Raw File
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from IPython.display import Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CNTK 106: Part A - Time series prediction with LSTM (Basics)\n",
    "\n",
    "This tutorial demonstrates how to use CNTK to predict future values in a time series using LSTMs.\n",
    "\n",
    "**Goal**\n",
    "\n",
    "We use simulated data set of a continuous function (in our case a [sine wave](https://en.wikipedia.org/wiki/Sine)). From `N` previous values of the $y = sin(t)$ function where $y$ is the observed amplitude signal at time $t$, we will predict `M` values of $y$ for the corresponding future time points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"http://www.cntk.ai/jup/sinewave.jpg\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Figure 1\n",
    "Image(url=\"http://www.cntk.ai/jup/sinewave.jpg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial we will use [LSTM](https://en.wikipedia.org/wiki/Long_short-term_memory) to implement our model. LSTMs are well suited for this task because their ability to learn from experience. For details on how LSTMs work, see [this excellent post](http://colah.github.io/posts/2015-08-Understanding-LSTMs). \n",
    "\n",
    "In this tutorial we will have following sub-sections:\n",
    "- Simulated data generation\n",
    "- LSTM network modeling\n",
    "- Model training and evaluation\n",
    "\n",
    "This model works for lots real world data. In part A of this tutorial we use a simple sin(x) function and in part B of the tutorial (currently in development) we will use real data from IOT device and try to predict daily output of solar panel. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import os\n",
    "import pandas as pd\n",
    "import time\n",
    "\n",
    "import cntk as C\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the block below, we check if we are running this notebook in the CNTK internal test machines by looking for environment variables defined there. We then select the right target device (GPU vs CPU) to test this notebook. In other cases, we use CNTK's default policy to use the best available device (GPU, if available, else CPU)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Select the right target device when this notebook is being tested:\n",
    "if 'TEST_DEVICE' in os.environ:\n",
    "    if os.environ['TEST_DEVICE'] == 'cpu':\n",
    "        C.device.try_set_default_device(C.device.cpu())\n",
    "    else:\n",
    "        C.device.try_set_default_device(C.device.gpu(0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two run modes:\n",
    "- *Fast mode*: `isFast` is set to `True`. This is the default mode for the notebooks, which means we train for fewer iterations or train / test on limited data. This ensures functional correctness of the notebook though the models produced are far from what a completed training would produce.\n",
    "\n",
    "- *Slow mode*: We recommend the user to set this flag to `False` once the user has gained familiarity with the notebook content and wants to gain insight from running the notebooks for a longer period with different parameters for training. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "isFast = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data generation\n",
    "\n",
    "We need a few helper methods to generate the simulated sine wave data. Let `N` and `M` be a ordered set of past values and future (desired predicted values) of the sine wave, respectively. \n",
    "\n",
    "- **`generate_data()`**\n",
    "\n",
    "> In this tutorial, we sample `N` consecutive values of the `sin` function as the input to the model and try to predict future values that is `M` steps away from the last observed value in the input model. We generate multiple such instances of the input signal (by sampling from `sin` function) each of size `N` and  the corresponding desired output as our training data. Assuming $k$ = batch size, `generate_data` function produces the $X$ and corresponding $L$ data and returns numpy arrays of the following shape:\n",
    "\n",
    "> The input set ($X$) to the lstm: $$ X = [\\{y_{11}, y_{12},  \\cdots , y_{1N}\\},\n",
    "        \\{y_{21}, y_{22}, \\cdots, y_{2N}\\}, \\cdots,\n",
    "        \\{y_{k1}, y_{k2}, \\cdots, y_{kN}\\}]\n",
    "$$\n",
    "> In the above samples $y_{i,j}$, represents the observed function value for the $i^{th}$ batch and $j^{th}$ time point within the time window of $N$ points. \n",
    "\n",
    "The desired output ($L$) with `M` steps in the future: $$ L = [ \\{y_{1,N+M}\\},\n",
    "        \\{y_{2,N+M}\\}, \\cdots, \\{y_{k,N+M}\\}]$$\n",
    "\n",
    "> Note: `k` is a function of the length of the time series and the number of windows of size `N` one can have for the time series.\n",
    "\n",
    "- **`split_data()`**\n",
    "\n",
    "> As the name suggests, `split_data` function will split the data into training, validation and test sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def split_data(data, val_size=0.1, test_size=0.1):\n",
    "    \"\"\"\n",
    "    splits np.array into training, validation and test\n",
    "    \"\"\"\n",
    "    pos_test = int(len(data) * (1 - test_size))\n",
    "    pos_val = int(len(data[:pos_test]) * (1 - val_size))\n",
    "\n",
    "    train, val, test = data[:pos_val], data[pos_val:pos_test], data[pos_test:]\n",
    "\n",
    "    return {\"train\": train, \"val\": val, \"test\": test}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def generate_data(fct, x, time_steps, time_shift):\n",
    "    \"\"\"\n",
    "    generate sequences to feed to rnn for fct(x)\n",
    "    \"\"\"\n",
    "    data = fct(x)\n",
    "    if not isinstance(data, pd.DataFrame):\n",
    "        data = pd.DataFrame(dict(a = data[0:len(data) - time_shift],\n",
    "                                 b = data[time_shift:]))\n",
    "    rnn_x = []\n",
    "    for i in range(len(data) - time_steps + 1):\n",
    "        rnn_x.append(data['a'].iloc[i: i + time_steps].as_matrix())\n",
    "    rnn_x = np.array(rnn_x)\n",
    "\n",
    "    # Reshape or rearrange the data from row to columns\n",
    "    # to be compatible with the input needed by the LSTM model\n",
    "    # which expects 1 float per time point in a given batch\n",
    "    rnn_x = rnn_x.reshape(rnn_x.shape + (1,))\n",
    "    \n",
    "    rnn_y = data['b'].values\n",
    "    rnn_y = rnn_y[time_steps - 1 :]\n",
    "    \n",
    "    # Reshape or rearrange the data from row to columns\n",
    "    # to match the input shape\n",
    "    rnn_y = rnn_y.reshape(rnn_y.shape + (1,))\n",
    "\n",
    "    return split_data(rnn_x), split_data(rnn_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us generate and visualize the generated data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ffoi9e/di5syZuOOOO7A0skt8woQJyI+cxDVv3jz069cP8yKHThQUFIR+PLv2TvWOHTRQ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\nYNo0KFo0dEQiOUMr1REDB8KVV9rYcSXUIvJ3ata0hOHFF+HOO21js0i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DFMC6quk4/dlp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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x29a87ebf048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 5 # input: N subsequent values \n",
    "M = 5 # output: predict 1 value M steps ahead\n",
    "X, Y = generate_data(np.sin, np.linspace(0, 100, 10000, dtype=np.float32), N, M)\n",
    "\n",
    "f, a = plt.subplots(3, 1, figsize=(12, 8))\n",
    "for j, ds in enumerate([\"train\", \"val\", \"test\"]):\n",
    "    a[j].plot(Y[ds], label=ds + ' raw');\n",
    "[i.legend() for i in a];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Network modeling\n",
    "\n",
    "We setup our network with 1 LSTM cell for each input. We have N inputs and each input is a value in our continuous function. The N outputs from the LSTM are the input into a dense layer that produces a single output. \n",
    "Between LSTM and dense layer we insert a dropout layer that randomly drops 20% of the values coming the LSTM to prevent overfitting the model to the training dataset. We want use use the dropout layer during training but when using the model to make predictions we don't want to drop values.\n",
    "![lstm](https://www.cntk.ai/jup/cntk106A_model_s3.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def create_model(x):\n",
    "    \"\"\"Create the model for time series prediction\"\"\"\n",
    "    with C.layers.default_options(initial_state = 0.1):\n",
    "        m = C.layers.Recurrence(C.layers.LSTM(N))(x)\n",
    "        m = C.sequence.last(m)\n",
    "        m = C.layers.Dropout(0.2, seed=1)(m)\n",
    "        m = C.layers.Dense(1)(m)\n",
    "        return m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training the network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define the `next_batch()` iterator that produces batches we can feed to the training function. \n",
    "Note that because CNTK supports variable sequence length, we must feed the batches as list of sequences. This is a convenience function to generate small batches of data often referred to as minibatch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def next_batch(x, y, ds):\n",
    "    \"\"\"get the next batch to process\"\"\"\n",
    "\n",
    "    def as_batch(data, start, count):\n",
    "        part = []\n",
    "        for i in range(start, start + count):\n",
    "            part.append(data[i])\n",
    "        return np.array(part)\n",
    "\n",
    "    for i in range(0, len(x[ds])-BATCH_SIZE, BATCH_SIZE):\n",
    "        yield as_batch(x[ds], i, BATCH_SIZE), as_batch(y[ds], i, BATCH_SIZE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Setup everything else we need for training the model: define user specified training parameters, define inputs, outputs, model and the optimizer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Training parameters\n",
    "\n",
    "TRAINING_STEPS = 10000\n",
    "BATCH_SIZE = 100\n",
    "EPOCHS = 20 if isFast else 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Key Insight**\n",
    "\n",
    "There are some key learnings when [working with sequences](https://www.cntk.ai/pythondocs/sequence.html) in LSTM networks. A brief recap: \n",
    "\n",
    "CNTK inputs, outputs and parameters are organized as tensors. Each tensor has a rank: A scalar is a tensor of rank 0, a vector is a tensor of rank 1, a matrix is a tensor of rank 2, and so on. We refer to these different dimensions as axes.\n",
    "\n",
    "Every CNTK tensor has some static axes and some dynamic axes. The static axes have the same length throughout the life of the network. The dynamic axes are like static axes in that they define a meaningful grouping of the numbers contained in the tensor but:\n",
    "- their length can vary from instance to instance,\n",
    "- their length is typically not known before each minibatch is presented, and\n",
    "- they may be ordered.\n",
    "\n",
    "In CNTK the axis over which you run a recurrence is dynamic and thus its dimensions are unknown at the time you define your variable. Thus the input variable only lists the shapes of the static axes. Since our inputs are a sequence of one dimensional numbers we specify the input as \n",
    "\n",
    "> `C.sequence.input_variable(1)`\n",
    "\n",
    "The `N` instances of the observed `sin` function output and the corresponding batch are implicitly represented in the dynamic axis as shown below in the form of defaults. \n",
    "\n",
    "> ```\n",
    "x_axes = [C.Axis.default_batch_axis(), C.Axis.default_dynamic_axis()]\n",
    "C.input_variable(1, dynamic_axes=x_axes)\n",
    "```\n",
    "The reader should be aware of the meaning of the default parameters. Specifiying the dynamic axes enables the recurrence engine handle the time sequence data in the expected order. Please take time to understand how to work with both static and dynamic axes in CNTK as described [here](https://www.cntk.ai/pythondocs/sequence.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# input sequences\n",
    "x = C.sequence.input_variable(1)\n",
    "\n",
    "# create the model\n",
    "z = create_model(x)\n",
    "\n",
    "# expected output (label), also the dynamic axes of the model output\n",
    "# is specified as the model of the label input\n",
    "l = C.input_variable(1, dynamic_axes=z.dynamic_axes, name=\"y\")\n",
    "\n",
    "# the learning rate\n",
    "learning_rate = 0.001\n",
    "lr_schedule = C.learning_rate_schedule(learning_rate, C.UnitType.minibatch)\n",
    "\n",
    "# loss function\n",
    "loss = C.squared_error(z, l)\n",
    "\n",
    "# use squared error to determine error for now\n",
    "error = C.squared_error(z, l)\n",
    "\n",
    "# use adam optimizer\n",
    "momentum_time_constant = C.momentum_as_time_constant_schedule(BATCH_SIZE / -math.log(0.9)) \n",
    "learner = C.fsadagrad(z.parameters, \n",
    "                      lr = lr_schedule, \n",
    "                      momentum = momentum_time_constant, \n",
    "                      unit_gain = True)\n",
    "\n",
    "trainer = C.Trainer(z, (loss, error), [learner])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are ready to train. 100 epochs should yield acceptable results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch: 0, loss: 0.22282\n",
      "epoch: 2, loss: 0.19430\n",
      "epoch: 4, loss: 0.16113\n",
      "epoch: 6, loss: 0.15103\n",
      "epoch: 8, loss: 0.11810\n",
      "epoch: 10, loss: 0.07352\n",
      "epoch: 12, loss: 0.06572\n",
      "epoch: 14, loss: 0.07864\n",
      "epoch: 16, loss: 0.09846\n",
      "epoch: 18, loss: 0.06972\n",
      "training took 12.9 sec\n"
     ]
    }
   ],
   "source": [
    "# train\n",
    "loss_summary = []\n",
    "start = time.time()\n",
    "for epoch in range(0, EPOCHS):\n",
    "    for x1, y1 in next_batch(X, Y, \"train\"):\n",
    "        trainer.train_minibatch({x: x1, l: y1})\n",
    "    if epoch % (EPOCHS / 10) == 0:\n",
    "        training_loss = trainer.previous_minibatch_loss_average\n",
    "        loss_summary.append(training_loss)\n",
    "        print(\"epoch: {}, loss: {:.5f}\".format(epoch, training_loss))\n",
    "\n",
    "print(\"training took {0:.1f} sec\".format(time.time() - start))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BzC7GrxiXAHeGEJLwGzgWKAUamdkSYPjGi1YRMx0FnAG8k+mJB+DqEMLTEWPt\nAdxjZiX4n98DIYQnI+ZJqt2BhzNjPmoDY0IIkyNnArgUGJNpkywCBkXOA/h/jPgq+oLYWQBCCK+b\n2QS8PbIu8+NtcVMB8JCZNcQzXbi1i+kagSAiknKxWzciIpJnKvQiIimnQi8iknIq9CIiKadCLyKS\ncir0IiIpp0IvIpJyKvQiIin3/wFgfI7swj4u9gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x29a87ea7ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A look how the loss function shows how well the model is converging\n",
    "plt.plot(loss_summary, label='training loss');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normally we would validate the training on the data that we set aside for validation but since the input data is small we can run validattion on all parts of the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# validate\n",
    "def get_mse(X,Y,labeltxt):\n",
    "    result = 0.0\n",
    "    for x1, y1 in next_batch(X, Y, labeltxt):\n",
    "        eval_error = trainer.test_minibatch({x : x1, l : y1})\n",
    "        result += eval_error\n",
    "    return result/len(X[labeltxt])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mse for train: 0.000098\n",
      "mse for val: 0.000095\n"
     ]
    }
   ],
   "source": [
    "# Print the train and validation errors\n",
    "for labeltxt in [\"train\", \"val\"]:\n",
    "    print(\"mse for {}: {:.6f}\".format(labeltxt, get_mse(X, Y, labeltxt)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mse for test: 0.000101\n"
     ]
    }
   ],
   "source": [
    "# Print validate and test error\n",
    "labeltxt = \"test\"\n",
    "print(\"mse for {}: {:.6f}\".format(labeltxt, get_mse(X, Y, labeltxt)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we used a simple sin(x) function we should expect that the errors are the same for train, validation and test sets. For real datasets that will be different of course. We also plot the expected output (Y) and the prediction our model made to shows how well the simple LSTM approach worked."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EE7rQPvafbPaysrmpqICAjENnbYIxE9uXFNMTccAnNt45VtHDSLD9tF1aZ2NF\nyhoq+rS3F4DjbaUUxLtm65IkYRDFvF+lvfaeHuiPdt3Wi1IKkKLslJZpX0OyogLQu27rlxQV0xF6\nwCdmTw9XtDEe2OvSTBjA0sSZixr4AnfffTcPPfQQ8fHxPProo8DZ0eubb74Zo9GIwWCgqKiIdevW\nzes75lqrMJXIyEgee+wxrrnmGuLj43nhhRe44oorTrtm06ZN9Pf3T6Z6TLz3O9WnM/vKPx+gevAg\nV2a4NrIGWJZczEfVHwO3ek+UC9TWQnDWIdYa/82l6yVJItVZzHtVH/P5S+eO3niTU2XjDMUcZaXe\ntQfH4rQFSBFtlFa0c96SRC+rm50DlmOkL1w0a7WVqVxcUMzvD/9u7gu9jBBgHj7MLZmutTnAkoQ1\nnLAeAG6Y81pvUlUFIdmHKE7/9twXI9t6smM1uysOcvmFl3lZ3eycKBthKOoUy9NcKwlVnFUEsfWU\n1/VSaDp70w81OdBQSvaypXMu4J5g88Ji/vf4n7ysam6EAKvjMJ/Ndt3WC2PXcLT1Y+BK7wlzgYoK\nCMk6zGrD9PXMzyRAF0D86ArePXWQC9Ze7GV1s3OsbIDhsFoWp7gWcNiYvwxnQjkW+xBZhunL76nF\n4abD5Ge4HnDYZCpGe0ufmcsvv5zLL7/8tGNn1qaOiIjg1VdfPe3YjTfeOPn3U089Nfn3pk2bsFqt\np117ZiR8KtNtPHP77bdz++23z/iZLVu2nKaxsLBQ9Xra5wI+Hanu64OBmENcsMB1p3pD7jKandpX\nFigrEzhTDrvsmALkR63geKv2W0F9WF1ObEAasaGxLl2vk3TEDi/1iQVc5d2HWZ7ieptfvGQxY9FV\ndPVqG2aXU24OuxwBA1ibtRSbQ/s2P3VKMJZYOi9bzw1fTmnTUS+qco0Pa0+QHGg6a8vjmQgKCCJy\nqJCdx7UvZ1jVP7/+5ZJlSxmJPsXQsLYPwsZG0OkPs34eTnWxcRnWEe379ZNlDkbijs5a8vJMskNW\ncNimfb/+Uf0R0oOLCA4Idun6sKAwwoZy2XVM+0LbtYOHWJPhWoQd4JLly7yoxo+fmfFpp7qiAgIN\nJ1iettTlz1y8rJCByJM4ndrOWZVWNyMFOMiInn2V9VSWGwqxDGn/sD7ecpwFMa63OYAhqIhDVm21\nj49Di66UTfmuP/AiQkIJHspk9zFt97evqgKdvpSVete1b15cRF+Y9vZysLqeUF0EyRHJLn9mSWoR\n5n7td4CruvXTAAAgAElEQVQ52X6Mgvj5PYDTAoo4UK9tu4+OQmdIKSXzsPXEqGgCRxPZd1LbFX+V\nlSBSS+flmF5YVERPsPa2fqCmmmhdKjGhMS5/pjC5kJpe7bWXdx5ncdL8bD1FKuKjWm21DwxAX+QR\nShbMYyCTPP2Oi378eBvfdqqrxxiLrCM/Id/lz+SkJqJzhHOoWtvc5KON5RiCC+a1sOD8BUV0Bmrv\naDQMlbPUMPOGDNOxKKGIyi5tO1+bDXSpZaxIn7vaylQSnUXsq9Q2ClZWPYAjtNnlnEGAJdl60I1R\n0aDtir/jTeUYQ+fX5uvzimjXae9o2EbKWZExP1vPiy2krF1b7WYzBKaVs9ww9wLuqcSNFbGnTNs+\n5nh1JyJowKVFihOctzCL8ZAObO3a1ks91VpOZvj87OW8nCJahPa23uQoZ1XWonl9Jje6iFOt2tpL\nTQ0EppWxOGV+fYwfP1rg00714bpaYkgnNDB0Xp+LHi5il8Z7fld3l5MfP78O7IKlJsZCG+kdGvSS\nqrlxOKA7uIzzcuenfXVmEXaHtm1eWysQ8RUsSpqf9uyIIo7atdV+0FxFgpRHgC7A5c/odBIRA0W8\ne0xb7XV95SxwcbHcBBctW8hwWC0jDu3SboaGYDCifN62vjK9iIYRbR2N6honjpgqFiQsmNfnjGFF\nlDZqay+l1kpSAhbOK+AQGKAjrL+Ad45qPJjpL6cweX72snlJAQPh5TiFdqtbu7vBEVvG6nk61cv0\nRdQPatvmVbVjOCLN5CXMXRXJjx+t8Wmn+kRzGRlh8+sEANKDF3NQ4+lZ+1g5y9Ln52hEhgcS1JfP\neye0y2FraICAlHKW6ucXjbmgqJDe0FOK1dB0hyPVLQToAkgMn99iySWpRdT2aWsvZW3lZEXM39bT\nAor4qE5b7S3j5azMnJ/25PhQAvqNfFihXdqN2SzbemHK/LRvKiiiO0jbNj9cYyWMeKJCoub1uaKk\nIqp6tNVe0V5OdtT8+kaQUxE+qNZWezvlFOfMM9qbHo00lMiReu3SbsxmkJLLKUyeX7++cUERHYHa\ntvmh2lqixPyDa378aIFPO9V1feUsSpxfJwCQH1dAVZd2G3qMjUF/aDlrTfN3kuIdheyr1C4KVlk9\nxnjM/FJuAJblJyBGw6lpa/SSsrkptVaQEjD/Nj8vt5B2SdvIo6W/goKU+TsapphCKjq00z44CMNR\n84/2AsSMFvJ+uXYP7PKaIZwRTeTE5czrc2sL9YwzSlNPm5eUzc0xWwX6oPnby+qsQlqc2tp6w1AF\ni9Pmrz0rsoCyNu369a4ucMSVsyprftolCaKGith9QjtbP1HdgwjundcaH4BNS7MYC2ynZ1i7tJvj\n9grSQ+ffv/jxowWKONWSJF0iSVKFJElVkiR9d5rzmyRJ6pYkqfST1/dcuW+rs4zVWfN3qov0eTSP\nardzmNUKuuRylqS5EWUPz+ekXbvo3cfVNUSOzz8qEBgIYQP5/EPDHdsqOsrJiZ7/w3rdohyGQ62M\njY95QZVrtFPB6uz5ay9MzcM+rF2b19YKpKRyiuYZ7QUwhC7gWIN22j+uqSTWaXK5JN0EYWESwf15\n/KNMO+3VXeWYYuff5usX5TEYUqvZjJIQ0Kmr4Dw3Ag4Lk/JoHNSwzWuckFBJwTzTywBSA/MptWrY\nr9eVk8j8Um4AYqJ1BPaa2F9Z6yVlc1PbU8GChPn3jX78aIHHTrUkSTrgl8BWoBC4QZKk6X4Be4UQ\nKz55/Wiu+46MwFBkOevy59+BFZtM9ARo1/ker+yBkF4yYuYXFQB5Ywxzr3baj9rK0Qe7FxVIkEwc\nrtdOe8NQOUWp8+98szNCoC+Nqhbr3Bd7gb4+GI2u4Lzc+WtfmW2iS9KuzUsr2wgIgKTw+a+2z4nN\npa5bw99pU5nbEbBYp4lDddppt41WzDu9DKAgNwoxEkVDd5MXVM1NRwc448tZlemGrWfl0S60c0wP\nVTUSLKLnVfljguxYE9Xt2jmmp1rKMYa7Z+vR47kcqNHO1pvHy1mR4Y9U+zk3UCJSXQxUCyEsQogx\n4AXgimmum9cQ2WwWSPG1LEwyzV/QQj2OgD76Rvrm/Vkl2F9TRex4Hjpp/s27xGCidUzDyGNXDbmx\n80v9mMAQZqKiVTvtXQEVnGea/8M6IADChkx8WKmN9uracYivYWHS/BadAZy3yMhocDPDjmEvKJub\ng3WVJIgFbm2fW5hmomlEO3sx99S4tCX8dOhDTZxq1ka7ENATVMF5pvnbS3AwBPeb+EgjWy+vHkFE\nN5Ab73qVmwnWLsxhKMSCw+nwgrK5OVRfSZJu/m0OsCjFpOmMkqWvmoVJ7vXrKUEmTti00T4+Dv2h\nFazNd6/d/5m5/fbb+e///m+tZUzLgw8+yE033QRAQ0MD0dHRqsyOZWdnT7uxjZoo4VQbgKn16xo/\nOXYmayVJOipJ0puSJM2Z03GsqhOdTiIuLG7eghITJXTduRyxaNMRlNnNpIbOL09zgmKTid6gas2m\nZ5uG6yhIy3brs3kJJix92rR5Tw84osysyJr/wxrkKPsRjaLshyvthDjjXN6AZCrG9ECknkzKm7VZ\nBFXeYsYQ7p6tr8410aPTztFoGTVTZHBPe06sCXOPNtpbW4HYOpZmzD/gABAnTBys1Ub7wSor4eN6\nlzcgmUpedij0J1PXoU251KrWOjIi3bOXFVm5dKGdrbc7zCxOd69fz4o2UdOljXabDaS4OgpS3evX\nfRUlnL9f//rX3HfffQopUp6JQEtGRga9vb1zBl727NlDRsb8Z/d9DbUWKh4GjEKIZcipIq/OdvEP\nfvADHvvVPQTtCeX999+f95dJEkSOmthfrU1HUNdlJifOvQ5sWX4CTid0DHYqrMo1uiUzK3Lc015k\nyKXVoWG0N7qB7Lgstz6fHm6iXKMo+5F6M3G6LLc+q9PJUXatIo+WHjO5Ce7Zy6oFesYCeugf7VdY\n1dwIAX0BZlbluqe9UG/SbN1GRc0IIrwVQ/R0sYu50YfmUdasTRrFcauZxAD32jw4GEIGTOzXyNYb\n+urJT3JPe/GCTIaD7Yw4RhRWNTcOBwwEm1llck/7olTtouwnq/oheICUiBRNvl8rfGn7b7W0CCHc\nmvGcL++//z4/+MEPJl9Ko4RTbQOmVvFP/+TYJEKIfiHE4Cd/vwUESZIUP9MNf/CDHxC35GJyt6yn\npKTELVHJgSbNFkE1D5vdjvbGx0vouk0csaqvvbMTnNFmlma4F41Zk5dLf1CNJlH2Q5V2Qpzxbpdd\nyk/Mw6pRlL2ypR5DuHv2ApCoy9Msyt466n4ETJ+mQ+rO4ZS9TmFVc9PcDMSZKdS76STlmujVaN3G\noaoGwscN815gOYEpTrt1G1WtZjKi3Lf1eJHHoXptBgRt42aWGN3TnpMZBD0ZVLfXKyvKBRoaQIo3\nsyDZPe0rs7Rbt3Gopp6o8SxVnC21uPnmm7FarVx22WVER0fzyCOPYLFY0Ol0PPnkk2RmZrJ582YA\nrr32WtLS0oiLi6OkpISysk+r39x6663cf//9wKdR3kcffZSUlBQMBgM7duyYUcMFF1zAvffey5o1\na4iJieHKK6+ku7sbYEYt+/fvZ/369cTFxbF8+XL27Nkzeb/6+npKSkqIiYlh69attLe3T56buJ/T\nKddp7+rq4ktf+hIGg4GEhASuuuoqBgcH2b59O3a7naioKKKjo2lubkYIwf/5P/8Hk8lEUlIS119/\n/aROgGeeeYasrCySkpL48Y9/7FL7l5SU+LxTfRAwSZKUKUlSMHA98NrUCyRJSpnydzEgCSFmDcWa\nu+vcjvYCZEaZqO5QvyMQAnokMyvdjIBJEkSNmfhYgyh7Ta0TEW11O9q7OD8GMRpBU7/6i6CO1dcT\nJ2W5/fml6SZax7V5WMvR3iy3P58RYaKiTX3t4+PQH+R+BEyng/BhE/ur1Lf1iupRRESzW4uJAZbl\nJTHOGF1DXQorm5vjVjOJge73jYvTtYuyN/TXk5eU5fbnDWEmyjXIZR8ZgeEQ9/v1oCAIHTTxsQa2\nfqq6H4J7SY1MdevzqxekMxbQycDogMLK5uZko5nk4CzVv9ebPP300xiNRt544w16e3v59re/PXlu\n7969VFRU8PbbbwOwfft2amtraW1tZcWKFXzhC1+Y8b7Nzc309fVht9t54okn+PrXv05PT8+M1z/z\nzDPs2LGD5uZmAgIC+Pd///fTzk/VYrfb+cxnPsP9999PV1cXjzzyCJ/73Ofo6OgA4POf/zyrV6+m\nvb2d733ve/zxj3887V5TB0U33ngjQ0NDlJeX09rayje/+U3Cw8N566230Ov19PX10dvbS2pqKo89\n9hivvfYa+/btw263ExcXxx133AFAWVkZd9xxB8899xx2u52Ojg5sttPiuZrgXqhjCkKIcUmS7gTe\nQXbS/yCEKJck6Tb5tPgdcLUkSbcDY8AQcN1c920aNnN52mK3deWnZPFa+5/c/ry7tLWBiDVTZHD/\noZcclMMpm/rRu8NVcm5vWFCYW5+PjwepO4cTDfXoC/QKq5udihYzhlT323xVXiYD1RbVpqCm0jpm\npij9fLc/b0rMYm//3xVU5Bp2O+ji6t2OgAEkBmRzvEF9Wz9ULef2uhvt1esl6MqmvLmeddnzX/fh\nCdXtZjKMWW5/flVuNn11FuUEzYOOcTNLjZe5/fmchCyO9e5XUJFr1NfL0d48N1OdAOKlHI5a1Lf1\ng9X1RDmz3Fo4D5Bp1CF6jNR1Wlmcqm4VjtpOM5n57rf5bEgPKtPPiwfcm5k9c0ZXkiQefPBBwsI+\nff7ecsstk3/ff//9/OxnP6Ovr4+oqLM3fQoODub73/8+Op2Obdu2ERkZSWVlJcXFxdN+/0033cSi\nRfL/50MPPcSyZct4+umnp9Xy7LPPcumll7J161YANm/ezKpVq/jb3/5GSUkJhw4dYteuXQQFBXH+\n+edz2WXT/8abmpp4++236ezsJDo6GoDzz5/52ffb3/6Wxx9/nLS0tMk2yMzM5Nlnn+Xll1/msssu\nY/369ZP/hl/+8pcz3kstPHaqAYQQfwcWnHHst1P+fhx43PX7Qa/OzMqc6YqIuMYSYyZ/bFW/RFq9\nRY72ZsVmuX2P9Cgj5s5S5US5yJF6M/E69zswSYIop5EjdVa2FqxTUNncWPvMrC50X3tRfiS8Gk7b\nQDvJkfMvD+cuTif0B9azIucmt+9RlGHkLyfVt/Va8xhOD6K9AIbITGrb1Xc0jje4n9sLn0TZx4yU\n1lpZl71cQWVz09hfz8UeDGSW5MXh3DlK30jfvHdk9ITRURgOrWd5Tpbb91ikN/JujfoDgkpzPwT3\nux3tBUgNM1Ldqv4iy1M2M8kh7ttLcDCEDBsprVHfqbYN1LM2Ocsr93bXGfYm6enpk387nU7uvfde\nXnrpJdrb25EkCUmSaG9vn9apTkhIQKf7dOAUHh5Of//M61WmLgrMzMxkbGzstLSNqVosFgsvvvgi\nr7/+OiAPCBwOBxdeeOFkBHnqYCAzM5PGxrM3gmtsbCQ+Pn7SoZ4Li8XClVdeOfnvEkIQFBRES0sL\ndrv9tH9DeHg4CQkJLt3Xm/jkjoqdnSBi6yhyM1cTYHV+BkPBDTiFU0Flc3Oszk6wB9FegLxkI02D\n6jtJNe3uV3KYIDHISJlNfe3tjnq382MB4uJA6jNyslFd7S0tcgRsYYr72lfmGukPtKiey15aZyXM\nkeZ2tBcgJ8FIY58GA4IOMxmRnkXA4gOMnGxQX3vHuJmi9Cy3P5+WJkGPkYpmdbXbbLKtmzyI9q7M\nzaRPp36bH62vJ2o806NZrKw4Iw296ms3d5vJjPHM1uOkTI5b1R/MdOF+HrsvM5MdTT3+/PPP8/rr\nr7N79266u7upr69HCKFYP9/Q8OkAz2KxEBwcTGJi4rRaMjIyuPnmm+ns7KSzs5Ouri76+vr4zne+\nQ1paGl1dXQwNDU1eb7VOb+cZGRl0dnbS23v2Dp3TtYnRaOStt9467XsHBgZIS0sjLS3ttH/D4ODg\nZDqKlvikU222jCOiGzyK9i4yhSOGo2nua1VOmAucaKgnjiyP7lGYbqRzXP3Ot6Hfszx2AEOkkboO\ndbULAf2BZpZlZbl9D0mCyHEjh1WOgtXVjyEimua9ffBUli6IxemE7uGZ8+e8wSmbmQQPor0ABQYj\nHQ71bd0+6H7Vkgn0EUZq2tTV7nDAUKiZFdmeR9kPVaurvco86FFuL8CKBck4AnoZGhua+2IFqWiu\nJynIM3tZmGakdUR9W28aNpPnZtWSCVLDjFSqvDnW0BCMRZhZ7oGt+yqpqanU1Z0+Q3ems9zX10dI\nSAhxcXEMDAxwzz33KJqa+Oyzz1JRUcHg4CAPPPAA11xzzeT9z9Ry44038vrrr/POO+/gdDoZHh5m\nz5492O12jEYjq1at4oEHHmBsbIx//OMfkxHtM/9tqampbNu2jTvuuIPu7m4cDgf79u0DICUlhY6O\njtMc7ttuu41777130klva2vjtdfkJXtXX301b7zxBh9++CFjY2Pcf//9mpUinopPOtXHapsIHo9z\nu5IDQHg4BA7I07NqUtVmJjXUs05gVZ6RgUCr6gbS7qhnkZtVSyYwJRmx9avb5h0dQKz7lRwmSAzM\nVD3KfqSugVBHGkEBQW7fIz5eQtenftRUntnwrM2X5xjp16k/Jd7h9GzdA0B2fCaNKkce7XaQ4uo9\ndpLiA4ycnCGa5C2OmOuJGDe6ndsLn1SM6UtXPcpe12Um3cOZjaVZRnol9Z3qLmFmiQezvgCZsUas\n3epqb2gQEGcmx82F877M3XffzUMPPUR8fDyPPvoocHak9uabb8ZoNGIwGCgqKmLduvmlVM7lgN90\n00188YtfRK/XMzo6ys9//vMZP5uens5f//pXfvzjH5OUlERmZiaPPPLIZEWP5557jv3795OQkMBD\nDz3EF7/4xRm1PPPMMwQGBrJw4UJSUlImv3fBggXccMMN5OTkEB8fT3NzM3fddRdXXHEFW7ZsISYm\nhnXr1nHgwAEACgoKePzxx7nhhhvQ6/UkJCSclrKiFYrkVCtNWaONaMnzxolyGjlusfKZ5dMn6nuD\nhl4LeRmZHt2jKC8aMR5I51AXCeEzVh5UnD5dA0syPSu+Xphu5KV2lR949Q5EpGfRXpAjj2pH2U82\n1hPvZo3qqUSMZVJaZ+H8/CWei3IR24CFNfGe2fqKBUk43ulncGzQrc1v3MHphIHABpZmG+e+eBYW\n6Y28U6GuvVSbhxAh3R5Fe0GOPNaqbOtl9noSA7I8uockQehIJqW1VpZnqLfLXtOghYsTPLP1VQv0\njH7Qytj4mEeD6PkwNgbDIQ0syfKsb1yQauSjepXtxdyNTuckPky9Z6BaXH755Vx++eWnHTuzHnRE\nRASvvnr6lh433njj5N9PPfXU5N+bNm06K+XizEj4meTm5k67I2NmZua0talXr149474h2dnZ7N27\nd9pzZ94vNjZ2xnJ/TzzxBE888cRpx77xjW/wjW98Y9rrb7rppsmdGwHuueeeaa9TE5+MVNe02EgK\ncW9jg6kkBGZS3qTudH7biA1TsmcDguhoCOg3ckzFTqynB0SkjQVpnmlfkStH2dXkeF0zwY5Ejx9U\n2fFG7AMqDwg6GkgJ83wXqbgA9XPZ20dt5KV6Zi9JSRJSbwZljepFq9vaQIq2kZvkWR+zPMdIn8qR\nx+P1NsLH9R5Fe0GOPKodZTd3NpAW4bmtx2LkZIO6/Xqnw8aCNM/sJTMjEPpTqWtXr+yX3Q662Eay\n4j37nS7JNNIj1LWXE/WNRDoz/qlqVPv558cnnWprt83t3cKmYog0Ut+pbkfQI2wUpHuuPcKhbuqK\nxSIgupH0GM+0L8tPYFwapne4TyFlc1NusxGjwMzGwjT183ttvTYyPGxzgLSwTOpUnCEQAvokG4sz\nPdMuSZ/k99aop73e4kRENKGP8qzs46oFaYwFtzM6PqqQsrmpsNuIDfDcXvJTjLSOquuYNvXbyIzz\n/HeaEqpuLrsQMBBgo8hDWw8IgJARdXPZa+tHESFdHu9IuCo/nZEQG+NO9Xb6q2y2ER/oua37ORv/\nQMV7+KRT3TJoIzvR8x9TTnwmdhWraAwPw1iIjUKjElF2IxVN6mmvMPciSTqiQ1wrdTMTsbFyfu8p\nFSOPNS2NisxsLM0yql5ZoG3Y84gpyJUFGvvVc5K6uoAoG/mpnmuPldSNsp80txEkoj1aswGQmhIA\nfWlUt5xdOspb1LXZSAnzvM2XZKqf39sxaiNPAXsxxmRi7VFP+8TMRl6K5wOCGGHkhIq57CfMTYSO\npxCgC/DoPjnGUBiKw9bTopCyubF02EiN8DvV3mD37t186Utf0lrGPyU+6VR3j9tYqPf8x7RIb6TD\noZ6j0dgIUmyjMpHHcHXze09YG4kSynRgYaNGjprV027tUWZmY3leKo6gLoYdwwqoco0eYWORAjMb\nC1KNtKkYebRYgChl2j0lzEitipHHUw2NROO5gyTn9xo5rGKUvbFPmf5lhSmdkeAm1SKPEzMbRQoE\nHPKSjbSOqGnrAhFpwxDlufakECPVKu6fUG5rJFbnue6gIAgaVHf21N5vIzPO71T7ObfwSad6OFiZ\nFIolWekM6NTLX6uzKDPVBnLk0aZi5LG62UZCkDIdWJzOyMlG9bQrNbORmqKDXgPVLepE2YeGYCxM\nGVsvMqbTJ9kVUOUaVeYBCBglLtTz3QQzY4xY+9SzF6XWbADEoG7VlbZhG7nJCsxsZATDYAIN3U0K\nqJqbnh4QCs1sLEo30CPU69dPmTsIFOEe7T0wQUaUEUuPerZe224jJUyZighRTiPHLOppV2pmw48f\nNfFJpzogzoYxVoHpfFMSjqAu1XIeT9Q3Eeb0fKoNIC81nY4x9R4c9Z2NpEUq0/kmhxkwt6vn4Ck1\ns6HTQeiogWNmdbQ3NIAuRpmc6mWmNEaDm1Xb7OiExUYkekVy83KT0mkfUc/WG7ptGKKVsfWkkHRq\n29TT3itsFGZ4rj0oCIKGDRwzq6PdapVTKJSY2VhhMjAcZFet5OipBhvRKOPc5SSm0zqknr009ioz\nswGQEGygplmdvnFiZqMgw+9U+zm38Emn2hmh0LRycgDSQAp1rc0KqJqbCptNkak2gMIMPf0qRh6b\nBmxkxSujPSPGgK1XnQfH6CgMBynX+UZLesoa1Gl3s8WBM7TN4/JoANkZITASTVNP+9wXK0BVc6Ni\nMxsFGXpVI4/NQ43kJCij3RCtp6FbHXvp7YXxcGWivQBRwsApizraq+uHEIGDJIR5vo3wgqwohIDu\nobN3ZfMGNa02EhSa2Vig19M9rl6/3jZsI0eBmQ2AtAgDli51fqft7SDF2DB5oD0zM3Nya2//y//K\nzPSsJKar+KRTrdNBVPDZe9vPF0mCkFE9R2rV6Qjq2pVZRASwLDeNkWD1ojGdYzYWeFgebYKcJD1t\nI+o8OGw25WY2ABJDDNS0qGMvJ8zNhDo9LwUIEBgIQUMGjqpk6/WdNtIiFbL1HAPDgerObCxQYGYD\nICtBr1rksaEBdLE2jyv0TBAfpKdKpcjjCYuNCKcyMxvh4RIBAwZOqDQgsHbZMChk60uy9QwGqGfr\nPaKRQoU2xMiM19M8oFKbT8xseJDHPnVbb+O/38rtv//95Htvvv7r4ZPEfX+hIvdyOgXSt4wcMdep\nov2f+VVfX6+cgc6CTzrV0ZJBkc4XIAqDapFHW6+NDIWcu5yMCHCE0tTTqcj9ZsPhgIGARsWivYvS\n9fQ61Wlzi0XgVGgREYA+Sr3Io1weTbkdoCKFnpMqORpN/TayFFpEtCg7FqEboXdoQJH7zcbQEIyE\nNFKgkKOxQG+gy6FOm9dbnIyHNXtcCnCC1Ag9lk51BgRVTTbiFZrZAAgf13NcpdSV5kEbWQrNbCw1\nJTMe3MGoY0yR+81GT48865uXooz2vFQ9HWPq2Hpt/QjjQd0kRyQrcr+UcPVSEqtbbCQGK9PmkgSh\nYwaO1qk3EPPjGT7pVCu1iAggMUSvWuRRqfJoINc0DRoycLTG+z+mpiYIjLN5vEHABEtz9AwFqdPm\nFfU96AggKsTzmQ2QI48tgyqlfyg4swFy5LGyWZ127xizke/hZhgThIZKBAzqOW72/qK5xkbZ1pXK\nM12cpV7k8VR9KyEiluCAYEXulxlvoKlfpQGBwuXRYgMMVNrV0d6lwMYvE8TFBCINJVPR6P2URKsV\nAmJtZMQo068XGg30S+r0LyctTUSIVEXWJwFkxOqx9ao3s6FXaGYDIEbSU96oXnqcH8/wSadar1DU\nceJe1i7v/5iEUK482gQRTj0nrd7XbrWCiG5ULNq7JDcZZ1APgyMjitxvNsoaldn4ZYIFaQY6Hep0\nYEouIgJIjTBg6fC+vQwPyxV6FhqU0x42rud4vffb3WoFZ2Qj6QotVFyRl4YjtJlxp/cXiFbYGxXZ\n+GWCvFQ9HaPq2LrS5dGSw/TUqbBAdGREXrOxUMF+PXRUzzEVIo/1FieOcLtiMxsrTHpGQ9RJSaxq\nblR0ZiM3WU+bSouhlZzZADklsbbVH6k+V/BJpzpHgfJoE2TF62ke9P6PqbMTiPZsYcWZxAXpqWry\n/o+ppn4YZ2AvSRFJitwvNESHbiiF43Xej8bUtipXHg2gKEvPgE6dDqxtRJnyaBMY4/TY+71v6w0N\nEBxvw6hQBAwgVmeg0ub9dq+s70XSCY83OZogPiYYaSSWysY2Re43G0qu2QB5MbRaZRg7x5RLQ4CJ\nxdDe197YCIHxNowKDn6jJT1ljd7XXm5pJ1hEKVIKECAzLQqcOuyd3l8gqvTMRkG6gV6hkq2PNyo2\nswHyYmhrtz9Sfa7gk061UouIAPLT9HSqkAcmT7U1KlK1ZILUcAP1Hd7/MZ2y2okkDZ2knDmEOfQc\nr1eh3buVbfMVJj2OUDvj496NxggBPU4bixSM9ualGOhQYYGoxQIoVB5tguQwPXUq5DyeamwkRkpX\nbLqR6B4AACAASURBVM0GyIuhj9Z6X7tSW9pPsCLPwEiw93U7HNCvU3YWLydZT+uwOjMbIlJZW08I\n0asSeSy3NRKn4MyGJMllGI+okJJoH1B2ZmNpjl6VxdBDQzAarNxCaIDsRAOtKqUk+vEcn3SqlcpL\nBlicZVBlAxiLReAItyuWQgFyHpgaOY/VLTYSFFpYMUGMZFAlD6xlSJmNXyZIjotAcoZQ3dil2D2n\no71druSQo6CtF2To6cX7bW6uH2csuJW0yDTF7mmI1mPr8b6tKz2zARAl6Slr8H67K7XxywRZKXEQ\nOERT+6Bi95yOiTUbSjpJakUea+qHcQb1kRieqNg99VEGGlSIPNa120hWcGYD5MXQJyze194xquzM\nRmFWMs7QDnr7vbtAdHJmI1bJlEQ9XeP+SPW5gk861Uo6psty9YyF2vF2ymOltZNAQogIjlDsnqYU\nPe1qRB47begV2vhlgqQwPXVt3tUuhLyISImNX6aiRuRxYhGRkra+wmT4JOdRsVtOS3lDC2HEK1IK\ncIKcJHUijw0Kz2wAJAYbqGnxrr2Mj8ubYSwyKPc71ekkgob1Xo88Wq1yzWGl8thBLk03FOh9eylr\nsBOl8CxedoKeZhUij7ZeZZ07kBdDV3s5JXEyj13Bfj04MJCAkSSO1bYods/psFrlnUOV7NeXZBtU\nLcPoxzN806lWMoUiNgZ049Q19il2z+kot9kUXUQEsChDTx/e/zE1DzYqtvHLBOnRehq9nPPY3Q1E\nKZvHDp9siuHlBaIWi8ARpuy0cm5aEiKkm5Z27y4QrW5WfmZjod5AjwplGFuGbOQkKutopEV6P+ex\nuVmOgCn9O410GrxehrHe4sQRolwpQICizDSc4S0MDHo3WlLjhVm8vFQ93SqUYWwbaVR0ZgPk0nSW\nTu9qb2yEoATlytNOEO7Qc9zLu+XWWUYZD+pSrBQgwLIcPY4wG6Oj6uxZ4cczfNKpTolIUexekiTJ\nG8B4ORqjdHk0+GRTjCCb1yOPnWN2xcqjTZCVqKd1yPsRsMB4ZR1TgIRg75dhrLT0oJN0ii2YA9BJ\nOoJGUjlS490FopauRkVLRgEsydEz6OWcRyEmNn5RzrmDT8owenlTDKtV3tJeaVuPC9JTafeurZdb\nWwkhRrFSgABhwSHoxmI4Vu3dBaLWbhuGKGUHYUWZevq9vBja4ZBnNpSexTPG6bH3eddelNj4ZTpi\nAvSU27yr/VSDnQhSFCsFCBAfGYVEAJUWdXYQ9eMZPulUKzmtDHLk8aTVuz+mxl7ldjqbID8tFRHe\nSmfXuKL3nUpvLzjClc1fA1ikN9Dt5TwwuTya8p2vGmUY5Y1flNUNchlGb2+K0TxoI1PhiOniTD3O\ncDuDg94bQcp57HZFqwuBHHns9HLk0WoFR7hyZS8nSA3XU+/lyGOlwhu/TBDuMHC0zvu2nq1geTSA\n5bkGHKE2HA5Fb3saTU0QHG9XNI8dPlkMPer9WbzRELviA8iUMO9vAFPTrNzGL1MJHfN+YNCPMvik\nU600CcF6qr28HW/biA1TsrIRjeDAIALG4jlW06rofafS0ADBCXYM0cpG7xZn6xnych5YnWUUR6Cy\nU20gb8fb5OXIozcWEQHEBRq8autCQKfDRn6qwik3oRHoRDBl5m5F7zsVqxUC45Sr2zvB4kzvL4au\ntvSDzkFsaKyi9zXGGbB5OfJo6bCTpmB5tAlidHqvbgAzaesKz+KlRMdD0BB1Dd5bIGq1ygNIpW19\nUYaeXi+nJFZYOwiWwggPClf0vukxehq9vBja2m1TdJ+NCaJQZ+G/H8/5l3Cq0yINWLu8Z5BjY3LJ\nqPw0ZTswkLfjPeHF0nRWKxClfOdbZNQzHm5n0IuFBSptzURJyk61gVyGscvLG8DYe+2KlkebICVc\nT70XN4Bpb5cXWCodvQM5GnPMiwtEGxrkbZuVjoAtyZYXQ495sbDAxMyGkqUAQV4M7e3Io73fhlHh\niClAcpiBWi9uANPVBVKUcrvkTiCnJKZxtNZ7O4harTAepny/vixHz0iwzasL/6ua7V6Z2chJ0tPm\n5cXQzQN2xdc9wMTO0P5I9bmAIk61JEmXSJJUIUlSlSRJ353hmsckSaqWJOmoJEnLlPheV5Ejj977\nMdlsEJJow6jwwgqAuAADFV7MeZyYalOyPBpAXFgsUuAYFXX9it53KjUtNhJDlB/IFGUa6Pfyphit\nCpdHm8DbkcdPZzaU1x4t6anw4gYwZouDsaA2RddsAOhjkiC0m/qGUUXvOxVzu53kMOVtfVG6nj4v\nl6brGLVjSlFeuyFaT2OP92zdapUXzCmdcgMQKQyc8mJKYq1lmPGAfkVLAQLkJKVBZDMtrd7zqus7\nbKSGK9/mi9K9uxh6ohqV0jMbIFdEU6MMox/P8dipliRJB/wS2AoUAjdIkrTwjGu2AblCiDzgNuA3\nnn7vfMhP9e7W01YrBMQoW6N6guQwvVfzwKoaugmSlC0FCHI0JnTMu6utrd129F5w7hZn6nGE2Rke\nVvzWgFwyajDATl6q8o6GKdm7W083NABRNsUjYABJod7dFOP/s3fe8XGVV97/PjPqvbdRG1myNXJv\n4NBseoBsCkkg2bDpW5LdJW82QBLI7kuyyb6bkOxudgmQtoSEBJNAIEAgYAM2xeBu2ZJl1Rnd0ahY\nxZLVy8zz/vGMgmyrjDT33hnj+X0+fJi588wzR8fnnnueU+vbTpIgMnWv2bBarMRM5HKkyTjPo+d0\nO4Wp+vN8rd3GeKwHr0FlG4ODMBnvYVmO/rQvy7bRPWZsFE8m6e/tBeNTEus9HaRa83WPbMRGxRI1\nlcqx5h5d952JjqF2itL15/ma0gJGo4xrOdrbC5bUduyZ+tNemmnOZOgIgocenuqLgEYpZauUchLY\nDnzgrDUfAH4JIKXcC6QKIfR1F80D5Xk01qieSjBG+RamFhg6jrex05giIpgeimEc7V0jxiiwgpQ8\nSDxJq2aMpeHxQFxWO4U657EDrCyycVoaK+sTscYcIG3JNkNb0zV1tRsS2QBIooBaAwfAdI/pn4YA\n6mFNcjvt7cZYGm73tKzrT3ulzUa/z/gonhF6PS+xwNBi6JYeD9lxxsh6gq+Aoy5j+C4l9I4bE9ko\nzy2AZA+9vbpvDSjdGJNpjLysyLcZnpIYgT7Qw6i2Ae4Z79v81+Zb45lljWFYVWxjKsHD6Kgx+zu1\nCSat+hfMgT8PbNy4m8nV105+ojHKNyumgKaTxtA+NQWnpccQ5RttjSZ6KsOwQQGqiEj/3F5QE0TH\nY43rLNDsHsJnmdC9YA78relGDfSy9xvzwAPIjLbRYJDncXgYxmPbDfH2JsYkYpWx1LYYM0F0evCL\nEXxfa7cxGmVcy9EGdx8xIoH46Hjd9zY6JbFtwJjIBqiURKPaMPb1KXnRu0MPQEZ8BkSPUd9iTKHP\nnwe/GKDXV5XaGLZGjOrzAVGhJmA23HvvvX9+vW3bNrZt2xbUfoWpBZDYhavVi6NS36I2UAVzKXk5\nuhfMgRrHO2Cg57FjqJ0rDAi1gRri4zbIe9feDnHZ7RSnOQzZPxnVhvEW9OeNpoHXoMhGaYYNkeLB\n45GUlOgb+gVo7Gwno1L/gjmAFTYbj3pf0X3faXQOt7PZgAJLgPxEG5pBRXNuN8Rnt2NL2WLI/ole\nG0ddHt67NUP3vTUNJuOMkfXyHBske+juhhz9/Rk0drWTWWmMbqzIs/HsgUOG7A1wcqyd67KMoT03\nwYar1xhZ1zSIzWqnIPm9uu8thCB+qoBqp4dLL6rQff/WVsm4QZENR4ENX6KHgQFITdV9+wsKu3bt\nYteuXYbtr4dR7QGKZ7wv9F87e03RAmv+jJlGtR6IscYQ7U3jWEs3jso8XfcGf6it1BgFtrrUxni0\nynm06myze73QP9XOMgO8vQBlmYU83+AyZG9Ng+gMYz2PjZ0eYLPue7tavYxHndS9OBQgOTYZi7By\nvGWAkhL9vcmtfe3kJRjD8zUlNkasbUgJetvs4+OqQ49Rsl6SYeNNV5shexsx0n4m0qNsnGhvA1br\nvneLNs5U9KDuBXOA2jNmmEbXKDk5+nuTtVMe8nUecjSNVcXGpSQODsJUXLshhdAAxWk2ag3yVKsh\nR8bp9VQx3ZpOf6O6yT2IJVnoOtBrGvnJeciEbpytU6xbE5a+0PMGZztqv/nNb+q6vx7pH/uBciFE\niRAiBvgY8MxZa54BPgkghNgC9EspjYmtzwEjB8CoUJsxCqwsqxBSPHQaMCSvq0vlgBWnGaPAVhQY\nlwdmZBERKM9jq0FtGBs8J0m0puteMDeNBK+NYwblPHYMe3QfKDGN5fk2ZLKHvj799/Z4ID7HmDx2\nUJ7H3knjZN2baJysG+l5bOhoJ82ah0Xo371VeR7zOdpiTNqNao9mDM9XFRfiTfQwPKz/3m43xOe2\nYzNIXspzbIalJLrdMBln3AEyJ95Gi0ERpcZOD5nRxvA82hpNjDeToy2mmk0RLAFBazoppRf4B+Al\noBbYLqWsE0L8rRDib/xrngecQogm4MfAF4P93cUiM8ZGo0Gjp7tH2ynLNshjGp8J0SM0OPXPA9M0\niM02Jt8RlJd92O951BuaBmMxxuSvAZRmFtIxZIy8NHe3G1ZEBH7PY4f+tE9NQb/XmNxegLykPEjo\nocWlf0K4260mzBkl66tKbAwZNABGc0tGrR2G0V6cZjNs9LSrp50cgyIbAKkWmyGjpycnVc2GUbJe\nmGKD5HY0TX/lqGkQlWacXl9ZXGhYMbRLm2LM2kNukjF9DIpSCnEb1Iax9VQ7eUnGyXoKNo4bWAwd\ngT7QxX0gpfyTlHKFlLJCSvnv/ms/llL+ZMaaf5BSlksp10opjUsmmwP5iTZa+/QXyIEB8CYaMwwD\nlDcmwavywPSG2w0ixZiew6A8GiLFQ48B3Zea3UNIMUlqrDEJZqoNozHh/LYBY7ohTCMvwYarR395\n6ehQ3t4iA/qxA0RZooiZyuZoi/5hGVVEZJxRPTPnUW80tvUSazGmYA6gIreQHoPaMHoGjenfP42c\nOBvNBhRDt7dDnIGyHh8dj9WXwLEW/ZWj221sZGNVsY3JOA/j4/rv3dDeRYo1myiLMSkOZdk2Tho0\nAKZjyGPI4JdpZMXYaDLIMRiBfrggJiqCynk0wvOoaZCQq/+Y75lIsxRywgBvjJFFRAAFyQXIxC6c\nrfq3pmvq7CAzpsCQgjmAlf6cR7297FKq9mh2g4qIwO95NEDW3W415MgoeQGV81jbpv9hRtNgPMY4\nWS9MVUVzRngeWwyObBjVhtHnU4Nfygzy9oK/GNoAz6OR7dGmkSwLqWk1hvaxKOOcJUWpNkRqGwbc\nprh6PeQaGNlwFNoYkPoTPjEBgxgr6wUGtxyNQB9cMEb18jwbfQbkPGoaWNONNTRy4220GOB5bNV8\njFq6VNjdAMRYY4jxpnOs5aTue2v9HgoMyrsDJS+k6J/f29+vPKZGRTbAuJzHP0c2DOR7VqyNZgO8\nMS73OBNigOzEbN33BkiKScJKLMed+remaxsw9tBeaVMtR4d0Hn5qdM0GGOd51DQg2bjcXvCnJHbq\nT3uzexBhkSTHJOu+N/hb00WNGZKS2D5oXCtAUAfI8RgPEzoPP21rU861IgMjkKWZNjoNbMMYgT64\nYIzqquIChiz6ex41DXwJxhoaRWk22k7rf7pu6ugm0ZpGjDVG972nkSKMyQPrHG6nxKAiIlCDSJTn\nUd99NQ0Sc431gFUZ5HnUNDUdz0jabck2NAM8j42dHaRHG1MwN40kaeNYq773qZRqpH2ZAYNfplGY\nYsOS6lHTMnWEpkF8rrGGqcNmY8CAATDTQ46MlHWjiqFbutWQI6OieEIIQwbATE3BKW+7IUOOplGc\npmRd78Cv0fVJoAbAGDkZOgJ9cMEY1Ubl92oajEYbq3zLcwrpNsAb4+ppNzTUBsrz2HRSX0Pj9GmV\ntlJqwDTFaaTEpiAskhPO07ruq2kQZXBkY0W+DW+ih9P6ko7mloxYjCuYAyjLLqRrxID0j1Pt5BtY\nRAT+Now6e9m7u1XrSCO9vdmJ2fhiTtPkGtN1X00Dq4Ht0UAdIMdj9M/vdWlTjFmMK5gDKM0opH3Y\nAFkfMFa/gDEDYNrbISHXY6inOj85H1+C/imJmgYi2biUG1ApiSNRqr1uBOGLC8aotiXbkCn6ex6n\nC+aMmDA3DYdBA2DahzwUG9QebRqFyYW654G53ZBU4DG02E8IYUgbRk0DX6Kxyrcw1RjPY7Onjzir\ncQVzAJUFNvq9519kAyA/Sf9iaDMiGxZhIcGXxzGXvq3ppiMbRsp6cZoNS7pH9/zepo4uUqOzDCuY\nA9VCUu+URJ9PdaOyGzCRcCZyE2w4dU5J1LTpIUfG0R5jjSHWl06tU9+URE2DCQPrkwDsmUqvG9Fe\nNwL9cMEY1RnxGWAdp8Glb2PQ6SIio0JtoAwNvXMeR0dhSBjr7QWwZ9noGtFf+RpdRASQYUDOo4ps\nGJyDn5iLL7aPFtekrvs6+zzkxBvL85VFNsZ0znkcGFATLIsNNqpL0m26j552u42v2QDVhlFvz2Or\nJhmxGnufFiQX4EvowNXq03VfV187eYnGy/qQxYNPR9K7u43PYwcoSSvEo3MbRrcbLGnG63Uj2jC2\naj5GRKchA72mYUtWffz1dgxGoC8uGKNaCEGSLNC92trdb/wDryi1EGtam66ex7Y2SLa1U5BsnBIA\n/wAYnT2PbjdgYHu0aRQkFurueXS6x5kQxkyYm4bVYiXel0NNa4eu+3YMGtdibBrFaTas6W265jxq\nGiTbPIYNw5iGEZ5HMyIbAHkJhTh1HgDT0jaIxYJhBXMAcVFxxMhk6lr1zevrGPJQnG6svJRl2bCk\ntnFSR6eppkFiXjv5Buv18lwbPRP6hgc0DaYMrtkAyI6z0azzAJim9h4SolKIjYrVdd+ZSIlNQQhJ\nvUvnvL4IdMUFY1SDynls0NHzODUFvZPGe3vzk/Lxxp3UNQ/M7Ya4bDfFqcULLw4CVYWFjMe26Zrz\nqIqIjFe+pZk2OnTOeWzu6iAjJtfQgjnwex51HAAzOqrGfBst67YU1e+5tVW/imK3G6Kz3BSlFOm2\n52xYVVTIsFXfnEdNgzGDIxtgzACYlh4V2TAyigeqDePxNv1oHxhQB5kSA3sOAxSmFOpeDO12Q1Sm\n8XrdUaiKofUs/Nc0GIkyXtYLU2206VwM3drnMTyyIYQgBRu1kQEwYY0LyqjOT7Sh6Vht3dEBiflu\nStKMfVhHW6OJkxnUuvQbUappQJpmuPJVnkd9cx5dmpdBPOqhZCAqcvUfPe0+bTzPQQ2A0TPnsa0N\nUmxtFKcaK+vTrenqXPq1plODX4zne2mmDWtam645j662cUboNTSsDErW9R4A4xl0U5JmvKzr7Xls\nbYVkm5sig/VLRnwGMmqMRpd+rek0DbxJxst6Ra7+LUednkG8jKspwgaiPLuQrjH9HkhSQvuwG3uG\nsboRjJ0MHYE+uKCM6pIMfXMeNQ3i88wxktKsNuo8+ikCTYOJeONptyXbkIn6emOaO7tIjk4nLipO\nv01nQVWhjdFo/fJ7Jyehz6tRnm28vBSl2nTNeXS7ITbHHFlXnkd9ZX0s1njvnS1ZGRq6yvpJD9lx\nBVgtVv02nQUOm41B9MvvHR6GkWiNZSbIemGKjTYdi6E1DaKzNUrSSnTbczaoYugCXYuhlbfXHL1u\nSdVX1lt63eQnFBse2aj0t2HUy8t+6hSINI2yTONlvSBZX8dgBPrjgjKql+fZ6NXRG9PaCpZ045Uv\nQG58oa6eR80tGRSa4SHx6dZ0euaBtfZrFKUYr8CK021EpXto16kpQns7JNk0U7x35bk2enQcAKMi\nG62mGNWqDaOO96l7iiE6DM9Lzk7Mxhulb2s6syIb9iwVUdIrv9fthpQijRITaNd7AIymgUwxh++Z\nMYU0dOp3gHS1jTIuBshJzNFtz9mQn5zPVJy+rek8wxql6cbzvCLXhkzyMDCgz36apvS6GfISGQAT\n/rigjOpKm/I86pXfq2kwmWjOzVScZqNNR89jc3sPcdYEEmMSddtzNgghSBGF1Lr1eXD4fHBywhyv\ngN6eR02DuDyNklTjD2HTnke98nvdbnMiG6ByTd06eh6bujpIi8k2dMgRqNZ0SeRTq+lzCpuYgAHM\niWzYktXoaT1l3azIRqVNtWHUy/OoaTAaY84BskDnNozN3W1kx9kMr9mIscYQRzrHW/U5hQ0NwViM\nRnm28brRlqwOkHrKenSWOXp9eV5BZABMmOOCMqqL0wqJznTr1llA02DYas6DY1mOje5xHT0a/Rq2\nJOPpBsjWcQBMVxfE52qUZRivwPKS8vDG9NLSqk/+h6aBxYQ8dgB7ZiHWjDa6dErDV5EN41MoQHVF\n0DPnURswJ7IB08XQ+tDu8ZgX2bCl2JiK0681naaBTDVH1ityCiHVzSmd0vBd2hRDdBo6CXIapRk2\nOnUcdtQ2ZI68AGRYCznRrg/tZkY2ClMK8Sa26VYMrWngM6FmA6CyoJDJeDcj+k+Ij0AnXFBGdWla\nKTK1VbcTarNnACmmSI9L12fDebCqsJhBoemS8ygldIyY4+0FKE4pQRto1WUvTYOEfHMUmNViJUkW\ncEzTp5ehpsFEgjkesJK0EkSaSzdZb2rvJj4qiYToBH02nAcrC4vpl626eB69Xuie0CjPMkfWC5NK\ncPXrJ+txuebIelxUHHFkUKtTG0ZNg/FYc2S9NK0US4aOev1kOxmxOURbo/XZcB5UFhTTO6UP4ePj\nMCDNk/WCxBJael267OV2Q0y2OfKSGpeKVVipa9WnylJFNkxylqSXEpXl0n2wVwT64YIyqvOS8vBF\nnaZRpwEwzl6NgsQSwwsrAJbn2LFmOnXxPJpZWAGwIsdO17hLl700DawZ5igwgNxYO/VdTl32atUk\nQyZFNopSipiK66SlVZ8BMK0mRjaqCuzIVCf9/cHvNR3ZKEk3vjIfoCLbTseoPvLidoNIN0/Ws6NK\nOd6hl6z7GBRthtdsgDKqpxJb9fOyD7RSnGJ8JAxgdaGd8QSnLp5HjweSCs3zVJdl2PGM6CMvZkY2\nADItdmo9+tDu0iYZEd2G9wYHsKfZ8Sa7dG05GoG+uKCMaouwkEoJR90uXfbzDGvYTSisAHUzyTSn\nLt4YtxsSC8wJ5QOsKbbTL5y6eB41DaYSzfFoAJSk2Gkd0Ef5tnj6sQoLqXGpuuw3H6Kt0SSRzzEd\nBEZKaB9pZZlJhzB7mh1Lhj6yriIb5sn6qkI7fVI/Q2PSpDx2gMJkO85+fWhv6uwiKTrN0JH204iP\njidWplHjCt7LPjUFvVPmdC0BWJZhJyrLqYvn0e2GOJPy2AGqCkrp8eon6+Ox5tFuS7TT3KuTrJ/0\nkBmbZ+hI+2mkx6djsVioc+nYyzACXXFBGdUAeXF2GrqDv5kGBmAqUaPMpFBbfnI+vpgBXXqaahpE\nZ5qofPPtkO7Upaep2w3DJrSMmsbyHDud4zoZ1X0aBSZ5ewGyo+3Ud7qC3qe3V3W5WZZljveuOLWY\nqfgOXbzsbjdYTIxsrC60M5nkZGgo+L1aNcmgxTzaK7LstOvkeWzt1yhMNk/Ws6Ls1Okg6+3tkFig\nUWqSt7c0rRRvkj5edk1TEUiz5GVtsZ3RWKcuLUdb3V6GRLvhswemYU8vpW3Ypcte7tPmOXkAMkQp\nNTp52SPQHxecUV2aWop22hX0Pm43JNvMKawAv5ddllCtuYLey+0GX3IrRQYP8phGaVopIl0fz2NL\n2xCTYsTQMd8zsbqolH5cuuzVPtyKPcM85VucXKqL59HlMq9lFCgve6LMp9oVvMBoGkyZlMcOUJau\n0rT08Dy2dPQRbY0iJTYl+M0CwCqbnVPSFfQ+Ph90jWmUZZqjXwAKE+209AUv65oG8fnmyUtiTCIx\npFDjCn5i0PTsAbP0enmmHWuWU5fC/6bODpKj0w0d8z0TVQV2enXwsk9OwimfxjKTnGsABfF2mnoi\nRnW44oIzqlfk2jk5oY/yjc5poTStNHiiAkRujD75vS4XDMU0syx9WfBEBQA9vexNvS0UJpaZkscO\nsLLAji/VGXRP04EB8KW2sDy7TB/CAkBFtp2OMX3kxZplrqxnR9mp0yG/1+mSnI5qpizdHL4Xpxbj\nje+gxRW8l725t4XiZHPuUVBpWuMJTkZHg9vn5EmIzW2hIss8WV+WWapLfq+mgUh3mirrmRa7Lp5H\nZ6uX05ZW7Gl2HahaGHp62V0DLZSmmifr60rsDMc4mZoKbh+PBxKLWijPME/W7el23EMu034vgsXh\ngjOq15bYGdAhv1fTYCqliYrMCn0ICwAlqfrk99a3nsInxg0fEDANi7CQ4ivmSKsr6L3aRppYnlke\nPFEBoizdrouXvbUVEouaqMgwj/bVRXb60ceonkhqoiLDPFkvTLLjPKWDrLd1EWeNJy0uTQeqFka0\nNZoEXz7VruBc1VKCZ6yJyhwzZb1UFy+7pkG8zVx5WWnTx/OoaTCWYK5etyXok997ot1NWky2KXns\noLzssTKVo87gctm9XuiabKIqzzxZr8hSEaWOINPwNQ1i85ooN1GvO/LtdE9GPNXhigvOqF5ZYEem\nuoLuLOBqlQzGmHsz6ZXf29jbTHFSuWneXoCcGDsnOoOjfWgIRuObqMo3j+f5yfnI2AEanMF52TUN\nLFnmysvqolImEoPvLOB0+Ri0tpjm7QV/fq8OXTSa+pooTTGP5wBZVnvQXTS6u8Ga1URljnneu+LU\nYrwJHTiDzGVvbQUyzZX1dSV2RmNdTAYZIGhpnWDI0maqp7osw07bsA6e6oEmytLMlfUMi51ajyuo\nPTwedQhbkWUe7aVppXiTg/eyaxr40s2W9VIGo/Qp/I9Af1xwRrU9TRXNBet5rHf3EGWxkhGfoQ9h\nAWCNTp5H93AzK7LNVb5FyXZcQeb3Op2QVNxsqrfXIiwk+4qpDtLL7nQqb6+ZyndZhuqiEaznsxvo\nIwAAIABJREFU8US7h+ToDMOnb86EHl00pIT2sWYcuebKuh75vU4nxBeaKy/Ky57HkSC97E6n8vaa\nSXtFlh1LppP2IIdZnuhsJSu20PDpmzNRVWCnZyo4efF64eRkMytN9PaCP783SC+7ywWx+ebKS2JM\nIjEyhWPO4HLZnU4YiTOX9so8O5Z0F93dpv1kBIvABWdUZ8RnYLH4qG0JrhVFfXcTJUnmhQhBpa5M\nJrUE5XkcHITxhCYceeZ5wABWZJfRMd4S1B5Op/LemanAAHKi7RzvbA5qjybnJMNRblM9YAXJBciY\nARpcwbWiaD7ViN1kb+/6UjtjcS1B5Tz29KjogNlGdXlWGZ6R4GTd5QKRYb6sZ1nKqG0PjvZG5yjj\nlh7TOjkAFKUW4UvooNkVXCuKllPme3s32MsYim4JarBXezvEFjSZ7ixR+b3B63VfmvmyniHsHG0L\nTq+fcPXjs4yZlkoJyjHoS3XhbPWa9psRBI4LzqgWQpDhq+Rg64mg9mkbaWSFifmOACuyKiCzEadr\n6drX5YKEoiYqTMxLBthYuoJToj6oPZxOGDfZ2wtgT66keSA4ealtayUzusC06nbwd4zxVrDfuXS+\nSwkd4004TPaArcxdAVn1uN1Lj3E6nRBfYL68rC9aQQ/ByYvTqVKdzKa9JGkFjX3B0V7X2UJuXClW\ni1UnqhZGjDWGpKkSDrQ0LXkPnw86pxpZZWJ6GcBa2wpEVn1Qg71cLpXbuyzDXGfJusJKTnqDk5cW\np2Qkttl0WS+Kr6S+JzjaT5xsojDB3FTKxJhE4rzZHGxymfabEQSOoIxqIUS6EOIlIUS9EOJFIcSs\nUy2EEC4hRLUQ4rAQYl8wv6kHCuMc1HTVLfn707m9qwrMVQIpsSnEejPYV7/03BWn0/zcXoBLlzsY\nTz0elJe90TnGmLXLtJZR01id56B9YunyAtDS34Q91VyeAxREOzjavnTae3tBZDZRZbK3NzsxG6uI\n4kD90sOzTicQAm/v5ZUORhLrgsrvrXedZsoyRH6S8VPaZqIqx4F7LDhZdw40UZ5uvqznRTk43LZ0\n2js6lGFqZnEogC3ZBrHDVDecWvIeTid4Q+DtvWyFg8G4uqC87PVaD1HWKNLj0/UjLABUZjlwjQQn\n662D5hbOTyNbODioBUd7BMYgWE/114CdUsoVwCvA1+dY5wO2SSnXSykvCvI3g0ZlViUtp5cukE4n\nJBQ1sNzECvFpZOFgb8vxJX+/pUUymljH8szlOlK1MJZl2hFJnRxvXLpVXdvRRE5sqSmTq2ZiS7mD\nU9aly4uU0D7ewMp88+WlIt1BU//SvTGtrRBrazC1G8I0Mn1VvN0czH0qGY6vN532lXnLIc1JcxBt\n9epONmCLrzDVAwZwcZmDHrF0nvt80OWtZ7XNfHlZllpJfd/SaW9pgeh882VdCEHaZCV7GpZOe5Nz\niuEY872964sqkRn1tHmWnopwoucExYnmy8umEgfdvqXzfGIC+q31rC40n3Z7koO67uC87BEYg2CN\n6g8Aj/hfPwJ8cI51Qoff0g0bih10BXEzOZ3gy6phVc4qHakKDKWJDo53L53249pJhMVnugcsyhJF\n4kQ5b5xYeipCy1ANjgzzeX55pYPJtDqGhpaWitDbCzK7ho1F5tO+vtBB++TS5cXlAm9GaGS9KN7B\nsY6l037MrRFvTTa1mBggNiqW+Iki3jy+9FQE10gNK7PN5/kVVQ7Gk+uWPCWvvR2ibTWsKzCf9jX5\nDjxBeNmdTphIDY2s22IdVAcRUappayY9Kp+kmCQdqVoYybHJxExl8lZd65L30MZqWJO7WkeqAsPW\nlQ5GEk4s2cuuaRBbVMvaPPPlZVWeA2004qkORwRr6OZIKbsApJSdwFzZ+hLYIYTYL4T46yB/M2hs\nrXIwFFe35JY0Dc0TjMY3U5lVqS9hAWBlroPW4aXfTLUnaylNWGW6Bwwgz+rg0BJDVlJCp6+GTcXm\nK7DcZJWKsO/40lIRnE6Ith0LycP6skoHp2OWLi/1zmHGYjyme8AAKjMdtAwuPSpzoreGZUnm8xxU\neHafc2l89/mgx1LDRaXm027PKETEDnGscWk9R51OsOaHxjB9T4WDU1FBOBycp/BGDZg6cnoay9Or\naOoP4j7tr6E8daWOFAWOTOlYckRpYgIGYmvYXGo+7VX5dmRSJ02tS4ueOp1ATmhk/eIyB71BRJQi\nMA4LxtGFEDuA3JmXUEbyN2ZZPpeZeqmUskMIkY0yruuklG/M9Zv33nvvn19v27aNbdu2LUTmorCu\npAyZ1I67c5Ti/MU3yj/ibiAjvYS4qDhd6QoEm+0Ofnn0l0v+vmukhktC4AEDKEt2cKJnaYqgrw98\n2TVsKr5NZ6oCQ8qEgz0NJ7jqosV7+FtaJOOptazMNv/B8Z7ly/EmO+k9NUlmevSiv3/EU0duxgrT\nU24ANpdW8YcTzyz5+9pYLTfmhsbQCCai1NGhDNP1tn/QmaqFIYQgaayS1+rq2LjyPYv+fnOLl7Gk\nE1RlVxlA3fy43LGCyZR6RkZ9JMQv3l9U3V5LYelKLML8oOqGIgevNL225O97JmrZGoLoAKiIUk1n\nHXDTor/rdkN0YQ1r8z+kP2ELIMoSRcJoOa/V1rPcvn7R329oGWc83hkS59rWlZWMJdUxNSWJijLf\nQXY+Y9euXezatcuw/Rd8Ukopr53rMyFElxAiV0rZJYTIA07OsUeH///dQoingIuAgIxqIxBliSJ+\npIJXjh7n0/kbF/39ut5jlBebH64CuGpVFaM7j+PzSSyWxd1MUkK3qOFi+zqDqJsfa/Kr+FXX40v6\nrtMJltzQeAUAbNFVHGyrAa5c9HcPtWjEiiQyEzL1J2wBxEfHETNWxK5jDXz4isUbmCd6j7HcHhpZ\n31pVxdDupXmqfT7oi6phy7Jt+hIVIFbmVvFs3Z+W9N1QesAA8qxVHGitBRZvVB90NpMszE9DAMhM\nSiVqMoM3a11cu2nxg4oaTx+jMiM0sn55ZRX/8lbtkr47OQmn42rYsmyu7Etj4ciq4nXn20v6bkuL\nxJsZOlnPFlW87azh8yzeqD7oqiczrszUnubTKMrIxkIUB+rb2bLSZvrvn88421H7zW9+U9f9gz2S\nPwN82v/6U8Afzl4ghEgQQiT5XycC1wE1Qf5u0Mj1beSN5kNL+q42XsPa/NAoAXtuNpapJPY1Lr43\n6KlT4Ms6xuaS0Hjvtq7YQG/MwSV9t655mKmE0KQhAKzM2Ehd/9JoP9pRQ1FsaOQFIHtqI7sbl0a7\ne6KGDYWhoX11iQ2El1q3Z9Hf7ewES14NG2yhkfXLl22gO2pp+qWm6RS+mNCkIQA4UjdS07c0eTl2\n8hgl8aHhOUDG+EZeqVsa7aFKLwPYsqIMb/QptJ6eRX/X7QZrwTHW5oWG75eVbaRTLE3Wq1s6sVog\nNzF34cUGYHnSRo52L4324z012JNCw3MhBKkjG9l5fGmyHoFxCNao/i5wrRCiHrga+HcAIUS+EOI5\n/5pc4A0hxGHgbeBZKeVLQf5u0KhI3ER194FFf09KOBV3kK3LF3+y1QupQ5t5qXbxtDc0TSJzjrI+\nPzS0b129jCnrAJ2DswY05sWelkPkyNUhSUMA2FKyCY9cPM8BGoYPsDprg84UBY6yuI0c6lw87VNT\nMJBwkG2VoYlsWCyCpNObePHY4mmvaxzFl17Pmtw1BlC2MK5e62A8xkP/6MCiv/tW6wHy2RCSNASA\niwo3oU3tX9J3W0YPsi43dLJeGrOJ/Z7Fy8v4OIykHmTbitDoxugoCwkDG/lT9eKNpGMNp/ElayFJ\nuQG4evVqRuIaGZlcfG7yXvcBCq0bQ1LjA7AxfxPO8aXpddfEAdbnh07Wi6I28ba2NNojMA5BaW0p\nZZ+U8hop5Qop5XVSyn7/9Q4p5fv8r51SynX+dnqrpZT/rgfhwWJTwSZalnAznTwp8eXv48qKiw2g\nKjAUWTfztrb4h96rtTUkTZWSEptiAFULIznJQkzPpiUdCI5072NFYuh4fmXVKoZjWhiaWPx0wk7r\nXq5YFjra1+duomlk8Q9rp8sLBQe5zB66LpgFbOZN5+Jl/ZW6I6RNVRIfvfiaCT2QnRmFtXsduxoW\n7wWr7t3HytTQ8fxKxzoGYo4zPjW+6O+ejN7LthDqxjVZm6gfWrx+aWwZh5xjXFS4+HRAvZDr3cRr\nzUvQ6/UHyZpaR7R18TUTeqDEFovoqWJPy5FFf7fm1D5WZ4RQr1duoC/mCFO+xY9u7Y3byzUrQkf7\nqvRN1A1EPNXhhrBpc2c2tq5YS39UHWNTY4v63q5jjUT7UshNCk24CmBl+iaODyxe+e7R9lEaHdo2\n4VkTm9jdsPiHXvP4Xi4uCh3tK8pj4OQqDnoW9+CYmJCMpO/jxrWho/2Kig30WKsX/eB4+Vgt8ZMF\npg9lmImq1M3U9C1eXva27WVZXOgeeEJAxtgmXq5b/H3aOrWXS0tDR/vK5QlwqpyjXccW9b2hYS/j\nmQe4YXXoZP3Sso10ioP45OL6pL1cW03ieAWJMYkGUbYwKpI2Ud29eHk50LmX5Ymh47nFAmnDm9l5\nfPH3aZvcyxXLQkf7uso0GCzgxCInK/b0TTKVdYRrV24yiLKF8R5/9FQutY1ZBIbggjWqHRXxWE6t\n4Ejn4oykl+v3kucN3QMP/DeT79CijaS603tZlx1a2pfFb+ZA595Ff68vfh83rA4d7XFxkNC/mR3H\nF0f76zUtWGUcZVmhKyZZvTwFy2ARxxZpJL3eshcbWwyiKjBcVLiJ1qn9izaS6of3sjEvtAdIe8xm\n9rUvboCslJKB5L0hPYSlpkLMyc3sPLE4Wd9x5ATRk9nkpphfkDuNDSuyEWPp1Pcsrh/+6y17KbaG\nVl42F2ymZWLfoo2k5tF9XFQQWr1eZN3MW+7FyYvX52ModT/v3xA62rOzQXRs4tWGxdH+/KGjxI3Z\nSYlLNoiyhbF5hQ3vlAVXvytkNERwLi5Yo9pmA9myjRcbXlnU9/Z1vcbK5EsNoiowrKnIIGbYzsH2\nxYV+2qJ2ce2KywyiKjBclHs59SNvLOpAUOtx4bWMcllVaIoUp1Hs28rOllcX9Z1nju0mezS0PC8t\nBW/LNnY2L472Q32vsTrtEmOIChDrK/KxjGUu6kAgpaQzdjfXO0LL941ZW6kZ3LWoA8He5nqYimWd\nvchAyhaGbXIbLzUsTl5eqH2NvInQ6ka7HXzObbziXBztR069xvrM0NK+aVkpvsloGnobAv6OT/o4\nGf8aN64KrayvS9/Kkf5XF3UgeKXmGNaxLJblzTXewngIAXlj23jhxOLk5aX61yjwhlZeyssFwrV4\nWZ9c+qDXCALABWtUW62QO3I1L5x4OeDvSClp9O7gqtJrDKRsYZSXg2y+hp0tOwP+TsupFibkKNet\nC11lPsC6ihzix+3s9wQe5nz8wE5Se68hyhpacV2XeiXVp15n0hu4Vnq9bQcr4+bsSmkKYmIgo/9q\nnq9bnKw7xU6uLQst7RUVYG1dnKwf767DOx7LlWuXGUjZwthQXkjUZBbVndUBf+d3B3eS0X/tottl\n6o3VSVezv+dVvL7Ax0+/2bmD1YmhlZfkZEjsupo/LkLWvT4vmvUV3rsitHq9okIQ07Y4WT/QdgQ5\nlM2lqwsNpGxhbCorwzcZs6g0it9X7yB7MLTyArAy/mre6np5UQeCvd07WJ8SWtozMsCqXc0L9YHL\nOsD118Mri/MlRrAIXLBGNcCa1Cuo7t3H6ORoQOub+pqY8E5y1WqHwZTNj4ICoOUa/tQQuPJ9+uhO\norRryM4O7cO6shKi3Vcv6sGxs3kHy0RoH3gAa8qzSZ4qY397YAcCn/RRN/4yW4tCT/vKxCvZ2/k6\nE97A5k/XnKzBN57AZSsX3+9XT5SUwMSJa3ixMXB5efLwTmLbryE1NfSyHt++OCNpl7aT5VGhl5e1\nZQXEeXMCTo+b8k3RNPUqV9tDT3tl7FW80bYr4APBoY5DyKE8Ll0d2n6/5eUwUnMNLzUvTtaTTl5D\nnPlzyM5AVZUg6eTVvOwM3MB73bOTqtjQG9XrS8tgKo7j3YH1xB+fGsfle4Nry68ymLL5IQRURF3F\nLtcrizoQNDTAstD6G97VuLCN6hUp5PrWB/zQ+2PD88jG61m+PLQPayHAkXAFhzoP0j8W2Djhp2qf\no3DsekLUuejPWLECBg5dz3ONfwxo/YR3giODO9mSdZ3BlC0MhwOSu67nuYbnFl4MHGg/gGU8gy2O\nEoMpWxhrKzLJopLdrt0BrX+u4Xl8DddRFlqbGqsVyqOuZE/bnoA7rzxb/xylU9cbTNnCcDhg8Mj1\n/DFAWR+dHKV2eBeX5F1tMGULw+GA9N7AZf0t91tEDZew2ZFnMGULY92yApKljT3uPQGt/8NxpdeL\nQ9MW/M+IjYWiqavZ5dwVcAH9H5ueo0yGXtYrK2G0JnB5GRwfpHHsLS61LX6Ylt5wOCCrP3DaX2t9\njZiBKjY4MgymbGGsLy0jypfMgfbAikSHh9V04qLQZpe9q3FBG9UOB+R038rjtYFN+fvl4e2ktt1C\nkvnDws7BquVJVMZcw+/rfr/g2v6xfg727GZj0vtNoGx+JCdD9tCVNPU04zzlXHD9juYdJI052Lg8\n9FOjHA4YO3gLj9c+HpBn4PGax7GeuIUVK0wgbgE4HJDfd0vAsv7o4e1kdN5CQoLBhAWAVcvSKY+5\nlGfqFx5ZfnL4JLX9+9icdqMJlM2PzEyI91xHdedRPKcXHmDzfOPzpI1sYl1F6HJMp+FwwFT1rWyv\n3R6QrG+v2Y6suYXly00gbgFUVkLR6cD0upSS3xzdTtHpW7BaTSBuAay251Ics57nG59fcK3ntAfn\nUA0XZ4Xe21tQAN66m9jjfouekYUH2DxT/wzppy9n7Yo0E6ibHw4HUBu4HfBYzXamqsND1h0OsI8E\nTvuJEyoiYrmgLT9jcUGz1uGA8UMf4bmG5xZsXO885aTlVBOrk0LvRQL14LD1fZzHah5bcO1TdU9R\n7L2aleWh6U99NhwrotmS+hG212xfcO1jNY+R2HIrFRUmELYAysqgt3Y9FqwLpoB4fV621zzOxKGP\nURjadEdAybrv2C08deKpBfsPn+g5QedQFxsyrjCJuvlRWQklg4HJ+hPHn6Bk4gYc5WFwGgAcy2O5\nOO0D/Lb2twuu3V67nZiGj4WFrC9fDh37tzA6OcrRrqPzrp30TvK72iew1t1KTujPAzgcIGpv5Ynj\nTyxYEF3dVc3Q+FjIuyJNo7ISlo0GJuu/rf0txaMfwLE81gTK5ocQ4ChP5KKMG3ji+BMLrn+s5jGs\ndeEh6ytWgGfPFXQMdSzYNWZ8apyn6p4mxX0LqakmETgPKishpuFWflv724AKoo8fh5WhLat61+OC\nNqorK6H5aC6XFl/Go0cfnXftgwceZH3UbVRWhKbB/tlwOGCy9n1Ud1bPWy0upeT+/feT7vps2NxM\nDgeUD32Knx766bwPva6hLv7Y+Ef6Xv9YWHh7o6JgWZnghvzP8MD+B+Zd+2zDs2RE2VieXhUWXoHK\nSmg5XMyGvA0LejUe2P8Aa3yfYmVVGLju8BtJ9R9kj3vPvO2jpJQ8sP8Bkps+F1ayXjn2KX588Mfz\nPvTaTrfxcsvL9Lz2EeU5CzHi48FWILip8FM8eODBedc+WfcktrhKHHnLQp5eBornrYfLqcisWDCS\n98D+B1g19WlWhDilbxoOB0Q3foSXW16mfbB9znU+6ePBAw8SVxc+er2yElZPfZoHDzw4b3Sj5VQL\nb7e9Te+bHwwLb29qKqSnWvlA6ScXlPXHah6jPGETDlsYeEpQ8tJ2aBW5SbkBpa8cPw5VoRm8ecEg\nDB73oUNqKqSkwCeX3cEP3vrBnAZe/1g//3v4fyls+xKVlSYTOQccDmisi+cLm77A9/d8f851r7pe\nZXB8kO49N7JqlYkEzoPKShht3IItxcbvan8357r/2fc/3FjyUeK82WHhAQPF9zUTf8cz9c/Qdrpt\n1jVSSr735ve4Mu4rYSMvOTkgJXy+6g6+v+f7cxp4PSM9PHr0UbJa/jFslG9lJTTVJvP59Z/nB3t+\nMOe6F5peQAhBx56rw0rWvS1bSY5Nnjd95b/e/i/+ouSvyElJIyU8Ako4HLBZ/j2P1z5O11DXrGt8\n0sd9e+7jMkv4yHpREZw+DV9Yewf37blvTgOvY7CDJ44/QXrTF8Pi0A5KXpzH0/mrNX/Ff771n3Ou\n+8OJP5ASm4L2xmVhI+sOB0S1Xo9P+nix+cU51/3HW//B+4s+h92WFPICy2k4HHBp1D/yy+pf0jfa\nN+sar8/L9/d8ny2+8JH1ZcugvR1u33gH33vzewumakWMauNxQRvVoG6m1FNbsSXb5vQ+3rvrXm52\n3ExrdSmrV5tM4BwoKwOPB/567T/y9ImnZ63Sn/JN8U8v/hP/ctm38bRZKA9tm+c/w+FQuV33br2X\nu1+5m+GJ4XPWtPa38tCBh7gu/p6weWiAot3dkM4XNn2BO166Y9Y1v639LSOTI8S7Phw28iKEoj13\n6DqSYpL4+aGfz7runpfv4bY1t+E6VhA2HrDly6G5Gf5x85fZXrt91ir9Se8kd7x0B3df/B1O9QlK\nS82nczY4HHCiTnDv1nu5a8ddsxagNfY28osjv2Cr9athJ+sdTTl8dt1n+erOr8665lfVv8IqrFia\n3hc2sm6xqJC+feIvkFLyq6O/mnXd117+Gp/f8Hkaj2SzZo3JRM6Bad34lffcycNHHqaxt/GcNWNT\nY9y5407u2PAdpE+QF/raUEAdCOpPKFm/46U7Zu00dLz7OI/XPs7F3q+EjX4BxfeelkI+vurj3P3y\n3bOu+dmhn5ERn8HEiWvDRl6iopQtUCU+zMD4AL87PreTCqC2NpL+YTQiRrUDTpwQPHDTA/zra//K\n4Y7DZ3z+XMNz/O747/jOVf/GsWOEzc0UHa0GHfS1ZfHda77Lbb+/7YxOIFJKvrrjq+Ql5eHwfZSK\nCvWdcEBlJdTVwdVlV3NZ8WX8/fN/f8YJe2xqjI89+THuvOROuhtLws7QqKuDe664hwPtB3jkyCNn\nfN7c18yX/vQlHrjpAWqOWsNGXkDRXl8veOh9D3H3K3dTc7LmjM+fOP4ELzS9wL1bv0VdHWGRhgCQ\nkAB5eTDance3tn2LT/z+EwyOD/75cyklX37xy1RkVlA8+hdUVYVPIc60rN+0/CbW5q3lSy986QxZ\nH54Y5mNPfox/vuKfaa8vCEtZv3fbvexy7TqnBuJEzwnu3HEnD970IDXHLOEn6ycsPPS+h7hzx53n\n5Mr++uiveb31db665Z9pbAwf79109JTThdxz+T3c9tRtZ9T7SCn5h+f/gY0FG8k5fT2rVhEWKTfw\njqzf7LgZe7qdu3bcdcbng+ODfOyJj/HtK7+N+0ROWMr6d67+Dn9s/CNP1T11xufHuo7xjVe/wf03\n3k/NMRE2B0jwR/Iaovjx+37Ml/70JZr7mmddNzqqHHGRdnoGQ0oZVv8pkszDAw9I+dnPqtdP1D4h\ns7+XLX968KfyaOdR+d03viuzv5ct33K/JTVNytxcU0lbEB/5iJSPPiqlz+eT/+eF/yNX/milfL7h\neXnAc0B+6qlPyZU/Wil7hnvkI49I+fGPh5rad+DzSZmZKWV7u5RD40Nyy8+2yJsfv1m+7X5bvtzy\nsrz4pxfLTzz5Cen1eeWnPiXlT38aaorfwZEjUjoc6vXxk8dl3vfz5D0v3yOPdh6Vj1Y/Kgt+UCB/\ncuAnUkopi4qkbG4OIbFn4T/+Q8ovflG9/s3R38jc+3Llw4cfltWd1fI7r31H5tyXIw+2H5ROp5Q2\nW0hJPQfve5+UTz6pZP3vnv07ufbBtfLFphflvrZ98i+f/Eu57qF18tToKfnjH0v5mc+Emtp34PVK\nmZQkZW+vlANjA3LjjzfKW393q9zbtle+1PSS3PjjjfJzf/ic9Pl88tZbpfzVr0JN8Tt4+20p161T\nr6s7q2XOfTny3lfvlUc7j8pHjjwi876fJx858oj0+aTMypLS4wktvTPxb/8m5T/9k3r98OGHZf73\n8+Wvqn8lqzur5b2v3itz78uVRzuPyqNHpVyxIrS0no1rr5XyueeUrH/66U/LTT/ZJHc075B72/bK\nj/72o3LzTzbL02On5Q9/KOUXvhBqat/BxISUCQlSDg5KeWr0lFzz4Bp52+9vk/s9++ULjS/ItQ+u\nlV987ovS5/PJD35Qyt/9LtQUv4Ndu6R8z3vU6wOeAzL7e9ny27u/LY92HpU/P/RzmXNfjtx+bLv0\n+aRMSVH3c7jgX/5FyrvvVq8f2v+QtP3AJrcf2y4npibOWHf4sJQrV4aAwDCH3+bUz4bVczNdCDLZ\nqH77bSnXr3/n/d62vfL9j71fVt5fKT/x5CdkfU+9lFLKP/5RKbtwwr/9m5Rf+Yp67fP55KPVj8rL\n/vcyufqB1fKul+6S/aP9Ukop77xTym9/O4SEzoJrrlEPDimlHJ0clfe+eq9c++BaefFPL5YP7n9Q\nen1eKaWUGzdK+dZbIST0LEw/OIaG1Hv3gFt+5unPyMr7K+X1v7pevtzyspRSylOnlDHl9YaQ2LMw\n88EhpZRvam/Km359k3Tc75CffOqTsrlPnQD+8Acpr78+RETOgX/5FynvuUe99vl88uHDD8tLfn6J\nXP3Aavn1nV+Xp8dOSymlvP12KX/wgxASOgsuu0zKnTvV6+GJYfmNl78h1zy4Rm752Rb5s4M/kz6f\nT0qpHniHD4eQ0LMwMiJlfLyU4+PqveuUS37yqU/Kyvsr5Q2P3iBfc70mpZSyo0Mdkv1/RljgT3+S\n8sor33m/27VbvvfR90rH/Q756ac/LV2nXFJKKX/9a+WcCCfcdZeU//qv6rXP55M/PfhTueVnW+Sa\nB9fIf37ln+XQuFI+f/3XUv7oRyEkdBZs2iTlG2+o10PjQ/JrO74mVz+wWl7y80vkLw7wi6LKAAAg\nAElEQVT/4s+yXl4uZV1dCAk9C/39Sl9PTan3zX3N8rbf3yYr76+U7/vN++QebY+UUkqnU8qCgtDR\nORueflrKG2545/3O5p1y2y+2ybruMxn8yCNS3nqrycSdB4gY1Trj7AfHXPh//+8dz0e44OwHx1x4\n73vVjRdOmPngmAuTk8qAHRgwh6ZAsWmTlHv2zL/mtdekvPhic+gJFP39UiYmvvPgmAszPR/hgqef\nlvLGGxdet22blC++aDw9i8Htt0t5333zrxkbkzIuTsrRUXNoChSrVkl56ND8a156SfE9nNDVJWVq\n6sKG/le/KuW3vmUOTYFi+3YpP/ShhdddfLGUu3cbT89i8Dd/I+X//M/8a4aG1DN3ctIcmgJFebmU\nx4/Pv+aZZ9TzNJygaVLm5S287vbbpfze94yn53yD3kZ1mGQehg7x8SrRv7Z2/nXV1eGTTz2N9evh\n8GHV1WEuSAn798OmTebRFQg2bIBDh+Zfc/w4FBYSNt0QprFhAxw8OP+acJSX1FSVm9wwdwdGQP1t\nGzeaQ1OgWL9+YXnx+dSaDRvMoSlQBEL70aOqIDNcuiFMI5D79MiR8JP1nBxISgLnAvOlqqsJq/xY\nCIznk5Nw7JiSrXBCILJ+6JDieVSUOTQFikD4Ho56vbBQyUNHx/zrwlGvvxtxwRvVENjNtG8fbN5s\nDj2BIicHEhPB5Zp7TWsrxMSALfQDCc/A9IFgPuzfH348h8DkZe9euOgic+hZDAKhPRyVb1HRwg+O\nhgY1xTAryzy6AsGGDeevrAdiJO3bd37K+rTDIdxoX7ZMjZLum72zGwA1NVBSoibUhhPOZ1kPVK+H\nG+1CLEy716sOBOHmcHg3ImJUs7BAdndDTw9h05tyJhZ66IWrAisvh97e+R8c4Up7oMr34vAY0nYG\nFqK9o0MZr8XF5tEUCAJ5cITjwRf8w0haYWho7jXhSvv5foCcz8BrblaRyoIC82gKBBYLrFs3P+0H\nDoSnvKxerVoCjs8ztPV81etSnr96vb4ecnMhLfRT4d/1iBjVqNSIvXvn/nz6gRcubbpmYvNmePvt\nuT8PVwVmsShv6Hx8D0cvEqgHR2MjDJ/bXhtQB4XOzvBp0zUTgcj6xo3h06ZrJhaiPVxlPToa1q5V\nhtBcCFfa169XaQZzGUkdHeo+CJce+DOxkLyEq4EE569ej49XzqeFDr/hqNenDdOpOYb8ulzqXi4M\nj2GKZyAQ3RhuKaDvVoShmWg+Nm9WJ7nTp2f/fO9e2LLFXJoCxRVXwGuvzf35nj3nJ+1DQ+rfZN06\nc2kKBHFxytjYs2f2z6cNU2t4TPk+A+95j8qBHRmZ/fPdu9W/SzjiiisUfXMh3GV9Ltr7+kDTCKu+\nvdNITlZG0v79s38+7aUOx0PYZZcp+ibOnUECKKM1nOXl3ajXu7qUvIfLBMuZyMxUaWZzRQimD2Hh\nKOtXXAFvvKHSPGbD7t1w+eXm0nShImJUA7GxyrB+443ZP9+1SynocMTFF6siy8HBcz8bGlIG1CWX\nmE9XINi6dW7l+/rr6mQdH28uTYFi27a5jaRdu8JXgSUmKk/7XF6w3bvVv0s44tJLVb732LlDCenr\nU9GDcPSAgeLpXPKye7f622JizKUpUGzbpmR6NoSzrKelKQ/6XBGC3bvDV69ffjm89ZZKxTobnZ1q\niEe4FSlOYz5Zf+UV9Xk4Rn1hftrD2Q7IyVFpTNXVs38eznr93YYwFW3zMdfNNDioTq7h6r2Lj1dh\nq9m8ptOGaUKC+XQFgi1blBKYzWv6yitw1VXm0xQotm6d29DYsQOuvdZUchaFuWR9YEBFB8IxrAzK\na1pVNXuYc/dudXgMV8P00ktVBGO2NIrzQdbnMjTCXdbnOvx2dIDbHb4h8YwMKC2dPY3i1VfVv0k4\nRsJAHQjefHP2NIpwl/X5DpDhLutz3adtbUq3h2M64rsREaPaj2uugT/96dzru3crIyNcDVNQN/oL\nL5x7fceO8FZgCQmKtzt3nvtZuNN+ySWqDdqpU2de7+mBpqbwDc2CkvXnnz/3+ksvKU9MbKz5NAWK\nuWR9587wlpfUVNWKa7YH9s6dcPXVppMUMK64Qh1kzi609HiU1zScOwrMpden5SXc2rrNxPmq17Oz\nVZvaN98887qU4X+fbtumnFGjo2deb2lRzp9wTNGaxlzy8sIL6j4I1+jAuw1BsVkI8REhRI0QwiuE\nmFO1CiHeK4Q4IYRoEEJ8NZjfNApbtqh8r6amM6///vfwvveFhqZA8eEPw5NPqj6905BSXfvgB0NH\nVyCYpn0mmpqUJymcDdPERPVwePbZM68//TRcd50qaAlXbN2q+ve2tp55/amn4EMfCg1NgeLDH4Yn\nnjizN7vXq2gPd1m/+eZzZb22VhX6hWsoH9SB4NJLzz2IPfUU3HBD+HpMQR1WqquVbp+Jp56Cm24K\nDU2BYjbdODkJzzwDH/hAaGgKFLPRfuiQkpWVK0NDUyDIzlb34ksvnXn9979X8hKO+dTTeO97VTSs\nt/fM6+eDXn83IdizyzHgQ8Cc5UNCCAtwP3A9sBL4uBAi7JrTWa3qoff44+9cGxtTRtKtt4aOrrmw\na4bLq6pKhcZn5sm+/bZKDQm3wQZn40MfUobpzDzZxx9XSlkPL9KuuWJ5OuAjHzlTXgAeeww+/nHD\nflIXREcrA/SJJ965NjgIzz67K+wf1uvXq8PjkSPvXHv9dZVTuHy5OTQsVaY+/GGlT2YWzm3fDh/9\naPh7kT784dll/S//cv7vGXn/BYK4OLjxxjNlvb8fXn5Z6ftwwWx82rJF1QrU1b1zbedOlSdeUmIe\nbUvBzTcrQ3Rm4dzjj8MttwRnmJohT7Pp9d/8Jvz1ekKC8lY//bR6v2vXLrq7VWroDTeElrYLCUGp\ncillvZSyEZjvNrkIaJRStkopJ4HtQFg+uv/mb+DBB9956P3616oQMNwGp8C5yuXzn4cf/vCd9//9\n3+paOJ+sQfH2kkvgkUfU+4kJ9W/w+c/rs7+RSvjmm1VXhPp69b62Vv13442G/aRu+Nzn4P7738l7\n/OUvoahoF3l5oaVrIQhxrqz/8If6yUsgWKpM2e0qBeSxx9T7sTH42c/gs5/VjzajcMstKhVuetDU\noUMq0rFQjmmojWqAv/1bpQ+nI3k//7kyMsKpZ+9sfLJYlGzMptfDHVVVKid82ls9NAQPPwyf+Uxw\n+5ohT3/5lyplyONR7/fsUWl+27YZ/tNB43OfU/IipeLVT36iDsThNpX43Qwz/CM2wD3jfZv/Wthh\n3Tr10Pv+95WH4JvfhHvuCTVVgeGv/1rla775plICr76qDgnnA77+dfj2t1XY6j/+Q3nXwzlPcxoJ\nCXD77XDnnSos+5WvwD/9U/iNmp4N73mPMvL++7/VcKPvfEeF+M8HfPGLKhVh/34l83v3Bv+wNgt3\n3w333qu8pf/+7+rQHs7h8GmkpMDf/d07sn7HHXDXXeGd5jSNK65Q7dIeekilld13n9I55wNuv115\n2aurVUpCbS3cdluoqQoMd98N3/iGioJ95zsqr7eiItRULYyMDHWY+epXlZPnzjuVvIRzmtM0rr9e\n3ZMPP6yKE//rv9S9GoF5WDDALoTYAeTOvARI4B4p5bOzf+v8xUMPKSV8333whS+Ebwuds5GcrG6k\nv/gL5ZF59NHz53R66aXKKCovV3/HfP1Zww133aVy2XJz1UHgy18ONUWB42c/U/nV3/qWOgzMzMkP\nZ6SlwU9+oh4gUqpQbWJiqKkKDFddpdI97HZITz+/ZP0b31CGUW6uOpT9/d+HmqLAIITSjVddpQy9\nu+9Ww3jOB2Rnw49+pLykQqiUivPh0A4qYvenP6lUlcxMlaZ1vuCb34Qrr4S8PMX78yE6AEpGHnlE\n3af9/fDd76qJrhGYByFnVvwsdRMhXgW+IqU8pwGQEGILcK+U8r3+918DpJTyu3PsFTxBEUQQQQQR\nRBBBBBFEsACklLolyurZUGguovYD5UKIEqAD+BgwZ8q/nn9cBBFEEEEEEUQQQQQRmIFgW+p9UAjh\nBrYAzwkhXvBfzxdCPAcgpfQC/wC8BNQC26WUdXPtGUEEEUQQQQQRRBBBBOcbdEn/iCCCCCKIIIII\nIoggggsZYdMd9XwYEGMkhBA/F0J0CSGOzriWLoR4SQhRL4R4UQiROuOzrwshGoUQdUKI62Zc3yCE\nOOrn43+Z/XcYDSFEoRDiFSFErRDimBDidv/1CK/OghAiVgixVwhx2M+r/+u/HuHVLBBCWIQQh4QQ\nz/jfR/g0C4QQLiFEtV+u9vmvRXh1FoQQqUKI3/n/7lohxMURPp0JIcRyvxwd8v9/QAhxe4RPs0MI\n8WWhBu4dFUL8WggRE+HVuRBCfMn/zDPfRpBShvw/lHHfBJQA0cARoDLUdJnMg8uAdcDRGde+C9zl\nf/1V4N/9r6uAw6ic+FI/76ajDnuBzf7XzwPXh/pv05lPecA6/+skoB6ojPBqTn4l+P9vBd5G9Y2P\n8Gp2Xn0ZeBR4xv8+wqfZ+dQCpJ91LcKrc/n0C+Az/tdRQGqET/PyywK0A0URPs3KnwL/vRfjf/84\n8KkIr87h00rgKBCLeu69BCwzi0/h4qk+bwbEGAUp5RvAqbMufwDwj0XhEWB6EPP7UbnpU1JKF9AI\nXCSEyAOSpZT7/et+OeM77wpIKTullEf8r4eAOqCQCK9mhZRyxP8yFqU0JBFenQMhRCFwI/CzGZcj\nfJodgnOjnBFezYAQIgW4XEr5MID/7x8gwqf5cA3QLKV0E+HTXLACiUKIKCAe8BDh1dlwAHullONS\n1fS9BtyM4ofhfAoXo/q8GRBjMnKklF2gjEkgx3/9bH55/NdsKN5N413NRyFEKcq7/zaQG+HVufCn\nNBwGOoEdfgUR4dW5+E/gTtShYxoRPs0OCewQQuwXQkx38I3w6kzYgR4hxMP+1IafCCESiPBpPtwK\n/Mb/OsKnsyClbAd+AGiov3tASrmTCK/ORg1wuT/dIwHlLCnCJD6Fi1EdQWCIVJX6IYRIAp4AvuT3\nWJ/NmwivACmlT0q5HuXNv0gIsZIIr86AEOImoMsfAZmvpecFzacZuFRKuQH1sPp7IcTlRGTqbEQB\nG4Af+Xk1DHyNCJ9mhRAiGuUx/J3/UoRPZ0EIkYbySpegUkEShRCfIMKrMyClPIFK9diBStk4DHhn\nW2rE74eLUe0Bime8L/Rfu9DRJYTIBfCHIk76r3tQJ69pTPNrruvvKvhDX08Av5JS/sF/OcKreSCl\nPA3sAt5LhFdn41Lg/UKIFuAx4CohxK+AzgifzoWUssP//27gaVT6XkSmzkQb4JZSHvC/fxJlZEf4\nNDtuAA5KKXv87yN8OhfXAC1Syj5/WsNTwCVEeHUOpJQPSyk3SSm3Af2o2itT+BQuRvWfB8QIIWJQ\nA2KeCTFNoYDgTE/ZM8Cn/a8/BfxhxvWP+St/7UA5sM8f0hgQQlwkhBDAJ2d8592E/wWOSyl/OONa\nhFdnQQiRNV3hLISIB65F5aBHeDUDUsq7pZTFUsoylO55RUr5V8CzRPh0BoQQCf4oEUKIROA64BgR\nmToD/jCzWwix3H/patSchgifZsfHUQfaaUT4dC40YIsQIs7/N14NHCfCq3MghMj2/78Y+BAqrcgc\nPhlRfbmU/1AetHpUkvjXQk1PCP7+36Aqn8dRN89ngHRgp58vLwFpM9Z/HVWlWgdcN+P6RtRDrhH4\nYaj/LgP4dCkqlHMEFdY55JedjAivzuHVaj9/jqCqoe/xX4/wam6ebeWd7h8RPp3LH/uMe+/YtK6O\n8GpWXq1FOYyOAL9Hdf+I8OlcPiUA3aiisOlrET7Nzqv/6/+7j6KK7aIjvJqVT6+hcqsPA9v+P3v3\nHVdl9Qdw/HMAFXErmjhQceTKvRe4Z6m599bMUstylOX4ZaVZpmW5cs8sNQe4BUfumVsxUHGhooKy\nOb8/DuLCREHuBb7vXvfF5Xkenud7T8j93vOc8z2J+Tsli78IIYQQQggRT9Yy/EMIIYQQQogkS5Jq\nIYQQQggh4kmSaiGEEEIIIeJJkmohhBBCCCHiSZJqIYQQQggh4kmSaiGEEEIIIeJJkmohhBBCCCHi\nSZJqIYQQQggh4kmSaiGEEEIIIeIpQZJqpdRvSqnrSqlj/3HMFKXUOaXUEaVUmYS4rhBCCCGEENYg\noXqq5wANn7dTKdUYKKi1Lgz0A6Yl0HWFEEIIIYSwuARJqrXWO4GA/zikOTA/+ti9QCal1BsJcW0h\nhBBCCCEsLbHGVOcGLj32vV/0NiGEEEIIIZI8O0sH8DSllLZ0DEIIIYQQIvnTWquEOldiJdV+QN7H\nvs8TvS1WWkte/SKjR49m9OjRlg7DKkVFwYkTsGMHTJs2mqio0Xh7Q+HCULo0FCsGBQs+emTJkjDX\n1Rpu34Z//zWPCxfg+HE4dgzOnoX8+aFcOaheHWrUgBIlwNY2Ya6dEOR3Km6kneJO2ipupJ3iRtop\n7hKqrfz9Yfdu+Ptv8/XQIciYEUqWhLfeguLFwcUFnJ0hTx5InTr+sQNERMDFi3DuHJw/b76eOgWH\nD4NS5r20XDmoWtW8n2bO/GrXUSrB8mkgYZNqFf2IzWpgALBMKVUFuKO1vp6A1xYpmNZw5gx4eMDW\nrbBrF2TNCjVrmkR29GjzD9/e/vXGoRRky2YeFSo8uS8sDE6fhgMHYOdOmDwZrl83fxAaNIBGjaBo\nUXMOIYQQwhLu3QNPT9iwATZtghs3oHJl8171+efmvS1r1tcfh52dSdZdXKDhY2UwtAY/P5PcHzwI\nkyZBhw5QpAi4ukKdOubh4PD6Y4w17oQ4iVJqMeAGZFNKXQRGAakBrbWeobV2V0o1UUqdB+4DPRLi\nuiLlCg01CfS6deDuDuHh0KQJdOkCM2aAk5M5bvRo82nW0lKnhlKlzKNnT7Ptxg3Tm75xo/nDYGNj\nkutmzaB+fUiTxrIxCyGESP68veHPP2HtWtMTXKWKSWSXLze90TZWtKKJUqZHPE8eeOcdsy0sDPbv\nBy8v+P576NjRdKo1awZNm5pe9MSSIEm11rpjHI75ICGuJQw3NzdLh5DowsNhyxZYtgz++ssM43j7\nbVi1yvzDj62X15rbKUcOaNXKPLQ2t7Y8PGD8eOja1fxBaNs28RJsa24rayLtFHfSVnEj7RQ30k5x\n96K2On3aJM1//glXr0LLlvDZZ1CrluV6eV9V6tRmWGX16uY13LljOqvWroUvvjDDPNu3h3btIFeu\n1xuLsrbxy0opbW0xCcvR2tzi+e038wegcGHzD6N1a/NJNbm6csX8sVu+3IzLbtvW9HBXrChDRIQQ\nQry827dh6VKYNw8uXYI2bUynTvXq1jW/JyFFRJi72kuWmM640qWhUyfznpoxoxlTnZATFSWpFlbp\n1i1YtMgk0/fumYSySxczRjqluXQJ5s+HOXNMj3XPnqYnO3t2S0cmhBBJW/78+fH19bV0GOI1y5cv\nH6dP+7B+vXk/3bbN9M7PmSNJtUjGjh0zk/j+/NOMke7VC2rXTvwxXZFRkQRHBBMcHsyD8Ac8CH8Q\n8/3jHs4ctlE2OKRywCGVA+lSpTNfU6fDzibh5gJrbcZgz55tPnG3aAEffmgdY8aFECIpiu6ptHQY\n4jV7+v/zjRtmDHbbtpJUi2QmKspMOPzxRzPO6/33oW/f19MTeyfkDr53fLl49yK+d325dPcS/g/8\nufng5hOPu6F3sbezxyGVA2nt0sYkzPZ29jGJ9OO/p5E6kuDwYO6H3+dB+APuh93nfvh9UtmkwtHB\nEUcHR7Kny052h+w4OjjyRro3yJc5H/ky5SN/5vzkypALW5u433+7dQtmzYKpUyFvXhg0yNzGS663\n8IQQ4nWQpDpleN7/Zxn+IZKNsDBzG2b8eFNjcvBgM8YrvnUug8ODOXvrLKdunuKU/ylO3zrN6Zun\n8bnjQ5SOIl+mfOTLnA/njM44Z3ImR7ocMYnvw0dm+8wvleTGRmtNSEQINx/cjEnc/e/74//An2tB\n17h49yI+d3zwvevLzQc3yZ0hNwWyFKC4Y3GKZ3/0yJ7u+Z8uIiJg9Woz4/nGDRg2zAyTkcohQgjx\nYpJUpwySVItkKyTEDGEYP97UZh450hRvf5UJeA/CH3Dk2hEOXjnIgasHOHjlIN4B3rhkcaGYYzHz\nyF6Moo5FKZC5AJntMyd4sfeEEBoRyqV7l/C+7c2pm6c46X+Sk/4nOeF/AjsbO8o7ladCrgpUyFWB\nirkqkitDrmdex/bt8PXXZmLjJ59Anz6QLp2FXpAQQiQBklSnDJJUi2QnOBhmzoQJE6BsWZNMV678\ncue49eAWOy7uYLvvdrb7buek/0mKZy9OhVwVKO9UnvK5ylMyR0lS2ybQsk4WprXmSuAVDl49yIEr\nBzhw5QD7r+zHzsaOGs41cM3nims+V0rkKIGNMgPPDx6Eb74x468//RQGDIC0aS38QoQQwgpJUp0y\nSFItko3ISFPCZ9QoKF8evvwy7pPrQiJC2O67Hfdz7mz5dwu+d3yplrcatfLVwjWfKxVyVSCNXcoa\n66C1xveuLzt8d+Dl64Wnjyd3Qu5QK18t6rvUp2mRpjhncubECfPB5cAB0+Y9ephVqoQQQhjJMan2\n8vKic+fOXLp0ydKhWA1JqkWSpzWsWQMjRoCjoxnuUaXKi3/u8r3LrD27Fvdz7nj6eFLqjVI0KdyE\n+i71KetUNkEraiQXfvf88PTxZIP3BjzOe5AzfU6aFm5K08JNsblSlS9H2nHpEvzvf2bcujWtkCWE\nEJaSXJPqLl26cPHiRUuHYjUkqRZJ2p49ZujBnTvw7bemPN5/DWW+EniF5SeWs+zEMs7cOkOTwk1o\nUqgJDQs1JGvarIkXeDIQGRXJPr99rDu3jnXn1uF3z4/WxVtTKKQ9i7+tga2NDZMnx+0DjhBCJGcp\nPamOjIzENgWUjUqspFr6q0SCunoVunUz5d169oQjR6Bp09gT6oDgAH7d/yuuc10p+UtJDl87zBe1\nvuDqkKssaLmADm91kIT6Fdja2FI1b1W+qvMVh/sdZk/vPeTNmJd5/h9ytUNeMrf/iHf676NTZ83l\ny5aOVgghxNMmTJhAmzZtntg2aNAgBg8eDMDcuXMpXrw4GTNmpFChQsyYMSPO57axseGXX36hSJEi\nFClSBIDBgwfj7OxMpkyZqFixIjt37gQgNDQUBwcHbt++DcC4ceNIlSoVQUFBAHz55Zd8/PHH8X69\nyYUk1SJBhIXBxInw1lvg5GTqTffo8Wzd5CgdxdZ/t9JpRScKTC6Al68XQ6oO4eqQq8xtMZfGhRsn\nm0mG1sIliwsjao7g6HtH2dRlE1XKZCR9tw5sLlSaN7tOYcTY2wQHv/g8QgghEkf79u3x8PDg/v37\nAERFRbF8+XI6deoEwBtvvIG7uzv37t1jzpw5fPTRRxw5ciTO5//rr7/Yv38/J0+eBKBSpUocO3aM\ngIAAOnbsSJs2bQgLCyNNmjRUqlQJLy8vALZv307+/PnZtWsXYHrFXV1dE/KlJ2ky/EPE28aNMHAg\nuLiYBVyiP/g+ISA4gJmHZjL94HTSpUpH73K96fRWJ7I5ZEv8gAVROgpPH09+3D6L9d7upPFtyphm\nA/iodVWrLDkohBCvw4uGfyTUn8NXSWtq1apF37596dy5M5s2beL999/n3LlzsR7bsmVL6tSpw4cf\nfvjC4R82NjZs27btP5PhrFmz4uXlxVtvvcWXX37JvXv3+P7778mTJw+fffYZV69eZdSoUWTJkgU/\nPz+yZMny8i8wEcnwD2H1btyATp3gvfdML7W7+7MJ9embp3l/3fu4THHh+I3jLGm1hKPvHWVg5YGS\nUFuQjbKhToE6rO62mKvDvelUuyLD9nbBcUQVft2xlPDIcEuHKIQQFqd1wjxeRYcOHViyZAkAS5Ys\noWPHjjH7PDw8qFq1KtmyZSNLlix4eHhw8+bNOJ87T548T3w/ceJEihcvTpYsWciSJQv37t2LOZ+r\nqyvbtm3j0KFDlCpVivr16+Pp6cmePXsoXLiw1SfUiUmSavHStIa5c81Qj9y54Z9/oFmzJ4/ZdXEX\nTRY1wXWuK9kdsnPy/ZPMbzmfSrkrSU+olcnmkI1p3QcTMOYsdew+Y+CCaeT42oXxO78jKCzI0uEJ\nIUSK1KZNGzw9PfHz82PlypUxSXVYWBitW7dm6NCh+Pv7ExAQQOPGjV9qwuXj78M7d+7ku+++448/\n/iAgIICAgAAyZswYc75q1apx5swZVq5ciaurK0WLFuXixYu4u7vL0I+nSFItXsr581CvHvz0E6xf\nbxZyebhqn9aarf9upfa82nRZ2YUWRVvgO9iXMbXH4JTBybKBixdKn86W5V815+hgTwrsXs2EBQfJ\n94MLX+/4mnuh9ywdnhBCpCiOjo64urrSo0cPXFxcePPNNwGTVIeFheHo6IiNjQ0eHh5s3Ljxla8T\nGBhIqlSpyJYtG2FhYYwdO5bAwMCY/WnTpqV8+fJMnTo1JomuVq0a06ZNk6T6KZJUiziJiHhUZ7pp\nU9i716yK+NDWf7dSY04N+q/rT48yPTjzwRn6lu+LvZ295YIWr6R4cTiwtizjyi4larYXf3iewmWy\nC2M8x3A35K6lwxNCiBSjY8eObNmyJWaCIkD69OmZMmUKbdq0IWvWrCxdupTmzZvH+ZxP3y1u2LAh\nDRs2pEiRIhQoUAAHBwfy5s37xDGurq5ERkZSqVKlmO+DgoKoVatWPF5d8iMTFcULnT1ryuQ5OMCs\nWVCgwKN9R68dZdjmYZy/fZ7/1f4fbUu0xdYm+de8TCl8fKBXL7gZdY783f7Hnpsb+Lzm57xX4T2p\n0iKESPKSY51q8SyZqCgsLirKDPOoVs1MSNy06VFC7XPHhy4ru9BoUSPeLvI2JwecpMNbHSShTmby\n54fNm6F/u8Ls+mQ+HcI34X7Wg2JTi7Hs+DJ5MxJCCCGiSU+1iJWvr1m85cEDmJ5u1N4AACAASURB\nVDfvUVWPB+EPGL9zPFP3T+WDSh8wpOoQMqTJYNlgRaJ42Gv94AG8/90Wfjw5lFQ2qZjaZCrlc5W3\ndHhCCPHSpKc6ZZCeamERWpskukIFqF8fdu40CbXWmlWnV1HilxKcvnWaw/0OM9pttCTUKUj+/OZu\nRfv28HHLugxItZ++5fvRdHFT+q/tz+3g25YOUQghhLAY6akWMe7ehf794dgxWLwYSpUy271vezPA\nfQCX7l3ip8Y/UadAHcsGKizun3+gY0coVgy+/TGA7w+P5I9TfzCuzjh6lu2JjZLP60II6yc91SmD\n9FSLRPWwmkfmzLB/v0moI6Mi+WH3D1SeVZm6BepypN8RSagFYGqU798PuXKBW5UstHaYikcnD2Ye\nmkmdeXU4f/u8pUMUQgghEpX0VKdwUVGm1vSkSTBtGrRsabafuHGCXqt7YW9nz6x3ZlEoayHLBiqs\n1vr1Zvx9164wekwkvxyazNc7vubzmp8zsPJAmbwqhLBa0lOdMiRWT3WCJNVKqUbAj5ie79+01uOf\n2u8K/AVciN60Qmv91XPOJUl1Irl6Fbp0gbAwWLgQnJ0hIiqC8TvH8+PeH/mq9lf0Kd9HbuWLF/L3\nN0l1YCAsXQohDufpvbo3oZGhzGk+h6KORS0dohBCPEOS6pQhyQz/UErZAD8DDYESQAelVGzvoNu1\n1uWiH7Em1CLxrF8P5cpBzZqwdatJqH3u+OA2142tPls51PcQ/Sr0k4RaxEn27LBunVkYqEIFOL+v\nEFu7baVLqS7UnFOTX/f/Km9cQgghkrWEyJgqAee01r5a63BgKRDb0j4J9klAvLrISBg1ypRGW7bM\nPLezg0XHFlFpZiVaFm3Jpi6byJsp74tPJsRjbGxgxAj4/Xfo0wdGfm5D37Lvs7PHTmYdnkWLZS24\n+eCmpcMUQohkzcvL65kVERNT7dq1mT17NgCLFy+mUaNGr/2avr6+2NjYEBUV9dqv9V8SIqnODVx6\n7PvL0dueVlUpdUQptU4pVTwBrite0s2b0KQJeHnBwYNQqxbcC71HpxWdGLdjHBu7bGRItSHSOy3i\npVYt8/t18CDUqQPpQ99kd6/dFM1WlDLTyrDJe5OlQxRCiGTt6aXILaVjx46sX7/+hceNGTOGrl27\nxuta1vCa7RLpOgcBZ631A6VUY2AVUOR5B48ePTrmuZubG25ubq87vmRv715o2xY6dICvvjK908eu\nH6P1762pU6AOB/oewCGVg6XDFMlEjhzg4QHffGOGgyxYkJrx9cfTsFBDuq7sSvcy3RnjNkYmMQoh\nhBWLjIzE1jb5/J329PTE09Pz9V1Aax2vB1AFWP/Y98OBYS/4mX+BrM/Zp0XCiYrS+ueftc6eXetV\nqx5tn3N4jnac4KgXHl1oueBEirBtm9ZOTlpPmGB+H68HXdd15tXRdefV1TeCblg6PCFECmatOcf4\n8eN169atn9g2cOBAPWjQIK211nPmzNHFihXTGTJk0AULFtTTp0+POc7T01PnzZv3uedWSukpU6Zo\nFxcXnT17dv3pp5/G7Js7d66uXr26/uijj3S2bNn0F198obXW+rffftPFihXTWbNm1Y0aNdK+vr4x\nP7Nx40ZdtGhRnTlzZv3BBx9oV1dX/dtvv8Wcr0aNGjHHHj9+XNevX19nzZpV58yZU3/zzTd6/fr1\nOnXq1Dp16tQ6ffr0ukyZMlprre/evat79eqlnZycdJ48efTIkSN1VFSU1lrryMhIPWTIEO3o6KgL\nFiyop06dqm1sbHRkZGSsr/l5/5+jt8c7F374SIik2hY4D+QDUgNHgGJPHfPGY88rAT7/cb5YX7h4\neYGBWnfooHXp0lqfP2+2PQh7oHv/1VsX/bmoPnHjhGUDFCnGxYtaV6yodZs25vcyIjJCf7b5M533\nh7x618Vdlg5PCJFCWWvO4evrq9OlS6eDgoK01iaJdHJy0vv27dNaa+3u7q7//fdfrbXW27dv1w4O\nDvrw4cNa67gl1XXq1NF37tzRly5d0kWKFHkiCbazs9NTp07VkZGROiQkRK9atUoXLlxYnzlzRkdG\nRupx48bpatWqaa219vf31xkyZNArVqzQERERetKkSdrOzu6J89WsWVNrrXVgYKB2cnLSkyZN0qGh\noTooKCjm9YwePVp36dLliThbtGih+/fvr4ODg7W/v7+uXLmynjFjhtZa619//VUXK1ZM+/n56YCA\nAF27dm2rSKrjPfxDax2plPoA2MijknqnlFL9ooOdAbRWSvUHwoFgoF18ryv+2/nz0KIFVK4Mu3dD\n2rRw6e4lWixrQeGshdnXe58sMS4STd68sH07fPABVKkCK1faMq7uOKrmrUrLZS35otYXDKg4wCrG\nxAkhxENqTML8TdKjXq76kbOzM+XKlWPlypV07tyZLVu2kC5dOipWrAhA48aNY46tWbMmDRo0YMeO\nHZQpUyZO5x8+fDiZMmUiU6ZMDB48mCVLltCzZ08AcufOzfvvvw9AmjRpmD59OiNGjKBIkSIxPztu\n3DguXbqEp6cnJUuWpGX0IheDBw/m+++/j/Waa9euxcnJicGDBwOQOnXqmNfztBs3buDh4cHdu3dJ\nkyYN9vb2DB48mJkzZ9KnTx+WL1/O4MGDyZUrFwAjRozAy8srTq/9dUqQMdVa6/XAm09tm/7Y86nA\n1IS4lnixjRtN/ekxY+C998y2PZf30Or3VgyqPIhPq30qyYtIdPb2MHMmzJgB1avD7NnQrFkzdvfa\nzTtL3uH4jeP81PgnUtmmsnSoQggBvHwynJA6dOjAkiVL6Ny5M0uWLKFjx44x+zw8PBg7dixnz54l\nKiqK4OBgSpUqFedz58mTJ+Z5vnz5uHLlSsz3T1cO8fX1ZdCgQQwZMgQwIxyUUvj5+XHlypVnjn9e\n5ZFLly5RsGDBOMXn6+tLeHg4Tk5OMdfUWuPs7AzwzHXz5csXp/O+blLmIRnRGr7/Hrp3hz/+eJRQ\nzz86n3eWvMP0ZtMZWn2oJNTCYpSCfv3gr7/M7+fo0ZA/kwt/9/obv0A/GixswK0HtywdphBCWFyb\nNm3w9PTEz8+PlStXxiTVYWFhtG7dmqFDh+Lv709AQACNGzd+qbUALl16VLTt4sWLMT2+8GwVDWdn\nZ6ZPn87t27e5ffs2AQEBBAUFUaVKFZycnLh48eJzz/24vHnz4u3tHeu+p6+ZN29e7O3tuXXrVsw1\n79y5w7FjxwBwcnJ64jq+vr5xeNWvnyTVyURwsFnRbtEi2LPHLOoSGRXJpxs/ZazXWLZ120azIs0s\nHaYQAFStCgcOwJYtZpgSoRlZ1W4VlXNXpvKsypz0P2npEIUQwqIcHR1xdXWlR48euLi48OabZkBA\nWFgYYWFhODo6YmNjg4eHBxs3bnypc3/33XfcuXOHS5cuMXnyZNq3b//cY/v168fXX3/NyZPm7/Ld\nu3f5448/AGjatCknT55k1apVREZGMnnyZK5duxbreZo1a8a1a9eYMmUKYWFhBAUFsW/fPgDeeOMN\nfHx8Yj4Y5MyZkwYNGvDRRx8RGBiI1poLFy6wfft2ANq2bcuUKVPw8/MjICCA8ePHx3rNxCZJdTJw\n+bKpDRwRATt3mtURg8KCaL60OQevHmRv772UyFHC0mEK8YScOU1SnSsXVKsGvj62fFvvW0a5jsJt\nrhvu59wtHaIQQlhUx44d2bJlC506dYrZlj59eqZMmUKbNm3ImjUrS5cupXnz2Nbce77mzZtTvnx5\nypUrx9tvvx0znjo2LVq0YPjw4bRv357MmTNTqlSpmNrT2bJlY/ny5QwbNgxHR0e8vb2pUaNGrOdJ\nnz49mzZtYvXq1eTMmZMiRYrElLdr06YNWmuyZctGhQoVAJg3bx5hYWEUL16crFmz0qZNm5iEvU+f\nPjRs2JDSpUtToUIFWrVq9VKv/3VRL3O7IDEopbS1xWTN/v4b2rSBgQNh6FBze/1a0DWaLm5KmTfK\nMK3ZNBmjKqya1jB1qqmfvmwZuLrC7ku7eff3dxnjNoa+5ftaOkQhRDKllHqpYRPJgY2NDefPn8fF\nxcXSoSSa5/1/jt6eYGNipac6CZs1y9w6nzkThg0zCfWZm2eo9ls1mr/ZnFnvzJKEWlg9pUxVkAUL\nzAJFM2dC1bxV2dFjBxN2TeCLrV+kuDc9IYQQSY/0VCdBUVEmif7rL1izBqKHWbHr4i5a/d6Kb+p+\nQ4+yPSwbpBCv4OxZePttaNwYJk6E26E3aLa4GcWzF2fm2zPlQ6IQIkGlxJ5qW1tbzp07Jz3VJHxP\ntSTVSczDCYnXrsGqVZAtm9n+58k/eW/deyxsuZCGhRpaNkgh4iEgAB7OmVm2DFI53KfdH+0Ijwrn\njzZ/SH11IUSCWLoUOnRIeUl1SiTDP8Qzbt6EevXAzg42bXqUUM84OIOB6weyofMGSahFkpclC6xb\nB0WLmoVi/HzSsar9KvJlyofrXFdu3L9h6RCFEEmY1jBqFAwfbulIRHIjSXUSce6cKUPm6mrK5tnb\nm+3jd47n253f4tXdi3JO5SwbpBAJxM4OJk+Gjz825SF3brdjerPpNCvSjJpzanLx7sUXn0QIIZ4S\nHGzuhG3aBHv3WjoakdxIUp0E7NplEotPP4WvvwYbG7O60IjNI5h3dB47euygUNZClg5TiATXty8s\nWWImMM6frxhbeyz9yvej5pyanL111tLhCSGSkKtXTcdUqlSwdSu88YalIxLJTYIsUy5en+XLYcAA\nmD8fGjUy2yKjIvnA/QMOXD3A9h7bcXRwtGyQQrxGdeqApyc0awbe3jBmzMdkSpPJ1LLu5E6ZnGUs\nHaIQwsodOQLvvGNWdP3sM1N1CCBXnlyyynAKkFjLmEtSbaW0NtUPpkyBjRuhTHTeEB4ZTtdVXbkW\ndI0tXbeQMU1GywYqRCIoXhx274bmzU1iPXt2LzLZZ6LBggasbLeS6s7VLR2iEMJKubtD9+7wyy/Q\nuvWj7evPryd8YDibWm2inks9i8Unkg8Z/mGFIiLg/fdh4UKTSDxMqEMiQmi5rCX3w+7j3tFdEmqR\norzxBmzbBmFhZsKuW47WLGi5gBbLWrDR++WW6BVCpAzTp0OvXqYE7eMJ9fITy+m2qht/tf9LEmqR\nYCSptjJBQY9643bsgDx5zPbg8GDeWfIO6VOn58+2f5I2VVrLBiqEBaRNa8rsVa9uJu666IasareK\nzis6s+bMGkuHJ4SwEg/Xc/jhB9i50/y9eGjRsUUMWj+IjZ03UjVv1eefRIiXJEm1FblyBWrVAicn\nU1IsY3RH9IPwBzRb0owc6XKw8N2FsgCGSNFsbODbb2HoUKhRA6J8q7Ou4zp6r+nNylMrLR2eEMLC\nQkKgQwczyf/vv6FgwUf75h+dz9DNQ9ncdTOlc5a2XJAiWZKk2kocPw7VqpnbUzNnmtnJAEFhQTRd\n3JQ8GfMwr8U87GxkGLwQAH36mKXNW7WCs54V8ejkQf91/Vl+YrmlQxNCWMitW2Z4GMDmzY/WcwCY\nc3gOn235jC1dt1A8e3HLBCiSNcnQrMDmzdCxI/z4o/n6UGBoIE0XN6Vw1sLMeHsGtja2lgtSCCvU\noIEpjdWsGfTsWY71fTbQeHEjIqIi6PBWB0uHJ4RIROfPQ5Mm8O67j8rPPjTr0CzGeI1hS9ctvOn4\npuWCFMmaJNUWNneuGfe1fLmpn/nQvdB7NF7UmBLZSzCt2TRslNxUECI2JUvCnj3w9ttw4UJp3Mdt\nounSBkRERdCldBdLhyeESAS7d5tkevRoUzbvcdMPTGfcjnFs7bqVwtkKWyQ+kTIoa1vzXimlrS2m\n10Fr849/wQJT7qdo0Uf77obcpeHChpRzKsfPTX6WhFqIOLh/39zpCQqCr2ee4t1V9fhf7f/Rs2xP\nS4cmhHiN/vgD+veHefNMT/Xjpu6byoS/J7C161YKZi0Y+wlEiqWUQmudYIXKpafaAsLCoHdvOHPG\nfLp+fFWngOAAGi5sSJU8VZjcaLIUpRcijtKlgxUr4KOPoOfbxViwZCvdttQjIiqCvuX7Wjo8IUQC\n09pU95g0yaznULbsk/un7J3CpD2T8OzmSYEsBSwTpEhRJKlOZAEBZmJVxoym5q6Dw6N9t4NvU39B\nfWo51+KHhj9IQi3ES7K1hcmTzaNL4zeZumQbg3bUJTwynAGVBlg6PCFEAomIgEGDYPt2U+HD2fnJ\n/ZN2T+KnfT+xrds28mfOb5EYRcojSXUi8vExt6YaNIDvvzcJwEM3H9yk/oL61CtQjwn1J0hCLcQr\nUgoGDzZvsn1aFeKbaZ6M212HiKgIBlUZZOnwhBDxFBRkSuaFhJga1JkyPbl/4t8TmXZgGp7dPXHO\n5Bz7SYR4DWSwbiI5cMAsWNGvn6ny8XhC7X/fnzrz6tCoYCNJqIVIIO++C2vWwBcfFKCnjSdT9k3h\nh90/WDosIUQ8XLsGbm7g6GjmIz2dUH+781umH5wuCbWwiARJqpVSjZRSp5VSZ5VSw55zzBSl1Dml\n1BGlVJmEuG5SsWYNNG4MU6ea21WPux50ndrzatP8zeZ8XfdrSaiFSEBVqpierIU/56PeZU9+2f8L\nE3ZNsHRYQohXcPq0WRnxnXdg9uxH6zk8NG77OOYcmYNXdy/yZMxjmSBFihbv4R9KKRvgZ6AucAXY\nr5T6S2t9+rFjGgMFtdaFlVKVgWlAlfheOymYOhXGjTMrJFaq9OS+q4FXqTu/Lu1KtGOU2yjLBChE\nMlewoBlz2aJFXorm8WImtYmIiuCzmp9ZOjQhRBzt2GEWRxs/Hrp3f3b/WK+xLDm+BM9unjhlcEr0\n+ISAhOmprgSc01r7aq3DgaVA86eOaQ7MB9Ba7wUyKaXeIBmLioIhQ+Cnn0xP2dMJ9ZXAK9SeV5uO\nb3WUhFqI1yxbNti0CTKQm0wrvJh7aAFjvcZaOiwhRBwsX24m+C9Y8GxCrbVm1LZRLDuxjG3dtklC\nLSwqIZLq3MClx76/HL3tv47xi+WYZCM4GNq2hYMHTQ+Zi8uT+/3u+eE2143uZbozstZIywQpRApj\nbw+LFkGDak6Ez9rGgsPL+HLbl6SEuvhCJEUPS+Z99JEpmdegwdP7NSO3jmTF6RVs67aNnOlzWiZQ\nIaJJ9Y8E5u9vxnu5uMCGDZAmzZP7L929RO15telXvh+fVv/UMkEKkULZ2JjliwsUyMnnX29j0YC6\nREZF8lWdr2Q+gxBWJDISPv4YtmyJvWSe1pphm4ex0Xsj27ptw9HB0TKBCvGYhEiq/YDHf93zRG97\n+pi8LzgmxujRo2Oeu7m54ebmFt8YE8XZs6ZkXocOMHasKe31ON87vtSZX4cBFQfwcdWPLROkEII+\nfSBv3hx06rONRQPMAjHf1vtWEmshrEBwMHTqZNZ12LkTMmd+cr/WmiEbh+Dp48mWrlvI5pDNMoGK\nJMfT0xNPT8/Xdv54L1OulLIFzmAmKl4F9gEdtNanHjumCTBAa91UKVUF+FFrHetExaS6TPnOnWYS\nxbhx0KvXs/t97vhQe15tBlceLLVyhbASR49C41a3UF3r065ybb5vMFESayEs6OZNePttM8H4t9+e\nvdurtWbQ+kHsubyHDZ03kCVtFssEKpKFhF6mPN5jqrXWkcAHwEbgBLBUa31KKdVPKdU3+hh34F+l\n1HlgOvB+fK9rTZYtMzVx58+PPaG+EHABt7luDKk6RBJqIaxI6dKwzzMbmVdvYeGO7Qz0GCxjrIWw\nEG9vqFYNatc276dPJ9RROooB7gPYf2U/m7pskoRaWJ1491QntKTUU601TJhgyuatXQulSj17zPnb\n56k7vy7Dqw+nf8X+iR+kEOKF7t2DFu3vcKhEQ9pWr8C05j9ho2RtLCESy7590Lw5jBoF77337P4o\nHUW/Nf04dfMU7p3cyZgmY+IHKZKdhO6plqT6FUVEwIABsHevqUGdO5ZaJudunaPO/Dp8UesL+pbv\nm/hBCiHiLDwcer1/lxUOjWlZrRTz2v4iibUQiWD1anOXd/ZsM/TjaZFRkfRe05sLARdY13Ed6VOn\nT/wgRbJkdcM/UqLAQPMP/+JFU5A+toT6xI0T1J5Xm9GuoyWhFiIJSJUK5s3IxJAcG1jueYLW8/oS\npaMsHZYQydovv5ieaXf35yfU3f/qju8dX9w7uktCLaya9FS/JD8/aNYMKlY0wz6eXiYV4OCVgzRd\n3JSJDSbSuVTnxA9SCBEvsxcG8d72ptQu64J7v1nY2thaOiQhkpWoKPjsM1ixAjw8zMTEp4VFhtF5\nRWcCQgL4q/1fOKRySPxARbImPdUWdOwYVK0K7drB9OmxJ9Q7L+6k8aLG/Nr0V0mohUiienZOz+r2\n7mw75EvN77sTERVh6ZCESDZCQ6FzZ3On9++/Y0+oH4Q/oMXSFoRFhrGmwxpJqEWSIEl1HG3cCPXq\nmYmJw4c/W4MaYJP3Jloua8nCdxfSsljLxA9SCJFgGtVJx95Bazlyzp+SY9sQHB5i6ZCESPLu3IFG\njSAsDDZvBsdY1my5F3qPRgsbkc0hG8vbLMfezj7xAxXiFUhSHQe//QZdu8Kff0L79rEfs+r0Kjqt\n6MTKditpULBB7AcJIZKUsiUdODN6Nf5X01DgiybcCgy0dEhCJFkXL0L16lCmjClFmzbts8fcfHCT\nOvPqUDJHSea1mEcq21huCQthpSSp/g9RUTBiBHzzDXh5Qc2asR+38NhC3lv7Hh6dPKjhXCNxgxRC\nvFZ5c6XG5/tFpL1fhAKj63D+yk1LhyREknPwoKlB3bs3TJoEtrFMU/C754frXFfqu9RnapOpUn1H\nJDkyUfE5goOhWze4cgVWrYr9FhXAD7t/YNKeSazvtJ4SOUokbpBCiEQTEaGpNnIkR8NXsK3nRqqV\nyGvpkIRIElavNsn09OnQ8jkjI71ve9NgYQP6lOvD8BrDEzdAkWLJRMVE4O8PdeuaT9LPG/MVpaP4\ndOOnzDw0k109d0lCLUQyZ2en2PftOBrl6EWtOTX50/OspUMSwqppDT/+CP37m/UcnpdQH7hygJpz\najK02lBJqEWSJkn1U06fhipVoE4dWLQI7GOZHxEWGUa3Vd3YdWkXO3vsxDmTc+IHKoSwiL+GfcJ7\nxb6kjbsrE5futXQ4QliliAj48EOYNctU+KhYMfbjPM55xFTM6lehX+IGKUQCs7N0ANbE09OUy/v2\nW+jRI/ZjgsKCaPV7K+zt7NncdbOU+REiBfq5V09c1ubg053NOHtlFjM+bm7pkISwGoGBZlJ/eDjs\n2gWZMsV+3JzDcxixZQSr26+mat6qiRukEK+B9FRHmzcP2raFJUuen1BfDbxK7Xm1cc7ozJ9t/5SE\nWogU7ONmzVjRyoPZ1/tTZ/hPRMnii0Jw+bKZ1J87txnyEVtCrbXmq+1fMXb7WLy6e0lCLZKNFD9R\nUWsYNQoWLjR/AIoVi/24I9eO0Hxpc3qX7c3IWiNRsRWqFkKkOEd8fKj+S2NyPWjCkQnfkc5B+ipE\nynT4MLzzDgwcCJ98Evt6DmGRYQxYN4CDVw/i3smdnOlzJn6gQkRL6ImKKTqpDg2Fnj3B29vMTs6R\nI/bjVp9ZTa/VvZjaZCptS7RNlNiEEEnHtbsBlP66BRH3snNw5Hzy55a7WCJlWbPGvJ/++iu0bh37\nMTcf3KT1763JZJ+JhS0XkiFNhsQNUoinSPWPBHLjhqnwERYG27bFnlBrrfn+7+/pv64/6zquk4Ra\nCBGrnJmy4PvVRnLlSMub42vgefiipUMSIlFoDZMnQ79+sHbt8xPqk/4nqTyrMlXyVGFF2xWSUItk\nKUUm1ceOQaVKULv281d1CosMo9/afsw/Np/dvXZTKXelxA9UCJFk2KdKw7HR82nu0om6Syrz85od\nlg5JiNcqLAz69jWrDv/9N1SuHPtx7ufccZvrxijXUXxb71tsbWJZ+UWIZCDFDf9YtQr69IEpU6BD\nh9iPuRJ4hTbL2+Do4Ci3qIQQL+3r3zcw8mBXehUYy8z3pEyYSH78/aFVK8iSxcxJyhDL26TWmh92\n/8DE3RP5s+2fVMtbLfEDFeI/yJjqV6S1KZU3dSqsXPn8mpnbfbfT4c8O9K/Qn89qfibLpAohXsma\nv8/x7u/NKZfVle2fTSaNXWpLhyREgvjnH2je3JTN++orsInlbTIwNJCeq3tyIeACK9quIF/mfIkf\nqBAvIEn1KwgJMUuknjljeqpz5372GK01k/dO5pud3zCvxTwaFWqUoDEIIVKe0//eo+p3nbHJeIOd\nA5dRLJckFiJpW70aevUyKyV26hT7MSdunKDV761wzefK5MaTsbeLZRU1IayATFR8SVevgqurWd3J\nyyv2hPpuyF06/NmB+Ufns6fXHkmohRAJomiBjPh9v4r8D1pR6qdKzN651tIhCfFKtIbx482S42vX\nPj+hXvLPEtzmuTG8xnCmvz1dEmqRoiTrpPrgQTNx4u23zaIuDrFUudpzeQ9lp5cla9qs7Oq5iwJZ\nCiR+oEKIZMshrQ0HJn9K/6wr6LPqfTrM/pTwyHBLhyVEnIWEQNeu8PvvsHdv7BMS74fdp++avnyx\n7Qs2ddlE9zLdEz1OISwt2SbVCxdCo0YwaRKMHPlsEfooHcU3O76h+dLmfN/ge35p+gtpU8VSBkQI\nIeJJKZjyaXWW1TnEip3HefPbWnjf9rZ0WEK80OXL5m5vaCjs2AF58jx7zMErByk3oxyhkaEc6neI\nMjnLJH6gQliBZDemOjzcrOTk7m4mJJYs+ewxl+9dpvuq7oRFhrHo3UXkzZQ3HhELIUTcnT0XRa1P\np3C39Ff80PQb3qvYW1ZoFVbJy8tUyRo4EIYNi71zauLfE5n490SmNJ5C+5LtLROoEK9IJir+h+vX\noW1bSJ8eFi2CzJmf3K+1Zs6ROQzbPIxBlQcxosYIqZcphEh0gYHQvM8J9uXuQrW3cjO/9UxZrllY\njYcLunzzDSxYAA0aPHuM921veq/pTURUBAtbLpTqHiJJsqqJikqpLEqpkuTT+wAAIABJREFUjUqp\nM0qpDUqpTM85zkcpdVQpdVgptS8+13yevXtNmTw3N7Nc6tMJ9eV7l2m6uCk/7/uZLV23MLLWSEmo\nhRAWkSEDbF5cgsHp97Dnr1KU+KkMS48vxdo6OUTK8+ABdO4M8+bBnj3PJtSRUZFM3jOZyrMq06xw\nMzy7eUpCLUS0ePVUK6XGA7e01hOUUsOALFrr4bEcdwEor7UOiMM5X7qneuZM+PxzmDUL3nnnyX1R\nOoo5h+cwfMtwPqz0ISNqjCCVbaqXOr8QQrwua9ZA18/2kLZtH8q6OPNL018kSREWceECtGwJpUrB\n9OnPTu4/ffM0vVb3wlbZ8ts7v1E4W2HLBCpEArGq4R9KqdOAq9b6ulIqJ+CptS4ay3H/AhW01rfi\ncM44J9WhoWas144dZvz0m28+uf/Y9WP0X9efiKgIZjSbQemcpeN0XiGESEwXLsC7bcKIqvIdfs6T\n+MJ1JB9W+lDupolEs349dOtmJvZ/8MGT46eDw4MZv2s8P+/7mTFuY+hfsb8sjCaSBasa/gHk0Fpf\nB9BaXwNyPOc4DWxSSu1XSvWJ5zUB8yZUvTrcumWGfjyeUAeGBjJkwxDqza9Ht9Ld2N1rtyTUQgir\n5eICu3emplLo52T+82+WHPqLSrMqseviLkuHJpK5yEgYNQp69oTly+HDDx8l1FprVp9ZTYlfSnDC\n/wSH+x1mQKUBklAL8Rx2LzpAKbUJeOPxTZgkeWQshz+vi7m61vqqUio7Jrk+pbXe+bxrjh49Oua5\nm5sbbm5uT+xfsQLee898on78D0CUjmLB0QWM3DaSei71OP7+cXKke16eL4QQ1iNtWjOEbfbsIgwd\ntpUO45bQ/s/21HSuyfh646VKkUhw165Bx47m+aFDkPOxubLnb59n0PpBeN/2Znqz6dQvWN8yQQqR\ngDw9PfH09Hxt54/v8I9TgNtjwz+2aa2LveBnRgGBWusfnrP/ucM/QkNh6FCzTOqyZVCp0qN9Wy5s\n4ZNNn5DWLi0TG0ykWt5qr/qyhBDCog4fhtatoUHT+2R9ZzzTDk1lUOVBDKk6hHSp01k6PJEMbNkC\nXbpAnz7w5ZdgGz3S6Mb9G/zP638sOb6ET6t9ykdVPyK1bWrLBivEa2Jtwz9WA92jn3cD/nr6AKWU\ng1IqffTzdEAD4PjLXujff6FmTfD1NZ+oHybU/1z/h6aLm9J3bV8+r/k5u3rukoRaCJGklS1rVoS9\nejEdG4aP5Y/6Bznpf5JCPxXip70/ERoRaukQRRIVGQljxpiEev5889zWFoLCghjrNZZiU4tho2w4\nNeAUw2oMk4RaiJcQ36R6PFBfKXUGqAt8C6CUclJKrY0+5g1gp1LqMLAHWKO13vgyF1m1yiyL2qGD\nmZCYJYtJptssb0P9BfWp71KfUwNO0bp4a1lEQQiRLGTObP7ede8ObRvkp2nwUtw7urPBewNv/vwm\ncw7PISIqwtJhiiTk+nVo2BC2bYMDB6BePbO8+A+7f6DIT0U4ffM0+/vsZ3LjyWRPl93S4QqR5Fj1\n4i8PHjxaHXHpUqhSxSTTY7ePZYfvDj6p9gn9K/SX26FCiGTt6FFo3x4qVIBffoFjAbv4fOvn+AX6\nMbTaULqW7koauzSWDlNYMQ8P6NXLPEaNguDIQKbun8qkPZOo6VyTkbVGyvLiIsWxtuEfr82RI+YN\n5M4dOHxYE5RjM00WNaH+gvpUzl0Z74HefFLtE0mohRDJXunSpmfR3h7KlYM0N6qzrds2Zr8zm1Vn\nVlFgcgG+2/Ud90LvWTpUYWWCg03p2X79YPFiGDDsGmN3fInLFBf+ufEPW7tu5Y+2f0hCLUQCsMqe\n6okTNd9+CxMnhaHeWsoPu38gPCqcj6t8TKdSnbC3s7d0mEIIYRG//27qCA8dCh9/DDY2cPTaUSb8\nPYEN5zfQtXRX3q/4PoWyFrJ0qMLCjh6FTp2gRAnoP/YQc05NZvWZ1XQo2YHBVQZTJFsRS4cohEVZ\n1eIvr4NSSpetd5aK/Wayymceb+V4iyFVh9CoUCMZLy2EEICPj1lK2tYW5s6FAgWit9/xYdqBacw+\nPJvyucozoOIAGhdqLIvIpDBRUTB5Moyb8IBWX6zgVNoZ+Nzx4YNKH9C7XG+yps1q6RCFsAopIqnO\nPiE73Up3o0/5PvJJWgghYhEZCT/8ABMmwNdfQ+/ej2r2h0SEsOz4Mn7e/zPXg67TpVQXupbuypuO\nb/73SUWS5+OjaTv4IBez/UZIoWVUda5Mr7K9aP5mc1LZprJ0eEJYlRSRVIeEh8ikGyGEiIMTJ6Br\nV7Nwx8yZkCvXk/uPXT/GvCPzWPTPIvJnzk+30t1oV7Kd9FYmMxdu/8snc5az2mcRGR3vMahWT3qW\n6y6LBgnxH1JEUm1tMQkhhDULD4evvoJp0+DHH02lkKdHy0VERbDReyPzj87H47wHVfJU4d2i79K8\naHNyps8Z+4mFVfO548PyE8tZePh3Tl31JfPVdxnfpR3d3FxlKXEh4kCSaiGEELHavx969ID8+U3p\nPWfn2I8LCgti/fn1rDi1Ao/zHpTMUZKWRVvSuFBjijoWlfkrVioyKpK9fntxP+eO+zl3Lt27RFHd\nkmNL2jKsnRtDP7HDzs7SUQqRdEhSLYQQ4rnCwsw46x9/hC++MJVCbP9jnmJoRChb/t3CqtOr2OC9\nAa01DQo2oEHBBtRzqSfDRCzM944vnj6ebPDewAbvDeTJmIcmhZpQMk0TZo6qyoMgO+bOheLFLR2p\nEEmPJNVCCCFe6MwZ6NsXQkJg1ix4660X/4zWmrO3zrLBewMbvTey3Xc7LllcqOFcg5rONanhXIPc\nGXO//uBTKK01FwIusN13O16+Xnj6eBIcEYxbfjfqFqhLk8JNcEydh2++galTYeRI86FJeqeFeDWS\nVAshhIiTqCiYPRs++8yspDdyJKR7ifWywiLDOHz1MDsu7mDnxZ3svLiTDGkyUDl3Zco5laO8U3nK\nOpWV3uxXdC3oGvv99rPPbx/7r+znwJUD2NvZU8O5Bm753XDL78ab2d6MGY6zeTO8/775gDR5MuTJ\nY+EXIEQSJ0m1EEKIl3LtGnzyCXh5wXffQbt2z05kjAutNWdunWG/334OXT3EoWuHOHz1MNkcslHO\nqRxv5XiLYo7FKOpYlCLZipA2VdqEfzFJUGBoICf9T3LC/wTHbxyP+RoSEULFXBXNI7f56pTB6Zmf\n9/Mzi/3s2gU//wzNmlngRQiRDElSLYQQ4pXs3AkffggZM8JPP0GpUvE/Z5SO4vzt8xy8cpCT/ic5\ndfMUp26e4kLABZzSO1EsezEKZilI/sz5yZcpn/maOR/Z0mZLNhMitdb4P/DnQsCFZx7eAd7cDr5N\nUceilMxRkhLZS5hHjhLky5TvP9sgOBgmTjTj4997z9xxeJk7DUKI/yZJtRBCiFcWGWnqWY8aBa1b\nw+jRkD17wl8nIiqCCwEXOH3zNBcCLuBzxwffu7743PHB544P4ZHh5Mucj5zpc/JGujfMI/2jr9kd\nspPJPhOZ0mQik30m0timSbQkXGvN/fD7BAQHcCfkDgEhAQQEB3Ar+BZXA69yNcg8rgRe4WrgVa4F\nXSNd6nS4ZHGhYJaCuGRxiXkUyFwA50zOL7WqpdawfLnpna5Y0Uw8fbhqphAi4UhSLYQQIt5u3YIx\nY2DxYhg8GD76KHF7Qe+G3OXi3YtcC7rG9fvXuR503XyNfn7zwU3uht7lbshd7obeRWv9RJJtb2dP\nGts0pLFLQ2rb1DHP09imwc7GDq01UToKjUZrzcP/onQUoRGhBEcEExweTEhECMER0V/Dg7kXeo87\nIXdIZZuKzPaZyWKfhSxps5DFPgtZ02bFKb0TThmcYr7mypCLnOlz4pDKIUHaZc8ek0zfu2fGTbu6\nJshphRCxkKRaCCFEgvH2hs8/h+3bTe91z56QygpXsw6JCOFe6L2YJDskIoTQiFBCI0MJiwyLeR4a\nEUpEVAQ2ygalFAr1xFcbZYO9nT32dvaktUtL2lRpn3ieIXUGMttnTvRVfY8fN/8fDh82/x+6d//v\nUohCiPiTpFoIIUSC278fhg0zk+JGj4a2bSWpSwwXLpgkeuNGGD4c+vcHe3tLRyVEypDQSbWsYyqE\nEIKKFWHLFjOB8aefzGIiCxZARISlI0uezp2D3r2hUiUoXBjOnzdDcCShFiLpkqRaCCEEYMrsNWhg\nSrf98gv89hsULWpqXYeHWzq65OHIEVPSsFo1U2f6zBn48kvIkMHSkQkh4kuGfwghhHguLy/43//g\n9Gmzel+fPpAtm6WjSlq0flQj/PBhGDLErHYpibQQliVjqoUQQiS6I0dMNYpVq0xP66BBUKyYpaOy\nbg8ewKJFZjhNWJipstK9uwzxEMJaSFIthBDCYq5fh19/hWnTzHLZvXtDixaQJnGLZVi106fN0Jm5\nc6FqVbPgTr16r7aKpRDi9ZGkWgghhMWFhMDKlSZ5PHoUOnaEXr0SZpXGpOjePVi2DObMgX//hS5d\nzCqILi6WjkwI8TySVAshhLAqFy6YZHLuXMic2QwPadfOVLVIzh48AA8Ps/rh+vVQty706AGNGoGd\nnaWjE0K8iCTVQgghrFJUFPz9t+mx/eMPcHKCVq2gaVMoXTp5DH+4c8fUlP7zT5NIV6wIbdrAu+++\nnuXehRCvj1XVqVZKtVZKHVdKRSqlyv3HcY2UUqeVUmeVUsPic01heHp6WjqEJEHaKe6kreJG2un5\nbGygRg0zMe/yZejSxRN/f5N05sljKoesWGGWSE8qIiPhwAH46ivz2vLmNb3ydeua2tKbN0O/fvFL\nqOV3Km6kneJO2soy4lun+h+gJeD1vAOUUjbAz0BDoATQQSlVNJ7XTfHkH0zcSDvFnbRV3Eg7xY2t\nLdy968mPP5qFTjw9oWRJmDHDjDMuUcKMOV682AwfsZYblEFBsHWrKSPYqJEpH9ili/kg8OWXcOOG\nGfLRt2/C9UzL71TcSDvFnbSVZcRr1JfW+gyAUv95U68ScE5r7Rt97FKgOXA6PtcWQgiRdBQubMrw\nDRpkVmk8ehS2bzfDRIYNg8BAM0SkTBnztXBhk3w7OZke8IR2/z74+JiE/9ixR4/Ll00M1aubpH/+\nfMiRI+GvL4RIfhJjKkVu4NJj31/GJNpCCCFSIDs7KF/ePD76yGy7edMk2keOmIVSfvsNvL1NVY0C\nBczwkezZTYKbI4fpQU6b1tR8trd/VNIvLMw8wsMhONj0MD983LwJly6Z6hyBgZAvHxQsaCqWtGoF\nY8ZAkSKQKpXl2kYIkXS9cKKiUmoT8MbjmwANfK61XhN9zDZgiNb6UCw/3wpoqLXuG/19Z6CS1nrg\nc65nJTcBhRBCCCFEcpaQExVf2FOtta4fz2v4Ac6PfZ8netvzrpcM5ocLIYQQQoiUJCFHqj0vGd4P\nFFJK5VNKpQbaA6sT8LpCCCGEEEJYVHxL6rVQSl0CqgBrlVIe0dudlFJrAbTWkcAHwEbgBLBUa30q\nfmELIYQQQghhPaxu8RchhBBCCCGSmtdQqOjVyAIxT1JK/aaUuq6UOvbYtixKqY1KqTNKqQ1KqUyP\n7RuhlDqnlDqllGpgmagTn1Iqj1Jqq1LqhFLqH6XUwOjt0laPUUqlUUrtVUodjm6nUdHbpZ1ioZSy\nUUodUkqtjv5e2ikWSikfpdTR6N+rfdHbpK2eopTKpJRaHv26TyilKks7PUspVST6d+lQ9Ne7SqmB\n0lbPUkp9FL343jGl1CKlVGppp2cppQZFv+clTn6gtbb4A5PcnwfyAamAI0BRS8dl4TapAZQBjj22\nbTwwNPr5MODb6OfFgcOYiaf5o9tSWfo1JFI75QTKRD9PD5wBikpbxdpWDtFfbYE9mNKW0k6xt9VH\nwEJgdfT30k6xt9MFIMtT26Stnm2nuUCP6Od2QCZppxe2mQ1wBcgrbfVM2+SK/reXOvr7ZUA3aadn\n2qkEcAxIE/2+txEo+DrbyVp6qmMWiNFahwMPF4hJsbTWO4GApzY3B+ZFP58HtIh+/g5mrHqE1toH\nOEcKqQWutb6mtT4S/TwIOIWpMCNt9RSt9YPop2kwfzQ00k7PUErlAZoAsx7bLO0UO8WzdzylrR6j\nlMoI1NRazwGIfv13kXZ6kXqAt9b6EtJWsbEF0iml7IC0mKpq0k5PKgbs1VqHajO/bzvwLqY9Xks7\nWUtSHdsCMbktFIs1y6G1vg4mmQQervP1dPv5kQLbTymVH9O7vwd4Q9rqSdFDGg4D14BNWuv9SDvF\nZhLwKeZDx0PSTrHTwCal1H6lVO/obdJWTyoA3FRKzYke1jBDKeWAtNOLtAMWRz+XtnqM1voK8D1w\nEfOa72qtNyPt9LTjQM3o4R4OmM6SvLzGdrKWpFq8GpllGk0plR74AxgU3WP9dNuk+LbSWkdprcti\nevIrKaVKIO30BKVUU+B69N2P/6qZn6Lb6THV9f/Zu++4qso/gOOfw1JRUJY4wY2zzPXLCWaouM09\ncJajtKzMHCVaOXLmKNPcK7e5FUeAK0dpmttU3IqAiAy5cJ/fH0dx4UiBw/i+X6/74t5zDud87+Fy\n7/c+5/s8j1IV0D+sPtI0rSbymnqSFVAB+PH+uYoCBiLn6Zk0TbNGbzVcfn+RnKtHaJqWC71V2h29\nFCS7pmkdkPP0GKXUSfRSj63ARvTSjoSkNk2uY6aVpPo/TRCTid3QNM0VQNO0PMDN+8uvoH/7eiBT\nnb/7l79WAAuUUmvuL5Zz9QxKqTtAAFAfOU9Pqg400TTtHPAr8I6maQuA63KenqaUunb/ZwjwG/ql\nUnlNPe4ycEkpdfD+45XoSbacp2fzAf5USt26/1jO1ePeBc4ppcLulzWsBqoh5+kpSqk5SqlKSikv\n4DZ6v6sUO09pJamWCWKSpvF4a9laoMv9+52BNY8sb3u/929hoBiwP7WCTANmA8eVUpMeWSbn6hGa\npjk/6OGsaVo2wBu9/lzO0yOUUoOVUm5KqSLo70M7lFK+wDrkPD1G0zTb+1eI0DQtO1AXOIq8ph5z\n/zLzJU3TStxfVAd9zgY5T8/WDv1L7QNyrh53EXhb07SsmqZp6K+p48h5eoqmaS73f7oBzdFLilLu\nPBndO/ORXpr10b9BnAEGGh2P0bf7f/irwD30f6CugAOw7f558gdyPbL9IPSeqieAukbHn4rnqTr6\n5ZzD6Jd2/rr/WnKUc/XYeSp3/9wcRu8NPeT+cjlPzz5nnjwc/UPO09Pnp/Aj/3dHH7xvy7lK8ly9\nid54dBhYhT76h5ynpM+VLRAC2D2yTM7V0+fJ7/5zPoLe2c5azlOS5ykIvbb6EOCV0q8nmfxFCCGE\nEEKI15RWyj+EEEIIIYRItySpFkIIIYQQ4jVJUi2EEEIIIcRrkqRaCCGEEEKI1yRJtRBCCCGEEK9J\nkmohhBBCCCFekyTVQgghhBBCvCZJqoUQQgghhHhNyZJUa5o2S9O0G5qmHXnONpM1TTujadphTdPK\nJ8dxhRBCCCGESAuSq6V6DlDvWSs1TfMBiiqligM9gZ+T6bhCCCGEEEIYLlmSaqXULiD8OZs0Bebf\n33YfkFPTNNfkOLYQQgghhBBGS62a6vzApUceX7m/TAghhBBCiHRPOioKIYQQQgjxmqxS6ThXgIKP\nPC5wf9lTNE1TqRKREEIIIYTI1JRSWnLtKzmTau3+LSlrgY+ApZqmvQ3cVkrdeNaOlJK8Wjw0bNgw\nhg0bZnQYIo2R10XaExICW7fCli2wYwfExkLVqvqtcmUoUwby5AEt2T7Cnj7+558P4403hnHgAAQF\ngaUleHqClxc0aAD5pfAwU5L3C5EULZnfjJIlqdY0bTHgBThpmnYR8ANsAKWUmqGU2qhpWgNN084C\nUUDX5DiuEEIIY50+DcuXw2+/6fdr14Z69eCrr6BYsZRLoJPi4gJFikD//vpjpeDff/Xkevt2GDgQ\nChWCxo2hSRN4663UjU8IkbElS1KtlGr/Etv0SY5jCSGEMFZwMCxaBMuWwY0b0LIljBkD1auDjY3R\n0T2kaXpiX6wYdOsG8fGwezesXw+tWoGVFXToAO3b69sIIcTrkI6KIs3z8vIyOgSRBsnrInXdu6cn\n0XXrQsWKcPkyTJqk/5wyRW+hTgsJ9fNeF1ZWeinI2LFw9izMn6+XjFSrppeozJkD0dGpF6tIPfJ+\nIVKDltbqlzVNU2ktJiGEyKyuXIGpU2HWLChXDrp3h+bNIVs2oyNLPiYTbN4MP/8M+/aBry/07g0l\nShgdmRAiJWmalqwdFdNkS3VcnNERCCFE5nb4MHTqpCfSUVGwZ49el9y+fcZKqAGsrfU66w0b4MAB\nyJoVataEpk315y0yhkKFCqFpmtwy4a1QoUKp8hpLky3VBQsq+veH998HW1ujIxJCiMwjMBC+/RZO\nnoS+faFHD3BwSP7jKKWIuBfBlTtXuBJ5hfCYcCLuRXA79jYRsfrP6Pho4s3xmBJM+k+zCbMyY2Np\nQxbLLGSxyoKNhQ1ZrbKSM2tOHLM5PnZzze5KAfsCZLHK8p/ji46GuXNh3DjIlw++/BIaNZKOjenZ\n/VZJo8MQBnjW3/7+8mT7r06TSfX+/YpRo/QWgk8/1d/YJbkWQoiUs2sX+PnBhQvw9dd6i/Tr1kib\nEkycCz/HqdBTnA49zalbp/g3/F+uRF7h8p3LWGqW5LfPTz67fDhlcyJX1lzkypqLnFlykjNrTrJb\nZ8fKwgorCyusLa2xsrBCQyMuIY64hDjuJdwjLiGO2PhYImIjCIsJIyw2jLCYMEKjQ7kRdYOrkVdx\nyOqAW0433HK64Z7TnZLOJSnlUopSzqVwsnV67nOIj4eVK2HkSP18fPedXlcuyXX6I0l15pWpk+oH\nMR07BsOH6721hw7Ve29bWxscoBBCZCD79unvr6dP68m0r++rvc9GxUVx+PphDl0/xF/X/uLQ9UOc\nvHWS/Hb5KeFUAg8nDzycPSjqUJQC9gXIb58f+yz2yf+EnpBgTuD63etcunOJixEXOR9+npOhJzkR\ncoITt06QxTIL5VzLUSlvJSrlq0Tl/JVxz+mO9kTWbDbDihX6ucqdW0+ua9VK8fBFMpKkOvPK1El1\nVFwUttYPm6YPHNDHF718GUaMgBYtpJVACCFeR3Cw/r66c6eeTHft+t9apsNiwth1cRdBwUHsvLiT\nf27+Q2mX0lTIU4EKeSvwVt63KJe7HNms024BtlKKa3evceTGEQ5cOcDBawc5cOUAcQlx1HCrgVch\nL7wKefGG6xtYaHoXpPh4WLwYhg0DDw+YMAFKlTL2eYiXI0l15pWpk+rsI7JTOX9l3i38LnWL1qVS\nvkqAxtat+odAtmz6EE4VKhgdrRBCpC+RkTBqFEyfrpfWffEFZM/+4t9LMCew/8p+Np7ZyMazGzkT\neoa3C7xNTbea1HKvRZX8VdJ0Av1fXLlzhZ0XdxJwIYCACwGERIfg6e5Jg+INaFSiEXly5CEuDn76\nSW/oaddOT7IdHY2OXDyPJNWZV6ZOqiPvRRIUHMS2c9vYeGYjd+Pu0qxkM5qXbE6NgrVYMM+aIUPg\nvff0S3BOzy+JE0KITE8pfVzmQYPA21tPBgsUeP7vxMbHsvnsZlYcX8Hms5vJZ5ePBsUb0KB4A6oW\nqIq1Zeaox7sWeY3t57ez/vR6tvy7heKOxWlcojHNSjYjj0U5hg7V666HDoVevfTxsEXak5aT6sKF\nCzNr1izeeeed19rPvHnzmDlzJjt37kymyDKGTJ1UPxnTiZATrD65mtUnV3M+/DzNSzbnvaKd2fBz\ndZYv0xg+HD74ACwtDQpaCCHSsBMn9HGX796FadOgcuVnbxuXEMe2c9tYemwpa0+tpXye8rQu3ZpG\nJRpRMGfB1As6jTIlmNh1cRfrTq9jxfEV5Myak/Zl21Peqh1jhxTi9m2YMQMqVTI6UvGkzJBUz507\nl9mzZxMUFPTSv6OUeqoPQUaTWkk1Sqk0ddNDerbg28Fq9M7RqtTUUqropKKq95LhqmKd86pqVaWO\nHXvurwohRKYSHa3UkCFKOTkpNXmyUvHxz9721K1Tqv+W/ir32Nyq2qxqatIfk9SVO1dSL9h0KMGc\noIIuBKle63opp++dVPVZ1VX3qTNV7vxR6pNPlLpzx+gIxaNelF8YxdfXV1lYWChbW1tlZ2enxo4d\nq5RSau/evapatWoqV65cqnz58iogICDxd+bMmaOKFCmi7OzsVJEiRdTixYvViRMnVNasWZWVlZXK\nkSOHcnBwSPJ4Xl5easiQIap69erK1tZW/fvvv2rOnDmqVKlSys7OThUtWlRNnz49cXtPT0+1atUq\npZRSu3btUpqmqY0bNyqllNq+fbsqX758Sp2aZPOsv/395cmXwybnzpIloJd80ZvNZrX/8n710YaP\nlPMYZ1V6ZH1lX3GD8huWoO7de6ldCCFEhhUQoFTRokq1aqXU5ctJbxNrilWLjixSXnO9lOtYV/Xl\n1i/VmdAzqRtoBnEv/p5ac3KNariooXIY5ahKffaxylP2hFqzxujIxANpNalWSqlChQqpHTt2JD6+\ncuWKcnJyUps3b1ZKKbVt2zbl5OSkbt26paKiopS9vb06c0b/X71+/bo6fvy4UkqpuXPnqpo1az73\nWF5eXsrd3V2dOHFCJSQkKJPJpDZu3KjOnz+vlFIqKChI2draqkOHDimllBo6dKj6+OOPlVJKjRw5\nUhUrVkwNHDgwcV2/fv2S70SkkNRKqtPkjIovQ9M0KuevzNQGU7n06SW+8GmDW5evGRtbAve2E/l9\nT6TRIQohRKqLjoZPPtHHmZ44EZYtg/z5H98mLCaMkTtHUmhSIeYcnsNHlT/i4qcXGf3uaIo5FjMm\n8HTOxtKGJh5NWN9+PX/1+pNmDbJzr50XbTe9wzs9NxEenjbLDsRDmpY8t1elHilPWLhwIQ0bNqRe\nvXoA1KlTh0qVKrFx40YALC0tOXr0KLGxsbi6ulLqPw5B06VLF0q74/lLAAAgAElEQVSWLImFhQVW\nVlb4+PgkzjpYs2ZN6tatm1iX7enpSWBgIABBQUEMGjQo8XFgYCCenp6v/qQzmHSbVD8qq1VWupTv\nwpGPDuLfez6Fqv9BnbVFqOXnx/WIUKPDE0KIVLFnD5QvD7duwdGj+tTbjwq+HczHmz6m2ORinAk7\ng39Hf7b6bqVl6ZbYWL7mTC8iUaFchRhZZyTXv7zIlG7dOJL7S1z9yjNw0WLizfFGhyeeQb96//q3\n5BAcHMyyZctwdHTE0dERBwcHdu/ezbVr17C1tWXp0qVMmzaNvHnz0rhxY06dOvWf9l+w4OP9IzZt\n2kTVqlVxcnLCwcGBTZs2cevWLQCqVq3K6dOnuXnzJn///TedOnXi0qVLhIaGsn//fmrJgO2JMkRS\n/YCmaVR3q8bez5eys8sezt+6QoExxem2pD83o24aHZ4QQqSI2FgYMEAfw3/0aFi06PHh3S5FXKL3\n+t5UmFEBW2tb/vnwH+Y0nUM513LGBZ0J2Fja0L1yR0K++ZthNUfzw87pOPqV4Oc/5kpyLR7zZEfB\nggUL0qlTJ8LCwggLCyM8PJzIyEgGDBgAgLe3N/7+/ly/fh0PDw969OiR5H5e5nhxcXG0bNmSAQMG\nEBISQnh4OD4+Pokt59myZaNixYpMmjSJsmXLYmVlRdWqVZkwYQLFihXDUcaSTJShkupHVS9ZnItT\nZzI8z9/8uvweRcaXwu/3YUTek7IQIUTGcfw4VKkC587BkSP6UKMPXIu8Rt+NfXnz5zfJmTUnp/qc\nYvS7o8lnl8+4gDMhTdMY3MqHG98HUv3mfD6dP4eiE8qy/NhyzMpsdHgiDciTJw/nzp1LfNyxY0fW\nrVuHv78/ZrOZ2NhYAgMDuXr1Kjdv3mTt2rVER0djbW1Njhw5sLDQ0zlXV1cuX76MyWR66WPHxcUR\nFxeHs7MzFhYWbNq0CX9//8e2qVWrFlOnTk0s9fDy8nrssdBl2KQa9NqmIX0LcnjkFIpsO8jMVf9S\ndFJxJu+bTFxCnNHhCSHEK1MKfvkFPD31Gurly8HFRV8XY4rhu6DvKDutLNaW1pzsc5LR747G2dbZ\n2KAzuZw5YdP0Giz2DiBiyWQ+Xfk9lWZUIvBCoNGhCYMNHDiQb7/9FkdHRyZMmECBAgVYs2YNI0eO\nxMXFBXd3d8aNG4fZbMZsNjNhwgTy58+Ps7MzQUFBTJs2DYB33nmHMmXKkCdPHnLnzp3ksZ5szc6R\nIweTJ0+mVatWODo6smTJEpo2bfrYNp6enty9ezex1OPBY0mqH5cuxqlODiaTPuPVzHVHKPTBl0Ro\n55nsM5m6Resm+7GEECIl3b4NPXrAqVOwZMnDabKVUvz6z68M2j6IyvkqM8Z7DEUcihgbrEjSpUvQ\ntp3irtsKwip+QVW3Koz1Hot7LnejQ8uw0vI41SJlpdY41Rm6pfpR1tb6DGLzx75B8MiNVA4fS+8N\nvXlv6XtcuH3B6PCEEOKl7N0Lb70Frq6wb9/DhPp4yHFqza3FhL0TWNh8IStar5CEOg0rWBACAzQa\nF2lFwqQT2N4tS8UZFfH73Y8YU4zR4QkhXkGmSaofqFcP/jyoEby1MYU3HqOEfQUqzajE97u+l44j\nQog0SymYPBmaNYMffoApUyBrVr3U46sdX+E515N2Zdux7/191HSvaXS44iVYWcF338H82dnwHzKU\n9pGHOBZynDd/flNKQoRIhzJN+ceT4uPBzw/mzYPxs8/zy/UPuB17m9lNZ/OG6xspfnwhhHhZUVF6\nucfx47ByJRS53wD9+/nf+WDdB1TIW4Ef6v8gHRDTsRs3oG1bsLGBjt+tYfCuPvgU82GM9xhyZc1l\ndHgZgpR/ZF5S/pHCrKz0cpCZM+Fj38I0u7OVnhV7UWd+Hfx+95OOjEKINOHMGXj7bb2Ebc8ePaGO\nMcXQb3M/Oq7uyMR6E1nWapkk1Omcqyts3QrlysHQ1k1ZWO0frCysKPtTWTaf3Wx0eEKIl5Bpk+oH\n6tfXP6imT9fY++P77O18iIPXDlJtVjVOh542OjwhRCa2di1Urw4ffQRz5kC2bHDw6kEqzKjA9bvX\nOdr7KI09Gr94RyJdsLKCcePg+++hZaOc/O/WTyxovoAe63rQd2Nfok3RRocohHiOTJ9UAxQtqnf+\niYyEDo0L8HPN9XQt35Xqs6sz+9BsuVwkhEhVZjN89RX06QPr1kGvXqAwMyJoBA0WNcDP048lLZfg\nmE0mXciIWreGgAD9aurysbU50O1vbsXcotKMSvx17S+jwxNCPEOy1FRrmlYf+AE9SZ+llPr+ifWe\nwBrgwcjmq5RS3z1jX6lSU50UpfTZyKZMgWXLIFeJf2i3sh0lnUvyS+NfpK5NCJHi7t6Fjh0hLAxW\nrIDcueFm1E18V/sSY4phcYvFFLAvYHSYIhVERICvL9y5o9fSb7m6mE82f8LXtb6mb5W+Lz17ntBJ\nTXXmlW5qqjVNswCmAvWAMkA7TdNKJrFpkFKqwv1bkgm10TQNBg2CWbP0Wcn2/FaWAx8cwDW7K5Vm\nVOLIjSNGhyiEyMCCg/VyD2dn2LZNT6iDgoOoML0ClfJWYkfnHZJQZyI5c8Lq1fC//+m38pbt+aP7\nH8w5PIe2K9vKDMFCpDHJUf5RBTijlApWSpmAJUDTJLZLN1+pfXxg924YPx6GfJmVSfWm8k3tb6gz\nvw4Ljyw0OjwhRAa0Zw9UrQpduugzJVpbK8bsHkPr5a2Z2WQmI+qMwMrCyugwRSqztNRrrL/+Gry8\n4PS+ouzptoecWXJS+ZfKHLt5zOgQhXjM8OHD8fX1BeDSpUvY29unyhWCwoULs2PHjhQ/zvMkR1Kd\nH7j0yOPL95c9qaqmaYc1TdugaVrpZDhuiipeXK+z/usvvdW6SeH27Oi0g+GBw+mzsY+MDiKESDbz\n5+vjT8+aBZ9+CjHx0XRY1YFlx5Zx4IMD1C9W3+gQhcE6d9Zbrbt1g+k/ZmN6oxkMqjEIr3lerDy+\n0ujwxGtKroRw3rx51Kxp/Dj1D0qTChYsyJ07d15YqhQYGEjBggVTI7QUlVrNHn8CbkqpaE3TfIDf\ngBLP2njYsGGJ9728vPDy8krp+JLk6AhbtkDv3lCzJqxbV46DHxzEd7UvdRfUZWXrlTjZOhkSmxAi\n/TObYfBgWL5c75hWujRcirhEs6XNKOlckp1dd5LNOpvRYYo0onp1vbGnSRN9zPIff+zMG65v0HRJ\nU46FHOPrWl9LnXUmp5RK1tdAQkIClpaWyba/Z0nuuJ8lICCAgICAlDuAUuq1bsDbwOZHHg8EvnzB\n75wHHJ+xTqU1ZrNSo0crlT+/UgcPKhWfEK++8P9CFZtcTJ0MOWl0eEKIdCgmRqnWrZWqUUOpkBB9\n2Z6Le1TecXnVmF1jlNlsNjZAkWbduaNUo0ZKeXsrFRGh1NU7V9X/fvmfar28tYqKizI6vDQrLeYX\nSinl6+urLCwslK2trbKzs1Njx45VSim1d+9eVa1aNZUrVy5Vvnx5FRAQkPg7c+bMUUWKFFF2dnaq\nSJEiavHixerEiRMqa9asysrKSuXIkUM5ODgkeTwvLy81aNAgVaVKFWVvb6+aNWumwsPDlVJKXbhw\nQWmapmbNmqXc3NyUp6fnC2M5f/688vT0VPb29qpu3bqqT58+ytfX97H9JSQkKKWUCgsLU127dlX5\n8uVTjo6Oqnnz5ioqKkply5ZNWVpaqhw5cig7Ozt17do1ZTab1ahRo1TRokWVs7OzatOmTWKcSik1\nf/585e7urpydndWIESNUoUKF1Pbt25N8zs/6299f/tq58INbciTVlsBZwB2wAQ4DpZ7YxvWR+1WA\nC8/ZX5JPPC1YuVIpZ2elfvtNfzzrr1kq99jcatu/24wNTAiRroSGKlWzpp5Ux8Toy1YeX6lcxrio\nDac3GBucSBdMJqV69VLqzTeVunxZqRhTjOqwsoOqOL2iunrnqtHhpUlpOb8oVKiQ2rFjR+LjK1eu\nKCcnJ7V582allFLbtm1TTk5O6tatWyoqKkrZ29urM2fOKKWUun79ujp+/LhSSqm5c+eqmjVrPvdY\nXl5eqkCBAur48eMqOjpatWjRQnXs2FEp9TAJ7ty5s4qOjlaxsbHPjUUppapWrar69++v4uLiVFBQ\nkLKzs3ssqbawsEhMqhs0aKDatm2rIiIiVHx8vAoKClJKKRUQEKAKFiz4WJw//PCDqlq1qrp69aqK\ni4tTvXr1Uu3atVNKKXXs2DGVI0cOtWvXLhUXF6c+++wzZW1tbXhS/drlH0qpBE3T+gD+PBxS74Sm\naT3vBzsDaKlpWm/ABMQAbV73uEZ47z1wc9MvvV27Br16daOoQ1HarGjD6HdH06V8F6NDFEKkcefP\n652hGzfWO6BZWMCUfVMYvXs0mztupkLeCkaHKNIBKyv46Sf9NVStGmzYkJUFzRfwXdB3VJ9dnc0d\nN1PC6ZlVliIJ2vDkKT9Qfq/WKU890plv4cKFNGzYkHr16gFQp04dKlWqxMaNG2nRogWWlpYcPXqU\nAgUK4Orqiqur6386lq+vL6VKlQLg22+/pXz58syfPx/Q66GHDx9OtmzZXhiLl5cXBw8eZPv27Vhb\nW1OzZk0aN056Qqpr166xZcsWwsLCsLe3B3hu/ff06dP58ccfyZs3LwBDhw7F3d2dhQsXsnLlSho3\nbkz16tUTn8PUqVP/0zlICclSU62U2gx4PLFs+iP3fwR+TI5jGa1SJdi1S5+J8fJl+PZbTwK7BFJ/\nUX1u3L3BgOoDpKZNCJGkgwehaVN96M4+fcCszHzh/yXrz6xnd7fdFMpVyOgQRTqiaTBwoN7Y8847\nsGSJxtfvfE1++/zUmlOLNW3X8L8C/zM6zHTjVZPhlBAcHMyyZctYt24doCfc8fHxvPPOO9ja2rJ0\n6VLGjh1Lt27dqFGjBuPGjcPDw+MFe33o0U6B7u7umEwmbt26lbisQIGHQ3c+L5arV6/i4OCQmIA/\n2N/ly5efOubly5dxdHRMTKhf5hw0b94cCwuLxONaW1tz48YNrl69+thzsLW1xcnJ+D5uMqPiKyhS\nRB9yb+tWvSd2kZwe7O62m4VHF/K5/+eYldnoEIUQacyGDdCggd662KcP3Iu/R/uV7dl3ZZ8k1OK1\ntG8PS5dC27awcCF0e6sbs5rMotGvjdhweoPR4YmX8GRjXMGCBenUqRNhYWGEhYURHh5OZGQkAwYM\nAMDb2xt/f3+uX7+Oh4cHPXr0SHI/z3Lp0sNB24KDg7GxscHZ2TnJeJ4XS968eQkPDycmJiZx+4sX\nLyZ5zIIFCxIWFsadO3de+PwB3Nzc2LRp02PHjYqKIm/evOTNm/ex5xAdHU1oaOhLPfeUJEn1K3Jx\ngR07ICRELwex1/IR1CWIA1cP4LvaV4bcE0Ik+uUXeP99fcrxpk0h2hRNkyVNiDfH4+/rL9ONi9dW\nuzb8/jsMGQKjRkGD4g1Z32497697n9mHZhsdnniBPHnycO7cucTHHTt2ZN26dfj7+2M2m4mNjSUw\nMJCrV69y8+ZN1q5dS3R0NNbW1uTIkSOxNdfV1ZXLly9jMpmee7yFCxdy8uRJoqOj8fPzo1WrVomJ\n7aNlKC+Kxc3NjUqVKuHn54fJZGLXrl2JLdoPPNhfnjx58PHx4cMPP+T27dvEx8ezc+fOxLhDQ0Mf\nS7h79uzJ4MGDE5P0kJAQ1q5dC0DLli1Zv349e/bswWQyMXTo0LQxW2ZyFmgnx4003JEgKSaTUt27\nK1WpklI3bigVHRetmvzaRNVbUE96YQuRyZnNSo0YoVThwkrd71OkbsfcVjVm11CdV3dWpgSTsQGK\nDOfKFaXKlVOqXz+lEhKUOnXrlHKf6K4m/THJ6NAMl5bzizVr1ig3Nzfl4OCgxo8fr5RSav/+/crT\n01M5Ojqq3Llzq0aNGqlLly6pa9euKU9PT5UrVy7l4OCgateurU6cOKGUUiouLk41atRIOTo6KhcX\nlySP5eXlpQYPHqyqVKmicubMqZo2bapCQ0OVUk93LHzgWbEopdS5c+dUzZo1lZ2dnapbt67q27fv\nMzsqhoeHq86dOytXV1fl6OioWrRokXiM7t27KycnJ+Xg4JA4+sfEiROVh4eHsre3V8WKFVNDhgxJ\n3H7+/PnKzc1NOTs7q5EjR6rChQsb3lFRU2khs3+EpmkqrcX0IkrB8OH6Z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Pnp9XEJcbRe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\nzMxK9D9jLvFt8QiDfwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x29a886f8b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# predict\n",
    "f, a = plt.subplots(3, 1, figsize = (12, 8))\n",
    "for j, ds in enumerate([\"train\", \"val\", \"test\"]):\n",
    "    results = []\n",
    "    for x1, y1 in next_batch(X, Y, ds):\n",
    "        pred = z.eval({x: x1})\n",
    "        results.extend(pred[:, 0])\n",
    "    a[j].plot(Y[ds], label = ds + ' raw');\n",
    "    a[j].plot(results, label = ds + ' predicted');\n",
    "[i.legend() for i in a];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Not perfect but close enough, considering the simplicity of the model.\n",
    "\n",
    "Here we used a simple sin wave but you can tinker yourself and try other time series data. `generate_data()` allows you to pass in a dataframe with 'a' and 'b' columns instead of a function.\n",
    "\n",
    "To improve results, we could train with more data points, let the model train for more epochs, or improve the model itself."
   ]
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