{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "collapsed_sections": [
        "ePHkrDq0hegj",
        "pgdmHMMChlqt",
        "sCIrDkAHjlPW",
        "hOXHIyMhnsmY"
      ]
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "QU-hHve9dWV0"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Data\n",
        "np.random.seed(0)\n",
        "true_mu = 2.0\n",
        "sigma = 1.0\n",
        "data = np.random.normal(true_mu, sigma, size=20)"
      ],
      "metadata": {
        "id": "Tv1Gf2mAddRK"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 1--Analytical posterior"
      ],
      "metadata": {
        "id": "ePHkrDq0hegj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Prior\n",
        "mu0 = 0.0\n",
        "tau = 1.0\n",
        "\n",
        "# Posterior (analytic)\n",
        "n = len(data)\n",
        "sigma2 = sigma**2\n",
        "tau2 = tau**2\n",
        "post_var = 1 / (n/sigma2 + 1/tau2)\n",
        "post_mean = post_var * (np.sum(data)/sigma2 + mu0/tau2)"
      ],
      "metadata": {
        "id": "2KH7R0z5dgHP"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Grid for plotting\n",
        "mu_grid = np.linspace(-1, 4, 500)\n",
        "\n",
        "prior = norm.pdf(mu_grid, mu0, tau)\n",
        "likelihood = np.exp(-0.5 * np.sum((data[:, None] - mu_grid)**2, axis=0) / sigma2)\n",
        "likelihood /= likelihood.max()  # normalize for visualization\n",
        "posterior = norm.pdf(mu_grid, post_mean, np.sqrt(post_var))\n",
        "\n",
        "# Plot\n",
        "plt.plot(mu_grid, prior, label=\"Prior\")\n",
        "plt.plot(mu_grid, likelihood, label=\"Likelihood (scaled)\")\n",
        "plt.plot(mu_grid, posterior, label=\"Posterior\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 391
        },
        "id": "fXBDhfGYdj4n",
        "outputId": "b695b8fa-3c36-4e05-ac3b-0a7c4487177c"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Posterior predictive\n",
        "def predictive_density(x_vals, mu_samples, sigma):\n",
        "    densities = []\n",
        "    for x in x_vals:\n",
        "        densities.append(np.mean(norm.pdf(x, mu_samples, sigma)))\n",
        "    return np.array(densities)\n",
        "\n",
        "posterior_samples = np.random.normal(post_mean, np.sqrt(post_var), size=1000)\n",
        "predictive_samples = np.random.normal(posterior_samples, sigma)\n",
        "\n",
        "x_grid = np.linspace(-1, 5, 300)\n",
        "\n",
        "plt.hist(predictive_samples, bins=30, density=True)\n",
        "plt.plot(x_grid, predictive_density(x_grid, posterior_samples, sigma), color=\"red\")\n",
        "plt.title(\"Posterior Predictive\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "jwEhRp5XdweM",
        "outputId": "2d667e65-9951-4b90-802e-1630be696621"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 2-- Metropolis-Hastings MCMC"
      ],
      "metadata": {
        "id": "pgdmHMMChlqt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Log posterior (unnormalized)\n",
        "def log_posterior(mu, data, sigma, mu0, tau):\n",
        "    log_likelihood = -0.5 * np.sum((data - mu)**2) / sigma**2\n",
        "    log_prior = -0.5 * (mu - mu0)**2 / tau**2\n",
        "    return log_likelihood + log_prior"
      ],
      "metadata": {
        "id": "rX1H0--Kd64r"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# MH sampler\n",
        "def metropolis_hastings(init, n_samples, proposal_std, data, sigma, mu0, tau):\n",
        "    samples = []\n",
        "    mu_current = init\n",
        "\n",
        "    for _ in range(n_samples):\n",
        "        mu_proposal = np.random.normal(mu_current, proposal_std)\n",
        "\n",
        "        log_alpha = (\n",
        "            log_posterior(mu_proposal, data, sigma, mu0, tau)\n",
        "            - log_posterior(mu_current, data, sigma, mu0, tau)\n",
        "        )\n",
        "\n",
        "        if np.log(np.random.rand()) < log_alpha:\n",
        "            mu_current = mu_proposal\n",
        "\n",
        "        samples.append(mu_current)\n",
        "\n",
        "    return np.array(samples)"
      ],
      "metadata": {
        "id": "ZhcjWg-Lh0by"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Run sampler\n",
        "samples = metropolis_hastings(\n",
        "    init=0.0,\n",
        "    n_samples=5000,\n",
        "    proposal_std=0.5,\n",
        "    data=data,\n",
        "    sigma=sigma,\n",
        "    mu0=mu0,\n",
        "    tau=tau\n",
        ")"
      ],
      "metadata": {
        "id": "zv7j-nkEiAcI"
      },
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# ---- Plot ----\n",
        "plt.hist(samples[1000:], bins=40, density=True, alpha=0.5, label=\"MH samples\")\n",
        "\n",
        "# True posterior for comparison\n",
        "from scipy.stats import norm\n",
        "x = np.linspace(-1, 4, 300)\n",
        "true_post = norm.pdf(x, post_mean, np.sqrt(post_var))\n",
        "plt.plot(x, true_post, label=\"True posterior\")\n",
        "\n",
        "plt.legend()\n",
        "plt.title(\"Metropolis-Hastings vs True Posterior\")\n",
        "plt.xlim(1,4)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 403
        },
        "id": "6N8lm6RviD9j",
        "outputId": "bfb13168-5715-4469-8b7d-8366b06a042b"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "burn_in = 1000\n",
        "\n",
        "plt.figure(figsize=(8, 4))\n",
        "plt.plot(samples, linewidth=0.8, label=\"Chain\")\n",
        "plt.axvline(burn_in, linestyle=\"--\", label=\"Burn-in\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"mu\")\n",
        "plt.title(\"MCMC Trace Plot with Burn-in\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "lPtwTYz5iGnF",
        "outputId": "e3818bbc-2140-4a48-bb6f-2d4cea09f8b9"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 3-- Variational Inference (ELBO)"
      ],
      "metadata": {
        "id": "sCIrDkAHjlPW"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Variational parameters (initialize)\n",
        "m = 0.0\n",
        "log_s = 0.0  # we optimize log std for stability"
      ],
      "metadata": {
        "id": "-RUmBbpai_PH"
      },
      "execution_count": 70,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "lr = 0.01\n",
        "n_steps = 5000"
      ],
      "metadata": {
        "id": "Lsk2gN-Hjqsl"
      },
      "execution_count": 71,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "elbo_history = []\n",
        "m_trace = []"
      ],
      "metadata": {
        "id": "SM7S4nFLkeyQ"
      },
      "execution_count": 72,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "for step in range(n_steps):\n",
        "    # Sample from q using reparameterization\n",
        "    eps = np.random.randn(1000) # this number of samples is important!!\n",
        "    s = np.exp(log_s)\n",
        "    mu_samples = m + s * eps\n",
        "\n",
        "    # Compute log terms\n",
        "    log_likelihood = -0.5 * np.sum((data - mu_samples[:, None])**2, axis=1) / sigma**2\n",
        "    log_prior = -0.5 * (mu_samples - mu0)**2 / tau**2\n",
        "    log_q = -0.5 * ((mu_samples - m)**2) / s**2 - np.log(s)\n",
        "\n",
        "    elbo = np.mean(log_likelihood + log_prior - log_q)\n",
        "    elbo_history.append(elbo)\n",
        "\n",
        "    # Gradients (manual, simple version)\n",
        "    grad_m = np.mean((mu_samples - m)/s**2 * (log_likelihood + log_prior - log_q))\n",
        "    grad_log_s = np.mean(((mu_samples - m)**2 / s**2 - 1) * (log_likelihood + log_prior - log_q))\n",
        "\n",
        "    # Update\n",
        "    m += lr * grad_m\n",
        "    log_s += lr * grad_log_s\n",
        "\n",
        "    m_trace.append(m)\n"
      ],
      "metadata": {
        "id": "yGJgbMSjkhAs"
      },
      "execution_count": 73,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# ---- Plot ELBO ----\n",
        "plt.plot(elbo_history)\n",
        "plt.title(\"ELBO during optimization\")\n",
        "plt.xlabel(\"Step\")\n",
        "plt.ylabel(\"ELBO\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 416
        },
        "id": "p_0H4hn5ks6q",
        "outputId": "7f6d2681-59f5-4121-c863-6527fc668659"
      },
      "execution_count": 74,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# ---- Compare distributions ----\n",
        "from scipy.stats import norm\n",
        "\n",
        "x = np.linspace(-1, 4, 300)\n",
        "\n",
        "vi_dist = norm.pdf(x, m, np.exp(log_s))\n",
        "true_post = norm.pdf(x, post_mean, np.sqrt(post_var))\n",
        "\n",
        "plt.plot(x, vi_dist, label=\"Variational\")\n",
        "plt.plot(x, true_post, label=\"True posterior\")\n",
        "plt.legend()\n",
        "plt.title(\"VI vs True Posterior\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 411
        },
        "id": "GOg_aMdokvq1",
        "outputId": "0f4b4ba7-d0d8-4e0f-d581-4758f8fda0cb"
      },
      "execution_count": 75,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(m_trace)\n",
        "plt.axhline(post_mean, linestyle=\"--\", label=\"True posterior mean\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Variational mean (m)\")\n",
        "plt.title(\"VI mean convergence\")\n",
        "plt.legend()\n",
        "plt.ylim(2,3)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 492
        },
        "id": "RYFnWVCpk7kq",
        "outputId": "40857b9c-9d16-49d9-c75a-403184992fde"
      },
      "execution_count": 76,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 4-- SBI (NPE)"
      ],
      "metadata": {
        "id": "hOXHIyMhnsmY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.optim as optim"
      ],
      "metadata": {
        "id": "ibg3N-9u34-O"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# ---- simulator ----\n",
        "def simulator(mu, sigma=1.0):\n",
        "    return mu + np.random.randn(*mu.shape) * sigma"
      ],
      "metadata": {
        "id": "jVgXGnd44J-F"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# ---- generate dataset ----\n",
        "N = 50000\n",
        "mu_train = np.random.normal(0, 2, size=(N, 1))\n",
        "x_train = simulator(mu_train)"
      ],
      "metadata": {
        "id": "nEUNrCn_4XXd"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# ---- transform to torch objects ---\n",
        "mu_train = torch.tensor(mu_train, dtype=torch.float32)\n",
        "x_train = torch.tensor(x_train, dtype=torch.float32)"
      ],
      "metadata": {
        "id": "XLo7ERYI4qc1"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# ---- network: x -> (mean, log_var of posterior over mu)\n",
        "class NPE(nn.Module):\n",
        "    def __init__(self):\n",
        "        super().__init__()\n",
        "        self.net = nn.Sequential(\n",
        "            nn.Linear(1, 64),\n",
        "            nn.ReLU(),\n",
        "            nn.Linear(64, 64),\n",
        "            nn.ReLU(),\n",
        "        )\n",
        "        self.mean_head = nn.Linear(64, 1)\n",
        "        self.logvar_head = nn.Linear(64, 1)\n",
        "\n",
        "    def forward(self, x):\n",
        "        h = self.net(x)\n",
        "        return self.mean_head(h), self.logvar_head(h)"
      ],
      "metadata": {
        "id": "7WlYTYoN42_Z"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# ---- initialization of the network ----\n",
        "model = NPE()\n",
        "opt = optim.Adam(model.parameters(), lr=1e-3)"
      ],
      "metadata": {
        "id": "KYJjBAsZ5Xeq"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# ---- training ----\n",
        "for step in range(5000):\n",
        "    idx = np.random.randint(0, N, size=128)\n",
        "\n",
        "    x_batch = x_train[idx]\n",
        "    mu_batch = mu_train[idx]\n",
        "\n",
        "    pred_mean, pred_logvar = model(x_batch)\n",
        "\n",
        "    loss = 0.5 * (\n",
        "        pred_logvar +\n",
        "        (mu_batch - pred_mean)**2 / torch.exp(pred_logvar)\n",
        "    ).mean()\n",
        "\n",
        "    opt.zero_grad()\n",
        "    loss.backward()\n",
        "    opt.step()"
      ],
      "metadata": {
        "id": "-2u4s6_p5oSZ"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# ---- posterior prediction ----\n",
        "x_test = torch.tensor([[1.0]])\n",
        "mean, logvar = model(x_test)\n",
        "\n",
        "print(\"posterior mean:\", mean.item())\n",
        "print(\"posterior std:\", torch.exp(0.5 * logvar).item())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c03F2LaM65V8",
        "outputId": "46d941d9-955a-4d5e-f7fa-5ab930acdde8"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "posterior mean: 0.7606245279312134\n",
            "posterior std: 0.879869282245636\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# ---- choose one observed dataset ----\n",
        "true_mu = 1.5\n",
        "x_obs = true_mu + np.random.randn(1, 1)  # simulator observation\n",
        "x_obs_t = torch.tensor(x_obs, dtype=torch.float32)"
      ],
      "metadata": {
        "id": "EjNWfcCf7dkX"
      },
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# ---- get predicted posterior parameters ----\n",
        "with torch.no_grad():\n",
        "    mean, logvar = model(x_obs_t)\n",
        "\n",
        "mean = mean.item()\n",
        "std = np.exp(0.5 * logvar.item())\n",
        "print(\"predicted posterior mean:\", mean)\n",
        "print(\"predicted posterior std:\", std)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oxV_KfsC7mD3",
        "outputId": "dc42c3bb-a997-496f-8b48-33835a9060c4"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "predicted posterior mean: 1.5145552158355713\n",
            "predicted posterior std: 0.8663194316080745\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# ---- sample from learned posterior ----\n",
        "posterior_samples = np.random.normal(mean, std, size=5000)"
      ],
      "metadata": {
        "id": "VE-b05_f90qv"
      },
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# ---- \"corner plot\" style visualization (1D case) ----\n",
        "plt.figure(figsize=(7, 4))\n",
        "plt.hist(posterior_samples, bins=40, density=True, alpha=0.6, label=\"NPE posterior\")\n",
        "\n",
        "# true parameter\n",
        "plt.axvline(true_mu, color=\"red\", linestyle=\"--\", label=\"True parameter\")\n",
        "\n",
        "# learned mean\n",
        "plt.axvline(mean, color=\"black\", linestyle=\"-\", label=\"Posterior mean\")\n",
        "\n",
        "plt.title(\"Neural Posterior Estimation (NPE)\")\n",
        "plt.xlabel(\"mu\")\n",
        "plt.ylabel(\"density\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 340
        },
        "id": "Vlnw7IliCZBl",
        "outputId": "a64675d0-c3d4-4b6e-b8f2-9b5b3ddab5e1"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 700x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import torch\n",
        "\n",
        "# ---- choose one observed dataset ----\n",
        "true_mu = 1.5\n",
        "x_obs = true_mu + np.random.randn(1, 1)  # simulator observation\n",
        "\n",
        "x_obs_t = torch.tensor(x_obs, dtype=torch.float32)\n",
        "\n",
        "# ---- get predicted posterior parameters ----\n",
        "with torch.no_grad():\n",
        "    mean, logvar = model(x_obs_t)\n",
        "\n",
        "mean = mean.item()\n",
        "std = np.exp(0.5 * logvar.item())\n",
        "\n",
        "# ---- sample from learned posterior ----\n",
        "posterior_samples = np.random.normal(mean, std, size=5000)\n",
        "\n",
        "# ---- \"corner plot\" style visualization (1D case) ----\n",
        "plt.figure(figsize=(7, 4))\n",
        "plt.hist(posterior_samples, bins=40, density=True, alpha=0.6, label=\"NPE posterior\")\n",
        "\n",
        "# true parameter\n",
        "plt.axvline(true_mu, color=\"red\", linestyle=\"--\", label=\"True parameter\")\n",
        "\n",
        "# learned mean\n",
        "plt.axvline(mean, color=\"black\", linestyle=\"-\", label=\"Posterior mean\")\n",
        "\n",
        "plt.title(\"Neural Posterior Estimation (NPE)\")\n",
        "plt.xlabel(\"mu\")\n",
        "plt.ylabel(\"density\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 340
        },
        "id": "6wlYUFV2nwfs",
        "outputId": "43647beb-7222-40fd-b091-2ded189afc24"
      },
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 700x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# --- coverage plot ----\n",
        "M = 50\n",
        "n_samples = 2000\n",
        "\n",
        "alphas = np.linspace(0.05, 0.95, 19)\n",
        "coverage = []\n",
        "\n",
        "for alpha in alphas:\n",
        "    count = 0\n",
        "\n",
        "    for _ in range(M):\n",
        "        # ---- sample true parameter ----\n",
        "        mu_true = np.random.normal(0, 1)\n",
        "\n",
        "        # ---- simulate observation ----\n",
        "        x_obs = simulator(np.array([mu_true]))[0]\n",
        "        x_obs_t = torch.tensor([[x_obs]], dtype=torch.float32)\n",
        "\n",
        "        # ---- posterior from NPE ----\n",
        "        with torch.no_grad():\n",
        "            mean, logvar = model(x_obs_t)\n",
        "\n",
        "        mean = mean.item()\n",
        "        std = np.exp(0.5 * logvar.item())\n",
        "\n",
        "        # ---- sample posterior ----\n",
        "        posterior_samples = np.random.normal(mean, std, size=n_samples)\n",
        "\n",
        "        # ---- compute credible interval ----\n",
        "        lower = np.percentile(posterior_samples, (1 - alpha) / 2 * 100)\n",
        "        upper = np.percentile(posterior_samples, (1 + alpha) / 2 * 100)\n",
        "\n",
        "        # ---- check coverage ----\n",
        "        if lower <= mu_true <= upper:\n",
        "            count += 1\n",
        "\n",
        "    coverage.append(count / M)"
      ],
      "metadata": {
        "id": "8PEKZj4pGvaL"
      },
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "coverage = np.array(coverage)\n",
        "\n",
        "# Standard error (binomial)\n",
        "stderr = np.sqrt(coverage * (1 - coverage) / M)\n",
        "\n",
        "# Confidence band (±1σ; you can also use 2*stderr for ~95%)\n",
        "lower = coverage - stderr\n",
        "upper = coverage + stderr\n",
        "\n",
        "plt.figure(figsize=(6, 6))\n",
        "\n",
        "# Uncertainty band\n",
        "plt.fill_between(alphas, lower, upper, alpha=0.3, label=\"Uncertainty (±1σ)\")\n",
        "\n",
        "# Estimated coverage line\n",
        "plt.plot(alphas, coverage, marker='o', label=\"Estimated coverage\")\n",
        "\n",
        "# Ideal diagonal\n",
        "plt.plot([0, 1], [0, 1], linestyle=\"--\", label=\"Ideal (y = x)\")\n",
        "\n",
        "plt.xlabel(\"Nominal coverage\")\n",
        "plt.ylabel(\"Empirical coverage\")\n",
        "plt.title(\"Coverage Plot\")\n",
        "\n",
        "plt.xlim(0, 1)\n",
        "plt.ylim(0, 1)\n",
        "plt.grid(alpha=0.3)\n",
        "\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        },
        "id": "lTq2vWS2IqWl",
        "outputId": "220196fb-4bef-4ba6-cdb7-f25babd2703b"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x600 with 1 Axes>"
            ],
            "image/png": 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esXU3KsmGJRdA5VGI7wMzv2ixQAQkGHFjtVpRFIW0tDRCQkJauzsdhgQjLc/TZx4fH8/Bgwex2WwSjAjRTu06WulRu8JKc91v2K3wziXHApG+xwKReB/2sHGde5KtHp197lF0HhIcCtG+ORQVh4epnwnhQXW/ERAI5z8Hyacdm5pp2UAEZGRECCGEaLeOlNfQIzaU6BC92yqak2mApMggTu8e4/6GqsLxX0h6TYKMc6GVfhmXIQAhhBCiHVJVldzSarRaDVeO6Fpnm+Njn49M6eeevFq4G147y7mM97hWnBWQkREPfb+zoPFGPjSxX2LjjTqJ9PR0br/99gZ3Z/anN954gw8//JBvv/22Ve4PsGLFCu699142bdok04hCCAAKKizUWJ0lKIZ1iyYtOphDZTVubZLqqjNSuBveuhCqimDFfXD1hy3Z7TrJp1oHMWHChDp/WC9ZsqTN7MGj1Wr53//+5/V5GzZs4IYbbvC4/erVq9FoNJSXl3t9r1OZzWYeeughHnnkkSZf49VXX2XChAlEREQ0uV+TJ09Gr9fz3nvvNbkfQoiO5WBJlevvxhobh8udgch1Y9JZcMVpfDDnDNbec7Z7IFKw07lqpqoIkgbC1IUt3e06STAi/M5qrX/JmSfi4+NbbXXTxx9/TEREBGPGjKm3zaxZs3j00Ufrfb+6uprJkydz//33N6svs2bN4sUXX2zWNYQQHUOxyYLJbHe93nCwFFWFHnGhjOoZx0WDUxjVM9Z9aqZgp7OgWXUxJA2CGcsgJKaOq7c8CUY6mVmzZjF16lSef/55kpOTiY2N5ZZbbsFmO5H4ZLFYuOeee0hLS8NgMJCRkcEbb7zhen/79u386U9/IiwsjMTERKZPn05xcbHr/QkTJnDrrbdy++23ExcXx+TJk8nMzATgkksuQaPRkJ6eDkB2djYXX3wxiYmJhIWFMWLECL7//nu3Pqenp7NgwQLXa41Gw+uvv84ll1xCSEgImZmZLFu2DICDBw+6thiIjo5Go9Ewa9Ys3n77bWJjY7FYLG7Xnjp1KtOnT6/3eS1dupQpU6Z48YRru/3227n33ns544wz6m3z7bffMmzYMAwGAxqNxu3PcVOmTOH3338nOzu7Wf0RQrR/OSeNigD8ur8EgDN61FNHpGCHc2qmuhiSB8OMz9tMIAISjHRKq1atIjs7m1WrVvHWW2+xZMkSlixZ4np/xowZfPDBB7z44ovs2rWLV155xVWhs7y8nLPPPpshQ4bw+++/s2LFCgoKCrj88svd7vHWW28RGBjIunXrWLhwIT///DMAixcv5ujRo2zYsAFwbpZ4/vnns3LlSv744w8mT57MlClT3PYkqstjjz3G5ZdfztatWzn//PO55pprKC0tJS0tjU8++QSAPXv2cPToUV544QUuu+wyHA6HK2gBKCwsZPny5Vx77bX13mft2rUMHz7c84fbBCUlJVx22WX06tWLTZs2sXr1ajIzMxk4cCDvvPOOq13Xrl1JTEzkp59+8mt/hBBtm7HaRlnViV8gjxprOFhSjVYDI9Kj6z7pmwegusS5fLeNBSIgCaydUnR0NP/5z3/Q6XT06dOHCy64gJUrVzJnzhyysrL46KOP+O6775g4cSIAPXr0cJ37n//8hyFDhvDUU0+5jr355pukpaWRlZVFr169AMjMzOTZZ58FThTgAoiKiiIpKcl17uDBgxk8eLDr9RNPPMFnn33GsmXLuPXWW+v9GmbNmsVVV10FwFNPPcWLL77I+vXrmTx5MjExzv9kCQkJbvkyV199NYsXL+ayyy4D4N1336Vr165MmDChznuUl5djNBpJSUlxO/7ee+/xl7/8xfXaYrGg0Wh4/vnnXce+/vprxo4dW2//T/b+++8TEBDAG2+84ZqOeuGFF7jooos477zz3NqmpKSQk5Pj0XWFEB3TwVNGRX7bXwrAgJRIwoP0BAZo0Z5a9v3Pb8K3D8GkJyE4qoV66jkJRjqh/v37u1XbTE5OZtu2bQBs3rwZnU7H+PHj6zx3y5YtrFq1qs69TLKzs13ByLBhwzzqi8lk4tFHH2X58uUcPXoUu91OTU1NoyMjgwYNcv09NDSUiIgICgsLGzxnzpw5jBgxgry8PFJTU1myZAmzZs2qt/BXTY0zGSwoyL1Q0EUXXcTIkSNdr++55x5SU1O57bbbXMdSU1Mb7MvJ9u3bx2mnneaWFzNmzBjsdju7du0iIeFESebg4GDZN0mITqzKYqeo8sR0s6qq/HrAfYomNizQ+WZ16YkRkJAYmPpSi/bVGxKMdBAREREYjcZax8vLy4mMjHQ7ptfr3V5rNBoURQGcP+waYjKZmDJlCs8880yt95KTT2Rsh4aGetTvefPm8d133/H888+TkZFBcHAwf/7znxtNem3oa6jPkCFDGDx4MG+//TbnnXceO3bsYPny5fW2j42NRaPRUFZW5nY8PDyc8PBwt9cxMTFkZGQ0eP/66PX6WjtEH399aon20tJS4uNbvjqiEKJtOHVUZF+RiWKTFUOAlsFpzs/6+DADHNkM70yFsx6A0+e0fEe9JDkjHUTv3r3ZtGlTreObNm1yjVZ4YuDAgSiKwpo1a+p8f+jQoezYsYP09HQyMjLc/jQWgNT1Q3fdunXMmjWLSy65hIEDB5KUlMTBgwc97m9dAgOdvxWcei+A66+/niVLlrB48WImTpxIWlpag9fp168fO3fWvRumr/Tv358tW7ZQVXXiQ2bdunVotVq3fzuz2Ux2djZDhgzxa3+EEG2T2eagoMJ9f5lfj03RDOsWjSFAh1YLMRW74O2LoaYMtn4IDntdl2tTJBjpIG666SaysrK47bbb2Lp1K3v27GH+/Pl88MEH3HnnnR5fJz09nZkzZ3Lttdfyv//9jwMHDrB69Wo++ugjAG655RZKS0u56qqr2LBhA9nZ2XzzzTfMnj27zh/+p1575cqV5Ofnu0YbMjMz+fTTT9m8eTNbtmzh6quvbnSEozHdunVDo9Hw5ZdfUlRUhMlkcr139dVXc/jwYV577bUGE1ePmzRpEmvXrnU7VlNTQ35+vuvPP/7xD2688Ua3YyeP7OTn57N582b27dsHwLZt29i8eTOlpc4Pkauuuorw8HBmzpzJ9u3bWbVqFbfddhuzZs1ym6L59ddfMRgMjBo1qlnPRwjRPh0qrebkj0e7Q2HDQefnyBndnVM0yVV7CHj3YjCXQ5cRMO1T0LX9SZC238M2oq1XRO3Rowc//vgjDzzwABMnTsRqtdKnTx/++9//MnnyZK+utXDhQu6//35uvvlmSkpK6Nq1q6tGRkpKCuvWreOee+7hvPPOw2Kx0K1bNyZPntxoZdDnn3+eO++8k9dee43U1FQOHjzI/Pnzufbaaxk9ejRxcXHcc889VFRUNPk5gDNf47HHHuPee+9l9uzZzJgxw7VaKDIykv/7v/9j+fLlTJ06tdFrXXfddQwfPhyj0eia7vrwww+ZPXt2g+etWrXKlRi7aNEiHnvsMdd748aNA5wri2bNmkVQUBArVqzgr3/9KyNGjCAkJIQ///nPzJ8/3+2aH3zwAddcc43sKC1EJ2RzKK6iZsdtyzNSbXUQGaynT1I4EaVb6f3TdWAxQpfTYdonEBTRSj32jkZVPdzur4OoqKggMjKSsrKyWpVJzWYzBw4coHv37rWSFkXTebqdfUs555xz6N+/v8cFxC677DKGDh3Kfffd5+ee1a+4uJjevXvz+++/071790bbe/rM5XvedxRFobCwkISEBCnZ30I60zM/UFxFdqHJ7djCNdlszCnjvH6JXN+9lCE/XoveVglpZ8C0j8EQXs/Vmq68vJzo6GiMRiMREb4LdDr2v54QJykrK+Ozzz5j9erV3HLLLR6f99xzz9W5eqglHTx4kJdfftmjQEQI0bEoisqhUvdVdNVWO1sOlQPOVTTRReudgUjXUX4LRPxJpmlEpzFkyBDKysp45pln6N27t8fnpaen89e//tWPPWvc8OHD/V58TQjRNuWV12C1u+fSbcwpw66opEQFkRYdTE7MHMJikkgedUW7C0RAghHRiTR3lY4QQrQ0VVXJLa1dW+jX/aX00xxkULchrqnYwOHTwWBo6S76hAQjQgghRBtVUGGhxuq+UrHEZCG0cCNvBT5DTVE/ttvfQBMYSnRIYCv1svkkGBFCCCHaqFOLnAEU7lzD24H/IExjxnZs2W5MaGDtEvDtiAQjQgghRBtUYrJgMrsXLIss2sC1B+cRqjGzP2wYB8e+ihIQfKIEfDslwYgQQgjRBp06KhJVtIHBP16PHjPrlAGUT3gVQ4BzC4+4sPaZK3KcLO0VQggh2hhjjY2yKpvrdVTRBk77aQ56Rw0/OQbwn8QnMIQ4V82EBQUQpNfVd6l2QYIRIYQQoo3JOWVUxB4QiqIN5BcGcb1tHkN7prjea++jIiDBiN84FJVfskv4fHMev2SX4FDaX6HbJUuW1KpS29a1xz4LIcTJqix2iiotbsdM0f34aODrzDLPRRcYzIDUE7uxx7XzfBGQYMQvVmw/ypnP/MBVr/3K35Zu5qrXfuXMZ35gxfajfrvnrFmz0Gg0tf54ui9Neno6CxYscDt2xRVXkJWV5YfeupMAQgghTsgpqUZVIbrwVyKLfncd/yo/HAuBjEiPQa9z/vgO0GmIDNa3Vld9RhJYfWzF9qPc9O4mTh0HyTeauendTSycNpTJA5L9cu/JkyezePFit2OGZhTACQ4OJjg4uLndEo1QVRWHw0FAgPx3FKKzM9sc5FfUEF3wM6etvRFVo+P3sz+gJCyTTbnO3c7P6B7jah8XZmgTe341l4yMNEJVVaqtdo/+VJptPLJsR61ABHAde3TZTirNNo+u5+0ehgaDgaSkJLc/0dHRrq/j0UcfpWvXrhgMBlJSUrjtttsAmDBhAjk5Odxxxx2uERWoPWLx6KOPctppp/Hmm2/StWtXwsLCuPnmm3E4HDz77LMkJSWRkJDAk08+6dav+fPnM2TIEMLCwkhLS+Pmm2/GZHJu+LR69Wpmz56N0Wh03fvRRx8FwGKxMG/ePFJTUwkNDWXkyJGsXr3a7dpLliyha9euhISEcMkll1BSUtLoczp8+DBXXXUVMTExhIaGMnz4cH777TfX+wsXLqRnz54EBgbSu3dv3nnnHdd7V199NVdccYXb9Ww2G3Fxcbz99tuAc/Oup59+mu7duxMcHMzgwYP5+OOPXe1Xr16NRqPh66+/ZtiwYRgMBtauXUt2djYXX3wxiYmJhIWFMWLECL7//nu3ex09epQLLriA4OBgunfvzvvvv19rVKu8vJzrr7+elJQUIiMjOfvss9myZUujz0UI0foOlVYTdXQdp639CzqHmbL4EVSF92DLISNmm0JcWCA9E07sldUR8kVARkYaVWNz0O/hb3xyLRXIrzAz8NFvPWq/8/FJhAT65p/ok08+4V//+hdLly6lf//+5Ofnu35AffrppwwePJgbbriBOXPmNHid7Oxsvv76a1asWEF2djZ//vOf2b9/P7169WLNmjX8/PPPXHvttUycOJGRI0cCoNVq+de//kVGRgYHDhzg5ptv5u677+bll19m9OjRLFiwgIcffpg9e/YAuDalu/XWW9m5cydLly4lJSWFzz77jMmTJ7Nt2zYyMzP57bffuO6663j66aeZOnUqK1as4JFHHmmw/yaTifHjx5OamsqyZctISkpi06ZNKIpz34fPPvuMv/3tbyxYsICJEyfy5ZdfMnv2bLp06cJZZ53FNddcw2WXXYbJZHL185tvvqG6uppLLrkEgKeffpp3332XRYsWkZmZyY8//si0adOIj49n/Pjxrr7ce++9PP/88/To0YPo6GgOHTrE+eefz5NPPonBYODtt99mypQp7Nmzh65duwIwY8YMiouLWb16NXq9nrlz51JYWOj2NV522WUEBwfzxRdfEBMTw6uvvso555xDVlYWMTExCCHaJptDoWrXdwxeeyM6h4Wi5LPYOvrfqLpAfj3g/EVrZPdYtMd+YdRoaPf1RY6TYKQD+fLLL2vtLnv//fdz//33k5ubS1JSEhMnTkSv19O1a1dOP/10AGJiYtDpdISHh5OUlNTgPRRF4c033yQ8PJx+/fpx1llnsWfPHr766iu0Wi29e/fmmWeeYdWqVa5g5Pbbb3dtZ9+9e3f+/ve/c+ONN/Lyyy8TGBhIZGQkGo3G7d65ubksXryY3NxcUlKcWePz5s1jxYoVLF68mKeeeooXXniByZMnc/fddwPQq1cvfv75Z1asWFFv/99//32KiorYsGGD6wdzRkaG6/3nn3+eWbNmcfPNNwMwd+5cfv31V55//nnOOussJk2aRGhoKJ999hnTp093XfOiiy4iPDwci8XCU089xffff8+oUaMA6NGjB2vXruWVV15xC0Yef/xxzj33XNfrmJgYBg8e7Hr9xBNP8Nlnn7Fs2TJuvfVWdu/ezffff8+GDRtcm+a9/vrrZGZmus5Zu3Yt69evp6CgAJ1OR0BAAM8//zz/+9//+Pjjj7nhhhsa/PcVQrSeki1fM/DHv6BTrBSlnM3WUS+i6gKpNNvYkVcBwMiTpmgig/Wu3JH2ToKRRgTrdex8fJJHbdcfKGXW4g2NtlsyewSnd2/8N9RgL9eNn3XWWSxcuNDt2PEfuJdddhkLFiygR48eTJ48mfPPP58pU6Z4naeQnp5OePiJHSETExPR6XRotVq3Yyf/tv7999/z9NNPs2fPHioqKrDb7ZjNZqqrqwkJCanzPtu2bcPhcNCrVy+34xaLhdjYWAB27drlGo04btSoUQ0GI5s3b2bIkCH1jhDs2rWr1g/sMWPG8MILLwAQEBDA5Zdfznvvvcf06dOpqqri888/Z+nSpQDs27eP6upqtyADwGq1MmTIELdjp+7CazKZePTRR1m+fDlHjx7FbrdTU1NDbm4uAHv27CEgIIChQ4e6zsnIyHBNxQFs2bIFk8lEXFyc27VramrIzs6u97kIIVqXcuh3Er6chVaxUphyDttGvYCqc456bDhYhkNV6RYbQkrUiTy+2A4yRQMSjDRKo9F4PFUyNjOe5Mgg8o3mOvNGNEBSZBBjM+PR+WEPgdDQULff8k+WlpbGnj17+P777/nuu++4+eabee6551izZg16veeZ2Ke21Wg0dR47Pu1x8OBBpkyZwl/+8heefPJJYmNjWbt2Lddddx1Wq7XeYMRkMqHT6di4cSM6nXtQdurojzd8kZB7zTXXMH78eAoLC/nuu+8IDg52rVo6nguzfPlyUlNT3c47NZk4NDTU7fW8efP47rvveP7558nIyCA4OJg///nPWK1Wj/tmMplITk5m1apVrtGo4zlAsmJJCO+YbQ4MAdoWSRA9EtQTQ+JoVG0A285Y4ApEAH7d75yiOaN7rNs5HWFJ73ESjPiQTqvhkSn9uOndTWjALSA5/q38yJR+fglEPBEcHMyUKVOYMmUKt9xyC3369GHbtm0MHTqUwMBAHA5H4xfx0saNG1EUhWeffZbAwEA0Gg0fffSRW5u67j1kyBAcDgeFhYWMHTu2zmv37dvXLfEU4Ndff22wP4MGDeL111+ntLS0ztGRvn37sm7dOmbOnOk6tm7dOvr16+d6PXr0aNLS0vjwww/5+uuvueyyy1wBWb9+/TAYDOTm5rpNyXhi3bp1zJo1yzXaYzKZOHjwoOv93r17Y7fb+eOPPxg2bBjgHIkpKytztRk6dCj5+fkEBASQnp7uFowIITynKCq/HxuRSAg3kBgRRHSI3i//n1RVJdfooGb0f5yvTwpECirM7C+uQqPBbUTdoNcSHtT+l/QeJ8GIj00ekMzCaUN57IudHDWaXceTIoN4ZEo/vy3rBecURn5+vtuxgIAA4uLiWLJkCQ6Hg5EjRxISEsK7775LcHAw3bp1A5zTLz/++CNXXnklBoOh1jB/U2VkZGCz2XjppZe4+OKL+fnnn1m0aJFbm/T0dEwmEytXrmTw4MGEhITQq1cvrrnmGmbMmME///lPhgwZQlFREStXrmTQoEFccMEF3HbbbYwZM4bnn3+eiy++mG+++abBKRqAq666iqeeeoqpU6fy9NNPk5yczB9//EFKSgqjRo3irrvu4vLLL2fIkCFMnDiRL774gk8//bTWqparr76aRYsWkZWVxapVq1zHw8PDmTdvHnfccQeKonDmmWdiNBpZt24dERERbkHOqTIzM/n000+ZMmUKGo2Ghx56yDXCBNCnTx8mTpzIDTfcwMKFC9Hr9dx5550EBwe7PiAnTpzIqFGjuOSSS3jqqafo27cvR48eZfny5VxyySW1poaEEHXLKa3GbHP+kpRXVkNeWQ0GvZaE8CASIwxEhfhgVGLPCshZS+HIB6i2OkBX+5q/HSgFoF9yhFs9kY6yiua4jpH50sZMHpDM2nvO5oM5Z/DClafxwZwzWHvP2X4NRABWrFhBcnKy258zzzwTcA7Rv/baa4wZM4ZBgwbx/fff88UXX7jyLx5//HEOHjxIz549iY+P91mfBg8ezD//+U+ef/55Bg4cyHvvvcfTTz/t1mb06NHceOONXHHFFcTHx/Pss88CsHjxYmbMmMGdd95J7969mTp1Khs2bHCtLDnjjDN47bXXeOGFFxg8eDDffvstDz74YIP9CQwM5NtvvyUhIYHzzz+fgQMH8o9//MM1FTR16lReeOEFnn/+efr3788rr7zC4sWLmTBhgtt1rrnmGnbu3Elqaipjxoxxe++JJ57goYce4umnn6Zv375MnjyZ5cuX07179wb7Nn/+fKKjoxk9ejRTpkxh0qRJbvkhAG+//TaJiYmMGzeOSy65hDlz5hAeHk5QUBDgnCL76quvGDt2LHPmzKF3795ceeWV5OTkkJiY2OD9hRBOFruj1iZ1ABabwqHSan4/WMbavcXsLaikwmyr4woe2PM1fDgNfv43pvXv1tlEVdUTUzQ93KdoOsoqmuM0qrfFLNq5iooKIiMjKSsrqzWHbjabOXDgAN27d3d9uIvmU1W1Vv6C8I3Dhw+TlpbG999/zznnnOM67ukzl+9531EUhcLCQhISEtwSuoX/+OuZ7zxSwZHyGo/bhwTqSIgIIikyiDCDBxMOu5fDRzNBsWHpdRFrBz2Nqq095bK/yMRTX+8mMEDL/MsGuzbD02phfK+EVpnyLy8vJzo6GqPRSEREhM+uK9M0QrQjP/zwAyaTiYEDB3L06FHuvvtu0tPTGTduXGt3TYgOocJs46jR80AEoNrq4GBxFQeLqwg1BJAYYSApMqjuxQ+7voT/zgLFBv0vZfvwZ1FrlNrtgF/3O6dohqRFue3KGxUS2Gq5h/4iwYgQ7YjNZuP+++9n//79hIeHM3r0aN577z2vVkQJIeq3t6CS5swXVFns7C+ys7+oivCgABKPjZgE6XWw64tjgYgdBvwfxj+9RFlORZ3XsSsK6w86g5FRp0zRxHewfBGQYESIdmXSpElMmuRZ3RshhHcKK82UVTUxB6QOlWY7lWYT+wpNxFHK4E+uQ6PYYeBlMHUROUdN9Z6740gFJoud8KAA+ia7T4d0tORVkGBECCGEQFFU9hXUHxw0VzEx7Bj+JDEF6zg69GliyywUVVrqbX88cXVk9xi3KZkQg47gQO8KYrYHEowIIYTo9A6VVTuX1/qYRrG5klPzu11EfreLoEahrKb+wKfG6mDzoXKgrkJnHW9UBGRprxBCiE7Oalc4UFx7KW9zJRz6ipHfXkxgTYFX523KLcPmUEmKCKJbrHuVaglGhBBCiA5of7EJu8O3VS4Sc5cz4Nc7CavYR9q+970690RtkRi3pfk6nYao4I6ZrC7TNEIIITotk8VOXpl3S3kbk5j7JQN+m4dGVTiS/n9k97/N43PLqq3szq8EYOQpUzSxoYFoO9iS3uMkGBFCCNFpZTVzKe+pEnO+YMD6u9CoCnnd/8yu4X8HjeeTEOsPlKICGfFhxIe7T8l01CkakGmaTmXChAncfvvtrXLNs88+m/ff926osiUVFxeTkJDA4cOHW7srQogWUmyyUGryfFfsxiTlfH5SIHKZ14EIuE/RnKqjlYA/mQQjHcSsWbOYOnVqa3ejTsuWLaOgoIArr7yytbtSr7i4OGbMmMEjjzzS2l0RQrQAVVXJKqj02fU0Divddy5Eoyoc7nE5u4Y/4XUgcrismkNlNei0GoanuwcjEcF6DAEdb0nvcRKMCL/797//zcyZM9v8fh2zZ8/mvffeo7S0tLW7IoTws8NlNVRbfLeUV9UFsmn8Evb3u5Xdwx73OhCBE+XfB6VG1trjpiOPioAEI56zVtX/x2b2om2NZ22bqaqqihkzZhAWFkZycjL//Oc/a7WxWCzMmzeP1NRUQkNDGTlyJKtXr3a9X1JSwlVXXUVqaiohISEMHDiQDz74wKt+FBUV8cMPP3DBBRe4jl177bVceOGFbu1sNhsJCQm88cYb3n2hHrr22msZNGgQFouzyJDVamXIkCHMmDHD1aZ///6kpKTw2Wef+aUPQoi2weZQ2O+jpbxBVXmuv1tCktg/4LYmBSKKqvLbgbp36IWOnS8CksDquadS6n8v8zy45r8nXj+XAbbqutt2OxNmLz/xesFAqC6p3e5RY9P6ecxdd93FmjVr+Pzzz0lISOD+++9n06ZNnHbaaa42t956Kzt37mTp0qWuH8KTJ09m27ZtZGZmYjabGTZsGPfccw8REREsX76c6dOn07NnT04//XSP+rF27VpCQkLo27ev69j111/PuHHjOHr0KMnJyQB8+eWXVFdXc8UVV9R5ndzcXPr169fgve6//37uv//+Ot978cUXGTx4MPfeey//+te/eOCBBygvL+c///mPW7vTTz+dn376ieuuu86jr08I0f4cKK7CZq97c7rjFEUlq7ASY42NyGA9vRLCa61kST7wCX1/f4gdI5+loOuF9VzJM1kFlZRV2wjW6xjUJdLtvcAALZEddEnvcRKMdEAmk4k33niDd99917Wt/FtvvUWXLl1cbXJzc1m8eDG5ubmkpDgDrXnz5rFixQoWL17MU089RWpqKvPmzXOd89e//pVvvvmGjz76yONgJCcnh8TERLcpmtGjR9O7d2/eeecd7r77bgAWL17MZZddRlhYWJ3XSUlJYfPmzQ3eKyamdsLXcWFhYbz77ruMHz+e8PBwFixYwKpVq2ptgZ2SksIff/zh0dcmhGh/qq12DpfV88viMRtzyli6IZey6hP71ESH6LlyRFeGdYsGIGX/x/T9/QE0qESWbG52MHJ8imZ4t2j0OveRlY4+RQMSjHju/iP1v6c5Janorn0NtD1l+O72bU3vUz2ys7OxWq2MHDnSdSwmJobevXu7Xm/btg2Hw0GvXr3czrVYLMTGOocIHQ4HTz31FB999BF5eXlYrVYsFgshIe4VARtSU1NDUFBQrePXX389r776KnfffTcFBQV8/fXX/PDDD/VeJyAggIyMDI/vW5dRo0Yxb948nnjiCe655x7OPPPMWm2Cg4Oprm74g0oI0X7tLTChNDAosjGnjIVrsmsdL6u2sXBNNjeN78kUx3f0+/1BAHIzppN12gPN6pPNobAxpwzonFM0IMGI5wJDW7+tD5lMJnQ6HRs3bkSncw+mjo9OPPfcc7zwwgssWLCAgQMHEhoayu23347V6vlSuLi4OMrKymodnzFjBvfeey+//PILP//8M927d2fs2LH1Xqe50zQAiqKwbt06dDod+/bVHTCWlpYSHx/f4H2EEO1TaZW1wc3pFEVl6YbcBq9hXf8G/dRXAcjNnOEMRDTNK0S25XA5NTYHMSGBZCa6jw5rNBATKiMjoh3q2bMner2e3377ja5duwJQVlZGVlYW48ePB2DIkCE4HA4KCwvrDQLWrVvHxRdfzLRp0wDnD/OsrKxGg4KTDRkyhPz8fMrKytx+yMfGxjJ16lQWL17ML7/8wuzZsxu8TnOnacAZXO3evZs1a9YwadIkFi9eXOu+27dvZ8KECQ1eRwjR/niylDersNJtauZUV+tW8pDqTLLPzZxJ1mn3NzsQgRNTNCN7xKA95XpRIfpa0zYdkQQjHVBYWBjXXXcdd911F7GxsSQkJPDAAw+45W306tWLa665hhkzZvDPf/6TIUOGUFRUxMqVKxk0aBAXXHABmZmZfPzxx/z8889ER0czf/58CgoKvA5G4uLi+Pnnn7n44ovd3rv++uu58MILcTgczJw5s8HrNHea5o8//uDhhx/m448/ZsyYMcyfP5+//e1vjB8/nh49egBQXV3Nxo0beeqpp5p8HyFE23TEaMZktjfYxlhTfyACkKlxFkX8LfFKKn0UiJjMdrblORcsdNYpGpClvR3Wc889x9ixY5kyZQoTJ07kzDPPZNiwYW5tFi9ezIwZM7jzzjvp3bs3U6dOZcOGDa7RlAcffJChQ4cyadIkJkyYQFJSkteF1XQ6HbNmzapzSfDEiRNJTk5m0qRJriRafzCbzUybNo1Zs2YxZcoUAG644QbOOusspk+fjsPhrDXw+eef07Vr1wani4QQ7Y/doZBdaGq0XWMrVh6zz+AG6x28HT4Hm+KbGvK/55TiUFTSooNJjQqu9X5nCUY0qurLqvxtX0VFBZGRkZSVlREVFeX2ntls5sCBA3Tv3r3OpEvRNEePHmXAgAFs3LiR9PR013GTyURqaiqLFy/m0ksvbb0OHnPGGWdw2223cfXVV7d2V5pNVVXsdjsBAQFuu36eSr7nfUdRFAoLC0lISGjzBf46Ck+f+b7CSg4WN56Yrigq93y61W2q5hztRn5SBmHFPVAJMwQwqmcs4zLjSI6sHUR46h9f72ZfkYnLhnVhUv8kt/eCA3WMyYhr8rX9oby8nOjoaIxGY63ViM0h/2OE3yUlJfHKK6+Qm+tMDDv+AfLEE08QFRXFRRdd1Mo9dO5Nc+mll3LVVVe1dleEED5UY3WQW+rZCjmtVsM5fRJcr2fqvuGNwH/ykv4FdDhHUId3iyY6RI/JYue7nQU89PkOnlmxm1/2l2BtpHbJqYoqLewrMqEBRnbvXHvRnEpyRkSLuPjiiwkIcH675ebm0r17d7p06cKSJUtcx1tTXFycq+aJEKLj2FfY8FLeU2UVOKdzrtev4EHd2wDsVbsQEWzgytO7MaxbNIqisv2IkR+zitmaV87eQhN7C018EJjLqB6xjOsVX+eUy6mOV1ztkxxOVEjtwKOzTNGABCOiFaSnp9PJZgeFEK2gvNpKQYW58YbH7C82sTXPyHUBX/Og7h0A1iXPQMn4K88kRrgqsGq1GgZ1iWJQlyjKqq2s21fMT3uLKamysnJ3ISt3F9IzPpRxveIZ3i261gZ3iuJc2bNqTxEAp9cxKqLTaoipI0DpqCQYEUII0SEdH+Xw1LItR7hO9xUPBbwLwIG+N1Ez4Hb6NJB3FR0SyIWDUjh/QDI7j1bw494iNh8qJ7uoiuyiKpauP8QZPWIY1yuetOiQOqu7fv7HEUL0Aa7qrgDRoYG1ys93ZBKM1EF+axedhXyvi47qqLGGikaW6p4su8jE8PyPeEjvDET297uF/f1v83j5rlarYUBqJANSIymvtvJzdgk/7i2i2GRl1Z4iVu0pIjHcQEEdRdfKa05Udz0ekMR1onwRkGDEjV7vzJaurq4mOLjp2dFCtBfHq+meWoVXiPbMoajs82Ap78m+2HKEICUdsyaII32v8yoQOVVUSCDnD0xm8oAkdh+t5Me9RWzKLaszEDnZ0g25DEmLQqvVdKp8EZBgxI1OpyMqKorCwkIAQkJCGlwWKTzj6TJT4TuePHNFUSgqKiIkJKRNJBEL4SsHS6qw2DzPWs0uMrH9SAVaTR9WjP8fYQk9fNIPrUZDv5QI+qVEsCmnjJfr2PPmZGXVNrIKKxmeHkOQvnP9giCfQKdISnKu8z4ekIjmU1UVRVHQarUSjLQQT5+5Vqula9eu8u8iOgyzzUFuieebXaZlLeF/2UlAHKN7xhGWkO6Xftk8XNJjrLF1uikakGCkFo1GQ3JyMgkJCdhsns83ivopikJJSQmxsbFSDKqFePrMAwMD5d9EdCj7Ck04PKyOmr5zIRnb/8XjahjrNc9zwcCBfutXY9VdT27X2aZoQIKReul0OplH9xFFUdDr9QQFBckPvhYiz1x0RsYaG/lGz5bydt/5Mj23LwDgDfv59O7Zg/hw/wUBvRLCiQ7RN7gRX3SInn7JER4HLh2JfEoJIYToEPY2sivvcd13/McViDxru5xFyiVcMCjZjz1zrra5ckTXBttcOaIrCRFBnXLaVIIRIYQQ7V5BhZnyBkYdjuu+49/03PEiAG8GzeBlx1TGZMS2yNTIsG7R3DS+J9Eh7iMf0SF617LezlQC/mQyTSOEEKJdUxSVvR4UOEs+8Ck9d/wbgF+6/5XHd41Cp9VwwUD/joqcbFi3aIakRZFVWImxxkZksJ5eCeFotRo0GogN7Xz5IiDBiBBCiHYut6was83RaLvCLpNIOfAxxSln81juWKCSMzPiiG3hhFGtVkOfpNo73kYE6wkM6JwTFhKMCCGEaLdsDoWD5Z4t5XXoQ9k04S12F5rZvX4POq2G8wck+bmHnuuMq2iOk2BECCGE35htDirNdr9cW1UU8sqqcWjC6k76VFV6bl+Aog3kQP9bnIe0ej7f4iw+NrYVRkUa0hnrixwnwYgQQgifsjsUCistHDXWUFblv3pNqqriqLajC63zTXpum0/33a8AUJJ0JhWxg9mdX0FWgYkArYbzWzBXpDEGvZbwoM63pPc4CUaEEEI0m6qqlFRZyTeaKaq0eFx4zE+dIWPb86Tvfg2APac9SEXsYFRVZdmWIwCMzYwjJrTtjER01sTV4yQYEUII0WQVZmehsXyjGavd8/1g/EZVydj6HOl7Xgdg95CHOJw53fn3/ErXqMifBrSdURGAuPC2Exi1BglGhBBCeMVsc5BvNHPUaKbK4p98kCZRVTK3PEO3rDcB2D3kYQ5nTjv21olRkXGZ8W1qVESrhZiQttOf1iDBiBBCiEY5FJXCSmcAUlZlRW3FWZj6RBZvPBGIDH2EwxnXuN7bdbSSvYXHc0U8W0HTOykci10hr7wGmx9HfaJCAgnQdc4lvce1+lf/0ksvkZ6eTlBQECNHjmT9+vUNtl+wYAG9e/cmODiYtLQ07rjjDsxmz/YiEEII4TlVVSkxWdieZ+THrCJ25FVQamqbgQiAMX44e4Y8yK6hj7kFIqqq8vmWPADG94onyoNRiOBAHV2ig8lICOPMjDh6J4UTEuif/criOnm+CLTyyMiHH37I3LlzWbRoESNHjmTBggVMmjSJPXv2kJCQUKv9+++/z7333subb77J6NGjycrKYtasWWg0GubPn98KX4EQQnQ8lcfzQCrMWGxtIA+kIaqKzl6Fog8D4FDmjFpNdh6tILuoCr1Ow588rCvSNSbEtVxYp9WQFhNCl+hgiiot5JRWY/Sg9LynOnu+CLRyMDJ//nzmzJnD7NmzAVi0aBHLly/nzTff5N57763V/ueff2bMmDFcffXVAKSnp3PVVVfx22+/tWi/hRCio7HYHRQYLRwx1mDyU10Qn1NV+u6cT7RxO5vGL8FuiKqjyYlcEU9HRQJ0GlKigmsd12g0JEQEkRARRHm1lZySaopNlmaNFIUE6ggJlIyJVnsCVquVjRs3ct9997mOabVaJk6cyC+//FLnOaNHj+bdd99l/fr1nH766ezfv5+vvvqK6dOn13sfi8WCxWJxva6oqACcW6wrShuP+DsIRVFQVVWedwuSZ97ySivN7C+sxBEYSkJECDpt29951aGoFFdaOFphprSN5oHUS1Xp/ccTdM35CBUN0YW/UthlUq1m248YXaMik/oloXrwRaZGBaNBRWlgeXJEUAADUyOotto5VFbN0fKmLWeODdO3q/+n/uprqwUjxcXFOBwOEhMT3Y4nJiaye/fuOs+5+uqrKS4u5swzz0RVVex2OzfeeCP3339/vfd5+umneeyxx2odLyoqwmq1Nu+LEB5RFAWj0Yiqqmi1rZ6m1CnIM285qqqSX2GmwGjGYa7CaLaj02qIDNYTExpImCGgzW0JbzLbKK22UV5tpR39HDxBVem74zm65n6CiobtA+/naPRIqCo/pZnKsk3OXJFx3SMIV6twVDV8aa0WDDaFwkLPSswDRGsgLEKhxGSh2GTF7vA8KNGG2igsrPG4fWszGo1+uW67GhtavXo1Tz31FC+//DIjR45k3759/O1vf+OJJ57goYceqvOc++67j7lz57peV1RUkJaWRnx8PFFRUS3U885NURQ0Gg3x8fHyg7GFyDNvGWabg51HKyiza9CGBKGqoAuJQqPRUAFUVEGQVUdSpIGkiCBCDa33kVtttZNfYSbfaKHGCqBHExyCf1Iy/UhV6PPH46QdC0S2DXyA/N7T0NUR8G3LM3KgzEKgTsP5p3VDF9x4hdPkKANdkiOb1LVUnDsI51eaySmpptrS8OZ9Op2G7l3i0LaDUbTjAgP9k9/Sav8z4uLi0Ol0FBQUuB0vKCggKanuBKOHHnqI6dOnc/311wMwcOBAqqqquOGGG3jggQfq/NA1GAwYDLUzlbVarXxItyCNRiPPvIXJM/evYpOFHUcqsNkV18iHRqNx/TnOYlfIKakhp6SGiGA9yZFBJEYEtcjurDaHQkGFsyBZ+UkJl21tpMZjxwKRLtkfoKJhx4inORJ/FrpTnjm454pM6J1ApId1PNLjwpv1f0arhS7RoXSJDqWo0kJuaVW9JfFjQw0EBLSvcNBfnyetFowEBgYybNgwVq5cydSpUwHnb3MrV67k1ltvrfOc6urqWg9Cp3P+Q3oyDyiEEM2lKCrZRSZySjwfxj+uosZGRY2NvYWVxIYaSI4KIi7U4NPfjFVVpdh0rCy7ydw+p2HqEWguIe7ID6ho2Hn6PzjabWqtqZnjtuUZOVhSTWCAlsn9PVtBExvmnFbzlfhwA/HhBow1NnJLqimsNLvl5cSFy5Le41p1mmbu3LnMnDmT4cOHc/rpp7NgwQKqqqpcq2tmzJhBamoqTz/9NABTpkxh/vz5DBkyxDVN89BDDzFlyhRXUCKEEP5SY3Ww/Yix2cs6FQWKKi0UVVrQB2hJjDCQHBlMpAfTCPVpc2XZ/cAaHM/GCe8QUbaDgq4XUF/G7cmjImf1jifCw+faNSbEZ309WWSwnoFdIqmxhnGorJq88hocDpXYNlQFtrW1ajByxRVXUFRUxMMPP0x+fj6nnXYaK1ascCW15ubmuo2EPPjgg2g0Gh588EHy8vKIj49nypQpPPnkk631JQghOonCCjM7j1Z4lZzoCZtd4XBpDYdLawgx6EiODCY5MoggfeO/YJltDgoqnFVR281yXG+pCmHluzFF9wOgJjydmvD0Bk/Z2oRRkbCgAGLD/DtSERyoo1diON3jnFM4nvwbdxYatZPNb1RUVBAZGUlZWZkksLYQRVEoLCwkISFB8hdaiDxz31EUlazCSg6XNrziQVVVHFXl6EKjmp2TodE4S4QnRwaREG5wKxXuUFSKKp31QNpqWXafURX6bXiApNxlbBnzMiXJ493fruOZq6rK37/aRU5JNZP7J/HnYV08ulX/1AiSI2vXFhHuysvLiY6Oxmg0EhER4bPrtqvVNEII0ZKqLHa25RlbfNRBVaGsykpZlZU9Wg3x4QbiwgyUVlkpqDTj8PHoTJukOOj3+wOkHPwUVaMlwFbp0WlbDhvJKanGEKBlUv/Exk8ADHotSRFBzemtaCYJRoQQog5HjTXsPlrZpEJWvuRQVFcuSKehOOi34T5Scv6HotGxY+TzzhyRRpycK3J2nwTCgzzPFWm3K4w6CAlGhBDiJA5FZdfRis71w78tURz033AvyTmfo2h0bD/jnxSmne/RqZsPlZNbemxUpJ9nuSI6nYbUOkq/i5YlwYgQQhxTabaxLc/YaLEq4SeKg/4b7iE5Z9mxQORfFKZN9ujUk0dFzumbQFiQZz/eUqOC3XJyROuQYEQIIYBDpdXsLazsUHU52itFE8D2Uf+qc6+Z+vxxqJxDZTUE6bWc19ezURGNxn/LeYV3JBgRQnRqNofCrqMVFFZYGm8s/EurY8eIZziUMZ2K2MEen6acPCrSJ9HjUZHECM+WUAv/k7EpIUSnZayxsf5AqQQirUij2End9z4ox6bGtDqvAhGAP3LLOVxWQ7Bex7n9PFtBA9A1VkZF2goZGRFCdEo5JVVkF5lkWsaPjtdoMdbYiAzW0ysh3K30vUax0/+3O0k69DURZdvZNeIp765dUElJWSVf7CoHjuWKeFjOPTo0kAgPV9sI/5NgRAjRqVjtCjuPVlBcKaMh/rQxp4ylG3IpO6l0fnSInitHdGVYt2g0io0Bv84j8fDXKFo9RSnnNOvaAAle7PUiuSJti0zTCCE6DUVR+e1AiQQifrYxp4yFa7JrBQtl1TYWrsnmjwNFDPh1risQ2Tr63xSnehaM1HdtgDfXHWRjTlmj1wg1BBAvm9S1KTIyIoToNCrMNiw2mZfxJ0VRWboht973A7AzeP0dJGrWY9foeafLE+wu7w/lBY1fW1X5cuvRBtss3ZDLkLSoBndCllyRtkeCESFEp1HXb9PCt7IKKxt8zvP1CzlPsx6LGsBfrLezOqsrcMhn9y+rtpFVWEmfpLr3TQkM0JIspd/bHAlGhBCdRnm1tbW70GHZFYUth4x8cWyJbX0+dZzJBO1mng65i5qo0Yz04h7FJgvZRVWNtjPW1B8MpcWENDhqIlqHBCNCiE6joR9SomkKKsz8tLeYddnFVHqwoeBqZQhjLS8wZ/xQzqln9KI+u/MreP7brEbbRQbXvUpGp9XQJVpKv7dFEowIITqFSrMNe2fY7bYF2BwKmw+V82NWEbvyT+ymGxmsZ3TPGH7eV4rR7Az8ArHxaMASXnFMIUd1VkbVhkTTKyHc6/v2SggnOkTf4DRQdIi+3msnRwWhl9LvbZIEI0KITqFc8kWaLb/CzE9ZRazLLsFkcY6CaID+qRGMy4xnUJdIArRa0mPDWLgmm0BsLNQv4BzdH4zU7uY867M40HHliK5NmirRajVcOaIrC9dk19umvmtL6fe2TYIRIUSn4M8pmuMFuMrKK4mO0tErMbzd5CU0VpjM5lDYlFPGj3uL2VNwYhQkOkTPmIw4xmbEERvmvkx2WLdobh3bhZEb/sZY/qBGDeQh+2wiQoJcdUaaali3aG4a37PBGiZ1iQ83EBIoP/LaKvmXEUJ0Cv4aGaldgKuw0R+MbUVDhcmSI4P4aW8xP2cXU2V1lmrXaGBgaiTjMuMZmBqJrp6AS+uwMOvQg8TxBzatgU8yn2d04ihmJfgmSBvWLZohaVHHAsByoqOiGg0Au8WENvu+wn8kGBFCdHhmmwOzzeHz6x4vwHWq48W9bhrfs80GJI31/WQxIYGMzYxjTEYcMaGBDV5X67AwaN3NxOX/hEMXxNaxr5KUcAae7aPrOa1WQ++kcBzhDnSh4Wg09QciUSF6IkOk9HtbJsGIEKLD88eoSGPFvcCzAlytwZO+AwzuEsn4XvEMSIn0+GvI2PrPY4FIMJvHvkpZgjeLd/1DckXaPkkrFkJ0eOU1vq8v0lhxLzhRgKut8aTvAOf2S2RQF++Cqf39bqYsbhh/jH2tTQQiIYE6Kf3eDsjIiBCiw/PHyIinCbH7Ck30Tmx4GqElHSqt5qttDZdUP87jpF/FAVodAHZDFBvPet+ZYNIGpMWEtJlnL+onwYgQokOzORRMHhTj8pan28//b/MRNuaUMa5XPCO7x7TKig6zzcH6g6X8tLeYA8WNVzA9rr7iYSfT2msYvPZGirqcx+GMa5wH28gPf32AlpQoKXLWHkgwIoTo0PwxKlJttfP9zsY3dgvUaXAoKofKanjvt1z+u/EwI7pFM65XPD3iQv3+G3tOSRU/7i3m1/0lWOzODQJ1Wg2ndYlkT4HJVSukLg0VDztOa6/mtLU3ElP4K5GlWynoMhlbUKxPv4bmSI0KrnfFj2hbJBgRQnRoRh/nixwpr+Hl1dnkV5jRakBpoKjrdWf2oHdSOL/uL+HHrCKOGM2syy5hXXYJqVHBjO8Vzxk9fDtaUmN1joKsySoit7TadTwx3MC4XvGM6hFLRLC+3tU0xzVWmExrr+a0n/5CTNFv2ANC+WPcG20qENFqIS1GRkXaCwlGhBAdmi9HRjbllvHG2gNY7AoxIYHcPKEnJVXWRgtwTeybyDl9EsguquLHvUVsOFhKXnkN76/P5b8bDzG8WwzjesWRER9W52hJY4XJVFXlQEkVP2UVs/5gqWsUJECrYWjXaMb1iquVt9LU4mHgDESG/HQD0UXrjwUib2KMG9L0B+sHSRHBGAJ0rd0N4SEJRoQQHZaiqFSYmx+MKIrK51uOsPxY4mfvxHD+Mq4HEcF60uNCPSrApdFoyEgIIyMhjCuGp/HbAefoRV55Db/sL+GX/SWkRAYxNjOeUT1jCTM4P54bKkzWNzmc3/aX8uPeIg6V1bjeT4oMYlxmHKN6xBLeQG6Lq3hYA4HOqXS2Kk5bewPRRRuw68PYNO5NKmJPa8pj9atusbKctz2RYEQI0WFVmG0oSvOuUWWx89ra/WzPqwDg3L6J/HlYF7dcBG8KcAGEGgI4u08CZ/WO50CxM69j/cFSjhjNfPj7IT7ZdJhh3aJJjgzif5uP1Dr/eGGyAK0G+7F5ogCthuHp0YzLjCczoe4RlrpotRr6eLF7bkLeNycFIoupiB3s8bktJS7cQKhBfry1J/KvJYTosJo7RXO4rJqXVmdTVGkhUKdl5qhujOzhu7wIjUZDj/gwesSHcfnwLvx2oJQfs5yjHL8dKG30fLuikhxpYHyvBM7ocWI0xZ+Opl9KYE0xZQkj22QgAtBNipy1OxKMCCE6rPJmbI634WApi38+iNWuEBcWyM0TMvxayTMkMICzeicwoVc8OSXVLNuSx9ZjozENueb0bvRJ9nxkoyl0NhOgwaF37u+S0/cGv96vOcKDAohupGS9aHskGBFCdFjl1d6vpHEoKp/+cZhvdjiX7vZLjuCGsT0IC2qZj0uNRkN6XCgje8R6FIwYfZAT0xCdzcSQH69D1Qbwx9jXUALa9qhDt1jZEK89kmBECNEhmSx27I4G1t3WodJs49Uf97Mr31nCfXL/JC4dktoqe8t4UnDMm3ZNobNWMuSn64gq2YwtMJLgqsNURfby2/2aK0ivIzFCSr+3RxKMCCE6JG9HRXJKqnh5dTYlVVYMAVpmj05neHqMn3rXuF4J4USH6BvcQ8aTwmRNpbNWMvTHa4ks3YItMJJN45e06UAEnBviSen39kk2yhNCdEjeJK/+kl3CP1bspqTKSkK4gfv/1LdVAxFwrnK5ckTXBts0VpisqQKsFQz9cTaRpVuwBkaxafxbVEb39/l9fClApyElKqi1uyGaSEZGhBAd0qnBSF2FwxRU/vv7YVbuLgRgYGokc8Z2b5X9Y+rSnMJkTRVgrWDIj7OJLN3mDEQmvIUpqq/P7+NrqVHBBOjk9+v2qm38jxNCCB8y2xyYbQ7X67oKh0UG6wkJ1HHUaAZgyqBkpgxOQdvGhvmbUpisOQw1BQSbDrWrQMRZ+r1tJ9aKhkkwIoTocE4eFalvDxZjjQ1jjQ29TsMNY3swpKvvRxl8xdvCZM1RFZnJpvFLQKPFFNWnRe7ZXAnhBoL0Uvq9PZNgRAjR4ZQf2xxPUVSWbshtsG1IoI7BXaJaoFdtV4ClnBBTjquImSm6Xyv3yDv+rP8iWoZMsAkhOpzjIyNZhZUNrkYBMNbYySqsbIlutUkBlnKGrpnF0DWziCze2Nrd8Vp4cECD+++I9kFGRoQQHYrNoVBlsQPOqRhPeNquo9Fbyhi6Zhbh5buwGGKx630/FRQTFui3WiiqqqA12/1ybdGyJBgRQnQoxhob6rFaZ22hcFhbpbeUHgtEdmMJimPT+LepiszwybV1Wg1JkUGkxYT4db8cRVEoLKz22/VFy5FgRAjRoZycvNrahcPaKr25lKFrZhJu3IMlKI6NE96mOqL5gUhwoI4u0cGkRAWjl2W2wgvy3SKE6FBOrrzamoXD2irn1MzxQCSejRPeaXYgEh0ayKC0SEb3jKVbbKgEIsJrMjIihOgwFEWl4pSN44Z1i+aGsd159acDbsf9WTisLbMHhGIOSSHQUnZsRKRHk67TUlMxonOQ7yAhRIdRYbahKLWPH99SPliv5ZqR3YgK8W/hsLZM1QWydfS/MZgLMYd28fr8IL1zKiY1WqZihO9IMCKE6DDq248mu7AKgD7JEZzRI7Ylu9QmBJqLST7wKTl95oBGg6oL9DoQiQ7VkxYdQny4QTajEz4nwYgQosMor2eJ7r4iEwAZ8WEt2Z02IbCmiKFrZhBWkY1WsXKg/60en6vTakiMCCItJlhqeQi/kmBECNFhnJy8epyqqmQfD0YSOlcwElhTyLDVMwit3I85OIn8bhd5dN7xqZiUqGACA2QqRvifBCNCiA7BZLFjd6i1jhdWWqg02wnQajpV2XBnIDKd0MoDmEOS2TjhHWrCGl5ZFBWip2uMTMWIlifBiBCiQ6hrVAROTNGk+3nJqU6rISJUT5VWg1I7JmpRgTUFx0ZEDlATksKmCW/XG4hotZAUESxTMaJVSTAihOgQ6k9edQYjPRNC/XZvg17LwNQIzBUq0bGxFFRYOVRWTY3V4bd71kfjsDJ0zaxjgUgqGye8jTksrVY7mYoRbYkEI0KIDqG+/WX2Ffo3eTUsKIDT0qII1GkwV4Bep6VrbAhpMcEUm5xBSamp7lEbf1B1gRzoezM9ty9g04S3aq2akVUxoi2SYEQI0e6ZbY46RyGqLHaOGM0A9PRDMBIXbmBASgQBOi3KKQVONBoN8eEG4sMNVFnsHCqr5qjRjKOOvBZfK+g2haIu56HoDICsihFtnwQjQoh2r75RkeOraBLDDUT4eDO8rrEhZCaEeTS6EGoIoE9SBBnxYRw1mjlUWk21D6dwDFVH6LvxIXaOeAprcCIAis4ge8WIdkOCESFEu1dWT/JqdpGz2FlPHy7p1Wigd1I4XaK9X5kToNOSFhNCWkwIxSYLh0qrKWnmFE5QVR5DV08npOow/TY8wOZxrxMdGkhaTDDxYTIVI9oHCUaEEO1efcmrvs4XCdBpGJgaSWyYodnXigszEBdmoNpq51BpDUeMNV5P4QRV5TFs9XSCqw5THdaV8onPcUZarOwVI9od+Y4VQrRrdodClcVe+7iicKDEOTLii2JnwYE6BqdF+fwHfUhgAL2TwukZH+qcwimrptrS+BROUNVhhq2eQXDVYWyR3dHP+oKM6NqrZoRoDyQYEUK0a+U1NtQ6BhQOl9ZgtSuEBOpIigxq1j0iQ/QM6hKJIUDXrOs05OQpnBKThUNlNZSYLHV+bUGmQ4z4cQaGqjzUmJ7oZ30JESl+65sQ/ibBiBCiXat3iuZY8mrP+DC0zcibSIoMol9yRIvu8BsbZiA2zECN1cGhsmqOlNdgd6jodBpSIoPJWP84OlMexGagmfmFBCKi3ZNgRAjRrhlr6qm8erzYWXzTi511jw/1y5JgTwUH6uiVGE7P+DBKqizEhAQSoNPCpYvgyzvgwgUQkdxq/RPCVyQYEUK0W4qiUlFTO1+kuZvjabXQNzmC5MjgZvfRF3RaDQlBKhxfnhuRAld/2LqdEsKHZOG5EKLdqjTbcdSxEUxplZWyahtaDXSP9W5kRB+gZWjX6DYTiABQkg3/OR22fdzaPRHCLyQYEUK0W+X1TdEcGxXpGhOCQe950mmIQceI9GiiQgJ90j+fKMmGJReCMRd+mg+OunNkhGjPZJpGCNFu1b85nvdLeqNDAxnUJbJtVSot3gdvXQiVRyG+D8z4H+iknLvoeCQYEUK0W+X1bY530koaT6REBdM3ObxtVSst3uscETHlQ3xfmLkMwhJau1dC+IUEI0KIdqnKYsdmV2odN9ucy2Gh8WBEo3GOnnTzMq/E74qy4K0pzkAkoR/MWAZh8a3dKyH8plnjkWaz2Vf9EEIIr9S3H82B4ipUFWJCA4kJrT/3Q6fVMLBLZNsLRAC2f3wsEOkPM7+QQER0eF4HI4qi8MQTT5CamkpYWBj79+8H4KGHHuKNN97weQeFEKIujRU7a2g/GoNey7D0aBLCm1eZ1W8m3AcTH3NOzYTGtXZvhPA7r4ORv//97yxZsoRnn32WwMATv3UMGDCA119/3aedE0KI+hjryxcpbLi+SFhQACPSY4gIamOJoKUHwG5x/l2jgTNvl0BEdBpeByNvv/02r776Ktdccw063Yklc4MHD2b37t0+7ZwQQtTFbHNQY629mZyiqOwvOraSpo6REZ1Ww/Bu0QR5sdy3RRTugjfOhY9mnghIhOhEvA5G8vLyyMjIqHVcURRsNln/LoTwv/pGRY4Ya6ixOTAEaEmNrl20LCI4wFlOvS0p2OlcNVNVBBV5YKtu7R4J0eK8/l/Zr18/fvrpp1rHP/74Y4YMGeKTTgkhREPqzRc5NkXTIy4UXR0b20UGt6FiZgAFO5x1RKqLIXkwzPgcgqNbu1dCtDivl/Y+/PDDzJw5k7y8PBRF4dNPP2XPnj28/fbbfPnll/7ooxBCuCmvZyVNdlHDxc4ig9tQnkj+NnjrIqgpheTTnAXNJBARnZTXIyMXX3wxX3zxBd9//z2hoaE8/PDD7Nq1iy+++IJzzz3XH30UQggXu0PBZKm9OR6cvFNvGw9GTg5EUoZIICI6vSYVPRs7dizfffedr/sihBCNMtbYUGvvjYexxkaRyYIG6BFfu3ZISKCOwIA2ki9irXImqqYMhemfQXBUa/dIiFYlFViFEO1KWSP5IilRwYQE1v5oi2groyIAXc+AWV9ATE8JRISgCcFIdHR0nfs3aDQagoKCyMjIYNasWcyePdsnHRRCiJMZG9mpt83mixzZDBotJA9yvk4d1qrdEaItaVIC65NPPsmf/vQnTj/9dADWr1/PihUruOWWWzhw4AA33XQTdrudOXPm+LzDQojOS1FUKmrqzhfJLmy48mpUSCsGI0f+gLcvdgYjs1dAQp/W64sQbZDXwcjatWv5+9//zo033uh2/JVXXuHbb7/lk08+YdCgQbz44osSjAghfKrSbMeh1E4YsdoVckqd9TnqGhnR6TSEGVppVjpvE7wzFcxGSBsJESmt0w8h2jCvs7m++eYbJk6cWOv4OeecwzfffAPA+eef79qzRgghfKW8nimanJIqHIpKZLCeuLDatUQigvR1Ti/7Xd5GeHvqsUDkDJj2CQRFtHw/hGjjvA5GYmJi+OKLL2od/+KLL4iJiQGgqqqK8PDw5vdOCCFO0tjmeD3jQ+sMOlolX+TwRnj7ErAYoesomPYxGORzUYi6eD1u+dBDD3HTTTexatUqV87Ihg0b+Oqrr1i0aBEA3333HePHj/dtT4UQnV55PWXgswvbWLGz/G3OqRlLBXQdDdf8Fwz17yIsRGfn9cjInDlzWLNmDaGhoXz66ad8+umnhISEsGbNGq677joA7rzzTj788EOPrvfSSy+Rnp5OUFAQI0eOZP369Q22Ly8v55ZbbiE5ORmDwUCvXr346quvvP0yhBDtTJXFjs2u1DququpJIyNtJBiJ7g6JA6DbGAlEhPBAkzK6xowZw5gxY5p98w8//JC5c+eyaNEiRo4cyYIFC5g0aRJ79uwhISGhVnur1cq5555LQkICH3/8MampqeTk5BAVFdXsvggh2rb6RkUKKi2YLHYCtBq6xYTUer9Vip0ZwpxBiEYDgbULsAkh3DUrvdxsNmO1uieURUR4npw1f/585syZ46pJsmjRIpYvX86bb77JvffeW6v9m2++SWlpKT///DN6vfM3nfT09KZ/AUKIdqO+/WiOFzvrHhda5468LVbsLPdXQnd9D5MedL6W0RAhPOZ1MFJdXc3dd9/NRx99RElJSa33HQ6HR9exWq1s3LiR++67z3VMq9UyceJEfvnllzrPWbZsGaNGjeKWW27h888/Jz4+nquvvpp77rkHnU5X5zkWiwWLxeJ6XVFRAYCiKChK7SFf4XuKoqCqqjzvFtQRn3lZlRW1jjrw+worAWfyal3vRwbr/P8ccn9B895lhNuqcCRloAy+0r/3E0DH/D5v6/z1rL0ORu666y5WrVrFwoULmT59Oi+99BJ5eXm88sor/OMf//D4OsXFxTgcDhITE92OJyYmsnv37jrP2b9/Pz/88APXXHMNX331Ffv27ePmm2/GZrPxyCOP1HnO008/zWOPPVbreFFRUa1RHeEfiqJgNBpRVRWtto3sDdLBdbRnbrUrmMoq6nxvX4HzePdwDY6q8lrv2012Cq0mv/VNf/R3opfPQWOvpipxOBWxI9EUFvrtfuKEjvZ93h4YjUa/XNfrYOSLL77g7bffZsKECcyePZuxY8eSkZFBt27deO+997jmmmv80U/A+Y2XkJDAq6++ik6nY9iwYeTl5fHcc8/VG4zcd999zJ071/W6oqKCtLQ04uPjJdekhSiKgkajIT4+Xj4wWkhHe+aFFWZ0obW/jiqLnfxKZy5JZloiuiD3jzSdTkPX1Dj/1RjJWYfmqxvQ2KtRuo+n4uwXiE9O6xDPvD3oaN/n7UFgYO06Pr7gdTBSWlpKjx49AGd+SGlpKQBnnnkmN910k8fXiYuLQ6fTUVBQ4Ha8oKCApKSkOs9JTk5Gr9e7Tcn07duX/Px8rFZrnQ/JYDBgMBhqHddqtfLN24I0Go088xbWkZ650eyoM6DYX+xc0psUEVRnbkhkcGC9U7jNdnAtvH852Kqhx1lwxXtoyio7zDNvLzrS93l74K/n7PVVe/TowYEDBwDo06cPH330EeAcMfFmpCEwMJBhw4axcuVK1zFFUVi5ciWjRo2q85wxY8awb98+tzmrrKwskpOT/RatCSFaX2PJqz3j616x4rclvZUF8N6xQKTnOXDVB6AP9s+9hOgEvA5GZs+ezZYtWwC49957eemllwgKCuKOO+7grrvu8upac+fO5bXXXuOtt95i165d3HTTTVRVVblW18yYMcMtwfWmm26itLSUv/3tb2RlZbF8+XKeeuopbrnlFm+/DCFEO2F3KJgsdW+O12o79YYnwrmPQca5cOX7EogI0UxeT9Pccccdrr9PnDiR3bt3s3HjRjIyMhg0aJBX17riiisoKiri4YcfJj8/n9NOO40VK1a4klpzc3PdhoTS0tL45ptvuOOOOxg0aBCpqan87W9/45577vH2yxBCtBPGGht1LJLBrigcLHZujtdixc5U1Vk7BOD0OTD8OpDpASGazatgxGazMXnyZBYtWkRmZiYA3bp1o1u3bk3uwK233sqtt95a53urV6+udWzUqFH8+uuvTb6fEKJ9qa/Y2aHSGqwOhdBAHUmRQbXeDzH4uNhZ9g+w+h9w1VIIce7DJYGIEL7h1f8kvV7P1q1b/dUXIYSopd7N8QpPlIDX+ntzvH0r4YOr4NBvsHa+764rhACakDMybdo03njjDX/0RQgh3KiqSkU9IyMtli+y73tnIGI3Q68/wdkP+ea6QggXr3NG7HY7b775Jt9//z3Dhg0jNNQ9i33+fPmtQQjhGxVmOw6ldsKIqqpkF7bA5nh7v4elV4PDAr0vgMuWQICs3BPC17wORrZv387QoUMB57Lak/mtsJAQolMy1jNFU1JlpbzGhk6jIT2u9uZ4Op2GMEOztt6CrG/hw2vAYYU+F8KfF0sgIoSfeP2/ddWqVf7ohxBC1FJWT32R46MiXWNDMATULmoWGaxv3i9Hdit8fbcEIkK0kCangu/bt49vvvmGmpoagDo3qBJCiOaobyXN8XwRvxU7CwiEaZ84l+7K1IwQfud1MFJSUsI555xDr169OP/88zl69CgA1113HXfeeafPOyiE6JyqLHZs9rp3CD2+ksbnyavVpSf+HtsTLpwPOj8VThNCuHgdjNxxxx3o9Xpyc3MJCTkxV3vFFVewYsUKn3ZOCNF51TcqYrY5OFzuHJHN8GXy6u6vYMFAZ66IEKJFeZ0z8u233/LNN9/QpUsXt+OZmZnk5OT4rGNCiM6tvv1osotMqCrEhQUSFVJ7+iTEoEOv8/L3rN3L4aOZoNhgx6fQ67ymdFkI0URej4xUVVW5jYgcV1paWufuuEII0RT1raTJLnLu1OuzJb27voCPZjgDkQH/Bxf9x7vzhRDN5nUwMnbsWN5++23Xa41Gg6IoPPvss5x11lk+7ZwQonOy2B1UWx11vufKF6knGKlrtKReO5fBf2eBYocBf4ZLXgVdM5cECyG85vX/umeffZZzzjmH33//HavVyt13382OHTsoLS1l3bp1/uijEKKTqW9URFFU9hcfW0nT3OTVnZ/Df2eD6oCBl8PUhRKICNFKvB4ZGTBgAFlZWZx55plcfPHFVFVVcemll/LHH3/Qs2dPf/RRCNHJ1Je8mldeg9mmEKTX0iUquNb7Op2G0MDadUfqlPWtMxAZdAVcskgCESFaUZP+90VGRvLAAw/4ui9CCAFAWVXdyavH64v0iAtDq617czyPi51d9CKkjYAh00HrYQAjhPALr0dGMjIyePTRR9m7d68/+iOE6OTsDgWTxV7neyd26m1isbPc30A5loui1cGwWRKICNEGeB2M3HLLLSxfvpzevXszYsQIXnjhBfLz8/3RNyFEJ1RsslJfQefs5uzUu+1jWDwZ/nfTiYBECNEmNKno2YYNG9i9ezfnn38+L730EmlpaZx33nluq2yEEMJbdofC3sLKOt8rr7ZSbLKi0TinaepSbzCy9b/w6RxQlWMVVWVTTyHakibvTdOrVy8ee+wxsrKy+OmnnygqKmL27Nm+7JsQopPJLqrCYqunBPyxUZEuUcEE15GkWm+xsy0fwmc3OAORoTNgyr9B2+SPPiGEHzQrfXz9+vW8//77fPjhh1RUVHDZZZf5ql9CiE7GWGPjcFl1ve9nFzZc7CwquI76IluWOqdlVAWGzoQLF0ggIkQb5HUwkpWVxXvvvccHH3zAgQMHOPvss3nmmWe49NJLCQur+0NCCCEaoqoqu49W1JsrAidGRurNFwk5ZYpm8wfOQATVmah6wb8kEBGijfI6GOnTpw8jRozglltu4corryQxMdEf/RJCdCKHy2qoNNe9ggbAalfILXGOmnhcBj4k1pkfMmQanP9PCUSEaMO8Dkb27NlDZmamP/oihOiEzDaHa9SjPgdLqnCoKpHBeuLCak/HBOg0hBlO+TjrdR7MWQUJ/SQQEaKN8zoYOR6IbNy4kV27dgHQr18/hg4d6tueCSE6hb0FJhyOBuZnOGk/moSwOouaRRwfFdn6EaQOg9hj1aCTBvi0r0II//A6GCksLOSKK65gzZo1REVFAVBeXs5ZZ53F0qVLiY+P93UfhRAdVLHJQkGFudF2x0dO6it2FhWsh41vwRe3QXgK/GUNhCX4tK9CCP/xeuzyr3/9KyaTybU5XmlpKdu3b6eiooLbbrvNH30UQnRADkVlT37dNUVOpqoq2YUNJ68mZH3gDEQA+l0EofJLkRDtidcjIytWrOD777+nb9++rmP9+vXjpZde4rzzzvNp54QQHdeB4ipqrI1XQs2vMFNldaDXaegaHVLr/dTspYRtfNj5YuRNMPlp8HR/GiFEm+D1yIiiKOj1tasc6vV6FKXuYkVCCHGyKoud3NIqj9oezxfpHhdKwClFzVL3vU/f44HIGbdIICJEO+V1MHL22Wfzt7/9jSNHjriO5eXlcccdd3DOOef4tHNCiI5pd34Fnv7ukl1Ud7GzxNzl9N30qPPFqFth0pMSiAjRTnkdjPznP/+hoqKC9PR0evbsSc+ePenevTsVFRX8+9//9kcfhRAdyJHyGsqqbB6331dPvkhJ4hgqovpROewmOO/vEogI0Y55nTOSlpbGpk2b+P7779m9ezcAffv2ZeLEiT7vnBCiY7HaFfYWNlxT5GSVZhv5x1bb9Dxlczy7IYrfz36fkb26SCAiRDvXpL1pNBoN5557Lueee66v+yOE6MD2FZqw2T3PLTs+RZMUGURYUABpWW+jarQczpwGgNYQSmhQPTv1CiHaDa+naW677TZefPHFWsf/85//cPvtt/uiT0KIDqi82sqR8hqvzsk+vh9NfBhd9yym9+a/0+ePx4ko2QzUUQJeCNEueR2MfPLJJ4wZM6bW8dGjR/Pxxx/7pFNCiI5FUVR2HW28psipjueLTFe/oNeWpwE40PcmKmIGAxKMCNFReD1NU1JSQmRkZK3jERERFBcX+6RTQoiOJbe0mipL/Rvh1cXuUDhYUsX1uuVMynsPgP39bmF//9tcOSISjAjRMXg9MpKRkcGKFStqHf/666/p0aOHTzolhOg4aqwODhR7VlPkZLml1cxmGQ/qjwcit7J/wN9cgYhGI8GIEB2F1yMjc+fO5dZbb6WoqIizzz4bgJUrV/LPf/6TBQsW+Lp/Qoh2bk9BJQ6l4Y3w6mLN+ZX79R8AkN3/rxzo/1e390MCA2oVQRNCtE9eByPXXnstFouFJ598kieeeAKA9PR0Fi5cyIwZM3zeQSFE+1VYYaa40tKkc1eZumOz/R99kyMIOCUQARkVEaIjadLS3ptuuombbrqJoqIigoODCQure/MqIUTnZXco7CnwPmlVo9hQNAHsKzKx0fF/3N2/N73qaBcVIsGIEB1Fs8Y44+PjJRARQtRpf3EVFpt3+1V13/kyQ9fMory8HGONDZ1WQ3psaJ1tZWREiI6jSSMjQgjRkAqzjUOl1V6d033HS/Tc8QIAAfu+BnrRLSaEwIDavzMF6DSEGuTjS4iOQrK/hBA+paoqu49WonqRs9p9x79dgcjegfP43OGsZdQzoe6RVxkVEaJjkWBECOFTh8tqqKjxfCO8HttfpOcO5yabewfdRU7fG9h3UuXVukgwIkTHIuOcQgifsdgdrhLujVJVeux4kR47XwIga9A95Pa5jmqrnbwyZ9n4nvGSLyJEZ+BRMFLXXjT1ue2225rcGSFE+7a3wITd4dn8TKC5mC77nAXNsgbfS27va1EUlR+zilCBiKAAIurYBE+KnQnR8XgUjPzrX//y6GIajUaCESE6qRKThXyj2eP21uB4Nk14i6jiTRzOuIaNOWUs3ZBLWbVziqfCbOeeT7dy5YiuDOsW7Tov1CDFzoToaDwKRg4cOODvfggh2jFFUdmT70FNEVUlqOow5rA0AExRfTFF9WVjThkL12TXal5WbWPhmmxuGt/TFZDIqIgQHY/8eiGEaLYDJVVUWx0NN1JVMrY9zxnfTiGy6HfXYUVRWboht8FTl27IRTlWUl6CESE6niYlsB4+fJhly5aRm5uL1Wp1e2/+/Pk+6ZgQon2ostjJKWlkIzxVJWPrc6TveR2AMGMWxvjhAGQVVrqmZupTVm0jq7CSPkkRUnlViA7I62Bk5cqVXHTRRfTo0YPdu3czYMAADh48iKqqDB061B99FEK0YbvzK1EaKrSqqmRsfZb0PW842w95mLyMq11vGz1cBmyssaEP0BISKIsAhehovJ6mue+++5g3bx7btm0jKCiITz75hEOHDjF+/Hguu+wyf/RRCNFGHTXWUFZlrb+BqpK55R+uQGTX0Ec5nDnNrYmn0y6RwXqZohGig/I6GNm1a5drd96AgABqamoICwvj8ccf55lnnvF5B4UQbZPNobC3oIGaIqpKr81P0y1rMQC7hj7mNiJyXK+E8EaDjOgQvUfthBDtk9fBSGhoqCtPJDk5mezsExnwxcXFvuuZEKJN21dowmqvf35Go9oJrnImpu4a9jh5GVfV2U6r1RDTSB7IlSO6otVqJBgRooPyevL1jDPOYO3atfTt25fzzz+fO++8k23btvHpp59yxhln+KOPQog2prza6qqSWh9Vq2frqBeJKfyFkuTx9bb7I7eMAyXVaIGwoAAqzHbXe9EheledEY3GWQhNCNHxeP0/e/78+ZhMzqHZxx57DJPJxIcffkhmZqaspBGigyutcgYhRaZ6ipupKgl531KYeh5oNKi6wAYDkRqrg/fXO0dPJg9IYuppqWQVVmKssREZ7Jya0Wo1gBQ7E6Ij8zoY6dGjh+vvoaGhLFq0yKcdEkK0LTaHwtFyM4fLq6m2NFBLRFXpvekx0rLfJzdzFllD7m/02p9tzqOs2kZ8uIELB6Wg1WrokxRRZ1uZohGi4/I6GNmwYQOKojBy5Ei347/99hs6nY7hw4f7rHNCiNZjrLFxuKyawgoLDqWR/WZUhd6bHict+31UNFRG9W70+vuLTazaXQjA9JHdCAxoeNRD6osI0XF5PeZ5yy23cOjQoVrH8/LyuOWWW3zSKSFE63AoKnnlNaw/UMqGA6UcLTd7FIj02fioKxDZOeJpjnb/vwZPsSsK7/ySgwqc0SOGfil1j4acTEZGhOi4vB4Z2blzZ53FzYYMGcLOnTt90ikhRMuqstjJK6/hSHmNx7vuAscCkUfosv9DZyBy+j84mn5Jo6d9v7OQQ2U1hAbquGJ4WqPtpdiZEB2b1/+7DQYDBQUFbrkjAEePHiUgQD4shGgvFEWlyGThcFkjhcsa0GfTY65AZMfpz5CfPrXRc4oqLSzbcgSAy4anER7U+IiHjIoI0bF5PU1z3nnncd9992E0Gl3HysvLuf/++zn33HN92jkhhO+ZbQ72FZpYu6+YbYeNTQ5EAMrihqNo9ewY+axHgYiqqrz3Ww5Wh0LvxHDG9Iz16D4SjAjRsXk9lPH8888zbtw4unXrxpAhQwDYvHkziYmJvPPOOz7voBCi+VRVpaTKyuGyGkpMFlQvZmIaUtBtCuVxw7CEpnjUfsPBMrYfqSBAq2H6Gd3QaDQenSfBiBAdm9fBSGpqKlu3buW9995jy5YtBAcHM3v2bK666ir0evnAEKItsdoV8itqyCuvocbawLJcTykOeu54kcM9r8ISkgTgcSBSZbHzwQZnTZELBiaTFBnk0XkajQQjQnR0TUryCA0N5YYbbvB1X4QQPqKqKrml1ewoK0ZVPRt9aJTioN/v95Ny8DPi877jt/M+R9V6HiR8sukwlWY7SZFBTB6Q5PF5oYYAdFoffQ1CiDbJo2Bk2bJl/OlPf0Kv17Ns2bIG21500UU+6ZgQoun2FpooNVnRhYbg4UxIwxQH/TbcR0rO/1A0Ovb3/6tXgUhWQSU/7nXuXTXjjG7ovaikKvVFhOj4PApGpk6dSn5+PgkJCUydOrXedhqNBofDB0PBQogmO1Jew6HShveN8YrioP+Ge0jOWYai0bH9jH9RmDbZ49NtDoV3fs0BYGxGHL0Sw726vUzRCNHxeRSMKIpS59+FEG2LscbG7vwK311QcdB//T0k5y5D0QSwfdS/KOwyyatLrNiRz1GjmfCgAP48rIvXXZBgRIiOz6ulvTabjXPOOYe9e/f6qz9CiCay2B1sPVyOL39fyNg+3xWIbGtCIJJfYWb51qMAXDkijVCDd2lqUuxMiM7Bq2BEr9ezdetWf/VFCNFEiqKy7bARi823I5e5mTMwRWSybdQCirwMRFRV5d1fc7ArKv1TIjg9Pcbr+8uoiBCdg9dFz6ZNm8Ybb7zhj74IIZooq7CS8mqbby52UhESa3Aiv533OUVdzvP6Mj9nl7A7v5JAnZZpIz2vKXIyCUaE6By8Hv+02+28+eabfP/99wwbNozQ0FC39+fPn++zzgkhGpdXXsNhHyWsahQb/X+7m6KUsynoNgUAVev9NEml2cZHvzs31JwyOJn4cEOT+hMlwYgQnYLXnzLbt293bZSXlZXl9l5TfvMRQjSdsdrGHh8lrGoUGwN+nUvi4W+IP7KSsoQzsAbHN+laH/1+mCqrgy7RwZzbL7Fp/dFAhAQjQnQKXgcjq1at8kc/hBBestgdbM3zTcKqRrEx8Jc7SMj7FkWrZ+uoF5ociOw8UsEv+0vQADNGdSNA6/VsMABhUuxMiE5D0tSFaId8mbCqcVgZ+OsdJOR9h0MbyNYxL1GSPL5J17LaFd75zVlT5KzeCfSIC2tyvyKl2JkQnYZHwcill17KkiVLiIiI4NJLL22w7aeffuqTjgkh6renwDcJqxqHlYG//I2EIyuPBSIvU5I8rsnX+3LrEYoqLUSH6LlkSGqz+hYVHNis84UQ7YdHwUhkZKQrHyQyMtKvHRJCNOxwWTV5Zb5JWE3OWeYKRLacuZDSpLHN6tc3OwoAuOr0rgQH6prVN1lJI0Tn4VEwsnjx4jr/LoRoWeXVVrIKKn12vSPd/4+QymxKE8dQmnRmk6+jqCrv/JqDQ1U5LS2KoV2jm9WvwABts4MZIUT70eSckcLCQvbs2QNA7969SUhI8FmnhBC1mW0Oth42NjthVeOwAqDqAkGjYd/ge5rdtzVZRWQXVWEI0HL16V2bfT0ZFRGic/E6zb2iooLp06eTmprK+PHjGT9+PKmpqUybNg2j0eiPPgrR6SmKyrY8I1Z78yIRrcPC4J9vYdDPf3UFJc1VXm3l0015AFw6JJWY0ObnekgwIkTn4nUwMmfOHH777Te+/PJLysvLKS8v58svv+T333/nL3/5iz/6KESntzu/EmMzE1a1DguD1t1M3NE1xBT+QliFb/aY+mDDIWpsDrrHhXJWb9+MkEowIkTn4vU0zZdffsk333zDmWeemF+eNGkSr732GpMne76tuBDCM4dKqzlS3ryEVVcgkv8TDl0Qm8e+SmV0/2b3bcvhcjbmlKHVwIwzuqH1QV0QKXYmROfjdTASGxtb54qayMhIoqObl7QmhHBXXm1lb2HzEla1djOD191MbMFaHLpgNo99lbKEkU2+nqKoZBVWUlxp4ZM/nNMz5/ZLJC0mpFn9PC4yWC/FzoToZLyepnnwwQeZO3cu+fn5rmP5+fncddddPPTQQ03qxEsvvUR6ejpBQUGMHDmS9evXe3Te0qVL0Wg0TJ06tUn3FaIt80XCqtZhZvC6m1yByB9jX2tWILIxp4x7Pt3K899mseSXHCrNdrQa6Brtm0BEo4HMxHCfXEsI0X54PTKycOFC9u3bR9euXena1Zk1n5ubi8FgoKioiFdeecXVdtOmTY1e78MPP2Tu3LksWrSIkSNHsmDBAiZNmsSePXsaXKFz8OBB5s2bx9ixTa+LIERbpSgqWw83P2E1pPIAkSV/YA8IYfPY1yiPH9Hka23MKWPhmuxaxxUVXlt7gACdlmHdmjc6mhYTIvkiQnRCXgcjvh6FmD9/PnPmzGH27NkALFq0iOXLl/Pmm29y77331nmOw+Hgmmuu4bHHHuOnn36ivLzcp30SorXtyq+goqb5FVZNUX35Y+zraFCbFYgoisrSDbkNtlm6IZchaVFNzhsJ0uvoGd/08vFCiPbL62DkkUce8dnNrVYrGzdu5L777nMd02q1TJw4kV9++aXe8x5//HESEhK47rrr+Omnnxq8h8ViwWKxuF5XVDh3OFUUBcUXO4yJRimKgqqq8rw9dLismiPNqLCqtdcQXJVHhS4WVVUpjxvmfENVm3zNrIJKyhpZzVNWbSOroJLeSU2bZumdGIoGFUVpej9bk3yftzx55i3PX8+6WRvlmUymWh2LiIjw+Pzi4mIcDgeJie5bjCcmJrJ79+46z1m7di1vvPEGmzdv9ugeTz/9NI899lit40VFRVitvqmzIBqmKApGoxFVVdE2cQfXzsJktpFdVNXkuEFnr+G0jXcSXrGXX097nirNIDQ0PRlUVVVyyy18sa3Eo/Zl5eU4wh1e3yc6VI+jGgqrvT61zZDv85Ynz7zl+auemNfByIEDB7j11ltZvXo1ZrPZdVxVVTQaDQ6H9x9EnqqsrGT69Om89tprxMXFeXTOfffdx9y5c12vKyoqSEtLIz4+nqioKD/1VJxMURQ0Gg3x8fHygdEAs83B7oNlaJu4W63WXs2QDX8lpmQj9oBQ9DoNupAo175S3qi2Olh/oJQf9xZxyItRmuioKHSh3o2M6AO0DO4eQ2BA+/7ekO/zlifPvOUFBvpnA0uvg5Fp06ahqipvvvkmiYmJTfqgOy4uLg6dTkdBQYHb8YKCApKSkmq1z87O5uDBg0yZMsV17PjITEBAAHv27KFnz55u5xgMBgwGQ61rabVa+eZtQRqNRp55AxyKyra8CuwOtUn/p3S2Kk5bewPRRRuw68PYNPYNjEHp6DQaj6+nqioHiqv4cW8x6w+WupJnA7QahnaNYufRSkwWe73nR4fo6ZUY7nX/eyeFExTYrEHaNkO+z1uePPOW5a/n7PUnwJYtW9i4cSO9e/du9s0DAwMZNmwYK1eudCXGKorCypUrufXWW2u179OnD9u2bXM79uCDD1JZWckLL7xAWlpas/skRGvYdbSCSnP9P+gborOZOO2nOUQXb3QGIuMWY4wZBFXlHp1fbbXz6/5S1mQVkXdScbXkyCDGZcYzqkcsYUEB9a6mOe7KEV29Tl6NCQskOTLYq3OEEB2P18HIiBEjOHTokE+CEYC5c+cyc+ZMhg8fzumnn86CBQuoqqpyra6ZMWMGqampPP300wQFBTFgwAC3849PtZx6XIj2IrekmnyjufGGddDZTAz56Xqiijdh04fzx7g3KY8eRFZ+JWXllURH6eiVGF4rSFBVlX1FJn7aW8zvB8uwOpyjIHqdhuHdYhjXK46M+DC3UY5h3aK5aXxPlm7IdUtmjQ7Rc+WIrl4v69VpNfRN8jzHTAjRcXkdjLz++uvceOON5OXlMWDAAPR69/ntQYMGeXW9K664gqKiIh5++GHy8/M57bTTWLFihSupNTc3V4bfRIdVWtW8CquqRouq0TkDkfGLWVWZxtJVW08KFgrdggWTxc6v+0v4MauIIycFQKlRwYzvFc/I7jGEGur/WBjWLZohaVFkFVZirLERGaynV0LtYMcTPePDCA7UeX2eEKLj0aiqd3n7v/76K1dffTUHDx48cRGNpkUSWH2hoqKCyMhIysrKJIG1hSiKQmFhIQkJCRJYHqMoKvkVZvYWmrA1s7CZzlZFUNVhfjQmNDiNkpkQxoHiKuzHls4GBmg5PT2GsZlx9IgLbVb+l7cigvWMSI9u0Xv6m3yftzx55i2vvLyc6OhojEajV6tnG+P1yMi1117LkCFD+OCDD5qdwCpEZ1NjdZBXXk1eubnJQYjOWkni4RUc6XEZAA59KJURvVj6/dYGz9tbaAIgLTqYccdGQUJaIXFUo4G+yd4nugohOi6vP4lycnJYtmwZGRkZ/uiPEB1SicnCobIaSkyW5tQeQ2etZOiP1xJZugW91UhOn+sByCpsvCgZwLSRXRnfK75VA4FusaGEB0nJdyHECV4HI2effTZbtmyRYESIRtgcCkfLzRwuq6ba2vzpywBrBUN+vJbI0q1YA6MoTRztes/oYen44EBdqwYiIYE6esSFttr9hRBtk9fByJQpU7jjjjvYtm0bAwcOrJXAetFFF/msc0K0RyaLnUOlzhUyDh+VNncGIrOJLN2GNTCKTeOXYIru53rf083lWnsTur7JEU3eu0YI0XF5HYzceOONgHN/mFO1hwRWIfxBVVUKKy0cLqumrKr5G9ydLMBqZMia2USWbXcGIhPewhTV161Nr4RwIoP0GM313zs6xLnypbWkRAUTHeqf6o1CiPbN62BENiQS4gSL3UFeWQ155TVYbL7/v6FRbCcCEUM0m8a/hSmqTx39UGhsMUFTipL5ikGvJTNRduQVQtStY9RgFqKFlVdbOVxWQ2GlGX/G56pWz9H0SwmuPsLG8W9RFVW72KBDUXnlp2zKqm2EBOrQ67RuOSRNLUrmS70Tw9HrZOmlEKJuHgcj559/Ph988AGRkZEA/OMf/+DGG2901eooKSlh7Nix7Ny50y8dFaK1OY7VBjlcWt3k0u1NcThzGvndLsIeWPea/v9uPMT2vAoCdVrmntuLrtEhZBVUUlZeTnRUVJ0VWFtSfLiBhIigVru/EKLt8/hXlW+++QaLxeJ6/dRTT1FaWup6bbfb2bNnj297J0QbUGN1sLegkp/2FrHrSNP3kPGU3lJG/9/uQm8pcx2rLxBZk1XE97sKAbj2zHTSY0PRajX0TgpnRFo4vZNaNxAJ0Dn7IoQQDfF4ZOTUQq1eFm4Vol3KKaliX6GpWbVBvKG3lDJ0zSzCy3ejt5Sxedzr9bbddbSC937LAWDqaSkM7xbTMp30QkZCGEF6KfkuhGiY5IwIUY8Sk6XlA5HVMwk37sESFE/WaffV2za/wszCNdkoKpzRI4YLBia3TCe9EB2qp0t0SGt3QwjRDngcjGg0mlrFkqScs+iozDYH249UtFwgYi5l6JoTgcjGCW9THdGzzrYmi51/r9xLtdVBz/hQZo5Kb3P/F7VaZ00RIYTwhFfTNLNmzcJgMABgNpu58cYbCQ11VlM8OZ9EiPZMUVS2HjY2ewM7T+nNJQxbM5MwYxaWoIRjgUiPOtvaFYVFa7IpqLQQExrIzRMy2uQqle5xYa2y740Qon3y+NNi5syZbq+nTZtWq82MGTOa3yMhWtnu/EoqPCyv7gv9199NmDELc3ACmya8Q3V49zrbqarKB+sPsTu/EkOAltvOzmj1iqp1CQsKoFuMTM8IITzncTCyePFif/ZDiDYhr7yGI+U1LXrPPUMeRv/bPLaPfI6a8PR6263cXciarCI0wA3jerTJfAznjrxS8l0I4R0ZRxXimAqzjT35FS1zM8UBWucqk5rwbmw45yPnT/J6bMsz8uHvhwD487AuDO4S1RK99FpaTEibHK0RQrRtbW+yWYhWYHMobDts9Gs11eMCawoZ+f0lxB5dfeJgA4FIXnkNr/yYjarCmRlxnNcv0f+dbIIgvY6e8VLyXQjhPQlGRKenqirb84zUWP2/yWNgTQHDVk8nvHw3vf54Co3ScG5KpdnGv3/Yi9mm0CsxjGkju7a5lTPH9UkORyfTM0KIJpBpGtHp7S+uosRk9ft9DNX5DF09g1DTQWpCUtg87nVUbf1TGjaHwkursik2WYkPN3Dz+AwC2uDKGYCkyCDiwgyt3Q0hRDslwYjo1IoqLRwoqvL7fdwDkVQ2Tngbc1have1VVeXtX3LYV2QiWK/jtrMzCAtqm/9d9QFaeiVKyXchRNO1zU83IVpAtdXOjiNGv9/HUJ3PsNXTCTHlOAORs97BHNqlwXNW7Mjnl/0laDVw4/geJEcG+72fTdUrMYzAgLY5YiOEaB/kE0R0So5jhc3sDv+XWO2y711nIBLaxaNA5I/cMj7dlAfAVSO60j8l0u99bKrYsMA2HSgJIdoHGRkRndKuoxWY/Lz77nHZA+5AoyoczrgGc2hqg21zS6p5be0BVOCs3vGc1SehRfrYFDqthj5JUvJdCNF8EoyITudQaTX5RrNf7xFoLsYaGO2sJaLVsW/w3Y2eU15t5d+r9mK1K/RPjuDKEV392sfm6hkfRnCg7MgrhGg+maYRnYqx2sbewkq/3iOoKo/hKy+n/4Z7nMXNPGC1K7y0OpuyahtJkUH8ZXyPNr1MNjJET1qMTM8IIXxDRkZEp2GxO9iaV+7XwmZBVYcZtnoGwVWHQaNFby3HFhRbq52iqGQVVmKssREZpGd1ViEHiqsIDXSunGmLm8xpNBATGkhqVDBxYYY2W+9ECNH+tL1PPCH8wFnYrAKLzX+RSJDpkDMQqc6jKiydTRPerjMQ2ZhTxtINuZRVuxc802rg5gkZJIQH+a2PTRESqCM5KpjkyCCC9DItI4TwPQlGRKewr9BEWZX/CpsFm3IZunoGwdVHXIGIJSSpVruNOWUsXJNd5zUUFUyWlkmqbYxOqyE+3EBqVDDRoYGt3R0hRAcnwYjo8AorzOSUVPvt+sGmXIatnk5Q9VGqwruzccLbWINr7x+jKCpLN+Q2eK2lG3IZkhbVarveRgTrSYkKIikiqM1WexVCdDwSjIgOrcpiZ8dR/+7EG2w6RKC5+Fgg8g7W4LqX42YVVtaamjlVWbWNrMLKFl0yqw/QkhwZREpUMGEG+UgQQrQ8+eQRHZbdobD1sBGHnwublSaNYfPYVzFFZNYbiJjMdtbuLfboesaahgMWXzg1GbW1RmKEEAIkGBEd2K6jlVT5KQcjuPIgADXh6QCUJo6p1UZVVfYUVPJjVjGbcsuwK54FRZHB9W+e11ySjCqEaIskGBEdUm5JNQUV/ilsFlx5kGGrpwEaNk54l5rwbm7vV9TY+Dm7hJ/2FlFQaXEdT4sOpqTKSrW1/toj0SF6eiX4dtM5SUYVQrR1EoyIDqesyuq3wmYhFfsZtnoGBnMhpohM7PowABRVZU9+JWuyivjjUDmOY6MghgAtI7vHMK5XPOmxoQ2upgG4ckRXn02ZBAdq6ZEcRnJkiCSjCiHaNAlGRIditjnYlmdE9UGaiFthsmA9pwUXMWzNTGcgEtmLjePfoliNYN22o/y0t5gi04lRkPTYEMb1iuf09Bi36ZBh3aK5aXzPWnVGokP0XDmiK8O6RTe/4xzbwC4wnMSoELRaCUSEEG2bBCOiw1AUle15Rqz25hc2O7UwWU9NHlcYnsRAOZWRvXi/93/45tcythw6iONY5BOs13FGjxjGZsbTNSak3msP6xbNkLQot0CnV0K4z0ZEwoMCGJASQWmJZwmzQgjR2iQYER3G3kIT5Y0snfXEqVMpPTRHWBr4d+Ixskvpyg3Guzn044kf9D3jQxmbGc+IbtEYPEwK1fppx9vgQB2ndY0iQFbHCCHaEQlGRIeQbzRzqLT5hc3qKkxWokZQoEZTpEZxjfU+ygghWK9lVM84xmXG0SW6/lGQlhSg03BaWhSGAB2KPzfgEUIIH5NgRLQIh6Jgcyho/VDyo9rqYJePCpvVVZjMSBjXWO9Hg0o5zpUufxnXkwGpkT65py9otXBaWhShUrRMCNEOySeX8Lsjxhp25FWgLdO2+Z1ejxcc66U5xFDtXpY6znYeJ8ytXZW1bewhc1z/lEiiQmTZrhCifZJgRPjVvkITB4pMPlnd0hIig/X01uTyfuCTxGoqqVKD+EIZXWe7tiIzMYzEiLa1068QQnhDghHhF4qisvNoBflG/xQe85ehgXlcHfgkMZpKtird+VEZVKuNPwqTNVWXmGC6xYa2djeEEKJZJBgRPmdzKGw9XE5Zlf/3WPGlsPJdDFw1g1BNJVuUHky33kvFKdMz4NvCZM0RH26gd2LbCIqEEKI5JBgRPlVjdfDHoTKqLfWXPG+Lwsp2MnjVTIIdRjYrPXgx+Vl0RSr4sTBZc0QE6xmQGtnmc3CEEMITEowInzHW2NhyqNwnRcdaUqC5mCGrZ2KwG9ms9OTfqc9x1Zn9uVLFb4XJmiMkUMdpaVHo2kBfhBDCFyQYET5RVGlhe57RtSdLe1JKFIsdf2Kk8juPRj7BjaP7odFo0GjwS2Gy5tAHaDmtaxSBAVLiXQjRcUgwIprtUGk1WQWV7WbFzMnsDoWX1+wjq/oikkMv5u6zBqFvo5vKabUwuEskIYHy31YI0bG0zU9d0W7sLahkT377C0QiSrcyaO2N/PeXPWQVmAjW67jxnH6EB7WdJbsn02hggNQSEUJ0UPIrlmgSRVHZfsRIYYWl8cZtTETJFob8eC16WyWj7AZ+0EznL+N6kBoV3Npdq1dmQjgJUktECNFBSTAivGa1O5fu+mJTupYWUbKFoT/OJsBmYoPSm3/Z/8wVI9LaVGn3U3WNDaFrbNvY/0YIIfxBghHhlWqrnc255VRb29fSXYCIks0M/fFaZyCi9mGm9W5G9ErjnD4Jrd21eiVEGMhMqF3rRAghOhIJRoTHyqutbDlsxNbOlu4CRBb/wZAfryXAXsVG+jHTMo9uSfFcdXpam63VERWiZ0CK1BIRQnR8EowIjxRWmNl+xEh73Jleo9jo/9s8AuxVbNYNYFrVXCIiIrlxfE8CtG0zhzskUMegLlFtoq6JEEL4W9v8JBZtSk5JFVsPt89ABEDV6tky+j/8GnQmV1XNRRMYym1nZxJqaJuxeGCAliFdo6WWiBCi02ibn8aiTVBVlT0FlRwurWntrjSJ1m5GCXCuQPnwUOT/t3ff4VFW6d/AvzOTKZlMMpm0SSGFJJAEEhIJAQERC4qrIqzrj2IBFbFQ3DWrC1iIFAE7KyIuWFAXNzZ0XeFFhRUViEtnKSH0hJJGSK8z85z3j8AsQ+qkzGSS7+e6vJZ55jznOXOYTW7u0/BNyXQoZDL8aWRUlz3lViGXITHUG+4qhbObQkTkMPynFzXKIgnsP1vqsoGId+FODN9wM/SFu7Ar+yK+2XceAHDvkDDEBXWtXVUvk8mA+BA99O5dc68TIqLOwswINVBrtmBfTgnKa8zObkqbeBfuRNKv0+BmroL/wffwwflHAQCj4gIwsq+/k1vXtL5GT/h7qp3dDCIih2MwQjYqa83Ym1OCGpPrLd0FAO+CHbjm12lQWKqR5z8MEwofRp1FQnyIF8Ynhzq7eU2K8NMi1Id7iRBRz8RghKyKK+uw/2wJzBYX29v9EkPBf5D066NQWKpREHAd7i+fhfwaC4K9NXhsRFSXXZkSqNcgOsDT2c0gInIazhkhAEB1nQV7zxS7biCSn4GkSxmRC4Ej8KR4BseLLdCp3TDrxj5ddkKowUOJfl10DgsRkaMwM0IAgDPFVS67dBcAQk5+BoWlBheCRmKh9ln8dqgIbnIZZtwQ1SXnYajc5AjUa9Dbz6PLZmyIiByFwQjBbJFwrsQ1V81cdmjwK6jQx+AL1Tj8c/s5AMDkoeHoY+w6wx9yOeCnUyNI7w4/nYo7qxIRXcJghHC+pAaWThqekSSBo/nlKC4ph8Fbgb5Gzw7LBGjLjqPCIxJHCytQWm3CZvnd+CzjDADgd/GBGBbl1yHPaS9PjRuCvd1h9NJwIzMiokYwGOnhhBA4U1zVKXXvzi5G+s4cFFtP9y2AQavExJQwJIcb2lW3T96vGPDrE/hC3IzXau4H8L8Ap7evFr+/JqRd9bfX5WGYIL0GnhruG0JE1Bz+M62HK6yoRXUnnMC7O7sYK38+cUUgUq+4yoSVP5/A7uziNtftm/sLBvz6BNxEHXwtBXCDbftPFVVhb05Jm+tvK7m8/pTdxFBvjOjjh75GTwYiREStwMxID5dT1PFZEUkSSN+Z02yZtf/JhsFDCbmd8yZ6XdiKhAN/hpuow/eWQZhpehLmRr7G6TtzcE2oYw6a83JXIkivQaBeA6WC8T0Rkb0YjPRgZTUmlFyVuegIRwvKG2REGj7bjMUbjthV7w3yvfib8k24yczYaEnBTNOsRgMRoD4Dc7SgHLGBnbNsVuUmR5BegyBvd+i66IF7RESugj9Fe7DOyIoAQGl16wIcD5UCarfW7f8xQuzCq+JNqGDGD2IIZppmNBmI2NuO1pLLAX9dfQaEq2GIiDoOg5EeqsZkQUF5TafU7dXKeRJP3BDV6syFMScHyv9IyA+5DccjXoR508kW7+moA+c4DENE1LkYjPRQZ4urO2WTs6o6MzYdzm+xnEGrRF87tkDPD7sTte5GlPomIRpuMGiVzQ4F2Vt/U+KCvRDi7d7ueoiIqGn8Z14PZJFEp2xydr6kGos3HMH+c6Voad7oxJSwFieX+ub+DHVVnvV1iX8KhFwJuVyGiSlh7a6/JVEBOgYiREQOwGCkB8otrYbJ3LFpkT05xXhpQybyympg0Cox93dxeGJkFAxa26ESg1aJJ0ZGtbjPiP/ZH5C49QkM3DIZypqLDd5PDje0q/6WhPpo0dvPo111EBFR63CYpgfKudhxE1clSeCf+89j/YFcAEBfow6PXx8FL3clevt54JpQ70s7sJbA4O3dqh1Y/c9+j4SMpyAXZpT7xMOsanxeSXK4ob7+gnKUVpugd68fmmlvRsTopUFMYNfZRp6IqLtjMNLDXKioRVVtx2xyVllrxuqtJ3HwXBkAYFRcAO5J7gU3+f8SbnK5DDGBnrB4WqDw8GxxBUrA2e8Rn/EnyIUFuWFjcHjwyxDypr+mcrmsQ5fv+uhU6B/MU3SJiByJwUgP01FZkbPFVVix5QQKy2uhUsgxeWg4ro30bVedAWf+H+J/S60PRMLvwqGUlwF565b+dgRPjRsGhOh5ii4RkYMxGOlBKmrNuFhR1+56dp6+iA+3n0adWYKfToXpN0QjzEfbrjr9zv/7ikBkLA6lLHVoIKJVKZAU5g03Lt0lInI4BiM9SHs3ObNIAuv2nsX3h+qX7sYFeeKxEVHQadr/NSoz9Ee1Lgylvkk4PGixQwMRlZsc14QZWr0BGxERdSwGIz1EnVlCXlnbl/OW15iw6peTyMwrBwDc1j8Qd18T0mFDGnXuRuy66R8wKfUODUQUChmuCfOGu4qBCBGRszAY6SHOFle1eZOz7KJKvLPlBIoq66B2k+OhYREYFOHT7jYZs/8FGQTywu8CAJjU7a/THnI5kNjLmyfrEhE5GYORHkCSBM4Wty0rknGiCB//dhomi0CApxozbohGiKH9G4EFZn+L/jv+AgCo0oWhzDep3XXaQyYD+gfr4eOhcuhziYioIQYjPUBeWQ3qmtnkTJJEg706JAh8sessNh8pAAAkhOgxbURvaFXt/8oEnv4G/XfOgUxIOBs5HmU+A9pdp736Gj1h9NI4/LlERNRQlwhGVqxYgVdffRV5eXlITEzE8uXLMXjw4EbLrl69Gh9//DEOHjwIAEhOTsbixYubLE/NL+fdnV2M9J05Nue86N2V0KoUyC2tP0hvzIAgjEkMhrwDTqkNOr0O/XbMhQwCZyMn4kjyi4DMsStYIvw8ENrO1T9ERNRxnL6O8bPPPkNqairS0tKwZ88eJCYmYvTo0SgoKGi0/JYtWzBp0iT89NNPyMjIQGhoKG699VacO3fOwS13DcWVdaioMTf63u7sYqz8+USDA+dKq03ILa2BUiHDjBuiMDYppOMDkahJTglEgr3dER2gc+gziYioeU4PRt544w1MmzYNDz30EPr164d3330XWq0WH3zwQaPl165di+nTpyMpKQmxsbF47733IEkSNm/e7OCWu4amsiKSJJC+M6fZe7UqBRJ7eXdIO/QlB9F/57OQQeBM1L04MjDN4YGIv6cacUHc5p2IqKtx6jBNXV0ddu/ejblz51qvyeVyjBo1ChkZGa2qo6qqCiaTCT4+ja/EqK2tRW1trfV1WVn91uWSJEFq6/ISF1FVZ0ZheQ2EaPje0fzyBhmRq5VWm3E0v7zd57QIIVDi1Q850Q9ALsw4cs08ADI02rBO4q1Vol+QJ4QQEA58rrNIkgQhRLf/jncl7HPHY587Xmf1tVODkQsXLsBiscBoNNpcNxqNOHLkSKvqmD17NoKDgzFq1KhG31+yZAnmz5/f4HphYSHq6tq/G2lXdra4GuaK2kbfKy4pb1UdxSUlsHi24ywbISBkgFRXhcN9noAMMqCqtO31tYFGKUeQQYeiC4UOfa4zSZKE0tJSCCEglzs9AdojsM8dj33ueKWlnfPzu0tMYG2rpUuXIj09HVu2bIFG0/jKiLlz5yI1NdX6uqysDKGhofD394e3t7eDWup4JouEw8VFUHg0vgzX4K0A0Pi8HNty3lB4tC0zEnLyM/if/wn7rv0rzAJQeHi3eFBeR9MoFUgO94ZG2bM2NZMkCTKZDP7+/vwh7SDsc8djnzueStU52yE4NRjx8/ODQqFAfn6+zfX8/HwEBgY2e+9rr72GpUuXYtOmTRgwoOmloWq1Gmq1usF1uVzerb+8ecXVkASa/OXf1+gJg1bZ7FCNQatEX2PLJ+02JuREOuJ2zwMABJ/5FmcCboFMJnNoMKJ0k2NguAFatUvH3G0mk8m6/fe8q2GfOx773LE6q5+d+renUqmQnJxsM/n08mTUoUOHNnnfK6+8goULF2Ljxo0YNGiQI5rqUoQQOHOx+U3O5HIZJqaENVtmYkpYm7Z7Dzn+qTUQye77IM5H3GN3He2lkMuQ1MsbHj00ECEiciVO/0mdmpqKKVOmYNCgQRg8eDCWLVuGyspKPPTQQwCAyZMnIyQkBEuWLAEAvPzyy5g3bx4+/fRTREREIC8vDwCg0+mg03HJJgAUlNeixtTyPA/PJg64M2iVmJgShuRwg93P7nV8LWL31M/Rye77MI4lzra7jvaSyYCEXnrotdzmnYjIFTg9GJkwYQIKCwsxb9485OXlISkpCRs3brROas3JybFJC61cuRJ1dXW45x7bf22npaXhxRdfdGTTu6zmNjm70j/3nQcAXN/HD4N7+9jswNqWjEivY39H7N4FAIDTMY/g+IBn6iMDB69eiQvygp+u4dAcERF1TU4PRgBg5syZmDlzZqPvbdmyxeb16dOnO79BLqy0yoTSFpbsAsCRvDJk5ZfDTS7DnQOC231Gi7KmCNEHXgcAnI6ZhuMDnq4PRBwsOkCHYO/2n51DRESO0yWCEeo4rcmKCCHw7f76rMiIPn4dclicSeOLvSNWwzd/O072n+WUQCTMV4sIPw+HP5eIiNqHwUg3UmOyoKC8psVyR/LKcTS/Am5yGX4XH9SuZyprL8Kkrt9wrtR/EEr9nTOhOFCvQV8jd1clInJFDEa6kTMXq1qcnnFlVuT6Pv7tyoqEZX2AiMx3sWfkGlQY+jVb1kOtgLuHslOW9mqUCsQFenV4vURE5BgMRroJs0XCuZLml/MC9VmRYwWXsiIJze/l0pywI++j739fBgD45v3aZDCidJMjzqiDVA0EBBi4FwARETXAYKSbyC2tgdnSfFpECPG/FTR9/WHQti0rEn7kPfT57ysAgJP9ZiI77rFGy/noVOgX5AWVQoaCluMkIiLqoRiMdAP1m5y1PHH1cG4ZjhdWQKmQ4fb4tmVFwjNXoc+B1wAAJ/rPwqn+sxqUkcuBKH8dwn3rJ5PyECsiImoOg5FuoLCiFlV1zW9yduVckZF9/eHdhqxIROa7iD7wBgDgRP8ncap/w+XYWpUC8b308NJwwzEiImodBiPdQGuyIofOl+FEYSWUChlu629/VkQmmeCbtxUAcCL+TzjVb3qDMsHe7ogJ9ISiDRumERFRz8VgxMWV15hQXNn8JmdXZkVu6BvQpqyIkCux77q/wf/cj8iLGGfznptChrggLxi9Gj85mYiIqDlc2uDisotalxU5eaESKoUct9k5V8S7YIf1zxalR4NAxFurxLWRvgxEiIiozRiMuLBac8ubnAkh8M/Lc0Vi/KF3b/1cjt6HlmPQlvvR+9DbDd6TyYBIfw8khxugUSrsazgREdEVOEzjws5crEZLC1UOnCvFqctZkdbOFRECkYfeQuThFQAASWF76Jy7SoH4YJ6KS0REHYPBiIuSJNHiJmdXzhW5sbVZkasCkWMD/oLs2EesbwfqNYgN9ISbgkk1IiLqGAxGXFRuWQ1M5ubTIv89V4rTRVVQuckxujVZESEQefCviMx8BwBwNHE2cmKmAgAUChliAz0RpOeJuERE1LEYjLionBYmrl6ZFbkpJgBerciKRB1cht6ZKwEARxPnICfmYQCAXqtEfLAe7irODSEioo7HYMQFFVXUorLW3GyZ/WdLkV1UBbWbHKP7G1tVb617AAAgK+lZnOn7IGQyINzXA1H+Hp1ywB0RERHAYMQl5bSwyZntXJEAeLZyN9Sz0fehxC8ZFd6xUCvliA/Ww9COU32JiIhag7MQXUxlrRlFFXXNltl3pgQ5F1uRFRECoUc/hrK22HqpwjsWAV5qXBvpy0CEiIgcgsGIi7EnK3JzbDNZESEQ/d9XELNvEa75+SHILHVQyGWIC/bCgF7eUHK1DBEROQiHaVxInVlCXmnzm5ztPVOCM8XV0CjluLVfEytohECf/S8j/OgHAIDzkf8HhUqNlAgfeKj5lSAiIsfibx4XcrygAhZJNPm+ZJMVMUKnaeSvVwj02b8E4UfXAAAyB87HuehJiPHXMRAhIiKn4G8fF3GhohbnW9jkbG9OCc5eyorc0q+RuSJCoO++xQg79hEAIDN5Ac5FTYRO44ZeBu4fQkREzsFgxAWYLBIyc8uaLXNlVmRUrBG6RrIcvQ+vsAYih5MX4nzUBABAjNGTS3eJiMhpOEvRBWTllaPW1Pxuq3tyinGupBruSkXjWREAeWFjUKMNwuFBi6yBiNFLw1UzRETkVMyMdHEF5TUtTlqVhMC/9ucCAEbFBTQ596PaMxzbb/t/kNy0AACFXIY+Rl3HNpiIiMhOzIx0YXVmCUdyy1sstzu7iayIkNB370vwO/+T9dLlQAQAIvw8oFFyi3ciInIuBiNdWFZeOepaOAxPkgT+dWmuyC39jNCqLmVFhITYPfMRduwjJGQ8CVV1gc197ioFwn20V1dHRETkcBym6aIKymqQX9b88AwA7MouxvnSGmhVCoyKqz9bBkJC7O409Dr5GQRkyExeiLpL585c1seog1zOSatEROR8DEa6oFqzBZl5LQ/PSJLAv/57KSsSdykrIiTE7p6HXic/h5DJcWjwy8gLH2tzn49OhQBPTae0nYiIyF4MRrqgrLxymFoYngGAndkXkXspK3JzXAAgJMTteh4hp768FIi8grzwu2zukcvrl/ISERF1FZwz0sXkldagoKy2xXL1WZH6FTS3XporEnT6a2sgcnDwqw0CEQDoZdByp1UiIupS+FupC6k1W3Akr/nNzS7bcfoi8kpr4KFS4ObY+hU0ueHjYCjchaLA4cgPu7PBPSo3OSL9PDq0zURERO3FYKQLycwth9nS9Nkzl1mumCsyup8/3C//LcoVODx4SZP3RQfo4MbTeImIqIvhb6Yu4nxJNS6Utzw8A9RnRfLLauGpkiG1chn675wNSJZm7/FyVyLYm+fPEBFR18NgpAuoMVlwNL/l1TNAfVbku/3nIYeENd4foNeZb2HMWQ+v4gPN3hcTyEmrRETUNXGYpgvIzC1rcXhGkgSOFpRj5+mLuFBehbfU7yK5bBskmRsODn0TZb5JTd4b5K2B3l3Zwa0mIiLqGAxGnOxcSTWKKuqaLbM7uxjpO3NQXGWCAha8qXwHd8oyYJEpcHDoMhT2urXJexUKGaIDeP4MERF1XQxGnKg1wzO7s4ux8ucTAAAFLFimXIExit9gEgrMqHsSUZYUJDdzf6SfB9RuPH+GiIi6Ls4ZcaJD58tgaWZ4RpIE0nfmWF/HybJxq3wX6oQC001/xA9SCtJ35kCSGq9Dq1Yg1MDzZ4iIqGtjZsRJzlysQnFl88MzRwvKUVxlsr4+KCLxmCkVCliwWarPhxRXmXC0oByxgV4N7o8xevL8GSIi6vIYjDhBdZ0FxwsqWixXWm2CG8zwRyly4QsA2CIlNVruav6eavjq1O1uKxERUWfjMI0THM4thaWJoZUrGdQyLFcuxzp1GsJleU2Wu3qljFwO9OX5M0RE5CKYGXGwnKIqFFc2zGRcTWapwx1Hn0W4YidqhRvCZfnIFoENyhm0SvQNsA08wnw84K7ipFUiInINDEYcqKrOjBOFLQ/PyCx16LftSQQV/Bu1QolHTan4RUpstOzElDCbeSFqpRy9ef4MERG5EA7TOIgQAofPl7U4PCOz1CFh+ywE5dUHIn9WzEbvIXfBoLUdijFolXhiZBSSww021/sEeELBSatERORCmBlxkJyLVSipan54Rmapw4Dts+Cf+xNqhBLTpadx/a33oJdBi2FRfjhaUI7SahP07vVDM1evlPHWKhGo13TmxyAiIupwDEYcoLK2dcMzCksNaovPoUYoMc30NK654ffodWmfELlc1ujy3ctkMp4/Q0REronBSCcTQuDQ+TJIUstl9xRI+FPp04jGWUQmj8KAXt6tfk6wtzs8NTx/hoiIXA/njHSy00VVKGtkH5DL5JZa+J/bhHPF1Vj160mUCB3co67DLXHGVj/DTSFDlD/PnyEiItfEzEgnqqg149SFpodn5JZaDNg2HX55v2KDfBpqTDcixuiJ+4aEQSZr/STUKH8dVG6MK4mIyDUxGOkkQggcOlfa5PCM3FyDxG3T4Zu/FdVQY3+NEQGeajwxMgpuitYHFjqNG3oZ3Duo1URERI7Hf053klMXKlFeY270vfpA5An45m9FjUyNB2v/gv2KBMy6KRo6jX3xYYzR064sChERUVfDYKQTlNWYcLqostH35OZqJG57HL7521Arc8fkmr9gJ+Lw+MhIBOnty3AYvTQweKg6oslEREROw2Ckg0lS/eZmjQ3PyCQzErc+Dt/87aiTu+P+mmewQ8RhUkoY+gfr7XqOQi5DHyMnrRIRketjMNLBzpdWo6KJ4Rkhd0OJ/2CYFFpMqZuNnSIWN8UE4MbYALufE+HnAY2S588QEZHr4wTWDmayNL/d+97e0zDjcCyOmPXoH+yFCSmhdj/DXaVAuI+2rU0kIiLqUpgZ6WRycxX67FsChakStWYL3v7pOI5U6xGk1+Cx6yPbdI5MH6OuwVbwREREroqZkU6kMFUiaeujMBTuhLb8NJ6Q/oLTRVXQqd0w66ZoaFX2d7+PToUAT54/Q0RE3QczI51EYapE0q/TYCjcCbNSh4/c7sGu7GIo5DJMvyGqTQGFXF6/lJeIiKg7YTDSCRSmCiT9+ggMF3bBpPTEJ9HL8PYxAwDggSHh6NuGgEImA2IDveChZjKLiIi6F/5m62Cyugpc8+sj8L6wByalJ74b8A5eynADIDC6nxHX9fGzu06FXIaEXnr46dQd32AiIiInYzDSwfx/nAmPC3tgUnrhp5RVSNsuh1kyI6mXN/4wsJfd9Snd5EgK9YbenSfyEhFR98Rhmg5kkQR+C3scRepQfBa3HAv2qFBWY0YvgzseGdHb7hUw7ioFUiIMDESIiKhbY2akIwiBjYfyMP9fh5FbWgMFFsOyQwGgBhqlHLNujLZ7gzKdxg1Jod7c2IyIiLo9BiPtVV2Cog8m4P2ztyJXxAIALPhfAFFjknC6qAq+dsz3MHiokNhLb9fpvURERK6Kv+3ao7oE4pPfw7fwN7yhXAklGt8GPn1nDiSp+Z1ZLzN6aXBNqDcDESIi6jH4G6+tqouBT8ZBdn4PLgodHjWlwtREoqm4yoSjBeUtVhnqo0V8iBd3VyUioh6FwzRtUV0MfDwOyN2HWpUB95bPxhER1uwtpdWmZt+PDtAhws+jAxtJRETkGpgZsVfVReDjsUDuPkDriyO3rm0xEAHQ5IoYmQzoF+zFQISIiHosBiP22rYMyN0PaP2AKd8hfuAwBOk1aG5gxaBVom9Aw11XFXIZEkO9Eezt3mnNJSIi6uoYjNjrxueBpPuBB78DjP2gkMuQNqYfADQZkExMCWswD0TpJsfAcAN3VSUioh6PwUhr1JQB4tJqGDcVMG4FEBBnffu2+CCsvH8gAvW2h98ZtEo8MTIKyeEGm+vczIyIiOh/OIG1JZUXgI/uAiKuA373cv0kj0bcFh+EW/oF4tt953A4twx69/qhmaszItzMjIiIyBaDkeZUFAIf3wUUHAaqLgAjUgHPwCaLK+QyJIUZ4KlpPOPBzcyIiIgaYjDSlIpC4KMxQGEmoAusnyPSTCDSEqOXBv2DuYcIERHR1RiMNKai4FIgcgTwDAKmfAf4Rbe5ulAfLWICG66mISIiIgYjDZXn1wciF7IAz+D6jIhvVJur42ZmREREzWMwcrVzu4GiY+0ORGQyIC7Ii3uIEBERtYDByNVibwf+bw1gjG9zIKKQy5DQS889RIiIiFqBwQgAlOcBQgK8gutf9xvb5qpUlzYz4x4iRERErcNgpCwX+OjO+mDkwfX/C0jaKITDMkRERHbp2RtelJ0H1twBFB0HLCbAUufsFhEREfU4XSIYWbFiBSIiIqDRaDBkyBDs2LGj2fJffPEFYmNjodFokJCQgA0bNtj/0MuByMUTgD6sPitiiGjbByAiIqI2c3ow8tlnnyE1NRVpaWnYs2cPEhMTMXr0aBQUFDRafvv27Zg0aRKmTp2KvXv3Yty4cRg3bhwOHjxo13Nl/5gAXDwJeIcBD60HDOEd8XGIiIjITjIhLp8A5xxDhgxBSkoK3n77bQCAJEkIDQ3FrFmzMGfOnAblJ0yYgMrKSnz33XfWa9deey2SkpLw7rvvtvi8srIy6PV6lM7xhJcxon75rndYh30eakiSJBQUFCAgIAByudPj3x6Bfe547HPHY587XklJCQwGA0pLS+Hl5dVh9Tp1AmtdXR12796NuXPnWq/J5XKMGjUKGRkZjd6TkZGB1NRUm2ujR4/GN99802j52tpa1NbWWl+XlpbW/686BNLvPwXgBZSUtOtzUPMkSUJZWRlUKhV/YDgI+9zx2OeOxz53vJJLvy87Oo/h1GDkwoULsFgsMBqNNteNRiOOHDnS6D15eXmNls/Ly2u0/JIlSzB//vwG18PmHwHmJ7Sx5URERD1XUVER9Hp9h9XX7Zf2zp071yaTUlJSgvDwcOTk5HRoR1LTysrKEBoaijNnznRoWo+axj53PPa547HPHa+0tBRhYWHw8fHp0HqdGoz4+flBoVAgPz/f5np+fj4CAxs/ITcwMNCu8mq1Gmp1w51Q9Xo9v7wO5uXlxT53MPa547HPHY997ngdPSzm1EE2lUqF5ORkbN682XpNkiRs3rwZQ4cObfSeoUOH2pQHgB9//LHJ8kRERNS1OX2YJjU1FVOmTMGgQYMwePBgLFu2DJWVlXjooYcAAJMnT0ZISAiWLFkCAPjjH/+IkSNH4vXXX8cdd9yB9PR07Nq1C6tWrXLmxyAiIqI2cnowMmHCBBQWFmLevHnIy8tDUlISNm7caJ2kmpOTY5MOGjZsGD799FM8//zzePbZZ9GnTx988803iI+Pb9Xz1Go10tLSGh26oc7BPnc89rnjsc8dj33ueJ3V507fZ4SIiIh6Ni7MJiIiIqdiMEJEREROxWCEiIiInIrBCBERETlVtwxGVqxYgYiICGg0GgwZMgQ7duxotvwXX3yB2NhYaDQaJCQkYMOGDQ5qafdhT5+vXr0aI0aMgMFggMFgwKhRo1r8O6KG7P2eX5aeng6ZTIZx48Z1bgO7IXv7vKSkBDNmzEBQUBDUajX69u3Lny92srfPly1bhpiYGLi7uyM0NBRPPfUUampqHNRa1/fLL79gzJgxCA4Ohkwma/Lctytt2bIFAwcOhFqtRnR0NNasWWP/g0U3k56eLlQqlfjggw/EoUOHxLRp04S3t7fIz89vtPy2bduEQqEQr7zyijh8+LB4/vnnhVKpFAcOHHBwy12XvX1+7733ihUrVoi9e/eKzMxM8eCDDwq9Xi/Onj3r4Ja7Lnv7/LJTp06JkJAQMWLECDF27FjHNLabsLfPa2trxaBBg8Ttt98utm7dKk6dOiW2bNki9u3b5+CWuy57+3zt2rVCrVaLtWvXilOnTonvv/9eBAUFiaeeesrBLXddGzZsEM8995xYt26dACC+/vrrZsufPHlSaLVakZqaKg4fPiyWL18uFAqF2Lhxo13P7XbByODBg8WMGTOsry0WiwgODhZLlixptPz48ePFHXfcYXNtyJAh4rHHHuvUdnYn9vb51cxms/D09BQfffRRZzWx22lLn5vNZjFs2DDx3nvviSlTpjAYsZO9fb5y5UoRGRkp6urqHNXEbsfePp8xY4a46aabbK6lpqaK4cOHd2o7u6vWBCN/+ctfRP/+/W2uTZgwQYwePdquZ3WrYZq6ujrs3r0bo0aNsl6Ty+UYNWoUMjIyGr0nIyPDpjwAjB49usnyZKstfX61qqoqmEymDj94qbtqa58vWLAAAQEBmDp1qiOa2a20pc+//fZbDB06FDNmzIDRaER8fDwWL14Mi8XiqGa7tLb0+bBhw7B7927rUM7JkyexYcMG3H777Q5pc0/UUb9Dnb4Da0e6cOECLBaLdffWy4xGI44cOdLoPXl5eY2Wz8vL67R2didt6fOrzZ49G8HBwQ2+0NS4tvT51q1b8f7772Pfvn0OaGH305Y+P3nyJP7973/jvvvuw4YNG3D8+HFMnz4dJpMJaWlpjmi2S2tLn9977724cOECrrvuOgghYDab8fjjj+PZZ591RJN7pKZ+h5aVlaG6uhru7u6tqqdbZUbI9SxduhTp6en4+uuvodFonN2cbqm8vBwPPPAAVq9eDT8/P2c3p8eQJAkBAQFYtWoVkpOTMWHCBDz33HN49913nd20bmvLli1YvHgx3nnnHezZswfr1q3D+vXrsXDhQmc3jVrQrTIjfn5+UCgUyM/Pt7men5+PwMDARu8JDAy0qzzZakufX/baa69h6dKl2LRpEwYMGNCZzexW7O3zEydO4PTp0xgzZoz1miRJAAA3NzdkZWUhKiqqcxvt4tryPQ8KCoJSqYRCobBei4uLQ15eHurq6qBSqTq1za6uLX3+wgsv4IEHHsAjjzwCAEhISEBlZSUeffRRPPfccx1+7D01/TvUy8ur1VkRoJtlRlQqFZKTk7F582brNUmSsHnzZgwdOrTRe4YOHWpTHgB+/PHHJsuTrbb0OQC88sorWLhwITZu3IhBgwY5oqndhr19HhsbiwMHDmDfvn3W/+666y7ceOON2LdvH0JDQx3ZfJfUlu/58OHDcfz4cWvgBwBHjx5FUFAQA5FWaEufV1VVNQg4LgeDgsewdYoO+x1q39zari89PV2o1WqxZs0acfjwYfHoo48Kb29vkZeXJ4QQ4oEHHhBz5syxlt+2bZtwc3MTr732msjMzBRpaWlc2msne/t86dKlQqVSiS+//FLk5uZa/ysvL3fWR3A59vb51biaxn729nlOTo7w9PQUM2fOFFlZWeK7774TAQEBYtGiRc76CC7H3j5PS0sTnp6e4h//+Ic4efKk+OGHH0RUVJQYP368sz6CyykvLxd79+4Ve/fuFQDEG2+8Ifbu3Suys7OFEELMmTNHPPDAA9byl5f2PvPMMyIzM1OsWLGCS3svW758uQgLCxMqlUoMHjxY/Pbbb9b3Ro4cKaZMmWJT/vPPPxd9+/YVKpVK9O/fX6xfv97BLXZ99vR5eHi4ANDgv7S0NMc33IXZ+z2/EoORtrG3z7dv3y6GDBki1Gq1iIyMFC+99JIwm80ObrVrs6fPTSaTePHFF0VUVJTQaDQiNDRUTJ8+XRQXFzu+4S7qp59+avTn8+V+njJlihg5cmSDe5KSkoRKpRKRkZHiww8/tPu5MiGYuyIiIiLn6VZzRoiIiMj1MBghIiIip2IwQkRERE7FYISIiIicisEIERERORWDESIiInIqBiNERETkVAxGiIiIyKkYjBBRk9asWQNvb+8OrfP06dOQyWTYt29fh9ZLRK6LwQhRF/bggw9CJpNh6dKlNte/+eYbyGSyTn/+hAkTcPTo0U5/DhH1bAxGiLo4jUaDl19+GcXFxQ5/tru7OwICAhz+3K7IZDI5uwlE3RaDEaIubtSoUQgMDMSSJUuaLffVV1+hf//+UKvViIiIwOuvv27zfkREBBYtWoTJkydDp9MhPDwc3377LQoLCzF27FjodDoMGDAAu3btst5z9TDNiy++iKSkJHzyySeIiIiAXq/HxIkTUV5ebi2zceNGXHfddfD29oavry/uvPNOnDhxwq7PXFtbi9mzZyM0NBRqtRrR0dF4//33re///PPPGDx4MNRqNYKCgjBnzhyYzWYAwKpVqxAcHAxJkmzqHDt2LB5++GHr63/+858YOHAgNBoNIiMjMX/+fGsdACCTybBy5Urcdddd8PDwwEsvvQSLxYKpU6eid+/ecHd3R0xMDP7617/aPMdsNuPJJ5+0fv7Zs2djypQpGDdunLWMJElYsmSJtZ7ExER8+eWXdvURUbfS3hP+iKjzXD5dd926dUKj0YgzZ84IIYT4+uuvxZX/9921a5eQy+ViwYIFIisrS3z44YfC3d3d5vTM8PBw4ePjI959911x9OhR8cQTTwgvLy9x2223ic8//1xkZWWJcePGibi4OCFJkhBCiA8//FDo9XprHWlpaUKn04m7775bHDhwQPzyyy8iMDBQPPvss9YyX375pfjqq6/EsWPHxN69e8WYMWNEQkKCsFgsQgghTp06JQCIvXv3Nvm5x48fL0JDQ8W6devEiRMnxKZNm0R6eroQQoizZ88KrVYrpk+fLjIzM8XXX38t/Pz8rKc+X7x4UahUKrFp0yZrfUVFRTbXfvnlF+Hl5SXWrFkjTpw4IX744QcREREhXnzxRes9AERAQID44IMPxIkTJ0R2draoq6sT8+bNEzt37hQnT54Uf//734VWqxWfffaZ9b5FixYJHx8fsW7dOpGZmSkef/xx4eXlZXNK8qJFi0RsbKzYuHGjOHHihPjwww+FWq0WW7Zsae7rQNRtMRgh6sIuByNCCHHttdeKhx9+WAjRMBi59957xS233GJz7zPPPCP69etnfR0eHi7uv/9+6+vc3FwBQLzwwgvWaxkZGQKAyM3NFUI0HoxotVpRVlZm85whQ4Y0+RkKCwsFAHHgwAEhRMvBSFZWlgAgfvzxx0bff/bZZ0VMTIw1YBJCiBUrVgidTmcNeMaOHWvtKyGE+Nvf/iaCg4Ot7998881i8eLFNvV+8sknIigoyPoagPjTn/7U5Oe6bMaMGeIPf/iD9bXRaBSvvvqq9bXZbBZhYWHWv8eamhqh1WrF9u3bbeqZOnWqmDRpUovPI+qOOExD5CJefvllfPTRR8jMzGzwXmZmJoYPH25zbfjw4Th27BgsFov12oABA6x/NhqNAICEhIQG1woKCppsR0REBDw9Pa2vg4KCbMofO3YMkyZNQmRkJLy8vBAREQEAyMnJac3HxL59+6BQKDBy5MhG38/MzMTQoUNtJvAOHz4cFRUVOHv2LADgvvvuw1dffYXa2loAwNq1azFx4kTI5fU/8vbv348FCxZAp9NZ/5s2bRpyc3NRVVVlrXfQoEENnr9ixQokJyfD398fOp0Oq1atsn620tJS5OfnY/DgwdbyCoUCycnJ1tfHjx9HVVUVbrnlFpvnf/zxx3YPZxF1F27ObgARtc7111+P0aNHY+7cuXjwwQfbVIdSqbT++fIv88auXT3foqk6Lt9zZfkxY8YgPDwcq1evts7diI+PR11dXava6O7u3qpyzRkzZgyEEFi/fj1SUlLw66+/4s0337S+X1FRgfnz5+Puu+9ucK9Go7H+2cPDw+a99PR0PP3003j99dcxdOhQeHp64tVXX8V//vOfVretoqICALB+/XqEhITYvKdWq1tdD1F3wmCEyIUsXboUSUlJiImJsbkeFxeHbdu22Vzbtm0b+vbtC4VC4bD2FRUVISsrC6tXr8aIESMAAFu3brWrjoSEBEiShJ9//hmjRo1q8H5cXBy++uorCCGswdO2bdvg6emJXr16AagPKO6++26sXbsWx48fR0xMDAYOHGitY+DAgcjKykJ0dLRdbdu2bRuGDRuG6dOnW69dmc3Q6/UwGo3YuXMnrr/+egCAxWLBnj17kJSUBADo168f1Go1cnJymsz+EPU0DEaIXEhCQgLuu+8+vPXWWzbX//znPyMlJQULFy7EhAkTkJGRgbfffhvvvPOOQ9tnMBjg6+uLVatWISgoCDk5OZgzZ45ddURERGDKlCl4+OGH8dZbbyExMRHZ2dkoKCjA+PHjMX36dCxbtgyzZs3CzJkzkZWVhbS0NKSmplqHYYD6oZo777wThw4dwv3332/zjHnz5uHOO+9EWFgY7rnnHsjlcuzfvx8HDx7EokWLmmxbnz598PHHH+P7779H79698cknn2Dnzp3o3bu3tcysWbOwZMkSREdHIzY2FsuXL0dxcbE1cPL09MTTTz+Np556CpIk4brrrkNpaSm2bdsGLy8vTJkyxa7+IuoOOGeEyMUsWLCgwTDKwIED8fnnnyM9PR3x8fGYN28eFixY0ObhnLaSy+VIT0/H7t27ER8fj6eeegqvvvqq3fWsXLkS99xzD6ZPn47Y2FhMmzYNlZWVAICQkBBs2LABO3bsQGJiIh5//HFMnToVzz//vE0dN910E3x8fJCVlYV7773X5r3Ro0fju+++ww8//ICUlBRce+21ePPNNxEeHt5sux577DHcfffdmDBhAoYMGYKioiKbLAkAzJ49G5MmTcLkyZMxdOhQ6HQ6jB492mb4Z+HChXjhhRewZMkSxMXF4bbbbsP69ettghqinkQmhBDObgQRUXclSRLi4uIwfvx4LFy40NnNIeqSOExDRNSBsrOz8cMPP2DkyJGora3F22+/jVOnTjXIzhDR/3CYhoioA8nlcqxZswYpKSkYPnw4Dhw4gE2bNiEuLs7ZTSPqsjhMQ0RERE7FzAgRERE5FYMRIiIicioGI0RERORUDEaIiIjIqRiMEBERkVMxGCEiIiKnYjBCRERETsVghIiIiJzq/wPpIdmZyn9LlwAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "C5z4kQE7JZ8_"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}