week01/intro_to_pytorch/Seminar_1_PyTorch_Basics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8bab2952-db79-4139-a35c-0e4de926a16b",
   "metadata": {},
   "source": [
    "# Introduction to Deep Learning with PyTorch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "759cf58a-5e03-4b9a-87d7-588e4249df83",
   "metadata": {},
   "source": [
    "[PyTorch](https://pytorch.org/) is one of the frameworks to create, train, and inference Deep Neural Network (DNN) models. Besides, it allows you to do a lot of math and linear algebra operations (The syntax is similar to NumPy).\n",
    "\n",
    "The official documentation has a lot of [examples and tutorials](https://pytorch.org/tutorials/), which are very helpful for the beginners. We advise you to have a look at them. Here are some useful links:\n",
    "\n",
    "* [Basics](https://pytorch.org/tutorials/beginner/basics/intro.html): several tutorials on basic PyTorch stuff\n",
    "* [Training a classifier](https://pytorch.org/tutorials/beginner/blitz/cifar10_tutorial.html)\n",
    "\n",
    "This seminar is partially built on these tutorials and [this seminar](https://github.com/markovka17/dla/blob/2023/week01/seminar.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3ca88987-7ef2-496d-830e-cacbb9edd478",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Some imports\n",
    "\n",
    "# computation stuff\n",
    "import torch\n",
    "import numpy as np\n",
    "\n",
    "# plotting stuff\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='retina' # makes the quality higher\n",
    "\n",
    "import seaborn as sns\n",
    "sns.set_style(\"whitegrid\") # improves the quality of matplotlib images and adds grid"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1090b1c-46f9-468e-908f-5e7c8df9811a",
   "metadata": {},
   "source": [
    "## Creation of Tensors\n",
    "\n",
    "Tensors, basically, are generalization of matrices to more than 2 dimensions: $T \\in \\mathbb{R}^{D_1 \\times D_2 \\times D_3 \\times ... \\times D_n}$ (Note: `PyTorch` also supports tensors in $\\mathbb{C}$). `PyTorch` supports several creation techniques:\n",
    "\n",
    "* From existing iterable array-like object: Python List, NumPy array, etc.\n",
    "* Using built-in functions (similar to NumPy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "36f238ef-77e4-4988-b31e-7ec7589d0578",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3] tensor([1, 2, 3])\n"
     ]
    }
   ],
   "source": [
    "iterable_object = [1, 2, 3]\n",
    "tensor = torch.tensor(iterable_object)\n",
    "print(iterable_object, tensor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c7cfe588-b629-4765-b520-bfd930f73a22",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3] tensor([1, 2, 3])\n"
     ]
    }
   ],
   "source": [
    "iterable_object = np.array([1, 2, 3])\n",
    "tensor = torch.tensor(iterable_object)\n",
    "print(iterable_object, tensor)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3eb761e5-3777-4b87-8cb0-c919a80a5c87",
   "metadata": {},
   "source": [
    "Built-it methods are preferred to save memory and increase speed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d18feb19-7819-4de7-8060-588b6586e4e9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2] tensor([0, 1, 2])\n"
     ]
    }
   ],
   "source": [
    "numpy_array = np.arange(3)\n",
    "tensor = torch.arange(3)\n",
    "print(numpy_array, tensor)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b570d1e-ed4c-455a-a072-7fcd0e901bb8",
   "metadata": {},
   "source": [
    "For each tensor object, we can access some meta information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b14d7828-57f3-435e-92b0-b51d2bbbf507",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type of elements: torch.int64\n",
      "Size (or shape) : torch.Size([3])\n",
      "Number of dimensions: 1\n"
     ]
    }
   ],
   "source": [
    "print(f\"Type of elements: {tensor.dtype}\")\n",
    "print(f\"Size (or shape) : {tensor.size()}\") # equivalent to tensor.shape # Note that we do not have () here\n",
    "print(f\"Number of dimensions: {tensor.dim()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f9721c1-f33e-45f6-8494-baaa953b7b33",
   "metadata": {},
   "source": [
    "We can create multi-dimensional tensors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "23ca6671-372e-41ce-b14b-f7d624509435",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Zeros tensor: tensor([[[0., 0., 0., 0., 0.],\n",
      "         [0., 0., 0., 0., 0.]],\n",
      "\n",
      "        [[0., 0., 0., 0., 0.],\n",
      "         [0., 0., 0., 0., 0.]],\n",
      "\n",
      "        [[0., 0., 0., 0., 0.],\n",
      "         [0., 0., 0., 0., 0.]]])\n",
      "Shape: torch.Size([3, 2, 5])\n",
      "-----------\n",
      "\n",
      "Random N(0, 1) tensor: tensor([[[ 0.3452, -1.8426, -0.5053, -0.1491,  0.5294],\n",
      "         [ 0.5500, -1.2011,  1.2593, -0.6449,  0.3399]],\n",
      "\n",
      "        [[-2.1666,  2.4026,  0.3618,  1.5458, -0.5531],\n",
      "         [ 0.0579,  0.6697, -0.7179,  0.1489,  0.0243]],\n",
      "\n",
      "        [[-0.2898, -0.3655, -0.0576, -0.6845, -1.7430],\n",
      "         [ 2.4222,  1.2887, -0.4693, -0.3146,  1.0934]]])\n",
      "Shape: torch.Size([3, 2, 5])\n"
     ]
    }
   ],
   "source": [
    "desired_shape = (3, 2, 5) # or [3, 2, 5]\n",
    "\n",
    "tensor = torch.zeros(desired_shape)\n",
    "print(f\"Zeros tensor: {tensor}\")\n",
    "print(f\"Shape: {tensor.shape}\")\n",
    "print(\"-----------\\n\")\n",
    "\n",
    "tensor = torch.randn(desired_shape)\n",
    "print(f\"Random N(0, 1) tensor: {tensor}\")\n",
    "print(f\"Shape: {tensor.shape}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fb385a9-5b8f-4240-9d95-81ad4c25fc03",
   "metadata": {},
   "source": [
    "It is also possible to reshape the tensors. In PyTorch, there are 2 methods for this: `view` and `reshape`. They have the same syntax and the first one is preferred, however, the former does not work sometimes (you will get a `Runtime Error`). In such a case, usually you can replace `view` with `reshape` and everything will work fine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "019826ae-5f6d-4b34-8f64-ecd87f9bd1f1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Orig: tensor([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n",
      "\n",
      "Reshape: tensor([[0, 1, 2, 3, 4],\n",
      "        [5, 6, 7, 8, 9]])\n",
      "Reshape shape: torch.Size([2, 5])\n",
      "\n",
      "View: tensor([[0, 1, 2, 3, 4],\n",
      "        [5, 6, 7, 8, 9]])\n",
      "View shape: torch.Size([2, 5])\n",
      "\n",
      "Orig again: tensor([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n",
      "Orig shape: torch.Size([10])\n"
     ]
    }
   ],
   "source": [
    "tensor = torch.arange(10)\n",
    "print(\"Orig:\", tensor)\n",
    "print()\n",
    "\n",
    "tensor_reshape = tensor.reshape(2, 5)\n",
    "print(\"Reshape:\", tensor_reshape)\n",
    "print(\"Reshape shape:\", tensor_reshape.shape)\n",
    "print()\n",
    "\n",
    "tensor_view = tensor.view(2, 5)\n",
    "print(\"View:\", tensor_view)\n",
    "print(\"View shape:\", tensor_view.shape)\n",
    "print()\n",
    "print(\"Orig again:\", tensor)\n",
    "print(\"Orig shape:\", tensor.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08df4048-a329-401b-9320-21b18cf85500",
   "metadata": {},
   "source": [
    "Multi-dimensional reshapes are also supported:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "89aeb8f5-b95e-4b07-9875-69808e644042",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Old shape: torch.Size([100])\n",
      "New shape: torch.Size([2, 5, 10])\n"
     ]
    }
   ],
   "source": [
    "tensor = torch.arange(100)\n",
    "tensor_3d = tensor.view(2, 5, 10)\n",
    "print(\"Old shape:\", tensor.shape)\n",
    "print(\"New shape:\", tensor_3d.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d94b8020-b130-4151-9238-1a6b11068e65",
   "metadata": {},
   "source": [
    "Sometimes you may want to swap some dimensions or permute them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "aba7401b-ee24-4c60-acc7-07786db02088",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([2, 10, 5])\n",
      "\n",
      "torch.Size([5, 10, 2])\n"
     ]
    }
   ],
   "source": [
    "tensor_3d_v2 = tensor_3d.transpose(-1, -2) # swap the two last dimensions\n",
    "print(tensor_3d_v2.shape)\n",
    "print()\n",
    "\n",
    "# use permute if you want to change more than 2 dimensions\n",
    "tensor_3d_v3 = tensor_3d.permute(1, 2, 0) # put the 1 dim to the 0 place, 2 dim to the 1 place and 0 to the last place\n",
    "print(tensor_3d_v3.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40d16e4d-fd74-4532-a55c-7aa08db9a82f",
   "metadata": {},
   "source": [
    "The common operation is to add extra dimension (to satisfy required shape conditions for a given operation. For example, your layer want 3D input but you only have 2D input)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6f730e1b-975e-481a-9282-451323ccdaf2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([2, 5])\n",
      "torch.Size([2, 1, 5])\n",
      "torch.Size([2, 1, 5])\n"
     ]
    }
   ],
   "source": [
    "tensor = torch.arange(10).view(2, 5)\n",
    "print(tensor.shape)\n",
    "\n",
    "tensor_unsqueeze = tensor.unsqueeze(1) # add imaginary dimension at the first index\n",
    "print(tensor_unsqueeze.shape)\n",
    "\n",
    "# you can also do it like this\n",
    "tensor_new_axis = tensor[:, None, :]\n",
    "print(tensor_new_axis.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2015ddfd-f966-4d56-8c4d-cb5801c579b0",
   "metadata": {},
   "source": [
    "And in fact, there are many other useful functions that often come in handy.\n",
    "For example, `.chunk`, `.unfold`, `.flatten`, `.scatter`, `.gather`, ....\n",
    "\n",
    "So, feel free to dive into the PyTorch documentation and find out more yourself :)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83cac640-91e9-42f6-b773-06153fa8f6a8",
   "metadata": {},
   "source": [
    "# Tensor operations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5da6432f-6ba5-45ff-8e97-f93c161c78e3",
   "metadata": {},
   "source": [
    "`PyTorch` and `NumPy` syntax are similar. You can do many operations on tensors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "86e95e22-9366-4113-8d75-5f8fc0d444f0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([10, 100, 1000])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(tensor(0.0014), tensor(1427.5685), tensor(4.6509), tensor(-4.5790))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# aggregation funcs\n",
    "\n",
    "tensor = torch.randn(10, 100, 1000)\n",
    "print(tensor.shape)\n",
    "tensor.mean(), tensor.sum(), tensor.max(), tensor.min()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81ed62ce-1c0a-437c-a026-3ff11056f494",
   "metadata": {},
   "source": [
    "Note that aggregation funcs have `dim` and `keepdim` arguments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0a489216-c5be-4361-9772-f9a055a76574",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([100, 1000])\n",
      "torch.Size([1000])\n"
     ]
    }
   ],
   "source": [
    "# take mean over 0 dimension\n",
    "print(tensor.mean(dim=0).shape)\n",
    "\n",
    "# or over 0 and 1 dimensions\n",
    "print(tensor.mean(dim=(0, 1)).shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6c5fdb47-1ed9-440f-bc7e-f5f869856f5c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1, 100, 1])\n"
     ]
    }
   ],
   "source": [
    "# take mean over 0 and 2 dimensions and keep dimensions (i.e., the number of dimensions stays the same)\n",
    "print(tensor.mean(dim=(0, 2), keepdim=True).shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5ea3e73c-791c-4f76-ae54-66e07a3de501",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(999.1323)\n"
     ]
    }
   ],
   "source": [
    "# Frobenius norm\n",
    "print(tensor.norm(p='fro'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "154b3b6b-f38b-442e-93b7-8bace66bd6aa",
   "metadata": {},
   "source": [
    "Linear algebra is also similar to `NumPy`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5e8bb430-e061-4ee2-a4c4-6f0cc77085f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = torch.randn(10, 20)\n",
    "B = torch.randn(20, 30)\n",
    "\n",
    "C1 = A.matmul(B)\n",
    "\n",
    "# or\n",
    "C2 = A @ B\n",
    "\n",
    "# or\n",
    "C3 = torch.matmul(A, B)\n",
    "\n",
    "assert torch.equal(C1, C2)\n",
    "assert torch.equal(C2, C3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1239ec48-d1f2-4036-8ca0-5339116ec785",
   "metadata": {},
   "source": [
    "# Automatic Differentiation\n",
    "\n",
    "Gradient automatic computation using back-propagation:\n",
    "1. Create a tensor/tensors which requires gradient: `a = torch.tensor(..., requires_grad=True)`\n",
    "2. Define some differentiable scalar function `loss = whatever(a)`\n",
    "3. Request backward pass `loss.backward()`\n",
    "4. The gradient is available as `a.grad`\n",
    "    \n",
    "Note the loss must be a function of at least one tensor which requires gradient.\n",
    "For more information see https://pytorch.org/docs/stable/autograd.html\n",
    "\n",
    "Let's look on a simple example\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "4e958a07-d6b8-4256-9801-017f9d697595",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x: tensor([-2.9637e-04,  5.2876e-01, -3.9855e-01, -2.9846e-02])\n",
      "y: tensor([ 0.5001, -0.7062,  1.0790, -0.2472])\n",
      "dp / dx: tensor([ 0.5001, -0.7062,  1.0790, -0.2472])\n",
      "dp / dy: tensor([-2.9637e-04,  5.2876e-01, -3.9855e-01, -2.9846e-02])\n"
     ]
    }
   ],
   "source": [
    "x = torch.randn(4, requires_grad=True)\n",
    "y = torch.randn(4, requires_grad=True)\n",
    "z = x * y + 10\n",
    "p = z.sum()\n",
    "p.backward()\n",
    "print('x:', x.data)\n",
    "print('y:', y.data)\n",
    "print('dp / dx:', x.grad)\n",
    "print('dp / dy:', y.grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d68487cf-33fc-4752-bda5-0b11ef581bd7",
   "metadata": {},
   "source": [
    "**Detaching variables.**\n",
    "\n",
    "`.detach()` returns a copy of a variable, through which back-propagation doesn't pass.\n",
    "\n",
    "If you average or just store batch losses during the optimization, you'd better detach those losses before averaging or storing.\n",
    "Otherwise the computational graphs for each batch would be stored in memory as well as batch losses, so you run out of memory very fast.\n",
    "\n",
    "Also there is in-place version (`.detach_()`) which doesn't create detached copy of the variable, but detaches variable itself from its computational graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a42f24f3-5b8b-4fe4-b9b7-f88b2253081d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x: tensor([ 0.1702, -0.6234,  2.3864, -0.7037])\n",
      "y: tensor([ 0.8170, -0.3600, -0.1344,  0.5552])\n",
      "dp / dx: tensor([ 0.8170, -0.3600, -0.1344,  0.5552])\n",
      "dp / dy: None\n"
     ]
    }
   ],
   "source": [
    "x = torch.randn(4, requires_grad=True)\n",
    "y0 = torch.randn(4, requires_grad=True)\n",
    "y = y0.detach()\n",
    "z = x * y + 10\n",
    "p = z.sum()\n",
    "p.backward()\n",
    "print('x:', x.data)\n",
    "print('y:', y.data)\n",
    "print('dp / dx:', x.grad)\n",
    "print('dp / dy:', y.grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29c801d0-3ff8-4489-931a-a020ea53b23e",
   "metadata": {},
   "source": [
    "You can also reset the gradient of a specific variable.\n",
    "\n",
    "**Important**: without resetting, the gradients will sum\n",
    "\n",
    "For example, $(x^2)' = 2x, (\\frac{1}{x})' = \\frac{-1}{x^2}$. If we do not reset, we will get $2x + \\frac{-1}{x^2}$, see code below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "393c73a3-2e3c-495e-86d0-ca8878392cb4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x: tensor([1., 1., 1., 1.], requires_grad=True)\n",
      "dp / dx: tensor([2., 2., 2., 2.])\n",
      "x: tensor([1., 1., 1., 1.], requires_grad=True)\n",
      "dp / dx: tensor([1., 1., 1., 1.])\n"
     ]
    }
   ],
   "source": [
    "x = torch.tensor([1., 1, 1, 1], requires_grad=True)\n",
    "y = x ** 2\n",
    "p = y.sum()\n",
    "p.backward()\n",
    "print('x:', x)\n",
    "print('dp / dx:', x.grad)\n",
    "y = 1 / x\n",
    "p = y.sum()\n",
    "p.backward()\n",
    "print('x:', x)\n",
    "print('dp / dx:', x.grad) # will actually be 2x + (-1 / x^2) because we did not reset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "ee2c4795-a541-42db-b652-d6be10a43a02",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x: tensor([1., 1., 1., 1.], requires_grad=True)\n",
      "dp / dx: tensor([2., 2., 2., 2.])\n",
      "x: tensor([1., 1., 1., 1.], requires_grad=True)\n",
      "dp / dx: tensor([-1., -1., -1., -1.])\n"
     ]
    }
   ],
   "source": [
    "x = torch.tensor([1, 1, 1, 1.], requires_grad=True)\n",
    "y = x ** 2\n",
    "p = y.sum()\n",
    "p.backward()\n",
    "print('x:', x)\n",
    "print('dp / dx:', x.grad)\n",
    "x.grad.zero_()         # zero gradients\n",
    "y = 1 / x\n",
    "p = y.sum()\n",
    "p.backward()\n",
    "print('x:', x)\n",
    "print('dp / dx:', x.grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e11db77-afbc-4843-9551-bc24cdd70fa4",
   "metadata": {},
   "source": [
    "For memory saving, gradients are stored only for so called leaf-variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "bd1e8196-904c-4f29-8254-ac15ab6bb737",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x: tensor([-1.4009,  0.0221, -1.0029, -0.5139], requires_grad=True)\n",
      "y: tensor([-0.4009,  1.0221, -0.0029,  0.4861], grad_fn=<AddBackward0>)\n",
      "p: tensor(1.1044, grad_fn=<SumBackward0>)\n",
      "x.grad: tensor([1., 1., 1., 1.])\n",
      "y.grad: None\n",
      "p.grad: None\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_25547/3752779638.py:11: UserWarning: The .grad attribute of a Tensor that is not a leaf Tensor is being accessed. Its .grad attribute won't be populated during autograd.backward(). If you indeed want the .grad field to be populated for a non-leaf Tensor, use .retain_grad() on the non-leaf Tensor. If you access the non-leaf Tensor by mistake, make sure you access the leaf Tensor instead. See github.com/pytorch/pytorch/pull/30531 for more informations. (Triggered internally at aten/src/ATen/core/TensorBody.h:489.)\n",
      "  print('y.grad:', y.grad)\n",
      "/tmp/ipykernel_25547/3752779638.py:12: UserWarning: The .grad attribute of a Tensor that is not a leaf Tensor is being accessed. Its .grad attribute won't be populated during autograd.backward(). If you indeed want the .grad field to be populated for a non-leaf Tensor, use .retain_grad() on the non-leaf Tensor. If you access the non-leaf Tensor by mistake, make sure you access the leaf Tensor instead. See github.com/pytorch/pytorch/pull/30531 for more informations. (Triggered internally at aten/src/ATen/core/TensorBody.h:489.)\n",
      "  print('p.grad:', p.grad)\n"
     ]
    }
   ],
   "source": [
    "# Don't pay attention to UserWarning from Python\n",
    "\n",
    "x = torch.randn(4, requires_grad=True)  # leaf variable\n",
    "y = x + 1                               # not a leaf variable\n",
    "p = y.sum()                             # not a leaf variable\n",
    "p.backward()\n",
    "print('x:', x)\n",
    "print('y:', y)\n",
    "print('p:', p)\n",
    "print('x.grad:', x.grad)\n",
    "print('y.grad:', y.grad)\n",
    "print('p.grad:', p.grad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a276ef90-560f-4f38-aaa6-21282372f334",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x.grad: tensor([1., 1., 1., 1.])\n",
      "y.grad: tensor([1., 1., 1., 1.])\n",
      "z.grad: None\n",
      "p.grad: None\n",
      "x.is_leaf: True\n",
      "y.is_leaf: True\n",
      "z.is_leaf: False\n",
      "p.is_leaf: False\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_25547/3528970621.py:8: UserWarning: The .grad attribute of a Tensor that is not a leaf Tensor is being accessed. Its .grad attribute won't be populated during autograd.backward(). If you indeed want the .grad field to be populated for a non-leaf Tensor, use .retain_grad() on the non-leaf Tensor. If you access the non-leaf Tensor by mistake, make sure you access the leaf Tensor instead. See github.com/pytorch/pytorch/pull/30531 for more informations. (Triggered internally at aten/src/ATen/core/TensorBody.h:489.)\n",
      "  print('z.grad:', z.grad)\n",
      "/tmp/ipykernel_25547/3528970621.py:9: UserWarning: The .grad attribute of a Tensor that is not a leaf Tensor is being accessed. Its .grad attribute won't be populated during autograd.backward(). If you indeed want the .grad field to be populated for a non-leaf Tensor, use .retain_grad() on the non-leaf Tensor. If you access the non-leaf Tensor by mistake, make sure you access the leaf Tensor instead. See github.com/pytorch/pytorch/pull/30531 for more informations. (Triggered internally at aten/src/ATen/core/TensorBody.h:489.)\n",
      "  print('p.grad:', p.grad)\n"
     ]
    }
   ],
   "source": [
    "x = torch.randn(4, requires_grad=True)  # leaf variable\n",
    "y = torch.randn(4, requires_grad=True)  # leaf variable\n",
    "z = x + y    # not a leaf variable\n",
    "p = z.sum()  # not a leaf variable\n",
    "p.backward()\n",
    "print('x.grad:', x.grad)\n",
    "print('y.grad:', y.grad)\n",
    "print('z.grad:', z.grad)\n",
    "print('p.grad:', p.grad)\n",
    "print('x.is_leaf:', x.is_leaf)\n",
    "print('y.is_leaf:', y.is_leaf)\n",
    "print('z.is_leaf:', z.is_leaf)\n",
    "print('p.is_leaf:', p.is_leaf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f13f126e-aeea-4822-846c-0b013f232ebc",
   "metadata": {},
   "source": [
    "One can use `.retain_grad()` to save gradients for non-leaf variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "70863af2-a2c9-4e89-80fa-f25d4836c145",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dp / dx: tensor([ 1.3745, -0.3364, -1.3568, -1.1700])\n",
      "dp / dz: tensor([2.1605, 0.4119, 0.2898, 4.8588])\n",
      "dp / dw: tensor([1.0803, 0.2059, 0.1449, 2.4294])\n",
      "y grad: None\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_25547/3606136174.py:13: UserWarning: The .grad attribute of a Tensor that is not a leaf Tensor is being accessed. Its .grad attribute won't be populated during autograd.backward(). If you indeed want the .grad field to be populated for a non-leaf Tensor, use .retain_grad() on the non-leaf Tensor. If you access the non-leaf Tensor by mistake, make sure you access the leaf Tensor instead. See github.com/pytorch/pytorch/pull/30531 for more informations. (Triggered internally at aten/src/ATen/core/TensorBody.h:489.)\n",
      "  print('y grad:', y.grad) # None, because we did not retain graph for y\n"
     ]
    }
   ],
   "source": [
    "x = torch.randn(4, requires_grad=True)   # leaf variable\n",
    "z = torch.randn(4, requires_grad=True)   # leaf variable\n",
    "w = z * 2      # not a leaf variable\n",
    "y = x * w + 1  # forward pass before retaining gradient is ok\n",
    "p = y.sum()\n",
    "\n",
    "w.retain_grad()\n",
    "\n",
    "p.backward()\n",
    "print('dp / dx:', x.grad)\n",
    "print('dp / dz:', z.grad)\n",
    "print('dp / dw:', w.grad)\n",
    "print('y grad:', y.grad) # None, because we did not retain graph for y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b4449a3-6fa4-4272-aa1b-334cab97dd87",
   "metadata": {},
   "source": [
    "Note that even if there are non-leaf variables which require gradient in the computational graph, `.backward()` fails.\n",
    "For correct work at least one of the leaf variables **must** require gradient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "3617922a-2c22-4952-8320-db668af84acf",
   "metadata": {},
   "outputs": [
    {
     "ename": "RuntimeError",
     "evalue": "element 0 of tensors does not require grad and does not have a grad_fn",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[23], line 9\u001b[0m\n\u001b[1;32m      6\u001b[0m y \u001b[38;5;241m=\u001b[39m x \u001b[38;5;241m*\u001b[39m w \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m1\u001b[39m  \u001b[38;5;66;03m# forward pass before retaining gradient is ok\u001b[39;00m\n\u001b[1;32m      7\u001b[0m p \u001b[38;5;241m=\u001b[39m y\u001b[38;5;241m.\u001b[39msum()\n\u001b[0;32m----> 9\u001b[0m \u001b[43mp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mbackward\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/miniconda3/envs/env9/lib/python3.9/site-packages/torch/_tensor.py:522\u001b[0m, in \u001b[0;36mTensor.backward\u001b[0;34m(self, gradient, retain_graph, create_graph, inputs)\u001b[0m\n\u001b[1;32m    512\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m has_torch_function_unary(\u001b[38;5;28mself\u001b[39m):\n\u001b[1;32m    513\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m handle_torch_function(\n\u001b[1;32m    514\u001b[0m         Tensor\u001b[38;5;241m.\u001b[39mbackward,\n\u001b[1;32m    515\u001b[0m         (\u001b[38;5;28mself\u001b[39m,),\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    520\u001b[0m         inputs\u001b[38;5;241m=\u001b[39minputs,\n\u001b[1;32m    521\u001b[0m     )\n\u001b[0;32m--> 522\u001b[0m \u001b[43mtorch\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mautograd\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mbackward\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    523\u001b[0m \u001b[43m    \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mgradient\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mretain_graph\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcreate_graph\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43minputs\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43minputs\u001b[49m\n\u001b[1;32m    524\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/miniconda3/envs/env9/lib/python3.9/site-packages/torch/autograd/__init__.py:266\u001b[0m, in \u001b[0;36mbackward\u001b[0;34m(tensors, grad_tensors, retain_graph, create_graph, grad_variables, inputs)\u001b[0m\n\u001b[1;32m    261\u001b[0m     retain_graph \u001b[38;5;241m=\u001b[39m create_graph\n\u001b[1;32m    263\u001b[0m \u001b[38;5;66;03m# The reason we repeat the same comment below is that\u001b[39;00m\n\u001b[1;32m    264\u001b[0m \u001b[38;5;66;03m# some Python versions print out the first line of a multi-line function\u001b[39;00m\n\u001b[1;32m    265\u001b[0m \u001b[38;5;66;03m# calls in the traceback and some print out the last line\u001b[39;00m\n\u001b[0;32m--> 266\u001b[0m \u001b[43mVariable\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_execution_engine\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_backward\u001b[49m\u001b[43m(\u001b[49m\u001b[43m  \u001b[49m\u001b[38;5;66;43;03m# Calls into the C++ engine to run the backward pass\u001b[39;49;00m\n\u001b[1;32m    267\u001b[0m \u001b[43m    \u001b[49m\u001b[43mtensors\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    268\u001b[0m \u001b[43m    \u001b[49m\u001b[43mgrad_tensors_\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    269\u001b[0m \u001b[43m    \u001b[49m\u001b[43mretain_graph\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    270\u001b[0m \u001b[43m    \u001b[49m\u001b[43mcreate_graph\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    271\u001b[0m \u001b[43m    \u001b[49m\u001b[43minputs\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    272\u001b[0m \u001b[43m    \u001b[49m\u001b[43mallow_unreachable\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m,\u001b[49m\n\u001b[1;32m    273\u001b[0m \u001b[43m    \u001b[49m\u001b[43maccumulate_grad\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m,\u001b[49m\n\u001b[1;32m    274\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n",
      "\u001b[0;31mRuntimeError\u001b[0m: element 0 of tensors does not require grad and does not have a grad_fn"
     ]
    }
   ],
   "source": [
    "# will not work because leafs do not require grad\n",
    "\n",
    "x = torch.randn(4, requires_grad=False)   # leaf variable\n",
    "z = torch.randn(4, requires_grad=False)   # leaf variable\n",
    "w = z * 2      # not a leaf variable\n",
    "y = x * w + 1  # forward pass before retaining gradient is ok\n",
    "p = y.sum()\n",
    "\n",
    "p.backward()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "c75de536-37ad-4e99-8519-39bd0094abc7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# will work because at least one leaf variable requires grad\n",
    "\n",
    "x = torch.randn(4, requires_grad=False)   # leaf variable\n",
    "z = torch.randn(4, requires_grad=True)   # leaf variable\n",
    "w = z * 2      # not a leaf variable\n",
    "y = x * w + 1  # forward pass before retaining gradient is ok\n",
    "p = y.sum()\n",
    "\n",
    "p.backward()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "03437945-b8c3-4da2-ae54-be2df54cc871",
   "metadata": {},
   "outputs": [],
   "source": [
    "# will work because at least one leaf variable requires grad\n",
    "\n",
    "x = torch.randn(4, requires_grad=True)   # leaf variable\n",
    "z = torch.randn(4, requires_grad=False)   # leaf variable\n",
    "w = z * 2      # not a leaf variable\n",
    "y = x * w + 1  # forward pass before retaining gradient is ok\n",
    "p = y.sum()\n",
    "\n",
    "p.backward()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "56e1cd4f-c097-412d-aba4-68c0eed78b41",
   "metadata": {},
   "outputs": [
    {
     "ename": "RuntimeError",
     "evalue": "can't retain_grad on Tensor that has requires_grad=False",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[26], line 8\u001b[0m\n\u001b[1;32m      5\u001b[0m y \u001b[38;5;241m=\u001b[39m x \u001b[38;5;241m*\u001b[39m w \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m1\u001b[39m  \u001b[38;5;66;03m# forward pass before retaining gradient is ok\u001b[39;00m\n\u001b[1;32m      6\u001b[0m p \u001b[38;5;241m=\u001b[39m y\u001b[38;5;241m.\u001b[39msum()\n\u001b[0;32m----> 8\u001b[0m \u001b[43mw\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mretain_grad\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     10\u001b[0m p\u001b[38;5;241m.\u001b[39mbackward()\n",
      "\u001b[0;31mRuntimeError\u001b[0m: can't retain_grad on Tensor that has requires_grad=False"
     ]
    }
   ],
   "source": [
    "# will not work\n",
    "x = torch.randn(4, requires_grad=False)   # leaf variable\n",
    "z = torch.randn(4, requires_grad=False)   # leaf variable\n",
    "w = z * 2      # not a leaf variable\n",
    "y = x * w + 1  # forward pass before retaining gradient is ok\n",
    "p = y.sum()\n",
    "\n",
    "w.retain_grad()\n",
    "\n",
    "p.backward()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "5bdc2eba-e8ef-47dd-bc17-c9d65329d02d",
   "metadata": {},
   "outputs": [
    {
     "ename": "RuntimeError",
     "evalue": "can't retain_grad on Tensor that has requires_grad=False",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[27], line 8\u001b[0m\n\u001b[1;32m      5\u001b[0m y \u001b[38;5;241m=\u001b[39m x \u001b[38;5;241m*\u001b[39m w \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m1\u001b[39m  \u001b[38;5;66;03m# forward pass before retaining gradient is ok\u001b[39;00m\n\u001b[1;32m      6\u001b[0m p \u001b[38;5;241m=\u001b[39m y\u001b[38;5;241m.\u001b[39msum()\n\u001b[0;32m----> 8\u001b[0m \u001b[43mw\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mretain_grad\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     10\u001b[0m p\u001b[38;5;241m.\u001b[39mbackward()\n",
      "\u001b[0;31mRuntimeError\u001b[0m: can't retain_grad on Tensor that has requires_grad=False"
     ]
    }
   ],
   "source": [
    "# will not work, because w relies on z, not on x\n",
    "x = torch.randn(4, requires_grad=True)   # leaf variable\n",
    "z = torch.randn(4, requires_grad=False)   # leaf variable\n",
    "w = z * 2      # not a leaf variable\n",
    "y = x * w + 1  # forward pass before retaining gradient is ok\n",
    "p = y.sum()\n",
    "\n",
    "w.retain_grad()\n",
    "\n",
    "p.backward()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "89deadf6-e1b7-4a4d-ae80-10cb84a67956",
   "metadata": {},
   "outputs": [],
   "source": [
    "# will work\n",
    "x = torch.randn(4, requires_grad=False)   # leaf variable\n",
    "z = torch.randn(4, requires_grad=True)   # leaf variable\n",
    "w = z * 2      # not a leaf variable\n",
    "y = x * w + 1  # forward pass before retaining gradient is ok\n",
    "p = y.sum()\n",
    "\n",
    "w.retain_grad()\n",
    "\n",
    "p.backward()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "469c123e-d851-4248-bbb0-b17985d183d0",
   "metadata": {},
   "source": [
    "# Datasets\n",
    "\n",
    "To train or inference your DNN model, you need input data (and ground truth \\ desired output data for training). In `PyTorch`, you need two objects for this.\n",
    "\n",
    "1. `Dataset`: the ordered set of all data that you have. Given the index $i$, returns $X_i$ (or anything else from `data[i]`, for example $Y_i$) from the dataset\n",
    "2. `DataLoader`: an iterable object that combines your data into batches: $B = (\\text{item}_1, ... \\text{item}_{\\text{batch size}})$, "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "bd395810-47f4-4c3d-bbcf-405dbbdf8d71",
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch.utils.data import DataLoader, Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c842e04-43ad-4b2a-9ca2-c945871f1418",
   "metadata": {},
   "source": [
    "The `Dataset` is a class that initiates our data somehow in the constructor. It also has two main methods `__getitem__` and `__len__`.\n",
    "Let's make a simple dataset, where one element is a vector of size 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "0fafea3b-4588-4984-95c6-a2a6a2360305",
   "metadata": {},
   "outputs": [],
   "source": [
    "class SimpleDataset(Dataset):\n",
    "    \n",
    "    def __init__(self, data: torch.Tensor):\n",
    "        self.data = data\n",
    "    \n",
    "    def __getitem__(self, index: int):\n",
    "        return self.data[index]\n",
    "\n",
    "    def __len__(self):\n",
    "        return len(self.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "79bfa014-ffac-4717-80df-48b1976a166a",
   "metadata": {},
   "outputs": [],
   "source": [
    "example_data = torch.randn(1000, 10) # X = 1000 elements (vectors) of size 10\n",
    "simple_dataset = SimpleDataset(example_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "37629622-e0f4-4966-9efa-921df596a61f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ 0.1542,  2.4574, -0.4700, -0.4856, -0.0843,  0.6401, -0.7215,  1.2653,\n",
       "         0.5506, -0.5688])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simple_dataset[10] # get X_10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "f15a8c3e-36b3-4850-820f-a0ca9efcbd24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(simple_dataset) # length of the dataset, i.e. the total number of elements"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5ee5e0d-6349-4a28-960e-340bb2fe0422",
   "metadata": {},
   "source": [
    "`DataLoader` is an iterable object (iterator, to be precise). It provides you with a sequence of batches. To access the batch, usually you work with a `for`-loop:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "86115e62-4972-4e08-afe7-a8ca8a0ecd31",
   "metadata": {},
   "outputs": [],
   "source": [
    "simple_dataloader = DataLoader(simple_dataset, batch_size=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "7cd367f9-3e24-48c3-a025-41765b641442",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([20, 10])\n"
     ]
    }
   ],
   "source": [
    "for i, element in enumerate(simple_dataloader): # enumerate allows to get batch index in the dataloader sequence\n",
    "    print(element.shape) # first dim is batch_size, the second and after are element shape\n",
    "    if i == 0: # break after the first element (for this example)\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "343fd5bd-8ac9-405b-8aa6-6a94aaacb944",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([20, 10])\n",
      "torch.Size([20, 10])\n"
     ]
    }
   ],
   "source": [
    "# one may use islice or next to get one batch from the dataloader\n",
    "\n",
    "batch = next(iter(simple_dataloader))\n",
    "print(batch.shape)\n",
    "\n",
    "from itertools import islice\n",
    "\n",
    "first_batch = list(islice(simple_dataloader, 0, 1))[0] # [0] because islice returns [batch]\n",
    "print(first_batch.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89836cbc-b969-4e16-a8cc-fbb7e194d61d",
   "metadata": {},
   "source": [
    "Note that here batch is a tensor, because we have the dataset returns only **one** object. If the dataset returns 2 objects, for example $x$ and $y$, the batch will be a tuple `(x, y)`. We can also work with batches as dictionaries, we will see it in the future lessons"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1509b27-3202-4bcb-a4fb-d9466a1cfe62",
   "metadata": {},
   "source": [
    "# Optimization (Training a model, finding local minima, etc.)\n",
    "\n",
    "Training a model is basically the task of finding local minima of the loss function. Before we move to Deep Neural Networks, let's see how we can find the minima of some function, for example, $f(x) = (x - 10)^2 + 14$. To do so, we will start from a random point $x_s$ and repeat the following steps:\n",
    "\n",
    "1. Calculate the loss: here, it is $f(x_s)$ itself\n",
    "2. Do one step of gradient descent: we will use `torch.optim.SGD` with some learning rate (a.k.a. step size)\n",
    "3. Set $x_s$ to its updated value from the previous step\n",
    "\n",
    "We will repeat these steps `NUM_STEP` times. Let's look at the code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "924cbe50-98f5-46b4-b938-869f57fb1a38",
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(x):\n",
    "    return (x - 10) ** 2 + 14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8e897488-9d62-4502-b035-528349450fbf",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 432,
       "width": 589
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = torch.linspace(-100, 100, 100)\n",
    "y = func(x)\n",
    "\n",
    "plt.plot(x, y)\n",
    "plt.scatter([10], [14], label='Minimum', c='red')\n",
    "plt.legend()\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "833b810e-ef36-4d0c-a467-de6df8fff8b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "from IPython import display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "50786435-dc94-44d6-9926-89f5e8a9f044",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AoIwqX768vvnmG02ZMkU9e/bM9Zf6hIQErVixQk8++aSef/55p64wyKz1Ikn3339/nk+Zy9StWzf78e7du/Pt//DDDxeqj2MhY2erX7++BgwYYD8vqaubvL29syWTsnIscF6/fv08ExJSxsquTAUpSt++ffs8k4SS1Lx5c8MqpaxzFxkZqSNHjkiSmjRpkm+MUkaSJfOpedeuXdPx48fz7O+4Wi0/69at07Fjx3Ts2LESW68pk81m0y+//KIXX3xRR48elaenp7p06aJHHnlEAwcOVPv27eXu7q6TJ09q4sSJevjhh3XmzJkcx8q6ndDT07NAMTiuDMtc/QgAcA3UbAIAoIzr06eP+vTpo+joaG3fvl179+7VoUOHdPjw4WyrCdatW6cnnnhCc+fOdUohbccnl23fvl3nzp3L9x6bzWY/Pn/+fJ59K1WqpPr16+c7ZmZyQZKOHDkim81WoMTXjRg7dqyWLFmilJQU7dy5U5s3b1avXr2K5bVuVIMGDfJNCDg+7r4gxeUd+8fFxeXb33FO8ut3+PBhSbInljLt27fPfpyUlFTgelyOWykvXLiQZ5Iqc1VcaWK1WvXqq69q+fLlkjJqvL377ruqVq2aoV9ISIhef/117d27V6dOndJTTz2l3377TZUqVTL0y7qdMDU1VeXKlcs3DsckVUFXQwEASgaSTQAAQJIUGBioe++9V/fee68k2Z/8tmjRIi1ZssReu+nEiRP64osvDFuYbpTjI+03btxY6Psdiw7npCCFiLP2S0lJUXx8fLE8lU7KeKz8o48+ai/Q/sUXX5S4ZFOFChXy7ZNZg6mg/TO3D0oqUB2wgs5dzZo17ceZxaQzOX6/wsPDNWfOnAKN6Si/lXyBgYGFHrOk++GHH+yJpsxaXI7znalBgwaaNm2aBg0apDNnzujChQv68ssv9c9//tPQr3z58obzpKSkAiWbHFcz5balEwBQMrGNDgAA5MjDw0OdOnXSRx99pNmzZxt+2fv111+dsq2lICtc8pKenp7n9YKuhvDx8TGcZ60x42xjxoyxv2ZwcLDWrFlTrK9XWIVd1VUcq8AKOneO38us83bt2rUix5Hfd6wgSRNXkvlUvkwvv/xyjommTOXLlzfUUXNMTGfKLCaf6dKlSwWKxbGf48o4AEDJx8omAACQrw4dOmjMmDH67LPPJGX8QhocHKzOnTsXaVzHJM8333yTrWB5URU0IZaYmGg4z7oSw9mqVKmiYcOG2X+p//LLL9W3b99i27qXX5Hrkqigc+e41TPrvDl+v4KCgvTtt986J7hSbP/+/fYVgz4+Prr11lvzvcexjlpCQoLOnDljqNFVuXJl+fv728c9d+6cGjdunOeYycnJhpVqjRo1KtT7AACYi5VNAACgQHr37m04L8jj6/Pj+GhzZ4yXVX41nXLq5+XlVezJJkkaNWqUfave8ePH9fvvvxf43sJuSSvqCjIzFKR+l5RRUylT1lpBjt+vgq6mKesuXrxoP/b398/1wQGOsn7uOa0oc0wuZa2tlZNDhw7Zj93d3dWwYcN87wEAlBwkmwAAQIFk3S6UteivVPjtVG3btrUf79mz58YCy0N0dLSh2HNuHAtJt2zZsthWGDmqWLGinn76afv5119/ne+WrUyO9aRiYmLy7X/s2LFCx2e2/fv3F6if49w5PplOkmFVzpEjR7IVvEd2jtsXr127ZijIn5us30F/f/9sfbp27Wo/LsgTH3fu3Gk/bt++fY4/bwAAJRfJJgAAUCBHjx41nDsWZs7k+AthQVbc3HHHHfbj1atXF8vqkyVLlhSqj+MvxcXtqaeestezCQkJ0eLFiwt0X+3ate3HWeclJytXrryh+My0Z88ehYWF5dnnxIkThhUwXbp0MVyvW7eufUVNamqqFixY4PxASxnHf9cJCQk6cOBAvvds27bNfuzp6Znjz4a+ffvaj7du3WpYkZaTRYsW2Y/79euXbwwAgJKFZBMAAGXQjBkz9NdffxW4f2Jior777jv7eZUqVdSyZcts/RwLATtux8lN27Zt7QmCpKQkvfbaa4bHneclJSUl3yeFSRnvNa+kxaJFixQcHCwpY2XWI488UqDXdwY/Pz89++yz9vPJkycX6P23adPGvvpq//79OnXqVK5958yZoxMnThQ92JvMZrPpww8/zHVlTXp6uv71r3/Zzzt27JhjHSDHz/eLL74o1Cqv4tjaWdK1atXK8O/4yy+/zLPmV0JCgqEWVvv27XPchtq2bVu1adNGUsbcffrpp7mOOW/ePIWEhEjKqMP10EMPFfJdAADMRrIJAIAy6MCBA3r66ac1aNAgzZkzJ88VRfv379ewYcN0/Phxe9uzzz6bYy2XZs2a2Y/Xrl1boMTJxIkT7U8U27Jli4YNG5bnFqozZ85o0qRJCgoKynfrnaenp+Lj4zVy5EjDCphMCxcu1DvvvGM/f+SRR1S/fv18Y3amYcOGqWrVqpKkiIiIAiU4qlatai/KbLPZ9Le//S3bSpG0tDRNnz5dH374oUtuQfL09NT69ev1+uuvZ6s5FRsbq7/97W/2FTUWi0V/+9vfchznwQcftH9W8fHxGjp0qObOnZvrdzMuLk5Lly7V8OHD9cEHHzjxHWUUKW/evLmaN2+u119/3aljO4ubm5tGjBhhP9+yZYtefvnlHH9GnD17Vs8884wh2Tlq1Khcx37llVfsx8uWLdOnn36q1NRUQ58VK1boo48+sp+PHDlSgYGBN/ReAADm4Wl0AACUYQcPHtTBgwf1/vvvq169emrSpIkqVaokDw8PRUdH68iRIwoPDzfcc+edd2rYsGE5jnfbbbfJ29tbSUlJOnLkiO677z516dJF/v7+9pU4PXv2VK9evez3NGvWTJ999pkmTJigxMRE7d+/X0OGDFG9evXUqlUrBQQEKCUlRZcvX9axY8cKtGIqU/v27RUQEKDVq1dr0KBBateunRo1aqSUlBTt27fPsOKpcePG+sc//lGYj88pvL29NWbMmEInNiZMmKDt27fLarXq6NGjuvvuu9WtWzdVr15dMTEx2rVrly5fvixfX1+98sorTk+cFLfnnntOs2bN0m+//abVq1erW7duqly5sqKiorR9+3ZD/aXnnntOnTp1ynEcd3d3ffHFFxo5cqQOHz6suLg4vfvuu/rkk0/Url07Va9eXe7u7oqNjdWZM2d0+vRp+xbQu++++6a816J66623dPDgQUOb46q/yMjIHFcH/etf/7KvNnI0atQobdmyRbt375YkrVq1SuvXr1eHDh1Up04dWa1WnTlzRgcOHDDUGRs6dKj69OmTa5zdu3fX888/b18JNXXqVC1ZskSdOnVSuXLldOjQIUNSu2fPnhozZkwBPwUAQElCsgkAgDKoe/fuOnDggCGRFBoammcxbW9vb40ePVrPPfec4WlojipUqKDXX39d7733nmw2m8LCwrJtYfP19TUkm6SM2k1z587Vm2++aV+BlF88tWvXVo0aNfJ9rx9//LHS0tK0fv167d27V3v37s3W59Zbb9WkSZNUoUKFfMcrDkOGDNH06dMVERFR4HtuvfVWffDBB3rnnXeUnp6upKQk/fnnn4Y+VatW1RdffFHgwuMlSe3atfX9999r/PjxioqK0tq1a7P1cXd317PPPqsJEybkOValSpX0yy+/6N///rcWLFigtLQ0xcXFafPmzbne4+3trVtuuaXI7+NmCA0NzbN2V2pqao7XcyuYXq5cOU2ZMkUffPCBfvvtN0kZ21YdazM58vT01PPPP6/nn38+31hfeukleXl5afLkyUpNTVVkZKRWrFiRrd/999+v999/P9efNQCAko2f3gAAlEFDhgzRkCFDdPz4ce3cuVP79u3T6dOnde7cOftjy8uXL68qVaqoefPm6tq1q+655x4FBATkO/bjjz+uZs2aad68edq/f78iIyOVmJiY71OtWrRooUWLFmnz5s1as2aN9uzZo8jISF27dk1eXl6qVKmSGjZsqFtvvVW9evVS+/btC/TUOD8/P3377bdauXKlfvvtNx07dkyXLl2Sv7+/mjdvrv79++vhhx8u0CPei4uXl5deeOEFvfXWW4W675FHHlG7du00Y8YMbdu2TVFRUSpXrpzq1Kmju+66S48++qgCAwML9PSvkqhDhw5aunSp5s2bp9WrVysiIkIJCQmqVq2aunXrpqFDhxY4IeTt7a333ntPzz77rJYuXapt27YpJCREMTExslqtqlChgurWrasWLVqoW7duuu222wxP/Str/Pz89H//938aNWqUFi9erD179ig0NFRXr16Vm5ub/P391aRJE3Xp0kWDBg1S9erVCzSuxWLRCy+8oLvvvlvz58/Xli1bdP78eaWlpalq1apq166dBgwYoB49ehTzOwQAFCeLrSDPMwUAAHAR27dvt9ec6dKli2bPnm1yRAAAAGULBcIBAAAAAADgNCSbAAAAAAAA4DQkmwAAAAAAAOA0JJsAAAAAAADgNCSbAAAAAAAA4DQkmwAAAAAAAOA0FpvNZjM7CAAAAAAAAJQOrGwCAAAAAACA05BsAgAAAAAAgNOQbAIAAAAAAIDTkGwCAAAAAACA05BsAgAAAAAAgNOQbAIAAAAAAIDTeJgdAJCV1WpVYmKiJMnDw0MWi8XkiAAAAAAAKH1sNpvS0tIkST4+PnJzc86aJJJNKHESExN19OhRs8MAAAAAAKDMaNGihcqXL++UsdhGBwAAAAAAAKdhZRNKHA+P61/LFi1ayNPT08RoCiY1NdW+GstVYoYRc+j6mEPXxvy5PubQ9TGHro85dG3Mn+tzxTl0jNnxd/GiItmEEsexRpOnp6e8vLxMjKbwXDFmGDGHro85dG3Mn+tjDl0fc+j6mEPXxvy5PlecQ2fWS2YbHQAAAAAAAJyGZBMAAAAAAACchmQTAAAAAAAAnIZkEwAAAAAAAJyGZBMAAAAAAACchmQTAAAAAAAAnIZkEwAAAAAAAJyGZBMAAAAAAACchmQTAAAAAAAAnIZkEwAAAAAAAJzGw+wAAAAAAKAorFar4uLidPXqVaWkpCg9Pd3skExhtVrtx2fOnJGbG2sLXAnz5/rMmEN3d3f5+vqqYsWK8vb2LvbXKyiSTQAAAABc1rVr1xQRESGbzWZ2KKaz2Wzy8Mj4FS89Pd3wiy9KPubP9Zkxh2lpaUpOTtaVK1cUEBCgmjVrymKxFPvr5odkEwAAAACXlFOiyWKxyN3d3cSozJW5kqIsfwaujPlzfTd7DtPS0uzHsbGx8vLyUpUqVW7Ka+eFZBMAAAAAl2O1Wg2JJj8/PwUGBsrX17dE/FXfDFarVYmJiZIkHx8ftmG5GObP9Zkxh+np6YqJiVFkZKQkKSoqSv7+/vLy8ir2184L314AAAAALicuLs6QaKpTp47Kly9fZhNNAMomd3d3Va5cWZUrV7a3xcXFmRhRBpJNAAAAAFzO1atX7ceBgYEkmQCUaf7+/vbj+Ph4EyPJQLIJAAAAgMtJSUmRlFGjydfX1+RoAMBc5cqVsyfdM38+molkEwAAAACXk56eLiljCwmrmgCUdY4PRygJTzIk2QQAAAAAAACnIdkEAAAAAAAApyHZBAAAAAAAAKch2QQAAAAAAACnIdkEAAAAAAAApyHZBAAAAAAw1aJFi9S8eXM1b95c4eHhxfY6ma/x9ddfF9trAJA8zA4AAAAAAFDybd++XSNGjLCf+/r66q+//pKPj0+e9yUlJalnz56Ki4uzt82aNUtdu3YttlgBmIuVTQAAAABQFDabtHat9OSTUrNmUoUKkptbxv9v1iyjfe3ajH6lSEJCgtasWZNvv7Vr1xoSTQBKP1Y2AQAAAMCNSE6WpkyRJk2Sjh3Lfj0uTjpxIuP/Zs2SmjeXxo6VnntO8vK6+fE6Ubly5ZScnKwlS5aof//+efZdsmSJ4Z6cDBw4UAMHDnR6nFkdy2meADgdK5sAAAAAoLCOHJHat5fGj8850ZSTY8cy+rdrJx09WqzhFbegoCBJ0l9//aWoqKhc+12+fFlbtmyRJPXt2/emxAbAfGV2ZdPly5d14MABHThwQMHBwQoODlZMTIwkacCAAfr444/zHSMxMVGbNm3Sli1bdPDgQYWGhiohIUF+fn5q0KCBevXqpccee0xVq1YtUEyJiYn66aeftHLlSoWFhSklJUU1atTQ7bffruHDh6t27doFGiciIkKzZ8/Wn3/+qQsXLsjLy0t169bVvffeqyeeeCLfPdWZ9uzZo59//lm7d+/WpUuX5O/vrxYtWmjAgAF64IEHCjRGWZKUZtWVJKtal7Ll0QAAAMhi2zbpvvukK1du7P4jR6QePaQVK6Ru3Zwb203Ss2dP7dq1S1FRUfr999/11FNP5dhv+fLlSktLU9WqVdWjRw+tWLHi5gYKwBRlNtnUo0ePIt1/9OhRPf7440pISMh2LSYmRvv27dO+ffs0c+ZMffDBB7rvvvvyHO/s2bMaPXq0QkJCDO1nzpzRmTNnNH/+fH366ae644478hxn3bp1evXVVw17ohMTExUbG6uDBw9q/vz5mjJliurXr5/nOF9//bUmT54sq9Vqb7t06ZI2b96szZs3a9myZfrqq69Urly5PMcpK/aExuiZZVFKSrOpz8l9mv50F7m7WcwOCwAAAM525Ih0773S//9D9Q27ciUjYfXXX1KLFk4J7WZyd3fX/fffr5kzZ2rJkiW5Jpsyt9A98MADcnd3z3W8RYsW6Y033pCUUeOpTp06huvDhw/Xjh071KVLF82ePVsXL17U9OnTtW7dOl28eFE+Pj5q3bq1RowYoT59+uT6Os2bN5ckjRs3Ti+++GKeMVSrVk1z5szRsmXLdPbsWbm7u6t58+Z65plndPvtt9vvi4uL0y+//KLff/9doaGhcnNzU5s2bTR69Gh17979ht5vpvDwcPuKsH//+9/Zthq+/vrrWrx4sWrXrq1169YpKirK/rlcuHBB/v7+6tChg8aNG6emTZsaxp05c6Y2bdqk8+fPy8/PT927d9dLL72kevXq5fr5AQXFNjpJtWrVUq9evQp1T1xcnD3R1KFDB73yyiuaMWOGFi9erGnTpunRRx+Vm5ub4uLi9Pe//10bNmzIcyzHRNOQIUM0c+ZMzZ07VxMmTJCvr6/i4uI0YcIEHTlyJNdxDh8+rAkTJiguLk6+vr6aMGGC5s6dq5kzZ2rIkCGSpJCQEI0ePTrPAn1z587VN998I6vVqnr16unDDz/U/PnzNWnSJPsTI/7880+9+eabhfrMSrPvN55RUlrGiqYNJy5pyb4IkyMCAACA0yUnS4MGFT3RlOnKFWngQCklxTnj3WQPPfSQpIzfQ06cOJHt+smTJ3Xo0CFDX2fYvXu3HnroIc2cOVOhoaFKTk5WTEyMNm/erNGjR2vatGlFfo24uDgNGzZMH3/8sQ4dOqS4uDjFxsZqx44deu655zRz5kxJ0rlz5/TYY4/p008/1ZEjRxQfH69r167pr7/+0tNPP62lS5cWOZaCOnr0qAYMGKDp06crJCRESUlJioyM1MqVKzVkyBDt2rVLkrR161Y9/PDDmj17tkJCQpScnKzLly9r+fLleuSRR3KcS6CwyuzKprFjx6pNmzZq06aNqlSpYsgYF4Sbm5vuvfdejRs3Tk2aNMl2vVevXrrttts0btw4paen61//+pduu+02WSzZV7tMmzbNnmh69dVXNWrUKPu19u3bq0uXLho+fLgSExP10Ucfafbs2TnG9OGHHyopKUkeHh6aPn262rdvb7/WvXt31a9fX5988olCQkI0Y8aMbJl8KWNV1qeffiopIwk3b948BQYG2q/fcccdGjt2rNavX6/ly5dryJAhPLJUko+X8a80C3aHa2CHnP86AQAAABc1ZUrGyiZnOnJE+v57KYf/Ni/pWrVqpaZNm+rEiRNasmSJ/v73vxuuZ65qatasmVq2bJnnH84LKjIyUmPHjpWbm5teeeUVdezYUZ6entqzZ48mTZqkq1ev6rPPPtNtt91mWMlTWO+8844OHTqkoUOH6s4775S/v7+OHDmir776SpGRkfq///s/9ejRQ6+//rrCwsI0evRo9e7dWz4+PtqzZ4++/vprXbt2Tf/85z/Vs2dPVa5cucjvPS+JiYkaO3asUlNT9be//U2dO3eWu7u7Nm3apO+++04JCQl67bXXNGPGDI0dO1YVKlTQ+PHjdeuttyotLU1//PGHfvzxR8XGxuqtt97Sr7/+WqzxovQrs8mm8ePHF+n+Dh06qEOHDnn26devn+666y6tWrVKoaGhOnz4sG655RZDn9TUVHvyqHHjxho5cmSOrzVo0CDNmzdPO3bs0IEDB9S2bVtDnwMHDtgz1YMGDTIkmjKNHDlSixYt0qlTpzRr1iyNGTNGnp6ehj7z58/XtWvXJEl///vfDYkmKWO57D//+U9t3LhR6enpmjZtGskmSXe1qqYVBy/az7eevqyImETVrliw+lgAAAAo4Ww26ZtvimfsSZOkceOkHP4wXdI99NBD+vTTT7V8+XK98sor9j+u22w2LVu2zN7HWUJCQlS7dm398ssvql69ur29bdu2at26tYYNG6a0tDTNmzdPb7/99g2/zoEDB/TNN9+oX79+9rbWrVurTZs2GjBggKxWq5588knFxcXpp59+0q233mrv16ZNGzVo0ECjR49WfHy8li1blus2Q2eJjo6WzWbT/PnzDdvgbr31VlWqVEnvv/++IiIi7DWFf/nlF8Pveh07dpS7u7umTZum/fv36/Dhw2rVqlWxxozSjW10xcwxERMaGprt+vbt2+3JnYcfflhubjlPiePe3DVr1mS77tg2aNCgHMdwc3PTww8/LEm6evWqtm/fnq3P2rVrJUl+fn668847cxynRo0a9r3HW7duzXNLXlnRt3lVlfe8/h8HNpu0eE+4iREBAADAqdatk44fL56xjx2T1q8vnrGL2YMPPig3NzedP3/e8PvF9u3bdf78ebm5ual///5Ofc23337bkGjK1KlTJ3vSZ/fu3UV6jXvvvdeQaMrUokULdezYUVJGgufJJ580JJoy9enTx/6Ap8xFAcUtt3pLgwYNstfajY6O1ltvvZVtUYEkPf744/bjmxUzSi+STcUsxWH/dU4F8Rx/CHbp0iXXcVq3bm1/ityePXtyHcfX1zfb6ilHnTt3th9nHSclJUUHDhyQJLVr105eXl65jpMZa0pKig4ePJhrv7KinKe7etb1NrQt3BMhG0+mAwAAKB1mzXLt8YtJ9erV7X9gz9w253jcrVu3HBNDN8rf399QnDurzN+FwsLCivQ6999/f67XWjgUdM+rX7NmzZwSS0FYLBbde++9OV7z9va2PyAqICBAvXv3zrFf3bp1Vb58eUk3J2aUbmV2G93NsmPHDvtx48aNs10/deqU/bhRo0a5juPh4aF69erp2LFjhnuyjlOvXj15eOQ+rY6vkXWckJAQpaen5xtLTuN0K6ZHtqamphbLuM6WmpqqOxr46I/Tifa2M5fitf1UlDrUq2heYCgwx++aq3zvYMQcujbmz/Uxh67P1ebQarXa/7Dn+ATl4mLZulXFucnN9tdfshXxfTj+odNmszn9c8lt/AcffFBbt27VH3/8oYkTJ0qSVq1aZb+W2S+v+PKLPfN6ZtIkt/fm7+8vSYqPj8/z/ef1GlLG71W53e/n51egfhUqVMg1lpzeb0HbchqnUqVK8vf3zzeWevXqyWaz5fpHcX9/f8XHxysuLu6m/LsqbYr732BBY7BarYaFL3kprp/3JJuK0dGjR+1PoWvWrFmOyaYLFy5IyliRlPmDMTc1a9bUsWPHFB0drZSUFPvKo+TkZF25ckVSxha3vAQEBMjX11cJCQn2184aS0HGcbyedRxnOnr0aLGN7WxNAz1Vy89d5+LS7W0/rD2o5zsFmBgVboQrfe+QM+bQtTF/ro85dH2uMoceHh5yc3NTYmJi/p2LyPf8+eJ9gQsXnPo+kpKSnDZWpuTkZPtxSkqKPd7evXvL29tbcXFxWrlypWw2m+Lj4+Xj46PevXvb+zn+8pucnGx4v47XkpKSsn0Wmb+0e3l55fk5Zf7x3Gq15tkvNTU123XHGCwWS673Z75Gptz6ZSYe0tLS8nytnN5v5vw5zqPjZ541lnLlyhXo+5Pf55cpp88HhVMc/wbzk56ebp+74ODgm/76jthGV0xSUlL01ltv2f/xT5gwIcd+8fHxkjKSTfnJ3EbneF/W48KMk5CQkGMsBRnH8XrWccoqi8Wi2xsYC4L/FZak5HS20gEAALg8h/9WLhYuXAfV19dXd9xxhyTp999/1++//y4p40nWjr/DACg7WNlUTN5//317LaMBAwYoKCgox36Zfx3I+lS4nDjWUHL8q4LjcWHGyZppLcw4jrEUZ8a2RYsWBXpPZktNTdXRo0fVp76PfjkYp8z0UkKaTRfcq+mBNnmvFIP5MudQcp3vHYyYQ9fG/Lk+5tD1udocnjlzRunp6XJ3d785CY3y5Ys3IeTnV+T3YbPZ7P9t7u3tbX8ynLNkFpmWMn4fcIx30KBB+t///qdt27bZ2wYOHGjo4/g7RLly5XK95u3tne2zyHyQkpubW56fk+P3Nr9+Wa/nF0NhXyOzZq/FYsnWL6fPMqf5c9yGlfUzz+81HBX088v8zty0f1elTHH/G8yPu7u7PD095e3trYYNGxboHsef/c5EsqkYfP/995o/f76kjMdevvPOO7n2zfwhU5B9ko5LLR1/ODkeF2Ycb29jQevCjOMYS9ZxnMnT0zPPQuUlTRVfd3VvFKi/Tkfb237bf0EDO2Z/KgRKLlf73iE75tC1MX+ujzl0fa4wh25ubvZfxHN7orNT1awpnThRbMNbatSQpYjvwzExYbFYnP65OP7inHX8Hj16qGrVqoqKipIkVatWTT179jT0yev+vK45Xs/vfTmOk1+/3F4jv9cpzGvkNlZmDSVJunbtmuH77HiP4xPNnfG5OKsfclbc/wYLIvN1zf4ZzrfHyebOnavPPvtMUkYR7SlTpuS5JS2z2n9BtqI57pnNvC/rcWHGyRpXYcZxvF6QrXtlyYD2tQznm09E6ULszd+vCwAAACfq3r14x+/Ro3jHL2bu7u566KGH5OXlJS8vLz300EMkK/JQp04d+3FeT/devnz5zQgHcDr+9TvR8uXL9d5770mSateurRkzZigwMDDPezILbSckJOjq1at59j3//4sSBgYGZluCWrFiRUn5F+uOjY21J4qyFgEvTNHvwhQTL2vubFlNfuWuLxq02qTFeyNMjAgAAABFNmKEa49/E7z66qsKDg5WcHCw/v73v5sdTonWtGlT++9wc+bMyfHJYStWrNDKlStvcmSAc5BscpK1a9fqH//4h6xWq6pWraqZM2cWKAnj+IS606dP59ovLS1NYWFh2e7J1KRJE0lSaGio0tLSch3H8TWyjtOgQQP7nt+8YslvnLLO18td92Wp0bRwT3iujxcFAACACwgKkpo3L56xmzeX/n+BbZQNHh4eevTRRyVJx48f14gRI7R27VodPXpUW7Zs0VtvvaVXXnlF7du3NzlS4MaQbHKCrVu36uWXX1ZaWpoqVqyoGTNmqF69gtXo6dixo/14x44dufY7ePCgfUVShw4dch0nISFBhw4dynWcnTt32o+zjuPl5aW2bdtKkvbt25djdj1rrF5eXmrdunWu/cqqQR3qGM5PRsbpQHisSdEAAACgyCwWaezY4hl77NiM8VGmPP/882rXrp0kae/evRo3bpyGDh2qF198UYsWLVKnTp30wQcfmBskcININhXRnj179MILLyglJUUVKlTQtGnT1LRp0wLf36VLF3txuN9++y3X1S+LFi2yH/fr1y/bdce2hQsX5jiG1WrVb7/9Jkny9/dX165ds/Xp27evJCkuLk6rV6/OcZwLFy5o69atkqTu3bvLz88vx35lWecGgaoXaKxltWB3uEnRAAAAwClGj5ZatnTumC1bSs8959wx4RJ8fHz0448/asKECWrWrJm8vb3l5+enW265RW+//bZmzpzJE+Hgsiw29vZIksLDw+2JlgEDBujjjz/O954jR45oxIgRunr1qnx9ffXDDz8YVioV1JdffqnJkydLytjnPGrUKMP1vXv3atiwYUpLS1OXLl00e/bsHMd54okntGvXLnl4eOinn37KtuTyhx9+0CeffCJJGjdunF588cVsY8TExKhfv366du2aateurYULF6pSpUr26+np6Ro7dqzWr18vSZo1a1aOSauiSElJUXBwsKSMp/mZXUW/IHKK+Ys1x/XFmutPLAnw8dSOt/qqnIe7WWEiD674vYMRc+jamD/Xxxy6PlebwxMnTigtLU0eHh6F+mNvkR05IvXsKV25UvSxKlWS/vpLatGi6GMp44/LmQ8D8vHxoUC3i2H+XJ/Zc3gjPxeL62e/R/5dSqddu3YZHiN5xeF/LM6ePWtYSSRJAwcONJyHhobqmWeesRf1fumll1ShQgUdP34819esXLmyKleunK39mWee0YoVKxQSEqJPPvlEoaGhuu++++Tt7a3t27fru+++U1pamry9vfXmm2/mOv5bb72lxx9/XElJSRo5cqTGjBmjrl27KikpSStWrNC8efMkZdRmevrpp3Mco2LFivr73/+ud999VxERERoyZIjGjBmjZs2aKTIyUj/++KO2b98uSXrggQecnmgqTQZ1qGNINsUmpmrdkUjd26amiVEBAACgSFq2lFaskO67r2gJp0qVMsZxUqIJAEqSMptsWrBggRYvXpzjtT179mjPnj2GtqzJpl27duny5cv283//+9/5vmZuq4n8/Pw0ZcoUjR49WiEhIZo3b549MeTY59NPP1XLPJbttmrVSp9//rleffVVxcXF6bPPPsvWp0GDBpoyZUqeW98ee+wxRUZGavLkyQoNDc0xwdWnTx999NFHeb3dMq9uoK+6NgzU9jPR9rYFu8NJNgEAALi6bt0yViQNHJix0qmwWraUFi0i0QSg1CqzyaaSpn79+lq8eLHmzJmjlStXKjQ0VKmpqapRo4b69OmjESNGqHbt2vmOExQUpKVLl2rWrFn6888/dfHiRXl6eqpevXq65557NGzYsALt+x0/frx69eqlOXPmaPfu3bp06ZL8/f3VokULDRw4UA888IAz3napN6hjHUOy6c/jUYq6lqyqFcqZGBUAAACKrEULad8+6fvvpUmTpGPH8r+nefOMYuDPPSeV8G2KAFAU1GxCieNq9QKk3GOOS05T53+tUWJqur3v2/e31KjejUyJE7lzxe8djJhD18b8uT7m0PW52hyaVrMpJzabtH69NGtWxoqnCxekuDjJz0+qUUPq0UMaMUK6445ifeqc2fViUDTMn+szew6p2QSUEX7lPHRv6xpatDfC3rZgdzjJJgAAgNLEYpGCgjL+DwAgUqVAMRvUsY7h/OiFazp0LtakaAAAAAAAKF4km4Bi1r1RZdUK8Da0LdgdblI0AAAAAAAUL5JNQDFzc7NoYAfj6qal+84pNd1qUkQAAAAAABQfkk3ATTCwg/FJgpfjU7T+aKRJ0QAAAAAAUHxINgE3QaOqfupQr6KhbT5b6QAAAAAApRDJJuAmeaRjXcP5+qORuhSXbFI0AAAAAAAUD5JNwE3ywK015e15/Z9cmtWm3/ZGmBgRAAAAAADOR7IJuEn8vT11b+uahrb5u8Jls9lMiggAAAAAAOcj2QTcRIM7Gp9Kd+ziNQVHxJoUDQAAAAAAzkeyCbiJujWqrDqVfAxt83dRKBwAAAAAUHqQbAJuIjc3iwZ1MK5uWrIvQkmp6SZFBAAAAACAc5FsAm6yR7JspbualKbVhy+aFA0AAAAAAM5Fsgm4yeoG+qp7o8qGtl93hZkUDQAAAAAAzkWyCTDB4E7G1U2bT17SuZhEk6IBAAAAAMB5SDYBJri3dU35lfOwn9ts0qI9FAoHAAAAUPq9/vrrat68uYKCgswORZK0aNEiNW/eXM2bN1d4OL+XOYNH/l0AOJuPl7v631pTv+y4vn1uwe5wjb2jiSwWi4mRAQAAAPlLSUnRH3/8oY0bN+rAgQO6cuWK4uLi5Ofnp9q1a6tNmza6++671a1bN7m5scahJLHZbFq3bp1+//13HTx4UFFRUUpOTpavr69q1KihRo0aqW3bturVq5datGhhdrhwUSSbAJM80rGuIdkUcjlBO0OuqEvDQBOjAgAAwI2y2Wz6dte3mrlvpo5cOqKWVVrq6XZPa0ynMaXqD4p//PGHPv74Y0VERGS7FhMTo5iYGB06dEhz585VgwYN9MYbb+j222+/+YGWAkFBQYqIiNCAAQP08ccfF3m8S5cuafz48dq9e3e2a9euXdO1a9d04sQJrVq1Sp988olWrFihxo0bF/l1zbB9+3aNGDFCkjRr1ix17drV5IjKFpJNgEk61KuoRlXL63RUvL1t/q4wkk0AAAAuatTSUZq+b7r9fOe5ndp5bqd2n9+tHx78wcTInGfSpEn66quv7Oc9e/ZUUFCQGjduLH9/f8XGxurMmTNat26d/vrrL4WEhOjzzz8n2VQCpKSk6Omnn9bx48clSa1atdLAgQPVsmVLlS9fXnFxcTp16pR27typDRs26Nq1ayZHfPMMHDhQAwcONDuMUoVkE2ASi8WiwR3r6v9WHrW3/R58Xv988BaVL8c/TQAAAFeyIWSDIdHkaNreaRredrj6NOhzk6NyroULF9oTTZUrV9YXX3yhLl26ZOvXo0cPPfHEEzp+/Lj+/e9/Kzo6+maHihzMnz/fnmgaOHCgPvzww2xbHDt37qzHHntMKSkpWr58ufz9/c0IFaUAm2cBEw3sUFtuDiuqE1LStSL4vHkBAQAA4IZ8s/ObPK9P2jnpJkVSPC5evKgPPvhAkuTr66vZs2fnmGhy1KxZM02bNk0jR468GSEiH2vXrpUkeXh46I033sizlpaXl5cGDhyoqlWr3qzwUMqQbAJMVN3fW32aGX+Az9/N0w8AAABcSUJqglacWJFnnxUnVigxNfEmReR8M2fOVGJiRvzjx48vcB0fNzc3PfTQQ4a27du325/8tX379jzvz+z39ddfZ7v29ddf269LGTWHJk2apIcfflidOnVS8+bNtWjRokL3dbRmzRqNHz9et99+u9q0aaNOnTpp4MCB+uabbxQbG5tr3Fmftnb16lV9+eWXuv/++9WuXTt16tRJTzzxhJYuXZrj/SNGjFDz5s3tdbEWL15sjz/z/4YPH57nZ5fVuXPnJEmVKlVyyoql+Ph4TZkyRY8++qi6dOmi1q1b67bbbtP48eO1fv36Gx43PDzc/h5zmhNHQUFBat68uV5//fVs92fWa5Kuf56O/+c4dkGfRhcdHa3PP//c/r1p06aNgoKC9Oqrr2rXrl2FivX06dN6++23FRQUpNatW6tHjx4aO3as9u3bl+c4roK9OoDJhnSqq/XHouznO85EK+RSvBpUKW9iVAAAAMhNYmqigiODlZSWJEnaEbFDCakJed4TnxqvSTsnqUvtjNVA3h7ealOtjXw8fYo93qKy2WxavHixpIxVTYMHDzY5ouxCQkI0cuTIHIuW30jf2NhYjR8/Xtu2bTO0p6Sk6NChQzp06JB+/vlnTZ48We3atcvz9U6fPq1Ro0Zle71du3Zp165d2rdvn95555184y4qT09PSRlFwmNiYlSxYsUbHuvw4cN67rnnFBkZaWi/ePGiVq1apVWrVumuu+7Sp59+qnLlyhUl7BJj8+bNeumllxQXF2doj4iIUEREhJYuXaqhQ4fqb3/7W75PYFy9erVeffVVewJXki5fvqw1a9Zo/fr1+vTTT3XfffcVy/u4WUg2ASbr27K6Kvl66kpCqr1twe5w/f3u5iZGBQAAgKziU+L18sqXNWPfDKXb0gt9/6urXzWcu1vc9XS7p/XFPV+ovFfJ/UPjiRMndOXKFUlSx44d5efnZ3JE2Y0fP16RkZEaPny4goKC5O/vr7Nnz6pWrVqF7ptZSPvQoUNyd3fXAw88oD59+qhOnTpKTU3Vrl27NGPGDF2+fFmjR4/W4sWLVbt27RzjSkxM1PPPP6+YmBg9//zz6tGjh3x9fXXkyBF98803unDhgubMmaM77rhDPXv2tN/30UcfKSkpSc8884wiIyPVt29fvfzyy4axfXwKl6i85ZZbdPz4cdlsNk2cOFEff/yxypcv/Pfu4sWLeuqppxQbGyuLxaIBAwbo/vvvV8WKFXXy5EnNmDFDR48e1R9//KHXX39dn3/+eaFfoyiqV6+uZcuWKTg4WG+++aakjM+zTZs2hn41atQo8JhHjhzRmDFjlJqaKk9PTz3xxBMKCgqSj4+Pjhw5oilTpig8PFw///yzPD099dJLL+U61vHjx7VixQpVrVpVI0eOVOvWrWWz2bR582ZNmTJFycnJmjhxorp166bAQNd9eBTJJsBkXh5ueqhdbc38K8TetnBPuCbc2UzubqXnEbkAAACuzGazacC8AVp9erXTxky3peuHvT/obOxZrRq2ShZLyfxvv6NHrz/Q5pZbbjExktydOHFCU6dOVa9evextrVu3vqG+kyZN0qFDh+Tv768ZM2ZkG6dTp07q37+/Hn30UUVFRemzzz7Tf//73xxfKzo6WqmpqZo3b56aNm1qeL0uXbqof//+Sk5O1s8//2xINtWpU0dubm721Uj+/v5q1qxZIT6R7IYOHaolS5bIarXqjz/+0LZt23THHXeoU6dOatu2rZo2bSp3d/d8x/nwww/tWwg/+OADw0q31q1b67777tOoUaO0fft2rVixQg8//LD69Ll5xfE9PT3VrFkze4JUyvg8i/L5TZw4UampqXJ3d9d3331n+O60bdtW99xzj4YOHaqTJ09q9uzZeuCBB3L9/h06dEi33HKLZs2aZUjctmvXTvXq1dOrr76quLg4LV26VE899dQNx2w2ajYBJcDgTnUM5+djk7Tl5CWTogEAAEBWq06tcmqiydHq06v1x6k/imVsZ4iJibEfV65c2bxA8jBgwABDAuBG+8bHx2vOnDmSpJdeeinXhEHt2rX1wgsvSJJWrVqlhITct1G+9NJLhkRTpvr166tfv36SpD179hQo9qJo27at3n//fXsC6+rVq1qyZIkmTpyohx56SJ06ddLIkSP166+/5vp+Ll68qDVr1kiSevfuneOWSi8vL3300Ufy8MhY25L5ebqqAwcOKDg4WJI0ePDgHL87AQEBev/99yVJVqtVv/76a55jfvTRRzmuEOzfv7+qVasmSfnWgCrpSDYBJcAttQLUqqaxSB+FwgEAAEqO3ed2F+/454t3/KKIj4+3Hxd269bN0r9/f6f03blzp65duyZJuvvuu/Mcp3PnzpKk1NRUHTp0KMc+FotFDzzwQK5jZK4Ui4mJ0dWrV/N8PWcYPHiwli5dqoEDB2bbQpeQkKAtW7Zo4sSJuuuuu7Rx48Zs9+/YsUPp6RlbSB955JFcX6dOnTrq0aNHtntc0V9//WU/zus9d+zY0V44f8eOHbn2a9asmVq0aJHjNYvFolatWkmSwsLCbiTcEoNtdEAJMbhTHb237LD9fNWhC4pNSFWAr6eJUQEAAECSUq2p+XcqyvjpxTt+UTgmJRwLGpckmU+ZK2rfgwcP2o8LulJKkqKionJsr1SpkipVqpTrfQEBAfbj+Pj4IhXtLqhGjRrp3//+t95//30dPHhQ+/fv18GDB7Vz505duHBBUsb7GTNmjH744Qd70kjK2IKY6dZbb83zdW699VZt3LhRiYmJCgsLU4MGDYrl/RS3zPfs6empli1b5tm3bdu2OnXqlEJDQ5WSkiJvb+9sfRo1apTnGJnfCcckrytiZRNQQjzUrrY83a/v009Js2rp/vyfpgEAAIDi90Cz3FenuML4ReGYALl8+bJ5geTBMWlTlL43+v6SkpJybM9vJZjjU8usVusNvfaN8vT0VPv27fXUU0/p008/1YYNGzRz5kz7lr/09HS99957stls9nsKs6WySpUq9uPMGk+uKPM9V6xY0b41MDeZ79lms+W6Uq2g34mb/X1wNlY2ASVEYHkv3dmqulYEX7C3/borXMO7NzAvKAAAAEiSOtbsqOc6Pqfvd3/v9LHHdByjDjU7OH1cZ3Hc8pPbdjGzFaSwdUH6Om73Wrx4cb7JhUyFebJZSda9e3dNnz5d/fv3V0xMjEJCQnTkyBH71i6goEg2ASXI4E51Dcmm4IhYHT53Va1q+edxFwAAAIqbxWLRpPsmqZx7OX214yunjTu+y3h9dvdnJfZJdJLUtGlTVapUSVeuXNHu3bsVFxeXY3Hjgiroap68im4XF8ctb4GBgaUmiVQY1apVU58+fbRkyRJJ0tmzZ+3Jpqyr3GrWrJnrOJcuXX/gUWFWnhVmtdfN+I5kvueYmBilpaXlmYDMfM8Wi0X+/mX7dzi20QElyG1Nq6pmgHFf76+7XLswHAAAQGnh7uauL+/9UksfWypfT98ijeXr6atljy/Tl/d+KXe3gq/KMYPFYtGAAQMkZfxyP3/+/CKN51gDKq+i2CEhIUV6nRvhWJPnZjwhrqTKfCKaJEMi1PGpevv3789zjAMHDkjK2DZWt27dAr92Qb8fMTExhm19WTkrgZv5nlNTU3XkyJE8+2a+53r16snLy8spr++qSDYBJYi7m0WPdKxjaFu8N0JJqa779AYAAIDSpn/z/nqm/TNFGuOZ9s+U6DpNWT311FP2WjNfffWVTp06VaD7rFarli5damirXbu2/dixIHdWy5cvv4FIi6ZHjx729zlr1ixDvSIzlCtXTpKUkpJS5LEK814c58UxUdSlSxf7NsSFCxfmev+5c+fsT3FzvKcgAgIC7KuC8vp+/P7773m+p8zPTira5+dYID2v97x37177v4suXbrc8OuVFiSbgBJmcEdj1j82MVV/HL5oUjQAAADIymqzavHRxUUa47ejv5meyCiM6tWra+LEiZIyVjcNHz48z8e7S9LJkyc1atQoTZs2zdAeEBBgfyLcokWLclydsmvXLs2aNcs5wReCv7+/nnjiCUkZyYOPPvooz61cly5dKvJKr7xUrVpVkhQaGlrkscaNG6c5c+bku/Vs0aJF2rp1qySpVq1ahnpN1atXV79+/SRJGzdu1OLF2f8dpKSk6M0331RqasYTFjM/z8Lo1KmTJGnt2rU5vvfTp0/rq6/y3s6a+dlJRfv82rZtq9atW0uS5s+fb/9sHF27dk3vvPOOpIxtgIMHD77h1ystqNkElDD1KvuqR+PK+uvU9Sdh/LozTA/eWsvEqAAAAJBpZ8ROhV8NL9IYYVfDtPPcTnWp7TorIAYNGqQLFy7oq6++0uXLlzV8+HD16tVLQUFBaty4sfz9/RUbG6szZ85ow4YN2rRpk9LT0w0FxjM98cQTeuedd3Tp0iU98cQTeuGFF9SwYUPFxsbqzz//1M8//6zWrVtr7969N/19vvTSS9q5c6f279+vWbNmaceOHRoyZIhatGghX19fxcbG6uTJk/rrr7+0ceNGNWvWrNiSC+3bt9f27dsVHBysKVOm6LbbbrOvvPL29lb16tULPNb58+f1/vvv69NPP1VQUJA6deqkhg0bKiAgQMnJyTp9+rRWrlypDRs2SMrYhvbGG29k24725ptvatu2bYqNjdWbb76p3bt367777pO/v79Onz6t6dOn27eb3XvvverTp0+h3/fQoUO1bt06JSUlafjw4Ro3bpxatWqlhIQEbd26VbNmzVJgYKDc3NwUHR2d4xi1atVSjRo1dOHCBU2fPl01atRQw4YN7ausKleuXODaY//61780ePBgpaam6tlnn9Xw4cN1xx13yMfHR0eOHNGUKVMUFpZR/mT48OFq0qRJod9zaUOyCSiBHu1c15Bs2nzyksKiE1Q3sGi1AQAAAFB0O8/tdM44Ea6VbJKksWPHqmnTpvr4448VERGhzZs3a/Pmzbn2b9q0qV599dVs7YMHD9bGjRu1Zs0anTx5Un/7298M15s1a6avv/5avXr1cvp7yI+Xl5emT5+uN954Q3/88YeOHj2q999/P9f+RSmWnp+hQ4dq7ty5iomJ0X//+1/997//tV/r0qWLZs+eXeCxatSooUOHDikhIUHLly/Pc5tihQoV9Pbbb+uuu+7KcZyZM2fqueeeU2RkpObPn5/j6q677rpL//d//1fg+Bz17t1bw4cP1+zZs3XhwgW9/fbbhuu1atXSt99+q2effTbPcZ577jm99957Cg8P1wsvvGC49u9//1sDBw4sUDwtW7bUd999p5deeklxcXGaPn26pk+fnq3f0KFD9eKLLxZozNKOZBNQAt19Sw35e3voalKavW3+7nD97c5mJkYFAAAASYqKj3LKOJHxkU4Z52a76667dPvtt2vVqlXauHGjgoODFR0drfj4ePn5+al27dq69dZbdffdd6tr1645Fmp2c3PTV199pblz52rx4sX2Wjd169bVfffdp6eeekre3t7Z7rtZ/Pz89PXXX2vXrl367bfftGvXLkVGRio5OVl+fn6qW7eu2rZtqz59+hRrQqx69eqaP3++vv/+e+3cuVMXLlxQcnLyDY01efJknT59Wps3b9aePXt08uRJXbhwQQkJCSpXrpwqVqyopk2bqmfPnurfv78CAwNzHatVq1ZauXKl5syZozVr1ujMmTNKTExUpUqV1K5dOw0YMEBBQUE3+rYlSW+//bbatWunuXPn6siRI0pLS1PNmjV15513auTIkYYnB+Zm6NChqlKliubNm6cjR44oNjZWaWlp+d6Xk169emn16tX68ccftWHDBoWFhSklJUVVqlRRx44d9dhjj6lDhw5KTEy8ofFLG4vNlTYKo0xISUlRcHCwJKlNmzYuUcW/OGJ+Z8lBzdp61n5eK8Bbm/4RJHe3kvtYXFfmit87GDGHro35c33MoetztTk8ceKE/THkjk/IuhlWnVyle+bck2cfbw9vJaUl5T3OsFW6q3H2lSM3ymq12n/R9fHxMTxCHiUf8+f6zJ7DG/m5WFw/+/n2AiXUkE7GQuHnYpO0+eQlk6IBAABApjsa3qEONTvken1Ctwm6+PeLernry7n26VCzg+5ocEcxRAcA5iPZBJRQrWsH6JZa/oa2X3eGmRQNAAAAMnm5e2nF0BXqVc+4fappYFMtf3y5Prv7M/mX89fn93yu5Y8vV9NA4wqDXvV6acXQFfJ097yZYQPATUPNJqAEe7RzXb2z5JD9/I/DF3Q5LlmV/cqZGBUAAACq+1XXpqc3afe53QqNDVVF74rq06CP3CzGv+ff3+x+3dv0Xm0I2aCYpBjVC6injrU6mhQ1ANwcJJuAEuyhW2vrX78fUUqaVZKUmm7T4r0RGtW7kcmRAQAAQJI61uqYb/LIzeKmOxqyZQ5A2cE2OqAEC/D11L2taxjaft0VJur6AwAAAABKKpJNQAn3aJZC4ccvxmlfWIw5wQAAAAAAkA+STUAJ161RZdUN9DG0/bqLQuEAAAAAgJKJZBNQwrm5WTSko3F107L955WQkmZSRAAAAAAA5I5kE+ACHulUR26W6+dxyWn6/cB58wICAAAAACAXJJsAF1AzwEe3NatqaGMrHQAAAACgJCLZBLiIxzobt9LtDLmiU1FxJkUDAAAAAEDOSDYBLiKoRXVVLu9laGN1EwAAKKvc3d0lSWlpaUpPTzc5GgAwl9Vqtf8szPz5aCaSTYCL8PJw08AOtQ1tC3dHKDXdalJEAAAA5vH19bUfx8TEmBcIAJQAcXFxstlskiQfH598ehc/kk2AC3k0y1a6S3HJWn800qRoAAAAzFOxYkX7cWRkpCIjI5WUlGT/ZQsAygKr1aqrV6/qwoUL9rYKFSqYGFEGD7MDAFBwTapVUId6FbUnNMbeNm9nmO66pYZ5QQEAAJjA29tbAQEBio2NlSRdvnxZly9flsViKRFbSMxSkrbRoPCYP9d3s+cwPT3dkGT38fFR+fLlb8pr54VkE+BiHu1c15BsWn8sUudjE1UzwPylkgAAADdTzZo15eXlpaioKHubzWZTWlqaiVGZx2azKTU1VZLk6ekpi8VickQoDObP9Zk9hz4+PqpXr16J+O6QbAJczANta+n9ZYcVn5KRMbfapPm7wjW+b1OTIwMAALi5LBaLqlSpIn9/f8XFxSk+Pl4pKSmyWstmTUur1arExERJGSu/3NyomuJKmD/XZ8Ycuru7y8fHRxUqVFD58uVLRKJJItkEuJzy5Tz0YLta+mXH9SfRzdsZpnF3NJGbW8n4wQIAAHAzeXl5KTAwUIGBgWaHYqqUlBQFBwdLkho2bCgvL6987kBJwvy5PubwOlKlgAt6rHM9w3lETKI2nbxkUjQAAAAAAFxHsglwQW3rBKhlTX9D29wdoSZFAwAAAADAdSSbABdksVj0eJe6hrbVhy8q6lqySREBAAAAAJCBZBPgoh5qV1ventf/CadZbVq4J9zEiAAAAAAAINkEuKwAH0/d16amoW3ezjDZbDaTIgIAAAAAgGQT4NIe72IsFH7mUry2nY42KRoAAAAAAEg2AS6tU/1KalLNz9A2dyeFwgEAAAAA5iHZBLgwi8WixzobC4X/7+AFxSSkmBQRAAAAAKCsI9kEuLiBHerIy/36P+WUNKsW740wMSIAAAAAQFlGsglwcYHlvXTXLdUNbXN3UCgcAAAAAGAOkk1AKZC1UPixi9e0NyzGnGAAAAAAAGUaySagFOjeqLLqBfoa2ubuoFA4AAAAAODmI9kElAJubhY9mqVQ+LL953UtKdWkiAAAAAAAZRXJJqCUGNyxjtzdLPbzxNR0Ld1/zsSIAAAAAABlEckmoJSo5u+tvi2qGdrm7ggzKRoAAAAAQFlFsgkoRbIWCg+OiNXBiFiTogEAAAAAlEUkm4BS5LZmVVUrwNvQNncnhcIBAAAAADcPySagFHF3s2hwJ2Oh8CV7zykhJc2kiAAAAAAAZQ3JJqCUGdK5rizX64TrWnKafj9w3ryAAAAAAABlCskmoJSpXdFHfZpVNbT9soOtdAAAAACAm4NkE1AKPdbZWCh8T2iMjl64alI0AAAAAICyhGQTUAr1bVlNVSuUM7T9vJ3VTQAAAACA4keyCSiFPN3d9GiWQuGL90RQKBwAAAAAUOxINgGl1GNdshcKX76fQuEAAAAAgOJFsgkopepU8s1WKHwOhcIBAAAAAMWMZBNQig3tYiwUvj8sRofOxZoUDQAAAACgLCDZBJRiQS2qqYa/t6GNQuEAAAAAgOJEsgkoxTzc3TSks7FQ+JJ95xSfTKFwAAAAAEDxINkElHKPda4rN4dC4XHJaVq6/5x5AQEAAAAASjWSTUApV6uij+5oXs3QxlY6AAAAAEBxIdkElAFDuxoLhQdHxCo4nELhAAAAAADnI9kElAG3N6+mWgFZCoXvOGtSNAAAAACA0oxkE1AGuLtZ9Ghn4+qmJfvO6VpSqkkRAQAAAABKKw+zAzDL5cuXdeDAAR04cEDBwcEKDg5WTEyMJGnAgAH6+OOPCzXehg0b9Ouvvyo4OFjR0dEKDAxUmzZtNGTIEPXp06dAY6SlpWn+/PlatmyZTp8+rYSEBFWrVk09evTQ8OHD1bRp0wKNEx0drdmzZ2vNmjWKiIiQJNWuXVv9+vXTiBEjVKlSpQKNc/z4cf3000/666+/FBkZKV9fXzVq1Ej9+/fX4MGD5eFRZr8+LunRznX11boTSrfaJEkJKelauv+cnuha3+TIAAAAAAClSZnNFvTo0cMp41itVk2cOFELFiwwtF+8eFEXL17UmjVrNHjwYL3//vtyc8t9IVl0dLRGjx6t4OBgQ3tYWJjmzZunxYsX65133tHgwYPzjGf//v0aO3asoqKiDO3Hjx/X8ePHNX/+fE2ePFlt27bNc5xff/1V77//vlJTr698SU5O1u7du7V7924tWrRI33//vQIDA/McByVHjQBvBbWoptWHL9rbft4eqqFd6sliseRxJwAAAAAABcc2Okm1atVSr169bujezz//3J5oatWqlT777DPNnz9fn332mVq1aiVJmj9/vr744otcx0hPT9e4cePsiaa77rpLU6dO1fz58/X222+rcuXKSklJ0TvvvKMNGzbkOs758+c1ZswYRUVFycPDQ6NGjdKcOXM0Z84cjRo1Sh4eHoqKitKYMWN04cKFXMfZsGGD3n33XaWmpqpKlSp6++23NX/+fE2dOlV33XWXJOnAgQMaN26c0tPTC/uRwURZC4UfOndVBygUDgAAAABwojK7smns2LFq06aN2rRpoypVqig8PFx9+/Yt1BhnzpzR9OnTJUmtW7fWnDlz5O2dUYS5bdu2CgoK0rBhw3Tw4EFNmzZNgwYNUv362bcsLV68WLt375YkDR06VO+++679Wtu2bXXbbbdp4MCBiouL04cffqiePXvmuIXt888/V3R0tCTp008/1b333mu/1qlTJ91yyy2aMGGCLl++rC+++CLHrYKpqan64IMPZLVa5efnp19++UX16l1PUNx2221677339PPPP2v37t1asmSJBg4cWKjPDea5rWlV1a7oo4iYRHvbz9tDdWvdiuYFBQAAAAAoVcrsyqbx48frjjvuUJUqVW54jB9//FFpaWmSpIkTJ9oTTZl8fHw0ceJESRn1mGbOnJnjOJkJq4oVK+q1117Ldr1+/fp67rnnJElnz57V6tWrs/WJiorSsmXLJEm9evUyJJoy3XffffYVXEuWLMm21U6SVq9erbCwMEnSc889Z0g0ZXrttdcUEBAgSZo2bVqO7wklk7ubRY93qWtoW7r/nK5SKBwAAAAA4CRlNtlUVDabTWvXrpUkNWrUSO3atcuxX7t27dSwYUNJ0tq1a2Wz2QzXz5w5o1OnTkmS7rnnHvn4+OQ4zoABA+zHa9asyXZ93bp1slqtkqRBgwblGnfmKiSr1ap169Zlu575nrK+piMfHx/dc889kqSTJ0/qzJkzub4eSp4hnerKw+16jabE1HQt2RthYkQAAAAAgNKEZNMNCg8PV2RkpCSpc+fOefbt0qWLpIyi4eHh4YZrmdvnHPvlpGrVqmrQoIEkac+ePdmuO46TVzyO1/Iap2HDhqpatWqu4zjGmtM4KLmq+XurX8vqhrY520OzJUIBAAAAALgRZbZmU1GdPHnSftyoUaM8+zpeP336tOrWvb6NKXNVU0HHCQkJ0fnz55WQkCBfX99s8VSoUCHPJFG1atXk5+enuLg4w2tLUnx8vM6fP1/o95R1HGdyfBpeSeYYpyvEPKRjLa08dL1I/NEL17TzdJTaleHaTa42h8iOOXRtzJ/rYw5dH3Po+phD18b8uT5XnMPiipNk0w1yfJpbjRo18uzreD0zmZPTONWrG1ebZFWzZk1JGVv4Lly4YEj4XLx4sUCxZI5z4sSJbE+ku9H3lNeT7Yrq6NGjxTZ2cXGFmCvYbKpe3l0X468/TfDb1Qc1rnOAiVGVHK4wh8gbc+jamD/Xxxy6PubQ9TGHro35c31lfQ7ZRneD4uPj7ceOK4xy4liHKSEhIddxypcvX+Rx8ovFcRzH1856nt84jtezxoKSz81iUb9GxvpgW0ITdS3FalJEAAAAAIDSgpVNNyg5Odl+7OnpmWdfLy8v+3FSUlKxjpPfGI7jOL62JKWkpDglFmdq0aJFgd6T2VJTU+2Za1eJuWbDZP16eJNS0zNqNaVYpWPJFfV0x/omR2YOV5xDGDGHro35c33MoetjDl0fc+jamD/X54pz6BizM5FsukHlypWzH+e3x9ExiePt7Z3nOI7nhR0nMTGxQPstM8fJ+lqOCaSivCdn8vT0NMTlClwl5lqBXrr7lhpafuD61s55uyI0uk8TWSyWPO4s/VxlDpE75tC1MX+ujzl0fcyh62MOXRvz5/rK+hyyje4GOW55y28bWWJiov046/Y0x3Gybmu7kXEKsqUtc5ys2/YK854crxdk6x5KpmHdjKuYTl+K11+nLpsUDQAAAACgNCDZdIMKUyDb8Xpmke+cxsks8p2bzOLiFoslWwHvzOLiBSnWnTlObmMUZJzCFBNHydW1YaCaVvMztP207axJ0QAAAAAASgOSTTeoSZMm9uPTp0/n2dfxuuMT5CSpcePGhR6nZs2a2VYTZcZz7do1RUVF5TpGZGSk4uLisr22JPn5+dmTYYV5T1nHgeuwWCx6oms9Q9sfhy/q4tXiq8MFAAAAACjdSDbdoDp16qhatWqSpJ07d+bZN/N69erVVadOHcO1jh072o937NiR6xhRUVEKCQmRJHXo0CHbdcdx8orH8Vpe45w5cybPpJVjrDmNA9cxsGMd+Xi628/TrTbN3RFmYkQAAAAAAFdGsukGWSwW9e3bV1LGKp99+/bl2G/fvn32VUB9+/bNVni5YcOG9pVBK1euNNRlcrR48WL7cb9+/bJdDwoKkptbxnQuXLgw17gXLVokSXJzc1NQUFC265nvKetrOkpMTNTKlSslZayoatiwYa6vh5LP39tTD7evZWj7ZUeo0tKtJkUEAAAAAHBlJJuK4Mknn5S7e8aKkA8++EBJScatR0lJSfrggw8kSR4eHnryySdzHGfkyJGSpJiYGH3yySfZroeGhur777+XJNWvX1933nlntj5Vq1ZV//79JUmbN2+2J4Mc/e9//9PmzZslSQ899JCqVq2arc+dd96punXrSpK+//57hYaGZuvzn//8R7GxsZKkZ555Jsf3BNfyRFdjofALV5O05kikSdEAAAAAAFyZh9kBmGXXrl2GRMqVK1fsx2fPnrWvAMo0cODAbGM0bNhQzzzzjKZMmaKDBw/q8ccf17PPPqu6desqLCxMU6dO1eHDhyVlJGUaNGiQYywDBgzQwoULtWfPHs2ZM0eXLl3S4MGDFRAQoAMHDmjy5MmKi4uTm5ub3nrrLXl45DxtEyZM0KZNmxQdHa1XXnlFBw8e1O233y5J+vPPPzVjxgxJUmBgoF5++eUcx/D09NTEiRM1ZswYxcXF6fHHH9fzzz+vtm3bKjY2VvPnz9eqVaskZWy5e+ihh3IcB66lde0AtatbUfvCYuxtc7af1T2tKf4OAAAAACicMptsWrBgQa7bxPbs2aM9e/YY2nJKNkkZCZ7Lly9r4cKFOnz4sCZMmJCtzyOPPJJrckeS3N3dNWnSJI0ePVrBwcFatWqVPaGTycvLS++884769OmT6zg1a9bUd999p7FjxyoqKkpTp07V1KlTDX2qVq2qSZMm5fkEuT59+ui9997T+++/r0uXLtlXZzlq27atvvnmG/vKLri+Yd3qG5JNm05c0plL8WpYpbx5QQEAAAAAXE6ZTTY5i5ubmz766CPdfffdmjdvnoKDg3XlyhVVqlRJbdq00aOPPppngihTYGCg5s6dq19//VXLly/XqVOnlJiYqGrVqql79+4aMWKEmjZtmu84t956q5YuXapZs2Zp7dq1Cg8Pl5RR0Lxv37568sknValSpXzHGTJkiNq1a6fZs2dr69atioyMlI+Pjxo3bqz+/ftr8ODBua6wgmt6oG1NfbD8sGITU+1tP28/q7fub2ViVAAAAAAAV1NmswUff/yxPv74Y6eN16dPnwIllfLi4eGhoUOHaujQoUUaJ3ObXF6rqQqiWbNmOa5qQunk7emuwR3r6IfNZ+xt83eH65W7msvbkxVsAAAAAICCoUA4ALsnuhkLhcckpOr3A+dNigYAAAAA4IpINgGwa1ilvHo1qWJo+2n7WZOiAQAAAAC4IpJNAAyGdatnON8bGqND52JNigYAAAAA4GpINgEw6Neyuqr7lzO0/bQt1KRoAAAAAACuhmQTAAMPdzc93sW4uum3vRG6mpSayx0AAAAAAFxHsglANo91rid3N4v9PDE1XYv3RJgYEQAAAADAVZBsApBNjQBv3dmyuqHtp21nZbPZTIoIAAAAAOAqSDYByNGwbvUN5yci47TjTLRJ0QAAAAAAXAXJJgA56tG4shpWKW9o+2k7hcIBAAAAAHkj2QQgR25uFj3R1VgofOXB84q6lmxSRAAAAAAAV0CyCUCuHulYR+U8rv+YSE23ae4OVjcBAAAAAHJHsglArir6eumhdrUMbXO2hyot3WpSRAAAAACAko5kE4A8jejewHB+4WqSVh++aE4wAAAAAIASj2QTgDy1rh2g9vUqGtpmbT1rTjAAAAAAgBKPZBOAfI3oXt9wvvX0ZZ24eM2kaAAAAAAAJRnJJgD5uq9NTVUu72VoY3UTAAAAACAnJJsA5Kuch7se61LX0LZoT7iuJaWaFBEAAAAAoKQi2QSgQIZ2rS83y/Xz+JR0Ld4bYV5AAAAAAIASiWQTgAKpXdFH/VpWN7TN2npWNpvNpIgAAAAAACURySYABfZkjwaG85ORcdp66rI5wQAAAAAASiSSTQAKrEfjympctbyhjULhAAAAAABHJJsAFJjFYtHwbvUNbauPXNS5mESTIgIAAAAAlDQkmwAUyqCOdVTey91+nm616eftoSZGBAAAAAAoSUg2ASiUCt6eGtChtqFt7s5QJaelmxQRAAAAAKAkIdkEoNBGdG9gOL8Ul6KVBy+YEwwAAAAAoEQh2QSg0JpVr6CuDQMNbRQKBwAAAABIJJsA3KAnezQwnO8+e0UHI2LNCQYAAAAAUGKQbAJwQ+5sVV3V/csZ2mazugkAAAAAyjySTQBuiKe7m4Z2qW9oW7I/QrEJqSZFBAAAAAAoCUg2Abhhj3epKw83i/08KdWq+bvDTIwIAAAAAGA2kk0Ablg1f2/d26amoW32trOyWm0mRQQAAAAAMBvJJgBFMqK7cSvd2csJ+vN4pEnRAAAAAADMRrIJQJF0ql9JLWv6G9pm/kWhcAAAAAAoq0g2ASgSi8Wip3oYVzdtPB6lU1FxJkUEAAAAADATySYARfZQu9qq6OtpaJv1V4g5wQAAAAAATEWyCUCReXu667HO9QxtC3aH62pSqkkRAQAAAADMQrIJgFMM715fbpbr5/Ep6VqwK9y8gAAAAAAApiDZBMApalf00d231DC0zdoaIqvVZlJEAAAAAAAzkGwC4DRP9mhgOA+5nKANx6PMCQYAAAAAYAqSTQCcpmvDQLWoUcHQNpNC4QAAAABQppBsAuA0FotFT2VZ3bTheJRORcWZExAAAAAA4KYj2QTAqR5qV1sVfT0NbbNY3QQAAAAAZQbJJgBO5ePlrkc71zW0LdgdrmtJqSZFBAAAAAC4mUg2AXC64d3qy81y/Tw+JV0LdoebFxAAAAAA4KYh2QTA6epU8tVdrWoY2mZtPSur1WZSRAAAAACAm4VkE4Bi8WSWQuFnLsVrw4koc4IBAAAAANw0JJsAFItujQLVokYFQ9vMLSHmBAMAAAAAuGlINgEoFhaLJdvqpg3Ho3Q6Ks6cgAAAAAAANwXJJgDF5uF2tRXg42lom7X1rEnRAAAAAABuBpJNAIqNj5e7Hutc19C2YHe4riWlmhQRAAAAAKC4kWwCUKyGdasvN8v187jkNC3cHW5eQAAAAACAYkWyCUCxqhvoqztbVTe0zdp6VlarzaSIAAAAAADFiWQTgGKXtVD46Uvx2nAiypxgAAAAAADFimQTgGLXvVFlNa9ewdA2ffMZk6IBAAAAABQnkk0Aip3FYtHIXg0MbZtOXNLxi9fMCQgAAAAAUGxINgG4KR5qV1uVfD0NbTO2hJgTDAAAAACg2JBsAnBTeHu664mu9Q1ti/aE60p8ikkRAQAAAACKA8kmADfN8O715eFmsZ8np1n1845QEyMCAAAAADgbySYAN011f2890LamoW3W1hClpltNiggAAAAA4GwkmwDcVCN7NTScX7yarBXB502KBgAAAADgbCSbANxUbetUVKf6lQxt0zefkc1mMykiAAAAAIAzkWwCcNNlXd20PzxWe0JjzAkGAAAAAOBUJJsA3HR3taqu2hV9DG0ztpwxKRoAAAAAgDORbAJw03m4u+nJHvUNbf87eEHnYhJNiggAAAAA4CwkmwCY4tFO9eTr5W4/T7faNGvrWRMjAgAAAAA4A8kmAKYI8PXUIx3rGNp+2RGqhJQ0kyICAAAAADgDySYApnmqRwPDeWxiqhbtiTAnGAAAAACAU5BsAmCaRlX9FNSimqFtxpYzslptJkUEAAAAACgqkk0ATDWyZ0PD+amoeG08EWVSNAAAAACAoiLZBMBUPZtUVrPqfoa26VtCzAkGAAAAAFBkJJsAmMpisejpLKubNh6P0omL10yKCAAAAABQFCSbAJhuQPvaquTraWib8VeIOcEAAAAAAIqEZBMA03l7umto13qGtkV7wnUlPsWkiAAAAAAAN4pkE4ASYXi3BvJws9jPk1Kt+nlHqIkRAQAAAABuBMkmACVCjQBv3d+2pqFt5l8hSk5LNykiAAAAAMCNINkEoMQY1auR4TzqWrKW7T9vUjQAAAAAgBtBsglAidGmToC6Ngw0tP2w6bRsNptJEQEAAAAACotkE4ASZVRv4+qmoxeu6a9Tl02KBgAAAABQWCSbAJQofVtUU8Mq5Q1tUzedNikaAAAAAEBhkWwCUKK4uVk0sldDQ9ufx6J04uI1kyICAAAAABQGySYAJc4jHeqooq+noW3a5jMmRQMAAAAAKAySTQBKHB8vdw3rWt/QtmhvhC7FJZsUEQAAAACgoEg2ASiRRvSoLy/36z+iUtKsmr31rIkRAQAAAAAKgmQTgBKpWgVvPdiulqHtp21nlZSablJEAAAAAICCINkEoMQa1dtYKPxyfIoW740wKRoAAAAAQEGQbAJQYrWo4a/eTasY2qZtPiOr1WZSRAAAAACA/JBsAlCijerdyHB+MjJOG05EmRQNAAAAACA/JJsAlGi3Na2iptX8DG0/bDptUjQAAAAAgPyQbAJQolkslmy1m7acvKzD566aFBEAAAAAIC8eZgdQWqSkpGjJkiVauXKljh07ppiYGHl6eqpatWrq0KGDBg8erA4dOuQ7zoYNG/Trr78qODhY0dHRCgwMVJs2bTRkyBD16dOnQLGkpaVp/vz5WrZsmU6fPq2EhARVq1ZNPXr00PDhw9W0adMCjRMdHa3Zs2drzZo1iojIKMpcu3Zt9evXTyNGjFClSpUKNA5QVA+1q61PVh3TpbgUe9sPm0/rsyHtzAsKAAAAALKw2WxKo8QsySZniIiI0HPPPacTJ04Y2lNTUxUSEqKQkBAtWrRIw4cP11tvvSWLxZJtDKvVqokTJ2rBggWG9osXL+rixYtas2aNBg8erPfff19ubrkvSIuOjtbo0aMVHBxsaA8LC9O8efO0ePFivfPOOxo8eHCe72n//v0aO3asoqKMtXGOHz+u48ePa/78+Zo8ebLatm2b5ziAM3h7umt4twb6fM1xe9uy/ef0j3taqLq/t4mRAQAAAECGv05d1kvLopSSbtM/ksP0VK/GZodkGrbRFVFqaqoh0dS8eXN9/PHHmjdvnqZPn66xY8fK19dXkjR79mxNnTo1x3E+//xze6KpVatW+uyzzzR//nx99tlnatWqlSRp/vz5+uKLL3KNJT09XePGjbMnmu666y5NnTpV8+fP19tvv63KlSsrJSVF77zzjjZs2JDrOOfPn9eYMWMUFRUlDw8PjRo1SnPmzNGcOXM0atQoeXh4KCoqSmPGjNGFCxcK/ZkBN2JYt3oq53H9R1Zquk0//hViXkAAAAAA8P/FJ6fp5V+DFZtsVWKaTR+tPK7YxFSzwzINK5uKaO3atfZEU/v27TVnzhy5u7vbr/fs2VNBQUF67LHHlJqaqqlTp2rkyJHy8Lj+0Z85c0bTp0+XJLVu3Vpz5syRt3fGao22bdsqKChIw4YN08GDBzVt2jQNGjRI9evXzxbL4sWLtXv3bknS0KFD9e6779qvtW3bVrfddpsGDhyouLg4ffjhh+rZs6chjkyff/65oqOjJUmffvqp7r33Xvu1Tp066ZZbbtGECRN0+fJlffHFF/r4449v+PMDCqqyXzkN7FBHv+wItbfN2R6qcUFN5OvFjzIAAAAA5pm3M0wxDsml1HSr4Y/lZU3ZfedOsnfvXvvx6NGjDYmmTK1bt9btt98uSbp69apOnTpluP7jjz8qLS1NkjRx4kR7oimTj4+PJk6cKCmjHtPMmTNzjCUzYVWxYkW99tpr2a7Xr19fzz33nCTp7NmzWr16dbY+UVFRWrZsmSSpV69ehkRTpvvuu0+9evWSJC1ZsiTbVjuguDzTy1goPDYxVfN3hZsUDQAAAABIaelWTdt8xtAW1LyqvD2z5wfKCpJNRZSaej1zWbdu3Vz7OV5zvMdms2nt2rWSpEaNGqldu3Y53t+uXTs1bJjxi/batWtlsxkrjp05c8aexLrnnnvk4+OT4zgDBgywH69Zsybb9XXr1slqtUqSBg0alOv7GThwoKSMWlPr1q3LtR/gTE2q+SmoRTVD2w+bTyst3WpSRAAAAADKut+DzysiJtHQ9kzP7LuRyhKSTUWUmQCSMopw5ybzmsViUYMGDezt4eHhioyMlCR17tw5z9fq0qWLpIyi4eHhxtUcmdvnHPvlpGrVqvbX37NnT7brjuPkFY/jtZzGAYrLs70bGc7DohO18hC1wwAAAADcfDabTVM3nTa0NQ30VMd6Fc0JqISg0EkR3X///friiy8UFxenqVOnqk+fPtm20h0+fFh//vmnJOmBBx6Qn5+f/drJkyftx40aGX+Jzsrx+unTpw2rpRy35hVknJCQEJ0/f14JCQn2AuaO8VSoUEFVq1bNdYxq1arJz89PcXFx2bYFOpPjKrCSzDFOV4nZVXWo46fWtfx18NxVe9t3f57Snc0r5/ikx4JiDl0fc+jamD/Xxxy6PubQ9TGHro35c01bT0frYMRVQ9tDzcsrLS2tSL+f3CzF9V0j2VREgYGB+s9//qNXXnlFe/bs0SOPPKInn3xSDRo0UEJCgvbs2aPp06crNTVVt9xyi15//XXD/Y5Pc6tRo0aer+V4/fz587mOU7169TzHqVmzpqSMDOyFCxcMyamLFy8WKJbMcU6cOFGsT6Q7evRosY1dXFwxZldzVz2LDp67fn7w3FXNXbdbrauVc8r4zKHrYw5dG/Pn+phD18ccuj7m0LUxf67ji03RhvMafu7qUrtcmZ9Dkk1O0LdvXy1cuFAzZszQggUL9I9//MNwvUqVKnrppZc0ZMiQbLWU4uPj7ceOK4xy4nhvQkJCruOUL1++yOPkF4vjOI6vDdwM3Wp7q1r5OEXGp9vblhxLcFqyCQAAAADyczY2VXsvpBja+jcrL3cXWNFU3Eg2OUFKSoqWLFmSY+FuSbp06ZKWLl2qOnXqqG/fvoZrycnJ9mNPT888X8fLy8t+nJSUVKzj5DeG4ziOr+1sLVq0KFAsZktNTbVnrl0lZlf3XFKoPvj9mP18z4VkeVdvqKbV/PK4K3fMoetjDl0b8+f6mEPXxxy6PubQtTF/ruenRQcN55V8PXVH/YxFGa4yh47fO2ci2VRECQkJevbZZ7Vr1y65u7tr1KhRGjhwoOrWrauUlBTt379fkyZN0u7duzV27Fj94x//0NNPP22/v1y56ysx8tsrmZJyPWPq7e1tuJZ1HMfzwo6TmJhYoH2bmePk9VpF5enpaUiOuQJXjNkVPd61gb5ef1oxCde/qzO2hunTwbcWeWzm0PUxh66N+XN9zKHrYw5dH3Po2pi/ku9CbJKWBxtLyjzRpa7KeWTsHirrc8jT6Iro66+/1q5duyRJH374oV599VU1btxYXl5e8vPzU8+ePTVr1ix17dpVNptN//nPfwxZQ8ctb1m3tGWVmHj9UYpZt7k5jpPftraCjJNfLI7j5LdtDygOvl4eGtHN+DjRJfsidCE2KZc7AAAAAMA5Zmw5o9T06zubynm4aVjXunncUbaQbCoCm82mRYsWSZIaNGigAQMG5NjPw8NDL730kiTJarXa75GMhbjzK7TteD2zyHdO42QW+c5NZnFxi8WSrRB4ZnHxghT9zhynIMXEgeIwokcDlfO4/mMsNd2mGX+dMTEiAAAAAKXdtaRU/bw91NA2uFMdBZYvuyuZsiLZVASXLl1STEyMJKlVq1Z59m3durX9+PTp0/bjJk2a5NieE8frjk+Qk6TGjRsXepyaNWtmW9mUGc+1a9cUFRWV6xiRkZGKi4vL9trAzVTFr5wGdaxjaPt5W6iuJfGoWAAAAADF45cdobqWnGY/t1ikUb0a5XFH2UOyqQjc3d3tx+np6Xn0NNZj8vC4XiqrTp06qlatmiRp586deY6Reb169eqqU8f4C3bHjh3txzt27Mh1jKioKIWEhEiSOnTokO264zh5xeN4LadxgJvl2d6N5Piwh2vJaZq7I8y8gAAAAACUWilpVk3fHGJou+eWGmpQhfIyjkg2FUHFihXl55fx5Ku9e/cqLS0t176OyRnHRJHFYrE/oe706dPat29fjvfv27fPviKpb9++smR5lGLDhg3tK4xWrlxpqMvkaPHixfbjfv36ZbseFBQkN7eMr8XChQtzfT+ZWwHd3NwUFBSUaz+guDWsUl53tzJu5Zy+5YxS060mRQQAAACgtFp+4JwuXDXWiX32NlY1ZUWyqQjc3Nx0++23S8rYVvbdd9/l2C82Nlaffvqp/TzznkxPPvmkfZXUBx98oKQk4xc3KSlJH3zwgaSMVVFPPvlkjq8zcuRISVJMTIw++eSTbNdDQ0P1/fffS5Lq16+vO++8M1ufqlWrqn///pKkzZs3a+XKldn6/O9//9PmzZslSQ899JCqVq2aYzzAzTK6j/GH+/nYJC3bf86kaAAAAACURjabTVM2GsvWdG5QSR3qVTIpopLLI/8uyMsLL7ygtWvXKjExUV9//bUOHjyoAQMGqG7dukpOTtb+/fv1448/6ty5jF98u3fvrl69ehnGaNiwoZ555hlNmTJFBw8e1OOPP65nn31WdevWVVhYmKZOnarDhw9Lkp555hk1aNAgx1gGDBighQsXas+ePZozZ44uXbqkwYMHKyAgQAcOHNDkyZMVFxcnNzc3vfXWW4btfI4mTJigTZs2KTo6Wq+88ooOHjxoT5D9+eefmjFjhiQpMDBQL7/8ctE/RKCIOtSrpM4NKmlnyBV725SNpzWgfe1sqwABAAAA4EZsPHFJRy9cM7SNvo0axjkh2VREjRs31uTJk/W3v/1NV65c0fr167V+/foc+3br1k1ffvlljtcmTJigy5cva+HChTp8+LAmTJiQrc8jjzySZ3LH3d1dkyZN0ujRoxUcHKxVq1Zp1apVhj5eXl5655131KdPn1zHqVmzpr777juNHTtWUVFRmjp1qqZOnWroU7VqVU2aNIkn0aHEGH1bY+0M2WU/P3rhmjaeuKQ+zVh5BwAAAKDopmZZ1dS4ann1bVHNpGhKNpJNTtCjRw/973//04IFC7Rx40adPHlS165dk7u7u6pUqaI2bdrogQceyLHWUiY3Nzd99NFHuvvuuzVv3jwFBwfrypUrqlSpktq0aaNHH300zwRRpsDAQM2dO1e//vqrli9frlOnTikxMVHVqlVT9+7dNWLECDVt2jTfcW699VYtXbpUs2bN0tq1axUeHi4po95U37599eSTT6pSJZYKouTo26KaGlctr1NR8fa2KRtPkWwCAAAAUGQHI2K1+eQlQ9uzvRvJzY2dFDkh2eQklSpV0rPPPqtnn322SOP06dOnQEmlvHh4eGjo0KEaOnRokcbJ3CbHVjm4Ajc3i57t3UivLwq2t205eVkHI2LVunaAiZEBAAAAcHVTNxlXNVXxK6eH29c2KZqSjwLhAEqNh9vXVhW/coa277MsdQUAAACAwgi/kqDlB84b2p7qUV/enu4mRVTykWwCUGp4e7rr6Z4NDG0rgs8rLDrBnIAAAAAAuLwfNp1RutVmP/fxdNewbvVNjKjkI9kEoFQZ1rW+fL2u/4Uh3WrTtM1nTIwIAAAAgKu6HJesuTtDDW2Pd6mnir5eJkXkGkg2AShVAnw99Wjnuoa2uTtDFR2fYlJEAAAAAFzVj1vPKinVaj/3cLNoVO+GJkbkGkg2ASh1nunVUB4OT4VISrVq5l8h5gUEAAAAwOXEJ6fpxyy/RzzUrrZqVfQxJyAXQrIJQKlTp5KvHmxXy9D2418hik9OMykiAAAAAK5m7s4wxSamGtrG9GlkUjSuhWQTgFJpTJ/GhvPYxFT9siM0l94AAAAAcF1KmlU/bDI+2bpfy+pqWr2CSRG5FpJNAEqlZtUrqF/Laoa2aZvPKCXNmssdAAAAAJBh6f5zOh+bZGh7/nZWNRUUySYApdbztxtXN52PTdKSfREmRQMAAADAFVitNn234ZShrUuDQHWsH2hSRK6HZBOAUqtj/UB1aWD8H4TvNpyS1WozKSIAAAAAJd3ao5E6GRlnaBvDqqZCIdkEoFTLurrpVFS8Vh+5aFI0AAAAAEoym82mb/88aWhrXr2C7mheLZc7kBOSTQBKtdubV1WLGsYift/+eUo2G6ubAAAAABjtDLmiPaExhrYxtzeSxWIxJyAXRbIJQKlmsViyPZluX1iMtp+JNikiAAAAACVV1lVNtSv66IG2tUyKxnWRbAJQ6j3QtqbqVPIxtH3756lcegMAAAAoi46cv6r1x6IMbc/2bihPd1InhcUnBqDU83B30+jbjAX9NhyP0qFzsSZFBAAAAKCk+T7LE+gCy3vp0c71TIrGtZFsAlAmDO5YV5XLexnavttw2qRoAAAAAJQkYdEJWnbgvKHtye4N5OPlblJEro1kE4AywcfLXU/1aGBo+/3AOYVeTjAnIAAAAAAlxg+bTivdev0hQr5e7hrRvb6JEbk2kk0AyowR3RuovMNfJqw2acomajcBAAAAZdnluGTN2xVmaHuscz1VyrIzAgVHsglAmRHg66mhXY17rn/dFa6oa8kmRQQAAADAbD/+FaKkVKv93MPNolG9G5oYkesj2QSgTHmmVyN5ulvs5ylpVs3YcsbEiAAAAACYJT45TT9uPWtoe6hdbdWq6JPLHSgIkk0AypQaAd4a0L62oW32trOKS0ozKSIAAAAAZvl5e6hiE1MNbWP6NMqlNwqKZBOAMmf0bY1lub64SdeS0vTLznDzAgIAAABw0yWlpmvKJuMTqvu1rK6m1SuYFFHpQbIJQJnTpJqf7m5Vw9A2Y+tZJafbcrkDAAAAQGmzYHf2+q1j72hsUjSlC8kmAGXS87cb/0fkUlyK1p1JMCkaAAAAADdTWrpV320wPpm6Z5PKal+vkkkRlS4kmwCUSbfWrajeTasY2n47Fq80K6ubAAAAgNJu6f5zCr+SaGgbe0cTk6IpfUg2ASizXrjd+D8mlxKs2hiamEtvAAAAAKWB1WrT5D+Nq5ra16uo7o0qmxRR6UOyCUCZ1a1RoDrWNy6TXXwkXumsbgIAAABKrT8OX9TJyDhD29jbm8ji+BQhFAnJJgBllsVi0bgsS2XPxaXrj8ORJkUEAAAAoDjZbDZNWn/S0NaiRgX1bVnNpIhKJ5JNAMq025tXVaua/oa2bzeels3G6iYAAACgtNl04pKCI2INbS/cwaomZyPZBKBMs1gs2QoBHr0Qpz+PRZkUEQAAAIDiknVVU4PKvrq/TU2Toim9SDYBKPPuaV1DDav4Gtq+WX+S1U0AAABAKbIrJFrbz0Qb2p6/vbHc3VjV5GwkmwCUee5uFj3Xu6GhbffZK9p2OjqXOwAAAAC4mqyrmmoGeGtA+zomRVO6kWwCAEn929ZQFV/jj8TJf57MpTcAAAAAV3LoXKzWZymV8WzvRvLyIC1SHPhUAUCSp7ubHm5e3tC26cQl7Q+LMScgAAAAAE4zef0pw3lgeS893qWeSdGUfiSbAOD/C2roq4rljD8Wv1nP6iYAAADAlZ2KitOKg+cNbc/0aigfL3eTIir9SDYBwP9Xzt2i/llWN60+fFHHLlwzKSIAAAAARfXdn6fk+OyfCuU8NKxbffMCKgNINgGAg7sb+SjAx8PQRu0mAAAAwDWFX0nQ4r0RhrYRPeorwMfTpIjKBpJNAODAx9NNw7sa924v239OZy/HmxQRAAAAgBs1deNppVmvL2vy9nTT0z0b5nEHnIFkEwBkMaJbPfk67N+22qTvNpzK4w4AAAAAJU3UtWTN3RlmaHuscz1V8StnUkRlB8kmAMiioq9ntj3cC3aH63xsokkRAQAAACisqZtOKznNaj/3dLdo9G2NTIyo7CDZBAA5GNWrobw8rv+ITE23acrG0yZGBAAAAKCgouNT9NO2s4a2ge3rqFZFH5MiKltINgFADqr5e+vRTnUNbT9vD1XUtWSTIgIAAABQUNM2n1ZCSrr93N3NohfuaGxiRGULySYAyMVzfRrJw81iP09Os+qHTaxuAgAAAEqymIQU/fiXcVXTQ+1qqX7l8iZFVPaQbAKAXNSp5KtBHeoY2mZtPavLcaxuAgAAAEqqGVtCFJecZj+3WKSxdzQxMaKyh2QTAOThhTsay91hdVNiarqmbT5jYkQAAAAAcnM1KVUzthj/e/2BtrXUuKqfSRGVTSSbACAP9SuX10PtahnaZm09q5iEFJMiAgAAAJCbWX+F6GpSmqFtHKuabjqSTQCQj7F3NJHD4ibFJadp+pYQ0+IBAAAAkF18clq2XQj3tq6h5jUqmBRR2UWyCQDy0biqnx5oa1zdNGPLGV1NSjUpIgAAAABZ/bTtrK4kGP8bfVwQq5rMQLIJAApgXFATWRxWN11LStOPrG4CAAAASoTElHRNzfLk6H4tq+mWWgEmRVS2kWwCgAJoVr2C7mtd09A2bcsZw1MuAAAAAJjj5x2huhRnrKv6YlBTk6IBySYAKKCsS3BjElI1e+tZk6IBAAAAIElJqen6fsMpQ1ufZlV1a92K5gQEkk0AUFAta/rrrlbVDW1TN51WQgqrmwAAAACz/LorTJHXkg1t4/tSq8lMJJsAoBDG9zUuxY2OT9GcbaEmRQMAAACUbSlpVn33p3FVU4/GldWxfqBJEUEi2QQAhdK6doCCWlQztH2/8bSSUtNNiggAAAAouxbuCde52CRDW9Y/EOPmI9kEAIX0YpbaTZfikvXLDlY3AQAAADdTarpVk9afNLR1aRCobo0qmxQRMpFsAoBCal+vkno3rWJo+27DKVY3AQAAADfRb3sjFH4l0dD2IrWaSgSSTQBwA17KsjT34tVkzd8dblI0AAAAQNmSlm7V5Cy1mtrXq6heTarkcgduJpJNAHADOjUIVI/GxuW5364/qZQ0q0kRAQAAAGXH8gPndeZSvKFtfFBTWSwWkyKCI5JNAHCDXgwyrm46F5ukhXtY3QQAAAAUp7R0q75ae8LQ1qZ2gG5vXtWkiJAVySYAuEHdGgWqSwPjI1UnsboJAAAAKFbLDpzT6Syrml4MasKqphKEZBMA3CCLxZLtsarhVxK1iNVNAAAAQLHIWNVkfAJd69r+urNVdZMiQk5INgFAEfRsUlkd61cytH29jtVNAAAAQHFYuv9ctlpNL/dtxqqmEoZkEwAUgcVi0YR+zQxtETGJWsCT6QAAAACnSku36ut1xlVNbWoHqG/LaiZFhNyQbAKAIurZpLI6NzCubqJ2EwAAAOBcS/blsKqpH0+gK4lINgFAEVksFr2cw+qm+bvDTIoIAAAAKF0yVjUZn0DXtk6AglqwqqkkItkEAE7Qo3Hl7E+mW3dSyWnpJkUEAAAAlB6/7TunkMsJhjZWNZVcJJsAwAksFotevtP4ZLpzsUn6dRe1mwAAAICiyG1V0x3NWdVUUpFsAgAn6dG4iro2NK5umrye1U0AAABAUfy275zOsqrJpZBsAgAnylq76Xxskn7dSe0mAAAA4EbktKrpVlY1lXgkmwDAibo3rqxujbLUblp/SkmprG4CAAAACmvx3ogcVjU1Y1VTCUeyCQCcbEKW1U0XriZpHqubAAAAgEJJTbfq63UnDW231q2o25tXNSkiFBTJJgBwsq6NKqtH48qGtsl/nmR1EwAAAFAIi/dGKDSaWk2uiGQTABSDrLWbLl5N1twdoSZFAwAAALiW1BxqNbWrW1G3N2NVkysg2QQAxaBLw0D1bJJ1dRO1mwAAAICCWLwnQmHRiYY2VjW5DpJNAFBMsq5uiryWrJ+3s7oJAAAAyEtqulVfrzeuampfr6L6sKrJZZiWbLp06ZKOHj2qPXv26MCBAwoJCVFycrJZ4QCA03VuEKheTaoY2r7dwOomAAAAIC+L9oTnsKqJJ9C5Eo+b9UJ79uzRxo0btXPnTh0+fFhJSUk59qtTp47atm2rXr166fbbb1elSpVuVogA4HQT7myqzScv2c+jriVrzvZQPdOroYlRAQAAACVTclq6vlprfAJd+3oVdVvTKrncgZKoWJNNly5d0ty5c7Vo0SKdP3/e3m6z2XK9JywsTOHh4VqxYoXc3d3Vu3dvDR06VL179y7OUAGgWHSsH6jeTato04nrCadv/zypx7vUla/XTcv3AwAAAC5h3s4wRcQYVzVNYFWTyymW33QuXryo77//XgsWLFBqaqo9ueTu7q4mTZrolltuUeXKlRUQEKCAgAAlJSUpNjZWsbGxCgkJ0cGDB3XlyhWlpaVp/fr1+vPPP9WkSRONHTtW99xzT3GEDADF5uV+zQzJpktxKZq19azG9GlsYlQAAABAyZKUmq5v1hlXNXVpmPHHW7gWpyebvvnmG02bNk1JSUmy2WyqXLmy7r33Xt19991q06aNvL29CzROWFiYtm3bpmXLlmnXrl06ceKEJkyYoJkzZ+r9999Xs2bN8h8EAEqAjvUr6fbmVfXnsSh723cbTumJrvVUwdvTxMgAAACAkuOnbWcVec1Yy/mVO1nV5IqKJdkkST179tTTTz+tHj16yM2t8HXI69atq7p162rw4MG6ePGiFi5cqB9//FH79u3TH3/8QbIJgEt55c7mhmRTTEKqpm8O0Uv9mpoYFQAAAFAyxCenafKfpwxtvZtWUddGlU2KCEXh9KfR9enTR/+PvfuOr/ns/zj+PtlTIiRBEDFjq1mjtGitas0OirZadZcOXXcXHTrvDu3daotWjS4UVR3UKLe21Cb2iJAgg0jIknHO7w8/ab4yBCf55iSv5+PR+z75fK/vdT5yOXLyOdeYN2+evvjiC3Xp0uWqCk2XCg4O1sMPP6zff/9dTz75pAICAuyQKQCUnuY1/dSrabAh9vm6SCWlZZqUEQAAAFB2zPorSompxvfGT9zMJBNHZfeZTdOmTbN3l7m8vLz04IMPllj/AFCSnri5kX7bE6eLZyScO5+taf+L1L97h5ubGAAAAGCi5PQsTVtrnNXUs3GQrqvN6fSOyu4zmwAABWtUzVe3taxhiM36M0oJl6xLBwAAACqSL/44orMZ2YbYBGY1OTSKTQBQih7r0UDOTv9scJielaNPL1mbDgAAAFQUiamZmvnHEUOsb/NqalrDz6SMYA+lVmxavHjxVd139uxZPfHEE3bOBgDMUTfQR4NbhxhiX/19VCeT003KCAAAADDPtP8dVsr5f2Y1WSzShJ7ManJ0pVZseu655/T4448rOTm52Pds2LBBt912m3799dcSzAwAStcj3RvI1fmf2U2Z2VZ9vPqQiRkBAAAApS/+XIZm/xVliA1oFaIGwb7mJAS7KdVldMuXL9ftt9+u9evXF9kuKytLb731lu6//37FxsbKYrEU2R4AHEmtAC/d1a62ITZvU7SiE9NMyggAAAAofZ+uOayMLGvu185OFj3Wo4GJGcFeSq3YNGrUKElSbGysRo8erbfffltZWVn52h04cECDBw/W7NmzZbVaFRgYqOnTp5dWmgBQKsZ3ry93l3/+Cc622vThqoMmZgQAAACUnhNJ6fp6wzFDbEjrmqpT1dukjGBPLqX1RM8995y6deumZ599VvHx8Zo1a5b++usvvfvuu2rQ4ELl8ssvv9QHH3ygzMxM2Ww23XzzzXr11VdVubLjHHd44sQJff/991qzZo1OnDih1NRUBQQEKCQkRB06dFCfPn3UsGHh60/Xrl2r+fPnKyIiQomJiQoICFDz5s11xx13qFu3bsXKITs7WwsWLNDSpUsVGRmptLQ0BQUFqVOnThoxYkTu9/tyEhMTNXfuXK1cuVLHjx+XJIWEhKhnz54aOXKkQ40LUNYEV/LQiOtD9XmezRAXbY3Rv26sp3qBPiZmBgAAAJS8j38/pMycf2Y1uTpb9EiP+iZmBHsqtWKTJHXq1ElLly7Viy++qBUrVmj//v0aMmSIxo0bp7/++kt///23bDabvLy89Pzzz2vIkCGlmd41mzt3rt5//32lpRmXwsTGxio2NlZbtmxRSkqKXnjhhXz3Wq1WTZw4Ud9//70hHhcXp7i4OK1cuVJDhw7Vq6++KienwiekJSYmasyYMYqIiDDEo6OjNW/ePC1evFiTJk3S0KFDi/yz7NixQ+PGjVNCQoIhfuDAAR04cEALFizQJ598ohYtWhTZD4DCjb2xnr7ZeExpmTmSJKtN+mDlQX1093UmZwYAAACUnGOn0zR/U7Qhdnf72qpZ2cukjGBvpVpskiQ/Pz999NFH+v777/XGG28oLS1NU6ZMkSTZbDa1bNlS77zzjmrXrn2ZnsqWTz75RB9++KEkqU6dOrrjjjvUvHlz+fr6KikpSXv27NGKFSsKLRRNmTIlt9DUpEkTPfDAA6pVq5aio6P1+eefa8+ePVqwYIECAgIKPZ0vJydH48ePzy003XLLLRo6dKj8/f21Y8cOffrppzp9+rQmTZqkoKCgQmdKnTx5UmPHjlViYqJcXFx077336qabbpIk/f7775o1a5YSEhI0duxYLVq0SNWqVbum7x1QUVX1cdd9neto6u+Hc2NLd5zQwzfWU+PqlUzMDAAAACg5/119UNlWW+7X7i5OGncTs5rKk1IvNl3Ut29frVq1Sr///rukC4UmX19fvfHGGw5XaFq/fn1uoWnAgAF67bXX5OrqamjTsWNHjR49WpmZmfnuP3LkiGbOnClJatasmb7++mt5eHhIklq0aKHu3bvrnnvu0a5du/TFF19o8ODBCg0NzdfP4sWLtWXLFknSsGHD9NJLL+Vea9Gihbp27apBgwYpJSVFr7/+ujp37iwXl/x/BaZMmaLExERJ0rvvvqs+ffrkXmvbtq2aNm2qCRMm6PTp0/rggw/01ltvXdH3C8A/xtxQT3PWH9W5jH+Oe31/xQHNGNnWxKwAAACAknE4IUWLtsYYYiOuD1VwJQ+TMkJJKNXT6C7auXOnBg4cqDVr1kiSPD09JUkpKSkaMmSIFixYYEZaV8Vqterll1+WJIWHh+v111/PV2jKy83NLV9s9uzZys6+8IvmxIkTcwtNF3l6emrixImSLuzHNGvWrAL7vliw8vf31zPPPJPvemhoqB566CFJ0tGjR7VixYp8bRISErR06VJJUpcuXQyFpov69u2rLl26SJKWLFmSb6kdgOLz83LVgzfUNcRW7InTjugkcxICAAAAStD7Kw4oz6Qmebk5a+yN9cxLCCWiVItNNptNU6dO1bBhw3T06FHZbDYNHTpU69at0/PPPy83Nzelp6dr0qRJGj9+vM6cOVOa6V2VP/74Q1FRUZKkBx98sMCZQkWx2WxatWqVJKlu3bpq1apVge1atWqlsLAwSdKqVatks9kM148cOaLDhy8sxendu3duAe9SAwcOzH28cuXKfNdXr14tq/XCJm2DBw8uNO9BgwZJulBsW716daHtAFzefZ3rqLKXsUj97m/7TcoGAAAAKBm7jifr550nDbF7O9VRVR93kzJCSSm1YlNMTIyGDRumjz/+WNnZ2fL399fHH3+syZMny9vbWyNHjtTChQsVHh6eW4Dp37+/1q1bV1opXpVly5ZJkiwWi2688cbceFJSkqKiopSUlFTk/TExMYqPj5cktWvXrsi27du3l3Rh0/CYGOO0w4vL5/K2K0hgYKDq1KkjSdq6dWu+63n7KSqfvNcK6gdA8fl6uGpsN+OnOesOntKGyNMmZQQAAADY3zvLjR+oVvJw0UNdmdVUHpXank233Xab0tPTZbPZ1LlzZ7355psKCgoytKlfv74WLFigKVOmaNasWTp16pTGjBmjYcOG5S4jK2t27NghSQoJCZGPj4+WLl2q6dOn68CBA7ltLm4YPmLEiHzL6A4dOpT7uG5d41KaS+W9HhkZqVq1auV+fXFWU3H7iYqK0smTJ5WWliYvr392/L+Yj6+vrwIDAwvtIygoSD4+PkpJSTE8t71lZWWVWN/2lDdPR8kZRmaP4V1taujzdZFKSPlnX7e3f92r7x5oJ4vFUur5OCKzxxDXhvFzfIyh42MMHR9j6NjK+/htijqjtQeMW7A80KWOPF1sBe5t7IgccQxLKs9SKzalpaXJzc1NTz75pEaNGlVoO1dXVz3zzDPq1q2bnnvuOZ04cULffPNNmSw2Wa1WRUZGSpIqV66s1157TXPnzs3XLioqSv/5z3+0YsUKTZ8+XZUq/XPKVGxsbO7jy53qlvf6yZPGqYd5+wkODi6yn+rVq0u6sIQvNjbWUJyKi4srVi4X+zl48KDhue1t3759JdZ3SXHEnGFk1hgOaOChGdv++UG7LTpZX/62We1qsFnileJ16NgYP8fHGDo+xtDxMYaOrbyNn81m06u/Jxpi/u5OauN7Nvc09fKmvI3hlSq1ZXQNGzbUwoULiyw05dWhQwctWbJE/fr1K+HMrt65c+dy9zc6cOCA5s6dq8DAQL3zzjvauHGjduzYoa+++ip3H6Zt27bp+eefN/SRmpqa+zjvDKOC5N2HKS0trdB+vL29r7mfy+WSt5+8zw3g6vWo66kgb2dD7JuIFOVcskcbAAAA4Eg2nzyv/aeNM2iGNvGRh4spZ5ahFJTazKbvv/++wJPYiuLr66v33ntPN910UwlldW3S09NzH58/f16enp6aM2eOYaZQu3btNHv2bN15553at2+fVqxYoR07dqhly5a5911U1Cl2kvEku4yMDMM1e/dzuT7y9pP3ue0tPDy8WLmYLSsrK7dy7Sg5w6isjOEzOqmnFu7K/frY2WxFWatqQKsapuTjSMrKGOLqMH6OjzF0fIyh42MMHVt5HT+r1abn/7fBEKtZ2VOP9W8nt3JWbHLEMcybsz2VWrHpSgtNed166612zMR+Lv0zDRkypMD9kjw8PDRhwgQ99NBDkqRffvklt9jk7v7PrvuXWyuZdx2rh4dxWc2l/eT9+kr7SU9PL9a6zYv9FPVc18rV1fWa/u6YwRFzhpGZYzioTW19/udR7Ys9lxv77++RGtC6drn7YVySeB06NsbP8TGGjo8xdHyMoWMrT+P3w7bj2h+XYog9eUtD+XiV760iytMYXg1+c7kGPj4+hq+7dOlSaNuOHTvKxeVCbS/vmtS8S94uXdJ2qbwzqS5d5pa3n8staytOP5fLJW8/l1u2B6D4nJwserpXI0Ms5ky6vt14zKSMAAAAgKuTmW3V+ysOGGKNgn11W8sQkzJCabF7sSk+Pt7eXeaTkJBw+UalwM3NTQEBAblfF7Wptru7uypXrixJSkz8Z2O0vPdcbqPtvNcvbvJdUD8XN/kuzMXNxS0WS76cL24uXpxNvy/2U5zNxAEUX/fwILUNrWyIfbT6kFLPZ5uUEQAAAHDl5m2O1rFE40SGp3o1krMTpy2Xd3YvNt1888167bXXLlvwuBq//PKL+vfvr3nz5tm976tVv3793McXNwsvTE5OjiTlznC69P6LJ9sVJu/1S5fr1atX74r7qV69er6ZTRfzOXfuXJFFvfj4eKWkpOR7bgDXzmKx6Jne4YbYqZTz+vLPIyZlBAAAAFyZtMxs/XfVQUOsdW1/9WwcZFJGKE12Lzbl5OTo66+/1s0336x///vf+uOPPy5bhCnKyZMnNWPGDPXp00dPPvmkDh48WKbWPbZr1y73cXR0dKHtUlJSdObMGUn/zB6SpJo1ayoo6MKLbdOmTUU+18XrwcHBqlmzpuFamzZtch9v3Lix0D4SEhIUFRUlSWrdunW+63n7KSqfvNcK6gfAtWkfFqCbGgUaYtPWRupMamYhdwAAAABlx6y/opRwzniY1DO9w2WxMKupIrB7sWnp0qW64YYblJmZqR9//FEPPvigunbtqkmTJmnRokU6ePCgbEUc452YmKi1a9fq448/1vDhw9WjRw+9//77OnLkiIKCgvTaa6/pgQcesHfaV+2WW27JfbxixYpC261YsSL3z523oGOxWNSjRw9JF2Ycbd++vcD7t2/fnjsjqUePHvleoGFhYbkzjJYtW2bYlymvxYsX5z7u2bNnvuvdu3eXk9OFvxYLFy4s9M+zaNEiSZKTk5O6d+9eaDsAV++pS/ZuOnc+W5+tPWxSNgAAAEDxJKdl6bM1xvetXRsG6vq6VUzKCKXN7sWmsLAwTZ8+Xd98803uhtmnTp3SggUL9MILL+i2225Ty5Yt1bVrV/Xv31/Dhw/X4MGD1bNnT7Vv316dO3fW2LFjNXXqVG3ZskVWq1XBwcF66qmn9Ntvv2nIkCG5xZCyIDw8XF27dpUk/fzzz1q/fn2+NgkJCfrggw8kXdiRfvDgwYbro0aNkrOzsyRp8uTJysjIMFzPyMjQ5MmTJV1Ygjdq1KgCc7n//vslSUlJSXrnnXfyXT927JimTZsmSQoNDdXNN9+cr01gYKD69+8vSfrjjz+0bNmyfG1+/fVX/fHHH5Kk22+/XYGBgfnaALh2TWv46baWNQyxWX9FKTY5o5A7AAAAAPNN+99hnc0w7jf6zCUfpKJ8c7l8k6vTunVrzZgxQ0eOHNHChQu1bNkyxcTESJIyMzMVHx+v+Ph4WSyWAmc6ubm5qUuXLrrjjjvUtWvXMlVgutTzzz+v7du36+zZs3rooYc0atQodevWTe7u7tq5c6emT5+eu+H2Y489ZlhGJ10o0I0ePVrTp0/Xrl27dPfdd+vBBx9UrVq1FB0drRkzZmjPnj2SpNGjR6tOnToF5jFw4EAtXLhQW7du1ddff61Tp05p6NCh8vPz086dO/XJJ58oJSVFTk5OeuGFFwx7R+U1YcIErVu3TomJiXryySe1a9cu3XjjjZKkNWvW6Msvv5QkBQQE6PHHH7/2byCAQj1xc0P9EnFS2dYL/06ez7bqw1UH9eag5iZnBgAAAOQXfzZDX/4ZZYj1a15dzUL8zEkIpiixYtNFYWFheuqpp/TUU0/pxIkT2rx5s7Zt26bY2FidOXNGSUlJcnd3V0BAgAICAtSwYUO1adNGLVq0KFN7MxUlLCxMn376qR577DGdOnVK06dP1/Tp0w1tLBaLxo4dqwcffLDAPiZMmKDTp09r4cKF2rNnjyZMmJCvzZAhQ4os7jg7O2vq1KkaM2aMIiIitHz5ci1fvtzQxs3NTZMmTVK3bt0K7ad69er67LPPNG7cOCUkJGjGjBmaMWOGoU1gYKCmTp3KSXRACatT1Vt3tqulr/8+lhubvzlaD94QprqBPiZmBgAAAOT30epDSs/Kyf3a2cmiJ25paGJGMIPdi02rVq2SJHXs2DHfSWc1atTQbbfdpttuu83eT2u6tm3b6qefftJXX32llStXKiYmRllZWQoMDFT79u01YsQINWnSpND7nZyc9MYbb6hXr16aN2+eIiIidObMGVWuXFnNmzfXnXfeWWSB6KKAgAB99913mj9/vn766ScdPnxY6enpCgoKUseOHTVy5Eg1aNDgsv20bNlSP/74o+bMmaNVq1blzkqrWbOmevTooVGjRqly5cqX6QWAPTzao4EWbo1RRtaFwxZyrDa9v+KAPh7G5vwAAAAoO46dTtO3G48ZYkPb1FQ9PiStcOxebBo3bpycnJz0448/qn79+rnx5557ThaLRY8//nju6WvlTeXKlfXII4/okUceueo+unXrVqyiUlFcXFw0bNgwDRs27Jr6ubhMjqVygLmCK3no3k5hhs3Bf9p5UmO7JTMdGQAAAGXG+yv2527/IEluLk56rOflJzug/CmRjZAK2oNp8eLFWrx4sc6ePVsSTwkA5dq/utVTJQ/j5wP/Wb7fpGwAAAAAo13Hk/XD9hOG2MjrQ1Xdz9OkjGAmuxebLu6zlJaWZu+uAaDC8vNy1UPd6hli/zuQoL8OnzIpIwAAAOAfby/bZ/ja191FD99Uv5DWKO/sXmy6eNLa5s2b7d01AFRo93Wuo0Bfd0PsrV/3yWrNP5sUAAAAKC3rDiZo3UHjh6Bjb6ynAG/HOPQL9mf3PZs6duyo+fPn6/3339fOnTtVp04dubj88zTffPONAgICrrjf8ePH2zNNAHA4Xm4ueqxHA734w67c2M6YZP0ccVL9W9YwMTMAAABUVFarTW/9apzVFFzJXfd3DjMpI5QFdi82/etf/9Jvv/2mpKQkLV++3HDNZrPp22+/vap+KTYBgHRnu1qa+ecRRSak5sbeWb5fvZpWk5tLiWzDBwAAABRq6c4T2n3CuDfzhJ4N5enmbFJGKAvs/ptJ9erVtXjxYg0dOlQhISFycXGRzWaTxWKRdKHgdDX/AQAkV2cnPdMr3BA7lpimr/8+alJGAAAAqKjOZ+fonUsOrakf5KMhbWqalBHKCrvPbJIuFJwmT55siIWHh8tisWjp0qWqX59NwgDgavVqGqw2oZW15eiZ3NhHqw9pSJua8vVwNTEzAAAAVCRfbTimmDPphtgzvRrJxZkZ9xUdfwMAwMFYLBY918c4uykxNVPT1kaalBEAAAAqmrMZWfp49UFDrG1oZd3cJNikjFCWlMjMpoK8+eabkqRq1aqV1lMCQLnVtk6Abm4SrBV74nJjn/8RqREdQxVcycPEzAAAAFARTFt7WGfSsgyx5/qG526hg4qt1GY2DRw4UAMHDpSPj09pPSUAlGv/7h0uZ6d/fphnZFk1ZcUBEzMCAABARRCbnKEv/jhiiF3Y6uHKT55H+cQyOgBwUPWDfHRH21qG2PzN0ToYd86kjAAAAFARfLDygDKyrLlfOztZ9Ezv8CLuQEVDsQkAHNiEng3k6frPsbJWm/T2sv1F3AEAAABcvYNx5zR/c7QhdkfbWqoXyCom/INiEwA4sKBKHnrghjBDbOXeOG2KSjQpIwAAAJRnby/bL6vtn689XZ01oWcD8xJCmUSxCQAc3JiudRXg7WaIvfHLXtlstkLuAAAAAK7cpqhErdwbZ4g9cEOYgjigBpeg2AQADs7Xw1WP9TB+mrTtWJKW7Yo1KSMAAACUNzabTW/+stcQC/B205iudU3KCGUZxSYAKAfubl9boVW8DLH/LN+vrBxrIXcAAAAAxbd8d5y2HksyxB7tXl++Hq7mJIQyjWITAJQDbi5OerpXI0PsyKlUfbcpupA7AAAAgOLJyrHqP8v2GWK1A7w0rEOoSRmhrKPYBADlRL/m1dWypp8h9uHKA0o5n21SRgAAACgPvvn7mCJPpRpiT/VqJDcXSgooGH8zAKCcsFgserZPY0PsVEqmpq09bFJGAAAAcHTJ6Vn6YOUBQ6xlTT/d2ry6SRnBEVBsAoBypGO9KuoeHmSIzVgXqZPJ6SZlBAAAAEf2ye+HdCYtyxB7oV8TOTlZTMoIjoBiEwCUM8/1CZdznh/+GVlWvbN8v4kZAQAAwBFFJ6bpyz+jDLFeTYPVPizAnITgMCg2AUA50yDYV3e1q2WILdp6XLuOJ5uUEQAAABzRf5bvV2ae041dnPJv2wAUhGITAJRDE25uKB93F0PstZ/3yGazmZQRAAAAHMm2Y2e0dMcJQ2xEx1CFVfU2KSM4EopNAFAOVfVx179urGeIbYhM1Mq98SZlBAAAAEdhs9n0+s97DbFKHi56tHsDkzKCo6HYBADl1OguYQrx9zTE3vxlr7LyTIUGAAAALrVsV6w2Hz1jiD3SvYEqe7uZlBEcDcUmACinPFyd9UzvRoZY5KlUffP3MZMyAgAAQFmXmW3VW8v2GWK1A7w0slOoSRnBEVFsAoByrH+LGmpZ088Q+2DlASWnZxVyBwAAACqyOeujdPR0miH2797hcndxNikjOCKKTQBQjjk5WfTirU0MsTNpWZr6+yGTMgIAAEBZlZSWqY9WG98ntq7tr77Nq5mUERwVxSYAKOfa1QlQ76bGNwiz/oxSdGJaIXcAAACgIvpo9aF8M+Bf6NdEFovFpIzgqCg2AUAF8GyfcLk6//MmITMn/1p8AAAAVFxRp1I1Z32UIdavRXW1Ca1sTkJwaBSbAKACqFPVWyOur2OI/bzzpLZccsoIAAAAKqb/LN+nrBxb7tduzk56tne4iRnBkVFsAoAK4tEe9eXn6WqIvfbzHtlstkLuAAAAQEWwOSpRv0TEGmL3dq6jWgFeJmUER0exCQAqCH8vNz3Svb4htu1Ykn6OOGlSRgAAADCb1WrTaz/vNcT8vVw17sb6hdwBXB7FJgCoQEZ2rKPQKsZPqN5etk8ZWTkmZQQAAAAzLdlxXNujkwyxx3o0kJ+Xa8E3AMVAsQkAKhA3l/xr76MT0/Xln1HmJAQAAADTpGVm6+1f9xtiYVW9NbxDqEkZobyg2AQAFUzvZtXUro7xVJGPVx9U/LkMkzICAACAGT5bc1ixZ43vAV/s11huLpQKcG34GwQAFYzFYtHEW5sYYqmZOXp3+f5C7gAAAEB5E3MmTdP+F2mI3dCgqrqHB5mUEcoTik0AUAG1qOmvIW1qGmILtsRo1/FkkzICAABAaXp72X6dz7bmfu3sdOEDSYvFYmJWKC8oNgFABfVMr0bydnPO/dpmk15Zuls2m83ErAAAAFDSNkclaumOE4bY8A611TDY16SMUN5QbAKACiqokocevsl4pO2mqDP6aedJkzICAABASbNabXpl6R5DzM/TVRN6NjQpI5RHFJsAoAIb3SVMtQI8DbG3ft2njKwckzICAABASVq4NUYRl2yd8HjPBqrs7WZSRiiPKDYBQAXm4eqs5/s0NsSOJ6Vr+iWbRQIAAMDxpZ7P1n8uORSmXqC37rk+1KSMUF5RbAKACq53s2q6vm6AIfbpmsOKTc4o5A4AAAA4ok/WHFLCufOG2Iu3NpGrM6UB2Bd/owCggrNYLJp0a1M55Tl4JD0rR28v22deUgAAALCr6MQ0zVh3xBC7sVGgbmoUZFJGKM8oNgEA1KRGJd3ZrrYhtnjbcW09dsakjAAAAGBPb/66V5nZ1tyvXZwserFfExMzQnlGsQkAIEl68paG8nV3McReWbpHVqvNpIwAAABgDxsiT+uXiFhDbETHUNUP8jEpI5R3FJsAAJKkqj7uerRHA0NsR3SSfth+3KSMAAAAcK1yrDZN/mmPIebv5arHLnnfB9gTxSYAQK5RneoorKq3Ifb2sn1KPZ9tUkYAAAC4Ft9vidbuE2cNsSdubih/LzeTMkJFQLEJAJDLzcVJL/ZrbIjFnT2vT9ccNikjAAAAXK2zGVl6Z/l+Q6xhsI+Gta9dyB2AfVBsAgAYdA8P0g0Nqhpi09dFKjoxzaSMAAAAcDU+XHlQp1IyDbGJtzaRizOlAJQs/oYBAAwsFosm3dpEzk6W3FhmtlWv/7zXxKwAAABwJQ7GndPsv6IMsZ6Ng3RDg0BzEkKFQrEJAJBPg2Bf3dPBOL162e5YrTuYYFJGAAAAKC6bzaaXl+5Wdp5Thd1cnDTx1iYmZoWKhGITAKBAE25uqMperobYyz/uVma21aSMAAAAUBzLdsXqz0OnDbExN9RVaBXvQu4A7ItiEwCgQP5ebnqmd7ghdjghNd90bAAAAJQd6Zk5eu2S7Q9q+Hno4ZvqmZQRKiKKTQCAQt3Rtpaah/gZYh+sPKD4sxkmZQQAAICifLrmkI4npRtiz/drLC83F5MyQkVEsQkAUChnJ4teub2pIZaamaO3ft1nUkYAAAAozLHTafrsf5GGWMe6VdSveXWTMkJFRbEJAFCk1rUra0ibmobYom3HtTkq0aSMAAAAUJDJP+8x7K/p7GTRy7c1lcViKeIuwP4oNgEALuvfvcPl626cej1pyW7l5DnhBAAAAOZZeyBBK/bEGWIjrg9Vo2q+JmWEioxiEwDgsgJ93fX4zQ0NsT0nz+qbjcdMyggAAAAXZWZb9cqPuw2xKt5umnDJ+zegtFBsAgAUy8iOoWoY7GOIvffbfp1JzTQpIwAAAEjSl38eUeSpVEPs373D5efpalJGqOgoNgEAisXV2Ukv32bcLDwpLUvv/LbfpIwAAAAQdzZD/1110BBrWcs/356bQGmi2AQAKLZO9aqqXwvjaSbfbjymXceTTcoIAACgYnvr131KzcwxxF65ramcnNgUHOah2AQAuCIv9G0sT1fn3K9tNmnSkl2yslk4AABAqdoclajF244bYne0ralWtfzNSQj4fxSbAABXpIa/p8Z3r2+IbT2WlO+NDgAAAEpOjtWmly7ZFNzXw0XP9A43KSPgHxSbAABX7IEbwlSnipch9uav+3Q2I8ukjAAAACqWrzYc1e4TZw2xCT0bqqqPu0kZAf+g2AQAuGLuLs6a1L+JIXYq5bymrDhgUkYAAAAVR/y5DL273HhIS8NgH43oGGpSRoARxSYAwFXpHh6sHuFBhtjsv6K0+wSbhQMAAJSkN3/Zp3Pnsw2xybc3k6szv+KjbOBvIgDgqk3q30RuLv/8KLHapIk/sFk4AABASVl/+HS+vTIHXReiDnWrmJQRkB/FJgDAVQut4q2Hb6xniG09lqQFW6JNyggAAKD8ysy2auKSXYaYr4eLnuvb2KSMgIJRbAIAXJOx3eoVuFl4YmqmSRkBAACUTzP/PKJD8SmG2DO9GinQl03BUbZQbAIAXBMPV2e9enszQywpLUv/WbbPpIwAAADKn+NJ6fpw5UFDrHmIn4Z1YFNwlD0UmwAA16xrw0D1a17dEPtuU7S2HD1jUkYAAADly6tLdys9Kyf3a4tFmjygmZydLCZmBRSMYhMAwC4m3tpE3m7OhtiLP+xSdo7VpIwAAADKh9/3xWv57jhDbFj72mpVy9+chIDLoNgEALCLan4emnBzQ0Ns78mzmrP+qEkZAQAAOL6MrBy99ONuQyzA201P92pkUkbA5VFsAgDYzahOdRRezdcQe3/FAcWdzTApIwAAAMf2yZrDOpaYZog91ydc/l5uJmUEXB7FJgCA3bg6O+m1AcbNwlPOZ2vyT3tMyggAAMBxHTmVqs/WHjbE2oZW1uDWNU3KCCgeik0AALtqWydAd7Q1vgH6aedJrTuYYFJGAAAAjsdms+mlH3crM/uf/S+dnSyaPKCZnNgUHGUcxSYAgN0926ex/L1cDbFJS3brfHZOIXcAAAAgr193xep/B4wf1t3XqY4aV69kUkZA8VFsAgDYXYC3m/7dO9wQO3IqVdPXRpqUEQAAgOMoaBuC4EruevySw1iAsopiEwCgRNzZtla+43g//v2Qjp1OK/gGAAAASJL+u/qwTiYbD1iZeGsT+bi7mJQRcGUoNgEASoSTk0WvDWimvFsKnM+2auKSXbLZbOYlBgAAUIYdPpOlORuOGWI3NKiqfs2rm5QRcOUoNgEASkyzED+N7FjHEFt7IEFLd540JyEAAIAyLMdq02ebk2XN87mcm4uTJt/eTBYLm4LDcVBsAgCUqCduaajgSu6G2KtLdys5LcukjAAAAMqmXw6lKTIp2xB7tHt91anqbVJGwNWh2AQAKFGVPFz1cv+mhtiplEy9tWyfSRkBAACUPSeS0vXdrhRDrEGQj8Z0rWdSRsDVo9gEAChxvZtVU8/GQYbYtxuPaVNUokkZAQAAlB02m02v/rxPGTnGfS3fGNRcbi782g7Hw99aAECJs1gseuX2ZvJyczbEn18Uocxsq0lZAQAAlA3Ld8dq9f5Thtjd7WurXZ0AkzICrg3FJgBAqQjx99STtzQyxA7Gp2ja2sMmZQQAAGC+sxlZeunH3YZYVR83Pds73KSMgGtHsQkAUGru7VRHzUP8DLGPfj+kyISUQu4AAAAo395bvl9xZ88bYs/3aSQ/L1eTMgKuHcUmAECpcXay6M1BzeWU5+TezGyrXli8SzabrfAbAQAAyqFtx85ozoajhlirYDf1axZsUkaAfbiYnUB59c477+jzzz/P/XrOnDnq0KFDkfesXbtW8+fPV0REhBITExUQEKDmzZvrjjvuULdu3Yr1vNnZ2VqwYIGWLl2qyMhIpaWlKSgoSJ06ddKIESPUoEGDYvWTmJiouXPnauXKlTp+/LgkKSQkRD179tTIkSNVuXLlYvUDAJdqFuKn+zuH6fM/juTG1kee1sKtxzWkTU0TMwMAACg9WTlWPbcoQnk/b3Nzlsa0qSSLxVL4jYADoNhUAvbu3atZs2YVu73VatXEiRP1/fffG+JxcXGKi4vTypUrNXToUL366qtycip8MlpiYqLGjBmjiIgIQzw6Olrz5s3T4sWLNWnSJA0dOrTIfHbs2KFx48YpISHBED9w4IAOHDigBQsW6JNPPlGLFi2K/WcEgLwm3NxQv+6K1fGk9NzY6z/vUffwIAV4u5mYGQAAQOmY+ccR7Ys9Z4jd0cRHwd78mg7HxzI6O7tYOMrOzlaVKlWKdc+UKVNyC01NmjTR+++/rwULFuj9999XkyZNJEkLFizQBx98UGgfOTk5Gj9+fG6h6ZZbbtGMGTO0YMECvfjii6pSpYoyMzM1adIkrV27ttB+Tp48qbFjxyohIUEuLi564IEH9PXXX+vrr7/WAw88IBcXFyUkJGjs2LGKjY0t5ncFAIy83V00eUBTQ+xMWpZe+3mPSRkBAACUnujENE1ZecAQaxTso/4NvU3KCLAvik12NmfOHEVERKhu3boaMmTIZdsfOXJEM2fOlCQ1a9ZM3377rfr166cWLVqoX79++uabb9SsWTNJ0hdffKGjR48W2M/ixYu1ZcsWSdKwYcP00UcfqWvXrmrRooVGjBihb7/9Vj4+PrJarXr99deVnZ1dYD9TpkxRYmKiJOndd9/V008/rbZt26pt27Z6+umn9c4770iSTp8+XWTxCwAup3t4sPo1r26ILdp6XH8eOlXIHQAAAI7PZrNp4pJdysiy5sYsFmnybY3l4sTyOZQPFJvs6MSJE/rwww8lSa+88opcXS9/esDs2bNzCz8TJ06Uh4eH4bqnp6cmTpwo6cJ+TIUtz7tYsPL399czzzyT73poaKgeeughSdLRo0e1YsWKfG0SEhK0dOlSSVKXLl3Up0+ffG369u2rLl26SJKWLFmSb6kdAFyJl/o3ka+7car4C4sjlJGVY1JGAAAAJWvpzpNas9/4e9Q9HULVqpa/OQkBJYBikx29+uqrSktL08CBA9W+ffvLtrfZbFq1apUkqW7dumrVqlWB7Vq1aqWwsDBJ0qpVq/Kd2HTkyBEdPnxYktS7d295enoW2M/AgQNzH69cuTLf9dWrV8tqvVBdHzx4cKF5Dxo0SNKFJYOrV68utB0AXE5QJQ890yfcEIs6naaPVh80KSMAAICSk5iaqZd/3G2IBfm66+nejUzKCCgZFJvs5JdfftHvv/9e6MyigsTExCg+Pl6S1K5duyLbXixexcXFKSYmxnDt4vK5vO0KEhgYqDp16kiStm7dmu963n6KyifvtYL6AYArMbx9bbWu7W+ITVsbqd0nks1JCAAAoIS8unS3ElMzDbGXb2uqSh6XXxUDOBK2ubeDs2fP6o033pAkPfXUUwoICCjWfYcOHcp9XLdu3SLb5r0eGRmpWrVq5X59cVZTcfuJiorSyZMnlZaWJi8vr3z5+Pr6KjAwsNA+goKC5OPjo5SUFMNzl4SsrKwS7d9e8ubpKDnDiDE016v9G2vApxuUbb0wczPbatMzC3ZowZj2cnEu3ucijKFjY/wcH2Po+BhDx8cYlm1rDiToh+0nDLGbGwepZ6MLhzkxfo7PEcewpPKk2GQH77zzjhISEtS6detibQp+Ud7T3KpVq1Zk27zXT548WWg/wcHBRfZTvfqFzXhtNptiY2MNxam4uLhi5XKxn4MHD5b4iXT79u0r0f5LgiPmDCPG0BwDw720YE9q7te7T57Tm4v+1oBwnyvuizF0bIyf42MMHR9j6PgYw7IlLcuq55cbD0HxcrXoznq23BPF82L8HF9FH0OW0V2jzZs3a8GCBXJxcdErr7wii6X4pwekpv7zS1XeGUYFybsPU1paWqH9eHsXfVRmcfq5XC55+8n73ABwLQaH+6hmJeNnIPN2p+jEuYJPzwQAAHAUX0ek6FS61RC7t6WvKns6m5QRULKY2XQNMjMzNXHiRNlsNo0aNUoNGza8ovvPnz+f+/hyJ9e5ubnlPs7IyCjRfopzit7FfvI+d0kIDw8vVj5my8rKyq1cO0rOMGIMy4b3qyTpzs836eI5CJlWafbebH11Xys5XeYoYMbQsTF+jo8xdHyMoeNjDMumTVFntOzwZkOsY90APda/tWGyAuPn+BxxDPPmbE8Um67BtGnTFBkZqRo1amj8+PFXfL+7u3vu48utk8zM/GcTOQ8PjyL7yfv1lfaTnp5erDWbF/sp6rnswdXV1VAgcwSOmDOMGEPztK8XpPs6hWnmn0dyY5uPJmnB9liNuD602P0who6N8XN8jKHjYwwdH2NYNmRk5Wjij3sNMQ9XJ709uGWRv0sxfo6voo8hy+iu0uHDhzVt2jRJ0osvvlispWeXyrvk7dIlbZdKT0/PfXzpc+Xt53LL2orTz+VyydvP5ZbtAcCVeqpXQ9UK8DTE3vplr44npRdyBwAAQNn031UHFXnK+DvaU7c0Uu0qV/77I+BImNl0lWbPnq2srCzVqlVLGRkZ+vnnn/O1OXjwYO7jDRs26NSpCxvC3XTTTfLy8jJsxH25jbbzXr+4yfdFefuJi4sr8jS8i5uLWyyWfBuBBwcH69SpU8Xa9PtiP8XZTBwAroSXm4veGtRCwz//OzeWmpmjFxZH6Mt7213R3ngAAABm2X0iWdP+F2mItazlr/s6h5mUEVB6KDZdpYvLyKKjo/XEE09ctv0nn3yS+3jVqlXy8vJS/fr1c2ORkZEF3Vbg9bwnyElSvXr1DO0aN2582X6qV6+eb2ZT/fr1tXv3bp07d04JCQkKDAwssI/4+HilpKTke24AsJfO9avqzra1NG9zdG5szf4E/bD9uAZeV9PEzAAAAC4vO8eqZ77fqRyrLTfm6mzRfwa3kPNl9qEEygOW0ZmoZs2aCgoKkiRt2rSpyLYXrwcHB6tmTeMvWm3atMl9vHHjxkL7SEhIUFRUlCSpdevW+a7n7aeofPJeK6gfALCH5/s1VpCvcS+DV5bu0amUkj2YAAAA4FrNWHdEu0+cNcT+dWN9Narma1JGQOmi2HSV3nrrLe3fv7/I//JuGj5nzpzc+MVikcViUY8ePSRdmHG0ffv2Ap9r+/btuTOSevTokW8JSVhYWO4Mo2XLlhn2Zcpr8eLFuY979uyZ73r37t3l5HThr8TChQsL/bMvWrRIkuTk5KTu3bsX2g4AroWfp6teG9DMEEtKy9LLP+42KSMAAIDLi0xI0QcrDxhiDYJ8NO4mVoWg4qDYZLJRo0bJ2dlZkjR58mRlZGQYrmdkZGjy5MmSJBcXF40aNarAfu6//35JUlJSkt555518148dO5a7oXloaKhuvvnmfG0CAwPVv39/SdIff/yhZcuW5Wvz66+/6o8//pAk3X777YUutQMAe7ilaTX1a2Hcp+6nnSf12+7L7y0HAABQ2qxWm55dFKHz2dbcmMUivT2khdxdnE3MDChd7NlksrCwMI0ePVrTp0/Xrl27dPfdd+vBBx9UrVq1FB0drRkzZmjPnj2SpNGjR6tOnToF9jNw4EAtXLhQW7du1ddff61Tp05p6NCh8vPz086dO/XJJ58oJSVFTk5OeuGFF+TiUvDQT5gwQevWrVNiYqKefPJJ7dq1SzfeeKMkac2aNfryyy8lSQEBAXr88cft/e0AgHxe7t9Ufx46paS0rNzYiz/sUoe6VeTn6WpiZgAAAEZf/31UG48kGmL3dqqj1rUrm5QRYA6KTWXAhAkTdPr0aS1cuFB79uzRhAkT8rUZMmRIkcUdZ2dnTZ06VWPGjFFERISWL1+u5cuXG9q4ublp0qRJ6tatW6H9VK9eXZ999pnGjRunhIQEzZgxQzNmzDC0CQwM1NSpUzmJDkCpCPR110v9m2jCvB25sfhz5/XGz3v19pAWJmYGAADwj+jENL356z5DrGZlTz11SyOTMgLMQ7GpDHByctIbb7yhXr16ad68eYqIiNCZM2dUuXJlNW/eXHfeeWeRBaKLAgIC9N1332n+/Pn66aefdPjwYaWnpysoKEgdO3bUyJEj1aBBg8v207JlS/3444+aM2eOVq1apZiYGEkXNjTv0aOHRo0apcqVqcwDKD0DWoVoyfYTWrM/ITc2b3O0+jSvphsbBZmYGQAAwIXlc09/v0NpmTmG+JuDmsvbnV+7UfHwt74EPfLII3rkkUeK3b5bt27FKioVxcXFRcOGDdOwYcOuqZ+Ly+RYKgegLLBYLHp9YHPd8v5apeZ5E/fswggtn9CV5XQAAMBUX/19VBsijcvn7m5fWzc0YI9bVExsEA4AcAgh/p56oV8TQyz2bIZe+2mPSRkBAABIR0+n6s1fjMvnQvw99XzfcJMyAsxHsQkA4DDubl9LNzSoaogt2BKj1fviTMoIAABUZBeWz+1UepZx+dzbg1vI14OZ16i4KDYBAByGxWLRW4NbyOeSvQ+eXRih5PSsQu4CAAAoGXPWR+U7fW54h9rqcsmHY0BFQ7EJAOBQQvw9NfHWxoZY/Lnzeu2X/SZlBAAAKqKjp1P19jLj+48Qf08917dxIXcAFQfFJgCAw7mjbS11a2jccHPJjpPadCLDpIwAAEBFYrXa9PSC/Mvn3hmSfwY2UBFRbAIAOJwLy+may9fD+Gbusy1nde681aSsAABARTHrryhtjDIun7vn+trqVJ/lc4BEsQkA4KCq+3lq0q3G0+mSMqz6YvtZkzICAAAVwZFTqfrPcuPpczUre+q5PiyfAy6i2AQAcFhD2tRU9/AgQ2zdsQz9tifepIwAAEB5ZrXa9Mz3O5SRZZxJ/c6QlvJm+RyQi2ITAMBhWSwWvTmouSpdspzupaV7lZiaaVJWAACgvPryryhtijpjiI3sGKqO9aqYlBFQNlFsAgA4tOBKHnr5tqaG2OnUTE1assukjAAAQHl05FSq3rlk+VytAE/9u3e4SRkBZRfFJgCAwxt4XYh6hBtPp/tp50n9vPOkSRkBAIDyJDvHqgnztrN8Digmik0AAIdnsVj0av/G8nGzGOIv/hCh+HMZJmUFAADKi0/XHNb26CRD7N5OdXR9XZbPAQWh2AQAKBcCfd31wHWVDLEzaVl6dmGEbDabSVkBAABHFxGTrA9XHTTEwqp665nejUzKCCj7KDYBAMqNLrU81CHE3RBbvS9e326MNikjAADgyDKycjRh/nZlW//54MrJIr13R0t5ubF8DigMxSYAQLlhsVj0UBs/VfVxM8Rf+3mPok6lmpQVAABwVP9Ztl+H4lMMsfE31Vfr2pVNyghwDBSbAADlip+7k16/vYkhlpaZoyfmb1d2jrWQuwAAAIz+PHRKM/88Yog1D/HTIz0amJQR4DgoNgEAyp2bGgVqWIfahtjWY0n6bO1hkzICAACOJDk9S08t2GGIubs4acqdLeXqzK/RwOXwKgEAlEsv9G2s0CpehtgHKw9q1/FkkzICAACO4uUfd+tksvFE23/3Dlf9IF+TMgIcC8UmAEC55O3uovfvaCUnyz+xbKtNj8/broysHPMSAwAAZdovESe1eNtxQ6xz/Sq6t1MdcxICHBDFJgBAudUmtLLG3VTfEDsUn6K3l+0zKSMAAFCWxZ/N0POLIwwxXw8XvTOkpZzyfoIFoEgUmwAA5dqjPRqoWUglQ+zLP6P056FTJmUEAADKIpvNpmcW7lRSWpYh/urtTVXD39OkrADHRLEJAFCuuTo7acodreTuYvyR99SCHUq+5M0kAACouL7ZeExr9icYYn2bV9OAViEmZQQ4LopNAIByr0Gwr57tE26InUzO0KQfd5mUEQAAKEuiTqXqtZ/2GmKBvu56fUBzWSwsnwOuFMUmAECFMKpjHXWuX8UQW7L9hJbuOGFSRgAAoCzIyrHqsXnblX7JASL/GdJClb3dTMoKcGwUmwAAFYKTk0XvDm2pSh4uhviLP+zSiaR0k7ICAABm+3DlQe2ITjLEhneorZsaBZmTEFAOUGwCAFQY1f08NXlAM0MsOT1LE+ZtV47VZlJWAADALBsiT2vqmkOGWFhVbz3ft7FJGQHlA8UmAECFcnurEPVvWcMQ+/tIoj5be9ikjAAAgBmS0y584GTL83mTi5NFH97VSt7uLoXfCOCyKDYBACqc1wY0U8glRxi/v+KAth07Y1JGAACgNNlsNj2/OEInkzMM8ad6NVKLmv7mJAWUIxSbAAAVjp+nqz64q5Wc8hwuk2O16bHvtutcRpZ5iQEAgFKxYEuMfo44aYh1qldFY26oa1JGQPlCsQkAUCG1qxOgR7o3MMSOJabppSW7TcoIAACUhiOnUvXyj8af9/5ernr/jlZyyvtJFICrRrEJAFBhPdK9vtqEVjbEFm07rh+2HTcpIwAAUJIys6167LttSsvMMcTfHtxC1fw8TMoKKH8oNgEAKiwXZyd9cGcr+V6yCeiLP+zSsdNpJmUFAABKypSVB7QzJtkQu7t9bfVqWs2kjIDyiWITAKBCqxXgpdcHNTfEUs5n67F525SVYzUpKwAAYG9/HT6V7/TZeoHemnhrY5MyAsovik0AgArvtpY1NKRNTUNs27Ek/XfVQZMyAgAA9nQmNVNPzNshm+2fmKuzRR/edZ283FwKvxHAVaHYBACApJdva6o6VbwMsY9/P6QNkadNyggAANiDzWbTc4siFHs2wxB/ple4moX4mZQVUL5RbAIAQJKPu4s+vOs6ueQ5hcZmkybM267ktCwTMwMAANfiu03RWrY71hC7oUFVje4SZlJGQPlHsQkAgP/Xspa/nrylkSF2MjlDzy7aKVveefcAAMAh7I89p5d/3G2IBXi76b2hLeWU5wMmAPZFsQkAgDwe6lpXnepVMcR+3RWrr/8+ZlJGAADgaqRlZmvcN1t1Ptt44Mfbg1soqJKHSVkBFQPFJgAA8nBysuj9O1rJ38vVEH/1pz3afSK5kLsAAEBZM2nJbh2KTzHERnUM1c1Ngk3KCKg4KDYBAHCJan4eemdIS0MsM9uq8d9sU8r5bJOyAgAAxbVwS4y+3xJjiDULqaTn+zU2KSOgYqHYBABAAW5uEqz7Oxs3Dj1yKlUvLI5g/yYAAMqwQ/EpmrhklyHm4+6ij+9uLXcXZ5OyAioWik0AABTi2T7halnTeCTyku0nNH9ztEkZAQCAomRk5Wj8N1uVlpljiL8xqLnqVPU2KSug4qHYBABAIdxcnPTxsNby9XAxxF/6cbf2x54zKSsAAFCYV3/ao32X/Iy+u31t3dayhkkZARUTxSYAAIpQK8BL/xncwhDLyLJq3DdblZbJ/k0AAJQVS3ec0DeXnB7bKNhXL/VvYlJGQMVFsQkAgMvo07y6RnYMNcQOxado4g+7TcoIAADkdfR0qp5bFGGIebo6a+rw6+Thyj5NQGmj2AQAQDE837exmtaoZIgt3Jr/pBsAAFC6zmfnaNw3W/OdGDt5QDPVD/I1KSugYqPYBABAMXi4OmvqsNbycTfu3zTxh106GMf+TQAAmOXNX/Zp1/Gzhtig1iEa0qamSRkBoNgEAEAx1anqrTcHNTfE0rNyNP6bbUq/5NQbAABQ8pbvjtWsv6IMsXqB3pp8ezNzEgIgiWITAABXpH/LGhrWobYhtj/unF5Zyv5NAACUpqOnU/XUgh2GmPv/nyTrfclMZACli2ITAABXaNKtTRRezbgHxHeborWQ/ZsAACgVGVk5GvvVVp3LMO7T9FL/pmpcvVIhdwEoLRSbAAC4Qh6uzpo6vLW83Iyn27zwQ4T2njxbyF0AAMBeJi3Zle9nbv+WNXR3+1omZQQgL4pNAABchXqBPnpjoHH/powsq8Z+tUXJ6VkmZQUAQPk3b9Mxzd9snE1cP8hHbw1qLovFYlJWAPKi2AQAwFUacF2IRlwfaogdPZ2mpxbskM1mMykrAADKr13HkzVxiXGfRC83Z312D/s0AWUJxSYAAK7Bi7c2Vsta/obYij1xmva/SHMSAgCgnEpOy9K/vt6izGyrIf724BaqH+RbyF0AzECxCQCAa+Du4qxPhrdWZS9XQ/w/y/bpr8OnTMoKAIDyxWq16ckF2xWdmG6I39upjvq3rGFSVgAKQ7EJAIBrFOLvqQ/vuk55t4mw2qRHv92m2OQM8xIDAKCc+HTtYa3cG2+Ita7tr+f7NjYpIwBFodgEAIAddG0YqCd6NjTETqVkatw3W5WVYy3kLgAAcDl/HT6l937bb4gFeLtp6vDWcnPhV1qgLOKVCQCAnYy7qb5uahRoiG05ekZv/rLPpIwAAHBssckZevTbbbLmOXfDYpH+e9d1qu7naV5iAIpEsQkAADtxcrJoyp2tVLOy8c3vzD+P6KedJ0zKCgAAx5SVY9X4b7bqVEqmIf7kzQ3VpUFVk7ICUBwUmwAAsCN/Lzd9dk+bfNP6n/l+pw7FnzMpKwAAHM+bv+zT5qNnDLHu4UF6+Mb6JmUEoLgoNgEAYGfNQvw0+famhlhaZo4emrtFKeezTcoKAADHsXhbjGb+ecQQq1nZU+/f0VJOTpZC7gJQVlBsAgCgBNzZrrbuaFvTEDuckKon52+XNe/GEwAAwGDX8WQ9uzDCEHNzdtKnw9vI38vNpKwAXAmKTQAAlJBXb2+mJtUrGWLLd8dp6u+HTMoIAICy7XTKeT00d4vOZxtPcp08oKma1/QzKSsAV4piEwAAJcTD1Vmf3dNGfp6uhvh7Kw5o5Z44k7ICAKBsysqxatw3W3U8Kd0QH3F9qO5sV9ukrABcDYpNAACUoNpVvPTxsOt06fYSj8/brkPxKeYkBQBAGfTGL3u1ITLREGtXp7Im3trEpIwAXC2KTQAAlLAbGgTquT6NDbGU89kaM2ezzmZkmZQVAABlx8ItMfryzyhDrFolD30yPP8JrwDKPl61AACUggduCNOAVjUMschTqXr8OzYMBwBUbDtjkvTc4ks2BHdx0rQRbRTo625SVgCuBcUmAABKgcVi0VuDW6hZiHHD8NX74vX+igMmZQUAgLlO/f+G4JmXbAj++oBmalnL35ykAFwzik0AAJQSD1dnTRvRVlW8jcc2f/z7If0ScdKkrAAAMEdWjlUPf71VJ5MzDPF7O9XR0La1TMoKgD1QbAIAoBSF+Htq6vDWcr5kx/CnFuzQvtizJmUFAEDpe+2nPdp4xLgheIewAL3Qr3EhdwBwFBSbAAAoZdfXraJJl5ysk5aZozFztigpLdOkrAAAKD0LNkdr9vqjhlgNPw9NHd5ars78mgo4Ol7FAACYYGTHUA1tU9MQO5aYpke+3absHGshdwEA4Pi2HE3UC4t3GWLuLk6aNqKtqvqwIThQHlBsAgDABBaLRZMHNFOrSzY/XXfwlN74ZZ85SQEAUMJizqRpzJwtyrzkg5U3BzVX85p+JmUFwN4oNgEAYBIPV2d9dk/+Y51n/nlE3/x9zKSsAAAoGSnns/XA7M06nWpcMj66S5gGta5ZyF0AHBHFJgAATFTNz0Of3dNabpfsTzFpyS79deiUSVkBAGBfOVabHvt2m/bFnjPEb2wUqOf6hJuUFYCSQrEJAACTtQkN0JuDmhti2Vabxn61RZEJKSZlBQCA/fxn2T6t2hdviNUP8tF/775OLmwIDpQ7vKoBACgDBrepqX/dWM8QO5uRrdGzNys5LcukrAAAuHbzN0dr2v8iDbHKXq76YlRbVfJwNSkrACWJYhMAAGXE07c0Uq+mwYbYkVOp+tfXW5TFCXUAAAe08UiiXlgcYYi5Olv02T1tFFrF26SsAJQ0ik0AAJQRTk4WTbmzlZpUr2SI/3X4tF76cbdsNptJmQEAcOWOnU7TQ3M3KyvH+PPrtQHN1KFuFZOyAlAaKDYBAFCGeLm56It72+Y7oe6bv4/pyz+jzEkKAIArdC4jS6Nnb9KZS5aCP3hDmO5sV9ukrACUFopNAACUMdX9PPX5yLZydzH+mH7t5z36fX98IXcBAFA25FhteuTbbToYbzzkont4kJ7t09ikrACUJopNAACUQS1r+eu9O1oaYlab9Mg323Qg7lwhdwEAYL43ftmrNfsTDLFGwb768K5WcnaymJQVgNJEsQkAgDLq1hY1NKFnQ0Ms5Xy27p+1SadTzpuUFQAAhZuzPkpf/HHEEAvwdtPno9rKl5PngAqDYhMAAGXYoz3q67aWNQyxmDPpGj17s9Izc0zKCgCA/FbuidPLP+42xFydLZo2oo1qBXiZlBUAM1BsAgCgDLNYLPrPkBZqVcvfEN8enaTH521TjpUT6gAA5tsZk6RHvt2mS38svTmohdrVCTAnKQCmodgEAEAZ5+HqrOkj2yjE39MQX747Tq/9vMekrAAAuCA6MU33z9qs9CzjjNvHejTQkDY1TcoKgJkoNgEA4ACCfD305X3t5OvhYoh/+Wf+vTEAACgtyWlZum/WJp26ZC/Bwa1r6vGeDUzKCoDZKDYBAOAgGgb7avqItnJ1Np7k89rPe/RrxEmTsgIAVFTns3M0Zu5mHYpPMcQ71auiNwc1l8XCyXNARUWxCQAAB9KxXhW9O7SlIWazSY/P264tRxNNygoAUNHYbDY98/1O/X3E+LOnUbCvPhvRRm4u/KoJVGQul2+CokRERGjt2rXaunWrDh06pMTERLm6uiooKEitW7fW4MGD1bZt22L3t3btWs2fP18RERFKTExUQECAmjdvrjvuuEPdunUrVh/Z2dlasGCBli5dqsjISKWlpSkoKEidOnXSiBEj1KBB8aazJiYmau7cuVq5cqWOHz8uSQoJCVHPnj01cuRIVa5cudh/LgCA/dzeKkQxZ9L1zvL9ubHz2VY9MHuzFj3cWWFVvU3MDgBQEbz7234t2X7CEAvyddeX97VTJQ9Xk7ICUFZQbLoGw4cP1+bNm/PFs7KyFBUVpaioKC1atEgDBgzQ5MmT5ebmVmhfVqtVEydO1Pfff2+Ix8XFKS4uTitXrtTQoUP16quvysmp8E8JEhMTNWbMGEVERBji0dHRmjdvnhYvXqxJkyZp6NChRf7ZduzYoXHjxikhIcEQP3DggA4cOKAFCxbok08+UYsWLYrsBwBQMh6+sZ5izqTr243HcmNn0rJ075cbtehfnVTFx93E7AAA5dm3G49p6u+HDTFvN2fNvLedalxymAWAioli0zWIj4+XJAUFBal3795q27atqlevLqvVqu3bt2vmzJmKi4vTDz/8oOzsbL333nuF9jVlypTcQlOTJk30wAMPqFatWoqOjtbnn3+uPXv2aMGCBQoICNATTzxRYB85OTkaP358bqHplltu0dChQ+Xv768dO3bo008/1enTpzVp0iQFBQUVOlPq5MmTGjt2rBITE+Xi4qJ7771XN910kyTp999/16xZs5SQkKCxY8dq0aJFqlat2lV/DwEAV8disWjy7U0Vm5yu3/f/88HA0dNpGj17s7598Hp5ujmbmCEAoDxasz9eL/6wyxBzdrLo4+Gt1SzEz6SsAJQ1FJuuQd26dTVhwgT16tVLzs7GN/StWrXSbbfdprvvvltRUVH66aefdNddd6ldu3b5+jly5IhmzpwpSWrWrJm+/vpreXh4SJJatGih7t2765577tGuXbv0xRdfaPDgwQoNDc3Xz+LFi7VlyxZJ0rBhw/TSSy/lXmvRooW6du2qQYMGKSUlRa+//ro6d+4sF5f8fwWmTJmixMQLa6/fffdd9enTJ/da27Zt1bRpU02YMEGnT5/WBx98oLfeeutKv3UAADtwcXbSx8Na687p67Xr+Nnc+PboJD0+b5s+Gd5Gzk5szgoAsI+ImGSN+3qrcqw2Q3zy7c10U6Mgk7ICUBaxa9s1mDZtmvr27Zuv0HRRQECAnn322dyvly9fXmC72bNnKzs7W5I0ceLE3ELTRZ6enpo4caKkC/sxzZo1q8B+Lhas/P399cwzz+S7HhoaqoceekiSdPToUa1YsSJfm4SEBC1dulSS1KVLF0Oh6aK+ffuqS5cukqQlS5bkW2oHACg93u4umjmqnUIuWbawfHecXlm6WzabrZA7AQAoviOnUnXvlxuVmpljiP/rxnoa1qG2SVkBKKsoNpWwDh065D4+duxYvus2m02rVq2SdGGmVKtWrQrsp1WrVgoLC5MkrVq1Kt8vD0eOHNHhwxfWTffu3VuengWvlR44cGDu45UrV+a7vnr1almtVknS4MGDC/tjadCgQZIu7DW1evXqQtsBAEpeUCUPzbqvnXw9jLNV56w/qv+uOmRSVgCA8iLubIZGfPG3TqdmGuL9W9bQ07c0MikrAGUZxaYSlpn5zz/IBW3sHRMTk7v3U0FL7PJq3769pAubhsfExBiuXVw+l7ddQQIDA1WnTh1J0tatW/Ndz9tPUfnkvVZQPwCA0tUg2FfTR7SVq7Nx2dyUlQc0d8NRk7ICADi65PQsjZq5UTFn0g3xzvWr6N2hLeTEcm0ABaDYVMI2bdqU+7hevXr5rh869M8nznXr1i2yr7zXIyMjDdcuzmq6kn5OnjyptLS0AvPx9fVVYGBgoX0EBQXJx8cn33MDAMzTsV4VTbmzlSyXvO+ftGSXftp5ouCbAAAoREZWjh6cvVn7Ys8Z4s1CKmnaiLZyd+EgCgAFY4PwEmS1WjV9+vTcrwva/yg2Njb38eVOdct7/eTJk4X2ExwcXGQ/1atXl3RhCV9sbKyhOBUXF1esXC72c/DgQcNz21tWVlaJ9W1PefN0lJxhxBg6PsbwglvCq+qlfuF6+ad9uTGbTZowb7u8XS3qXK+KidkVjvFzfIyh42MMHZ89xzA7x6pH5u3UxqhEQzw0wFMzhl8nN4vVsIoD147XoONzxDEsqTwpNpWgWbNmaefOnZKkW265Rc2aNcvXJjU1Nfexl5dXkf3l3Yfp0hlJefvx9va+5n4ul0vefvI+t73t27fv8o3KGEfMGUaMoeOr6GPY3FO6s4mP5u1JyY1l5dj0r6+26ZUbA1Q/wNXE7C6voo9fecAYOj7G0PFdyxjabDZ9uuWsVh0xLp3z93DSv6/31okj+8V82ZLFa9DxVfQxZBldCdm4caPee+89SVKVKlX08ssvF9ju/PnzuY9dXYt+8+/m5pb7OCMjo0T7uVwfefvJ+9wAgLJhaBNv9a5n/OAgI8em19YlKuZstklZAQAcwTe7UvIVmrxcLZp4Q2UFezNfAcDl8S9FCTh48KDGjx+v7Oxsubu768MPP1SVKgUvW3B3d899fLnpa3mnqXp4eBTZT96vr7Sf9PT0Yk2lu9hPUc91rcLDw4tV+DJbVlZWbuXaUXKGEWPo+BjD/D5oZtMT30fol11xubFzmTa9tSFF8x5op2p+HkXcXboYP8fHGDo+xtDx2WMMZ68/pkX7jNtkuLs4acaI1mpXp7Jd8kTBeA06Pkccw7w52xPFJjuLjo7W/fffr+TkZDk7O+v9998v8lS3vEveLl3Sdqn09H8+Xbh0mVveflJTU4ssAF2un/T09Mvmkrefyy3buxaurq6GmViOwBFzhhFj6PgYw398cFdrnZu9SesOnsqNnUzO0P1zt2nBQx1V2bvsfZ8YP8fHGDo+xtDxXc0YLtl+XK//ut8Qc7JIHw9rrc4Ni94XFvbFa9DxVfQxZBmdHcXFxem+++5TfHy8LBaL3njjDfXs2bPIe/JuxH25jbbzXr+4yXdB/Vzc5LswFzcXt1gs+TYCv7i5eHE2/b7YT3E2EwcAmMPNxUmf3tNGLWv6GeKH4lN0/+xNSstkSR0AQFq9L05Pzt+RL/7moOa6uQmFJgBXhmKTnSQmJur+++9XdHS0JGnixIkaMGDAZe+rX79+7uPIyMgi2+a9nvcEOUmqV6/eFfdTvXr1fDObLuZz7tw5JSQkFNpHfHy8UlJS8j03AKDs8XF30Zf3tVfdQONM1G3HkvTQ3C06n51jUmYAgLLgr0OnNParrcq22gzxp3s10p3tapuUFQBHRrHJDs6dO6cHHnhAhw4dkiQ9+eSTGj58eLHurVmzpoKCgiRJmzZtKrLtxevBwcGqWbOm4VqbNm1yH2/cuLHQPhISEhQVFSVJat26db7refspKp+81wrqBwBQtgR4u2nu6A6qVsm4T9O6g6c07uttysqxmpQZAMBMW44m6oE5m5WZbfw5cH/nMD18Ix8qA7g6FJuuUXp6usaMGaPdu3dLksaOHasxY8YU+36LxaIePXpIujDjaPv27QW22759e+6MpB49eshisRiuh4WF5c4wWrZsmWFfprwWL16c+7igJX7du3eXk9OFvxYLFy4sNO9FixZJkpycnNS9e/dC2wEAyo4Qf0/NHd1e/l7GzSpX7o3ThHnblXPJJ9oAgPItIiZZ987cpLRM4wzXIW1q6sV+jfP9zgEAxUWx6RpkZmZq/Pjx2rp1qyRp5MiRmjBhwhX3M2rUKDk7O0uSJk+erIyMDMP1jIwMTZ48WZLk4uKiUaNGFdjP/fffL0lKSkrSO++8k+/6sWPHNG3aNElSaGiobr755nxtAgMD1b9/f0nSH3/8oWXLluVr8+uvv+qPP/6QJN1+++0KDAws1p8TAGC+BsG+mnVfe/m4G88I+WnnSf174U5ZKTgBQIWwP/acRsz8W+fOG/fu69eiut4e3EJOThSaAFw9TqO7Bk8++WRu0eX666/XkCFDdODAgULbu7q6KiwsLF88LCxMo0eP1vTp07Vr1y7dfffdevDBB1WrVi1FR0drxowZ2rNnjyRp9OjRqlOnToH9Dxw4UAsXLtTWrVv19ddf69SpUxo6dKj8/Py0c+dOffLJJ0pJSZGTk5NeeOEFubgUPPwTJkzQunXrlJiYqCeffFK7du3SjTfeKElas2aNvvzyS0lSQECAHn/88WJ+twAAZUWrWv768r52GvnFRqVn/fNp9vdbYuTh6qTJtzfj02wAKMeOnErV8M//VlJaliHeIzxIU+5oJWcKTQCuEcWma/Dbb7/lPt6wYYNuu+22ItuHhIRo9erVBV6bMGGCTp8+rYULF2rPnj0FzpAaMmRIkcUdZ2dnTZ06VWPGjFFERISWL1+u5cuXG9q4ublp0qRJ6tatW6H9VK9eXZ999pnGjRunhIQEzZgxQzNmzDC0CQwM1NSpUzmJDgAcVLs6AZoxsq3un73JsE/HVxuOydPVWc/3ZfkEAJRHMWfSNHzGBp1KOW+Id65fRVOHt5abC4tfAFw7ik1lhJOTk9544w316tVL8+bNU0REhM6cOaPKlSurefPmuvPOO4ssEF0UEBCg7777TvPnz9dPP/2kw4cPKz09XUFBQerYsaNGjhypBg0aXLafli1b6scff9ScOXO0atUqxcTESLqwoXmPHj00atQoVa5c+Zr/3AAA83RpUFWfDm+th+ZuMZxANGPdEXm6ueiJmxuamB0AwN7izmZo+Od/60SycduOtqGVNWNkW3m4OpuUGYDyhmLTNdi/f7/d++zWrVuxikpFcXFx0bBhwzRs2LBr6ufiMjmWygFA+dWjcbA+vOs6PfLtVuXdrum/qw7K09VZ/+IkIgAoF06nnNc9n/+to6fTDPHmIX6aeV87ebnxqyEA+2GOJAAAFVy/FtX17tCWunTV3NvL9mnWn0fMSQoAYDfJaVkaOXOjDsanGOKNgn015/72quThWsidAHB1KDYBAAANal1Trw9oni/+8tI9+nbjMRMyAgDYQ3Jalu754m/tPnHWEA+r6q25D7RXZW83kzIDUJ5RbAIAAJKkYR1qa+KtTfLFn1sUQcEJABzQxUJTxPFkQzzE31NfP9BBQb4eJmUGoLyj2AQAAHKN7hKmp3s1yhd/blGEvvmbghMAOIrk9CwN/2JDvkJTcCV3ff1AB9Xw9zQpMwAVAcUmAABgMO6m+nqke/188ecXR+irDUdNyAgAcCVSMq26d9YW7TpuXDoXXMld343pqDpVvU3KDEBFwZEDAAAgnydubihJ+mj1IUP8xR92yWazaUTHOiZkBQC4nHOZVr26NlGRSdmGeLVKHvp2zPUKo9AEoBQwswkAAORjsVj0xM0N9WiPBvmuTVyyW3PWR5V+UgCAIiWlZRVaaPqOQhOAUkSxCQAAFOhiwenxnvkLTpOW7NasP4+YkBUAoCBJaZm6d/aWQgtNLJ0DUJooNgEAgCI93rOhJvRsmC/+8tI9mvkHBScAMFtSWqaGf/639pw8Z4hX96PQBMAcFJsAAMBlPdazgZ68OX/B6dWf9ugLCk4AYJozqRcKTbtPGDcDr1bJnUITANNQbAIAAMXySI8GerpXo3zxyT/t0Yz/RZqQEQBUbPHnMnTX9A35Ck1VPJ301f1tFVqFQhMAc1BsAgAAxTbupvp6pnf+gtPrv+zVBysPyGazmZAVAFQ8MWfSdMdn67U/zrh0rqqnk169MUC1A7xMygwAKDYBAIAr9PCN9fVsn/B88Q9WHtRrP++l4AQAJSwyIUV3fLZeUafTDPHqfh565cYAVfNxMSkzALiAYhMAALhiY7vV0/N98xecvvjjiJ5bFKEcKwUnACgJe0+e1R3TNuhEcoYhXqeKl74d3ZZCE4AygWITAAC4KmO61tNrA5rJYjHGv9sUrce+26bMbKs5iQFAObU9Okl3Td+gUynnDfFGwb6aP7ajavh7mpQZABhRbAIAAFftnutDNeWOVnJ2Mlacftp5Ug/N3ayMrByTMgOA8mVD5GkNn7FByelZhniLmn76bsz1CvL1MCkzAMiPYhMAALgmA64L0afDW8vN2fi24vf9CRo1c6POZWQVcicAoDh+3x+vUTM3KjXTWMBvXydAXz/QQZW93UzKDAAKRrEJAABcs1uaVtOX97WTl5uzIf73kUTd8/nfOpOaaVJmAODYfok4qTFzNuv8JUuTuzYM1Oz728vXw9WkzACgcBSbAACAXXSuX1VzR3dQJQ/j5rQ7YpJ15/T1ij+bUcidAICCzN8UrfHfbFVWjvHQhd5Nq2nGyDbyvKTADwBlBcUmAABgN21CK+u7MR1V1ce4pONAXIqGfLZeR06lmpQZADgOm82mj1Yd1DMLd+rSwz0HXReij4ddJ3cXCk0Ayi6KTQAAwK6a1Kik+Q91VA0/42a1xxLTNOTTv7Q9OsmcxADAAeRYbZq4ZJfeW3Eg37V7rq+td4e2lIszv8YBKNv4VwoAANhd3UAfLfhXJ9Wp4mWIn07N1N3TN+j3/fEmZQYAZVdGVo7Gfb1VX204lu/awzfW0+Tbm8npktM/AaAsotgEAABKRIi/p+aP7aimNSoZ4ulZOXpg9mbN3xxtUmYAUPYkp2Vp5BcbtWx3rCFusUiv3NZUz/QOl8VCoQmAY6DYBAAASkyQr4fmPdRRNzSoaojnWG165vud+mjVQdlstkLuBoCK4WRyuoZO+0sboxINcTdnJ00d1lqjOtUxJzEAuEoUmwAAQInycXfRF6PaaeB1IfmuvbfigCYu2aWcS3fABYAK4mDcOQ365C8diEsxxH3dXTT7/vbq27y6SZkBwNVzuXwTAACAa+Pm4qT3hrZUcCUPfbb2sOHaVxuOKTY5Xfc3dpK7M0tEAFQcm6MSNXr2ZiWnZxniwZXcNeu+9mpcvVIhdwJA2cbMJgAAUCqcnCx6tk+4Xu7fRJduO7Jyb4JeWZuoc5lWc5IDgFK2bNdJDf/873yFpnqB3lr4r04UmgA4NIpNAACgVN3bOUxTh7WW2yVHd+8/naUXVp/WscQ0kzIDgJJns9n06ZrDGvvVVp3PNhbYW9f21/djO6lmZa9C7gYAx0CxCQAAlLq+zatrzuj28vUwrug/fi5HQ6Zv1MYjiYXcCQCOKzPbqn8v3Km3l+3Ld61n4yB9/cD1quztZkJmAGBfFJsAAIAprq9bRd+P7aRqlTwM8aS0LA3/fIO+3xJjUmYAYH9JaZkaOfNvzd+c/9+2u9vX0mf3tJGnm7MJmQGA/VFsAgAApmlUzVeLHu6kRsE+hnhWjk1PLdih/yzbJysn1QFwcEdOpWrQJ39pQ6Rx1qbFIj3fN1xvDGwuF2d+NQNQfvAvGgAAMFUNf099+0A7tanunu/aJ2sO6+GvtyotM9uEzADg2m2IPK2Bn/ypyFOphrinq7M+u6eNxnStJ8ulpyYAgIOj2AQAAEzn4+6if3f2V/+G+TfFXbY7VndO26C4sxkmZAYAV2/B5miN+OJvJaUZT5wLruSuBWM7qlfTaiZlBgAli2ITAAAoE5wtFt3bspIm39ZYLk7GT/kjjifr9o//1K7jySZlBwDFZ7Xa9PayfXr6+53KyjEuBW5SvZJ+GNdZzUL8TMoOAEoexSYAAFCm3Nm2pubc316VLjmpLvZshoZ+tl7LdsWalBkAXF7K+WyN/WqLPl1zON+1no2DtWBsR1X38zQhMwAoPRSbAABAmdOpflUtHtdZdaoYl9WlZ+Vo7Fdb9P6KA2wcDqDMOZyQogFT/9Rve+LyXXugS5imjWgjb3eXAu4EgPKFYhMAACiT6gX6aPHDndUhLCDftf+uOqgH52xWcnpWAXcCQOlbtTdOAz7+U4fiUwxxZyeL3hjYXC/e2kTOTmwEDqBioNgEAADKrMrebpo7uoPuaFsz37VV++I1YOqfOhB3zoTMAOACq9WmD1ce1OjZm3XuvPHkTH8vV82+r72GdahtUnYAYA6KTQAAoExzc3HS24NbaGIBswKOnErVgKl/6uedJ03KDkBFdi4jSw99tUVTVh7Id61x9UpaOr6LujSoakJmAGAuik0AAKDMs1gsGt0lTF+N7qAq3m6Ga2mZORr3zVa9+ete5bCPE4BScij+wv5MKwrYn+m2ljW06F+dVCvAq4A7AaD8o9gEAAAcRsd6VbT0kS5qWTP/keHT1kZq1MyNOpOaaUJmACqSFXviNGDqnzqckGqIO1mkF/s11od3tZKnm7NJ2QGA+Sg2AQAAh1LD31PzHupY4D5Ofxw6pVs/+kO7jiebkBmA8i7HatP7v+3Xg3M2K+WS/Zkqe7lq7ugOeuCGurJY2AgcQMVGsQkAADgcD1dnvT24hV4b0EyuzsZf6o4npWvwp3/p243HZLOxrA6AfcSfzdDwzzfov6sP5bvWpHol/Ti+izrXZ38mAJAoNgEAAAdlsVh0z/Wh+m5MRwX5uhuunc+26rlFEXr0u+06l5FlUoYAyot1BxPU97/rtCEyMd+121vV0EL2ZwIAA4pNAADAobUJrayfHumitqGV811buuOE+rOsDsBVurhsbuTMjTqVYtwPztnJohf7NdYHd7I/EwBcimITAABweEGVPPTNg9fr3k518l2LOp2mQZ/8pTnro1hWB6DY4s5maNiMC8vmLv2no4afh+Y/dD37MwFAISg2AQCAcsHNxUkv39ZUn93TRpU8XAzXMnOsmrRkt/711VYlp7OsDkDR/ncgQX0/XKe/j+RfNtc9PEg/P3qD2oQGmJAZADgGik0AAKBc6d2smn5+9Aa1rOWf79qy3bHq99912h6dVOp5ASj7snOsenf5fo36cqNOpxqXzbk4WfR833B9PrKtKnu7mZQhADgGik0AAKDcqRXgpQUPddSDN4TluxZzJl1DPv1Ln6+LlNXKsjoAF0QnpunuGRv08e8FL5ub91BHjelaT05OLJsDgMuh2AQAAMolNxcnvdCvib4Y1Vb+Xq6Ga9lWm177ea9GfblRsckZJmUIoCyw2Wz6fkuM+ny4TpuizuS73rNxkH557Aa1KeAQAgBAwSg2AQCAcq1H42D98ugNBZ5Wt+7gKd0yZa1+3HHChMwAmO1MaqYe/nqrnlqwQynnsw3XXP7/tLkZI9vK34tlcwBwJSg2AQCAcq+Gv6e+G3O9Hr6xXr5rZzOy9ei32/Tot9uUnMbm4UBFsfZAgnp98D/9uis237VaAZ6aP7Yjp80BwFWi2AQAACoEF2cnPdM7XF+N7qBqlTzyXf9xxwn1+uB/+uPgKROyA1Ba0jNz9NKSXRo1c6Piz53Pd31om5r65dEb1Lo2y+YA4GpRbAIAABVKlwZVtfzxrurfska+a7FnM3TPF3/r5R93KyMrx4TsAJSkXceTdetH6zR7/dF81yp7ueqze1rrnaEt5evhWsDdAIDiotgEAAAqHD8vV31093X68K5WquThku/6rL+i1O+/6xQRk2xCdgDsLSvHqo9WHdSAqX/qcEJqvuvdGgZq+eNd1btZdROyA4Dyh2ITAACosG5vFaLlE7qqS/2q+a4dTkjVwE/+1Hu/7df5bGY5AY5q1/Fk3fbxn3pvxQFlW22Gax6uTpp8e1PNuq+dggpYXgsAuDoUmwAAQIVW3c9Tc+5vr5f7N5G7i/GtUbbVpo9WH1LfD9dpc1SiSRkCuBoZWTl669d9un3qn9p78my+681D/PTTIzdoRMc6bAIOAHZGsQkAAFR4Tk4W3ds5TD8/2kXNQ/zyXT+ckKqh09Zr0pJd+Y5HB1D2bDySqL4frtNnaw8r55LZTE4WafxN9bXo4U6qH+RjUoYAUL5RbAIAAPh/9YN8tejhTnq0e325OBlnOths0pz1R3XL+2v1+754kzIEUJSU89ma+MMu3TFtvSJP5d+bKbyarxY/3FlP9WokV2d+FQKAksK/sAAAAHm4OjvpiVsaaekjXdSiZv5ZTieSM3TfrE167LttOp2S/9h0AOb4fX+8bnl/reZuyH/SnKuzRRN6NtSP47uoZS3/0k8OACqY/MevAAAAQI2rV9Kif3XSl39G6b0V+5WRZTVcX7L9hP53IEEv9W+q21vVYM8XwCTx5zL05i/7tHjb8QKvt6rlr/8MaaGGwb6lnBkAVFwUmwAAAArh4uykB7vW1S1Ng/X84gj9eei04fqZtCw9Pm+7FmyJ1sv9m6oBv8wCpSY7x6o5649qyooDOlfAXmoerk566pZGuq9zmJydKAYDQGmi2AQAAHAZoVW89dXoDlqwJUav/bRHZzOMv9j+eei0+ny4Tvd1rqNHezSQr4erSZkCFcPGI4matGSX9sWeK/B6p3pV9NagFqpdxauUMwMASBSbAAAAisViseiOtrV0Y6NAvfzjbv0SEWu4nm21aca6I/ph+wk93zdcA1qFsLQOsLPLLZnz9XDRC30b6852tXj9AYCJ2CAcAADgCgT5euiT4W00bUQb1fDzyHc94dx5TZi3Q3dMW6/dJ5JNyBAof7JzrPrijyPq8e7aQgtNg1qHaNWT3XRX+9oUmgDAZMxsAgAAuAq9mlbTDQ2q6pPfD2v6/yKVmWPcQHxT1Bn1/+gP3XN9qJ68uZH8vFhaB1yNvyNP66Ufdxe6ZC68mq8mD2imdnUCSjkzAEBhKDYBAABcJS83Fz3Vq5GGtKmpV5bu1u/7EwzXrTZpzvqj+mnnSU3o2UB3ta8tV2cmlgPFcTghRW//uk+/7Ykr8Lqvu4uevKWh7rk+VC68rgCgTKHYBAAAcI3qVPXWzHvbadXeeL3y025FJ6YbriemZmrikt2a+WeUnunVSL2bVWOZD1CIUynn9cHKA/p2Y7RyrLYC2wxuXVPP9glXoK97KWcHACgOik0AAAB2YLFY1LNJsLo0qKppayP1yZpDOp9tXFp35FSq/vX1VrWu7a/n+jZm2Q+QR3pmjj5fF6nP1h5WamZOgW0aV6+kybc3VVteOwBQplFsAgAAsCMPV2c91rOBBrUO0eSf9hS4BGjrsSQN/Wy9bm4SrH/3bqT6Qb4mZAqUDTlWmxZuidF7K/Yr7uz5AttU9nLV4z0baniH2iyZAwAHQLEJAACgBNQK8NL0kW21/vBpvfXrXu2IyX8y3Yo9cVq1N053tqutCT0bKKhS/tPtgPLKZrNpzYEEvf3rvkI3/3Z3cdLoLmEae2M9VfJgk30AcBQUmwAAAEpQx3pV9MO4zvo54qT+s2y/jiWmGa5bbdK3G4/ph23HNapTHT14Q5iq+LAPDcovm82m/x08pQ9WHtC2Y0kFtrFYpEHX1dSTtzRUDX/P0k0QAHDNKDYBAACUMIvFoltb1NAtTarpm7+P6r+rDykxNdPQJj0rR5+tPazZf0VpRMdQjelaV1UpOqEcKU6RSZJuaFBVz/VprCY1KpVecgAAu6LYBAAAUErcXJx0b+cwDW5TU9PWRurzPyKVkWXcRDw9K0fT/xepOeujdE+HUI3pVldBviyvg+MqbpEpvJqvnu/bWF0bBpZecgCAEkGxCQAAoJT5erjqqV6NdM/1ofpg5QHN3xytS094z8iy6vM/jmjuhqMa3iFUY7vVZU8nOJTiFplqBXjq0e4NNKh1TTk7WUovQQBAiaHYBAAAYJJqfh56a3ALjelaV1N/P6wfth9XziVVp/PZVs3884i++vuohrWvrTFd67KHDcq0HKtNK/bE6rO1kdoenVRou1oBnnrkpgYa2DpErpwwBwDlCsUmAAAAk9UN9NF7d7TUI93ra+rvh7RoW/6iU2a2VbP+itLcDUfVr3l1PXBDmFrU9DcnYaAAaZnZWrA5RjP/PKKjp9MKbUeRCQDKP4pNAAAAZUSdqt56Z2hLPdK9gT5Zc0jfb4lR9iVFpxyrTT/uOKEfd5xQ+zoBGn1DmHo2Dmb5EUwTfzZDs9dH6asNx5ScnlVoO4pMAFBxUGwCAAAoY2pX8dJbg1to3E319cmaw/p+S7Sycmz52m2MStTGqESFVvHS/Z3DNKRNTXm78/YOpWN/7Dl9vi5SS7afUGaOtdB2FJkAoOLh3QgAAEAZVSvAS28Oaq7x3etr+trDmr85RulZOfnaHT2dppd+3K33ftuvuzvU1siOdRTCvk4oAdk5Vq3eF6+v/j6m/x1IKLJts5BKevCGuurbvDpFJgCoYCg2AQAAlHEh/p565fZmmnBzQ32z8Zhm/xWluLPn87U7m5GtaWsjNf1/kerWMFB3tautHo2D+EUf1+x4UrrmbTymeZujC/y7l1eP8CA9cENdXV83QBYLyzsBoCKi2AQAAOAg/L3c9PCN9fVAl7r6OeKEPl93RLtPnM3XzmaT1uxP0Jr9CQr0ddeQNjV1V7taCq3ibULWcFQXZzF9u/GY1hxIkC3/Ss5cbi5OGtw6RKO7hKl+kG/pJQkAKJMoNgEAADgYNxcnDbyupga0CtGGyER98UekVu6NL7Btwrnz+nTNYX265rA616+iu9rV1i1Ng+Xu4lzKWcNRJKTl6MPVh7Vw6wnFns0osm2At5vuuT5UIzuGqqqPeyllCAAo6yg2AQAAOCiLxaKO9aqoY70qikxI0ay/orR463GdO59dYPs/D53Wn4dOK8DbTbe1rKH+LWuodW1/ljpBSWmZWro9Rt+tT9SehEzZVPR+TK1q+WtY+9q6rVUNebhSuAQAGFFsAgAAKAfqBvro1dub6dk+4fp550l9u/GYth5LKrBtYmqmZv0VpVl/RalmZU/1b1lD/VvUUOPqvhSeKpD0zByt3BunJdtPaO2B+AJPPMzL191FA64L0d3ta6tJjUqllCUAwBFRbAIAAChHvNxcNLRtLQ1tW0v7Y8/pu03HtGjrcSWnZxXYPuZMeu4yu/pBPurfooZua1VDYVXZ36k8ysqx6o9Dp/Tj9hNavjtWaZn5Tze81MVZTLe2rC4vN359AABcHj8tAAAAyqlG1Xz1Uv+m+nfvcC3bFatvNx7T30cSC21/KD5FU1Ye0JSVB9QspJL6Nq+uHuHBahjsU35mPNls0urV0pw50vr10smTUmqq5O0tVa8udewojRwpde8um6RPN3+qWdtnae+pvWpctbHua3WfxrYd61Dfj5Tz2Vp3IEEr98Zr9b44nUkruPCYl4+7iwZcV0N3t6+tpjX8SiFLAEB5QrEJAACgnPNwddaA60I04LoQRSakaMn2E1q644QiT6UWes+u42e16/hZ/WfZfoX4e6p7eJC6Nw5Sx7pVHHOPnvPnpenTpalTpf37819PSZEOHrzw35w5UqNGemBUZc3M3JDbZNOJTdp0YpO2nNyiz2/7vBSTv3IxZ9K0am+8Vu6N09+RicrMsV72HjcXJ7UOdtUNtT01smdr+Xp7lkKmAIDyiGITAABABVI30EcTbm6ox3s20O4TZ7V0x4XC04nkwk8dO56UrrkbjmruhqPydHVW5/pV1aNxkG5qFKRqfh6lmP1V2rtXGjz4wv8X09qM/ZqZWfC1L7Z9oREtRqhbnW52SvDaZedYtfN4slbtjdOqvfHaF3uuWPc5WaTO9avqtpY11L1hgKIO7pMkuTtiQREAUGZQbEKRjh8/rrlz52rNmjWKjY2Vm5ubatWqpT59+mj48OHy9OQTLwAAHJHFYlGzED81C/HTv3uHa+uxM1q644R+jjipUymFVFkkpWdd2FR65d44SVJ4NV91CAtQm9p+8snIkZ9HGStSbNgg9e0rnTlzRbd93L7o61M3TTW12JRjtWnPibPaEHla6yNPa9ORxEJPISzIdbX9dXvLGurXooYCfd0lSZmZhY87AABXgmITCrV69Wo9/fTTSklJyY2lp6crOTlZu3bt0oIFCzR9+nSFhoaamCUAALhWTk4Wta0ToLZ1AjTx1iZaH3lav+2O0+p98TqelF7kvftiz2lf7DnNXn/h65q+zrohaq861g/U9WEBCqpk4synvXulPn2kpKQrui3NVfqlQdFtfjn4i9Kz0uXpWjofvOVYbdp78kJxaUPkaf19JFHnMopfXHJ1tuj6ulXUIzxIPRoHq1aAVwlmCwCo6Cg2oUB79uzRhAkTlJGRIS8vLz300EPq0KGDMjIy9Msvv2j+/PmKiorSmDFjtHDhQvn4+JidMgAAsAMXZyfd0CBQNzQI1Ks2m/bHndPqffFavTdeW4+dkdVW9P0x53L07aYYfbspRpIUVtVbbUIrq3mIn5qFVFLj6pVK50Sz8+cvLJ0rRqEp3UWKCJYy/j+tjSFSmlvR96RmpWrqpqlqH3JhCpSHi4eaBzW3S/HJZrMp5ky6Io4nX/gvJlk7Y5J09gqKS5JU2ctVNzW6UFzq2rCqfD1crzk3AACKg2ITCvT6668rIyNDLi4umjlzpq677rrcax07dlRoaKjeeecdRUVF6csvv9QjjzxiYrYAAKAkWCwWhVerpPBqlfTwjfWVmJqptQfitWpvvNYeSCjWzJojp1J15FSqvt9yofjkZJHqBfrkLuFrVqOSmtSoZP9CyPTpl92jKdVVery39OV1Uo7TlT/F0yueNnztbHHWfa3u0we9P5C3m3ex+rDZbDqRnKGImGRFHE/Szphk7TqeXKwT4wrSIMhH3RsHqWfjYLWuXVnOTo5zah4AoPyg2IR8du7cqc2bN0uSBg8ebCg0XXT//fdr0aJFOnz4sObMmaOxY8fK1ZVPywAAKM8CvN008LqaGnhdTWXlWLUzJkkbIhP195FEbY5KVFpmzmX7sNqkg/EpOhifosXbjufGawd4qU5Vb9Wt6q06VbwUFuijsCreCqnseeUFE5tN+vjjoptIGniXtKLelXVdlBxbjj7f9rmOJh/V8nuWy2L5J+/U89k6cipVhxNSdORUqiITUhV5KkVHElKVWozvW2HqBnrr+rpV/v+/AAX5OsCG7QCAco9iE/JZuXJl7uPBgwcX2MbJyUkDBgzQe++9p7Nnz+rvv/9Wly5dSitFAABgMldnJ7UJDVCb0ACNu0lKTc/Qj+u2aU9Cpo5leGjrsaQr2rD6WGKajiWm6X8HEgxxN2cn1QrwVFhVH9UK8FSQr4eCfN0VVMk997G/l6uhsKPVq6UDB4p8vuX17VhosjnL2VZZzgqQs62K1h9w08Pf/SpvlxCdSEpXZEKqYs8WftrflQir6p1bWLq+bhUFm7knFgAAhaDYhHy2bNkiSfLy8lLTpk0LbdeuXbvcx1u3bqXYBABABebq7KSGVdzUsIqbmjdvLmcXV+05cVabjyYq4niydh8/q4Px5y6759OlMnOsOpyQqsMJqUU8t0WBPu4KrOShKt5u8t52QN69H5FXZrq8szLklZkun8x0eWVmyDsrXe7ZWVrcRPLMkSTL//93keX//9dFFpunnOT5///vJSebpyzylJPNS07ylJPNR862ADnJTxYZ1+H9usMmKebK/rCXqOzlqmYhfmpR00/NQ/zUqlZlVfOjuAQAKPsoNiGfw4cPS5Jq164tF5fC/4rUrVs33z0AAACS5OxkUfOafmpe0y83lp6Zo72xZ7X7eLJ2HT+riOPJOhB3TtlXWoG6RFbOhX2PTiT//+whz9pSy9qXvS8o85qe1q78PF3VPOTC96t5yIX/alb2NM7YAgDAQVBsgsH58+d15swZSVK1atWKbOvn5ycvLy+lpaUpNja2RPLJyrq6zTFLW948HSVnGDGGjo8xdGyMn+Mrzhg6S2pWzVvNqnnrzjY1JEmZ2VYdjL+wj1HU6TTDf1d6+lpZZ7FIIX4eCqvqrbCqXhf+v4qX6lb1VnAl93yFpdJ+LfA6dHyMoWNj/ByfI45hSeVJsQkGqan/TFH38vK6bHtPT0+lpaUpLS2tRPLZt29fifRbkhwxZxgxho6PMXRsjJ/ju5oxDLVIoVWlblUlyUs2m6fOZdp04ly2TqRk6+S5HCWm5+hMhlVnMqxKSs/R2cxrmxFlbzZlKcdyWn4eFjUPqK0AT2cFeDqpmo+LQnydVc3HRW7OFwtKWZKSpLQkJRyTEoro1wy8Dh0fY+jYGD/HV9HHkGITDM6fP5/7uDiny7m5uUmSMjLss+klAACAJFksFlVyt6iSu5vCq7oV2CbLalNyhlVnMnJ0Jv1CESo106pKX85RusVFaW4eSnX1UKqbV+7jNDdPnXdxlcUmSTYlekrn3G36p2xly/3PqjTZLOmyKl1WS5psSpfVki6b0mS1pMuqNOVYEv//v9Oy6pzuCrtLE5pOkLPFuTS+TQAAlEkUm2Dg7u6e+7g40+kyMy9sduDhUTKbVYaHhxer6GW2rKys3Mq1o+QMI8bQ8TGGjo3xc3xlaQxdX3lAlkOHit1+aUPpriFSWsE1rWLxcvXSV7cvUr8G/a6+E5OVpTHE1WEMHRvj5/gccQzz5mxPFJtg4O3tnfu4OEvj0tPTJRVvyd3VcHV1zZ095SgcMWcYMYaOjzF0bIyf4zN9DDt1kq6g2NT/gDR6m/RRh6t/ytHXjdbApgOvvoMyxvQxxDVjDB0b4+f4KvoYOl2+CSoSd3d3+fv7S9JlN/1OTk7OLUhdbjNxAACAUjNy5BU1t1qkxeHX9pQ/7PtBNlvZ2kMKAACzUGxCPvXr15ckHTt2TNnZhZ8CExkZmfu4Xr16JZ4XAABAsXTvLjVqVOzmm2pIMX7X9pTRZ6O16cSma+sEAIBygmIT8mnTpo2kC8vodu/eXWi7TZv+eUPVunXrEs8LAACgWCwWady4YjffFGKfp910nGITAAASxSYUoGfPnrmPFy5cWGAbq9WqH374QZJUqVIldehwDZscAAAA2NuYMVLjxsVqmmCnrSfjU+Pt0xEAAA6OYhPyadGihdq2bSvpQrFp27Zt+drMnDlThw8fliSNHDnSIXbZBwAAFYi7u7RwoVS58mWbdoq+fHcehe8skKtz7c7FSAwAgPKPYhMK9MILL8jDw0PZ2dm6//77NW3aNG3fvl0bNmzQpEmT9M4770iS6tSpo/vuu8/kbAEAAArQuLH0yy+XLTjdFCW1PlH49Qlb3RXXa6Ue7/B4oW1aV2+tm+rcdHV5AgBQzriYnQDKpiZNmmjKlCl6+umnlZKSovfffz9fmzp16mj69Ony8fExIUMAAIBiuP566a+/pEGDpL17C2ziliP98rU05A7pj9B/4g1OS1N211S/qSuk8HBNUQ/1rNtTE5ZP0MHEg7ntutTuou+Hfi9XZ2Z6AwAgUWxCEbp3764ff/xRc+bM0Zo1axQXFydXV1fVrl1bvXv31j333CNPT0+z0wQAAChaeLi0fbs0bZo0daq0f3++JsGp0rovpS3VpWN+kn9gLXUb8qSc3v2X5OaW265fw37q06CP1katVVJGkmr71VabGm1K8Q8DAEDZR7EJRQoJCdFzzz2n5557zuxUAAAArp6bm/TII9L48dLvv0tz5lyY8RQbK6WkSD4+UrVqatOpk9qMHCnddNOFU+0K4GRx0k1hLJkDAKAwFJsAAABQcVgsUvfuF/4DAAAlgg3CAQAAAAAAYDcUmwAAAAAAAGA3FJsAAAAAAABgNxSbAAAAAAAAYDcUmwAAAAAAAGA3FJsAAAAAAABgNxSbAAAAAAAAYDcUmwAAAAAAAGA3FJsAAAAAAABgNxSbAAAAAAAAYDcUmwAAAAAAAGA3FJsAAAAAAABgNxSbAAAAAAAAYDcUmwAAAAAAAGA3FJsAAAAAAABgNxSbAAAAAAAAYDcUmwAAAAAAAGA3LmYnAFzKZrPlPs7KyjIxk+LLm6ej5AwjxtDxMYaOjfFzfIyh42MMHR9j6NgYP8fniGOYN8+8v4tfK4vNnr0BdpCamqp9+/aZnQYAAAAAABVGeHi4vL297dIXy+gAAAAAAABgN8xsQpljtVqVnp4uSXJxcZHFYjE5IwAAAAAAyh+bzabs7GxJkqenp5yc7DMniWITAAAAAAAA7IZldAAAAAAAALAbTGq9zwAAHW9JREFUik0AAAAAAACwG4pNAAAAAAAAsBuKTQAAAAAAALAbik0AAAAAAACwG4pNAAAAAAAAsBuKTQAAAAAAALAbik0AAAAAAACwG4pNAAAAAAAAsBuKTQAAAAAAALAbik0AAAAAAACwG4pNAAAAAAAAsBuKTQAAAAAAALAbik0AAAAAAACwG4pNAAAAAAAAsBuKTQAAAAAAALAbik0AAAAAAACwG4pNAAAAAAAAsBsXsxMAyrLU1FTt2bNHO3fu1M6dOxUREaHjx49LkkJCQrR69eor6u/AgQP66quv9Ndffyk+Pl5eXl6qW7eu+vfvr6FDh8rFpXgvybVr12r+/PmKiIhQYmKiAgIC1Lx5c91xxx3q1q3bFf85K7KPPvpIH3/88RXdM378eD3yyCOGWExMjHr06FGs+wcOHKi33nrrip4ThRsxYoQ2btxYrLb79++/bBt7vU5RfDExMfr999+1ceNG7d+/X3FxcbJarapcubKaNWumfv36qVevXkV+73kNmuv48eOaO3eu1qxZo9jYWLm5ualWrVrq06ePhg8fLk9PT7NTrHAiIiK0du1abd26VYcOHVJiYqJcXV0VFBSk1q1ba/DgwWrbtm2RfSxatEjPPfdcsZ7vzTff1KBBg+yROv5fo0aNitWuffv2mjt3bpFteO9Y+q7k/clFc+bMUYcOHXK/5jVYsk6fPm34PS8iIkJJSUmSru69gj1eZ9nZ2VqwYIGWLl2qyMhIpaWlKSgoSJ06ddKIESPUoEGDK/1jmoZ3zEARxo4de8U/JAozf/58vfrqq8rKysqNnT9/Xlu2bNGWLVu0aNEiTZs2TQEBAYX2YbVaNXHiRH3//feGeFxcnOLi4rRy5UoNHTpUr776qpycmLhYUsLCwsxOASXEHq9TXJkPPvhAn332mWw2W75rF/9tW7VqlZo3b67//ve/qlGjhglZoiirV6/W008/rZSUlNxYenq6kpOTtWvXLi1YsEDTp09XaGioiVlWLMOHD9fmzZvzxbOyshQVFaWoqCgtWrRIAwYM0OTJk+Xm5mZCligNvHd0HE5OTqpTp47ZaVQonTp1sks/9nqdJSYmasyYMYqIiDDEo6OjNW/ePC1evFiTJk3S0KFD7ZJ3SaPYBBSTv7+/mjVrpq1btyotLe2K7l27dq1eeuklWa1WVa1aVWPHjlXLli2VlJSkBQsW6LffftPOnTs1fvx4zZ07V87OzgX2M2XKlNx/xJo0aaIHHnhAtWrVUnR0tD7//HPt2bNHCxYsUEBAgJ544olr/jNXBMOGDVOvXr2KbGO1WjV8+HClpKTIx8dHPXv2LLL9448/XuQMCz8/v6vKFUVr1qyZ3nzzzau+316vU1yZhIQE2Ww2eXl5qWfPnurYsaNCQ0Pl7u6uw4cPa+7cubmfNt53331atGiRvL29i+yT12Dp2bNnjyZMmKCMjAx5eXnpoYceUocOHZSRkaFffvlF8+fPV1RUlMaMGaOFCxfKx8fH7JQrhPj4eElSUFCQevfurbZt26p69eqyWq3avn27Zs6cqbi4OP3www/Kzs7We++9d9k+v/jiCwUFBRV6vVq1anbLH0Z33323hg0bVuj1omYO8t7RPG+88YbS09OLbHPo0CFNmDBBktSxY0cFBwcX2pbXYMmqUaOG6tatqz/++OOK77XH6ywnJ0fjx4/PLTTdcsstGjp0qPz9/bVjxw59+umnOn36tCZNmqSgoCCHmJFIsQkowq233qo777xTzZs3z/1Etnv37ldUbMrKytLkyZNltVrl4+Ojb7/9VrVr18693rVrV73yyiv65ptvtGXLFi1ZsqTAKbBHjhzRzJkzJV34pfrrr7+Wh4eHJKlFixbq3r277rnnHu3atUtffPGFBg8ezKfIxVClShVVqVKlyDZr167N/cS+d+/eud/3wgQHB6thw4Z2yxHF4+XlddXfd3u9TnHl/P399dRTT+nuu+/OV4ho1qyZbr31Vj355JP69ddfFRUVpS+//FLjx48vsk9eg6Xn9ddfV0ZGhlxcXDRz5kxdd911udcuFg7feeed3LG7dAkySkbdunU1YcIE9erVK19hvFWrVrrtttt09913KyoqSj/99JPuuusutWvXrsg+69Spo5o1a5Zk2ihElSpVrurfNN47mqtWrVqXbbNkyZLcx7fffnuRbXkN2t+4cePUvHlzNW/eXFWrVr2iJfkX2et1tnjxYm3ZskXShQ/DX3rppdxrLVq0UNeuXTVo0CClpKTo9ddfV+fOncv81g7MlQSKcOedd+rWW2+9ph+8K1asUHR0tCTpoYceMvwCe9EzzzyT+0n7F198UWA/s2fPVnZ2tiRp4sSJ+Qoenp6emjhxoqQLa31nzZp11TnDKO8bgQEDBpiXCEqMvV6nuHJPP/20HnzwwUJnvDg7O+ull16Sq6urJGn58uWlmR6KsHPnztylWoMHDzYUmi66//77Va9ePUkX9iLJu0QVJWfatGnq27dvoTMwAwIC9Oyzz+Z+zeuqfOK9Y9lmtVq1dOlSSRc+MLvllltMzqjiefTRR3XTTTepatWqV92HvV5nFwtW/v7+euaZZ/JdDw0N1UMPPSRJOnr0qFasWHHVOZcWik1ACVu1alXu44EDBxbYxtPTU71795Z0YTrtkSNHDNdtNltuP3Xr1lWrVq0K7KdVq1a5+wmtWrWqwD1QcGVSUlJyv/c1a9a87GaqcEz2eJ2i5FSuXDl3o9yLRUGYb+XKlbmPBw8eXGAbJyen3CL92bNn9ffff5dGaiiGvJsQHzt2zMRMUBJ471j2rV+/XnFxcZIuzJznIAXHY6/X2ZEjR3T48GFJRf9dyPseNe/P4LKKYhNQwi5OhwwLC1NgYGCh7dq3b5/7eOvWrYZrMTExufsvXG6a+8V+4uLiFBMTc1U54x+//vqrMjIyJF2Y3myxWEzOCCXBHq9TlKzMzExJYgPbMuTi68bLy0tNmzYttF3en1u8bsqOi68piddVecR7x7Lvhx9+yH18uSV0KJvs9Tq7+PM0b7uCBAYG5m4i7wg/T8v2Ij/AwaWmpurkyZOSLlS7i5L3+sXK9kWHDh0qsN3l+omMjCzWenEU7v/au/egKK8zjuM/UFS8EjHW+6VaITVhQtQxNGkdSBiq1U7VUKqJOBqxahI7bZIabWIYdTSRXBqbJtFcxtFMFTW1khglTbxNOlZaW9TgTBqBKF6CKLsodwj0D2bfLLKwLJy9KN/PXyzv2cNZdp49Z5/3XNqyhO7999/Xm2++aR3/PWDAAI0bN05JSUktfiFD++Tl5SkxMVH5+fmqqqrSbbfdprFjxyohIUE/+9nPrGVYNzIVp/Ceq1evKi8vT5KsJVktIQZ9wxEDw4YNa3HfCOImMP3rX/+yfm5NXC1fvlz5+fmy2+3q0aOHhg8frpiYGM2ePbvFTY3Rfvv379e+fft04cIFBQcH6/bbb1d0dLSmT5+ue++91+VzGDsGtrKyMmtmyuDBgxvNNGwOMRh4TMWZc9/Ymnq+/vprXbp0SeXl5erevbunzfYZbmMAXvTNN99YP7s7IcL5uvPz2lOP4ws02ub8+fPWfiT33HOPy318XMnJydG5c+dUXV2t0tJSnTlzRunp6ZoxY4ZWrlzZ6G4yzLly5YpOnjyp69evq7q6WoWFhTpw4ICWLVumX/ziF81+yTUVp/Ced955x9oPYfLkyW7LE4PeV1VVJZvNJsl93PTp08caDBM3gaGurk6bNm2yHrcmrrKyslRUVKSamhrZ7XadOHFCb731luLj47V9+3ZvNrfDO3PmjHJzc1VZWany8nKdPXtWf/vb3zR37lw99thjun79epPnMHYMbJ988ol14NC0adNaNXOeGAw8puLMuR53icOBAwdKaljCF+h9KjObAC8qKyuzfnaXdXa+fuNpd57U47zG15NT89DUnj17rDXVze3j46x379568MEHNXHiROvo9qKiIn3++efatWuXysvLlZ6errKyslYdM43WCQoKUkxMjCZNmqTIyEiFhYWprKxMOTk5Sk9PV25urs6cOaPk5GTt3LlTgwYNavR8U3EK7zhx4oS2bNkiqWGgNmvWrGbLEoO+40ncSA19U3l5OXETIDZv3qyTJ09Kajhe+84772y27NChQxUfH6/o6Gjry9L58+eVmZmpzMxMVVVV6fnnn1dQUJCSkpJ80v6OIjQ0VHFxcYqJidHIkSPVo0cPFRcXKysrS9u3b5fdbtenn36qJUuW6L333ms0g5exY2BzXkLnbuY8MRi4TMWZcz09evRocz2BhmQT4EXOd8+bW8Lj0KVLF+tnxx5BDlVVVUbqgWcyMjIkSV27dnV717d///46cuSIyw39Jk2apIcffljz5s3TxYsX9dFHH2nKlCkeH60K115//XX17t27ye/Hjx+v2bNn67nnntPu3bt15coVrV27Vq+//nqjcqbiFOZduXJFS5cuVW1trYKCgvTCCy80u2kmMehbnvRL0nexQ9z4X1ZWlpVsDQ8PV2pqarNl4+PjNX369CazLqKiojRlyhQdPHhQTzzxhGpqarRu3TrFxcW1uO8dPHPkyBGX/dt9992nOXPmKCUlRadPn1ZWVpa2bdum5ORkqwxjx8D1zTffKCsrS1LjjaNdIQYDm6k4u1XjlWQTbnqOE4raY926dZoxY4aB1jTm/GHg7rhn5y+8Nx6Z2bVrVyP13Mx8/T5nZ2fr66+/liQ98MAD6tWrV4vlnd9rV0aMGKG0tDQ9/PDDkhr2lOlIX3S9+f65Gog7hISEaM2aNcrOzlZ+fr7+/ve/q7CwsNEUZVNxeqvzdQyWlpZq4cKF1hTxJ598UjExMc2WJwZ9y5N+Sfoudjpa3ASar776So8//rhqa2vVtWtXvfbaawoPD2+2vLu+LzY2VkuWLNFrr72miooK7dq1S4sXLzbd7A6rpf6tX79+2rBhgyZPnqyamhq9//77jZJNjB0DV0ZGhurq6iS5n9VEDAY2U3F2Yz3Ojz2pJ9CwZxPgRc7TIN1Nc3S+fuM0TE/qqaioaLYetJ4n05tba/z48Ro9erSkhlMnHAMNeFfnzp310EMPWY8ddxMdTMUpzKmqqtKSJUuUk5MjSZo/f75SUlLaXS8xaI4ncSN91zcRN/5TUFCg+fPnq6SkRJ06ddIrr7zi9vSk1khKSrJmXThvOg7vGzp0qH70ox9Jks6ePavCwkLrGmPHwOU4fKZLly6aMmVKu+sjBv3HVJw51+O8pM7TegINM5tw0/v444/bXUf//v0NtKQp59kT7jZwa2mDOU82JXa+7thA7lbgy/e5urpa+/btk9Rw5/D+++9v9992GDVqlM6cOaOqqirZ7Xb17dvXWN2BzN9x6kgwSGo0GJfMxemtzlfvYW1trX7zm9/o2LFjkqTExEQtW7as3X/boaPGoGldu3ZVWFiY7Ha727gpKSmxBuEdLW4CRWFhoebNm6fLly8rKChIa9eu1YMPPmik7vDwcIWFhclmszX5fIX3jRo1SocPH5akRjN3GTsGplOnTlknmMXGxqpPnz7trpMY9B9TceZcT2FhYYtjE8fm4kFBQQHfp5Jswk2vNcf1+kvPnj01cOBAXbp0yTq2uznO1298Tc5flD2px93RmTcTX77Phw4dkt1ul9RwQkinTp2M1d2a00ZuRf6O05b+76bi9Fbni9dbV1en3//+9zp48KAkacqUKVq1apXRv9FRY9AbRo8erX//+986d+6camtr1bmz62FlR46bQFBcXKz58+eroKBAkvTcc88Zm7HrQFz5T3P/e8aOgckxq0kyN3NeIgb9xVScOfeNeXl5uuOOO9zWM3DgwICf2cQyOsDLxo0bJ0nKz89XUVFRs+Wcl/bcc889ja4NGTLEmhHgbnqs4/r3vvc9DRkypE1t7ui8sYTOITc3V1LD1OmwsDCjdaN5jruIkuvZNSbiFO23cuVK7d27V1LDHd+0tDQFB5sdqhCD5jjipry83Fry6Ipzv0Xc+Nb169e1YMEC6zPwySeftPYtM6W4uFg2m02S92aKo3mOzzSp8Uxdxo6Bp6amxurj+vbtq5/85CdG6iUG/cdUnDn6U6npdg/OioqKrD1lb4b+lGQT4GXOG9Du3r3bZZmKigrt379fUkOG/MZTKYKCgqx68vLylJ2d7bKe7OxsK9v9wAMPcJejDWw2m44cOSJJioyMVGRkpLG6jx8/rq+++kpSQ6di+ks0XKutrdUHH3xgPXa1R4mJOEX7rFu3Tjt37pQkxcTEaMOGDc3OlGkrYtAs52VYzjHmrK6uzkrg9+7dWxMnTvRF06CGz6yFCxdaicBFixZp4cKFxv9Oenq66uvrJbn+fIX3FBQU6B//+IckadiwYY2STYwdA8+RI0dUXFwsSZo6daqxPo4Y9B9TcTZy5EhrdtP+/fsb7cvkzHmMamoptDcxygK8LD4+XkOHDpUkbdy4UefOnWtSZv369SopKZEkPfrooy7rmTt3rrWca/Xq1U2OuqysrNTq1aslNWyIPHfuXGOvoSPZu3evdZqEJ7OaPv30U6ujd+Xs2bN66qmnrMezZ89ucxvxnX/+85+6du1as9dramr07LPPWnd+Y2NjXe5HYSpO0TZ/+tOftHnzZklSdHS03njjDbeny92IGPS9qKgojR8/XlJDsum///1vkzLvvfeeFX/Jycluj3SGGdXV1Xr88cf1n//8R1LD//63v/2tR3WcP39ep0+fbrHMwYMH9ec//1lSw6lIM2fObFuD0cSBAwdUW1vb7PUrV65o6dKl1pjF1WcaY8fA4ukSOmLw5mAqzubPny9JstvtSktLa3L93Llz2rhxoyRp+PDhio+PN/YavCWovqWRGdDBnT17VsePH2/0uxdffFF2u11hYWFNNq398Y9/rNtvv71JPYcPH9aiRYtUV1enfv36afHixYqKilJJSYl27typzMxMSQ132rdu3drsHkEvv/yyNm3aJEn64Q9/qJSUFA0dOlQFBQV6++23rQ7p17/+tX73u9+1+/V3RA899JBOnTqlzp076/Dhw+rXr1+rnhcREWF98EdFRWnAgAHq0qWLLl++rM8//1y7du2yNsidPHmy/vjHP3rxVXQczzzzjDIzMxUXF6eJEydq5MiR6tmzp8rKypSTk6MdO3ZYy0fCw8OVnp5uJZVuZCpO4ZmtW7dqzZo1khqmlr/66qtuj3oeOXJkk6QFMegfp0+f1qxZs1RZWanu3btr0aJFmjhxoiorK/Xxxx8rPT1dkjRixAh98MEH6tmzp59b3DE88cQT+uSTTyRJ9957r1asWNHijJWQkJAmszWPHTum5ORkRUdHKzY2VpGRkdamtQUFBcrMzFRmZqaV5F25cqXxJXodWVxcnGpqapSQkKC7775bgwcPVrdu3WSz2XTs2DGlp6dbS6fGjRunzZs3u0zSM3YMDCUlJbr//vtVXV2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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 454,
       "width": 589
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# requires_grad=True is required\n",
    "# this is our starting point\n",
    "current_solution = torch.randint(low=-100, high=100, size=(1,), dtype=torch.float32, requires_grad=True)\n",
    "\n",
    "# initialize a simple SGD\n",
    "# SGD will minimize only one variable — current_solution\n",
    "optimizer = torch.optim.SGD([current_solution], lr=1e-2)\n",
    "\n",
    "NUM_STEP = 200\n",
    "\n",
    "\n",
    "for i in range(NUM_STEP):\n",
    "    current_loss = func(current_solution)\n",
    "    \n",
    "    # zero out .grad of `current_solution` \n",
    "    # remember that otherwise your new gradients will be summed with the existing ones\n",
    "    optimizer.zero_grad()\n",
    "    \n",
    "    # compute new gradient by `current_solution`\n",
    "    current_loss.backward()\n",
    "    \n",
    "    # update current_solution\n",
    "    optimizer.step()\n",
    "\n",
    "    # some logging and visualization stuff\n",
    "    if i % 20 == 0:\n",
    "        display.clear_output()\n",
    "        \n",
    "        x = torch.linspace(-100, 100, 100)\n",
    "        y = func(x)\n",
    "\n",
    "        plt.plot(x, y)\n",
    "        plt.scatter([10], [14], label=\"Minimum\", c=\"red\", linewidths=3)\n",
    "        plt.scatter([current_solution.item()], [current_loss.item()],\n",
    "                    label=\"Current Solution\", marker=\"*\", c=\"green\", linewidths=3)\n",
    "        \n",
    "        plt.legend()\n",
    "        plt.title(f\"Step Number: {i}\")\n",
    "        plt.xlabel(\"x\")\n",
    "        plt.ylabel(\"f(x)\")\n",
    "        plt.show()\n",
    "        \n",
    "        time.sleep(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0ecd201-22e3-489b-a799-91a5c42f8ba4",
   "metadata": {},
   "source": [
    "# The General Pipeline\n",
    "\n",
    "Training pipeline for your DNN model is similar to the example with some function above. To train your model you will need:\n",
    "\n",
    "1. Define your model\n",
    "2. Define a `Dataset` and `DataLoader`. Make sure you have at least 2 splits: train\\test, so you can monitor performance on unseen data\n",
    "3. Choose an optimizer. We advise you to use `torch.optim.Adam` or `torch.optim.AdamW` (if you use weight decay). Your optimizer should work with `model.parameters()` to optimize model weights. Basically, we will have `model.parameters()` instead of `[current_solution]` in the example above.\n",
    "4. Choose a scheduler. That is, control learning rate (step size) for your optimizer. There are plenty of them in `torch.optim.lr_scheduler`. We advise you to use [CosineAnnealing](https://pytorch.org/docs/stable/generated/torch.optim.lr_scheduler.CosineAnnealingLR.html#torch.optim.lr_scheduler.CosineAnnealingLR) or [OneCycleLR](https://pytorch.org/docs/stable/generated/torch.optim.lr_scheduler.OneCycleLR.html#torch.optim.lr_scheduler.OneCycleLR). The latter uses warm-up technique (the learning rate goes from low value to high during the first several steps and then the scheduler decreases the learning rate as usual), which is essential for Transformer-based models. The absence of scheduler is equivalent to a constant learning rate.\n",
    "5. Iterate over your dataloader (for DNNs you reuse the same dataloader (the data shuffles) several times, a.k.a. epochs). For each batch, compute the loss, do `.backward`, run `optimizer.step()` to update weights and `scheduler.step()` to update learning rate. **Do not forget to zero gradients between batches via calling `oprimizer.zero_grad()` after `step()` or at the beginning of the for-loop**. Do some logging (recommended).\n",
    "6. Finish, your model is trained.\n",
    "\n",
    "The choice of the scheduler and optimizer depends on the task. There is no such setting that works all the time, you should try several settings and choose the one that works best for your task. However, usually `Adam`, `AdamW` and one of the mentioned schedulers should do the work (You may need to tune `learning_rate` and `weight_decay`. Do not forget to think about the total number of training steps)\n",
    "\n",
    "If you want to work with a model from some paper, the best starting point would be to use the **same** optimizer and scheduler (with the **same** hyperparameters, i.e., learning rate, weight decay, etc.), as was done by the authors. However, if the paper is rather **old** and do not use Adam\\AdamW (or at least SGD), it is better to use our **suggested** schedulers and optimizers instead (unless you are sure what and why you are doing). The exception is the case when you want to **exactly reproduce** the results from the paper. In such a case, you must use the paper authors' setting to get the authors results.\n",
    "\n",
    "**We will have a look at this pipeline in the next lesson**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1fb87f97-4c30-4d54-a390-82e00bb1759d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
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