{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torchvision.transforms as transforms\n",
    "import torch.nn as nn\n",
    "import torchvision\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "import urllib\n",
    "import numpy as np\n",
    "import PIL\n",
    "import torch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#intialize the device\n",
    "device = torch.device(\"cuda:1\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This will show the noise when we train the model how accurately it models the noise as the image structure of pixel(32*32)\n",
    "def plot_noise_distribution(true_noise, predicted_noise):\n",
    "    plt.hist(true_noise.cpu().numpy().flatten(), density = True, alpha = 0.8, label = \"true noise\")\n",
    "    plt.hist(predicted_noise.cpu().numpy().flatten(), density = True, alpha = 0.8, label = \"predicted noise\")\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This will also show the distribution of the noise which like a gaussian and the model will try to fit to that Gaussian noise\n",
    "def plot_noise_prediction(true_noise, predicted_noise):\n",
    "    plt.figure(figsize=(10,10))\n",
    "    f, a = plt.subplots(1, 2, figsize = (5,5))\n",
    "    a[0].imshow(reverse_transform(true_noise))\n",
    "    a[0].set_title(f\"true noise\", fontsize = 10)\n",
    "    a[1].imshow(reverse_transform(predicted_noise))\n",
    "    a[1].set_title(f\"predicted noise\", fontsize = 10)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Forward Process:\n",
    "$$\n",
    "q(x_{t}|X_{t-1})=\\mathcal{N}(x_{t};\\sqrt{1-\\beta_{t}}x_{t-1},\\beta_{t}I)\n",
    "$$\n",
    "A little trick\n",
    "$$\n",
    "\\alpha_{t}=1-\\beta_{t}\n",
    "$$\n",
    "$$\n",
    "\\bar{\\alpha_{t}}=\\Pi^{t}_{s=1}a_{s}\n",
    "$$\n",
    "Reparameterization technique:\n",
    "$$\n",
    "\\mathcal{N}(\\mu,\\sigma^{2})=\\mu+\\sigma.\\epsilon, \\epsilon ->\\mathcal{N}(0,1)\n",
    "$$\n",
    "Rewrite the process\n",
    "$$\n",
    "q(x_{t}|x_{t-1})=\\mathcal{N}(x_{t};\\sqrt{1-\\beta_{t}}x_{t-1},\\beta_{t}I)\n",
    "$$\n",
    "$$\n",
    "=\\sqrt{1-\\beta_{t}}x_{t-1}+\\sqrt{\\beta_{t}}\\epsilon\n",
    "$$\n",
    "$$\n",
    "=\\sqrt{\\alpha_{t}}x_{t-1}+\\sqrt{1-\\alpha_{t}}\\epsilon\n",
    "$$\n",
    "$$\n",
    "=\\sqrt{\\alpha_{t}\\alpha_{t-1}}x_{t-2}+\\sqrt{1-\\alpha_{t}\\alpha_{t-1}}\\epsilon\n",
    "$$\n",
    "$$\n",
    "...\n",
    "$$\n",
    "$$\n",
    "=\\sqrt{\\alpha_{t}\\alpha_{t-1}...\\alpha_{1}\\alpha_{0}}x_{0}+\\sqrt{1-\\alpha_{t}\\alpha_{t-1}...\\alpha_{1}\\alpha_{0}}\\epsilon\n",
    "$$\n",
    "$$\n",
    "q(x_{t}|x_{t-1})=\\sqrt{\\bar{\\alpha_{t}}}x_{0}+\\sqrt{1-\\bar{\\alpha_{t}}}\\epsilon\n",
    "$$\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Backward:\n",
    "$$\n",
    "1: repeat\n",
    "$$\n",
    "$$\n",
    "2: x_{T} -> \\mathcal{N}(0,1)(noise)\n",
    "$$\n",
    "$$\n",
    "3: for\\hspace{0.5cm} (t=T,....,1) \\hspace{0.5cm} do\n",
    "$$\n",
    "$$\n",
    "4:z->\\mathcal{N}(0,1) \\hspace{0.5cm} if \\hspace{0.5cm} (t>1) \\hspace{0.5cm} else (z=0)\n",
    "$$\n",
    "$$\n",
    "x_{t-1}=\\frac{1}{\\sqrt{\\alpha_{t}}}\\left(x_{t}-\\frac{1-\\alpha_{t}}{\\sqrt{1-\\bar{\\alpha_{t}}}}\\epsilon_{\\theta}(x_{t},t)\\right)+\\sigma_{t}z\n",
    "$$\n",
    "$$\n",
    "end \\hspace{0.5cm} for\n",
    "$$\n",
    "$$\n",
    "return \\hspace{0.5cm} x_{0}\n",
    "$$\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The main algorithm where we code the forward addition of noise and reverse denoising\n",
    "#We will use the linear schedule following the DDPM paper with initial as 0.0001 and final as 0.02 but the time steps are different as 400 steps\n",
    "\n",
    "\n",
    "class DiffusionModel:\n",
    "    def __init__(self, initial_schedule=0.0001, final_schedule=0.02, timesteps = 400):\n",
    "        self.initial_schedule = initial_schedule\n",
    "        self.final_schedule = final_schedule\n",
    "        self.timesteps = timesteps \n",
    "        self.betas = torch.linspace(initial_schedule, final_schedule, timesteps)# divide the initial and final schedule into the number of time steps\n",
    "        self.alphas = 1 - self.betas # Alpha is defined as in the paper 1-beta\n",
    "        self.alphas_cumprod = torch.cumprod(self.alphas, axis=0) # Cummulative product of the alphas using pyTorch\n",
    "        \n",
    "    # Now we define the forward for adding the noise which has nothing to do with machine learning\n",
    "    # This will have two outpus the first is the image with added and the second is the noise added which is sent to the device    \n",
    "    def forward(self, x0, t, device):\n",
    "        noise = torch.randn_like(x0) # x0 is the size of the image, we make the noise of the same size\n",
    "        # For a given t we calculate the square root cummulative product\n",
    "        sqrt_alphas_cumprod_t = self.get_index_from_list(self.alphas_cumprod.sqrt(), t, x0.shape) \n",
    "        # For a given t we calculate the square root cummulative product\n",
    "        sqrt_one_minus_alphas_cumprod_t = self.get_index_from_list(torch.sqrt(1. - self.alphas_cumprod), t, x0.shape) \n",
    "        # According to the algorithm we have the mean with reparamaterization trick    \n",
    "        mean = sqrt_alphas_cumprod_t.to(device) * x0.to(device)\n",
    "        #similarly we have the variance\n",
    "        variance = sqrt_one_minus_alphas_cumprod_t.to(device) * noise.to(device)\n",
    "        \n",
    "        #The reparamertization trick gives the noise added image as mean+variance remember the noise in the algorithm is given as $\\epsilon$\n",
    "        return mean + variance, noise.to(device)\n",
    "    \n",
    "    @torch.no_grad()\n",
    "    #We start the backward process here the x will be the noisy image at time t and model is UNet(here)\n",
    "    def backward(self, x, t, model, **kwargs):\n",
    "        betas_t = self.get_index_from_list(self.betas, t, x.shape) #We find the beta as we will not be learning this\n",
    "        sqrt_one_minus_alphas_cumprod_t = self.get_index_from_list(torch.sqrt(1. - self.alphas_cumprod), t, x.shape) #calculate the same as before\n",
    "        sqrt_recip_alphas_t = self.get_index_from_list(torch.sqrt(1.0 / self.alphas), t, x.shape) # This is the factor in front as written as above\n",
    "        #Finally calculate the mean,the model will be UNet $\\epsilon_{\\theta}$\n",
    "        mean = sqrt_recip_alphas_t * (x - betas_t * model(x, t, **kwargs) / sqrt_one_minus_alphas_cumprod_t) \n",
    "        posterior_variance_t = betas_t #the variance remains as before\n",
    "\n",
    "        if t == 0:\n",
    "            return mean #when you reach t=0 return the mean (no noise any more)\n",
    "        else:\n",
    "            #the z in the algorithm z~N(0,1)\n",
    "            noise = torch.randn_like(x)\n",
    "            #$\\sigma$ which is the squareroot of posterior_variance_t  \n",
    "            variance = torch.sqrt(posterior_variance_t) * noise \n",
    "            return mean + variance #return the final t-1 time stamp image\n",
    "        #this will give you the value(say beta) with the image size at a particular time used above\n",
    "    @staticmethod\n",
    "    def get_index_from_list(values, t, x_shape):\n",
    "        batch_size = t.shape[0]\n",
    "        result = values.gather(-1, t.cpu())\n",
    "        return result.reshape(batch_size, *((1,) * (len(x_shape) - 1))).to(t.device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "image_shape = (32, 32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# Image to tensor with scaling to -1 to 1 to match the noise which is N(0,1)\n",
    "transform = transforms.Compose([\n",
    "    transforms.Resize(image_shape), # Resize the input image\n",
    "    transforms.ToTensor(), # Convert to torch tensor (scales data into [0,1])\n",
    "    transforms.Lambda(lambda t: (t * 2) - 1), # Scale data between [-1, 1] \n",
    "])\n",
    "\n",
    "# Getting back image from tensor to Image\n",
    "\n",
    "reverse_transform = transforms.Compose([\n",
    "    transforms.Lambda(lambda t: (t + 1) / 2), # Scale data between [0,1]\n",
    "    transforms.Lambda(lambda t: t.permute(1, 2, 0)),\n",
    "    transforms.Lambda(lambda t: t * 255.), # Scale data between [0.,255.]\n",
    "    transforms.Lambda(lambda t: t.cpu().numpy().astype(np.uint8)), # Convert into an uint8 numpy array\n",
    "    transforms.ToPILImage(), # Convert to PIL image\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Load the image\n",
    "#the image is in the same folder 23cs461/assignmet/arpan\n",
    "diffusion_image = PIL.Image.open('cat.jpg')\n",
    "diffusion_torch_image = transform(diffusion_image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "diffusion_model = DiffusionModel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x1000 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 10000x10000 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#lets see 5 images at some particular time\n",
    "image_no = 5\n",
    "batch_torch_image = torch.stack([diffusion_torch_image] * image_no)\n",
    "t = torch.linspace(0, diffusion_model.timesteps - 1, image_no).long()\n",
    "batch_noisy_image, _ = diffusion_model.forward(batch_torch_image, t, device)\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "f, a = plt.subplots(1, image_no, figsize = (100,100))\n",
    "\n",
    "for i, img in enumerate(batch_noisy_image):\n",
    "    a[i].imshow(reverse_transform(img))\n",
    "    a[i].set_title(f\"Iteration: {t[i].item()}\", fontsize = 100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "class SinusoidalPositionEmbeddings(nn.Module):\n",
    "    def __init__(self, dim):\n",
    "        super().__init__()\n",
    "        self.dim = dim\n",
    "\n",
    "    def forward(self, time):\n",
    "        # Get the device of the input 'time' tensor\n",
    "        device = time.device\n",
    "\n",
    "        # Calculate half of the specified dimension for sine and cosine embeddings\n",
    "        half_dim = self.dim // 2\n",
    "\n",
    "        # Compute a scalar value for the embeddings\n",
    "        embeddings = math.log(10000) / (half_dim - 1)\n",
    "\n",
    "        # Calculate a tensor of exponential values for frequency representation\n",
    "        embeddings = torch.exp(torch.arange(half_dim, device=device) * -embeddings)\n",
    "\n",
    "        # Generate embeddings by multiplying 'time' with the frequency values\n",
    "        embeddings = time[:, None] * embeddings[None, :]\n",
    "\n",
    "        # Combine sine and cosine embeddings and concatenate them along the last dimension\n",
    "        embeddings = torch.cat((embeddings.sin(), embeddings.cos()), dim=-1)\n",
    "\n",
    "        # Return the computed sinusoidal position embeddings\n",
    "        return embeddings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#These blocks are needed for the UNet architecture.\n",
    "\n",
    "class Block(nn.Module):\n",
    "    def __init__(self, channels_in, channels_out, time_embedding_dims, labels, num_filters=3, downsample=True):\n",
    "        super().__init__()\n",
    "\n",
    "        # Initialize the Block module with various parameters\n",
    "        self.time_embedding_dims = time_embedding_dims\n",
    "        self.time_embedding = SinusoidalPositionEmbeddings(time_embedding_dims)\n",
    "        self.labels = labels\n",
    "\n",
    "        # If labels are used, create a linear layer for label processing\n",
    "        if labels:\n",
    "            self.label_mlp = nn.Linear(1, channels_out)\n",
    "\n",
    "        self.downsample = downsample\n",
    "\n",
    "        # Create convolutional layers for downsample or upsample\n",
    "        if downsample:\n",
    "            self.conv1 = nn.Conv2d(channels_in, channels_out, num_filters, padding=1)\n",
    "            self.final = nn.Conv2d(channels_out, channels_out, 4, 2, 1)#kernal stride and padding\n",
    "        else:\n",
    "            self.conv1 = nn.Conv2d(2 * channels_in, channels_out, num_filters, padding=1)\n",
    "            self.final = nn.ConvTranspose2d(channels_out, channels_out, 4, 2, 1)\n",
    "\n",
    "        # Batch normalization layers for feature normalization\n",
    "        self.bnorm1 = nn.BatchNorm2d(channels_out)\n",
    "        self.bnorm2 = nn.BatchNorm2d(channels_out)\n",
    "\n",
    "        # Second convolutional layer\n",
    "        self.conv2 = nn.Conv2d(channels_out, channels_out, 3, padding=1)\n",
    "\n",
    "        # Linear layer for processing time embeddings\n",
    "        self.time_mlp = nn.Linear(time_embedding_dims, channels_out)\n",
    "\n",
    "        # Rectified Linear Unit (ReLU) activation function\n",
    "        self.relu = nn.ReLU()\n",
    "\n",
    "    def forward(self, x, t, **kwargs):\n",
    "        # Apply the first convolutional layer and batch normalization\n",
    "        out = self.bnorm1(self.relu(self.conv1(x)))\n",
    "\n",
    "        # Process time embeddings using a linear layer and add to the output\n",
    "        out_time = self.relu(self.time_mlp(self.time_embedding(t)))\n",
    "        out = out + out_time[(..., ) + (None, ) * 2]\n",
    "\n",
    "        # If labels are used, add processed labels to the output\n",
    "        if self.labels:\n",
    "            label = kwargs.get('labels')\n",
    "            out_label = self.relu(self.label_mlp(label))\n",
    "            out = out + out_label[(..., ) + (None, ) * 2]\n",
    "\n",
    "        # Apply the second convolutional layer and batch normalization\n",
    "        out = self.bnorm2(self.relu(self.conv2(out)))\n",
    "\n",
    "        # Apply the final convolutional layer\n",
    "        return self.final(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#The channel sizes are given in the sequence_channels\n",
    "\n",
    "class UNet(nn.Module):\n",
    "    def __init__(self, img_channels = 3, time_embedding_dims = 128, labels = False, sequence_channels = (64, 128, 256, 512, 1024)):\n",
    "        super().__init__()\n",
    "        self.time_embedding_dims = time_embedding_dims #here we use the time embeddings\n",
    "        sequence_channels_rev = reversed(sequence_channels)\n",
    "        \n",
    "        #The UP and DOWN sampling\n",
    "        self.downsampling = nn.ModuleList([Block(channels_in, channels_out, time_embedding_dims, labels) for channels_in, channels_out in zip(sequence_channels, sequence_channels[1:])])\n",
    "        self.upsampling = nn.ModuleList([Block(channels_in, channels_out, time_embedding_dims, labels,downsample=False) for channels_in, channels_out in zip(sequence_channels[::-1], sequence_channels[::-1][1:])])\n",
    "        self.conv1 = nn.Conv2d(img_channels, sequence_channels[0], 3, padding=1)\n",
    "        self.conv2 = nn.Conv2d(sequence_channels[0], img_channels, 1)\n",
    "\n",
    "    # The forward\n",
    "    def forward(self, x, t, **kwargs):\n",
    "        residuals = []\n",
    "        out = self.conv1(x)\n",
    "        for down_sample in self.downsampling:\n",
    "            out = down_sample(out, t, **kwargs)\n",
    "            residuals.append(out)\n",
    "        for up_sample, residual in zip(self.upsampling, reversed(residuals)):\n",
    "            out = up_sample(torch.cat((out, residual), dim=1), t, **kwargs)\n",
    "            \n",
    "        return self.conv2(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Information for training\n",
    "total_epochs = 2000\n",
    "print_frequency = 500\n",
    "learning_rate = 0.001\n",
    "batch_size = 128\n",
    "information = True\n",
    "\n",
    "unet = UNet(labels=False)\n",
    "unet.to(device)\n",
    "optimizer = torch.optim.Adam(unet.parameters(), lr=learning_rate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 0 | Train Loss 1.0317939519882202\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x1000 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 500 | Train Loss 0.011262591928243637\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x1000 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1000 | Train Loss 0.009885832667350769\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x1000 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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dq5qaGte+mJgYt3O++OILrV27Vh06dHBt8fHxcjgcOnDggHbt2qV27dpp2LBhrnP69eunTp061VnHzp07NWTIEFdYaYgvvvhCFRUVuvTSS91qOXDggPbv3y9J2rVrl2JjY93Oi4uLa1D/gwYNcv185tU2Z2aJdu3apWuvvdat/bXXXqtdu3bV2ldKSop27typvn376sEHH9R7773n0TguBmZYAACtSvv27d0+V1RU6L777tODDz54VtvLL79c3333nce/w9/f3+NzKioqFBYWpry8vLOO1ReOGuqSSy5x/Xwm1Dkcjkb1NXToUB04cEDvvvuuPvjgA911112yWq3asGHDRR9HXQgsAIAWo6CgwO3zp59+qj59+sjb27vOc4YOHapvv/3W7ZLNb/Xr108///yztm3b5roktGfPHpWWltbZ56BBg/Tss8/qxx9/rHWWxcfHx23W50wddrtd7dq1c1sP8lv9+/dXQUGBkpKS3MZ4vvr376+PP/5YycnJrn0ff/yxBgwYUOc5gYGBSkxMVGJiou644w4lJCToxx9/bNA4LgYCC9BWnOMZG0tKK5qoEKDxCgsLZbPZdN9992n79u1atmyZFi9eXO85Dz/8sK6++mpNmTJF9957r9q3b69vv/1W77//vpYvX66+ffsqISFB9913n1auXKl27dpp+vTp9c6ijB8/Xo899pjGjh2rzMxMhYWFaceOHQoPD1dcXJwiIyN14MAB7dy5U5dddpk6duwoq9WquLg4jR07VosWLdIVV1yho0eP6p133tGtt96qmJgYTZs2TSkpKYqJidG1116rl156Sd9884169ux5Xt/bQw89pLvuuktDhgyR1WrV22+/rTfeeEMffPBBre2XLFmisLAwDRkyRF5eXnr99dcVGhqqTp06NWgcFwNrWAAALUZSUpL+8Y9/aMSIEXrggQc0bdq0cy7yHDRokDZv3qzvvvtO1113nYYMGaL09HSFh4e72jz33HMKDw/XqFGjdNttt2nSpEnq1q1bnX36+PjovffeU7du3fSHP/xBAwcO1MKFC10zPbfffrsSEhJ0/fXXq2vXrnrllVdksVi0adMm/e53v1NqaqquuOIKjRs3Tj/88IPrBcKJiYmaM2eOZs2apWHDhumHH37Q5MmTz/t7Gzt2rJYuXaqsrCxdeeWVWr16tZ577jmNHj261vYdO3bUokWLFBMTo+HDh+vgwYPatGmTvLy8GjSOi4GXHwJtxTlmWPYWt6wZFl5+2Dgt+eWHo0ePVnR0tNvj8tEy8PJDAADQJhBYAACA8Vh0CwBoEWq7jRZtBzMsAADAeAQWAABgPAILALRBreAGUbQgF+LfG4EFANqQM49vP3XqVDNXgrbkzL+3374+wFMsugWANsTb21udOnVyvRQvICDA7WWCwIXkdDp16tQpFRcXq1OnTvW+QuFcCCwA0MaEhoZK+vVNvsDF1qlTJ9e/u8YisABAG2OxWBQWFqZu3brpp59+au5y0Mpdcskl5zWzcgaBBUCLZOKrBGzLttR57O2pI5uwkobx9va+IH9IgKbAolsAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4zUqsKxYsUKRkZHy8/NTbGystm7dWmfbN954QzExMerUqZPat2+v6OhovfDCC25tnE6n0tPTFRYWJn9/f1mtVu3du7cxpQEAgFbI48Cyfv162Ww2ZWRkaPv27Ro8eLDi4+NVXFxca/suXbro0UcfVX5+vr788kulpqYqNTVVf//7311tFi1apKeeekqrVq1SQUGB2rdvr/j4eJ0+fbrxIwMAAK2Gxel0Oj05ITY2VsOHD9fy5cslSQ6HQxEREZo6dapmz57doD6GDh2qm2++WfPnz5fT6VR4eLhmzJihmTNnSpLKysoUEhKitWvXaty4cefsr7y8XEFBQSorK1NgYKAnwwHajtWj6j28t7iiiQppvWydltZ57O2pI5uwEqBl8OTvt0czLNXV1dq2bZusVuuvHXh5yWq1Kj8//5znO51O5ebmas+ePfrd734nSTpw4IDsdrtbn0FBQYqNjW1QnwAAoPVr50nj48ePq6amRiEhIW77Q0JCtHv37jrPKysrU/fu3VVVVSVvb289/fTT+v3vfy9Jstvtrj7+uc8zx/5ZVVWVqqqqXJ/Ly8s9GQYAAGhhPAosjdWxY0ft3LlTFRUVys3Nlc1mU8+ePTV69OhG9ZeZmal58+Zd2CIBAICxPLokFBwcLG9vbxUVFbntLyoqUmhoaN2/xMtLvXv3VnR0tGbMmKE77rhDmZmZkuQ6z5M+09LSVFZW5toOHTrkyTAAAEAL41Fg8fHx0bBhw5Sbm+va53A4lJubq7i4uAb343A4XJd0oqKiFBoa6tZneXm5CgoK6uzT19dXgYGBbhsAAGi9PL4kZLPZlJycrJiYGI0YMULZ2dmqrKxUamqqJCkpKUndu3d3zaBkZmYqJiZGvXr1UlVVlTZt2qQXXnhBK1eulCRZLBZNnz5dCxYsUJ8+fRQVFaU5c+YoPDxcY8eOvXAjBQAALZbHgSUxMVElJSVKT0+X3W5XdHS0cnJyXItmCwsL5eX168RNZWWl7r//fh0+fFj+/v7q16+fXnzxRSUmJrrazJo1S5WVlZo0aZJKS0s1cuRI5eTkyM/P7wIMEQAAtHQeP4fFRDyHBWgAnsNy0fEcFsAzF+05LAAAAM2BwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGI7AAAADjEVgAAIDxCCwAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgvEYFlhUrVigyMlJ+fn6KjY3V1q1b62z7zDPP6LrrrlPnzp3VuXNnWa3Ws9qnpKTIYrG4bQkJCY0pDQAAtEIeB5b169fLZrMpIyND27dv1+DBgxUfH6/i4uJa2+fl5Wn8+PH68MMPlZ+fr4iICI0ZM0ZHjhxxa5eQkKBjx465tldeeaVxIwIAAK2Ox4FlyZIlmjhxolJTUzVgwACtWrVKAQEBWrNmTa3tX3rpJd1///2Kjo5Wv3799Oyzz8rhcCg3N9etna+vr0JDQ11b586dGzciAADQ6ngUWKqrq7Vt2zZZrdZfO/DyktVqVX5+foP6OHXqlH766Sd16dLFbX9eXp66deumvn37avLkyTpx4kSdfVRVVam8vNxtAwAArZdHgeX48eOqqalRSEiI2/6QkBDZ7fYG9fHwww8rPDzcLfQkJCTo+eefV25urh5//HFt3rxZN910k2pqamrtIzMzU0FBQa4tIiLCk2EAAIAWpl1T/rKFCxfq1VdfVV5envz8/Fz7x40b5/p54MCBGjRokHr16qW8vDzdeOONZ/WTlpYmm83m+lxeXk5oAQCgFfNohiU4OFje3t4qKipy219UVKTQ0NB6z83KytLChQv13nvvadCgQfW27dmzp4KDg7Vv375aj/v6+iowMNBtAwAArZdHgcXHx0fDhg1zWzB7ZgFtXFxcnectWrRI8+fPV05OjmJiYs75ew4fPqwTJ04oLCzMk/IAAEAr5fFdQjabTc8884zWrVunXbt2afLkyaqsrFRqaqokKSkpSWlpaa72jz/+uObMmaM1a9YoMjJSdrtddrtdFRUVkqSKigo99NBD+vTTT3Xw4EHl5ubqj3/8o3r37q34+PgLNEwAANCSebyGJTExUSUlJUpPT5fdbld0dLRycnJcC3ELCwvl5fVrDlq5cqWqq6t1xx13uPWTkZGhuXPnytvbW19++aXWrVun0tJShYeHa8yYMZo/f758fX3Pc3gAAKA1sDidTmdzF3G+ysvLFRQUpLKyMtazAHVZParew3uLK5qokNbL1mlpncfenjqyCSsBWgZP/n7zLiEAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGI7AAAADjEVgAAIDxCCwAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4zUqsKxYsUKRkZHy8/NTbGystm7dWmfbZ555Rtddd506d+6szp07y2q1ntXe6XQqPT1dYWFh8vf3l9Vq1d69extTGgAAaIU8Dizr16+XzWZTRkaGtm/frsGDBys+Pl7FxcW1ts/Ly9P48eP14YcfKj8/XxERERozZoyOHDniarNo0SI99dRTWrVqlQoKCtS+fXvFx8fr9OnTjR8ZAABoNSxOp9PpyQmxsbEaPny4li9fLklyOByKiIjQ1KlTNXv27HOeX1NTo86dO2v58uVKSkqS0+lUeHi4ZsyYoZkzZ0qSysrKFBISorVr12rcuHHn7LO8vFxBQUEqKytTYGCgJ8MB2o7Vo+o9vLe4ookKab1snZbWeeztqSObsBKgZfDk77dHMyzV1dXatm2brFbrrx14eclqtSo/P79BfZw6dUo//fSTunTpIkk6cOCA7Ha7W59BQUGKjY2ts8+qqiqVl5e7bQAAoPXyKLAcP35cNTU1CgkJcdsfEhIiu93eoD4efvhhhYeHuwLKmfM86TMzM1NBQUGuLSIiwpNhAACAFqZJ7xJauHChXn31Vb355pvy8/NrdD9paWkqKytzbYcOHbqAVQIAANO086RxcHCwvL29VVRU5La/qKhIoaGh9Z6blZWlhQsX6oMPPtCgQYNc+8+cV1RUpLCwMLc+o6Oja+3L19dXvr6+npQOAABaMI9mWHx8fDRs2DDl5ua69jkcDuXm5iouLq7O8xYtWqT58+crJydHMTExbseioqIUGhrq1md5ebkKCgrq7RMAALQdHs2wSJLNZlNycrJiYmI0YsQIZWdnq7KyUqmpqZKkpKQkde/eXZmZmZKkxx9/XOnp6Xr55ZcVGRnpWpfSoUMHdejQQRaLRdOnT9eCBQvUp08fRUVFac6cOQoPD9fYsWMv3EgBAECL5XFgSUxMVElJidLT02W32xUdHa2cnBzXotnCwkJ5ef06cbNy5UpVV1frjjvucOsnIyNDc+fOlSTNmjVLlZWVmjRpkkpLSzVy5Ejl5OSc1zoXAADQenj8HBYT8RwWoAF4DstFx3NYAM9ctOewAAAANAcCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGI7AAAADjEVgAAIDxCCwAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACM1665CwBaq1uWbWnuEtwsKa1o7hIAoNGYYQEAAMZrVGBZsWKFIiMj5efnp9jYWG3durXOtt98841uv/12RUZGymKxKDs7+6w2c+fOlcVicdv69evXmNIAAEAr5HFgWb9+vWw2mzIyMrR9+3YNHjxY8fHxKi4urrX9qVOn1LNnTy1cuFChoaF19nvllVfq2LFjrm3LFrOm0wEAQPPxOLAsWbJEEydOVGpqqgYMGKBVq1YpICBAa9asqbX98OHD9cQTT2jcuHHy9fWts9927dopNDTUtQUHB3taGgAAaKU8CizV1dXatm2brFbrrx14eclqtSo/P/+8Ctm7d6/Cw8PVs2dP3X333SosLKyzbVVVlcrLy902AADQenkUWI4fP66amhqFhIS47Q8JCZHdbm90EbGxsVq7dq1ycnK0cuVKHThwQNddd51OnjxZa/vMzEwFBQW5toiIiEb/bgAAYD4j7hK66aabdOedd2rQoEGKj4/Xpk2bVFpaqtdee63W9mlpaSorK3Nthw4dauKKAQBAU/LoOSzBwcHy9vZWUVGR2/6ioqJ6F9R6qlOnTrriiiu0b9++Wo/7+vrWux4GAAC0Lh7NsPj4+GjYsGHKzc117XM4HMrNzVVcXNwFK6qiokL79+9XWFjYBesTAAC0XB4/6dZmsyk5OVkxMTEaMWKEsrOzVVlZqdTUVElSUlKSunfvrszMTEm/LNT99ttvXT8fOXJEO3fuVIcOHdS7d29J0syZM3XLLbeoR48eOnr0qDIyMuTt7a3x48dfqHECAIAWzOPAkpiYqJKSEqWnp8tutys6Olo5OTmuhbiFhYXy8vp14ubo0aMaMmSI63NWVpaysrI0atQo5eXlSZIOHz6s8ePH68SJE+ratatGjhypTz/9VF27dj3P4QEAgNagUe8SmjJliqZMmVLrsTMh5IzIyEg5nc56+3v11VcbUwYAAGgjjLhLCAAAoD4EFgAAYDwCCwAAMF6j1rAAAM62pHRa3QdXd2i6Qjxx3+bmrgBoEGZYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGI7AAAADjEVgAAIDxCCwAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOO1a+4CgBZr9ah6Dy8prWiiQgCg9WOGBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHg+OA4AmsLfYzAcJ2pZtqXX/21NHNnElQP2YYQEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjNeowLJixQpFRkbKz89PsbGx2rp1a51tv/nmG91+++2KjIyUxWJRdnb2efcJAADaFo8Dy/r162Wz2ZSRkaHt27dr8ODBio+PV3Fxca3tT506pZ49e2rhwoUKDQ29IH0CAIC2xePAsmTJEk2cOFGpqakaMGCAVq1apYCAAK1Zs6bW9sOHD9cTTzyhcePGydfX94L0CQAA2haPAkt1dbW2bdsmq9X6awdeXrJarcrPz29UAY3ps6qqSuXl5W4bAABovTwKLMePH1dNTY1CQkLc9oeEhMhutzeqgMb0mZmZqaCgINcWERHRqN8NAABahhZ5l1BaWprKyspc26FDh5q7JAAAcBG186RxcHCwvL29VVRU5La/qKiozgW1F6NPX1/fOtfDAACA1sejGRYfHx8NGzZMubm5rn0Oh0O5ubmKi4trVAEXo08AANC6eDTDIkk2m03JycmKiYnRiBEjlJ2drcrKSqWmpkqSkpKS1L17d2VmZkr6ZVHtt99+6/r5yJEj2rlzpzp06KDevXs3qE8AANC2eRxYEhMTVVJSovT0dNntdkVHRysnJ8e1aLawsFBeXr9O3Bw9elRDhgxxfc7KylJWVpZGjRqlvLy8BvUJAADaNovT6XQ2dxHnq7y8XEFBQSorK1NgYGBzl4O2YvWoeg/vLa5ookKAxrN1Wlrr/renjmziStAWefL3u0XeJQQAANoWAgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGI7AAAADjEVgAAIDxCCwAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4zUqsKxYsUKRkZHy8/NTbGystm7dWm/7119/Xf369ZOfn58GDhyoTZs2uR1PSUmRxWJx2xISEhpTGgAAaIU8Dizr16+XzWZTRkaGtm/frsGDBys+Pl7FxcW1tv/kk080fvx4TZgwQTt27NDYsWM1duxYff31127tEhISdOzYMdf2yiuvNG5EAACg1fE4sCxZskQTJ05UamqqBgwYoFWrVikgIEBr1qyptf3SpUuVkJCghx56SP3799f8+fM1dOhQLV++3K2dr6+vQkNDXVvnzp0bNyIAANDqeBRYqqurtW3bNlmt1l878PKS1WpVfn5+refk5+e7tZek+Pj4s9rn5eWpW7du6tu3ryZPnqwTJ07UWUdVVZXKy8vdNgAA0Hp5FFiOHz+umpoahYSEuO0PCQmR3W6v9Ry73X7O9gkJCXr++eeVm5urxx9/XJs3b9ZNN92kmpqaWvvMzMxUUFCQa4uIiPBkGAAAoIVp19wFSNK4ceNcPw8cOFCDBg1Sr169lJeXpxtvvPGs9mlpabLZbK7P5eXlhBYAAFoxj2ZYgoOD5e3traKiIrf9RUVFCg0NrfWc0NBQj9pLUs+ePRUcHKx9+/bVetzX11eBgYFuGwAAaL08Ciw+Pj4aNmyYcnNzXfscDodyc3MVFxdX6zlxcXFu7SXp/fffr7O9JB0+fFgnTpxQWFiYJ+UBAIBWyuO7hGw2m5555hmtW7dOu3bt0uTJk1VZWanU1FRJUlJSktLS0lztp02bppycHC1evFi7d+/W3Llz9fnnn2vKlCmSpIqKCj300EP69NNPdfDgQeXm5uqPf/yjevfurfj4+As0TAAA0JJ5vIYlMTFRJSUlSk9Pl91uV3R0tHJyclwLawsLC+Xl9WsOuuaaa/Tyyy/rT3/6kx555BH16dNHGzdu1FVXXSVJ8vb21pdffql169aptLRU4eHhGjNmjObPny9fX98LNEwAANCSWZxOp7O5izhf5eXlCgoKUllZGetZ0HRWj6r38N7iiiYqBGg8W6elte5/e+rIJq4EbZEnf795lxAAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgvHbNXQDQULcs29LcJbhZUlrR3CUAQJvBDAsAADAegQUAABiPwAIAAIxHYAEAAMZj0S0AtGFLSqfVfmB1h6YtpKHu29zcFaCZMMMCAACMR2ABAADGI7AAAADjsYYFZlg96pxNeFAbALRdzLAAAADjMcMCADjL3mIzZzRt9byi4+2pI5uwEjQ1ZlgAAIDxCCwAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHiNCiwrVqxQZGSk/Pz8FBsbq61bt9bb/vXXX1e/fv3k5+engQMHatOmTW7HnU6n0tPTFRYWJn9/f1mtVu3du7cxpQEAgFbI48Cyfv162Ww2ZWRkaPv27Ro8eLDi4+NVXFxca/tPPvlE48eP14QJE7Rjxw6NHTtWY8eO1ddff+1qs2jRIj311FNatWqVCgoK1L59e8XHx+v06dONHxkAAGg1LE6n0+nJCbGxsRo+fLiWL18uSXI4HIqIiNDUqVM1e/bss9onJiaqsrJSf/vb31z7rr76akVHR2vVqlVyOp0KDw/XjBkzNHPmTElSWVmZQkJCtHbtWo0bN+6cNZWXlysoKEhlZWUKDAz0ZDgwxepR52xi6svYADQdW6eldR7j5Yctjyd/vz16W3N1dbW2bdumtLQ01z4vLy9ZrVbl5+fXek5+fr5sNpvbvvj4eG3cuFGSdODAAdntdlmtVtfxoKAgxcbGKj8/v9bAUlVVpaqqKtfnsrIySb8MHP/fmpvqPby/pLKJCgGAC+fP9il1HtvxaBMW4oG0oMdr3f/av8c1cSXmOfN3uyFzJx4FluPHj6umpkYhISFu+0NCQrR79+5az7Hb7bW2t9vtruNn9tXV5p9lZmZq3rx5Z+2PiIho2EAAAGgyCbXuDXq4icsw2MmTJxUUFFRvG48CiynS0tLcZm0cDod+/PFHXXrppbJYLM1YmbnKy8sVERGhQ4cOcdnsAuO7vbj4fi8uvt+Lh+/23JxOp06ePKnw8PBztvUosAQHB8vb21tFRUVu+4uKihQaGlrrOaGhofW2P/OfRUVFCgsLc2sTHR1da5++vr7y9fV129epUydPhtJmBQYG8l+ci4Tv9uLi+724+H4vHr7b+p1rZuUMj+4S8vHx0bBhw5Sbm+va53A4lJubq7i42q/FxcXFubWXpPfff9/VPioqSqGhoW5tysvLVVBQUGefAACgbfH4kpDNZlNycrJiYmI0YsQIZWdnq7KyUqmpqZKkpKQkde/eXZmZmZKkadOmadSoUVq8eLFuvvlmvfrqq/r888/1l7/8RZJksVg0ffp0LViwQH369FFUVJTmzJmj8PBwjR079sKNFAAAtFgeB5bExESVlJQoPT1ddrtd0dHRysnJcS2aLSwslJfXrxM311xzjV5++WX96U9/0iOPPKI+ffpo48aNuuqqq1xtZs2apcrKSk2aNEmlpaUaOXKkcnJy5OfndwGGCOmXy2gZGRlnXUrD+eO7vbj4fi8uvt+Lh+/2wvL4OSwAAABNjXcJAQAA4xFYAACA8QgsAADAeAQWAABgPAJLG1ZVVaXo6GhZLBbt3LmzuctpFQ4ePKgJEyYoKipK/v7+6tWrlzIyMlRdXd3cpbVIK1asUGRkpPz8/BQbG6utW7c2d0mtQmZmpoYPH66OHTuqW7duGjt2rPbs2dPcZbVaCxcudD3CA41HYGnDZs2a1aDHIaPhdu/eLYfDodWrV+ubb77Rk08+qVWrVumRRx5p7tJanPXr18tmsykjI0Pbt2/X4MGDFR8fr+Li4uYurcXbvHmzHnjgAX366ad6//339dNPP2nMmDGqrOSlqBfaZ599ptWrV2vQoEHNXUqLx23NbdS7774rm82m//7v/9aVV16pHTt21PkqBJyfJ554QitXrtT333/f3KW0KLGxsRo+fLiWL18u6ZenakdERGjq1KmaPXt2M1fXupSUlKhbt27avHmzfve73zV3Oa1GRUWFhg4dqqeffloLFixQdHS0srOzm7usFosZljaoqKhIEydO1AsvvKCAgIDmLqfVKysrU5cuXZq7jBalurpa27Ztk9Vqde3z8vKS1WpVfn5+M1bWOpWVlUkS/04vsAceeEA333yz279jNF6LfFszGs/pdColJUX//u//rpiYGB08eLC5S2rV9u3bp2XLlikrK6u5S2lRjh8/rpqaGtcTtM8ICQnR7t27m6mq1snhcGj69Om69tpr3Z5AjvPz6quvavv27frss8+au5RWgxmWVmL27NmyWCz1brt379ayZct08uRJpaWlNXfJLUpDv9/fOnLkiBISEnTnnXdq4sSJzVQ5UL8HHnhAX3/9tV599dXmLqXVOHTokKZNm6aXXnqJV8xcQKxhaSVKSkp04sSJetv07NlTd911l95++21ZLBbX/pqaGnl7e+vuu+/WunXrLnapLVJDv18fHx9J0tGjRzV69GhdffXVWrt2rdv7tXBu1dXVCggI0IYNG9xegpqcnKzS0lK99dZbzVdcKzJlyhS99dZb+uijjxQVFdXc5bQaGzdu1K233ipvb2/XvpqaGlksFnl5eamqqsrtGBqGwNLGFBYWqry83PX56NGjio+P14YNGxQbG6vLLrusGatrHY4cOaLrr79ew4YN04svvsj/MDVSbGysRowYoWXLlkn65dLF5ZdfrilTprDo9jw5nU5NnTpVb775pvLy8tSnT5/mLqlVOXnypH744Qe3fampqerXr58efvhhLr01EmtY2pjLL7/c7XOHDh0kSb169SKsXABHjhzR6NGj1aNHD2VlZamkpMR1LDQ0tBkra3lsNpuSk5MVExOjESNGKDs7W5WVlUpNTW3u0lq8Bx54QC+//LLeeustdezYUXa7XZIUFBQkf3//Zq6u5evYseNZoaR9+/a69NJLCSvngcACXEDvv/++9u3bp3379p0VAJnM9ExiYqJKSkqUnp4uu92u6Oho5eTknLUQF55buXKlJGn06NFu+5977jmlpKQ0fUFAA3BJCAAAGI+VgAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAY7/8BMAeGZ2DtJOoAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1500 | Train Loss 0.007045763544738293\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x1000 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for epoch in range(total_epochs):\n",
    "    mean_epoch_loss = []\n",
    "    \n",
    "    batch = torch.stack([diffusion_torch_image] * batch_size)\n",
    "    t = torch.randint(0, diffusion_model.timesteps, (batch_size,)).long().to(device)\n",
    "\n",
    "    batch_noisy, noise = diffusion_model.forward(batch, t, device) \n",
    "    predicted_noise = unet(batch_noisy, t)\n",
    "    \n",
    "    optimizer.zero_grad()\n",
    "    loss = torch.nn.functional.mse_loss(noise, predicted_noise) \n",
    "    mean_epoch_loss.append(loss.item())\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    \n",
    "    if epoch % print_frequency == 0:\n",
    "        print(f\"Epoch: {epoch} | Train Loss {np.mean(mean_epoch_loss)}\")\n",
    "        if information:\n",
    "            with torch.no_grad():\n",
    "                plot_noise_prediction(noise[0], predicted_noise[0])\n",
    "                plot_noise_distribution(noise, predicted_noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vGg6qTwbGlTF89TZWnM4aJc4HLFJwxWSHCx+C1ukcJuiuzcOdaif23iDYDtexqnbsbJwz9HbAflFhIbj0d5MzVih3Plom2B8nYFPq7n/ZFZiI6MdoTGr622C1sPmbhYJ97B178Gk2/y5o7ketQMsKHwna1nYXBHuzIy4PVu+4jWONwibgjg7YxNzZ+XPQfKZ8Jdg7juI8yGm7WGBbJhXSBekt3n2XYZ4GHCQMIwMHCcPIwEHCMDLo7cR9UsfWpKxVuRNU8JpL4Hvhm+mCvdoHl4BqmuGutwMTzEAruou9sl7ZKE62fzqKSbbBBZgES2iHyayCKipmVW2wb5XhvP6CnXUTl6t2O+cA2syBB0DbXn4NtOlDogU7aTrupCVtwp26IrQ4YW7Ydgdon96JFOz+OzqAzzENnjPvYdiM3PR2f9AiLPGhSGSfv+zIG4sPC/YWthbswhIdvbd/JU/cGeZpwEHCMDJwkDCMDBwkDCOD3lYBl9X7icoUlTtdNcjCJkmjTcRdoaJjsDfUHXPMavuV7AKtR0/c1njQ7+IW0vdOYaPtbvctQQtrhBP8AwcHgjbC61fQvPvFCPbx5VPAZ2kULrmNX5YGWnJ/rCLwiGgr2L9dqA8+Yz5dD5rzNGxU/XMbrDbopxGbdA9eMxd83ph7BrTxnbE6oPt67Obp0zIAtPbLxd5eLw/bBz6724h/P3kFxUT7wa1K+ErCMDJwkDCMDBwkDCMDBwnDyKC3E/eiXb9RuUFlJjR1TRPw2XNVXHIbk4mZ6BbjcWtlixs4sfMtbAbamMkvifYvuIQ1Y/ZvoB2Y9i1oMS7YzNvoc2xyXfvTEMFWdeoCPlFNcMLc1RO3tri7B8/HnGxxkhsXjRn32v2wEuBbH8zoH02ZD5rvgWJxrEkh4KOeUQ+08W9hRr9ZLu7UNSofe2qdOS/aK96bAT6TWolLJorLsCfZ4+ArCcPIwEHCMDJwkDCMDBwkDCOD3k7cT5xTk5Fl5cS9tAeWwdsaiaXyiRqcWLubvAVa3bO4RfKfm3GSuD0wQbCLu5eDT/c2kaDd6Im7R7Vw+hG0ROkr0FZ8JzbDnhyGTaN79ssC7frxP0CLX+AO2ufHxf5cXfZgD6xFDTNA+7gNPqC4fAUfdrjPFh+KbL2KGf1917Bv2EktHv+dI1NAU+zF77jXt2IDraZFuDbeRi02IteVloHP4+ArCcPIwEHCMDJwkDCMDHo7JxkVdZVMTSqX3iqm45LP6P5ite2+blbgo2lbBFpgCibQvumJ84MvD4lLT98cj8e6F4/HWrHFCbSbtzqCpjiO/6P6dxR/R+0fccMe9eb3QCvbirsT+6zAnmNXfhLf+0oQ3r+/Pe4z0Kx/TQEt8N4XoB13EJN0Q7s3AJ8lr+JcJjkIezF3PGsEWkgp9j6bP16s/l6dgcuzTa6Jm/hQuZaIcGOoquArCcPIwEHCMDJwkDCMDNUKkrCwMHJzcyNLS0uysbEhX19funxZXLFWVFREQUFBVLt2bbKwsCB/f3/KycF+tgzzolCtiXtSUhIFBQWRm5sblZaW0syZM6lnz56Unp5O5uYPex9NnTqV9u7dS7GxsaRWqyk4OJj8/Pzo+PHj1RqY9fUvyMxYWWGvuYRJtbvvfyDYvx/0Bx+Pnbhs1qVeW9C0i7AKNaQ8UbD7/N4SfI4l4sZBu4P+BO3VMOwrVfvKO6AlBIlLZxtosW9Va2NMamaEYpX09ObhoE0Ys06wb3QbDT5dnI+AZm2Py3D3BmCDcvtrqwX7TCr2wGrjkQBa7kp8AGLcAPuX0Wb87Dc6nRDsw1uweXj0bLVg5xeV0SIsFq6SagXJ/v3iouCoqCiysbGhtLQ08vLyIo1GQxERERQTE0PdunUjIqLIyEhq2rQppaSkUPv27avz6xhGL3iiOYlG83BPbWtrayIiSktLo5KSEvL2rnxM16RJE3JycqLk5OQqj6HT6SgvL094MYw+8Y+DpLy8nKZMmUIdO3akFi1aEBFRdnY2KRQKsrKyEnxtbW0pOxsXBRE9nOeo1eqKl6MjdshgmJrkHwdJUFAQXbhwgbZt2/ZEAwgNDSWNRlPxyszMfKLjMczT5h9l3IODg2nPnj109OhRqlevcimmnZ0dFRcXU25urnA1ycnJITs7uyqPpVQqSalUgj7T+lUyVFYuU7W06gc+K92GCXbdK7hsNmAJ7np0oXkD0Cz2YzXsgGZiwA7uNxx8Bm/A96WtxJ1wQ8bihHPA6hLQLjUUnwS6TcaHDCcCsUrXtMc60GbVx5np159NEGyHr3DXLL+BmNE3V2Dfrdh4zMx72KQL9p4VWG1rlRUK2sSbzqBNWoBNzEN7487JnQvFLHz8etwRuU6rzYKdV4Dfx+Oo1pVEkiQKDg6muLg4SkhIIGdn8YO5urqSsbExxcfHV2iXL1+mjIwM8vT0/OvhGOaFoFpXkqCgIIqJiaFdu3aRpaVlxTxDrVaTqakpqdVqCgwMpJCQELK2tiaVSkUTJ04kT09PfrLFvLBUK0jWrXt4Se/SpYugR0ZG0jvvvENERMuXLydDQ0Py9/cnnU5HPj4+tHYtPgNnmBeFagXJ39nvx8TEhMLDwyk8HBNZDPMiorel8o1SnKiWUeUORq/PswafPi8fEux7/rjE91Z3zHRfGTUEtI9aYsPs7OVtBPvrWdgcu3sZNvIunH0ftIix2OT62yr8lr/2iWD7pmMjaZszH4N2f8h50Nb6YznQzs1ir6wFcZhd77DqNGjDIjFz7rMYt7L++kpfwZYaYlPwacW41HjGm7iFd90sK9AWv4Hjbd1J/Of927lW4PNRU7HvWbFUQET491IVXODIMDJwkDCMDBwkDCMDBwnDyKC3E/fGA7WkMKnM1k5ahtsV+/3qK9g5X2A5fuaEg6C1HYwZ/paO74BmFrJVsL+5ZgM+RefGg/aNC/b6On19J2g9woeB1qREnMzXbY7bTDc+gBP3MfmpoOkG1gZtUOcFgv1BEq5Tr22sAS31ATbpnvQxLkMIWBgm2L63rcDHxKsxaIXtV4C2ZgtOrIuDcLexYRsjBHvmK/j9hhwTS/gL8ktoK65yqBK+kjCMDBwkDCMDBwnDyKC3c5JfP9NSLYPKHk7Rxz4CnwZHxV5Tv29pAz6NorHHb6cxWLmbnoG7187dIybjRrgXgI/14Z9AO56Eywc83seNa1QuWNE67A3xMxi3w/9jmRt/B019+E3QdvriJkEfzjkl2MtTsGL5DbIFreWqCNBqn8RE4d1hYi+rBidwp93oxljZnH4El2dPmoI9lXV+34MWNFrsjeyZjt/lL5FNBftBsY6I9oJfVfCVhGFk4CBhGBk4SBhGBg4ShpHBQPo79e/Pkby8PFKr1eT9Sy7VemQTn2JvbJRcOHeEYE88uRJ8jFe7gGZxGCf4y/rhJO61AeIE8zUKAh+rY+agaTvg5LKpLSZDX1oeAFqPLWIT8HrrPgWf/Wdxwjyz/QPQtjvjkt5Ti8QE6eLmOP5GpVjx66V7CbR2edjEvE9OkmC7G2NC8/MJuL7o5g3cxCfjGjbztj+Elc1W2wwEe+yKE+CztoOYCNaWFVKjn0aSRqMhlUoF/o/CVxKGkYGDhGFk4CBhGBk4SBhGBr3NuNe/dooU5pWTyoJ9uMutl4PYxHn1UOwX1TDjVdC6euFOuFYTLoL2+vIlgt3KD3t4tZtlD1pbCRtCHziJlam3zYtBW6kVM9uqH7Fitvb32Kh6Y8Qu0E5uwt9p1qa1YLe2xn5mTXJwIvvFYOysqTX0Aa17gVhtO2GyBfh4jMJz9vuv2EtsSF+sPJ5fchu0vrfF3Xc3bm4APtdfEZd655dIRFgsUSV8JWEYGThIGEYGDhKGkYGDhGFk0NuM+4j0M6SwrJz0KUf/AL5TO4i9iFV1cSIc0Xg+aF85GYD22q4eoGlzxOz3EAnXexanLwEt2bg5aNF9sP9XTn/cPar8RrBgv7oZJ+kPzLAUfPJOnPg65OJ4j9j0EuyEDwaDz1e/3ACtdN890OpYYcn+L/YNBdvZHislplvsAO1We1zSsDq4F2gD2uHDiLfcxWqAg5a409XGj8UtyB9IZTRB8zNn3BnmacBBwjAycJAwjAwcJAwjg95m3IP2bSUL08pJWk4MTnLfdhTXkn95AntU/ZmHpeBLe+Emp8lnvUBbcEbM7jpnYJ+p6bc3gNZpF6Zy+9p9AlqHHriV9bHrYhPqEe2xkXQrj0OgjdqJ/+9enbcftMFG4o5VE8wagk/Z/D6g9RqAn2m5GR5/um0zwT70KpbYf5c+B7Sx03BJQ8sduDPBH8dwmUByt7/0HjiBa/tHrDQT7LwHpTQBT22V8JWEYWTgIGEYGThIGEYGDhKGkUFvJ+5vPviWDKXKGD5yASeAh4aLO0+N241Nz2YE1gGt/odfgzZr5DTQTp4SJ/2dloaBT+7ovqA1absbtO2jcavmuu2vgKbZIf6OGA+sDuiUiv/bzLzUoH19xgy0tZvFbaVrLQAXWnQCy9H7OOF687eysMx+cvk5wR63DD/3/Xu4HXXpOmyOXeaIGXfn+hNBm2nrK9iNY93Ap3GE2JyuPL+YiLDJeFXwlYRhZOAgYRgZqhUk69atIxcXF1KpVKRSqcjT05N++KGy8LCoqIiCgoKodu3aZGFhQf7+/pSTgy1gGOZFolpzknr16tHixYupUaNGJEkSbd26lQYOHEhnz56l5s2b09SpU2nv3r0UGxtLarWagoODyc/Pj44fx8115GjkYUe1zCuH18iqNfhMqB0t2Ct+aAY+cb9hxWmjfYWgXdFgJeikOeJmOUfHdwKfS+1xI54OiSdBU+xrD9o7Qbhz7zbrEMH+SfUB+CxfiJsETQrD/lw/zL4J2owLVwW7ubEOfL6c9S5oM4dgArZn/mjQ1g8X+3/V6YUJ001NHEDr8bI7aIM6YlX3xR24C3PqAvF4Ge3zwGfeZDvBflCqozHgVTXVCpL+/cUGa4sWLaJ169ZRSkoK1atXjyIiIigmJoa6detGRESRkZHUtGlTSklJofbt8Y+EYV4E/vGcpKysjLZt20YFBQXk6elJaWlpVFJSQt6PdFps0qQJOTk5UXIy/hf6DzqdjvLy8oQXw+gT1Q6S8+fPk4WFBSmVSho3bhzFxcVRs2bNKDs7mxQKBVlZWQn+tra2lJ2d/djjhYWFkVqtrng5OmJXDoapSaodJI0bN6Zz585RamoqjR8/nkaOHEnp6en/eAChoaGk0WgqXpmZmf/4WAzzLKh2MlGhUFDDhg8rR11dXenUqVO0cuVKCggIoOLiYsrNzRWuJjk5OWRnZ/eYoxEplUpSKnFJpvUHP5OxUWUiLei3fPAZNFhscn3lMi7VVabi7lSp9mtAcy4bC1qdWysEu/41nHCuWIvNn108FaAttP4ctEOT8DZ05pn1gr3oeCz4+B2YAJq3Hy6TPZmPvbh2378l2B3y8crd9mus+N2QjTv+Fp/CpGmatb9gK9VDwefcROzXlT51KWjh87Cx+cFXMDk5/JzYyLz27+vBx/y2eP7zS/DhzeN44jxJeXk56XQ6cnV1JWNjY4qPj6/42eXLlykjI4M8PT2f9NcwTI1RrStJaGgo9e7dm5ycnEir1VJMTAwlJibSgQMHSK1WU2BgIIWEhJC1tTWpVCqaOHEieXp68pMt5oWmWkFy584devvtt+n27dukVqvJxcWFDhw4QD16POw0snz5cjI0NCR/f3/S6XTk4+NDa6u4HWGYF4lqBUlEBO7A+igmJiYUHh5O4eG4ouzv8p8ORyVlYqcjnYT3kAXFok9pOc5bHkiYLCsoxy5KZVIRaIW6UsEuysPkllSEj6yLJC1opQ/wvSTheLXF4njLtPg+3QOcZxWU4WcqKkO/4hIx2ZdXivf4+eV4zool/Jx5+fid5BuL50xrgOe1tLgENKkIz1mhVI7vJfxMxlrxd5gU4GeS/jIHKfh/++901NK7vlu3bt3ix8DMcyMzM5Pq1cPtwx9F74KkvLycsrKyyNLSkrRaLTk6OlJmZqZsAzHm6ZOXl/evPf+SJJFWqyUHBwcyNPzvz6/0bj2JoaFhRWQbGDx8BPyfgkqmZvi3nn+1GtfgVAWXyjOMDBwkDCODXgeJUqmkuXPnVpmRZ549fP4foncTd4bRN/T6SsIw+gAHCcPIwEHCMDJwkDCMDBwkDCOD3gZJeHg4NWjQgExMTMjDw4NOnsQOJMyTExYWRm5ubmRpaUk2Njbk6+tLly+L2zP8r7eK0ssg2b59O4WEhNDcuXPpzJkz1KpVK/Lx8aE7d+7U9ND+dSQlJVFQUBClpKTQoUOHqKSkhHr27EkFBZXVtlOnTqXdu3dTbGwsJSUlUVZWFvn5+dXgqJ8zkh7i7u4uBQUFVdhlZWWSg4ODFBYWVoOj+t/gzp07EhFJSUlJkiRJUm5urmRsbCzFxsZW+Fy6dEkiIik5Obmmhvlc0bsrSXFxMaWlpQmtiQwNDcnb2/u/tiZing4ajYaIiKytHzaB+6etov5N6F2Q3Lt3j8rKysjW1lbQ5VoTMU9OeXk5TZkyhTp27EgtWrQgIvrHraL+TehdqTxTcwQFBdGFCxfoxx9/rOmh6BV6dyWpU6cOGRkZwdMTudZEzJMRHBxMe/bsoSNHjggr9ezs7CpaRT3K/9L3oXdBolAoyNXVVWhNVF5eTvHx8dya6BkgSRIFBwdTXFwcJSQkkLOzuMEOt4oi/Xy6tW3bNkmpVEpRUVFSenq6NGbMGMnKykrKzs6u6aH96xg/frykVqulxMRE6fbt2xWvwsLCCp9x48ZJTk5OUkJCgnT69GnJ09NT8vT0rMFRP1/0MkgkSZJWr14tOTk5SQqFQnJ3d5dSUlJqekj/SoioyldkZGSFz4MHD6QJEyZIL730kmRmZiYNGjRIun37ds0N+jnD60kYRga9m5MwjL7BQcIwMnCQMIwMHCQMIwMHCcPIwEHCMDJwkDCMDBwkDCMDBwnDyMBBwjAycJAwjAz/B0NdiW/OizKLAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0fhZ8J2EYGdhJGEYGdhKGkUFv1yTHf9xHhmaVHXG3lGGTmnnvzxbG8aHYqXblRxjEm/H6RdDWBuHaZc9GsXNszHw8Dru2LRbH/soUD45tvhYG2qBwtGs1LVsYL0l5BDbTL24HzSMTs2iHdsW6W3Wni4HChv7YUfin15uCVv8CBuhGPMSaY2uTxOu49JtksPnPIsy+DS4MBe2EdhxonZpuAW1kD/F6vNvaHWxCzMWM5fKCP18nnu8kDCMDOwnDyMBOwjAysJMwjAx6u3D3/dmUzEwqg2ab+uLx0aPffSWMp7yGgbcfDmFgbLT/eNCCvsZaTZc/PiCMNZOwHlVMC3/Qmg2aD1r6PVyk3zD4AedxN0cYnzHGgONgIwysrnDAAhp183SgxfuIH3n+IiwurSqpB5qVKRYZnxKIn8kHy6OFsduYxWCj3Y21yhqOwACg1gmDsj1N8fiu4oh4bZtexk5XjQ+Ix5RLdRLhJ141fCdhGBnYSRhGBnYShpGBnYRhZNDbFtXTX3InlaJykelTPwJs093ECPuaXVjUeYjtS6BFxWAWcOaHuaB9U1/cCLg+Bot234p7HbTrhAvr9+P3gGa9th1oN/qKEeWMGfj6Lsk5oGmMsIzsHCvcaEjZLkaedZ4GYONgcxu0TabjQYuaj5Ht4F7i60XljwabpS5Y16vc+jJoJY9xA6R391DQuny3QhhPboutv1s/FP9+SnWFdHbV29yimmFqAnYShpGBnYRhZGAnYRgZ9Hbh/nOqmqwsKxeB9WZgSnfMZTEi+8WmBWBzNg5TvAd3w4LTM/Y5gHbizAlhLDlhFcqkE7jgjNliCNoYA+zklHUZO3O53BZrJg9weg1svPOngRYcbA1a81vNQQuYL16P6X3QppXCFrTk9nVB65KExbDzJPH4wrX9V8FmbDFuMvxsgtr8mRhdfym1I2gvXxXnq/DGrmUBD8QsgrInZXRtxo+8cGeYmoCdhGFkYCdhGBnYSRhGBr1Nlf+qwJRMf+PDniZFYGPfVWxNnLZvIdj4mluD9uaVlaC9vRq7Ux2wEs+0W5q1Bpu7TTA6vYyw9bSLBZ43r3MwBbSZyf2FcdIujN7HzcXaU8v9NKB5O2JkfkrjscLYfKEn2ITEYmHw/HvYdrtuKGY4JPiJZ/5b2ONRgtjOWK+g0e46oE1YjR2rBlquBe2CsRjVP5l2Bmzq3RaPHJQWlxIRtvquCr6TMIwM7CQMIwM7CcPIoLfBxF7Hb5GRhWWF3s74fbB9PVQ8errkyzVgcyoKs4BPBWNG8SN7PObbb6G4HjB0wIDaniOYRVs/HTvhXq3nA1pUOgYdbzUbKYyj91wHm4yvsPlP4kGsgeXYMw004yHi2mWJEdbwshyDNci2mGL93s9NLUC7aStmHg8Y9F+wOfIG1j0L//pl0M4dw+uY5/0OaKc2iEHlIz9gE6L9ncXP8kmhRD6jSzmYyDA1ATsJw8jATsIwMlTLSUJCQsjFxYUsLS3J1taWPD09KS1N/N5bVFREvr6+VLduXbKwsKARI0ZQdnb2M16RYfSfai3c+/fvT15eXuTi4kKlpaX04Ycf0pUrVyg1NZXMzZ8ufH18fOjIkSMUHh5OarWa/Pz8SKFQ0LlzGHiqil8X7j3mvE1GJpVHTY/exAY65wYtFcZ11mJ2bN95mD28bgk2cHnnAwzaDXssBhP7jpiAc+iXCtorFzDY99X7WLdqx81ZoBmpxMLakVOwYY970EegWU9Vg/bD93h0VmthLYy/34JHiIddwILZA/Zgwe8vpmMG8azN4gZCB8fhYJNXiMdrXXJUoL3aDzOIf/wEA4x374kNkh4ewyzmSCsPcQ7lZdQgJ+1PLdyrFXGPjRULiIWHh5OtrS0lJydT9+7dSaPR0ObNmykiIoJ69376R7F161Zq3bo1JSQkUOfO2EaZYfSdv7Um0Wiebifa2NgQEVFycjKVlJSQu3tlgYBWrVqRk5MTnT+P5wWIiHQ6HeXl5QkPhtEn/rKTlJeXU0BAAHXt2pXatm1LRERZWVmkVCrJ2tpasLWzs6OsrKwqXyckJITUanXFw9ERy3UyTG3yl53E19eXrly5QpGRkX9rAkFBQaTRaCoeGRn4nZNhapO/lAXs5+dHhw8fptOnT1PDhpWZuPb29lRcXEy5ubnC3SQ7O5vs7e2rfC2VSkUqFS7anC7tIKVxZTR71phvwGbxinxhbBO2DGxif8LFtv++UaAZvIw1nlr7ixmtjy9jAerSm9i1yS92BGiDXFeDppgyCJ97VMwi6GmI2b2lDx+DZvTpHdC2P8Io+bzupcK4w52uYDM4GDsKd7SKBq3vcoyIz7xtI4zfPIZfswfbY8ffbzZglNxitRK0dyeuAK3OZDHD+pefcMGfYddTGBdIJUSEGQlVUa07iSRJ5OfnR1FRUXT8+HFq0qSJ8HNnZ2cyNjam+Pj4Ci0tLY3u3r1Lbm5uv385hvlHUK07ia+vL0VERNDBgwfJ0tKyYp2hVqvJ1NSU1Go1eXt7U2BgINnY2JCVlRX5+/uTm5sb72wx/1iq5SQbN24kIqKePXsK+tatW2n8+PFERLR69WpSKBQ0YsQI0ul05OHhQRs2bKiRyTJMbVAtJ/kzcUcTExMKCwujsDAMPjHMPxG9TZVP2HGRLMwqU7ETvTG15eHX4vFUaTAWwg7ZFwDa6LR7oF2fMRm0/XPE/yHp+RjD0Wbiwrr4KC5yvU/hkdhJjzFa7/dQ7AI1cAW2eF7xDqb/x07ALXaHC7jA/2WkWPR72eFXwKalxhW03nlYN2xyALaQ/vyieAw6f+pxsBl2B69P2Glj0NqNOAHarawY0LrMFrMlRnbCLIV3L2iFcUnhE/p6wixOlWeYmoCdhGFkYCdhGBnYSRhGBr2tu3W7x1Ays6r04dHFmL7dsp14pr1/i7FgE7DlAGh7f8G09aGvlIB2sr2YXt21136wUScGgNZg1BDQeqrKQPtsJJ6Zb9hKLKK9/RjmsvXIweLe4wfjufGA4I2grZkidqcq24lR84yr80DzWdIMtHqTA0DrMv60MH74AdbdyriMGxaaCR+Dlp64D7S0BNxgeWK9VRg3f+co2DSLE2ts6UgLNs+C7yQMIwM7CcPIwE7CMDLobTAx/vxDMreoDPKse4ANXeb+6CmMr/dBm+wjF0Cr3+gaaEOuYv2s+DcOCOPEZMyO9R9YD7SY+q1AK/4mGLSfVViLa1tHcR6vDvwZbHqtwud9mo3zT8sxA+1+AzFoV7CsB9jsD7IE7VzMetB+XoHdiNs0EzO6R2vDwcZ3Hdb6mp+P3Ynt2+Ex5VIvPKLtbirW3Qq68wXYWOWMEcZF+Tpa1mQ1BxMZpiZgJ2EYGdhJGEYGdhKGkUFvg4k2O1PIUlVZxPpmczz+en+iWDOqybdnwWa2F/4fuDDzIWhl738IWsst3YVx40lxYHN+dlvQliThZV3cfB1oRsOxGLYqRQzare/zA9j8sBpricXm4YJWdWQmaJ8Y/CKMF93BfZtgzZuguUl4fDrRG0+b1rcSOyA7dusCNickbOLz/Z0U0CZ8jJ9d/UNYv+1uN3FRftQJM5sX2IsZy4VSARHh31RV8J2EYWRgJ2EYGdhJGEYGdhKGkUFvI+5j/PqRUlUZHb60Eosz298UI8omy7COksI5FLS207FWlllBEGhnJbHCy+oMjE6P3YcL8teqODI8xxQj508mY5R5RT9xbh8sxqi5UWt30I7v+QW0zqPw+Gvhp2InrbklWBfLUIEbINbGuAngNRjf+y/9xKzfkJ/xqHQDBRYn312Mn923Hh+AdjsOu3xN04gbJfvKMBPg9a7i9S8oKKQuvd7miDvD1ATsJAwjAzsJw8jATsIwMuhtxN1p2DxSmVfW3VrVugHYvOQsRtyjUxeCzbEgb9B25WF6+5IIXKwee1PcLJg2FBfuB48tBe2lNzEVf8dL34L2KD4cNG2/FGG8c5kd2NzecwO0QruboDUPfhu0Du+JR2KTHuPx2pUtNoE243EgaM0oALT+w8WNhx87YuvvKYRHCfp+gcenDa+MR+0lX9D2vSFG/kuuY5bCuUMHhHGerhhsngXfSRhGBnYShpGBnYRhZGAnYRgZ9HbhHvF/PqQwMqwYj1p9EGyOPxALZke6HgCbxWkYyd2nwRpe3xzCNnSB28TK+DENsFtXbmIT0A4e6AvavSWNQesxE6Ppa03FwtSZGHSmOfHYgnmKFUa/i9bguXS66icMbxB2+Hqv51ugxaf/BFrqbRfQGn46XRjvbOwBNi4tQkAr9MVOV9c/wOutCsXC4KNMxPc0aOJKsEmaLn5O2ifYtexZ8J2EYWRgJ2EYGdhJGEYGdhKGkUFvF+6FLv6kUFV2LHo0GDsc3Y87LIx1UdhNqqUxnv32cMX08JdbYEGzYb/sEMbrPukDNkE7W4I2/cEc0Lb1tQZN3cQTtIbLOghjVbdwsFnVzhC00UsxSj6xCxbRvm47VBgvm4Hn/X2NqmgC69cCpM9fxy5c7beKmyL9twwFm0lWmAlwiUpBm78RtaNtsEtW6js9hbFLfewE9miaWFiwkDDC/yz4TsIwMrCTMIwM1XKSjRs3Urt27cjKyoqsrKzIzc2NYmIqvwYVFRWRr68v1a1blywsLGjEiBGUnY0NQRnmn0S1ju9GR0eToaEhtWjRgiRJom3bttGKFSvo0qVL1KZNG/Lx8aEjR45QeHg4qdVq8vPzI4VCQefOYa2kZ/Hr8d2dh8aTmbmyQg+4+TXYemwQM4PdugwAm+CGuI7og2WfqMi9ALRNLmLdrY88GoNNbP3hoH2xAI/l3ojFwNt/zfH79YPpYpbrrlgMeu0s+RE088cYZGveEwtT2/yuWdGZfpg5HdEe63ots8Is4+L2WJ/LO1yc/7XpmDm9YN5c0FacwACm3y187r49+D5vfHBVGAeVYhOlLk3FwGRJeTkde5Dzp47vVmvhPnjwYGG8dOlS2rhxIyUkJFDDhg1p8+bNFBERQb17P+0ktXXrVmrdujUlJCRQ585VLAYZ5h/AX16TlJWVUWRkJGm1WnJzc6Pk5GQqKSkhd/fKIgWtWrUiJycnOn8ed5N+RafTUV5envBgGH2i2k5y+fJlsrCwIJVKRVOnTqWoqCh65ZVXKCsri5RKJVlbWwv2dnZ2lJWFt8hfCQkJIbVaXfFwdMQegQxTm1TbSVq2bEkpKSmUmJhIPj4+NG7cOEpNxUaRf5agoCDSaDQVj4wMTDRkmNqk2sFEpVJJzZs/Pdbq7OxMFy9epDVr1tDo0aOpuLiYcnNzhbtJdnY22dtjNuevqFQqUqlUoB8N2ENKw8ruTfMi8BhuS7NEYTz3q0Fgc3raIdB6N8IjpSfOvAHazTNiLS7nbz8Dm7Ssq6DFWJ0ErfVAzAzusNACtLMp4rFS38FYT0u3qA1or07B480b7viBdjNKPOo6bwP+nzyjwbpkh7zGgGb7aUfQFF6hwthtDn6LsL7WHbT9hqj1ScCOvAvSIkFrOlPsiBW5BTOPRx0Vg6GStpio7+dgVxV/O05SXl5OOp2OnJ2dydjYmOLj4yt+lpaWRnfv3iU3N6w+zjD/FKp1JwkKCqIBAwaQk5MT5efnU0REBJ08eZLi4uJIrVaTt7c3BQYGko2NDVlZWZG/vz+5ubnxzhbzj6ZaTpKTk0Njx46lzMxMUqvV1K5dO4qLi6O+fZ9+lVi9ejUpFAoaMWIE6XQ68vDwoA0bNjyXiTPMi6JaTrJ58+Y//LmJiQmFhYVRWFjYH9r9Eb/GNovLxRjnkwIMqmlLxQS40nIMCOYX4fPKVZggmK/D5xaQuD4ozCsEm5L8ItCKDPC1CqVy0MqKMI6bpxW3wEvy8vH1dfhahfllODctaqWFv3tPpZhE+KS4imtWgHZlxViWp7hQ/J1PSvH6lElPcK6EW/8GWpxHaTG+p+Ji8XPRSjhXSVtc5fjPxNL1rmD2vXv3eBuYeWFkZGRQw4YN/9BG75ykvLyc7t+/T5aWlpSfn0+Ojo6UkZEhmzrA1Dx5eXn/2usvSRLl5+eTg4MDKRR/vH+ld+dJFApFhWcbGDzdAv41oZKpHf6t11+tVv8pO06VZxgZ2EkYRga9dhKVSkULFiyoMiLPPH/4+j9F7xbuDKNv6PWdhGH0AXYShpGBnYRhZGAnYRgZ2EkYRga9dZKwsDBq3LgxmZiYUKdOnejChQu1PaV/JSEhIeTi4kKWlpZka2tLnp6elPa7dhX/66Wi9NJJdu/eTYGBgbRgwQL67rvvqH379uTh4UE5OTnyT2aqxalTp8jX15cSEhLo6NGjVFJSQv369SOtVlthM2PGDIqOjqa9e/fSqVOn6P79+zR8OJZS+tci6SGurq6Sr69vxbisrExycHCQQkJCanFW/xvk5ORIRCSdOnVKkiRJys3NlYyNjaW9e/dW2Fy7dk0iIun8+fO1Nc0Xit7dSYqLiyk5OVkoTaRQKMjd3f0PSxMxNYNGoyEiIhsbGyKiv1wq6t+E3jnJw4cPqaysjOzsxP7lcqWJmL9PeXk5BQQEUNeuXalt27ZERH+5VNS/Cb1LlWdqD19fX7py5QqdPXu2tqeiV+jdnaRevXpkaGgIuydypYmYv4efnx8dPnyYTpw4IZzUs7e3rygV9Vv+lz4PvXMSpVJJzs7OQmmi8vJyio+P59JEzwFJksjPz4+ioqLo+PHj1KSJ2KWWS0WRfu5uRUZGSiqVSgoPD5dSU1OlyZMnS9bW1lJWVlZtT+1fh4+Pj6RWq6WTJ09KmZmZFY/CwsIKm6lTp0pOTk7S8ePHpaSkJMnNzU1yc3OrxVm/WPTSSSRJktatWyc5OTlJSqVScnV1lRISEmp7Sv9KiKjKx9atWytsnjx5Ik2bNk2qU6eOZGZmJg0bNkzKzMysvUm/YPg8CcPIoHdrEobRN9hJGEYGdhKGkYGdhGFkYCdhGBnYSRhGBnYShpGBnYRhZGAnYRgZ2EkYRgZ2EoaR4f8BcLbzoVd/6vEAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9zUnqW0eTUZ3KGHaIGAw+zlvELtc9+dbg4z/9NmhBrfHk1W2OuKX32HqxI/f0ITxV9/XB2PFr1gTziG9scW5Y6q12oNXZKh7a8zAPi5xRN7CwGmXdH7QO23Br7pfHxWJlc/tvwCeAsGAXPR8Hcu97gKcA234pFhh3FyaCj2YAfmZuzpagxbqeA830HBaMB3s8L9jXO3UCn7MufoKdXwAuvwvfSRhGBg4ShpGBg4RhZOAgYRgZDKQ/6nuvBXJyckilUlFMWieqY1m5rvD899hZeyxb1JLPYkGwfsuVoPUq14BmNw8TzAed2gm26ft4NNIbPy0GbbyrCrQ1VZzkdL8/nkR1bPsGwR7cDguC3/q2Am3Io1LQ/GJwS+yil8Rtyt7ftQef4SdOg7bn+wWgJb3lAVq8n1hI7bsb54GZGWPhsElj3Obb0x2z67A8XACxa9JBsI+dwo7ii+biwG9JJ5EUVUxarZasrHCb8JPwnYRhZOAgYRgZOEgYRgYOEoaRQW8T96QxfmShrJz/lNsW52Jde0tMuF7wfgl8HNZgd2zJCJw15XQSO0Ib24jHMjtMsgMfWzwAirxvYGX+yFsPQTt4+hZoWpOtgu26BxcLPhyOx27XcWgJ2uhh6Ld63kzBbj0K52l9vr8ctBsz80Cze4QLA90HTBbsNRNxIufJA7ild+cue9DaxrUA7Y3T+NmWfif+bVjvx+S+w28aj4sLi2llyEZO3BmmJuAgYRgZOEgYRgYOEoaRQW8T90RFHFkYVB7XXL/RIfD94bUvBFt3rzP4mOjMQVP0dwYt6iGetLTZTRysbSq9BT7dLmJCnrB5L2gqwvlZ3TbgTLBHfcRW+TaHjoGPW5NzoDUJ7QPacB8868U1WqzWd7bB2V/N83Cx4NhNPDpD9yOefvVt2Leiz2138MkqfRE0zVF8z33zMJl/sH8JaGMPir+D0jF4ktYvJ8XOiJziPGq8yp0Td4apCThIGEYGDhKGkYGDhGFk0Ns97o/mrqJis8qKe/l5rNzWfVc8ovrzUtynXn4Kj4F2v+cEWqgtJm/HdySIPg9twOdqbE/QFiQFgjb3CLaVLxyISaiZqrVgBzTCtu8xMdh+7nP1S9AGuDUHbfaL4rDt8c64sBG1ERcBPliK17FxHc4Xm+InLqZM+FgBPkX2A0Dr4ILdBxNicWFjztJ5oH0XMVSwe7yDFXeFzzTRLsJh4r8H30kYRgYOEoaRgYOEYWTQ25zkuPl1Utap3NLp2KYN+DRNDBLscb0x/+ipxWLfDkf8/vtDKX4UzU6KJ9+W9Z0IPv0OeYHWuBvOv139xhzQ+n6E3cgTR4szd4/1GQI+LYLx9NpWL+Ic5I9O1wGt9Thx7laXmz+AT6AtHhP+sQpnlSXNcQbtmK04A2vAC5iT9DbHz+Kl3fj/9ZW81aDNKFkL2vvNugt2959x22+fmFOCXVKKnc6/B99JGEYGDhKGkYGDhGFkqFaQREZGkoeHB1laWlKDBg3Iz8+P0tPTBZ+ioiIKDg6munXrkoWFBQUEBJBGgyN8GOafQrUS98TERAoODiYPDw8qLS2lSZMmUbdu3SgtLY3MzR8XpcaOHUv79u2j7du3k0qlopCQEPL396djx7Cb9Y/wKuhI5lLl6bt0HoteIx3mCnaz6HHg88Od10GL+340aAunjgKtx/FJgn1oEhYTz7hiQU2Zgt2rJT9jMa7ZJJw1dcJI3LI68gw2abeY9jW+fvga0PLycW/xovNiMa7u5MHgcy3rAmguNq+AtvluKmih18WB1rOi1oNP99exS7fbEWfQFAH4s79ugHPCzPqKXcX5574Hn7I1/QS7sExH3xEWJquiWkFy4MABwV67di01aNCAUlNTqXPnzqTVaikmJoY2bdpEXl6PV31iY2OpZcuWlJKSQq+8gh80w+g7fysn0WofL0Xa2Dz+HzY1NZVKSkrI27ty132LFi3IycmJkpPxDHQiIp1ORzk5OcKDYfSJvxwk5eXlFBoaSh06dCBXV1ciIsrKyiKFQkHW1taCr62tLWVl4aYdosd5jkqlqng4OmKPFsPUJn85SIKDg+nixYu0ZcuWv3UB4eHhpNVqKx6ZmVjIYpja5C9V3ENCQmjv3r2UlJREDg6VJ5/a2dlRcXExZWdnC3cTjUZDdnY4s4qISKlUklKpBP2QQT1SGphW2BckrAwHLxQ7a7/pvAN8xi/AIdpeR1EzHIpDnEOdxblboxerwUcTmg3aXotI0D7tXx+086twGPbwd8Rq+pBMXLBwOYndseae2FG8Y7wfaFOyxZOonFriwO9G0TiDzGsO/o52TrkBWkSUmLf+dAuvXzVyOGjJk3AF9PwV7LDuEDoItI+TftNhveMs+GybL54ynF9QTDQU3KqkWncSSZIoJCSEdu7cSQkJCeTi4iL8u7u7O5mYmFB8fOUKR3p6OmVkZJBajX9gDPNPoFp3kuDgYNq0aRPt3r2bLC0tK/IMlUpFZmZmpFKpKDAwkMLCwsjGxoasrKxo1KhRpFareWWL+cdSrSBZvvzxbbhLly6CHhsbS4MHDyYiooULF5KhoSEFBASQTqcjHx8fWrZsGTHMP5VqBcmfmT5kampK0dHRFB0d/ZcvimH0Cb1tlU/1bE0mFpWt3ikrcG6VxzyxYnpj+3jwGX8Xj4s26tMVtEmTdKBN2S22vEf44QlTjRvhttxJ8/GI5AZf43bRpVW0wfc6OUKwLdxw3ljLmzgYvIcxzhw7nPg5aN6fiQly68XO4GN1rx9opQFvgJZ3HxdANo0QK+z5xvhZbA0/A9rksZikv+bbFLTmQQ6g9YgRtzCcT8KOgVNvi/O/CnMKiQi3PFcFNzgyjAwcJAwjAwcJw8jAQcIwMuht4t7zZBKZmVVWeUd2xWXkxTniwOYNXngy0rD+WBVu4oP/N8xuex+0Rm3E/ev7V+Ke8XeWzgUt8wMD0BqUYrLduxMOjl62VWwF73LyMvhcG4dV8iJ1XdAOrsT2eZeCMYKtSMLnnbuFc70u9p8Bmn3MQtA+l8TOgtLjceAzxRIT970HcLD2zkv4u9s6oQi0CZ2nC/bzwfngU+R+WLDLCnnuFsPUGBwkDCMDBwnDyKC3OUnn695kqazsIP1pzl3wWd1rgmDveaEj+HRvhUUqjXQRtLzZeJhNs0tiISz/Gm77bbZlDGils9NAy7TDltOBPUxA80sQZwF3N1eBzxIja9DundwK2mcPg0FLCxA7IQ7qPgKf0w6YH3y90Ba0W/2xwNtvqHiIj+HNyeBTcAI7NzwndAPtaNk20L5btxK0IxFi8TPGG+eqmb0qnk5ckCsRlnKrhu8kDCMDBwnDyMBBwjAycJAwjAx6e/ru7gE3yFxhWaGvPNULfC/NFwdkd0/rAD6ur+PA7O4JuBU1bwyuYXQaKBby9mf4gk+zcZiYnm/8CLT+9UxBS76bAtqPz4k7ONN2PQ8+7wfh6w/xwsHda775GbRfmooLAcO34UE/AY0HgvaqP8768vmkMWirHorF0BFftwWfIwdwWPWdWDxEyXefJWgbJVwoMU8Wn+sz+1XwaRElFprLyoop/cfNfPouw9QEHCQMIwMHCcPIwEHCMDLobcV90OnFZGBUmWC3+Aq3cuZfeU6wl/piUpc+EavO5rM3gfYgux1o/rtLBXt4z3jw+eln7ARY/DOeLtv9+k7QUhvjDKmb7uLMrjWr8fXvGE8CrUtHHL4ttcXPzPybDMEefBAHhYdk4AysLfWwMv9QfQK06BGJgh38Yl/wObveB7Q9R7BLwS8AF0r2fDgWtGl1xJMNFnTELb4HbosD20t15ZSOTRZVwncShpGBg4RhZOAgYRgZOEgYRga9rbifMdhLFgaVrfJfpGEyGTdur2C/2hYTyZTpVbRb21qA9uNiPBErIVScIXW3Hlb0vb7Fba31d+Pcp1av49biH17FVvP174qnNEWtxMWIjm9/DNqeyTjkOqEMT3Jqtk78zIb3wtcftzUdtIvN8ESvvT/iSVduLq6CHVwQCD7B6XjE9qwIPLa6cNV80NTj8bSxg3P2CbbJMWfwKd4obiMuzCui8Z0ncMWdYWoCDhKGkYGDhGFk4CBhGBn0tuLu8OY4sjKprCKb6iLAp1OOOAz7/rTe4NM1DqvfR9plg3bhNk7B/yIpSrCXtsCj6hwSMHE3a4LnQ85YjJpXcX/QglzFNv5dBs3AJ9kBK+nvX8FZU01SG4J2v4e4dWCU4xfgk3EJ99U3fgsXQDac+x9oR8vExYhmyivg09cT55I9fK0LaKtUp0Hb1bo1aHsixUNr/XCEAU1Y/Z5g5xXnEtEEdKwCvpMwjAwcJAwjAwcJw8jAQcIwMuht4n7bPZYsTCsr42Ujb4LPoDLxqOPht6o42ekEjiDrXICDr394ExPYmYe/Euz+Z3DPddRK3MMdGDsONJuOeEpWdDdMHL9QiAPwbg5diu/pEQOaizUei72h02rQPt0ivt7JODwuetLCINCMh+OJYVdbKED7cZB4Mlf0NFwQ6XN0F16rEk8fG+6L1fodVQynK+wuXsfJabvBR6nZKNglJcXg83vwnYRhZOAgYRgZqhUky5cvp7Zt25KVlRVZWVmRWq2m/fv3V/x7UVERBQcHU926dcnCwoICAgJIo8HGRIb5J1GtLuA9e/aQkZERNW3alCRJonXr1tG8efPo7Nmz1Lp1awoKCqJ9+/bR2rVrSaVSUUhICBkaGtKxY8fkX/z/+bULOOWyL1lYVg6Uvt1rNvh29Tol2H5uWGQzcD4K2uiFWBjrdxC/oxYGi9tk13WqBz7GTe1A+1I6Bdo65U3QnL1Bogd+4nwx12ycu1Xkuwe07K7ZoI0ux4NqXDeKn9HObdvB513fs6C5X20AWn4V+cxPS8RtuLEP/MDn7ZfxwCSrQGvQPM4lgvbdMDyNeFqKmPe8p5gCPl0eiV3Y+eVF9OZPM/9UF3C1EvcePXoI9uzZs2n58uWUkpJCDg4OFBMTQ5s2bSKv/x+UFhsbSy1btqSUlBR65ZVXqvNWDKM3/OWcpKysjLZs2UL5+fmkVqspNTWVSkpKyNu78r/HFi1akJOTEyUnJ//u6+h0OsrJyREeDKNPVDtILly4QBYWFqRUKmnEiBG0c+dOatWqFWVlZZFCoSBra2vB39bWlrKysG/pVyIjI0mlUlU8HB0dq/1DMMzTpNpB0rx5czp37hydOHGCgoKCaNCgQZSWhuNg/izh4eGk1WorHpmZ2ETIMLVJtYuJCoWCmjR53Onp7u5Op06dokWLFlHfvn2puLiYsrOzhbuJRqMhOztMbn9FqVSSUokDrF/b0oYMTCv1MxMxCS3sKRYP3dbNBJ8Vn/YBbXopblmt/8kR0M5PFAdOu2//CXw8vdqBZvfG26DFfYUdylvr4uDrkN/U/9782RV8FP5loGk71QdtqDF2EM/I6C7YruOwSPh5BL7nzNm4/fjsqvdBKwoWP7NSo+7gE18UAto5CYuEPd2wS1rjlwTap3HizDHVRGfwSdeECnZhUQ5RJP69VMXfrpOUl5eTTqcjd3d3MjExofj4ygFu6enplJGRQWq1+g9egWH0m2rdScLDw8nX15ecnJwoNzeXNm3aRIcPH6a4uDhSqVQUGBhIYWFhZGNjQ1ZWVjRq1ChSq9W8ssX8o6lWkNy7d48GDhxId+/eJZVKRW3btqW4uDh6/fXHk0YWLlxIhoaGFBAQQDqdjnx8fGjZsmVP5cIZ5llRrSCJicHGuicxNTWl6Ohoio7GprY/y6+1TUmnE/S8gjx8vxzxu7musABfryQXtLxSc9DKinBnX45UKPqU6cCnuBhf37gAd94VFJeCZlKKuUVxufgexjlV/UxF+LwcPBgn1xg/s2Kd6FdUgNdfWob15fyCKnLCHPTT/ebzKDGq4mcsLAStrAxfv4jwZy/OR7+CcvE9jQvx91RYJJYWinSPn/Nnaul6N3fr9u3bvAzMPDMyMzPJwQEHbD+J3gVJeXk53blzhywtLSk3N5ccHR0pMzNTtnWAqXlycnL+tZ+/JEmUm5tL9vb2ZGj4x+tXerefxNDQsCKyDQwef235taGSqR3+rZ+/SoUDL6qCW+UZRgYOEoaRQa+DRKlU0tSpU6usyDNPH/78H6N3iTvD6Bt6fSdhGH2Ag4RhZOAgYRgZOEgYRgYOEoaRQW+DJDo6mpydncnU1JTat29PJ0/i5iDm7xMZGUkeHh5kaWlJDRo0ID8/P0pPF89M/K+PitLLINm6dSuFhYXR1KlT6cyZM+Tm5kY+Pj5079692r60fx2JiYkUHBxMKSkpdPDgQSopKaFu3bpRfn5lV/TYsWNpz549tH37dkpMTKQ7d+6Qv79/LV71M0bSQzw9PaXg4OAKu6ysTLK3t5ciIyNr8ar+G9y7d08iIikxMVGSJEnKzs6WTExMpO3bt1f4XL58WSIiKTk5ubYu85mid3eS4uJiSk1NFUYTGRoakre39x+OJmJqBq328fHRNjaPj4L+q6Oi/k3oXZDcv3+fysrKyNbWVtDlRhMxf5/y8nIKDQ2lDh06kKvr42EQf3VU1L8JvWuVZ2qP4OBgunjxIh09iqNh/8vo3Z2kXr16ZGRkBKsncqOJmL9HSEgI7d27lw4dOiTs1LOzs6sYFfUk/6Xfh94FiUKhIHd3d2E0UXl5OcXHx/NooqeAJEkUEhJCO3fupISEBHJxcRH+nUdFkX6ubm3ZskVSKpXS2rVrpbS0NGnYsGGStbW1lJWVVduX9q8jKChIUqlU0uHDh6W7d+9WPAoKCip8RowYITk5OUkJCQnS6dOnJbVaLanV6lq86meLXgaJJEnSkiVLJCcnJ0mhUEienp5SSkpKbV/SvxIiqvIRGxtb4VNYWCiNHDlSeu6556Q6depIvXr1ku7evVt7F/2M4f0kDCOD3uUkDKNvcJAwjAwcJAwjAwcJw8jAQcIwMnCQMIwMHCQMIwMHCcPIwEHCMDJwkDCMDBwkDCPD/wGhkMv3BcoEoQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Get back the image from the noise again\n",
    "with torch.no_grad():\n",
    "    img = torch.randn((1, 3) + image_shape).to(device) #start with a noise(same as the image size with randn)\n",
    "    for i in reversed(range(diffusion_model.timesteps)): #for the reverse time step T->0\n",
    "        t = torch.full((1,), i, dtype=torch.long, device=device)\n",
    "        img = diffusion_model.backward(img, t, unet.eval())# do the backward\n",
    "        if i % 50 == 0: #400/50=8 images\n",
    "            plt.figure(figsize=(2,2))\n",
    "            plt.imshow(reverse_transform(img[0]))\n",
    "            plt.show()"
   ]
  }
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