diff --git a/Lab3-policy-gradient.ipynb b/Lab3-policy-gradient.ipynb
index 4529e50..3ddadb5 100644
--- a/Lab3-policy-gradient.ipynb
+++ b/Lab3-policy-gradient.ipynb
@@ -28,17 +28,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "[2017-09-12 22:50:43,560] Making new env: CartPole-v0\n"
-     ]
-    }
-   ],
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
    "source": [
     "import gym\n",
     "import tensorflow as tf\n",
@@ -103,14 +97,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/Users/andrew/miniconda2/envs/cedl/lib/python3.5/site-packages/tensorflow/python/ops/gradients_impl.py:95: UserWarning: Converting sparse IndexedSlices to a dense Tensor of unknown shape. This may consume a large amount of memory.\n",
+      "C:\\Users\\user\\Anaconda3\\envs\\gym\\lib\\site-packages\\tensorflow\\python\\ops\\gradients_impl.py:95: UserWarning: Converting sparse IndexedSlices to a dense Tensor of unknown shape. This may consume a large amount of memory.\n",
       "  \"Converting sparse IndexedSlices to a dense Tensor of unknown shape. \"\n"
      ]
     }
@@ -152,7 +146,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 4,
    "metadata": {
     "collapsed": true
    },
@@ -214,6 +208,7 @@
     "            Sample solution should be only 1 line.\n",
     "            \"\"\"\n",
     "            # YOUR CODE HERE >>>>>>\n",
+    "            a = r - b\n",
     "            # <<<<<<<<\n",
     "\n",
     "            p[\"returns\"] = r\n",
@@ -258,97 +253,97 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Iteration 1: Average Return = 14.85\n",
-      "Iteration 2: Average Return = 15.59\n",
-      "Iteration 3: Average Return = 16.61\n",
-      "Iteration 4: Average Return = 17.43\n",
-      "Iteration 5: Average Return = 17.08\n",
-      "Iteration 6: Average Return = 17.24\n",
-      "Iteration 7: Average Return = 21.3\n",
-      "Iteration 8: Average Return = 21.42\n",
-      "Iteration 9: Average Return = 20.62\n",
-      "Iteration 10: Average Return = 26.82\n",
-      "Iteration 11: Average Return = 28.0\n",
-      "Iteration 12: Average Return = 28.41\n",
-      "Iteration 13: Average Return = 28.96\n",
-      "Iteration 14: Average Return = 28.15\n",
-      "Iteration 15: Average Return = 30.64\n",
-      "Iteration 16: Average Return = 36.2\n",
-      "Iteration 17: Average Return = 38.13\n",
-      "Iteration 18: Average Return = 34.5\n",
-      "Iteration 19: Average Return = 40.37\n",
-      "Iteration 20: Average Return = 35.78\n",
-      "Iteration 21: Average Return = 47.81\n",
-      "Iteration 22: Average Return = 47.21\n",
-      "Iteration 23: Average Return = 43.34\n",
-      "Iteration 24: Average Return = 46.1\n",
-      "Iteration 25: Average Return = 50.25\n",
-      "Iteration 26: Average Return = 51.02\n",
-      "Iteration 27: Average Return = 59.81\n",
-      "Iteration 28: Average Return = 57.49\n",
-      "Iteration 29: Average Return = 61.39\n",
-      "Iteration 30: Average Return = 62.26\n",
-      "Iteration 31: Average Return = 61.98\n",
-      "Iteration 32: Average Return = 62.16\n",
-      "Iteration 33: Average Return = 59.89\n",
-      "Iteration 34: Average Return = 73.46\n",
-      "Iteration 35: Average Return = 78.51\n",
-      "Iteration 36: Average Return = 72.79\n",
-      "Iteration 37: Average Return = 78.74\n",
-      "Iteration 38: Average Return = 86.95\n",
-      "Iteration 39: Average Return = 94.08\n",
-      "Iteration 40: Average Return = 97.58\n",
-      "Iteration 41: Average Return = 103.42\n",
-      "Iteration 42: Average Return = 101.17\n",
-      "Iteration 43: Average Return = 112.39\n",
-      "Iteration 44: Average Return = 115.09\n",
-      "Iteration 45: Average Return = 134.65\n",
-      "Iteration 46: Average Return = 138.92\n",
-      "Iteration 47: Average Return = 147.15\n",
-      "Iteration 48: Average Return = 152.35\n",
-      "Iteration 49: Average Return = 149.66\n",
-      "Iteration 50: Average Return = 148.15\n",
-      "Iteration 51: Average Return = 144.82\n",
-      "Iteration 52: Average Return = 144.43\n",
-      "Iteration 53: Average Return = 153.21\n",
-      "Iteration 54: Average Return = 163.66\n",
-      "Iteration 55: Average Return = 154.28\n",
-      "Iteration 56: Average Return = 155.07\n",
-      "Iteration 57: Average Return = 161.53\n",
-      "Iteration 58: Average Return = 166.28\n",
-      "Iteration 59: Average Return = 174.05\n",
-      "Iteration 60: Average Return = 172.8\n",
-      "Iteration 61: Average Return = 170.78\n",
-      "Iteration 62: Average Return = 179.58\n",
-      "Iteration 63: Average Return = 174.84\n",
-      "Iteration 64: Average Return = 175.74\n",
-      "Iteration 65: Average Return = 174.99\n",
-      "Iteration 66: Average Return = 187.7\n",
-      "Iteration 67: Average Return = 178.94\n",
-      "Iteration 68: Average Return = 182.74\n",
-      "Iteration 69: Average Return = 181.42\n",
-      "Iteration 70: Average Return = 182.19\n",
-      "Iteration 71: Average Return = 184.58\n",
-      "Iteration 72: Average Return = 181.9\n",
-      "Iteration 73: Average Return = 184.29\n",
-      "Iteration 74: Average Return = 188.8\n",
-      "Iteration 75: Average Return = 190.46\n",
-      "Iteration 76: Average Return = 188.89\n",
-      "Iteration 77: Average Return = 187.9\n",
-      "Iteration 78: Average Return = 190.19\n",
-      "Iteration 79: Average Return = 186.28\n",
-      "Iteration 80: Average Return = 189.1\n",
-      "Iteration 81: Average Return = 188.16\n",
-      "Iteration 82: Average Return = 191.32\n",
-      "Iteration 83: Average Return = 192.03\n",
-      "Iteration 84: Average Return = 195.45\n",
+      "Iteration 1: Average Return = 20.45\n",
+      "Iteration 2: Average Return = 18.67\n",
+      "Iteration 3: Average Return = 19.21\n",
+      "Iteration 4: Average Return = 20.59\n",
+      "Iteration 5: Average Return = 23.19\n",
+      "Iteration 6: Average Return = 21.18\n",
+      "Iteration 7: Average Return = 24.79\n",
+      "Iteration 8: Average Return = 23.09\n",
+      "Iteration 9: Average Return = 25.96\n",
+      "Iteration 10: Average Return = 27.52\n",
+      "Iteration 11: Average Return = 27.33\n",
+      "Iteration 12: Average Return = 31.51\n",
+      "Iteration 13: Average Return = 33.2\n",
+      "Iteration 14: Average Return = 33.66\n",
+      "Iteration 15: Average Return = 33.37\n",
+      "Iteration 16: Average Return = 42.08\n",
+      "Iteration 17: Average Return = 37.26\n",
+      "Iteration 18: Average Return = 43.06\n",
+      "Iteration 19: Average Return = 40.63\n",
+      "Iteration 20: Average Return = 40.84\n",
+      "Iteration 21: Average Return = 40.37\n",
+      "Iteration 22: Average Return = 45.1\n",
+      "Iteration 23: Average Return = 43.67\n",
+      "Iteration 24: Average Return = 46.74\n",
+      "Iteration 25: Average Return = 46.12\n",
+      "Iteration 26: Average Return = 44.35\n",
+      "Iteration 27: Average Return = 49.1\n",
+      "Iteration 28: Average Return = 48.62\n",
+      "Iteration 29: Average Return = 51.33\n",
+      "Iteration 30: Average Return = 51.07\n",
+      "Iteration 31: Average Return = 50.5\n",
+      "Iteration 32: Average Return = 54.02\n",
+      "Iteration 33: Average Return = 52.56\n",
+      "Iteration 34: Average Return = 57.02\n",
+      "Iteration 35: Average Return = 55.55\n",
+      "Iteration 36: Average Return = 59.29\n",
+      "Iteration 37: Average Return = 57.34\n",
+      "Iteration 38: Average Return = 62.87\n",
+      "Iteration 39: Average Return = 63.65\n",
+      "Iteration 40: Average Return = 64.12\n",
+      "Iteration 41: Average Return = 60.31\n",
+      "Iteration 42: Average Return = 63.77\n",
+      "Iteration 43: Average Return = 65.99\n",
+      "Iteration 44: Average Return = 63.3\n",
+      "Iteration 45: Average Return = 64.73\n",
+      "Iteration 46: Average Return = 65.91\n",
+      "Iteration 47: Average Return = 67.49\n",
+      "Iteration 48: Average Return = 68.8\n",
+      "Iteration 49: Average Return = 67.64\n",
+      "Iteration 50: Average Return = 68.82\n",
+      "Iteration 51: Average Return = 70.26\n",
+      "Iteration 52: Average Return = 78.53\n",
+      "Iteration 53: Average Return = 73.5\n",
+      "Iteration 54: Average Return = 80.04\n",
+      "Iteration 55: Average Return = 77.22\n",
+      "Iteration 56: Average Return = 84.89\n",
+      "Iteration 57: Average Return = 82.58\n",
+      "Iteration 58: Average Return = 87.67\n",
+      "Iteration 59: Average Return = 88.29\n",
+      "Iteration 60: Average Return = 90.95\n",
+      "Iteration 61: Average Return = 99.53\n",
+      "Iteration 62: Average Return = 94.45\n",
+      "Iteration 63: Average Return = 107.04\n",
+      "Iteration 64: Average Return = 112.56\n",
+      "Iteration 65: Average Return = 123.9\n",
+      "Iteration 66: Average Return = 132.01\n",
+      "Iteration 67: Average Return = 146.82\n",
+      "Iteration 68: Average Return = 146.05\n",
+      "Iteration 69: Average Return = 152.7\n",
+      "Iteration 70: Average Return = 152.27\n",
+      "Iteration 71: Average Return = 157.93\n",
+      "Iteration 72: Average Return = 157.28\n",
+      "Iteration 73: Average Return = 160.44\n",
+      "Iteration 74: Average Return = 161.47\n",
+      "Iteration 75: Average Return = 167.08\n",
+      "Iteration 76: Average Return = 163.13\n",
+      "Iteration 77: Average Return = 167.54\n",
+      "Iteration 78: Average Return = 171.92\n",
+      "Iteration 79: Average Return = 175.66\n",
+      "Iteration 80: Average Return = 184.96\n",
+      "Iteration 81: Average Return = 182.74\n",
+      "Iteration 82: Average Return = 184.35\n",
+      "Iteration 83: Average Return = 185.37\n",
+      "Iteration 84: Average Return = 196.11\n",
       "Solve at 84 iterations, which equals 8400 episodes.\n"
      ]
     }
@@ -371,14 +366,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
      "data": {
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NnnIp+h+voj98xxgdFmnB9It7UAHNf2mdyjTlMpx5X6H/9TZE90N1YIkjFR6J6Z7Fxl/w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\nDTX+jM4LWgjRo/i85iLaToVFoC66Cv3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oduwQatxFbe5ScxZATAx624XZe5HgYjI1/mL0UZkxJsJPNzdD3TmIiYGKs2iP+dORtceD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\nh7d5/iNHjgRuJycnB/4eFxdHU1MTHo+H9PR0li1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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1107bac18>"
+       "<matplotlib.figure.Figure at 0x1abb2765e10>"
       ]
      },
      "metadata": {},
@@ -386,9 +381,9 @@
     },
     {
      "data": {
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DUS1DoFsfq0sWos7USVgsWrSI/fv3k5eXx8yZM5k0aRIjRoy4oAsKYP/+/axZswY3Nzds\nNhv3338/3t6Vr+IlRE1ow0CvfBUOfYe67zFU526O51TrMNTd0RZWJ4T1ZFnVn8npsDkNrZ10brZ9\ncaD/fQ5n01E334lt3B01ft+G1k7OIu1kTqPvhhLCKlpr9Kq/2xcFKi+HLj2xTZwGfQdbXZoQLknC\nQjROPx5Fb/kMNWg4auwkVIhMxyHE5UhYiEZJ79oKNhvq9vtQ3jIdhxCVkTW4RaOjtUbv2gZdekpQ\nCGGShIVofH46AeknUTI+IYRpEhai0dG7toGyofoMtLoUIeoNCQvR6OhdW6FzN5SPv9WlCFFvSFiI\nRkWf/BFOpaL6SReUEFUhYSEaFb17GyiF6nPh5H9CiEuTsBCNit71FXTogvILrPzFQggHCQvRYOmS\nEvTB79AF+fbHZ05C2jHpghKiGuSmPNEg6cICjEXPwLFDoGzQLhyaNgNA9ZGwEKKqJCxEg6ML8zEW\n/Q1+PIqaPB3y89DffwNH9kPn7qjAYKtLFKLekbAQDYouzMeIewZSj2Gb+RSq98/3UoyfjC4uAjc3\nawsUop6SsBANhi4t/TUoHpiD6nVNhefVz91QQoiqkwFu0XB8vweOH0ZNnXVBUAghakbCQjQYeu9O\naNIU1W+o1aUI0eBIWIgGQWuN/nYnXN0L5eFhdTlCNDgSFqJhOPkjZGWgevS3uhIhGiQJC9Eg6L07\nAVDd+1lciRANU51cDRUfH8/u3bvx9fUlNjYWgDVr1rBhwwZ8fOyLz0yePJm+ffsCsHbtWjZu3IjN\nZmPatGn07t27LsoU9ZjeuxPatkcFBFldihANUp2ExfDhw7nhhhtYunRphe1jx45l/PjxFbalpaWx\nbds2Xn75ZbKzs5k3bx6vvPIKNpucBImL0wX5cOR71A1/sLoUIRqsOvkJ3LVrV7y9vU29Njk5mcGD\nB+Ph4UHLli0JCQnhyJEjTq5Q1Gd6/x4wDFQP6YISwlksvSlv/fr1bNmyhfDwcKZMmYK3tzdZWVl0\n6tTJ8ZqAgACysrIsrFK4vL3J0LwFhF9ldSVCNFiWhcXo0aO57bbbAFi9ejUrV64kOjq6Su+RmJhI\nYmIiADExMQQFVb+/2t3dvUb7Nxau1k7aMMjYl0LTfhH4tmxldTkOrtZOrkrayRxXaCfLwsLPz8/x\n9ciRI1mwYAFgP5M4e/as47msrCwCAgIu+h5RUVFERUU5HmdmZla7nqCgoBrt31i4WjvpowfR53Io\n6dTdpepytXZyVdJO5jiznUJDQ029zrJR4+zsbMfXO3bsICwsDID+/fuzbds2SktLSU9P59SpU3Ts\n2NGqMoWL03t3gbKhuve1uhQhGjRTZxb5+fl89NFHnDhxguLi4grPPfvss5Xuv2jRIvbv309eXh4z\nZ85k0qRJ7Nu3j+PHj6OUIjg4mOnTpwMQFhZGREQEjz76KDabjXvvvVeuhBIO+ttk9Feb0Hm5kJcL\nmachvDPK28fq0oRo0JTWWlf2ovnz51NWVkZERASenp4Vnhs+fLizaquykydPVntfOR02x6p20uXl\n6LUr0evXgl8ABIVACx+Utw9q8AhUx651XtPlyOfJHGknc1yhG8rUmcWhQ4d4/fXX8ZA5d4QFdE4W\nxvKFcGgfaviNqEn3yfxPQtQxU2HRrl07zp49S0hIiLPrEaICffonjIV/geIi1L2PYhs03OqShGiU\nTIVF9+7def755xk+fHiFq5gARowY4ZTChNBGOcaKV6CsDNvTL6HaXGF1SUI0WqbC4sCBAwQGBrJ3\n794LnpOwEM6iN30CPxxA/Wm2BIUQFqs0LLTWzJw5k6CgINxk/WJRR3TGafSHK6F7P5R0PQlhuUqv\nSVVK8fjjj6OUqot6hEBrjbHyVbDZsN0TLZ89IVyAqRsYrrzySk6dOuXsWoQAQP/vczjwLWriNFRA\nsNXlCCEwOWbRrVs3nn/+eSIjIy+Yn0TGLERt0kWF6PdXwFU9UMOut7ocIcTPTIXFwYMHadmyJd9/\n//0Fz0lYiNqkt22EogJsf5gq3U9CuBBTYfHMM884uw4h0IaB3vRfaN8Z1b5T5TsIIeqMqTELwzAu\n+UeIWrN/D5z5CTVinNWVCCF+x9SZxeTJky/53OrVq2utGNG4GRv/Az5+qP5DrC5FCPE7psLi1Vdf\nrfA4OzubhIQE+vfv75SiROOj00/Bd7tQY29Hucu8T0K4GlPdUMHBwRX+dO7cmYceeoh169Y5uz7R\nSOjNn4DNhoqUK6CEcEXVXiiisLCQc+fO1WYtopHSJcXorYmovoNRfoFWlyOEuAhT3VBLliypcBlj\nSUkJ33//PcOGDXNaYaLx0Ns3Q2EBasRYq0sRQlyCqbD4/dTkTZo0YdSoUfTs2dMpRYnGQxcWoP+7\nBq7oCB2utrocIcQlmAqL3r1706nThde9HzlyRNbHFjWi338LcrKwPfAXuQlPCBdmasziueeeu+j2\n+fPn12oxonHR+1LQ//scdf0tchOeEC7usmcWv9x0p7V2/PnFmTNnZMpyUW26qBBj5RIIaYsaf+n7\neIQQruGyYfHbm/HuuOOOCs/ZbDZuueUWUweJj49n9+7d+Pr6EhsbC8Dbb7/Nrl27cHd3p1WrVkRH\nR9O8eXPS09OZPXu2YxHxTp06MX369Cp9U8L16fdXQHYWtqdiUB6eVpcjhKjEZcPi1VdfRWvN3/72\nN5599lm01iilUErh4+ODp6e5/+TDhw/nhhtuYOnSpY5tPXv25M4778TNzY1Vq1axdu1a7r77bsA+\noL5w4cIafFvClelD+9BbPkONvgXVoYvV5QghTLhsWAQH29cSiI+PB+zdUrm5ufj7+1fpIF27diU9\nPb3Ctl69ejm+7ty5M9u3b6/Se4r6S2/fBM28UDffaXUpQgiTTF0NVVBQwOuvv8727dtxd3fn7bff\nZufOnRw5cuSC7qnq2LhxI4MHD3Y8Tk9P58knn6RZs2bccccdXH21XFLZUGit0d/uRHXtg/JsYnU5\nQgiTTIXF8uXLad68OfHx8Tz66KOA/Wxg5cqVNQ6LDz/8EDc3N8cNfv7+/sTHx9OiRQuOHj3KwoUL\niY2NxcvL64J9ExMTSUxMBCAmJuaChZmqwt3dvUb7NxY1bafSHw6SlZtFi8HX0awBt7d8nsyRdjLH\nFdrJVFjs3buX1157DXf3X1/u4+NDbm5ujQ6+efNmdu3axdy5cx3X2Ht4eODhYZ9ILjw8nFatWnHq\n1Ck6dOhwwf5RUVFERUU5HmdmZla7lqCgoBrt31jUtJ2M/30BSpF/ZWcKGnB7y+fJHGknc5zZTr9c\nTFQZU/dZeHl5kZeXV2FbZmZmlccufmvPnj2sW7eOp556iiZNfu2OOHfunOOS3TNnznDq1ClatWpV\n7eMI16K/3QlXdkL5+FldihCiCkydWYwcOZLY2FjuuOMOtNYcOnSId955h1GjRpk6yKJFi9i/fz95\neXnMnDmTSZMmsXbtWsrKypg3bx7w6yWy+/fvZ82aNbi5uWGz2bj//vvx9vau/ncoXIY+lwPHD8t9\nFULUQ6bC4uabb8bT05M33niD8vJy/v73vxMVFcWYMWNMHeSRRx65YNul1u4eNGgQgwYNMvW+on7R\n3+0CrVE9BlhdihCiiioNC8Mw2Lx5M6NGjTIdDkLo4iLw8ET99i7/b3eCXwC0C7euMCFEtVQ6ZmGz\n2Vi5cqVj0FmIyuiSEoz/92eM5x9DFxbYt5WVofenoHr0lwkDhaiHTA1w9+vXj507dzq7FtFA6PUf\nQsZp+OkExqvz0CUlcGQ/FBWieshSvELUR6bGLEpLS3n55Zfp3LkzgYGBFX4zfOihh5xWnKh/9NkM\n9PoPUP2HQt8I9PKXMF5bgGrZGtzd4epelb+JEMLlmAqLsLAwwsLCnF2LaAD0+28BoG6bhgoMxigs\nQK+KRwN07YNq2szS+oQQ1WMqLCZOnOjsOkQDoA9+h975JeqmyahA+7xitsgbMAry0GvfRvUeaHGF\nQojqMhUWQlRGG+UY7y6HgGDU9bdWeE7deBuqe19o296i6oQQNWVqgFuIyuikzyDtGLaJ01BNKk4Q\nqJRCteuAssnHTYj6Sv73ihrT6Sftixl17Q39hlhdjhDCCSQsRI3o8nKMN+LA3R3b1D/LPRRCNFCm\nxiy01mzYsIGtW7eSl5fHSy+9xP79+8nJyamwDoVofPRnH8DRg6j7H0f5B1pdjhDCSUydWaxevZpN\nmzYRFRXlmCY3MDCQdevWObU44dr0iSPoj99BDRiG7ZprrS5HCOFEpsIiKSmJp556iiFDhji6GVq2\nbHnBUqmi8dDFhRivvwwt/FB3zbS6HCGEk5kKC8MwaNq0aYVtxcXFF2wTjYM+lYbx/BNw5iS2aQ+j\nmrewuiQhhJOZCos+ffqwcuVKSktLAfsYxurVq+nXr59TixOup/irTRjzH4O8XGyzn0V17WN1SUKI\nOmAqLKZMmUJ2djZTp06lsLCQKVOmkJGRwV133eXs+oSL0FpjfPBPcl/8PwgNw/bXOJTM8yREo2Hq\naigvLy+eeOIJcnJyyMzMJCgoCD8/WRazsdBao/+9DL35U5qNvpmSCVNQMmW9EI2KqbD4ZU1sHx8f\nfHx8HNtsckdug/fboFDX30qLGY9x/uxZq8sSQtQxU2ExefLF10x2c3PD39+fgQMHMmnSJBnwbmB+\nHxTqD3+Um+6EaKRMhcW0adNITk5mwoQJBAYGkpmZyUcffUTfvn0JDQ3lvffeY8WKFcycKZdQNiR6\n7UoJCiEEYDIs/vvf/7JgwQK8vLwACA0NpUOHDsyZM4clS5bQrl07nnrqqcu+R3x8PLt378bX15fY\n2FgA8vPziYuLIyMjg+DgYGbPno23tzdaa9566y1SUlJo0qQJ0dHRhIfLus11SZ/4Af3ZWtTQURIU\nQghzV0MVFhZSUlJSYVtJSQmFhYUA+Pn5cf78+cu+x/Dhw3n66acrbEtISKBHjx4sXryYHj16kJCQ\nAEBKSgqnT59m8eLFTJ8+nddff930NyRqThvlGKvioYUPauI0CQohhLmwiIyM5LnnniMxMZE9e/aw\nYcMG5s+fT2RkJADffPMNoaGhl32Prl274u3tXWFbcnKy4z0iIyNJTk4GYOfOnVx77bUopejcuTMF\nBQVkZ2dX+ZsT1aO3rIfjh1ET/4Ty8q58ByFEg2eqG+ruu+8mJCSEbdu2kZ2djZ+fH9dffz1RUVEA\ndOvWjWeffbbKB8/NzcXf3x+wn53k5uYCkJWVRVBQkON1gYGBZGVlOV4rnEefy0Z/+DZ06YkaGGl1\nOUIIF2EqLGw2G6NHj2b06NEXfd7T07PGhSilqtzdkZiYSGJiIgAxMTEVAqaq3N3da7R/Q5G7ainF\npSUEPjgH9+DgC56XdjJH2skcaSdzXKGdTC+rmpOTw5EjR8jLy0Nr7dg+YsSIah/c19eX7Oxs/P39\nyc7OdtzDERAQ4JjdFuDs2bMEBARcsH9UVJTj7AaosE9VBQUF1Wj/hkAf3o+RtB41ZhI5Tb3hIu0h\n7WSOtJM50k7mOLOdKhtC+IWpsNixYwdLliyhdevWpKamEhYWRmpqKl26dKlRWPTv35+kpCQmTJhA\nUlISAwYMcGz/7LPPGDJkCIcPH8bLy0u6oOqA3vwpeHmjxky0uhQhhIsxFRarV68mOjqaiIgIpk2b\nxosvvsimTZtITU01faBFixaxf/9+8vLymDlzJpMmTWLChAnExcWxceNGx6WzYJ+4cPfu3Tz88MN4\nenoSHR1dve9OmKaLC9F7vkINGnHBGtpCCGEqLDIzM4mIiKiwLTIykunTpzNlyhRTB3rkkUcuun3u\n3LkXbFNKcd9995l6X1E12igHQNncKm7fvR3On0dFDLegKiGEqzN16ayPjw85OTkABAcHc+jQIc6c\nOeOYM0rUH8aiv2G8tvCC7Xr7JghqBR2utqAqIYSrM3VmMXLkSA4cOMCgQYMYO3Yszz77LEopxo0b\n5+z6RC3SZaVwaB+Ul6H3pzjWotA5Z+HAt6ixk+QGPCHERZkKi/HjxztmmI2MjKRbt24UFxfTtm1b\npxYnatmpNCgvA2XDWPMmtr8uQrm5ob/eAlqjBl1ndYVCCBdVaTeUYRjcc889jlXywH4ZlwRF/aN/\nPAqAmnAkt/EjAAAWbElEQVQX/HQC/eUX9u3bN0H7zqhW5i6hE0I0PpWGhc1mIzQ0lLy8vLqoRzhT\n6lFo0hR1w63QuRt63b/Qh/dD2nHUoOFWVyeEcGGmuqGGDh3KggULuPHGGwkMDKzQr929e3enFSdq\nl049Cm2vRNncsE26F2P+Yxjxz4ObG2rAtVaXJ4RwYabC4vPPPwfgvffeq7BdKcWrr75a+1WJWqcN\nA1KPoQYOB0Bd0REVMQK9bQP0ugbVwsfaAoUQLs1UWCxdutTZdQhnO5sORYUQ1t6xSd1yN/roQWwj\nxlpYmBCiPjA9N1RZWRmHDx8mOzubwYMHU1xcDCBLqdYXvwxut/t1ESnlF4jbvHirKhJC1COmwuLH\nH39kwYIFeHh4cPbsWQYPHsz+/ftJSkpyTNEhXJv+8SjYbNDmCqtLEULUQ6bu4F6+fDm33347ixYt\nwt3dni9du3blwIEDTi1O1B6dehRah6E8aj6dvBCi8TEVFmlpaQwbNqzCtqZNm1a6lKpwIalHUWGy\njrkQonpMhUVwcDBHjx6tsO3IkSOEhIQ4pShRu/S5HMjJqjC4LYQQVWFqzOL2228nJiaGUaNGUVZW\nxtq1a/niiy+YMWOGs+sTtSH1GFBxcFsIIarC1JlFv379ePrppzl37hxdu3YlIyODxx9/nF69ejm7\nPlELfpnmQ84shBDVZerM4ty5c7Rv317WmKivUo9CYEtU8xZWVyKEqKdMhUV0dDTdunVj6NChDBgw\nQO6tqGd06lGQwW0hRA2Y6oaKj4+nb9++fP7550yfPp1Fixaxc+dOysvLnV2fqCFdXARnTqKkC0oI\nUQOmzix8fHy4/vrruf7668nIyGDr1q28++67/P3vf+eNN95wdo2iJtKO29eqkMFtIUQNmJ7u4xe5\nubnk5OSQl5dH8+bNnVGTqCFdVAgZpyDjtH1tbZBuKCFEjZgKi7S0NL788ku2bt3K+fPniYiI4Ikn\nnqBjx441OvjJkyeJi4tzPE5PT2fSpEkUFBSwYcMGfHzsM6FOnjyZvn371uhYDZ3WGn44gPHFOkjZ\nDvo366Nf0RECgqwrTghR75kKi7/+9a8MHDiQ6dOn061bN8cSqzUVGhrKwoULAfuKfDNmzOCaa65h\n06ZNjB07lvHjx9fKcRo6vXcXxsfvwLFD4OWNGn0zqv1VEBwCQa1QXnIGKISoGVNhsXz5csecUM6y\nd+9eQkJCCA4OdupxGhqdcRrj1Xn2S2PvnIkaPALVRK5WE0LULlMJ4O7uTk5ODkeOHCEvL8/e5fGz\nESNG1EohW7duZciQIY7H69evZ8uWLYSHhzNlyhS8vb1r5TgNjf7sQ7DZsD35Asov0OpyhBANlNK/\n/cl/CTt27GDJkiW0bt2a1NRUwsLCSE1NpUuXLjzzzDM1LqKsrIwZM2YQGxuLn58fOTk5jvGK1atX\nk52dTXR09AX7JSYmkpiYCEBMTEyNJjZ0d3enrKys2vtbofxsBpkzb6PZyHH4zHyiTo5ZH9vJCtJO\n5kg7mePMdvL0NDcTtakzi9WrVxMdHU1ERATTpk3jxRdfZNOmTaSmptaoyF+kpKTQvn17/Pz8ABx/\nA4wcOZIFCxZcdL+oqCiioqIcjzMzM6tdQ1BQUI32t4Kx+g0wyikZPqbOaq+P7WQFaSdzpJ3McWY7\nhYaGmnqdqZHqzMxMIiIiKmyLjIxky5YtVa/sIn7fBZWdne34eseOHYSFhdXKcRoSfS4HveUz1KDr\nUEGtrC5HCNHAmb4pLycnBz8/P4KDgzl06BAtWrTAMIzKd65EcXEx3377LdOnT3dsW7VqFcePH0cp\nRXBwcIXnhJ1OXAelpagb/2B1KUKIRsBUWIwcOZIDBw4waNAgxo4dy7PPPotSinHjxtW4gKZNm/Lm\nm29W2DZr1qwav29Dpgvy0Zs+QfUfigppa3U5QohGwFRYTJgwwfF1ZGQk3bp1o7i4mLZt5QeVFfQX\nCVBchBpzm9WlCCEaiWrdPBEUJHcDW0V//w36k/dR10Si2srkgEKIulE7t2KLOqGzMjD+sRBC2qDu\necDqcoQQjYiERT2hS0sxli2AslJsD/wF1dTL6pKEEI2IhEU9od/9Bxw7hG3aI6jWMlYkhKhbEhb1\ngN79FXrLetSNf0D1jah8ByGEqGUSFi5Oa43xn3ft4xQT7ra6HCFEIyVh4er2pUDqMdT1t6JsblZX\nI4RopCQsXJzx2QfgF4gaNNzqUoQQjZiEhQvTPxyAg3tRoyeg3D2sLkcI0YhJWLgw47MPoHkL1LDR\nVpcihGjkJCxclD75I+z5GjViLKppM6vLEUI0cs5dK1WYprWG8+ehvAzKy9GfvAeeTVDX1XyyRiGE\nqCkJCxdhvPI3+5VPv6FG3oRq4WNNQUII8RsSFi5Apx2HfSmoAcPgyk7g5g6enqh+QyrdVwgh6oKE\nhQvQW9aDuzvqzhkobzmTEEK4HhngtpguKUFv34zqO0SCQgjhsiQsLKZ3/g+KClCR11tdihBCXJKE\nhcX0lvXQOgw6dbO6FCGEuCQJCwvptGNw9CDq2tEopawuRwghLsklBrgffPBBmjZtis1mw83NjZiY\nGPLz84mLiyMjI4Pg4GBmz56Nt7e31aXWKp20Htw9UBEjrC5FCCEuyyXCAuCZZ57Bx+fXAd6EhAR6\n9OjBhAkTSEhIICEhgbvvbjhTdOuSYvTXm1H9h6Cat7C6HCGEuCyX7YZKTk4mMjISgMjISJKTky2u\nqHbpr5OgqBB17Q1WlyKEEJVymTOL+fPnAzBq1CiioqLIzc3F398fAD8/P3Jzc60sr1bp8yXo/6yG\nKzpCx6utLkcIISrlEmExb948AgICyM3N5bnnniM0NLTC80qpiw4AJyYmkpiYCEBMTAxBQUHVrsHd\n3b1G+1dFwQcryc/OxP/Rv+EZHFwnx6wtddlO9Zm0kznSTua4Qju5RFgEBAQA4Ovry4ABAzhy5Ai+\nvr5kZ2fj7+9PdnZ2hfGMX0RFRREVFeV4nJmZWe0agoKCarS/WfpcDsb7/4Re13AupB3UwTFrU121\nU30n7WSOtJM5zmyn3/9yfimWj1kUFxdTVFTk+Prbb7+lXbt29O/fn6SkJACSkpIYMGCAlWXWGv3x\nO3C+BNttU60uRQghTLP8zCI3N5eXXnoJgPLycoYOHUrv3r3p0KEDcXFxbNy40XHpbH2nT6Wit6xH\nRd6ACmlrdTlCCGGa5WHRqlUrFi5ceMH2Fi1aMHfuXAsqch7j/RXQpCnqpslWlyKEEFVieVg0Bjr1\nGMbH78C3yahb/4hq4Wt1SUIIUSUSFk6kf/oR46N/we6voJkX6qY7UKNutrosIYSoMgkLJ9GFBRgL\nngK0PSRGjkc1b1jTlQghGg8JCyfRWxOhqADb/8WiruxkdTlCCFEjll862xBpoxy94WPo1BUJCiFE\nQyBh4Qx7dsDZdGwjx1tdiRBC1AoJCycwNnwEgS2h90CrSxFCiFohYVHL9I8/wKF9qBFjUW5uVpcj\nhBC1QsKilunEj+033g0dZXUpQghRa+RqqBrQJSXob3eggkIgNAyKi9DJW1DDrkd5yWWyQoiGQ8Ki\nBvTq5ej/fY7+ZUPzFlBWhhoxzsqyhBCi1klYVJPel4L+3+eo68aguvRCnzwBaSegdRgqpI3V5Qkh\nRK2SsKgGXViAsXKJPRgm/gnl4YnqG2F1WUII4TQywF0N+v23IDsL29SHUR6eVpcjhBBOJ2FRRY7u\np9ETUOFXWV2OEELUCQmLKtCHvsNYsdje/XTznVaXI4QQdUbGLH5H79qK8dmHqF4DUAOuRbUKRedk\noT9Ygd6+GQKCsd33qHQ/CSEaFQmL39DnSzDeXQ4lJeh1/0av+ze0C4f0U1BWiho7CXXjRFSTJlaX\nKoQQdUrC4jf0pk8gJwvb489DcAh655fo3dugSy9st01FtQq1ukQhhLCEhMXPjIJ89KfvQ7c+qKu6\nA6BGT4DREyyuTAghrGdpWGRmZrJ06VJycnJQShEVFcWYMWNYs2YNGzZswMfHB4DJkyfTt29fp9ZS\nuO4dKMjDdssUpx5HCCHqI0vDws3NjXvuuYfw8HCKioqYM2cOPXv2BGDs2LGMH18360HoczkUfvwu\nqt8Q1BUd6uSYQghRn1gaFv7+/vj7+wPQrFkz2rRpQ1ZWVp3XoT95D33+PLYJd9X5sYUQoj5wmfss\n0tPTOXbsGB07dgRg/fr1PP7448THx5Ofn++04+qzGeikT2k6YgwqpK3TjiOEEPWZ0lrryl/mXMXF\nxTzzzDPceuutDBw4kJycHMd4xerVq8nOziY6OvqC/RITE0lMTAQgJiaG8+fPV/nYZT+dIO+NRfjP\n+v/AP7Bm30gj4O7uTllZmdVluDxpJ3OkncxxZjt5epq7Z8zysCgrK2PBggX06tWLceMunNo7PT2d\nBQsWEBsbW+l7nTx5stp1BAUFkZmZWe39GwtpJ3OkncyRdjLHme0UGmrulgBLu6G01ixbtow2bdpU\nCIrs7GzH1zt27CAsLMyK8oQQQvzM0gHugwcPsmXLFtq1a8cTTzwB2C+T3bp1K8ePH0cpRXBwMNOn\nT7eyTCGEaPQsDYsuXbqwZs2aC7Y7+54KIYQQVeMyV0MJIYRwXRIWQgghKiVhIYQQolISFkIIISol\nYSGEEKJSlt+UJ4QQwvXJmcXP5syZY3UJ9YK0kznSTuZIO5njCu0kYSGEEKJSEhZCCCEqJWHxs6io\nKKtLqBekncyRdjJH2skcV2gnGeAWQghRKTmzEEIIUSlLJxJ0BXv27OGtt97CMAxGjhzJhAkTrC7J\nJWRmZrJ06VJycnJQShEVFcWYMWPIz88nLi6OjIwMgoODmT17Nt7e3laXaznDMJgzZw4BAQHMmTOH\n9PR0Fi1aRF5eHuHh4cyaNQt390b/342CggKWLVtGamoqSikeeOABQkND5TP1O//5z3/YuHEjSinC\nwsKIjo4mJyfH0s9Uoz6zMAyDN954g6effpq4uDi2bt1KWlqa1WW5BDc3N+655x7i4uKYP38+69ev\nJy0tjYSEBHr06MHixYvp0aMHCQkJVpfqEj755BPatGnjeLxq1SrGjh3LkiVLaN68ORs3brSwOtfx\n1ltv0bt3bxYtWsTChQtp06aNfKZ+Jysri08//ZSYmBhiY2MxDINt27ZZ/plq1GFx5MgRQkJCaNWq\nFe7u7gwePJjk5GSry3IJ/v7+hIeHA9CsWTPatGlDVlYWycnJREZGAhAZGSntBZw9e5bdu3czcuRI\nwL6o1759+xg0aBAAw4cPl3YCCgsL+f777xkxYgRgXyq0efPm8pm6CMMwOH/+POXl5Zw/fx4/Pz/L\nP1ON+rw4KyuLwMBf190ODAzk8OHDFlbkmtLT0zl27BgdO3YkNzcXf39/APz8/MjNzbW4OuutWLGC\nu+++m6KiIgDy8vLw8vLCzc0NgICAALKysqws0SWkp6fj4+NDfHw8J06cIDw8nKlTp8pn6ncCAgK4\n6aabeOCBB/D09KRXr16Eh4db/plq1GcWonLFxcXExsYydepUvLy8KjynlEIpZVFlrmHXrl34+vo6\nzsLEpZWXl3Ps2DFGjx7Niy++SJMmTS7ocpLPFOTn55OcnMzSpUt57bXXKC4uZs+ePVaX1bjPLAIC\nAjh79qzj8dmzZwkICLCwItdSVlZGbGwsw4YNY+DAgQD4+vqSnZ2Nv78/2dnZ+Pj4WFyltQ4ePMjO\nnTtJSUnh/PnzFBUVsWLFCgoLCykvL8fNzY2srCz5XGE/cw8MDKRTp04ADBo0iISEBPlM/c7evXtp\n2bKlox0GDhzIwYMHLf9MNeoziw4dOnDq1CnS09MpKytj27Zt9O/f3+qyXILWmmXLltGmTRvGjRvn\n2N6/f3+SkpIASEpKYsCAAVaV6BLuvPNOli1bxtKlS3nkkUfo3r07Dz/8MN26dWP79u0AbN68WT5X\n2LuYAgMDOXnyJGD/odi2bVv5TP1OUFAQhw8fpqSkBK21o52s/kw1+pvydu/ezT//+U8Mw+C6667j\n1ltvtbokl3DgwAHmzp1Lu3btHN0CkydPplOnTsTFxZGZmSmXOf7Ovn37+Pjjj5kzZw5nzpxh0aJF\n5Ofn0759e2bNmoWHh4fVJVru+PHjLFu2jLKyMlq2bEl0dDRaa/lM/c6aNWvYtm0bbm5uXHnllcyc\nOZOsrCxLP1ONPiyEEEJUrlF3QwkhhDBHwkIIIUSlJCyEEEJUSsJCCCFEpSQshBBCVErCQjRKjz76\nKPv27bPk2JmZmdxzzz0YhmHJ8YWoDrl0VjRqa9as4fTp0zz88MNOO8aDDz7IjBkz6Nmzp9OOIYSz\nyZmFEDVQXl5udQlC1Ak5sxCN0oMPPsif/vQnXnrpJcA+XXZISAgLFy6ksLCQf/7zn6SkpKCU4rrr\nrmPSpEnYbDY2b97Mhg0b6NChA1u2bGH06NEMHz6c1157jRMnTqCUolevXtx77700b96cJUuW8OWX\nX+Lu7o7NZuO2224jIiKChx56iHfeeccxz8/y5cs5cOAA3t7e3HzzzY41l9esWUNaWhqenp7s2LGD\noKAgHnzwQTp06ABAQkICn376KUVFRfj7+3PffffRo0cPy9pVNFyNeiJB0bh5eHhwyy23XNANtXTp\nUnx9fVm8eDElJSXExMQQGBjIqFGjADh8+DCDBw9m+fLllJeXk5WVxS233MLVV19NUVERsbGxvPfe\ne0ydOpVZs2Zx4MCBCt1Q6enpFep45ZVXCAsL47XXXuPkyZPMmzePkJAQunfvDthntn3ssceIjo7m\n3Xff5c0332T+/PmcPHmS9evX88ILLxAQEEB6erqMgwinkW4oIX4jJyeHlJQUpk6dStOmTfH19WXs\n2LFs27bN8Rp/f39uvPFG3Nzc8PT0JCQkhJ49e+Lh4YGPjw9jx45l//79po6XmZnJgQMHuOuuu/D0\n9OTKK69k5MiRjon1ALp06ULfvn2x2Wxce+21HD9+HACbzUZpaSlpaWmOuZZCQkJqtT2E+IWcWQjx\nG5mZmZSXlzN9+nTHNq11hUWygoKCKuyTk5PDihUr+P777ykuLsYwDNMT4WVnZ+Pt7U2zZs0qvP8P\nP/zgeOzr6+v42tPTk9LSUsrLywkJCWHq1Km89957pKWl0atXL6ZMmSLToQunkLAQjdrvF9oJDAzE\n3d2dN954w7EqWWXeeecdAGJjY/H29mbHjh28+eabpvb19/cnPz+foqIiR2BkZmaa/oE/dOhQhg4d\nSmFhIf/4xz/417/+xaxZs0ztK0RVSDeUaNR8fX3JyMhw9PX7+/vTq1cvVq5cSWFhIYZhcPr06ct2\nKxUVFdG0aVO8vLzIysri448/rvC8n5/fBeMUvwgKCuKqq67i3//+N+fPn+fEiRNs2rSJYcOGVVr7\nyZMn+e677ygtLcXT0xNPT89Gv8qccB4JC9GoRUREAHDvvffy1FNPAfDQQw9RVlbGo48+yrRp03j5\n5ZfJzs6+5HtMnDiRY8eO8cc//pEXXniBa665psLzEyZM4IMPPmDq1Kl89NFHF+z/5z//mYyMDGbM\nmMFLL73ExIkTTd2TUVpayr/+9S/uvfde7r//fs6dO8edd95ZlW9fCNPk0lkhhBCVkjMLIYQQlZKw\nEEIIUSkJCyGEEJWSsBBCCFEpCQshhBCVkrAQQghRKQkLIYQQlZKwEEIIUSkJCyGEEJX6/wG3Vkil\nyo892QAAAABJRU5ErkJggg==\n",
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x5MiRC75/WFgYOTk5F3y9J5Aycsxdy0hnZmA8Go+6+U70lvVQWoLl8YXg7Y3x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\nEg8Ob/psAAAAAElFTkSuQmCC\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1107ba828>"
+       "<matplotlib.figure.Figure at 0x1abb2765208>"
       ]
      },
      "metadata": {},
@@ -428,6 +423,152 @@
     "Modify the code to compare the variance and performance before and after adding baseline. And explain wht the baseline won't introduce bias. Then, write a report about your findings and explainations. "
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Iteration 1: Average Return = 30.5\n",
+      "Iteration 2: Average Return = 30.97\n",
+      "Iteration 3: Average Return = 34.39\n",
+      "Iteration 4: Average Return = 34.49\n",
+      "Iteration 5: Average Return = 39.38\n",
+      "Iteration 6: Average Return = 39.56\n",
+      "Iteration 7: Average Return = 38.52\n",
+      "Iteration 8: Average Return = 47.56\n",
+      "Iteration 9: Average Return = 45.63\n",
+      "Iteration 10: Average Return = 47.82\n",
+      "Iteration 11: Average Return = 43.86\n",
+      "Iteration 12: Average Return = 50.8\n",
+      "Iteration 13: Average Return = 49.57\n",
+      "Iteration 14: Average Return = 52.1\n",
+      "Iteration 15: Average Return = 53.25\n",
+      "Iteration 16: Average Return = 56.55\n",
+      "Iteration 17: Average Return = 57.8\n",
+      "Iteration 18: Average Return = 55.13\n",
+      "Iteration 19: Average Return = 54.48\n",
+      "Iteration 20: Average Return = 55.56\n",
+      "Iteration 21: Average Return = 60.33\n",
+      "Iteration 22: Average Return = 61.28\n",
+      "Iteration 23: Average Return = 65.61\n",
+      "Iteration 24: Average Return = 66.02\n",
+      "Iteration 25: Average Return = 71.55\n",
+      "Iteration 26: Average Return = 66.51\n",
+      "Iteration 27: Average Return = 70.45\n",
+      "Iteration 28: Average Return = 66.59\n",
+      "Iteration 29: Average Return = 76.95\n",
+      "Iteration 30: Average Return = 74.85\n",
+      "Iteration 31: Average Return = 76.25\n",
+      "Iteration 32: Average Return = 82.77\n",
+      "Iteration 33: Average Return = 82.44\n",
+      "Iteration 34: Average Return = 90.91\n",
+      "Iteration 35: Average Return = 93.65\n",
+      "Iteration 36: Average Return = 100.23\n",
+      "Iteration 37: Average Return = 104.6\n",
+      "Iteration 38: Average Return = 111.54\n",
+      "Iteration 39: Average Return = 109.77\n",
+      "Iteration 40: Average Return = 128.62\n",
+      "Iteration 41: Average Return = 129.4\n",
+      "Iteration 42: Average Return = 150.79\n",
+      "Iteration 43: Average Return = 160.3\n",
+      "Iteration 44: Average Return = 153.7\n",
+      "Iteration 45: Average Return = 158.81\n",
+      "Iteration 46: Average Return = 158.52\n",
+      "Iteration 47: Average Return = 160.79\n",
+      "Iteration 48: Average Return = 159.55\n",
+      "Iteration 49: Average Return = 168.21\n",
+      "Iteration 50: Average Return = 171.06\n",
+      "Iteration 51: Average Return = 167.63\n",
+      "Iteration 52: Average Return = 168.45\n",
+      "Iteration 53: Average Return = 175.41\n",
+      "Iteration 54: Average Return = 173.7\n",
+      "Iteration 55: Average Return = 174.66\n",
+      "Iteration 56: Average Return = 186.83\n",
+      "Iteration 57: Average Return = 182.37\n",
+      "Iteration 58: Average Return = 188.43\n",
+      "Iteration 59: Average Return = 188.83\n",
+      "Iteration 60: Average Return = 188.65\n",
+      "Iteration 61: Average Return = 190.42\n",
+      "Iteration 62: Average Return = 188.67\n",
+      "Iteration 63: Average Return = 185.52\n",
+      "Iteration 64: Average Return = 190.54\n",
+      "Iteration 65: Average Return = 184.61\n",
+      "Iteration 66: Average Return = 186.75\n",
+      "Iteration 67: Average Return = 191.3\n",
+      "Iteration 68: Average Return = 186.89\n",
+      "Iteration 69: Average Return = 189.24\n",
+      "Iteration 70: Average Return = 186.92\n",
+      "Iteration 71: Average Return = 189.76\n",
+      "Iteration 72: Average Return = 191.05\n",
+      "Iteration 73: Average Return = 191.01\n",
+      "Iteration 74: Average Return = 190.58\n",
+      "Iteration 75: Average Return = 186.59\n",
+      "Iteration 76: Average Return = 188.17\n",
+      "Iteration 77: Average Return = 194.91\n",
+      "Iteration 78: Average Return = 192.14\n",
+      "Iteration 79: Average Return = 192.46\n",
+      "Iteration 80: Average Return = 194.36\n",
+      "Iteration 81: Average Return = 194.98\n",
+      "Iteration 82: Average Return = 190.75\n",
+      "Iteration 83: Average Return = 193.96\n",
+      "Iteration 84: Average Return = 194.34\n",
+      "Iteration 85: Average Return = 194.81\n",
+      "Iteration 86: Average Return = 195.32\n",
+      "Solve at 86 iterations, which equals 8600 episodes.\n"
+     ]
+    }
+   ],
+   "source": [
+    "sess.run(tf.global_variables_initializer())\n",
+    "\n",
+    "n_iter = 200\n",
+    "n_episode = 100\n",
+    "path_length = 200\n",
+    "discount_rate = 0.99\n",
+    "baseline = None\n",
+    "\n",
+    "po = PolicyOptimizer(env, policy, baseline, n_iter, n_episode, path_length,\n",
+    "                     discount_rate)\n",
+    "\n",
+    "# Train the policy optimizer\n",
+    "loss_list, avg_return_list = po.train()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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fUz3bkN5YYySiPSOIMkYWOSOwblTt8alenLEULxgIIRArViNPvoqUEtmkyp6T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\n++Zg3nrrLQA2btxIdHQ0n332Ga+99ppP5xqNRux2Oy0tLWpAqq2t9Tm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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x1abb4cc7c18>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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3x6D8ZTcCIari9HkWMTExzJ8/H29vb+bPn090dDQXX3xxjW6ek5NDUJC9nzgo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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x1abb4d3e630>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "util.plot_curve(loss_list, \"loss\")\n",
+    "util.plot_curve(avg_return_list, \"average return\")"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -453,6 +594,321 @@
     "If you answer is right, your will solve CartPole with roughly ~ 80 iterations."
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# set the hyperparameter for generalized advantage estimation (GAE)\n",
+    "LAMBDA = 0.98 # \\lambda\n",
+    "class PolicyOptimizer_actor_critic(PolicyOptimizer):\n",
+    "    def __init__(self, env, policy, baseline, n_iter, n_episode, path_length,\n",
+    "        discount_rate=.99):\n",
+    "        PolicyOptimizer.__init__(self, env, policy, baseline, n_iter, n_episode, path_length,\n",
+    "            discount_rate=.99)\n",
+    "    \n",
+    "    def process_paths(self, paths):\n",
+    "        for p in paths:\n",
+    "            if self.baseline != None:\n",
+    "                b = self.baseline.predict(p)\n",
+    "                b[-1] = 0 # terminal state\n",
+    "            else:\n",
+    "                b = 0\n",
+    "            \n",
+    "            \"\"\"\n",
+    "            1. Variable `b` is the reward predicted by our baseline\n",
+    "            2. Calculate the advantage function via one-step bootstrap\n",
+    "                    A(s, a) = [r(s,a,s') + \\gamma*v(s')] - v(s)\n",
+    "            3. `target_v` specifies the target of the baseline function\n",
+    "            \"\"\"\n",
+    "            r = util.discount_bootstrap(p[\"rewards\"], self.discount_rate, b)\n",
+    "            target_v = util.discount_cumsum(p[\"rewards\"], self.discount_rate)\n",
+    "            a = r - b\n",
+    "            \n",
+    "            p[\"returns\"] = target_v\n",
+    "            p[\"baselines\"] = b\n",
+    "            p[\"advantages\"] = (a - a.mean()) / (a.std() + 1e-8) # normalize\n",
+    "\n",
+    "        obs = np.concatenate([ p[\"observations\"] for p in paths ])\n",
+    "        actions = np.concatenate([ p[\"actions\"] for p in paths ])\n",
+    "        rewards = np.concatenate([ p[\"rewards\"] for p in paths ])\n",
+    "        advantages = np.concatenate([ p[\"advantages\"] for p in paths ])\n",
+    "\n",
+    "        return dict(\n",
+    "            observations=obs,\n",
+    "            actions=actions,\n",
+    "            rewards=rewards,\n",
+    "            advantages=advantages,\n",
+    "        )"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Iteration 1: Average Return = 18.37\n",
+      "Iteration 2: Average Return = 18.64\n",
+      "Iteration 3: Average Return = 18.61\n",
+      "Iteration 4: Average Return = 20.39\n",
+      "Iteration 5: Average Return = 21.79\n",
+      "Iteration 6: Average Return = 23.28\n",
+      "Iteration 7: Average Return = 26.5\n",
+      "Iteration 8: Average Return = 26.41\n",
+      "Iteration 9: Average Return = 38.14\n",
+      "Iteration 10: Average Return = 39.46\n",
+      "Iteration 11: Average Return = 43.6\n",
+      "Iteration 12: Average Return = 56.31\n",
+      "Iteration 13: Average Return = 60.37\n",
+      "Iteration 14: Average Return = 74.8\n",
+      "Iteration 15: Average Return = 77.94\n",
+      "Iteration 16: Average Return = 88.85\n",
+      "Iteration 17: Average Return = 85.66\n",
+      "Iteration 18: Average Return = 89.34\n",
+      "Iteration 19: Average Return = 97.0\n",
+      "Iteration 20: Average Return = 94.19\n",
+      "Iteration 21: Average Return = 86.07\n",
+      "Iteration 22: Average Return = 97.74\n",
+      "Iteration 23: Average Return = 91.69\n",
+      "Iteration 24: Average Return = 90.21\n",
+      "Iteration 25: Average Return = 92.39\n",
+      "Iteration 26: Average Return = 89.37\n",
+      "Iteration 27: Average Return = 87.73\n",
+      "Iteration 28: Average Return = 81.14\n",
+      "Iteration 29: Average Return = 95.13\n",
+      "Iteration 30: Average Return = 88.92\n",
+      "Iteration 31: Average Return = 90.05\n",
+      "Iteration 32: Average Return = 94.35\n",
+      "Iteration 33: Average Return = 95.83\n",
+      "Iteration 34: Average Return = 94.58\n",
+      "Iteration 35: Average Return = 97.66\n",
+      "Iteration 36: Average Return = 107.71\n",
+      "Iteration 37: Average Return = 94.41\n",
+      "Iteration 38: Average Return = 85.35\n",
+      "Iteration 39: Average Return = 95.1\n",
+      "Iteration 40: Average Return = 96.84\n",
+      "Iteration 41: Average Return = 104.97\n",
+      "Iteration 42: Average Return = 97.64\n",
+      "Iteration 43: Average Return = 102.49\n",
+      "Iteration 44: Average Return = 113.19\n",
+      "Iteration 45: Average Return = 110.21\n",
+      "Iteration 46: Average Return = 110.11\n",
+      "Iteration 47: Average Return = 114.36\n",
+      "Iteration 48: Average Return = 130.16\n",
+      "Iteration 49: Average Return = 132.27\n",
+      "Iteration 50: Average Return = 135.63\n",
+      "Iteration 51: Average Return = 133.3\n",
+      "Iteration 52: Average Return = 138.79\n",
+      "Iteration 53: Average Return = 141.04\n",
+      "Iteration 54: Average Return = 144.74\n",
+      "Iteration 55: Average Return = 146.45\n",
+      "Iteration 56: Average Return = 140.39\n",
+      "Iteration 57: Average Return = 147.39\n",
+      "Iteration 58: Average Return = 153.11\n",
+      "Iteration 59: Average Return = 141.86\n",
+      "Iteration 60: Average Return = 148.21\n",
+      "Iteration 61: Average Return = 141.57\n",
+      "Iteration 62: Average Return = 142.29\n",
+      "Iteration 63: Average Return = 148.51\n",
+      "Iteration 64: Average Return = 140.74\n",
+      "Iteration 65: Average Return = 149.14\n",
+      "Iteration 66: Average Return = 152.47\n",
+      "Iteration 67: Average Return = 149.24\n",
+      "Iteration 68: Average Return = 138.4\n",
+      "Iteration 69: Average Return = 140.74\n",
+      "Iteration 70: Average Return = 141.23\n",
+      "Iteration 71: Average Return = 133.87\n",
+      "Iteration 72: Average Return = 141.9\n",
+      "Iteration 73: Average Return = 136.04\n",
+      "Iteration 74: Average Return = 145.07\n",
+      "Iteration 75: Average Return = 137.5\n",
+      "Iteration 76: Average Return = 137.77\n",
+      "Iteration 77: Average Return = 146.0\n",
+      "Iteration 78: Average Return = 145.29\n",
+      "Iteration 79: Average Return = 145.52\n",
+      "Iteration 80: Average Return = 145.19\n",
+      "Iteration 81: Average Return = 140.74\n",
+      "Iteration 82: Average Return = 141.58\n",
+      "Iteration 83: Average Return = 155.41\n",
+      "Iteration 84: Average Return = 149.82\n",
+      "Iteration 85: Average Return = 149.35\n",
+      "Iteration 86: Average Return = 151.23\n",
+      "Iteration 87: Average Return = 151.5\n",
+      "Iteration 88: Average Return = 154.62\n",
+      "Iteration 89: Average Return = 152.32\n",
+      "Iteration 90: Average Return = 163.26\n",
+      "Iteration 91: Average Return = 161.27\n",
+      "Iteration 92: Average Return = 153.37\n",
+      "Iteration 93: Average Return = 146.51\n",
+      "Iteration 94: Average Return = 155.09\n",
+      "Iteration 95: Average Return = 153.72\n",
+      "Iteration 96: Average Return = 150.84\n",
+      "Iteration 97: Average Return = 151.8\n",
+      "Iteration 98: Average Return = 157.12\n",
+      "Iteration 99: Average Return = 151.62\n",
+      "Iteration 100: Average Return = 152.22\n",
+      "Iteration 101: Average Return = 149.63\n",
+      "Iteration 102: Average Return = 147.91\n",
+      "Iteration 103: Average Return = 152.14\n",
+      "Iteration 104: Average Return = 142.41\n",
+      "Iteration 105: Average Return = 146.01\n",
+      "Iteration 106: Average Return = 146.08\n",
+      "Iteration 107: Average Return = 140.91\n",
+      "Iteration 108: Average Return = 152.31\n",
+      "Iteration 109: Average Return = 150.13\n",
+      "Iteration 110: Average Return = 153.66\n",
+      "Iteration 111: Average Return = 159.03\n",
+      "Iteration 112: Average Return = 161.19\n",
+      "Iteration 113: Average Return = 159.77\n",
+      "Iteration 114: Average Return = 155.77\n",
+      "Iteration 115: Average Return = 163.07\n",
+      "Iteration 116: Average Return = 159.13\n",
+      "Iteration 117: Average Return = 160.18\n",
+      "Iteration 118: Average Return = 157.42\n",
+      "Iteration 119: Average Return = 157.94\n",
+      "Iteration 120: Average Return = 160.62\n",
+      "Iteration 121: Average Return = 165.97\n",
+      "Iteration 122: Average Return = 169.01\n",
+      "Iteration 123: Average Return = 162.06\n",
+      "Iteration 124: Average Return = 158.46\n",
+      "Iteration 125: Average Return = 157.93\n",
+      "Iteration 126: Average Return = 154.82\n",
+      "Iteration 127: Average Return = 158.02\n",
+      "Iteration 128: Average Return = 158.43\n",
+      "Iteration 129: Average Return = 158.97\n",
+      "Iteration 130: Average Return = 155.2\n",
+      "Iteration 131: Average Return = 156.32\n",
+      "Iteration 132: Average Return = 157.74\n",
+      "Iteration 133: Average Return = 152.66\n",
+      "Iteration 134: Average Return = 151.86\n",
+      "Iteration 135: Average Return = 159.88\n",
+      "Iteration 136: Average Return = 160.81\n",
+      "Iteration 137: Average Return = 160.78\n",
+      "Iteration 138: Average Return = 162.45\n",
+      "Iteration 139: Average Return = 168.18\n",
+      "Iteration 140: Average Return = 154.28\n",
+      "Iteration 141: Average Return = 154.41\n",
+      "Iteration 142: Average Return = 158.33\n",
+      "Iteration 143: Average Return = 157.41\n",
+      "Iteration 144: Average Return = 155.62\n",
+      "Iteration 145: Average Return = 160.26\n",
+      "Iteration 146: Average Return = 161.08\n",
+      "Iteration 147: Average Return = 159.65\n",
+      "Iteration 148: Average Return = 159.3\n",
+      "Iteration 149: Average Return = 163.87\n",
+      "Iteration 150: Average Return = 157.24\n",
+      "Iteration 151: Average Return = 156.31\n",
+      "Iteration 152: Average Return = 154.99\n",
+      "Iteration 153: Average Return = 157.0\n",
+      "Iteration 154: Average Return = 157.87\n",
+      "Iteration 155: Average Return = 161.16\n",
+      "Iteration 156: Average Return = 162.85\n",
+      "Iteration 157: Average Return = 159.98\n",
+      "Iteration 158: Average Return = 165.98\n",
+      "Iteration 159: Average Return = 160.04\n",
+      "Iteration 160: Average Return = 164.62\n",
+      "Iteration 161: Average Return = 161.65\n",
+      "Iteration 162: Average Return = 163.17\n",
+      "Iteration 163: Average Return = 167.49\n",
+      "Iteration 164: Average Return = 167.75\n",
+      "Iteration 165: Average Return = 172.5\n",
+      "Iteration 166: Average Return = 163.51\n",
+      "Iteration 167: Average Return = 166.19\n",
+      "Iteration 168: Average Return = 164.78\n",
+      "Iteration 169: Average Return = 172.07\n",
+      "Iteration 170: Average Return = 165.18\n",
+      "Iteration 171: Average Return = 163.92\n",
+      "Iteration 172: Average Return = 163.87\n",
+      "Iteration 173: Average Return = 159.09\n",
+      "Iteration 174: Average Return = 159.76\n",
+      "Iteration 175: Average Return = 158.48\n",
+      "Iteration 176: Average Return = 158.18\n",
+      "Iteration 177: Average Return = 156.48\n",
+      "Iteration 178: Average Return = 162.21\n",
+      "Iteration 179: Average Return = 161.7\n",
+      "Iteration 180: Average Return = 162.1\n",
+      "Iteration 181: Average Return = 172.95\n",
+      "Iteration 182: Average Return = 172.49\n",
+      "Iteration 183: Average Return = 168.28\n",
+      "Iteration 184: Average Return = 178.22\n",
+      "Iteration 185: Average Return = 174.47\n",
+      "Iteration 186: Average Return = 175.37\n",
+      "Iteration 187: Average Return = 172.74\n",
+      "Iteration 188: Average Return = 170.63\n",
+      "Iteration 189: Average Return = 171.42\n",
+      "Iteration 190: Average Return = 170.09\n",
+      "Iteration 191: Average Return = 162.79\n",
+      "Iteration 192: Average Return = 171.33\n",
+      "Iteration 193: Average Return = 163.03\n",
+      "Iteration 194: Average Return = 167.17\n",
+      "Iteration 195: Average Return = 165.31\n",
+      "Iteration 196: Average Return = 164.29\n",
+      "Iteration 197: Average Return = 158.58\n",
+      "Iteration 198: Average Return = 161.52\n",
+      "Iteration 199: Average Return = 161.87\n",
+      "Iteration 200: Average Return = 154.18\n"
+     ]
+    }
+   ],
+   "source": [
+    "sess.run(tf.global_variables_initializer())\n",
+    "\n",
+    "n_iter = 200\n",
+    "n_episode = 100\n",
+    "path_length = 200\n",
+    "discount_rate = 0.99\n",
+    "# reinitialize the baseline function\n",
+    "baseline = LinearFeatureBaseline(env.spec) \n",
+    "sess.run(tf.global_variables_initializer())\n",
+    "po = PolicyOptimizer_actor_critic(env, policy, baseline, n_iter, n_episode, path_length,\n",
+    "                     discount_rate)\n",
+    "\n",
+    "# Train the policy optimizer\n",
+    "loss_list, avg_return_list = po.train()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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Y7+9D+9oJ3HUL+sSRwbdvb4X2VvQ7uwGwNv0A/cbOuE5ttbWYiemxHjwdz7GrE+rrUGXT\nojZRl34SLAuUwvUPd8G8C9B/3A6Afv5pdPWzcdmVaERcRkvAH53MB/FchOSnJ4a4hD8MvbULvekH\ncOCdER1O+/0EHlwXvAHHRYctLt2J9aB04ynzs7MD6o5D3TH0wSGus8XOaxzaj248jX51O3p3qMpO\n+/1Y1b/B+vfvY9W8POS5rfZW80vDqegPB3qOU2KIS2k56rKrUCuvRRV6UHMXQv1JdMMpU2HW3IB2\n1pmKge7vQzfVD2ljIhBxGS2BQOQSxw5Z2eByibgIyYsjKL2RnosTrtEtZgSTPn1iZMdrbjCJ5j1v\nxG1SMEyV6IniDafNz04fdNrnHCox3mqPo+poQ+/cBhCRSNcv/Bf6iX9H73oZ/fzTQ57asvNKur4u\n+kNHXNLTAWJ6LgCuL3wV11+avj911jnmeNv+G7Q2Xk3L4GNc9H8+ivWd28a94kzEZbQE/NE9LthD\nNHNyRVyE5KW3x/zs6Q7lX/x+6O8zv7fZN9SRiktQjE7Gb1MwLJbgnEuDfWPv7AiFrocQF90amnWo\nX7RzGi1h7722HWafg/rkGjh+CO18twOP09sT+t4bT0d/bofF1OJLIC0dyqYOfzEz54ByoV/ZGnqv\n8TTWS7/H+skGUxXoHL++Dr3zBfP/fIQe6Vgh4jJaBvNcwDRSSs5FSFJ0rLAYhOL+rfYT9jBiEfJ0\n7KflkYpRLIKey8jFxdq5DX34vdGdJ9xzcYoIhvJcWppMJCI1NdRe4IjpyaNw7BDqostQc+Yaz2Ew\ne5yQGEBDDM/FDgeqz34B13ceRjmr2g6BysyCqTPNd5adY2xqOIV+eSv6jy9iPfpAsJlb//ZXJoyf\nkoreW4t+989Yjz+E9o2ssOFMEHEZLQG/+YOLRU6uiekKQjLiCIplRVZNORVLbfbNdhBx0XXHaf3u\n17H+frVZIdF5um84HX8TpJ1z0SP0XHRXJ/qx/4O1/utYL/0+4rPAv30XK0ZyW1sBcHIOnR2h6EJb\ntLjo/j4jnq1NkF9kqrMAPCVmAkd3F/r1P4ByoSo/Dmeda/azvQLd1Yn13BMhT8bJKWEEIAonLJab\njyoZ2bRhAGWfVy28yIjH6ZNw/BCUTYPdr6Of/in60HvoP25DXfZJqDgX/c5urN/8Ar3nTcjIHPG5\n4kXEZbQEArET+mAqxsRzEZKVcG8l/KnducE5PSf1deaGPADrF4/St+dPYGmTDHfCRAF/6OY9DPrI\nQXS9ES9tBUI3+gGei9Ya6+Wt6IEJb+fpPzcP/bMfBZ/Atdaw5w30e3ujT9rSHOxP052+0DkHeC66\npwvrn/7aJO9bm6GgCDX7bADU0uX2Pk3oN16BuQtQBUWonFwom4Z+/120ZZmw1LObwVme2BGXKdOh\nPpa4+CAtHZWWPsS3FgNbXKiYC55i9J93QV8fauVfoZb/Bbr6Wawf/ou5hk9/HvWRRXD0IOzfg7pq\n9ejPFwciLqMl4B80LKbcknP5sKJ7e7B++X9H/ASeUFusANaPHzTls38KK58NF5fwp3anUqu12TzR\nBvzQeBq950/oumNmyd3+PjjwDllX/CV4S+D0yYi8xGDezkCsRx/A+sn/MS86fSYhDdFhsdMn0f/x\niPESwq/NPo/65GdN5/rRg+b9rk6zcmOYpxDErhQjPd3Oudj/Rjva0H4/+uA+U2114qgR2r215rso\n9Jgqrb/4K9RHzjf71B2HUydQ55wXPLyqmGtKnJ/4d9j9urHHnhOmbXvUWecaYXLyWw5dncHQ1mhQ\nC5bAgkrUoovAWxacP6ZmzkFd8zcmd9Pehuvv/gmV4w7Zn1dgPJlxQMRllOhAYMiwmIjLh5T33ka/\n8F/gLPI0BLrxNPpPf0ycLc2N6JqX0DUvYf34wVCCN0xcIhLWnT6zTWcHzPmIee/Z/8R66DtYd92C\n9aP74eA+6O8jfUEllJabm3xLE0ybZbavD4mL9vcT+Lf15gk/DN3dZcpxD+4z53eEID0jus/FsW9g\n6MquuFKVHzfHPHwAAMvJ/8RokgyGo6afZTwFJ4eiNRzYi7X+f5t8xYnD5u0jB6C1CVXgQU2bheuz\nN0KhWbFRv/2mOf+0maETVMwFXwd623Ooy66CgqKQ2DrX6HgajafRzQ0E7vlHE1rs6jRrQY0SlVdA\nyj/cZWwsLjVvZmRC6RRURgauO+7F9bX7UWfPM5/NOhtmzkF99guo9IxRny8eZPzLaLE9lxi9tiah\n39ON9vtRgwmQkFT0vPIC1q6duG74+zM6jm63cwddPtRw2/72V+idL+D64VMjHuGhm+pRnpKRGWPf\nmNWFl6Jf3W5CSeUzBg+LdXcGb+Lq3AXot980HsPUmeb1tuew/P3gcpE2fxHqtT+g33sHsrJQH1mE\nbmqISOrr//4V/GknOi0NteRjofOENS3qN19Dlc8wL4rLTFlz+PU69jmhOof6k1DgQRV4oGSKEQLA\nckJ0vhieS8Mp0/g8fba5roxM84Do96PffNVsc/Cd0E3emUJc4Akdo6DI2GUP/WTqrOBH6sKPQ0sT\n6oKlqOmzCXzvRKicu70NlZmNmjoTDejdr5tmzGOH0Pv3oLs7zX3jTPDa4jL9rGBztyryQlFoCWOV\nkkLKt39wZucZJeK5jJZAIGYpMiCTkScJ1ku/x/rVYwD0vv4SesfvosMVI0BbFtrxVDrsqqAR5Nz0\n0ffN31GMhHJMe3e+gPWNv0MfH9lidNppAJy70Pw8ZW50eqC4ZNmVSV2dwZu4mjY7eJNVK69FffZG\ns93bb8Kss3Fl50DJFNMr09psbmAlU9CnTqBrX8N69j/Rv33SnG9A6W2wI96dZ8J1jhAUl5mHsvDJ\nAPZ3oweIi66vg1KT+FYz54DtuQQccen0ReeLGk6ZhLw734TfOtpN4htzswdMzuTkUVMh5lBYFPxV\npWeYf99N9ZCRZY7nfJaZjevqz6Omm+S/KpsKp06YPFBHK678AiPu+UXop//DVJalpRtBjdNzCUcV\nl9nfR8UZHWesEXEZLUPkXJwRMJLUjx9tWVgv/ndCSyX17tfRr+0AwOpoN7H7U3GU0+7bjfXgOvTR\ng2B7LsNNxdb+frDDLzQPv3657u8zCWJAHxph+a3juZy7wOznrBPS2x0SlLYWc7NMTzc3OMdTKCgy\nY95Lp6KWXGyeui81MXo118TtVWlYL0aBx7x+ZzfWD+9DP/dLU2F1wdLovo4ThyErG3XplbB/D9rJ\nExSXmRBVeK/IoJ5LHapkivl95hzTnd7eGgqLaR317083njZP9zlu83lbM2qqHdZyChHq68xNf0Fo\neXUV7rk43w3AtJlDD7MsmxoMv+mONlz5haisbFzr/y+u2+7Edcu3YNYcU8rd5UPFkXOJPJ/deOmE\n3pIEEZfRMkS1mHLnmV86E19D/oHl/XfR//loYnMSXT7wtZuKJKcU9uTol5LVjpA0nA7zXIbJuZ08\nZhoXAT0gFBTzHDueNyKkXBFhpSFpbYbUNPN0nV8UEs6ebsgvNL/7+yEzyzwQdflCYaj8Qlx/979w\nrb0nFGKputrE6y80eQ7HcwBQhV5YWAnTZqH+di2uHz1Fyp0bUDMqoK0loitcHz8M5TNQF11qyqF3\nPG8+sJ+8I5L6QXEJ64rv6jQ5DFtc1Kw55oMjB7FawrzAgUn9hlOo4imhyAKYG7Kyb38z7Cf+3h4z\nWsUJJxUURR6n0IiNCguJxSIovqePm6S6/Z2r1DTUwgtRiz6KKiw2/1/jTOhHnG/qTFxfX4+q/Njw\nG48jSZMYqK2t5bHHHsOyLK644gpWrVoV8Xl/fz8bN27k/fffJzc3l9tvv52SEuOa/vrXv2bbtm24\nXC7+5m/+hkWLFiXO0IAflTlIjXiuERe978+oOfMSZ8MHGL3PXtcjkd5fV6epiOrtDlbzMMKlZLXW\ncPqkCX3YoTTd0ohuH1lYTB97P/RiiJEdwe1f/C2cPc/kB44fHny7QAD9y/+LunKV8VwKPWZqRNnU\nUPy/pztSbDKzIRBAd3Wi2prNpG93XtRTuSr0RMbri7zBnAWFRbhmXAgfXRZpkJMHaKqHKdPN93bi\nCOrCS03obdbZxlPIygHnoSys0i4odu2taMsyNtllyMF+EFsU9JEDIc8FIpL6ursLfO1QXBpaFgMg\nLx/yC6C1GbX8U+if/wgsy+RGZs4xN/4Bnosq9Jr9w5P5sbDFRZ86AR1tqLnnRW9T5IU3mgB9xmEx\nICnvN0nhuViWxaZNm/jmN7/Jhg0beOWVVzh+/HjENtu2bSMnJ4dHHnmElStXsnmzCRUcP36cnTt3\n8oMf/IBvfetbbNq0CSuRU12H6nOZNhsWLUU/uzmqwUsYGSFxSWDVndM70dFuwmKArhuZ56J3voB1\n11fNHK4+O08TVvmku4ax+8hBE7PPzBo2LKY7O6D+JGpBJWraLDhxOPbYdjCDDLf/1lSJtTYFn7pN\n/P+42a+3G5Uf9jSemWWemrvtsFhe4YjWLlGuFLPWCASrqKK2ccTFCY212E/p9lO/uvRK835uHsoJ\n1YV7Lo7HYlnQ2kRg/f/GeuLfzXuO55KVbcTzyAGT0M/MMp+Hh1TtSjFVXBbhuaicXCO0YMqKnTDZ\n1Jm4LroMFi01nfDhON/pMJ4L3hJzjzh1HHwhzyWCIq95wAkEzjyhn6QkhbgcOHCAsrIySktLSU1N\n5ZJLLqGmpiZim127drF8+XIAli5dyp49e9BaU1NTwyWXXEJaWholJSWUlZVx4MCBxBk7RIe+crlw\nfeVrUDHXjF0QRoXu7zMlr5DYoghHXNpbQ4tljXCdcr3rFRO397WDE/JpaQrlXAbxXKyXtxL4wZ1G\nPKfPhqJi9HA5FztZrWadbUp+fR2DFwE4T+vHD5unceepu2yaud6ONuO5uHODf7/KCYt1+kzifGAY\naChKp5rjOF7HQGxxCSb17ZCek+tQF11qqrZy840HBaHFzLQ2YmcnzfXeWvN34TRIOsJGKKkfaGkK\nCoQOD4s5PS7essibeE6uud6sHCguM02GJVNQeQWoyo+Tcss3oy5JnTXX2DRj9pBfjXKlmCKHfX+G\nQCCmuKhwUR4DzyUZSQpxaW5uxuMJuaAej4fm5uZBt0lJSSE7O5uOjo6ofYuKiqL2HVOGmi2GHVc9\n69zImUKTFO3vx3py07jMIQLMDcSZiTQKcdHtrSOe+Kr9/uC6JsEZWtlu05UeNvAv5r7dXbDPHi/f\n1wv95py6pTEU5x/E49KvVMM7u6HumKnqKfIOGxYLzs+aWRF6Wj4+SN7F6VQ/fth4UuGeC5in6J5u\n83SfYT+RZ2aZZHKXz4ScRiEurqXLUctXmtBbLPILTUWULS7asdsOKanMbNT1X8FVdXWoyMBp5uzq\nNCFHp/rJ7nZXn///UNffjMoI69OYNcd4NqeOh5L0vvCRK7a4FZdG5lxycnF96hpcX7wF5XKhPnsj\nrm9vGPKa1XmLSVn/7yOb/3X2PLDLpAf1XJxtzzShn6QkRc4llqs/8I92sG0GDRPEoLq6murqagDW\nr1+P1xvbpR+KjqXLSCsuJXOIfTvLyvH19VKUk40ra/g/xLEiNTU1rmsajP4D79C89VnyFiwm89JP\nJNwu39EDdLpSSJ02E1d/H4UjvJbGu76KSs+g4DsPkTLMDdJqb8VJo2d3tNAJZMxfRG/NyxT0dZE2\nZfByzp5XXqDNTsbnZWXSl5pKF6DqjqMDflAK1dUZda26r5f6wwfIuPhytL8f9yc/Q/fW39B77CXy\n25vo/t2zZF7+KdLnLgjuk5qaSvrJI/jLZ+CdMQursIgGILulgZwY30uX0nSAERGtyZk6gxyvl8C8\nhTQCOc31dFgWOUUeurJzsDo7yCosQvv9dL9eD1qTe80XyR7mOw/+v/zk1ea/IWgsLSe1rYUCr5e2\nxjr6vKUUz5gV2uBqM0I+0HCKRsCdmkKW14u/q50mIGfuAjr/9EfY9xYqM5via74YFbbrW7iElic2\ngd9P9rSZdGW7yfT3kWdfR7uvlR53HsUzZqEDfpwhNUXTZ5LiHWHfUBzof7yT/qs+S//bb5Kz9DKy\n0iPztFZ6WvDvMK+snIwx/Hc7Usb6fhF1/IQdeRR4PB6amkIdw01NTRQWFsbcxuPxEAgE6Orqwu12\nR+3b3NwqtkJBAAAgAElEQVRMUVHsG0xVVRVVVVXB142NwydUo/jU58j1eofc10oxc3uaDr8frEEf\nD7zD2DVadL35p9hefxrfGRx3pHYF3noDps/Gn2cSrSPZR3d3YdWZ/Fzjuptx3fUQKi1t8O3DxpR0\n2qW9fTPPhpqXaXl7N66c/EH3tf5QHfy9vf402pki7Hh23lJ042ka6utRLhd6dw26ucHkS/z99C++\nGLVoKW2Ale1Gt7XQ/NN/g92v0/37LahLrkB98VZUSgper5fe/W+jzl0Q+h4KPHTuf5vuGN+Ldcq+\nLvthqzM9k+7GRjQpkJ6B78/m6b8zYKHtDu1uDagUs09KCp3nLKRrmO98NH9jgUIvgZNHaWxsJHDw\nXZgyPea+utuUIHc01NPZ2Ig+bEa6dNvhL93ZARVzaYoRkdB5HlAKtKYrLQPtzqWnoZ4++zyBY4fB\nUxI6b1Y2dHfR3NePGsN/KzEpLofl5eSkZ0Zdt9balIH39dHeH0i8LTGI935RXj6yAZtJERarqKig\nrq6O+vp6/H4/O3fupLKyMmKbJUuWsH37dgBeffVV5s+fj1KKyspKdu7cSX9/P/X19dTV1TFnzpwJ\nuIoQKs++QU320JgTakrwKoFg+ls4cgA1+xzUaJYucHo4FlSa32ONNQ8nfBCiM6fKKWkdasGl/j70\nn2tCU3D7ekProDiUTTM36u4udG8v1n88jP7Fj02XPEDFR0LbFhabn2/VoC6+HPUXnzPFAo/cg/Xb\nX9Hz0laTd5h1dmifqTPQdlWbtfOFyLXTB4QuncS9crlg2qzQQMfMrFDiOzMbcuyQzLwLQqX0Y4Ty\nlkBjventOXUicmRKOI49dkI/WClWUh4MmSl7zEzUOTKzgn0eKr/INGh2tKFPHDH5nobTkQ942W4z\nKHKcRqAMhlIq9DcgYbHEkZKSwk033cR9992HZVlcfvnlTJ8+nSeeeIKKigoqKytZsWIFGzdu5Lbb\nbsPtdnP77bcDMH36dC6++GLWrl2Ly+Xib//2b3GNoOIloeQVmJ8dk1xcnJvnKNbaGC3askxFUEOd\nyQnMPttUVA2chjvY/rbXouYuMJNhe4fJvXSHiZYzD6vI/kc+yIJPgIn7d3ehPnYF+v13jfAOyPOo\nKdOMDZ0d6NrXTB5GudB/eB7KpqJyQ16RKrLLWrVGXbwC9ZHzsXLz0Vs2o99+EydroMLERZVNQx/Y\nitYavfU30NcDV/yl+dDXYaqfOjtM3qowlIdU02cbmzE3Y+2MW8/MCnakq4GlxGOBt8w8mLy7xxTC\nDFJlpVwpJrnvlCI7jZP5RZBXaP7+pp816GnUrDmmITO/0BQINJ7G2nCXOWZTAyy5OLRxTq6p0EoG\nirxmbE72B7NaLCnEBWDx4sUsXrw44r1rr702+Ht6ejpr166Nue/q1atZvXp1Qu0bFfZNRLe3Djtn\nKpkJJslHeKOP6xz/8YiZm3XJCsDcTHXjabP8rhUwY0cq5qIG+wd46hikpKCmzTI3674hBALQnfa1\nKFeolNidZ25EQ4iLrnnJ9IAsvNA+Ty+6L4bnAtDSZJa+/cj5qAKPWVMj3GuBUAmvOw/sCbuuqquh\n6mp0Tze5Jw7RfuDdyK7rsqnGxuaGoMemtTa5R1+76dvILzSTgsNzTzPCbswRnkuW6Y+47CrUoqVD\nfm/xoBYsQf/qJ1jP/NS8njpEf0hmNrruOIHvfs14/Nk5JnGfXwinTwzquQBw9nzY9Qp4ilHuvOBI\nlyBh1WW4cyHGcgITQbBvZhzzsuNJ0ojLB4pc23NpjzFEbzIxDmExfeIIHDlgEuKZWeYG6gjJ6ZNY\nD9+D+txNpjkw1v51J+zwiR1aGMr7gJDn4i0xPRApKXYFVSb0DL5Urd79uhFA5zxOWCyvIBj+VKVT\nzXDCt2qgow3XJz5jSo5f/wPMvyDyoEVes+DUBUujhleqzCwyP3oZvorIxjhVNs0+/q5gVR0dbcYG\nX7sRP08Jur0lYr0ONf2sUPNgRhYqIwttn0d5ilFf+OrQ31mcqCnTzZTlA++Yvo+hlvDNyoY9b5j/\nH9luM9oFUPmFaKWC05djnudjVXguvYIWUtBOaC87B+aeD3/aGeq5AVyf/nyUxzlhfGQhNJ7+wA65\n/WBe1QSj0tLMTWiy51ycDvQEhsWC39GBd+DcBShXCtoWF33EJHYJXzdkIKeOmYWY7Goc3ds7tLfo\neC7FU6DhFC53nol/Z2QGS5Sj+PMu6OtFVV5qymshFBbzlpoek5wc0/UN6L1mLDtnzUXluHE9+FhU\nP4hKz8D1j3dHehXDYd+cI9ZoaW4IiovylKBWfxH1iQFCXD7TeGraMnmWMM8l0ahLrzSrNJZNRaUO\nXmgRzK1c+knU9V8Jvb/oo6isbNQQKycql4sUrxcaG4NRA7XkY6jPfhFdPgPCutfVnI8Mdphxx7X0\nclh6+USbkTCSIqH/gSSvIPbCRZOJYM4lMZ6L1tqIi1127uQXlNOP4IxKaYst0trvN3OjpkwHp/dh\nmLAY3T5ISTUjySGUB8nIDC1NO/A8zriUs841CfL09JC4ZGab/9e5BaE+iuOHTWOe3bSncvNj9oOo\n+RdE5GGGJb/ICML+PaH3nPlkvg7jubjzUFOmRZ4nIyPkNWRmmv9gfMRlycdNiGvGMBN7s7JNon3l\n51BKBb8v10WX4frCLSM/odPf89HlqNw8XJ+5fsjqQSFxiOeSKHLzQ/OmJitOcjxRnkuXz8xqu/BS\n9K6XUefMN+/bFUz6mBkxrwfrSm+oM8nZsmmhNcEHE4ijB02OpdMeFGjPgXPl5mPB0DmX9hbIdodu\nUukZ5rvp6zU3/OJS4zmF5YWGvZnGgVLKdMYfORAaONncYL6DLt/g3fLYobG6Y5FNlBnjIC4ZGbjW\nPRjZwBgD16eugWW+6EnEoz3f4otRt/8zOH9LwoQh4pIo8gpGPFIkaRmmWkz39YKvI+gFjBqnKmjR\nR3Gt+VKoa9m5SR+1PZfBRNqpFCubFgyLDVYtZj31OLQ0oqafZY6f44hLni0uWRGDE8PRba2hacJg\nxMXOuaj0dNTf/KPJn6SkBPsomJWYcng1ZZpZIOvsefBOrZlP5kwFyB2ilPi8xXBgr/G0cvOMtzjM\nDX/MbC6bNvw2ztozZ3qutPTo/JYwIYi4JAiVl49+988TbcaZMUxYTP9+C3rbc6T84GfxHd9ZoCq/\nEOUpDr3v3PScm+bANT2c8+95w4SopkwzP5UaPCzW2gyn69C5+cZzsZ/yg2GpzMzB53a1t4TKyyEk\nLn19kJ4RmtILRri6u8zMq0RgT9xV5TPQp0+YJk2nx2UIsXBdfDlcbMf3P3o5qmwaaigxEoQzRHIu\niSK3wPQ72ONCJiXBarHu2GN2Gk9BRxs6zr6BYNgw/MYN0XX/Xb6ouV/a145+dbuJrWdmmZBRekZE\naEs3NYSGQ7a3moT24QMmB+AOhcUAkzAeuI67Q1sLaoDnop2cS1hVFhC6wScgLAaE8inlM0x/TnNj\ncIGykTZBqowMMwlYEBKIiEuicLr0Y63pPVlwxEVbMSupgotlDXZTHo6guESO+lFpacYTgVDSeUBo\nTL+81YSlVvxl6M0B4mI99n+wfvqIESbHC+rvMz0zbiMCLufpfcicS2ukjWFhsaCdDu68iGT+mDP3\nfNTS5aj5i1FFxSah73guY9xhLwhnwojDYnv27KGkpISSkhJaWlrYvHkzLpeL66+/noKCguEP8CFD\n5RWY3oL2tqhFhyYLEevKd3WFRqM7dIaJSzw30/ZWM7Y91viL7FzoazLjT/a9ZUJTduhM9/ehX/xv\nU7oc3v8wUCDaW00/yMBJCVk5wRyKy2k2HERcdE+3eT9/QFisu8sWl8gxIq7VXxh+SsAZoHLcqL81\nzcS60GtWe3RKtd3jk0MRhJEwYs9l06ZNwbEqP/3pTwkEAiilePTRRxNm3KQm2Eg5iSvGwpvNYiX1\nnSfmwfpDBqCPHyLwndtCa3y0mVxGzLHtThnv7HNC2zrH+d2vobkR18q/itwnIxMdfmPv7TbzwloH\n5FJyclDeUly3fpvMj9mDTDOyoL/PTAUIpz1sFIlDemZIWNMixUXNnBOqeks0Tp7KWaEyRzwXIXkY\nsbg0Nzfj9XoJBALs3r2br3zlK3z5y19m//79ibRv8mLnEfQE97roQ+9h/ef/P6qlCYKEjzfpjjFI\ncpRhMb3jd3DiCHrrs+Z1e0tIhAdiezPqrHNC22LnUf7nV7DkEtRHzo/cJz0jMqHf3R25PPB0e5Gn\nLFu4zr8otDZIxiDVZq1O0UHITpWeERLWCRyAqOyZaPq9t01hQcbEDmMUhHBGLC5ZWVm0trayd+9e\npk2bRqbdiOWfzAnrRJKbHJOR9Z9rzDrsA0ROnzhqVkYcalxKf19o3MkAz0VbVmhy8QjERfv96F0v\ng1LoV6rRnT7z3cRaSAlCifFZtufijLd/ZSv0+3F97qbofcJCW1rrkF32oltqnl2imhMjDOc0Fg70\nwhzPJTznkpERmrc2MOcynsyoMEn9UyckJCYkHSMWl6uuuop169bx8MMP88lPfhKAffv2MXXqEPOC\nPsxkZUNq2sRPRna8jwHj5PU7tWZlxNMnhti3N3jz1wOHV3Z3mkQ/DD/PC0xPhq8ddfX10NuD/sPv\noL0VNbBSzEbluI1XkF9oEtWO53LyqEmYe2Is9JSRGfI8+nqD9ulDjrgsso8d40bsNBQOmC+mnekA\nA/tcHAZWi40jKseN694fmdUZV//1hNkhCLEYcUJ/1apVXHTRRbhcLsrKzPoIRUVF3HzzzQkzbjKj\nlDIVYxOdc+kPE5fw3osWOwk81HDNvl77yfh4dM7FF1rOV/d0w8F96B3Po274+5jhGf3aDtPlftVq\n9P496OpnTWgpL7bnoi5fCecsMN9jfmHoJn/yGJRPj71PRibaCYuFe1MnjxhPaO5C1BduMWu/RO2b\nYQowBgple4sZSx8uSGHeyoSvC5Kegbr8LybUBkGIxahKkcvLy4PCsmfPHlpbW5kxY0ZCDPtAkFsw\n4TmX4PDJ5kjPxfFkhrSvvy/U3xElLmGLU/V0o9+qQf9xG/pnG2Pmd/S7e1DnLUGlpuG6+vNGdC0r\nsgorDDVzDi57DL+ZPNxieobqT5pZYrEI91zC7bUsUzjgcuG67JOxBcHxXAaGxZyig/A1gsL3n8iw\nmCAkMSMWl7vvvpt9+/YBsGXLFh566CEeeughnnnmmYQZN+kJG8c+YTgVXwPERTuey1Bhu74+88Tu\nckV36Yd5LvR0m9lWGA9F//HFiE2t7k4z2dj2ONScecERHYOFxcJR+YXmJu/MEhvEc4lI6A8UieHO\nM8hsMj2wx8U5T6zfBUEIMmJxOXbsGOecY5KrL7zwAnfffTf33XcfW7duTZhxkx2Vlz/ha7oEe1Va\nBoytd3Iww4XF0jNMUn9gQr8zzHPp7TbJ/eIy09PzTm3EtgF7ad7wab2uz37RLJg1xAqDQQo90NqM\nfn+/fZxBvGU7oa/tpYYBk/eCyA77mPs6nsuAsFhbS3TRQXrY+Pc0ERdBiMWIxcUJdZw6dQqAadOm\n4fV66exM/Prqk5ZcM3Y/rjLgscJO6OuWhuBb2rJCvR+DhMW0ZZkGxPR0exjjQM/FFheXy4TFOu2p\nvKXl6IZTEZv6Txw1v5SGxEXNrCDlX3+CKi1nONTCiyDgRz//lJkfNtggxPQMEwLz+0M5F0fQBsnt\nBMl01oOJzrlECZOExQRhWEac0D/33HP5yU9+QktLCxdeeCFghCY3V0ogByWvwKwd3tUZXwf7WOCE\nxcI9F1+bsYshci7OLK/0DMjKRnd1mhUWz11g5nD5Osyqge58cyPv7IDcfFRBkdkujMDxI2axqpIp\nMU40AirmGq/o1Anwlg7ez+GEtvp6TJEB9oDHY4cGze1E7RtWLaZ7e4znEj5Uk7DkP0hYTBAGYcTi\ncsstt/Bf//Vf5OXlcfXVVwNw8uRJ/uIvzqxSxefzsWHDBhoaGiguLuaOO+7A7Y6+EW/fvj2Y31m9\nejXLly+nt7eXH/zgB5w+fRqXy8WSJUu44YYbzsieMSW812WixCUsLKYtyySmHaFRrsFzQo4opdlh\nsb1vYv15F+pL/4j62BXGc8nJhawsE0rq8qFKp5qVGdtb0b09wdUD/SePgrck7kWblFKojy5HP/dL\ns+rkYITnTZzx+eV2CG04zyUjRp/L8cOgNWra7Mhtk6QUWRCSmRGLS25uLtdff33Ee4sXLz5jA7Zs\n2cKCBQtYtWoVW7ZsYcuWLdx4440R2/h8Pp566inWr18PwDe+8Q0qKytJS0vj05/+NOeddx5+v597\n7rmHN998kwsuSI71HILzxTpaQ+GZ8cYRiYDfhMDyC0P5linTBl8ts9/eLz3ddMs7k4/tOVa606x8\nSFq68RI6fUZAHe+k4VRw3fPAiaODh7JGiFpqxEUNlsyH0E2/tzcYFlMzzPrxaoD3EUVqmgnxhU9V\nHtjZP/A8A38XBCHIiHMufr+fJ598kltvvZUbbriBW2+9lSeffPKMO/RrampYtmwZAMuWLaOmpiZq\nm9raWhYuXIjb7cbtdrNw4UJqa2vJyMjgvPPM6PDU1FRmz55NU9MQ662PN3lJ0KXf3xd6KnfKj23P\nRc2oAN8gOSGn+TI9A3XRZagrV5mktyNGvg7TFZ6ZZfIx3Sb0p7ymVJ1Gk3fRloX/5FFU2Zk126rS\nclx/vw5VdfXg24R7H93dxjObvxjX//oXGGbEvFLKXF94zuX4ISOsRQOESXIugjAsI/Zcfv7zn3Pw\n4EG+/OUvU1xcTENDA08//TRdXV186UtfituAtrY2CgtNyKKwsJD29vaobZqbm/F4QpOFi4qKaG6O\nHEbY2dnJG2+8MWSYrrq6murqagDWr1+P1xvfCoqpqakj2jeQ6qIRyLECZMd5rjO1qyHgx1U+Hf+h\n98j195Hp9dLR00VXaio5Z8/F9+qLeNw5uLIiJx73dzTTDOR5vGQuNeLf+FYNaX095Hu9NHZ3klo+\nA20F8B8+gKU1OSVlZM2dTwOQ3dlBjtdLoL6Oxr5e3HPOPfPv4MpPD/lxb0kprUB+ZiY9StOTlU1x\ncTEUrxh0n/DvrCE7m3QF+fbr5lPHYdbZFBVHiou/s40mAFcK3tKy2IM3z5CR/o2NN2LX6ElW2xJt\n14jF5dVXX+XBBx8MJvDLy8uZPXs2X/va14YVl3vvvZfW1uin9+uuu2501oYR/g86EAjw0EMP8alP\nfYrS0tJB96mqqqKqqir4urGxcdBth8Lr9Y5oXx0IgFL46o7TFee5ztQuq6cHPbsUDr1H+5H38c2Z\nj3XyGOQX0ZlinrqbDr+PKi6LtL2+HoCOnh589jEDObkEGuvpb2wk0N6KNets6O1FN5ltOzV09fRC\nVg6dRw7S3diIfmeP+SynIOHfge42Xkdbw2l0SzM6I3PY/0/h35mVlk5vWyuNjY1oy8I69B7qY1VR\nx9Bddl4mLT1hnvJI/8bGG7Fr9CSrbfHaVV4+fIUnjEJczqSc9s477xz0s/z8fFpaWigsLKSlpYW8\nvOix4UVFRezduzf4urm5mXnz5gVfP/roo5SVlbFy5cq4bUwEKiXFnos1gb0u/b1mbfrUNLOwFHZY\nrNBjlmIGE7YbIC4RCX2H3HxoOGX+FnztJiymXKb8FzOzSykFxWXBcmRdZ5chTxmHGXRhCX3d0x1a\naGzE+2cFq8xoPGVCZOHrxQS3s78TCYkJwqCMOOdy8cUX88ADD1BbW8vx48epra3lwQcfZOnSpWdk\nQGVlJTt27ABgx44dwTLncBYtWsTu3bvx+Xz4fD52797NokVmCOEvf/nLMw7NJZTc/NByvuOM1jq4\nzjslU9CnT5oPmhtQBZ5QNVuspH5YzsVB5eabbbu7TII/Jy80TRhCFXHFpdBgr9ly8hgqrwA1XLXW\nWJDh9KrYCf1Ri0vYSpbHDgOgBibzIfSdSDJfEAZlxJ7LjTfeyNNPP82mTZtoaWmhqKiISy65hGuu\nueaMDFi1ahUbNmxg27ZteL1e1q41q+wdPHiQrVu3cvPNN+N2u1mzZg3r1q0D4JprrsHtdtPU1MQz\nzzzD1KlT+frXvw6Y6c1XXHHFGdk0puQVTNxkZL/dq5KWbqq1ThwxHfuN9fDRZcG1VHRHG1FZg/Bq\nMYfcAuOxOIt9FRVHJsCz7XVSiqega19HWwH0yaOkzTgLa+yvLhrHo+izS5EH5JGG3z8rWHyh9+8x\nq2SWx5gG4HhzUoYsCIMypLjs2bMn4vX8+fOZP38+WutgzmPfvn3Biq14yM3N5a677op6v6KigoqK\niuDrFStWsGJFZGLW4/Hw5JNPxn3u8UDl5qPt9UTGnaD3kY6aMg1d+yocfR+0ZZYHdtaPj+FZaWff\n8BtoXj5YFvrIAQBUSRk6fJS/Mzm4bKopfa47ASePkrr8U4QtO5Y40sP7XLqhoGjo7QegMjLRvd3o\n/n70aztQi5bGHHKpUlKM8IjnIgiDMqS4/Nu//VvM9x1hcURm48aNY2/ZBwVvKfxpJ7q/DzXeT7pB\n7yMDymxhePNV897UmebGmZk1SFgsbF8HJ4x2yF591FsGRw6GPnc8l3POQwP6jy9AdxepM84aJ3EJ\n73PpQmWO1nMxU5V17avQ2YH6+CeGPpfkXARhUIYUlx/+8IfjZccHFjVrjqkaO/q+GWOSAPTRgzB1\nVvQHYUl5NWWaueHvetl4I06zY25+KBcTTn/I63FQuaYAQB/cB9k5qBw32slrpGcEO/BVcRl4S9Ev\n/R6A1Bkx8hYJQLlcxt6+nvhyLplZ0NmOfv4ZE/IbuIxyOOkZEhYThCEY1XouQhzYy/TqwwcScnjd\n3Ij1L2vRb7wS/aEd2lLp6VBqV2s11UP5DJQrxXx20WWw542oeWAxq8WcsfV1x4zXAihnmnB25Hgb\n9ZHzg0sBp45k8vFYkW4vddwdh7jMnAMBC44eRC27KnINl1jnkbCYIAyKiEuiKfSYkSuJyru0NILW\noSnH4fSH8iYqM8uMuAeTb7FRK6+FqTOxfvZDdPhY/b4+U2acGubcOmExrU1FGIRu4ANnp81daH7m\nF+HKjS4vTxgZmeiOdrPE8SjDYq6LL8f1o6dw/eDnqE8NXaiiLv0E6sJLz8RSQfhAI+KSYJRSMOts\n9OH9iTmBM/p+4Eh8CCX0nfCNM4IlXFzS0nDd8PdmvZRdL4f27e81hQDh3efuXDPyHkJjXoLiEjkd\nWzniMtQssESQk2sGTsLoPRdMaE3l5g3bde+6ag2ujy6Lw0BB+HAg4jIOqFlz4NQJdNfYr32jHXGJ\ndez+yKS8sodHqoGNgXM+AiXlZp374L59UTkF5bKbQgFKBojLwLBYXgHq459AjfMNWF2wFOrtHFLW\n6MVFEISxQcRlHFCzzja/HBmbvIvu68V6/GF0W0uo0iuWuAz0XCrmml6OATkQM9J+GezfE1r+uLc3\ndjWUHRoLei5246KKsaSA669vw/Wxqqj3E4m6+PLQ73F4LoIgjA0iLuPBDNOvo08cGZvjHT+MfqUa\n/fafoMN4LjpGWEwPqPhSF12G68HHYgqBWroMtEa/stV09vf3xU5YO3mX4oFhsQlar2YAylMSyveM\nthRZEIQxY8Qd+sIZ4M4zyfGO6InPceHMv2ppCvNcfNHbDaj4UkoN2rWuSsrhnPPQz/4n+o8vmvVZ\niqInpqq8ArTLFSwOICMTZp2Nmn3OGV3SWKI+/gn0vrdMIYUgCBOCiMs4oFwukwz3jbG4tDYNk3OJ\nng82FK5bv42u+QP6rV3Q3YU6/6LojeZfYJLedhWZUoqUb31/tFeQUNRFl6GmzkANtWqlIAgJRcRl\nvHDnoTvHRlycyb063HOJVS0WoxFyKFRWNuqyq+CyqwbdxvWxKhjnPMpoUUrBwKWJBUEYV0Rcxouc\nXLN641jgrA/f0hjyWMI8F93dBW3N0Ql9QRCEcUIS+uOFO2/sw2ItTaE8Tk83OmCWnNa/ewbr/n8y\nneqpqUN3mguCICQAueuMEyo3bww9F1tcOtrMevH2WBbdZXs0zQ1mzZXmhsjxLYIgCOOEiMt4kWMS\n+meyomcQR1wc7CGUlu0Zaac8+fRJmdwrCMKEIOIyXrjzzBonvd3DbzscA8RFlZg1rbVTjuwk+U+f\nlHyLIAgTgojLeOGMTRmDXhfd2w0pKaE3HM+l0xYXJ7fT2y3iIgjChCDiMk4otz3YcSzyLt1dYHsr\nAKrU9lw67WOHFw7IWHhBECaACS9F9vl8bNiwgYaGBoqLi7njjjtwu6NHiWzfvp1nnnkGgNWrV7N8\n+fKIzx944AHq6+v5/veTq6EviOO5jEWvS0+3GeXf3GAqwpywWKcP3dcbua695FwEQZgAJtxz2bJl\nCwsWLODhhx9mwYIFbNmyJWobn8/HU089xf3338/999/PU089hc8XGnfy2muvkZmZOZ5mjx5bXPRY\nlCM7qywWesDlAm8JAFZnR3TYTarFBEGYACZcXGpqali2zIxlX7ZsGTU1NVHb1NbWsnDhQtxuN263\nm4ULF1JbWwtAT08Pzz33HGvWrBlXu0dNMCw2BuLS221WgCzwGNHKzAblQnf6wGcn850ZYuK5CIIw\nAUy4uLS1tVFYaAYMFhYW0t4effNtbm7G4/EEXxcVFdHcbFZe/OUvf8mnP/1p0pP9JpqVY4ZXjkXO\nxfZc1LwLzH8uF2Rlm4S+47nYY/WVJPQFQZgAxiXncu+999La2hr1/nXXXRf3MZVSHD58mFOnTvGl\nL32J+vr6Yfeprq6muroagPXr1+P1Rk/9HQmpqalx7Vufm0emv5+8OM8LoLWmvqeH7CIP7hu/Eny/\nMTcPujpxY9EOZJ87n679e8jIzSP/DM43FsT7fY0HyWqb2DU6ktUuSF7bEm3XuIjLnXfeOehn+fn5\ntLS0UFhYSEtLC3l50eutFxUVsXfv3uDr5uZm5s2bx/79+zl06BC33HILgUCAtrY2vvOd7/Cd73wn\n5jYOwqAAABdcSURBVLmqqqqoqgoNXWxsbIzrerxeb1z76mw33Y2n6YvzvAC6txesAF0aesKOE8jI\nJOBrp6fuBADdxSbJ32vpuK9zrIj3+xoPktU2sWt0JKtdkLy2xWtXeXn58BuRBNVilZWV7Nixg1Wr\nVrFjxw4uvPDCqG0WLVrEL37xi2ASf/fu3Vx//fW43W6uvPJKAOrr63nggQcGFZakwD0GI2B67REv\nA1dZzMqxcy7t4HKhps5Ag+RcBEGYECZcXFatWsWGDRvYtm0bXq+XtWvXAnDw4EG2bt3KzTffjNvt\nZs2aNaxbtw6Aa665Jma5ctLjzoOGujM7htOdnzFAXLJzsBpPm+58dx4UFZv3JeciCMIEMOHikpub\ny1133RX1fkVFBRUVFcHXK1asYMWKFYMep6SkJHl7XGyUOxd9eP+ZHcQWl4Hrw6tsN7r9XTNXLDcf\ncnJRV65Cnf/RMzufIAhCHEx4tdiHihz3mYfFHM9lYFisYi5WWwu89za481BK4frcTajZZ5/Z+QRB\nEOJAxGU8ycgCfz/aCsR/DEdcnD4WG3XBUjNvrLMD5Y4uihAEQRhPRFzGkwy7W763N+5D6O7YCX3l\nziN9oV0MkZsf9/EFQRDGAhGX8STdHlETPvtrtPQOktAHMj9m56TEcxEEYYIRcRlPMmxx6TsDcRks\n5wJkfPQyKPSiZp4V//EFQRDGgAmvFvswoTIyTO/JGYTFQuISPajT5c4j5V9/Ev+xBUEQxgjxXMaT\nsQiL9XRDRibKlTL8toIgCBOEiMt4MlZhsRghMUEQhGRCxGU8GYNqMeO5iLgIgpDciLiMJ3ZYTJ9B\nWEx3d4rnIghC0iPiMp6MRVjs+BFU2bSxsUcQBCFBiLiMJ2cYFtMtTdDaBDLSRRCEJEfEZTwZZbWY\nrq8jsP5/o9vthdYOmaGXavY5ibBOEARhzBBxGUdUaiqkpI44LKYP7IWD+9Bvv2leH95v9p8hTZKC\nICQ3Ii7jTUbGyMNibS3m58F3ANDv74dps1CyRosgCEmOiMt4k5458ibK1mYA9IF3zCTlIwckJCYI\nwqRAxGW8Sc+AvpF5LrrNiAsnj8KBd0yPiyTzBUGYBIi4jDcZGSPvc2lrMcsUa421aYMZ+zJ/cWLt\nEwRBGAMmfHClz+djw4YNNDQ0UFxczB133IHb7Y7abvv27TzzzDMArF69muXLlwPg9/vZtGkTe/fu\nRSnFddddx9KlS8fzEkZHxijDYvMWwVu7oLkBtfqLqPzCxNonCIIwBky4uGzZsoUFCxawatUqtmzZ\nwpYtW7jxxhsjtvH5fDz11FOsX78egG984xtUVlbidrt55plnyM/P56GHHsKyLHw+30RcxshJz4Tu\nzmE301pDWwtq8cXoGWdBlw9V9ZlxMFAQBOHMmfCwWE1NDcuWLQNg2bJl1NTURG1TW1vLwoULcbvd\nuN1uFi5cSG1tLQAvvvgiq1atAsDlcpGXl+QLZWWMMOfS3Qn9fZBfhOvv1+H62ndRaWmJt08QBGEM\nmHDPpa2tjcJCE+opLCykvb09apvm5mY8Hk/wdVFREc3NzXR2Gg/giSeeYO/evZSWlnLTTTdRUFAw\nPsbHgcrIHFnOxa4UI78Q5SlOrFGCIAhjzLiIy7333ktra2vU+9ddd13cx1RKEQgEaGpq4txzz+Wv\n//qvee655/jZz37GbbfdFnOf6upqqqurAVi/fj1erzeuc6empsa9b3teAb39fcPu33vyMK1Awcyz\nSB/huc7ErkSSrHZB8tomdo2OZLULkte2RNs1LuJy5513DvpZfn4+LS0tFBYW0tLSEjOsVVRUxN69\ne4Ovm5ubmTdvHrm5uWRkZHDRRRcBsHTpUrZt2zbouaqqqqiqqgq+bmxsjOdy8Hq9ce9raY3u6R52\nf+voIQDacKFGeK4zsSuRJKtdkLy2iV2jI1ntguS1LV67ysvLR7TdhOdcKisr2bFjBwA7duzgwgsv\njNpm0aJF7N69G5/Ph8/nY/fu3SxatAilFEuWLAkKz549e5g2LcknBmdkQl+vSdgPhRMWK5DqMEEQ\nJh8TnnNZtWoVGzZsYNu2bXi9XtauXQvAwYMH2bp1KzfffDNut5s1a9awbt06AK655ppgufINN9zA\nxo0befzxx8nLy+OrX/3qhF3LiEjPBK2hry80JTkWbS2QkYXKzB4/2wRBEMaICReX3Nxc7rrrrqj3\nKyoqqKioCL5esWIFK1asiNquuLiYf/7nf06ojWOKIyh9PcOLi/S0CIIwSZnwsNiHjoyRjd3XrU0S\nEhMEYdIi4jLeBNd0GabXpaMdcvMTb48gCEICEHEZZ1R4WGwoerol3yIIwqRFxGW8GWFYjN5uyMxK\nvD2CIAgJQMRlvBlBWExrDT09kCHiIgjC5ETEZbyxw2J6qLBYfx9oSzwXQRAmLSIu481IwmI93eZn\nZmbi7REEQUgAIi7jjR0W0797hsCdXzXLFw/EEZ4MERdBECYnE95E+aHDqRY7dcL89LVD3oB+Fttz\nURIWEwRhkiKey3iTlo669ErURZeZ1+3R06LptcNiktAXBGGSIuIyziilcH3xVtSyq8wb7W3RGzk5\nFwmLCYIwSRFxmShyzYJmOqbnYudcJCwmCMIkRcRlosizV8uMIS66RxL6giBMbkRcJorsHEhJhY4h\nwmIy/kUQhEmKiMsEoZQygymHSuhLn4sgCJMUEZeJJK8APZjn4nJBatr42yQIgjAGiLhMJHkFg3gu\nPZCZZbwbQRCESYiIywSihgqLSY+LIAiTGBGXiSSvADpazRTkMHRPt1SKCYIwqZnw8S8+n48NGzbQ\n0NBAcXExd9xxB263O2q77du388wzzwCwevVqli9fDsDLL7/Mr3/9a5RSFBYWctttt5GXlzeelxA/\nefng90N3J2SHXbMdFhMEQZisTLjnsmXLFhYsWMDDDz/MggUL2LJlS9Q2Pp+Pp556ivvvv5/777+f\np556Cp/PRyAQ4PHHH+fuu+/me9/7HjNnzuT555+fgKuIkwG9LvrUCXRHu0noi+ciCMIkZsLFpaam\nhmXLlgGwbNkyampqorapra1l4cKFuN1u3G43CxcupLa2Fq01Wmt6e3vRWtPV1UVRUdF4X0LcqKC4\ntKG1xvr+t9C//qlZKEw8F0EQJjETHhZra2ujsNBMBS4sLKS9vT1qm+bmZjweT/B1UVERzc3NpKam\n8uUvf5l/+qd/IiMjgylTpvB3f/d3g56rurqa6upqANavX4/X643L5tTU1Lj3Dad/+iyagVwCpKWl\n0NjaTGrjaaz+XtLyC8gf5TnGyq6xJlntguS1TewaHclqFySvbYm2a1zE5d5776W1Nboq6rrrrov7\nmEop/H4/v//973nggQcoLS3lJz/5Cb/+9a9Zs2ZNzH2qqqqoqqoKvm5sbIzr3F6vN+59w9GW+dl+\n4jjKb1701x2HgB8LNepzjJVdY02y2gXJa5vYNTqS1S5IXtvitau8vHxE242LuNx5552Dfpafn09L\nSwuFhYW0tLTETMYXFRWxd+/e4Ovm5mbmzZvH4cOHASgrKwPg4osv5tlnnx1b4xOJOw+UgvZWdKDf\nvNfaZMbCSFhMEIRJzITnXCorK9mxYwcAO3bs4MILL4zaZtGiRezevRufz4fP52P37t0sWrSIoqIi\njh8/HgylvfXWW0ydOnVc7T8TVEoKFE9BH34PThwNfRDwS0JfEIRJzYTnXFatWsWGDRvYtm0bXq+X\ntWvXAnDw4EG2bt3KzTffjNvtZs2aNaxbtw6Aa665JliufM0113D33XeTkpKC1+vllltumbBriQe1\nsBK9/X/QpeWQlQ3dXeYDaaIUBGESM+Hikpuby1133RX1fkVFBRUVFcHXK1asYMWKFVHbXXnllVx5\n5ZUJtTGRqIUXoqt/AyeOoC68FF3z0v9r7+6Doir3OIB/9yysvLosC7Hq1Wsipt5R0qBGRM1Am7KZ\n1CtM1KRrmE4L0khO1j+NM8boDBCVL5OVMshoCZNk/dH4hy8wSQ2E0AtKCakDw8uyLoIK6L489w/G\nkyhry205B+r7+Wv37Fn363Mezu88z9mzZ+AFTosR0Rim+rTYP17M7D8Kycy5gG7cwGNOixHRGMbi\nojKNnz/wn3kDjyf9G4gc+HKChiMXIhrDWFxGAWnhMmDCZOBfU4GIqIGFHLkQ0Rim+jkXAjRzHoN2\nzmMDjyNNEADPuRDRmMaRy2gTMTAtxpELEY1lHLmMMpq4hQMXUprGzvU6RET3YnEZZTR6AzT/Xad2\nDCKiv4TTYkRE5HMsLkRE5HMsLkRE5HMsLkRE5HMsLkRE5HMsLkRE5HMsLkRE5HMsLkRE5HMaIYRQ\nOwQREf29cOTyf3jrrbfUjjAk5hq+0ZqNuYZntOYCRm+2kc7F4kJERD7H4kJERD6n3b59+3a1Q4xF\n06ZNUzvCkJhr+EZrNuYantGaCxi92UYyF0/oExGRz3FajIiIfI73cxmGuro6FBYWwu12IykpCStX\nrlQti81mw969e3Ht2jVoNBokJyfj2WefRUlJCU6ePInx48cDANLS0jB//nxFs2VkZCAgIACSJEGr\n1WLXrl24ceMGCgoK0NnZicjISGzZsgUhISGKZWptbUVBQYH83Gq1IjU1FTdv3lSlvfbt24dz585B\nr9cjPz8fADy2kRAChYWFqK2txbhx42CxWEZsOmOoXMXFxaipqYGfnx+ioqJgsVgQHBwMq9WKLVu2\nYOLEiQCAmJgYbNy4UbFcD+rrZWVlOHXqFCRJwvr16/Hoo48qlqugoACtra0AgN7eXgQFBSE3N1fR\n9vK0f1C0jwnyisvlEpmZmaK9vV04HA6xdetW0dzcrFoeu90umpqahBBC9Pb2iqysLNHc3CyOHj0q\njh8/rlouIYSwWCyiu7t70LLi4mJRVlYmhBCirKxMFBcXqxFNCDGwLTds2CCsVqtq7VVfXy+amppE\ndna2vMxTG9XU1IicnBzhdrvFr7/+Kt5++21Fc9XV1Qmn0ylnvJOro6Nj0HojaahcnrZdc3Oz2Lp1\nq7h9+7bo6OgQmZmZwuVyKZbrbkVFRaK0tFQIoWx7edo/KNnHOC3mpcbGRphMJkRFRcHPzw8JCQmo\nrq5WLY/BYJCPLAIDAzFp0iTY7XbV8vyZ6upqLFmyBACwZMkSVdvu559/hslkQmRkpGoZZs+efd/I\nzVMb/fDDD1i8eDE0Gg1mzJiBmzdvoqurS7FcsbGx0Gq1AIAZM2ao0s+GyuVJdXU1EhIS4O/vj4ce\neggmkwmNjY2K5xJC4LvvvsPChQtH5LMfxNP+Qck+xmkxL9ntdhiNRvm50WjExYsXVUz0B6vVikuX\nLmH69OloaGjAiRMnUFFRgWnTpmHt2rWKTj/dkZOTAwBYtmwZkpOT0d3dDYPBAGCg4/f09Cie6Y6z\nZ88O+oMfDe0FwGMb2e12REREyOsZjUbY7XZ5XSWdOnUKCQkJ8nOr1Yo333wTgYGBeOGFFzBr1ixF\n8wy17ex2O2JiYuR1wsPDVSmIFy5cgF6vx4QJE+RlarTX3fsHJfsYi4uXxBBfqtNoNCokGay/vx/5\n+fkwm80ICgrC8uXLsWbNGgDA0aNHcejQIVgsFkUz7dixA+Hh4eju7sa7774rzzGPBk6nEzU1NXjx\nxRcBYFS0158ZLX3v2LFj0Gq1WLRoEYCBndO+ffsQGhqK33//Hbm5ucjPz0dQUJAieTxtu6HaSw33\nHsSo0V737h88GYk+xmkxLxmNRly9elV+fvXqVVWOHO/mdDqRn5+PRYsW4YknngAAhIWFQZIkSJKE\npKQkNDU1KZ4rPDwcAKDX6xEfH4/Gxkbo9Xp5mN3V1SWfhFVabW0tHn74YYSFhQEYHe11h6c2MhqN\nsNls8npq9L0zZ86gpqYGWVlZ8k7H398foaGhAAaul4iKikJbW5timTxtu3v/Vu12u9wnleJyuVBV\nVTVolKd0ew21f1Cyj7G4eCk6OhptbW2wWq1wOp2orKxEXFycanmEEPjoo48wadIkPPfcc/Lyu+dJ\nq6qqMHnyZEVz9ff3o6+vT378008/YcqUKYiLi0N5eTkAoLy8HPHx8YrmuuPeo0m12+tuntooLi4O\nFRUVEELgt99+Q1BQkKLFpa6uDsePH8e2bdswbtw4eXlPTw/cbjcAoKOjA21tbYiKilIsl6dtFxcX\nh8rKSjgcDlitVrS1tWH69OmK5QIGzutNnDhx0FS6ku3laf+gZB/jRZTDcO7cORQVFcHtdmPp0qVY\nvXq1alkaGhrwzjvvYMqUKfKRZFpaGs6ePYvLly9Do9EgMjISGzduVHRH1NHRgby8PAADR2+JiYlY\nvXo1rl+/joKCAthsNkRERCA7O1vxcxu3bt3Ca6+9hj179shTBLt371alvd5//32cP38e169fh16v\nR2pqKuLj44dsIyEEDhw4gB9//BE6nQ4WiwXR0dGK5SorK4PT6ZS3152v0H7//fcoKSmBVquFJElI\nSUkZsQOuoXLV19d73HbHjh3D6dOnIUkSzGYz5s2bp1iup556Cnv37kVMTAyWL18ur6tke3naP8TE\nxCjWx1hciIjI5zgtRkREPsfiQkREPsfiQkREPsfiQkREPsfiQkREPsfiQuSF7Oxs1NfXq/LZNpsN\nL7/8snyNBNFYwK8iEw1DSUkJ2tvbkZWVNWKfkZGRgU2bNmHu3Lkj9hlEI40jFyIFuVwutSMQKYIj\nFyIvZGRk4JVXXpF/fcDPzw8mkwm5ubno7e1FUVERamtrodFosHTpUqSmpkKSJJw5cwYnT55EdHQ0\nysvL8fTTT+PJJ5/E/v37ceXKFWg0GsTGxiI9PR3BwcHYvXs3vv32W/j5+UGSJKxZswYLFixAZmYm\nPvvsM2i1WtjtdnzyySdoaGhASEgInn/+eSQnJwMYGFm1tLRAp9OhqqoKERERyMjIkK+2/vLLL/HN\nN9+gr68PBoMBGzZswJw5c1RrV/r74q8iE3nJ398fq1atum9abM+ePQgLC8OHH36IW7duYdeuXTAa\njVi2bBkA4OLFi0hISMCnn34Kl8sFu92OVatWYdasWejr60N+fj5KS0thNpuxefNmNDQ0DJoWs1qt\ng3J88MEHmDx5Mvbv34/W1lbs2LEDUVFRcpGoqanBG2+8AYvFgs8//xwHDx5ETk4OWltbceLECezc\nuRPh4eGwWq08j0MjhtNiRH/BtWvXUFdXB7PZjICAAOj1eqxYsQKVlZXyOgaDAc888wy0Wi10Oh1M\nJhPmzp0Lf39/jB8/HitWrMD58+e9+jybzYaGhga89NJL0Ol0mDp1KpKSklBRUSGvM3PmTMyfPx+S\nJGHx4sW4fPkyAECSJDgcDrS0tMDpdMo30iIaCRy5EP0FNpsNLpdr0L3QhRCDfg337pswAQM3BSss\nLMSFCxfQ398Pt9vt9Y94dnV1ISQkBIGBgYP+/btvFaDX6+XHOp0ODocDLpcLJpMJZrMZpaWlaGlp\nQWxsLNauXav4z9HTPwOLC9Ew3HsDJaPRCD8/Pxw4cEC+FfCfOXLkCAAgLy8PoaGhqKqqwsGDB716\nr8FgwI0bN9DX1ycXGJvN5nWBSExMRGJiInp7e/Hxxx/j8OHD2Lx5s1fvJRoOTosRDYNer0dnZ6d8\nrsJgMCA2NhaHDh1Cb28v3G432tvbHzjN1dfXh4CAAAQHB8Nut+Prr78e9HpYWNh951nuiIiIwCOP\nPIIjR47g9u3buHLlCk6fPi3fHfJBWltb8csvv8DhcECn00Gn00GSuAugkcGeRTQMCxYsAACkp6dj\n27ZtAIDMzEw4nU5kZ2dj/fr1eO+99wbdyOpeKSkpuHTpEtatW4edO3fi8ccfH/T6ypUr8cUXX8Bs\nNuOrr7667/2vv/46Ojs7sWnTJuTl5SElJcWra2IcDgcOHz6M9PR0vPrqq+jp6UFaWtpw/vtEXuNX\nkYmIyOc4ciEiIp9jcSEiIp9jcSEiIp9jcSEiIp9jcSEiIp9jcSEiIp9jcSEiIp9jcSEiIp9jcSEi\nIp/7H2+bC2ob44ElAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x1abb4d610f0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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UyjB0kNWsPSVEAPLb1Nn169cTGxtLz5496x13OBz1WhpxcXE4HA5JFgFIf/J3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\nhYWIiDhSWIiIiCOFhYiIOPoKItijqxqaeLoAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x1abb4d61a58>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "util.plot_curve(loss_list, \"loss\")\n",
+    "util.plot_curve(avg_return_list, \"average return\")"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -477,7 +933,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 23,
    "metadata": {
     "collapsed": true
    },
@@ -523,6 +979,7 @@
     "            Sample solution should be only 1 line. (you can use `util.discount` in policy_gradient/util.py)\n",
     "            \"\"\"\n",
     "            # YOUR CODE HERE >>>>>>>>\n",
+    "            a = util.discount(a, self.discount_rate*LAMBDA)\n",
     "            # <<<<<<<\n",
     "            p[\"returns\"] = target_v\n",
     "            p[\"baselines\"] = b\n",
@@ -543,7 +1000,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 24,
    "metadata": {
     "scrolled": true
    },
@@ -552,90 +1009,82 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Iteration 1: Average Return = 25.12\n",
-      "Iteration 2: Average Return = 31.17\n",
-      "Iteration 3: Average Return = 30.07\n",
-      "Iteration 4: Average Return = 31.98\n",
-      "Iteration 5: Average Return = 36.77\n",
-      "Iteration 6: Average Return = 36.22\n",
-      "Iteration 7: Average Return = 43.52\n",
-      "Iteration 8: Average Return = 45.12\n",
-      "Iteration 9: Average Return = 50.86\n",
-      "Iteration 10: Average Return = 58.81\n",
-      "Iteration 11: Average Return = 58.87\n",
-      "Iteration 12: Average Return = 65.66\n",
-      "Iteration 13: Average Return = 69.72\n",
-      "Iteration 14: Average Return = 76.32\n",
-      "Iteration 15: Average Return = 77.74\n",
-      "Iteration 16: Average Return = 78.17\n",
-      "Iteration 17: Average Return = 94.97\n",
-      "Iteration 18: Average Return = 89.34\n",
-      "Iteration 19: Average Return = 98.15\n",
-      "Iteration 20: Average Return = 103.35\n",
-      "Iteration 21: Average Return = 106.54\n",
-      "Iteration 22: Average Return = 109.03\n",
-      "Iteration 23: Average Return = 113.63\n",
-      "Iteration 24: Average Return = 119.11\n",
-      "Iteration 25: Average Return = 115.67\n",
-      "Iteration 26: Average Return = 126.51\n",
-      "Iteration 27: Average Return = 131.33\n",
-      "Iteration 28: Average Return = 138.83\n",
-      "Iteration 29: Average Return = 143.7\n",
-      "Iteration 30: Average Return = 146.15\n",
-      "Iteration 31: Average Return = 146.41\n",
-      "Iteration 32: Average Return = 157.34\n",
-      "Iteration 33: Average Return = 160.51\n",
-      "Iteration 34: Average Return = 159.67\n",
-      "Iteration 35: Average Return = 169.42\n",
-      "Iteration 36: Average Return = 170.71\n",
-      "Iteration 37: Average Return = 174.41\n",
-      "Iteration 38: Average Return = 172.93\n",
-      "Iteration 39: Average Return = 173.29\n",
-      "Iteration 40: Average Return = 177.32\n",
-      "Iteration 41: Average Return = 177.14\n",
-      "Iteration 42: Average Return = 179.85\n",
-      "Iteration 43: Average Return = 181.82\n",
-      "Iteration 44: Average Return = 182.0\n",
-      "Iteration 45: Average Return = 181.89\n",
-      "Iteration 46: Average Return = 183.19\n",
-      "Iteration 47: Average Return = 183.87\n",
-      "Iteration 48: Average Return = 183.26\n",
-      "Iteration 49: Average Return = 183.27\n",
-      "Iteration 50: Average Return = 189.11\n",
-      "Iteration 51: Average Return = 181.45\n",
-      "Iteration 52: Average Return = 186.91\n",
-      "Iteration 53: Average Return = 188.84\n",
-      "Iteration 54: Average Return = 189.76\n",
-      "Iteration 55: Average Return = 189.51\n",
-      "Iteration 56: Average Return = 186.36\n",
-      "Iteration 57: Average Return = 190.55\n",
-      "Iteration 58: Average Return = 189.35\n",
-      "Iteration 59: Average Return = 189.84\n",
-      "Iteration 60: Average Return = 187.14\n",
-      "Iteration 61: Average Return = 191.82\n",
-      "Iteration 62: Average Return = 189.32\n",
-      "Iteration 63: Average Return = 190.74\n",
-      "Iteration 64: Average Return = 188.13\n",
-      "Iteration 65: Average Return = 190.99\n",
-      "Iteration 66: Average Return = 189.23\n",
-      "Iteration 67: Average Return = 186.98\n",
-      "Iteration 68: Average Return = 188.0\n",
-      "Iteration 69: Average Return = 191.68\n",
-      "Iteration 70: Average Return = 188.03\n",
-      "Iteration 71: Average Return = 193.07\n",
-      "Iteration 72: Average Return = 191.96\n",
-      "Iteration 73: Average Return = 189.53\n",
-      "Iteration 74: Average Return = 186.71\n",
-      "Iteration 75: Average Return = 190.05\n",
-      "Iteration 76: Average Return = 191.1\n",
-      "Iteration 77: Average Return = 193.49\n",
-      "Iteration 78: Average Return = 188.66\n",
-      "Iteration 79: Average Return = 191.49\n",
-      "Iteration 80: Average Return = 191.68\n",
-      "Iteration 81: Average Return = 193.19\n",
-      "Iteration 82: Average Return = 193.87\n",
-      "Iteration 83: Average Return = 195.04\n",
-      "Solve at 83 iterations, which equals 8300 episodes.\n"
+      "Iteration 1: Average Return = 19.91\n",
+      "Iteration 2: Average Return = 18.4\n",
+      "Iteration 3: Average Return = 19.53\n",
+      "Iteration 4: Average Return = 22.78\n",
+      "Iteration 5: Average Return = 23.65\n",
+      "Iteration 6: Average Return = 25.54\n",
+      "Iteration 7: Average Return = 27.71\n",
+      "Iteration 8: Average Return = 32.29\n",
+      "Iteration 9: Average Return = 28.77\n",
+      "Iteration 10: Average Return = 33.15\n",
+      "Iteration 11: Average Return = 34.87\n",
+      "Iteration 12: Average Return = 40.8\n",
+      "Iteration 13: Average Return = 41.48\n",
+      "Iteration 14: Average Return = 43.07\n",
+      "Iteration 15: Average Return = 47.6\n",
+      "Iteration 16: Average Return = 47.86\n",
+      "Iteration 17: Average Return = 46.81\n",
+      "Iteration 18: Average Return = 46.03\n",
+      "Iteration 19: Average Return = 53.02\n",
+      "Iteration 20: Average Return = 50.85\n",
+      "Iteration 21: Average Return = 56.04\n",
+      "Iteration 22: Average Return = 57.77\n",
+      "Iteration 23: Average Return = 54.57\n",
+      "Iteration 24: Average Return = 62.82\n",
+      "Iteration 25: Average Return = 65.64\n",
+      "Iteration 26: Average Return = 64.68\n",
+      "Iteration 27: Average Return = 64.74\n",
+      "Iteration 28: Average Return = 72.81\n",
+      "Iteration 29: Average Return = 74.57\n",
+      "Iteration 30: Average Return = 86.19\n",
+      "Iteration 31: Average Return = 85.78\n",
+      "Iteration 32: Average Return = 93.65\n",
+      "Iteration 33: Average Return = 97.91\n",
+      "Iteration 34: Average Return = 125.64\n",
+      "Iteration 35: Average Return = 113.59\n",
+      "Iteration 36: Average Return = 122.85\n",
+      "Iteration 37: Average Return = 131.33\n",
+      "Iteration 38: Average Return = 124.59\n",
+      "Iteration 39: Average Return = 122.64\n",
+      "Iteration 40: Average Return = 136.92\n",
+      "Iteration 41: Average Return = 141.61\n",
+      "Iteration 42: Average Return = 146.41\n",
+      "Iteration 43: Average Return = 157.23\n",
+      "Iteration 44: Average Return = 165.37\n",
+      "Iteration 45: Average Return = 163.88\n",
+      "Iteration 46: Average Return = 160.78\n",
+      "Iteration 47: Average Return = 166.6\n",
+      "Iteration 48: Average Return = 178.25\n",
+      "Iteration 49: Average Return = 166.47\n",
+      "Iteration 50: Average Return = 168.98\n",
+      "Iteration 51: Average Return = 166.51\n",
+      "Iteration 52: Average Return = 168.31\n",
+      "Iteration 53: Average Return = 164.27\n",
+      "Iteration 54: Average Return = 174.25\n",
+      "Iteration 55: Average Return = 175.09\n",
+      "Iteration 56: Average Return = 175.08\n",
+      "Iteration 57: Average Return = 171.07\n",
+      "Iteration 58: Average Return = 179.65\n",
+      "Iteration 59: Average Return = 176.71\n",
+      "Iteration 60: Average Return = 184.62\n",
+      "Iteration 61: Average Return = 187.19\n",
+      "Iteration 62: Average Return = 185.63\n",
+      "Iteration 63: Average Return = 184.89\n",
+      "Iteration 64: Average Return = 182.38\n",
+      "Iteration 65: Average Return = 187.64\n",
+      "Iteration 66: Average Return = 193.47\n",
+      "Iteration 67: Average Return = 189.34\n",
+      "Iteration 68: Average Return = 187.74\n",
+      "Iteration 69: Average Return = 186.09\n",
+      "Iteration 70: Average Return = 189.64\n",
+      "Iteration 71: Average Return = 192.96\n",
+      "Iteration 72: Average Return = 191.75\n",
+      "Iteration 73: Average Return = 188.43\n",
+      "Iteration 74: Average Return = 192.56\n",
+      "Iteration 75: Average Return = 195.96\n",
+      "Solve at 75 iterations, which equals 7500 episodes.\n"
      ]
     }
    ],
@@ -658,14 +1107,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 25,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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NnnIp+h+voj98xxgdFmnB9It7UAHNf2mdyjTlMpx5X6H/9TZE90N1YIkjFR6J6Z7Fxl/w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\nDTX+jM4LWgjRo/i85iLaToVFoC66Cv3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j0WCWVU+6sMvX6YygaLkYhsGrr77KAw88wPLly/nwww/Jz89vdsyGDRsYOHAgK1as4Oqr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\nIYQQfvf/exhjlzORwH0AAAAASUVORK5CYII=\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1278b4d30>"
+       "<matplotlib.figure.Figure at 0x1abb4d4cc18>"
       ]
      },
      "metadata": {},
@@ -673,9 +1122,9 @@
     },
     {
      "data": {
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DUS1DoFsfq0sWos7USVgsWrSI/fv3k5eXx8yZM5k0aRIjRoy4oAsKYP/+/axZswY3Nzds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\nyo892QAAAABJRU5ErkJggg==\n",
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o71agevTH6Na7zP1VYC1o2QHVUpr8hBDFeex9FuL66MP70Ivn2Tuv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\nAABJRU5ErkJggg==\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x127a02390>"
+       "<matplotlib.figure.Figure at 0x1abb4cdce80>"
       ]
      },
      "metadata": {},
@@ -713,7 +1162,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.5.3"
+   "version": "3.5.4"
   }
  },
  "nbformat": 4,
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diff --git a/policy_gradient/policy.py b/policy_gradient/policy.py
index 99fecf3..c91ddcb 100644
--- a/policy_gradient/policy.py
+++ b/policy_gradient/policy.py
@@ -30,6 +30,8 @@ def __init__(self, in_dim, out_dim, hidden_dim, optimizer, session):
         Sample solution is about 2~4 lines.
         """
         # YOUR CODE HERE >>>>>>
+        fc = tf.layers.dense(self._observations, hidden_dim, tf.tanh)
+        probs = tf.layers.dense(fc, out_dim, tf.nn.softmax)
         # <<<<<<<<
 
         # --------------------------------------------------
@@ -72,6 +74,7 @@ def __init__(self, in_dim, out_dim, hidden_dim, optimizer, session):
         Sample solution is about 1~3 lines.
         """
         # YOUR CODE HERE >>>>>>
+        surr_loss = tf.reduce_mean(-log_prob * self._advantages)
         # <<<<<<<<
 
         grads_and_vars = self._opt.compute_gradients(surr_loss)
diff --git a/policy_gradient/util.py b/policy_gradient/util.py
index 61ef302..fdb3742 100644
--- a/policy_gradient/util.py
+++ b/policy_gradient/util.py
@@ -32,6 +32,10 @@ def discount_bootstrap(x, discount_rate, b):
     Sample code should be about 3 lines
     """
     # YOUR CODE >>>>>>>>>>>>>>>>>>>
+    b[0] = 0.0
+    b_t_next = np.roll(b,-1)
+    y = x + discount_rate*b_t_next
+    return y
     # <<<<<<<<<<<<<<<<<<<<<<<<<<<<
  
 def plot_curve(data, key, filename=None):
diff --git a/report.md b/report.md
index 1e5017e..b914621 100644
--- a/report.md
+++ b/report.md
@@ -1,3 +1,194 @@
+
+# 江愷笙 <span style="color:black">(106062568)</span>
+
+Here is the [github page](https://petersci.github.io/homework3-policy-gradient/) of my report.
+
 # Homework3-Policy-Gradient report
 
 TA: try to elaborate the algorithms that you implemented and any details worth mentioned.
+
+## Overview
+
+>Policy gradient methods are a type of reinforcement learning techniques that rely upon optimizing parametrized policies with respect to the expected return (long-term cumulative reward) by gradient descent. They do not suffer from many of the problems that have been marring traditional reinforcement learning approaches such as the lack of guarantees of a value function, the intractability problem resulting from uncertain state information and the complexity arising from continuous states & actions.
+## Implementation
+
+In this homework we have to use policy gradient method to solve the cartpole problem.
+* Problem 1
+
+In problem 1 we have to use tensorflow to construct DQN for the policy gradient. Here we have to add the softmax layer to obtain the probability distribution.
+
+```python
+fc = tf.layers.dense(self._observations, hidden_dim, tf.tanh)
+probs = tf.layers.dense(fc, out_dim, tf.nn.softmax)
+```
+
+* Problem 2
+
+In problem 2 we have to define our lost for the neural network, here the loss function is surrogate loss. However, we have to take care that for the optimizer in tensorflow, the task is to minimize the loss (gradient descent), but in policy gradient, we have to maximize the surrogate loss (gradient asscent). So here we take the negative number of the loss to minimize this negative number, which equals to maximize its positive number.
+
+<table border=1>
+<tr>
+<td>
+<img src="imgs/surrogate_loss.PNG"/>
+</td>
+</tr>
+</table>
+
+```python
+surr_loss = tf.reduce_mean(-log_prob * self._advantages)
+```
+
+the surrogate loss should take the average number over N episode and each time step, so we use tf.reduce_mean to obtain the average number.
+
+* Problem 3
+
+Here in problem 3 we use baseline to reduce the variance. So we replace the loss function by the formula shown below.
+
+<table border=2>
+<tr>
+<td>
+<img src="imgs/baseline.PNG"/>
+</td>
+</tr>
+<tr>
+<td>
+<img src="imgs/baseline2.PNG"/>
+</td>
+</tr>
+</table>
+
+```python
+a = r - b
+```
+
+* Problem 4
+
+In problem 4 we remove the baseline to see what is the difference between problem 3 and 4, I will discuss it in Results.
+
+To remove the baseline, just replace 
+
+```python
+baseline = LinearFeatureBaseline(env.spec)
+```
+
+by
+
+```python
+baseline = None
+```
+
+* Problem 5
+
+In problem 5 we have to implement a simple actor critic algorithm by replacing the first formula below in problem 3 with the second formula.
+
+<table border=3>
+<tr>
+<td>
+<img src="imgs/baseline2.PNG"/>
+</td>
+</tr>
+<tr>
+<td>
+<img src="imgs/actor.PNG"/>
+</td>
+</tr>
+</table>
+
+We have to add the original reward to the discounted baseline at the next time step, so we have to left shift the baseline by 1.
+
+```python
+b[0] = 0.0			# let the first value to 0, after we shift left, it will be the last value
+b_t_next = np.roll(b,-1)	# shift left by 1
+y = x + discount_rate*b_t_next	# new R
+return y
+```
+
+* Problem 6
+
+Finally, we introduce generalized advantage estimation (GAE), which uses a hyperparameter lambda to comprimise two methods in problem 3 and 5.
+
+<table border=4>
+<tr>
+<td>
+<img src="imgs/GAE1.PNG"/>
+</td>
+</tr>
+<tr>
+<td>
+<img src="imgs/GAE2.PNG"/>
+</td>
+</tr>
+</table>
+
+```python
+a = util.discount(a, self.discount_rate*LAMBDA)
+```
+
+## Installation
+* Anaconda
+* Ipython notebook
+* Python3.5
+* OpenAI gym
+* Tensorflow
+* to run the code, open Lab3-policy-gradient.ipynb by using Ipython notebook and execute each block.
+
+## Results
+* Problem 1~3
+
+<table border=5>
+<tr>
+<td>
+<img src="imgs/problem3_1.PNG" width="45%"/>
+<img src="imgs/problem3_2.PNG" width="45%"/>
+</td>
+</tr>
+</table>
+
+* Problem 4
+
+<table border=6>
+<tr>
+<td>
+<img src="imgs/problem4_1.PNG" width="45%"/>
+<img src="imgs/problem4_2.PNG" width="45%"/>
+</td>
+</tr>
+</table>
+
+Here we prove why baseline won't produce bias.
+
+<tr>
+<td>
+<img src="imgs/bias.PNG"/>
+</td>
+</tr>
+
+We add baseline by subtracting the baseline function B(s). Since the operation is linear, we can only consider the term in the figure above which is related to B(s). Since that the baseline function B(s) only depend on s, we can take it outside the sigma which sum over all the actions. And the summation over all the policies is equal to 1, so the gradient on a constant is 0, thus the baseline won't introduce bias. 
+
+By comparing problem 3 and 4, we can find that without baseline, the result will have bigger variance. Since we subtract the value function of the current state from the reward, we obtain the advantage which shows how much the current action is better than we usually do at this state. The baseline compensate the variance introduced from different states.
+
+* Problem 5
+
+<table border=7>
+<tr>
+<td>
+<img src="imgs/problem5_1.PNG" width="45%"/>
+<img src="imgs/problem5_2.PNG" width="45%"/>
+</td>
+</tr>
+</table>
+
+* Problem 6
+
+<table border=8>
+<tr>
+<td>
+<img src="imgs/problem6_1.PNG" width="45%"/>
+<img src="imgs/problem6_2.PNG" width="45%"/>
+</td>
+</tr>
+</table>
+
+In problem 6 we introduce a hyperparameter lambda, which value is between [0,1]. If lambda is 0, then this GAE algorithm will reduce to actor critic algorithm as we implemented in problem 5, who has lower variance but introduce bias. On the other hand, if lambda is 1, it will have higher variance, but it is more accurate on the value function (less bias). Thus lambda makes a compromise between bias and variance.
+
+