a2c_discrete_monte-carlo.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Synchronous Advantage Actor-Critic (A2C) Monte-Carlo\n",
    "\n",
    "This is the A2C algorithm with a discrete action space (only works on environments with discrete actions) and Monte-Carlo parameter updates. Synchronous Advantage Actor-Critic (A2C) is an actor-critic method which runs multiple environments in parallel. A2C is a synchronous version of the asynchronous algorithm A3C. The updates will be performed in a Monte-Carlo way (parameter updates will only be performed at the end of the episode). This implementation is closer to a pure policy gradient approach than actor-critic, since bootstrapping is only used in the odd case that the environment doesn't enter a terminal state before the steps limit. \n",
    "\n",
    "The advantage function, $A^{\\pi}$, following policy $\\pi$ is defined by:\n",
    "$$A^{\\pi} = Q^{\\pi}(s_t, a_t) - V^{\\pi}(s_t),$$\n",
    "where $Q^{\\pi}(s_t, a_t)$ is the action-value function following policy $\\pi$ and $V^{\\pi}(s_t)$ is the state-value function following policy $\\pi$. The advantage function essentially measures the advantage gained (or lost) by taking the action $a_t$ in state $s_t$ over the average return of all immediate actions, and then following policy $\\pi$ in the following states. We don't know the absolute value of the advantage, $A^{\\pi}$, hence we need to find an advantage estimate, $\\hat{A}$, as a substitute.\n",
    "\n",
    "The advantage estimate used in A2C/A3C is given by:\n",
    "$$\\hat{A}_{t} = G_t - \\hat{v}(S_t, w),$$ \n",
    "where $G_t$ is the discounted return for terminal episodes or the bootstrapped return for non-terminal episodes, and $\\hat{v}(S_t, w)$ is the value estimate given state $S_t$ and parameters $w$. The bias-variance trade-off can be finetuned by altering the discount rate $\\gamma$. Larger discount/decay rates lead to higher variance and lower bias and lower discount/decay rates lead to lower variance and higher bias. \n",
    "\n",
    "\n",
    "We will be using autograd to perform gradient descent on the policy and value functions. We only need to construct the objective functions (loss functions) and their derivatives will be calculated automatically. We will be using the Adam optimizer for both policy and value gradient updates. The loss functions will be combined into a single loss function. Autograd traces the paths of all the parameters for the gradient calculation, so combining the losses won't impact the gradient calculations. \n",
    "\n",
    "The policy objective function is given by:\n",
    "$$L_{t}^{PF} = -\\hat{E_t}[\\log(\\pi_\\theta(a_t | s_t))\\hat{A}_{t}].$$\n",
    "\n",
    "The value objective function is given by:\n",
    "$$L_{t}^{VF} = \\hat{E_t}[\\hat{A}_{t}^2].$$\n",
    "\n",
    "The final objective function is given by:\n",
    "$$L_{t} = \\hat{E_t}[L_{t}^{PF} + c_{1}L_{t}^{VF} - c_{2}S_{\\pi_{\\theta}}(s_t)],$$\n",
    "where $S_{\\pi_{\\theta}}(s_t)$ is the entropy of the policy function, and $c_{1}$, $c_{2}$ are the objective coefficients. Increasing $c_{1}$ will increase the update size on the value function (the same effect as increasing the learning rate) and increasing $c_{2}$ will make the policy function less deterministic. Decreasing the coefficients will have the opposite effect. \n",
    "\n",
    "\n",
    "\n",
    "For more information on A2C/A3C, see the original A3C paper [1] [Asynchronous Methods for Deep Reinforcement Learning](https://arxiv.org/abs/1602.01783), the notebook [2] [RL-Adventure-2 Actor-Critic Notebook](https://github.com/higgsfield/RL-Adventure-2/blob/master/1.actor-critic.ipynb).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import gymnasium as gym\n",
    "from IPython.display import Video\n",
    "import jax\n",
    "import flax.linen as nn\n",
    "from jax import value_and_grad\n",
    "import jax.numpy as jnp\n",
    "import optax\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from vec_env.subproc_vec_env import SubprocVecEnv\n",
    "# Print numpy array floats with 2 decimal places\n",
    "np.set_printoptions(precision=2, suppress=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Type of environment, options include:\n",
    "# CartPole-v1, MountainCar-v0\n",
    "ENV_TYPE = \"CartPole-v1\"\n",
    "# Choose number of parallel environments, \n",
    "# don't exceed the number of computer threads\n",
    "num_envs = 10\n",
    "\n",
    "# Save videos from training\n",
    "SAVE_VIDEOS = False\n",
    "VIDEOS_ROOT_DIR = './videos/a2c_discrete_monte-carlo/'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_env(env_id):\n",
    "    \"\"\"\n",
    "    Returns a single environment object, \n",
    "    which will be used for parallel execution.\n",
    "    \"\"\"\n",
    "    def _init():\n",
    "        env = gym.make(env_id)\n",
    "        return env\n",
    "    return _init"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create multiple envs for parallel execution\n",
    "envs = SubprocVecEnv([make_env(ENV_TYPE) for _ in range(num_envs)])\n",
    "\n",
    "num_actions = envs.action_space.n\n",
    "obs_dims = envs.observation_space.shape\n",
    "obs_upper_bounds = envs.observation_space.high\n",
    "obs_lower_bounds = envs.observation_space.low"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create The Policy "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\u001b[3m                               _policy_fn Summary                               \u001b[0m\n",
      "┏━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━┓\n",
      "┃\u001b[1m \u001b[0m\u001b[1mpath   \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mmodule    \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1minputs         \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1moutputs        \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mparams           \u001b[0m\u001b[1m \u001b[0m┃\n",
      "┡━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━┩\n",
      "│         │ _policy_fn │ \u001b[2mfloat32\u001b[0m[10,4]   │ \u001b[2mfloat32\u001b[0m[10,2]   │                   │\n",
      "├─────────┼────────────┼─────────────────┼─────────────────┼───────────────────┤\n",
      "│ Dense_0 │ Dense      │ \u001b[2mfloat32\u001b[0m[10,4]   │ \u001b[2mfloat32\u001b[0m[10,256] │ bias:             │\n",
      "│         │            │                 │                 │ \u001b[2mfloat32\u001b[0m[256]      │\n",
      "│         │            │                 │                 │ kernel:           │\n",
      "│         │            │                 │                 │ \u001b[2mfloat32\u001b[0m[4,256]    │\n",
      "│         │            │                 │                 │                   │\n",
      "│         │            │                 │                 │ \u001b[1m1,280 \u001b[0m\u001b[1;2m(5.1 KB)\u001b[0m    │\n",
      "├─────────┼────────────┼─────────────────┼─────────────────┼───────────────────┤\n",
      "│ Dense_1 │ Dense      │ \u001b[2mfloat32\u001b[0m[10,256] │ \u001b[2mfloat32\u001b[0m[10,2]   │ bias: \u001b[2mfloat32\u001b[0m[2]  │\n",
      "│         │            │                 │                 │ kernel:           │\n",
      "│         │            │                 │                 │ \u001b[2mfloat32\u001b[0m[256,2]    │\n",
      "│         │            │                 │                 │                   │\n",
      "│         │            │                 │                 │ \u001b[1m514 \u001b[0m\u001b[1;2m(2.1 KB)\u001b[0m      │\n",
      "├─────────┼────────────┼─────────────────┼─────────────────┼───────────────────┤\n",
      "│\u001b[1m \u001b[0m\u001b[1m       \u001b[0m\u001b[1m \u001b[0m│\u001b[1m \u001b[0m\u001b[1m          \u001b[0m\u001b[1m \u001b[0m│\u001b[1m \u001b[0m\u001b[1m               \u001b[0m\u001b[1m \u001b[0m│\u001b[1m \u001b[0m\u001b[1m          Total\u001b[0m\u001b[1m \u001b[0m│\u001b[1m \u001b[0m\u001b[1m1,794 \u001b[0m\u001b[1;2m(7.2 KB)\u001b[0m\u001b[1m   \u001b[0m\u001b[1m \u001b[0m│\n",
      "└─────────┴────────────┴─────────────────┴─────────────────┴───────────────────┘\n",
      "\u001b[1m                                                                                \u001b[0m\n",
      "\u001b[1m                        Total Parameters: 1,794 \u001b[0m\u001b[1;2m(7.2 KB)\u001b[0m\u001b[1m                        \u001b[0m\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "class _policy_fn(nn.Module):\n",
    "    \"\"\"\n",
    "    Policy function is an MLP used to choose the \n",
    "    best possible discrete action given the observations from the state.\n",
    "    Each discrete action is given a probability from 0-1.\n",
    "    The probability distribution can then be used \n",
    "    to stocastically choose the next action.  \n",
    "    \"\"\"\n",
    "    num_actions: int\n",
    "\n",
    "    @nn.compact\n",
    "    def __call__(self, x):\n",
    "        x = nn.Dense(256)(x)\n",
    "        x = jax.nn.relu(x)\n",
    "        x = nn.Dense(self.num_actions)(x)\n",
    "        return jax.nn.softmax(x)\n",
    "\n",
    "# Create the model object\n",
    "policy_fn = _policy_fn(num_actions=num_actions)\n",
    "# Display the model details\n",
    "dummy_x = envs.reset()\n",
    "dummy_x = jnp.array(dummy_x)\n",
    "rng_key = jax.random.PRNGKey(64)\n",
    "print(policy_fn.tabulate(rng_key, dummy_x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\u001b[3m                               _value_fn Summary                                \u001b[0m\n",
      "┏━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━┓\n",
      "┃\u001b[1m \u001b[0m\u001b[1mpath   \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mmodule   \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1minputs         \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1moutputs        \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mparams            \u001b[0m\u001b[1m \u001b[0m┃\n",
      "┡━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━┩\n",
      "│         │ _value_fn │ \u001b[2mfloat32\u001b[0m[10,4]   │ \u001b[2mfloat32\u001b[0m[10,1]   │                    │\n",
      "├─────────┼───────────┼─────────────────┼─────────────────┼────────────────────┤\n",
      "│ Dense_0 │ Dense     │ \u001b[2mfloat32\u001b[0m[10,4]   │ \u001b[2mfloat32\u001b[0m[10,256] │ bias: \u001b[2mfloat32\u001b[0m[256] │\n",
      "│         │           │                 │                 │ kernel:            │\n",
      "│         │           │                 │                 │ \u001b[2mfloat32\u001b[0m[4,256]     │\n",
      "│         │           │                 │                 │                    │\n",
      "│         │           │                 │                 │ \u001b[1m1,280 \u001b[0m\u001b[1;2m(5.1 KB)\u001b[0m     │\n",
      "├─────────┼───────────┼─────────────────┼─────────────────┼────────────────────┤\n",
      "│ Dense_1 │ Dense     │ \u001b[2mfloat32\u001b[0m[10,256] │ \u001b[2mfloat32\u001b[0m[10,1]   │ bias: \u001b[2mfloat32\u001b[0m[1]   │\n",
      "│         │           │                 │                 │ kernel:            │\n",
      "│         │           │                 │                 │ \u001b[2mfloat32\u001b[0m[256,1]     │\n",
      "│         │           │                 │                 │                    │\n",
      "│         │           │                 │                 │ \u001b[1m257 \u001b[0m\u001b[1;2m(1.0 KB)\u001b[0m       │\n",
      "├─────────┼───────────┼─────────────────┼─────────────────┼────────────────────┤\n",
      "│\u001b[1m \u001b[0m\u001b[1m       \u001b[0m\u001b[1m \u001b[0m│\u001b[1m \u001b[0m\u001b[1m         \u001b[0m\u001b[1m \u001b[0m│\u001b[1m \u001b[0m\u001b[1m               \u001b[0m\u001b[1m \u001b[0m│\u001b[1m \u001b[0m\u001b[1m          Total\u001b[0m\u001b[1m \u001b[0m│\u001b[1m \u001b[0m\u001b[1m1,537 \u001b[0m\u001b[1;2m(6.1 KB)\u001b[0m\u001b[1m    \u001b[0m\u001b[1m \u001b[0m│\n",
      "└─────────┴───────────┴─────────────────┴─────────────────┴────────────────────┘\n",
      "\u001b[1m                                                                                \u001b[0m\n",
      "\u001b[1m                        Total Parameters: 1,537 \u001b[0m\u001b[1;2m(6.1 KB)\u001b[0m\u001b[1m                        \u001b[0m\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "class _value_fn(nn.Module):\n",
    "    \"\"\"\n",
    "    Value function is an MLP used to predict the expected return (value) \n",
    "    given the observations from the state.\n",
    "    The value can then be used for bootstrapping, and/or \n",
    "    calculating the advantage from action chosen in the state. \n",
    "    \"\"\"\n",
    "    @nn.compact\n",
    "    def __call__(self, x):\n",
    "        x = nn.Dense(256)(x)\n",
    "        x = jax.nn.relu(x)\n",
    "        x = nn.Dense(1)(x)\n",
    "        return x\n",
    "\n",
    "# Create the model object\n",
    "value_fn = _value_fn()\n",
    "# Display the model details\n",
    "print(value_fn.tabulate(rng_key, dummy_x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_model(policy_variables, env, rng_key):\n",
    "    \"\"\"\n",
    "    Runs a single episode following the policy function, \n",
    "    then returns the episodes rewards and steps.\n",
    "    Args:\n",
    "        policy_variables: Policy functions model parameters.\n",
    "        env: Environment used to interact with.\n",
    "        rng_key: Random number generator key.\n",
    "    Returns:\n",
    "        steps: Number of environment steps.\n",
    "        episode_rewards: List of rewards from the episode.\n",
    "    \"\"\"\n",
    "\n",
    "    terminated, truncated = False, False\n",
    "    episode_rewards = []\n",
    "    steps = 0\n",
    "\n",
    "    state, _ = env.reset()\n",
    "    while not (terminated or truncated):\n",
    "        steps += 1\n",
    "        # Select the action following the parametrized policy\n",
    "        action_dist = policy_fn.apply(policy_variables, state)\n",
    "        rng_key, subkey = jax.random.split(rng_key)\n",
    "        action = jax.random.choice(subkey, jnp.arange(num_actions), p=action_dist)\n",
    "        action = np.array(action)\n",
    "        next_state, reward, terminated, truncated, info = env.step(action)\n",
    "\n",
    "        episode_rewards.append(reward)\n",
    "\n",
    "        state = next_state\n",
    "    episode_rewards = np.array(episode_rewards)\n",
    "    return steps, episode_rewards\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_returns(\n",
    "    gamma, next_value, rewards, done\n",
    "):\n",
    "    \"\"\"\n",
    "    Get discounted returns from rewards for each environment.\n",
    "    Args:\n",
    "        gamma: trajectory discount (scalar).\n",
    "        next_value: value functions bootstrapped return for next state.\n",
    "        rewards: agent rewards of taking actions in the environment.\n",
    "        done: flag list for end of episode, \n",
    "            False indicates terminated, and True not terminated.\n",
    "    Returns:\n",
    "        Array of returns for each environment at each step.\n",
    "    \"\"\"\n",
    "    batch_size = len(done)\n",
    "    rewards = jnp.array(rewards)\n",
    "    done = jnp.array(done)\n",
    "\n",
    "    R = jnp.squeeze(next_value)\n",
    "    returns = []\n",
    "\n",
    "    for t in reversed(range(batch_size)):\n",
    "        R = rewards[t] + (gamma * R * done[t])\n",
    "        returns.append(R)\n",
    "\n",
    "    returns = jnp.array(list(reversed(returns)))\n",
    "    return returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss_fn(value_variables, policy_variables, rng_key, gamma, max_steps, env_returns, env_steps):\n",
    "    \"\"\"\n",
    "    Runs a single episode in a Monte-Carlo way, \n",
    "    then calculates the actor and critic losses, \n",
    "    which are then combined and returned.\n",
    "    The gradients on this loss function are then used \n",
    "    to update the policy and actor functions.\n",
    "    Args:\n",
    "        value_variables: Value functions model parameters.\n",
    "        policy_variables: Policy functions model parameters.\n",
    "        rng_key: Random number generator key.\n",
    "        gamma: Discount rate for discounting returns.\n",
    "        max_steps: Limit on the number of steps in an episode.\n",
    "        env_returns: List containing the returns from all environments each episode.\n",
    "        env_steps: List containing the steps from all environments each episode.\n",
    "    Returns:\n",
    "        Combined loss of the value and actor functions.\n",
    "    \"\"\"\n",
    "    terminated, truncated, term_or_trunc = jnp.repeat(False, num_envs), jnp.repeat(False, num_envs), jnp.repeat(False, num_envs)\n",
    "    episode_log_probs = []\n",
    "    episode_values = []\n",
    "    episode_rewards = []\n",
    "    done_flag = []\n",
    "    steps = 0\n",
    "\n",
    "    states = envs.reset()\n",
    "    states = jnp.array(states)\n",
    "    # Generate an episode following the policy\n",
    "    while not term_or_trunc.all() and steps < max_steps:\n",
    "        steps += 1\n",
    "        # Select the action following the parametrized policy\n",
    "        action_dists = policy_fn.apply(policy_variables, states)\n",
    "        # Stocastically choose the next action based on the probability distribution\n",
    "        actions = []\n",
    "        for dist in action_dists:\n",
    "            rng_key, subkey = jax.random.split(rng_key)\n",
    "            action = jax.random.choice(subkey, jnp.arange(num_actions), p=dist)\n",
    "            actions.append(action)\n",
    "        actions = np.array(actions)\n",
    "        \n",
    "        next_states, rewards, terminated, truncated, info = envs.step(actions)\n",
    "        # Check if env was terminated or truncated in this episode or one of the previous episodes \n",
    "        # We only want one episode per environment\n",
    "        term_or_trunc = jnp.array([term or trunc or t_or_t for term, trunc, t_or_t in zip(terminated, truncated, term_or_trunc)])\n",
    "        done_flag.append(jnp.invert(term_or_trunc))\n",
    "        # If the episode previously ended, then set the reward to 0, \n",
    "        # we're ignoring rewards after the environment terminated\n",
    "        rewards = jnp.array([reward if not t_or_t else 0 for reward, t_or_t in zip(rewards, term_or_trunc)])\n",
    "        episode_rewards.append(rewards)\n",
    "        # Log probabilities are needed for the actor loss\n",
    "        log_probs = jnp.array([jnp.log(dist[action_index]) for dist, action_index in zip(action_dists, actions)])\n",
    "        episode_log_probs.append(log_probs)\n",
    "        # Entropy is used in the loss function to prevent the model from becoming too deterministic\n",
    "        entropy = jnp.array([-jnp.sum(dist * jnp.log(dist)) for dist in action_dists])\n",
    "        # Estimate the values given the states, then set all terminated states value to 0\n",
    "        values = value_fn.apply(value_variables, states)\n",
    "        values = jnp.squeeze(values)\n",
    "        # We're ignoring values after the environment terminated\n",
    "        values = [value if not t_or_t else 0.0 for value, t_or_t in zip(jnp.array(values), term_or_trunc)]\n",
    "        values = jnp.array(values, dtype=jnp.float32)\n",
    "        episode_values.append(values)\n",
    "\n",
    "        states = next_states\n",
    "\n",
    "    env_returns.append(list(np.array(episode_rewards).sum(axis=0)))\n",
    "    env_steps.append(list(np.array(done_flag).sum(axis=0)))\n",
    "\n",
    "    # Calculate the returns then \n",
    "    next_values = value_fn.apply(value_variables, next_states)\n",
    "    returns = get_returns(gamma, next_values, episode_rewards, done_flag)\n",
    "    episode_values = jnp.array(episode_values)\n",
    "    advantages = returns - episode_values\n",
    "    # Calculate actor and critic losses, then add entropy \n",
    "    episode_log_probs = jnp.array(episode_log_probs)\n",
    "    actor_loss = -(advantages * episode_log_probs).mean(axis=0)\n",
    "    critic_loss = (advantages**2).mean(axis=0)\n",
    "    loss = (actor_loss + 0.5 * critic_loss - 0.001 * entropy).mean()\n",
    "\n",
    "    return loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learn The Optimal Action-Value Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ubuntu22/repos/reinforcement-learning-algorithms/venv-pre/lib/python3.10/site-packages/gymnasium/wrappers/rendering.py:415: UserWarning: \u001b[33mWARN: Unable to save last video! Did you call close()?\u001b[0m\n",
      "  logger.warn(\"Unable to save last video! Did you call close()?\")\n",
      "/home/ubuntu22/repos/reinforcement-learning-algorithms/venv-pre/lib/python3.10/site-packages/gymnasium/wrappers/rendering.py:282: UserWarning: \u001b[33mWARN: Overwriting existing videos at /home/ubuntu22/repos/reinforcement-learning-algorithms/videos/a2c_discrete_monte-carlo folder (try specifying a different `video_folder` for the `RecordVideo` wrapper if this is not desired)\u001b[0m\n",
      "  logger.warn(\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 0\n",
      "\tTest Episode 0 Return: 20.00 Steps: 20.00\n",
      "\tReturns: [np.float64(11.0), np.float64(13.0), np.float64(20.0), np.float64(15.0), np.float64(35.0), np.float64(10.0), np.float64(26.0), np.float64(54.0), np.float64(13.0), np.float64(10.0)]\n",
      "\tAverage Return: 20.70\n",
      "\tLoss: 58.08\n",
      "Episode: 1\n",
      "\tReturns: [np.float64(14.0), np.float64(32.0), np.float64(33.0), np.float64(18.0), np.float64(81.0), np.float64(23.0), np.float64(38.0), np.float64(74.0), np.float64(21.0), np.float64(19.0)]\n",
      "\tAverage Return: 35.30\n",
      "\tLoss: 143.06\n",
      "Episode: 2\n",
      "\tReturns: [np.float64(50.0), np.float64(73.0), np.float64(61.0), np.float64(42.0), np.float64(31.0), np.float64(42.0), np.float64(30.0), np.float64(43.0), np.float64(36.0), np.float64(39.0)]\n",
      "\tAverage Return: 44.70\n",
      "\tLoss: 177.27\n",
      "Episode: 3\n",
      "\tTest Episode 1 Return: 78.00 Steps: 78.00\n",
      "\tReturns: [np.float64(29.0), np.float64(37.0), np.float64(56.0), np.float64(41.0), np.float64(39.0), np.float64(44.0), np.float64(53.0), np.float64(79.0), np.float64(33.0), np.float64(56.0)]\n",
      "\tAverage Return: 46.70\n",
      "\tLoss: 182.41\n",
      "Episode: 4\n",
      "\tReturns: [np.float64(30.0), np.float64(141.0), np.float64(41.0), np.float64(28.0), np.float64(76.0), np.float64(37.0), np.float64(54.0), np.float64(57.0), np.float64(114.0), np.float64(48.0)]\n",
      "\tAverage Return: 62.60\n",
      "\tLoss: 289.06\n",
      "Episode: 5\n",
      "\tReturns: [np.float64(113.0), np.float64(75.0), np.float64(46.0), np.float64(33.0), np.float64(30.0), np.float64(42.0), np.float64(148.0), np.float64(94.0), np.float64(89.0), np.float64(97.0)]\n",
      "\tAverage Return: 76.70\n",
      "\tLoss: 392.63\n",
      "Episode: 6\n",
      "\tTest Episode 2 Return: 168.00 Steps: 168.00\n",
      "\tReturns: [np.float64(53.0), np.float64(115.0), np.float64(43.0), np.float64(78.0), np.float64(58.0), np.float64(36.0), np.float64(72.0), np.float64(66.0), np.float64(99.0), np.float64(98.0)]\n",
      "\tAverage Return: 71.80\n",
      "\tLoss: 362.61\n",
      "Episode: 7\n",
      "\tReturns: [np.float32(44.0), np.float32(135.0), np.float32(107.0), np.float32(42.0), np.float32(60.0), np.float32(143.0), np.float32(81.0), np.float32(69.0), np.float32(200.0), np.float32(151.0)]\n",
      "\tAverage Return: 103.20\n",
      "\tLoss: 547.97\n",
      "Episode: 8\n",
      "\tReturns: [np.float32(132.0), np.float32(126.0), np.float32(200.0), np.float32(122.0), np.float32(101.0), np.float32(114.0), np.float32(200.0), np.float32(61.0), np.float32(172.0), np.float32(198.0)]\n",
      "\tAverage Return: 142.60\n",
      "\tLoss: 960.42\n",
      "Episode: 9\n",
      "\tTest Episode 3 Return: 161.00 Steps: 161.00\n",
      "\tReturns: [np.float32(81.0), np.float32(169.0), np.float32(200.0), np.float32(58.0), np.float32(200.0), np.float32(166.0), np.float32(200.0), np.float32(88.0), np.float32(135.0), np.float32(200.0)]\n",
      "\tAverage Return: 149.70\n",
      "\tLoss: 1099.12\n",
      "Episode: 10\n",
      "\tReturns: [np.float32(86.0), np.float32(200.0), np.float32(88.0), np.float32(56.0), np.float32(188.0), np.float32(87.0), np.float32(200.0), np.float32(90.0), np.float32(116.0), np.float32(121.0)]\n",
      "\tAverage Return: 123.20\n",
      "\tLoss: 724.96\n",
      "Episode: 11\n",
      "\tReturns: [np.float32(94.0), np.float32(190.0), np.float32(168.0), np.float32(63.0), np.float32(200.0), np.float32(69.0), np.float32(200.0), np.float32(93.0), np.float32(200.0), np.float32(200.0)]\n",
      "\tAverage Return: 147.70\n",
      "\tLoss: 1074.65\n",
      "Episode: 12\n",
      "\tTest Episode 4 Return: 85.00 Steps: 85.00\n",
      "\tReturns: [np.float32(200.0), np.float32(199.0), np.float32(152.0), np.float32(200.0), np.float32(200.0), np.float32(70.0), np.float32(200.0), np.float32(57.0), np.float32(200.0), np.float32(200.0)]\n",
      "\tAverage Return: 167.80\n",
      "\tLoss: 1330.62\n",
      "Episode: 13\n",
      "\tReturns: [np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(76.0), np.float32(200.0), np.float32(63.0), np.float32(200.0), np.float32(200.0)]\n",
      "\tAverage Return: 173.90\n",
      "\tLoss: 1452.14\n",
      "Episode: 14\n",
      "\tReturns: [np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(73.0), np.float32(157.0), np.float32(200.0), np.float32(200.0), np.float32(200.0)]\n",
      "\tAverage Return: 183.00\n",
      "\tLoss: 1523.60\n",
      "Episode: 15\n",
      "\tTest Episode 5 Return: 500.00 Steps: 500.00\n",
      "\tReturns: [np.float32(200.0), np.float32(200.0), np.float32(161.0), np.float32(200.0), np.float32(200.0), np.float32(75.0), np.float32(200.0), np.float32(141.0), np.float32(200.0), np.float32(200.0)]\n",
      "\tAverage Return: 177.70\n",
      "\tLoss: 1380.71\n",
      "Episode: 16\n",
      "\tReturns: [np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(75.0), np.float32(200.0), np.float32(93.0), np.float32(200.0), np.float32(200.0)]\n",
      "\tAverage Return: 176.80\n",
      "\tLoss: 1417.36\n",
      "Episode: 17\n",
      "\tReturns: [np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(200.0)]\n",
      "\tAverage Return: 200.00\n",
      "\tLoss: 1686.60\n",
      "Episode: 18\n",
      "\tTest Episode 6 Return: 500.00 Steps: 500.00\n",
      "\tReturns: [np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(77.0), np.float32(200.0), np.float32(200.0), np.float32(200.0), np.float32(200.0)]\n",
      "\tAverage Return: 187.70\n",
      "\tLoss: 1504.69\n"
     ]
    }
   ],
   "source": [
    "# Number of episodes to train on\n",
    "episodes = 19\n",
    "# Sliding window for episode evaluation (needs to be less than episodes)\n",
    "episode_window = 3\n",
    "# Episode will terminate before max_steps\n",
    "max_steps = 200\n",
    "# Discount ratio\n",
    "gamma = 0.99\n",
    "# Step size\n",
    "policy_alpha = 0.01\n",
    "value_alpha = 0.01\n",
    "\n",
    "policy_variables = policy_fn.init(rng_key, dummy_x)\n",
    "policy_optimizer = optax.adam(learning_rate=policy_alpha)\n",
    "policy_opt_state = policy_optimizer.init(policy_variables)\n",
    "\n",
    "value_variables = value_fn.init(rng_key, dummy_x)\n",
    "value_optimizer = optax.adam(learning_rate=value_alpha)\n",
    "value_opt_state = value_optimizer.init(value_variables)\n",
    "\n",
    "# Create multiple envs for parallel execution\n",
    "envs = SubprocVecEnv([make_env(ENV_TYPE) for _ in range(num_envs)])\n",
    "if SAVE_VIDEOS:\n",
    "    # Create a single environment for testing\n",
    "    os.makedirs(VIDEOS_ROOT_DIR, exist_ok=True)\n",
    "    test_returns = []\n",
    "    test_steps = []\n",
    "    env = gym.make(ENV_TYPE, render_mode=\"rgb_array\")\n",
    "    env = gym.wrappers.RecordVideo(\n",
    "        env=env, \n",
    "        video_folder=VIDEOS_ROOT_DIR,\n",
    "        episode_trigger=lambda episode: episode % 1 == 0,\n",
    "        video_length=0,\n",
    "        name_prefix=f\"{ENV_TYPE}\",\n",
    "        fps=30\n",
    "        ) \n",
    "env_returns = []\n",
    "env_steps = []\n",
    "losses = []\n",
    "\n",
    "for episode in range(episodes):\n",
    "    print(f\"Episode: {episode}\")\n",
    "    # Perform 6 tests and record them at even intervals\n",
    "    if SAVE_VIDEOS and episode % (episodes // 5) == 0:\n",
    "        test_step, test_rewards = test_model(policy_variables, env, rng_key)\n",
    "        test_returns.append(np.sum(test_rewards))\n",
    "        test_steps.append(test_step)\n",
    "        test_episode = episode // (episodes // 5)\n",
    "        print(f\"\\tTest Episode {test_episode} Return: {test_returns[test_episode] :.2f} Steps: {test_steps[test_episode] :.2f}\")\n",
    "\n",
    "    # Run a forward pass on the parallel envs (will last an entire episode) and \n",
    "    # calculate the gradients for value and policy functions \n",
    "    loss, (value_grads, policy_grads) = value_and_grad(loss_fn, argnums=(0, 1))(\n",
    "        value_variables, \n",
    "        policy_variables, \n",
    "        rng_key, \n",
    "        gamma, \n",
    "        max_steps,\n",
    "        env_returns,\n",
    "        env_steps\n",
    "    )\n",
    "    # Update value function weights\n",
    "    value_updates, value_opt_state = value_optimizer.update(value_grads, value_opt_state, value_variables)\n",
    "    value_variables = optax.apply_updates(value_variables, value_updates)        \n",
    "    # Update policy function weights\n",
    "    policy_updates, policy_opt_state = policy_optimizer.update(policy_grads, policy_opt_state, policy_variables)\n",
    "    policy_variables = optax.apply_updates(policy_variables, policy_updates)\n",
    "\n",
    "\n",
    "    losses.append(loss)\n",
    "    print(f'\\tReturns: {env_returns[-1]}')\n",
    "    print(f\"\\tAverage Return: {jnp.array(env_returns[-1]).mean() :.2f}\")\n",
    "    print(f\"\\tLoss: {loss :.2f}\")\n",
    "\n",
    "        "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot The Results\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(ncols=1, figsize=(6, 5))\n",
    "axs.set_title(\"Loss\")\n",
    "loss_moving_average = (\n",
    "    np.convolve(\n",
    "        losses, np.ones(episode_window), mode=\"valid\"\n",
    "    )\n",
    "    / episode_window\n",
    ")\n",
    "axs.plot(range(len(loss_moving_average)), loss_moving_average)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For cartpole rewards are assigned for the time spent in a non-terminal state. The episode length and rewards will be identical in this case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7AwBAQ8UsdXbPPvusli5dqh49emjixIlq06aNsrOztXHjRv3000+nLN/OxNXVVY8//rjuuOMOXXDBBbr66quVkpKiOXPmqFmzZlVWRzVr1kz+/v6aPXu2fHx85OXlpR49epx0/dAzufjiixUWFqY+ffooNDRUO3fu1CuvvKLhw4dXfn8BVDNT7vkHoNac6TbG+sNtc0/cxvj55583XnzxRSMiIsJwc3Mz+vXrZ2zZsqXKMf98G+MlS5YYI0aMMMLDww1XV1cjPDzcuPbaa409e/ZUeV56erpx0003GUFBQYarq6vRvn37U962Nysry7jhhhsMX19fw8/Pz7jhhhuMTZs2nfI2v/v27TNuvPFGIywszHBxcTGaNGli/OMf/zC++OKLM35f/vh6T+V8jhsSEmJIMtLT0yu3rVq1ypBk9OvX76T9d+zYYQwePNjw9vY2goKCjIkTJxpbtmw56fWNHTvW8PLyOmW+48ePG3feeacRGBhoeHl5GZdeeqlx4MCBKrdmLikpMe6//34jPj7e8PHxMby8vIz4+HjjtddeO+P3BgAA/A+z1On9ce74Y8bJkycbERERhouLixEWFmZceOGFxptvvlm5z9KlSw1Jxueff17luSe+h3/OOHPmTCMqKspwc3Mzunfvbqxevdro0qWLMXTo0Cr7ffPNN0abNm0MZ2fnKscZMGCA0bZt25Pyjx071oiKiqr8/I033jD69+9vBAYGGm5ubkazZs2M+++/38jNzT3r9wLAX2MxjBq4ihyAOiclJUUxMTF6/vnndd9995kdBwAAoE5hlqo9drtdwcHBGjlypN566y2z4wD4G7imFAAAAADAIRUXF590N74PPvhA2dnZGjhwoDmhAFQbrikFAAAAAHBIv/76q6ZOnaqrrrpKgYGB2rhxo9555x21a9dOV111ldnxAPxNlFIAAAAAAIcUHR2tiIgIzZw5U9nZ2QoICNCNN96oZ599Vq6urmbHA/A3cU0pAAAAAAAA1DquKQUAAAAAAIBaRykFAAAAAACAWlcnryllt9t1+PBh+fj4yGKxmB0HAADUY4ZhKD8/X+Hh4bJa6/b5PGYoAABQG851fqqTpdThw4cVERFhdgwAANCAHDhwQE2bNjU7xt/CDAUAAGrT2eanOllK+fj4SKp4cb6+vianAQAA9VleXp4iIiIq54+6jBkKAADUhnOdn+pkKXViubmvry8DFQAAqBX14e1uzFAAAKA2nW1+qtsXRgAAAAAAAECdRCkFAAAAAACAWkcpBQAAAAAAgFpHKQUAAAAAAIBaRykFAAAAAACAWkcpBQAAAAAAgFpHKQUAAAAAAIBaRykFAAAAAACAWkcpBQAAAAAAgFpHKQUAAAAAAIBaRykFAAAAAACAWkcpBQAAAAAAgFpHKQUAAAAAAIBaRykFAAAAAACAWkcpBQAAAAAAgFpHKQUAAOqk9LxifbHhoN5dlWx2FAAAgDqhzGbXupRsvbR4j5KOFpgdR85mBwAAADgXRaXlSkjK1oq9R7Vqb6b2ZlQMUr7uzhrbO1pOVovJCQEAAByLYRjad7RQq/Ye1arETP2alK2CknJJFTNUbLC3qfkopQAAgEOy2Q1tO5SrVXuPauXeTG1MPaYym1H5uMUidWjqr37Ng1RcZpOXG2MNAABAVkGJVu/L0so9R7U6MVOHc4urPB7g5ao+zYPUItTHpIT/w/QGAAAcxoHsIq3cm6mVe4/ql31Zyj1eVuXxiAAP9W0erH5xQerdLFD+nq4mJQUAAHAMxWU2rU85ppWJFavJfzucV+VxV2erukU3Ur+4YPVtHqQ2jX1ldZAV5pRSAADANLnHy7RmX6ZW7s3UqsRM7c8qqvK4j7uzejcLVL+4iiIqKtDLpKQAAACOwW43tCstX6sSK1aTr03OVkm5vco+rRv7ql9ckPo2D1L3mAC5uziZlPbMKKUAAECtKbPZtSk1p+IteYmZ2nIgR/b/vSNPzlaLOkc2Ut+4IPWNC1KHJn5yduK+LAAAoGFLyy3Wyt+vC7U6MVOZBaVVHg/1dVPf5sHq3yJIvZsFKdjHzaSk54dSCgAA1JiKi2sWVKyE2pupX5OyVFhqq7JPs2CvyuXkPZsFyptrQwEAgAausKRcCclZlTPUiRu8nODp6qSesYHq2zxI/eKC1DzEWxaLY7wl73ww9QEAgGqVVVCiVYkVA9SqxEwdOcXFNfs2r1gJ1bd5kML9PUxKCgAA4BhsdkNbD+Zo1d5MrUzM1KY/3eDFapHa/36Dl75xQeoc2UiuznV/NTmlFAAA+FtKym1al3xMK3+/S96OIydfXLN7dEBlCeVIF9cEAAAwy4HsIq3YW3Fx8jPd4KV/XMVb8vw8XUxKWnMopQAAwF+SU1SqD9fs15xfUpRVWPW6BnXl4poAAAC1yTAMrUnK0hvLk7R8z9Eqj/m6O6t3s4qVUA3lBi+UUgAA4LwcyC7SO6uS9dn6Ayr6/fpQwT5uGtCi4g55denimgAAALWh3GbXot/S9MbyJG07lCup4i15XaMCGvQNXiilAADAOdl+KFdvrkjSgm1HZPv9lnltGvvqlgGxuqR9Y7k0sCEKAADgbI6X2vT5hgN6e2WyUrOLJEnuLlZd3TVCE/rGNIjVUGdCKQUAAE7LMAytSszUmyuStHJvZuX2fnFBmtQ/Vn2bB9XJO70AAADUpOzCUr3/S4o+WJOiY0UV14pq5Omisb2jdWOvaAV4uZqc0DFQSgEAgJOU2+xasO2I3lieVHnhcierRcPbN9ak/rFq18TP5IQAAACOJzWrSG+vStJn6w+ouMwuqeKC5RP7xeqqLhHycOU6m39EKQUAACoVlpTrs/UVS8wP5RyXJHm4OOmabhVLzCMCPE1OCAAA4Hi2HszRGyuStHDbEf1+lQO1b+KnWwbEamjbsAZ3rahzRSkFAACUWVDy+xLz/ZW3Iw70ctW43tG6vmeUGrHEHAAAoArDMLR8z1G9sTxJa5KyKrcPaBGsWwbEqldsIJc5OAtKKQAAGrDkzEK9tTJJX2w4qNLyiiXm0YGemtg/VqM6N5W7C0vMAQAA/qjMZte3Ww7rzRVJ2pWWL0lytlp0WXy4JvaPVevGviYnrDvOe/3YihUrdOmllyo8PFwWi0Vff/11lccLCgo0ZcoUNW3aVB4eHmrTpo1mz55dZZ/i4mJNnjxZgYGB8vb21qhRo5Senv63XggAADh3m1KP6dYPN+iCF5dpbkKqSsvtio/w1+zrO2vJvQM1pkcUhVQ1Yn4CAKDuKygp19srkzRg+lLd89kW7UrLl5erk27uG6MVDwzSS9d0pJA6T+e9UqqwsFDx8fEaP368Ro4cedLj99xzj37++Wd99NFHio6O1o8//qjbb79d4eHhuuyyyyRJU6dO1YIFC/T555/Lz89PU6ZM0ciRI7V69eq//4oAAMAp2e2Glu7O0BsrkrQ2Obty+4WtQjSpf6y6xwSwxLyGMD8BAFB3ZeQV671fUvTRr/uVX1wuSQr2cdNNfaI1pnuU/DxdTE5Yd1kMwzD+8pMtFs2fP1+XX3555bZ27drpmmuu0aOPPlq5rUuXLho2bJieeuop5ebmKjg4WHPnztWVV14pSdq1a5dat26tNWvWqGfPnmf9unl5efLz81Nubq58fWkhAQA4k5Jym77ZfFhvrUjS3owCSZKLk0WXd2yiSf1jFRfqY3JCx1bdc4dZ81NNvBYAAOqzxIwCvbUiSfM3HVKpreIyB7HBXrqlf6wu79REbs6sKj+dc505qv2aUr1799Z///tfjR8/XuHh4Vq2bJn27Nmj//znP5KkDRs2qKysTIMHD658TqtWrRQZGXleQxUAADizvOIyzUtI1burk5WeVyJJ8nFz1nU9InVTnxiF+bmbnBAnMD8BAOA41qdk640VSVq8439vk+8a1UiT+sdqcOtQWa2sLK8u1V5KzZo1S5MmTVLTpk3l7Owsq9Wqt956S/3795ckpaWlydXVVf7+/lWeFxoaqrS0tFMes6SkRCUlJZWf5+XlVXdsAADqjbTcYr23OlkfJ6SqoKRiiXmor5vG94nRtT0i5evOEnNHUxPzk8QMBQDAubLbDS3ema43VyRpw/5jldsvahOqW/rHqmt0gInp6q8aKaV+/fVX/fe//1VUVJRWrFihyZMnKzw8vMrZvfMxbdo0PfHEE9WcFACA+mVPer7eXJGkbzYfUpmt4t35cSHemtQ/ViM6NpGr83nf3wS1pCbmJ4kZCgCAsykus+nrTYf05sokJR0tlCS5Olk1snMT3dwvVs1DvE1OWL9Vayl1/Phx/fOf/9T8+fM1fPhwSVKHDh20efNmvfDCCxo8eLDCwsJUWlqqnJycKmf70tPTFRYWdsrjPvzww7rnnnsqP8/Ly1NERER1RgcAwKHY7IZyj5cpu7BUx4pKK/4sLFV20e9/Fpb9b/vvf5648KYkdY8J0K0DYjWwRQhLzB1cTc1PEjMUAKDhOV5q+8O8dKo56k/zVVFp5ck8H3dn3dAzSuN6RyvEl8sc1IZqLaXKyspUVlYmq7XqmVgnJyfZ7RUXBevSpYtcXFy0ZMkSjRo1SpK0e/dupaamqlevXqc8rpubm9zc3KozKgAAtcYwDOWXlP9pOCr7U8n0x+GoTDlFpbKf561ILBZpaNswTeofq06RjWrmxaDa1dT8JDFDAQDqttJyu3KKKualimKp7DSz0//KpuNltvP+Oo393DWhb4xGd4+Ut1u1v6EMZ3De3+2CggIlJiZWfp6cnKzNmzcrICBAkZGRGjBggO6//355eHgoKipKy5cv1wcffKCXXnpJkuTn56cJEybonnvuUUBAgHx9fXXHHXeoV69eXKQTAFBnHSss1S/7srQuJVsZ+cUnDU7l59sw/c7H3VmBXq5q5OWqAM/f//RyVSNPVwV4ufz+Z8X2YB83rhfloJifAAA4md1uaMeRPK1KzNSe9PzfT9hVnLg7Vliq/JLysx/kFFycLJUzUsCf5yhPlyrzVCMvV4X5usuJleWmsBiGcV5T8rJlyzRo0KCTto8dO1Zz5sxRWlqaHn74Yf3444/Kzs5WVFSUJk2apKlTp8piqfiPXFxcrHvvvVfz5s1TSUmJhgwZotdee+2My8//iNsZAwDMVlxm04b9x7QqMVOr9mZq++Fcne1fVE9XpyolUuVQdFLZ5KpGvxdOLk5cB8ps1TF3OML8VF2vBQCAv+NAdlHl/PTLvkwdKyo74/5WiyrLo4qZyaXqzOT55+LJRd5uzpX/fsIc5zpznHcp5QgYqAAAte3EmbzViZlalZiptcnZKim3V9mnRai3ejcLUnSgZ2XJFPCHssndxcmk9Pg76tPcUZ9eCwCgbsgpKtWafVlamZip1YmZ2p9VVOVxbzdn9YwNUKfIRgryrpiZAr3/Vzb5urtwfcw66FxnDt4sCQDAaRw8VqTViZlauTdTv+zLUnZhaZXHQ3zc1Ld5kPrGBalP8yCFckFMAADQwJWU/76afG9FCbX1UNXV5E5WizpF+KtvXJD6Ng9SfIQ/K8MbMEopAAB+l3u8TGv2VayEWp2YpeTMwiqPe7o6qWdsYGURFRfizdJwAADQoNnthnal5WtV4lGtSszS2uQsFZdVXU3ePMS7Yn5qHqQesQHy4RqY+B2lFACgwSopt2nj/pyK1VCJmdp2MKfKHe+crBZ1jPBXn+ZB6hcXpPim/nJ15kweAABo2A7nHNeqvSdO5GUq60+ryYN/X03e5/ciKsyP1eQ4NUopAECDYRgVZ/JOvCVvbXL2SbcNbhbs9ftKqGD1iA3gbnYAAKDByysu05p9WRXX1tybqaRTrCbvERPw+4m8YLUIZTU5zg2lFACgXjuS+8czeVnKLCip8niQt2vlWbw+zYMU7u9hUlIAAADHUFpu16bUY5WrybccqLqa3GqR4iP8K9+S1ymyEavJ8ZdQSgEA6p1fk7K0cNsRrUrM1L6jVc/kebg4qXtMgPr9fnHyVmE+nMkDAAANXm5Rmb7YeFCr9h5VQnK2ikqrriaPDfKqvLlLz9hA+Xmwmhx/H6UUAKBeeXPFPj3z/a7Kz60WqX1Tf/X7fSVU5yh/uTk7mZgQAADAsRzJPa4xbyco6Q8n8wK9/rCaPC5ITVhNjhpAKQUAqBcMw9CMn/bq5SV7JUkjOoZrWLsw9YoNkp8nZ/IAAABOJTWrSNe9/asOHjuuxn7uuqlPtPo2D1arMB9ZrawmR82ilAIA1HmGYeiZ73fqrZXJkqT7h7TU5EHNTU4FAADg2BIzCnT92wlKyytWdKCnPrq5h5o28jQ7FhoQSikAQJ1mtxt69Jvt+jghVZL02D/aaHzfGJNTAQAAOLYdh/N0wzsJyiosVVyItz6+uYdCfN3NjoUGhlIKAFBnldvseuCLrfpq0yFZLNKzI9vrmm6RZscCAABwaJtSj2nsu2uVV1yudk189cH4HgrwcjU7FhogSikAQJ1UWm7XXZ9s0sLtaXKyWvTS1fEa0bGJ2bEAAAAc2q9JWZowZ50KS23qEtVI793UTb7uXH8T5qCUAgDUOcVlNt320QYt3X1Urk5WvXJdJ13cNszsWAAAAA5t2e4M3fLhBpWU29W7WaDeurGrvNyoBWAe/t8HAKhTCkrKNfH99VqTlCV3F6vevKGr+rcINjsWAACAQ1u0PU13zNuoMpuhC1qF6LUxneXu4mR2LDRwlFIAgDoj93iZxr23VptSc+Tt5qx3x3VT95gAs2MBAAA4tK83HdK9n2+RzW5oePvG+s81HeXqbDU7FkApBQCoG7IKSnTDO2u140ie/Dxc9MH47oqP8Dc7FgAAgEObm5Cqf329TYYhjercVM+Nai9nJwopOAZKKQCAw0vPK9aYtxOUmFGgIG9XfTihh1o39jU7FgAAgEN7e2WSnlqwU5J0Q88oPXFZW1mtFpNTAf9DKQUAcGgHsos05u0EpWYXKczXXR9P7KFmwd5mxwIAAHBYhmHolZ8T9eLiPZKkW/rH6qFhrWSxUEjBsVBKAQAcVtLRAo15O0FHcosVGeCpj2/uoYgAT7NjAQAAOCzDMPTcot2avXyfJOmei1rojguaU0jBIVFKAQAc0q60PF3/9lplFpSoWbCXPr65p8L83M2OBQAA4LDsdkNPfPub3l+zX5L0yPDWurlfrMmpgNOjlAIAOJytB3N047trlVNUpjaNffXBhO4K8nYzOxYAAIDDstkNPfjlVn2x4aAsFumpy9tpTI8os2MBZ0QpBQBwKOtSsnXTe+tUUFKujhH+ev+m7vLzdDE7FgAAgMMqs9l196ebtWDrEVkt0otXx+uKTk3NjgWcFaUUAMBhrNx7VBM/WK/iMrt6xATonXHd5O3GP1UAAACnU1xm05S5G/XTzgy5OFk0c3QnDWvf2OxYwDlh0gcAOITFO9I1+eONKrXZNaBFsGZf30Uerk5mxwIAAHBYRaXlmvjBeq1OzJKbs1Wzb+iiQS1DzI4FnDNKKQCA6f675bCmfrpZNruhoW3D9PK1HeXmTCEFAABwOnnFZRr/3jqt339Mnq5OemdsN/VqFmh2LOC8UEoBAEz12boDevCrrTIM6YpOTfT8lR3k7GQ1OxYAAIDDyi4s1dh312rboVz5ujtrzvju6hzZyOxYwHmjlAIAmGbO6mQ9/u0OSdJ1PSL11Ih2slotJqcCAABwXBn5xbr+7QTtSS9QgJerPpzQXW3D/cyOBfwllFIAAFO8tixR0xftliTd3DdG/xreWhYLhRQAAMDpHMo5rjFv/aqUrCKF+rrp45t7qHmIj9mxgL+MUgoAUKsMw9CLP+7RK0sTJUl3XhinqYPjKKQAAADOICWzUGPeTtChnONq2shDc2/uqchAT7NjAX8LpRQAoNYYhqEnv9uh91anSJIeGtZKtw5oZm4oAAAAB7cnPV9j3k7Q0fwSxQZ56aObeyjc38PsWMDfRikFAKgVNruhf83fpk/WHZAk/d+ItrqhV7S5oQAAABzc9kO5uuGdBB0rKlOrMB99OKGHgn3czI4FVAtKKQBAjSuz2XXf51v0zebDslqk6VfG68ouTc2OBQAA4NA27M/WuHfXKb+kXPFN/fT++O7y93Q1OxZQbSilAAA1qqTcpilzN2nxjnQ5Wy16eXQnDe/Q2OxYAAAADu2XxEzd/MF6FZXa1D06QO+M6yofdxezYwHVilIKAFBjjpfaNOnD9Vq5N1Ouzla9PqazLmwdanYsAAAAh/bzrnTd+tFGlZbb1S8uSG/e0FUerk5mxwKqHaUUAKBG5BeXacKc9Vqbki0PFye9Pbar+jQPMjsWAACAQ1uw9Yju+mSTyu2GLmoTqleu6yQ3Zwop1E+UUgCAaldms2v8nHVal3JMPm7Oeu+mbuoaHWB2LAAAAIe2ZGe67pi3UXZDuiw+XC9eHS8XJ6vZsYAaQykFAKh2L/64p6KQcnfWvIk91a6Jn9mRAAAAHNqR3OO69/MtshvSqM5NNf3KDnKyWsyOBdQoKlcAQLVaufeoZi/fJ0maPqoDhRQAAMBZ2OyG7v5ks3KKytSuia+eGdmOQgoNAqUUAKDaZBaU6J7PtkiSrusRqWHtucseAADA2by6NFEJydnydHXSrGs7cw0pNBjnXUqtWLFCl156qcLDw2WxWPT111+ftM/OnTt12WWXyc/PT15eXurWrZtSU1MrHy8uLtbkyZMVGBgob29vjRo1Sunp6X/rhQAAzGW3G7r3sy06ml+iFqHeenR4G7MjAQ6D+QkAcDrrUrI146c9kqT/G9FOMUFeJicCas95l1KFhYWKj4/Xq6++esrH9+3bp759+6pVq1ZatmyZtm7dqkcffVTu7u6V+0ydOlXffvutPv/8cy1fvlyHDx/WyJEj//qrAACY7p1VyVq+56jcnK2adW1nblsM/AHzEwDgVHKKSnXXvE2yG9IVnZpoVJemZkcCapXFMAzjLz/ZYtH8+fN1+eWXV24bPXq0XFxc9OGHH57yObm5uQoODtbcuXN15ZVXSpJ27dql1q1ba82aNerZs+dZv25eXp78/PyUm5srX1/fvxofAFBNth7M0ajXf1GZzdBTl7fT9T2jzI4EVJvqnjvMmp9q4rUAAP46wzB060cb9MNv6YoO9NR3d/aTtxv3IkP9cK4zR7VeU8put2vBggVq0aKFhgwZopCQEPXo0aPKEvUNGzaorKxMgwcPrtzWqlUrRUZGas2aNdUZBwBQC/KLy3THvE0qsxka1i5MY3pEmh0JqFOYnwCgYfooIVU//JYuFyeLZl3bmUIKDVK1llIZGRkqKCjQs88+q6FDh+rHH3/UFVdcoZEjR2r58uWSpLS0NLm6usrf37/Kc0NDQ5WWlnbK45aUlCgvL6/KBwDAfIZh6NGvt2t/VpGa+Hvo2ZEdZLFwpxjgfNTU/CQxQwGAo9qVlqf/+26HJOnBoa3Uvil3K0bDVK1VrN1ulySNGDFCU6dOlSR17NhRv/zyi2bPnq0BAwb8peNOmzZNTzzxRLXlBABUj682HtLXmw/LyWrRy6M7ys/TxexIQJ1TU/OTxAwFAI7oeKlNd8zdpNJyuwa2DNb4PjFmRwJMU60rpYKCguTs7Kw2barecal169aVd48JCwtTaWmpcnJyquyTnp6usLCwUx734YcfVm5ubuXHgQMHqjM2AOAvSDpaoEe/2S5JuvvCOHWNDjA5EVA31dT8JDFDAYAjevK7HdqbUaBgHze9cFW8rFZWmaPhqtZSytXVVd26ddPu3burbN+zZ4+ioiouetulSxe5uLhoyZIllY/v3r1bqamp6tWr1ymP6+bmJl9f3yofAADzlJTbdMe8TSoqtalnbIBuH9Tc7EhAnVVT85PEDAUAjmbB1iOatzZVFos045qOCvJ2MzsSYKrzfvteQUGBEhMTKz9PTk7W5s2bFRAQoMjISN1///265ppr1L9/fw0aNEiLFi3St99+q2XLlkmS/Pz8NGHCBN1zzz0KCAiQr6+v7rjjDvXq1euc7xwDADDXcwt367fDeWrk6aIZ13SSE2f4gDNifgIAHMgu0kNfbZUk3Tqgmfo0DzI5EWA+i2EYxvk8YdmyZRo0aNBJ28eOHas5c+ZIkt59911NmzZNBw8eVMuWLfXEE09oxIgRlfsWFxfr3nvv1bx581RSUqIhQ4botddeO+Py8z/idsYAYJ6fd6Vr/Jz1kqS3b+yqwW1CTU4E1KzqmDscYX6qrtcCADh/ZTa7rnljjTam5qhTpL8+u6WXXJyq9Y1LgEM515njvEspR8BABQDmSM8r1rCXVyq7sFTjekfr8cvamh0JqHH1ae6oT68FAOqS53/YpVeX7pOPm7O+v6ufIgI8zY4E1KhznTmoZgEA58RmN3T3J5uVXViqNo199fAlrcyOBAAA4PB+SczUa8v2SZKmjWpPIQX8AaUUAOCcvL4sUWuSsuTp6qRZ13WSm7OT2ZEAAAAcWlZBie7+dLMMQxrdLUL/6BBudiTAoVBKAQDOasP+bP3np72SpCcua6tmwd4mJwIAAHBshmHovs+3KCO/RM1DvPXvS7nsAfBnlFIAgDPKPV6mO+dtls1uaETHcF3ZpanZkQAAABzeu6tTtHT3Ubk6W/XKdZ3k4coqc+DPKKUAAKdlGIYe/mqrDuUcV2SAp566vJ0sFovZsQAAABza9kO5enbhTknSo8Nbq1UYN5cAToVSCgBwWvPWHtD329LkbLVo5rWd5OPuYnYkAAAAh1ZQUq475m1Smc3QxW1CdX3PKLMjAQ6LUgoAcEp70vP1xLe/SZLuH9JSHSP8zQ0EAABQBzz2zXYlZxaqsZ+7pl/ZgVXmwBlQSgEATlJcZtOUuRtVUm5X/xbBmtgv1uxIAAAADm/+poP6auMhWS3Sy6M7yd/T1exIgEOjlAIAnOT/vtuhPekFCvJ204tXxctq5QwfAADAmSRnFuqR+dslSXdeGKfuMQEmJwIcH6UUAKCKhduO6OOEVEnSS1fHK9jHzeREAAAAjq203K47521SYalN3WMCdMcFcWZHAuoESikAQKVDOcf14JdbJUm3DIhV/xbBJicCAABwfM//sEvbDuXK39NFL4/uKCdWmQPnhFIKACBJKrfZdde8TcorLld8hL/uu7il2ZEAAAAc3tLdGXprZbIkafqoDmrs52FyIqDuoJQCAEiSZi7Zq/X7j8nbzVmzRneSixP/RAAAAJxJRl6x7vtsiyRpbK8oXdw2zOREQN3CbxwAAK3Zl6VZSxMlSU9f0U6RgZ4mJwIAAHBsdruhez7boqzCUrUK89HDl7Q2OxJQ51BKAUADl11Yqrs/3STDkK7q0lQjOjYxOxIAAIDDm71in1YlZsrDxUmvXNdJ7i5OZkcC6hxKKQBowAzD0ANfbFF6Xolig730xIi2ZkcCAABweBtTj+nFH/dIkh6/rI2ah/iYnAiomyilAKABm/NLin7amSFXJ6tmXdtJnq7OZkcCAABwaLnHy3TnvE2y2Q39o0NjXd01wuxIQJ1FKQUADdT2Q7ma9v0uSdI/L2mltuF+JicCAABwbIZh6J/zt+ngseOKCPDQMyPby2KxmB0LqLMopQCgASosKded8zap1GbX4NahGts72uxIAAAADu+z9Qe0YOsROVstmjm6k3zdXcyOBNRplFIA0AA9/t/flJRZqDBfdz1/ZQfO8AEAAJxFYka+/v3f3yRJ917cUp0iG5mcCKj7KKUAoIH5ZvMhfb7hoCwWacbojmrk5Wp2JAAAAIdWXGbTlLmbVFxmV9/mQbqlf6zZkYB6gVIKABqQ/VmF+tf87ZKkOwY1V8/YQJMTAQAAOL5nvt+pXWn5CvRy1UtXx8tqZZU5UB0opQCggSgtt+vOeZtUUFKubtGNdOeFcWZHAgAAcHg//JamD9bslyS9eHW8QnzdTU4E1B+UUgDQQLz4425tOZgrPw8XzRjdSc5O/BMAAABwJodzjuuBL7ZKkib2i9HAliEmJwLqF34jAYAGYPmeo3pjRZIk6blRHdTE38PkRAAAAI6t3GbX3Z9sVu7xMnVo6qf7h7QyOxJQ71BKAUA9l5FfrHs/2yxJur5npIa2CzM3EAAAQB0w6+dErU3Jlperk2aO7iRXZ359Bqobf6sAoB6z2w3d+9kWZRaUqlWYjx4Z3sbsSAAAAA4vISlLs37eK0l6+or2ig7yMjkRUD85mx0AAFAzDmQX6aXFe7Ryb6bcXayadW0nubs4mR0LAADAYZXb7Ppu6xE9/f1O2Q1pVOemurxTE7NjAfUWpRQA1DPJmYV6dWmi5m86JJvdkCQ9cVlbxYX6mJwMAADAMZXZ7Jq/6ZBeW5qolKwiSVLzEG89OaKtycmA+o1SCgDqib3p+XplaaK+3XJYv3dR6hcXpDsvjFO36ABzwwEAADigknKbvtxwSK8tS9TBY8clSY08XTShb4zG9o6Wlxu/MgM1ib9hAFDH7TySp1d+TtT324/I+L2MurBViKZc0FydIhuZGw4AAMABFZfZ9Om6A5q9fJ+O5BZLkoK8XTWxX6yu7xlFGQXUEv6mAUAdte1grmb+vFeLd6RXbhvSNlR3XBCndk38TEwGAADgmI6X2vRxwn69uSJJGfklkqRQXzfd0r+Zru0eKQ9Xrr8J1CZKKQCoYzamHtOsJXu1dPdRSZLFIg1v31hTLmiuVmG+JqcDAABwPAUl5fpwzX69vTJJWYWlkqRwP3fdNrCZruoawc1gAJNQSgFAHVFxa+JErUrMlCRZLdKIjk00eVAzNQ/hIuYAAAB/lnu8TO//kqJ3Vycrp6hMkhQR4KHJA5trZOemcnW2mpwQaNgopQDAgRmGoV/2ZenlJXu1NjlbkuRstWhk5ya6fWBzRQd5mZwQAADA8eQUlerdVcl675cU5ReXS5Jig7x0+6DmGtExXC5OlFGAI6CUAgAHZBiGlu05qllL9mpjao4kycXJoqu6Rui2Ac0UEeBpbkAAAAAHlFVQordXJeuDX1JUWGqTJMWFeGvKBc31jw7hcrJaTE4I4I8opQDAgRiGocU70vXK0kRtPZgrSXJztura7pG6ZUCsGvt5mJwQAADA8WTkFevNFUn6OCFVx8sqyqjWjX11xwXNNbRtmKyUUYBDopQCAAdgtxta9FuaZv2cqJ1H8iRJHi5Our5npCb2j1WIj7vJCQEAABzPkdzjmr1sn+atO6DScrskqUNTP91xQZwGtw6RxUIZBTgySikAMJHNbui7rYf1ys+J2ptRIEnycnXSjb2jdXPfGAV6u5mcEAAAwPEcyC7S68v36Yv1B1VqqyijOkf6684L4zSgRTBlFFBHnPfV3VasWKFLL71U4eHhslgs+vrrr0+776233iqLxaIZM2ZU2Z6dna0xY8bI19dX/v7+mjBhggoKCs43CgDUWWU2u77YcFAXvbRcd32yWXszCuTj7qw7L4zT6ocu0INDW1FIAfUI8xMAVI+UzELd//kWDXphmeYmpKrUZlePmAB9fHMPfXlbbw1syeoooC4575VShYWFio+P1/jx4zVy5MjT7jd//nz9+uuvCg8PP+mxMWPG6MiRI1q8eLHKysp00003adKkSZo7d+75xgGAOqW03K4vNx7Ua8sSdSD7uCTJ39NFE/rEaGyfaPm6u5icEEBNYH4CgL8nMaNAry5N1DebD8luVGzrFxekOy6IU/eYAHPDAfjLzruUGjZsmIYNG3bGfQ4dOqQ77rhDP/zwg4YPH17lsZ07d2rRokVat26dunbtKkmaNWuWLrnkEr3wwgunHMIAoK4rLrPp8/UH9PqyfTqcWyxJCvRy1cT+sbq+Z5S83Xg3NVCfMT8BwF+zKy1Ps35O1Pfbjsj4vYwa1DJYd1wYp86RjcwNB+Bvq/bfgux2u2644Qbdf//9atu27UmPr1mzRv7+/pUDlSQNHjxYVqtVCQkJuuKKK6o7EgDUmuIym1Kzi5SSWajU7CLtzyrS/uwi/XYoV1mFpZKkEB83Teofq+t6RMrTlTIKAPMTgIbNMAxl5JdUzE1ZFTNUSlbFPLXtUG7lfhe3CdUdF8SpfVM/E9MCqE7V/tvQc889J2dnZ915552nfDwtLU0hISFVQzg7KyAgQGlpaad8TklJiUpKSio/z8vLq77AAHCecovKtD+7UClZRUrNKqwsnvZnFSo9r+S0z2vs567bBjbT1V0j5O7iVIuJATi6mpifJGYoAI6j3GbXoZzj/5ubMgu1P7tIqVlFSs0u0vEy2ymfZ7FIl7RrrCkXNFfrxr61nBpATavWUmrDhg16+eWXtXHjxmq9uNy0adP0xBNPVNvxAOBM/ni2LiWrUKl/KJ32ZxUp93jZGZ/v4+6s6EAvRQZ6KirAU9GBXooK9FSnyEZydT7v+0sAqOdqan6SmKEA1K7jpbbfV4qfWO1UMTulZhfp0LHjKj9xMahTsFqkJo08KmaoAE9FBXoqMsBLbcN9FRHgWYuvAkBtqtZSauXKlcrIyFBkZGTlNpvNpnvvvVczZsxQSkqKwsLClJGRUeV55eXlys7OVlhY2CmP+/DDD+uee+6p/DwvL08RERHVGR1AA1Nms+twzvFTrnZKzS5ScZn9jM8P8XGrHJaiAj1///BSVICn/D1duOsLgHNWU/OTxAwFoPrlFJVWzk2pWSdWjhdpf/aZV4xLkpuztbJwivr9pF3k7yfwmjTykIsTJ++AhqZaS6kbbrhBgwcPrrJtyJAhuuGGG3TTTTdJknr16qWcnBxt2LBBXbp0kST9/PPPstvt6tGjxymP6+bmJjc3bo0O4K/LLCjRu6uSte1QrvZnFelQznHZzvNs3R+HJ64FBaC61NT8JDFDAfh7DMPQTzsz9O2Ww5Wrns5nxXh0oKeiAk78by+F+LjJauXEHYD/Oe/fqgoKCpSYmFj5eXJysjZv3qyAgABFRkYqMDCwyv4uLi4KCwtTy5YtJUmtW7fW0KFDNXHiRM2ePVtlZWWaMmWKRo8ezZ1jAFS7wpJyvb0yWW+u2KfC0qrXKvjf2br/rXbibB2AmsD8BKCu2bA/W88u3KV1KcdOeuyPK8ajAz0rLlnAinEAf8F5l1Lr16/XoEGDKj8/sSR87NixmjNnzjkd4+OPP9aUKVN04YUXymq1atSoUZo5c+b5RgGA0yqz2fXJ2lS9vGSvMgsq7nrXvomfxvSIVHSQF2frANQq5icAdUViRr6mL9qtH3ekS6o4iXdDzyh1iwlgxTiAamcxDOP0719xUHl5efLz81Nubq58fbkDA4D/MQxD329L0/M/7FJKVpEkKSrQU/cPaalL2jWmhAJw3urT3FGfXguA6pWeV6wZP+3Rp+sOyG5UXMrgqi4RmnpRC4X5uZsdD0Adc64zBxU3gHpjzb4sPbtwp7YczJUkBXq56q7BcRrdLZK73gEAAJxCXnGZ3li+T++sSq680ctFbUL1wJCWigv1MTkdgPqOUgpAnbfzSJ6eW7RLy3YflSR5ujppYr9YTewfK283fswBAAD8WUm5TR+u2a9XliYqp6ji4uVdohrpoWGt1C06wOR0ABoKflsDUGcdPFakl37co/mbD8kwJGerRdf1iNQdF8Qp2Ie7TQEAAPyZ3W7omy2H9MIPe3Qo57gkqVmwlx4c2koXtQnlIuUAahWlFIA651hhqV5dmqgP1uxXqa1imfnwDo1138UtFRPkZXI6AAAAx2MYhlbszdSzC3dp55E8SVKor5umDm6hK7s0lTN3HQZgAkopAHXG8VKb3vslWa8v26f84nJJUq/YQD00rJXiI/zNDQcAAOCgth7M0bMLd+mXfVmSJB83Z906sJnG94mRh6uTyekANGSUUgAcXrnNri83HtR/Fu9VWl6xJKlVmI8eGtZKA1oEs8wcAADgFFIyC/X8j7u1YOsRSZKrk1U39orS5EHN1cjL1eR0AEApBcCBGYahn3ZmaPqiXdqbUSBJauLvoXsvbqHLOzaR1UoZBQAA8GeZBSWauWSv5iakqtxuyGKRrujYRPdc3EJNG3maHQ8AKlFKAXBI61Oy9ezCXVq//5gkyd/TRVMGNdf1PaPk7sIycwAAgD8rKCnX2yuT9NaKJBWW2iRJA1oE68GhrdQm3NfkdABwMkopAA4lMSNfzy3arcU70iVJ7i5Wje8To1sGNJOfh4vJ6QAAABxPmc2uT9am6uUle5VZUCpJ6tDUTw8NbaXezYNMTgcAp0cpBcAhpOUWa8ZPe/TZ+gOyG5LVIl3dNUJ3D26hMD93s+MBAAA4HMMw9P22ND3/wy6lZBVJkqICPXX/kJYa3r4x190E4PAopQCYKvd4md5Yvk/vrk5WcZldknRxm1A9MLSlmof4mJwOAADAMf2yL1PPLdylLQdzJUlB3q6668I4je4eKRcnq8npAODcUEoBMEVJuU0frtmvV5YmKqeoTJLUJaqRHh7WSl2jA0xOBwAA4Jh2HsnTswt3afmeo5IkT1cnTeofq4n9YuXlxq93AOoWfmoBqFV2u6FvthzSCz/s0aGc45Kk5iHeenBoKw1uHcIycwAAgFM4eKxIL/24R/M3H5JhSM5Wi67rEak7LohTsI+b2fEA4C+hlAJQawzD0M0frNfPuzIkSaG+brrnohYa1bmpnFlmDgAAcEprk7N1/TsJKi2vuNTBPzo01n0Xt1R0kJfJyQDg76GUAlBrViVm6uddGXJ1turuwXG6qXeMPFydzI4FAADgsAzD0LMLd6q03K4uUY302D/aKD7C3+xYAFAtKKUA1JpXlyZKkq7rHqnbBzY3OQ0AAIDjS0jO1sbUHLk6W/X6mM4K8eWuxADqD94vA6BWbNh/TL8mZcvZatGk/rFmxwEAAKgTTpzUu6pLUwopAPUOpRSAWvH6soqBamTnJgr39zA5DQAAgOPbdjBXK/dmyslq0S39m5kdBwCqHaUUgBq380ieftqZIYtFumUAAxUAAMC5eO33k3qXdmisyEBPk9MAQPWjlAJQ415ftk+SdEm7xmoW7G1yGgAAAMeXmFGgRb+lSZJu41qcAOopSikANWp/VqG+23pYknTbQFZJAQAAnIvZy/fJMKTBrUPVMszH7DgAUCMopQDUqNnLk2Q3pAEtgtWuiZ/ZcQAAABzeoZzj+nrTIUnS7YM4qQeg/qKUAlBj0vOK9eWGg5KkyYNYdg4AAHAu3lqRpHK7od7NAtU5spHZcQCgxlBKAagxb69MUqnNrq5RjdQ9JsDsOAAAAA4vs6BE89amSpJu51pSAOo5SikANeJYYak+TqgYqFglBQAAcG7eXZWsknK74pv6qU/zQLPjAECNopQCUCPeX5OiolKbWjf21cCWwWbHAQAAcHh5xWX6cM1+SdLtg5rLYrGYnAgAahalFIBqV1BSrvdWp0iSbh/YjIEKAADgHHy4Zr/yS8oVF+Kti1qHmh0HAGocpRSAajcvIVW5x8sUHeipS9o3NjsOAACAwzteatO7q5IlSbcNbCarlZN6AOo/SikA1aqk3Ka3ViZJqhionBioAAAAzuqz9QeUVViqpo08dGl8uNlxAKBWUEoBqFZfbjikjPwShfm664pOTc2OAwAA4PDKbHa9uaLipN4t/WPl4sSvaQAaBn7aAag25Ta73lixT5I0sX+sXJ35EQMAAHA232w+rEM5xxXk7aarukaYHQcAag2/MQKoNgu2HdH+rCI18nTRtd0ZqAAAAM7GZjf02rJESdKEvjFyd3EyOREA1B5KKQDVwjAMvb6sYpXUTX1i5OnqbHIiAAAAx/fjb2lKOlooH3dnXd8z0uw4AFCrKKUAVIufd2VoV1q+vFydNLZXtNlxAAAAHJ5hGHrt95N643pHy8fdxeREAFC7KKUA/G2GYejVpRXLzq/vGSU/TwYqAACAs1m5N1PbDuXK3cWqcb2jzY4DALWOUgrA35aQnK2NqTlydbZqQt8Ys+MAAADUCSeuJXVt90gFeruZnAYAah+lFIC/7cQqqau7NlWIr7vJaQAAABzfhv3Z+jUpWy5OFk3sF2t2HAAwBaUUgL9l28FcrdybKSerRbf0b2Z2HAAAgDrhtaUV15K6olMThft7mJwGAMxBKQXgbzmx7Pyy+HBFBHianAYAAMDx7TySpyW7MmSxSLcO4KQegIbrvEupFStW6NJLL1V4eLgsFou+/vrrysfKysr04IMPqn379vLy8lJ4eLhuvPFGHT58uMoxsrOzNWbMGPn6+srf318TJkxQQUHB334xAGpXYka+Fv2WJkm6bSADFQCcDvMTgD96/fc77l3SrrFig71NTgMA5jnvUqqwsFDx8fF69dVXT3qsqKhIGzdu1KOPPqqNGzfqq6++0u7du3XZZZdV2W/MmDH67bfftHjxYn333XdasWKFJk2a9NdfBQBTvL4sSYYhXdQmVC1CfcyOAwAOi/kJwAkpmYX6bmtF6cxJPQANncUwDOMvP9li0fz583X55Zefdp9169ape/fu2r9/vyIjI7Vz5061adNG69atU9euXSVJixYt0iWXXKKDBw8qPDz8rF83Ly9Pfn5+ys3Nla+v71+ND+BvOHisSAOfX6Zyu6H5t/dWp8hGZkcCgBpR3XOHWfNTTbwWAOfv4a+2ad7aVA1sGaw5N3U3Ow4A1IhznTlq/JpSubm5slgs8vf3lyStWbNG/v7+lQOVJA0ePFhWq1UJCQk1HQdANXlrRZLK7YZ6NwukkAKAasb8BNRP6XnF+nLDQUnS7QObm5wGAMznXJMHLy4u1oMPPqhrr722shlLS0tTSEhI1RDOzgoICFBaWtopj1NSUqKSkpLKz/Py8mouNICzyiwo0SfrDkiSJg9ioAKA6lRd85PEDAU4mrdXJqnUZle36EbqHhNgdhwAMF2NrZQqKyvT1VdfLcMw9Prrr/+tY02bNk1+fn6VHxEREdWUEsBf8e6qZJWU2xUf4a/ezQLNjgMA9UZ1zk8SMxTgSI4VlurjhFRJ0u2c1AMASTVUSp0YqPbv36/FixdXef9gWFiYMjIyquxfXl6u7OxshYWFnfJ4Dz/8sHJzcys/Dhw4UBOxAZyDvOIyfbhmvyTp9oHNZLFYTE4EAPVDdc9PEjMU4Ejm/JKiolKb2jT21cAWwWbHAQCHUO1v3zsxUO3du1dLly5VYGDVVRS9evVSTk6ONmzYoC5dukiSfv75Z9ntdvXo0eOUx3Rzc5Obm1t1RwXwF3y4Zr/yS8oVF+Kti1qHmh0HAOqFmpifJGYowFEUlJRrzi8pkqTbB3FSDwBOOO9SqqCgQImJiZWfJycna/PmzQoICFDjxo115ZVXauPGjfruu+9ks9kqr3MQEBAgV1dXtW7dWkOHDtXEiRM1e/ZslZWVacqUKRo9evQ53zkGgDmOl9r07qpkSRUDldXKQAUA54L5CWjY5iWkKvd4mWKCvDSsXWOz4wCAw7AYhmGczxOWLVumQYMGnbR97NixevzxxxUTE3PK5y1dulQDBw6UJGVnZ2vKlCn69ttvZbVaNWrUKM2cOVPe3t7nlIHbGQPmmLM6WY9/u0NNG3lo2X0D5exU4zfwBADTVcfc4QjzU3W9FgDnp6Tcpn7PLVVGfomeG9Ve13SLNDsSANS4c505znul1MCBA3WmHutcOq6AgADNnTv3fL80ABOVltv15ookSdItA5pRSAHAeWB+AhquLzccUkZ+iRr7ueuKTk3NjgMADoXfKgGck282H9Lh3GIFebvpqi4MVAAAAGdTbrNr9vJ9kqSb+8XK1ZlfvwDgj/ipCOCsbHZDr1cOVDFyd3EyOREAAIDjW7DtiFKzi9TI00XXdo8wOw4AOBxKKQBn9eNvaUo6Wihfd2eN6cF1EAAAAM7Gbjf02tKKk3rj+8TI07Xab3wOAHUepRSAMzIMQ68uq7hj1Nje0fJxdzE5EQAAgOP7eVeGdqfny8vVSTf2ijY7DgA4JEopAGe0cm+mth/Kk4eLk27qc+q7QwEAAOB//nhS7/peUfLz5KQeAJwKpRSAM3p1acVAdW33SAV4uZqcBgAAwPH9mpStTak5cnW2akJfTuoBwOlQSgE4rQ37s5WQnC0XJ4sm9megAgAAOBev/b5K6uquTRXi425yGgBwXJRSAE7rxMU5R3ZqqsZ+HianAQAAcHxbD+Zo5d5MOVktuqV/M7PjAIBDo5QCcEo7j+Rpya4MWSzSLQNizY4DAABQJ5w4qXdZfLgiAjxNTgMAjo1SCsApvb6sYqC6pH1jxQZ7m5wGAADA8SVm5OuHHWmSpNsGskoKAM6GUgrASVIyC/Xd1sOSpNsZqAAAAM7J68uSZBjSxW1C1SLUx+w4AODwKKUAnOSNFftkN6SBLYPVNtzP7DgAAAAO7+CxIn2z+ZAk6fZBzU1OAwB1A6UUgCrScov15YaKgWoyAxUAAMA5eWtFksrthvo0D1THCH+z4wBAnUApBaCKt1cmqdRmV/foAHWLDjA7DgAAgMM7ml+iT9YdkCRNHshJPQA4V5RSACodKyzV3LWpkqTbBnEtKQAAgHPx7upklZTbFR/hr17NAs2OAwB1BqUUgEpzfklRUalNbRr7amCLYLPjAAAAOLzc42X6aM1+SdLkgc1ksVhMTgQAdQelFABJUkFJueb8kiKp4lpSDFQAAABn99Gv+5VfUq4Wod4a3DrU7DgAUKdQSgGQJM1LSFXu8TLFBnlpaLsws+MAAAA4vOOlNr27KlmSdNvAZrJaOakHAOeDUgqAistsemtlkiTp1gHN5MRABQAAcFafrktVVmGpmjby0KUdws2OAwB1DqUUAH258aAy8kvU2M9dl3dqYnYcAAAAh1dabtebKypO6t0yoJmcnfjVCgDOFz85gQau3GbXG8srBqqJ/WLl6syPBQAAgLP5ZvMhHc4tVpC3m67q0tTsOABQJ/HbJ9DALdh2RKnZRQrwctXo7hFmxwEAAHB4Nruh15fvkyRN7BcjdxcnkxMBQN1EKQU0YHa7odeWVgxUN/WOlqers8mJAAAAHN8Pv6Up6WihfN2dNaZnlNlxAKDOopQCGrCfd2Vod3q+vN2cdWOvaLPjAAAAODzDMPTaskRJ0rje0fJ246QeAPxVlFJAA2UYhl79faC6vmeU/DxdTE4EAADg+FbszdT2Q3nycHHSuD4xZscBgDqNUgpooH5Nytam1By5Ols1vm+02XEAAADqhNeWVpzUu7Z7pAK8XE1OAwB1G6UU0ECdWHZ+TdcIhfi4m5wGAADA8a1PyVZCcrZcnCya2J9VUgDwd1FKAQ3Q1oM5Wrk3U05Wiyb1jzU7DgAAQJ3w2rKKG8SM7NRUjf08TE4DAHUfpRTQAL38015J0oj4cEUEeJqcBgAAwPFtPZijn3dlyGqRbh3YzOw4AFAvUEoBDcwviZlasitDTlaLJl/Q3Ow4AAAADs8wDD313U5J0oiOTRQT5GVyIgCoHyilgAbEZjf01IKKger6HpFqFuxtciIAAADH98Nv6Vqbki03Z6vuH9LS7DgAUG9QSgENyJcbD2rHkTz5uDvrrsEtzI4DAADg8ErL7Zq2sOKk3qT+sQr351pSAFBdKKWABqKwpFwv/LBbknTnBXHcwhgAAOAcfLAmRfuzihTs46ZbB3AtKQCoTpRSQAPxxookZeSXKDLAUzf2jjI7DgAAgMM7VliqmUsqbhBz70Ut5OXmbHIiAKhfKKWABuBI7nG9uaLiFsYPDWslN2cnkxMBAAA4vpeX7FVecblahfnoqq4RZscBgHqHUgpoAF74YY+Ky+zqGtVIw9qFmR0HAADA4SUdLdBHv+6XJD0yvI2crBaTEwFA/UMpBdRz2w7m6suNByVJj/yjjSwWBioAAICzmbZwl8rthi5oFaK+cUFmxwGAeolSCqjHDMPQUwt2SJJGdAxXxwh/cwMBAADUAb/sy9TiHelyslr0z0tamR0HAOotSimgHvtxR7oSkrPl5mzVA0MZqAAAAM7Gbjf09IKdkqTrukeqeYiPyYkAoP4671JqxYoVuvTSSxUeHi6LxaKvv/66yuOGYeixxx5T48aN5eHhocGDB2vv3r1V9snOztaYMWPk6+srf39/TZgwQQUFBX/rhQCoqrTcrmcX7pIk3dwvRk38PUxOBAANF/MTUHd8temQfjucJx83Z909OM7sOABQr513KVVYWKj4+Hi9+uqrp3x8+vTpmjlzpmbPnq2EhAR5eXlpyJAhKi4urtxnzJgx+u2337R48WJ99913WrFihSZNmvTXXwWAk3z0634lZxYqyNtVtw1sbnYcAGjQmJ+AuqGotFzP/1BxUm/KBc0V6O1mciIAqN8shmEYf/nJFovmz5+vyy+/XFLFWb7w8HDde++9uu+++yRJubm5Cg0N1Zw5czR69Gjt3LlTbdq00bp169S1a1dJ0qJFi3TJJZfo4MGDCg8PP+vXzcvLk5+fn3Jzc+Xr6/tX4wP1Vk5RqQY8v0y5x8v0zBXtdV2PSLMjAUCdVd1zh1nzU028FqC+mfHTHs34aa+aNvLQT/cMkLuLk9mRAKBOOteZo1qvKZWcnKy0tDQNHjy4cpufn5969OihNWvWSJLWrFkjf3//yoFKkgYPHiyr1aqEhIRTHrekpER5eXlVPgCc3swlico9XqaWoT66umtTs+MAAM6gpuYniRkKOB/pecV6Y3mSJOmhYa0opACgFlRrKZWWliZJCg0NrbI9NDS08rG0tDSFhIRUedzZ2VkBAQGV+/zZtGnT5OfnV/kRERFRnbGBeiU5s1Af/poiSfrX8NZyduJ+BgDgyGpqfpKYoYDz8cIPu3W8zKbOkf4a3r6x2XEAoEGoE7+tPvzww8rNza38OHDggNmRAIf17MKdKrMZGtgyWP1bBJsdBwBgImYo4NxsP5SrLzYelCQ98o82slgsJicCgIahWkupsLAwSVJ6enqV7enp6ZWPhYWFKSMjo8rj5eXlys7Ortznz9zc3OTr61vlA8DJfk3K0g+/pctqkf55SWuz4wAAzkFNzU8SMxRwLgzD0NMLdsowpEvjw9U5spHZkQCgwajWUiomJkZhYWFasmRJ5ba8vDwlJCSoV69ekqRevXopJydHGzZsqNzn559/lt1uV48ePaozDtCg2O2GnlqwQ5J0bfdItQj1MTkRAOBcMD8B5vppZ4bWJGXJ1dmqB4a0NDsOADQozuf7hIKCAiUmJlZ+npycrM2bNysgIECRkZG6++679dRTTykuLk4xMTF69NFHFR4eXnmHmdatW2vo0KGaOHGiZs+erbKyMk2ZMkWjR48+5zvHADjZ/E2HtP1QnrzdnDX1ohZmxwEA/AHzE+CYymx2Tft+pyRpQt8YRQR4mpwIABqW8y6l1q9fr0GDBlV+fs8990iSxo4dqzlz5uiBBx5QYWGhJk2apJycHPXt21eLFi2Su7t75XM+/vhjTZkyRRdeeKGsVqtGjRqlmTNnVsPLARqm46U2Pf/DbknS5EHNFeTtZnIiAMAfMT8BjunjX/crKbNQgV6uun1gM7PjAECDYzEMwzA7xPnKy8uTn5+fcnNzuTYCIGnmkr16afEeNfH30JJ7B3ALYwCoRvVp7qhPrwX4u3KLyjTghaXKKSrT01e005geUWZHAoB641xnjjpx9z0Ap5eeV6zXl+2TJD04rBWFFAAAwDmY9fNe5RSVKS7EW9d0jTA7DgA0SJRSQB334o+7dbzMpk6R/rq0Q2Oz4wAAADi8lMxCvb8mRZL0r+Gt5ezEr0UAYAZ++gJ12I7Defp8w0FJ0iPD28hisZicCAAAwPE9t2iXymyG+rcI1sCWIWbHAYAGi1IKqKMMw9BTC3bIMKR/dGisLlGNzI4EAADg8NYmZ2vh9jRZLdK/LmltdhwAaNAopYA66uddGfplX5Zcnax6cGgrs+MAAAA4PLu94qSeJF3TLVItw3xMTgQADRulFFAHldnsevr7nZKkm/pGKyLA0+REAAAAju+bLYe09WCuvFyddM9FLcyOAwANHqUUUAfNTUhV0tFCBXi5avKg5mbHAQAAcHjHS22avmi3JOn2Qc0V7ONmciIAAKUUUMfkHi/TjJ/2SJKmXtRCvu4uJicCAABwfO+sStKR3GI18ffQhL4xZscBAIhSCqhzXl2aqGNFZWoe4q1ru0WYHQcAAMDhZeQX67Vl+yRJDwxtKXcXJ5MTAQAkSimgTtmfVag5q1MkVdwtxtmJv8IAAABn89KPe1RUalN8hL8u7RBudhwAwO/4jRaoQ55btEulNrv6xQVpYMtgs+MAAAA4vJ1H8vTp+gOSpEeHt5bVajE5EQDgBEopoI5Yn5Kt77elyWqR/jW8tSwWBioAAIAzMQxDTy/YKcOQhrdvrK7RAWZHAgD8AaUUUAfY7Yb+b8FOSdLVXSPUKszX5EQAAACOb9nuo1qVmClXJ6seHNrK7DgAgD+hlALqgG+3HtaWAznydHXSPRe3MDsOAACAwyuz2fXUgh2SpHF9ohUZ6GlyIgDAn1FKAQ6uuMym5xbukiTdPrCZQnzcTU4EAADg+D5Zm6p9RwvVyNNFkwc1NzsOAOAUKKUAB/fOqmQdzi1WuJ+7bu4Xa3YcAAAAh5dXXKb//LRXkjT1ohby83AxOREA4FQopQAHdjS/RK8tTZQk3T+0pdxdnExOBAAA4PheXZqo7MJSxQZ76drukWbHAQCcBqUU4MBeWrxHhaU2dWjqpxHxTcyOAwAA4PAOZBfpvVUpkqR/XdJaLk78ygMAjoqf0ICD2pWWp0/XpUqSHhneRlarxeREAAAAju/ZRbtUarOrT/NAXdAqxOw4AIAzoJQCHNTTC3bKbkjD2oWpe0yA2XEAAAAc3ob92Vqw9YgsFulfl7SRxcJJPQBwZJRSgANatjtDK/dmysXJooeGtTI7DgAAgMMzDEP/991OSdJVXZqqTbivyYkAAGdDKQU4mHKbXU8vqBioxvaKVlSgl8mJAAAAHN+3W49o84Ecebo66d6LW5odBwBwDiilAAfzyboD2ptRIH9PF91xQZzZcQAAABxecZlNzy3cJUm6dUAzhfq6m5wIAHAuKKUAB5JfXKb/LN4jSbr7wjj5ebqYnAgAAMDxvbs6WYdyjivM110T+8WaHQcAcI4opQAH8tqyfcoqLFVskJfG9IwyOw4AAIDDyywo0WtL90mS7h/SUh6uTiYnAgCcK0opwEEcyC7SO6uSJUkPX9JaLk789QQAADib/yzeo4KScrVr4qsrOjUxOw4A4DzwWy/gIKb/sFul5Xb1ig3U4NYhZscBAABweHvS8zVvbaok6ZHhbWS1WkxOBAA4H5RSgAPYmHpM3245LItF+tfw1rJYGKgAAADO5ukFO2U3pCFtQ9UzNtDsOACA80QpBZjMMAw99d0OSdKVnZuqXRM/kxMBAAA4vuV7jmr5nqNycbLooWGtzY4DAPgLKKUAky3YdkQbU3Pk4eKk+4a0NDsOAACAwyu32fX0goqTejf0jFZMkJfJiQAAfwWlFGCi4jKbnl24S5J0y4BYhfq6m5wIAADA8X22/qD2pBfIz8NFd17Y3Ow4AIC/iFIKMNGcX1J08Nhxhfq6aVL/WLPjAAAAOLz84jK9tHi3JOmuC+Pk7+lqciIAwF9FKQWYJLOgRK/+nChJun9IK3m6OpucCAAAwPG9vmyfMgtKFRPkpet7RpkdBwDwN1BKASYoLrPp9o82Kr+kXG3DfTWyUxOzIwEAADi8xTvSNXv5PknSQ8NaydWZX2cAoC7jpzhQy8ptdt0xb5PWpmTLx81ZL1wVL6vVYnYsAAAAh7Y2OVtT5m6U3ZCu7NJUF7cJNTsSAOBvopQCapFhGPrX/O1avCNdrs5WvTW2q1o39jU7FgAAgEPbeSRPE95fp5Jyuy5sFaJnR7aXxcJJPQCo6yilgFr0/A+79en6A7JapFnXdlLP2ECzIwEAADi0A9lFGvvuWuUXl6trVCO9cl1nOTvxawwA1Af8NAdqyburkvXasoprIDxzRXsNaRtmciIAAADHlllQohvfXauM/BK1DPXRO2O7ycPVyexYAIBqQikF1IKvNx3Sk9/tkCTdP6SlRnePNDkRAACAYysoKddN761Tcmahmvh76P3x3eXn6WJ2LABANar2Uspms+nRRx9VTEyMPDw81KxZM/3f//2fDMOo3McwDD322GNq3LixPDw8NHjwYO3du7e6owAOYdnuDN33+RZJ0rje0bp9YDOTEwEAHA3zE1BVSblNt3y4XtsO5SrAy1UfTuiuMD93s2MBAKpZtZdSzz33nF5//XW98sor2rlzp5577jlNnz5ds2bNqtxn+vTpmjlzpmbPnq2EhAR5eXlpyJAhKi4uru44gKk2pR7TbR9tVLnd0GXx4XrsH224KCcA4CTMT8D/2OyG7vlsi1YnZsnT1Unvjeum2GBvs2MBAGqAc3Uf8JdfftGIESM0fPhwSVJ0dLTmzZuntWvXSqo4yzdjxgw98sgjGjFihCTpgw8+UGhoqL7++muNHj26uiMBpkjMyNf4Oet0vMymfnFBeuGqeFmtFFIAgJMxPwEVDMPQE9/+pgVbj8jFyaI3buii+Ah/s2MBAGpIta+U6t27t5YsWaI9e/ZIkrZs2aJVq1Zp2LBhkqTk5GSlpaVp8ODBlc/x8/NTjx49tGbNmlMes6SkRHl5eVU+AEd2OOe4bnxnrY4VlSk+wl+zr+8iV2cu4QYAOLWamJ8kZijUPTOXJOqDNftlsUgvXd1R/eKCzY4EAKhB1b5S6qGHHlJeXp5atWolJycn2Ww2Pf300xozZowkKS0tTZIUGhpa5XmhoaGVj/3ZtGnT9MQTT1R3VKBGHCss1Y3vrtXh3GLFBnvpvXHd5OVW7X/VAAD1SE3MTxIzFOqWj37dr//8VFHMPn5pW10aH25yIgBATav2pRufffaZPv74Y82dO1cbN27U+++/rxdeeEHvv//+Xz7mww8/rNzc3MqPAwcOVGNioPoUlZZr/PvrlJhRoDBfd304oYcCvFzNjgUAcHA1MT9JzFCoO77fdkSPfrNdknTnBc01tne0uYEAALWi2pdv3H///XrooYcqr23Qvn177d+/X9OmTdPYsWMVFhYmSUpPT1fjxo0rn5eenq6OHTue8phubm5yc3Or7qhAtSqz2XX7xxu1KTVHfh4u+mBCdzXx9zA7FgCgDqiJ+UlihkLd8Etipu7+ZLMMQ7q2e6SmXtTC7EgAgFpS7SulioqKZLVWPayTk5PsdrskKSYmRmFhYVqyZEnl43l5eUpISFCvXr2qOw5QK+x2Qw98sVXLdh+Vu4tV747rqhahPmbHAgDUEcxPaKi2H8rVpA83qNRm19C2YXrq8nbcqRgAGpBqXyl16aWX6umnn1ZkZKTatm2rTZs26aWXXtL48eMlSRaLRXfffbeeeuopxcXFKSYmRo8++qjCw8N1+eWXV3ccoMYZhqFnvt+p+ZsOyclq0WtjOqtLVIDZsQAAdQjzExqilMxCjXtvrQpKytUzNkAzRneUE3cqBoAGpdpLqVmzZunRRx/V7bffroyMDIWHh+uWW27RY489VrnPAw88oMLCQk2aNEk5OTnq27evFi1aJHd39+qOA9S4N1Yk6e1VyZKk6aM66IJWoWd5BgAAVTE/oaHJyCvWDe8mKLOgVG3DffXWjV3l7uJkdiwAQC2zGIZhmB3ifOXl5cnPz0+5ubny9fU1Ow4asM/WH9ADX2yVJP3rktaa2D/W5EQAgOpWn+aO+vRaUHflHi/T6Dd/1c4jeYoK9NQXt/ZWsA/XPgOA+uRcZ45qv6YU0FD8tCNdD3+1TZJ0S/9YCikAAICzKC6zaeIH67XzSJ6CvN304fgeFFIA0IBRSgF/wbqUbE2eu1E2u6EruzTVQ8NamR0JAADAoZXb7Lpz3iatTc6Wj5uz3h/fTZGBnmbHAgCYiFIKOE+70vI0Yc46lZTbdWGrED07sj13iQEAADgDwzD0yNfb9eOOdLk6W/XW2K5qG+5ndiwAgMkopYDzcCC7SDe+s1Z5xeXqGtVIr1zXWc5O/DUCAAA4kxd+3K1P1h2Q1SLNHN1JPWMDzY4EAHAA/DYNnKOsghKNfXetMvJL1DLUR++M7SYPV+4SAwAAcCbvrU7Wq0v3SZKevqK9hrYLMzkRAMBRUEoB56CgpFw3zVmnpMxCNfH30Pvju8vP08XsWAAAAA7tm82H9MS3OyRJ913cQtd2jzQ5EQDAkVBKAWdRUm7TrR9u0NaDuQrwctUHE7orzM/d7FgAAAAObfmeo7r3sy2SpHG9ozV5UHOTEwEAHA2lFHAGdruhez/bolWJmfJ0ddJ747qpWbC32bEAAAAc2uYDObrtow0qtxu6LD5cj/2jDTeGAQCchFIKOA3DMPTEt7/pu61H5OJk0Rs3dFF8hL/ZsQAAABxaYkaBbnpvrYpKbeoXF6QXroqX1UohBQA4GaUUcBqzfk7U+2v2y2KRXrq6o/rFBZsdCQAAwKEdyT2uG99J0LGiMsVH+Gv29V3k6syvHACAU+NfCOAUPk7Yr5cW75EkPX5pW10aH25yIgAAAMeWU1SqG99Zq8O5xYoN9tJ747rJy83Z7FgAAAdGKQX8ycJtR/TI19slSXde0Fxje0ebGwgAAMDBHS+1afycddqbUaAwX3d9ML67ArxczY4FAHBwlFLAH/yyL1N3fbJZhiFd2z1SUy9qYXYkAAAAh1Zms+v2jzdoY2qO/Dxc9MGE7mrayNPsWACAOoBSCvjd9kO5mvTBBpXa7BraNkxPXd6Ou8QAAACcgd1u6MEvtmrp7qNyd7Hq3XFd1SLUx+xYAIA6glIKkJSSWahx761VQUm5esYGaMbojnLiLjEAAABnNG3hTn216ZCcrBa9NqazukQFmB0JAFCHUEqhwcvIL9aN765VZkGp2jT21Vs3dpW7i5PZsQAAABzaG8v36a2VyZKk6aM66IJWoSYnAgDUNdwOAw1aalaRJn24XqnZRYoM8NSc8d3k4+5idiwAAACHZbcbend1sqYt3CVJ+uclrTSqS1OTUwEA6iJKKTRIhmHo44RUPfP9ThWV2hTk7aYPJ3RXiI+72dEAAAAc1sFjRXrgi636ZV+WJGlS/1hN6t/M5FQAgLqKUgoNzuGc43rwy61auTdTktQ9JkAvXhWviADuEgMAAHAqhmHos/UH9H/f7VRBSbk8XJz00LBWurFXlNnRAAB1GKUUGgzDMPTVxkN6/NvflF9cLjdnqx4Y2ko39Y6WlYuaAwAAnFJ6XrEe+rLiDnuS1DWqkV64Kl7RQV4mJwMA1HWUUmgQMvKL9c+vtuunnemSpI4R/nrx6ng1C/Y2ORkAAIBjMgxD/91yWI9985tyj5fJ1dmq+y5uoQl9Y7lLMQCgWlBKod5bsPWIHvl6m44VlcnFyaKpF7XQpH6xcnbi5pMAAACnklVQoke+3q6F29MkSR2a+unFq+IVF+pjcjIAQH1CKYV661hhqR79Zru+23pEktSmsa9euiZercJ8TU4GAADguBZtP6J/zd+urMJSOVstuvPCON02sJlcOKEHAKhmlFKol37aka6HvtqmzIISOVktmjyouaYMai5XZ4YpAACAU8ktKtO//7tdX28+LElqFeajF66KV7smfiYnAwDUV5RSqFfyisv05Lc79MWGg5KkuBBvvXh1vDo09Tc3GAAAgANbujtDD325Vel5JbJapNsGNtOdF8bJzdnJ7GgAgHqMUgr1xsq9R/XAF1t1JLdYFos0qV+spl7UQu4uDFMAAACnkl9cpqcX7NQn6w5IkmKDvfTiVfHqFNnI5GQAgIaAUgp1XmFJuaYt3KmPfk2VJEUHeuqFq+LVNTrA5GQAAACO65d9mbr/8606lHNcFos0vk+M7h/SkhN6AIBaQymFOi0hKUv3f7FVqdlFkqSxvaL04LBW8nTl/9oAAACncrzUpucW7dKcX1IkSREBHnrhynj1iA00NxgAoMHhN3fUScVlNj3/w269uzpZhiE18ffQ81d2UO/mQWZHAwAAcFgb9mfrvs+3KjmzUJI0pkek/nlJa3m58WsBAKD28a8P6pzNB3J0z2eblXS0Ypi6pmuEHvlHa/m4u5icDAAAwDEVl9n0n5/26K0VSbIbUmM/dz03qoP6twg2OxoAoAGjlEKdUVpu18wle/XaskTZDSnEx03PjeqgQa1CzI4GAADgsLYdzNW9n2/WnvQCSdKozk312KVt5OfBCT0AgLkopVAn7Dicp3s+26xdafmSpMs7huvxy9rK39PV5GQAAACOqcxm1ys/J+qVpYmy2Q0Febtp2sj2uqhNqNnRAACQRCkFB1dus2v28n16ecleldkMBXi56unL22lY+8ZmRwMAAHBYu9Pydc9nm/Xb4TxJ0vAOjfV/I9opwIsTegAAx0EpBYeVmJGvez/boi0HcyVJQ9uG6akr2inI283kZAAAAI7JZjf05ook/WfxHpXa7PL3dNH/jWinS+PDzY4GAMBJKKXgcGx2Q++uStbzP+5Wabldvu7OenJEO43oGC6LxWJ2PAAAAIeUdLRA936+RZtScyRJg1uH6JmR7RXi425uMAAAToNSCg5lf1ah7vt8i9alHJMkDWwZrGdHdlCYH8MUAADAqdjthub8kqLpP+xScZldPm7O+vdlbTWqcxNO6AEAHBqlFByC3W7o44T9eub7XTpeZpOXq5Meu7SNru4awTAFAABwGgeyi3T/F1v0a1K2JKlfXJCeG9VB4f4eJicDAODsKKVgurziMt0xd5OW7zkqSeoVG6jpV3ZQRICnyckAAAAc18JtR3Tf51tUWGqTp6uT/nlJa43pEckJPQBAnUEpBVMdPFak8XPWaU96gdxdrHp4WGvd0DNKVivDFAAAwKkYhqG3ViZp2sJdMgype3SAXrgqXpGBnNADANQt1po46KFDh3T99dcrMDBQHh4eat++vdavX1/5uGEYeuyxx9S4cWN5eHho8ODB2rt3b01EgQPbdjBXV7z2i/akFyjEx01f3NpbY3tHU0gBABok5ieci3KbXY9+s13PfF9RSN3YK0pzJ/agkAIA1EnVXkodO3ZMffr0kYuLixYuXKgdO3boxRdfVKNGjSr3mT59umbOnKnZs2crISFBXl5eGjJkiIqLi6s7DhzUTzvSdfUba3Q0v0Stwnz09eQ+atfEz+xYAACYgvkJ56KgpFwTP1ivj35NlcUiPTK8tZ64rK2cnWrkPDMAADXOYhiGUZ0HfOihh7R69WqtXLnylI8bhqHw8HDde++9uu+++yRJubm5Cg0N1Zw5czR69Oizfo28vDz5+fkpNzdXvr6+1RkftWDO6mQ9+d0O2Q2pf4tgvXpdJ/m4u5gdCwCAU6qNuaM25ieJGaouS8st1vg567TjSJ7cXayacU0nDW0XZnYsAABO6Vxnjmo/rfLf//5XXbt21VVXXaWQkBB16tRJb731VuXjycnJSktL0+DBgyu3+fn5qUePHlqzZs0pj1lSUqK8vLwqH6h7bHZDT367Q49/W1FIXds9Qu+M7UohBQBo8GpifpKYoeqLHYfzdPmrq7XjSJ6CvF31yaReFFIAgHqh2kuppKQkvf7664qLi9MPP/yg2267TXfeeafef/99SVJaWpokKTQ0tMrzQkNDKx/7s2nTpsnPz6/yIyIiorpjo4YVlZbr1o826N3VyZKkB4e20jNXtJcLy80BAKiR+UlihqoPlu3O0FWzf1FaXrGah3hr/u191DHC3+xYAABUi2q/+57dblfXrl31zDPPSJI6deqk7du3a/bs2Ro7duxfOubDDz+se+65p/LzvLw8hqo6JCO/WDe/v15bD+bK1dmqF6+K16Xx4WbHAgDAYdTE/CQxQ9V1cxNS9eg322WzG+oVG6jZ13eRnycrzAEA9Ue1L1Np3Lix2rRpU2Vb69atlZqaKkkKC6tYapyenl5ln/T09MrH/szNzU2+vr5VPlA37EnP1xWv/qKtB3PVyNNFc2/uQSEFAMCf1MT8JDFD1VV2u6FpC3fqn/O3yWY3NLJzE70/vjuFFACg3qn2UqpPnz7avXt3lW179uxRVFSUJCkmJkZhYWFasmRJ5eN5eXlKSEhQr169qjsOTLQ6MVOjXv9Fh3KOKybIS/Nv76Ou0QFmxwIAwOEwP+GE4jKb7pi3SW8sT5IkTR3cQi9eFS9XZy55AACof6r97XtTp05V79699cwzz+jqq6/W2rVr9eabb+rNN9+UJFksFt1999166qmnFBcXp5iYGD366KMKDw/X5ZdfXt1xYJLP1x/Qw19tU7ndULfoRnrzhq5q5OVqdiwAABwS8xMkKaugRBM/WK+NqTlycbLouVEdNLJzU7NjAQBQY6q9lOrWrZvmz5+vhx9+WE8++aRiYmI0Y8YMjRkzpnKfBx54QIWFhZo0aZJycnLUt29fLVq0SO7u7tUdB7XMMAy9tHiPZv2cKEm6ND5cz1/ZQe4uTiYnAwDAcTE/Yd/RAt303jqlZhfJ191Zb9zQVb2aBZodCwCAGmUxDMMwO8T5ysvLk5+fn3Jzc7k2ggMpKbfpwS+26uvNhyVJkwc1070XtZTVajE5GQAAf119mjvq02upTxKSsjTpww3KPV6miAAPvTeum5qH+JgdCwCAv+xcZ45qXymFhimnqFSTPtygtcnZcrJa9MwV7XRNt0izYwEAADi0bzYf0v2fb1Wpza6OEf56e2xXBXm7mR0LAIBaQSmFv21/VqFumrNOSUcL5ePmrNeu76x+ccFmxwIAAHBYhmHolZ8T9eLiPZKkoW3D9J9rOsrDlUseAAAaDkop/C0b9h/TxA/WK7uwVOF+7nr3pm5qFcbbAQAAAE6nzGbXP7/aps83HJQkTewXo4eHteaSBwCABodSCn/Z99uOaOqnm1VSble7Jr56Z2w3hfpysVUAAIDTyT1epts/3qDViVmyWqQnLmurG3pFmx0LAABTUErhvBmGoTdXJGnawl2SpMGtQ/Ty6E7ycuP/TgAAAKdz8FiRxs9Zpz3pBfJ0ddIr13XSBa1CzY4FAIBpaBFwXsptdv37v7/p44RUSdK43tF69B9t5MRycwAAgNPaejBHE95fr6P5JQr1ddM7Y7upXRM/s2MBAGAqSimcs4KSck2Zu1HLdh+VxSI9OryNxveNMTsWAACAQ1u8I113ztuk42U2tQrz0Xs3dVNjPw+zYwEAYDpKKZyTtNxi3TRnnXYeyZO7i1Uvj+6kIW3DzI4FAADg0N5bnawnv9shw5D6twjWq9d1ko+7i9mxAABwCJRSOKsdh/M0fs46peUVK8jbVe+M7ab4CH+zYwEAADgsm93QUwt26L3VKZKka7tH6skRbeXiZDU3GAAADoRSCme0dHeGpny8UYWlNjUP8dZ747opIsDT7FgAAAAOq6i0XHd9slmLd6RLkh4a1kq39I+VxcI1OAEA+CNKKZzWxwn79dg3v8lmN9S7WaBev76L/DxYbg4AAHA6GfnFuvn99dp6MFeuzla9dHW8/tEh3OxYAAA4JEopnMRuN/TcD7v0xvIkSdKozk01bWR7uTqz3BwAAOB09qTn66b31ulQznE18nTR22O7qktUgNmxAABwWJRSqKK4zKZ7P9uiBduOSJLuuaiF7rigOcvNAQAAzmB1YqZu/WiD8ovLFRPkpffGdVN0kJfZsQAAcGiUUqiUVVCiiR+s18bUHLk4WTT9yg66olNTs2MBAAA4tM/XH9DDX21Tud1Qt+hGevOGrmrk5Wp2LAAAHB6lFCRJCUlZuuuTzUrLK5afh4veuKGLesYGmh0LAADAYRWX2fTEtzs0b22qJOmy+HBNv7KD3F2cTE4GAEDdQCnVwNnshl75OVEvL9kjuyHFBnvpzRu6qnmIt9nRAAAAHNbe9HxNmbtJu9PzZbFId1wQp7svjJPVyiUPAAA4V5RSDVh6XrHu/mSz1iRlSaq4oPmTI9rKy43/WwAAAJyKYRj6fP1BPfbf7SousyvI200zrumovnFBZkcDAKDOoX1ooJbtztC9n21RVmGpPF2d9NTl7TSyM9ePAgAAOJ384jI98vV2fbP5sCSpX1yQXrq6o4J93ExOBgBA3UQp1cCU2ex64YfdemNFkiSpdWNfvXJdJzUL5u16AAAAp7PtYK7umLdRKVlFcrJadO/FLXRr/2a8XQ8AgL+BUqoBOZBdpDvmbdLmAzmSpLG9ovTwJa25GCcAAMBpGIah91anaNrCnSqzGWri76GZ13ZUl6gAs6MBAFDnUUo1EN9vO6IHv9yq/OJy+bo7a/qV8RraLszsWAAAAA7rWGGp7v9iq37amS5JGtI2VNNHxcvP08XkZAAA1A+UUvVccZlN//fdDn2cUHGr4i5RjfTy6I5q2sjT5GQAAACOa11Ktu6ct0lHcovl6mTVI/9orRt6Rsli4e16AABUF0qpeiwxo0BT5m7UrrSKWxXfNqCZpl7UQi5OVrOjAQAAOCSb3dDryxL1n5/2ymY3FBvkpVnXdVLbcD+zowEAUO9QStVDhmHoiw0H9dg3v+l4mU1B3q76zzUd1S8u2OxoAAAADisjr1hTP9us1YlZkqSRnZro/y5vJy83RmYAAGoC/8LWMwUl5Xpk/jZ9/futivs2D9JL18QrxMfd5GQAAACOa/meo7rn083KKiyVp6uT/m9EO43q0tTsWAAA1GuUUvXI9kO5umPeJiVnFsrJatE9F7XQbQO4VTEAAMDplNnseuHH3XpjeZIkqVWYj14d01nNgr1NTgYAQP1HKVUPGIah939J0TPf71Kpza5wP3fNvLaTukZzq2IAAIDTOZBdpDs/2aRNqTmSpBt6Rulfw1vL3cXJ3GAAADQQlFJ1XE5Rxa2KF++ouFXxRW1C9fyVHeTv6WpyMgAAAMe1aPsRPfDFVuUVl8vH3VnTR3XQsPaNzY4FAECDQilVh63//VbFh3+/VfE/L2mlsb2juVUxAADAaRSX2fT0gp368Nf9kqROkf6aObqTIgI8TU4GAEDDQylVB9nthl5fvk8vLd4jm91QdKCnXrmus9o14VbFAAAAp7PvaIGmzN2knUfyJEm3Dmimey9uIRcnq8nJAABomCil6piM/GLd8+kWrUrMlCRd3jFcT13RXt7cqhgAAOC0vthwUI99s11FpTYFernqpWs6akCLYLNjAQDQoNFk1CEr9x7V1E83K7OgVB4uTnpyRFtd2aUpb9cDAAA4jcKScj369XZ9temQJKl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      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Code used from: https://gymnasium.farama.org/tutorials/blackjack_tutorial/#visualizing-the-training\n",
    "fig, axs = plt.subplots(ncols=2, figsize=(12, 5))\n",
    "axs[0].set_title(\"Episode rewards\")\n",
    "reward_moving_average = (\n",
    "    np.convolve(\n",
    "        np.array(env_returns).mean(axis=1), np.ones(episode_window), mode=\"valid\"\n",
    "    )\n",
    "    / episode_window\n",
    ")\n",
    "axs[0].plot(range(len(reward_moving_average)), reward_moving_average)\n",
    "axs[1].set_title(\"Episode lengths\")\n",
    "length_moving_average = (\n",
    "    np.convolve(\n",
    "        np.array(env_steps).mean(axis=1), np.ones(episode_window), mode=\"valid\"\n",
    "    )\n",
    "    / episode_window\n",
    ")\n",
    "axs[1].plot(range(len(length_moving_average)), length_moving_average)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(ncols=2, figsize=(12, 5))\n",
    "axs[0].set_title(\"Test Returns\")\n",
    "axs[0].plot(range(len(test_returns)), test_returns)\n",
    "axs[1].set_title(\"Test Lengths\")\n",
    "axs[1].plot(range(len(test_steps)), test_steps)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing Videos"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test Episode 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test Episode 0 Return: 20.0\n"
     ]
    }
   ],
   "source": [
    "test_episode = 0\n",
    "print(f\"Test Episode {test_episode} Return: {test_returns[test_episode]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/a2c_discrete_monte-carlo//CartPole-v1-episode-0.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-{test_episode}.mp4\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test Episode 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test Episode 1 Return: 78.0\n"
     ]
    }
   ],
   "source": [
    "test_episode = 1\n",
    "print(f\"Test Episode {test_episode} Return: {test_returns[test_episode]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/a2c_discrete_monte-carlo//CartPole-v1-episode-1.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-{test_episode}.mp4\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test Episode 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test Episode 2 Return: 168.0\n"
     ]
    }
   ],
   "source": [
    "test_episode = 2\n",
    "print(f\"Test Episode {test_episode} Return: {test_returns[test_episode]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/a2c_discrete_monte-carlo//CartPole-v1-episode-2.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-{test_episode}.mp4\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test Episode 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test Episode 3 Return: 161.0\n"
     ]
    }
   ],
   "source": [
    "test_episode = 3\n",
    "print(f\"Test Episode {test_episode} Return: {test_returns[test_episode]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/a2c_discrete_monte-carlo//CartPole-v1-episode-3.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-{test_episode}.mp4\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test Episode 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test Episode 4 Return: 85.0\n"
     ]
    }
   ],
   "source": [
    "test_episode = 4\n",
    "print(f\"Test Episode {test_episode} Return: {test_returns[test_episode]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/a2c_discrete_monte-carlo//CartPole-v1-episode-4.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-{test_episode}.mp4\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test Episode 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test Episode 5 Return: 500.0\n"
     ]
    }
   ],
   "source": [
    "test_episode = 5\n",
    "print(f\"Test Episode {test_episode} Return: {test_returns[test_episode]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/a2c_discrete_monte-carlo//CartPole-v1-episode-5.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-{test_episode}.mp4\")"
   ]
  }
 ],
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