333.560296 195.872993 \r\nL 333.587689 55.653925 \r\nL 333.685086 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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(rewards)"
   ]
  },
  {
   "source": [
    "From this graph, it is not possible to tell anything, because due to the nature of stochastic training process the length of training sessions varies greatly. To make more sense of this graph, we can calculate **running average** over series of experiments, let's say 100. This can be done conveniently using `np.convolve`:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2814cc63488>]"
      ]
     },
     "metadata": {},
     "execution_count": 22
    },
    {
     "output_type": "display_data",
     "data": {
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110.421698 \r\nL 116.97379 100.967522 \r\nL 116.979883 101.257861 \r\nL 117.092611 107.246111 \r\nL 117.120031 106.3388 \r\nL 117.135264 104.941542 \r\nL 117.184011 116.434143 \r\nL 117.187058 116.440191 \r\nL 117.260178 117.625744 \r\nL 117.244945 114.298938 \r\nL 117.287598 115.678051 \r\nL 117.336345 105.95773 \r\nL 117.403372 110.669696 \r\nL 117.406419 110.669696 \r\nL 117.500866 98.608515 \r\nL 117.421652 111.812908 \r\nL 117.58008 100.30821 \r\nL 117.613593 105.570611 \r\nL 117.66234 97.441108 \r\nL 117.677574 97.586278 \r\nL 117.756787 86.80138 \r\nL 117.829908 93.442893 \r\nL 117.988335 105.752073 \r\nL 117.991382 103.889062 \r\nL 118.076689 113.905771 \r\nL 118.088876 110.488234 \r\nL 118.119343 112.61739 \r\nL 118.161996 108.54659 \r\nL 118.180276 108.570784 \r\nL 118.183323 108.334884 \r\nL 118.229023 113.137581 \r\nL 118.253397 115.901854 \r\nL 118.28691 109.919653 \r\nL 118.326517 111.982272 \r\nL 118.442291 101.83854 \r\nL 118.366124 113.542846 \r\nL 118.460571 103.495894 \r\nL 118.463618 103.876965 \r\nL 118.524552 97.997592 \r\nL 118.673839 87.884104 \r\nL 118.536738 98.348419 \r\nL 118.698213 90.708864 \r\nL 118.85664 106.768261 \r\nL 118.859687 106.683579 \r\nL 118.899294 103.949549 \r\nL 118.932807 110.960036 \r\nL 118.966321 120.595674 \r\nL 119.051628 113.433969 \r\nL 119.094281 114.480401 \r\nL 119.139982 110.814866 \r\nL 119.152168 111.65564 \r\nL 119.267942 95.953119 \r\nL 119.207009 113.349287 \r\nL 119.286222 100.290063 \r\nL 119.465977 111.050767 \r\nL 119.469023 109.998286 \r\nL 119.511677 108.117129 \r\nL 119.548237 112.677877 \r\nL 119.660964 116.845457 \r\nL 119.612217 110.578965 \r\nL 119.673151 115.974439 \r\nL 119.761505 114.2445 \r\nL 119.694478 118.496762 \r\nL 119.779785 116.101462 \r\nL 119.804158 118.285056 \r\nL 119.880326 114.861471 \r\nL 119.990006 111.776615 \r\nL 119.926026 119.198415 \r\nL 120.00524 112.865388 \r\nL 120.03266 113.343238 \r\nL 120.063127 109.217999 \r\nL 120.081407 109.804727 \r\nL 120.224601 96.805991 \r\nL 120.300768 90.636279 \r\nL 120.346468 94.773615 \r\nL 120.349515 95.160734 \r\nL 120.407402 88.482929 \r\nL 120.413495 87.751031 \r\nL 120.462242 91.186714 \r\nL 120.486615 90.866131 \r\nL 120.489662 92.075878 \r\nL 120.510989 86.692503 \r\nL 120.599343 91.985147 \r\nL 120.718163 95.729316 \r\nL 120.64809 86.166262 \r\nL 120.727303 94.767566 \r\nL 120.840031 89.263216 \r\nL 120.858311 89.946723 \r\nL 120.995412 97.525791 \r\nL 120.904011 87.956689 \r\nL 121.001505 97.283841 \r\nL 121.022832 96.461213 \r\nL 121.031972 98.58432 \r\nL 121.175166 108.607077 \r\nL 121.178213 107.609035 \r\nL 121.303127 96.309994 \r\nL 121.312267 97.380621 \r\nL 121.315313 97.846374 \r\nL 121.379294 93.823964 \r\nL 121.40976 95.475269 \r\nL 121.525534 103.653161 \r\nL 121.458507 92.196853 \r\nL 121.586468 102.36478 \r\nL 121.592561 101.052204 \r\nL 121.662635 106.048461 \r\nL 121.693102 103.066434 \r\nL 121.711382 106.314606 \r\nL 121.790596 102.721656 \r\nL 121.796689 103.362822 \r\nL 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107.699766 \r\nL 123.639932 97.652814 \r\nL 123.655166 101.052204 \r\nL 123.7161 94.555861 \r\nL 123.74352 95.922875 \r\nL 123.75266 94.912736 \r\nL 123.82578 104.022134 \r\nL 123.83492 101.602639 \r\nL 123.920227 107.445719 \r\nL 123.947647 103.03619 \r\nL 123.950694 102.89102 \r\nL 123.972021 106.223874 \r\nL 123.975068 106.169436 \r\nL 124.051235 109.012342 \r\nL 123.999441 104.143109 \r\nL 124.084748 107.246111 \r\nL 124.124355 105.068566 \r\nL 124.103028 108.165519 \r\nL 124.194429 107.088844 \r\nL 124.200522 107.482012 \r\nL 124.206615 106.15129 \r\nL 124.212709 106.786407 \r\nL 124.310203 103.75599 \r\nL 124.255362 108.849026 \r\nL 124.328483 104.475789 \r\nL 124.343716 103.18136 \r\nL 124.39551 109.078878 \r\nL 124.401603 108.921611 \r\nL 124.407697 109.242194 \r\nL 124.41379 110.373308 \r\nL 124.48691 103.489845 \r\nL 124.489957 103.719697 \r\nL 124.648385 112.502464 \r\nL 124.50519 103.374919 \r\nL 124.654478 111.558861 \r\nL 124.718458 107.7784 \r\nL 124.748925 112.829095 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129.230596 86.450553 \r\nL 129.264109 92.577924 \r\nL 129.34637 97.979446 \r\nL 129.306763 91.229055 \r\nL 129.38293 95.426879 \r\nL 129.398163 89.015218 \r\nL 129.498704 93.043676 \r\nL 129.559638 87.914347 \r\nL 129.605338 92.432754 \r\nL 129.651038 89.67453 \r\nL 129.721112 95.838193 \r\nL 129.803372 85.779143 \r\nL 129.836886 92.813824 \r\nL 129.861259 93.442893 \r\nL 129.882586 86.093678 \r\nL 129.97094 76.657648 \r\nL 129.900866 88.755122 \r\nL 130.004453 77.673836 \r\nL 130.028827 76.331016 \r\nL 130.07148 87.206645 \r\nL 130.242095 120.027092 \r\nL 130.245141 118.883881 \r\nL 130.333495 129.826047 \r\nL 130.373102 121.980835 \r\nL 130.528483 98.935146 \r\nL 130.531529 99.298071 \r\nL 130.601603 94.682884 \r\nL 130.635117 88.277272 \r\nL 130.699097 99.419045 \r\nL 130.702144 99.11056 \r\nL 130.711284 102.945459 \r\nL 130.796591 94.440935 \r\nL 130.799638 95.106296 \r\nL 130.827058 91.356079 \r\nL 130.918458 91.725052 \r\nL 130.921505 92.825922 \r\nL 130.979392 87.593764 \r\nL 131.025092 91.537541 \r\nL 131.079932 89.015218 \r\nL 131.098213 93.563868 \r\nL 131.119539 93.430796 \r\nL 131.131726 94.99137 \r\nL 131.186566 88.343808 \r\nL 131.22008 91.622223 \r\nL 131.226173 90.835887 \r\nL 131.27492 95.106296 \r\nL 131.360227 98.560125 \r\nL 131.317574 93.104164 \r\nL 131.390694 96.406774 \r\nL 131.402881 94.31996 \r\nL 131.451628 100.205381 \r\nL 131.485141 99.122657 \r\nL 131.488188 99.709385 \r\nL 131.555215 93.787671 \r\nL 131.567402 94.07801 \r\nL 131.674036 80.359475 \r\nL 131.713643 81.000641 \r\nL 131.80809 90.212867 \r\nL 131.747156 79.506603 \r\nL 131.838557 85.767046 \r\nL 131.841603 85.724705 \r\nL 131.847697 86.65621 \r\nL 131.984797 98.475442 \r\nL 131.987844 96.727357 \r\nL 132.060964 107.391281 \r\nL 132.088385 102.388975 \r\nL 132.091431 102.31639 \r\nL 132.106665 104.318522 \r\nL 132.112758 102.739802 \r\nL 132.243765 122.204638 \r\nL 132.246812 120.341627 \r\nL 132.252905 118.02496 \r\nL 132.277279 123.831748 \r\nL 132.350399 123.620042 \r\nL 132.356493 123.795456 \r\nL 132.359539 123.081705 \r\nL 132.40524 128.344106 \r\nL 132.49664 117.365648 \r\nL 132.499687 117.795108 \r\nL 132.56976 112.175832 \r\nL 132.825682 93.406601 \r\nL 132.575854 113.028704 \r\nL 132.831775 95.172832 \r\nL 132.837869 95.553902 \r\nL 132.840915 94.434886 \r\nL 132.871382 91.610126 \r\nL 132.947549 95.753511 \r\nL 132.996296 88.827707 \r\nL 133.06637 93.557819 \r\nL 133.300964 105.425441 \r\nL 133.087697 92.100073 \r\nL 133.319244 105.032273 \r\nL 133.361898 94.828054 \r\nL 133.441112 100.277966 \r\nL 133.450252 100.973571 \r\nL 133.456345 98.493589 \r\nL 133.462439 95.795852 \r\nL 133.520326 106.375093 \r\nL 133.553839 103.090629 \r\nL 133.556886 102.897069 \r\nL 133.575166 107.990106 \r\nL 133.578213 107.736059 \r\nL 133.715313 120.964647 \r\nL 133.733593 119.053246 \r\nL 133.767107 129.033662 \r\nL 133.840227 118.248764 \r\nL 133.855461 119.295195 \r\nL 133.879834 113.016606 \r\nL 133.882881 113.167825 \r\nL 134.071775 97.955251 \r\nL 134.093102 101.723614 \r\nL 134.105289 103.27814 \r\nL 134.190596 100.011822 \r\nL 134.196689 97.646765 \r\nL 134.294183 101.772004 \r\nL 134.29723 101.40908 \r\nL 134.464797 76.923792 \r\nL 134.571431 72.012218 \r\nL 134.540964 77.135498 \r\nL 134.583618 73.234063 \r\nL 134.623225 75.756386 \r\nL 134.601898 71.963828 \r\nL 134.690252 73.923619 \r\nL 134.699392 72.012218 \r\nL 134.778606 82.464435 \r\nL 134.888286 90.624182 \r\nL 134.827353 81.974488 \r\nL 134.900473 88.712781 \r\nL 135.037574 80.123574 \r\nL 135.04062 80.395767 \r\nL 135.071087 84.696419 \r\nL 135.110694 79.028753 \r\nL 135.165534 84.000815 \r\nL 135.189908 82.319266 \r\nL 135.226468 87.80547 \r\nL 135.272168 85.482755 \r\nL 135.290448 85.017002 \r\nL 135.305682 89.214826 \r\nL 135.360522 87.865957 \r\nL 135.366615 89.505165 \r\nL 135.439736 85.452511 \r\nL 135.467156 84.490762 \r\nL 135.494576 88.997071 \r\nL 135.531136 88.960779 \r\nL 135.66519 109.992238 \r\nL 135.668237 108.87927 \r\nL 135.683471 107.548548 \r\nL 135.747451 117.293063 \r\nL 135.765731 113.506554 \r\nL 135.768778 113.597285 \r\nL 135.780964 111.208034 \r\nL 135.927205 89.487019 \r\nL 136.055166 70.481887 \r\nL 136.070399 73.572792 \r\nL 136.149613 84.871833 \r\nL 136.186173 76.107213 \r\nL 136.19836 73.959911 \r\nL 136.274527 85.355732 \r\nL 136.518262 107.076746 \r\nL 136.283667 83.033017 \r\nL 136.530448 104.070524 \r\nL 136.637082 98.269785 \r\nL 136.652316 98.638758 \r\nL 136.676689 103.489845 \r\nL 136.731529 94.89459 \r\nL 136.835117 84.279056 \r\nL 136.874724 88.035322 \r\nL 136.87777 89.202728 \r\nL 136.956984 82.077316 \r\nL 136.969171 82.416045 \r\nL 136.984404 81.351468 \r\nL 137.042291 89.359996 \r\nL 137.109318 93.775574 \r\nL 137.084945 85.912215 \r\nL 137.158065 90.787497 \r\nL 137.267746 95.112344 \r\nL 137.182439 89.553555 \r\nL 137.298213 91.92466 \r\nL 137.404846 79.464262 \r\nL 137.423127 83.940327 \r\nL 137.46578 87.678447 \r\nL 137.490154 82.10756 \r\nL 137.535854 85.083538 \r\nL 137.593741 83.97662 \r\nL 137.566321 87.684495 \r\nL 137.599834 86.438456 \r\nL 137.694281 94.840151 \r\nL 137.627254 85.688412 \r\nL 137.721701 90.231014 \r\nL 137.724748 88.984974 \r\nL 137.797869 95.100247 \r\nL 137.825289 91.622223 \r\nL 137.931923 95.735364 \r\nL 137.916689 91.513346 \r\nL 137.941063 94.138498 \r\nL 138.069023 79.252556 \r\nL 137.956296 95.330099 \r\nL 138.093397 81.726489 \r\nL 138.227451 93.182797 \r\nL 138.291431 96.71526 \r\nL 138.239638 91.622223 \r\nL 138.340178 93.769525 \r\nL 138.343225 93.588063 \r\nL 138.361505 98.445199 \r\nL 138.373692 99.794067 \r\nL 138.449859 92.590021 \r\nL 138.492512 87.055427 \r\nL 138.556493 92.807776 \r\nL 138.775854 109.865214 \r\nL 138.788041 107.850985 \r\nL 138.794134 107.965911 \r\nL 138.797181 107.554597 \r\nL 139.083569 87.255035 \r\nL 139.098802 88.132102 \r\nL 139.202389 93.340065 \r\nL 139.129269 84.817394 \r\nL 139.22067 93.049725 \r\nL 139.24809 91.283494 \r\nL 139.269416 94.731274 \r\nL 139.403471 107.0586 \r\nL 139.290743 93.21909 \r\nL 139.412611 105.274223 \r\nL 139.504011 98.578271 \r\nL 139.531431 101.342544 \r\nL 139.537525 103.689454 \r\nL 139.583225 95.318002 \r\nL 139.635018 99.431143 \r\nL 139.708139 97.132623 \r\nL 139.671579 102.328488 \r\nL 139.732512 100.683231 \r\nL 139.897033 117.268868 \r\nL 139.915313 114.323133 \r\nL 139.988434 119.36778 \r\nL 140.006714 116.966432 \r\nL 140.061554 118.956466 \r\nL 140.0189 115.944195 \r\nL 140.070694 118.732663 \r\nL 140.092021 124.757205 \r\nL 140.165141 117.438233 \r\nL 140.186468 121.702593 \r\nL 140.414969 105.165345 \r\nL 140.192561 122.355856 \r\nL 140.454576 107.82679 \r\nL 140.472856 111.964126 \r\nL 140.49723 105.364954 \r\nL 140.56121 105.588757 \r\nL 140.667844 112.079052 \r\nL 140.680031 109.756337 \r\nL 140.740964 115.284883 \r\nL 140.789711 110.754379 \r\nL 140.838458 110.808817 \r\nL 140.908532 106.411385 \r\nL 140.911579 106.598896 \r\nL 140.954232 102.927313 \r\nL 140.963372 103.151116 \r\nL 141.088286 92.571875 \r\nL 141.09438 94.235278 \r\nL 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284.011235 86.958647 \r\nL 284.075215 81.266785 \r\nL 284.148335 78.520659 \r\nL 284.093495 83.522964 \r\nL 284.190989 79.379579 \r\nL 284.200129 80.359475 \r\nL 284.264109 73.082844 \r\nL 284.367697 66.241722 \r\nL 284.379883 69.804429 \r\nL 284.501751 75.091025 \r\nL 284.41949 67.130887 \r\nL 284.507844 74.782539 \r\nL 284.584011 73.536499 \r\nL 284.550498 77.788762 \r\nL 284.623618 74.340981 \r\nL 284.626665 74.328884 \r\nL 284.629711 74.764393 \r\nL 284.663225 78.145637 \r\nL 284.730252 73.137283 \r\nL 284.733299 73.282452 \r\nL 284.846026 64.711392 \r\nL 284.748532 74.939806 \r\nL 284.900866 67.45147 \r\nL 284.910006 70.493985 \r\nL 284.97094 60.326058 \r\nL 284.99836 63.501645 \r\nL 285.02578 59.775623 \r\nL 285.101947 64.142811 \r\nL 285.108041 63.28389 \r\nL 285.150694 66.907084 \r\nL 285.181161 61.312002 \r\nL 285.220768 64.118616 \r\nL 285.330448 74.4922 \r\nL 285.357869 72.604994 \r\nL 285.379195 70.058476 \r\nL 285.427942 79.313043 \r\nL 285.430989 78.986411 \r\nL 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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "#code block 12"
   ]
  },
  {
   "source": [
    "## Varying Hyperparameters and Seeing the Result in Action\n",
    "\n",
    "Now it would be interesting to actually see how the trained model behaves. Let's run the simulation, and we will be following the same action selection strategy as during training: sampling according to the probability distribution in Q-Table: "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# code block 13"
   ]
  },
  {
   "source": [
    "\n",
    "## Saving result to an animated GIF\n",
    "\n",
    "If you want to impress your friends, you may want to send them the animated GIF picture of the balancing pole. To do this, we can invoke `env.render` to produce an image frame, and then save those to animated GIF using PIL library:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "360\n"
     ]
    }
   ],
   "source": [
    "from PIL import Image\n",
    "obs = env.reset()\n",
    "done = False\n",
    "i=0\n",
    "ims = []\n",
    "while not done:\n",
    "   s = discretize(obs)\n",
    "   img=env.render(mode='rgb_array')\n",
    "   ims.append(Image.fromarray(img))\n",
    "   v = probs(np.array([Qbest.get((s,a),0) for a in actions]))\n",
    "   a = random.choices(actions,weights=v)[0]\n",
    "   obs,_,done,_ = env.step(a)\n",
    "   i+=1\n",
    "env.close()\n",
    "ims[0].save('images/cartpole-balance.gif',save_all=True,append_images=ims[1::2],loop=0,duration=5)\n",
    "print(i)"
   ]
  }
 ]
}