8-2-recurrent-neural-networks.ipynb

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    "# Recurrent Neural Networks (RNN)\n",
    "\n",
    "&copy; 李浩东 haodongli@zju.edu.cn\n",
    "\n",
    "- Sequence Models\n",
    "- Text Preprocessing\n",
    "- Language Models and the Dataset\n",
    "- Recurrent Neural Networks\n"
   ]
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    "$$\n",
    "x_{t} \\sim P\\left(x_{t} \\mid x_{t-1}, \\ldots, x_{1}\\right)\n",
    "$$\n",
    "\n",
    "- Music, speech, text, and videos are all sequential in nature. If we were to permute them they would make little sense. The headline dog bites man is much less surprising than man bites dog, even though the words are identical."
   ]
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    "- In order to achieve this, we could use a regression model.\n",
    "\n",
    "$$\n",
    "x_{t} \\sim P\\left(x_{t} \\mid x_{t-1}, \\ldots, x_{1}\\right) \\sim P\\left(x_{t} \\mid x_{t-1},  x_{t-2},\\ldots, x_{t-\\tau}\\right)\n",
    "$$\n",
    "\n",
    "- Such models will be called autoregressive models, as they quite literally perform regression on themselves."
   ]
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    "- The second strategy, shown in the figure below, is to keep some summary $h_t$ of the past observations, and at the same time update $h_t$ in addition to the prediction $\\hat{x}_{t}$. This leads to models that estimate ${x}_{t}$ with $\\hat{x}_{t}=P\\left(x_{t} \\mid h_{t}\\right)$ and moreover updates of the form $h_{t}=g\\left(h_{t-1}, x_{t-1}\\right)$. Since $h_t$ is never observed, these models are also called latent autoregressive models.\n",
    "\n",
    "![sequence-model.svg](./images/8/sequence-model.svg)\n"
   ]
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    "- Both cases raise the obvious question of how to generate training data. One typically uses historical observations to predict the next observation given the ones up to right now. Obviously we do not expect time to stand still. However, a common assumption is that while the specific values of $x_t$ might change, at least the dynamics of the sequence itself will not. This is reasonable, since novel dynamics are just that, novel and thus not predictable using data that we have so far. Statisticians call dynamics that do not change stationary. Regardless of what we do, we will thus get an estimate of the entire sequence via:\n",
    "\n",
    "$$\n",
    "P\\left(x_{1}, \\ldots, x_{T}\\right)=\\prod_{t=1}^{T} P\\left(x_{t} \\mid x_{t-1}, \\ldots, x_{1}\\right)\n",
    "$$\n",
    "\n",
    "- Note that the above considerations still hold if we deal with discrete objects, such as words, rather than continuous numbers. The only difference is that in such a situation we need to use a classifier rather than a regression model to estimate it."
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    "# Markov Models\n",
    "\n",
    "- Recall the approximation that in an autoregressive model we use only $x_{t-1}, \\ldots, x_{t-\\tau}$ instead of $x_{t-1}, \\ldots, x_{t-1}$ to estimate $x_t$. Whenever this approximation is accurate we say that the sequence satisfies a Markov condition. In particular, if $\\tau=1$, we have a first-order Markov model and $P(x)$ is given by:\n",
    "\n",
    "$$\n",
    "P\\left(x_{1}, \\ldots, x_{T}\\right)=\\prod_{t=1}^{T} P\\left(x_{t} \\mid x_{t-1}\\right) \\text { where } P\\left(x_{1} \\mid x_{0}\\right)=P\\left(x_{1}\\right)\n",
    "$$\n"
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    "- Such models are particularly nice whenever $x_t$ assumes only a discrete value, since in this case dynamic programming can be used to compute values along the chain exactly. For instance, we can compute $P\\left(x_{t+1} \\mid x_{t-1}\\right)$ efficiently:\n",
    " \n",
    "$$\n",
    "\\begin{aligned}\n",
    "P\\left(x_{t+1} \\mid x_{t-1}\\right) &=\\frac{\\sum_{x t} P\\left(x_{t+1}, x_{t}, x_{t-1}\\right)}{P\\left(x_{t-1}\\right)} \\\\\n",
    "&=\\frac{\\sum_{x t} P\\left(x_{t+1} \\mid x_{t}, x_{t-1}\\right) P\\left(x_{t}, x_{t-1}\\right)}{P\\left(x_{t-1}\\right)} \\\\\n",
    "&=\\sum_{x_{t}} P\\left(x_{t+1} \\mid x_{t}\\right) P\\left(x_{t} \\mid x_{t-1}\\right)\n",
    "\\end{aligned}\n",
    "$$\n"
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    "- In fact, if we have a Markov model, we can obtain a reverse conditional probability distribution, too. In many cases, however, there exists a natural direction for the data, namely going forward in time. It is clear that future events cannot influence the past. Hence, if we change $x_t$, we may be able to influence what happens for $x_{t+1}$ going forward but not the converse. That is, if we change $x_t$, the distribution over past events will not change. Consequently, it ought to be easier to explain $P\\left(x_{t+1} \\mid x_{t}\\right) $\n",
    " rather than $P\\left(x_{t} \\mid x_{t+1}\\right) $."
   ]
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  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ed99d5db",
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   "outputs": [
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     "name": "stdout",
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     "text": [
      "1.11.0\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "from torch import nn\n",
    "import matplotlib.pyplot as plt\n",
    "from torch.utils.data import DataLoader\n",
    "import torch.backends.cudnn as cudnn\n",
    "import torch.optim as optim\n",
    "import requests\n",
    "import collections\n",
    "from torch.nn import functional as F\n",
    "import re\n",
    "# import time\n",
    "import math\n",
    "import random\n",
    "from torch.utils import data\n",
    "import hashlib\n",
    "import os\n",
    "print(torch.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e3da6dcc",
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0, 1000.0)"
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     "execution_count": 2,
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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = 1000  # Generate a total of 1000 points\n",
    "time = torch.arange(1, T + 1, dtype=torch.float32)\n",
    "x = torch.sin(0.01 * time) + torch.normal(0, 0.2, (T,))\n",
    "plt.figure(figsize=(12, 6))\n",
    "plt.plot(time, x, '-b')\n",
    "plt.xlim(1, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7fae4077",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "30 20\n",
      "30 20\n"
     ]
    }
   ],
   "source": [
    "def generate_date(tau):\n",
    "    features = torch.zeros((T - tau, tau))\n",
    "    for i in range(tau):\n",
    "        features[:, i] = x[i: T - tau + i]\n",
    "    labels = x[tau:].reshape((-1, 1))\n",
    "    num_workers = 0\n",
    "    batch_size, n_train = 20, 600\n",
    "    train_loader = DataLoader(dataset=data.TensorDataset(features[:n_train], labels[:n_train]), \n",
    "                              batch_size=batch_size, shuffle=True, num_workers=num_workers)\n",
    "    train_iter = iter(train_loader)\n",
    "    test_loader = DataLoader(dataset=data.TensorDataset(features[n_train:], labels[n_train:]), \n",
    "                              batch_size=batch_size, shuffle=True, num_workers=num_workers)\n",
    "    test_iter = iter(test_loader)\n",
    "    print(len(train_loader), len(test_loader))\n",
    "    print(len(train_iter), len(test_iter))\n",
    "    return train_loader, test_loader, features\n",
    "\n",
    "train_loader, test_loader, features = generate_date(tau=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b221073c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 0.9129,  1.4217,  0.6786,  0.5357],\n",
      "        [ 0.3694,  0.3018,  0.3527,  0.6734],\n",
      "        [ 0.1396, -0.3484, -0.3318,  0.3335],\n",
      "        [ 1.2910,  0.7567,  1.1020,  1.1510],\n",
      "        [-0.6803, -0.6971, -0.7796, -0.3869],\n",
      "        [-0.6435, -0.5256, -0.6300, -0.5475],\n",
      "        [ 0.2834,  0.3532,  0.4497,  0.2817],\n",
      "        [ 0.9646,  1.1996,  0.7468,  1.3165],\n",
      "        [-1.0178, -1.0986, -1.3208, -1.3482],\n",
      "        [ 0.1829,  0.1130, -0.0066,  0.0979],\n",
      "        [ 0.0174, -0.2091,  0.3615,  0.1878],\n",
      "        [-0.8771, -1.0745, -1.1865, -0.8613],\n",
      "        [-0.6647, -0.9520, -0.8991, -0.9913],\n",
      "        [ 1.1012,  0.9812,  1.3224,  0.7805],\n",
      "        [ 0.7449,  0.9660,  0.6778,  0.5861],\n",
      "        [ 0.7645,  0.6381,  0.7783,  0.2462],\n",
      "        [ 0.3315,  0.2322,  0.1001,  0.5734],\n",
      "        [ 0.6303,  0.3578,  0.5908,  0.7649],\n",
      "        [ 0.9270,  0.9531,  0.8100,  0.7802],\n",
      "        [-1.0004, -0.8097, -0.6716, -1.0671]])\n",
      "tensor([[ 0.9197],\n",
      "        [ 0.5742],\n",
      "        [-0.2718],\n",
      "        [ 1.2469],\n",
      "        [-0.6670],\n",
      "        [-0.5339],\n",
      "        [ 0.2200],\n",
      "        [ 0.7036],\n",
      "        [-0.9049],\n",
      "        [ 0.2362],\n",
      "        [ 0.0244],\n",
      "        [-1.0070],\n",
      "        [-0.7042],\n",
      "        [ 1.1377],\n",
      "        [ 0.4639],\n",
      "        [ 0.8699],\n",
      "        [ 0.2883],\n",
      "        [ 0.7811],\n",
      "        [ 0.9399],\n",
      "        [-0.6647]])\n"
     ]
    }
   ],
   "source": [
    "datas, targets = next(iter(train_loader))\n",
    "print(datas)\n",
    "print(targets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cd1e6b04",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def simple_mlp():\n",
    "    net = nn.Sequential(nn.Linear(4, 32),\n",
    "                        nn.ReLU(),\n",
    "                        nn.Linear(32, 1))\n",
    "    return net\n",
    "\n",
    "class SimpleMLP(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(SimpleMLP, self).__init__()\n",
    "        self.model = simple_mlp()\n",
    "    def forward(self, x):\n",
    "        x = self.model(x)\n",
    "        return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "45541b58",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def train_model(model, name, epoch_num=500, device='cuda', learning_rate=0.01, train_loader=train_loader, test_loader=test_loader):\n",
    "    def init_weights(m):\n",
    "        if type(m) == nn.Linear or type(m) == nn.Conv2d:\n",
    "            nn.init.xavier_uniform_(m.weight)\n",
    "    model.apply(init_weights)\n",
    "    if device == 'cuda':\n",
    "        print(\"Use CUDA for training.\")\n",
    "        model = torch.nn.DataParallel(model) # make parallel\n",
    "        cudnn.benchmark = True\n",
    "    \n",
    "    model.to(device)\n",
    "    # specify loss function\n",
    "    criterion = nn.MSELoss(reduction='none')\n",
    "    # specify optimizer\n",
    "    optimizer = optim.Adam(model.parameters(), learning_rate)\n",
    "    train_losslist = []\n",
    "    valid_losslist = []\n",
    "\n",
    "    for epoch in range(1, epoch_num+1):\n",
    "        # keep track of training and validation loss\n",
    "        train_loss = 0.0\n",
    "        valid_loss = 0.0\n",
    "\n",
    "        model.train()\n",
    "        for data, target in train_loader:\n",
    "            data, target = data.to(device), target.to(device)\n",
    "            optimizer.zero_grad()\n",
    "            output = model(data)\n",
    "            loss = criterion(output, target)\n",
    "            loss.sum().backward()\n",
    "            optimizer.step()\n",
    "            train_loss += loss.sum().item()*data.size(0)\n",
    "\n",
    "        model.eval()\n",
    "        for data, target in test_loader:\n",
    "            data, target = data.to(device), target.to(device)\n",
    "            output = model(data)\n",
    "            loss = criterion(output, target)\n",
    "            valid_loss += loss.sum().item()*data.size(0)\n",
    "\n",
    "        train_loss = train_loss/len(train_loader.dataset)\n",
    "        valid_loss = valid_loss/len(test_loader.dataset)\n",
    "        train_losslist.append(train_loss)\n",
    "        valid_losslist.append(valid_loss)\n",
    "        print(\"Epoch ->\", epoch, \"\\t train_loss ->\", train_loss, \"\\t\\t\\t valid_loss ->\", valid_loss)\n",
    "    \n",
    "    os.mkdir(\"./result/\") if os.path.exists(\"./result/\") == False else print(\"./result/ exists.\")\n",
    "    torch.save(model.state_dict(), './result/' + name + '.pt')\n",
    "    return train_losslist, valid_losslist, model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1b112dfb",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['sm_37', 'sm_50', 'sm_60', 'sm_61', 'sm_70', 'sm_75', 'sm_80', 'sm_86', 'compute_37'] cuda\n",
      "Use CUDA for training.\n",
      "Epoch -> 1 \t train_loss -> 2.590431062380473 \t\t\t valid_loss -> 1.2389005639336326\n",
      "Epoch -> 2 \t train_loss -> 1.1704057296117147 \t\t\t valid_loss -> 1.7951183860952205\n",
      "Epoch -> 3 \t train_loss -> 1.2141841918230056 \t\t\t valid_loss -> 1.2576977171079078\n",
      "Epoch -> 4 \t train_loss -> 1.1336304724216462 \t\t\t valid_loss -> 1.1760255363252428\n",
      "Epoch -> 5 \t train_loss -> 1.1412086109320323 \t\t\t valid_loss -> 1.1651216161371483\n",
      "Epoch -> 6 \t train_loss -> 1.2022289117177327 \t\t\t valid_loss -> 1.1709889817719508\n",
      "Epoch -> 7 \t train_loss -> 1.1765139768520991 \t\t\t valid_loss -> 1.1640310149000148\n",
      "Epoch -> 8 \t train_loss -> 1.2275258978207906 \t\t\t valid_loss -> 1.397282317431286\n",
      "Epoch -> 9 \t train_loss -> 1.3512031773726145 \t\t\t valid_loss -> 1.2245428495936923\n",
      "Epoch -> 10 \t train_loss -> 1.1404260714848837 \t\t\t valid_loss -> 1.2579764302330787\n",
      "./result/ exists.\n"
     ]
    }
   ],
   "source": [
    "device = \"cuda\" if torch.cuda.is_available() else \"cpu\"\n",
    "print(torch.cuda.get_arch_list(), device)\n",
    "train_losslist, valid_losslist, model = train_model(SimpleMLP(), \"reg_sin_simplemlp\", \n",
    "                                                    10, device, learning_rate=0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ee1c0f9e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def plot_losses(train_losslist, valid_losslist):\n",
    "    plt.plot(train_losslist, '-bx')\n",
    "    plt.plot(valid_losslist, '-rx')\n",
    "    plt.xlabel('epoch')\n",
    "    plt.ylabel('loss')\n",
    "    plt.legend(['Training', 'Validation'])\n",
    "    plt.title('Loss vs. No. of epochs')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a4e03768",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_losses(train_losslist, valid_losslist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "009507a4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1f7017ba5b0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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UlVhWKBSKtkWxBL8PP8yvWPTLX5b+fDHWrGl8neZ4lkuJ5ULjh4pjVjSGEsvtjA1hFKRx1HX4178gFoMHH2z8OEol+DVXLDfleyqxrFAoFKUJ22H99SSMF6XffvITOPDA6Lr331/681DY7ra2WJbrhMWyHF+aMqupUOSiwjDaGRvas/zvf4vnn34aXac5nuUKksT/YlMetwCzSWLZcRoX1UosKxQKRWlkPHEFScp/UQnpFCQSVFBD7eJoPEUFSRhvi+S9bExysUTtMOEwDMcBw8hfJ5Lgl0yKahqh/biuCKPQtMKhGnK/TRl7FIpclGe5nbEhBKI0PIYh6m9CfgJHIePkOPDHP8Lnn4vXmUxQm7PTn6/hmD8dwTAmNymurCnfU1XDUCgUiii5oRXSS1tFNVpDvTCuqRQWdmQ9aau5NlpHOdcWh23/++8Lcfv668E2MuMKNy2Rn9t9SVJsP2c/hgEXXCDWkWK5UAiJEsuKlqDEcjujqUZh5Uq44YaWieuwZ3nlSmEAK+zxwuuQpdB2P/oIrr9elPgBIWZFbc4GNM9FdzJM4hL2Wdp4MftSxz1/vhgAlGdZoVAoAp5+GsrLYebM4L1UStjwIdwbxDDEYthYkc/KOspSTMs6yqXCMP77X/F4772B2E7cWLhpiRxX3Jk2mXX5+wGYNk08SoEf3pc8dCWWFS1BieV2RlONwv/+B2PHwrvvNn8f4ZjlPb4RBnDQS9cyE4s7uIgKknkGq4IkPWYIQS3j1zIZUZvTRccDNEDHoed3dpOPIZdPP4W+feHKK5VYVigUijCvvCIeX3steK+hQQjhGBn8Sb3jj6eWaAiGrKOMEa2jXMqzLJ+vWxeIba2ACF6xIr9es2cUr9fcWp7lU05RFTIUAiWW2xlNFcv19c1bP4wMudB16LMi6NpURooR3E0NlXRZGHgNpEeh93+vpYZK+qwTyzIZUWpoFJPwYnFcTSdFGR/uZDV6DMVaWcvY6XffzTGaySBxRaFQKNojsWwWU9g2NjTAUsoxcJG5cd5TT0VmCiGoo+zcEK2jXCpmOSyWl1IuHCO6HhHBjz4K22wD//lPdD/fXxrsJzdpr5BYlusUCr+Tx5G7nUKdXxXtEyWW2xlNFb/S2KyPWHYceC6V7dqU9UkYeMRJ8ewYmy++EOtJj4LuOsRJMWCtDQRG7R168+1JF/D+4SOopIbPdswp0lkAaSRzM6dlPN422wTrVJBk7aGVuNcE03+aBhdf3PzvrlAoFJsqMrEuLCgbGqArdbhogWc5k8mLWQYhZD8aPIaOR5m8/Xb+tqCwt7fniiQTGY2Og6fpMGGCL7ZvvVWs89FH0f0sOW9MJLkvjArDULQ2Siy3M5pqFKSxWR+x/MMPwqhdxgTc7KnmAQ4i3u2qq8R6clrN1Q3SJEiWWUA0wW/Hx6ewT3I60LTScY6D7y0Oe0CkWN5228CIh8V6ePrvzjub/90VCoViU6WYZ9nGIk3c9yyTSPgxy7ljxH/+I2Ym7747f1u568vnBy4XNjiGi+dk+GHCPf4snwyDyN1PuNxc7j6aG4ahQvIUjaHEcjuigiTbTW1aqMH6iGUpQn/4QTx2pQ4NEXPsojGNIdRi+kZQTqvNPW0cldTwZiKYvvPj2FwHwxEZ2E2JIdNfFxnTHf4kQjukYJZiubw8PwbO0YrHwCkUCsXmyNSp8Oab4rkUy7me5VpMBmKz7MyRMHIka56Y6ccs5wrN3Nm88LYqSHLU68EYJMeX/2UsMhh4CFHSaeFsGDgQkknicbFObpc/WWmp0DGoahiK1kbVWW4nSA9txztTcG8iElNWiNYIw5CVMLqxiAwxPCBNgmqqqCDJaQttvNcswKQWkzlHm9Q+DLuFYsukkNX1FI6RwHYt+jbhFi/+qg0pkSwSR5Y5MqmrE8s7dQqMphTrl/ezOeM2C2dA42EeCoVCsTkwfLh49LzCYRhyLKjF5Mvfm5T3gfqlwfJiYjk3RliOQWW1KagUY5Drmv62pzGUC7kr8OBlZ/k8T6wj82gkiTeTMNcGyyKzf9RmtzQMQyXzKYqhPMvthLCHNjfTuBCNeZb/8Q/R7rQQUizvu0IYx+FMATymMpxKagCooZIz374GjhS1kyEwyrlGdjrn8dmg4TwwrCbikS7FukMsSIiM6TTBlKH0LLtu1GjWYvJYTxEDl1sTWqFQKNoDUiznhmFI5HgQFtO54jNX1MrlcgwyPEesVF0dGV+e3a5KVLlAhOsRi4FlFRS3FSQ5/Ib8WssSWe6u12P5XmzlWVa0BOVZbidID62hp9CKhBqsWSOyf886q7RnOZOByy4TSXK5BewhEMvSOMZw/Fg3C5tuLCJBg8iuzrjcwcX0Yx5bf1QFBJnNe32X5F9UitqddoJZ3asAuOMO6NgR/vKX4t937YEm1NTw7YM2p0+0/ClDebyOk2805XErsaxQKNojxcIwJMuXi9y7s3ZPcgfVAHivCbudu750asht2YhQCwMHzfNg2jR2O118dhiTGZaewX84k7N5AB0XI7uBsJ2uIOmPIXo6BVnhHft3dXAMySS3OdUMYRqJhzPwdNSLrcSyoiUosdxOkKEG9w+36X6eVTAEY+RI+Ne/oEeP4p7l778PPL/LlxfelxSbft1NUjgYDGEaMTLZ2DTNr50cw2EEd+PePZ3bqGGRJ7y7PZYEYtvNpNj1YxtpEF/9axLK7Ui70zCOA5gmXyVMaicG74en53KNpjTqSiwrFIrNhY8+Ejb9nXdgv/2iy3Lte2NiefRo2OqdJJcYFiPJelROnkYFQQxzsZjlWkyq9aEMc+8W1j+TYY8vbIaxgMlcCCtgACKvxcATBtq2cRyxXb9pCQ1i/NAQLmjPo8P906hAOFOorGQE9eh4aB554RxKLCtaggrDaAccd1zwPLeOZJj33hOPrlvcs7z99rD77qX3J8VmLSbn7VLD3buMYxpDiZEhhoOBwxOcTCaUXW3gYaTrqUJMzY08MEnms0U4xEhj4BoJPt7VAmAYk3mJI+GaawpOwUHx0nHhsna5JY2+mpHk29Hj8V5TtZYVCsXmwYMPisf7789fVswxUCwM4+uvxeyg7qT9pO3c1tfdvkpyNePZ45tou+v3pyXp0AEcPWhc8k5Xi8HMALmt7LM0QbJ1NIyjgRguMRw01w3c144oZWdh46VS2VTBbDiHpkF5eZPCMDwvqMWvUIRRnuV2wHPPhRL8pqbg/6IJfosWwR57BAajQ4fSMcuRmLRkEmyb1KEWiSPF9sIGeEVPk3uXmSS+SnIe0/FIkSbBrVzFMxzPHVzsh2loeAxhGh+v6cu4b0aTyHqkpzKcrS+sYsprJhUkmcQo4mTAJVvXyOadTiZ77x3stzGxnMnkT+/VUEliYgP6JJ1hTGIqI5r1d1YoFIq2hnQKyHjkMNIpIpE2sZhn2fNkGTmDBBn/zaWUA8KRMXbmJYCD+3gZJGvIZITd3mdkJXs1pHB1Q2QVVlXx3h0m0Idjed53nNzCFfxAF8bXWGCakapFopuri3QqE4uB6+LFE9iOJQ4nniDjpHDRiOueENWjRzPA6c3LmCWbkiSTsNdeYng86qjG/rKK9oTyLG/mSCNQRTVl1BdM8Hvkkfzal02phlGBKM/mXnMtGauST+8TnoSwWN55Z2FgZRjIE5zM2/RmfxZESsqRfTTIcFL9DD/8wsBhEd341e0mc+dmvRpZYwmAYbCyr0Xv3jBsWP73LiSWK0hy5Gvj2faDwIMc9lpomQyTuCSvQ1UpCoV1KBQKxcZG2qWmiGUpJMO2LJUKPitt+b0MwyVru3WdrtTxs52EI8Pw0sRwMTLCkSFLgGrprE33HOjWDUyT3RYnuYzbcNDwNJ2buYrf82duJmg4Ej6WJzmJDAYZdBw9DieeCMOH882/RPJ3LSafTanhOsZxL8OEos4OaIe7dt72JLnj3IIFxf+engd//7uo9qRoPyixvJmzZIkQh0O4Fx0vkmUsWbUq+hnHaVqdZQsbUkHnvQ8n20BULCcS0Hu1mJY7hUc5nUc5hNlM5kI6s4IUCTLZ09DVdNIkeKJsMCkSpDHI6EElC5BJIjEcEBb89ttZ2UsY1Zdein4HyBfL+y4XHuRjX72WY/4c1F8OvBZiANBxCnaoKsZ22zUenqJQKBStwc47N93z2RzPslw317PcsaN4Xl+PbzPTlJHJtqdeSjlD9wwcGSL8ASgvx3FEK2t0HQdd1LNftAiSyVBeigeaxg90yTtGxwlm/k7hCRwMHucUPDSRkT59emScWrybGTRMMWJ+yMdL2feaIpZLjXu2Db/9LYwaVXwdxeaHCsPYzPnkEyFqY2T8piDakCGRpLhcsZzJNM2zbGPhxhPgpUi7CR5aanEcgffWwma/D8sZ/PFo4qTImlDfmPZlPpXUYGGzlHJOGlDHza9bfJgwSdIbC5v6gy1qXzf97Ynpvqw/OhaD3r39sLVwPHa/fiKxJVL26NUkw74aKypxeC5utsmJ9EiMYhJ3cAkx3SHllkVEemMsX1484VGhUChak6+/Fv+bghSHsQKjfa4zoVgYRseOognIgetkkl1KeIPR0FyXiYzm+c4TSFEG1IsUbs+D0aPpfhZMZDQ4Dh4auufBlCkwfTp13SZky8Wl0GIJ7JRV8PhzKyttwVp0NwM4uA0pEkkbmfydeinJTAYSJ4XnxfyQj9d+GvVUf/UV7LorPP986S6DucixcenS4usoNj+UWN7MWbxY3NUbuH5cMH37RtYpJJab4lmuxeSw+homnmZz2aMWX68xIZnkuMequYppxEihvyzW1fGych0/Nm0Gg32hCkBvqH0dWIb/3oXLbS7UF/A3V8Qwu2iirFA2mxrbxjnbLHisY8bAqaeK58OYjGZdQkUmg46Hg46bbXIihbiNxTm7vcTfTrE5Y1K23Fw2JrtY1Q2FQqFoy5QSy00Jwwh7lsOiVcwHamiuR5wUWzt1VFLDXzuNZcCqF4ghwh92my3C6jTPRUND81xwPEil2GJdne8wOfVmi9rfFq5sJCsryZyXGQzmCGah0YDjaixeV+6vv90z1ZTRIJwyThrmzoWqKjxPOHF+8rANu1kkvxL7uusuOPbY6D5LJcIXqkWt2PxRYnkzZ8UK0W7aQSeGi6vpaLKNXZZCYRhN7eBXi8nivYURdVYugMrR9F9Xn/U5BMLYQSdFGRO5lL7MZwaD8xLoZCF56UG+jUtJfJjmV+hoeMRwyWSlchqNeDZbulB95AqSVL5hs81PLCqASYyCTAYDyKCxaLv+rPlJP/Z/ZQETGU2CBlx0bnYnsfjcMdROEtvwKivRUikRT9JI10OFQqFoazQ1DOPBB4N19/4+CeNtsCwaGkxfLEdqJQPg4ek6aTfBdz0tap83ub18LFNXzULTUhiJBJ/1G8y2787CMFJkHANN10iQxtU05i4q9x0mp1QEx1JBsH/HMf2cF+nUkM6UO7gEnQwHThnFMGAqI1i9JudLvvEGVFZygTeBiYymw39T8HiCbf5QA9kmV7njXK4Q9ryg8IYSy+0TJZY3c1askHflZXik0OP5DUlWrybiXc1kzIKe5UJ32xUkOXliJaeQghWA5vqx0TL+1wM+YU/Oo5pagpCKCpKBVxno/nWSO7NTfB6i/rIIuHDIYJBGdOO7jAl0pc7Plk5nS95JsexXtvgiBbckWMR50Vg6NHarewvj1TeZhIaOQwwPD5cxSy7hvXm9AdOPyfbvHmxbiWWFQrHJ8PHHotsqNO5ZPuss0RCvgiQ3vFoJrzaArnNGx0nMLBeOjVpM3uo7lP7z7sbAI4POuopBHPPaWIbuJ2zjbMPkMibwm11m0OvawbzrjuCq/+vNc1fZXPygxWGdF3DRu5dAxmEio3mH3tRisvXW4jik/eZa4aQ4sHMNn2UFdXi8EAniWdvtiKTsd+jNM9tV0Z97hTcbxMCVSjEY4eHWs0nu271jU0wsF3otRbL8Oyqx3L5QCX6bOStWBJUormMcr43L947uulgYp3Fcy0ws9v7rRey9NNoiFAobBwsbIxNUrsATQlkm7Ul9fStX+kJZ7quGykjFiUM/FhU7xBRf1Fo9wclcxzgqqWEqIyLZ0uFycABXcgsdWCe244jRICNSSHwMN43uyf0EDVIML0P506IzlY0F8aAmaKGuhwqFQtFWCdfYb2qCn4VN3G0Qxj+T4eZVl9A/E9jpdw+qooEOpDFIUcZ3F42lFpMttxTLe65IMpHR/OSrGhg9mq4fCadIw2/GsGArk60a6sB10T2XOEGNZimWZagHjujOd/qq6sgxViASxpdSXjAp+3+rTM7Y1uZuRuIYZb79noFIHHd18fq7XhZAk8RyeOyTf8dCJegUmy+t4lnWNO1e4CTgO8/z9i+wXAMmAicAa4HzPc+b2xr7bq+sWCEu1q5dG18P8O/KD+lBXhxuz2/sSKm2XZ68m39o01lA0CIUChewX0o5nqbjeNJsCYH8Kj9lGdsyYOclTHYvYOo3wjMRjnnTqOeqHaqZ9UuT5N+TDPw8qNiRIZbt7pfx6zKHvQoQfI/EDhYguv4NYzKn86h/HFIgP80JnK49JpJOAFcTXQRTXoKJXMoV/DV7TB47PSu6QdVi8t39NeywMPhbKRQKxabC2rXB86bGLM/CwtV0DE8oRg2Hk5dVU56deVy6TzQk4s79hV3cZVGSMdjsuXIRCVKiRFwqxU4f2IBJLFuY4u1OFiQSOPUpMl5Q7UiKZRnqEcs6X36xdhp3ZrvzVVHtd4JNkeCv/JbL+TsxzSHliaTsTu8kGdTZ5v+owji3ihE9bLAsph5q8g69mXiqzYArLZZ+EdjzsDiuIIlp23CUhUwaDC/Xsy5G5VluX7RWGMY/gduB6iLLjwf2yf4/BLgz+6hoITvsIAxdodCIt96Cyy+HJ58MxLKky8Ik/LJSfDgbhzvLsDifBJpsEYpHzBN3/GGxHDasFSR9w6W5ju8LjmdDJ47kZRx0vO/L+Gjn3v7nwjFvOh4n101jQOe+LGAGhidSAB007uUCqqninF2yMWpfRYWqrPFMKkWPWIIKang9bXIB9wBB+IfmeQxnChkMiCdIp4T4/t++l9I7M58HP+rDD3ThCU7mVB4TWdzZblC1mHnZ4gqFQrGpEPYmN7UpSS0m/9r+twz5/i8AZNwYx349jeOzAvXJr2siIRGytNtPr6/kMFJkMoZwdmhgJBJ8sYfl71/XYWEXE2pq+O9Imxl1gW2XnulaTKYxlIu0u8Hz0MlwJbdwEk9lKyzLfJgUP9CFI3mJv5xgc8VTFvuzgEnrLsFY5zCCMqY7NSLTm2Dbbx5tMoAkPR8dTwUWum76YljOfHaoScGrYlypJVi+115w/k+SXI3NNyssyHXgKDZbWkUse573sqZp3UuscipQ7XmeB9RqmtZF07SdPM9rYvEbRS65Ri7MRRcJp+ubb+aL5fJ37Lw43FecMVRS44vfhJ4h7SWwPYu+oTvq3JjgMl9cg4fGh1pPerIQLRuKEcPFyaQ4eI3NA1mjIg3hCETMm+6k2fmmS9ghK7cz2UTAufTFwmb2Fhbvxkz4Kvo9LGy8hhSa66BlhT0e9EVMWPj3EJ5IDPSAtWcN55b7u7EkXc7tH44m7jRwNc/joJMhRpoEHhnIljCqIMmu51dCOoUbT6C/qBL8FArFpoMUyBUkOeBpG3paERtWyLNcQZKzvrsNNPB0nafdEzjVfQIDB48Uu39uExaJHecnuZ6x6OkGtKytncpwdh7QjVOHlrPLIzYVQCxmoutZj6xp8n+7mnwbh4qvRA6LVmv5262mios6TIdUCscxOJkn/BwWD+FQSZPwk/1eOdyEp4LurhqQoIHuX9isXWty663Bd9zu4yRcXknvhhQ1JLi5LphBlTOfetYrLp0mjiO89Nt/muTyT0VeTebDBCTVmNBe2FAxy7sAX4ZeL86+l4emaSM0TZujadqc77//foMc3OZMrlj+dl+LtJ7AC8XhrlwpROzF3MlAZvLeWeP41Q41vpGQSMMqDYoRCrvQ8djT+0hMr2VPqww6bixBbQcrcgzViJg3GdeMkxHCGp0XGMRliKzlcVzLXR9XcnAmv5OejcU6N4GjGaLVKZaInw5V4ZizxRE48Q5+YuDawVXcrI2hH/OIO/V+XHQMFwOHaQzhvn3HMe+8CVjYXMktaA314Dg49Sm+mG6v12+hUCgUGxJdD5wb/R6+FveoSkwtyWuvieWFPMsWNnEvJWIPPI9v2REnlvDtaN3+lr9+BUn2vWggR/M8eMLZkSZBNVV8tIsFo0dz+HMiPyX2RhLDCEIaVq4EM5TDQmWQw1KL8D4zbhz3xYdGqitlMLh/qwupzHp9Adati3Z3FSF4Bh/vYjF2LIwdG8Q69/nfLVBf7zfT6vWd7R+TLFHnaGJ89JubuPD999EwwpgX7YSbyzXXwLx5Lf7pFG2MDSWWtQLvFaxk6HneZM/z+nue13+77bb7kQ9r80SGZrz1FsyZE132qmtyRLqGe3Yf55dCk6XjZJWKb3tavK7nx2pJwyoNimg7KuSpjC/m+OOp2XMEj3AaUxjBI6NqmNcheuddi8iWdjHEwXoiqzqjl3EDY+lKnW+Q4l6KQ9bZed9RJi1e441j9p+E0ZTHlcagno5M2OFm7r+gxk8MrO9rclBKdDPUZDdDpKciRs3OVczf2qLv9NGM4xoR+5z1kjvEmN/FavmPolAoFBsYXc/xljbUU0U1//ynWJ4bWnfmixdxLM8CwqvsxYXwfWBYYEd/2C+w51VUo6UbkBEe75b190XsgPerhSj1HBI0ELtpLL3XJCNi+ZB1Nh00YeulJ9fHNGHMGP4dqyKV7RaYJsbF3MF1293JvLLgOLb/JEk3FpEhnm2FHeO3Zbfz6Q4mc+cSSiy/hr0WPOrbdRedrmsXseNnSX/8u4wJ1BwpxsfaUMzy2pokBzPbT2BPa8WTvtNpuOkmOEQFm242bKjScYuB3UKvdwWWbKB9tzukWL722vxl330nhKbb1WSYSV6sVoIU3GBwozGUyVSJ6alsIp2xlwWY7M8C3qY36e12pvr747mNSykjhY5Hw6NPcQS6n4DxbKyqYFx1V+rQs7nMnq7zgjuIB/YeS+2HYvsuOhk80lqCt7e1xBmUg4ybG7BH8DqceLK7A7t+bHNn1jvwyIDxnMuiyHSejJGexhC+7m5y/Lfj0dMpdL+JC7jAx+xJj9erIYmadlMoFJsEhpFTG9nzGMI06ldU8c03JosWBfknQ7mHxMJQFrdm8M3VE6gdazKsP9ycFY6/61B8f0sTO1PbIKoeme/f64tSAxdqXuAfzOKKuKhvvHIlpHYpR4/poklJIoG9zsrbZhKT42I1HJYJaix390SMc0ODOP5hD1SikyKDwRRG0PmiKv51n8m5Dmy1IMkViM6tMiTP//vgMPDjyfDJFH6Ojo5LigTTd4uGV+ivJ+lxocW+iLsLB50/bT+BcUXGAjkjWygpXrFpsqHE8uPAJZqmPYBI7Fup4pV/fHbfHZYtgxEjYPJk8d6yZeJRZh7LMA3hfcgak4zDeZm7+QXTmf/iBLhwNKRS7GIYzKSCI8m25fseqjk+EoMcJw1o2aoWKXb9xGannUw++SR6bNILrOsi0fCG+rGsTggjO5HR6Di46NywzQQ+3k4YpHAtaHnHX0GS7vfbVGTfk/8rSHLvokoSi1LMxAA0Yt9kst7wGGKSLoiRrqaKsji82cnivFgCNy1atgqvucd+LAR7IQycBjNncvubJpdeKv5+8m+pUCgUbQldD/JERnI3Gh4GGfb9VtjlQvknEs91cb4VDazCk7xlZcHzaqoYYUxFd0QdtcNXP+Pbad0TilHWttddlxgpDlhuAyY96pKc8/VocB1xoBMmUHth4Q5+8zuazFoVLPOyYnnZsmz5UiclSpcCi+hGzwEmxgPQ7askN39XSYIGDFwcotPpwmEjtqf7TpQUe3whjlFizLLRMin/72PgMnj5PZDszUspkwEDgi6H8pgVmxetEoahadr9CJ/bTzRNW6xp2gWapo3UNG1kdpWngU+Bj4EpwMWtsV9FYcKe3O22i7bylGHgUuDJZn7hltggYpATNLDf07firmsAx0FLpTgiK5Sl0biSW5lLX9LEfU+sli1WnybB970sHnoIunWLHqP0Ai/85Ti+vU9Md6VS4ZgwFw2PLpk6EonwNFpQn1m+d+BD0feuZjxVVPuhHAlSkdJ40xjC/+1zIw8dfTfXcqM/bRiLwVtbmMw/8lI0NFzA07TQ98JPirztNvE9vla3fAqFoo0iE/yqqSIT74Cjibjjr/a2gML5J/7/WIJveor1unQJttkh5FmuxWTJccNws6F4upcJmlvpoka9YwgLjGGQ0RPM62zhujBgrRC5MjaanM6yCxeKR8eJ7hMCsQzC8eJoQirrOvx8ZDm/+IX47nstDsYTB503GICrx/E0DUeP42S/uRzPZMjdJ7tZkf19tIuFpxkRr/QBqTfwjqpkjJXkv/+NHp8Sy5sfrVUN4+xGlnvAqNbYl6JxpFhOp4XBiMeDZTt8KsredKq3ANO3T/2YhwsYSIMh7p47ffexH4ogCr9H6xfvxSdMZDRPc4Jfei2DziuJQYxJjWXUviY77ADDh+eHhdRi8tkvTDodIF6nUoHHGVKkSfBKzBJ5iKHECi9UyF7G4sVJUUU15zFdZCpni9OF27KGk0+22t1k//1gwv+C44nFYN/lSfrW/s1PFHE9DxcDLeu10LJJkd408Rl9Q0X9KxQKRTORYrkWk0dG1bDVmzbjZlmc1kN4TaW91UKeZQd4gwFkbppAXTfhfd77v8HsXdizrGnwVWUV5U9Np6OeIkMC2xXrja+sYaxlc9cCi4cfhpnX21z5sMXbCZPVq2EmFm4sgeGmCjZ9GtorSXJkNbc58HmmLzp1/qyi6wZiGUSJUB3Adeh7zyVQ1RvDMHl/B4tjSeBlx5PfMIGh58Gn02xsT5Sau4uLfHsvQ/I+3ynq4e43ymQYd3AHF/tjio6Hl2rgOsay5u2xhD3RqmHJ5odqd72JE+5Zn0tDgxCAUixXkGTKZyIu2X1WlL1ZttxkGJMZxhRfCDtGnPedfejFe/57ubtYSWc6syobepHiW3akgQ7Es0bpju3HUrvYZHR238WOMRYLlqXTgcd5yB420z6z+Fg3OaosLKIb8NBYSjkgEjRcXDw0duCbkKCGNzmIg3nDF/AvMIgbEN2mBjr5d//xOPRdaaO5odbYRoy7et2OsWAexxwNe91QBaaZ1+FJoVAo2hrhm/mvupl8mjGpnQVnZT210t7mNvv4DRMYtq3Jfo9N5iUuIX6HQw1lVFJDh1DCtqZBXQ+xjf+OtLlzoUXtTLH8/W1M/qybXH2/6AvAGJMPbXB/gDVrxL6fHF3D6dvYeU2fKkgyEwvvrhQjAZaLOOFU9hi+9IKOgRY2hpcOxqh0Gqqr0XWTj7eL5rHUYnLQFjApVMp0Tz7hKkRN6YZsSN6hLpAUjqWllNM1K9SPYBZVVHMB92CQRnddBvEC3j9mweAgzll5ljc/lFjexEmnxU15IerrhWeh/ENx0XdjkS8mHUeEEyxdBJMY5Se9OWh80uNE9l74dCQJLvzoonEnI7kidhtOJuV7a6up8o1SXUdhNOJNEMvSoMtkiFpMzNNMav8O3bYQ309W0JB39rczCg8DnXS2EofDCTztt7VOk+AeLuAAFvgC/gbGAnA141m53MJxTDQt8MTHYlDbweLCeBluugEXneRZt/NU3QieXQDPHZZkr2ypIFmXU3kQFApFWyXciMR1xZgAsONnSe7I9hCrpoqLudO33x/saFH7jckl85IcPH0UOhk0V9QttrApK4t6XWUjk+8uMPlyQvD+nt8mWXG1zTDK6eXVQTJoALJ2rRDEu39mw+lWXtK0hU2cQADLuv1yVnHe/qY/bthY/uxfeJgxjODYwt1fw9Eew5jM5fwdDzGDeBkTqMXkF4uTeJWVjPNjnYVQP3ObGqqXVzGEe33xFMPFzY6nrSGW334buneHzp2Lr3PFFdCzJ1xwQcv3o2geSixv4mRmJUnMtiN35lL8NTTAEfEk/a6qpG82NEGKSVdP4P3U4sOB0dqUDjFWdtwxUjFChlxkwC8R9Bsm8Pm+J/DCOztSnW0NDfiPe2U9r7LFalPEcioVJPFdeLDFzreanHoq3HyzWN6Pef5xiVoZGd/zreMRI8MURrCIbr4X4R16+wIe8Ct+ZN5OMHH3GsrKTH8AicdhbpnJ9HNr+OTerCfiPjENeQfVVI67B9wMxOP02dbms2yLbeVlVigUG4pC1YWKERbLjiPqEVeQZPDtFka2ssMQpjGQmb6o7JZ1vuzyUXSWzcXAxmJYBzjmGHj+eWH7pMPAMIIktwqSXP9yJUZWbHrfaTAwQa9+M3nJERWWaqikw8MpeCrhlzGVyAoeOoE3wsmG0f3sHxZXV8GwYeL9Wkz+tvcd/Obji4lprgiVq6rCeE58Z12P2uilS4NjDDcxyeDSFaGk9/rShlTKr54hcmjqOcer5m26EQuNPWI8jaGHwkjWRywfeCAceii8+mrxdf76V/GoxPKGQ0VcbsJUkKTjyZUiGLiyUpR4C1FfDxUNNnommtx2HeMYd2QN6XkLOMl5FHTDr2E5itup7VGVraMsTg8XjRQx5jAgGwfsUUaKvd95jPOYXvDYpEFvjme5zzphQP+kX0v3Cyq54rAk++wTeM71nG2IxtyERL1YIVwtQ9ZftrAjSX8xN8U+X9mRxJFYTHi3P9vR5GbG+FU1aqhkBHehO2nxxVIphq+4BQiaISoUCsWGoFF7k0zC+PGQTPp2t4IkA14cT7dstzzdSftJy3Gi9Y3l9j/tZuHERH1jYtmxIRuz/OijgViVM4JhsWxhY7hCbIJwZtDQQOWSalwXEq9laz+7QSfZMLWY3IvYgZzx/B+DqKSGgy812XrrqOf1oW1GcASzWHHFTTBzJpim71mWjVmuZjwVJKmry4p5xoYqYIibgaWUczXjWVVWDolEVkYHDpkzVt7DUsqzRU9laVGNBQcNiYj9yIxj6PdoDCnqZdMYRdtBieVNGAs7r3U1RD3LK2PlaLqOpwfJbTczhp3qFtDhsgs5hNkYbprHOYUjeZmpjGBhFxHn9QKDfHGs4zGPfqQo8ye7tGy8cqSQfBY3x7NcjLBYPjQtDKiWY0Dl8vuMKhqy+2+gjFu4kjRxnOwEnIHLCO72K2NAtIrGEO7NtrU2yGgJ3tveiiSrxGLCyIUL9QfZ4lGOrn+CCpKk0zmDVxHD+MAD8NJLpf8WCoVCEeass2Dq1Oh7JWeykknhOMk6UHquCKoGHfH8tVz3cqUQe0bc94rKttGSdFrY3E93MHn4yAnYxiC0SZOYyghAVKbo2BH2yNa3l/YyLJb9Tng5h6dlj3/p/mK5qxsFk/tAhId4HToKe6138PNNJOecE6xbXy8E9upLx/iiVYrlQ7VoJaVjPp9MDZUM4oVsPotGmhh/5Td+59gzXhlN6s8TeIGjI9WQDC9DV+oYxSQyxHE1nQY6sKBvVeTY5ZhQQfT3aEwwq7C+tosSy5swNhZeXJTkKWRw+jYkGfPtaP/2WsZjARyyeAYQJO5twVp/mUy+uIGxpCjz25xWU0UlNUzmQhoow82WIQobWok06E3xLMtlL7qWX2Io/H3kVOIbMZOBzOQabmIgM/k9f+ZIXiLZ9dRsH0Ev6/Vu8AV8uIpG2LM+cp8aPiyPZnbH48JYpdP5Rl962YMZUA8Lmw7zkmg3j/fL1hUzjGefXbTZk0KhUBTkwQdFJaEwxTzLtbVwywk2XsiB0meF7dtA3RMzal2p455zbO5iJI9wGtMYEtlOfb2whTt9nuR0ezSWUwOjR/sOCGkzpV0Oi+UttsgeSzZxcDIjSREXgX6JBC/tXoXjwDd7iOWLR4zLC8Hwvw8m70yoYSrDeXG38/KWDxwY9A+QoXRh54wUy0d6wRgQJ8WglTMi5eRe4GiO5GV+oEswVjgpvKV12TEw4d9YOLoY76YygmPKXmL+YFF6dNEu+XHcUNyhVQw1S9l2UTHLmzC1mHw1vQbtJZtPu1kckROzbGET91LguaBpfjxWBUnWeMKqSfE3g8H+dnf9UiQE2lh5mcRyv9VU8eivbU6baEXu9iXhpDloWhhGLSZnblPDU1fakRhsaZRlgf3w/moxiaXXin2Evo8U8FLsytJB1VTxhmGyXwfY34EBTpJfZr9fLCZikOvrwSpLcuC66N/gtIEr6Dvz7+g4OMQ4mNkc+Jsb0N0MNSSYznn5hlF1+1MoFK1IxGs53vZt5WWXgb7C4vJEQsQjJxK8lrBYBKI8nJYt7eZZ/HwtdABO5CliZBjCvQzEphaRw5FIQPfPQ80+sq2oazH90DVp2xsaxGPYswyBra6mikv2t/nVZItP/mbiLhWx07WYLB9p0u3A4t91+XI4j+mUfZHCYjqViO5/knPOEU23pFgOx2hLsfySFh0DHnQHcyizAJHEPYPB/pgi1/P0BKlDxdg2MBvCB9BwRhW1/xHrvuaZzK404aEka64dz71PljP01DqwLDJdgtJ8JBJiPCjiQS/02yraHkosb8JUkCTxms1pd4iL2vsdkExy/tc2CSxRrB2DmOaCYWA7VtDWelkDDjrvsy9rLriMqfeM8Ld53cuVxEiRIkElNdzMmLx912JSNtbkt4fBz38eXXb77SISAZoXswyiUxNjogJTLi9W0/i5rQZzyMrnfaF8C1dEhH2u4O+YEEap+zdJrllSSTz7Xe+sqyGTMdllUZK/rwzel3+DrY+B0TNP40pu4RSe4FQeRU8HcX8ATiwYqJQrWaFQtDaOE4SXcW3W1tTU8OmnJksxmXPuBA75cgYMHszs8SafA5XU8EfLZvoXFnwKFz9cSYx16Mj6+Smu5BYG8wiplKhh/P6OFoP0BJ6bIhZqRS1FctizXEGSbe+22dOzIMd5UovJrvua/MoMku1kNYxdqm04wyrqVOg4W4bBOaGQv2BdOb6UEsuvefljAMAkLkHHYSKjeYfekbGi0/EWw/sFY4j8zNhewfYzGdj6vex4SgPG6y68oUNZGYnJQtTXYgrPuW3nlccr9tsq2iZKLG+iSGPZ8bYUNVlBRxKorOSidSkuIMFlTECTKjX7KKbkGvws3x58xGt79fa3a2ETd1PZwuv1VFFd0HMM0RrOkkMPhVGj4E9/CtYpRa5YLrR+2LNciOqyESwGBjODGQz2Y+skud5o14V334ULlwnPu2x08pOvbdJpk70XR9+XHhWZyHIST/qF6f3pOWKifF5DFa/dZKN1LQ+m3JR3WaFQtBKOE4SXhWexli4VCcn9qkeDm4JZs+i9ZW8+z9q/lw41ef1LOIPxxJyU34BKcjIiD6MWk3gcPupq8tsDazhwuc2If1vUHirsmBxSpF3u+lF2LPpbilOMBBXZjqiSs88OnCe6Lg650zvZz0xMwZ351TAkr8Ut9s96xdNefsifPIZ168RjoTCMQuXjulKHjhspRyfXqcXk/K758cMVJDl6js2zWcE9wE0y4JmxlFGPgSf+ltn6fFs/Vo0v6k2zyWOAEsttFyWWN1GksdTc4I571ROwVSoQeYOZge5lAA8yQRtSkcnrZj0KDju+byMv7KBkj4OOxxCmRUrDhSkklqWxak7McmNiuTHP8urVMJUReSK5GPLY/v21xfCs5yRNgs92t8jMh/ldLE7TEnheKhKTnU6Lv3s4g1pDtMSe5g3x/0ZrB8CWp1QGU2810alDhUKhaBbJpO+d1JZDNxbhoPuzhlgiWdnKVj/CEyJ6gGaz60UmU6fCLouSXLukmq34BkeP4bmeKOuGTGDzqKIaC5t3XYt02mSObtJxZ8C2ubgv3DEvsGNSqO78YXYschx0LxCeIGKY//1vIp9xXYi9GnymVMja32tNHqSG31fY/CmZH/KnaWKMKeZZzmTgEC+Z51XODc+zEbOuMtziu6+rcJxok5QaKunwtHBOXcYEJjKaso9F58NINT/PY9vHp1FRZNwshRLLbRclljdR5MWuaw14nuhod/kTvbkNEQaQJsEMBmPps4hpQrTZ64SxGMUkfwoqRRk/9LPI2gjRFrXLUM5ccTcGHgYZLohVY2WixgYKi+Ve2Wmq3NJxxWgNz/Lq1aX3kYsUy7WYXGPWEH9VfDdrd5NMBt7awuTSnjVs9170O6fTsJTywItA1rNsGMzN9PW33/CczZZ5SR1NNJqhQVF5pBUKhZ84nEqBYdAFjeGkMXABzfdESPvkoYPuCZuPxUl1SW53qhl63z0Yrpgec1ydxzmFD+jB5Yg8jAwxv4tfui7BrUtqWPM93PRVJbye4vZEgpueDm78pV3+wwsWNSQwjBReLIHdYPnHLhP+JLoOn3wCN35iMTD7Ga1IyNoWW8CiRbAIk1k/NaktUkgiHhdhHeFjks87vZPkEVlbH4NpDPWdP+HQDBDtt8uy4XSZ5+9h3dUXMIy+dKXOb+ilZ51Tg5mRDQ/xCna41ZxM5KahFB98IGo/H3aYqobRllFieROlFpOJXMrV/AUjG3d1ztIa/nBIDd0+tbn/GyHyyvr05vYzbDKHWdQeKS7cqYzwm3V0ZgUX3jeWYaHwhf90qOIUphMnhYPBuc40jGwb1IcvruHcOwJjGe4e+MQTMGiQeJ5bOq4p1TDkNnNpTCyvXQtdusCKFcF7++wDH31UeP1w6aWvdjN5IGvQBmXrLK9bBx9vZ3JPjqG7+Wa4mjrh0cHFAXRNR3PdSNzbN/tabBtK6vCOtAofSC7JpBg00mkxAqgEQYWi3RJO1PYTh7PGKyZv2D0xa+i+aDPAhYmMFl5lQ4cJE8hcKuKTDVd4QKWpNXA5iae4lat4nNOoopq+zKU/c0RtZC9FjyU28eUQc4WnWkul6DLfhuOjYlkKzxfG2Hy7r0XtOYHNki2pJeFk7kpqeO2PNgy0Ctq53XYTQhKIVC3KJexgCT//+ms4ckm0GtII7ua8bKJgODTjasZHOgbGvDSd7ruLyYg6yrKhl65D2hWOqCOYhUYDetY7D1nRrOu4ukE3Z1G2gkhpG77vvuLR85RnuS2jSsdtgnie8DZczt/AczHwSNBA3x9s3trC5J7tx/hG4INtTRgzBv2w/KQLUYD9FrZ543kmcyHDEHV4XnWFIbuOcUxjKIaX8cvudP/c9rchp8AkJ52Enyn9Y4RhFNsGwNZbR/8+l19eeL2dd4Zjjw1eb7VV8DweF59du5ZIs5IwIkwlli1SD3gumutSlo3vBvh8p2xSxzhRFil1UBMF7y23iEEx2/iE6uqmfU6hUGx2SBvqV1QwDGGkjFh02j8WI32YFSqT6QobUlfHoWlZ0UJ8QuZYyBA8WWLzPKbTnzkYuKJBlZZg4tsWj6+ycIzC5UnDtroWk/TlYyizorYu17McdobUYqL9fkxRh8D22wfPi9ljiI5B4e1//nm43rMYPIwivQFsLNIEtaeB0I2FR4IMT3M8H/xqHJXUMJURVFLDv35yIyO4m7sYyV2MhLvvhlNOQXMchjOZmVg4F17UpIYkEBXLv/516TFPsWFRYnkTxHVl7Gy0FekLaSvSUKOCJL/8QjTIKOSVHUy01rJ8vXatMGQ3M4ZqqnCNhF9r+eufWJFtFAuzyC0dV4xcsZzriYDC3uZc4nFhj6Qnoth+v/oqKqzDYll+ZtWqqHGeMSN4XovJNIbiofl/N9ndaQjTqCAp2qma4iYF04z8JkVJJoVrXqFQKAiEk19RYdw4sG1W/eICXGl/NA2GDKG+r+kLwwxC2DqHW3zvlYOmk0EnYyR4iSOyXlKdFGXI7qbRusODGLl34Hmdfm5w4x8Wtrl22TDEDF+YQmEYTWWHHYLnTRXLudsP6j2L3gAZCvcGkCXiZO3ptF6Gl6NUv2VHvvhl4IiqxWTiFmOYygiqqWIR3XBc8J58Es11iOFSRgp98l1wxBFBUegShMXybbc1urpiA6LCMDZBHEfeMZehaw1kPJ1R3M7LaZOKrDCTCQllH6WgMoFWIMlsBoM5lqDkmqy1vGZNsE4tJk/9tobZt4rYrnP3jm6jmFhuqWe5U6f8deRyz8tfFj6OiorodoshM6dz9yc/88EH0DcIQeZnP4t+vpoqzsuGqega6J6bbYiSoYpqdv+3TWZ1ObGVouZmqkcTPMu2Hf2ChgFVVUVXVygUmw6ffgoXXACPPRZt01yKsHB64AuTYy402XZb+GExxO4T9ifWIYFWVUUqFQjD07a2+d0zFpkGEZahuQ4OOg9U3MZ5r46ggvyEt3Cy2w2MxekS2Kzl+5pwVb4NyxWmuXWWIV8sNycmt7liuZjND9d7PqPc5qG64Hv36QPz50fXAxh9cJIer1dzAfdgkPFr9N+UiG77m2+CsTZBCm+UhuM6xMjxUGcycMkl0Lt3ydC68G8ufyeSlgrHawMosbwJkskEhvHX+9v8Y0HI6GVn8YM2zUGSma6bkXhdGaM84aczGP1KELOcK0pX7W9yc3b7Q3LOmESO8ZC0pCkJFB5IpAejlFjONaaFDOc224hHmTkNUU92WPiXMs61mJyQqMFM2RxxWjnHPj2aTIOI7x7CNGLPpTGec8UXKyvDfUDcqOQ2EZB4Hox/zeKqWBmxTIP43KRJykAqFJsJ110n7ocffzzaprkUYWF59tlw4oni89c9Y7Iwm5w27jmLmGmSXiLWe8Mw+Thu8jsT3OvGi6S0rB+6bLVoSlWosVM42e2HXiZdQraw0GwfRJ0qkJ9/AvliWSbiNYWmhmF8+aV4bEyI12JSv5vJ/LrgvYsugmefhUceia6bcWAR3RjF7XSlzr+xyHUOffstnEcQF51xswXpNAfXExVGZKy4k3a49Tibq1c2LpbDApzK4qX1FBsOJZY3QaRRqMWkdkH0Atp3eZKD19q8S7loHY0oKI9l+QXhw0xlBNffP4KpuxXfXywm2q4uWZI/9daYZ7m5CX6FPMvhfSaT8OKL8Ic/BPtPp5smlk84QTyGxXJ4vVWrgueljDPA67rJS5hs2Q+6n9Sb6gtsDmY2p/JYtOZmKkXsFZsKyGsiII3f3LnwhydNnqCG5J9sVQlDodjMkKFYjVUHChMWThY233xscc01JtOmgWx4cf3BYhCX299660CQru5vsSUJdD1Fxk0wb2ur6L6kgP797+H3vxfCXBKeiQuzfHn0dSHHSa5YlgJ7333huOOKHg4AO+4YPG/MHjeVXOG/5Zb5v0kFSW6dG23MJW8uctd13WgZuoyW4NfeBK7o+Qx7vfc4mvQv6zoNbhmP/WBxdfazs2eT/S0D5NhuhQS46gbbNlBieROk2B10BUmmfl5J3BMX+WVMYOD+dfxysgWmWTRerJh3WBKPw5lniuf//Gf+skJ4gY0oSVhMe15hz3I4DKOiQvyXYjmREGI5d/ovV9Q/+miQ2BcWy64rPM59+kSrZ3ToIMoW5d5cSOQ2UilY2cvEBsZyXbTmpq5DIsGqg4K4wGg5OcC2mfuRhRz8Vl9qRuKoFQrFpo8Us43Z2jCZTNTDmPogQeX4aDhdZlaSxY/a6EdYDGMB566dwb/qB+O91htesrmMCYw6o45rXrBId4iKre23h+++C17//vdw4435idvhKkNhcsWy5Mwz4b//Fc9zq1hIIT9uHJxxRunvv912wfOWiOXKymyJ+xC5Yrljx/wxzMIm5uY3pYLC413YM99xl3L6LZ7H3gsfj+QU0b8/lbMniO1ky4P+7gYLuyH6m8gbpKWU46KTwcNIJNAKlNZTbFiUWN4EKSaWLYLOc9DAYGbw2o5j/TvScHOPsAgsVZYHipfmgeJi+YorYOzYwMgV8yxLUSvFcinPcqEwjLIy4a3INaa56556avA87CnxPFi2TDy/8cbg/Q4dROmixkinhYGropoEGd84vsQRWDceR/owi92PNKlAxAXGjKxnubxceJBTKYZqBrO5g6mM4IMP4KCDGt+vQqHYdGiJWA536isk3CpIkji+kh2dFNytMZkM1MPhPA9WnK6Oy0QSzOlXw/xXTfbICYHo2TMqljt0COx02MkxeHDh4wt7fsPjwH/+I5wqQ4aI8m1hpO1tikMgPC41NkaBCAcO88ILjYeFdOyYP6YValgiKTbeyd+kZnElZdSje0GZPgD69aN2thmpmf2MY/A0J/AtO1JNFWD6rcwnMhodBxcd7W8TMJRXeaOjqmG0ZZJJ0Sc0p+xMoTacd3ARBzMbhxgZNAxcjuZ5rqsJsnCl6Mw1VIUMUdjI5LYQDVPM+F9/vRCi0rhUVhZeT+5HivdSnuVCyP3nepZLxTeHPcvhhIqrr4azzhLPmzpdmkoVvnlZSC+wLNY9a/stZCsJZZXPm+ePoLrncAcXU0EyEgqiUCg2D5orlteuFTNogYdRJ02COsq5mvF+aIbuCCGtO8II+RV60mm/u+vOH9roen68cLEayBDYxVtuiSY7h7n0UpGzVuh77befePzss+j7MgyjKWJ5jz2C56XEcjwunCxvv934NnO/c3l5vq2Xtvo6xkVCMLp3L/37BXlC0TJ9rhH3k7XDNbPLSHE6jzKSu5jJQEgmc26QROK4t7Su6D4VGw4lltsqyewd6LXXiseQYM7NmJ2JxUju4nQeRct6NwEMwPCyWbih8nG5hqqQAQgbkEKeZSlOmyoq99svKlKL0VzPsvQU5HqWi4VPADQ0BM9/9avgeSwGBx6Yv04hunUThjedFmK5mioaKMNBo4Ey5tIXKivpdMu11FDpC2YsS4RgfPONvy0N0STAwhbdCIvcJCkUik2DO+4IGjSBsBPQuL38/HN47jl49VXY8fOoh3EilzJRG804hE1ZSjmOFsNBw9WEkZQmMkPcL/fZYFoYRr5Yzh0Hwo4QOcaUCn8wjCCUIlfMyk6uYe8zBMdQyM5D8Df75BPh+S50bLksXx4xpyWRYvn884X3e8CA4qEVNzOGsyYEHt3334+umyu8pUc6jUFKS/AIp3EXI/nfH17yZ3dtLLxEwvcSadn/CURoXlDpKijX6vzUatqXU/yoqDCMNsi//gWHvGizT0ODUH0NDZEA/7An08KOdh7Kll+X4QAaZGvNiWoYUNqjEIuJ7XfpEkzRFfIsSw9wcxJWmlIvuVQ1jDAPPii8FH//u3jdWBhGGDkV+PXX+cZcbqcxYd+jh/BkyMZaok7nTD+jXHoQNMeJFsEPta3FMMBx8BAhGjYWn1+S5IRvK9HT+YmACoVi02DUqOjrJtVaR9TWvfdeuO++qIcxjUZf5vthdh4p+jEPKY893eBm53JO2nk+/1gy2O/QamMxNZuv0tpiObyNXIfLllsK0Z8bGtFYGMbTT4u/lRyjysrE8Fdq7ChWrSPM2LEiofCBB8Tr7beH884Tz0uNYeHydWVl0XW33jq/zKqMXf54Z4uHvhJ2+86dgGSSq7O/x9FaDdeV38KhSx/zvdAaHpSX+2OJ3M5SyrndtqEMNQ5sZJRYboOcey4Mo5wpZN2jrivmi7KExbLsPKRne9qLZhmBUvQAraxMeDT/LN4rZVzKysT2u3YNxHIhL7P0DDRHLIdF+XnnwfTp+es0tc7yz38uHqdMEY+5YRilPMtSCOd+BgIPSWNiWWZRp9Ow1YLAEN7MmGClWAzPdXG8GDaW6PBXXx98keHDAXj6KbhzTRW1y0ysL8bjkQKVBa1QbDZIz3Ihu7RyJfzwg8iRaGgQAiyTicbOOhisZQtcPUbahTRCnRqeIwSX6/ADXZh6xnNM/YfYrgwf2GorImJZhnBsv8oinCxYKAyjMbEcFrW5HHNM/nuNhWHE49ExpUsXUZ6tKY6WUvToAYccIkrvQfR4S9XkDycZyuOTbL21qBAVRlYV2Xp18F6nd5Lw20rGZatrXLZ2Av3XPuc7uDQgg0Zsxgy2yPSmAnGj1JkV3MD1xMc5cEuZ7zgp5QhS/HioMIw2Slfq8MIZeXVB3NKf/ywM3tWMB+BSbiOD4fewTxPHQSNFnFm9RvoXmTTUpcSyNI5hI9FanmX5dQYNElNghS765tZZlka3OdnSU6bA3nsXFuZN9SxvtZXwpnT7Kskhv69kHNfwEkcwjMlUkBTC2B8ZPfZnAUO4N1ompKoK7ryTp8qrGJ2+hSSH0JkVpPXC7WUVCsWmifQsh0PoJAMGiLAuECYjnRaiWXoYpzIc0DiFJwCPqQynkhqqqSKji+n6jC5mpsLdSSVbbYUfhiGra4zjWkY9IsLDJC3xLMuck+bEYkPxMIxcZEfA9RXL8vOFmmSVGsO6do2+zhXyxVi5Mnj+ziQbLyVmBOKkuIB7KKPe9yq7iJbavPACB4y2mMlAxnENV3OLmDUOzy5TetZU8eOhPMttgWwpGSmMrs7eVaJnr3DpGQa815IcdE81tzONGBlSJJjOedm4Vw8Xj3sYxhd0w8ai/1EmR2SdB00Ry7vtJnR5U8Vyc9qXguiOt8suxZcXMkBNmYJrToLfL34h/hdin33Eo4y5K8ZWWwnD2WOJjZZuwMDFw+UOLsYhRpwUXtrL/i4Og5lBjNCUgPwxkkkmzD+CeHbZIczm/l2uosMOXTjuZostlFdZodjkkWK5kGf5ww/Fo+cFy1dnPZO1mKKUGRliODieaJYhvca/PaCGrefbeIdZ1L5scmaX/O2HPcvh6hqOE62u0RKxvPfeMHQo/OY3TfgjICbT7rij8KxeIeR4sL4CUX43+RienS0llkv1FSh0Y1IIG4u0lkDLzhD0ZV6kxKiXnQs2XBfNSxMHv1a/H05pGIEGaMHf4rnnhBd8yJDmf1YhUGJ5Y5JMinTjJ57A8zy/Q8c40hi4kEFYOVkgOJmEQZWMoN7vCuRlwy/CpW6mUxWUFwr9wk0Ry3vtJdp/brtt8F5YLEuPa64HOJzMUooePUov33XX/PdKtbuWHo3mJPiV4qc/hddfzy/f9txzwc8A4m+YSMBb21j8XNfxHFFTU8dFz2ZEe4CnaaS9BPPowyBeCOLIXVcE0u25Z7Z+SfY7Att+OZ/jv3yOP78JVxWpIqJQKDYdwp7l2bNFSMBbb8EBBwTrrFsXiNRwVZxwOIanJ7Ady1/2/jYmMzE5Jmv/cgVcLCbslBR94W0RS2Cng22FHR9STDYmlg0D7rmn9DphbrsN/vrX4qVEc5FiWXpqm+qRzkV+fzmWhT38xcIwOnXKdwaFPei5f+sTThAx17nUYvL4r2t482823VjEcKZEcoo8NFwMDMPF0w3SaQ0vqwEyaBgxA26/3Q/Ha8nYNnkyvPeeEsvrgxLLrUB9PcyYAb/8ZdONAMmkX2cXxEXjptJoGsRCd5W4Ljz2mFBr550HDYEQc9D8nvXVVPkJHeFWpuE7Y3nhh8Xyk09GD6t7d/EoY+wgakx++EE8hsXyV18FraTXl1Botk8pz7JclmvUmyreCzFgQP57xxwjKm/IaUTLglmzYH5HkznnT6LvPZeg45AhBmi4ZIglDJadOpSr/9uXiYxGJuM4aOiemHbTYjEcDDQC6z0DUdhUTbcpFJsHYc/yQw+J5888ExXLdXWBEJJ2FqIJX70OLceaZfvvS5suY4GlgJNxyXPKLDQtWC+8rUOvsKgdX3iskMfRWp3zJLrevG3K8SiTEbOSLR1ncj3LYbGc61nu0kU0YunXL18sl/IslwrLSPc3uRlRZ/k8pgMNWTGsk6KMy5jA3X+sozZhccWV+Ml9XanjtzMstjsl+J1aIpZTKTWerC9KLLcCV18NEyeK0IVCSQ0Fse2IIhXiVycWj+GkUuihJD08z7e2rmGAK670WRzOGG6OiGNZdaHQ1FoiIYxqWCyH25pCYIzCWb5hAyGNePgOf+edG/22TabQzUYpz7L8frnTejvvLG5iWtPYy+N4+22R5T1pkihb9NE5Ixh9T5B9DuJ3uGKGRV0dDP7vWBI0EMMjg86n7MmefErMdfEch/+VncwBHT5gxUqNiVzGVEYAzbjxUigUbRLXFXYjnOAn7Vju9b1sWSDili8PBG/YAXJDshKdBlx0RjGJL3RhK2SScbevLCrA7/qXXpuAZI1fCQmCJLR//iS6//DxNDUM48fmr38VoR4nntj8kL8wzRHLu+4qHLnHHpvfpTA8njZHLMubpdxKF12p83/f686Fn3YL1pNcnFPnuqViuaWzrQqBEsutwOLF4jEc1N8oloUXj4vyYkAGg4u5g2um9+bps6u5gHuCknDZtsn07QuO42dlHsnL7M8CarN3rH5b1FA/+7BXWGYAlyoIf/DB4vHoo0UnJoh6lqXH9vzzm/Fd15NSCX5yWaEEk1JZzi2hb1/hTZbejm22EfVAFy8OBiBJLSa/TiXZ+8JK9gx5EdxYGbdmrmQio/FIoesGRzU8QzyVYVsSvEPvwjtXKBSbHI4jzHepBL+tthIxymHP8jbv59vzKqqJZdahAx4uk7iE3/3Qm1XAwz+IdbXfJajiPD8uGU9U1DGM/NyHUvaxrYjlLbcU3WDXl1Ixy7l/B8cJ6u/njunhG4pccVxILP/nP6JyU7hrbO5YIamuzv98BUm2us2G0631CsNQnuX1R4nlVqCYp6AU73Y2GZay+esB1Rx6KBxxl4gzfufsJFXAk5xIzyN3pOcv+wormm1moblOJL51MDOYyohI4ka4LWr4TliK5VIxy/vvL0rGde3qVzaLGJN9993wF12pMAx5bIUMyPpmUOfy2GMwd27gVd9mG+F5+MtfCq8ff9VGS4s6qQ4wh/58cuEEpk4SRm8wM+i60xb0WfQEhhfUY5aGVNOIJn+qZD+FYpPCcSA+J8mv19g8j4XrmnnjRefOQiwvWxbYsW6f2dnZKBdooIpqhnBvJNZVx+GAZTYdILD9mWgOi6MniFkW+iPBMc2ZI+JXS9lHKZabU+2oLSO/q6xuEQ73y/2OYSFdypvdFM+yTBQPi+Vc5AzCNu9bftk4OUNZQyUd/5qC2xPrVTpOeZbXHyWWW5HmiOXp08Ud5s++NfnmTqi9K+jGV5ZN2nNeLYPxVUIkJZNkXpudraIcXC0yvrVYP/tCYrmUZ9kw8mtLtraHthC2HZRPyqUpYRiFWk5LCsVBt4Rttom27d5mm6Ci3w47iHqgYVb2tdjGMNBdMRvQh7f4ICN+50mx0RhOivQigwwxNA3SXvC7VZBk0IxquHaa+HKqQYlCscnhvpqEkyu5Np3idyRILqzB86LXcOfOolJBXR3s+a0Ip9B+WJGtsCO6e+7AN37DKQ9w0UhRxpudLN4kEMdGPEG1I3JYqqim265wItHSaQcdJP7/97/RYy0UhtHaDoeNhfwev/ylyDuRDUkgXxCH83VKff9csVyo7Kmc8ZSJ8bmhNeEZYe9+g6FokSpXCVJobrTmvgrD2DgosbyRkDHB338Pa2uy8WYsinTj0zIpPv+nTXcgfbhFzMmKaDTepyfuqMv4dtEIeEII72ONGn7qRGPcCoVhlPIsFzIOG8K7cOSRxZc1JcGv0PQmwBNPRJNoWpNwskmhv+mKnibfHj+UHR+/Gx2PGGl2/VjI4biXQvMcXGAqw+l5dDecwy1qrzUZxmQmcQmx1zP4HbpSKVY/adNJiWWFYpNBf9mGVDDj182u5qgGm9cQiXcgRFYFSfrfW82QOdPQyeB9peGiYeAh5xJTJNC0FGnPYBpDqaYKvYNJLXAZExjMDAaMHUzt1UEiWdmiFFROp/feIiwvnNvRlDCMzU0s6zqMGBFdtmKFeJQzhU31LB96KAwcCDNnitelmlytW0fBUMnwjLDruOjIsnHBDIFhpNBCNfdVGMbGQYnljYSclhngJulwoujuk0F4GXXErW2aBOfeY/GiW43hpCIdf+7jHA786QiMB4NtftTV5JVvo2KquWEYhYzDhvAsl6IpnuViYvmkk36cY4Joeb0ttshfnkrByr36slN2LsDA5YGact6lN1oigduQIu2Kaia/ON5k9GioHJ9k0tpRxEPl5NA0MlqCY/5k8d+LCpfXUygUbY/UoRYdEgnS60SN3T1fmsaeToaBJHj0ixrA5MB1SSZQSYfZ9WjZkqCZbBFKHQcdjxN4hkv5B4MPr+PmWouXUsLO908JETaR0SRIYYydRUW21XWCFEa2E+hBq2ymYEbsVK4QDnuW//lPuO46UXd/c6CU6F+6VDzutFPzxPKee8KLL4qwvNWrxczoddeJsn9//7tYR3qW162L1riWoZKRsoCageuJsnEeGnPpSzVVPHKJzY6/sNY7Zll5ltcP1cGvFWjJHZsUyxYyrtXBwOFeLuAuRnIXIxnITDQNjGn3+NNvHvhhFj16RI1AY2XXWupZ3thiuVSC37nnisfjjttwxyNpzLPc0ACxFXU46GiIaiddqWNO3ISaGj741Tg/EVN6JY5wbXTc4Pc2DLjwQobvKdb7+usN8MUUCkWr0NBPXOvXMY5pDEVzM35+wm6f2gAcuEyIKFkBycmGWDzBybho2cZGGbpSx6yfjuHNROAQaWiAKqopo14k9KWjIszRDEgkeKuLBUS9n6UEpGXByy9vfjHLhVi2TDzutJN4DIvlpnjW5bgUj8MNN4iScxL591u3LgiVTGP4Y7isjnEd47i8n82l/AMXAx03W24Uvh0yJhJ+p8TyxkF5lluR5sQsS7FsY+HGs17GbM3kcKbs3d5FaE7aF0/v6734425TefJNk/Ly6MUc9nRKwkJXZjZL0VyItiyWCzFgwMabXmpMLD/7LPTb2mIXyiA79WZjib+nabLoB5Pa/xPrykGstoNFqr4MsuWh7hswiSF3jmDegWJ553eT8IKtEv4Uik2ATAYwgxq7w2PT8dIp0l6CL/e0AHhjS4shJNBowEPjcU7mVq4C4DieIx7KQznaiNrjXiuTDOHeoCNcLIbtBCLs+sNtjrvZ4v0/CFvRVLG8uVHqu44eLdoYDB4s0kKa6lkuto9wTpB8b926aNm4cKikrI5xsA6VCGdJDNf3PneYBzxt+za/pQl+Kgxj/VBiuRUIn4SvvCKmyWV5sTB1dSJGed99A7Fci8krY2t4dkx+QxGAXP1tu0fwwbam70UuJpY7dhT7KORZLiXq26JYLhWGsTEJZz8XEst//jOASQU1jOplM+k98ft2znobwuXu5G8zv6NJ5YrAoH78kcmQZJIh39isYwU9hv9d1NkuK1MJfwpFG8dxAvFVi8kzl9egvWRz02sWp+4iErf7rLR5iJ9xjnY/mudyHM9xK1cVFFfH5Yjlfj/YfuKfi4ZzzhBq7wlE2OxKk+PMwvXoS4VhbG6UEst9+sDXX4v8Figslkv9beS4JH+XcA8CuV+Z4FesbFwFSc783GYh5ZFE/aWUs/fISsik/CRvd8/m2/xUav3qVCuUWG5VNA0OP1w8LyTs+vWDRYvEsnXrAkG7aBfheSjEA4kqzmu4F8NNkyZONVVF485+/nN4/HHxfOutxbbDxyHFmaz5WYiNleBXirbqAQkbRSmW5W8aphaT7geY1L4nXkujWkgsG0bUoB7TkMQ7qpJL6huCFugg5l+z2dEKhWLD43mizvreexdfx3GCWr0VJNnxfZtXdhHC9/evTYbrLuHSdEaEYHjCOZKgwS8hmSuuDCNqD2cZFpeQQNdT6GUJMudWQaj9tKzQIIVSoSS09kBTxhBpgwuFYZQSmrliOTzjKD+/22KRxF/IIeYn/n0vZh8vYwJ7b13HoystLGz0dEo4SOrroboa97qWieVCvQgUTUfda7QCTfV4LloUPK+vDzyTsjLGSeVJrmY8FST99ebETf40yOZabmJg1oAW8g789reiHJBElrUJCzdpDBoaih9jIaOwscVqW/UsFxLLBx4o2rLmEg59qfCSMH4827yfzFse9hpVkOSqtWNx62W9VaKxzNnsaIVCseH5z39gn33g+eeLryPFshREBz16LaMeqWQYkzn+qVGQTmNkY5WDsnCGX0IyF12P2ogkJkO71aDfOA5qatAPiwqpkQcKW7PfD8LWhMeOtmZPf0yaMoZJMRkuHSfHnqZ4ZeU+dtwx+l4FSca+Usk4rqWGSipIMmZMsE448S9Oiq7U8dA+Y6jFFGGa4aSdadOIvRGMGyTF70sy9F4BVBjG+qM8y61Ac5uSvPIKvPGGCMf4+muRSVtBkv8sqySe04FP1+G9rU1WdgJrlQ3AFltEPQ3yMXznKMXy2rXBe00Ry4WMysaevimV4LcxKSSWNa1wTLh8r4IkDy2vhGtT7BtLUJH9nXPFsu9tcBrQcckABuChkcbgnv1u5yLlVVYoNhpvvy0e58yBY44pvM6NN8KoUYEg0j0Hw0kxmBlo2YwradYcNFzN4K/eb7CwAfK8kLme5YYGeGdHE8aI9fRQEtcDl4lKS6RSjPcSJKmhY8fiNqO9hmFIpA0OV1ZqSRjG9ttH92thE3dFZRIZh9ypU/A7FOqRIJun1CLKj+78xN1iR5kM8VdtyMbAU1kZuI1DYXnr1okZYXlMqVT7nVVoLZRYbkWaamxkqEbYs2xhE/fyO/DpOnT/OskNqwMhPX6NKDkE0WmisEhrTCz/7GeifXNLv8OGZGN7tosRbgUbFsthYymRf3sLmzgpcETOu/ydc8Vy4G1wyaBlm9G4oOuMcicxdf4ILvrxvppCoWgEKT7CNjaXadNELslKynHRcTWPjJ5ghjOYo2KzMNwGMq7OX/gt+xzUhS/WlHPZ+6MjtXj1Q03ee0/UAy4klsOe5rBjY7dPbKGSHAcja2s+U2K5KIXCFAqJ5UMPjYYm5orl8O9hGEIMp/UErhuI4V+FHC2FYtPP6Ros/+aYKnb+33RfFNdXWIAYIzLrsm3NQ01LQJQyPeYY8fYtt4jQElUNY/1oFZ+hpmnHaZr2gaZpH2uadnWB5ZamaSs1TZuf/X9da+x3U0cK2jVrYCnleJpOBj3SgW/ZMjBeCYR0nBQHrrD9bRTzLMtYtXAYxpVXCm/26afDjBlwzTU/3ndrTdpqGEbYgIbjyAvdwcvfxsYirSXAMPDiwe8sl8vfM1xmCLRs1VXQXId+zGvtr6JQKJqJvOZLiWUA55Ukt/FrDNJ4msa0PhOYygj+c+gEGDSIqztN4vf8mcd7jaFzQ11kSt7C5t//DvZlGHDIIcG20+niQnBJD0sYFsPA0YWtCduptmZPfwykjW6pWJaEb0JefVXo0lwK7UPT4HXNZPgeNUxlONMRrQNzu+jWYnIzIjbjasZzUCoIq1i+ryg/uOp341j3ZA31fYUgjowRoaYlkuefF8c5bJh43R5+7x+T9RbLmqYZwCTgeKAXcLamab0KrDrL87w+2f9/XN/9bg5Isbz9J6KovO45uOj8Vp8QmX6zscjoQX3Gz3e3/GVhz3KhMAwZDw0ivm7hwsKez7ZMWw3DCBP2LAP89KfR5dJzXIvJL8prYNw4vvt3jf8753qWpbdhKsOL7vOFF4Isa4VCsWFpqlg+6L1qymjAAHTXYeAn9zCMyZz56mioqWHcqtFUkCSTgXlb59fiDYsww4B77oHp04P3ilUr+n5vIbIYN46xh+d38GvL9rS1aI5YLhQ+16GDyEP5v/9r/PPFfgfDEDMA5zGd4Uyhhkp2/TI/xngYk3mJIxnHNYx6pNLPXXIcwDTp/KcxHHRJ0O5ajhF/KhtXsjKSjMFWnuX1ozXCMAYAH3ue9ymApmkPAKcC77XCtjcJpNFp7skoBe3un8tuSy4uGttpdZH1ajG5sm8N271r80y9xU/3LByzHL7YZYb25tDtbWPHTDeFXLH8zDOiMsmvfiVeh3+bNxMixtALNRgplOBXi+nHLvqJfbpBtVsFwNFHw4UXwl13tfrXUSgUjSCdE2vXIhKsbLtg/fNVq6Kf22fFG0xiLjHHBVzfg3zz/SZgMi9nSt4wgjHGMIIpdkkpkYZpgmnySXYyqlTc6uYYhrG+nmVdh/nzS38uNwwDoGdP4ZiS++73Q7R7304f2hByiFWQZBJB51Y3E1RECcdQL1wY1Rm1mLxXZnJ9ifQVWd1DieX1ozXE8i7Al6HXi4FDCqxnapr2FrAEuMLzvHdbYd9timItl4shL655nS1OznbtcTCYZViQs62PtzN5eFuTJUvg6JDBk8ZA16NxVMceK+6IBw1q9tdoc2yKnuWttoKDDw6Whw2x/B6FSsflVsPoxiIyxIE0LjrJsydRe19gGd9rN7ekCkXbQnrsdv2yQKJVSAhVU8UQ7iVBCg3Q8Xxb76JFwu4gSOqTN8qxWL5zRIbZieWFjy/sZJB2qb0lea2vZ7k5hPcxZ04w6yfjln8dSuJb2ceCfwXrW0Q7t2IY2BkLyNcVuaI315mUu748T9vy+Lkp0BpiudD9aO7PMhfY3fO81ZqmnQA8CuxTcGOaNgIYAdCtW7dWOLwfH3kSlqpfXAh5Uou4Yvln1Are4ZeVBRdFOO5MIhM/DENsNxaDE05o3vG0Vdpqgl+YQr9J2PiGn5cSy/K7+tUwSJHBYAojqKaKS7cRMW3S66S8BQrFxkGKkB5LbD+Rzk+0ygreCpJY2FzKbfRjHsONaeBk/Hq6XaljKeWR6hfhaz9FgszcQHyH6yXruhBOTRHLX2dnsbbbLngvVzwpz3LL9lHIs7zFFtE481ecaBLfhJ9GXcEi/jjo3JqYdDs37mUyaFC++G3sdwuXvgPlWW4tWkMsLwZ2C73eFeE99vE874fQ86c1TbtD07Sunuctzd2Y53mTgckA/fv3b3P3QiNHQrdu8Pvf5y9rrliWXXX2/cYmhihMb5DhCNfGzikZlEgU9g6EPctyPVk2ZnOhrSb4hZGGMmy4iollabTCxlk+z6+G4eABixA3jmfeVcnPQ5nyrqvKxykUGwMpSmZvYXF+IhF4lrOJVrmit5IathhWxaonbO5bYhUUxpcxgcHMIEGD3/JYf80mt/qRponSlStXFheCkeYls8TjUUcF7x12GPToIcaKdze7eV7BxhLLYQxD5A6FZwx6rYSnnjK59FL49NP8ihjJESZd3xKfb8yzrMTyhqE1okHfAPbRNG0PTdMSwFnA4+EVNE3bUdPET6pp2oDsfuvytrQJcPfd8Ic/RN+TF0up+sWFWLdOXKDJMpHU4WgiqePVuJW3blhsFfMsh9drrliW8dNtkU0hDKNQiaHwb1bIEId/o9wwjHCms5ymtbDRHSGgy6inimplABWKjYR0jtTXA+edB8OHRxKtqqimjPpIZYtFu5jcve2YiHCSN8UJGpjEJQziBQxcvzKSd6QViVmWyFCMpniWZcLxfvtFP//BB9FmVpsbGysMI/d91w1unsZxLVudVskJ2yQj3f5kRYzanBuj5ojlPfeE7t3FvmSDMxWG0Tqst2fZ87yMpmmXAM8h+ibc63neu5qmjcwuvws4A7hI07QMsA44y/M2n5+upWEYW24pLtBk9q7ypkqbP7xg8V4s31uYSIiwuH/+U3gDcgl7lqG4AS3G++/DkiWNr7cxaMthGGPHwsMPNy6Ww7+HPF/Cg1mxahjhRB8AVzPQPQcdjyFMY84PVWQyJp63ec0mKBRtnXQ6m5j1QSV8lPUqV4nk2wqSDOFedDw/JnEp5ezqRscJG4sMBhouHho6Tra2us4LDOIGxjLz0PyYZQiaIjVFLD/zjPBuFgq1kAJ6t93yl23qNEcst9R+NsWzDDmzhdlwnXi8+MxgS8TyZ5/lz2icWl/DCypkb71plToDnuc97XleD8/z9vI876bse3dlhTKe593ued5+nucd6Hlehed5r7XGftsazfUs//Wvwr6uXi3E0VsniLtKTYNHH42uW1YG994rDPSRRwbvFwrDgOZf+DvuCP36Ne8zG4q2XA3j+uvhrbcKi+Vi03qFbhMLFbTP9TTUYvLyXkNx0dAAgwx9V9occMD6e0UUCkXzSKeDZlLReGXxfgzHz0QxcJnIaHb+IllgnBBruehkiJPGIEUZNzCWWkxiMVrkWQ6vu9VWsMMOhde74grRVbaysqnffNOhOe2qWxqzXei3CVOwdn42XKeUU6slYhnyZyt+t24sFSSVWF5P2rAM2fRojlg++2zRwa+sLKiFLCsq6Dqcemo0vkzGLBe7uOQF29IwjLZMW/YsSwoZ4/BxhwVyIbHcVA/I/3aqooEOfnjGG1taLFyoptgUig1NOh1tMhSOV5bCSMplHY84KXb/zI6ME0JUZzCyFTKmMYTrGEclNXnT8bnPpWe5mM1oqpNB10X88uaIdFj8mPZxyhRxI9LYTcvrmsmEk2q4jnFo2XCdUnHS8nOuCw88ELwfeyMIsYB8sSzPvQw6Bi6W+wI1VHKIm1/bWdF0lFjOYdkycfI9/3zzPxs2gp9/nh9oH8YwgGSSX68Zz/6rxEksY5HlyR+erit2sedeKC0Nw2jLtGXPskT+DsW8E00tK9jY7za3TIRnyAF1fkeRJHQHF8FFF4l6r83gnXfgt79VYluhaC7ptJjt+fm2ovHHM1fUMHJ6MK3+LMeykH1JEyeTvbn9ZDcrMk7k5iZUUxWZTQJhUwp5L5sThtFeefllkYyf2zGvNRk6FL75prjtl79ZIgFXP2byx9QYP669lFNL/n5z5gjnGojGJT1HisYlNYjGJbn7lSF8LzAIB51Ytpb3kdjKzq8Hm5Gkah3mzhWPf/5ztPB7KQrFLO+xB1x8MUyaVPgz+9SJ2py/WZdiVDZTesstxQVUSCw3NoWSW46sNTzL773X/NCSH4NNwbMs//7FDKbMSA6vW4jGxLIM2ZGD6a9WJ5mKRRkpvLvAmzwF7c470EaMaNJxH3OMKCt11VUiFEehUDQN6QxJIpoM/VFLYjEe+pUzk0spQxjwFHFmbDOcO1ZXUbGTGbGphXITZLm5bU+3WN07GtMaFsDNCcNor/TuLf43h30KFrVtOWGxrOvR37DUOC0/V5cthSAbl2hOJivcROOSz7X8uOdaTG5gLEcwy6/tbCMSRTfHEoEbAiWWcyiUfNVUwkawgiR7PGDDOVbBNpQ//aQa6uuJ4eFlM6WlWJb7njoVDjhAPC8mlnNP/NYMw+jZc/230RpsSkb/xxLLd94pHMerV0ffP2i1TZx0UOzcdfBGXiReN0Ewy/NKeRwUiuYhnRkNDUAySKryRmnEQ/HKMTJ816EbcxpMBrj5ieDhm99wchZPJYhdGW1wEraFspKC8iy3HosXRxu+tAbyNys0Jue+V1sb7F9+Tt6U5TYucTGwsUqK3+mcB4jGOLWYys6vB+pyykGKh+bcfYU9y3JKfCYDGb3sWpE1kTM1XkGSwz++FzyRKe0Qw8bywzCkkevdG+64QzxvbBo/17OswjA2LI0ZofDvV2rd3BuDoUPFo+wGtXp1tCxQMmGRJi5aYSNShTTPhUsuaVJIhjzPlRFVKJqHFDGpFGAHSVW4Li66f02mSTC/i4Wui8/0z0RjTsOEk7P0TJAwKAnbh/Jy8Ri+EQ+zKdjNtsYuuwThLa1F2LOcS65Y7tYtcFLJz61YEe3m6qKTJsYobgfg0tXjC2qMGioZzhTOY7r/vkryazmbkaRqXVoyVbHLoiS3UkkZ9eh4wrMgM6RD3mULG90T6slFYxpDqMXMa5kMgcFrqmdZXpCbkje2MTaF7/JjhWHstJN4XLZMnAs9VyT5b6gs0OBVNQzE5kpu4TQeA3neOU7eeZfL0qVKLCsULSUslr0jReyxRwo9nuDihgn0Yx4gvHr6NibGEtjp8/xGJeH4ZBnD7JFCjwUJg4Vilrt2FY8rVhQ+vk3BbrYHSonlXHsfbjgmP/fD89FurnMPHsGlb1SxPwt4iSMxVjlQWRZpsx5taiVmrlXH1/VD3Xvm0JjoKfWZvRfbJGjAyFbW9EBcDVmDB8EdoqvFwDBI6x2oRtTmlCEUzRHLucdQVibuVjenuKRNwUPyY4nlX/xCPJ50kvhd+68OjGCcFH1/EEbwVq7izd1OJYMhJup0PXA9FeDhh0XrW9kGVxlRhaJ5hBO40/1NLthdJN4+d2UNUxnBxdzJxdxJLSbxuLgk9/giev3KNtcSGcN8HeOYPb4m72a3kFheubLw8W0KdrM9UEos575XSCyHha+Bw9ItRDfXSYzKFhp0RSxQaBYiXBHDQ2MpYixQTpGWozzLOZQKwwifaC+9BL16CcEh3397W4vT0PGycUUuGtqQIb7BqyDJTCzipPEwYPhw/vBWFbVJsVwKpbCRa4lneXMKwYBNw0PSmFgeMUI0lHn//eaJ5d69g/XjcXh+tcXvsp6nNAlmepY/5Vb2ZQoH0DRNqPNRo4Kd55Azu1t0KlehUBQmLJYbGuDr7iYPfGGyVQf8JD2ZtBePCzs2v4vFSaHr18bK266MYT4ilDPSEs+yEsttg6aGYWhadJ3c+szynFmul3M9YzHI+PHLmmFEnHIgqrGczBPo2RrfAPqf6+AYq+SMo6Iw6nLKoZToCQuKY48N4okl73QyGcWkbKkgnQatg9/RCWT70xQGHoYrNlbXIzhpd99dlIh5+OFgm831LCcSm1eNZdi0xHIxttkGnn668XVLfddYLOp5klO40vNg4BDHAS97smQyTY5dVmJZoWgeUixXkITx4zlgjbjOtn4vaGssy3vFYsKWv7WFuH7/0XVcXghGLoXsRKGYZRWG0bZpaoJfx45R3SE/J23+VIbzLMdyxku/ZhD/Qwe/OyS/+U3EKVdDJafyGLFsR0jZSj0+rnAelaJxNjMf5PrTVLHc0JA//dXQAFMZwTv0popqum4LZ4aW6/I2UDJ3Lgfvk2Q6ojh5IgH//nd0m/JiKuaxLORZ3tzE8qbgIWlKFZVCv8t770V/w1KzAvLz4ex5CDwPWjhWXlIkdjl3IFZiWdGesW2RF/CznzX9MzKhu4ZKEuNT3KIlWMcErJdmkKCBGK4fLzofE12HdevE9dtrO7CW2oB4bRiNd2qDqH1RnuVNg6Z6lsMhGOHPSYZwLwlSaC6BRxnIoBPr0sU/fwLniSwgoOGio+OgOW7BPCpF46jLKYdSoie3ycjatdHXNTXB8/OYzul1U3CPqmT1/5I88gj8O1ZFA2X4NnHOHEb8R3geOncuLIjPPFOUDLvllqYdd1mZCsPYGDQl1l0axrBQ7dkT9t03fzulPg/RihjS8/Dg1hdme4GFKDA9V2g/6yOWFy8Whf9V3LNiU2XgQBg8uHmfke2uZTxpzGvgDi6m11fPY+DioEdCLQxDiOUKkkz6QHieX9QqWfdikqOPzt9+oeupkGc5V2RJlFhuG7SGWJaz0vInladGBp20VgaW5euTcKObBhJM5kJGMYkUZXg5nSYVTWczk1XrT1M9yyAMX/gzB6VFnFo3FvkGNF2f4k/H2IzHBEwGMpPrGcsxvIDmuhhZz8PiDoXv8srK8sM9wuQe54gRcPjhjX/PTYlNwei3VCzn8u23jX8+XIs1nFH/WQeTmSv7cpd+CYaXEdb29tub5EFYH7H8q1+JTlmnnQYDBrR8OwrFpoRsdy3jSQFi2frKMsX7MiZQi8lx4HuWj8cm7oqwKbwUsVob182/RnfYIX+fYQEVj8Ndd8GRRxY+vk3BydAeKCWWw46SxjzLYWYzgHu4gK7U8dFOFg+ZJulVYlmhRjcA79Abu6raLySgaB5KLOdQTMisXQvffx99T4pliAqYDAYZYn6NzZlYkYSPGQzmaH2m2F88gd1gtdoJfMgh4v/mxKYgliW5YnnKFFi0SDxvilhesqT4MjljUKws0PLlIgyo/7m9ufAntvAe5Ahl1y28/6aK5W+/hS23jLaPlTWglWdZ0Z6Q7a6lMDmY2ZzOo0C23jnQlTp/fcMQ44iNRcZI4DopMlqCmGXhvhhsd9Qo+PnPo3a8UIIfwIUXFj++Tclubs6UilkeOlSE31x4Yb5YDv9+1VQxhGnESeFoCX7jTfBF8F7Zz4Vj6HOFsiTxwHQRhjF9upgKV6EYTUaJ5RyKhWHsvz989ln0vbVr4Ycf4OOP4RfYfpwaeExhBIvo5k/BhYU0aOA6ENP58vIJ1P7JZL8OrXPcmyObQhm8Yn//YcOC503x9EixPH06bL11dJk0trnZ0fIck53BZmVMhl5hFjTOP/mJuOk755zo+00VyzvuCN27R6+FTeH3UShaGylOZA7BMCZzCo+LUl5AKqfaRThm+a4zavjmQZvPu1ncb0Y7q5WVwRFHFN5nc7zFSiy3DUp5ljUNBg0Sz3PFctiu1mZnpS1svtzDgk/hasZjY7E02+46EkNfoI63hS1WchwVt9wClFjOIVw67r//FY0bLrooXyiDMHyWJZYtpRwDFw8wcFlBZ25mDCBOaukJ1LKG1MADT2OneB3l5XDrrS073vYiVE45BYYM2dhHUZymhGF06CA8sn/7W/F1evaETz4RiUZh7y1EE/zC02xf727CF8F6990nDO+UKfnb//jj6PFKGusQGebzz5u+rkLR1hk5svF1Xn1ViJ6KiuC9dFpc0/X1QqTI8lwZDJ7gZG7lqohnT8YsA6zoaXIzJj2yM4rhWZlSZUubI5ZVGEbboJRYhuCmpljsuUTelA2ujwri8+tFM5LcGPrwrCMIJwvxBJBSccstQN175hAWPT//OVx8cfF1166FeaJJE12pw0HzKxFczt/9dqbhAuEuOg4xHE0E2pcda7F0KRx/fOsc9+bKY4+JmNi2yq67isd+/Yqvo+uwahUMH158nfvugzfeyBfKEJ3Gq8VkKaLe5qjE5Lx1H3qo9PGqahgKhTjv7747//2GBliwIHg9ZoxIYg2TSgXXaSBShOp9gwF5U+DSswzBrJEUyWGx3NLSkrkoz3LboDGxLJc3JpYl/X6INrY5pN4Gghj6TNYt5xCLzGzUYrL8oRoYN06FYLQAdTnlUMpDGK5AANGYZRsLN1uJQAN0HCxsP35oIpfiYqBlW5bM7TdcnbCbEQcdBHPmwLXXrt92OneG/v0LLwsb22FMZjIXcizPc8VHFzKMqGDWNEQtzfHjVZ1lhaIIxWZJRo2CAw4IwqJSKVEqVNOCOOF0WsTvQ7QCQbFmIzJmGfLFclggl4r9b44AVmK5bdDaYvlFN3quvbGFBckkW90+nv1ZQFCfNv+uq6GfKe78mqE77rhDnPdr1jT5I5slKgwjh2JiuVAs0LJ10RPuSU7iZJ5AwyNFGUsp9z/joqHjZmtvOvzQpVurCuXN3bO8KXDQQT/u9jt1Cp4PZgYQ1Nv8uT6DqW7QqW+AkxTTbOm0cEnnxKf9GJ5ldQ4qNjU++qjw+7NmicdV2QoDmYx4XkGSbSfbcL5FOm36nuViFQjChMXrhvAsqzCMtkGpBD8oHYZx5pkiHDTMzProudZdA8eqZLtMiklZnWHg4WYddrWYvtMu9oYF2yHGgwIJ4IW46SbxuHx5cHPYHlFiOYdiYrlQLNC/1kY75sgEvmkMpZqqyGdkj3YxPWLw5V5Wqxxve4lZVgivs2QGgzmW533fwePxwdAQLP9FqjrI+EuloLr6RxPL6hxUbKrkiuVddoEvvojmroC4Pn6yLMmDWTuPZTA2PpSXd6/i3awwzm0WlEtYLMtruZBnuZBYbknMsvIstw3Wx7P8n//k21fXjZ5r1hfj8Uih4aCjoaGJ+svZGY6wPtHPNMQGMxlxQE2Y3ZbVjtr7zZe6nHIoKJaTSbqxiAwxf+pjKeWMWDbev2OTotjAYRHd/JhSD3CzAtnz/9xaqxmy3XYTjzvv3DrbU7RdwmJ5KiMYwd28zgA+PeA03tN7R9ZtTL/mNthRYRiK9sg330RfL1kCa15IMqJO2HY5DjgO9F0Z2HlSKc5ZczeTFlrcwUV+aF4uYU9cWGzkimUVs7z50loJfsUIcqK0bCCoi4vu1/gO6xMtnc6viNEIMty0OUngmyPqcsoht3RcBUnSR1YynCmAx1SGcxkTmMhoxqy9lhoqWUp5XrxaBUlu49JsqL2HgYOelcwGGXb/zG6V473wQnjkETj//FbZnKINExbLIIrMH8AC9ljwBE+sq4wM2P/tWCVqUGkaDZRxzvNVkc/mxp8psaxoj8jJFxC2/g4uovOpA/nNcmHby+aKayqTgf9lhChxsreiOh4JL8UI7qaGyjzB/Otfw/33B6/D4lUKo6aKZeVZ3nRpqmd5iy0a31ahbdRichkT/PICBqDj+jW+wwUGPF0XBfub0clPiWWBupxyyJ1+s7DR0tl2pmTYg085nmcoo54YDgkaGMwMLmMC1zHOr2toYRMn7Ren13Hx0HxBvXhvq1WOV9dFlQg1Fb75k1t3WXoMdE9kRVvY/rK5ZSbMnAk33YTFTO77NDrV9mOIZRWzrGgLrF4drWRRinAjhxoqGcHdkGoghkMZ9Wz1cDUghIIUJW522JSnu4HnX39nnQXduon3NS1oJARRoSu781Vl72HDnS9LJfipmOVND5nUud12hZc3J8Ev12EC4ty9gHvQcP0cFk03Ikmmz3IsHhqa54kTc3jzCwy0d4eKEss5yLsnKT7Dd2UGLoP4H6fzKDqeX1N5EC8wkdGRxA4bizRxPPArZLjoTGU4ldTw7Z6qCoaieYQT/CA4N13dgHg0Az+dRhhCy/KrsshzexiT+fNLhzCD031vmBLLis2FwYNFJYuw17gYch1542n4jaqF57jLo9MgmfSvj67UoeVUGQjHh+6yC9x8s3i/Q06jqfBsZfnk8aytSfrJU3/5i+jmBioMY3Nj6VLxWKh9OQgH75ZbFl8eZscdo68rSDITi0OY7QtlTzf4YfztfmJfDZWcymNiltt1hcjp1vwCA8qzrIiQe1cvs5zn0B8PLdvEOhoTGsP1PQtnnBF8biA2rzPAF8vheGZlyBTNJdfzIM/NL0eMI/5SDUkvMH6rViFKxlVWMg4xpZx6KemXnOu5SrTmfYkjqSDZJLFcrBW3vLFUYlnRFpg5Uzw2pf26FMvh0m+ebggvHKA5GbBt//oQJUJ136Z7aCzvN4jfHiBmFGMx+MUvYOJEuO666L4MI/Bg62OvpeNJleivi5vVRCKoplPqOlKl4zY9GhPLZWXwzjvBzVIpZD1/Se4MtgcsPW047gUj/OWRm0BN88MvPvhA2O5nn23a91CeZUUEefeUa2j6MB8t602GwFsM4KD5noWysuAztZjcwwX+SWzgspRyQE2RKZpPrEDtmlpMVo0K6mYeeaR4P5WC9As2pILi9fpfbuFP2a6S0rjGSFNFNfs9Xroe81dfiUoBpWjvngdF26BQHHAxZItgC9sPpfv0ijtooINfwYjycv/crsVkFJMgFieDjhPrwHa3j2XpPuL6i8XE2PHrX+fHoOp6IF60AglWpW46VQe/TZfGxDJA9+7FY5r33z94nmuDc2ewU5Sx8tQqf1vhm8AGEnxSeSHmuhoWdjH9m8pHHmna92jv9l2VjsshNwwDoIpq/+7NQWMWh3MoSXQcMsT8UnG1mPQqi25PdPbTieGSQfeD7tVdv6K5FKvTGe72V1MDt90Gv/kNDP+Xxb3xBI4j6nwnnnmUrtn15HjsYDCEaSQezcCzxUsJLVqU80YyGdTqzIYetXdjqmgbNEcs774kyd059fN/tit8mDiWo1NP4Dou7qWj6bNlb5Zkz/OpjOD6f/dm0s9teg6zqDJN30lS7BoFYfOleIkZ+S2HmzJDozzLmx7LlonH3BCKprJgQXBu5IplOYNdhYitr6aKew8Ozsfc+t/1S03mA6+8EtQQzw3vK0Z79ywrsZxDrliuIMkQ7vVjlDPEWEgv7uNXdKUurwB9WY5YFsaxDI9UpLOTMmSK5lLIswxRY2cYUC4mL5j+oUn3Y2poeN7mVB6NxLWtYQs+pzsf0oNTeALdC3m6CohlWWsTxDWRObISw02hJRLsv1cNScwmiROF4sdGis2mnI/7fhOtn19FNb1HTyfu1ku/Mk46RUWDzdMhO//WFiY2cPwXNiTBMALPcphttxWPe+0FCxcK8XLqljX87w92XlMIOSaU8iw3J5FbjTFti65dG1+nMXLDMCC/vnc8Xvymbf588bjddrB4sXgedraUor07Q5RYziE3DMPCzpZ/AwdR1WI4U3wvRLg7jo1FIhEVGsU6O6kpMkVz2W8/8RiLRe/ycz0D4YzplSuhB4tEIwUCj3KCNPvyAXvzMRli6DroJUoJhcWyhQ1pUQSfVIp+P9iA2e6NqaJt0ZTzcX4Xi5+RwCOFg0Ff5hJzGzCyzhEHDUdP8LJmRT734k0isSrxTBpq4vQYZEM2ZjnMIYfA44/D0UfDySdn99nRhDH5N6RSCJcS+c0Ry2qMaRv84Q/w978Xd3Y0h8ZC4QC22UacJ4kE9Evldx6uxSSVElVjoOliub17ltW9Zw65hiqohmHgEEPD82NALWyGMZmXOJJxXEMNleyzND/usxaTmxkTuftTd/2K5nLQQaK72EUXRd/PjXWTYrmCJDe/bjGSu+jLfEA0yHmJI7Kt10UTnWkM4dVjx5UsJRQWy+FrgkSCuVtbYtvKs6zYiLguvPZa9HVjvL2lcGY8wckYOPTnDQxcMmhkMJjF4by2z3kR4d25M/SeV00ZKZHql0px2KdiGryQIDr5ZFEZo7G2x6XCMG64QTw2pRavRI0xbYMbb8wv1dlSSsU9V5Dkasaz7QdCg5SVRTsPh8uLdn43yU9nicY7MnH8iSeCmsqS8HmvxLIigjw5ZP1N6Rl+cL9xjGISKcr8xI/OrGASo4iTJoZLggZ6LLGbtB9lyBQtoVu3qMdIxp2FkfWYxaxIkCkt6n17dOV7MsT883guffm8uyVCMIok+YXFsrwmbu08jocuqmFuQsUsKzY+EybAYYcFr5tTDeMknszW0vdwINs02OVIXuaI9+/m2fojGMZkKkhyfWI8neujrf/0rNAt5T2UNr/YOqXE8ujR4v1SMdHF9qfYfChUZxmCKivjuBZtUCUkk5SVRRP8wg3TBo2v5JQ3RJWkn7w8mcWjxvOnU5Jcfnl0u2Hx7Djwxhtw8MH5oro9oMIwcpADfvguqhaT/U2Tqe+K15O4BB2Hy/kbejZEQzSZNPhqHwtmNr4fNUWmaCnhcyf2RhJq7Uj8ozSoMlNaz4ZgyBncXrwvSmShoeOKTpOTNSAj3NQhD/PUqfCPf4iEQSAScvT7H8bA34JjUWJZsTFZuDD6uinnYyolbir1cEOH7LNYNhRDxyNOhju4GIcY8aWZrPiIEyeDVpbgjZ5VsLC0XZdCtyWe5ZagxpjNj2I3WpWGTcIJWrFj2yQSpu/YOHkrmydWizDQqxmPnkmhZ5uqDXzoEjRcakhwzbwaZML2l18GTkMQmujSS2HOHHjrLaio+NG/bptC3XvmUEgsA3TpIh67UpedwnazQlkjg0aaGKO43S8h1Bjqrl/RUsLNDcpOrIRrr4XKSt8rLD3LMlP6EU7DQUc62vRsKJE8j+Ok0Z2UOPnr66G62t/X8OEiG3vt2qj3olB7XxWGodiY5AqJppyP6XSQhJ3xbyc9dDwy/qugTn6CBoxs+NI9XMBbP78JZs5k0S7C7pcSujJcqphYLpXg1xLUGLP5UUwsf7Bj4EGWVVbCFTHu7DIm0jDNiYkwOhcdzXPQXRGmUVZrc8EF4nPduonEVInjBLqoJTdiK1dCz55BkuGmhrqccsgNw5BIsRzt6Odl/+k8yUm8Q++8ahjFUIZM0VKkobKwhRchp2ZreKquFpPBPMLhvMLdjKSBMt8rlvan5+K4etYKex5Mm5YXjrFsWTT+rYx6v1yRpJAnb80a4TH7z39a6csrFEXIFaFNDcOQ3rcXOBoHHQNw0PmUvbMhGYFgls8dYlRTxUdniBrn8pos5c1urLxca3uW1Riz+VFMpC7dR5zD1xHknoS1SPicq8XkvxfWcNfOIrTUMcpw9SBM4957C+8jkwmuqZaIZduG99+H669v/mfbAupyyqGYWJYCJDCsg7L1k4WX7lQeo4ZKdvyseGOHMGqKTNFS5LljYwkvgmFEarYWumGrxeRi7mQgM7mOcQzEjjyfc8AFwWidyUSaJQB8953YXybbC0rHYwjTIt7lQuJElifK7WamULQ2uV63poZhgLg+bmAsqezNZIoybuVKUnTEQc/Ow8gADY1pDKEW0xchTRHLjXmWVRiGojGK/abbbAMfbGPS9S9Bg6pw4nfuOffZjia/WzGGqYzgqWMm8O1+lVzGhEgRglw6v5vkvK9FUmD4ODyvebOKm2qnVxWznIP80aVYljGaO39hIWN5pGE9glloiHqcBh5xUuyw0PbXA5G9vHateH7QQTB3rjhZ1F2/oqXIc6cWE16ogZfsvJqtxajFZH4HM68U3OLt+oqU/ZRolmD+3qLvl8E6338vPjuNoYzgbgw8DDJY2L6BLSQUpIBp75nUih+floRhSLEMhct8vkNvLjvApubtciYymjiitnh1qgoIRIi8JlvDs9xa4UxqjNn8KCaWy8qC5ifh9yS510bqpSS/XmuzlHJOeH40MTfFRGbxDr0LCuYKklRcU0lFKsVwEny9oAYOFOv95jeivXtjIri1bwY3NEos5xD2LMsYzQQpvH8kqMjWKITAsFZRzRCmYZAhTYJPdrMi2+vcWYjlLl1EYHyPHvDRR8qQKVpO2GBqh5pwaNPi5CWdO4vQ5PD57c5MMDwzgTOtOo75k0XtoSa1dwY1nb/7Tny2mirOYzrxnCY70Hyx7HniOivW5lWhaA5hEVpBks6TbBhs+TeRy5bBgw/CyJHBwB1udy0Fclgs1GKyaw+Th96Gd+iNhc2Zf7OovcSM7FNek6VuCje0Z1mNMZsfxcRyIRtaLAyjgiRXv1BJHNHZNZZx0XH90nKFxLKF7ScFeqTYco4N54j1Jk4U66TTpau1NKdGeFtEXU45yAG/oSEao2k4QY1CSe7UdiU1fLZj9ETbckvxKE9cecKoKTJFS2nKIHjwwcWXyXNRnN8N4vzONNCVOk5JjsEZEO0GBcKzDMFNojzfw4a1kEcsHNmRy113iWNZsqTx76NQNIa8MZM3gdv+PZr4es45cPHFImFVcsCa0kmrEJy7sl7+FpX514fc9/p4lls7wU+NMZsfxRL8ConlYmEYFjZxL5VN8nZAA1fTSZNgKeVczfi8nBUbC08X7dkcYqzqZ/nLpI2XM+iNsal6lpVYzkEau/r6IJnP0QxcI+pFCxNuOiLrD8qKBFttJYqSv/iieC0NorrrV7SUpgyCs2fD//1f4WUdOojHpZRj4GZjkF0OZjYHZ5KReP1csQzifLexsLAj4qKQUJACutCyf/5TPC5a1Pj3USgaQwoJ6eTQ3Gji62efRdf7/HM4YHl+04ZLLolud6/vRbMHea6H2xZLQSKvyVIhFI15lnv0EI9NiKYqyYAB4nFT9+Qp8gnb/qeeCm7AColleT5B9JxbSjkuOhk0kYHieXiazkQuZSKjGcc1cISoKx7G8/u/epHzXO67MbG8qZ+PSrLlEBbLtZj8Z0QN3g3jeP7qmpLB75JjjxWPxx8vHj1PtLvs1Uu8VmJZsb409dwpVsBeGtiu1OGg+wWzTuUxnnMqcV4JBLA0snV1QYeoYUwu6I0rJBRycwDCNDSIRyneFYr1QZ6r0snh5SS+yva+cnDfY4/8pg3vbWfx058G26wgyY3JSsZxDS9zODM4nS4L86+P5lTDKHb99u8Pn3xCnlhvLs89B6+/vumLE0U+hhGcR4cfDuefL54XEst33hncOMnztIIkExktPMpouGiiC6Xn0Zf52ZlGFzIZJnGJb9stbHTHyeaqOGz5hu3vR267qY1KlGd5MyEchgGw+1kmsWvHsPwnTbvdHzRITNsdfbR4vWJFdLkKw1CsL009dzp1Kvy+NLayvqyTlcsySVV7yfbXlYawfybJTCxu5A/cwcV++Ea4hWopz3KhMAx5jamYZUVrID3GMlTo21HRFu6rVwuxsPWdwTRzbljR/I4m22wTbNPCJu4KARHD4XQeJXb0QF9EtKQaRimxsOee6y9yu3QJRJJi88Iw4JprxPOysuDGq1jJWnmuyfM0CC11kQURHXRc3WAtW+Ch+f5jHce37Uspx9N1MohwjZV9LX8f8rprqmdZieXNBDm4y2oBudNsYeSyMWOi7xsG7LijeF5XF12mPMuK9aWp504xsSw9uVIoTOZC0nqZ712rr7D8daWRraKaMlIY2VKJHprfLnsp5UDLxbJC0RqE4zlrMfl26JhITMP+q0R8ctcJIpZZCt5wGJ2uExHLNhaupkfqLJMKbhDl9XHWWeL5uecWPz4paFTzHkVLkWLZ84T+kGNBMYeDFKby2sjtEyGCKzQ0z+MUHkfDxUMDXSdFGTYWw5jMJC5BczJ46FzGBFb2Cq4rFYbRDDRNO07TtA80TftY07SrCyzXNE37R3b525qm9WuN/f4Y5HqWcz0HYbbaSjwWCrrfYQfxuGZN9H15wiixrGgp6+NZ3nffqBdCJqlevG+QpLr2wPwEplxe5TBcDHRcJjKaCpIlwzBKiWXVJlvxY5B7Xv3UicYy5yZsg7DPYbFci8nF3iS/vjgAiSB/RV4fe+4pwqP33bf48TTFs6xQFOLSS8VjruCU51JjYlmep7WYnLNj0CfCwEPHRXfTxHAxsr5lD3iWY9mfBUxilOjyioeGS1fqIrZebrupCX6bKust2TRNM4BJwPFAL+BsTdN65ax2PLBP9v8I4M713e+PhTSw8ofv2FE8FhK3MomvkFiWnuVcVBiGYn1piVj+6CNYuFDMPheasrvnvcC7VijBr5oqGrIhGw2UsZBefrts2c2vkOiV7xVapsSyojXJvVmTDXEkubHMhRK2dT0/1n8qIziCWXx01EhRd27mTD9/pVSprFyUZ1nRUiZOLGwnpROiqWIZ4INtgwY8GQwyWhxXM6KzJ67LqTzGJEahZwP1hB/aEO2yQ8fSXLG8qd4stoZ/cwDwsed5n3qelwIeAE7NWedUoNoT1AJdNE3bqRX23eqEPcsVJNl5uohvKyRQpFEtJJa3377w9lUYhmJ9aUmC3957C69Xly75YnmvvaKvw40awh6JgcxkMhcyjSHMpW9eN7/tP8kvu6U8y4oNRe55dOqpItlNIsOOlowUscyFErY1TVS7GD48+n4tJvNG3Cmypsz8KeimoDzLipaiaYXtfmNiWdrfsEbp0EGczyeWiZbXR3o2F3l3+PZcnp7S6+wSI4OOq8e4vMPt1GJGrjW57cYS/Db1mOXWaEqyCxDq9cVi4JAmrLML8HXuxjRNG4HwPtOtW7dWOLzmIU8CWauz44QU3JGg6w01kGNcpeeukHehscLzSiwrWkpTPcuyxndusk9u9YlcT1rYs5x7I3ge00mQIkWCpzmBU3nM7+a3y0c2uddIKS+aFOVKLCtag0Ln0ezZItl6+nTxuhaTJeeZ7Ny/8DbOPVfY5smTYcqU6LJCThHlWVZsTKRYbmqCX/j5vA4m9d1Mapfgd6usopod+IbTYk/hZjJkiHEpt9GVOva/yGLadGHf22PpuNYQy4X+BLn3Dk1ZR7zpeZNBFPjr37//Br8HkQbXr9XpiPi27d61AZMOHYLkv1KeZYBDD4XDDou+J0WyCsNQtJSm3mhpmmivvsce0fdzDasUz7KTWXyOhRS9q1YFy65nrF9ayCPFt+xImgSQwkVnq2WLRJxHyPOmxLJiQ1HoXHMceOYZGDo0+l643bvk5pvhqquKb7+QzW6OWFaeZUVr01TPcvg8Ddf77rMuv3tlBUlO8Z7JijbNb4E9ftfCYXXtJQyjNcTyYmC30OtdgdyeXE1Zp00gTy5ZuNvTPbREguUHWoDw1uWK5WKC4NVX899TnmXF+tKcG62+ffPfyxXLZWXR1tfayKC1+/Ll4WUNGLh++aC59GUI9wIeCdIcOHsyVP5/e2ce50R9///nZybJLqCA7KIIiqKCLYqIom60anDxrFb98m21rS7iQbVoRdtaaT3wi9/it6394oEnStle6vdHvWotltR41KxKPSreihZPlAVBjt0kM5/fH59MZpJNdrMHsMf7+XjkkWQyVzKZmde85/V+vxfllesqJ4omYlnoCkp5OguFhOvmJ14fdZRpGrX99q1HvySyLHQ3vP98ezzL3rg1Osn/vlJLKHun0OvIGiMBjjFluGRyLbAdp7hYbm/puJ5KV0i254HRSqlRSqkIcDrwUME4DwF12aoYNcA6rXULC0Z3wHEKCndbFsybx4Zx5uTvVcAAXywXVrxoDRHLQmfp7H+n0IYRieS3dldpv1LA3mvyI8oOFkuZTC1xqmk0rbK99dJuXsc0KE8YiHgQuoJCsVxDkq89PZftlydbjOcdsx+aleT76013vrYuQjsrliWyLHQ1nmWuI5Hlr2UShN1Ui3r5Lw+OkVZ+ox4vETaTKS6WvfmV25Skp9LpyLLWOqOUuhBYAtjA3VrrV5VS52c/vw34C3AC8A6wCZjW2eVuKRynoHC3VtDYiD3afO75QKFjYllEstBZOmvhKRZZzlUKIIUVjpBo9utrWqSxAQdTe/MaZueSo1JEIBtxdpWFFeiYBuVFjSWyLJRLU1Ppjo/Biy7vbkjFkylI+ndKwBfLNSQ54ZeTUJkUXyfCX1c8TqHnPkhwv9tpJ1i1SiLLwralI9UwvHGfHxAj82UE102RIcJqqricubxZGWMKccZ/4dszwOw3BznGtjHotRicZIZ7AUCxYZSB1vovGEEcHHZb4LUGZnTFsrY0jpMvHMLZk7+dvYILimUvwa899QU9sSwHTKGjdPaCq3///PcVFX6lgBgJTrkuBpeQra+ZCZQNgouZxxk3R3l1FjR86U+zmipOm9TI5GtjZXuWPUQsC+XwzDMmB2TJEjjmmJafB/9HXsDD1g5uxkTN6m6J8v3vm/E2bTKNdqxMMwqooJkxDfW0JpaDkeVkEp58sn0Xrt70PVUsCN0P7z9f6qKtsClJcNzl20e5eq846skEqrqKG1bPJEKK9KoIJ/WLcx353dZ2ft+36nFVBI4wdjsvut2WDvLWpaf+/yXOWYDj+MLh14P8dqneQTEY1eiIWPauwkQsCx2lVEJpuZx9tilyX9gq1etktnq08a0F62ua+puaaho5+GD4xjfyp1nAdJ44NL9jGohYFrqOp582z3/7W/HPg/81L+DhKBs3ZG4l7/ZxksuZy6Z4kj//uf3LD+53o0bB1Kntm16O/UJX40WWS50TWossh8Pw3jBz/B4WaszZ8MI6RU1TIm8+kQjs/m/fqmdlfLtde8VyT0XEcgHeibuBKAuH+Sd/T1gE/5RVVe2ff0+vNShse0q1sS6XkSPhxhth0iTzvtCWkU5n2/ziF6r36imvpgrbLn5wLhQB77zTst17MUQsC+XgHYNLHTuD/yMv4PHng+fw6A/jABzzi1rmcCW1c2tZck2SeupwwxFcFM1EeDta1+ryO2t/amv9BaG9eGK51H+zLbHsDX91qLm4TGOTsSLE3VjefCIReHu4P44b8u123joUq6UfxDs/eOv097+beuY9ZX8QsVxA8ITvde8D/88YFAlTpsCsWfCLX8Af/gB33dX2/MWGIXSWwrrIHaUwsuyRThuxMYP5OFg5wexiUU0jtl38tp/jYO5PzzWNfEaPhlNOaXs9RCz3XTZuhO9+t2W3vWK0FZkN/o+8MojrI1UMfTWRtVyYqFiEZq5mNgDv353ggYn/zSQSfLZnaQsGdP6OjkSWha6mrchysaYknq4JiuV/DzcXl1cxh58d0rJhTygEK3byx/n7T/2KR15kuVyx7FFbCwsW9Byx3CWe5d5E8IDbvz/m5J9IMHBYDIi2uEL7+c/N629/u7z5S2RZ6Cxem/XO4v0XC8Xyt75lnheY3kDZJD+HFBUkiPHdEpHliS/cAb++0OxEFRV5SVWFBP//Ipb7Ls89ZwINb70Fzz/f+rhtHTu9k3FeqcOnXLSy2J8Q2g6RcTU2LpNZyhE8xcaBcR7dfxYNy2BaifnusQesWNH5yLI3vSR5C11FR2wYnlgOhfzh228PS7J1lr+5S8v52LZZlleLeewe/mftFcuF+6/j9Ix9QsRyAcET9wGppLn8SaUYEzIZ1aGQf/LvyAaWW3FCZ+kqsexRqvsTGMG8nHF5heuLRZZrSHJKfAa42SNmc3OuPmcxgvuZiOW+i5cDsmxZ2+O2JZYLG0qZ5jmmpKGNw2dfP4+XH1jBZJbmGusMfjmBUtGi833hBZPQffLJ5n1nI8vjx8PFF5t8AUHoCsqNLAeP116CdzjsWzKChQsKE8C9+QfFcDBK3FEbRrF5dWd6gJ7fugRP3AdtSJi6sY6DymZUB/90nRHLPeUPInQ/usqG4REUyzWYJKga/Nq0XhKfJ3yLeZZjJFDBP7Vt5+pzFkPEct/mz3+G669v+wQbpFzPstdQKpPtQeYq00Tny1PquIbZpKjI1ZANT46VXN6ECTBmTOmyXO0lW7KfPffsmvkJQmciy1rDwQeb188+638eFM4etu3vXzUk2echY7WD8iPLwf022EGzp2ghEcsFBE/cbw2PmSOlbaPDJqM6+KfsSEea4483z7vt1qnVFPowXSWWgxEG8G9fz+FK4tTmCeYgxSLLCWI4oQqjCEIhuPnmllHlgJ9ZxHLf5o9/hJtuyt/2bd1tC3p+33/fvA/0v8F14Wu231DKxeahr17G3468lmOsOJmDornEv6uYQy3Gd9nWcdwTy157dkHoLnj7T0fEcjoNp50GO+wAP/qR/3lrkWXvHHHA/Veau+7JZIdsGKtXt/wO3R0RywUceaT/+qORUVM6bs4cPlho/JedvRV36aXw6aew116dm4/Qd+msd9Lj2GPN8z//aZ6DXfyCHZ2KLb9wP2ggyo3fiMO115oCtNOn531eQxJdWwtXmoOsfsYX4j0lsiB0HY5jxGfwBNvc3Po0wcjyE0+Y13ffnT/P4/sl6GcZC4ZCsyk0mKUTZ/FChV/+s/BOSVuIWBa6K52xYaTT5q7imjVwzjn+54WR5RqSXPjlXEZ+lMydIyzt5Lq1diTBLyiQe8rxX8RyAVdd5QvmykpMxuesWaQnmgNrezo2FUMp0/1JELY13/42DB0KF1xg3nu1aTNYaBSrKV4bsVQ1jHeGmn2lsNYyGCHuWZpIpbCeTOQ+6ymRBaHrKCaWN2xofZpgZLmYf9l1oaEyho74rXpfqYrR3GxEQUcvMj3P8ogRHZteELYU990H554LY8cW/7xYUxIvslxK3HpiuoYkt3ABjzOJS9ZeyU/jtaymihQRXMs2V5GxWLs9y4WvC+8wdVckwa8I3oG4mD+5s5FlQeguDBoEn33mv28gysXMy1W/uIGZLGcc/Y+K8ve/++N5TgsPr0zXoE9ilOqAliCGDkdQpCASIXVoLPdZTzhQCl2LJ5aD237DBqiuLj1NUCAXs044DrzUL8rHt8SZ/y2TkLrToCg7FYhl7/+6miqY28geq2JAtKQN5Mc/hrPOgh137MAXFYQtyFe/CnfeWfrztmwYxaisDLSLpykbOgHcFNU0Ukuc7+2VoHFcjB8GOvi1dRwP2jCC415xBSxaBEuXmh4A3RWRfkXwhHHwD+YdaDsbWRaE7kw1jVi4uWoBMRKMOi3Ko4+ag6jW+ZFlv0xXCueRCCSND7RQeDQQ5a1b4nzl0wTEYjQHatqKWO57uG7LyLLzdBL+mDDNDorcnSgWTS4sQWjbkDowynXZi7avZ8hFli2roKwcLlxhcYmq4AHilLrQU0qEstAzKSaWvchxYST46adN4m04HGgXj0YDLoq0ipDQpiJSw1tR7HfhEteI7hqSXPhqPVwA1NUV3X+D7a4LrRdvvw1nnGEcfN0VEctFKBZFLtaURBC2FRddtGW8Xp4VQ5MijUlqHZMtMaSUL5a9/SDoc1ZOM8yeDbNn4xzU8mD5rBVF/UeUvfcG5xN/uIjlvkehDaOGJLufWwsZc+eBeLzFCTfoWS5lw7Dt/CpF6TR5NozCsnK4Lrby/PnleZgFoafQWlOSwsjyYYeZx4IF+ecBFbKJjzyb2Svq8nz+jgNr18IhOsnjxKj4JAW3AQsXwuOPt9h/S3mWPbp7OV3xLBehmA1DxLLQnbjxRrj55q6fr1ctYAHnsYipAGy3Xf44tg1DhpjXQZ+zhWvupdXW4v6jZSWNs86Cr3zFvA4eLKvf9qtkCD0TrY1/stxScI5jpvGS+mIkUGnf055X5iJLOR38LCvfm5xKmWVkixqRIEYm0MYdwFWhVsscCkJPpTCyrFTbNoxw2LfkrdyrltD8m3h+2q15QtkrMbrur8bSFCad259K7b9BG0axfXjYsHZ/va2KiOUieAflYpFlsWEIfYGpLOI87iROLSdWGRHr7Re2Dbtkuzx5B9UV7GGcbd799SIHyyDBiOI3bvSrZIhg7pnce68pQ3X99eWN710sbdpknhPEcENZRZtNHCqkrciyZ8MIRpabm83f0YssNxBlIWd7LkxQimf2nlZ2ZQxB6EkUVsOw7dI2DI9w2ByXb2Amo1bEYeZMjoyY43Iw6W8OV7D71CMYyBekCZPbFS0Lqlomh7cVWe7uhQ9ELBfB25ClIsviXxN6M0FrRT8rRb9nE0BxsewdVPdgBQptDpSRCOnDYiXnH0zwiJHAzrQeURS6P6tWmeePPy5vfO/E6YnlBqLEZ5kynUELRl0d3HKLGadYNYzCeRYTy4XVMOqpIxOqNAMqK2kYUwd0/9vAgtBeCiPLoVB5keVciTjXHJdHf5TI+f2nczsVNJvyjE6GH/K/XMRN/H3gKWaf0hpmzmwR+ChVDcOjq5ttdTUilotQzOcTjCy/9hq8+ebWXy9B2BoEo3yqomWULyiWgx5QFwsmT4Z4PFdqsRibNvli2TQzaT2iKHR/vJNyuY2aCiPLAO/v3LL04G9/CzNmFF9W4etiNoymJl8sR/5pbh0D3P5NX5jvf4FZ3mGHlbfugtBTaE0stxZZ9ux1rrJAKSpGVOUl/QE5K5OFQzWNvNIv2w6wxN3FUtUwPNrTzXNbIA7cIrQVWa6qKnqXQRB6BQ1E+fL+OFWvJPIqE3hCyLJg++3N62AiiGtHsGfPhmgUpzF/npGIOX7WkMS5NkFkvxhgOqrde16cM3ZJlKyCIHR/OiqWN2/2hxXWWS48eXrTaJ2fWR/8vDCy/Npr5nnmIUm2O6WWOaRIEaE+HDfCHDgWiSoLvZOO2jA8e93t1oXgOgyePZPVzCNFBLxKMhjBnCFMghi7V+If6IsEPlqrhgGlI93dBRHLRSjWQjIcNn+0Yn3TBaG3oWuicGK+cP35z03N2eB+4SUExkiQcGL8mihR4IMP8ue3/fYwutHcxuv3ixTbRSLUYLpifrhrFC4XkdyT8U6EVpn3KotFlgvF8tq1+e+DkSnvRF9YDaMwsgzmAu3MFbOhuTlXEnH0Rwmk+oXQ2/H2j2Cwry0bhtexsppGlHbBdVEpv8by1cxmMkuzdxMVC5kGwIFfJmDePGhsLBr4aMuzLGK5B1IsslxZaax048dvm3UShK1JsaovP/qReXisWwfHHw/PPBPNJUgtXgx/+EPLSh1HhJNMZzYRmlGuC2lTrquBqJSO6wV4J8JyI8ve+MHI8kcf5Y/TGLg74Tj+cdl1i4vlYpHlc7mD+VyI/XkG0GSwSBPh4zGx8lZUEHowhXdMsjZ9bLt0Mq6nexLEcMMRk1MSiZDYbGosX8NsjuApNCkcK8IL7gRTu3xNCmYWL/sIbVfDELHcAykWWQa/DbYg9HbKqfoycGDLOy1VVfDTn+YPqyHJ71fVEs7evtPKQociJJwYIHWWewOdjSzvsw+8/nr+OEGx/Pnn+Sdb78TaWp3lGpLMZwZhMijMLeNlTOQS5nHaGIkqC72fQrEciZj9ozV/sHfsbyDKO7fF2fuTBMRiNBxq9pnnrCi1rrmb+NZOMcZ84ieE57zKrYhlkMhyr6FYZFkQ+hLhZUl4JtGmj7jwgvLRR1uOEyNBWJskwAwWn+87mbUXz6bhXDNfEcs9n84m+I0bB489ll8WLiiWP/qoeGS5cJ5BG0aMBBZuTigD7M/LgEn4E4TejidQd9kFfvhDOPvstqcJ6p6mCVE4K//4X1EBDZvN3UT7MzgISKsIWqcIt5Kk3VpkuaJCEvx6JIWmeEHoS5zLHYSPvtCoj4qKkrfVwBcmBxwAL7wAn37acpwEMTJWBO2aroDPHj+bYftIu+veRGfF8nGDkuy+JsGXv65iYMp4Hhsb/f/I2rVte5YLbRgm+bQCRRNWtrKyTYYYCSoqJLIs9H68/SMUgl/9qrxpihU2CBIc5jgmAv29PeOM+TjBFUtjJsHbMXeL5s6FU081+2spsVxDkuNIMPz1Kphb3O/cHRCxXIRSNgxB6O14t65VOqtGmptL3lYD/8BZWwvLl8MXX7Qcp4Eoc2Jx3L8nWE0VZ/4rQf89wEuwchzYc0847zy4/PKu/kbC1qCjnuVNm8x/7rsLa4Fm7B9ls/QqKoicHcf7j6xfn18NoxwbRgNRvrlDnBPX1nOuvZAwGdKOaeEeW5mEuYlue2IWhK6gWBnctigllkeNgvfeK261en/nKA+vjnJFdlf67DNTXveCC4xYLgw8evuyV7s50tyMvcyFF6w2AzTbCpGDRRAbhtBX8W5d57DtVmsfewdTr1JMMbEMsHJ4lHeAOLVULkmhH/erYVx3nRln1iwRyz2VzpSOi5HAyqSwcI1dIlundcfXEgTFcrHIcuE8QyGwn0tyOQkSxHhluyh/WRvFPb2OGfskqP1pDIDaubXgZEtcdcMTsyB0BYXVMMqhlFh+8UVzfJ8woeU0AweafXLJEpgyBTZuNMMHDWppuQhGloN1+oP7fmsBmm2FNCUpgkSWhb6Kd+sayzI7wM03l+VZtiwjlsvqCqUdVLYahtA76EyCX4IYOhwh452Osl0g39w5lht/3bryqmHs+2US65ha5nAlcWo5xDVdxFbtYRqeNBDNiXPpGin0djoilr3ScYXTDRoEu+1WvDTjGR/M5cBUkjPO8IUyGBHd3NxyGcGmVCla7vvdsTmVyMEiiGdZ6Kt4dZOT1ybKukXtHTg9sRykhqSpv0yMUCiaOzAqlYJwhERzLG+cBql722PpTGT5Fdtk3f9mWoJvnV/FhJHGt/j2PVEGDDAn3/Xr/XkHbRiFLXT3/yKBSpnMfE2KQzYn+H9E2WOVsV3UEMuJczLFmycIQm/B2z+6IrJcOKx/f9hvk7FRVLyS4hs6wunEeThwHB80yHTR9KghyZkfJRj4agyvKVUtcWbuUM8I+1O+9p/DTI/7bhZVBhHLRZHIstCXaSAKs8o7WKVS5jkUyhfLOS8aKTLYPPePs/kJddQS56qvJdjh1BhcSm6cFBFq8T2qQs+ivWI56Fm2bbC/FuU6oow9FCacaT5r+g1st50Zd4c3knx1lRG7rhvNRZaDdzIcB5ZXx+DDCOnN2WTSfjHfE+2miGf/Z6/fFGff1QnxLAu9mo5EloOVYopN5909GjECYm8niNCMrV0iNHO4k2ghlr3Icu6c8GEK9TPfhgdw8heLCOsULIoYsdwNERtGEcSzLAjl8fDD5vmII/LFsu9Fc6ggxddeu504tQA8duAs1uwdLRiniTrqt8E3ELqC9ib4BW0YoZARxQBffumP09xsGihMqkwy/d5aYn831orRq5MlxfLb1VGIx7mKOdQS58VK8z+zs7aLMMb+kznI2DJEKAu9mY6I5cGD/detRZZ32QUG8oWpnQ/YuKyPVOWNGxTLweO9yvg2vBgJQjqFTfe2RYlYLoJElgWhPL73PfN85JH5YtmzXDgY9WShc0IlnTb7WIIYGWx09vNpLIRkstPr9NBDsGZNp2cjtIPOeJZDIdMOHfLFclOTiXIdZSewnRS2NmJ37GeJnEgOimWv3TXRKNcxKxe1ShDDCUXAtkljqmF4LX8FoTfj1VXuShuGt4/HKpL8kF8DoAAXiyG6MW/coGfZ9yfbuCGzH3rDM5YZ3p1tUSKWiyCRZUEojxtvNIIl6FkOh33v8x18j2YqcJQvVDyx3ECUhZyNi0IBYVJQ37no8mefwcknm4zsf/2rZQernsajj5rv0d3pjGfZto3/0bKKR5ZfrY6RtiK5/9BLg2O5yHIiYUoWevMsdnJvIMpjl8Vhjok2NxAVsSz0CW691exT5V7EFlJsf/L29YM35zf9cbB5JhzLGzcc9sWyd064fcQcnrjKt2A0EOVnh8S5bficbl2ZRsRyESSyLPQ1hg7t+LTefuKJZS+buoEo3+dWJvE4mavmcPd34rxdFc2JZYB66kgTzkWXWdi56LLX5CKRgPHjzex6MiecYL5Hd6ejnmUw/x+ljBVjwwZ/uBdZ/vfwKD/YJ85jhxuxu3z7aF5EuabGn2epCNr6ffxqGICIZaFPYNu+xamj0xeSq3c+pAoXmwwK1woxg5tZtw4uZy41JHPjBqthNBBl4bBZuE7+eCt2inJH1Swz0ty5XXKHsasROVgEiSwLfY033zQ1NPfYo+PzCEaWgzQQJXJ1lAsV/HoPU/bL28e86PJ0bjeGjEymUzU2C+vvNjSU1+JVMCxeDMOGwWGHtW+6oGfZceC66+DCC41nsRjBro3eCXn77YtHlg/KJBn2WYJ3x5mKKbFM/nb2TsZeu+sgnogvbG8tYlkQ2qaUWK4hyeQ/z0Th4GLz1H/OZ/l944hvqKWCFDoS4YLUPI56tpHwmBjBxO19v0wy6b9rmRRI7B67Hr71QT1MWmh27m5Y/1zEchE60vVGEHoyO+xgHp2hf3/zXCiWlfIjjuEweZFlMNHlqSwiTIpwJz1rhXWegzU/BwyASy+FOXM6PPtez3/+p3lur30lGFl+5BG44gpYsQLuuqv4+MHt7x1nt9uupWd5YjrJNS/WYjsp3Psi/J44mUw0Tyx7/9tSNgwQsSwIHaHY/pTJkEuatXBJoxjQ1JhL4LNxINPMrXwf6xkX/XyEGh7P3dU5YL3XhMiUd6yjnrOfWETIaUJn29J3x8YkYsMogkSWBaH9VFaa53DYRB6822yWhbmtNncuE9NJ0un8yKDnZbuK9nnWfv97OP74/GGFkeWgWN60Ca69tv3fS2ibYIKfV05w/frS47cQy8kkF22Yy4iV/u3X5mY4cEOCkGsy6G0nW8kik39R5GXvF7NheOsVbLQA7Ut4EoS+SqnIcoIYbiiCa9moSIRPvxLLJfC5lpnIxsFCY6Wb8yodPdffTJvG5CAAhJxUNtUbkxTeDRP9JHZaBBHLgtB+vGjdgakk91BLhGZcLP7XvRRqb4JUigVuhKtHxHGcfEHckC1Q/8PRUF3m8s44o+Ww1sSysOUIRqI9K0Rhm9sgwc8mppNQW8v5m1OkP46w8t44I0+L0tQEbw6L4bwTwc2k0HaERMYk9wW3syeWHQdGr/abjwSb3BRGlgVBKM1dd8FPf9ryIhPMvttAlMd+EueE/gmsWIw1r0dpAGqJ8/cz6+n32ztKzvv3K6Icdmaclb9N5CpinGMvwnVSONgs5GwuiHe/xiQilosgCX6C0H68yPKUjfVUshkL0Lj8UP8KmgHXzZX+KhTLHkOHdq6CRSmx3JpwEzqPt81c17fc/OlPsGQJHHtsy/GDkeVocwJS5vatq1PcenqCuadFaW6GlSOi3DolzoDF9YzZG3iVPLFcQ5Lz1iYgGWP8JrjssVp4zG8+siormEUsC0L5nH126VwPb99dNzYK3zb7V+htM2zt3lH67Z0AyKuSUU9+o5Hv/zZK0Mc876Q4ax/wO7le0L10MiA2jKJIu2tBaD+VlUa8fHvzgtyBUgEKnW3TZpOxIrwwMJYnljpCqaBDKc9yoYgWuhbvmJmrdZzluOP8183NUF0Nt9ySL5aXbReDiKmz6pUXBL8aRiQC38ks4rDX7iROLfusN1YeryPY1HeuhNpapmyqJ+TmNx/xELEsCF2Dd0wdOdIf5tk1dtoJY5+oqCCDRZoQF3BL3l2eYqwcYWqjg6mSoZ+Rahg9AoksC0L7qayEOuoJkcGrIKYBlxD2zTdDYyOX3hdDOXDoby9gMZ+yimHUU9fmwbSQhgb/dVCgeX5Zj2JiubVEMKFjBCPLpWq6rlsHjY0wY0b+sdW2galTSSyFe9+ZQIwE+hlobo7y1S+SHP3y7FxL3TApDvwywd8y0fyEolQKHQbHimCTIu0Y0V2qGoYgCB1j4ECTj3Doof4wbz/bccfsgGOP5ZVHPuaW9DksYHre9OdyB1NYzGKmsJxxxEiw/b9j1IBph00KJks1jB6BeJYFof3s+mGSI7g7F1UGyGBzacXN3DTdHDDtPyX51T9jRHSKfbLjTGMhF3Ej1TSSIMaSJdGit+5LESwZVo5YbmwMHNR7CI4Da9eayGx3xDtmBm0YpcYBsz1qSJpM+BUL4c4MR2qbr6EIkYHJEU535vGDh2YSyjSjcHGwSBPhvs9jPPtXGLJHjNSKCJAiFIlwT7iO1SfU8aOJCWp/GuOf4Sgjsssr5r0UBKH9vPGGucAN7uerV5vnGp00keVUiv2Bm3iZ5YzLBUPO5Q7uwLR9PZbHSBPGwsV5NMIOTM21w9ZSDaNnIZFlQSif4W8nCGUbXLvAsxzMETzF7/r5kYUD1iUI6XTWnkG2c18z87mQOVxJnFpmH5dk82b49FP4wx/aXm5QhJUSy0F7hndg70ncdx+MGuU3XelueNvAcVqK5S++yB8HfAvFdG4nopvBcbDdNOHsydLd3MR3U3dhO6Y8lYPFy0MnU0scgJ/ouexnvcJfqqfy2MjzIB7nyXSUVXuY5iN3vxZl5Up/eeU2SxEEoXV23rllsGHVKvM8YV0id7D1urIG7VBTWJz7DCBEOlfpBsydoTQ2OtzLqmEopYYA9wK7A+8D39Jary0y3vvAl4ADZLTWEzuz3K2FRJaFvsZLL3W8Bu36CTFSv4+gSZEmwiXMo4EoQwKX5K/uGCP9dhgLX9W62Fg4hHBRNFFHPe+/H+W734UXXzS+1/vvh8mTYbfdWiYA9utnavqOGpXfLQqKR5Y3b+7Y99uWrFpluttt2ODXs+5OeL+v67ZMpvz4Y1OxIiiWfQuFzt2FUGic7H/BQjOBF9FWCFdDyo3wm91ms+/nrzCfC7FIY78DGkWKMJ/+EsZvhgEDTCTqq1/d4l9ZEIQsJ55oGhHtflYMngwbWxTk5SAALGYKx/JYbp93sXCBjBWh3q1j3Yl1DHqonu+cCiX6GW0zOhtZvhyIa61HA/Hs+1JM0lrv31OEMkhkWeh7jB8PY8Z0bNrmA0y95Gss05a4gSg1JJnZ5LcvXbFjlEkkuI3zuZ9T2FR3Pt/nFjKEci2vz+VOMrfewQcfmPlu3AjnngtHHGHeB1siezz5pHkujCx7wq0niuXgRYEnNLdWouKQIe0bP2jDKFxH731QLCeIkcEmqKtdLP7JgbgoFGDh8u7ex/PJ2FouZh7D17zCbVxAmHQuymOhqSDFjvffTpxaUzouwP/9H3zrW+YiC+Dxx+Ef/2jfdxMEoXUOO8wcr/b4btTYJ84/n3sGnc+kQDMSgAVMZzq38ywHk8ZEI10s5u6YDawMgaksYuC9d0Jtbbdqe91ZOXgy5C4bFgEJ4CednOc2p6rK+Brl1p0glE9lpam/+RxRXPxb7ZFNKag1CRvhcDRXUxlg022woB4O4EW+x21YQAiHsfMvZOL24/gr0ZyFwhPP3m39IJ4QKxTLHj1RLAcjtMVE/5Zc3toW9wdbJxhZLkcsG1SuYgqWhWtXcFf6HPbjFcKYmqt7vvUolpvhJhKEVjhYuHmVVrzrCQtNmBR7fpAgWJJq4kS4915/id3szq4g9D6iUYhGufZJeG1dy48XMJ1qGpnIPwllOwBWq0YAxjWaO07KdbpdF7/OiuWdtNafAGitP1FKlUqb0cBjSikN3K61LlmxWik1HUz65MhgbZKtyPPPw3PPbZNFC0KPxauz7Iku71Z7CP/AFw6bA18NSWIkCD0fA6LUU8e5agFKm0oaSjsclknwV0xzCvAjresCB2BvPtVvm/mUEstBz3JPEctBcen9poWl8bbU8jo6bTGx7K1zoQ0jRAYbyGARmjyZB/edzYJfR3MZ8iNZyfecO7G0QxgXlW2F69/C9b2Ppp5riDXjYx3/EoIgdBle0rV3jF5NVS6J2+v2B81oFKdfWEVTGEIVMVIPR7CsFFY36+LXplhWSi0FhhX56GftWM5hWuuPs2L6b0qpN7TWTxYbMSuk7wCYOHFiJ9oTdJxRo8xDEITyKfQ6Bw+IIaWgqirXCtsrEWQfF6Ema9m464D5nPPP72PhktEhnrZjQEtx60WWg/Ph+gh8I04q1TIK4Tg9M7JcTCxvychyZ+YdTPAr14aRO1kqC6ZMYZ1ttp1356GGJOeFF0EmRdq1USjsrM/Z/Bym7Y2FxgFeYjz9O+i3FwSha7Ht4DG6KbvfKpqppJY4FzMvm3/gMPTamfw4Po5/uMbKt6guwZjpsW4TVYYyPMta68la632LPB4EVimldgbIPn9WYh4fZ58/A+4HDu66ryAIQnfAiyx7NBDlYuahsY3amzmT0auTLSLOXrb05zuOwyGEEUAOu65/BYAbbvDnOXiwuTMHMNn252M5JnJdLLLc1CRiuRzaO++1a+HMM02kv5QNo4YkO//GeNaD38f7b7jYWNr8N3b9MN+f2ECUt26J8/45c5hEghiP8+x2R+Ni4ZXJdlWIDBYWMJFlHH5N9/I5CkJfxbK8u4vN2YwUsNFUZJO4q2nEwiWEm7vz2K+f2e9fO3lWtxLK0PkEv4eAqdnXU4EHC0dQSg1QSm3vvQaOAZZ3crmCIHQzCsUyQDWNKLIlElIp9vowkYsqprFRET9ber81CUKksTG+5flcSA1Jfvtbf37r1sGVV5rXE46uwsUig4Vjm1t2pcRy0L6waZOZT2HljGI88ABMm1buL9C1bG0bRqFYbsuWMXcu/O53cMcdxW0YXlRp97tNh72KF/JFrHeytLMnyxFvJ1osY4cTonx+zqxctHneoNmkVQVpbFw7xLJhX2cZE3GwTDWVVBPU13fwFxAEoauwLFhNFZCfY2ChmcZCVlOVOw+QtVx4dye7Y0Cjs2L5OuBopdTbwNHZ9yilhiul/pIdZyfgaaXUy8BzwCNa6792crmCIHQzionl3O122xwQ/zUkRgPmVttVzIF4PJfs98GeMVys3IHVIpNXozPId/dIcvLSH2CTRqN4aso8iEaLCuBikeXBg+GYY9r+TqeeCr/5TdvjbQm2dWS5uRlWrvQj+YV4NZ8rK4tHlr07CFY2WWfA8/6MakgykpVkCOEo899YW8RvvNNO+f+rJFEu2S/OAs4DFAd98jD78xIOtvnfaA0LF0p0WRC2MeM3JbmBmXhZBl7+sAJsMlTTmHceIBrtvWJZa92ota7VWo/OPq/JDv9Ya31C9vUKrfX47GMfrfV/d8WKC4LQvShWn7mBKCcPiMMcc0Bcvr3vS72O/Fttq0dHuZ5LAXN4tdEcxHPU0FL4XLxDPVamOReFrl75IlC8GkYpG8aTRbMmug/bWiynUqZe8aRJxcf3fsd+/YpHlr0LJdcyYviL/WOAH3E+jzsBzTNjTVORNXv7/4UaklzOXKxnk3liubkZ3hwSZSUjsd0MNg42Dm8z2q+skcmUVviCIGwVJm7wbHIaB4vnOJhmzF0hr/5y4XnAqyHf68SyIAiCR6mWws+HTFe1wshvDUmYOzcnhvv3h/UMxsXKVTk4hQeJU9tCMBdGsYd++AIkk73es7w1bRjNza13DPSqlAQjy4UJfouYyvtHGzG8bqw5IU4KeNZtHDYNHQnRaK7aiSemr8XYNwa+6m/7/TYmOf39uaymCicUwVFGLo/mbb9SRijUrbLoBaEv8tJg326XURVcwjwm8TjvT/Pr8BfSnSPL0nZDEIQuwatLPmyYaVVdDE/MeoKIK1PEiVBLnAEDotxPjAyhXIc/C02EZmIkchUSYiSwhwxEWzau62ABO32wDGprGX5SnGCd3RqSDLolweavxHLDh76T5HISWa/0lk0i+de/zIH/kEPaP+22jiy35ekuFVlOpwsqlTwegavrcuM8E4mRSvmdHj8fGwOgosJ8Xkc9FdnseTZvZvCdvwDup4YkD2+uJfJeijOI8PR/zmPtO42sen4l53GnEctKGZN5N0sOEoS+xuuDjd0uRoL1+8doeNHskx9PjdKwsPg0IpYFQegTxOOw996wyy7+sGAnOk+AeX5WHIcwpiJGv34mievBIWfzn2tuyxYGM+2wE8TyyxA97PngLFw0tjZJYqP+ncATwN74/W5tZrhlcS7zWc44Llhci03KeKmT8S0qrMaPb/kblEt3Estat2zSFDyhedOO+jTJQR8k2J6Vueixm26G2bMZcNJsIMrL/aNcnJrHFBazmClM3M/8/sccAxdOTDJt2d1Z57qh8q8PcC53UE1jbp6aFNunGvnD+Fksfz7JVBYBzdi2BRMmdNVPIghCB7EsvwzkcTv5w72LYi/wEQxahEJw//0wduxWX902ERuGIAhdxlFHwYgR+cOCQtG7dR9M/PP8a95B9JGqOppVPzJYZLD5M18HWpYhMtrNtKZwlQWRCK8OjeWW5Y2vtItyMsznQuqoJ+QYwRUmVdTb+tln8Morpb/D1mJb2jBqSLL9fN8iU6wyhieWMxnz+bncwU/+ciRH/u0KpnE3GUxZN6VdWLqU/X9k7DSHKpP4M5k4NzCTPVaZZVgW/PDABCEcgrpcAf89YXHuP5PJeh7X7hfDdc0J+ec7mhKFKluiUBL8BKH7YAWUZkWFH8iYw5XmDmNgfz3lFBgzZuuvY1uIWBYEYYtSLLLsVcRgju9fC4fNZ69sF+WC0XHuZDoOIb7Bw8SpZTVVedUyTBIgaLRpbDFvHm/s4EeJExRW13DYiU/RypSbS1O8Q9See8J+++UP60x3u3LRGm680W81vbUjy54Q905kO910Zc4vXkyke37mTAb2XpNkPjOwdRpLu4RI8xLjWcZEs21cF5U2dxCOcH3PcpgUI1ckcvPcONETxPlh7OYTp+T+M3fuav4zm8ZHc7/R1w9pJGz7JQolwU8Qti3B436hWA7W2i8VtOhuiFgWBKHLGTLEfx08UO6xh3l+9lm49UWT+Hfq/0QZOTI/QfDfw03Fg5ApLkaYFAfwIs9wKOC3PNYoE2nWGhob86wDDUSZwXy0HcZVFhlCnMCjoB1cLC5mXlELxoYNLb/P1hDLTz8NF18MF1xg3nsCOfh6a9gwchF518n5xYslTnqRZceB8WsTWLiBixjNQTzP/ryEtmxQCm2HSBDjhYF+4k+aCBsPiuXm2XyAEcRX8t9w2WXGm3H77Ww+Yzpgtumi4abucv/+/u/y2diY+QPZfs1WQRC2HcGE3W+969+lqqjw7yx6x4CesL+KZ1kQhC5n2TJzN/yhh0ytXI/6enjqKTg40MPzssvM45FHzHulYNAgcpHkTLZN6rnciYVRrQpwUWQIoXDRdgQ7FmNz4O57DUmqaeS5upvpv7mRf9xjEsFCuKRRVNNY9vcJCteO8NlnptrHdtuVHseL1K5ZY563lQ1jNVXYuFnR67KaqqLL9Sw1mQws2y5GHRUomnJ+YxuNJg1u9mope/Z8fXCU2g/iOb/ivIn+BUs47Psc5/6Pv6z+H/qvvd+iXz//9bqxUWOYTyTMiVcS/ARhm+Pdpap4vZnTsJjBfCoqpufuEnnHgGQP2F8lsiwIQpczahR897vm9fDh/vBBg+DEE4tP40WWlYJxG4yv1RPHIZxsqTEfHY4wg5u5ijnceZpJ1PMEZ9ATN/F3M/lk7xj11JFWkbw6n+XiCdfVq02xhS++KHtSwFwwTJzYcvjmzaZl9Mcf+5EYL5FuWyX4VdOIky3f52BRTWNRsRz0LL/Uz5z8lu90NBqVizArMJ5lrVGuQ4wEE9N+Yk8DUQYM8OfpWXEK8eqvgv87RSL+bxQKYQTyrO7XJlcQ+iJa+3epbFzCmLyRAf8yEQ2vxnKxEnLdERHLgiBsETxLRFAst0ZQLO+3xvO0mXbIFjpPgKEUnxw7jQVM5zpmGaE3d24uWSzoibOcFNXLTem5qSPi3K3OYxFTAbjhhvwyd6US+TxR9n//Zzr6XX55+b+Dx5tvthz24IOmZfSll3YfsWxukVbgWjYpKkgQa1MsO445+d03djaZUGXAc6xRaLAs3FCE1VRxy1vmIuaJUC13TEuyzz7+PEMl7nUGxbL3Wyjlv7btltMIgrBtKZY30u/ZxDZeq44hYlkQhC3CJ5+Y58LqGKXwoopKwbu7Gk+bVxch13ACjAm6spLPjqsDTBT5gsW1cOWV3PCqSUhLEMNRIZzsdJv6VwFGkJ+pF3EedxKnlntmJvM61HnJdYW4Lrz8sumkDPCXv5T3ndrCa66yeXN5Ynlr2DC8W6SvnuYnX3qe5bVr/Yugdev86bxpXx8c5YaT4izlaBwsbEx0OjNpMk9cGaeaRsKuuYgJuSnOG53IK0lXKrLsVUoB/7ewLP83suRMJgjdCq39vBFHhclgkaIC66jYtl61DiGHGEEQtggbN5rn3XYrb3xP8CgFH400gu0OvkeKcE4oK9uG6dMhHmdjtj5vjAS2k63ZrFPUUU8d9Vg6gwVYrkP0jz+ghiTR5vws7BgJ3njDX4dSzVQcx5Tvff558/6DD9r+PuWUmwsW4e8ukWUwJ7mXT/BvkabT5kJhyBCorTXr661fJuMLaNeFt6ujXMNsUtnWtikq+NWA2Xy2Z9REqS1jhXHslok9pcRyUFDPnGme99gjXzgLgtB98I5nC5jOnMlPcCXXUkuc8BE9w3ZRiCT4CYKwRfjhD42gmj69vPGDYrGiwk/0ApjO7aajG8BI0x7Zfsa8TRAjY0WwSeE4NtNYSJhUzroBYGeMMP7XkBipjyJAMxrFakzE2XWN4PKipYW4bvtrLZcjbL3IclNT62I5KEy3FK01JXn8cZgxw7z+xz/gw2zCXQ1JJt1Xz9CP4RbqWPUg1O6c4BVivPDLOI/82HiTB2yMclb2OyRGTuW992HAOXXUFfiLS4nlIFOnmgeIWBaE7krwePnujlF+nz2WFzY36imIWBYEYYswcCBce2354xeKZY8XmIBDCMtyUIGyYJ5PtYEo9QfM4zx1FyuWbWC0+0a2EoNv3XBCERKZGAN2jHIx85jPhVg43MBMljOO5uYo/fqRVyItWAGjI6XjymnZ6p042hLLW9OGcS53MIXFVP59CmCudAoj7itXGqH8ODEqnk2xP/At7kJjEfokw7kqQr/D4hzOLACODcGQN7OZ8e+naCbCvU5di3Uo5VkuhdgwBKF7UqrOck9FxLIgCN2CYmK5Br8qhrYs1Lx5uWoHnliuIcnUf14EboqvZOeVwcJRIeKRE+g3ahgf19bBfDjzw7lsYiUWLiFcdNaKkcmYeQbFclCs3nxz+d/jvffMdwgmpZXCW0bQ1rAtbRjncgd38D0z4A+P8XPeZT2DGfJmDAJZ6x98YOwvYdK56H2YNBplLlS012jAb2O742vGAmNnLTBjP0/kzRPajiwfcED+e4ksC0L3p6dGk4OIWBYEoVswbJh5PvJIXyz7VS1ctFbQ6NdG9sRyjAQh14RcTbkzWMpk/nrQbB5ZE+WgCXCck41qvpkyflksFC4ONgliXJYVoUGxHBSmP/95+d/j/PONOLzllrbH9QRxU5O/7GJiefdPk1xOgp1WxCgUmADvvGPqV0+bVv56FpLJwBQWm3XAROV/wi9xUbiLK7g3m+wHJnkzQYwMNhaZ3DQZQri4pIkQDviR9/0ySf8vV5IhhG2DsiMc9KMYhbQmlpubW4rikSPNc7AJjiAI2x6JLAuCIGwB9tzTlFfbc0/T9hn8Tk+aFKGCzmyeWE4QI63CRLRRm2kqWMwUDvsiwRpg/aYoIz7zo5oaHXAzm2dPGAd9uh3t2vfFF0bsezaMGvy6woVC11vu5s2+xaJQLNeQ5CeP1WKTwl0QYe1JcXY4IX8+hxximpmcdVbHoziZDCxmCsfymJ9QiSaExnFMJz9PLDc1GfvLQnUu0/VtWJho/l2cw0pG5jUaqCHJNf+oJeymSGGz6TvnMeCCuqL1kFuzYQQ7PHr8+tcwaRIcdljHvrMgCFue3lDasRfofUEQegtjxpgDqxdZ9sqYXcUcmv4czxNYQc/yjw5MsHnq+dzG+VzEjdzATM5860ruWFHLyI+SbKg03QAdLFwsFBobjU0ma8Mw8yplwwhSQ5JbuMD0pU4mW3yeShnh2dQUbI5yBU9wBNxxR964QRtGKbEcI0HIMRU8VCbFPV+vh7lz85btdf3rjKc5kzGZ69O5nbfZK1cbVQNamQh8DUkuZy7D3ksSDsM94ToyoX5ksr/rC0zguqxPmblzcxcKISeFpR1zsbLryJKNQ9p7Uu3XD771rY5/Z0EQtgy9LbLcC76CIAi9jWCCn9fpyf5avsAKCquX+0X5/Jpb+T63Uk1jLoocclNM+qCe45dkfc/K4nouzZU18zr5Wc8mYe5cBr7mC1BPQHsCsYZkLqntfG6D224zYc0CweyJ5c2b/Q5WoWwHK77//bzxy7FheNU+jH3EVPvgyitNDbciy+4o3vddwHSmUp8TwRlsnhnydb7BAzzBkczhCs75Yy1fs5MsC0f5w8HzcLGxcJjPDH7OT4hj6l7HqWU1VWTsCK5lfm/n8FjHV1IQhB5BUCxfcUXxcZ55xuR49ATEhiEIQrcjKJY9Cm/RB8VyUxO5VteedUOpFI6KkMmA7aSwcXFQrGcwtcSJkWA1VdRRz9DTFoKT4RgrQk3Wm+s4fmQ4QjMuFs9wKBFSORMHqWwiWyBSmkqZ9W9qMuuS7WFnpnEcqK/Pje8J1Kam0pHlBqL8rCZO+JkEI1nJedxpPiyx7I4SjEo3EOWmk+P0X1zPNBZyaONDHI7JplOAm2nmDKueI3WC6pUrsXAIodFk+DG/yn4BlzApqmnknpp5HLPyLpIfDOdoCdEIQq/HE8sPPujnFhTSkzrTi1gWBKHbUUwsF97KC4rlZctg6VLz2rNuXDI+wfLqGG+8AadYd4Pj4lo2CSeW894+ziQiNKOyItPSpjoGwIAf1fO/vECEpqwQdDmSJ4FA2+1Iy8Yazc3GHrB5s1mXhzmJU3mg6Pf0BLHrtp7g98p2UdYDddSTIUTILr7srogse7xVFWUICUKks5VDfFuGqxTfSS0kRIbMh3b+BQEalxDYirRjWlx/J3kRITfFqQDfeNQUbm7lTHnccR3/HoIgdB+84/Tvf9/+0pDdCbnGFwSh21FMLBcSFMtawxNPmNeHWcYn+9bwGB+NjLJhA7iuCjTONtRRTwXN/kFQKRzbiLvHidH/t7dxCM/lajYHUwJdgIMPLir6UqaZIF98Yd7/ksto9lp3RyJQ59cXDgriQr9x8LPRq02E+zzuBDScdx7E40WXHeSLL+Dee1v8dEUp1pRkNVXYWaEM5ntnsHl55EmEyBDC+JAf5iTSeC1tK5nBzTDHtMuuphHbNSXmlLeSiUTJ9Vi/Hh56qLx1FgShe+JFlr3j9He+07PzC3qwzhcEobfSXrEM8Nlnpk7wLe6FKBzcJRXcfGqcHb9IYJPBQqPdTF5Vhzy++lXuOXIB1bfm1w92AW2mxkZnBWEF/QM1n4N4nuVly/xhCzkbgAtumuALxWg0zxc98W8JaoihlJlnUCyPa/TbdGvIdTH0UMqcnArF8imnmIuIww+H4cNb+TFp2USluRl2phEHKy+y7BDi5WHHM3blErROkSbCL7mMX3JZrupHA1HunAUNP83+JoSpILtyRSLiQbbfvvX1FASh+1MoloOsWLFlGyxtCUQsC4LQ7WivWK6ogF0+SDKfGYTIGFHnNDP2swTXZD3MlmpGK8VqbVpc11PH2Swgkq0TzNtvkz7URFOtbDQZjEBMY3M35/ACE6imkaftGE+VsBF4YjmZDHqeU2Sw0T9QqEzGCMZ4HMeJ5sapiKeIE+HaxjgQzesg2KhMNY8MmjQRQkfGqF9kIjX9+pUWy160vZwyeO+8k/++udmrpRzCzgpdBYRIceC/F1M/+CJ2W/sSi5mSu/hoIMrPfgb/daQ/nwaiTCJBHfUAnPe3OkI9yawoCEKHKSaWR43a+uvRWUQsC4LQ7WivWN5+ezh2VT12VihrAMvm4zExGp40La5vty7EcvwW1w1EeYQTOZUHTBQ5nebov8ykmQNaRFMtXFYykgXZ9s9hC6OGEwkTJS1Isstk4I034Hz8iLDChWbtj5RI4OwUzTVesbXpbHf4e/UwN8EOzTHAiOlL/22qebhYXMw8/mNdlLPOgr/+Faqr/U52pTzL5URx3nor/71Xc/ol9udgnsPK/q42mn0//Rv78RgOFkfwVO73BJgyBSZMyJ9XA9Hc5+d/re11EQShZ9NaZLknImJZEIRuR3vF8hHhJKdtvjsn6DLY/GnSzaz9ihFo1TSCdrEwFRo8K8YqhuXNc5ePn2caL5EhjIknu2SwSGO8zJczlwQxQi6mdFsqlYsSEzXR4HTaiOVxG5LshulaBxqbQKg4FIJYjMwrfvUOSOFgU/vBQrgyQ61tKnPESBDSpothBtNlz02OA6Lcc48/yxqSVN2RgDNjLewh5YjlN9+Ec84xYve//gv2+CzJ/2UrgZjufMZ17NWo1pDXMtwTw61tuxqSqOsSLS4wBEHoXXhiuScn9QXpJV9DEITeRGttjz3yxLJOZKO34KBYwHm8d8B0RvU3nyeIocMRnFSKtI5ku+kZK8Y0FuYEoelYl2EZE3mRA3iBCRzAi+zEp9zEDwiRIUWEeneqn8kXKOHmidJxG5L8KWOEpkbxBl/hK7xBCNd4JqZNg2gU5yW/esdFg+rZb92TjHVfB3SuMofpUBgB3YyNy2SWwnVP5UrcgW/36Hd7Cu6y4eyzSX+7Dq9jYOj5JPwpUVKkbthgPN977QXHHw+/+AXs+57fajyDxVIms5gp3MyMXItrbdY093tCabHsrSNX5l9gCILQ++htkWWphiEIQrcjWCburLPg/PNbjhM8CL821ERn09ikVSX11BEO53cCfO3GOE/UmgoNDVl7Q4wEF3Ejt3M+GbsCBwsbl4ksYyqLAJjKIk7mQSpoJoRjBLDGCD7bhkiEVV+NsWqVb4M4aGMiW3LOJYTD3rxJhjDatqGyMlcRI+gl/o91d7MPr2WLsIG2QrlkubrhcZYyOWcPsRy/xF0NSa5mthH8bla83347oeNqc41Udj+3Fn3FFXBEyy6CABs3mudBg8xzRQX87kP/N01RwTXMZjnjctF4LwHyBSbkJUyWEsue3STvAkMQhF5NbxHLElkWBKHb4YnlMWNg4cLi4wQPwitHRKl9xVgWGveN0fBKlGNCRs96NB8QpWF1lIal+Yl3KSLUEufjWB2nvTGbr3y0NGcvmMLibDdAnY2igo3LC0xAL61DPZGAqirmnZogAfx5tRGNnzpVeSXnLDQLmMbpl45k40Exdj00yr/+Ra7xydXMzqvAAbB6l/Hwvvn8oI0JFjOFI3gKTQrsCAk3ltc0xQ54rNEampuJYRqZqObNZrjrmjbdANOn55blVcLo1888V1TAEieaa97iRY7Nspog+1sA3MU5edslKJbvu88vF+XZTUJ2qs2KGIIg9Gx6W2RZxLIgCN0O7wAbrAhRahyAgQPhr9kksqOGmmGhArEcDvv+OS/KaUqxmSjt2rUxNqv+aFTOp+wJVEUTFjpn8zieR1k+v5Eh9heMuOdq5uCYqsOXnE0NdRzAi7iAjRGVDjb11PH1A2HFXQlqgCf/B458t57vsZAQqRYVOIa+/zyPEwMUoS+M/eMGLmICL6FPnELD/VEuZ27OKuGgsHJzACyb1W4VVzM7l/SYE8wXXgjjxuVsEJ5Yrqw0z8GIvBc19pelyaD4tP+eXLPpx7mkR4+gWP7mN4214513fLtJck5CPMuC0EcobCbVUxGxLAhCt2PkSBg2DK6/vvQ4hdUwPDyxVkwse9N4UU5NKpe8d/MLMWMTAFwUN3ARyxnHIqayE5/ydR4hQhoLzak8gPOHB7Gz4jQEprza727nce5GofOSDWdwMwDDz6xleDpFAkXoDxqlXVRWhAeFMphotIk266xfrpkf8r9YuOiHn6KGcXnfw8EmHFbYThosi3U/v5kDLnsxF7H2IuMKTAZifX32x0hg7RwDonmR5ULylqUizJtQz4J/tBS8hdMGrSYNRGGWiGRB6O14kWWlWh+vpyBiWRCEbkdlJXzySevjlBLLXnQ0HM5PFAyKZS/K6VkMYtm2zkGh+iOu5xJuyCX1PcLXOZkHA5Ug/EhwTuhqI3CBXBR6AeexgOlczlxIp7Jd78xEhSJWY5qgWBjB7kWKzTgKC8dEkR0/+W8RUwHjHf7x4S8yZgwwYQL2ky9yNnflItYOJtJtZqjhzjvNQ2v2CldQQ5ydVgBzE3z1ixgUNG4J/mbvj4yR2sn//LXXYOxY8zp4gQLl1XgWBKF3IWJZEAShGxA8CJcbWQ6WMQpaDADShLECzTcsXKycXznFKobRTGXOH5xB5YSzh7Ys0m4IULhkcO0I9Y5J5jMNPmxsnNwy/DbSVlbQWthoLOWaeWhT19hB8TAncRxL0KTQdoSBmS94giOxcHCwOBeN/biGp0OgFNs1pyAQtW5hHQyoWCvVTB31HDRrEWRS/JAIDweqbRT+Zru6cGjgQmSXXYpvl4LFCILQRxCxLAiC0M3o399/XY4NoxCvy9wvq3/BIasfRqGz9ZGN6E0ToZ466qkjRoLVVFFNIwfxXC7anMFi48GTOa5hNmB80dsfH6Phz353u4WczXRuy3mZvfrFv62YzlvNIxnJSs7DRHs1KhtHdvNaStdRzyEjPuXH//4VNi4KcjWclSZXkiMYtfbee7QYpl124lOsdApch5DKr51cyMaN+b+tF80vhtfSWxCEvoOIZUEQhG5GUKx5gjgcbj2yXEgDUS7f+37sdUkOTfsVIDy7Q7Cls0cNSY5jCeGs93nltNk0NJiydIXrBaau81QWEaEpGzG2SFHBn7ar48/NZrqz1CJCVgrXijAjPY9qGnPLryHJVBZR+e/N2brQ+cI350km39rhZKPgAMq2cR1tvM8F89CRCCqdIkOEhBMr+VutWdPS4lIKEcuC0HcRsSwIgtBNCIpSL/s6FMoXcaFQ22WMGhth1XZRnlzrC+JS0VXvs1ri1GGS5Y566xVuoZ5pLCREBveBCP8XsDMEfb+rqeIAXsRS/jo3EOU7O8a5/+IEv3svxoI785ftVfHwkgeD5N4r5Yd1sjzN4bzOWE46Eda+8Slj33mghV/6BB5l9RU3sqPVyBWPxGgokrwXpNCbfOyxsGRJy/HEhiEIfQ9deIDq4YhYFgShx1NKLLdlw6ishKYm//3nnxtLx9q15S23hiR1OXGcxr7eZa9sYp6CXCJeUHB7r3PT6Qx1qxdxVFZUP2ebihErr2m5PL81dlNeHWfv2UFhh0JGobpuTkDX8CyzuI5318B/v3NEC7FtrBwZKjY0wtxZvPx429+9MJr8yCPFhbGIZUHou0hkWRAEoZvglTwDXyyXY8Po3z9fLDc2wujR5S3TawhSEajBbBLpdLaqhcINRUikY21Oh/ZFtWdbKGZfaCDKxczjFnUhjk5jQ66+cgYLHarAvnkeNDay5q/PMfhJ46e2yZiOf8+QawsOpvKGQxjbckm7ETjSrGtzc9vfv/C3tO3ikXsRy4LQ99h1V3j99dbzGXoSIpYFQeix/OlPpmTZG2/4w9oTWQ6KbA+v5XNbeJaIYHc/As8OFs+ePo+G3xa3UnjTOZiaFaupAiCdzk7vmHX+8Y/h5z/3p6+mEaVdQkAGi6VMZjFTqKaRN6piHLExyiWz4IPBSfo96fupPQ92sOpHigquG34jk8Y1cvmSGPEjzLqWI5abmmDECPjoo9bHE8+yIPQ9/vhHY8vaY49tvSZdg4hlQRB6LKeeap7ff98fVsqzXCzyGayi4REsQ9cawSYdADZOzt5gku80A9ONuXXxRGNwOjebeGfhcgMzWc44Xs0YwZrJmPUttDskiJFWEbQ2IvgaZvs2j1XwwKWwfj3U1ES5IFBL2hvnpAEJ/mOj8VjXU8f6wVGogYYlfhToBz+A73639e+/YYOJHAUj88WQyLIg9D2GDIFvf3tbr0XXIWJZEIQeTzmeZW9YkGKR5YEDy1tmYbLefGYQJhNoLmLz5YExuMeI8vXrW07nlYqzcQln226/lDai1nHM+haucwNRTh4Q58AN+SI4yOzZcOCB8M+CWtIAy8JRlgaGnbYhSc3jCc63q7D+pxFiMb7znSjr18MFF7T83uGwiX5v3GguLNq6uPDE8i67tB2FFgRB6I50Siwrpb4JzAa+ChystV5WYrzjgBswdfEXaK2v68xyBUEQgpRTOi74mUexyHK5YhlaNjaZz4VYZHCzLa6/uZ/5rKIiv0iFN10NSc5iEQSsEk1NxgaxywdJfpxJMPKjGIXd9B5vivK3Vqp0APzzn/nvx4+Hl1+GL77wh9WQZOEHtURWNnMsLlxhmZWNxxk0qPj8b7gBvv99E1luD2++WbyNtiAIQnens5Hl5cB/ALeXGkEpZQPzgaOBD4HnlVIPaa1f6+SyBUEQgK6NLJdrwyhkAdNZzrg828PpWXFu22YdN2/On6aBKKcPjXNMJMHvPvKjxKsfTjLj/lqsTAp9V4RbC7rpdcQHfPTRRiyDifJ++KHxT4d1CjtbcxnXNU1NEgm+dVmUFSvgoYfguef8+QwebJ43bixvuf36me9dWelvG0EQhJ5Ep8Sy1vp1ANV6bZCDgXe01iuy494DnAyIWBYEoUsop84ytJ7g54m6YGR5331h+fLy16Mw0uwtz7KKi2WAl/tH+Xx4lIaPYORIWLkSmpcksJ0UNg5upok66lut9wxw7bXG8nD11cU/HzrUf+19R8//rHRTtuE25oeLxbBt+NnP4Mkn8+ez884t59cazz0Hf/ubCGVBEHouW+PwNQL4IPD+w+wwQRCELqFU6bi2xHJQZHtVMIJieenSzq1XoVguRrBZipc5/sbOMVxleu4prZnGwlxXwFKEQjBgQOnPq6v91170vIEoVw2chw6eClw3b7p99smfz777wh/+AHfd1erq5I1/ySXljSsIgtAdaVMsK6WWKqWWF3mcXOYyioWdS/Z2UUpNV0otU0ot+/zzz8tchCAIfZlSkeXCm16FNoygTcOzFwRtGG11/GuLcsSybfvrtfvu5vmFSJSn9jobjco1DImRaHVZ4XDrYnnXXf3XwQuCHZxGLFz/QJ3JQMJf1nXX5XfmC4VMlvuQIa2ujiAIQq+hTbGstZ6std63yOPBMpfxIRA4TLML8HEry7tDaz1Raz1xaLn3+QRB6NOUEsuFFIrfYmI5KCTbEssvvQS77VZ6nYqJ5cMPb7lO3njbbWfsDR9+CE+NqqNZVeJadl6d5FKUI5a9i4dgYuPToRhpFfYjGJEIxPxlRSJwzDH++MV+V0EQhN7M1rBhPA+MVkqNUkpFgNOBh7bCcgVB6COUK5YLfbNBm0YxG0ZbPtuqqtLtXEuJ5WLWEG9dQyEjllevNm6I+7efyttHnkdtQYJfMdoSyzvu6H8evEh41opy2cQE9+94Ppx/Pjz+OERLL0vEsiAIfY3Olo47FbgJGAo8opR6SWt9rFJqOKZE3Ala64xS6kJgCaZ03N1a61c7veaCIAhZggI06FkuRBcYwDprw2itlWtFRXGxXCg2g57lUMgI8B3fTfLTV2qxnRT8IwLUtb4i5HuWKypaduEbPNh8vmFD/vd2HPjXgCgv7h3lP25tczEilgVB6HN0thrG/cD9RYZ/DJwQeP8X4C+dWZYgCEIpgtHd1iLL5Yjl9tgwKitLR5ZLieW2IsvV1TDmrQShXDUM06ykrcjy0KG+WO7fv6VYtizffhGsd5zJmGpxrQn/wvUVBEHoS0gxH0EQehXBKG0hhWK5szaM1sRye2wYhZHlpekYGStCBhs31LZfGUxyoCeWS9kxitkwNm82HfkKa1KXovVKoYIgCL0PEcuCIPQqOmvD2G47f1hrUVQvItxaZDm4TqXEciiUHw2vroYl66P89JA4tw2fQ3JOcb/yKafkt6PebTc/clzsu0PxyLLrwqZNpafxmDtXLBiCIPRNRCwLgtAruPHG/OYXxYRdQQnhPLEcjZrH0KEwejTceWfrkWVP/LYmlr3lWZYf1W2t9rMXWc5kIEmU3+06iy/3LW6/OPVUuOUW//3gwf66BNfp7rtNFz7wo+aFUeQNG9oWy5dfbiLQgiAIfQ2JEwiC0Cu46CLz/OKL5rlcG8Yll8B++5lqac88Y4a/9VbLaWtrIR7337cllisr88WyZ/NoTSzbtt88ZNUqGDasdDQ3WP7NY+RIM/311xsxDXDWWf46evPuiFgWBEHoq4hYFgShV1EYWX7oIV9Y7rJL/rjhMPz61+XNd+nSfGFcTmTZcfx18qK6xaph6ECn6R12MK8//9ysbykR60Wqn3nGj/hWVprpggTXz7OaBG0YIGJZEAShNUQsC4LQqzj4YJg82RenJ53kfzZmDKxYYSKv8+eXn9RWjLbEcm1tfmTZWx9PQHsU2jC8+W7caN63FVlupSRyC7yyeIVe7OZmEcuCIAilEM+yIAi9isMPN97lUiJz1CjjCYb2i+WKCmPZgNbF8ttvG4/vhAkmCe/ee32xvHkznHOOP26wZFso5Ed9XTe/rFwhrTUgKYUnljdubPmZiGVBEITiiFgWBKHPccEFRigHo87l0NQEv/mNed1aXeK99jIi2rZNEt5ee+WL5QULjJgG30cM+WLZe98ez3JbeGJ5/Xp44w24+mr/MxHLgiAIxREbhiAIfY7x41s27WiNmhr/teeJbsuGUUhQLIMvgquqYM0af1hQLLcWWQ52GiwXb5ovv4S994aDDvI/E7EsCIJQHBHLgiAIrfDhh37SHfh+386KZU+sB+ddLLJcKGJnzIDTT4dddy1vucXWwbNhBJclYlkQBKE4IpYFQRBaYcSI/PcdFcuex9gTy+vXm+eBA/OrYQTtHcUiy6EQfO1r5S2zkJNOgjPPhDlzzHsRy4IgCG0jYlkQBKEdFNowjjoKXn217ek8j/GmTebZE8te/WUoz7NcWCu6FA8/DG++mT+sshLq6/33wWV1pjKIIAhCb0bEsiAIQjsojCxffz0MGQLXXNP6dJ5Ybmoyz+vWmefCyHKhZ7mwzFu5YvnEE82jNSSyLAiC0DZSDUMQBKEdFIrlcBj23LPt6XbbzVThuP9+8z5owwjOuzCyXCiWy1lWuYhYFgRBaBsRy4IgCO2g0IYB5UV7LcuUkRs/3ry/6iqT3Ddhgj+9UqXF8s47my6CXlvvrkDEsiAIQtuIDUMQBKEdFEaWIV8sl9tR7+ij/ZJxHkrle4dt2xfnWpuugF2JiGVBEIS2kciyIAhCOygmlr221occAkuWtH+eQbEdFMyhkC+WvWV0JSKWBUEQ2kbEsiAIQjtoTSyPHduxZiEeXhk6T8Tatl9yrqujysHlgIhlQRCEUogNQxAEoR0U8ywffrh5/va3OzbPQs9zZaXpshcKwXbbwVtvdawJSVuIWBYEQWgbEcuCIAjtYNAgmDjRJOZ5jBlTfkm3cghGlgFGj+66eQcJ1nAWsSwIglAcEcuCIAjtIByG55/v2nkGq2GAL5YLG5J0NcHugyKWBUEQiiOeZUEQhG7G1hLLQUQsC4IgFEfEsiAIwjamVGS5sCHJlkTEsiAIQnFELAuCIHQzvIjy1owsB+s7C4IgCD4ilgVBELYx//VfsMceflUNTyRvjciyl6i4efOWX5YgCEJPRMSyIAjCNubAA+Hdd02lDfBF8taILP/mN7DffnDQQVt+WYIgCD0RqYYhCILQzSgUzVuS/faDl1/e8ssRBEHoqUhkWRAEoZtx4IHmedWqbbsegiAIgohlQRCEbsfBB5vnd9/dtushCIIgiA1DEASh23HssfCDH8CMGdt6TQRBEAQRy4IgCN2MUAhuuGFbr4UgCIIAYsMQBEEQBEEQhJKIWBYEQRAEQRCEEohYFgRBEARBEIQSiFgWBEEQBEEQhBKIWBYEQRAEQRCEEohYFgRBEARBEIQSiFgWBEEQBEEQhBKIWBYEQRAEQRCEEohYFgRBEARBEIQSiFgWBEEQBEEQhBKIWBYEQRAEQRCEEohYFgRBEARBEIQSiFgWBEEQBEEQhBIorfW2XoeSKKU+B/69lRdbDazeyssUtj6ynfsGsp37BrKd+waynfsG22o776a1Hlrsg24tlrcFSqllWuuJ23o9hC2LbOe+gWznvoFs576BbOe+QXfczmLDEARBEARBEIQSiFgWBEEQBEEQhBKIWG7JHdt6BYStgmznvoFs576BbOe+gWznvkG3287iWRYEQRAEQRCEEkhkWRAEQRAEQRBKIGI5gFLqOKXUm0qpd5RSl2/r9RE6hlJqV6XU40qp15VSryqlLs4OH6KU+ptS6u3s8w6BaWZlt/ubSqljt93aC+1FKWUrpV5USv05+162cy9DKTVYKfX/lFJvZPfrqGzn3odS6pLsMXu5UuqPSqlK2c49H6XU3Uqpz5RSywPD2r1dlVIHKqVeyX52o1JKba3vIGI5i1LKBuYDxwNjgW8rpcZu27USOkgG+KHW+qtADTAjuy0vB+Ja69FAPPue7GenA/sAxwG3ZP8PQs/gYuD1wHvZzr2PG4C/aq2/AozHbG/Zzr0IpdQI4AfARK31voCN2Y6ynXs+v8FsoyAd2a63AtOB0dlH4Ty3GCKWfQ4G3tFar9Bap4B7gJO38ToJHUBr/YnW+oXs6y8xJ9YRmO25KDvaIuCU7OuTgXu01s1a6/eAdzD/B6Gbo5TaBfg6sCAwWLZzL0IpNRA4ArgLQGud0lp/gWzn3kgI6KeUCgH9gY+R7dzj0Vo/CawpGNyu7aqU2hkYqLVOapNsVx+YZosjYtlnBPBB4P2H2WFCD0YptTswAXgW2Elr/QkYQQ3smB1Ntn3PZR5wGeAGhsl27l3sAXwOLMzabRYopQYg27lXobX+CPgVsBL4BFintX4M2c69lfZu1xHZ14XDtwoiln2KeV+kVEgPRim1HbAYmKm1Xt/aqEWGybbv5iilTgQ+01r/s9xJigyT7dz9CQEHALdqrScAG8nesi2BbOceSNazejIwChgODFBKndHaJEWGyXbu+ZTartt0e4tY9vkQ2DXwfhfMLSChB6KUCmOE8u+11n/KDl6VvZVD9vmz7HDZ9j2Tw4BvKKXex9imjlJK/Q7Zzr2ND4EPtdbPZt//P4x4lu3cu5gMvKe1/lxrnQb+BByKbOfeSnu364fZ14XDtwoiln2eB0YrpUYppSIYg/lD23idhA6QzZC9C3hda/3rwEcPAVOzr6cCDwaGn66UqlBKjcIkDjy3tdZX6Bha61la61201rtj9te/a63PQLZzr0Jr/SnwgVJq7+ygWuA1ZDv3NlYCNUqp/tljeC0m30S2c++kXds1a9X4UilVk/1/1AWm2eKEttaCujta64xS6kJgCSYL926t9avbeLWEjnEYcCbwilLqpeywnwLXAfcppc7BHJi/CaC1flUpdR/mBJwBZmitna2+1kJXIdu593ER8PtsIGMFMA0T7JHt3EvQWj+rlPp/wAuY7fYippPbdsh27tEopf4IxIBqpdSHwNV07Dh9AaayRj/g0exj63wH6eAnCIIgCIIgCMURG4YgCIIgCIIglEDEsiAIgiAIgiCUQMSyIAiCIAiCIJRAxLIgCIIgCIIglEDEsiAIgiAIgiCUQMSyIAiCIAiCIJRAxLIgCIIgCIIglEDEsiAIgiAIgiCU4P8DqRcCssv8aWoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tau, n_train = 4, 600\n",
    "onestep_preds = model(features)\n",
    "plt.figure(figsize=(12, 6))\n",
    "plt.plot(time, x.detach().numpy(), '-b')\n",
    "plt.plot(time[tau:], onestep_preds.cpu().detach().numpy(), '.r')\n",
    "plt.legend(['data', '1-step preds'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00310c59",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- The one-step-ahead predictions look nice, just as we expected. Even beyond `604 (n_train + tau)` observations the predictions still look trustworthy. However, there is just one little problem to this: if we observe sequence data only until time step 604, we cannot hope to receive the inputs for all the future one-step-ahead predictions. Instead, we need to work our way forward one step at a time:\n",
    "\n",
    "$$\n",
    "\\begin{split}\\hat{x}_{605} = f(x_{601}, x_{602}, x_{603}, x_{604}), \\\\\n",
    "\\hat{x}_{606} = f(x_{602}, x_{603}, x_{604}, \\hat{x}_{605}), \\\\\n",
    "\\hat{x}_{607} = f(x_{603}, x_{604}, \\hat{x}_{605}, \\hat{x}_{606}),\\\\\n",
    "\\hat{x}_{608} = f(x_{604}, \\hat{x}_{605}, \\hat{x}_{606}, \\hat{x}_{607}),\\\\\n",
    "\\hat{x}_{609} = f(\\hat{x}_{605}, \\hat{x}_{606}, \\hat{x}_{607}, \\hat{x}_{608}),\\\\\n",
    "\\ldots\\end{split}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4d7d42e6",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "multistep_preds = torch.zeros(T)\n",
    "multistep_preds[: n_train + tau] = x[: n_train + tau]\n",
    "for i in range(n_train + tau, T):\n",
    "    multistep_preds[i] = model(multistep_preds[i - tau:i].reshape((1, -1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f75dd428",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1f701805550>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 6))\n",
    "plt.plot(time, x.detach().numpy(), '-b')\n",
    "plt.plot(time[tau:], onestep_preds.cpu().detach().numpy(), '.r')\n",
    "plt.plot(time, multistep_preds.cpu().detach().numpy(), '-.g', linewidth=2)\n",
    "plt.legend(['data', '1-step preds', 'multi-step preds'])\n",
    "# plt.ylim(-4, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "918311a1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Let us take a closer look at the difficulties in -step-ahead predictions by computing predictions on the entire sequence for $k=1, 4, 16, 64$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ab676c28",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1f704cd7f40>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "max_steps = 64\n",
    "\n",
    "features = torch.zeros((T - tau - max_steps + 1, tau + max_steps))\n",
    "# Column `i` (`i` < `tau`) are observations from `x` for time steps from\n",
    "# `i + 1` to `i + T - tau - max_steps + 1`\n",
    "for i in range(tau):\n",
    "    features[:, i] = x[i: i + T - tau - max_steps + 1]\n",
    "\n",
    "# Column `i` (`i` >= `tau`) are the (`i - tau + 1`)-step-ahead predictions for\n",
    "# time steps from `i + 1` to `i + T - tau - max_steps + 1`\n",
    "for i in range(tau, tau + max_steps):\n",
    "    features[:, i] = model(features[:, i - tau:i]).reshape(-1)\n",
    "\n",
    "steps = (1, 4, 16, 64)\n",
    "plt.figure(figsize=(12, 6))\n",
    "plt.plot(time, x.detach().numpy(), '--')\n",
    "for step in steps:\n",
    "    plt.plot(time[tau + step - 1: T - max_steps + step], features[:, (tau + step - 1)].cpu().detach().numpy(), '.')\n",
    "plt.legend([\"original\"] + [str(step) + '-step preds' for step in steps])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2436a0ab",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Text Preprocessing\n",
    "\n",
    "- Load text as strings into memory.\n",
    "- Split strings into tokens (e.g., words and characters).\n",
    "- Build a table of vocabulary to map the split tokens to numerical indices.\n",
    "- Convert text into sequences of numerical indices so they can be manipulated by models easily.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "32f959a3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def download(url, sha1_hash, cache_dir=os.path.join('.', 'data')):\n",
    "    os.makedirs(cache_dir, exist_ok=True)\n",
    "    fname = os.path.join(cache_dir, url.split('/')[-1])\n",
    "    if os.path.exists(fname):\n",
    "        sha1 = hashlib.sha1()\n",
    "        with open(fname, 'rb') as f:\n",
    "            while True:\n",
    "                data = f.read(1048576)\n",
    "                if not data:\n",
    "                    break\n",
    "                sha1.update(data)\n",
    "        if sha1.hexdigest() == sha1_hash:\n",
    "            return fname  # Hit cache\n",
    "    print(f'Downloading {fname} from {url}...')\n",
    "    r = requests.get(url, stream=True, verify=True)\n",
    "    with open(fname, 'wb') as f:\n",
    "        f.write(r.content)\n",
    "    return fname"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b6327be4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "text lines -> 3221\n",
      "the time machine by h g wells\n",
      "twinkled and his usually pale face was flushed and animated the\n"
     ]
    }
   ],
   "source": [
    "txt_file = download('http://d2l-data.s3-accelerate.amazonaws.com/' + 'timemachine.txt', '090b5e7e70c295757f55df93cb0a180b9691891a')\n",
    "def read_time_machine():  #@save\n",
    "    \"\"\"Load the time machine dataset into a list of text lines.\"\"\"\n",
    "    with open(txt_file, 'r') as f:\n",
    "        lines = f.readlines()\n",
    "    return [re.sub('[^A-Za-z]+', ' ', line).strip().lower() for line in lines]\n",
    "\n",
    "lines = read_time_machine()\n",
    "print(\"text lines ->\", len(lines))\n",
    "print(lines[0])\n",
    "print(lines[10])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "425b3940",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Tokenization\n",
    "\n",
    "- The following tokenize function takes a list (lines) as the input, where each element is a text sequence (e.g., a text line). Each text sequence is split into a list of tokens. A token is the basic unit in text. In the end, a list of token lists are returned, where each token is a string."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9e2ef63f",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['the', 'time', 'machine', 'by', 'h', 'g', 'wells']\n",
      "[]\n",
      "[]\n",
      "[]\n",
      "[]\n",
      "['i']\n",
      "[]\n",
      "[]\n",
      "['the', 'time', 'traveller', 'for', 'so', 'it', 'will', 'be', 'convenient', 'to', 'speak', 'of', 'him']\n",
      "['was', 'expounding', 'a', 'recondite', 'matter', 'to', 'us', 'his', 'grey', 'eyes', 'shone', 'and']\n",
      "['twinkled', 'and', 'his', 'usually', 'pale', 'face', 'was', 'flushed', 'and', 'animated', 'the']\n"
     ]
    }
   ],
   "source": [
    "def tokenize(lines, token='char'):  #@save\n",
    "    \"\"\"Split text lines into word or character tokens.\"\"\"\n",
    "    if token == 'word':\n",
    "        return [line.split() for line in lines]\n",
    "    elif token == 'char':\n",
    "        return [list(line) for line in lines]\n",
    "    else:\n",
    "        print('ERROR: unknown token type: ' + token)\n",
    "\n",
    "tokens = tokenize(lines, token='word')\n",
    "for i in range(11):\n",
    "    print(tokens[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47534960",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Vocabulary\n",
    "\n",
    "- The string type of the token is inconvenient to be used by models, which take numerical inputs. Now let us build a dictionary, often called vocabulary as well, to map string tokens into numerical indices starting from 0. To do so, we first count the unique tokens in all the documents from the training set, namely a corpus, and then assign a numerical index to each unique token according to its frequency. Rarely appeared tokens are often removed to reduce the complexity. Any token that does not exist in the corpus or has been removed is mapped into a special unknown token \"\\<unk>\". We optionally add a list of reserved tokens, such as \"\\<pad>\" for padding, \"\\<bos>\" to present the beginning for a sequence, and \"\\<eos>\" for the end of a sequence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "eddf3c11",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "class Vocab:  #@save\n",
    "    \"\"\"Vocabulary for text.\"\"\"\n",
    "    def __init__(self, tokens=None, min_freq=0, reserved_tokens=None):\n",
    "        if tokens is None:\n",
    "            tokens = []\n",
    "        if reserved_tokens is None:\n",
    "            reserved_tokens = []\n",
    "        # Sort according to frequencies\n",
    "        counter = count_corpus(tokens)\n",
    "        self._token_freqs = sorted(counter.items(), key=lambda x: x[1],\n",
    "                                   reverse=True)\n",
    "        # The index for the unknown token is 0\n",
    "        self.idx_to_token = ['<unk>'] + reserved_tokens\n",
    "        self.token_to_idx = {token: idx\n",
    "                             for idx, token in enumerate(self.idx_to_token)}\n",
    "        for token, freq in self._token_freqs:\n",
    "            if freq < min_freq:\n",
    "                break\n",
    "            if token not in self.token_to_idx:\n",
    "                self.idx_to_token.append(token)\n",
    "                self.token_to_idx[token] = len(self.idx_to_token) - 1\n",
    "\n",
    "    def __len__(self):\n",
    "        return len(self.idx_to_token)\n",
    "\n",
    "    def __getitem__(self, tokens):\n",
    "        if not isinstance(tokens, (list, tuple)):\n",
    "            return self.token_to_idx.get(tokens, self.unk)\n",
    "        return [self.__getitem__(token) for token in tokens]\n",
    "\n",
    "    def to_tokens(self, indices):\n",
    "        if not isinstance(indices, (list, tuple)):\n",
    "            return self.idx_to_token[indices]\n",
    "        return [self.idx_to_token[index] for index in indices]\n",
    "\n",
    "    @property\n",
    "    def unk(self):  # Index for the unknown token\n",
    "        return 0\n",
    "\n",
    "    @property\n",
    "    def token_freqs(self):  # Index for the unknown token\n",
    "        return self._token_freqs\n",
    "\n",
    "def count_corpus(tokens):  #@save\n",
    "    \"\"\"Count token frequencies.\"\"\"\n",
    "    # Here `tokens` is a 1D list or 2D list\n",
    "    if len(tokens) == 0 or isinstance(tokens[0], list):\n",
    "        # Flatten a list of token lists into a list of tokens\n",
    "        tokens = [token for line in tokens for token in line]\n",
    "    return collections.Counter(tokens)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4de51712",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('<unk>', 0), ('the', 1), ('i', 2), ('and', 3), ('of', 4), ('a', 5), ('to', 6), ('was', 7), ('in', 8), ('that', 9)]\n",
      "words: ['the', 'time', 'machine', 'by', 'h', 'g', 'wells']\n",
      "indices: [1, 19, 50, 40, 2183, 2184, 400]\n",
      "words: ['twinkled', 'and', 'his', 'usually', 'pale', 'face', 'was', 'flushed', 'and', 'animated', 'the']\n",
      "indices: [2186, 3, 25, 1044, 362, 113, 7, 1421, 3, 1045, 1]\n"
     ]
    }
   ],
   "source": [
    "vocab = Vocab(tokens)\n",
    "print(list(vocab.token_to_idx.items())[:10])\n",
    "for i in [0, 10]:\n",
    "    print('words:', tokens[i])\n",
    "    print('indices:', vocab[tokens[i]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "13098303",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "170580 28\n",
      "32775 4580\n"
     ]
    }
   ],
   "source": [
    "def load_corpus_time_machine(max_tokens=-1, token='char'):  #@save\n",
    "    \"\"\"Return token indices and the vocabulary of the time machine dataset.\"\"\"\n",
    "    lines = read_time_machine()\n",
    "    tokens = tokenize(lines, token)\n",
    "    vocab = Vocab(tokens)\n",
    "    # Since each text line in the time machine dataset is not necessarily a\n",
    "    # sentence or a paragraph, flatten all the text lines into a single list\n",
    "    corpus = [vocab[token] for line in tokens for token in line]\n",
    "    if max_tokens > 0:\n",
    "        corpus = corpus[:max_tokens]\n",
    "    return corpus, vocab\n",
    "\n",
    "corpus, vocab = load_corpus_time_machine(token='char')\n",
    "print(len(corpus), len(vocab))\n",
    "corpus, vocab = load_corpus_time_machine(token='word')\n",
    "print(len(corpus), len(vocab))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c99bbba",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Language Models\n",
    "\n",
    "- Assume that the tokens in a text sequence of length $T$ are in turn $x_{1}, x_{2}, \\ldots, x_{T}$. Then, in the text sequence, $x_{t}(1 \\leqslant t \\leqslant T)$ can be considered as the observation or label at time step $t$. Given such a text sequence, the goal of a language model is to estimate the joint probability of the sequence:\n",
    "\n",
    "$$\n",
    "P\\left(x_{1}, x_{2}, \\ldots, x_{T}\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfa87930",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- The obvious question is how we should model a document, or even a sequence of tokens. Suppose that we tokenize text data at the word level. Let us start by applying basic probability rules:\n",
    "\n",
    "$$\n",
    "P\\left(x_{1}, x_{2}, \\ldots, x_{T}\\right)=\\prod_{t=1}^{T} P\\left(x_{t} \\mid x_{1}, \\ldots, x_{t-1}\\right)\n",
    "$$\n",
    "\n",
    "$$\n",
    "P(\\text { deep, learning, is, fun })=P(\\text { deep }) P(\\text { learning } \\mid \\text { deep }) P(\\text { is } \\mid \\text { deep, learning }) P(\\text { fun } \\mid \\text { deep, learning, is })\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8ed34f8",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "-  The probability of words can be calculated from the relative word frequency of a given word in the training dataset. For example, the estimate $\\hat{P}(\\text{deep})$ can be calculated as the probability of any sentence starting with the word “deep”. A slightly less accurate approach would be to count all occurrences of the word “deep” and divide it by the total number of words in the corpus.\n",
    " \n",
    "$$\n",
    "\\hat{P}(\\text { learning } \\mid \\text { deep })=\\frac{n(\\text { deep }, \\text { learning })}{n(\\text { deep })}\n",
    "$$\n",
    "\n",
    "\n",
    "- where $n(x)$ and $n(x, x') $ are the number of occurrences of singletons and consecutive word pairs, respectively.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38764763",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Unfortunately, estimating the probability of a word pair is somewhat more difficult, since the occurrences of “deep learning” are a lot less frequent. In particular, for some unusual word combinations it may be tricky to find enough occurrences to get accurate estimates.\n",
    "-  Things take a turn for the worse for three-word combinations and beyond. There will be many plausible three-word combinations that we likely will not see in our dataset. Unless we provide some solution to assign such word combinations nonzero count, we will not be able to use them in a language model. If the dataset is small or if the words are very rare, we might not find even a single one of them."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3bbfd20",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- A common strategy is to perform some form of Laplace smoothing. The solution is to add a small constant to all counts. Denote by $n$ the total number of words in the training set and $m$ the number of unique words. This solution helps with singletons, e.g., via:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\hat{P}(x) &=\\frac{n(x)+\\epsilon_{1} / m}{n+\\epsilon_{1}} \\\\\n",
    "\\hat{P}\\left(x^{\\prime} \\mid x\\right) &=\\frac{n\\left(x, x^{\\prime}\\right)+\\epsilon_{2} \\hat{P}\\left(x^{\\prime}\\right)}{n(x)+\\epsilon_{2}} \\\\\n",
    "\\hat{P}\\left(x^{\\prime \\prime} \\mid x, x^{\\prime}\\right) &=\\frac{n\\left(x, x^{\\prime}, x^{\\prime \\prime}\\right)+\\epsilon_{3} \\hat{P}\\left(x^{\\prime \\prime}\\right)}{n\\left(x, x^{\\prime}\\right)+\\epsilon_{3}}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "- Here $\\epsilon_{1}$, $\\epsilon_{2}$ and $\\epsilon_{3}$ are hyperparameters.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49c4751b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Unfortunately, models like this get unwieldy rather quickly for the following reasons. First, we need to store all counts. Second, this entirely ignores the meaning of the words. \n",
    "- For instance, “cat” and “feline” should occur in related contexts. It is quite difficult to adjust such models to additional contexts, whereas, deep learning based language models are well suited to take this into account. \n",
    "- Last, long word sequences are almost certain to be novel, hence a model that simply counts the frequency of previously seen word sequences is bound to perform poorly there."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ade813c3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Markov Models\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&P\\left(x_{1}, x_{2}, x_{3}, x_{4}\\right)=P\\left(x_{1}\\right) P\\left(x_{2}\\right) P\\left(x_{3}\\right) P\\left(x_{4}\\right) \\\\\n",
    "&P\\left(x_{1}, x_{2}, x_{3}, x_{4}\\right)=P\\left(x_{1}\\right) P\\left(x_{2} \\mid x_{1}\\right) P\\left(x_{3} \\mid x_{2}\\right) P\\left(x_{4} \\mid x_{3}\\right) \\\\\n",
    "&P\\left(x_{1}, x_{2}, x_{3}, x_{4}\\right)=P\\left(x_{1}\\right) P\\left(x_{2} \\mid x_{1}\\right) P\\left(x_{3} \\mid x_{1}, x_{2}\\right) P\\left(x_{4} \\mid x_{2}, x_{3}\\right)\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "- The probability formulae that involve one, two, and three variables are typically referred to as unigram, bigram, and trigram models, respectively.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "137c83c3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('the', 2261),\n",
       " ('i', 1267),\n",
       " ('and', 1245),\n",
       " ('of', 1155),\n",
       " ('a', 816),\n",
       " ('to', 695),\n",
       " ('was', 552),\n",
       " ('in', 541),\n",
       " ('that', 443),\n",
       " ('my', 440)]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vocab.token_freqs[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ba029c31",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "freqs = [freq for token, freq in vocab.token_freqs]\n",
    "plt.plot(freqs)\n",
    "plt.xlabel('token: x')\n",
    "plt.ylabel('frequency: n(x)')\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fb9244b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- We are on to something quite fundamental here: the word frequency decays rapidly in a well-defined way. After dealing with the first few words as exceptions, all the remaining words roughly follow a straight line on a log-log plot. This means that words satisfy Zipf’s law, which states that the frequency $n_i$ of the $i^{\\text{th}}$ most frequent word is:\n",
    "\n",
    "$$\n",
    "\\begin{gathered}\n",
    "n_{i} \\propto \\frac{1}{i \\alpha} \\\\\\\\\\Rightarrow\\quad\n",
    "\\log n_{i}=-\\alpha \\log i+c,\n",
    "\\end{gathered}\n",
    "$$\n",
    "\n",
    "- Where $\\alpha$ is the exponent that characterizes the distribution and $c$ is a constant.\n",
    "- But what about the other word combinations, such as bigrams, trigrams, and beyond?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "799fe4bd",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[((4, 1), 309),\n",
       " ((8, 1), 169),\n",
       " ((2, 12), 130),\n",
       " ((2, 7), 112),\n",
       " ((3, 1), 109),\n",
       " ((1, 19), 102),\n",
       " ((11, 7), 99),\n",
       " ((6, 1), 85),\n",
       " ((14, 2), 78),\n",
       " ((4, 5), 73)]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bigram_tokens = [pair for pair in zip(corpus[:-1], corpus[1:])]\n",
    "bigram_vocab = Vocab(bigram_tokens)\n",
    "bigram_vocab.token_freqs[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ef8611f5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[((1, 19, 71), 59),\n",
       " ((1, 19, 50), 30),\n",
       " ((1, 177, 65), 24),\n",
       " ((11, 63, 6), 16),\n",
       " ((11, 7, 5), 15),\n",
       " ((103, 3, 26), 15),\n",
       " ((63, 6, 13), 14),\n",
       " ((2, 107, 33), 14),\n",
       " ((2, 47, 1), 13),\n",
       " ((2, 110, 6), 13)]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trigram_tokens = [triple for triple in zip(\n",
    "    corpus[:-2], corpus[1:-1], corpus[2:])]\n",
    "trigram_vocab = Vocab(trigram_tokens)\n",
    "trigram_vocab.token_freqs[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0052b695",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24746d89ca0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bigram_freqs = [freq for token, freq in bigram_vocab.token_freqs]\n",
    "trigram_freqs = [freq for token, freq in trigram_vocab.token_freqs]\n",
    "\n",
    "plt.plot(freqs)\n",
    "plt.plot(bigram_freqs)\n",
    "plt.plot(trigram_freqs)\n",
    "plt.xlabel('token: x')\n",
    "plt.ylabel('frequency: n(x)')\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.legend(['unigram', 'bigram', 'trigram'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc03b725",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- This figure is quite exciting for a number of reasons. First, beyond unigram words, sequences of words also appear to be following Zipf’s law, albeit with a smaller exponent $\\alpha$, depending on the sequence length.\n",
    "- Second, the number of distinct $n$-grams is not that large. This gives us hope that there is quite a lot of structure in language. Third, many $n$-grams occur very rarely, which makes Laplace smoothing rather unsuitable for language modeling. Instead, we will use deep learning based models."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f227c61",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Long Sequence Data\n",
    "\n",
    "- When sequences get too long to be processed by models all at once, we may wish to split such sequences for reading. Now let us describe general strategies. Before introducing the model, let us assume that we will use a neural network to train a language model, where the network processes a minibatch of sequences with predefined length, say $n$ time steps, at a time. Now the question is how to read minibatches of features and labels at random.\n",
    "- The figure below shows all the different ways to obtain subsequences from an original text sequence, where  and a token at each time step corresponds to a character.\n",
    "\n",
    "![timemachine-5gram.svg](./images/8/timemachine-5gram.svg)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54a271ee",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Random Sampling\n",
    "\n",
    "- However, if we pick just one offset, there is limited coverage of all the possible subsequences for training our network. Therefore, we can start with a random offset to partition a sequence to get both coverage and randomness. \n",
    "- In random sampling, each example is a subsequence arbitrarily captured on the original long sequence. The subsequences from two adjacent random minibatches during iteration are not necessarily adjacent on the original sequence. For language modeling, the target is to predict the next token based on what tokens we have seen so far, hence the labels are the original sequence, shifted by one token.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "63fb9048",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def seq_data_iter_random(corpus, batch_size, num_steps):  #@save\n",
    "    \"\"\"Generate a minibatch of subsequences using random sampling.\"\"\"\n",
    "    # Start with a random offset (inclusive of `num_steps - 1`) to partition a\n",
    "    # sequence\n",
    "    corpus = corpus[random.randint(0, num_steps - 1):]\n",
    "    # Subtract 1 since we need to account for labels\n",
    "    num_subseqs = (len(corpus) - 1) // num_steps\n",
    "    # The starting indices for subsequences of length `num_steps`\n",
    "    initial_indices = list(range(0, num_subseqs * num_steps, num_steps))\n",
    "    # In random sampling, the subsequences from two adjacent random\n",
    "    # minibatches during iteration are not necessarily adjacent on the\n",
    "    # original sequence\n",
    "    random.shuffle(initial_indices)\n",
    "\n",
    "    def data(pos):\n",
    "        # Return a sequence of length `num_steps` starting from `pos`\n",
    "        return corpus[pos: pos + num_steps]\n",
    "\n",
    "    num_batches = num_subseqs // batch_size\n",
    "    for i in range(0, batch_size * num_batches, batch_size):\n",
    "        # Here, `initial_indices` contains randomized starting indices for\n",
    "        # subsequences\n",
    "        initial_indices_per_batch = initial_indices[i: i + batch_size]\n",
    "        X = [data(j) for j in initial_indices_per_batch]\n",
    "        Y = [data(j + 1) for j in initial_indices_per_batch]\n",
    "        yield torch.tensor(X), torch.tensor(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "3c4181f9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X:  tensor([[5, 6, 7, 8, 9],\n",
      "        [0, 1, 2, 3, 4]]) \n",
      "Y: tensor([[ 6,  7,  8,  9, 10],\n",
      "        [ 1,  2,  3,  4,  5]])\n",
      "X:  tensor([[20, 21, 22, 23, 24],\n",
      "        [15, 16, 17, 18, 19]]) \n",
      "Y: tensor([[21, 22, 23, 24, 25],\n",
      "        [16, 17, 18, 19, 20]])\n",
      "X:  tensor([[25, 26, 27, 28, 29],\n",
      "        [10, 11, 12, 13, 14]]) \n",
      "Y: tensor([[26, 27, 28, 29, 30],\n",
      "        [11, 12, 13, 14, 15]])\n"
     ]
    }
   ],
   "source": [
    "my_seq = list(range(35))\n",
    "for X, Y in seq_data_iter_random(my_seq, batch_size=2, num_steps=5):\n",
    "    print('X: ', X, '\\nY:', Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "840d2d12",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def seq_data_iter_sequential(corpus, batch_size, num_steps):  #@save\n",
    "    \"\"\"Generate a minibatch of subsequences using sequential partitioning.\"\"\"\n",
    "    # Start with a random offset to partition a sequence\n",
    "    offset = random.randint(0, num_steps)\n",
    "    num_tokens = ((len(corpus) - offset - 1) // batch_size) * batch_size\n",
    "    Xs = torch.tensor(corpus[offset: offset + num_tokens])\n",
    "    Ys = torch.tensor(corpus[offset + 1: offset + 1 + num_tokens])\n",
    "    Xs, Ys = Xs.reshape(batch_size, -1), Ys.reshape(batch_size, -1)\n",
    "    num_batches = Xs.shape[1] // num_steps\n",
    "    for i in range(0, num_steps * num_batches, num_steps):\n",
    "        X = Xs[:, i: i + num_steps]\n",
    "        Y = Ys[:, i: i + num_steps]\n",
    "        yield X, Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "323be2d7",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X:  tensor([[ 1,  2,  3,  4,  5],\n",
      "        [17, 18, 19, 20, 21]]) \n",
      "Y: tensor([[ 2,  3,  4,  5,  6],\n",
      "        [18, 19, 20, 21, 22]])\n",
      "X:  tensor([[ 6,  7,  8,  9, 10],\n",
      "        [22, 23, 24, 25, 26]]) \n",
      "Y: tensor([[ 7,  8,  9, 10, 11],\n",
      "        [23, 24, 25, 26, 27]])\n",
      "X:  tensor([[11, 12, 13, 14, 15],\n",
      "        [27, 28, 29, 30, 31]]) \n",
      "Y: tensor([[12, 13, 14, 15, 16],\n",
      "        [28, 29, 30, 31, 32]])\n"
     ]
    }
   ],
   "source": [
    "for X, Y in seq_data_iter_sequential(my_seq, batch_size=2, num_steps=5):\n",
    "    print('X: ', X, '\\nY:', Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f38a519c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "class SeqDataLoader:  #@save\n",
    "    \"\"\"An iterator to load sequence data.\"\"\"\n",
    "    def __init__(self, batch_size, num_steps, use_random_iter, max_tokens):\n",
    "        if use_random_iter:\n",
    "            self.data_iter_fn = seq_data_iter_random\n",
    "        else:\n",
    "            self.data_iter_fn = seq_data_iter_sequential\n",
    "        self.corpus, self.vocab = load_corpus_time_machine(max_tokens)\n",
    "        self.batch_size, self.num_steps = batch_size, num_steps\n",
    "\n",
    "    def __iter__(self):\n",
    "        return self.data_iter_fn(self.corpus, self.batch_size, self.num_steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e9564e39",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def load_data_time_machine(batch_size, num_steps,  #@save\n",
    "                           use_random_iter=False, max_tokens=10000):\n",
    "    \"\"\"Return the iterator and the vocabulary of the time machine dataset.\"\"\"\n",
    "    data_iter = SeqDataLoader(batch_size, num_steps, use_random_iter, max_tokens)\n",
    "    return data_iter, data_iter.vocab"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c99f45ce",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Recurrent Neural Networks\n",
    "\n",
    "- We have introduced $n$-gram models, where the conditional probability of word $x_t$ at time step $t$ only depends on the $n-1$ previous words. If we want to incorporate the possible effect of words earlier than time step $t-(n-1)$ on $x_t$, we need to increase $n$. However, the number of model parameters would also increase exponentially with it, as we need to store $|V|^n$ numbers for a vocabulary set $V$. Hence, rather than modeling $P\\left(x_{t} \\mid x_{t-1}, \\ldots, x_{t-n+1}\\right)$ it is preferable to use a latent variable model:\n",
    "\n",
    "$$\n",
    "P\\left(x_{t} \\mid x_{t-1}, \\ldots, x_{1}\\right) \\approx P\\left(x_{t} \\mid h_{t-1}\\right)\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2eb26bf",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- where $h_{t-1}$ is a hidden state (also known as a hidden variable) that stores the sequence information up to time step $t-1$. In general, the hidden state at any time step $t$ could be computed based on both the current input $x_t$ and the previous hidden state $h_{t-1}$:\n",
    "\n",
    "$$\n",
    "h_{t}=f\\left(x_{t}, h_{t-1}\\right)\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7405c481",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- For a sufficiently powerful function $f$, the latent variable model is not an approximation. After all, $h_t$ may simply store all the data it has observed so far. However, it could potentially make both computation and storage expensive.\n",
    "- Recall that we have discussed hidden layers with hidden units. It is noteworthy that hidden layers and hidden states refer to two very different concepts. Hidden layers are, as explained, layers that are hidden from view on the path from input to output. Hidden states are technically speaking inputs to whatever we do at a given step, and they can only be computed by looking at data at previous time steps.\n",
    "- Recurrent neural networks (RNNs) are neural networks with hidden states."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88cd541d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Let us take a look at an MLP with a single hidden layer. Let the hidden layer’s activation function be $\\phi$. Given a minibatch of examples $\\mathbf{X} \\in \\mathbb{R}^{n \\times d}$ with batch size $n$ and $d$ inputs, the hidden layer’s output $\\mathbf{H} \\in \\mathbb{R}^{n \\times h}$ is calculated as:\n",
    "\n",
    "$$\n",
    "\\mathbf{H}=\\phi\\left(\\mathbf{X} \\mathbf{W}_{x h}+\\mathbf{b}_{h}\\right)\n",
    "$$\n",
    "\n",
    "- where $\\mathbf{W}_{xq} \\in \\mathbb{R}^{d \\times h}$ is the weight parameter, and $\\mathbf{b}_h \\in \\mathbb{R}^{1 \\times h}$ is the bias parameter.\n",
    "- Next, the hidden variable $\\mathbf{H}$ is used as the input of the output layer. The output layer is given by:\n",
    "\n",
    "$$\n",
    "\\mathbf{O}=\\mathbf{H W}_{h q}+\\mathbf{b}_{q}\n",
    "$$\n",
    "\n",
    "- where $\\mathbf{O} \\in \\mathbb{R}^{n \\times q}$ is the output variable, $\\mathbf{W}_{hq} \\in \\mathbb{R}^{h \\times q}$ is the weight parameter, and $\\mathbf{b}_q \\in \\mathbb{R}^{1 \\times q}$ is the bias parameter of the output layer. If it is a classification problem, we can use $\\text{softmax}(\\mathbf{O})$ to compute the probability distribution of the output categories."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4bb5faa5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Assume that we have a minibatch of inputs $\\mathbf{X}_{t} \\in \\mathbb{R}^{n \\times d}$ at time step $t$. In other words, for a minibatch of $n$ sequence examples, each row of $\\mathbf{X}_t$ corresponds to one example at time step $t$ from the sequence. Next, denote by $\\mathbf{H}_t\\in \\mathbb{R}^{n \\times h}$ the hidden variable of time step $t$. \n",
    "- Unlike the MLP, here we save the hidden variable $\\mathbf{H}_{t-1}$ from the previous time step and introduce a new weight parameter $\\mathbf{W}_{hh} \\in \\mathbb{R}^{h \\times h}$ to describe how to use the hidden variable of the previous time step in the current time step. Specifically, the calculation of the hidden variable of the current time step is determined by the input of the current time step together with the hidden variable of the previous time step:\n",
    "\n",
    "$$\n",
    "\\mathbf{H}_{t}=\\phi\\left(\\mathbf{X}_{t} \\mathbf{W}_{x h}+\\mathbf{H}_{t-1} \\mathbf{W}_{h h}+\\mathbf{b}_{h}\\right)\n",
    "$$\n",
    "\n",
    "- Compared with:\n",
    "\n",
    "$$\\mathbf{H}=\\phi\\left(\\mathbf{X} \\mathbf{W}_{x h}+\\mathbf{b}_{h}\\right)$$\n",
    "\n",
    "- this one adds one more term $\\mathbf{H}_{t-1} \\mathbf{W}_{h h}$ and thus instantiates $h_{t}=f\\left(x_{t}, h_{t-1}\\right)$. From the relationship between hidden variables $\\mathbf{H}_{t}$ and $\\mathbf{H}_{t-1}$ of adjacent time steps, we know that these variables captured and retained the sequence’s historical information up to their current time step, just like the state or memory of the neural network’s current time step. \n",
    "- Therefore, such a hidden variable is called a hidden state. Since the hidden state uses the same definition of the previous time step in the current time step, the computation is recurrent. \n",
    "- Hence, neural networks with hidden states based on recurrent computation are named recurrent neural networks. Layers that perform the computation in RNNs are called recurrent layers."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a05a5c8",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- For time step , the output of the output layer of RNN is similar to the computation in the MLP:\n",
    "\n",
    "$$\n",
    "\\mathbf{O}=\\mathbf{H W}_{h q}+\\mathbf{b}_{q}\n",
    "$$\n",
    "\n",
    "- Parameters of the RNN include the weights $\\mathbf{W}_{x h} \\in \\mathbb{R}^{d \\times h}, \\mathbf{W}_{h h} \\in \\mathbb{R}^{h \\times h}$, and the bias $\\mathbf{b}_h \\in \\mathbb{R}^{1 \\times h}$ of the hidden layer, together with the weights $\\mathbf{W}_{hq} \\in \\mathbb{R}^{h \\times q}$ and the bias $\\mathbf{b}_q \\in \\mathbb{R}^{1 \\times q}$ of the output layer. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbf88d10",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![rnn.svg](./images/8/rnn.svg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4dbde8a1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 1.3129, -1.2245,  2.8187, -2.7141],\n",
      "        [-2.1283,  1.8983, -1.7776, -0.9191],\n",
      "        [-0.7369, -1.8983,  4.0983,  4.2379]])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([[ 1.3129, -1.2245,  2.8187, -2.7141],\n",
       "        [-2.1283,  1.8983, -1.7776, -0.9191],\n",
       "        [-0.7369, -1.8983,  4.0983,  4.2379]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# A trick\n",
    "X, W_xh = torch.normal(0, 1, (3, 1)), torch.normal(0, 1, (1, 4))\n",
    "H, W_hh = torch.normal(0, 1, (3, 4)), torch.normal(0, 1, (4, 4))\n",
    "print(torch.matmul(X, W_xh) + torch.matmul(H, W_hh))\n",
    "torch.matmul(torch.cat((X, H), 1), torch.cat((W_xh, W_hh), 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7db9f3f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Recall that for language modeling, we aim to predict the next token based on the current and past tokens, thus we shift the original sequence by one token as the labels. Bengio et al. first proposed to use a neural network for language modeling\n",
    "- Let the minibatch size be one, and the sequence of the text be “machine”. To simplify training in subsequent sections, we tokenize text into characters rather than words and consider a character-level language model. The figure below demonstrates how to predict the next character based on the current and previous characters via an RNN for character-level language modeling.\n",
    "\n",
    "![rnn-train.svg](./images/8/rnn-train.svg)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bb94c60",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![rnn-train.svg](./images/8/rnn.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "430eb7ef",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Last, let us discuss about how to measure the language model quality, which will be used to evaluate our RNN-based models in the subsequent sections. One way is to check how surprising the text is. A good language model is able to predict with high-accuracy tokens that what we will see next. Consider the following continuations of the phrase “It is raining”, as proposed by different language models:\n",
    "    - “It is raining outside”\n",
    "    - “It is raining banana tree”\n",
    "    - “It is raining piouw;kcj pwepoiut\n",
    "- We might measure the quality of the model by computing the likelihood of the sequence. Unfortunately this is a number that is hard to understand and difficult to compare. After all, shorter sequences are much more likely to occur than the longer ones, hence evaluating the model on Tolstoy’s magnum opus War and Peace will inevitably produce a much smaller likelihood than, say, on Saint-Exupery’s novella The Little Prince. What is missing is the equivalent of an average."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf9a4524",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Information theory comes handy here. We have defined entropy, surprisal, and cross-entropy when we introduced the softmax regression. If we want to compress text, we can ask about predicting the next token given the current set of tokens. A better language model should allow us to predict the next token more accurately. Thus, it should allow us to spend fewer bits in compressing the sequence. So we can measure it by the cross-entropy loss averaged over all the  tokens of a sequence:\n",
    "\n",
    "$$\n",
    "\\frac{1}{n} \\sum_{t=1}^{n}-\\log P\\left(x_{t} \\mid x_{t-1}, \\ldots, x_{1}\\right)\n",
    "$$\n",
    "\n",
    "- where $P$ is given by a language model and $x_t$ is the actual token observed at time step $t$ from the sequence. This makes the performance on documents of different lengths comparable. For historical reasons, scientists in natural language processing prefer to use a quantity called perplexity. In a nutshell, it is the exponential of the euqation above:\n",
    "\n",
    "$$\n",
    "\\exp \\left(-\\frac{1}{n} \\sum_{t=1}^{n} \\log P\\left(x_{t} \\mid x_{t-1}, \\ldots, x_{1}\\right)\\right)\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b938acac",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Perplexity can be best understood as the harmonic mean of the number of real choices that we have when deciding which token to pick next. Let us look at a number of cases:\n",
    "    - In the best case scenario, the model always perfectly estimates the probability of the label token as 1. In this case the perplexity of the model is 1.\n",
    "    - In the worst case scenario, the model always predicts the probability of the label token as 0. In this situation, the perplexity is positive infinity.\n",
    "    - At the baseline, the model predicts a uniform distribution over all the available tokens of the vocabulary. In this case, the perplexity equals the number of unique tokens of the vocabulary. In fact, if we were to store the sequence without any compression, this would be the best we could do to encode it. Hence, this provides a nontrivial upper bound that any useful model must beat."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "fd5b7cc6",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[1, 0, 0],\n",
      "        [0, 0, 1]])\n",
      "len(vocab) -> 28\n",
      "torch.Size([5, 2, 28])\n"
     ]
    }
   ],
   "source": [
    "batch_size, num_steps = 32, 35\n",
    "train_iter, vocab = load_data_time_machine(batch_size, num_steps)\n",
    "print(F.one_hot(torch.tensor([0, 2])))\n",
    "print(\"len(vocab) ->\", len(vocab))\n",
    "X = torch.arange(10).reshape((2, 5))\n",
    "print(F.one_hot(X.T, 28).shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e89b3797",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def get_params(vocab_size, num_hiddens, device):\n",
    "    num_inputs = num_outputs = vocab_size\n",
    "\n",
    "    def normal(shape):\n",
    "        return torch.randn(size=shape, device=device) * 0.01\n",
    "\n",
    "    # Hidden layer parameters\n",
    "    W_xh = normal((num_inputs, num_hiddens))\n",
    "    W_hh = normal((num_hiddens, num_hiddens))\n",
    "    b_h = torch.zeros(num_hiddens, device=device)\n",
    "    # Output layer parameters\n",
    "    W_hq = normal((num_hiddens, num_outputs))\n",
    "    b_q = torch.zeros(num_outputs, device=device)\n",
    "    # Attach gradients\n",
    "    params = [W_xh, W_hh, b_h, W_hq, b_q]\n",
    "    for param in params:\n",
    "        param.requires_grad_(True)\n",
    "    return params"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "659b0600",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Build RNN Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "e0ff9e00",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "def init_rnn_state(batch_size, num_hiddens, device):\n",
    "    return (torch.zeros((batch_size, num_hiddens), device=device), )\n",
    "\n",
    "def rnn_fw(inputs, state, params):\n",
    "    # Here `inputs` shape: (`num_steps`, `batch_size`, `vocab_size`)\n",
    "    W_xh, W_hh, b_h, W_hq, b_q = params\n",
    "    H, = state\n",
    "    outputs = []\n",
    "    # Shape of `X`: (`batch_size`, `vocab_size`)\n",
    "    for X in inputs:\n",
    "        H = torch.tanh(torch.mm(X, W_xh) + torch.mm(H, W_hh) + b_h)\n",
    "        Y = torch.mm(H, W_hq) + b_q\n",
    "        outputs.append(Y)\n",
    "    return torch.cat(outputs, dim=0), (H,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "95bfd0d7",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "class RNN:\n",
    "    \"\"\"A RNN Model implemented from scratch.\"\"\"\n",
    "    def __init__(self, vocab_size, num_hiddens, device, get_params, init_state, forward_fn):\n",
    "        self.vocab_size, self.num_hiddens = vocab_size, num_hiddens\n",
    "        self.params = get_params(vocab_size, num_hiddens, device)\n",
    "        self.init_state, self.forward_fn = init_state, forward_fn\n",
    "\n",
    "    def __call__(self, X, state):\n",
    "#         print(X.T)\n",
    "#         print(X.shape)\n",
    "        X = F.one_hot(X.T, self.vocab_size).type(torch.float32)\n",
    "        return self.forward_fn(X, state, self.params)\n",
    "\n",
    "    def begin_state(self, batch_size, device):\n",
    "        return self.init_state(batch_size, self.num_hiddens, device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "a38e165e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['sm_37', 'sm_50', 'sm_60', 'sm_61', 'sm_70', 'sm_75', 'sm_80', 'sm_86', 'compute_37'] cuda\n",
      "True <class 'tuple'>\n",
      "torch.Size([10, 28]) 1 torch.Size([2, 512])\n"
     ]
    }
   ],
   "source": [
    "num_hiddens = 512\n",
    "device = \"cuda\" if torch.cuda.is_available() else \"cpu\"\n",
    "print(torch.cuda.get_arch_list(), device)\n",
    "rnn = RNN(len(vocab), num_hiddens, device, get_params, init_rnn_state, rnn_fw)\n",
    "state = rnn.begin_state(X.shape[0], device)\n",
    "print(isinstance(state, tuple), type(state))\n",
    "Y, new_state = rnn(X.to(device), state)\n",
    "print(Y.shape, len(new_state), new_state[0].shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "0415e9c4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def predict(prefix, num_preds, net, vocab, device):\n",
    "    \"\"\"Generate new characters following the `prefix`.\"\"\"\n",
    "    state = net.begin_state(batch_size=1, device=device)\n",
    "    outputs = [vocab[prefix[0]]]\n",
    "    get_input = lambda: torch.tensor([outputs[-1]], device=device).reshape((1, 1))\n",
    "    for y in prefix[1:]:  # Warm-up period\n",
    "        _, state = net(get_input(), state)\n",
    "        outputs.append(vocab[y])\n",
    "    for _ in range(num_preds):  # Predict `num_preds` steps\n",
    "        y, state = net(get_input(), state)\n",
    "        outputs.append(int(y.argmax(dim=1).reshape(1)))\n",
    "    return ''.join([vocab.idx_to_token[i] for i in outputs])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "a1e2745c",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'time traveller oidxoqrjz '"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict('time traveller ', 10, rnn, vocab, device)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e381cecf",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Gradient Clipping\n",
    "\n",
    "- For a sequence of length $T$, we compute the gradients over these $T$ time steps in an iteration, which results in a chain of matrix-products with length $O(T)$ during backpropagation. It might result in numerical instability, e.g., the gradients may either explode or vanish, when $T$ is large. Therefore, RNN models often need extra help to stabilize the training.\n",
    "- Generally speaking, when solving an optimization problem, we take update steps for the model parameter, say in the vector form $\\mathbf{x}$, in the direction of the negative gradient $\\mathbf{g}$ on a minibatch. For example, with $\\eta > 0$ as the learning rate, in one iteration we update $\\mathbf{x}$ as $\\mathbf{x} - \\eta\\mathbf{g}$. Let us further assume that the objective function $f$ is well behaved, say, Lipschitz continuous with constant $L$. That is to say, for any $\\mathbf{a}$ and $\\mathbf{b}$ we have:\n",
    "\n",
    "$$\n",
    "|f(\\mathbf{a})-f(\\mathbf{b})| \\leq L\\|\\mathbf{a}-\\mathbf{b}\\|\n",
    "$$\n",
    "\n",
    "- In this case we can safely assume that if we update the parameter vector by $\\eta\\mathbf{g}$, then:\n",
    "\n",
    "$$\n",
    "|f(\\mathbf{x})-f(\\mathbf{x}-\\eta \\mathbf{g})| \\leq L \\eta\\|\\mathbf{g}\\|\n",
    "$$\n",
    "\n",
    "- which means that we will not observe a change by more than $\\eta\\mathbf{||g||}$. This is both a curse and a blessing. On the curse side, it limits the speed of making progress; whereas on the blessing side, it limits the extent to which things can go wrong if we move in the wrong direction."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb5757b7",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Sometimes the gradients can be quite large and the optimization algorithm may fail to converge. We could address this by reducing the learning rate $\\eta$. But what if we only rarely get large gradients? In this case such an approach may appear entirely unwarranted. One popular alternative is to clip the gradient $\\mathbf{g}$ by projecting them back to a ball of a given radius, say $\\theta$ via:\n",
    "\n",
    "$$\n",
    "g \\leftarrow \\min \\left(1, \\frac{\\theta}{\\|\\mathbf{g}\\|}\\right) \\mathbf{g}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "a6f37a81",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def grad_clipping(net, theta):  #@save\n",
    "    \"\"\"Clip the gradient.\"\"\"\n",
    "    if isinstance(net, nn.Module):\n",
    "        params = [p for p in net.parameters() if p.requires_grad]\n",
    "    else:\n",
    "        params = net.params\n",
    "    norm = torch.sqrt(sum(torch.sum((p.grad ** 2)) for p in params))\n",
    "    if norm > theta:\n",
    "        for param in params:\n",
    "            param.grad[:] *= theta / norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "e55194a0",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import time\n",
    "def train_epoch(net, train_iter, loss, optimizer, device, use_random_iter):\n",
    "    \"\"\"Train a net within one epoch\"\"\"\n",
    "    state, start_time = None, time.perf_counter()\n",
    "    metric = [0, 0]\n",
    "    loss_sum = 0\n",
    "    size = 0\n",
    "    for X, y in train_iter:\n",
    "        size += 1\n",
    "    for X, Y in train_iter:\n",
    "        if state is None or use_random_iter:\n",
    "            # Initialize `state` when either it is the first iteration or\n",
    "            # using random sampling\n",
    "            state = net.begin_state(batch_size=X.shape[0], device=device)\n",
    "        else:\n",
    "            if isinstance(net, nn.Module) and not isinstance(state, tuple):\n",
    "                # `state` is a tensor for `nn.GRU`\n",
    "                state.detach_()\n",
    "            else:\n",
    "                # `state` is a tuple of tensors for `nn.LSTM` and\n",
    "                # for our custom scratch implementation\n",
    "                for s in state:\n",
    "                    s.detach_()\n",
    "        y = Y.T.reshape(-1)\n",
    "        X, y = X.to(device), y.to(device)\n",
    "        y_hat, state = net(X, state)\n",
    "        l = loss(y_hat, y.long()).mean()\n",
    "        loss_sum += l\n",
    "        if isinstance(optimizer, torch.optim.Optimizer):\n",
    "            optimizer.zero_grad()\n",
    "            l.backward()\n",
    "            grad_clipping(net, 1)\n",
    "            optimizer.step()\n",
    "        else:\n",
    "            l.backward()\n",
    "            grad_clipping(net, 1)\n",
    "            optimizer(batch_size=1) # Since the `mean` function has been invoked\n",
    "        metric[0] += l * y.numel()\n",
    "        metric[1] += y.numel()\n",
    "    return math.exp(metric[0]/metric[1]), metric[1]/(time.perf_counter() - start_time), loss_sum/size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "76751cbb",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def sgd(params, lr, batch_size):\n",
    "    \"\"\"Minibatch stochastic gradient descent. Defined in :numref:`sec_linear_scratch`\"\"\"\n",
    "    with torch.no_grad():\n",
    "        for param in params:\n",
    "            param -= lr * param.grad / batch_size\n",
    "            param.grad.zero_()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "97ee7bbe",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def train_rnn(net, train_iter, vocab, lr, num_epochs, device, use_random_iter=False):\n",
    "    \"\"\"Train a model\"\"\"\n",
    "    loss = nn.CrossEntropyLoss()\n",
    "    loss_list = []\n",
    "    # Initialize\n",
    "    if isinstance(net, nn.Module):\n",
    "        optimizer = torch.optim.SGD(net.parameters(), lr)\n",
    "    else:\n",
    "        optimizer = lambda batch_size: sgd(net.params, lr, batch_size)\n",
    "    # Train and predict\n",
    "    for epoch in range(num_epochs):\n",
    "        ppl, speed, l = train_epoch(net, train_iter, loss, optimizer, device, use_random_iter)\n",
    "        loss_list.append(l.cpu().detach().numpy().sum())\n",
    "        if (epoch + 1) % 25 == 0 or epoch == 0:\n",
    "            print(predict('time traveller', 50, net, vocab, device))\n",
    "            print(\"Epoch ->\", epoch + 1, \"\\t\\t\\tLoss ->\", l)\n",
    "    print('perplexity ->', ppl, \"-*-*-*-\", speed, 'tokens/sec on', device)\n",
    "    print(predict('time traveller', 50, net, vocab, device))\n",
    "    print(predict('traveller', 50 + 5, net, vocab, device))\n",
    "    return loss_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "5e229d7f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def plot_losses(loss_list):\n",
    "    plt.figure(figsize=(20, 10))\n",
    "    plt.plot(loss_list, '-bx')\n",
    "    plt.xlabel('epoch')\n",
    "    plt.ylabel('loss')\n",
    "    plt.title('Loss vs. No. of epochs')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "a8e03b24",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time traveller                                                  \n",
      "Epoch -> 1 \t\t\tLoss -> tensor(3.2657, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller the the the the the the the the the the the the t\n",
      "Epoch -> 25 \t\t\tLoss -> tensor(2.4908, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travellere the the the the the the the the the the the the \n",
      "Epoch -> 50 \t\t\tLoss -> tensor(2.2883, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travellere the the the the the the the the the the the the \n",
      "Epoch -> 75 \t\t\tLoss -> tensor(2.1909, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller and the the the the the the the the the the the t\n",
      "Epoch -> 100 \t\t\tLoss -> tensor(2.1230, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travellere and and and and and and and and and and and and \n",
      "Epoch -> 125 \t\t\tLoss -> tensor(2.0727, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller and the the the the the the the the the the the t\n",
      "Epoch -> 150 \t\t\tLoss -> tensor(2.0153, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller and and the the the the the the the the the the t\n",
      "Epoch -> 175 \t\t\tLoss -> tensor(1.9479, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller at in the ghat and have and the that these the th\n",
      "Epoch -> 200 \t\t\tLoss -> tensor(1.8707, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller ourd and the time traveller ourd and the time tra\n",
      "Epoch -> 225 \t\t\tLoss -> tensor(1.7279, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller of the thing s arall or the fill tracell same the\n",
      "Epoch -> 250 \t\t\tLoss -> tensor(1.4753, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller bet and the time traveller dewe mith his in the g\n",
      "Epoch -> 275 \t\t\tLoss -> tensor(1.2242, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller pereat in tha flle wather saco the grave thavelle\n",
      "Epoch -> 300 \t\t\tLoss -> tensor(0.9787, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller ffre dine ti noous it in ass if eredinger as wa h\n",
      "Epoch -> 325 \t\t\tLoss -> tensor(0.7369, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller come the bouthe buine ffreew yhr gereatthred hit \n",
      "Epoch -> 350 \t\t\tLoss -> tensor(0.5201, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller came back anduiney filbes sthey ubuin expaysedce \n",
      "Epoch -> 375 \t\t\tLoss -> tensor(0.3837, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller come the gat ee that ale ingtome wathe one ur ato\n",
      "Epoch -> 400 \t\t\tLoss -> tensor(0.2849, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller cald twhe bogit bote mod t is the three dimension\n",
      "Epoch -> 425 \t\t\tLoss -> tensor(0.2002, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller after the pauserequired for the proper assimilati\n",
      "Epoch -> 450 \t\t\tLoss -> tensor(0.1134, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travellerif s aga beree by a couve buthed heare hea sime tr\n",
      "Epoch -> 475 \t\t\tLoss -> tensor(0.0767, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 500 \t\t\tLoss -> tensor(0.0957, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 525 \t\t\tLoss -> tensor(0.0795, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 550 \t\t\tLoss -> tensor(0.0562, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 575 \t\t\tLoss -> tensor(0.0747, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 600 \t\t\tLoss -> tensor(0.0515, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 625 \t\t\tLoss -> tensor(0.0732, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 650 \t\t\tLoss -> tensor(0.0447, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 675 \t\t\tLoss -> tensor(0.0458, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 700 \t\t\tLoss -> tensor(0.0584, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 725 \t\t\tLoss -> tensor(0.0574, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 750 \t\t\tLoss -> tensor(0.0296, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 775 \t\t\tLoss -> tensor(0.0593, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 800 \t\t\tLoss -> tensor(0.0437, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 825 \t\t\tLoss -> tensor(0.0480, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 850 \t\t\tLoss -> tensor(0.0452, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 875 \t\t\tLoss -> tensor(0.0394, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 900 \t\t\tLoss -> tensor(0.0419, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 925 \t\t\tLoss -> tensor(0.0409, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 950 \t\t\tLoss -> tensor(0.0304, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 975 \t\t\tLoss -> tensor(0.0319, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1000 \t\t\tLoss -> tensor(0.0342, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1025 \t\t\tLoss -> tensor(0.0316, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1050 \t\t\tLoss -> tensor(0.0253, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1075 \t\t\tLoss -> tensor(0.0296, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1100 \t\t\tLoss -> tensor(0.0252, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1125 \t\t\tLoss -> tensor(0.0311, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1150 \t\t\tLoss -> tensor(0.0289, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1175 \t\t\tLoss -> tensor(0.0285, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1200 \t\t\tLoss -> tensor(0.0186, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1225 \t\t\tLoss -> tensor(0.0257, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1250 \t\t\tLoss -> tensor(0.0237, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1275 \t\t\tLoss -> tensor(0.0222, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1300 \t\t\tLoss -> tensor(0.0246, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller tered wit sard ily thaverisy cuvelyer io is atery\n",
      "Epoch -> 1325 \t\t\tLoss -> tensor(0.1075, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1350 \t\t\tLoss -> tensor(0.0585, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1375 \t\t\tLoss -> tensor(0.0340, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1400 \t\t\tLoss -> tensor(0.0300, device='cuda:0', grad_fn=<DivBackward0>)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1425 \t\t\tLoss -> tensor(0.0257, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1450 \t\t\tLoss -> tensor(0.0223, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1475 \t\t\tLoss -> tensor(0.0307, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1500 \t\t\tLoss -> tensor(0.0224, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1525 \t\t\tLoss -> tensor(0.0186, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1550 \t\t\tLoss -> tensor(0.0231, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1575 \t\t\tLoss -> tensor(0.0302, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1600 \t\t\tLoss -> tensor(0.0251, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1625 \t\t\tLoss -> tensor(0.0239, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1650 \t\t\tLoss -> tensor(0.0247, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1675 \t\t\tLoss -> tensor(0.0246, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1700 \t\t\tLoss -> tensor(0.0238, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1725 \t\t\tLoss -> tensor(0.0219, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1750 \t\t\tLoss -> tensor(0.0243, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1775 \t\t\tLoss -> tensor(0.0247, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1800 \t\t\tLoss -> tensor(0.0193, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1825 \t\t\tLoss -> tensor(0.0228, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1850 \t\t\tLoss -> tensor(0.0209, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1875 \t\t\tLoss -> tensor(0.0162, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1900 \t\t\tLoss -> tensor(0.0210, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1925 \t\t\tLoss -> tensor(0.0200, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1950 \t\t\tLoss -> tensor(0.0226, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1975 \t\t\tLoss -> tensor(0.0246, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 2000 \t\t\tLoss -> tensor(0.0244, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "perplexity -> 1.0246825922988203 -*-*-*- 110833.61474677507 tokens/sec on cuda\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "traveller with a slight accession ofcheerfulness really this is \n"
     ]
    }
   ],
   "source": [
    "num_epochs, lr = 2000, 0.5\n",
    "loss_list = train_rnn(rnn, train_iter, vocab, lr, num_epochs, device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "ebc02c37",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_losses(loss_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ecb6585",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Use torch.nn.RNN()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "3f1ac207",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1, 32, 512])\n",
      "torch.Size([35, 32, 512])\n",
      "torch.Size([1, 32, 512])\n"
     ]
    }
   ],
   "source": [
    "rnn_layer = nn.RNN(len(vocab), num_hiddens)\n",
    "init_state = torch.zeros((1, batch_size, num_hiddens))\n",
    "print(init_state.shape)\n",
    "X = torch.rand(size=(num_steps, batch_size, len(vocab)))\n",
    "Y, state_new = rnn_layer(X, init_state)\n",
    "print(Y.shape)\n",
    "print(state_new.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "35275776",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "class RNNModel(nn.Module):\n",
    "    \"\"\"The RNN model.\"\"\"\n",
    "    def __init__(self, rnn_layer, vocab_size, **kwargs):\n",
    "        super(RNNModel, self).__init__(**kwargs)\n",
    "        self.rnn = rnn_layer\n",
    "        self.vocab_size = vocab_size\n",
    "        self.num_hiddens = self.rnn.hidden_size\n",
    "        # If the RNN is bidirectional (to be introduced later), `num_directions` should be 2, else it should be 1.\n",
    "        if not self.rnn.bidirectional:\n",
    "            self.num_directions = 1\n",
    "            self.linear = nn.Linear(self.num_hiddens, self.vocab_size)\n",
    "        else:\n",
    "            self.num_directions = 2\n",
    "            self.linear = nn.Linear(self.num_hiddens * 2, self.vocab_size)\n",
    "\n",
    "    def forward(self, inputs, state):\n",
    "        X = F.one_hot(inputs.T.long(), self.vocab_size)\n",
    "        X = X.to(torch.float32)\n",
    "        Y, state = self.rnn(X, state)\n",
    "        # The fully connected layer will first change the shape of `Y` to (`num_steps` * `batch_size`, `num_hiddens`). \n",
    "        # Its output shape is (`num_steps` * `batch_size`, `vocab_size`).\n",
    "        output = self.linear(Y.reshape((-1, Y.shape[-1])))\n",
    "        return output, state\n",
    "\n",
    "    def begin_state(self, device, batch_size=1):\n",
    "        if not isinstance(self.rnn, nn.LSTM):\n",
    "            # `nn.GRU` takes a tensor as hidden state\n",
    "            return  torch.zeros((self.num_directions * self.rnn.num_layers, batch_size, self.num_hiddens),device=device)\n",
    "        else:\n",
    "            # `nn.LSTM` takes a tuple of hidden states\n",
    "            return (torch.zeros((self.num_directions * self.rnn.num_layers, batch_size, self.num_hiddens), device=device),\n",
    "                    torch.zeros((self.num_directions * self.rnn.num_layers, batch_size, self.num_hiddens), device=device))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ce548c0",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Use torch.nn.RNN()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "34eaa353",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'time travellerjkkeejeeee'"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rnn_net = RNNModel(rnn_layer, vocab_size=len(vocab))\n",
    "rnn_net = rnn_net.to(device)\n",
    "predict('time traveller', 10, rnn_net, vocab, device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "e8ad4d77",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time travellereeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee\n",
      "Epoch -> 1 \t\t\tLoss -> tensor(3.0871, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travellere and and and and and and and and and and and and \n",
      "Epoch -> 25 \t\t\tLoss -> tensor(2.3187, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller the the the the the the the the the the the the t\n",
      "Epoch -> 50 \t\t\tLoss -> tensor(2.1041, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller and the the thas ans of the that in thave that ma\n",
      "Epoch -> 75 \t\t\tLoss -> tensor(2.0062, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travellere mancenis thithed and har ghes anoul that icale s\n",
      "Epoch -> 100 \t\t\tLoss -> tensor(1.9162, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller and ar anow youre ion ano stowe this loulhestire \n",
      "Epoch -> 125 \t\t\tLoss -> tensor(1.6112, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller asting wio nesther if that ion is four whath le w\n",
      "Epoch -> 150 \t\t\tLoss -> tensor(1.1728, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller ourde wor andthreat mave at carsome tha e and a m\n",
      "Epoch -> 175 \t\t\tLoss -> tensor(0.7931, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller fred thes ather me sime traveller ags alw you but\n",
      "Epoch -> 200 \t\t\tLoss -> tensor(0.5358, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller proceed d any t me time soa laves atwer and dome \n",
      "Epoch -> 225 \t\t\tLoss -> tensor(0.3615, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller fur sowe ther tase phe lanse was axnot mask feorl\n",
      "Epoch -> 250 \t\t\tLoss -> tensor(0.2797, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 275 \t\t\tLoss -> tensor(0.1188, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller fur no in and tie yor aclof absthrensther so deas\n",
      "Epoch -> 300 \t\t\tLoss -> tensor(0.1235, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller fur ai in way h ao li g ou spas fhine bxe hat fof\n",
      "Epoch -> 325 \t\t\tLoss -> tensor(0.1052, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller sure an hor aiman at move atoul ink in the glyere\n",
      "Epoch -> 350 \t\t\tLoss -> tensor(0.0734, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller fit so in wall genely in the filbew of en as alo \n",
      "Epoch -> 375 \t\t\tLoss -> tensor(0.0756, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 400 \t\t\tLoss -> tensor(0.0666, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 425 \t\t\tLoss -> tensor(0.0480, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 450 \t\t\tLoss -> tensor(0.0659, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller fith o inilitanig sury is of spe travelleryoumcan\n",
      "Epoch -> 475 \t\t\tLoss -> tensor(0.0572, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 500 \t\t\tLoss -> tensor(0.0446, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 525 \t\t\tLoss -> tensor(0.0524, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 550 \t\t\tLoss -> tensor(0.0318, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 575 \t\t\tLoss -> tensor(0.0538, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 600 \t\t\tLoss -> tensor(0.0499, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 625 \t\t\tLoss -> tensor(0.0451, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 650 \t\t\tLoss -> tensor(0.0375, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 675 \t\t\tLoss -> tensor(0.0415, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 700 \t\t\tLoss -> tensor(0.0381, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 725 \t\t\tLoss -> tensor(0.0357, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller fith o inifatrey oou tainve gab ta t otel ane ofm\n",
      "Epoch -> 750 \t\t\tLoss -> tensor(0.0438, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 775 \t\t\tLoss -> tensor(0.0577, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 800 \t\t\tLoss -> tensor(0.0488, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 825 \t\t\tLoss -> tensor(0.0362, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 850 \t\t\tLoss -> tensor(0.0292, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 875 \t\t\tLoss -> tensor(0.0297, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 900 \t\t\tLoss -> tensor(0.0292, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 925 \t\t\tLoss -> tensor(0.0370, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 950 \t\t\tLoss -> tensor(0.0311, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 975 \t\t\tLoss -> tensor(0.0231, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1000 \t\t\tLoss -> tensor(0.0241, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1025 \t\t\tLoss -> tensor(0.0303, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1050 \t\t\tLoss -> tensor(0.0304, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1075 \t\t\tLoss -> tensor(0.0278, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1100 \t\t\tLoss -> tensor(0.0228, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1125 \t\t\tLoss -> tensor(0.0267, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1150 \t\t\tLoss -> tensor(0.0268, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1175 \t\t\tLoss -> tensor(0.0173, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1200 \t\t\tLoss -> tensor(0.0271, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1225 \t\t\tLoss -> tensor(0.0307, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1250 \t\t\tLoss -> tensor(0.0257, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller fithed in familh imuthicesorlshith tanepsocr f ac\n",
      "Epoch -> 1275 \t\t\tLoss -> tensor(0.0283, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1300 \t\t\tLoss -> tensor(0.0268, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1325 \t\t\tLoss -> tensor(0.0259, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1350 \t\t\tLoss -> tensor(0.0239, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1375 \t\t\tLoss -> tensor(0.0245, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1400 \t\t\tLoss -> tensor(0.0299, device='cuda:0', grad_fn=<DivBackward0>)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1425 \t\t\tLoss -> tensor(0.0240, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1450 \t\t\tLoss -> tensor(0.0226, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1475 \t\t\tLoss -> tensor(0.0278, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1500 \t\t\tLoss -> tensor(0.0240, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1525 \t\t\tLoss -> tensor(0.0227, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1550 \t\t\tLoss -> tensor(0.0164, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1575 \t\t\tLoss -> tensor(0.0199, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1600 \t\t\tLoss -> tensor(0.0245, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1625 \t\t\tLoss -> tensor(0.0233, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1650 \t\t\tLoss -> tensor(0.0213, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1675 \t\t\tLoss -> tensor(0.0202, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1700 \t\t\tLoss -> tensor(0.0203, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1725 \t\t\tLoss -> tensor(0.0202, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1750 \t\t\tLoss -> tensor(0.0240, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1775 \t\t\tLoss -> tensor(0.0230, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1800 \t\t\tLoss -> tensor(0.0178, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1825 \t\t\tLoss -> tensor(0.0249, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1850 \t\t\tLoss -> tensor(0.0219, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1875 \t\t\tLoss -> tensor(0.0207, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time travelleryou can show black is white by argument said filby\n",
      "Epoch -> 1900 \t\t\tLoss -> tensor(0.0169, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller fir so it will beicone four uf emit do cane t whe\n",
      "Epoch -> 1925 \t\t\tLoss -> tensor(0.0191, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller for so it will be convenient to speak of himwas e\n",
      "Epoch -> 1950 \t\t\tLoss -> tensor(0.0260, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 1975 \t\t\tLoss -> tensor(0.0215, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "Epoch -> 2000 \t\t\tLoss -> tensor(0.0210, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "perplexity -> 1.0212559638748901 -*-*-*- 499128.1968430898 tokens/sec on cuda\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "traveller with a slight accession ofcheerfulness really this is \n"
     ]
    }
   ],
   "source": [
    "num_epochs, lr = 2000, 0.5\n",
    "loss_list = train_rnn(rnn_net, train_iter, vocab, lr, num_epochs, device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "ed139d37",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_losses(loss_list)"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}