Lab3-policy-gradient.ipynb

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   "source": [
    "# Automatically reload changes to external code\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
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   "cell_type": "markdown",
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   "source": [
    "In this assignment, you will solve a classic control problem - CartPole using policy gradient methods.\n",
    "\n",
    "Policy gradient method is a family of RL algorithms that parameterizes the policy directly. The simplest advantage that policy parameterization may have over action-value parameterization is that the policy may be a simpler function to approximate.\n",
    "\n",
    "First, you will implement the \"vanilla\" policy gradient method, i.e., a method that repeatedly computes **unbiased** estimates $\\hat{g}$ of $\\nabla_{\\theta} E[\\sum_t r_t]$ and takes gradient ascent steps $\\theta \\rightarrow \\theta + \\epsilon \\hat{g}$ so as to increase the total rewards collected in each episode. To make sure our code can solve multiple MDPs with different policy parameterizations, provided code follows an OOP manner and represents MDP and Policy as classes.\n",
    "\n",
    "The following code constructs an instance of the MDP using OpenAI gym."
   ]
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   "source": [
    "import gym\n",
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "from policy_gradient import util\n",
    "from policy_gradient.policy import CategoricalPolicy\n",
    "from policy_gradient.baselines.linear_feature_baseline import LinearFeatureBaseline\n",
    "\n",
    "np.random.seed(0)\n",
    "tf.set_random_seed(0)\n",
    "\n",
    "# CartPole-v0 is a MDP with finite state and action space. \n",
    "# In this environment, A pendulum is attached by an un-actuated joint to a cart, \n",
    "# and the goal is to prevent it from falling over. You can apply a force of +1 or -1 to the cart.\n",
    "# A reward of +1 is provided for every timestep that the pendulum remains upright. \n",
    "# To visualize CartPole-v0, please see https://gym.openai.com/envs/CartPole-v0\n",
    "\n",
    "env = gym.make('CartPole-v0')"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 1: construct a neural network to represent policy\n",
    "\n",
    "Make sure you know how to construct neural network using tensorflow.\n",
    "\n",
    "1. Open **homework2/policy_gradient/policy.py**.\n",
    "2. Follow the instruction of Problem 1."
   ]
  },
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    "## Problem 2: compute the surrogate loss\n",
    "\n",
    "If there are $N$ episodes in an iteration, then for $i$ th episode we define $R_t^i = \\sum_{{t^′}=t}^T \\gamma^{{t^′}-t}r(s_{t^′}, a_{t^′})$ as the accumulated discounted rewards from timestep $t$ to the end of that episode, where $\\gamma$ is the discount rate.\n",
    "\n",
    "The pseudocode for the REINFORCE algorithm is as below:\n",
    "\n",
    "1. Initialize policy $\\pi$ with parameter $\\theta_1$.\n",
    "2. For iteration $k = 1, 2, ...$:\n",
    "    * Sample N episodes $\\tau_1, \\tau_2, ..., \\tau_N$ under the current policy $\\theta_k$, where $\\tau_i =(s_i^t,a_i^t,R_i^t)_{t=0}^{T−1}$. Note that the last state is dropped since no action is taken after observing the last state.\n",
    "    * Compute the empirical policy gradient using formula: $$\\hat{g} = E_{\\pi_\\theta}[\\nabla_{\\theta} log\\pi_\\theta(a_t^i | s_t^i) R_t^i]$$\n",
    "    * Take a gradient step: $\\theta_{k+1} = \\theta_k + \\epsilon \\hat{g}$.\n",
    "    \n",
    "    \n",
    "Note that we can transform the policy gradient formula as\n",
    "\n",
    "$$\\hat{g} = \\nabla_{\\theta} \\frac{1}{(NT)}(\\sum_{i=1}^N \\sum_{t=0}^T log\\pi_\\theta(a_t^i | s_t^i) *R_t^i)$$\n",
    "\n",
    "and $L(\\theta) = \\frac{1}{(NT)}(\\sum_{i=1}^N \\sum_{t=0}^T log\\pi_\\theta(a_t^i | s_t^i) *R_t^i)$ is called the surrogate loss. \n",
    "\n",
    "We can first construct the computation graph for $L(\\theta)$, and then take its gradient as the empirical policy gradient.\n",
    "\n",
    "\n",
    "1. Open **homework2/policy_gradient/policy.py**.\n",
    "2. Follow the instruction of Problem 2."
   ]
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     "text": [
      "/home/smilewater/anaconda3/envs/tensorflow-gpu/lib/python3.6/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"
     ]
    }
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   "source": [
    "tf.reset_default_graph()\n",
    "sess = tf.Session()\n",
    "# Construct a neural network to represent policy which maps observed state to action. \n",
    "in_dim = util.flatten_space(env.observation_space)\n",
    "out_dim = util.flatten_space(env.action_space)\n",
    "hidden_dim = 8\n",
    "\n",
    "# Initialize your policy\n",
    "with tf.variable_scope(\"policy\"):\n",
    "    opt_p = tf.train.AdamOptimizer(learning_rate=0.01)\n",
    "    policy = CategoricalPolicy(in_dim, out_dim, hidden_dim, opt_p, sess)\n"
   ]
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   "source": [
    "# Problem 3\n",
    "\n",
    "Use baseline to reduce the variance of our gradient estimate.\n",
    "\n",
    "Change the loss term: \n",
    "\n",
    "$$L(\\theta) = \\frac{1}{(NT)}(\\sum_{i=1}^N \\sum_{t=0}^T log\\pi_\\theta(a_t^i | s_t^i) *R_t^i)$$\n",
    "\n",
    "into this one\n",
    "\n",
    "$$L(\\theta) = \\frac{1}{(NT)}(\\sum_{i=1}^N \\sum_{t=0}^T log\\pi_\\theta(a_t^i | s_t^i) *(R_t^i-V_t^i))$$\n",
    "\n",
    "where $V_t^i$ is the baseline prediction for at the $t$ timestep $i^{th}$ trajectory. In this part, we use a simple linear function to parameterize value function. (You're encouraged to see the details in ```policy_gradient/baselines/linear_feature_baseline.py```)\n",
    "\n",
    "1. Fill in the function `process_paths` of class `PolicyOptimizer` below."
   ]
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   "source": [
    "class PolicyOptimizer(object):\n",
    "    def __init__(self, env, policy, baseline, n_iter, n_episode, path_length,\n",
    "        discount_rate=.99):\n",
    "\n",
    "        self.policy = policy\n",
    "        self.baseline = baseline\n",
    "        self.env = env\n",
    "        self.n_iter = n_iter\n",
    "        self.n_episode = n_episode\n",
    "        self.path_length = path_length\n",
    "        self.discount_rate = discount_rate\n",
    "\n",
    "    def sample_path(self):\n",
    "        obs = []\n",
    "        actions = []\n",
    "        rewards = []\n",
    "        ob = self.env.reset()\n",
    "\n",
    "        # sample a batch of trajectory\n",
    "        for _ in range(self.path_length):\n",
    "            a = self.policy.act(ob.reshape(1, -1))\n",
    "            next_ob, r, done, _ = self.env.step(a)\n",
    "            obs.append(ob)\n",
    "            actions.append(a)\n",
    "            rewards.append(r)\n",
    "            ob = next_ob\n",
    "            if done:\n",
    "                break\n",
    "\n",
    "        return dict(\n",
    "            observations=np.array(obs),\n",
    "            actions=np.array(actions),\n",
    "            rewards=np.array(rewards),\n",
    "        )\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",
    "            # `p[\"rewards\"]` is a matrix contains the rewards of each timestep in a sample path\n",
    "            r = util.discount_cumsum(p[\"rewards\"], self.discount_rate)\n",
    "            \n",
    "            \"\"\"\n",
    "            Problem 3:\n",
    "\n",
    "            1. Variable `b` is the values predicted by our baseline\n",
    "            2. Use it to reduce variance and then assign the result to the \n",
    "                    variable `a` (baseline reduction)\n",
    "\n",
    "            Sample solution should be only 1 line.\n",
    "            \"\"\"\n",
    "            # YOUR CODE HERE >>>>>>            \n",
    "            a = r - b            \n",
    "            # <<<<<<<<\n",
    "\n",
    "            p[\"returns\"] = r\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",
    "        )\n",
    "\n",
    "    \n",
    "    def train(self):\n",
    "        loss_list = []\n",
    "        avg_return_list = []\n",
    "        for i in range(1, self.n_iter + 1):\n",
    "            paths = []\n",
    "            for _ in range(self.n_episode):\n",
    "                paths.append(self.sample_path())\n",
    "            data = self.process_paths(paths)\n",
    "            loss = self.policy.train(data[\"observations\"], data[\"actions\"], data[\"advantages\"])\n",
    "            avg_return = np.mean([sum(p[\"rewards\"]) for p in paths])\n",
    "            print(\"Iteration {}: Average Return = {}\".format(i, avg_return))\n",
    "            loss_list.append(loss)\n",
    "            avg_return_list.append(avg_return)\n",
    "            # CartPole-v0 defines \"solving\" as getting average reward of 195.0 over 100 consecutive trials.\n",
    "            if avg_return >= 195:\n",
    "                print(\"Solve at {} iterations, which equals {} episodes.\".format(i, i*100))\n",
    "                break\n",
    "\n",
    "            if self.baseline != None:\n",
    "                self.baseline.fit(paths)\n",
    "        return loss_list, avg_return_list"
   ]
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     "name": "stdout",
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     "text": [
      "Iteration 1: Average Return = 23.1\n",
      "Iteration 2: Average Return = 25.71\n",
      "Iteration 3: Average Return = 27.85\n",
      "Iteration 4: Average Return = 29.22\n",
      "Iteration 5: Average Return = 28.85\n",
      "Iteration 6: Average Return = 34.52\n",
      "Iteration 7: Average Return = 33.67\n",
      "Iteration 8: Average Return = 34.11\n",
      "Iteration 9: Average Return = 37.76\n",
      "Iteration 10: Average Return = 36.64\n",
      "Iteration 11: Average Return = 39.82\n",
      "Iteration 12: Average Return = 48.9\n",
      "Iteration 13: Average Return = 46.26\n",
      "Iteration 14: Average Return = 49.97\n",
      "Iteration 15: Average Return = 52.68\n",
      "Iteration 16: Average Return = 52.51\n",
      "Iteration 17: Average Return = 50.02\n",
      "Iteration 18: Average Return = 56.16\n",
      "Iteration 19: Average Return = 52.54\n",
      "Iteration 20: Average Return = 51.38\n",
      "Iteration 21: Average Return = 62.91\n",
      "Iteration 22: Average Return = 56.09\n",
      "Iteration 23: Average Return = 59.28\n",
      "Iteration 24: Average Return = 62.36\n",
      "Iteration 25: Average Return = 61.02\n",
      "Iteration 26: Average Return = 71.19\n",
      "Iteration 27: Average Return = 73.18\n",
      "Iteration 28: Average Return = 74.94\n",
      "Iteration 29: Average Return = 81.41\n",
      "Iteration 30: Average Return = 76.44\n",
      "Iteration 31: Average Return = 84.26\n",
      "Iteration 32: Average Return = 92.12\n",
      "Iteration 33: Average Return = 94.37\n",
      "Iteration 34: Average Return = 90.26\n",
      "Iteration 35: Average Return = 111.77\n",
      "Iteration 36: Average Return = 111.8\n",
      "Iteration 37: Average Return = 123.52\n",
      "Iteration 38: Average Return = 133.57\n",
      "Iteration 39: Average Return = 136.4\n",
      "Iteration 40: Average Return = 157.49\n",
      "Iteration 41: Average Return = 150.17\n",
      "Iteration 42: Average Return = 151.71\n",
      "Iteration 43: Average Return = 151.58\n",
      "Iteration 44: Average Return = 155.21\n",
      "Iteration 45: Average Return = 161.79\n",
      "Iteration 46: Average Return = 167.62\n",
      "Iteration 47: Average Return = 165.44\n",
      "Iteration 48: Average Return = 173.7\n",
      "Iteration 49: Average Return = 173.44\n",
      "Iteration 50: Average Return = 179.46\n",
      "Iteration 51: Average Return = 185.48\n",
      "Iteration 52: Average Return = 181.74\n",
      "Iteration 53: Average Return = 184.86\n",
      "Iteration 54: Average Return = 192.51\n",
      "Iteration 55: Average Return = 193.36\n",
      "Iteration 56: Average Return = 191.39\n",
      "Iteration 57: Average Return = 187.99\n",
      "Iteration 58: Average Return = 193.92\n",
      "Iteration 59: Average Return = 192.35\n",
      "Iteration 60: Average Return = 191.66\n",
      "Iteration 61: Average Return = 194.92\n",
      "Iteration 62: Average Return = 193.95\n",
      "Iteration 63: Average Return = 196.12\n",
      "Solve at 63 iterations, which equals 6300 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 = LinearFeatureBaseline(env.spec)\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()"
   ]
  },
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vQ/niMmAKKQFqjTts1NOQfdgc/v5iur01YE2JRMQlxiirTQL6gpCq1Fb1iwQYCyaEW0xr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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efe3c03fef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7du0CoLi4mOLi4noLTAhXVX7mR/TWD1HDYlBt2jk6HCHqhF1PFj/88ANLly7F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\nsRBCCFEtKRZCCCGqJcVCCCFEtf5/lwpDoWOdEIoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efe3c03f7f0>"
      ]
     },
     "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": {},
   "source": [
    "# Verify your solutions\n",
    "\n",
    "if you solve the problems 1~3 correctly, your will solve CartPole with roughly ~ 80 iterations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 4\n",
    "\n",
    "Replacing line \n",
    "\n",
    "`baseline = LinearFeatureBaseline(env.spec)` \n",
    "\n",
    "with \n",
    "\n",
    "`baseline = None`\n",
    "\n",
    "can remove the baseline.\n",
    "\n",
    "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": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1: Average Return = 31.14\n",
      "Iteration 2: Average Return = 36.33\n",
      "Iteration 3: Average Return = 35.4\n",
      "Iteration 4: Average Return = 37.23\n",
      "Iteration 5: Average Return = 40.81\n",
      "Iteration 6: Average Return = 43.13\n",
      "Iteration 7: Average Return = 42.91\n",
      "Iteration 8: Average Return = 42.55\n",
      "Iteration 9: Average Return = 42.96\n",
      "Iteration 10: Average Return = 43.78\n",
      "Iteration 11: Average Return = 53.83\n",
      "Iteration 12: Average Return = 48.12\n",
      "Iteration 13: Average Return = 51.31\n",
      "Iteration 14: Average Return = 49.7\n",
      "Iteration 15: Average Return = 50.57\n",
      "Iteration 16: Average Return = 49.59\n",
      "Iteration 17: Average Return = 58.61\n",
      "Iteration 18: Average Return = 55.72\n",
      "Iteration 19: Average Return = 51.83\n",
      "Iteration 20: Average Return = 65.14\n",
      "Iteration 21: Average Return = 62.36\n",
      "Iteration 22: Average Return = 67.12\n",
      "Iteration 23: Average Return = 65.77\n",
      "Iteration 24: Average Return = 74.15\n",
      "Iteration 25: Average Return = 74.43\n",
      "Iteration 26: Average Return = 76.3\n",
      "Iteration 27: Average Return = 89.68\n",
      "Iteration 28: Average Return = 91.29\n",
      "Iteration 29: Average Return = 105.11\n",
      "Iteration 30: Average Return = 108.53\n",
      "Iteration 31: Average Return = 109.26\n",
      "Iteration 32: Average Return = 120.05\n",
      "Iteration 33: Average Return = 122.64\n",
      "Iteration 34: Average Return = 131.23\n",
      "Iteration 35: Average Return = 127.43\n",
      "Iteration 36: Average Return = 132.21\n",
      "Iteration 37: Average Return = 137.94\n",
      "Iteration 38: Average Return = 130.96\n",
      "Iteration 39: Average Return = 142.17\n",
      "Iteration 40: Average Return = 155.78\n",
      "Iteration 41: Average Return = 154.87\n",
      "Iteration 42: Average Return = 155.03\n",
      "Iteration 43: Average Return = 162.96\n",
      "Iteration 44: Average Return = 160.3\n",
      "Iteration 45: Average Return = 168.68\n",
      "Iteration 46: Average Return = 179.22\n",
      "Iteration 47: Average Return = 180.15\n",
      "Iteration 48: Average Return = 187.18\n",
      "Iteration 49: Average Return = 187.2\n",
      "Iteration 50: Average Return = 186.34\n",
      "Iteration 51: Average Return = 189.86\n",
      "Iteration 52: Average Return = 189.12\n",
      "Iteration 53: Average Return = 194.31\n",
      "Iteration 54: Average Return = 192.36\n",
      "Iteration 55: Average Return = 193.99\n",
      "Iteration 56: Average Return = 186.96\n",
      "Iteration 57: Average Return = 194.65\n",
      "Iteration 58: Average Return = 190.04\n",
      "Iteration 59: Average Return = 195.29\n",
      "Solve at 59 iterations, which equals 5900 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": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yrjsp+NxjCfflEk0tcFkV/oyZo2NuX9+E+NAn4Fgv8tCz/uelYUD/OURreMM/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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efe37346400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pieLiYjIyMkhPT6d169aVvo8Q1UmfPQP7dqKu7SUztYVHc+rJ4rbbbnOMRoqJ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\nQgghKvT/AZBtQwkb2T0hAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efe372eae10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "util.plot_curve(loss_list, \"loss\")\n",
    "util.plot_curve(avg_return_list, \"average return\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yrjsp+NxjCfflEk0tcFkV/oyZo2NuX9+E+NAn4Fgv8tCz/uelYUD/OURreMM/\nYSlQ3k9ork7/OSWMWUAWvlTQRkeTMrL/rBIRxHk3Ggslmw74UZp5MGGeTuV8WZt48Bkdixkmi1Z/\nLVp4Dfytq2lZDes2zj9fUQUzM8jpCBWyU2XELIETbHSWg2xaGgYMDsQlIkiZppXqsx92qRI4RcXq\nc42B2Pp+uOY65Hf/BunyGSqnQwlVQkUEJvXhCdCy/1zafj+LAW10NKlz4Wy4PDRZ6ptg2Dlfy2zY\npXJUQluNl1fA9GT8vUB8BqrAXMyNJiaYjhJeY34BX2x9f/CddIWvLE8mvB3T06kO93RwO7Nakj7r\nDLtUsm5jHHLpFJkv/NmPdMbI0QkcY7Fg+dSfgGFg/N1T/iKfQERPB3xigtAE6P7zSpiwTNBGR5MS\n0uOGUU/0O7tEqW9UORNOh2//rnDlGszXX4szV0f6w2um0YkimzbXdAqLwl9b/w51R3pLcBdHYd4R\nj6ff6Mho4bX6JvU+LdCjZVGTgFw6ZZrNwp8XY+fohCAamhEf/QN4/SjywE+V1y8ssGJV5AH2Jn+L\nA/C1bfC4lo2IAPKg9trY2Bjd3d0MDg5SX1/P9u3bqagIT5A6evQo+/btwzAMtm7d6m/WttD4oaEh\ntm/fzu/+7u/ygQ98IGvzWjYscGeXKMLehAQVYmtqCa9GYBJYlaAqglEKxTQ6C3o6qoFbpPpxlt/c\nCr+5NXyMaXQy4un4wosV1UFPi4Zm9T45BoAIibZLAOlIQC6dKtU25d1e7lc5OmtiJDmHILbchXz1\nReT396nvbGOzUsRF2ra+UX1uQ1fgqoplVf7GJOeezv79+2lvb2fPnj20t7ezf//+sG0Mw2Dv3r3s\n3LmT7u5uDh48SH9/f1zj/+7v/o6bblqaP8p8YL6wYbo8HZ+s1BQThFYj8OFvhBWvVNmnXiuwm0Yn\n2prOVJiIYEF8RkdmohTOyDBUVIYXu1wOLQ6uDCiBSkBDvUwhhFAKtvN96jsVQ7kWaazlk3+sKmGf\n7wtPCg3EHpwA7W+R0BLFM1qC5Nzo9Pb2smXLFgC2bNlCb29v2DZ9fX00NTXR2NiI1Wpl8+bN/u1i\njX/55ZdpaGigpaUlCzNZplw4C7b69JXvqKpRLX7NGmwj7nARAQS0N4hTTDAxBsWliEqfgciA0WEs\n/bk6cmQYKmvCXyivVC3Al7DRkVcuQn1T1vrLiKaV8NYp9SBWjk6ksbZ6xO/dpx7E8vp97RmkKQLp\nP6cqqMdTZurxAAAgAElEQVTjrS8Rcm50PB4PtbXqDa+pqcHj8YRt43K5qKubbyVbV1eHy+WKOX5q\naoof/ehH/O7v/m6mp7CskRfOxv6RJYhqcdCkFD7jo+D1xgyvxV1pemIMysuxmMYxitGR01MRRQQx\nKS9XGe2ZEhKErufge5/ql7hs2jGQndCaSVMLSANQRiRRxOZ3Y/nsQ4gtd0XfpqxcCU9MT6f//LJa\nz4Esrek89thjDA8Phz1/9913Bz0WQiSsr482/p/+6Z943/veR0kk6WsIPT099PT0ALB7927s9uTd\neavVmtL4fCPWfOTMNI4rlyh/51Yq0jhn98qrMBwDVAmJC6hqWUVJyP6NkiIGgXIhKY/j2G7vLEZV\nDYW+9gBlFiKes9uYQ1ZUYktwPo7ySkq8M1TFGGeMjYCwzBu+OBgaH6XwmuuojrDf4dbVeE+/viS/\nc3W1tTgGL1N2y7uozNLcptZtwLzlta3bQEFtXcztI/KeD0Z8OvAzcja3YvE4qamtxTHwNmV3fThr\nc0wXqXznsmJ0HnnkkaivVVdX43a7qa2txe12U1UVro232Ww4nU7/Y6fTic1mizm+r6+PX/3qVzzz\nzDOMj48jhKCoqIi77gq/C+nq6qKrq8v/eGgovCBfvNjt9pTG5xux5iPP94Exx2RdI1NpnLNRVYs8\ndpjhc28BMGqxMhayf2kYIATjjstMxnHsuWEXFJUwJwQUFjHhHIx4znOjI1BWnvBnKMsrmXIOMhNj\n3NxXH4FLF7D8t4eJt3rDnNuFUVwa8XyMahvScZnZyUmcESIEixW73c7Q6ZPgnWWyqobpLP2eZJnv\n2lNYhMtrINJ43MDfkVFTh/fcaYbeOA4zM0zWNWZtjuki0nVhxYr4vNKch9c6Ozs5cOAAAAcOHGDT\npk1h27S1tTEwMIDD4cDr9XLo0CE6Oztjjv/yl7/MN77xDb7xjW/w3ve+lw996EMRDY4meeSFNIsI\nTOqbYHpqXqQQIbwmLBbVUiDu8Nr4fEOuktIFhAQJhtcgvqKfVy6Bx4XxFzuQRw4tuEs5PaXUdBHC\na4AqzSMN5qL0aFnUZFMubdLoK/xpq08p4rIgZouD877yUcssvJZzo7Nt2zaOHTvGgw8+yPHjx/1S\naJfLxeOPPw5AQUEB9957L7t27WL79u3cdttttLa2xhy/2JAetyrJvpjoP6cW3U0ZcpoQZrXp06+r\nJyLl6YBaSI+3/tr4GKK8XP1dWh7T6IhEhQSgxAQx1GvSMMDjQvxmF7Suwfir3Rg/+V7EKsV+ouXo\n+DCTVedCu14uAeQV31pVFo2OKCxSC/0JiggSxmxxcOKIUrw1t2b2eHlGzvN0KisrefTRR8Oet9ls\n7Nixw/+4o6ODjo6OuMcH8rGPfSz1E80g0jAw/vov4NQJLKvWzpdAz3PkhbOwclX61UX1vpLyZ06q\nnjUReu8AUF7pT7JbkImxeU+ntCyGem0ycgmcBRAVVf4714iMetSF5qo1WP7zZ5F/uwf5w39QbZI/\n8UB4xQWIWgLHj9/o9MNVaxM+57zGcUmpGCOJSDKI5ZMPQpx9eJJF1KtcNHmsFxpXKmO3jMi5p6MB\n+cLP4NQJ9feJIzk+m/iQUkL/2bQlhQZh9jEZG4l90Ymz0rT0zqpKzQFGJ2rttankw2uMjUT3XIbV\nmqSoqUMUFiE+/d8R7/995IvPYnz9/4s8bgFPh6oaKC5hbqA/8fPNc6Sv0Ge25NImYv1GxFVrMnsQ\n86ZyYnzZhdZAG52cI4edyO//LaxvV5WDjy8Oo4NrUK2TpHs9B19/EzM3J1poDRDx9tQxvaHyAKMT\nwdORXi94ZyFKNnlMKqrU2JkoRT/dPiGML9FRCIHlA7+P+OA98PqrEcvZzJfAifwemLJp78CFxM83\n33EMZDW0llVq68As7qmNjiabSCkxnnkavF4s/+UBRHsnnDyGjHbhyifSXP4mDF+ILVI1Aj/x9tQx\nE0h9no4oKYtcBmcmerHPBVmgFI4cNo1OsOcmbrpNvX7q1+GDTKNTWR3+mjm+aSVz/VHaJqeInJ1F\nnj2N8dxPMP52D8bffx1p9jfKIHLOC0OXEVko9JkL/C0OWH4iAsiDNZ1lzSsvwtGXEB/5pFLpbLwZ\n+Ysfw5snIJF2uzlAFTZUveIzgbA3IfveiB1eK6uAiTGkYcQOw/g8HX/pnLLyyAU/zdYESQgJREWV\nqqk1NhK5WKTbpRaNQ0Nlza0qNPfm8fC6biPDqsJ2aAmcoPEtzB05iGVmOvraV4IYv/wZ8sBPlVBk\nzquerKiE6WnkKy9i+fgfITrfmdA+pTGnuq3GUb5/znFZrX8tVU8HVDkcx8Cy9HS00ckRcnwM4389\nDVetQfy2T3G3fiMUFSGPH06sx3sOkBfOqRIlJUl4BfFgigkilcAxKa9UlZanJubXayJhhtfKTPWa\nWtMJM1ZmL51k1WsQXcE27ISqWnWXG4CwWOCa65G+Nb1A5Ig7+nqOSXOreg+uXEpbZQj5Hz+E2RnE\nb38QsXotrL5GtXO+fBHj290YT/854tWXEPf8oQpxxoHx9V1gsVDw3/7Hgtuaa1RZlUtnGdGyCnnx\nfFbqyuUbOryWI+T3vg2jHiyf/GP/3Z8oLIJrb0CeOBJbSpsP9J/NyHqOH7Mw4kLhNVgwxCbHQ9Z0\nSsrUhdoMp5n4eukkZUh9PXWi5erIYaeK5UdArG8Hp2O+Y6VJlBI4QWPNkvyX3k7whCMjDUNVWd70\nTiwf+STi5t9E+HrLiOYWLP/vnyM+eA/yyEGMP/3j+IUvF96C115G/vrVBTedM9eoslkCJ8uID9yD\n5eEnM5sPlKdoo5MD5BuvIQ/2IO78EOKqtqDXRPvNMHhZ3bnmKXJqEgYvp69xWwTEqrVQYI3Z3Mp/\nl72QmMDv6QQICQAmQsQEZi+dVDydaOfidkYNFQpfF9Iwb2dkOLpc2qRxpQrbXU6Tgm1kWAkiTAVh\nCKKgAMvv3I1lxxNQWo6x58tKaRYDOTcHHrU+ZXx/nwq1xcA7cEGtqy0090WMKC5BJFNmZwmgjU4O\nMH7+I7DZEe+/O+w1sVGF1eSJw9k+rfi5eB6kjF3CPUXEyquwPPVdxMqrom8Up6cT1eiEyqb94bUk\nPJ2yctW8K1pVgmEnIlooZeUqdW4RjM6Cnk5hEQWNK5DpUrD5mueJBRIkxao2LPf+P8pjHFjAyxoZ\nVoU0r30H9J9DvvhczM3nLvWrnjTL0AtYDmijkwvcTmhdE3HhV9gbobk1r6XT/vI3mVKu+YiYMBmI\nz9NZsNL0+LhqzOZbkBem0QmRTUuzVXUyyaGWAmUEIxgdOTWpjlUTJbxmscA11wV5OnJmGqZilMAJ\noKBlNaQpV0ea0u14OmfalBGVbmfs7XzKPcvW98PV65D7vxNToTk3cGFJr+csd+I2OidOnMDhUHdB\nbrebr3/963zzm9+MWD1aswAj7phhE9F+M5w6oS5W+ciFs+rOPony72mlLAFPJ1BoUOoTFITKpqdS\nEBJA9FI4UeTSgYh1G8ExMC+tXigxNABryyq4ckmFsVLF5+nEZXQqqqHACu4FilUG5ChZPvopGHYi\ne/4l4qbS61XqNW10lixxG529e/di8Sl9/v7v/565uTmEEDz99NMZO7mliDTm1IUpVtLjxptVH5mT\nx7J4ZvEjfSKCnIc/TEOyQCkcOTE2r1wDJSQAZKhsejqFPB2IXvTTPV+NIBpivW9d502ft7NQCZwA\nrC2rlbQ5HYU/nQ7VVCwOwyssFrVOtYCnE5ijJNZthBtuQf7795GjESpjD10BYw6WaI6OJgGj43K5\nsNvtzM3N8dprr/GHf/iH3HfffZw6dSqT57f0GB1R8e1YnQKvuQ6KS/MyxCYNAy6ez1xSaAKIwkLl\nlcQjJAjsYeMPr4V4On6jk2S+S0VVxHPxJ1TGMDq0Xq3Oy0wSHXGr/+M1OgCXU1/XkUOO+Lwck1o7\n0rWApzPsVB5RhUpytXzkUzAzjfzx/54/rpTIN49j/MPXARDNMdbyNIuauPN0SktLGR4e5sKFC7S0\ntFBSUoLX68Xr9Wby/JYecdzBCmshXDcvnc65RxHI4GV1cc6XpLZ4qhJMjPvbBAOxhQQFVvX+J4Go\nqEKeOx3+ghl+iqFWEpYCWHsd8tRxILAEThxrOr4EXTnQj7gxsXMOw+lIKEte1NZFnnMgbhdU1/pz\nokRzC+KddyKf/yly6/vBeQXjx9+FvtehupbK+z7HxNXx9RvSLD7iNjp33XUXO3bswOv18qlPfQqA\nkydPsnLlykyd29LE47uDrV5AldTeiXz1Jbh0AWIpuLJNf4bL3yRKWeXCQoKJMURZgDS9uERVUwit\nvzY1lfx6DihPx1f0M+hGYdgJZeULhqzE+o3I44eRHndACZyFjY6lvEKFuVJUsJk5Otx4S/yDau3w\n6ksxb44i5SiJD/w+8lfPYez6nPocau2I3/8M4p2/TdmKlUwssqZmmviJ2+hs27aNW265BYvFQlOT\nStyz2Wx89rOfzdjJLUWkP2wSI7wGiOs7VPnzE4djy4azjLz4trpgr8iTc4rH0xkfD1rTERaLWtcJ\nNTozU0kp1/xUVKm1uOlJ/7oRgHS7YofWzPNat1F95qd+rYxOWcXCCj6T5lbkpRTDawvk6ESktk6N\nGRuFyvCuv4AyuiHlkkR1LWLbx5HP/wfio59C3LY1/rlqFjUJlcEJbEd64sQJLBYL1113XUonMDY2\nRnd3N4ODg9TX17N9+3YqKsJLmhw9epR9+/ZhGAZbt271N2uLNf78+fP89V//NZOTkwghePzxxykq\nynHvijjDJsJmh5bVal3nPR/OwonFydBlqK3Lnx4g5RWqJ00UpGkEQsvklEboHppsWwMTX1UCRkeC\njA7DzriMDle1qeOfOoEcXThHJxDR3Io8+IvUwrFx5ugEHddmVzXn3EPRjY7bhbg+vBeWpesD0PWB\nJE5Us5iJW0jwpS99iZMnTwKwf/9+vva1r/G1r32NH/zgBymdwP79+2lvb2fPnj20t7ezf//+sG0M\nw2Dv3r3s3LmT7u5uDh48SH9/f8zxc3NzPPXUU9x333189atf5U//9E+xxiqcmC08wypnJI5SK6L9\nZuh7PXrDsRwgh64kttCcYVR7gxiezmRwhWk/peXIECGBnE4tvCaiVSUYdiJiyKX94wsKYO21Kl8n\njsTQIJpblHFdSL4cg4RydEzMhNcoCjY5OaHOa5lm32vCidvoXLhwgXXr1gHwi1/8gi996Uvs2rWL\nn//85ymdQG9vL1u2bAFgy5Yt9Pb2hm3T19dHU1MTjY2NWK1WNm/e7N8u2vjXXnuNq666itWrVwOq\nw6glyw2hIhJPEUcf4voOVW237420HV66ncw98kfIZOW1Qw6VwJovlFXA+Gj0WnX+umvlwc+XlM7n\n5ZhMT6a+pgNBCaL+EjDxeDr48nUuvQ0D/XHJpf3jzJbHqSSJJpKjY+IzJjKasTPl0nHOX7P0ifsq\nbP6oL19WF6uWlhbsdjvj4xH6kiSAx+Ohtlatb9TU1ODxhGv3XS4XdXXzX9q6ujpcLlfM8QMDAwgh\n2LVrFw899BA/+tGPUjrPdCETuYNtVCINGaHBV9L0n1PhqP5zCQ+V3ll1Eckno1Ne6WueNhP59dC2\nBial5UrVFsj0lDJGyeIzOkG5Oh63ksgnYnRAGa5EPR1IrRxOAjk6fqpqVO23aLk6ceQoaZYXcceb\n1q9fz7e//W3cbjebNm0ClAGqrFy4tPljjz0WsXLB3XcH1x4TQqQkDw4cPzc3x8mTJ3n88ccpLi7m\ny1/+MmvWrKG9vT1sXE9PDz09PQDs3r0buz35cuNWqzXm+KHxUawrV1ETxzGkzYbDWkjp5CiVKZxT\nIJPCYASosBZQGsc+A+fjHejHKSWVq9fGNTYbTDQ2MQrYigspiHBO02/3MQxUr2ihyG73z2e4phav\n0xH0WQ3NzlJYVU11knMzSooYBMqlQblvH7OuK7iA6lVrKI7nM6++FUdRMcxMU9a0gop4P6Or1zJY\nUUmJe4iqJM/fPeLGaFxBXYLjB231FE2MRnzfJr0zjAC1a9ZijXO/C/2GFiNLbU6pzCduo/PAAw/w\n4x//mKqqKj7wAbX4d+nSJd773vcuOPaRRx6J+lp1dTVut5va2lrcbjdVVeGLkTabDadz/k7K6XRi\ns9lijq+rq2PDhg3+xzfddBNnz56NaHS6urro6uryPx5KQa5pt9tjjp9zDWG0bYj/GDY7kxfOM50m\nCakxoCoCjw45GI9jn4HzkadVmG+suCyusdnAjKq5+s8jIjjuxoASGXhmvYihIf98DEsBcnw06HOY\nmxjHQCT9+UvDAGFh/PIAk+Z7du4MACMFVkS8+227Ft54jQlrEVNxfkZOpxPZuJLJc6eZSfL85wYu\nIlpWJzx/o7qWqcsXmY0wzrhwDgC3FHHPf6Hf0GJkqc0p0nwChWaxiDu8VllZyT333MPHPvYxSnyy\n0o6ODt73vvclcKrhdHZ2cuDAAQAOHDjg96ICaWtrY2BgAIfDgdfr5dChQ3R2dsYcf8MNN3DhwgWm\np6eZm5vjjTfeoKWlJaVzTRXpnVWLzImETeoakGasPR2YoZ8kxAn+MF8+hdf89deihHknogkJIkim\npydTUq8Ji0Up2MYD1nTccVQjCN2PL8QmFpDVh41rbk16Tcefo5OAcs1/3Jq66OG1YZeSfqepq6lm\n8RO3p+P1evnBD37A888/7/csbr/9dj784Q+npArbtm0b3d3dPPvss37JM6h1nKeffpodO3ZQUFDA\nvffey65duzAMgzvuuIPW1taY4ysqKnjf+97Hjh07EEJw00030dERLtvMKiO+9aoFEkMDEXUNyONp\nbHNgGp3QbPx4GHKociZxKLGyxkI9dULbGpiUlMHsDNI7i7AWqjXL6ankS+CYVFQFr+n4S8BEkRNH\nQNx0K/K5f4eWBFuBN7fACz9Hjo4gIsiX5dRkdNVkMjk6JrV2OH44olw7VvM6zfIkbmvxne98hzNn\nznDfffdRX1/P4OAg//zP/8zExIS/QkEyVFZW8uijj4Y9b7PZ2LFjh/9xR0dHRKMRbTzA7bffzu23\n3570uaUdX2JoQnewdfXgcSNnZ9KSG+O/ICZTwXroiuoDZFm4z33WCGhvEHE1cGIMiorCEw/9laYn\nobJQCRGkTC1PB5SnMxZgAIdV8zaRgHJSrFxFwRN/m/ChRfNVKmdm4AJUXh/0mjzWi/HNr2B55P9H\nrIxgzJLI0fFjs8PMtPIqy0OMe4zmdZrlSdy/hJdeeokvfvGL3HDDDaxYsYIbbriBz3/+87z44ouZ\nPL9Fgxx2YfT8C3OxpMgJ1NPyY/NdBEJbGSeLWdk3tMJyHMihK/kVWoP5i1y0StPjY+FeDoQX/TQb\nuKVSkQD8pXBMZDYvuqaCLaTwp5QS40f/CHNzyNePRhyaVI6OD38HzEiy6WGXVq5pgkhYMq2Jwogb\n+d1vMRsjp0b6667F7+n47zxdaVrX8d2Fy6TCa1fyK0cHVF5NgTVqeE2G9tLxIUKLfk6n0Ko6cL8h\nRge3M3sXXVs9FBWHr+ucOAJvnwEhkH2vRx6bTI6OSZQEUTk3p260dHhNE0DcRue2227jz/7szzh6\n9Cj9/f0cPXqUv/iLv+DWW2/N5PktHuyqHt1cjJIsSXk6vouATJenk2R4TU5PKy8pj6oRgJLJU1Ye\nW0gQ09MJNjoiTeE1KaW6URt2zl+UM4ywWKBpZVCujpQS48f/G+oaEJveBadfj3wDmUyOjkm0BNEE\nc5Q0y4O413Q+/vGP88///M/s3bsXt9uNzWZj8+bNfPSjH83k+S0aRFk5VFQyd/lS9I1GhqG0PLG1\nmZo6lXyXBgWbNIz59YZE1WvOPFSumZRXRhcSjI+pdbFQohidVD0dKqpUQ7WpSXXBnZnOqvBCNLUG\nezNvHIWzpxD/+Y/U9+jl58ExAI3B8taE++gEUlULIkKC6LBODNWEE9PonDhxIujx9ddfz/XXXx+k\nUjl58iQbN27M3BkuJuxNzF2J4el43Akp18BXj6vWnhajw+S4uhBC4kICX8w/78JrAOUVkTt2AkyO\nI8pWhz9fanYPnVAChHSu6YDyKM0qCdm86Da3wMsH/Eo141+/CzV1iN/sgqHLqop13+uIEKOTaB+d\nQITVqr7X7hBvPI423ZrlR0yj85d/+ZcRnzcNjml8vv71r6f/zBYhor6JubfPRH1djrgXbGkQkbr6\n9OTqjPouzEXFCUum8zJHx4dYcRXylRcjV1iOsqbjrwJtCgmmUmxVbZ5LRZVSkI2N+HOEsnmnL5pb\n1fGvXEROTcHp1xF334coLEQ2rlRe4enX4Tfnk6GT6qMTSq1diSYCSCZHSbP0iWl0vvGNb2TrPJYG\n9U3MHTmExetVd3+hjHiSan4mbA2q8nCqmN6AvTFxz8npgKKixNajssXV6+CXPwsLG0ljToXPIq7p\nmJJpZXxlOsNroJq5mWt42VxID6jBJg89C1U1iHfdCfjWfNZuQIaKXVLJ0TGprQsXMCSRo6RZ+uRB\n2eUlRH0TGHPgirLoP+JOSLnmp64e3E7VGyYVTKNT3wTTU+qiHCeqpUFjfrXO9iGuVtXP5VtvBr9g\nViMIzR0BlbdjLQxY00lXeM2XNzQ2Oi8hzmaeSkMzFBQgD/4C3ngNceeHgqoBiLUblBc0GlBYN5Uc\nHXO/tfZwyXQSOUqapY/+NqQRUd+s/hgKz9WRM9PqApeMp1DXoNZihqOUGokTc93Dvy6TyLpOnvXR\nCWJFqwqLnQ01OlGqEZiUlkWQTKeqXgtY03G7oKIqqw3vhLUQ6pvh5DGoqERsuSv49bW+posB3k4q\nOTp+au0wNRnU+ymrOUqaRYM2OumkXl3MpSNCgmgycmkfoi5NCaKB4TVI2OjkpYgAVIWE1WuRb50K\nfsEnow5ra2ASWH/NXNNJ1UCUliuV2NiIKgGTi/UMX4hNdH0wvOzNqrVgLQxWuKWSo2MSKUFUJ4Zq\nIqCNTjqpqVMhmwieDr7EUJFUeM3M1UlRTDA2oi6q5jnEWZVAToypUFWeGh3whdj6zyFnA/rqmJ5O\naAM3k5Ky+TtzXwO3VENBQoj5qgQ5qjsm2jZAtQ3x7t8Jf62wEFZfgzwdYnSSzdEx9xuSIDqfo6SN\njiYYbXTSiLBYKGhsjtyV0+/pJGF0bL4fdDqMTkVVeDb+QgyZMf88Njpr1qv8mLff8j8n4wmv+Y3O\ndOoiAhOz6KfbichBeEncuQ3L438z/zmHvn7NBnj7jEr4JcUcHZPQBNHJCRWy1J6OJgRtdNJMQdNK\niGB05kvgJBFeKyyCalvKRkeOjaqFblMuHG94zS+XztM1HVAKNkAGruuYrarLong6peXBtdfSZnQq\nlWc76snJRVcIEV7gNPD1tdepNujnfOFIp2M+hJsspnF1+YyOv021XtPRBKONTpopaFRGJ6zUiOnp\nVFQnt+O6emQ0VVy8jHpU6MeM88fp6eRzjo6JqLEpjzBwXWcBT0eUlvoNr5yeSl1EYFJRBRfPq7/z\nMbzUtgEAefr1lProBCKshWq90jQ2ZjWCfJy/Jqdoo5NmCppWqgtZaIb8iFuFtpLsPSTqGtISXhOV\n1UHZ+HExdEWNiRamyheuXhcsm54YA2th9AZiQZ7OVOpyaR+iospvzPLxoivKK2DlKiUmSEeOjkmt\n3R9e04mhmmhoo5NmrE0r1R8hITbpGU4uR8ekrgFcg+rONFl8azqJhtek05G3OTqBiKvXg9Mxn5QZ\nqb9LICVlMDmpvNKpdIbXApIh8/SiK9ZugLfe9H9PU8nR8VNrn6+/psNrmigk3/IzTYyNjdHd3c3g\n4KC/82dFRfiF4ujRo+zbtw/DMNi6dSvbtm2LOd7r9fJXf/VXnD17FsMwuP322/nQhz6U8fkU+DLi\n5eBltbhtMjqcWjZ/XT14vcpjSuJCJr1edRFOIrzG0BWVdJjniKvXqRIwZ0/BDbcgo/XSMSkrU/lP\n01PqX7qqQQcanTz0dABYuwEO/BR5rFc9TkMOlqitQ546rh4MO6G8Urep1oSRc09n//79tLe3s2fP\nHtrb29m/f3/YNoZhsHfvXnbu3El3dzcHDx6kv78/5viXXnoJr9fLk08+ye7du+np6cHhSFNPmhiY\nRidMTOBxI1IwOinn6kz4qjBXVKkiokVFcUmmpZR5naMTxKq1YLHM5+tMjEUXEUBwpenpqZQkw0GY\nLbQLi/I2JGkmicpfHVBPpCPxt9YOE+PIqUmdGKqJSs6NTm9vL1u2bAFgy5Yt9Pb2hm3T19dHU1MT\njY2NWK1WNm/e7N8u1vipqSnm5uaYmZnBarVSVhZZQppORHGJUpoFGB0pZfIlcExsKebqjM4bHUCF\nluLwdKTHrcrzLwKjI4qL1VqFqWCLVuzTpCRAOj49mb41nUrfe1xjy9+QZF2D8pjdQynn6Pgxvbph\nJwy78tfL0+SUnIfXPB4PtbXqYlxTU4PH4wnbxuVyUVc3/wWuq6vj9OnTMcffeuutHD58mM985jPM\nzMzwyU9+MmLYDqCnp4eenh4Adu/ejd2efJjFarVSuKIVhoew+fZjTI4zODNDedNKypPct1FexiBQ\nPjmW1D5mLl/ADdSsbKHIbmeovIJCaVC9wL4M38J89ZprKE7hfckWI9fdyNQvf0adzcbQ1CRFV9cF\nzdFqtfo/3+nGZoaB6qJC3NPTlNbUUpmGOc6uvAoXUFjf5P8OZJLAOSXC8MYbmX7hF1gbV1CXhvOc\nWd2GG6gyvIyMuCm6ZsOC369IJDuffGapzSmV+WTF6Dz22GMMDw+HPX/33XcHPRZCpHRnGDi+r68P\ni8XC008/zfj4OI8++ijt7e00NobfsXd1ddHVNV/qfWgoQq/3OLHb7Xhr6pBvvObfj7yiGruNW4uY\nTGHfVFQyfuFcUvuQF1U3SY8hEUNDzBUWMzfsZnaBfVVcUuNGCksQqZx7ljCar0JOjDP069cwxkaY\nLhJk4XcAAB0HSURBVCgM+jztdvv85zI7C4Dn4gWYnWHSkEynYY5yTok9vBXVKX2X4iVwTolgtLYB\nv2Cu2paW85QWdTnxnDmFHHYxXVKe1H6TnU8+s9TmFGk+K1asiLJ1MFkxOo888kjU16qrq3G73dTW\n1uJ2u6mqCi+DbrPZcDrni106nU5sNlvM8S+88AI33ngjVquV6upq1q9fz5kzZyIanbRT3wQvPouc\nmVYLqf4SOCm2BbA1JN222t/kzAyvlcYXXpvzGczFEF4DEGvW+RqVvRG9rYGJr72BP3E3nXk6kPfN\ny8TaDUp4ka6kXzOcdu40SJn389fkhpyv6XR2dnLggFrMPHDgAJs2bQrbpq2tjYGBARwOB16vl0OH\nDtHZ2RlzvN1u93c+nZqa4vTp06xcuTIbU1JGB+bzakaTL/YZRF198rk6ptEpN9d0SuOSTM85BpT4\nILRwZL7SuFIZkzdeUxe+aHXXYF5IYMp80yUkKClFvOfDiE23p2d/maJlNeI3tiBuvDUtuxOFRaoE\nkE/IoYt9aiKRc6Ozbds2jh07xoMPPsjx48f9UmiXy8Xjjz8OQEFBAffeey+7du1i+/bt3HbbbbS2\ntsYcf9dddzE1NcXnPvc5duzYwR133MGqVauyMidhGh1ftWn/nXQyddcC91unmq+FVTuIh7ERdTH0\nlUcRiRidReLlgK9R2eq1yF+/qp6IR0jg8SUypsnoCCGwfPRTiFVtadlfphCWAiyf/u8qZydd1NbN\nV2PQRkcTgZwLCSorK3n00UfDnrfZbOzYscP/uKOjg46OjrjHl5SU8LnPfS69JxsvPqMjhy4jADzD\nqty9r8FX0tTVKyXZ2ChUJtiN0UwMNQksdhmDuSsDiBVXJXiiuUVcvR75xmvq75hGR3lvZpvlRePN\n5TO2erhwVv2t1WuaCOTc01mSVFaru2ZTNj06rGSploKUduvP1XElHmKToUaneGFPRxoGc4OXF5Wn\nA2pdx08MoyMsFmV40uzpLGf8ZX+suk21JjLa6GQAIQTUNyEdA4AvvJbqeg4oTweSW9cZHVHG0KS0\nDLyzfgVXRIZdqi7XIjM6ZsVpIHYZHFDrP/41He3ppIwZUqvO4xwlTU7RRidT1DfNtwTwpJgYauIr\nyiiHkjA6YyOIwPBePPXXnGYfnTxuaRABUVUzbygXqghQWqaqb0PakkOXNWYpIR1a00RBG50MIeqb\nVIsDw4DRYURlGjydsnIVDkqmxUHYms7C9dcWQ0uDaAjT24nH6Jjo8FrKmOE1rVzTRCPnQoIlS32T\nCk0Nu5SQIA2ejhAC6hoSLoUjZ6ZVQcsAoyNKSlWORixPxzQ66ajLlWXE5ncryXRRUewNg4yODq+l\njOnpaKOjiYI2OhlC2JvURf3tPtVGOdXEUJNk+uqMhdRdg/nwWiwF29AVLDa7yr9YZIiNNyM23rzw\ndiVl+AXoxboicsrY7KrgaevVuT4TTZ6ijU6maPDJpvtOqsfpCK8Boq5eNd9KBF9iqAiVTIMqdBkF\n6RrEWt9ECh188h/zfSiwqu6XmpQQRcVY/vzbqsK2RhMBvaaTKWz1ICzIM28AINIhJADl6UyMx9/1\nE+arEQR5Or4clVj7GRnGstTDJL5SOHo9J32IomKtXNNERRudDCGshSrUcK5PPZEuo2Mz++rEH2Lz\n112rjBBei1V/bdSDJV3nna+YggqtXNNosoI2OpmkoVmJCSA9eToEyJcTKfwZydMxL7ZRGrlJYw7G\nRrAs9UZcfk9Hiwg0mmygjU4G8XfbLLCmr4OkL0FUOq/EP2ZsBIQIPoci3519NPXa2AhIufQ9HdPj\n0+E1jSYraKOTSeqb1f/VNemLcVfWKBnwUIJGp6xCtan24S8BEy28NqISJpe60RGl2uhoNNlEG50M\nIup9nk6alGvgy9WxNyED2mEvyNho5DpYJTGKfo4uD6PjV6/pYp8aTVbQRieT+D2dNF+4G1aAr65b\nPKhinxEqXMdobyBHVA+g5WJ0hPZ0NJqsoI1OJvF5OmmTS/sQDc3zJXbiIbTYp0lpGTJaeM30dJaN\nkEAbHY0mG+Q8OXRsbIzu7m4GBwepr69n+/btVFSEL7ofPXqUffv2YRgGW7du9Tdre/HFF/ne977H\nxYsX+cpXvkJb23zjrB/+8Ic8++yzWCwW/uAP/oAbb7wxa/MCXy+XG26BDTekd8cNzTA7A8NOlQ+0\nEGMexOq14c/HauQ2MgwFBYjyCph2pXS6eY2p4tPqNY0mK+Tc09m/fz/t7e3s2bOH9vZ29u/fH7aN\nYRjs3buXnTt30t3dzcGDB+nv7wegtbWVz3/+82zYENz9sL+/n0OHDvHVr36Vhx9+mL1792LE6xmk\nkYL/9j+wbHpXWvcpGnxhuzhCbFLK8GKfJqVl0Y3OqAcqqpXgYCnj93R0CRyNJhvk/IrS29vLli1b\nANiyZQu9vb1h2/T19dHU1ERjYyNWq5XNmzf7t2tpaWHFihUR97t582YKCwtpaGigqamJvr6+zE4m\nWzSo+cp41nWmJ8HrjWh0RHFpVCGBHPVEDsktMURhEeLu+xC3/lauT0WjWRbkPLzm8XiorVVrHjU1\nNXg8nrBtXC4XdXXz5Vjq6uo4ffp0zP26XC6uueYa/2ObzYbLFTlM1NPTQ09PDwC7d+/GbrcnPA8T\nq9Wa0vh4kDYbjsIiSseGqVzgWHNXLjEEVDavoDRk2xGbjanpqYjn65ocR9jrszKfbBJxPr/3B7k5\nmTSxLD6jRc5Sm1Mq88mK0XnssccYHh4Oe/7uu+8OeiyEyEnNpq6uLrq6uvyPh4aGkt6X3W5PaXz8\nB2pk4twZphc4lnz7PABj0sJ4yLaGtCAnxxkcHAx73+ecgwhbPV6vNzvzyRJZ+3yyyFKb01KbDyy9\nOUWaT6SIUySyYnQeeeSRqK9VV1fjdrupra3F7XZTVRUeBrLZbDidTv9jp9OJzRZbVRU6xuVyLThm\nUdHQHJ9s2l8CJ4pk2jBgZiZ8TWOZhNc0Gk12yfmaTmdnJwcOHADgwIEDbNq0KWybtrY2BgYGcDgc\neL1eDh06RGdn54L7PXToELOzszgcDgYGBli7NoKCa5Ei6pthcEAJBWIQsdinSZTuoXJ6Cmam05rU\nqtFoNJAHazrbtm2ju7ubZ5991i+ZBuWZPP300+zYsYOCggLuvfdedu3ahWEY3HHHHbS2tgLw8ssv\n8+1vf5uRkRF2797N6tWrefjhh2ltbeW2227jc5/7HBaLhf/6X/8rlqWkxGpsVh6KxxW7S2OkYp8m\n/krTk8EJrL7EUKq0p6PRaNJLzo1OZWUljz76aNjzNpuNHTt2+B93dHTQ0dERtt0tt9zCLbfcEnHf\nH/7wh/nwhz+cvpPNI0RDs+p46RhY2OhYLPPS4MB9+FtWhyjYfImhIk2VsTUajcZkCd36LzN8JXbk\nlUuxt/Pl6EQUaJRGaVltejp6TUej0aQZbXQWK7Z61TJhMLaYQEZLDIWojdykz9PRazoajSbdaKOz\nSBEFBVDfuHCC6FiUumsw37I6tCqB39OJYqw0Go0mSbTRWczUxyGbHo1SYRqidw8d9UBJKaJIl4bR\naDTpRRudRYzw5erElE2PjSASDK8x6klbe22NRqMJRBudxUxDM0xPzYfDQpCGEb2BG0BhERQUhBX9\nlCPDWkSg0WgygjY6i5gFq01PjoM0ohodIYQq6R+qXhv1aBGBRqPJCNroLGYWqjY9GiMx1KS0LDy8\nNjKM0ImhGo0mA2ijs5ipa1DhMUeUXB1fNYKoazoAJaVB6jVpzKmQnA6vaTSaDKCNziJGFBQowxPN\n04lVd80ktHvo2KgKyWkhgUajyQDa6Cx2GpqjhtdkrLprJqVlwWs6OjFUo9FkEG10FjmiYUX0atOu\nQfV/DKMjSkJaVvuUcHpNR6PRZAJtdBY7Dc3KUxkN7rgqDQP50nOw9jpEcUn08SWlQUKC+RI42uho\nNJr0o43OIieqbPqN12DwMuK3/lPsHZSUBVckMI2OXtPRaDQZQBudxY5ZbTrE6BjP/TtUViM6Nsce\nX1oK05MqkRRUeM1igbKKTJytRqNZ5uS8n87Y2Bjd3d0MDg76m7hVVIRf8I4ePcq+ffswDIOtW7ey\nbds2AF588UW+973vcfHiRb7yla/Q1tYGwLFjx3jmmWfwer1YrVY+8YlPsHHjxqzOLSvYG0BYgqpN\nS9cQvPYy4j0fQhQWxh7vK/rJ9JQSFfjaVIul1PBOo9HkDTm/suzfv5/29nb27NlDe3s7+/fvD9vG\nMAz27t3Lzp076e7u5uDBg/T39wPQ2trK5z//eTZs2BA0prKykoceeognn3ySBx54gKeeeior88k2\nwlqoDE9AXx35y58BEnH7exbeQUlwTx1dAkej0WSSnBud3t5etmzZAsCWLVvo7e0N26avr4+mpiYa\nGxuxWq1s3rzZv11LSwsrVqwIG3P11Vdjs9kAZZhmZmaYnZ3N4ExySP28bFp6vcroXN+BqG9aeGxp\nSNFPn6ej0Wg0mSDnRsfj8VBbWwtATU0NHo8nbBuXy0Vd3XxL5rq6OlwuV9zH+NWvfsWaNWsoXCjU\ntEgJqjb92svgcWFZSEBgjvVXmvaJCUY9uk21RqPJGFlZ03nssccYHg6vhHz33XcHPRZCRG6rnAIX\nLlzgmWee4eGHH466TU9PDz09PQDs3r0bu92e9PGsVmtK45Nh/Oq1jD33E+qKi/Ac6sFb34j9t96j\nKhYswExjE26gqqiQYrsdx6iH0oYmKn1zyMV8MslSmw8svTkttfnA0ptTKvPJitF55JFHor5WXV2N\n2+2mtrYWt9tNVVV4IqPNZsPpdPofO51Of+gsFk6nkyeeeIIHHniApqbooaauri66urr8j4eGhhbc\ndzTsdntK45NBlqtw2NBz/4E8dhix7eM43e74xs7MADBy5TJc7EdOTTJZWMy0bw65mE8mWWrzgaU3\np6U2H1h6c4o0n0jLHJHIeXits7OTAwcOAHDgwAE2bdoUtk1bWxsDAwM4HA68Xi+HDh2is7Mz5n7H\nx8fZvXs399xzD9dee21Gzj1v8OXqyB99BwoKEO/87fjH+sJrcmoyoASOXtPRaDSZIedGZ9u2bRw7\ndowHH3yQ48eP+6XQLpeLxx9/HICCggLuvfdedu3axfbt27nttttobW0F4OWXX+azn/0sp06dYvfu\n3ezatQvg/7Z370FR1f8fx59ngQ0FWXcXdUfRaSS+ZXmZHDDxp5GB3WzKG07ZbdPKEqUwHbGZrIkM\nZpQwHRzM8ZZjNloj5R/VjE3RlE1S6mgqJo6ShLQsC6vAErB7fn8Qa4j65bIXz37fj3/knD1n9/Ni\nkDfncz7n8+Grr76iurqaTz/9lOXLl7N8+fJr3i8KCbFDQFHAYUe5OxnFYOz+uR1DppuvzGqgyLxr\nQgg/CfpzOgMGDGDVqlVd9ptMJlauXOndHj9+POPHj+9y3IQJE5gwYUKX/bNnz2b27Nm+bexNSomI\nANMgqLX99xkIrtZRdFxNV1YglYEEQgg/CXrRET4Sd2t7AflPzx6AVcIj2petbna1P6MDIJN9CiH8\nRIpOiNA9/xp4PL0b/dcx6WfHPZ1oKTpCCP+QohMilKg+zJUW2a990s/LTrilH8ott/iuYUII8S9S\ndAT064/6twvlEtK1JoTwKyk64p8rnSbUlr9lEIEQwq+CPmRa3AQi+7ff05HJPoUQfiZFR7TPv/bP\n6qOKFB0hhB9J95rwdq/R2ADyYKgQwo+k6Ij21UMbLrV/Lfd0hBB+JN1r4spCbiCj14QQfiVFR1xZ\nyA3kno4Qwq+k6Igr86+B3NMRQviVFB1xZfVQkO41IYRfSdER7QMJABQdRA0IbluEECFNio6AW/4p\nOgNiUHTyIyGE8J+gD5luaGigoKCAmpoaBg0aRFZWFtHRXSevPHr0KNu2bcPj8ZCamupd7O2nn35i\n7969/Pnnn7z33nvEx8d3Os9ut5OVlUV6ejqPPfZYQDJpTsdAAhlEIITws6D/WVtcXMyYMWNYv349\nY8aMobi4uMsxHo+HLVu28MYbb1BQUMCPP/5IZWUlAMOHD2fZsmWMGjXqmu+/Y8cO7r77br9m0LyO\nezryjI4Qws+CXnRKS0tJSUkBICUlhdLS0i7HlJeXY7FYGDJkCOHh4UyaNMl7XFxcHEOHDr3mex86\ndIjBgwcTFxfnvwCh4J/Ra7JMtRDC34JedJxOJ0ajEYCBAwfidDq7HONwODCbzd5ts9mMw+G44fs2\nNzfz+eefk56e7tsGh6LIyPZ/B8QEtx1CiJAXkHs6OTk51NfXd9n/xBNPdNpWFKV3K19ew549e5g+\nfTqRHb9Qb+DAgQMcOHAAgLy8PGJjY3v9ueHh4X06P1garUvQj00k4qq2azXP9YRaHgi9TKGWB0Iv\nU1/yBKTovPnmm9d9zWAwUFdXh9FopK6ujpiYrn9tm0wmamtrvdu1tbWYTKYbfmZ5eTk///wzu3bt\norGxEUVR0Ov1PPTQQ12OTUtLIy0tzbttt9u7E+uaYmNj+3R+0PzfNFwAV7Vds3muI9TyQOhlCrU8\nEHqZrpXnerc5rhb00WuJiYmUlJQwY8YMSkpKSEpK6nJMfHw8Fy9exGazYTKZOHjwIJmZmTd833fe\necf79Z49e4iMjLxmwRFCCBE4Qb+nM2PGDI4dO0ZmZibHjx/3DoV2OBzk5uYCEBYWxvz581m9ejVZ\nWVkkJyczfPhwoH2wwMsvv8zvv/9OXl4eq1evDloWIYQQN6aoqqoGuxE3m6qqql6f+79wGa1loZYH\nQi9TqOWB0MvUl+61oF/pCCGE+N8hRUcIIUTASNERQggRMFJ0hBBCBIwUHSGEEAEjo9eEEEIEjFzp\n+Fh2dnawm+BTkufmF2qZQi0PhF6mvuSRoiOEECJgpOgIIYQImLC333777WA3ItSMHDky2E3wKclz\n8wu1TKGWB0IvU2/zyEACIYQQASPda0IIIQIm6EsbhIqjR4+ybds2PB4Pqamp3tmytWTjxo0cPnwY\ng8FAfn4+AA0NDRQUFFBTU8OgQYPIysoiOjo6yC3tHrvdTmFhIfX19SiKQlpaGo888ohmM7W0tPDW\nW2/R1taG2+1m4sSJzJ07V7N5/s3j8ZCdnY3JZCI7O1vTmTIyMoiMjESn0xEWFkZeXp6m8wA0NjZS\nVFTEhQsXUBSFV155haFDh/Yukyr6zO12q4sXL1arq6vV1tZWddmyZeqFCxeC3aweO3HihHr27Fl1\n6dKl3n07d+5U9+3bp6qqqu7bt0/duXNnsJrXYw6HQz179qyqqqra1NSkZmZmqhcuXNBsJo/Ho7pc\nLlVVVbW1tVVduXKlevr0ac3m+bf9+/er69atU3Nzc1VV1fbP3aJFi1Sn09lpn5bzqKqqbtiwQT1w\n4ICqqu0/ew0NDb3OJN1rPlBeXo7FYmHIkCGEh4czadIkSktLg92sHrvzzju7/KVSWlpKSkoKACkp\nKZrKZTQavTc7+/Xrx7Bhw3A4HJrNpCiKd/l1t9uN2+1GURTN5ulQW1vL4cOHSU1N9e7TeqaraTlP\nU1MTp06d4v777wfal6qOiorqdSbpXvMBh8OB2Wz2bpvNZs6cORPEFvmO0+nEaDQCMHDgQJxOZ5Bb\n1Ds2m41z585x2223aTqTx+NhxYoVVFdX8+CDD5KQkKDpPADbt2/n6aefxuVyefdpPVNOTg46nY5p\n06aRlpam6Tw2m42YmBg2btxIRUUFI0eOxGq19jqTFB3RbYqioChKsJvRY83NzeTn52O1Wunfv3+n\n17SWSafTsWbNGhobG1m7di1//PFHp9e1lufXX3/FYDAwcuRITpw4cc1jtJYpJycHk8mE0+nk3Xff\n7bK4mdbyuN1uzp07x/z580lISGDbtm0UFxd3OqYnmaTo+IDJZKK2tta7XVtbi8lkCmKLfMdgMFBX\nV4fRaKSuro6YmJhgN6lH2trayM/PZ8qUKdxzzz2A9jMBREVFcdddd3H06FFN5zl9+jS//PILR44c\noaWlBZfLxfr16zWdqeP/vsFgICkpifLyck3nMZvNmM1mEhISAJg4cSLFxcW9ziT3dHwgPj6eixcv\nYrPZaGtr4+DBgyQmJga7WT6RmJhISUkJACUlJSQlJQW5Rd2nqipFRUUMGzaMRx991Ltfq5kuXbpE\nY2Mj0D6S7dixYwwbNkyzeQDmzZtHUVERhYWFvPbaa4wePZrMzEzNZmpubvZ2EzY3N3Ps2DFGjBih\n2TzQ3nVmNpupqqoC4Pjx48TFxfU6kzwc6iOHDx9mx44deDwepk6dyqxZs4LdpB5bt24dJ0+e5PLl\nyxgMBubOnUtSUhIFBQXY7XbNDfUsKytj1apVjBgxwnvp/+STT5KQkKDJTBUVFRQWFuLxeFBVleTk\nZObMmcPly5c1medqJ06cYP/+/WRnZ2s2019//cXatWuB9m6pyZMnM2vWLM3m6XD+/HmKiopoa2tj\n8ODBLFq0CFVVe5VJio4QQoiAke41IYQQASNFRwghRMBI0RFCCBEwUnSEEEIEjBQdIYQQASNFR4g+\nWLp06XWfpPc3u93OM888g8fjCcrnC9EbMmRaCB/Ys2cP1dXVZGZm+u0zMjIyWLhwIWPHjvXbZwjh\nb3KlI8RNwO12B7sJQgSEXOkI0QcZGRnMnz/f+xR6eHg4FouFNWvW0NTUxI4dOzhy5AiKojB16lTm\nzp2LTqfju+++45tvviE+Pp7vv/+eBx54gPvuu49NmzZRUVGBoiiMGzeOBQsWEBUVxYYNG/jhhx8I\nDw9Hp9MxZ84ckpOTWbx4Mbt37yYsLAyHw8HmzZspKysjOjqaxx9/nLS0NKD9SqyyshK9Xs+hQ4eI\njY0lIyOD+Ph4AIqLi/nyyy9xuVwYjUZeeOEFxowZE7TvqwhdMuGnEH0UERHBzJkzu3SvFRYWYjAY\nWL9+PX///Td5eXmYzWamTZsGwJkzZ5g0aRKbN2/G7XbjcDiYOXMmo0aNwuVykZ+fz969e7FarSxZ\nsoSysrJO3Ws2m61TOz744AOGDx/Opk2bqKqqIicnB4vFwujRo4H2GZ1ff/11Fi1axCeffMLWrVtZ\nvXo1VVVVfP311+Tm5mIymbDZbHKfSPiNdK8J4Qf19fUcOXIEq9VKZGQkBoOB6dOnc/DgQe8xRqOR\nhx9+mLCwMPR6PRaLhbFjxxIREUFMTAzTp0/n5MmT3fo8u91OWVkZTz31FHq9nltvvZXU1FTvhIwA\nd9xxB+PHj0en03Hvvfdy/vx5oH25hNbWViorK71za1ksFp9+P4ToIFc6QviB3W7H7Xbz0ksvefep\nqtppsb/Y2NhO59TX17N9+3ZOnTpFc3MzHo+n25NC1tXVER0dTb9+/Tq9/9mzZ73bBoPB+7Ver6e1\ntRW3243FYsFqtbJ3714qKysZN24czz77bMgszyFuLlJ0hPCBqxewMpvNhIeHs2XLFsLCwrr1Hrt3\n7wYgPz+f6OhoDh06xNatW7t1rtFopKGhAZfL5S08dru924Vj8uTJTJ48maamJj788EN27drFkiVL\nunWuED0h3WtC+IDBYKCmpsZ7L8RoNDJu3Dg++ugjmpqa8Hg8VFdX37C7zOVyERkZSf/+/XE4HOzf\nv7/T6wMHDuxyH6dDbGwst99+Ox9//DEtLS1UVFTw7bffMmXKlP/a9qqqKn777TdaW1vR6/Xo9XpN\nrWwptEWKjhA+kJycDMCCBQtYsWIFAIsXL6atrY2lS5fy/PPP8/7771NXV3fd90hPT+fcuXM899xz\n5ObmMmHChE6vz5gxg88++wyr1coXX3zR5fxXX32VmpoaFi5cyNq1a0lPT+/WMz2tra3s2rWLBQsW\n8OKLL3Lp0iXmzZvXk/hCdJsMmRZCCBEwcqUjhBAiYKToCCGECBgpOkIIIQJGio4QQoiAkaIjhBAi\nYKToCCGECBgpOkIIIQJGio4QQoiAkaIjhBAiYP4feH+nhbT+jEsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efe107d9f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pieLiYjIyMkhPT6d169aVvo8Q1UmfPQP7dqKu7SUztYVHc+rJ4rbbbnOMRoqJ\niaFDhw4UFRXRpEkTp24yf/58UlNTyc/PZ+LEiQwfPpyhQ4cyb9481q5d6xg6C9C0aVOio6OZNm0a\nhmEwbtw4GQklXJbemQw2m/RXCI9XYbEwTZNRo0bxzjvv4PPrPsGX2+Y1ZcqUco8/+eST5R4fNmwY\nw4YNu6x7CGEFvX0LBIVC8zZWhyJEtarwV3bDMIiKiiI/P78m4hHCbejz52BXCuranih5+hUezqlm\nqD59+vD8889zyy23EBYWVqpttmPHjtUWnBAuLfUHOH9OmqBEreBUsfjqq68A+OCDD0odV0rx6quv\nVn1UQrgBvX0L1K0HbeUXJuH5nCoWFy7TIYQAbbOhd2xFdeqO8vaxOhwhqp3TDa0lJSXs2bOHpKQk\nAIqKiigqKqq2wIRwaft3wZl81LXRFZ8rhAdw6sni6NGjPP/88/j4+JCVlUXv3r1JTU1lw4YNjiGv\nQng6XVIMO7dhbl4LO76Huv7Q4VqrwxKiRjhVLBYvXsxf//pXbrjhBsaOHQvYFwd87bXXqjU4IVyB\nPnUS/fXH6OSNcCYfAoNR/YegbhiE8qtrdXhC1AinisXx48fp27dvqWN+fn6ylaqoFcwFz8AvJ1Bd\neqJ694f216K8vKwOS4ga5VSxiIiI4ODBg7Rq1cpxLC0tjcjIyGoLTAhXoE8chZ+PoO6ZgHHjEKvD\nEcIyThWLv/71r8TFxTFw4EBKSkpYuXIlX3/9NRMmTKju+ISwlE6xD+iQuRSitnNqNFS3bt144okn\nOH36NO3bt+fUqVM89thjdO7cubrjE8JSettmaH01Kjis4pOF8GBOPVmcPn2aFi1a8MADD1R3PEK4\nDJ1xAo4fQg0fZ3UoQljOqWIxadIkOnToQJ8+fejRowd+fn7VHZcQltPbNgOguspcCiGcaoZauHAh\nXbt25auvvmL8+PHMnz+f77//HpvNVt3xCWEZnZIEzdugwhpYHYoQlnOqWAQGBjJo0CBmzZpFfHw8\nzZs35/3332f8+PHVHZ8QltBZGXD4J1TX3laHIoRLuOx1lfPy8sjNzSU/P5969epVR0xCWE6n/NoE\n1U2aoISAy5iUt2nTJr799lvOnz9PdHQ006dPl+1OhcfSKUnQpAWqgXP7Ewvh6ZwqFv/85z/p2bMn\n48ePp0OHDrLNqfBoOjcL0vagbr/H6lCEcBlOrw3l7e3UqUK4Pb19C4D0VwhxAacqgLe3N7m5uaSl\npZGfn4/laGTyAAAXW0lEQVTW2vFa//79qy04IaygtyVBo6aoqGZWhyKEy3CqWGzdupVXXnmFRo0a\ncezYMZo2bcqxY8do166dFAvhUXR+HuzfjRp8p9WhCOFSnCoWy5cvZ9KkSURHRzN27FheeOEF1q1b\nx7Fjx67o5idOnGDevHmOjzMyMhg+fDhnz55lzZo1BAYGAjBixAi6du16RfcSwhl6+xbQpjRBCfEH\nThWLzMxMoqNLDyGMiYlh/PjxjB49utI3j4qKYs6cOQCYpsmECRO47rrrWLduHUOGDOG2226r9HsL\nURl6WxJERELTFlaHIoRLcapYBAYGkpubS3BwMBEREezfv5/69etjmmaVBbJz504iIyOJiIiosvcU\nwhnaZoMfvsNc+8mvTVB3oZSyOiwhXIpTxWLAgAHs3buXXr16MWTIEGbOnIlSiltvvbXKAvn222+5\n/vrrHR+vXr2ajRs30rJlS0aPHk1AQECV3UsIAJ1/Gr3pK/T6zyE7E8IaoO4ai5J9K4QoQ+kLhzY5\nKTMzk6KiIpo0aVIlQZSUlDBhwgTi4+MJDg4mNzfX0V+xfPlycnJymDRpUpnrEhMTSUxMBCAuLu6K\ndu7z9vampKSk0te7GsnndyVHD3L2o6WY+afRZ05jnj2DLjiDeToXbDZ8r+lG3SF3Uaf79TW6A558\njVyfp+VUXj6+vr7OXVuZG4aHh1fmsovavn07LVq0IDg4GMDxN9ifap5//vlyr4uNjSU2NtbxcWZm\nZqVjCA8Pv6LrXY3kY6e1xox/Cn45AZGNoV4AKrIJ+NdD1Q9GXdcXW+OrOAOcycmp+sAvQb5Grs/T\nciovn6go51YpcImZdn9sgsrJySEkJASwD9tt2rSpVaEJd5eyGY4eQI2dgtFbhnkLUVmWF4uioiJ2\n7NhRagXb//znPxw+fBilFBEREbK6ragUbdowP37XPsGuV4zV4Qjh1iwvFn5+frz11luljj388MMW\nRSM8id6yAdKPYUx8HGXUXF+EEJ5IVgQUHkmXFKM/WQbNWsK1ssy4EFdKioXwSHpTImT+gjF0JEpW\nSRbiisn/IuFx9Plz6M+WQ+uroWM3q8MRwiNIsRBuS+efRpcUlz2+/gvIzcYYOkpmYgtRRSzv4Bai\nMvRPqZjznwQvb1THbtD5OtQ13cFQ6C8+hPZdUH/qaHWYQngMKRbC7ejjhzBfmQUhEai2HdA/fAfJ\n36C9vCGiIZw5jTF0pNVhCuFRpFgIl6L37UJvXI368932mdZ/fP3UScz5M6GOH8bUmaiwBuiRf4OD\n+9E/fIf+cSvq+lhUi7YWRC+E55JiIVyKufpD2JWCTtmMGjIcdfMwlLcPAPp0Dub8p6D4PMY/4lBh\nDQDscyhaX41qfTXcOcbC6IXwXFIshMvQZ8/Anh9R18fCuSL0x++iv9+EMWoyZt0umC/NhNwsjGmz\nUY1ly1MhapIUC+Ey9I/fgc2GirkF1aINulc/zHcXYT7/ONkNGtnnTUz+X1SrdlaHKkStI8VCuAy9\nLQlCI6B5awBU5+sw2nZEr1yKbdPXqDGPoK6ReRNCWEHmWQiXoAsLIHU7qmvvUnMjVF1/jHsm0GBZ\nIkavGy2MUIjaTYqFcAl6RzKUlKC69S73deUlD8FCWEmKhXAJetu3EBwKLf9kdShCiHJIsRBVSp88\nju3//o65/gu0aTp3TVEh7EqxN0HJon9CuCT5nymqlP7kfTh2CP3uvzDnPYk+dbLia3Zug+LzqK7l\nN0EJIawnxUJUGX3yZ3TyJtSgO1CjJsPhnzBnPoK57rNLP2Vs+xbqB0Gbq2suWCHEZZFeQ1Fl9OoP\nwdsbddNQVGAIukNXzCWvot97Df39txj3T3HMunZcc+4cetc2VK9+spudEC5MnixEldBZGegt61F9\nb0IFhgCgwiIwpjyNuu9hOHYQ87np6KMHS1+4OwXOFaG6XW9B1EIIZ0mx8EC6uBhdUlKz91z9EaBQ\ng+4odVwphdFnIMbjL4DhhTnnf9B7fvz9um1JEFAf2spy4kK4MikWHsh8dTZZ0+5DFxXUyP10bhZ6\n09eo3v1RoRHlnqMaN8OY8QKENcB8aSbmdxvQxefRO7aiuvRCeUkTlBCuTIqFh9FHDkDqdmzHDqGX\nLEBrXf33/CoBTBvqljsveZ4KDcf4x3PQqh36jXjMN+KhqPCiE/GEEK7D8g7uyZMn4+fnh2EYeHl5\nERcXx5kzZ5g3bx6nTp0iIiKCqVOnEhAQYHWobkGvWQV16uJ/610U/HcJtGmPunHIxc8vPo/y8a38\n/fJPozesRl13AyoissLzlX8AxpSn0W/Os0/E868H7TpV+v5CiJphebEAeOqppwgMDHR8nJCQwDXX\nXMPQoUNJSEggISGBkSNl57OK6NM56ORvUH0HEXDPeAp+2oNe/ia6eZsymwHp4mL0f99Br/kEmrSw\nNyH1vMHROV3qXNOEjHQwFEQ0KrV2k05cZZ8jUcFTxYWUjy+Mnw5ftID6gY79KoQQrsslisUfJScn\n8/TTTwMQExPD008/LcXCCXr9avv6Sv1vRRkGxv1TMGdNxXztBYx/zkPVq28/7+TPmIvnwNGDqJ4x\n6F9OoFe8if7wbejQFRV9I5gmHEmzN2sdOwiFv/Z/BARCq3aoVu1QzVqh130KXaNRUZe3v4QyDNSQ\n4VX9KRBCVBOXKBazZs3CMAwGDhxIbGwseXl5hITYf8MNDg4mLy+v3OsSExNJTEwEIC4ujvDw8ErH\n4O3tfUXXW00Xnyfzmy/x6RZNSMfOeHt7E3FVC4off5bsJ/6G99IFBD/xAkUbviT/9bkoH1+CnniB\nOj36AFBy7BCF61dTtGE15utz7G/q44t389b4xAzCp1U7tGmjeN8uivfuwvbjVn7rDQm9dzw+1fy5\nc/evT3k8LSdPywc8L6crycfyYjFr1ixCQ0PJy8tj9uzZREVFlXpdKVWq2eNCsbGxxMbGOj7OzMys\ndBzh4eFXdL3VzM3r0LnZlPQZRGZm5u/5hDRADb+f8++9RsbU0XD0ILTtgDHuUfJDw8n/Lee69eGW\nu2DQMIwD+8CvLjRqivb25jxw/rcbdbUXFyP/NBzcB9pGXv1QqObPnbt/fcrjaTl5Wj7geTmVl88f\nf+ZejOXFIjQ0FICgoCB69OhBWloaQUFB5OTkEBISQk5OTqn+DFGW1tre9xDZBDpcW+Z11W8wpO2x\nL8Vx2z2oIXdddLa0MrygTfsK76nqB0LnHlccuxDCPVg6dLaoqIjCwkLHv3fs2EGzZs3o3r07GzZs\nAGDDhg306CE/lC7pwB44koYacGu5T2FKKdS4qRhxb2D8+W5ZVkMIcdksfbLIy8tj7ty5ANhsNvr0\n6UOXLl1o1aoV8+bNY+3atY6hs+LidOIn4F8PFd3/oucowwtCPaftVQhRsywtFg0bNmTOnDlljtev\nX58nn3zSgojcj84+hd6+GRV7O6qOn9XhCCE8lMzgdnN63eegQfW/+MQ7IYS4UpZ3cNcm+ucjcPaM\nfaTRhX98fC864stxrdaQnwvHD6OPHYKjh9DHDsLJn+HanmWW/hZCiKokxaIG6J+PYK5cCj9uLf8E\nb28ICIL6gVA/CBUQBL6+6Pw8yMuB0zmQlwu2C1aSDQ2Hpi1R3Xqj+t9aM4kIIWotKRbVSGf+gl71\nHnrLevCrixo60r7sRlGhfd/pc4VQVGh/2jiTh84/Dfl59q1Iz5+D+sEQFIxq1BSCQiAoBNX4Kmja\nAhUgw4mFEDVHikU10OeK0CuXojd8Acqw7xx3819K/YC/dKOTEEK4FikWVUxnZWC++gz8fATVJxZ1\n690oGbIqhHBzUiyqkP4pFfNfz0FJCcYj/0R17GZ1SEIIUSWkWFQR85uv0O8ugrAGGA//LyqyidUh\nCSFElZFicYV0SQn6g7fQaz+F9tdijJ+OqicbNQkhPIsUi4vQxcXg5YUyyp+3qE/noDd+hd6wGnKz\n7DOo7xwje0kLITySFIty6Ix0zLh/QPF5+HWXOdWiLbRoC1kZ6LWf2bcEtZVA+y4Yox9CXSP9E0II\nzyXF4g90wVnMV2eDaaJ69UMf+gn91Uq0zfb7SXX9Uf1uQfUbjIpsbF2wQghRQ6RYXEDbbJivvQAZ\nJzCm/h/qT9fYj58/B8cOoQ/tgzp1UT36ovzqWhytEELUHCkWF9Ar3oTU7ajRDzkKBYDyrePYd1oI\nIWojWXX2VwWrP0Kv/RQ18HaMvjdZHY4QQrgUKRaATt1O/uJ50KkH6s4xVocjhBAup9YXC51+HHPR\nC3g3bY7x4KOy5agQQpSj1hcLfOtAizYEP/ECys/f6miEEMIl1fpiocIi8Jr6f3g1aGR1KEII4bJq\nfbEQQghRMSkWQgghKmTpPIvMzEwWLFhAbm4uSiliY2MZPHgwK1asYM2aNQQG2jcLGjFiBF27drUy\nVCGEqNUsLRZeXl6MGjWKli1bUlhYyIwZM+jUqRMAQ4YM4bbbbrMyPCGEEL+ytFiEhIQQEhICQN26\ndWncuDHZ2dlWhiSEEKIcLrPcR0ZGBocOHaJ169bs3buX1atXs3HjRlq2bMno0aMJCCi7R0RiYiKJ\niYkAxMXFER5e+e1Lvb29r+h6VyP5uD5Py8nT8gHPy+lK8lFaa13F8Vy2oqIinnrqKYYNG0bPnj3J\nzc119FcsX76cnJwcJk2aVOH7nDhxotIxhIeHk5mZWenrXY3k4/o8LSdPywc8L6fy8omKinLqWstH\nQ5WUlBAfH0/fvn3p2bMnAMHBwRiGgWEYDBgwgAMHDlgcpRBC1G6WPllorVmwYAEBAQGMGTPGcTwn\nJ8fRl/Hpp5+SlpbGlClTLIpSCCGEpU8W+/btY+PGjezatYvp06czffp0UlJS+M9//sOjjz7KY489\nxu7du7nvvvuqPZYZM2ZU+z1qkuTj+jwtJ0/LBzwvpyvJx9IO7nbt2rFixYoyx2VOhRBCuBbL+yyE\nEEK4Pq+nn376aauDcBUtW7a0OoQqJfm4Pk/LydPyAc/LqbL5uMTQWSGEEK5NmqGEEEJUyGVmcFvl\nhx9+4O2338Y0TQYMGMDQoUOtDumyLVy4kJSUFIKCgoiPjwfgzJkzzJs3j1OnThEREcHUqVPLnQXv\nii62wKS75nT+/HmeeuopSkpKsNls9OrVi+HDh7ttPhcyTZMZM2YQGhrKjBkz3DqnyZMn4+fnh2EY\neHl5ERcX59b5AJw9e5ZFixZx7NgxlFL87W9/IyoqqnI56VrMZrPphx56SJ88eVIXFxfrxx57TB87\ndszqsC7b7t279YEDB/S0adMcx5YuXapXrlyptdZ65cqVeunSpVaFd9mys7P1gQMHtNZaFxQU6Ece\neUQfO3bMbXMyTVMXFhZqrbUuLi7W//M//6P37dvntvlc6JNPPtHz58/Xzz33nNbavb/vJk2apPPy\n8kodc+d8tNb6lVde0YmJiVpr+/femTNnKp1TrW6GSktLIzIykoYNG+Lt7U3v3r1JTk62OqzL1r59\n+zK/GSQnJxMTEwNATEyMW+UVEhLi6IS7cIFJd81JKYWfnx8ANpsNm82GUspt8/lNVlYWKSkpDBgw\nwHHM3XP6I3fOp6CggD179tC/f3/Avi5UvXr1Kp1TrW6Gys7OJiwszPFxWFgYP/30k4URVZ28vDzH\nLPjg4GDy8vIsjqhyLlxg0p1zMk2Txx9/nJMnTzJo0CDatGnj1vkAvPPOO4wcOZLCwkLHMXfPadas\nWRiGwcCBA4mNjXXrfDIyMggMDGThwoUcOXKEli1bMmbMmErnVKuLRW2hlEIpZXUYl62oqIj4+HjG\njBmDv79/qdfcLSfDMJgzZw5nz55l7ty5HD16tNTr7pbPtm3bCAoKomXLluzevbvcc9wtp1mzZhEa\nGkpeXh6zZ88us8Ceu+Vjs9k4dOgQ999/P23atOHtt98mISGh1DmXk1OtLhahoaFkZWU5Ps7KyiI0\nNNTCiKpOUFCQY42tnJwcxyq+7qK8BSbdPSeAevXq0aFDB3744Qe3zmffvn18//33bN++nfPnz1NY\nWMjLL7/s1jn99n8/KCiIHj16kJaW5tb5hIWFERYWRps2bQDo1asXCQkJlc6pVvdZtGrVivT0dDIy\nMigpKSEpKYnu3btbHVaV6N69Oxs2bABgw4YN9OjRw+KInKe1ZtGiRTRu3Jhbb73Vcdxdczp9+jRn\nz54F7COjduzYQePGjd02H4B77rmHRYsWsWDBAqZMmULHjh155JFH3DanoqIiR3NaUVERO3bsoFmz\nZm6bD9ibmMLCwhxbN+zcuZMmTZpUOqdaPykvJSWFf//735imyY033siwYcOsDumyzZ8/n9TUVPLz\n8wkKCmL48OH06NGDefPmkZmZ6XZD/vbu3cuTTz5Js2bNHI/II0aMoE2bNm6Z05EjR1iwYAGmaaK1\nJjo6mjvvvJP8/Hy3zOePdu/ezSeffMKMGTPcNqdffvmFuXPnAvbmmz59+jBs2DC3zec3hw8fZtGi\nRZSUlNCgQQMmTZqE1rpSOdX6YiGEEKJitboZSgghhHOkWAghhKiQFAshhBAVkmIhhBCiQlIshBBC\nVEiKhaiVpk2bdtGZx9UtMzOTUaNGYZqmJfcXojJk6Kyo1VasWMHJkyd55JFHqu0ekydPZsKECXTq\n1Kna7iFEdZMnCyGugM1mszoEIWqEPFmIWmny5Mncf//9jlm73t7eREZGMmfOHAoKCvj3v//N9u3b\nUUpx4403Mnz4cAzDYP369axZs4ZWrVqxceNGbrrpJvr168drr73GkSNHUErRuXNnxo0bR7169Xjl\nlVfYtGkT3t7eGIbBnXfeSXR0NA899BDLli3Dy8uL7OxsFi9ezN69ewkICOD2228nNjYWsD/5HD9+\nHF9fX7Zu3Up4eDiTJ0+mVatWACQkJPDFF19QWFhISEgIDzzwANdcc41ln1fhuWr1QoKidvPx8eGO\nO+4o0wy1YMECgoKCePnllzl37hxxcXGEhYUxcOBAAH766Sd69+7N4sWLsdlsZGdnc8cdd3D11VdT\nWFhIfHw8H3zwAWPGjOHhhx9m7969pZqhMjIySsXx0ksv0bRpU1577TVOnDjBrFmziIyMpGPHjoB9\nhddHH32USZMm8f777/PWW2/xzDPPcOLECb788kuee+45QkNDycjIkH4QUW2kGUqIC+Tm5rJ9+3bG\njBmDn58fQUFBDBkyhKSkJMc5ISEh3HLLLXh5eeHr60tkZCSdOnXCx8eHwMBAhgwZQmpqqlP3y8zM\nZO/evdx77734+vrSvHlzBgwY4FjoDaBdu3Z07doVwzC44YYbOHz4MGBf9ry4uJjjx4871v6JjIys\n0s+HEL+RJwshLpCZmYnNZmP8+PGOY1rrUptkhYeHl7omNzeXd955hz179lBUVIRpmk4vNpeTk0NA\nQAB169Yt9f4HDhxwfBwUFOT4t6+vL8XFxdhsNiIjIxkzZgwffPABx48fp3PnzowePdpjltkXrkWK\nhajV/rjxS1hYGN7e3rz55pt4eXk59R7Lli0DID4+noCAALZu3cpbb73l1LUhISGcOXOGwsJCR8HI\nzMx0+gd+nz596NOnDwUFBbz++uu8++67PPzww05dK8TlkGYoUasFBQVx6tQpR1t/SEgInTt3ZsmS\nJRQUFGCaJidPnrxks1JhYSF+fn74+/uTnZ3NJ598Uur14ODgMv0UvwkPD+dPf/oT7733HufPn+fI\nkSOsW7eOvn37Vhj7iRMn2LVrF8XFxfj6+uLr6+tWO7kJ9yLFQtRq0dHRAIwbN47HH38cgIceeoiS\nkhKmTZvG2LFjefHFF8nJybnoe9x1110cOnSI++67j+eee47rrruu1OtDhw7lv//9L2PGjGHVqlVl\nrv/73//OqVOnmDBhAnPnzuWuu+5yak5GcXEx7777LuPGjePBBx/k9OnT3HPPPZeTvhBOk6GzQggh\nKiRPFkIIISokxUIIIUSFpFgIIYSokBQLIYQQFZJiIYQQokJSLIQQQlRIioUQQogKSbEQQghRISkW\nQgghKvT/AZBtQwkb2T0hAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efe3729d208>"
      ]
     },
     "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": {},
   "source": [
    "# Problem 5: Actor-Critic algorithm (with bootstrapping)\n",
    "\n",
    "The baseline reduction lowers the variance without the cost of introducing bias. Are there any others that can reduce the variance of the policy?\n",
    "\n",
    "In this part, you will implement a simple actor-critic algorithm. Try to overwrite the `process_paths` in `PolicyOptimizer_actor_critic`. Note that the `PolicyOptimizer_actor_critic` inherit the class `PolicyOptimizer`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "We use the one-step bootstrap for the advantage function, which change the $A_t^i=(R_t^i-V_t^i)$ in problem 3 into:\n",
    "\n",
    "$$A_t^i = r_t^i + \\gamma*V_{t+1}^i - V_t^i$$\n",
    "\n",
    "Open **policy_gradient/util.py ** to implement the function `discount_bootstrap`\n",
    "\n",
    "If you answer is right, your will solve CartPole with roughly ~ 80 iterations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 6: Generalized Advantage Estimation\n",
    "\n",
    "In Problem 3, we calculate the advantage function with **the total return substract the baseline** \n",
    "\n",
    "In Problem 5, we calculate the advantage function based on Problem 3, and **replace the total return with the immediate reward plus estimated baseline**\n",
    "\n",
    "Here, we use a novel advantage function called \"Generalized Advantage Estimation\", which introduces one hyperparameter $\\lambda$ to compromise the above two estimation methods.\n",
    "\n",
    "Assume the $\\delta_t^i$ represent the i-step bootstrapping (e.g. $\\delta_t^i=r_t^i + \\gamma*V_{t+1}^i - V_t^i$). The generalized advantage estimation will be:\n",
    "\n",
    "$$A_{t}^{GAE} = \\sum_{l=0}^{\\infty} (\\gamma\\lambda)^l \\delta_{t+1}$$\n",
    "\n",
    "Please see [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://arxiv.org/abs/1506.02438) for details.\n",
    "\n",
    "\n",
    "If you answer is right, your will solve CartPole with roughly ~ 80 iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "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",
    "            \"\"\"\n",
    "            Problem 6 (Skip this when doing Problem 5): \n",
    "            \n",
    "            1. in Problem 3, we calculate the advantage function with the total \n",
    "                       return substract the baseline \n",
    "               in Problem 5, we calculate the advantage function based on Problem 3. \n",
    "                       And replace the total return with the immediate reward plus estimated baseline\n",
    "            2. Here, we use a novel advantage function called \"Generalized Advantage Estimation\", \n",
    "                       which introduces one hyperparameter to balance the above two estimation methods.\n",
    "            Currently, the variable `LAMBDA` is the default hyperparameter for GAE. \n",
    "                        (You're encouraged to try other \\lambda=[0,1])\n",
    "            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",
    "            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": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1: Average Return = 33.84\n",
      "Iteration 2: Average Return = 33.11\n",
      "Iteration 3: Average Return = 35.03\n",
      "Iteration 4: Average Return = 32.34\n",
      "Iteration 5: Average Return = 35.16\n",
      "Iteration 6: Average Return = 34.93\n",
      "Iteration 7: Average Return = 38.91\n",
      "Iteration 8: Average Return = 42.21\n",
      "Iteration 9: Average Return = 45.39\n",
      "Iteration 10: Average Return = 48.1\n",
      "Iteration 11: Average Return = 48.3\n",
      "Iteration 12: Average Return = 45.51\n",
      "Iteration 13: Average Return = 46.66\n",
      "Iteration 14: Average Return = 47.17\n",
      "Iteration 15: Average Return = 49.21\n",
      "Iteration 16: Average Return = 55.6\n",
      "Iteration 17: Average Return = 55.31\n",
      "Iteration 18: Average Return = 52.71\n",
      "Iteration 19: Average Return = 56.32\n",
      "Iteration 20: Average Return = 53.8\n",
      "Iteration 21: Average Return = 59.44\n",
      "Iteration 22: Average Return = 69.45\n",
      "Iteration 23: Average Return = 69.4\n",
      "Iteration 24: Average Return = 64.78\n",
      "Iteration 25: Average Return = 73.06\n",
      "Iteration 26: Average Return = 75.37\n",
      "Iteration 27: Average Return = 76.08\n",
      "Iteration 28: Average Return = 77.29\n",
      "Iteration 29: Average Return = 89.76\n",
      "Iteration 30: Average Return = 102.25\n",
      "Iteration 31: Average Return = 109.21\n",
      "Iteration 32: Average Return = 116.09\n",
      "Iteration 33: Average Return = 113.61\n",
      "Iteration 34: Average Return = 119.45\n",
      "Iteration 35: Average Return = 131.53\n",
      "Iteration 36: Average Return = 141.05\n",
      "Iteration 37: Average Return = 137.32\n",
      "Iteration 38: Average Return = 137.71\n",
      "Iteration 39: Average Return = 141.81\n",
      "Iteration 40: Average Return = 147.04\n",
      "Iteration 41: Average Return = 141.29\n",
      "Iteration 42: Average Return = 144.4\n",
      "Iteration 43: Average Return = 151.2\n",
      "Iteration 44: Average Return = 159.15\n",
      "Iteration 45: Average Return = 160.67\n",
      "Iteration 46: Average Return = 171.2\n",
      "Iteration 47: Average Return = 173.46\n",
      "Iteration 48: Average Return = 172.61\n",
      "Iteration 49: Average Return = 175.46\n",
      "Iteration 50: Average Return = 175.79\n",
      "Iteration 51: Average Return = 178.24\n",
      "Iteration 52: Average Return = 180.15\n",
      "Iteration 53: Average Return = 182.54\n",
      "Iteration 54: Average Return = 185.4\n",
      "Iteration 55: Average Return = 183.67\n",
      "Iteration 56: Average Return = 181.63\n",
      "Iteration 57: Average Return = 187.26\n",
      "Iteration 58: Average Return = 187.13\n",
      "Iteration 59: Average Return = 187.77\n",
      "Iteration 60: Average Return = 184.64\n",
      "Iteration 61: Average Return = 185.67\n",
      "Iteration 62: Average Return = 183.85\n",
      "Iteration 63: Average Return = 181.55\n",
      "Iteration 64: Average Return = 183.12\n",
      "Iteration 65: Average Return = 181.58\n",
      "Iteration 66: Average Return = 182.7\n",
      "Iteration 67: Average Return = 181.76\n",
      "Iteration 68: Average Return = 180.24\n",
      "Iteration 69: Average Return = 178.67\n",
      "Iteration 70: Average Return = 186.68\n",
      "Iteration 71: Average Return = 184.21\n",
      "Iteration 72: Average Return = 184.12\n",
      "Iteration 73: Average Return = 183.47\n",
      "Iteration 74: Average Return = 187.55\n",
      "Iteration 75: Average Return = 186.6\n",
      "Iteration 76: Average Return = 187.03\n",
      "Iteration 77: Average Return = 187.28\n",
      "Iteration 78: Average Return = 188.16\n",
      "Iteration 79: Average Return = 190.24\n",
      "Iteration 80: Average Return = 187.83\n",
      "Iteration 81: Average Return = 187.88\n",
      "Iteration 82: Average Return = 184.74\n",
      "Iteration 83: Average Return = 186.59\n",
      "Iteration 84: Average Return = 185.23\n",
      "Iteration 85: Average Return = 186.89\n",
      "Iteration 86: Average Return = 191.24\n",
      "Iteration 87: Average Return = 190.06\n",
      "Iteration 88: Average Return = 188.38\n",
      "Iteration 89: Average Return = 190.98\n",
      "Iteration 90: Average Return = 191.4\n",
      "Iteration 91: Average Return = 193.72\n",
      "Iteration 92: Average Return = 195.02\n",
      "Solve at 92 iterations, which equals 9200 episodes.\n"
     ]
    }
   ],
   "source": [
    "#from policy_gradient import util\n",
    "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": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
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LuuYrAKhv/QAmXYr+5EOYeAmWX/4WNWyUxz3q4jQ4ddxrfsY93zJ+itfnqMgoLHf/EsIs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\nCNEJM2bMAOD222/ngQceAOCee+7B6XTys5/9jB/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efdd868afd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+x6VuKNM0ad26da1tZWVlJ2wTotFsWQ9HCzAuvNi5SfXqh99jCzwYlBC+y6WW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\nnf4f8f4yPAK/wlsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efe10779e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "util.plot_curve(loss_list, \"loss\")\n",
    "util.plot_curve(avg_return_list, \"average return\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}