4_symbolic_learning.ipynb

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    "# Symbolic Regression using KANs\n",
    "\n",
    "This is Part 4 of the tutorial series on KAN. \n",
    "\n",
    "In our previous notebooks, we looked at the fundamental components of KANs, including spline activation functions and how to perform backpropagation in a network using such functions. We also explored the unique advantages of KANs, such as their capability for continual learning and enhancing model capacity.\n",
    "\n",
    "In this notebook, we will learn how to train KANs when specific activation functions are predetermined and fixed to a symbolic formula. If a user is able to identify a spline that matches a certain symbolic function, that activation can be fixed to the identified symbolic formula, while the rest of the KAN continues to be trained.\n",
    "\n",
    "Let's dive into this scenario.\n",
    "\n"
   ]
  },
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   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from utils import eval_basis_functions, get_coeff, single_stacked_kan_training"
   ]
  },
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   "source": [
    "## Dataset\n",
    "\n",
    "Let's create a dataset using the function example provided by the authors: $ f(x, y) = e^{\\sin(\\pi x) + (y+0.5)^2} $."
   ]
  },
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     "text": [
      "Training dataset:  1280\n",
      "Test dataset:  713\n"
     ]
    }
   ],
   "source": [
    "fn = lambda x: torch.exp(torch.sin(torch.pi * x[:, :1]) + torch.pow(x[:, 1:] + 0.5, 2))\n",
    "\n",
    "x1 = torch.linspace(-1, 1, steps=40)\n",
    "x2 = torch.linspace(-1, 1, steps=40)\n",
    "x1, x2 = torch.meshgrid(x1, x2, indexing='ij')\n",
    "x_eval = torch.stack([x1.flatten(), x2.flatten()], dim=1)\n",
    "y_target = fn(x_eval) #+ torch.randn((x_eval.shape[0], 1))*0.1\n",
    "\n",
    "# test and train split\n",
    "n_training = int(x_eval.shape[0] * 0.8)\n",
    "training_idxs = np.random.randint(x_eval.shape[0], size=n_training)\n",
    "test_idxs = [i for i in range(x_eval.shape[0]) if i not in training_idxs]\n",
    "x_training = x_eval[training_idxs]\n",
    "x_test = x_eval[test_idxs]\n",
    "y_training = y_target[training_idxs]\n",
    "y_test = y_target[test_idxs]\n",
    "\n",
    "print(\"Training dataset: \", n_training)\n",
    "print(\"Test dataset: \", len(test_idxs))"
   ]
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    "### Basic functions\n",
    "\n",
    "Let's define some basic functions\n",
    "1. `initialize_KAN` to setup a KAN using the parameters provided\n",
    "2. `eval_KAN` to evaluate KAN for a given x\n",
    "3. `eval_x_symbolically` to evaluate x given only the symbolic functions\n",
    "4. `set_symbolic_fn` to set a particular activation function in KAN to a specified symbolic function"
   ]
  },
  {
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    "def initialize_KAN(KAN, k, grid_range, grid_size):\n",
    "    \"\"\"\n",
    "    Returns the ingredients necessary to evaluate a KAN.\n",
    "    Note: we use a single grid for all the activation functions.\n",
    "\n",
    "    Args:\n",
    "        KAN: List of integers corresponding to neurons in each layer\n",
    "        k: spline order\n",
    "        grid_range: range of grid. e.g, [-1, 1]\n",
    "        grid_size: number of control points\n",
    "    \"\"\"\n",
    "    grid = torch.linspace(grid_range[0], grid_range[1], steps=grid_size).unsqueeze(dim=0)\n",
    "    \n",
    "    # initialize the coefficients and symbolic functions\n",
    "    coefs, masks, symbolic_functions = [], [], []\n",
    "    for in_dim, out_dim in zip(KAN, KAN[1:]):\n",
    "        coef = torch.zeros((in_dim, out_dim, grid_size + k - 1), requires_grad=True)\n",
    "        mask = torch.ones((in_dim, out_dim))\n",
    "        coefs.append(coef)\n",
    "        masks.append(mask)\n",
    "    \n",
    "        symb_fns = [[lambda x:x for _ in range(out_dim)] for _ in range(in_dim)]\n",
    "        symbolic_functions.append(symb_fns)\n",
    "        \n",
    "    return coefs, masks, symbolic_functions, grid\n"
   ]
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    "def eval_KAN(x, coefs, masks, symbolic_functions, grid, k):\n",
    "    \"\"\"\n",
    "    Acts as the model.forward to evaluate x according to the given KAN.\n",
    "    \n",
    "    Args:\n",
    "        x: Batch x input_dimensions\n",
    "        coefs: list of coefficients of size (in_dim, out_dim, h), where in_dim and out_dim are determined by the KAN structure, h is determined by the grid\n",
    "        masks: list of masks to be used to combine spline activation and symbolic activations. Each mask is (in_dim, out_dim). A value of 1 means use spline. \n",
    "        symbolic_functions: list of list symbolic functions. Each inner list represents symbolic function corresponding to a specific input dimension. \n",
    "        grid: grid for spline estimation\n",
    "        k: order of spline\n",
    "    \"\"\"\n",
    "    x_in = x\n",
    "    for coef, mask, symb_fns in zip(coefs, masks, symbolic_functions):\n",
    "        # spline activations\n",
    "        bases = eval_basis_functions(x_in, grid, k)\n",
    "        y_sp = torch.einsum('ijk, bik -> bij', coef, bases)\n",
    "\n",
    "        # symbolic activations\n",
    "        y_symb = eval_x_symbolically(x_in, symb_fns)\n",
    "\n",
    "        # combine the two outputs\n",
    "        y = mask[None, ...] * y_sp + (1-mask[None, ...]) * y_symb\n",
    "\n",
    "        # add along the input dimensions\n",
    "        x_in = y.sum(dim=1) # B x output_dimension\n",
    "\n",
    "    return x_in\n",
    "        \n",
    "    "
   ]
  },
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   "cell_type": "code",
   "execution_count": 5,
   "id": "c6a6b910-948d-4a1b-9564-55b08f9c4a0a",
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   "source": [
    "def eval_x_symbolically(x_eval, symbolic_fns):\n",
    "    \"\"\"\n",
    "    Evaluates `x_eval` using functions specified in `symbolic_fns`.\n",
    "\n",
    "    Args:\n",
    "        x_eval: batch x number of dimensions\n",
    "        symbolic_fns: list of list of symbolc functions. \n",
    "    \"\"\"\n",
    "    in_dim = len(symbolic_fns)\n",
    "    out_dim = len(symbolic_fns[0])\n",
    "    postacts = []\n",
    "    for i in range(in_dim):\n",
    "        postacts_ = []\n",
    "        for j in range(out_dim):\n",
    "            symb_fn = symbolic_fns[i][j]\n",
    "            postacts_.append(symb_fn(x_eval[:, i]))\n",
    "        postacts.append(torch.stack(postacts_, dim=1))\n",
    "    \n",
    "    return torch.stack(postacts, dim=1) # stack so that the input_dim is intact\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
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   "id": "45a3d9a4-d11a-4518-ae78-bb684a606ef3",
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   "source": [
    "def set_symbolic_fn(symbolic_functions, masks, i, j, k, fn, use_affine=False):\n",
    "    \"\"\"\n",
    "    Sets the symbolic function in the layer i, neuron j's kth output.\n",
    "    \n",
    "    Args:\n",
    "         symbolic_functions:  list of list symbolic functions. Each inner list represents symbolic function corresponding to a specific input dimension. \n",
    "         masks: list of masks to be used to combine spline activation and symbolic activations. Each mask is (in_dim, out_dim). A value of 1 means use spline. \n",
    "         i: layer index\n",
    "         j: neuron index (input)\n",
    "         k: output index\n",
    "         fn: function to use\n",
    "         use_affine: whether to use SymbolicKANLayer or not\n",
    "\n",
    "    Returns:\n",
    "        modified symbolic_functions and masks\n",
    "    \"\"\"\n",
    "    if use_affine:\n",
    "        symb_fn = SymbolicKANLayer(fn)\n",
    "    else:\n",
    "        symb_fn = fn\n",
    "\n",
    "    symbolic_functions[i][j][k] = symb_fn\n",
    "    masks[i].data[j][k]= 0\n",
    "\n",
    "    return symbolic_functions, masks"
   ]
  },
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    "### Section 1: Training a KAN without symbolic formulae\n",
    "\n",
    "Let's train a KAN without any symbolic functions.\n",
    "\n",
    "To effectively model our function with a KAN, we need to configure the activation functions as follows:\n",
    "\n",
    "1. **Mapping $ y $ to $ y^2 $**: This function will square the value of $ (y + 0.5)^2 $.\n",
    "2. **Mapping $ x $ to $ \\sin(\\pi x) $**: This function will apply the sine transformation scaled by $ \\pi $ to $ x $.\n",
    "3. **Combining the Results**: Add the results of 1 and 2 to obtain a new intermediate value $ z $.\n",
    "4. **Exponential Activation**: Map $ z $ to $ e^z $, computing the exponential of $ z $.\n",
    "\n",
    "This sequence requires a [2, 1, 1] KAN structure:\n",
    "- Two inputs ($ x $ and $ y $) are first transformed to one intermediate output $ z $,\n",
    "- Then $ z $ is transformed to the final output $ e^z $.\n",
    "\n",
    "To facilitate batch processing, we use a `mask`:\n",
    "- Where `mask=1`, the model applies the spline activation functions.\n",
    "- Where `mask=0`, the model uses the predefined symbolic functions."
   ]
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     "text": [
      "Val loss:  23.45651\tTrain loss:  19.97607\tBest Val loss: inf\n",
      "Val loss:  10.82449\tTrain loss:  7.26333\tBest Val loss: 10.15026\n",
      "Val loss:  7.03033\tTrain loss:  4.89028\tBest Val loss: 7.22423\n",
      "Val loss:  5.07032\tTrain loss:  3.52273\tBest Val loss: 5.22234\n",
      "Val loss:  4.38844\tTrain loss:  2.88212\tBest Val loss: 4.29603\n",
      "Val loss:  6.74622\tTrain loss:  3.41262\tBest Val loss: 3.49717\n",
      "Val loss:  5.79401\tTrain loss:  3.53381\tBest Val loss: 3.06012\n",
      "Val loss:  4.57888\tTrain loss:  2.88980\tBest Val loss: 2.63679\n",
      "Val loss:  3.17205\tTrain loss:  2.02335\tBest Val loss: 2.31600\n",
      "Val loss:  2.94587\tTrain loss:  1.96406\tBest Val loss: 2.19677\n",
      "Val loss:  2.25482\tTrain loss:  1.66901\tBest Val loss: 2.05615\n",
      "Val loss:  2.61979\tTrain loss:  1.94571\tBest Val loss: 1.91652\n",
      "Val loss:  3.83012\tTrain loss:  4.02219\tBest Val loss: 1.83981\n",
      "Val loss:  1.83867\tTrain loss:  1.38823\tBest Val loss: 1.75930\n",
      "Val loss:  2.05491\tTrain loss:  1.90978\tBest Val loss: 1.75930\n",
      "Val loss:  4.05904\tTrain loss:  4.57036\tBest Val loss: 1.68105\n",
      "Val loss:  3.83731\tTrain loss:  4.52541\tBest Val loss: 1.68105\n",
      "Stopping: No further improvements...\n"
     ]
    }
   ],
   "source": [
    "# KAN setup\n",
    "k = 3\n",
    "grid_range = [-1, 1]\n",
    "grid_size = 10\n",
    "KAN = [2, 1, 1]\n",
    "\n",
    "coefs, masks, symbolic_functions, grid = initialize_KAN(KAN, k, grid_range, grid_size)\n",
    "\n",
    "# training hyperparameters\n",
    "lr = 0.01\n",
    "early_stopping_iterations = 1e4\n",
    "early_stopping_imrpovement_threshold = 200\n",
    "\n",
    "losses = {'train': [], 'val': []}\n",
    "i=0\n",
    "verbose = True\n",
    "best_loss = np.inf\n",
    "while True: \n",
    "    # randomly shuffle indices\n",
    "    shuffled_idxs = torch.randperm(x_training.shape[0])\n",
    "    y_pred = eval_KAN(x_training[shuffled_idxs], coefs, masks, symbolic_functions, grid, k)\n",
    "    \n",
    "    loss = torch.mean(torch.pow(y_pred - y_training[shuffled_idxs], 2))\n",
    "    loss.backward()\n",
    "    losses['train'].append(loss.item())\n",
    "\n",
    "    for coef in coefs:\n",
    "        if coef.grad is not None:\n",
    "            coef.data = coef.data - lr * coef.grad\n",
    "            coef.grad.zero_()\n",
    "\n",
    "    \n",
    "    with torch.no_grad():\n",
    "        y_test_pred = eval_KAN(x_test, coefs, masks, symbolic_functions, grid, k)\n",
    "        val_loss = torch.mean(torch.pow(y_test_pred - y_test, 2))\n",
    "\n",
    "    losses['val'].append(val_loss.item())\n",
    "    if i% 100 == 0 and verbose:\n",
    "        print(f\"Val loss: {val_loss.item(): 0.5f}\\tTrain loss: {loss.item(): 0.5f}\\tBest Val loss:{best_loss: 0.5f}\")\n",
    "        \n",
    "    if best_loss > val_loss.item():\n",
    "        best_loss = val_loss.item()\n",
    "        best_model = (coefs, masks, symbolic_functions)\n",
    "        n_no_improvements = 0\n",
    "    else:\n",
    "        n_no_improvements += 1\n",
    "        if n_no_improvements > early_stopping_imrpovement_threshold:\n",
    "            print('Stopping: No further improvements...')\n",
    "            break\n",
    "\n",
    "    i += 1\n",
    "    if i > early_stopping_iterations:\n",
    "        print('Stopping: Iteration limit reached...')\n",
    "        break\n"
   ]
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    "#### Visualizing individual activation functions\n",
    "\n",
    "As we visualize the activation levels, we observe that the response of `x1` closely resembles a quadratic function. Given this observation, it could be advantageous to explicitly fix this activation to a quadratic form. Doing so might simplify the model structure and potentially improve both the training efficiency and model accuracy by directly incorporating our insights into the function's behavior. Let's proceed to implement this fixed quadratic activation for `x1`."
   ]
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     "text": [
      "validation loss:  1.68105\n"
     ]
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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coefs, masks, symbolic_functions = best_model\n",
    "print(f\"validation loss: {best_loss: 0.5f}\")\n",
    "\n",
    "fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(10, 5), dpi=100)\n",
    "\n",
    "x = torch.linspace(-1, 1, steps=100).unsqueeze(dim=1)\n",
    "bases = eval_basis_functions(x, grid, k=3)\n",
    "\n",
    "ax = axs[0]\n",
    "y_out_0 = torch.einsum('ijk, bij->bk', coefs[0][0:1].transpose(2, 1), bases)\n",
    "y_out_1 = torch.einsum('ijk, bij->bk', coefs[0][1:2].transpose(2, 1), bases)\n",
    "ax.plot(x.numpy(), y_out_0.detach().numpy(), label=\"Activation (x0): (0, 0)\")\n",
    "ax.plot(x.numpy(), y_out_1.detach().numpy(), label=\"Activation (x1): (0, 1)\")\n",
    "ax.legend()\n",
    "\n",
    "ax = axs[1]\n",
    "y_out_final = torch.einsum('ijk, bij->bk', coefs[1].transpose(2, 1), bases)\n",
    "ax.plot(x.numpy(), y_out_final.detach().numpy(), label=\"Activation (y): (1, 0)\")\n",
    "\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbfccc5e-4981-47b5-bc24-8ef331183b5c",
   "metadata": {},
   "source": [
    "### Section 2: Training KANs with activation fixed to identified Symbolic formula\n",
    "\n",
    "Let's fix $y$ to a symbolic formula, $y^2$ or a learnable variant thereof. We do this as following --\n",
    "\n",
    "1. We define symbolic layers that holds a potential symbolic function for that activation function\n",
    "2. Upon fixing an activation function to a formula, we replace that function. We also modify `mask` to indicate where symbolic activation function is to be used. \n",
    "3. Upon the model forward, we compute all outputs for the symbolic layer using the previous layer's output. \n",
    "4. Finally, we combine the outputs using the `mask`.\n",
    "\n",
    "Let's see how we process a symbolic layer. Here, we have two dimensions on the input and 3 dimensions for the output, i.e., We have a layer that takes in 2 inputs and outputs 3 dimensions. As a result, we have 2x3 activations, and hence symbolic functions.\n",
    "\n",
    "### batch processing\n",
    "\n",
    "To incorporate a fixed symbolic formula, such as \\((y + 0.5)^2\\), into our KAN model, we will follow these steps:\n",
    "\n",
    "1. **Define Symbolic Layers**: Establish layers that can hold potential symbolic functions for each activation. This allows for direct embedding of known mathematical relationships.\n",
    "\n",
    "2. **Activation Function Replacement**: Adjust the `mask` to indicate where the symbolic activation function should be used.\n",
    "\n",
    "3. **Model Forward Pass**: During the model's forward pass, compute all outputs for the symbolic layer using the output from the previous layer. This ensures that the fixed symbolic transformations are applied correctly.\n",
    "\n",
    "4. **Output Combination**: Use the `mask` to combine the outputs appropriately, merging the results from both the symbolic and spline-based activation functions."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5dffe625-11c6-4380-9d99-34d25649613b",
   "metadata": {},
   "source": [
    "### Section 2.1 Affine Transformations of Symbolic Functions\n",
    "\n",
    "The authors proposed using symbolic activation functions so that, given a function, one only needs to learn the affine transformations of the input and the output to predict it accurately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cdb402b1-f0b0-42d0-bfe6-a0c1a65e3186",
   "metadata": {},
   "outputs": [],
   "source": [
    "class SymbolicKANLayer(nn.Module):\n",
    "    def __init__(self, fn):\n",
    "        super().__init__()\n",
    "        self.fn = fn\n",
    "        \n",
    "        # learnable parameters\n",
    "        self.affine = torch.nn.Parameter(torch.zeros(4), requires_grad=True)\n",
    "        \n",
    "    def forward(self, x_eval):\n",
    "        return self.affine[0] * self.fn(self.affine[1]*x_eval + self.affine[2]) + self.affine[3]\n",
    "\n",
    "    def step(self, lr):\n",
    "        \"\"\"\n",
    "        Performs a step of gradient descent using the learning rate `lr`\n",
    "        \"\"\"\n",
    "        if self.affine.grad is not None:\n",
    "            self.affine.data = self.affine.data - lr * self.affine.grad\n",
    "\n",
    "    def zero_grad_(self):\n",
    "        \"\"\"\n",
    "        Zeroes out the gradients in-place.\n",
    "        \"\"\"\n",
    "        self.affine.grad.zero_()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "12206cf7-4343-4fec-9581-55d238d08568",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Val loss:  24.83722\tTrain loss:  19.97608\tBest Val loss: inf\n",
      "Val loss:  18.14330\tTrain loss:  13.52023\tBest Val loss: 18.33046\n",
      "Val loss:  10.25327\tTrain loss:  7.36032\tBest Val loss: 10.29337\n",
      "Val loss:  7.19448\tTrain loss:  5.00078\tBest Val loss: 7.23424\n",
      "Val loss:  5.21834\tTrain loss:  3.65003\tBest Val loss: 5.18963\n",
      "Val loss:  3.98071\tTrain loss:  2.79763\tBest Val loss: 3.98080\n",
      "Val loss:  3.09984\tTrain loss:  2.22271\tBest Val loss: 3.11376\n",
      "Val loss:  2.53218\tTrain loss:  1.82276\tBest Val loss: 2.54068\n",
      "Val loss:  2.12870\tTrain loss:  1.53761\tBest Val loss: 2.10287\n",
      "Val loss:  1.80931\tTrain loss:  1.32303\tBest Val loss: 1.78779\n",
      "Val loss:  1.56597\tTrain loss:  1.15745\tBest Val loss: 1.55182\n",
      "Val loss:  1.37366\tTrain loss:  1.02722\tBest Val loss: 1.37356\n",
      "Val loss:  1.22497\tTrain loss:  0.92524\tBest Val loss: 1.22758\n",
      "Val loss:  1.10913\tTrain loss:  0.84370\tBest Val loss: 1.11060\n",
      "Val loss:  1.01548\tTrain loss:  0.77832\tBest Val loss: 1.01621\n",
      "Val loss:  0.93924\tTrain loss:  0.72614\tBest Val loss: 0.93992\n",
      "Val loss:  0.87724\tTrain loss:  0.68405\tBest Val loss: 0.87789\n",
      "Val loss:  0.82657\tTrain loss:  0.64967\tBest Val loss: 0.82696\n",
      "Val loss:  0.78440\tTrain loss:  0.62121\tBest Val loss: 0.78501\n",
      "Val loss:  0.74874\tTrain loss:  0.59757\tBest Val loss: 0.74907\n",
      "Val loss:  0.71831\tTrain loss:  0.57780\tBest Val loss: 0.71832\n",
      "Val loss:  0.69235\tTrain loss:  0.56113\tBest Val loss: 0.69258\n",
      "Val loss:  0.67036\tTrain loss:  0.54692\tBest Val loss: 0.67056\n",
      "Val loss:  0.65103\tTrain loss:  0.53469\tBest Val loss: 0.65100\n",
      "Val loss:  0.63399\tTrain loss:  0.52412\tBest Val loss: 0.63414\n",
      "Val loss:  0.61951\tTrain loss:  0.51491\tBest Val loss: 0.61964\n",
      "Val loss:  0.60669\tTrain loss:  0.50685\tBest Val loss: 0.60687\n",
      "Val loss:  0.59541\tTrain loss:  0.49978\tBest Val loss: 0.59552\n",
      "Val loss:  0.58539\tTrain loss:  0.49354\tBest Val loss: 0.58548\n",
      "Val loss:  0.57642\tTrain loss:  0.48797\tBest Val loss: 0.57650\n",
      "Val loss:  0.56821\tTrain loss:  0.48297\tBest Val loss: 0.56828\n",
      "Val loss:  0.56092\tTrain loss:  0.47846\tBest Val loss: 0.56081\n",
      "Val loss:  0.55413\tTrain loss:  0.47439\tBest Val loss: 0.55419\n",
      "Val loss:  0.54801\tTrain loss:  0.47069\tBest Val loss: 0.54812\n",
      "Val loss:  0.54246\tTrain loss:  0.46730\tBest Val loss: 0.54253\n",
      "Val loss:  0.53706\tTrain loss:  0.46415\tBest Val loss: 0.53699\n",
      "Val loss:  0.53246\tTrain loss:  0.46126\tBest Val loss: 0.53247\n",
      "Val loss:  0.52824\tTrain loss:  0.45858\tBest Val loss: 0.52831\n",
      "Val loss:  0.52439\tTrain loss:  0.45609\tBest Val loss: 0.52439\n",
      "Val loss:  0.52079\tTrain loss:  0.45376\tBest Val loss: 0.52083\n",
      "Val loss:  0.51746\tTrain loss:  0.45159\tBest Val loss: 0.51750\n",
      "Val loss:  0.51442\tTrain loss:  0.44955\tBest Val loss: 0.51445\n",
      "Val loss:  0.51160\tTrain loss:  0.44763\tBest Val loss: 0.51163\n",
      "Val loss:  0.50899\tTrain loss:  0.44583\tBest Val loss: 0.50902\n",
      "Val loss:  0.50658\tTrain loss:  0.44413\tBest Val loss: 0.50660\n",
      "Val loss:  0.50434\tTrain loss:  0.44252\tBest Val loss: 0.50435\n",
      "Val loss:  0.50224\tTrain loss:  0.44099\tBest Val loss: 0.50226\n",
      "Val loss:  0.50028\tTrain loss:  0.43954\tBest Val loss: 0.50029\n",
      "Val loss:  0.49846\tTrain loss:  0.43816\tBest Val loss: 0.49846\n",
      "Val loss:  0.49674\tTrain loss:  0.43685\tBest Val loss: 0.49675\n",
      "Val loss:  0.49513\tTrain loss:  0.43560\tBest Val loss: 0.49517\n",
      "Val loss:  0.49366\tTrain loss:  0.43441\tBest Val loss: 0.49364\n",
      "Val loss:  0.49225\tTrain loss:  0.43328\tBest Val loss: 0.49225\n",
      "Val loss:  0.49091\tTrain loss:  0.43219\tBest Val loss: 0.49091\n",
      "Val loss:  0.48966\tTrain loss:  0.43115\tBest Val loss: 0.48965\n",
      "Val loss:  0.48847\tTrain loss:  0.43015\tBest Val loss: 0.48846\n",
      "Val loss:  0.48737\tTrain loss:  0.42919\tBest Val loss: 0.48736\n",
      "Val loss:  0.48633\tTrain loss:  0.42827\tBest Val loss: 0.48629\n",
      "Val loss:  0.48528\tTrain loss:  0.42739\tBest Val loss: 0.48531\n",
      "Val loss:  0.48437\tTrain loss:  0.42654\tBest Val loss: 0.48437\n",
      "Val loss:  0.48349\tTrain loss:  0.42573\tBest Val loss: 0.48347\n",
      "Val loss:  0.48263\tTrain loss:  0.42494\tBest Val loss: 0.48264\n",
      "Val loss:  0.48184\tTrain loss:  0.42419\tBest Val loss: 0.48185\n",
      "Val loss:  0.48108\tTrain loss:  0.42346\tBest Val loss: 0.48109\n",
      "Val loss:  0.48035\tTrain loss:  0.42276\tBest Val loss: 0.48037\n",
      "Val loss:  0.47966\tTrain loss:  0.42208\tBest Val loss: 0.47959\n",
      "Val loss:  0.47891\tTrain loss:  0.42143\tBest Val loss: 0.47890\n",
      "Val loss:  0.47824\tTrain loss:  0.42080\tBest Val loss: 0.47823\n",
      "Val loss:  0.47761\tTrain loss:  0.42019\tBest Val loss: 0.47761\n",
      "Val loss:  0.47700\tTrain loss:  0.41960\tBest Val loss: 0.47701\n",
      "Val loss:  0.47641\tTrain loss:  0.41903\tBest Val loss: 0.47641\n",
      "Val loss:  0.47578\tTrain loss:  0.41845\tBest Val loss: 0.47578\n",
      "Val loss:  0.47518\tTrain loss:  0.41790\tBest Val loss: 0.47519\n",
      "Val loss:  0.47465\tTrain loss:  0.41737\tBest Val loss: 0.47465\n",
      "Val loss:  0.47413\tTrain loss:  0.41685\tBest Val loss: 0.47413\n",
      "Val loss:  0.47416\tTrain loss:  0.41634\tBest Val loss: 0.47381\n",
      "Val loss:  0.47366\tTrain loss:  0.41583\tBest Val loss: 0.47366\n",
      "Val loss:  0.47318\tTrain loss:  0.41534\tBest Val loss: 0.47318\n",
      "Val loss:  0.47270\tTrain loss:  0.41486\tBest Val loss: 0.47271\n",
      "Val loss:  0.47226\tTrain loss:  0.41440\tBest Val loss: 0.47226\n",
      "Val loss:  0.47186\tTrain loss:  0.41395\tBest Val loss: 0.47187\n",
      "Val loss:  0.47142\tTrain loss:  0.41351\tBest Val loss: 0.47142\n",
      "Val loss:  0.47099\tTrain loss:  0.41308\tBest Val loss: 0.47097\n",
      "Val loss:  0.47059\tTrain loss:  0.41267\tBest Val loss: 0.47059\n",
      "Val loss:  0.47024\tTrain loss:  0.41227\tBest Val loss: 0.47028\n",
      "Val loss:  0.46983\tTrain loss:  0.41188\tBest Val loss: 0.46983\n",
      "Val loss:  0.46946\tTrain loss:  0.41150\tBest Val loss: 0.46946\n",
      "Val loss:  0.46915\tTrain loss:  0.41113\tBest Val loss: 0.46915\n",
      "Val loss:  0.46879\tTrain loss:  0.41077\tBest Val loss: 0.46880\n",
      "Val loss:  0.46843\tTrain loss:  0.41042\tBest Val loss: 0.46844\n",
      "Val loss:  0.46808\tTrain loss:  0.41008\tBest Val loss: 0.46808\n",
      "Val loss:  0.46773\tTrain loss:  0.40975\tBest Val loss: 0.46774\n",
      "Val loss:  0.46741\tTrain loss:  0.40943\tBest Val loss: 0.46742\n",
      "Val loss:  0.46710\tTrain loss:  0.40912\tBest Val loss: 0.46710\n",
      "Val loss:  0.46686\tTrain loss:  0.40882\tBest Val loss: 0.46678\n",
      "Val loss:  0.46656\tTrain loss:  0.40852\tBest Val loss: 0.46646\n",
      "Val loss:  0.46613\tTrain loss:  0.40824\tBest Val loss: 0.46614\n",
      "Val loss:  0.46593\tTrain loss:  0.40796\tBest Val loss: 0.46589\n",
      "Val loss:  0.46559\tTrain loss:  0.40769\tBest Val loss: 0.46561\n",
      "Val loss:  0.46537\tTrain loss:  0.40743\tBest Val loss: 0.46537\n",
      "Val loss:  0.46511\tTrain loss:  0.40717\tBest Val loss: 0.46511\n",
      "Stopping: Iteration limit reached...\n"
     ]
    }
   ],
   "source": [
    "# KAN setup\n",
    "k = 3\n",
    "grid_range = [-1, 1]\n",
    "grid_size = 10\n",
    "KAN = [2, 1, 1]\n",
    "\n",
    "coefs, masks, symbolic_functions, grid = initialize_KAN(KAN, k, grid_range, grid_size)\n",
    "\n",
    "# training hyperparameters\n",
    "lr = 0.01\n",
    "early_stopping_iterations = 1e4\n",
    "early_stopping_imrpovement_threshold = 200\n",
    "\n",
    "# setup the symbolic forms\n",
    "# A few candidate options\n",
    "# symbolic_functions, masks = set_symbolic_fn(symbolic_functions, masks, 0, 0, 0, lambda x: torch.sin(torch.pi * x), use_affine=False)\n",
    "# symbolic_functions, masks = set_symbolic_fn(symbolic_functions, masks, 0, 0, 0, lambda x: torch.sin(x), use_affine=True)\n",
    "# symbolic_functions, masks = set_symbolic_fn(symbolic_functions, masks, 0, 1, 0, lambda x: torch.pow(x, 2), use_affine=True)\n",
    "symbolic_functions, masks = set_symbolic_fn(symbolic_functions, masks, 0, 1, 0, lambda x: torch.pow(x + 0.5, 2), use_affine=False)\n",
    "# symbolic_functions, masks = set_symbolic_fn(symbolic_functions, masks, 1, 0, 0, lambda x: torch.exp(x), use_affine=False)\n",
    "\n",
    "\n",
    "losses_symb = {'train': [], 'val': []}\n",
    "i=0\n",
    "verbose = True\n",
    "best_loss = np.inf\n",
    "while True:    \n",
    "    # randomly shuffle indices\n",
    "    shuffled_idxs = torch.randperm(x_training.shape[0])\n",
    "    x = x_training[shuffled_idxs]\n",
    "    y_pred = eval_KAN(x_training[shuffled_idxs], coefs, masks, symbolic_functions, grid, k)\n",
    "    loss = torch.mean(torch.pow(y_pred - y_training[shuffled_idxs], 2))\n",
    "    loss.backward()\n",
    "    losses_symb['train'].append(loss.item())\n",
    "\n",
    "    # backpropagate \n",
    "    for coef in coefs:\n",
    "        if coef.grad is not None:\n",
    "            coef.data = coef.data - lr * coef.grad\n",
    "            coef.grad.zero_()\n",
    "\n",
    "    for symb_layer in symbolic_functions:\n",
    "        for neuron in symb_layer:\n",
    "            for out_symb in neuron:\n",
    "                if isinstance(out_symb, SymbolicKANLayer):\n",
    "                    out_symb.step(lr)\n",
    "                    out_symb.zero_grad_()\n",
    "\n",
    "    with torch.no_grad():\n",
    "        y_test_pred = eval_KAN(x_test, coefs, masks, symbolic_functions, grid, k)\n",
    "        val_loss = torch.mean(torch.pow(y_test_pred - y_test, 2))\n",
    "\n",
    "    losses_symb['val'].append(val_loss.item())\n",
    "    \n",
    "    if i% 100 == 0 and verbose:\n",
    "        print(f\"Val loss: {val_loss.item(): 0.5f}\\tTrain loss: {loss.item(): 0.5f}\\tBest Val loss:{best_loss: 0.5f}\")\n",
    "\n",
    "    if best_loss > val_loss.item():\n",
    "        best_loss = val_loss.item()\n",
    "        best_model = (coefs, masks, symbolic_functions)\n",
    "        n_no_improvements = 0\n",
    "    else:\n",
    "        n_no_improvements += 1\n",
    "        if n_no_improvements > early_stopping_imrpovement_threshold:\n",
    "            print('Stopping: No further improvements...')\n",
    "            break\n",
    "\n",
    "    i += 1\n",
    "    if i > early_stopping_iterations:\n",
    "        print('Stopping: Iteration limit reached...')\n",
    "        break\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ea3b3e47-4612-43d2-8c32-87f6563ed9f8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "validation loss:  0.46511\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11f0a2fd0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ALy8vdOvWDT///DO2b9+OV1555aFjb968ic6dO9f6enK5XCPFka+vL86cOYPS0lL1vuPHj8PDw0M9jA4oz62np4f27dvXeQZqOi7H38f9glI0M9JDD2fLermmxgujiRMn4quvvsKSJUvQqVMnhIaG4ujRo+oxqYmJibh79666fa9evbB9+3asW7cO3t7e+P3337F37956WWeAiIiIHu3gwYO4f/8+pk+fjg4dOlTaxo8fj/Xr1wMAli5dih07dmDp0qWIiIjAjRs38MUXX6jP4+zsjDNnziAlJQUZGRnVXm/cuHHIzc3FrFmzMHDgwEr37LRp0wZXrlzBsWPHEB0djf/7v//D5cuXKx3v7OyMsLAwREVFISMjo9IH+wpvvPEGkpKSMGfOHERGRmLfvn1YunQp5s2b91T36wwcOBB5eXkIDw9/6LlXX30Vn3/+OQRBwNixYx96/uzZsxg2bJj6cUpKCjw9PXHp0qVqr9e5c2dYW1vj/PnzlfbL5XKEhoYiJiYGAHDjxg2Ehoaqe3cexwsvvACZTIbp06cjPDwcO3fuxHfffffQbMJnz55F375962XaddJeFcPoBre1g66Gp+lWE7SMQqEQAAgKhULsKERETQ7/Bletpp9LYWGhcOvWLaGwsFCEZE/mmWeeEUaMGFHlc8HBwQIA4fr164IgCMIff/whdOrUSZDJZIK1tbUwbtw4ddugoCChY8eOgr6+vlDxkWTjxo2Cubn5Q+edMGGCAEDYsGFDpf1FRUVCQECAYG5uLlhYWAizZs0SFi5cKHh7e6vbpKenC0OHDhVMTEwEAMLJkyeFuLg4AYBw7do1dbtTp04J3bt3F2QymWBvby8sWLBAKC0tVT/fv39/4e233650/dGjRwsvv/xyjT+vCRMmCAsXLnxof25urmBkZCS88cYbDz2XnJws6OnpCUlJSep9FZlPnjxZ4/Xef/99YdKkSZX2LV26VADw0LZx48ZKr+9Rr+X69etCnz59BH19faF58+bC559//lAbDw8PYceOHTWepzH+u6f6o1KphF4rAoVWCw4Kf4XLn+pctXlfkgjCf/p2G7mcnByYm5tDoVDAzEzzs1cQEdE/+De4ajX9XIqKihAXFwcXFxfRb5onzQgLC8PQoUMRGxsLExMT9f74+Hi0bt0aly9fRpcuXSods2DBAty/fx/r1q2r9fXkcjnat2+Pq1evPnTfUk1atWqFjz/+GAEBAbW+ZoUjR47g3XffRVhYmHr9p6rw3z3V5GaKAs/8cA6GelJcWzIUBrWYGOa/avO+VE/9UkRERERNU8eOHfHFF18gLi4OAFBaWgq5XI7FixejZ8+eDxVFAGBra1tp7abasLe3x/r165GYmPjYx4SHh8Pc3BxTp059omtWyM/Px8aNG2ssiogepWIYXX93m6cqimqL/2qJiIiINOzfvTDnz5/HwIED4e7ujt9//73K9u++++5TXW/MmDG1at++fXuEhYU91TUB4LnnnnvqcxBVFEZ+HepnNroKLIyIiIiI6tGAAQMemqWOiMrF3stDdFoedHUkGORRv4URh9IREREREVGDcPRmeW9RbzdrmBvpPaJ13WJhRERE1ADUtEgokbbhv3eqzuEb5cv4DO9g/4iWdY9D6YiIiEQkk8mgo6OD1NRU2NjYQCaTQSKRiB2LSCMEQUBJSQnu3bsHHR0dyGQysSNRA5KYWYDw1BxIdSQY1p6FERERUZOio6MDFxcX3L17F6mpqWLHIaoXRkZGaNmy5VMtnkva58jN8t6inq6WsDSu/6KZhREREZHIZDIZWrZsibKyMiiVSrHjEGmUVCqFrq4ue0bpIYcf3F/k38FBlOuzMCIiImoAJBIJ9PT0oKdXvzcbExE1BCnZhbielA2JBPBrX7+z0VVg/yUREREREYmqYja67q0sYWtqIEoGFkZERERERCSqIxWz0XnV/6QLFVgYERERERGRaNJyinAl4T4AwF+EaborsDAiIiIiIiLRVPQWdW5pAQdzQ9FysDAiIiIiIiLRHHpQGD3T0VHUHCyMiIiIiIhIFHcVhbgcXz6MboSI9xcBLIyIiIiIiEgkh2+Uz0bXrVUzUYfRASyMiIiIiIhIJIfCUgEAIzuKs6jrv7EwIiIiIiKiepeSXYirieWLuo7wYmFERERERERNUMVsdN2dLWFnJs6irv/GwoiIiIiIiOrdwbCK2ejE7y0CWBgREREREVE9S8oqQGhS+TA6MRd1/TcWRkREREREVK+O3CzvLerhbAlbU/GH0QEsjIiIiIiIqJ4duF5eGI3yFndR139jYURERFpjxYoV6N69O0xNTWFra4sxY8YgKiqqUpuioiK8+eabsLKygomJCcaPH4+0tLQazysIApYsWQIHBwcYGhpiyJAhuH37tiZfChGR1orLyMeNFAWkOhIMbyDD6AAWRkREpEVOnz6NN998ExcvXsTx48dRWlqKYcOGIT8/X93mnXfewYEDB7B7926cPn0aqampGDduXI3n/fLLL/H9999j7dq1CA4OhrGxMfz8/FBUVKTpl0REpHUOXi9fu6i3mzWsTPRFTvMPXbEDEBER1ZWjR49Werxp0ybY2toiJCQE/fr1g0KhwPr167F9+3YMGjQIALBx40a0bdsWFy9eRM+ePR86pyAIWLlyJRYvXozRo0cDALZs2QI7Ozvs3bsXkyZN0vwLIyLSIgceLOo6qoHMRleBPUZERKS1FAoFAMDS0hIAEBISgtLSUgwZMkTdxtPTEy1btkRQUFCV54iLi4NcLq90jLm5OXx8fKo9pri4GDk5OZU2IiICouS5iE7Lg0yqg2HtG84wOoCFERERaSmVSoW5c+eid+/e6NChAwBALpdDJpPBwsKiUls7OzvI5fIqz1Ox387O7rGPWbFiBczNzdWbk5PTU74aIiLtcODBMLr+HjYwN9QTOU1lLIyIiEgrvfnmm7h58yZ+++23er/2okWLoFAo1FtSUlK9ZyAiamgEQfhnGF0Dmo2uAgsjIiLSOrNnz8bBgwdx8uRJtGjRQr3f3t4eJSUlyM7OrtQ+LS0N9vZVD+mo2P/fmetqOkZfXx9mZmaVNiKipu5GigIJmQUw1JNiSFtbseM8hIURERFpDUEQMHv2bOzZswd///03XFxcKj3ftWtX6OnpITAwUL0vKioKiYmJ8PX1rfKcLi4usLe3r3RMTk4OgoODqz2GiIgetj+0vLdocFtbGMka3hxwLIyIiEhrvPnmm9i6dSu2b98OU1NTyOVyyOVyFBYWAiifNGH69OmYN28eTp48iZCQEEybNg2+vr6VZqTz9PTEnj17AAASiQRz587F8uXLsX//fty4cQNTp06Fo6MjxowZI8bLJCJqdFQqAQfDGt6irv/W8Eo1IiKiJ7RmzRoAwIABAyrt37hxIwICAgAA3377LXR0dDB+/HgUFxfDz88PP/74Y6X2UVFR6hntAOD9999Hfn4+Zs6ciezsbPTp0wdHjx6FgYGBRl8PEZG2uBSfBXlOEUwNdDHAw0bsOFWSCIIgiB2iLuXk5MDc3BwKhYJjuomI6hn/BleNPxciauoW/XkDOy4lYkK3FvjyOe96u25t/v5yKB0REREREWlMSZkKR26WD6N71ru5yGmqx8KIiIiIiIg05uzte8guKIW1iT58W1uJHadaLIyIiIiIiEhj9j9Y1PWZjg6Q6khETlM9FkZERERERKQRBSVlOH6rfB24Zzs1zNnoKrAwIiIiIiIijTgRkY6CEiWcLA3R2clC7Dg1YmFEREREREQaUbGo67PejpBIGu4wOoCFERERERERaUB2QQlOR6cDaNiz0VVgYURERERERHXuyE05SpUCPO1N4WFvKnacR2JhREREREREdW5faAoAYHSnht9bBLAwIiIiIiKiOnZXUYjguCwAwChvB5HTPB4WRkREREREVKcOXr8LQQC6OzdDi2ZGYsd5LCyMiIiIiIioTu27Xj6M7tlGMowOYGFERERERER1KCY9DzdTcqCrI8FIr8YxjA5gYURERERERHVo//XytYv6trGGpbFM5DSPj4URERERERHVCUEQsL+RzUZXQaOFUVZWFqZMmQIzMzNYWFhg+vTpyMvLq/GYAQMGQCKRVNpef/11TcYkIiIiIqI6EJasQHxmAQz0dDC0nZ3YcWpFV5MnnzJlCu7evYvjx4+jtLQU06ZNw8yZM7F9+/Yaj5sxYwY++eQT9WMjo8YxkwURERERUVO2L7R8GN2wdvYw1tdoqVHnNJY2IiICR48exeXLl9GtWzcAwA8//IARI0bgq6++gqOjY7XHGhkZwd7eXlPRiIiIiIiojilVAg6ElRdGoztV/1m/odLYULqgoCBYWFioiyIAGDJkCHR0dBAcHFzjsdu2bYO1tTU6dOiARYsWoaCgoNq2xcXFyMnJqbQREREREVH9CorNxL3cYlgY6aFvGxux49SaxnqM5HI5bG1tK19MVxeWlpaQy+XVHvfCCy+gVatWcHR0RFhYGBYsWICoqCj8+eefVbZfsWIFPv744zrNTkREREREtbP3waQLI70cINNtfHO81bowWrhwIb744osa20RERDxxoJkzZ6r/28vLCw4ODhg8eDBiY2PRunXrh9ovWrQI8+bNUz/OycmBk5PTE1+fiIiIiIhqp6hUiaM3yzs/GttsdBVqXRi9++67CAgIqLGNq6sr7O3tkZ6eXml/WVkZsrKyanX/kI+PDwAgJiamysJIX18f+vr6j30+IiIiIiKqWycj05FXXAZHcwN0a9VM7DhPpNaFkY2NDWxsHj1m0NfXF9nZ2QgJCUHXrl0BAH///TdUKpW62HkcoaGhAAAHh8azai4RERERUVNSMYzu2U7NoaMjETnNk9HY4L+2bdvC398fM2bMwKVLl3D+/HnMnj0bkyZNUs9Il5KSAk9PT1y6dAkAEBsbi2XLliEkJATx8fHYv38/pk6din79+qFjx46aikpERERERE9IUViKk5H3ADTO2egqaPSuqG3btsHT0xODBw/GiBEj0KdPH6xbt079fGlpKaKiotSzzslkMpw4cQLDhg2Dp6cn3n33XYwfPx4HDhzQZEwiIiIiInpCx27KUaJUwd3OBJ72pmLHeWIaXXXJ0tKyxsVcnZ2dIQiC+rGTkxNOnz6tyUhERERERFSH9l0vH0Y3ulNzSCSNcxgdoOEeIyIiIiIi0l7pOUUIis0EADzr3XiH0QEsjIiIiIiI6AkdDLsLlQB0bmkBJ0sjseM8FRZGRERERET0RPZfTwUAjG7kvUUACyMiIiIiInoCCZn5CE3Kho4EGNmRhRERERERETVB+0PLe4t6u1nDxlRf5DRPj4URERERERHViiAI2PdgGF1jn3ShAgsjIiIiIiKqlYi7uYhJz4NMVwd+HezFjlMnWBgREREREVGtVEy6MMjDFmYGeiKnqRssjIiISGucOXMGo0aNgqOjIyQSCfbu3VvpeYlEUuX2v//9r9pzfvTRRw+19/T01PArISJquARBwIEHhdEoLRlGB7AwIiIiLZKfnw9vb2+sXr26yufv3r1baduwYQMkEgnGjx9f43nbt29f6bhz585pIj4RUaNwNTEbKdmFMJZJMbitrdhx6oyu2AGIiIjqyvDhwzF8+PBqn7e3rzwOft++fRg4cCBcXV1rPK+uru5DxxIRNVUVvUXD2tvDQE8qcpq6wx4jIiJqktLS0nDo0CFMnz79kW1v374NR0dHuLq6YsqUKUhMTKyxfXFxMXJyciptRETaQKkScDDsLgBglLeDyGnqFgsjIiJqkjZv3gxTU1OMGzeuxnY+Pj7YtGkTjh49ijVr1iAuLg59+/ZFbm5utcesWLEC5ubm6s3Jyamu4xMRieLinUxk5BXDwkgPfdxsxI5Tp1gYERFRk7RhwwZMmTIFBgYGNbYbPnw4nn/+eXTs2BF+fn44fPgwsrOzsWvXrmqPWbRoERQKhXpLSkqq6/hERKKoGEY3vIM9ZLraVUrwHiMiImpyzp49i6ioKOzcubPWx1pYWMDd3R0xMTHVttHX14e+fuNfBZ6I6N9KylQ4clMOQLtmo6ugXWUeERHRY1i/fj26du0Kb2/vWh+bl5eH2NhYODho19h6IqJHOXv7HhSFpbA11YePi5XYceocCyMiItIaeXl5CA0NRWhoKAAgLi4OoaGhlSZLyMnJwe7du/Hqq69WeY7Bgwdj1apV6sfz58/H6dOnER8fjwsXLmDs2LGQSqWYPHmyRl8LEVFDU7Go68iODpDqSEROU/c4lI6IiLTGlStXMHDgQPXjefPmAQBefvllbNq0CQDw22+/QRCEagub2NhYZGRkqB8nJydj8uTJyMzMhI2NDfr06YOLFy/Cxka7bjomIqpJUakSx2+lAQCe6ah9w+gAQCIIgiB2iLqUk5MDc3NzKBQKmJmZiR2HiKhJ4d/gqvHnQkSN3ZEbdzFr21U0tzDEuQUDIZE0jh6j2vz95VA6IiIiIiKq0cEb5WsXjezo0GiKotpiYURERERERNUqKCnD3xHpAIBnOmrvxDMsjIiIiIiIqFp/R6ajsFSJlpZG8GpuLnYcjWFhRERERERE1Tp4vXwY3TNaPIwOYGFERERERETVyCsuw8mo8mF0I7V4GB3AwoiIiIiIiKoRGJGG4jIVXK2N0c5Bu2fVZGFERERERERVOtBEhtEBLIyIiIiIiKgKOUWlOBN9DwAwUksXdf03FkZERERERPSQvyPSUaJUwc3WBB72pmLH0TgWRkRERERE9JBDDxZ1HeGl3ZMuVGBhREREREREleQVl+H0g2F0I7zsRU5TP1gYERERERFRJYERaSh5MBudh532D6MDWBgREREREdF/HLkhB1A+jE7bZ6OrwMKIiIiIiIjU8v+1qOvwJjKMDmBhRERERERE/3IyKh3FZSq0sjLS+kVd/42FERERERERqR3+12x0TWUYHcDCiIiIiIiIHigoKcPJyAez0XVoGtN0V2BhREREREREAIC/wtNQWKpEi2aG6NC86QyjA1gYERERERHRA1uC4gEAz3d1alLD6AAWRkREREREBOBmigJXE7OhJ5Vgso+T2HHqHQsjIiIiIiLCr0EJAAD/Dg6wNTUQOU39Y2FERERERNTEKQpKse96CgBgqm8rkdOIg4UREREREVETtzskCUWlKnjam6Jbq2ZixxEFCyMiIiIioiZMpRLw68XyYXRTfZ2b3KQLFVgYERERERE1Yadv30NCZgFMDXQxprOj2HFEw8KIiIiIiKgJW382DkD5FN1GMl2R04iHhRERERERURN1I1mBczEZkOpIMK23s9hxRMXCiIiIiIioifrpTCwAYFRHBzhZGomcRlwsjIiIiIiImqCEzHwcvnEXADCzX2uR04iPhRERERERURP089k7UAlAf3cbtHM0EzuO6FgYERERERE1MRl5xdh9JRkA8Hp/9hYBLIyIiIiIiJqcTefjUVymgreTBXq6Woodp0HQWGH06aefolevXjAyMoKFhcVjHSMIApYsWQIHBwcYGhpiyJAhuH37tqYiEhERERE1OdkFJdh8IR4A8Ho/1ya7oOt/aawwKikpwfPPP49Zs2Y99jFffvklvv/+e6xduxbBwcEwNjaGn58fioqKNBWTiIiIiKhJ+eVsHHKLy+Bpbwq/9vZix2kwNLaC08cffwwA2LRp02O1FwQBK1euxOLFizF69GgAwJYtW2BnZ4e9e/di0qRJVR5XXFyM4uJi9eOcnJynC05EREREpKWy8kuw8Xz5gq7vDHWHjg57iyo0mHuM4uLiIJfLMWTIEPU+c3Nz+Pj4ICgoqNrjVqxYAXNzc/Xm5ORUH3GJiKgBOnPmDEaNGgVHR0dIJBLs3bu30vMBAQGQSCSVNn9//0eed/Xq1XB2doaBgQF8fHxw6dIlDb0CIiLN+ulMLPJLlOjQ3AzD2tmJHadBaTCFkVwuBwDY2VX+H2RnZ6d+riqLFi2CQqFQb0lJSRrNSUREDVd+fj68vb2xevXqatv4+/vj7t276m3Hjh01nnPnzp2YN28eli5diqtXr8Lb2xt+fn5IT0+v6/hERBp1L7cYWy4kAADmDXXnvUX/UavCaOHChQ990/bfLTIyUlNZq6Svrw8zM7NKGxERNU3Dhw/H8uXLMXbs2Grb6Ovrw97eXr01a9asxnN+8803mDFjBqZNm4Z27dph7dq1MDIywoYNG6o9pri4GDk5OZU2IiKxrT0di8JSJTo5WWCgh63YcRqcWt1j9O677yIgIKDGNq6urk8UxN6+/MavtLQ0ODg4qPenpaWhU6dOT3ROIiKi/zp16hRsbW3RrFkzDBo0CMuXL4eVlVWVbUtKShASEoJFixap9+no6GDIkCGPHOZdca8tEVFDkJJdiF8vsreoJrUqjGxsbGBjY6ORIC4uLrC3t0dgYKC6EMrJyUFwcHCtZrYjIiKqjr+/P8aNGwcXFxfExsbigw8+wPDhwxEUFASpVPpQ+4yMDCiVyiqHedc0QmLRokWYN2+e+nFOTg7vgSUiUX11LAolZSr4uFiibxtrseM0SBqblS4xMRFZWVlITEyEUqlEaGgoAMDNzQ0mJiYAAE9PT6xYsQJjx46FRCLB3LlzsXz5crRp0wYuLi74v//7Pzg6OmLMmDGaiklERE3Iv2c49fLyQseOHdG6dWucOnUKgwcPrrPr6OvrQ19fv87OR0T0NG4kK7DnWgoAYPHIduwtqobGCqMlS5Zg8+bN6sedO3cGAJw8eRIDBgwAAERFRUGhUKjbvP/++8jPz8fMmTORnZ2NPn364OjRozAwMNBUTCIiasJcXV1hbW2NmJiYKgsja2trSKVSpKWlVdqflpamHgJORNSQCYKATw/fAgCM7dwcXi3MRU7UcGlsVrpNmzZBEISHtoqiCCj/H/Xve5YkEgk++eQTyOVyFBUV4cSJE3B3d9dURCIiauKSk5ORmZlZ6d7Wf5PJZOjatSsCAwPV+1QqFQIDA+Hr61tfMYmInlhgRDou3smCvq4O5vt5iB2nQdNYjxERkRgKSsqQmVeCjLxiFJYooRIAlSBAVyqBpbEMVsb6aGakB11pg1mtgOpQXl4eYmJi1I/j4uIQGhoKS0tLWFpa4uOPP8b48eNhb2+P2NhYvP/++3Bzc4Ofn5/6mMGDB2Ps2LGYPXs2AGDevHl4+eWX0a1bN/To0QMrV65Efn4+pk2bVu+vj4ioNkqVKqw4EgEAmN7HBc0tDEVO1LCxMCKiRulebjHCkrMRnpqD2Ht5uHMvH/EZ+cgtLnvksQZ6Onh7sDte6+fKFb+1zJUrVzBw4ED144oJEF5++WWsWbMGYWFh2Lx5M7Kzs+Ho6Ihhw4Zh2bJlle4Hio2NRUZGhvrxxIkTce/ePSxZsgRyuRydOnXC0aNHH5qQgYioofk1KAGx9/JhaSzDrAGtxY7T4EkEQRDEDlGXcnJyYG5uDoVCwTWNiLSESiUgOj0Xl+KyEByXhasJ93FXUVRte31dHVib6MNIJoVUp3yNtZIyJe4XlOJ+QQkq/uoN9rTF1xO8YWEkq6dXov34N7hq/LkQUX1Lzy3C4K9OI7e4DCvGeWFyj5ZiRxJFbf7+sseIiBqkpKwCnIvJwLmYDFyIycD9gtJKz0skgJuNCbxamKONrSlcrI3R2sYYDhaGMJZJq51xp0ypwu6QZCzdH47AyHSM/P4cfpzSBd5OFvXwqoiIiOrHF0eikFtcBu8W5pjYjcsFPA4WRkTUIOQXl+HinUycib6HM7czEJeRX+l5I5kUXVs1g4+LJbo5W8KruTmM9Wv/J0xXqoPJPVrCq7k53tx+FQmZBXhu7QUs8PfE9D4unMKUiIgavZCELPxxNRkSCfDx6A4cNv6YWBgRkSjKlCrcTM3B+ZgMnIm+h6uJ91Gq/Gdkr66OBJ1bWqCPmw36tLFCxxYW0KvDCRM6NDfHgTl9sOD3MBy5KcfyQxEIis3EV897o5kxh9YREVHjpFQJ+L+94QCAid2c0IkjIh4bCyMiqhfFZUqEp+YgJP4+guMyEXwn66GJEpwsDdGvjQ36udugV2srmBroaTSTmYEefpzSBVuDE7Hs4C0ERqZj+Hdn8d2kTvBxtdLotYmIiDRhW3ACbt3NgZmBLt7j9Ny1wsKIiDQqv7gM83dfR2BkOkrKVJWeMzXQRU9XK/RrY42+bWzgbG1c7/kkEgle6tkKXVpaYM72a7iTkY/JP1/EW4PbYM6gNpBy+AERETUSaTlF+PJoFADgPT8PWJnoP+II+jcWRkSkUf87FoUjN+UAAEtjGbq0bIZuzs3Qq7UV2juaN5jCo71j+dC6JfvC8cfVZKw8cRtBsZn4blJn2JsbiB2PiIjokT4+EI684jJ0crLACz6txI7T6LAwIiKNuRKfhc1B8QCAn17qimHt7Br05AbG+rr4eoI3+rSxwuI9NxEcl4UR35/F1xO8MdDDVux4RERE1QqMSMPhG3JIdSRYMc6rwXzx2Jhw6Xci0oiiUiXe/yMMggA837UF/NrbN+ii6N/Gdm6Bg2/1RTsHM2Tll2DaxstYcSQCpUrVow8mIiKqZ/nFZViyr3zChVf7uqCtA9dLexIsjIhII74PvI079/JhY6qPxSPbiR2n1lysjfHnG73wsm/5UISfTt/B5HUXIa9hYVkiIiIxfHs8GinZhWjRzBBvD24jdpxGi4UREdW5mykK/HTmDgBg+ZgOMDfS7OxymmKgJ8XHoztgzZQuMNXXxZWE+3jmh7M4H5MhdjQiIiIAwPWkbGw4HwcAWDamA4xkvFPmSbEwIqI6VapU4f3fw6BUCRjZ0QF+7e3FjvTUhns54MCcPmjrYIaMvBK8tD4Yq0/GQBCERx9MRESkISVlKiz4IwwqARjTyZH3wz4lFkZEVKd+Oh2LW3dzYGGkh4+fbS92nDrjbG2MPW/0woRuLaASymfbe3P7VeT/Zy0mIiKi+rL2dCwi5bmwNJZhySjtec8VCwsjIqozt9Ny8X1gDABg6ah2sNay9RMM9KT48jlvfDbWC3pSCQ7fkGP8mgtIzCwQOxoRETUxMem5WPX3P++5lsYykRM1fiyMiKhOKFUC3vs9DCVKFQZ62GBMp+ZiR9KYF3xa4reZPWFjqo9IeS5Grz6Hy/FZYsciIqImQqkSsOCPGyhRqjDI0xbPejuKHUkrsDAiojqx8XwcQpOyYaKvi0/HejWaqbmfVNdWljgwuw86tjDH/YJSTPk5GPtCU8SORURETcCWoHiEJNyHib4ulo/poPXvufWFhRERPbWEzHx89VcUAGDRCE84WhiKnKh+2JsbYOdMX/i1t0OJUoW3fwvF94G3OSkDERFpTFJWAb48Wv6eu3B403nPrQ8sjIjoqahUAhb8EYaiUhV8Xa0wuXtLsSPVK0OZFGumdMXMfq4AgG+OR2PJvnCoVCyOiIiobgmCgEV/3kBhqRI+LpZ4oUfTes/VNBZGRPRUtl9KxMU7WTDUk+Lz8V7Q0Wl63fk6OhJ8MKItlo1uD4kE+PViAubuDEVJmUrsaEREpEV2XUnCuZgM6Ovq4PPxHZvke64msTAioieWkl2IFYcjAADv+XmglZWxyInE9ZKvM76b1Bm6OhLsv56Kmb9eQWGJUuxYRESkBdJyirD8UPl77rvD3OFi3bTfczWBhRERPZGK7vz8EiW6tWqGgF7OYkdqEJ71dsTPL3eDgZ4OTkXdw4wtV1BUyuKIiIieztJ94cgtKoNXc3O80ttF7DhaiYURET2R3SHJOBN9DzJ25z9koIcttrziAyOZFOdiMlgcERHRUzl6U46j4XLo6kjwxfiO0JXyI7wm8KdKRLV2V1GIZQdvAQDeHeoON1sTkRM1PD1cLLFpWg8YyaQ4ezsDr/0awuKIiIhqTVFYiiX7bgIAXuvvinaOZiIn0l4sjIioVgRBwAd/3kBuURk6OVng1b6uYkdqsHq4WGJDQHcY6klxOvoe5uy4hjIlJ2QgIqLH98XRSKTnFsPV2hhzBrURO45WY2FERLXyx9UUnIwqH0L31fMdIeUQuhr1dLXC+oBukOnq4PitNPzfvnCuc0RERI/lcnwWtgcnAgA+G+cFAz2pyIm0GwsjInpsckURPjkQDgB4Z4g73GxNRU7UOPRqbY3vJ3WCjgTYcSkRK0/cFjsSERE1cCVlKny45wYAYHIPJ/R0tRI5kfZjYUREj0UQyhdyzSkqg3cLc8zoyxlxasO/gwM+Gd0BAPBd4G1sC04QORERETVk68/FITotD1bGMiz0byt2nCaBhRERPZadl5Nw+sEsdF9P8OaMOE/gxZ6t8Pbg8vHhS/aF40JMhsiJiIioIUrKKsB3gdEAgA9HtoW5kZ7IiZoGfrIhokdKyipQz0L33jAPDqF7CnOHtMHYzs2hVAl4Y/tVJGYWiB2JiIgaEEEQsHR/OIpKVejpaomxnZuLHanJYGFERDVSqQS8/3sY8kuU6O7cDK/04RC6pyGRSLBinBe8nSyQXVCKV7dcRl5xmdixiIiogTgWnoa/I9OhJ5Vg+ZgOkEg4yVF9YWFERDXaHBSPoDuZMNST4qvnvTkLXR0w0JNi3UtdYWuqj+i0PLyzM5Qz1REREYpKleoRGjP7uXKERj1jYURE1YpJz8XnRyIBAB+M8EQrK2ORE2kPOzMDrJv6zzTe+6+nih2JiIhEtu7MHaRkF8LB3ABvDnQTO06Tw8KIiKpUqlThnZ3XUVymQj93G7zYs5XYkbROJycL9WQMyw7egqKwVOREREQkltTsQvx4KgYAsGhEWxjJdEVO1PSwMCKiKv3wdwxupChgbqiH/z3XkWOcNWRGX1e0tjFGRl4JvjoWJXYcIiISyedHIlFUqkJ352YY1dFB7DhNEgsjInrItcT7WH2y/Fur5WM6wM7MQORE2kumq4PlY7wAAFuDExCalC1uICIiqneX47Ow/3oqJBJg6aj2/DJSJCyMiKiSvOIyzN0ZCqVKwLPejhjl7Sh2JK3n29oK4zo3hyAAH+65gTKlSuxIjdaZM2cwatQoODo6QiKRYO/evernSktLsWDBAnh5ecHY2BiOjo6YOnUqUlNrvr/ro48+gkQiqbR5enpq+JUQUVMhVxRhwe9hAIBJ3Z3Qobm5yImaLhZGRFTJR/vDkZBZgOYWhlg2uoPYcZqMD0a2hZmBLsJTc7AlKEHsOI1Wfn4+vL29sXr16oeeKygowNWrV/F///d/uHr1Kv78809ERUXh2WeffeR527dvj7t376q3c+fOaSI+ETUxiZkFeP6nC7iTkQ8HcwO8O8xD7EhNGu/qIiK1g2Gp+D0kGToS4NuJnbjSdj2yNtHHwuFt8cGeG/j6rygM97KHg7mh2LEaneHDh2P48OFVPmdubo7jx49X2rdq1Sr06NEDiYmJaNmyZbXn1dXVhb29fZ1mJaKm7XZaLqb8Eoz03GK0sjLC1uk+sDbRFztWk8YeIyICAKRkF2LRnzcAAG8OdEMPF0uREzU9k7o7oUtLC+SXKPHx/ltix2kSFAoFJBIJLCwsamx3+/ZtODo6wtXVFVOmTEFiYmKN7YuLi5GTk1NpIyKqcCs1BxN+CkJ6bjE87Eyx+zVfOFkaiR2ryWNhREQoU6rwzm+hyC0qQycnC7z1YAppql86OhJ8OtYLUh0JjobLERiRJnYkrVZUVIQFCxZg8uTJMDMzq7adj48PNm3ahKNHj2LNmjWIi4tD3759kZubW+0xK1asgLm5uXpzcnLSxEsgokYoPFWBF365iPsFpejYwhw7X+sJW05y1CCwMCIifBd4G5fis2Cir4vvJnWCnpR/GsTS1sEMr/ZxAQAs2ReOgpIykRNpp9LSUkyYMAGCIGDNmjU1th0+fDief/55dOzYEX5+fjh8+DCys7Oxa9euao9ZtGgRFAqFektKSqrrl0BEjdDNFAVe+DkY2QWl6ORkga2v+sDCSCZ2LHqAn36ImrhztzOw6sHU3J+N80IrK2ORE9HbQ9qguYUhUrIL8V3gbbHjaJ2KoighIQHHjx+vsbeoKhYWFnB3d0dMTEy1bfT19WFmZlZpI6Km7WaKAlN+CYaisBSdW1pgy/QeMDPgvbwNCQsjoiYsPbcIc3eGQhCAyT1a4llOzd0gGMl08fGz7QEA68/G4XZa9UO2qHYqiqLbt2/jxIkTsLKyqvU58vLyEBsbCwcHLsBIRI/ndloupm64BEVhKbq2aoYtr7AoaohYGBE1UUqVgHd2hiIjr/zGz6Wj2okdif5lSDs7DGlrhzKVgMV7b0IQBLEjNQp5eXkIDQ1FaGgoACAuLg6hoaFITExEaWkpnnvuOVy5cgXbtm2DUqmEXC6HXC5HSUmJ+hyDBw/GqlWr1I/nz5+P06dPIz4+HhcuXMDYsWMhlUoxefLk+n55RNQIxWfkY8ovwcjKL0HHFubYNK07TFkUNUicrpuoifr2eDTOx2TCUE+K1VM6w0BPKnYk+o+lo9rhXMw9BMdlYW9oCsZ2biF2pAbvypUrGDhwoPrxvHnzAAAvv/wyPvroI+zfvx8A0KlTp0rHnTx5EgMGDAAAxMbGIiMjQ/1ccnIyJk+ejMzMTNjY2KBPnz64ePEibGxsNPtiiKjRS8kuVE/J7Wlvii2v9GBR1ICxMCJqgk7cSlPfV/T5eC+42ZqKnIiq4mRphDmD2uB/x6Lw6aEIDPK0g7kh31BrMmDAgBp71x6n5y0+Pr7S499+++1pYxFRE5SVX4KX1gcjJbsQrjbG+HU6J1po6DiUjqiJScjMxzu7QgEAL/u2wuhOzcUNRDV6ta8LXG2MkZFXgm/+ihI7DhERPYb84jJM23QZd+7lw9HcANte9YGNKRdvbehYGBE1IYUlSry+9Spyi8rQpaUFPhzJ+4oaOn1dKZaN7gAA+PViAiLlXCiUiKghK1WqMGvbVVxPyoaFkR62TO8BB3NDsWPRY9BYYfTpp5+iV69eMDIyeuSK4hUCAgIgkUgqbf7+/pqKSNSkCIKA936/joi7ObA2kWH1lC6Q6fK7kcagt5s1/NvbQyUAH++/xYkYiIgaKEEQsOD3MJyJvgdDPSk2BnTncPVGRGOfikpKSvD8889j1qxZtTrO398fd+/eVW87duzQUEKipmX1yRgcDLsLXR0JVr/Qhd9eNTIfjmwLma4Ogu5k4li4XOw4RERUhe8Cb+PPaymQ6kjw45Qu6NyymdiRqBY0NvnCxx9/DADYtGlTrY7T19eHvb29BhIRNV3HwuX46q9oAMAnozvAx7X2a7eQuJwsjfBaP1f88HcMlh+KwAAPW84kSETUgPx5NRkrT5Qvyr18TAcM9LQVORHVVoMbR3Pq1CnY2trCw8MDs2bNQmZmZo3ti4uLkZOTU2kjon9E3M3BOztDAZRPtvCCT0txA9ETmzWgNRzMDZB8vxA/n7kjdhwiInrg4p1MLPgjDADwev/WmNyD77WNUYMqjPz9/bFlyxYEBgbiiy++wOnTpzF8+HAolcpqj1mxYgXMzc3Vm5OTUz0mJmrY7ioKMW3jZRSUKNGrtRUWP8PJFhozI5kuFg73BAD8eCoW6TlFIiciIqKEzHy89msISpUCRnjZ430/D7Ej0ROqVWG0cOHChyZH+O8WGRn5xGEmTZqEZ599Fl5eXhgzZgwOHjyIy5cv49SpU9Ues2jRIigUCvWWlJT0xNcn0iY5RaUI2HAZ8pwitLYxxo9TukBP2qC+C6En8Ky3Izq3tEBhqRIrA2+LHYeIqEnLKy7Dq5uvQFFYCm8nC3wzoRN0dCRix6InVKt7jN59910EBATU2MbV1fVp8jx0Lmtra8TExGDw4MFVttHX14e+PueFJ/q3kjIVZm0NQVRaLmxM9bFpWg8uKqclJBIJFg1viwk/BWHn5SRM7+OC1jYmYsciImpyVCoB7+wMxe30PNia6mPdS11572cjV6vCyMbGBjY2NprK8pDk5GRkZmbCwcGh3q5JpA1WHInA+ZhMGMvKpwp1sjQSOxLVoR4ulhjS1hYnItLx5dFI/PRSN7EjERE1OStPROP4rTTIdHWwbmo32JkZiB2JnpLGxtUkJiYiNDQUiYmJUCqVCA0NRWhoKPLy8tRtPD09sWfPHgBAXl4e3nvvPVy8eBHx8fEIDAzE6NGj4ebmBj8/P03FJNI6pUoVfg9JBgB8PaETOjQ3FzkRacL7/p7QkQDHwtMQknBf7DhERE3KsXA5vv87BgCwYqwXOjlZiBuI6oTGCqMlS5agc+fOWLp0KfLy8tC5c2d07twZV65cUbeJioqCQqEAAEilUoSFheHZZ5+Fu7s7pk+fjq5du+Ls2bMcKkdUC5fjs5BbVAZLYxmGtrMTOw5piLudKZ7r2gIA8PmRCC76SkRUT+Iz8jF/13UAwCu9XTD+wd9iavw0to7Rpk2bHrmG0b/fyA0NDXHs2DFNxSFqMv6OSAcADPSwhZQ3gGq1d4a6Y19oKi7H38epqHtcM4OISMMKS5R4fWsIcovL0N25GRaN8BQ7EtUhTlFFpGUCI8sLoyFt+SFZ2zmYG2KqbysAwMrA2+w1IiLSIEEQsHjvTUTKc2FtIsOqFzjbq7bh/00iLRJ7Lw9xGfnQk0rQp4212HGoHszs1xoGejq4npSN09H3xI5DRKS1dl1Jwh9Xk6EjAX6Y3IWTLWghFkZEWiQwIg0A0NPVCqYGeiKnofpgY6qPKT7lvUbfsdeIiEgjbqflYun+cADAu8M84NvaSuREpAksjIi0yIkH9xcN5r0mTcpr/V2hr6uDa4nZOBeTIXYcIiKtUlSqxOzt11BUqkLfNtaY1b+12JFIQ1gYEWmJ7IIS9bTNg9tyNrqmxNbUAC/4tAQAfHeCvUZERHVp+aFbiEorv6/o6wne0OHERlqLhRGRljgdfQ9KlQB3OxMu6NoEvd6/NWS6OriScB8XYjPFjkNEpBWO3pRj68VEAMA3EzrB1pT3FWkzFkZEWkI9jI69RU2SnZkBJnd3AgD8dOaOyGmIiBq/9JwiLPwzDADwWj9X9HO3ETkRaRoLIyItUKpU4XQUp+lu6l7t6wodCXAm+h6i5LlixyEiarQEQcD7f4Qhu6AU7R3N8O4wD7EjUT1gYUSkBYLvZCGnqAxWxjJ0cmomdhwSiZOlEfw72AMA1p9jrxER0ZPaFpyIU1H3INPVwcqJnSDT5UfmpoD/l4m0wLFwOQBgaDs7SHlTaJM2vY8rAGDvtVSk5xaJnIaIqPGJy8jHp4ciAAAL/D3Rxs5U5ERUX1gYETVyKpWAv26VF0Z+7e1FTkNi69qqGbq0tECJUoVfgxLEjkNE1KgoVQLm7QpFYakSvVpbYVovZ7EjUT1iYUTUyIWlKJCWUwxjmZQLzhGA8nuNAGDrxQQUlihFTkNE1HhsOBeHa4nZMNXXxf+e59TcTQ0LI6JGrmIY3QBPWxjoSUVOQw2BX3t7OFka4n5BKf64mix2HCKiRiEuIx9f/RUFAFj8TFs0tzAUORHVNxZGRI1cRWHEYXRUQaojwbReLgCALUHxXPCViOgRVCoBC34PQ3GZCn3crDGhm5PYkUgELIyIGrGY9FzcuZcPPakEAz24vgL9Y3zXFjDQ00F0Wh5CEu6LHYeIqEHbGpyAS/FZMJJJsWKcFyQSDqFrilgYETVix8LTAAC9WlvD1EBP5DTUkJgb6mFUR0cAwPZLiSKnISJquJLvF+DzI5EAymehc7I0EjkRiYWFEVEj9heH0VENJvu0BAAcCrsLRUGpyGmIiBoeQRCwdF84CkqU6O7cDC/1bCV2JBIRCyOiRuquohDXkxWQSMrXLyL6r85OFvC0N0VxmQp/XuMkDERE/3UsXI7AyHToSSX4bKwXZ6Fr4lgYETVSR26U9xZ1bdkMNqb6IqehhkgikeCFB71G24MTOQkDEdG/5BaVYun+cADAa/1acyFXYmFE1FgdvnEXADCyo4PISaghG9O5OQz1pLidzkkYiIj+7eu/opGWU4xWVkaYPchN7DjUALAwImqE7ioKceXBh9zhHVgYUfXMDPQwyrv83wgnYSAiKheSkIUtQfEAgOVjOnAdQALAwoioUTr8YBhdd+dmsDc3EDkNNXSTe/wzCUNukXZPwnDmzBmMGjUKjo6OkEgk2Lt3b6XnBUHAkiVL4ODgAENDQwwZMgS3b99+5HlXr14NZ2dnGBgYwMfHB5cuXdLQKyAiTYuS52L65itQCcDoTo7o24bLXVA5FkZEjZB6GJ0Xe4vo0To5WcDVxhjFZSr1FO/aKj8/H97e3li9enWVz3/55Zf4/vvvsXbtWgQHB8PY2Bh+fn4oKiqq9pw7d+7EvHnzsHTpUly9ehXe3t7w8/NDenq6pl4GEWlIQmY+XlwfjOyCUnRyssBnY73EjkQNCAsjokYmNbsQIQn3IZEAw1kY0WOQSCQY06k5AGBfaIrIaTRr+PDhWL58OcaOHfvQc4IgYOXKlVi8eDFGjx6Njh07YsuWLUhNTX2oZ+nfvvnmG8yYMQPTpk1Du3btsHbtWhgZGWHDhg0afCVEVNfkiiJM+SUY93KL4Wlvik3TusNYX1fsWNSAsDAiamSO3HwwjK6VJezMOIyOHs/oTuWLvZ6PyUB6bvW9I9osLi4OcrkcQ4YMUe8zNzeHj48PgoKCqjympKQEISEhlY7R0dHBkCFDqj0GAIqLi5GTk1NpIyLxpOcU4YVfLiL5fiGcrYywZXoPWBjJxI5FDQwLI6JG5lBYKgBghBcXdaXH18rKGJ1bWkAlAAeu3xU7jijk8vIvFezsKq/7ZWdnp37uvzIyMqBUKmt1DACsWLEC5ubm6s3Jyekp0xPRk7qXW4wXfgnGnXv5aG5hiK2v+sDWlF8s0sNYGBE1IqnZhbiamM1hdPREmspwuoZg0aJFUCgU6i0pKUnsSERNUmZeMab8chEx6XlwMDfAjhk90aKZkdixqIFiYUTUiFRMusBhdPQkRnZ0gFRHgrBkBWLv5Ykdp97Z25f3sqalVZ6AIi0tTf3cf1lbW0MqldbqGADQ19eHmZlZpY2I6ldGXjGm/BKM6LQ82JnpY8eMnmhpxaKIqsfCiKgR2fvgm/6KdWmIasPaRB9921gDAPZda3q9Ri4uLrC3t0dgYKB6X05ODoKDg+Hr61vlMTKZDF27dq10jEqlQmBgYLXHEJH40nOLMHndRUTKc2FrWl4UOVsbix2LGjgWRkSNREx6Hm6m5EBXR4KRHR3FjkONVMVwur2hqRAEQeQ0dS8vLw+hoaEIDQ0FUD7hQmhoKBITEyGRSDB37lwsX74c+/fvx40bNzB16lQ4OjpizJgx6nMMHjwYq1atUj+eN28efv75Z2zevBkRERGYNWsW8vPzMW3atHp+dUT0ONJyijBp3UXcTs+DvZkBdr7mC1cbE7FjUSPAOQqJGomK+0L6udvA0pgz6dCTGdbeDoZ6UiRmFSAsWQFvJwuxI9WpK1euYODAgerH8+bNAwC8/PLL2LRpE95//33k5+dj5syZyM7ORp8+fXD06FEYGPwzNDU2NhYZGRnqxxMnTsS9e/ewZMkSyOVydOrUCUePHn1oQgYiEl9qdiFe+Pki4jML0NzCENtn+KCVFXuK6PFIBC37yjAnJwfm5uZQKBQc001aQxAE9P/fKSRmFeD7yZ3xrDd7jOjJvbEtBIdvyPHGgNZ439+zTs/Nv8FV48+FSPMSMvPxws/BSMkuRItmhtgxoyecLHlPUVNXm7+/HEpH1AhcTcxGYlYBjGVSDG3Lb6np6fi1L5804Fh49dNNExE1JjHpuXh+bRBSsgvham2MXa/5siiiWmNhRNQI7H1wo7xfe3sYyqQip6HGbqCnLfSkEsTey0dMetObnY6ItEt4qgITf7qI9NxieNiZ4rfXesLRwlDsWNQIsTAiauBKlSocejBN9+jOzUVOQ9rAzEAPvq3LZ6djrxERNWZXE+9j8rqLyMwvQYfmZvhtZk8u3kpPjIURUQN39vY9ZOWXwNpEht6trcSOQ1rCr335kMy/bqU9oiURUcN0ISYDL/4SjJyiMnRr1QzbZ/REM05ORE+BhRFRA7fnWioA4JmOjtCV8leW6sbQdnaQSIDrSdmQK4rEjkNEVCt/R6YhYNNlFJQo0cfNGlum94CZgZ7YsaiR46csogZMUVCqHuo0rguH0VHdsTU1QJeWzQAAf93icDoiajwOhd3FzC0hKClTYWg7O/zycjcYybgCDT09FkZEDdj+sFSUlKngaW8Kr+bmYschLVMxnI73GRFRY/FHSDLm7LiKMpWAZ70d8eOULjDQ46REVDdYGBE1YLuvJAEAnu/mBIlEInIa0jYV03ZfvJOF7IISkdMQEdVs68UEvLv7OlQCMLGbE76d2Al6HGJOdYj/mogaqIi7OQhLVkBPKsGYTlzQlepeKytjeNqbQqkS8HdkuthxiIiqteFcHBbvvQkACOjljBXjvCDV4ReGVLdYGBE1ULuvJAMAhrS1g5WJvshpSFsNbmsLADgdfU/kJEREVVt7OhafHLwFAHitvyuWjmoHHRZFpAEsjIgaoJIyFfZcKy+MJnRzEjkNabP+7uWF0Znoe1CqBJHTEBFV9n3gbXx+JBIA8NbgNljo78mh5aQxLIyIGqDAiDTcLyiFnZk++raxFjsOabHOLS1gqq+L+wWluJmiEDsOEZHadydu45vj0QCA9/w8MG+oO4si0igWRv+xLzQF0zddRlxGvthRqAnb9WDShXFdWnDtItIoPakOeruVF99nOJyOiBqI7wNv49sT5UXRwuGeeHOgm8iJqCngJ67/+ONqCgIj03Hk5l2xo1ATlXy/QH2/x/NdW4ichpqCfu42AHifERE1DN8H/tNTtHC4J17v31rkRNRUsDD6jxEdyqevPXKD63qQOLYHJ0IlAL3drOBqYyJ2HGoC+rmX9xhdS8qGorBU5DRE1JStPR2rLooW+LMoovrFwug/hrW3h1RHghspCiRlFYgdh5qY4jIldl4uH0b3Us9WIqehpqJFMyO42ZpAqRJwISZD7DhE1ERtCYpXT7Twnp8HZg1gUUT1i4XRf1gay9DT1RIAOJyO6t3Rm3Jk5pfAzkwfQ9raiR2HmpB+bTicjojEs/tKEpbsCwcAzBnkxnuKSBQsjKowvIMDAOAwh9NRPfs1KAEA8EKPVpx0gepVf49/CiNB4LTdRFR/Dt+4iwV/hAEAXuntgnlD3UVORE2Vxj55xcfHY/r06XBxcYGhoSFat26NpUuXoqSkpMbjioqK8Oabb8LKygomJiYYP3480tLSNBWzSn7t7SGRAKFJ2UjJLqzXa1PTdSs1B1cS7kNXR4LJPbh2EdUvHxdL6Ovq4K6iCLfT88SOQ0RNxIXYDMz9LRQqAZjU3Qn/90xbTslNotFYYRQZGQmVSoWffvoJ4eHh+Pbbb7F27Vp88MEHNR73zjvv4MCBA9i9ezdOnz6N1NRUjBs3TlMxq2Rjqo8ezuXD6Y7eZK8R1Y+tweW9RX4d7GFrZiByGmpqDPSk6OlqBYDTdhNR/QhPVWDmlhCUKFUY3sEen471YlFEotJYYeTv74+NGzdi2LBhcHV1xbPPPov58+fjzz//rPYYhUKB9evX45tvvsGgQYPQtWtXbNy4ERcuXMDFixc1FbVKI7zKh9MducH7jEjzcopKsfdaCgBOukDi4bTdRFRfkrIKELDxMvKKy+DjYolvJ3aCVIdFEYmrXm9iUCgUsLS0rPb5kJAQlJaWYsiQIep9np6eaNmyJYKCgqo8pri4GDk5OZW2uuD/YNruKwn3IVcU1ck5iarz26VEFJQo4W5nAh+X6n9HiDRpaFs7vOfngUXD24odhYi0mKKgFC9vvIR7ucXwtDfFuqndYKAnFTsWUf0VRjExMfjhhx/w2muvVdtGLpdDJpPBwsKi0n47OzvI5VUPaVuxYgXMzc3Vm5NT3dybYWdmgG6tmgEAjnJ2OtKgkjIVNpyLBwC82teVwwhINC2tjPDmQDe0czQTOwoRaamSMhVe3xqCO/fy4WhugM2v9IC5oZ7YsYgAPEFhtHDhQkgkkhq3yMjISsekpKTA398fzz//PGbMmFFn4QFg0aJFUCgU6i0pKanOzj38wXC6g2EsjEhzDt1IhTynCDam+hjdyVHsOERERBohCAL+b+9NBN3JhLFMivUB3WHHe2qpAdGt7QHvvvsuAgICamzj6uqq/u/U1FQMHDgQvXr1wrp162o8zt7eHiUlJcjOzq7Ua5SWlgZ7e/sqj9HX14e+vv5j56+NZzo64NNDt3Al4T6SsgrgZGmkketQ0yUIAn46fQcAENDLGfq6HEpARETaac3pWOy8kgQdCfDDC53R1oG909Sw1LowsrGxgY2NzWO1TUlJwcCBA9WTKOjo1NxB1bVrV+jp6SEwMBDjx48HAERFRSExMRG+vr61jfrU7MwM0Ku1Nc7FZGBfaApmD2pT7xlIu52LyUCkPBdGMimm+LQUOw4REVGdUxSW4v/23sT+66kAgP97ph0GeXIRc2p4NHaPUUpKCgYMGICWLVviq6++wr179yCXyyvdK5SSkgJPT09cunQJAGBubo7p06dj3rx5OHnyJEJCQjBt2jT4+vqiZ8+emopao4qhTXuupXDRQ6pz686U9xZN6OYECyOZyGmIiIjq1sU7mRi+8gz2X0+FVEeC9/w8ENDLWexYRFWqdY/R4zp+/DhiYmIQExODFi1aVHquosAoLS1FVFQUCgoK1M99++230NHRwfjx41FcXAw/Pz/8+OOPmor5SP4d7LF4703E3stHeGoOOjQ3Fy0LaZeIuzk4ezsDOhJgeh8XseMQERHVmVKlCitPROPHU7EQBKCVlRG+ndgJXVo2EzsaUbU01mMUEBAAQRCq3Co4OztDEAQMGDBAvc/AwACrV69GVlYW8vPz8eeff1Z7f1F9MDXQw5C25d29FevMENWFH/6+DaB8zSzev0ZERNoiMbMAz68NwuqT5UXRhG4tcOitviyKqMGr13WMGqsxnZsDAPZfT4VSxeF09PQi7ubg8A05JBJgDu9dIyIiLXHgeipGfH8WoUnZMDXQxeoXuuDL57xhoq+xQUpEdYb/Sh9Df3cbWBjpIT23GEGxmejTxlrsSNTIfXfin94iD3tTkdMQERE9naJSJT4+cAs7LiUCALq1aoaVkzqhRTOOiKDGgz1Gj0Gmq4MRD9Y02hvK4XT0dMJTFTgaXt5bNHcwe4uIiKhxi0nPw+hV57HjUuKDkRBu+G1mTxZF1OiwMHpMYx8Mpzty4y7yi8tETkONWUVv0TMdHdHGjr1FRETUeO2/nopnV51DVFourE308esrPnh3mAd0pfyISY0P/9U+pm6tmsHZygj5JUocCrsrdhxqpG6mKPDXrTRIJMBbg9zEjkNERPREisuUWLrvJt7acQ0FJUr4ulrh8Nt9eLsBNWosjB6TRCLBhO5OAICdV5JETkON1f+ORQEARrG3iIiIGim5oggTf7qIzUEJAIDZA92w9VUf2JoaiJyM6OmwMKqF57q0gFRHgpCE+4hJzxU7DjUyJ6PScTr6HvSkErwz1F3sOERNlrOzMyQSyUPbm2++WWX7TZs2PdTWwIAfAKlpuhSXhWd+OIfQpGyYG+phQ0A3zPfzgFRHInY0oqfGWelqwdbMAAM9bHAiIh27riTjgxFtxY5EjUSpUoVPD0UAAF72dYaLtbHIiYiarsuXL0OpVKof37x5E0OHDsXzzz9f7TFmZmaIiopSP5ZI+CGQmhZBEPDrxQR8cuAWylQCPO1Nse6lbmhpxQkWSHuwMKqlid1b4kREOv4IScb8YR6Q6bLTjR5tx6VExKTnoZmRHuZwJjoiUdnY2FR6/Pnnn6N169bo379/tcdIJJJaLTZeXFyM4uJi9eOcnJzaByVqIErKVFiy7yZ+u1x+K8Gz3o74fLwXjGT8GEnahZ/qa2mghw1sTPWRmV+CvyPTxI5DjYCioBTfHI8GAMwb5gFzQz2RExFRhZKSEmzduhWvvPJKjb1AeXl5aNWqFZycnDB69GiEh4fXeN4VK1bA3NxcvTk5OdV1dKJ6kZVfghfXB+O3y0nQkQAfjPDEd5M6sSgircTCqJZ0pToY36UFAGDnZU7CQI/2XeBtZBeUwt3OBJO788MRUUOyd+9eZGdnIyAgoNo2Hh4e2LBhA/bt24etW7dCpVKhV69eSE5OrvaYRYsWQaFQqLekJL5fUOMTnZaLZ1edw6W4LJjq62L9y90xs19rDiUlrcVy/wlM6NYCa0/H4nT0PaRkF6K5haHYkaiBup6UjU0X4gAAi0e247oORA3M+vXrMXz4cDg6OlbbxtfXF76+vurHvXr1Qtu2bfHTTz9h2bJlVR6jr68PfX39Os9LVF/Ox2Tg9a0hyC0qQysrI/wytRtnUyWtx09pT8DVxgS+rlZQCcC2iwlix6EGqrhMifd+vw6VAIzu5Ih+7jaPPoiI6k1CQgJOnDiBV199tVbH6enpoXPnzoiJidFQMiJx7bqShJc3XEJuURm6OzfD3jd6syiiJoGF0RN6uVcrAMBvl5NQVKp8RGtqilb/HYPotDxYGcuwdFR7seMQ0X9s3LgRtra2GDlyZK2OUyqVuHHjBhwcHDSUjEgcgiDgm+PReP/3MJSpBDzr7Yhfp/ugmbFM7GhE9YKF0RMa0tYODuYGyMovweEbd8WOQw1MeKoCP56KBQB8MroDLPmmQtSgqFQqbNy4ES+//DJ0dSuPKp86dSoWLVqkfvzJJ5/gr7/+wp07d3D16lW8+OKLSEhIqHVPE1FDVqZU4YM9N/F94G0A5Yu2fjepEwz0pCInI6o/LIyekK5UB1N8WgKAeuVnIqB8CF3Ft23DO9hjZEd+q0zU0Jw4cQKJiYl45ZVXHnouMTERd+/+84XX/fv3MWPGDLRt2xYjRoxATk4OLly4gHbt2tVnZCKNKSpV4o1tV7HjUiJ0JMCnYztgvp8HJ1mgJkciCIIgdoi6lJOTA3NzcygUCpiZmWn0Whl5xei14m+UKFXY+2ZvdHKy0Oj1qHH4cM8NbAtOhIWRHo6/0x82prwBm5qO+vwb3Jjw50INVU5RKV7ddAWX4rMg09XB95M6w7/D46/ZRdTQ1ebvL3uMnoK1ib66N2BLULy4YahB2H0lCduCEyGRAN9O7MSiiIiIGqys/BJM+TkYl+KzYGqgi19f6cGiiJo0FkZPaapv+SQMB8PuIjOv+BGtSZvdTFHgw703AQBzB7tjoIetyImIiIiqlp5ThIk/BeFGigKWxjLsmNETPq5WYsciEhULo6fUyckCHVuYo6RMhW3BiWLHIZEoCkvx2q8hKClTYbCnLeYMchM7EhERUZVSsgvx/E9BuJ2eB3szA+x6zRcdmpuLHYtIdCyMnpJEIsH0Pi4AgM0X4jl1dxO1/3oqUrIL4WRpiG8mdoKODm9YJSKihif5fgEmrQtCQmYBnCwNsft1X7jZmogdi6hBYGFUB0Z4OaC5hSEy80vwx9VkseOQCIJiMwAAE7o6wdxQT+Q0RERED0vKKsCkdReRlFWIVlZG2PWaL5wsjcSORdRgsDCqA3pSHbzyoNfol7NxUKq0aqI/egRBEHDxThYAwLc1x2cTEVHDU95TdBHJ9wvhYm2MnTN94WBuKHYsogaFhVEdmdTdCWYGuojLyMfxW2lix6F6FJ2Wh6z8EhjqSdGxhYXYcYiIiCpJyynCCz8HIyW7vCjaMaMn7M0NxI5F1OCwMKojxvq6eOnBDHXrzsSKnIbqU8Uwum7OzSDT5a8UERE1HJl5xZjySzASswrQ0tKIRRFRDfgprg693MsZMqkOriZm40p8lthxqJ5UDKPryWlOiYioAckuKMGL6y8hJj0PDuYG2PaqD4siohqwMKpDtqYGGNelOQBg9ckYkdNQfVCpBFyMywTAwoiIiBqOS3FZGPn9OUTczYG1iT62verDiRaIHoGFUR17rX9r6EiAk1H3EJacLXYc0rBIeS6yC0phJJOiYwuuAUFEROIqKVPh8yORmLguCCnZhWhpaYTtM3zgasMpuYkehYVRHXOxNsaYTuW9Rt8H3hY5DWnaxTvlvUXdnS2hJ+WvExERiedmigKjV5/H2tOxEARgYjcnHH67L9ztTMWORtQo6IodQBvNHuSGvaEpOBGRjpspCq4mrcWC7nAYHRERiaukTIVVf9/Gj6diUaYSYGksw4pxXvBrby92NKJGhV9xa4CrjQme9XYEAHzHXiOtpVQJCH5QGHH9IiIiEsO1xPt4dtU5fP93DMpUAkZ6OeCvd/qxKCJ6Auwx0pDZg9pg3/VUHL+VhvBUBdo7stdI20TczUFOURlM9HXRwdFM7DhERNSE5BWX4atjUdgcFA9BAKyMZfhkdAeM7OggdjSiRos9RhriZmuCUR0f9BqdYK+RNqq4v6iHiyV0eX8RERHVk7/C5Rj6zWlsulBeFI3r0hzH5/VnUUT0lNhjpEFvDXbDwbBU/HUrDdcS76Nzy2ZiR6I6dDr6HgDAl/cXERFRPUi+X4CP9t/CiYg0AICTpSE+G+uFvm1sRE5GpB34NbcGudmaYnyXFgCAL45GQhAEkRNRXckrLkPwg4VdB7W1FTkNERFps1KlCj+djsXQb87gREQadHUkeGNAa/w1tz+LIqI6xB4jDXtnqDv2XU/FxTtZOB19DwM8+CFaG5yNvocSpQou1sZozbUhiIhIQ4LvZOL/9t1EdFoeAKCHsyWWj+3AKbiJNICFkYY5WhjiZd9W+PlsHL44GoV+bWygoyMROxY9pcDIdADAYE8WukREVPcy8oqx4nAk/riaDACwNJZh0XBPPNe1BSQSfo4g0gQWRvXgjQFu+O1SEiLu5uBAWCpGP1gAlhonpUrAyQeFEYfRERFRXVKpBOy4nIgvj0ZBUVgKiQSY3KMl3vfzgIWRTOx4RFqN9xjVg2bGMrzW3xUA8NVfUSguU4qciJ5GaFI2MvNLYGqgi+7OlmLHISIiLXErNQfj1lzAh3tuQlFYinYOZvhjVi98NtaLRRFRPWBhVE9e6eMCW1N9JGUVYuP5eLHj0FP4O7J8NqD+7jbQ4zTdRET0lApKyvDZ4QiMWnUOoUnZMNHXxZJn2mH/7N7owhltieoNP9XVEyOZLt739wQArPo7Bum5RSInoicVGFE+jG5IWzuRkxARUWN3KiodQ785g3Vn7kCpEjC8gz1OzOuPV/q4cI08onrG37h6NK5zc3i3MFevVk2NT/L9AkTKc6EjAQZ4cIpUIiJ6Mln5JXhnZygCNl5GSnYhmlsYYv3L3bDmxa6wNzcQOx5Rk8TCqB7p6EiwZFR7AMDukGTcTFGInIhq6+8Hky50a2XJ8d5ERPREDt+4i6HfnMaeaymQSIBXervgr3f6YTBHIhCJioVRPevaqhnGdHKEIAAfHwjnoq+NzIkHw+gGczY6IiKqpfv5JZiz4xre2HYVmfkl8LAzxZ+zemHJqHYw1udEwURiY2EkggXDPWGoJ8Xl+PvYF5oqdhx6TPdyi3E+JgMAMLQdv9UjIqLH93dkGoatPIMD11Mh1ZFgziA3HJjTB505uQJRg8HCSAQO5oaYPcgNALD80C0oCktFTkSP48D1VChVArydLOBqYyJ2HCIiagSKSpVYuu8mXtl0Bfdyi+Fma4I/Z/XCu8M8INPlxzCihoS/kSKZ0dcVrW2MkZFXwokYGom9oSkAyifRICIiepRIeQ5GrzqPzUEJAMrvJTo4pw+8nSzEDUZEVWJhJBKZrg6Wj/ECAGwNTkBoUra4gahGMel5CEtWQFdHgmc6Oogdh4iIGrjdV5IwetV5RKXlwtpEH5umdceSUe1goCcVOxoRVYOFkYh8W1thXOfmEATgwz03UKZUiR2JqrHnWjKA8kVdrUz0RU5DREQNVVGpEgt+D8N7v4ehuEyF/u42ODq3LwZ4cNIeooaOhZHIPhjZFmYGughPzcGmC/Fix6EqqFQC9l4rnyRjbBcOoyMioocJgoDAiDSMWX0eO68kQUcCzB/mjo0B3WHNL9SIGgUWRiKzNtHHohFtAQBf/RWFhMx8kRPRf12Kz0JKdiFM9XUxhGtMEBHRv6hUAg7fuIsR35/D9M1XECnPhZWxDL9O98HsQW2goyMROyIRPSaNFUbx8fGYPn06XFxcYGhoiNatW2Pp0qUoKSmp8bgBAwZAIpFU2l5//XVNxWwQJnV3gq+rFYpKVVj4xw2ubdTA7L1WPunCcC97jg0n0gIfffTRQ+8znp6eNR6ze/dueHp6wsDAAF5eXjh8+HA9paWGShAEHAuXY8T3Z/HGtquIuJsDY5kUr/V3xbF3+qG3m7XYEYmoljS2mlhkZCRUKhV++uknuLm54ebNm5gxYwby8/Px1Vdf1XjsjBkz8Mknn6gfGxkZaSpmgyCRSPD5eC/4rTyDoDuZ2HEpCS/4tBQ7FgEoKCnDoRt3AQBjO7cQOQ0R1ZX27dvjxIkT6se6utW/HV64cAGTJ0/GihUr8Mwzz2D79u0YM2YMrl69ig4dOtRHXGpgzkTfw1d/RSEsWQEAMNXXxbTezpjW2wXNjGUipyOiJ6Wxwsjf3x/+/v7qx66uroiKisKaNWseWRgZGRnB3t5eU9EapFZWxnjPzxPLDt7CZ4cjMMDDBo4WhmLHavJ+D0lGblEZWloawcfFUuw4RFRHdHV1H/t95rvvvoO/vz/ee+89AMCyZctw/PhxrFq1CmvXrtVkTGpgbiQr8MXRSJx7sNi3kUyKab2dMaOvKyyMWBARNXb1eo+RQqGApeWjP1xu27YN1tbW6NChAxYtWoSCgoJq2xYXFyMnJ6fS1lgF9HJGl5YWyCsuw6I/OaRObEqVgA3n4gAAr/R25jhxIi1y+/ZtODo6wtXVFVOmTEFiYmK1bYOCgjBkyJBK+/z8/BAUFFTtMdr03kRASnYh3tpxDaNWncO5mAzIpDp4pbcLzr4/EO/5ebIoItIS9VYYxcTE4IcffsBrr71WY7sXXngBW7duxcmTJ7Fo0SL8+uuvePHFF6ttv2LFCpibm6s3Jyenuo5eb6Q6Enz5XEfIdHVwOvoetl+q/o2aNO9ERBriMwtgZqCL57s13n9XRFSZj48PNm3ahKNHj2LNmjWIi4tD3759kZubW2V7uVwOO7vKE6/Y2dlBLpdXew1tem9qyvKLy/DVsSgM+uoU9l9PhUQCjO3cHIHv9seSUe24fAORlql1YbRw4cKHblr97xYZGVnpmJSUFPj7++P555/HjBkzajz/zJkz4efnBy8vL0yZMgVbtmzBnj17EBsbW2X7RYsWQaFQqLekpKTavqQGxc3WFO/7eQAAlh+MQHwGZ6kTyy9n7wAApvRsBWN9jY06JaJ6Nnz4cDz//PPo2LEj/Pz8cPjwYWRnZ2PXrl11dg1te29qagRBwJ5ryRj41SmsOhmD4jIVfFwscWB2H3w7sROcLLX73meipqrWn/beffddBAQE1NjG1dVV/d+pqakYOHAgevXqhXXr1tU6oI+PD4DyHqfWrVs/9Ly+vj709bXrG5tXervgREQaLt7Jwru7r2PXa76QchhXvQpNysbl+PvQk0oQ0MtZ7DhEpEEWFhZwd3dHTExMlc/b29sjLS2t0r60tLQa71HSxvempiI8VYGl+8JxJeE+AMDZygiLRrTFsHZ2kEj4XkykzWpdGNnY2MDGxuax2qakpGDgwIHo2rUrNm7cCB2d2o/cCw0NBQA4ODjU+tjGSkdHgq+e94b/yrMISbiPn87E4o0BbmLHalJ+ftBb9Kx3c9iZGYichog0KS8vD7GxsXjppZeqfN7X1xeBgYGYO3euet/x48fh6+tbTwmpPuQWleLrv6KxJSgeKqF8YoU5g9rglT7O0NflUg1ETYHG7jFKSUnBgAED0LJlS3z11Ve4d+8e5HJ5pTHZKSkp8PT0xKVLlwAAsbGxWLZsGUJCQhAfH4/9+/dj6tSp6NevHzp27KipqA1Si2ZGWDqqHQDguxO3cT+/5vWfqO4kZhbgyIMpul/t6yJyGiKqa/Pnz8fp06cRHx+PCxcuYOzYsZBKpZg8eTIAYOrUqVi0aJG6/dtvv42jR4/i66+/RmRkJD766CNcuXIFs2fPFuslUB0SBAEHw1Ix+OvT2HShvCh6pqMDAt/tj1kDWrMoImpCNHbjxPHjxxETE4OYmBi0aFF5/ZeK2dZKS0sRFRWlnnVOJpPhxIkTWLlyJfLz8+Hk5ITx48dj8eLFmorZoD3XtQU2XYhHeGoOfg9Jxox+ro8+iJ7a50cjoBKAfu42aOtgJnYcIqpjycnJmDx5MjIzM2FjY4M+ffrg4sWL6tEQiYmJlUY49OrVC9u3b8fixYvxwQcfoE2bNti7dy/XMNICyfcLsHjvTZyKugcAcLE2xrLRHdCnDRdnJWqKJIKWzQmdk5MDc3NzKBQKmJk1/g+1Oy4lYtGfN+BsZYS/3x3AKaM1LCg2E5N/vggdCXD47b7wtC//N6RUKlFaWipyOiLx6enpQSqt/ht0bfsbXFf4c2lYlCoBmy/E46u/olBQooRMqoM3BrbG6/1bw0CPPURE2qQ2f3851VYDN7qTIz47FIH4zAKcj81A3zaPd38X1Z5SJeDjA+EAgCk+reBpbwZBECCXy5GdnS1uOKIGxMLCAvb29rwRnRqlmPRczN8dhtCkbABAD2dLfDbOC262JuIGIyLRsTBq4IxkuhjXpTk2ByVg68UEFkYa9NvlRETKc2FuqId5Q90BQF0U2drawsjIiB8EqUkTBAEFBQVIT08H0LQmxaHGr0ypwrqzd7DyxG2UlKlgqq+LhSM8Mbl7S47GICIALIwahRd7tsLmoASciEjHXUUhHMwNxY6kdRQFpfjqWBQA4J0hbdDMWAalUqkuiqysrEROSNQwGBqW//1JT0+Hra1tjcPqiBqKmPRcvLvrOq4nKwAAAz1s8Nk4L76fElElGpuVjupOGztT+LhYQqkSsOMSFwmsa4Ig4KMD4bhfUIo2tiaY0rMVAKjvKTIy4kJ+RP9W8TvB++6ooVOpBPxy9g5GfH8O15MVMDXQxVfPe2NDQHcWRUT0EBZGjcSLDz6s/3YpEaVKlchptMuWoATsuZYCqY4En471gp608q8Fh88RVcbfCWoMku8XYPLPF7H8UARKylTo526D4+/0x3NdW/DfMBFViUPpGgm/9vawNtFHem4xjtyU41lvR7EjaYWQhCwsO3gLALBouCd6uFiKnIiIiJ7W3msp+L+9N5FbXAYjmRQfjmyLF3q0ZEFERDVij1EjIdPVwUsPeo1+OXsHWjbLuijSc4swa+tVlKkEPNPRAdP7cDFXIqLGTFFYird2XMPcnaHILS5Dl5YWOPJ2X0zxacWiiIgeiYVRI/Jiz5bQ19VBWLICl+KyxI7TqMkVRXh5w2Wk5xajja0JvhjfkW+aj2HTpk2wsLDQ+HXi4+MhkUgQGhqq8WuVlJTAzc0NFy5cqLNzZmRkwNbWFsnJyU90fGZmJmxtbREfH19nmR5HSUkJnJ2dceXKlXq9LlFduBKfhRHfncX+66mQ6kjwzhB37HrNF62sjMWORkSNBAujRsTKRB/PdW0BAPj57B2R0zRet1JzMGb1eUTczYG1iQw/vdQVxvraOao0KCgIUqkUI0eOrPWxzs7OWLlyZaV9EydORHR0dB2lKxcQEIAxY8ZU2ufk5IS7d++iQ4cOdXqtqqxduxYuLi7o1avXYx8jCAKWLFkCBwcHGBoaYsiQIbh9+7b6eWtra0ydOhVLly59okyffvopRo8eDWdnZ/W+xMREjBw5EkZGRrC1tcV7772HsrKyWp979erVcHZ2hoGBAXx8fHDp0iX1czKZDPPnz8eCBQueKDeRGJQqAd+duI0JPwUhJbsQLS2NsPt1X7w9pA10pfyYQ0SPj38xGpnpfVwgkQAnItIRey9P7DiNiiAI+CtcjufXXoA8pwhutibY80ZvuNpo76J+69evx5w5c3DmzBmkpqY+9fkMDQ1ha2tbB8lqJpVKYW9vD11dzRasgiBg1apVmD59eq2O+/LLL/H9999j7dq1CA4OhrGxMfz8/FBUVKRuM23aNGzbtg1ZWbXr3S0oKMD69esrZVIqlRg5ciRKSkpw4cIFbN68GZs2bcKSJUtqde6dO3di3rx5WLp0Ka5evQpvb2/4+fmp1yUCgClTpuDcuXMIDw+v1bmJ6psgCDgdfQ/PrjqHb09EQyUAYzs3x6G3+qBLy2ZixyOixkjQMgqFQgAgKBQKsaNozPRNl4VWCw4Ki/4MEzuKqJYfDBeeX3tB2HjujpCRW1RtO5VKJZyOShfG/3heaLXgoNBqwUFh8rogIbugpMbzFxYWCrdu3RIKCwsrnSu/uFSUTaVS1ernk5ubK5iYmAiRkZHCxIkThU8//fShNvv37xe6desm6OvrC1ZWVsKYMWMEQRCE/v37CwAqbYIgCBs3bhTMzc0FQRCEqKgoAYAQERFR6ZzffPON4OrqKgiCIJSVlQmvvPKK4OzsLBgYGAju7u7CypUr1W2XLl360HVOnjwpxMXFCQCEa9euqdueOnVK6N69uyCTyQR7e3thwYIFQmlpqfr5/v37C3PmzBHee+89oVmzZoKdnZ2wdOnSGn9Gly9fFnR0dIScnBz1vs2bNwvGxsZCdHS0et+sWbMEDw8PIT8/X1CpVIK9vb3wv//9T/18dna2oK+vL+zYsaPS+V1cXIRffvmlxgz/tXv3bsHGxqbSvsOHDws6OjqCXC5X71uzZo1gZmYmFBcXP/a5e/ToIbz55pvqx0qlUnB0dBRWrFhRqd3AgQOFxYsXV3ueqn43KjSFv8FPgj+XunU5LlOYsPaC+m96+yVHhT9CksSORUQNUG3+/mrn+CEtN7OfK05EpOGPkGS8O9QdVib6Ykeqd8F3MvHz2TgAwKW4LCw/FIHebtZwtzNBi2ZGsDHVR2p2IaLTchGWrECkPBdA+SQWL/u2wnt+npDp1r7DtLBUiXZLjtXpa3lctz7xg5Hs8X9ld+3aBU9PT3h4eODFF1/E3LlzsWjRIvW9VIcOHcLYsWPx4YcfYsuWLSgpKcHhw4cBAH/++Se8vb0xc+ZMzJgxo8rzu7u7o1u3bti2bRuWLVum3r9t2za88MILAACVSoUWLVpg9+7dsLKywoULFzBz5kw4ODhgwoQJmD9/PiIiIpCTk4ONGzcCACwtLR/q3UpJScGIESMQEBCALVu2IDIyEjNmzICBgQE++ugjdbvNmzdj3rx5CA4ORlBQEAICAtC7d28MHTq0ytdw9uxZuLu7w9TUVL1v6tSpOHjwIKZMmYILFy7g2LFj+OWXXxAUFAQjIyPcuXMHcrkcQ4YMUR9jbm4OHx8fBAUFYdKkSer9PXr0wNmzZ9W9P5s2bcK0adNqnDzl7Nmz6Nq1a6V9QUFB8PLygp2dnXqfn58fZs2ahfDwcHTu3Lna81UoKSlBSEgIFi1apN6no6ODIUOGICgoqFLbitxEDYlSVd7rv+7sHVxLzAZQ/jd9as9WeGOgGyyNZeIGJKJGj4VRI9TduRm8W5jjerICG8/HY76fh9iR6pUgCPjqrygAQE9XSxSUKBGWrMDp6Hs4HX2vymP0dXUwxacVXu/vClszg/qMK5r169fjxRdfBAD4+/tDoVDg9OnTGDBgAIDy+1gmTZqEjz/+WH2Mt7c3gPLiRCqVwtTUFPb29tVeY8qUKVi1apW6MIqOjkZISAi2bt0KANDT06t0fhcXFwQFBWHXrl2YMGECTExMYGhoiOLi4hqv8+OPP8LJyQmrVq2CRCKBp6cnUlNTsWDBAixZsgQ6OuVFbseOHdX39bRp0warVq1CYGBgtYVRQkICHB0fnvr+p59+QseOHfHWW2/hzz//xEcffaQuVuRyOQBUKlIqHlc8V8HR0RHXrl1TPzY3N4eHR82/r1VlksvlVV7v33keJSMjA0qlssrzREZGPpQ7ISHhsc5LpGlyRRH+uJqM3y4nIimrEAAgk+pgfNfmmDOoDRwtuFArEdUNFkaNkEQiwRsD3fDaryHYeD4O0/u4oFkT+qbsVPQ9XI6/D31dHayc2Bn25ga4nZaLczEZSL5fiOT7BUjPLYajuSHcbE3gZmsC39ZWsK6DnjVDPSlufeJXB6/iya79uKKionDp0iXs2bMHAKCrq4uJEydi/fr16sIoNDS02t6gxzVp0iTMnz8fFy9eRM+ePbFt2zZ06dIFnp6e6jarV6/Ghg0bkJiYiMLCQpSUlKBTp061uk5ERAR8fX0rzRzYu3dv5OXlITk5GS1btgRQXhj9m4ODQ6X7Z/6rsLAQBgYPF8rNmjXD+vXr4efnh169emHhwoW1ylvB0NAQBQUF6sdjx47F2LFjazymukz16b+5iepbfnEZTkSkYV9oKk5FpUP1oJPVwkgPL/VshZd8W8HWtGl8yUVE9YeFUSM1rJ0d2juaITw1B+vO3sECf89HH6QFBEHA1w96i6b6toK9efkbYxs7U7SxM63p0DohkUhqNZxNLOvXr0dZWVmlngdBEKCvr49Vq1bB3NwchoZP/y2rvb09Bg0ahO3bt6Nnz57Yvn07Zs2apX7+t99+w/z58/H111/D19cXpqam+N///ofg4OCnvnZV9PT0Kj2WSCRQqVTVtre2tsaNGzeqfO7MmTOQSqW4e/cu8vPz1cPtKnq20tLS4ODgoG6flpb2UMGXlZUFGxubWr0Ga2tr3L9/v9I+e3v7SrPHVVzv33ke57xSqVR93L/P899zPEluoqelKCjFqeh0HL0px9+R6Sgu++d3t4ezJSZ0d8JILwcYyh7/SyIiotrgrHSNlERSvkYDAGy+EI+MvGKRE9WPozfluJmSA2OZFLMGuIkdp0EqKyvDli1b8PXXXyM0NFS9Xb9+HY6OjtixYweA8t6VwMDAas8jk8mgVCofeb0pU6Zg586dCAoKwp07dyrdY3P+/Hn06tULb7zxBjp37gw3NzfExsbW+jpt27ZFUFBQpXtzzp8/D1NTU7Ro0eKRGavTuXNnREZGPnTPz4ULF/DFF1/gwIEDMDExwezZs9XPubi4wN7evtLPLicnB8HBwfD19a10nps3bz7W/T//zXTr1q1K+3x9fXHjxo1KvV/Hjx+HmZkZ2rVr91jnlclk6Nq1a6XcKpUKgYGBdZKbqLYEQUDE3Rz8dDoWE38KQpflx/H2b6E4clOO4jIVnK2MMHugGwLf7Y9dr/viua4tWBQRkUaxMGrEBre1RccW5igoUWLdGe1f10ipEvD18fI1dKb3deWNttU4ePAg7t+/j+nTp6NDhw6VtvHjx2P9+vUAgKVLl2LHjh1YunQpIiIicOPGDXzxxRfq8zg7O+PMmTNISUlBRkZGtdcbN24ccnNzMWvWLAwcOLBSL1WbNm1w5coVHDt2DNHR0fi///s/XL58udLxzs7OCAsLQ1RUFDIyMlBaWvrQNd544w0kJSVhzpw5iIyMxL59+7B06VLMmzdPfX/Rkxg4cCDy8vIqTU2dm5uLl156CW+99RaGDx+Obdu2YefOnfj9998BlH8pMXfuXCxfvhz79+/HjRs3MHXqVDg6OlZaj6mgoAAhISEYNmyYet+ePXsqDTOsip+fH8LDwyv1Gg0bNgzt2rXDSy+9hOvXr+PYsWNYvHgx3nzzTejrP/4Q0Xnz5uHnn3/G5s2bERERgVmzZiE/Px/Tpk2r1O7s2bOVchPVlfScIuy5lox3d12Hz2eBGP7dWaw4EonguCwoVQLc7Uwwa0BrHJzTByfnD8B8Pw+01uIlFYioYWFh1IhJJBK8M7S812hLUDzSc4secUTjtvViAmLS82BhpIdX+7qIHafBWr9+PYYMGQJzc/OHnhs/fjyuXLmCsLAwDBgwALt378b+/fvRqVMnDBo0qNJwrU8++QTx8fFo3bp1jcOqTE1NMWrUKFy/fh1Tpkyp9Nxrr72GcePGYeLEifDx8UFmZibeeOONSm1mzJgBDw8PdOvWDTY2Njh//vxD12jevDkOHz6MS5cuwdvbG6+//jqmT5+OxYsX1/bHU4mVlRXGjh2Lbdu2qfe9/fbbMDY2xmeffQYA8PLywmeffYbXXnsNKSkpAID3338fc+bMwcyZM9G9e3fk5eXh6NGjle4N2rdvH1q2bIm+ffuq9ykUCkRFRdWYycvLC126dMGuXbvU+6RSKQ4ePAipVApfX1+8+OKLmDp1Kj755BN1m/j4eEgkEpw6darac0+cOBFfffUVlixZgk6dOiE0NBRHjx6tNCFDUFAQFAoFnnvuuUf89IgeLb+4DCcj0/HJgVsY9u1p9PgsEO/svI4/riYjPbcYBno6GOBhg6Wj2uHs+wPx1zv9scDfEx2am1e6p5CIqD5IhJrmjW2EcnJyYG5uDoVCATMzM7HjaJwgCBi35gKuJWYjoJczPnq2vdiRNCI9twiDvzqN3OIyLBvTAS/1bKXxaxYVFSEuLg4uLi6i3wxPmhMWFoahQ4ciNjYWJiZ19810z5498dZbb6mnLq+NQ4cO4b333sPNmzcfu0fs5MmTGDduHO7cuYNmzZ58ccuJEyfC29sbH3zwQbVtavrdaGp/gx9XU/m5CIKAqLRcnIq6h9NR93AlIQulyn8+ZkgkQHtHM/R2s0ZfNxt0c24Gg1pMLENEVFu1+fvb8O8ipxpJJBLMH+aBKb8E49eLCXjBpyXc62ESgvq24nAkcovL0LGFOV7o0VLsOKRFOnbsiC+++AJxcXHw8vKqk3NmZGRg3LhxmDx58hMdP3LkSNy+fRspKSlwcnJ6rGMOHz6MDz744KmKopKSEnh5eeGdd9554nNQ01OqVOFSXBb+Cpfj+K00pCoqj15o0cwQfdtYo7ebNXq1tuYwaCJqsNhjpCVmbrmCv26lobebFbZO99GqIQhBsZmY/PNFSCTAvjd7o2MLi3q5LnuMiKrGHqPa07afi0ol4HJ8FvZdT8XhG3eRXfDPvYEGejrwdbXCAA9b9HO3gbOVkVa9JxFR48IeoyZo8ch2OBV9D+djMnH0phzDvRwefVAjUFKmwpJ9NwEAU3xa1ltRRERE5QVQQlYBbqYoECXPRUp2IVKyC3HnXn6l2VCtjGUY0tYOw9rbobebNYfHEVGjxMJIS7S0MsLr/Vzx/d8xWH4oAgM8bLViWtNVf9/G7fQ8WBnL8N6wprFWExGRWFQqAZHyXJyLuYdzMZm4lnAfucVlVbY1NdDF8A72GN2pOXq6WkGqw14hImrcWBhpkVkD3PDH1RSkZBdizelYzHswY11jFRSbiR9OxgAAPnq2PcyN9B5xBBER1VaZUoVL8Vk4ckOOo+Fy3MutvC6eTFcHbR3M0M7BDK2sjOBoYYjmFgZo72jOniEi0iosjLSIoUyKD0e2xRvbrmLNqRgMa2eHDs0fnrK5McjKL8HcndcgCMCEbi0wytvx0QcREdFji5TnYPeVZOwLTUFGXol6v5FMip6uVujtZo2erpZwtzOFnpSrexCR9mNhpGWGd7DHsHZ2+OtWGt767RoOzukDI1nj+t8sCALe230daTnFaG1jrLVTkBMR1bfCEiX2X0/BtuBEhCUr1PstjPTg184ew73s0au1NWS6LISIqOlpXJ+Y6ZEkEgm+GN8R15PP4M69fCw7eAsrxnUUO1at/HTmDgIj0yHT1cEPk7s0usKOiKihSckuxJYL8dh5JUk9g5yujgRD2trh+W4t0M/dhr1CRNTk8ROnFmpmLMO3Ezphyvpg7LiUhH5tbBrNLHV/hCTj8yORAIDFI9uinWPjn9aWiEgst1JzsO5MLA6E3YVSVb46R4tmhnipZys817UFrEz0RU5IRNRw8OshLdXLzRqv928NAFjwRxhup+U+9TkFQUCkPEf95lrXTtxKw/t/hAEApvdxwUs9W2nkOvTkNm3aBAsLC41fJz4+HhKJBKGhoRq/VklJCdzc3HDhwoU6PaezszOuXLnSYDI9rkmTJuHrr7+u9+tS3QpJyELAxksY8f1Z7A1NhVIloFdrK/w8tRtOvzcQr/VvzaKIiOg/WBhpsXlD3dG5pQVyisrw4vpgJGYWPPG5VCoBc3eGwn/lWUzdEIzcotJHH1QLl+Ky8Ob2q1CqBIzr3BwfjmjLBQHrQFBQEKRSKUaOHFnrY52dnbFy5cpK+yZOnIjo6Og6SlcuICAAY8aMqbTPyckJd+/eRYcOHer0WlVZu3YtXFxc0KtXr8c+5s8//8SwYcNgZWVVZQEnk8kwf/58LFiwoM4yZWVlYcqUKTAzM4OFhQWmT5+OvLy8Wp03PDwc48ePh7OzMyQSyUP/fwFg8eLF+PTTT6FQKB4+ATV4QbGZmLzuIsavCcKpqHvQkQDPdHTAgdl9sH1GTwxtZ8dptYmIqsHCSIvpSXWw4eXucLczQVpOMV745SLkiqJan0cQBHx0IBz7QlMBAOdjMjHhp4tIz6n9uaqyLzQFL60PRnGZCoM8bfHFcx2hwzfuOrF+/XrMmTMHZ86cQWpq6lOfz9DQELa2tnWQrGZSqRT29vbQ1dXsaF9BELBq1SpMnz69Vsfl5+ejT58++OKLL6ptM2XKFJw7dw7h4eF1kmnKlCkIDw/H8ePHcfDgQZw5cwYzZ86s1bkLCgrg6uqKzz//HPb29lW26dChA1q3bo2tW7fW6twkrktxWZi0LgiTf76IoDuZ0JNKMKm7E07OH4BVL3SBV4vGOUMpEVF9YmGk5ZoZy7B1ug+crYyQfL8QU365iOT7tes5+vZ4NLYEJUAiAd4Z4g5rExki7uZg7I8XnmqInlIlYMXhCLz9WyiKy1QY4GGD1S90adg3AAsCUJIvzibUbghjXl4edu7ciVmzZmHkyJHYtGnTQ20OHDiA7t27w8DAANbW1hg7diwAYMCAAUhISMA777wDiUSi7r3791C66OhoSCQSREZGVjrnt99+i9aty4dxKpVKTJ8+HS4uLjA0NISHhwe+++47dduPPvoImzdvxr59+9TXOXXqVJVD6U6fPo0ePXpAX18fDg4OWLhwIcrK/ll4csCAAXjrrbfw/vvvw9LSEvb29vjoo49q/BmFhIQgNja2Uo/ali1bYGJigtu3b6v3vfHGG/D09ERBQfnvzksvvYQlS5ZgyJAh1Z67WbNm6N27N3777bcaMzxOpoiICBw9ehS//PILfHx80KdPH/zwww/47bffalXwdu/eHf/73/8wadIk6OtXP4xq1KhRtc5N4riaeB8v/hKMCT8F4eKdLMikOnipZyucem8gPh/fEa2sjMWOSETUaHDyhSbA1swAW1/1wfNrgxB7Lx/DV57F0mfbY3yX5jUOVysqVeK7wNtYcyoWAPDJ6A54qWcrjO3cHFM3BCM+swAjfziH1/u3xhsDWtdqob/otFx8fCAc52MyAQCzBrTG/GEeDX+IR2kB8JlIayp9kArIHv9Dzq5du+Dp6QkPDw+8+OKLmDt3LhYtWqT+f37o0CGMHTsWH374IbZs2YKSkhIcPnwYQPlQMW9vb8ycORMzZsyo8vzu7u7o1q0btm3bhmXLlqn3b9u2DS+88AIAQKVSoUWLFti9ezesrKxw4cIFzJw5Ew4ODpgwYQLmz5+PiIgI5OTkYOPGjQAAS0vLhz7sp6SkYMSIEQgICMCWLVsQGRmJGTNmwMDAoFLxs3nzZsybNw/BwcEICgpCQEAAevfujaFDh1b5Gs6ePQt3d3eYmpqq902dOhUHDx7ElClTcOHCBRw7dgy//PILgoKCYGRk9Ng/fwDo0aMHzp49q3586tQpDBw4EHFxcXB2dn7sTEFBQbCwsEC3bt3U+4YMGQIdHR0EBwerC9q60qNHD3z66acoLi6usYAi8YSnKvDNX9EIjEwHAOhJJZjQzQlvDnSDo4WhyOmIiBonFkZNRItmRtj1mi/m7gxFSMJ9zN99HcdvyTF3iDs87U0rFUiCIOBYeBqWH7qF5PuFAIB3h7qrJ0NoaWWEP2b1wju7ruNM9D18H3gbe64lY4G/J4a0tauxQErKKsC3J6Kx51oKBAEw0NPB/57z5gKuGrB+/Xq8+OKLAAB/f///b+/ug5q60z2Af8NLAhQSpKBIQUVBtC5vuhahO6KViuvL6HS7Cuv1bayuVGxtq5XtnS1rZ7quterera46cxV0p7bbHWGdWpX1UtAqiC3iqmBpRQZ8i7aivCiIkOf+wfXcRggSIkkg389MZszJ75w8eTzkyZPfyTmora3F0aNHMWHCBADA+++/j6SkJKxdu1ZZJzIyEkBbc+Ls7AwvLy+Th1wBbYd3bdmyRWmMvvvuOxQXFyuHYbm6uhptPzg4GIWFhfjss88we/ZseHp6wt3dHffv3+/0ef76178iKCgIW7ZsgUqlwogRI3Dt2jWsWbMG7777Lpyc2mYZIyIikJ6eDgAIDQ3Fli1bkJuba7IxqqqqQkBA+31vx44diIiIwGuvvYasrCz84Q9/wJgxY0zGZ0pAQACqqqqU+x4eHggLC4Orq6vJdTqKSa/XtzuE0cXFBT4+PtDr9WbH9TgBAQFobm6GXq/H4ME8CYo9qfihAZuOfIcvzl4HADipgJfHBGLFC6EI8jGvcSciImNsjBxIkE9bc7TjWAU2H/kOOaU3kFN6AwE6N0wY0R/urs6orrmHyh/v4uLNth91D9S54T+njcT0COMPak97arB70VgcOq/He5+X4XJNI1L3lsDd1RkTR/jhFyF+8HJzgZurM1paDfim6jZOXrqFsut1yhFhU0b5Y/WUMAzz87R2KrrP1aNt5sZWz91F5eXlOHXqFLKzswG0fYieM2cOdu7cqTRGZ86cMTkb1FVJSUlYtWoVTp48iXHjxuHjjz/G6NGjMWLECGXM1q1bsWvXLlRXV6OxsRHNzc2Iiooy63kuXLiA2NhYowb++eefR0NDA65cuYJBgwYBaGuMfmrgwIG4efOmye02NjbCzc2t3fJ+/fph586dSExMRFxcHNLS0syK9yF3d3fl8DugbSbm0UMPuxqTNbm7t804/DT2vmLdunXIysrCt99+C3d3d8TFxWH9+vUICwszuU5mZiYWLVpktEyj0aCp6cn8zrIrrty+h//6n++x7/QVPDwx6IzIALyREIqhvek9lIjIjrExcjDOTiq8OiEEE4b3x6Yj5Th+8Udcq23C3qJqo3FqZycsHT8Ur04cZvICqyqVClPDB2L8cD9sz69AdslVXL3TiIPn9Dh4zvS32L8I8cXqxDBEBnk/yZdmHSqVWYez2crOnTvR0tJiNPMgItBoNNiyZQt0Op3y4dcS/v7+eOGFF7B3716MGzcOe/fuRUpKivL4p59+ilWrVmHjxo2IjY2Fl5cXNmzYgKKiIoufuyOPzsSoVCoYDAaT4319fXHu3LkOHzt27BicnZ1x/fp13L171+jQtq6qqamBn5+fWet0FJO/v3+7Bq+lpQU1NTWdzrR1V01NDQCYHXtvcPToUSxfvhxjx45FS0sL3nnnHUyePBllZWV46inTf9tarRbl5eXKfWueNfNyzT1M2ngUza1t+3LCyAF4a/JwjBzI67wRET1JbIwc1LMBWvz3grFoetCKwopb+Or7H+HsBAzy8UCQjweeDdCiv1fXvrX21LhgVWIY3po8HOev1uFw6XWUXqtDY3MrmloMMBgE4YE6xAT7YNzQpzFAa9tvw/u6lpYW7NmzBxs3bsTkyZONHps1axY++eQTLFu2DBEREcjNzW33TfhDarUara2tj32+uXPn4u2330ZycjIuXbqEpKQk5bETJ04gLi4Or776qrKsoqLC7OcZOXIk9u3bBxFRPpCeOHECXl5eCAwMfGyMpkRHR2Pbtm1G2wWAgoICrF+/Hp9//jnWrFmD1NRU7N692+ztnz9/HtHR0RbHFBsbizt37qC4uFg5pO/LL7+EwWBATEyM2XF1Je7AwED4+vo+8W3b2uHDh43uZ2Zmon///iguLsb48eNNrqdSqXqkCe2KIB8PxA57Gi0GA96aHIbRg/rZJA4ior6OjZGDc3N1xsQR/TFxhOWnYFapVAgP1PG0sDZ24MAB3L59G4sXL4ZOZ/x/8atf/Qo7d+7EsmXLkJ6ejkmTJmHYsGFISkpCS0sLDh48qFx7Z8iQITh27JhyBjNTH5JfeuklpKSkICUlBRMnTjSapQoNDcWePXuQk5OD4OBg/O1vf8PXX3+N4OBgZcyQIUOQk5OD8vJyPP300+1iBtrOCvfnP/8ZK1asQGpqKsrLy5Geno4333xT+X1Rd0ycOBENDQ0oLS1VrplUX1+PefPm4bXXXsMvf/lLBAYGYuzYsZgxYwZefvllAG0zKtXV1cpJIh7OJPj7+xt9eP7qq6+MTkxx6tQpzJ8/H7m5uXjmmWe6HNPIkSMxZcoULFmyBNu3b8eDBw+QmpqKpKSkDn8jZUpzczPKysqUf1+9ehVnzpyBp6cnQkJCjOJ+tKnuqx5er8nHx6fTcQ0NDRg8eDAMBgNGjx6NP/7xjxg1apTJ8ffv38f9+/eV+3V1dRbFue0/RpucvScioidE+pja2loBILW1tbYOhXq5xsZGKSsrk8bGRluHYpbp06fL1KlTO3ysqKhIAMi///1vERHZt2+fREVFiVqtFl9fX3nppZeUsYWFhRIRESEajUYevlVkZGSITqdrt93Zs2cLANm1a5fR8qamJlm4cKHodDrx9vaWlJQUSUtLk8jISGXMzZs35cUXXxRPT08BIHl5eVJZWSkApKSkRBmXn58vY8eOFbVaLf7+/rJmzRp58OCB8nh8fLy8/vrrRs8/c+ZMWbBgQaf5mj17tqSlpSn3Fy1aJOHh4dLU1KQs27hxo/j4+MiVK1eUPABod0tPT1fWKSgoEG9vb7l3756yLC8vTwBIZWWlWTGJiNy6dUuSk5PF09NTtFqtLFq0SOrr643GAJCMjAyT232Y10dv8fHxypjGxkbR6XRSWFhocjud/W30pvfg1tZWmTZtmjz//POdjisoKJDdu3dLSUmJ5Ofny/Tp00Wr1crly5dNrpOent5hrntDXoiI+hJz6pJKxMyLo9i5uro66HQ61NbWQqvl8dfUfU1NTaisrERwcLDNfwxPPefs2bN48cUXUVFRAU/PJ/cj9jlz5iAyMhLvvPOOVWKqrKzE8OHDUVZWhtDQULOf86Ft27YhOzsb//rXv0yO6exvoze9B6ekpODQoUM4fvy4WYdkPnjwACNHjkRycrLRjOBPdTRjFBQU1CvyQkTUl5hTl+z4SppERD0vIiIC69evR2Vl5RPbZnNzM8LDw/HGG29YLaaDBw9i6dKlFjVFQNsJLD766COLttEbpKam4sCBA8jLyzP7d2qurq6Ijo7GxYsXTY7RaDTQarVGNyIism+cMSIygTNGRB3rzTNGIoIVK1YgOzsb+fn53WokW1tbMWrUKEydOhWbNm3q0jr2nhcior7KnPdf/pKTiIgcxvLly7F3717s378fXl5eygVyf3oK+/nz5+OZZ57BunXrAADvvfcexo0bh5CQENy5cwcbNmxAVVUVXnnlFZu9DiIievLYGBERkcPYtm0bACgXOn4oIyMDCxcuBABUV1cbne3w9u3bWLJkCfR6Pfr164cxY8agoKAAzz77rLXCJiIiK2BjRPQYnV0glMgR9ea/ia4cPZ6fn290f/Pmzdi8eXMPRURERPaCjRGRCWq1Gk5OTrh27Rr8/PygVquterV7InsjImhubsYPP/wAJycnqNVqW4dERET0xLAxIjLByckJwcHBuH79unIhTyICPDw8MGjQIIsurktERGRv2BgRdUKtVmPQoEFoaWlBa2urrcMhsjlnZ2e4uLhw9pSIiPocNkZEj6FSqeDq6gpXV1dbh0JEREREPYTHQRARERERkcNjY0RERERERA6PjRERERERETm8Pvcbo4fXqKirq7NxJEREjufhe29XrhfkSFibiIhsw5y61Ocao/r6egBAUFCQjSMhInJc9fX10Ol0tg7DbrA2ERHZVlfqkkr62Nd6BoMB165dg5eXV7dOJ1tXV4egoCBcvnwZWq22ByLs25g/yzB/lmMOLWNp/kQE9fX1CAgI4HWOfoK1ybaYP8swf5Zh/ixjzbrU52aMnJycEBgYaPF2tFotd14LMH+WYf4sxxxaxpL8caaoPdYm+8D8WYb5swzzZxlr1CV+nUdERERERA6PjRERERERETk8NkaP0Gg0SE9Ph0ajsXUovRLzZxnmz3LMoWWYP/vE/xfLMH+WYf4sw/xZxpr563MnXyAiIiIiIjIXZ4yIiIiIiMjhsTEiIiIiIiKHx8aIiIiIiIgcHhsjIiIiIiJyeGyMiIiIiIjI4bExAvD+++8jLi4OHh4e8Pb27tI6IoJ3330XAwcOhLu7OxISEvD999/3bKB2qqamBnPnzoVWq4W3tzcWL16MhoaGTteZMGECVCqV0W3ZsmVWiti2tm7diiFDhsDNzQ0xMTE4depUp+P/8Y9/YMSIEXBzc0N4eDgOHjxopUjtkzn5y8zMbLefubm5WTFa+3Ls2DHMmDEDAQEBUKlU+Oc///nYdfLz8zF69GhoNBqEhIQgMzOzx+OkNqxNlmFtMg9rk2VYm7rPnmoTGyMAzc3N+PWvf42UlJQur/PBBx/gL3/5C7Zv346ioiI89dRTSExMRFNTUw9Gap/mzp2L0tJSHDlyBAcOHMCxY8ewdOnSx663ZMkSXL9+Xbl98MEHVojWtv7+97/jzTffRHp6Ok6fPo3IyEgkJibi5s2bHY4vKChAcnIyFi9ejJKSEsyaNQuzZs3C+fPnrRy5fTA3fwCg1WqN9rOqqiorRmxf7t69i8jISGzdurVL4ysrKzFt2jRMnDgRZ86cwcqVK/HKK68gJyenhyMlgLXJUqxNXcfaZBnWJsvYVW0SUmRkZIhOp3vsOIPBIP7+/rJhwwZl2Z07d0Sj0cgnn3zSgxHan7KyMgEgX3/9tbLs0KFDolKp5OrVqybXi4+Pl9dff90KEdqX5557TpYvX67cb21tlYCAAFm3bl2H42fPni3Tpk0zWhYTEyO//e1vezROe2Vu/rr6N+2IAEh2dnanY95++20ZNWqU0bI5c+ZIYmJiD0ZGj2JtMh9rk3lYmyzD2vTk2Lo2ccaoGyorK6HX65GQkKAs0+l0iImJQWFhoQ0js77CwkJ4e3vj5z//ubIsISEBTk5OKCoq6nTdjz/+GL6+vvjZz36G3/3ud7h3715Ph2tTzc3NKC4uNtpvnJyckJCQYHK/KSwsNBoPAImJiQ63nwHdyx8ANDQ0YPDgwQgKCsLMmTNRWlpqjXD7BO5/vQtr0/9jbeo61ibLsDZZX0/ufy4Wb8EB6fV6AMCAAQOMlg8YMEB5zFHo9Xr079/faJmLiwt8fHw6zcVvfvMbDB48GAEBATh79izWrFmD8vJyZGVl9XTINvPjjz+itbW1w/3m22+/7XAdvV7P/ez/dCd/YWFh2LVrFyIiIlBbW4sPP/wQcXFxKC0tRWBgoDXC7tVM7X91dXVobGyEu7u7jSKjjrA2/T/Wpq5jbbIMa5P19WRt6rMzRmlpae1+2PbozdQOSz2fv6VLlyIxMRHh4eGYO3cu9uzZg+zsbFRUVDzBV0GOLjY2FvPnz0dUVBTi4+ORlZUFPz8/7Nixw9ahkYNibbIMaxP1BaxN9qvPzhi99dZbWLhwYadjhg4d2q1t+/v7AwBu3LiBgQMHKstv3LiBqKiobm3T3nQ1f/7+/u1+XNjS0oKamholT10RExMDALh48SKGDRtmdry9ga+vL5ydnXHjxg2j5Tdu3DCZK39/f7PG92Xdyd+jXF1dER0djYsXL/ZEiH2Oqf1Pq9VytqibWJssw9r05LE2WYa1yfp6sjb12cbIz88Pfn5+PbLt4OBg+Pv7Izc3Vyk2dXV1KCoqMuvsQfasq/mLjY3FnTt3UFxcjDFjxgAAvvzySxgMBqWgdMWZM2cAwKiY9zVqtRpjxoxBbm4uZs2aBQAwGAzIzc1Fampqh+vExsYiNzcXK1euVJYdOXIEsbGxVojYvnQnf49qbW3FuXPnMHXq1B6MtO+IjY1tdwpeR93/nhTWJsuwNj15rE2WYW2yvh6tTRafvqEPqKqqkpKSElm7dq14enpKSUmJlJSUSH19vTImLCxMsrKylPt/+tOfxNvbW/bv3y9nz56VmTNnSnBwsDQ2NtriJdjUlClTJDo6WoqKiuT48eMSGhoqycnJyuNXrlyRsLAwKSoqEhGRixcvynvvvSfffPONVFZWyv79+2Xo0KEyfvx4W70Eq/n0009Fo9FIZmamlJWVydKlS8Xb21v0er2IiMybN0/S0tKU8SdOnBAXFxf58MMP5cKFC5Keni6urq5y7tw5W70EmzI3f2vXrpWcnBypqKiQ4uJiSUpKEjc3NyktLbXVS7Cp+vp65f0NgGzatElKSkqkqqpKRETS0tJk3rx5yvhLly6Jh4eHrF69Wi5cuCBbt24VZ2dnOXz4sK1egkNhbbIMa1PXsTZZhrXJMvZUm9gYiciCBQsEQLtbXl6eMgaAZGRkKPcNBoP8/ve/lwEDBohGo5FJkyZJeXm59YO3A7du3ZLk5GTx9PQUrVYrixYtMirclZWVRvmsrq6W8ePHi4+Pj2g0GgkJCZHVq1dLbW2tjV6BdX300UcyaNAgUavV8txzz8nJkyeVx+Lj42XBggVG4z/77DMZPny4qNVqGTVqlHzxxRdWjti+mJO/lStXKmMHDBggU6dOldOnT9sgavuQl5fX4Xvdw5wtWLBA4uPj260TFRUlarVahg4davQ+SD2LtckyrE3mYW2yDGtT99lTbVKJiFg+70RERERERNR79dmz0hEREREREXUVGyMiIiIiInJ4bIyIiIiIiMjhsTEiIiIiIiKHx8aIiIiIiIgcHhsjIiIiIiJyeGyMiIiIiIjI4bExIiIiIiIih8fGiIiIiIiIHB4bIyIiIiIicnhsjIiIiIiIyOH9LzwaADsAiOueAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coefs, masks, symbolic_functions = best_model\n",
    "print(f\"validation loss: {best_loss: 0.5f}\")\n",
    "\n",
    "fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(10, 5), dpi=100)\n",
    "\n",
    "x = torch.linspace(-1, 1, steps=100).unsqueeze(dim=1)\n",
    "bases = eval_basis_functions(x, grid, k=3)\n",
    "\n",
    "ax = axs[0]\n",
    "y_out_0 = torch.einsum('ijk, bij->bk', coefs[0][0:1].transpose(2, 1), bases)\n",
    "y_out_1 = torch.einsum('ijk, bij->bk', coefs[0][1:2].transpose(2, 1), bases)\n",
    "ax.plot(x.numpy(), y_out_0.detach().numpy(), label=\"Activation (x0): (0, 0)\")\n",
    "ax.plot(x.numpy(), y_out_1.detach().numpy(), label=\"Activation (x1): (0, 1)\")\n",
    "ax.legend()\n",
    "\n",
    "ax = axs[1]\n",
    "y_out_final = torch.einsum('ijk, bij->bk', coefs[1].transpose(2, 1), bases)\n",
    "ax.plot(x.numpy(), y_out_final.detach().numpy(), label=\"Activation (y): (1, 0)\")\n",
    "\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfef8395-c6b4-44aa-a973-5972f230ee03",
   "metadata": {},
   "source": [
    "**Note:** The curve for \\(x2\\) is zero everywhere because the coefficients for \\(x2\\) did not receive any gradients. This outcome is expected since we are masking all outputs related to \\(x2\\) with its symbolic function.\n",
    "\n",
    "**Observation:** We observe that the other activation functions are correctly learned to match their respective functional formulations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7c5b5d23-c588-4614-a3df-60e78471bda4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Loss')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(losses['val'][100:], label='wo_symbolic-val', linestyle='--', alpha=1.0, color='orange')\n",
    "plt.plot(losses_symb['val'][100:], label='w_symbolic-val', linestyle='--', alpha=1.0,  color='green')\n",
    "\n",
    "plt.plot(losses['train'][10:], label='wo_symbolic-train', linestyle='-', alpha=1.0, color='orange')\n",
    "plt.plot(losses_symb['train'][10:], label='w_symbolic-train', linestyle='-', alpha=1.0,  color='green')\n",
    "\n",
    "# plt.ylim(0,1)\n",
    "plt.legend()\n",
    "plt.title('Loss')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d48d7fe3-a3be-40f9-a761-f56cfa7e1faf",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "***Things to explore on your own***\n",
    "1. **Varying Grid Size**: Observe how the results change when the grid size is reduced.\n",
    "2. **Specific Activation Functions**: Analyze the impact of fixing the \\(0,0,0\\) activation to $\\sin(\\pi x)$\n",
    "3. **Exploring Quadratic Functions**: Explore the effects of setting \\(0,1,0\\) activation to $(x+0.5)^2$.\n",
    "\n",
    "***Observations***\n",
    "- **Impact of Incorrect Formulas**: If an activation is incorrectly fixed to a wrong formula, it can lead to worse outcomes, rather than compensating based on other activation functions. This is particularly problematic if the KAN structure lacks sufficient capacity.\n",
    "- **Noise and Symbolic Regression (SR)**: Fixing an output to a function in noisy conditions can cause other activation functions to overfit to the noise, casting doubt on the practicality of SR. Nonetheless, examining a few symbolic forms can provide valuable insights into the influence of certain variables."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d812d57-d314-4109-9675-cf57c138ebdc",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "We have explored how KANs can be used to infer symbolic formulas underlying datasets throughout this notebook.\n",
    "\n",
    "\n",
    "## Conclusion\n",
    "\n",
    "Inspired by the authors' original implementation and their accompanying arXiv paper, our goal was to gradually build a foundational understanding of KANs. While the code used in these notebooks may not exactly match the original, the concepts and techniques discussed should provide a solid basis for delving deeper into the original codebase. I hope that by following this series, you have gained a clear understanding of the basics of KANs and are now equipped to explore their application across various domains.\n"
   ]
  }
 ],
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