Nonlinear_Least_Squares_Optimization_for_Multi_Exponential_Decay_Models.ipynb

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      "source": [
        "# Nonlinear Least Squares Optimization for Multi-Exponential Decay Models\n",
        "\n",
        "Name: John Hodge\n",
        "\n",
        "Date: 04/21/24"
      ],
      "metadata": {
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      "cell_type": "markdown",
      "source": [
        "Non-linear system optimization using nonlinear least squares is a common technique used in various fields such as engineering, economics, and physics to fit a model to a set of data points. One illustrative example is the estimation of parameters in the exponential decay model, which is frequently used in physics and chemistry to describe how the intensity of a phenomenon decreases over time.\n",
        "\n",
        "### Exponential Decay Model Example\n",
        "\n",
        "Consider a scenario where you have observed data from a process that follows exponential decay, such as radioactive decay or the discharge of a capacitor in an RC circuit. The exponential decay model can be described by the following equation:\n",
        "\n",
        "$ y(t) = A \\exp(-\\lambda t) + \\epsilon $\n",
        "\n",
        "Where:\n",
        "- $ y(t) $ is the observed value at time \\( $t$ \\),\n",
        "- $ A $ is the initial intensity or amount,\n",
        "- $ \\lambda $ is the decay constant,\n",
        "- $ \\epsilon $ is the error term, which is usually assumed to be normally distributed.\n",
        "\n",
        "The goal is to estimate the parameters \\( $A$ \\) and \\( $\\lambda$ \\) that best fit the observed data. This is done by minimizing the sum of the squares of the residuals, where residuals are the differences between the observed values and the values predicted by the model.\n",
        "\n",
        "### Nonlinear Least Squares Optimization\n",
        "\n",
        "To perform the nonlinear least squares optimization:\n",
        "\n",
        "1. **Define the Objective Function**: The objective function $F(A, \\lambda)$ is defined as the sum of the squared differences between observed values \\( $y_i$ \\) and modeled values $\\hat{y}_i(A, \\lambda)$:\n",
        "\n",
        "   $ F(A, \\lambda) = \\sum_{i=1}^{n} [y_i - A \\exp(-\\lambda t_i)]^2 $\n",
        "\n",
        "2. **Choose Initial Guesses**: Start with initial guesses for \\( $A$ \\) and \\( $\\lambda$ \\). The accuracy of initial guesses can significantly affect the convergence of the optimization algorithm.\n",
        "\n",
        "3. **Optimization Algorithm**: Use an optimization algorithm like the Levenberg-Marquardt algorithm, which is well-suited for nonlinear least squares problems. This algorithm iteratively adjusts \\( $A$ \\) and \\( $\\lambda$ \\) to find the minimum of $F(A, \\lambda)$.\n",
        "\n",
        "4. **Convergence**: The optimization process continues until it converges, meaning that changes in the parameters no longer significantly reduce $F(A, \\lambda)$, or until a maximum number of iterations is reached.\n",
        "\n",
        "5. **Result**: The output is the estimated values of \\( $A$ \\) and \\( $\\lambda$ \\) that provide the best fit to the data under the exponential decay model.\n",
        "\n",
        "### Application Example\n",
        "\n",
        "If you have data from a chemical reaction where the concentration of a reactant decreases over time, you could use this model and method to estimate the speed of the reaction and the initial concentration. This information could be crucial for scaling up the reaction for industrial production or for studying reaction kinetics in detail.\n",
        "\n",
        "This example demonstrates how nonlinear least squares can be applied to real-world problems where the underlying relationships between variables are non-linear and the parameters of the model need to be estimated accurately to understand the system dynamics."
      ],
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      "cell_type": "markdown",
      "source": [
        "Next is a step-by-step tutorial on how to perform nonlinear least squares optimization using Python and the SciPy library. In this example, we'll use the exponential decay model described in the previous discussion. We'll fit this model to some synthetic data generated for this purpose.\n",
        "\n",
        "## Install Necessary Libraries\n",
        "\n",
        "First, ensure you have the necessary Python libraries installed. You can install them using pip if you haven't already:"
      ],
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      "cell_type": "code",
      "source": [
        "!pip install numpy scipy matplotlib"
      ],
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        },
        "id": "ru72kqXLRV4z",
        "outputId": "1009aa1e-78f9-4931-e3aa-401ccd0b84b1"
      },
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: numpy in /usr/local/lib/python3.10/dist-packages (1.25.2)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.10/dist-packages (1.11.4)\n",
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            "Requirement already satisfied: packaging>=20.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (24.0)\n",
            "Requirement already satisfied: pillow>=6.2.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (9.4.0)\n",
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            "Requirement already satisfied: python-dateutil>=2.7 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (2.8.2)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.7->matplotlib) (1.16.0)\n"
          ]
        }
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      "cell_type": "markdown",
      "source": [
        "## Import Libraries\n",
        "\n",
        "Import the required modules in your Python script or notebook:"
      ],
      "metadata": {
        "id": "g7y1WPa1SX6a"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.optimize import curve_fit"
      ],
      "metadata": {
        "id": "uH-GLfIFRPVX"
      },
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Step 3: Generate Synthetic Data\n",
        "\n",
        "For demonstration purposes, we'll create synthetic data using the exponential decay model with some added noise:"
      ],
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        "id": "hMB1HHFxSc56"
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    {
      "cell_type": "code",
      "source": [
        "# Parameters\n",
        "A_true = 10  # true amplitude\n",
        "lambda_true = 0.3  # true decay constant\n",
        "\n",
        "# Generate some data points\n",
        "np.random.seed(0)\n",
        "time = np.linspace(0, 10, 50)  # time from 0 to 10\n",
        "y = A_true * np.exp(-lambda_true * time) + np.random.normal(0, 0.5, time.shape)  # model with noise\n",
        "\n",
        "# Plot the data\n",
        "plt.scatter(time, y, label='Data with Noise')\n",
        "plt.plot(time, A_true * np.exp(-lambda_true * time), 'r-', label='True model')\n",
        "plt.xlabel('Time')\n",
        "plt.ylabel('Value')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.show()"
      ],
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      "execution_count": 46,
      "outputs": [
        {
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              "<Figure size 640x480 with 1 Axes>"
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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Define the Model Function\n",
        "\n",
        "Define the exponential decay function that will be used to fit the data:"
      ],
      "metadata": {
        "id": "PTTf-YkJTBie"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def exp_decay(t, A, lam):\n",
        "    return A * np.exp(-lam * t)"
      ],
      "metadata": {
        "id": "uk63hrCRTFgb"
      },
      "execution_count": 47,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Perform Nonlinear Least Squares Optimization\n",
        "\n",
        "Use curve_fit from SciPy to fit the model to your data:"
      ],
      "metadata": {
        "id": "Lq0hsgLwTHBr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Initial guess for the parameters\n",
        "initial_guess = [8, 0.1]\n",
        "\n",
        "# Perform the curve fitting\n",
        "params, cov = curve_fit(exp_decay, time, y, p0=initial_guess)\n",
        "\n",
        "# Extract the parameters\n",
        "A_est, lambda_est = params"
      ],
      "metadata": {
        "id": "8hxyxYq9TQwT"
      },
      "execution_count": 48,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Evaluate and Visualize the Fit\n",
        "\n",
        "Evaluate the fit and visualize it alongside the original data:"
      ],
      "metadata": {
        "id": "ZJe_Sm2ZTT2t"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create a smooth curve for the fitted model\n",
        "time_fine = np.linspace(0, 10, 400)\n",
        "y_fit = exp_decay(time_fine, A_est, lambda_est)\n",
        "\n",
        "# Plot the original data, true model, and fitted model\n",
        "plt.scatter(time, y, label='Data with Noise')\n",
        "plt.plot(time, A_true * np.exp(-lambda_true * time), 'r-', label='True model')\n",
        "plt.plot(time_fine, y_fit, 'b--', label='Fitted model')\n",
        "plt.xlabel('Time')\n",
        "plt.ylabel('Value')\n",
        "plt.title('Fit of Exponential Decay Model to Noisy Data')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "AKfneCwwTdlv",
        "outputId": "d9b254aa-ca71-4730-ac1b-eb82c11ddb14"
      },
      "execution_count": 63,
      "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": [
        "## Print the Estimated Parameters\n",
        "\n",
        "Finally, print the estimated parameters to see how close they are to the true values:"
      ],
      "metadata": {
        "id": "8W46_EYRTdBX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(f\"Estimated Amplitude (A): {np.round(A_est, 3)}\")\n",
        "print(f\"Estimated Decay Constant (λ): {np.round(lambda_est, 3)}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jixEyzzUTM33",
        "outputId": "6eb40484-066e-41fc-d21a-0e80df1b2544"
      },
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Estimated Amplitude (A): 10.699\n",
            "Estimated Decay Constant (λ): 0.315\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Results Analysis\n",
        "\n",
        "These values are very close to the true values used to generate the synthetic data (Amplitude = 10, Decay Constant = 0.3), indicating a good fit by the optimization process."
      ],
      "metadata": {
        "id": "OOO55i-MUAja"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Extend the model to include a second exponential term\n",
        "\n",
        "To extend the model to include a second exponential term, we'll adjust our function to have the form:\n",
        "\n",
        "$ y(t) = A_1 \\exp(-\\lambda_1 t) + A_2 \\exp(-\\lambda_2 t) + \\epsilon $\n",
        "\n",
        "This model captures more complex behaviors such as systems with multiple decay processes. Let's modify the code to fit this new model to the data."
      ],
      "metadata": {
        "id": "WZWiFB4wUMf3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Define the new exponential decay function with two terms:"
      ],
      "metadata": {
        "id": "aMD7YWPvUeeW"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Updated exponential decay function with two terms\n",
        "def exp_decay_two_terms(t, A1, lambda1, A2, lambda2):\n",
        "    return A1 * np.exp(-lambda1 * t) + A2 * np.exp(-lambda2 * t)"
      ],
      "metadata": {
        "id": "bZOXbvVVUjQL"
      },
      "execution_count": 51,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Update the synthetic data generation to reflect this new model:\n",
        "\n",
        "For simplicity, we'll adjust the amplitude and decay constants for the two terms and generate new synthetic data."
      ],
      "metadata": {
        "id": "NyX2HG_YUndd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Generate new synthetic data with two exponential terms\n",
        "np.random.seed(0)\n",
        "A1_true = 8  # true amplitude for the first term\n",
        "lambda1_true = 0.3  # true decay constant for the first term\n",
        "A2_true = 5  # true amplitude for the second term\n",
        "lambda2_true = 0.1  # true decay constant for the second term\n",
        "y_two_terms = A1_true * np.exp(-lambda1_true * time) + A2_true * np.exp(-lambda2_true * time) + np.random.normal(0, 0.5, time.shape)"
      ],
      "metadata": {
        "id": "4RedG8UaU2qA"
      },
      "execution_count": 53,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Perform curve fitting for the two-term model"
      ],
      "metadata": {
        "id": "VERFlbDyV1wu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Perform curve fitting for the two-term model\n",
        "initial_guess_two_terms = [7, 0.2, 4, 0.05]\n",
        "params_two_terms, cov_two_terms = curve_fit(exp_decay_two_terms, time, y_two_terms, p0=initial_guess_two_terms)\n",
        "A1_est, lambda1_est, A2_est, lambda2_est = params_two_terms\n"
      ],
      "metadata": {
        "id": "3ZAWP_AnU93M"
      },
      "execution_count": 54,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Create a smooth curve for the fitted model with two terms"
      ],
      "metadata": {
        "id": "8nsSW23JV4G8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create a smooth curve for the fitted model with two terms\n",
        "y_fit_two_terms = exp_decay_two_terms(time_fine, A1_est, lambda1_est, A2_est, lambda2_est)"
      ],
      "metadata": {
        "id": "8HggzPudVAhA"
      },
      "execution_count": 55,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Evaluate and visualize the Fit"
      ],
      "metadata": {
        "id": "qNbn2SgrV81Y"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Plotting for the two-term model\n",
        "plt.scatter(time, y_two_terms, label='Data with Noise')\n",
        "plt.plot(time, A1_true * np.exp(-lambda1_true * time) + A2_true * np.exp(-lambda2_true * time), 'r-', label='True model')\n",
        "plt.plot(time_fine, y_fit_two_terms, 'b--', label='Fitted model with two terms')\n",
        "plt.xlabel('Time')\n",
        "plt.ylabel('Value')\n",
        "plt.title('Fit of Dual Exponential Decay Model to Noisy Data')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "wDTV6PCjVDij",
        "outputId": "607f245f-5bf1-486c-c308-ee9a13cee982"
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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Varl79y7FixfXb387YHJ0dATQ9/24fv06QKKjG+zt7Q2eW1pa6vvAvJlmQn1Jkuvo0aOMGTOG48eP66u444SEhODg4PDeaSfk7ffS9evXCQkJIUeOHAkeH9dp/ebNmwDvHKJ7584dRo8ezdatW+OVy5uBWYMGDXB1dWXVqlXUq1cPrVbLmjVraNasWYre505OTtSvX5/Vq1cTERGBRqOJ1wE0zu3bt3Fzc4uXflzTQdzn9/bt25iYmFCgQAGD495+7z1+/JgXL16waNGiRKdXiCu/D2Xs756ffvqJFStWMHXqVGbPnp3g9UxMTOKNuHRxcSFLlixJXm/YsGHs2bOHSpUqUbBgQRo2bEiHDh2oXr26/piiRYtSsWJFVq1aRffu3QFdIFulSpVkj/JMSnh4uMHr/OrVK6ZMmcKSJUu4f/++QZ+o5P7DcPnyZX766Sf27dsX75+m1PinIz1IICNSTVw/kTc/4Il1StZoNKjVav3zlStX0rVrV5o3b86QIUPIkSMHarWaKVOm6P84paaoqCh9Z7mbN28SERGBtbV1ql8XMCiHN8V9iWm1WkDXT8bFxSXecW+PMEosvfd18+ZN6tWrR9GiRZkxYwa5c+fG3NycnTt3MnPmTH3+jOnt95JWqyVHjhwJ9lcA4gVuSdFoNDRo0IBnz54xbNgwihYtio2NDffv36dr164G96NWq+nQoQOLFy9m/vz5HD16lAcPHrzXf+MdOnSgR48ePHz4kMaNG6fZ5JNx99OxY0e6dOmS4DGlSpVKk7ykVP78+enYsSOLFi1Kso/H+0zgWKxYMa5evcr27dvx8fFhw4YNzJ8/n9GjR+unJgBdrcwPP/zAvXv3iIqK4sSJEwYddN9XTEwM165dMwi6+/bty5IlS+jfvz9Vq1bFwcEBlUpFu3btkvU5e/HiBbVr18be3p7x48dToEABLC0t8fX1ZdiwYanyWU0PEshkUin5oObNmxeAq1evGjRvREdHExgYmKwaivcR1wHZy8tLv83R0THB0Qq3b982yNvff/9N/vz52bhxo8G9xo2qSm1jxowhICCAadOmMWzYMIYPH86cOXPiHRdXO/Kma9euYW1trf9jam1tzdWrV+Mdd+XKFUxMTFI8z07cf9w5cuQw2muXkvfTtm3biIqKYuvWrQa1R6k1oiw8PJxNmzaRO3dufS1EgQIF2LNnD9WrVzeoOn9bXFldunQp0f+YL168yLVr11i2bJlB597EmnY7d+7M9OnT2bZtG7t27cLJycngPZ5cLVq0oGfPnpw4cYJ169YlelzevHnZs2cPYWFhBv+txzULxH2+8+bNi1ar5ebNmwY1IG+/9+JGNGk0mlR//6TGd89PP/3EypUr8fb2TvB6Wq2W69ev698roOvc/OLFC31+EmNjY0Pbtm1p27Yt0dHRfPnll0yaNIkRI0bomybbtWvHwIEDWbNmjX5+r7Zt26b4Pt72999/8+rVK4P30t9//02XLl2YPn26fltkZGS879DEyv/AgQM8ffqUjRs3UqtWLf32wMDAD85vRiJ9ZDIpGxsbgGQNYaxfvz7m5ubMmTPHoGryjz/+ICQkJMFRDR9q9erV/P7771StWpV69erptxcoUIATJ04QHR2t37Z9+3bu3r1rcH5cLcKb+T158uR7D29MiZMnTzJt2jT69+/PoEGDGDJkCPPmzePgwYPxjj1+/LhBW/Xdu3fZsmULDRs2RK1Wo1aradiwIVu2bDEYTfTo0SP9pGhvNwW9i5eXF/b29kyePDnBUR/vM0NoXG1Tct5PCb02ISEhLFmyJMXXfZdXr17RqVMnnj17xsiRI/Vf2G3atEGj0TBhwoR458TGxurvo2HDhtjZ2TFlyhQiIyMNjovLf0L3oyhKgk0XoKutKFWqFL///jsbNmygXbt27zXPjq2tLQsWLGDs2LE0bdo00eM+++wzNBpNvP/6Z86ciUqlonHjxgD6n28H3G+PQlKr1bRs2ZINGzYYjK6L8z7vn8S+j1Lju6dAgQJ07NiRhQsX8vDhQ4N9cZNdvn3PcZMpJnW9p0+fGjw3NzfHw8MDRVEMPmfZs2encePGrFy5klWrVtGoUSODebTex/nz5+nfvz+Ojo706dNHv12tVscbYj937tx4Q6cTK/+E3tvR0dHMnz//g/Kb0UiNTCYV18G0X79+eHl5oVarEx1e6OTkxIgRIxg3bhyNGjXiiy++4OrVq8yfP5+KFSt+cCe1v//+G1tbW6Kjo/Uz+x49epTSpUuzfv16g2O/+eYb/v77bxo1akSbNm24efMmK1eujNeu//nnn7Nx40ZatGhBkyZNCAwM5LfffsPDw0PfX+J9+Pr6snLlynjb44ZORkZG0qVLFwoVKsSkSZMA3dwq27Zt4+uvv+bixYv6Lw3Q9b3w8vKiX79+WFhY6L8g3qyKnjhxIrt376ZGjRr07t0bU1NTFi5cSFRUFD///HOK78He3p4FCxbQqVMnypUrR7t27XBycuLOnTvs2LGD6tWrp7iq28rKCg8PD9atW0fhwoXJmjUrJUqUSLBvScOGDTE3N6dp06b07NmT8PBwFi9eTI4cORLthJkc9+/f17824eHh+Pv7s379eh4+fMigQYPo2bOn/tjatWvTs2dPpkyZgp+fHw0bNsTMzIzr16+zfv16Zs+eTatWrbC3t2fmzJl88803VKxYkQ4dOuDo6Mj58+eJiIhg2bJlFC1alAIFCjB48GDu37+Pvb09GzZsSLIPUefOnRk8eDDAB31+EmvaeVPTpk2pU6cOI0eO5NatW5QuXZp///2XLVu20L9/f/1np0yZMrRv35758+cTEhJCtWrV2Lt3Lzdu3IiX5tSpU9m/fz+VK1emR48eeHh48OzZM3x9fdmzZw/Pnj1L0X2UKVMGtVqNt7c3ISEhWFhY6OcZSo3vnpEjR7JixQquXr1q0L+sdOnSdOnShUWLFumbVU6dOsWyZcto3rw5derUSTTNhg0b4uLiQvXq1XF2diYgIIB58+bRpEmTeP2TOnfurO/TlFAwnZTDhw8TGRmJRqPh6dOnHD16lK1bt+Lg4MCmTZsMmos///xzVqxYgYODAx4eHhw/fpw9e/aQLVs2gzQTK/9q1arh6OhIly5d6NevHyqVihUrVsQLjjK9NB8nJeJ5c4hhQhIaAhkbG6v07dtXcXJyUlQqVbKGYs+bN08pWrSoYmZmpjg7Oyu9evVSnj9/bnDM+wy/jntYWloquXLlUj7//HPlzz//THRo3/Tp05WcOXMqFhYWSvXq1ZUzZ87EGwqp1WqVyZMnK3nz5lUsLCyUsmXLKtu3b1e6dOmi5M2b1yA9jDD8Om5IeNxQ55MnTxqcf+bMGcXU1FTp1auXwXX79OmjrFy5UilUqJA+nwkNgfT19VW8vLwUW1tbxdraWqlTp45y7Ngxg2MSex/EDdt8O939+/crXl5eioODg2JpaakUKFBA6dq1q8Fw8C5duig2Njbx8pPQkOpjx44p5cuXV8zNzQ3KNKFjt27dqpQqVUqxtLRU3N3dFW9vb+XPP/9UACUwMFB/XEqGX8e9FiqVSrG3t1eKFy+u9OjRI95r8aZFixYp5cuXV6ysrBQ7OzulZMmSytChQ5UHDx7Ey2+1atUUKysrxd7eXqlUqZKyZs0a/X5/f3+lfv36iq2trZI9e3alR48eyvnz5xMdehwUFKSo1WqlcOHC77y3OO/6nL9ZFm8PRQ8LC1MGDBiguLm5KWZmZkqhQoWUX375xWAIuaIoyqtXr5R+/fop2bJlU2xsbJSmTZsqd+/eTfAz8ujRI6VPnz5K7ty5FTMzM8XFxUWpV6+esmjRIv0xyR1+rSiKsnjxYiV//vyKWq2O935NzndPQpIqs7ipBd4eMh0TE6OMGzdOyZcvn2JmZqbkzp1bGTFiRLzvo7ffmwsXLlRq1aqlZMuWTbGwsFAKFCigDBkyRAkJCYl37aioKMXR0VFxcHCIN6w/MXGf47iHmZmZ4uTkpNSqVUuZNGmSEhwcHO+c58+fK19//bWSPXt2xdbWVvHy8lKuXLmS4DQWiZX/0aNHlSpVqihWVlaKm5ubMnToUOWff/5JdLh2ZqRSlI8tNBMibahUKvr06WOUjn4ic3ny5Amurq6MHj2aUaNGpXd2RBqLjY3Fzc2Npk2b8scff6R3dj550kdGCCFSaOnSpWg0Gv3s1eLTsnnzZh4/fmzQOVykH+kjI4QQybRv3z78/f2ZNGkSzZs3/yRXGv6UnTx5kgsXLjBhwgTKli1L7dq10ztLAglkhBAi2caPH8+xY8eoXr06c+fOTe/siDS2YMECVq5cSZkyZfSL+Ir0J31khBBCCJFpSR8ZIYQQQmRaEsgIIYQQItP66PvIaLVaHjx4gJ2d3XutvyGEEEKItKcoCmFhYbi5uRmsnv62jz6QefDgQYrXshFCCCFExnD37l1y5cqV6P6PPpCJm1r67t27KV7TJikxMTH8+++/+qnRReqRsk4bUs5pQ8o5bUg5p43ULOfQ0FBy584db4mIt330gUxcc5K9vb3RAxlra2vs7e3lQ5LKpKzThpRz2pByThtSzmkjLcr5Xd1CpLOvEEIIITItCWSEEEIIkWlJICOEEEKITOuj7yMjhPg4aTQaYmJi0jsbKRYTE4OpqSmRkZFoNJr0zs5HS8o5bXxIOZuZmaFWqz84DxLICCEyFUVRePjwIS9evEjvrLwXRVFwcXHh7t27MrdVKpJyThsfWs5ZsmTBxcXlg14jCWSEEJlKXBCTI0cOrK2tM90fKa1WS3h4OLa2tklO8iU+jJRz2njfclYUhYiICIKDgwFwdXV97zykayBz6NAhfvnlF86ePUtQUBCbNm2iefPmCR773XffsXDhQmbOnEn//v3TNJ9CiIxBo9Hog5hs2bKld3bei1arJTo6GktLS/kDm4qknNPGh5SzlZUVAMHBweTIkeO9m5nS9dV9+fIlpUuX5tdff03yuE2bNnHixAnc3NzSKGdCiIwork+MtbV1OudECGEMcZ/lD+nvlq41Mo0bN6Zx48ZJHnP//n369u3LP//8Q5MmTdIoZ0KIjCyzNScJIRJmjM9yhq5v02q1dOrUiSFDhlC8ePH0zo6eRqtwKvAZAKcCn6HRKumcIyGEEOLTlKE7+3p7e2Nqakq/fv2SfU5UVBRRUVH656GhoYCu2soYQzX3BDxi6q4rPA9/xYQK0GvFKRxtrRjeuCj1izl/cPoivrjXLTMOtc1MMkM5x8TEoCgKWq0WrVab3tl5L4qi6H9mpnsYN24cW7ZswdfXN9Fjbt26RYECBTh79ixlypRJu8wlcP3SpUsDma+cM5sPfT9rtVoURSEmJiZeH5nkfhdl2EDm7NmzzJ49G19f3xRVPU2ZMoVx48bF2/7vv/8arV19YNHXv0+ooAVeEh14lp2BRkleJGL37t3pnYVPQkYuZ1NTU1xcXAgPDyc6Ojq9s5NsvXv3Zs2aNYDuHhwdHSlevDgtW7akQ4cOKeokuXr1akaMGMHt27dTK7sJ6tGjB126dNH/c9i7d29CQkJYtWqV/pjw8HBA1/8x7rjkKFWqFHfv3uXff/+lYsWK+u0jRozg4sWLbN++PVnpODg4cOXKFbJly0ZYWBiA/qdIXe9bztHR0bx69YpDhw4RGxtrsC8iIiJZaWTYQObw4cMEBweTJ08e/TaNRsOgQYOYNWsWt27dSvC8ESNGMHDgQP3zuNUzGzZs+EGLRmq0Cl6zDvEwNBIACxOFCRW0jDpjQpRWhQpwtrfkn/61UJtI+70xxcTEsHv3bho0aCCLv6WizFDOkZGR3L17F1tbWywtLd87HY1W4fStZwSHRZHDzoKK7llT9XNrZmaGl5cXf/75J7GxsQQGBnL48GFGjBjBjh072LJlC6amyfs6trS0RKVSGXUR3OR4+3pmZmaYmpoabLe1tQXAxsYmRfkzMTHB0tKSiRMnsn//fv12c3PzeNd4F0dHR0BXQxAWFoadnZ30qUpFH1rOkZGRWFlZUatWrXif6WQHw0oGASibNm3SP3/y5Ily8eJFg4ebm5sybNgw5cqVK8lONyQkRAGUkJCQD8rfsRtPlLzDtusfhX/cpmzevFkp/OM2g+3Hbjz5oOuI+KKjo5XNmzcr0dHR6Z2Vj1pmKOdXr14p/v7+yqtXr947jV0XHyhVJu8x+NxWmbxH2XXxgRFzaqhLly5Ks2bNFEVRFI1Gozx//lzRaDTK3r17FUBZvHix/tjp06crJUqUUKytrZVcuXIpvXr1UsLCwhRFUZT9+/crgMFjzJgxiqIoyvLly5Xy5csrtra2irOzs9K+fXvl0aNHieZp7ty5SvHixfXPN23apADKggUL9Nvq1aunjBw5UlEURRkzZoxSunRp/e9v52P//v1KYGCgAigbNmxQPD09FSsrK6VUqVLKsWPHkiyfvHnzKv369VPMzc2VHTt26Lf/8MMPSu3atfXPNRqNMm7cOCVnzpyKubm5Urp0aWXXrl36/XHXP3funKLRaJTAwEClffv2Svbs2RVLS0ulYMGCyp9//qk//s6dO0rr1q0VBwcHxdHRUfniiy+UwMDAJPMqDL35fn4fSX2mk/v3O107+4aHh+Pn54efnx8AgYGB+Pn5cefOHbJly0aJEiUMHmZmZri4uFCkSJE0z2twWKRRjxNCpD2fS0H0WulLUIjh5/RhSCS9VvricykoTfNTt25dSpcuzcaNG/XbTExMmDNnDpcvX2bZsmXs27ePoUOHAlCtWjVmzZqFvb09QUFBBAUFMXjwYEBXozZhwgTOnz/P5s2buXXrFl27dk302rVr18bf35/Hjx8DcPDgQbJnz86BAwf06R0/fhxPT8945w4ePJg2bdrQqFEjfT6qVaum3z9y5EgGDx6Mn58fhQsXpn379vGaDd6WL18+vvvuO0aMGJFoX4vZs2czffp0pk2bxoULF/Dy8uKLL77g+vXrCR4/adIkAgIC2LVrFwEBASxYsIDs2bPr78/Lyws7OzsOHz7M0aNHsbW1pVGjRpmq2VKk86ilM2fOULZsWcqWLQvAwIEDKVu2LKNHj07PbCUoh13yqrGTe5wQIm1ptArjtvmT0BjDuG3jtvmn+SjEokWLGjSV9+/fnzp16uDu7k7dunWZOHEif/31F6BranFwcEClUuHi4oKLi4u+Oadbt240btyY/PnzU6VKFebMmcOuXbv0/VbeVqJECbJmzcrBgwcBOHDgAIMGDdI/P3XqFDExMQYBShxbW1usrKywsLDQ58Pc3Fy/f/DgwTRp0oTChQszbtw4bt++zY0bN95ZFj/99BOBgYEG/W7eNG3aNIYNG0a7du0oUqQI3t7elClThlmzZiV4/L179yhTpgwVKlTA3d2d+vXr07RpUwDWrVuHVqvl999/p2TJkhQrVowlS5Zw584dfTAnMod0DWQ8PT1RFCXeY+nSpQkef+vWrXSb1bdSvqy4OljyZgvgrVt2vPzPCQAV4OpgSaV8WdMlf0KIpJ0KfBavJuZNChAUEqmfWiGtKIpi0Ldgz5491KtXj5w5c2JnZ0enTp14+vTpOzs+nj17lqZNm5InTx7s7OyoXbs2AHfu3EnweJVKRa1atThw4AAvXrzA39+f3r17ExUVxZUrVzh48CAVK1Z8r0ESpUqV0v8eN/V83FT0SXFycmLw4MGMHj06Xq1IaGgoDx48oHr16gbbq1evTkBAQILpdevWjXXr1lGmTBmGDh3KsWPH9PvOnz/PjRs3sLOzw9bWFltbW7JmzUpkZCQ3b95M9r2K9Jeh55HJSNQmKsY09QB0QUv4jRz071+XRztKgUb3JTSmqYd09BUig8qozcMBAQHky5cP0P2z9vnnn1OqVCk2bNjA2bNn9TOfJ9Xc8fLlS7y8vLC3t2fVqlWcPn2aTZs2vfM8T09PDhw4wOHDhylbtiz29vb64ObgwYP6YCil3uwsHhekJXdo7sCBA3n16hXz589/r2u/qUGDBgQGBjJgwAAePHhAvXr19E1x4eHhlC9fXt+9Ie5x7do1OnTo8MHXFmlHApkUaFTClQUdy+HiYIm1+xMcHSOJDbNCHejOgo7laFTi/Re9EkKkrozYPLxv3z4uXrxIy5YtAV2tilarZfr06VSpUoXChQvz4MEDg3PMzc3RaDQG265cucLTp0+ZOnUqNWvWpGjRosmqAYnrJ7N+/Xp9XxhPT0/27NnD0aNHE+wfk1Q+jMHW1pZRo0YxadIkgyG99vb2uLm5cfToUYPjjx49ioeHR6LpOTk50aVLF1auXMmsWbNYtGgRAOXKleP69evkyJGDggULGjwcHByMfl8i9Uggk0KNSrhyZFhdlnYvT7NmujZfs0vFaFBMghghMrKEmofflNrNw1FRUTx8+JD79+9z/vx5pkyZQrNmzfj888/p3LkzAAULFiQmJoa5c+fy33//sWLFCn777TeDdNzd3QkPD2fv3r08efKEiIgI8uTJg7m5uf68rVu3MmHChHfmqVSpUjg6OrJ69WqDQGbz5s1ERUXFa8Z5Ox8XLlzg6tWrPHnyxKgTKX777bc4ODiwevVqg+1DhgzB29ubdevWcfXqVYYPH46fnx8//PBDgulMnjyZLVu2cOPGDS5fvsz27dspVqwYAF999RXZs2enWbNmHD58mMDAQA4cOEC/fv24d++e0e5FpD4JZN6D2kRFpXxZ8fK6jaOjwtWrKv5fiyuEyKDebh5+U9zz1Gwe9vHxwdXVlfz589OqVSv279/PnDlz2LJli35G09KlSzNjxgy8vb0pUaIEq1atYsqUKQbpVKtWje+++462bdvi5OTEzz//jJOTE0uXLmX9+vV4eHgwdepUpk2b9s48qVQqatasiUqlokaNGoAuuLG3t6dChQrY2Ngkem6PHj0oUqQIFSpUwMnJKV5NyYcwMzNjwoQJREYaNvP169ePgQMHMmjQIEqWLImPjw9bt26lUKFCCaZjbm7OyJEjKVWqFLVq1UKtVrN27VpAt1jhoUOHyJMnD19++SXFihWje/fuREZGpvkcPeLDqBRF+agXCgoNDcXBwYGQkBCjvjljYmLYuXMnp09/zqRJasqVgzNnQOZdMr64sv7ss88y7ERtH4PMUM6RkZEEBgaSL1++954Qz+dSEOO2+Rt0/HV1sGRMU480aR7WarWEhoZib2+fohl9RcpIOaeNDy3npD7Tyf37nWFn9s0svv9ey8yZanx9YfduaNgwvXMkhEhKoxKuNPBw4VTgM4LDIslhp2tOko76QmROEsh8oGzZ4NtvYc0aePEivXMjhEgOtYmKqgWypXc2hBBGIPVtRjBmDAQGQps26Z0TIYQQ4tMiNTJGkCVLeudACCGE+DRJjYwRabWwYQMkMsmkEEIIIYxMAhkjGjgQWrWCiRPTOydCCCHEp0ECGSPq0kX3c+1akKU6hBBCiNQngYwRlS0LjRvrmpgmTUrv3AghhBAfPwlkjGzMGN3P5cvhv//SNy9CCCHEx04CGSOrXBkaNQKNRmplhBCfLnd3d2bNmpXs48eOHUuZMmVSLT/i4yWBTCqQWhkhRByVSmXwUKvVODo6olarUalUjB07Nr2zKESmJvPIpIIqVcDLC54/h9DQ9M6NECI9BQUF6X9ft24do0eP5tSpU9jZ2WFiYoKtra1+v6IoaDQaTE3lq1mI5JIamVSybh2cOAFSUyrEp83FxUX/cHBwQKVS4ezsjIuLC1euXMHOzo5du3ZRvnx5LCwsOHLkCF27dqV58+YG6fTv3x9PT0/9c61Wy5QpU8iXLx9WVlaULl2av//+O8m8uLu7M3HiRDp37oytrS158+Zl69atPH78mGbNmmFra0upUqU4c+aMwXkbNmygePHiWFhY4O7uzvTp0w32BwcH07RpU6ysrMiXLx+rVq2Kd+0XL17wzTff4OTkhL29PXXr1uX8+fMpK0whEiCBTCpxcJCVsIVIE4oCL1+m/UNRjHYLw4cPZ+rUqQQEBFCqVKlknTNlyhSWL1/Ob7/9xuXLlxkwYAAdO3bk4MGDSZ43c+ZMqlevzrlz52jSpAmdOnWic+fOdOzYEV9fXwoUKEDnzp1R/n9/Z8+epU2bNrRr146LFy8yduxYRo0axdKlS/Vpdu3albt377J//37+/vtv5s+fT3BwsMF1W7duTXBwMLt27eLs2bOUK1eOevXq8ezZs5QVlhBvkfrL96XRkOvAAahfH8zMEj0sJATmzoWOHcHdPc1yJ8SnIyIC3mieSTPh4WBjY5Skxo8fT4MGDZJ9fFRUFJMnT2bPnj1UrVoVgPz583PkyBEWLlxI7dq1Ez33s88+o2fPngCMHj2aBQsWULFiRVq3bg3AsGHDqFq1Ko8ePcLFxYUZM2ZQr149Ro0aBUDhwoXx9/fnl19+oWvXrly7do1du3Zx6tQpKlasCMAff/xBsWLF9Nc8cuQIp06dIjg4GAsLCwCmTZvG5s2b+fvvv/n2229TUFpCGJJA5j2pv/yS8rt2oXFxgWHDEj2uWzfYuBHu3IFFi9Iwg0KITKNChQopOv7GjRtERETEC36io6MpW7Zskue+WePj7OwMQMmSJeNtCw4OxsXFhYCAAJo1a2aQRvXq1Zk1axYajYaAgABMTU0pX768fn/RokXJ8sYidOfPnyc8PJxs2QxXHH/16hU3ZfZQ8YEkkHlP2i+/xGTXLkwmToTOncHVNcHjBg7UBTJLlsDIkZA3bxpnVIiPnbW1rnYkPa5rJDZv1eyYmJjom3bixMTE6H8P///97tixg5w5cxocF1fjkRizN2qQVf9v/05om1arTW723yk8PBxXV1cOHDgQb18WWXVXfCAJZN6T0qkTz375hazXrulqZJYvT/C46tWhXj3Yu1c3r4zUyghhZCqV0Zp4MgonJycuXbpksM3Pz08fcHh4eGBhYcGdO3eSbEYyhmLFinH06FGDbUePHqVw4cKo1WqKFi1KbGwsZ8+e1TctXb16lRcvXuiPL1euHA8fPsTU1BR3aWMXRiadfd+XiQkXe/RAUalgxQo4dizRQ+OmiViyBG7cSJvsCSEyr7p163LmzBmWL1/O9evXGTNmjEFgY2dnx+DBgxkwYADLli3j5s2b+Pr6MnfuXJYtW2bUvAwaNIi9e/cyYcIErl27xrJly5g3bx6DBw8GoEiRIjRq1IiePXty8uRJzp49yzfffIOVlZU+jfr161O1alWaN2/Ov//+y61btzh27BgjR46MN0JKiJSSQOYDvChUCKVrV92Tvn110/kmoEYN3Wy/sbGvgxohhEiMl5cXo0aNYujQoVSsWJGwsDA6d+5scMyECRMYNWoUU6ZMoVixYjRq1IgdO3aQL18+o+alXLly/PXXX6xdu5YSJUowevRoxo8fT9e47z5gyZIluLm5Ubt2bb788ku+/fZbcuTIod+vUqnYuXMntWrV4uuvv6Zw4cK0a9eO27dv6/vkCPG+VMrbDbEfmdDQUBwcHAgJCcHe3t5o6cbExLBz504+q1ABs+LFdcOTFi6ERHrfnz0LFSroasHPn4c3+taJd9CX9WefGbTlC+PKDOUcGRlJYGAg+fLlw9LSMr2z8160Wi2hoaHY29tjYiL/S6YWKee08aHlnNRnOrl/v+XV/VA5csC4cbrff/wR3pgTQaNVOH7zKVv87hOd5Slt2ih07KibY0YIIYQQH046+xpD796weDFcvgyjR8O8efhcCmLcNn+CQiL1h7mUsmRsMw/y5El4hJMQQgghUkZqZIzBzAzmzNH9vmABRzbspddKX4MgBuBRWCS9VvricykogUSEEEIIkVISyBhL3brQqhVotdgMHhhvDgiAuC3DlwTSrp3Cvn1pm0UhhBDiYyOBjDFNm4bG0oqyty7QNOBQgocowH8H3Fi3TsXIkclbruXNvjbHbz5Fo/2o+2cLIYQQySZ9ZIwpb16ude1Nsd+m8+P+P9lbsBIR5lbxDnOoeoMo/zycOGHC9u3QtGniSSbU18bVwZIxTT1oVEL62gghhPi0SY2MkYV+35+7Ds64hj+lz/G/EjxGbRtF2y5RAPz0EyQ2E7jPpaAE+9o8DJG+NkIIIQRIIGN0FYrlZF7T3gB8c3oTeZ8/MNivQlejMn2iJQ4OcOECTJgdFq/ZSKNVGLfNn4QakeK2jdvmL81MQgghPmkSyBiZ2kRFnaHfcMi9LBaaWEbtXazfp/r/zzFNPXDKrqJZ5zAAJoxT02/lBdovPkEN7334XAriVOCzeDUxb1KAoJBITgU+S/QYIYQQ4mMngUwqaFTSDdXsWcSaqKl/8zSeN08D4OJgyYKO5WhUwhWfS0EcMDuC2jYSTYg1YefzAK+bjfb4P0zWtYLDEg92hBAZn6enJ/3790+z6y1dujTDrDh969YtVCoVfn5+yT7HmOWV3Oun9WskUkYCmVRS84tamPT/AYBfTyxlXafSHBlWl0YlXPXNRiozLY51AnCoeRXbkneB181Gm/zuJ+s6Oewy5zTtQnxKunbtikqlQqVSoVarcXR0RK1Wc+PGDTZu3MiECRP0x7q7uzNr1iyD8zNS8PExyZ07N0FBQZQoUQKAAwcOoFKpDFbufl9du3alefPmH5xOSiX0/vnYSSCTikzGjoWcObG5d5vKqxegNtE1Lr3ZbGTj8YAs1W5gYv56wUkFePYyhqw25vrmqLfF9bWplC9rat6CEMJIGjVqRFBQEPfv3+fKlSvcv3+ffPnykTVrVuzs7NI7e58ktVqNi4sLpqYygPdt0dHR6Z2FZJNAJjXZ2b2e8feXX8DfH0i8OUhRQBul1j9vXsYNIF4w82Zfm7jgSAiRsVlYWODi4oKLiwvOzs64uLigVqsNmi08PT25ffs2AwYM0NfgHDhwgK+//pqQkBD9trFjxwIQFRXF4MGDyZkzJzY2NlSuXJkDBw4YXHfp0qXkyZMHa2trWrRowdOnT5PMZ1xzy19//UXNmjWxsrKiYsWKXLt2jdOnT1OhQgVsbW1p3Lgxjx8/1p+n1WoZP348uXLlwsLCgjJlyuDj42OQ9qlTpyhbtiyWlpZUqFCBc+fOxbv+pUuXaNy4Mba2tjg7O9OpUyeePHmSrDIOCQlBrVZz5swZfZ6yZ89OlSpV9MesXLmS3LlzG9yrn58ft27dok6dOgA4OjqiUqkMVvjWarUMHTqUrFmz4uLion8NEjJ27FiWLVvGli1bDF7HVq1a8f333+uP69+/PyqViitXrgC64MHGxoY9e/YAute3X79+5MiRA0tLS2rUqMHp06cTvW5C7584R44c0b+euXPnpl+/frx8+VK/393dnQkTJtC5c2fs7e359ttv9TWB27dvp0iRIlhbW9OqVSsiIiJYtmwZ7u7uZMuWjWHDhqHRvP5nfP78+RQqVAhLS0ucnZ1p1apVonk2BglkUluLFvD55xATA999B1ptgs1BUUEOBC2twbN/Xy+L3cDDhQUdy+HiYHj8m31thBA6L18m/oiMTP6xr169+9jUsnHjRnLlysX48eMJCgoiKCiIatWqMWvWLOzt7fXbBg8eDMD333/P8ePHWbt2LRcuXKB169Y0atSI69evA3Dy5Em6d+/O999/j5+fH3Xq1GHixInJysuYMWP46aef8PX1xdTUlA4dOjB06FBmz57N4cOHuXHjBqNHj9YfP3v2bKZPn860adO4cOECXl5efPHFF/q8hIeH8/nnn+Ph4cHZs2cZO3as/j7ivHjxgrp161K2bFnOnDmDj48Pjx49ok2bNsnKs4ODA2XKlNEHc5cvX0alUnHu3DnCw8MBOHjwILVr1453bu7cudmwYQMAV69eJSgoiNmzZ+v3L1u2DBsbG06ePMnPP//M+PHj2b17d4L5GDx4MG3atNHXwsW9jrVr1zYINA8ePEj27Nn1206fPk1MTAzVqlUDYOjQoWzYsIFly5bh6+tLwYIF8fLy4tmzhAd5JPT+Abh58yaNGjWiZcuWXLhwgXXr1nHkyBGDoApg2rRplC5dmnPnzjFq1CgAIiIimDNnDmvXrsXHx4cDBw7QokULdu7cyc6dO1m2bBlLly7l77//BuDMmTP069eP8ePHc/XqVXx8fKhVq1air5lRKB+5kJAQBVBCQkKMmm50dLSyefNmJTo6+t0H37qlKNbWigKK8scfSqxGq1SZvEdxH7Zdyfv/h0uXQ4quTkZRXLscUqpM3qPEarSKoihKrEarHLvxRNl87p5y7MYT/fZPRYrKWry3zFDOr169Uvz9/ZVXr17F2xf3+Uno8dlnhsfGfRwTetSubXhs9uzxj0mpLl26KGq1WrGxsdE/WrZsqSiKotSuXVv54Ycf9MfmzZtXmTlzpsH5S5YsURwcHAy23b59W1Gr1cr9+/cNtterV08ZMWKEoiiK0r59e+Wzt26+bdu28dJ6U2BgoAIov//+u37bmjVrFEDZu3evftuUKVOUIkWK6J+7ubkpkyZNMkirYsWKSu/evRVFUZSFCxcq2bJlM3jtFixYoADKuXPnFEVRlAkTJigNGzY0SOPu3bsKoFy9elVRlPjl9baBAwcqTZo0UTQajTJlyhSlTZs2SunSpZVdu3YpiqIoBQsWVBYtWmRwr3HX379/vwIoz58/N0izdu3aSo0aNeLd27BhwxLNR5cuXZRmzZoZbLtw4YKiUqmU4OBg5dmzZ4q5ubkyYcIEpW3btoqiKMrEiROVatWqKYqiKOHh4YqZmZmyatUq/fnR0dGKm5ub8vPPPyd63YTeP927d1e+/fZbg22HDx9WTExM9K9H3rx5lebNmxscs2TJEgVQbty4od/Ws2dPxdraWgkLC1MURVE0Go1Sr149ffobNmxQ7O3tldDQ0ETz+KakPtPJ/fstNTJpIW9eGDdO9/uQIaifPmFMUw/gdTORhUsoNh66Dr7PDxRj9Oevm43UJiqqFshGszI5qVogmzQnCZEJ1alTBz8/P3x9fTl06JDBf/vv4+LFi2g0GgoXLoytra3+cfDgQW7evAlAQEAAlStXNjivatWqyUq/VKlS+t+dnZ0BKFmypMG24OBgAEJDQ3nw4AHVq1c3SKN69eoEBATo81KqVCksLV/XML+dl/Pnz7N//36D+ylatCiA/p7epXbt2hw5cgSNRsPRo0epXbs2np6eHDhwgAcPHnDjxg08PT2Tldab3iwPAFdXV/39J1eJEiXImjUrBw8e5PDhw5QtW5bPP/+cgwcPAroamri83bx5k5iYGIMyNTMzo1KlSvoyTa7z58+zdOlSg3L18vJCq9USGBioP65ChQrxzrW2tqZAgQL6587Ozri7u2Nra6vf5uTkpC+LBg0akDdvXvLnz0+nTp1YtWoVERERKcpvSkkPp7Tyww+wYoVuBrwhQ2i0dCkLOpYzWH4gS62rRFx1JfJ2drgHlEw6SSHEa/9vOUiQWm34PKm/PyZv/Xt369Z7Z8mAjY0NBQsWRKvVEhoair29/QelFx4ejlqt5uzZs6jfusE3/8i8LzMzM/3vcX0t3t6mTWxa8vcUHh5O06ZN8fb2jrfP1TV5Tem1atUiLCwMX19fjh07hre3N25ubkydOpXSpUvj5uZGoUKFUpy3N+8d3u/+VSoVtWrV4sCBA1hYWODp6UmpUqWIiori0qVLHDt2LF5zmzGEh4fTs2dP+vXrF29fnjx59L/b2NjE25/QfSdVFnZ2dvj6+nLgwAH+/fdfRo8ezdixYzl9+nSqjbyTQCatmJnBwoVQrRosWwZdu9LI05MGHi6cCnxGcFgkOews+dtGxYzpMHQoNGwY/wtYCJGwBL6D0/xYYzA3NzfoOJnYtrJly6LRaAgODqZmzZoJplWsWDFOnjxpsO3EiRPGzTBgb2+Pm5ubvgYkztGjR6lUqZI+LytWrCAyMlJfK/N2XsqVK8eGDRtwd3d/75FEWbJkoVSpUvz666+YmZlRtGhRXFxcaNu2Ldu3b0+wf0wcc3NzgHhl/T4Ses1AV2O0ePFiLCwsmDRpEiYmJtSqVYtffvmFqKgofQ1MgQIFMDc35+jRo+TNmxeAmJgYTp8+neScNgldt1y5cvj7+1OwYMEPvq/kMDU1pX79+tSvX58xY8aQJUsW9u3bx5dffpkq10vXpqVDhw7RtGlT3NzcUKlUbN68Wb8vJiaGYcOGUbJkSWxsbHBzc6Nz5848ePAg8QQzuipVoGdP3e/ffQdRUfGajX4aqcLRES5dgt9/T9/sCiHSnru7O4cOHeL+/fv60Tru7u6Eh4ezd+9enjx5QkREBIULF+arr76ic+fObNy4kcDAQE6dOsWUKVPYsWMHAP369cPHx4dp06Zx/fp15s2bF28kkbEMGTIEb29v1q1bx9WrVxk+fDh+fn788INuPq0OHTqgUqno0aMH/v7+7Ny5k2nTphmk0adPH549e0b79u05ffo0N2/e5J9//uHrr79OUXDh6enJ6tWr9Z1ms2bNSrFixVi3bl2SgUzevHlRqVRs376dx48f6zsIvw93d3cuXLjA1atXefLkCTExMfq8+fv7c/nyZWrUqKHftmrVKipUqKCvFbGxsaFXr14MGTIEHx8f/P396dGjBxEREXTv3j3J6779/hk2bBjHjh3Td/q+fv06W7ZsidfZ1xi2b9/OnDlz8PPz4/bt2yxfvhytVkuRIkWMfq046RrIvHz5ktKlS/Prr7/G2xcREYGvry+jRo3C19eXjRs3cvXqVb744ot0yKkRTZkCzs5w9Sr8/HO83Y6Or7vT7NyZxnkTQqS78ePHc+vWLQoUKICTkxMA1apV47vvvqNt27Y4OTnx8/+/O5YsWULnzp0ZNGgQRYoUoXnz5pw+fVrfXFClShUWL17M7NmzKV26NP/++y8//fRTquS7X79+DBw4kEGDBlGyZEl8fHzYunWrvhnH1taWbdu2cfHiRcqWLcvIkSPjNSHF1epoNBoaNmxIyZIl6d+/P1myZMHk7Ta/JNSuXRuNRqMPFEAXLGg0miT7x+TMmZNx48YxfPhwnJ2dP+gPfY8ePShSpAgVKlTAycmJo0ePArp+RlmyZKFMmTL6JsDE8jZ16lRatmxJp06dKFeuHDdu3OCff/7B0dEx0esm9P4pVaoUBw8e5Nq1a9SsWZOyZcsyevRo3Nzc3vv+EpMlSxY2btxI3bp1KVasGL/99htr1qyhePHiRr9WHJWiKBli1UGVSsWmTZuSnAnx9OnTVKpUidu3bxu06yUlNDQUBwcHQkJCPrhN+k0xMTHs3LmTzz77LF574TutXQvt24OFBVy8CG+118bEwPbt0Lw5qKRf74eVtUi2zFDOkZGRBAYGki9fPoNOo5nJm31kUvLHWaSMlHPa+NByTuozndy/35mqj0zchFBJdRiKiooiKipK/zw0NBTQfUnHVe0ZQ1xa75Xml1+ibtAAk9270X73HZpdu+JFLJ9/DrGxxshp5vdBZS2SLTOUc0xMDIqioNVqjd7RNK3E/e8Ydx8idUg5p40PLWetVouiKMTExMTrtJ7c76JMUyMTGRlJ9erVKVq0KKtWrUo0nbFjxzIurm3mDatXr8ba2tpY2f1g1kFB1P3hB9TR0ZwdMIB7ibTbvnplyrFjbtSrdyeNcyhExmNqaoqLiwu5c+fWd8wUQmRe0dHR3L17l4cPHxL71n/vERERdOjQ4Z01MpkikImJiaFly5bcu3ePAwcOJHlDCdXI5M6dmydPnhi9aWn37t00aNDgvavhTaZMQT1mDEqOHMRevKjrIPOGV6+gRAlT7t5VsX17LA0bJvxS7Ql4xNRdV3gY+nr6Uhd7S4Y3Lkr9Ys7vlbeMxBhlLd4tM5RzZGQkd+/exd3dPdM2LSmKQlhYGHZ2dgZTyAvjknJOGx9azpGRkdy6dYvcuXMn2LSUPXv2zN+0FBMTQ5s2bbh9+zb79u17ZzBiYWGBhYVFvO1mZmap8uX8QekOHw5r16IKCMBs1Cjd8GyDtKF1a5gxA4YMMaVhQ922N/lcCqL36vP/XzX79ZvozvMoeq8+/1EtZZBar6EwlJHLWaPRoFKpMDExybT9HuKq3+PuQ6QOKee08aHlbGJiop+b5u3vneR+D2XoVzcuiLl+/Tp79uwhW7Zs6Z0l4zI3h99+0/2+aBG8tdgbwKhRkD07BATAggWG+zRahXHb/EmoniZu27ht/mi0GaLSTQijySAVyUKID2SMz3K6BjLh4eH4+fnh5+cHQGBgIH5+fty5c4eYmBhatWrFmTNnWLVqFRqNhocPH/Lw4cNMtbz4O9WqpZtTBqB793gr0mXJAnFrvI0dC28uXHsq8Jl+VuCEKEBQSCSnAhNeYEyIzCbuP7TUnvJcCJE24j7LH1ILnK5NS2fOnNEvmw4wcOBAALp06cLYsWPZunUrAGXKlDE4b//+/e+1VkaG5e0NO3bAf//pqmBmzDDY/c03MH++bnWD0aMhbtqd4LDEg5g3Jfc4ITI6tVpNlixZ9Ou6WFtbZ7r+D1qtlujoaCIjI6XJIxVJOaeN9y1nRVGIiIggODiYLFmyxBuxlBLpGsh4enomWa30yVQf29vrmpYaN4ZZs3QdY95YTE2thtmzoU4dXUtU9+5QrhzksEteZ8fkHidEZuDi4gKQ4gX7MgpFUXj16hVWVlaZLgjLTKSc08aHlnOWLFn0n+n3leE7+34yGjWCrl1h6VLo1g3OnYM3enB7eurm0FOrIW4yxkr5suLqYMnDkMgE+8moABcHSyrly5r6+RcijahUKlxdXcmRI0eGnvMmMTExMRw6dIhatWpl2E7VHwMp57TxIeVsZmb2QTUxcSSQyUhmzAAfH7hyBcaPh8mTDXYvXw5vrqOmNlExpqkHvVb6ogKDYCYuLh7T1AO1ifw3Ij4+arXaKF+CaU2tVhMbG4ulpaX8gU1FUs5pIyOUszQcZiSOjq+HJv38M5w9a7D77cVgY2OhUQlXFnQsh4uDYfORi4PlRzX0WgghhEiI1MhkNM2bQ9u2sG6dronp9GndMO033LkDAwbo1p6cP18XzDTwcOFU4DOCwyLJYadrTpKaGCGEEB87qZHJiObO1U0ec+ECTJ0ab3dgIGzcqOv4G1dpozZRUbVANpqVyUnVAtkkiBFCCPFJkEAmI3Jy0gUzoJtE5tIlg921a8NXX4GiQO/eIOuhCSGE+FRJIJNRtW0LzZpBTIyuiemtxbR++QXs7ODUKfjjj3TKoxBCCJHOJJDJqFQqXQeYLFl0/WRmzjTY7eqqG9gEuiWb3pzxVwghhPhUSCCTkbm5vQ5gRo2Cq1cNdn//PZQsCc+ewdCh6ZA/IYQQIp1JIJPRdekCXl4QFaWb0lej0e8yNX09Wnv/fggNTac8CiGEEOlEApmMTqXSLV9gawtHj8Zbh6l6ddiwAS5e1K10IIQQQnxKJJDJDPLk0a3BBPDTT7ph2W/48kuwsUn7bAkhhBDpTQKZzKJbN2jaFKKjoVMnXVPTW7RaXVNTQEA65E8IIYRIBxLIZBYqFSxerJtj5sIFGDMm3iEjRujmlenZU+aWEUII8WmQQCYzcXbW9ZcB3VpMR44Y7O7dG6yt4fBhmVtGCCHEp0ECmcymeXPo2lU3rW/nzhAWpt+VNy9MmKD7fehQePgwXXIohBBCpBkJZDKj2bN1UUtgIAwcaLCrXz8oVw5evNAtLCmEEEJ8zCSQyYzs7WHZMl2/md9/h23b9LtMTXWtTyYmsHatwS4hhBDioyOBTGZVu/br2phvvoHHj/W7ypd/vev773XLNQkhhBAfIwlkMrOJE6FECQgOhm+/1fWb+b/x46FVK9i8GczM0i+LQgghRGqSQCYzs7SEFSt0kcrmzbrmpv+zsoL166Fs2fTLnhBCCJHaJJDJ7MqUgXHjdL/36we3biV42MWLshaTEEKIj48EMh+DoUOhWjXdUOyuXePNhjd/vq7fzPDh6ZM9IYQQIrVIIPMxUKth+XLdgksHD+omy3tD0aK6Dr8LFsCBA+mTRSGEECI1SCDzsShQQDe/DOgWljxxQr+rbl3dsgUA3bvDy5fpkD8hhBAiFUgg8zHp1g3atgWNBtq3h5AQ/a6ff4bcueG//+DHH9Mxj0IIIYQRSSDzMVGpYOFCyJdP1+m3Z0/9kGx7e92akwBz5sD+/emXTSGEEMJYJJD52Dg4wJo1uil+162DP//U7/Lyet3E1LWrjGISQgiR+Ukg8zGqXPn16pF9+0JAgH7XtGlQvLhuHSZb23TKnxBCCGEkEsh8rIYOhfr14dUraNcOIiMBXfDi5wf9++vWYxJCCCEyM/lT9rEyMdENyXZyggsXYMgQ/S5T09eHvXwJz54ZnqrRKhy/+ZQtfvc5fvMpGq2CEEIIkRGZvvsQkWm5uuqCmcaNYd48XQ1Ns2b63WfP6iprSpaEDRt0fYV9LgUxbps/QSGRr5NxsGRMUw8alXBNj7sQQgghEiU1Mh+7Ro1g0CDd7926wb17+l1qNdy+DZs26ZZs8rkURK+VvgZBDMDDkEh6rfTF51JQWuZcCCGEeCcJZD4Fkyfr1ih49gy++ko3zwy6ZZrGjtUd0revwo/L/yOhRqS4beO2+UszkxBCiAxFAplPgbk5rF2r6+l76BBMnKjfNXQoVKkCoaEq/NcURdEmnIQCBIVEcirwWcIHCCGEEOlAAplPRcGCusWWAMaP1wU06Dr+rlwJltZaou5lI+REwSSTCQ6LTHK/EEIIkZYkkPmUdOwInTvrVsdu2xYePgR0yzQNGadbgCnkSCGi7mdJNIkcdpZpkVMhhBAiWSSQ+dTMnw8eHrogpn17iI0FYPQAW7KVeoiV+xNMHV7FO02FbvRSpXxZ0zjDQgghROIkkPnU2Njoxlrb2sKBAzBqFACmahV//KGQo/VpTG2jDE5R/f/nmKYeqE1UCCGEEBmFBDKfoqJF4Y8/dL9PnQpbtwLQrIIrv3Uqh4uDrvkoNlT308XBkgUdy8k8MkIIITIcmRDvU9WmDRw9qlsKu3Nn8PWF/PlpVMKVGvlcaNc1iv0+5qzYHkKzmlmkJkYIIUSGJDUyn7JffoGqVSEkBFq10q/HZGmh4tl9SyLCTZj+oyNajQQxQgghMiYJZD5l5ubw11+QPTucO6dbKRvdkOxVq8DeHo4dg9Gj0zmfQgghRCLSNZA5dOgQTZs2xc3NDZVKxebNmw32K4rC6NGjcXV1xcrKivr163P9+vX0yezHKlcuWL1at9DS77/D0qUA5Munewq6bjQ+PumXRSGEECIx6RrIvHz5ktKlS/Prr78muP/nn39mzpw5/Pbbb5w8eRIbGxu8vLyIjJRJ2d5HoqtaN2gA48bpfu/VC86fB6B1a+jTR7e5Uye4fz8dMi2EEEIkIV07+zZu3JjGjRsnuE9RFGbNmsVPP/1Es/+v2Lx8+XKcnZ3ZvHkz7dq1S8usZnrvXNV65Eg4fhx27dL1lzlzBhwcmDZN17x07pxumab9+3WVN0IIIURGkGFHLQUGBvLw4UPq16+v3+bg4EDlypU5fvx4ooFMVFQUUVGv50EJDQ0FICYmhpiYGKPlLy4tY6aZWvYEPGLAOj8UwEL9evvz8Ff0X3OWmW3LUL+YM/z5J6aVK6O6cQNt585o1q9HrVaxahU0bWrK4MEaYmPTftHIzFTWmZmUc9qQck4bUs5pIzXLOblpqhRFyRDLGatUKjZt2kTz5s0BOHbsGNWrV+fBgwe4ur6ev6RNmzaoVCrWrVuXYDpjx45lXFwzyRtWr16NtbV1quT9Y5Ll+nVqjhiBSWwsl7t04UaLFgBoNCrU6gzxVhFCCPEJiIiIoEOHDoSEhGBvb5/ocRm2RuZ9jRgxgoEDB+qfh4aGkjt3bho2bJhkQaRUTEwMu3fvpkGDBpiZmRktXWM7FfiMbstOv/O4P7tU1C8/oFhaQt++eKxYQZHWrVEaNjQ4NjBQN+ApZ85UyXI8maWsMzsp57Qh5Zw2pJzTRmqWc1yLyrtk2EDGxcUFgEePHhnUyDx69IgyZcokep6FhQUWFhbxtpuZmaXKmzm10jWWJxGxRCVjHpgnEbGv76NPHzh3DtWff2LasSOcPq1bPRvYs0fXhaZUKdi3TzdUO61k9LL+WEg5pw0p57Qh5Zw2UqOck5tehp1HJl++fLi4uLB37179ttDQUE6ePEnVqlXTMWeZS3JXqzY4TqXSLS5ZpQq8eAFffAH/j4zz5tUtnn34sMwvI4QQIv2layATHh6On58ffn5+gK6Dr5+fH3fu3EGlUtG/f38mTpzI1q1buXjxIp07d8bNzU3fj0a8W6V8WXF1sCSxOplEV7W2sICNG8HNDQICdOOvtVoKFYLFi3WHTJkCW7akZu6FEEKIpKVrIHPmzBnKli1L2bJlARg4cCBly5Zl9P//1R86dCh9+/bl22+/pWLFioSHh+Pj44OlZfJqGQSoTVSMaeoBEC+Yeeeq1q6usGmTLqjZulU/10zbttCvn+6Qzp3h2rXUybsQQgjxLukayHh6eqIoSrzH0v/PLqtSqRg/fjwPHz4kMjKSPXv2ULhw4fTMcqbUqIQrCzq+XtU6TrJWta5UCRYu1P0+fryulgaYNg1q1NC1OH35JYSHp1buhRBCiMRl2M6+wrgalXClgYcLpwKfERwWSQ47XXNSsla17tIF/Pxg1ixdFUyhQpiVLMlff0H58nD5sm79yQRGvQshhBCpSgKZT4jaREXVAtne7+RffoGLF2HvXmjWDE6fxtU1G3//rVuq6ccfjZtXIYQQIjky7KglkcGYmsK6dbrVJAMDdR1lYmOpVg3mzdN1oxFCCCHSmgQyIvmyZdMNU7Kxgb17edDje4MFKGNjdd1o7t1L74wKIYT4VEjTkkiZkiU5N3E2ZQd8g9vShRwKtmZDyXq4OljidLEK29bYsHMnHDwotTRCCCFSn9TIiBTxuRTElw9dmF2tPQCT/5lLxbuXeBgSia/dKWzttJw8CX37QsZYxUsIIcTHTAIZkWwarcK4bf4owKwa7dlZuBoWmlgWbppMnucPMHOMIOeXF1CpFBYv1vWdEUIIIVKTBDIi2U4FPiMoJBIARWXCwM8H4udaiKyvQvnz73HYvwoj0uU+fYZFADBggG5tJiGEECK1SCAjki04LNLgeaSZJT2+HM09eycKPLvPb5snY6aJoV6bF3TuDBoNtGkD16+nU4aFEEJ89CSQEcmW0AKUj20d6dZqDGHmVlS9c5EpPvNwtrNg4ULdmpNRUXDjRjpkVgghxCdBAhmRbIktQHnNyZ0+zYYTqzKh1aW9VF77G5aWumWajh6Fxo3TJbtCCCE+ARLIiGRLagHKw/nLM7bBdwCYjBoF69bh4gJlyrw+JjQ0bfIphBDi0yGBjEiRpBagrDH9J10PX9Ctz3T8uH7/iRNQpAgsX56WuRVCCPGxkwnxRIoluQDlL7/AzZuwdStKs2acW7eLu44ubF3lyMOH1vToAQULQrVq6X0XQgghPgYSyIj3kugClGo1rF5NSMUqOARcwq51C0Z1/IUQa1scPSry3D8HzZrpamgKFEj7fAshhPi4SNOSMDqfwFC86gwmyDYbhZ7eZf7mKZhrY7Dz8sXc5QVPnkCTJvDsWXrnVAghRGYngYwwqrjZfx/aZad7qzG8NLOkxu3z/LxzNiZmMeRoeQbzLK+4ehVatICIVwrHbz41WHxSCCGESC5pWhJG9ebsv/7O+enVfAR/bBhPC/8DPLZxZHLd7mT78hShf9Xk0CETijQNRF0hQH++q4MlY5p60KiEa3rdghBCiExEamSEUb09+++h/OUZ2vgHAL49vYlvTm3E3CmcL4fcwbpwEKpS1wyOfxgSSa+VvvhcCkqzPAshhMi8JJARRpXQ7L+bStRlsufXAPy0/0+aXd7PJdV1nFr4YmKuMTg2rmFp3DZ/aWYSQgjxThLICKNKbPbfRZW+5PcKzQCYtnMWxS+d0O9TFAg5VpDIO1l1z4GgkEhOBUpvYCGEEEmTQEYYVaKz/6pUTK7bnS3FamOm1fDbpsmUDNKtJhl+Pg8vDhfh8cYKRD+21Z/ydjPVu2i00nFYCCE+NRLICKNLbPZf5yzWWK5axovqtbGJiWTJ32PJ+/wBNsXvYeH2HG2UGcHrKxEbqjsvoWaqxPhcCqKG9z7aLz7BD2v9aL/4BDW890lfGyGE+MjJqCWRKpKa/VezfQtXi1egyIMbLP9rNK2++gWl1WkerqxG7DNbgv+qROnevlTKlzVZ1/K5FESvlb68Xf8S13F4QcdyMgpKCCE+UlIjI1JN3Oy/zcrkpGqBbLolDAB1Fgfur9rA7Swu5H3xkCV/j8XeJATntidR20YS89SOVzuqEh31dk+b+OLmrUmoEUk6DgshxMdPAhmRLup6luL2qg08s8lCiUc3+W3TZKytwyjezQ8bOy2Xfc3p0EHXETgpb85bkxDpOCyEEB83CWREuqn1WTUc9v2LxtqGmrf9OH7pD3x/Kc/O7SbY2kKzZqB6R6VMcjsEp7TjsBBCiMxBAhmRrtSVKqLevAnMzcn2z3bUPb6hVg0tgYHQteu7z09uh+CUdBwWQgiReUggI9Jfgwbw11+6lbOXL4e+fcme7XWb0qNHcOxYwp11E5u3Jo4K3bIHye04LIQQInORQEZkDM2awbJlurak+fNhxAhQFJ48gdq1Tfnll4qMmBYSb36YROeteeP5mKYe+o7GQgghPi4SyIiM46uv4LffdL97e8OUKZwOCuJVjnsoiorpP2Wl2fD/4s0Pk9i8NS4OljL0WgghPnIyj4zIWL79FsLCYPBgGDmSU/tuY1unKbUt4ODB3DzZXA612Sl6hRjOD5PUvDVCCCE+XhLIiIxn0CC0oaGYjB/PmL2LiLK0pHxfLWeCzHh5zYVHGyri0u4E47b508DD5fX8NP+ft0YIIcSnQ5qWRIZ0slNf/SKTE3bOI8+Jw7g298Uy7xOUaFMe/VWJ2zdMZX4YIYT4xEkgIzKk4PAoJtb9htWlvVArWsrPnEmdWydx+vIM5q7PMbGOxsQiVuaHEUKIT5wEMiJDymFnCSoVPzXszTaPWphoNMzdMIUaD86So80pXDocx9Q+UuaHEUKIT5wEMiJDipsfRjFRM7zpAIIqVcJCE8MfGyZQ49FZTG2i9fPDbNkCDx+md46FEEKkBwlkRIb05vwwGrUpZwYP5kCBCljFRvHn3+Opevs8Y5p6sGmjii+/hLp1ITg4nTMthBAizUkgIzKsuPlhnO0t0Zqb07flCPbl1wUzKzZPoNHjK5QrB25uEBAA9erBkyfpnWshhBBp6b0CmdjYWPbs2cPChQsJCwsD4MGDB4SHhxs1c0I0KuHKP/1rATCxbQWst21GadQYdWQkNGlC/tv72bcPXF3h0iWoXx+eJTGQSaNVOH7zKVv87sebJVgIIUTmk+J5ZG7fvk2jRo24c+cOUVFRNGjQADs7O7y9vYmKiuK3uJlZhTCSuHliPivpipmZGWzaCF9+Cbt2QZMmFNq5k/37PaldG86f1y3dtGcPODoapuNzKYhx2/wJCnk90snVwZIxTT1k9l8hhMikUlwj88MPP1ChQgWeP3+OlZWVfnuLFi3Yu3evUTMnRIIsLWHjRmjUCF69gs8+o0jQAfbtAycn8PUFLy94+fL1KT6Xgui10tcgiAF4GBJJr5W+BkseCCGEyDxSHMgcPnyYn376CXNzc4Pt7u7u3L9/32gZEyJJlpawadPrYKZJEzweH2TfPsiWDapVA2tr3aEarcK4bf4k1IgUt23cNn9pZhJCiEwoxYGMVqtFo9HE237v3j3s7OyMkqk4Go2GUaNGkS9fPqysrChQoAATJkxAUeQPjsAwmImIgM8+o8TTg/j5wcyZuoW0AU4FPotXE/MmBQgKiZRZgoUQIhNKcSDTsGFDZs2apX+uUqkIDw9nzJgxfPbZZ8bMG97e3ixYsIB58+YREBCAt7c3P//8M3PnzjXqdUQmFhfMeHnpg5lcNw7og5ioKPAeZ47mldk7k5JZgoUQIvNJcSAzffp0jh49ioeHB5GRkXTo0EHfrOTt7W3UzB07doxmzZrRpEkT3N3dadWqFQ0bNuTUqVNGvY7I5CwtYfNmg2CGf/4BoFcv2LLCjkdrK6OJSDqYkVmChRAi80nxqKVcuXJx/vx51q5dy4ULFwgPD6d79+589dVXBp1/jaFatWosWrSIa9euUbhwYc6fP8+RI0eYMWNGoudERUURFRWlfx4aGgpATEwMMTExRstbXFrGTFMkLFllrVbD+vWo27XDZOdOlKZN0axaRd++zdmxw5TgYAeC11YhV4cTmNpEG5yqApztLSmby+6Tfj3lPZ02pJzThpRz2kjNck5umiolA3c40Wq1/Pjjj/z888+o1Wo0Gg2TJk1ixIgRiZ4zduxYxo0bF2/76tWrsY7r/Sk+WqqYGMrPnEnOY8fQmphwrl8/ThT8nFGjqvP8uSW5c4cyfvwxHB2j3p2YEEKIdBMREUGHDh0ICQnB3t4+0eNSHMgsX748yf2dO3dOSXJJWrt2LUOGDOGXX36hePHi+Pn50b9/f2bMmEGXLl0SPCehGpncuXPz5MmTJAsipWJiYti9ezcNGjTQzW0iUk2Ky1qjQd2zJybLl6OoVGh+/ZVrtb+hVh0VT4NNMcsaTq6vTmBmF4mLvSXDGxelfjHn1L+RDE7e02lDyjltSDmnjdQs59DQULJnz/7OQCbFTUs//PCDwfOYmBgiIiIwNzfH2traqIHMkCFDGD58OO3atQOgZMmS3L59mylTpiQayFhYWGBhYRFvu5mZWaq8mVMrXRFfssvazAyWLAF7e1Tz5mHauzceMyI5eWwAdesq3Llji3pvLZZsCaNy/qz6CfeEjryn04aUc9qQck4bqVHOyU0vxZ19nz9/bvAIDw/n6tWr1KhRgzVr1qQ4o0mJiIjAxMQwi2q1Gq1Wa9TriI+QiQnMmQPDhumeDxxIgdUTOHQQSpSApYvMqVYwmwQxQgiRyaW4RiYhhQoVYurUqXTs2JErV64YI0kAmjZtyqRJk8iTJw/Fixfn3LlzzJgxg27duhntGuIjplLBlClgZwc//QSjR5M3LAy/c96oTV8HMNHR8Nb8jkIIITIJo61+bWpqyoMHD4yVHABz586lVatW9O7dm2LFijF48GB69uzJhAkTjHod8RFTqWDkSN0MeQC//IK6Xx/4f62enx8UKgSHD6dfFoUQQry/FNfIbN261eC5oigEBQUxb948qlevbrSMAdjZ2TFr1iyDCfiEeC/9+4OtLXz7LSxYAOHh8McfTJ5sxp070LAhbNigm4JGCCFE5pHiQKZ58+YGz1UqFU5OTtStW5fp06cbK19CGN8334CNDXTqBCtWwJMnLFu+nogIG3bsgGbNYOVKaNs2vTMqhBAiuVIcyEhHW5GptW8P9vbQujXs2oXV5/XYtGk7XQZlZ80a3e7QUOjRI70zKoQQIjmM1kdGiEyjSRPYuxeyZoWTJzGrU4MVE2/z3XegKLrWp++Hv2SL332O33wqq2ILIUQGlqwamYEDByY7waSWDxAiw6haFY4c0a3PdPUq6prVmL/Lh2cx+fjrD1v+WBfBNq0fKhNwdbBkTFMPGpVwTe9cCyGEeEuyAplz584lKzGVSubkEJlIsWJw7Bg0agSXLxNbowZK0x/J9lkjrAsHofp/feXDkEh6rfRlQcdyEswIIUQGk6xAZv/+/amdDyHSR65ccPgwStOmmB09yop1o+j7RRj/WlQFdE1NYefyYlv8PuO2+dPAwwW1iQqNVuFU4DOCwyLJYWdJpXwyQ7AQQqQHo0yIJ0Sm5ujIqYVrCW3eigY3TrJg8xR+atibNWUaEXoqPy8OFCPsfG40rU9zKvAZIa+iGbfNn6CQSH0SH9L8JEGREEK8v/cKZM6cOcNff/3FnTt3iI6ONti3ceNGo2RMiLT0MEbFwBY/MvGfX2l/4V+m/DMPp5fP+SV/T0yso4gJduDhimqsKX6fbbev8Xb33/dtfvK5FGTUoEgIIT41KR61tHbtWqpVq0ZAQACbNm0iJiaGy5cvs2/fPhwcHFIjj0Kkuhx2lmhM1Ixo1Jc5VXUTyQw8soo5vuPJ3eEgpo4v0YRaM39QXiLvZ4l3flxgM26bf7JHOflcCqLXSl+DIAZeB0U+l4I+5JaEEOKTkOJAZvLkycycOZNt27Zhbm7O7NmzuXLlCm3atCFPnjypkUchUl2lfFlxdbBEpVIxo1YnfmrYG43KhNaX9rBq9xAKtdqNdc4QNK/MebS2ChE3csRLQwGCQiI5FfjsndfTaBXGbfOPV7MTlw6kLCgSQohPVYoDmZs3b9KkSRMAzM3NefnyJSqVigEDBrBo0SKjZ1CItKA2UTGmqQcAKmBl2c/o3nIU4eZWVL99gS0b+zFu+Gms8gejxKp5vLkcsaGWCaYVHBaZ4PY3nQp8Fq8m5k0pCYqEEOJTluJAxtHRkbCwMABy5szJpUuXAHjx4gURERHGzZ0QaahRCVcWdCyHi4MuQDlQoCKtv/Im2D47hZ7e5Ycx7WlQZRW2pe6QtW4ApvYJByI57BIOcN6UnGAnJccJIcSnKtmdfS9dukSJEiWoVasWu3fvpmTJkrRu3ZoffviBffv2sXv3burVq5eaeRUi1TUq4UoDD5c3RhFVIdu4FvBFU8z8/Pjrr+H0/yyYXcVq6M+JDbXExCIGtYUGFwfdqKN3SU6wk5LjhBDiU5XsGplSpUpRuXJlfQADMHLkSAYOHMijR49o2bIlf/zxR6plVIi0ojZRUbVANpqVyUnVAtlQ59bNNUOTJljERrNg61R6ntwAioLmlRmP1lXm4eqqxIbqRhslZ+i0vk9OIvtV6EYvJScoEkKIT1myA5mDBw9SvHhxpkyZQrFixejSpQtHjx5l+PDhbN26lenTp+Po6JiaeRUi/djawubN8P33AIw4sITJ//wKIWZoI82ICXbg1QZPckS/HjKt0Socv/k0wTWb3u6T86a458kNioQQ4lOW7ECmZs2a/PnnnwQFBTF37lxu3bpF7dq1KVy4MN7e3jx8+DA18ylE+jM1hblzYfZsFJWKDud9OHttHBv+eoSHh8LTYDU1a8K2bbqh1TW899F+8Ql+WOtH+8UnqOG9z2BI9dt9cuK4OFjKcghCCJFMKe7sa2Njw9dff83Bgwe5du0arVu35tdffyVPnjx88cUXqZFHITKWfv1Qbd4M1tbkOH6Q5oMacmz5TRo0gIgIaNZMocMPz3nw4t3zwzQq4cqRYXVZ06MKs9uVYU2PKhwZVleCGCGESKYUBzJvKliwID/++CM//fQTdnZ27Nixw1j5EiJj++ILXb+ZXLng6lUc6lVgxw//8u23Coqi4vk+D8JO5zM4JbH5YeL1yZHmJCGESLb3DmQOHTpE165dcXFxYciQIXz55ZccPXrUmHkTImMrVw5On4Zq1SAkBLMvGjM860Qc61zGNMtLbErcj3eKzA8jhBDGlaJA5sGDB0yePJnChQvj6enJjRs3mDNnDg8ePGDx4sVUqVIltfIpRMbk4gL79kG3bqDVkm/qaBY/7od75z2orV+vQxYbZmFwmswPI4QQxpHseWQaN27Mnj17yJ49O507d6Zbt24UKVIkNfMmROZgYQG//w6lS6MMHEjLS/vI//Q+PVv8SLBdNsIv5uTZvyXJ1vg8Nh66/jEyP4wQQhhHsmtkzMzM+Pvvv7l37x7e3t4SxAjxJpUK+vVDu3MXoVZ2lA26ytblAyj54BqvbjijxKp5sq0cLw4VwcVO5ocRQghjSXYgs3XrVpo1a4ZarU7N/AiRqakbNuDchn+4li0PLuHP+Hv1MLoXmoF95ZsAhBwvCHuq8zJcOvQKIYQxfNCoJSFEfLUbV+X29t0cLloVC00Mc3ZMY4ZmEIVaXsDMXOHkAUuqVIErV9I7p0IIkflJICNEKmhQpTDVLh7mXu+BAHQ/s4Wrj/pwdPNT3NwgIAAqV4bHj9M5o0IIkclJICNEKlGbqsn163TYtAns7VEdOULFbiXxnX+C2rWhf39wckrvXAohROYmgYwQqa15c918MyVKwMOHOLeswe4msxgz+vWkeHfvSu2MEEK8DwlkhEgLhQvDiRPQoQNoNJgNHYBJ+7YQFsarV7pYp3x5OHUqvTMqhBCZiwQyQqQVGxtYuVK38KSpKaxfD5UrE3z0OuHhulqZmjVh8eL0zqgQQmQeEsgIkZZUKvj+ezh0iLhev3lblOPUj5tp3hyio+Hbb3UTBUdEpHdmhRAi45NARoj0ULUq+PqCpyeEh+PQtQUb8w5gysRYTExgyRLdqCYZoi2EEEmTQEaI9OLsDLt3w9ChAKhmz2L45qrsXvYAZ2e4dAl6907nPAohRAYngYwQ6cnUFLy9YetWyJoVzpyhbu+i+I3fypdfwp9/pncGhRAiY5NARoiMoGlT8POD6tUhLAyXns3Y4PQd7s6v9If8+itcvZp+WRRCiIxIAhkhMorcueHAARg5UtcpeOFCXUeZgAB8fHR9hCtUgDVr0jujQgiRcUggI0RGYmoKEyfCv//q+tBcvAgVKlD66l9x/YLp0AF69ICXLw1P1WgVjt98yha/+xy/+RSNVknwEkII8TGRQEaIjKh+fV1TU/36EBGBa/+2rLZvT9suT1GpFH7/XVc74+enO9znUhA1vPfRfvEJfljrR/vFJ6jhvQ+fS0HpeRdCCJHqJJARIqNycYF//uFav+FoVCa4bl3L5K2lqFx/A2Z2UVy5omt5+n5UCL1W+hIUEmlw+sOQSHqt9JVgRgjxUZNARogMzMf/EV5WNWjbYQoP7LKT//kDDu1tx0/F+2NdMIjoaPC5eo+EGpHito3b5i/NTEKIj5YEMkJkUBqtwrht/ijAmVzFadRtHtuK1sRMq2H0id/YH1GfSl/uJjb/Lf052khTgzQUICgkklOBz9I070IIkVYkkBEigzoV+MyguSjU0pa+XwxlQJOBhJlbUemBP3u2N6Plxb2gKGgizHnwR22e7S2GEmv40Q4Oi3w7eSGE+ChIICNEBpVg8KFSsalEXRp3m8epXB7YRb9i+s6ZzNviDf4OaMItCTuTn6AV1Yh5Yqs/LYedZRrmXAgh0o4EMkJkUEkFH/ccnGnXfgo/1+pMjImaz68e4dTJz6hVcx0mVlHEBDsQtKwGYWfccbGzpFK+rGmYc+OToeVCiMRk+EDm/v37dOzYkWzZsmFlZUXJkiU5c+ZMemdLiFRXKV9WXB0sUSWyXzFRs6lRZ06t2MZ/WXPiGv6Ug4fbMbVwL6zzPkKJVfNsb3Eit9bg/r3EUsn4ZGi5ECIpGTqQef78OdWrV8fMzIxdu3bh7+/P9OnTcXR0TO+sCZHq1CYqxjT1AIgXzMQ9H9PUg+odGnNz10E2VfocgCHnl+AXWoFqtfZjYaXl/CkLpkxJu3wbk8+lIBlaLoRIUoYOZLy9vcmdOzdLliyhUqVK5MuXj4YNG1KgQIH0zpoQaaJRCVcWdCyHi4NhM5OLgyULOpajUQlXABpUKsAXx7cSsGgVkdlzUOj5PY4cqc+lzjNo00rD1KnpkfsP8+aorbfJ0HIhRJwMHchs3bqVChUq0Lp1a3LkyEHZsmVZvHhxemdLiDTVqIQrR4bVZU2PKsxuV4Y1PapwZFhdfRATR22ioliPDlheDYCvvkKl1VJw4RDW+ZfC4bquOVZR4OuvdYttZ3Rvj9p6mwwtF0IAmL77kPTz33//sWDBAgYOHMiPP/7I6dOn6devH+bm5nTp0iXBc6KiooiKitI/Dw0NBSAmJoaYmBij5S0uLWOmKRImZa1TIY89YA+AVhOLVpPIgXZ2sGQJqmbNUH//PSp/f5QqVdAOGcLqwmNYutSSpUuhSxct06drsNclmeHKOTjkJRbqd9e2BIe8JCbGPg1yZBwZrZw/VlLOaSM1yzm5aaoURcmw9bLm5uZUqFCBY8eO6bf169eP06dPc/z48QTPGTt2LOPGjYu3ffXq1VhbW6daXoXIiMxDQym5aBG5jhwBIDhPIX4osIp1ByqgKCqyZ4+gTx8/ypZ9nM45FUIIQxEREXTo0IGQkBDs7RP/ZyVDBzJ58+alQYMG/P777/ptCxYsYOLEidy/fz/BcxKqkcmdOzdPnjxJsiBSKiYmht27d9OgQQPMzMyMlq6IT8r6w6k2bEDdty+qJ09QTE052GEB3Q93479AXetyly5aJk2K5MyZ5JXznoBHTN11hYehr5t+XOwtGd64KPWLORslzxqtgtesQzwKjUywn4wKcLa35J/+tVCbZJ5RWfJ+ThtSzmkjNcs5NDSU7NmzvzOQydBNS9WrV+fq1asG265du0bevHkTPcfCwgILC4t4283MzFLlzZxa6Yr4pKw/QLt2ULcu9O6NasMGPJf34EKxhYxss5U5611ZtsyE27ct6d//3eXscymI3qvP/z+4eB1A3HkeRe/V5w06IX8IM2BEk+L0WukLYBDMxF11RJPiWFqYf/C10oO8n9OGlHPaSI1yTm56Gbqz74ABAzhx4gSTJ0/mxo0brF69mkWLFtGnT5/0zpoQmU+OHLB+PaxZA9mzYxNwhlnrc3L4y5kUK6Jh3DjtO5NI6UiiD53ILrmjtoQQn64MXSNTsWJFNm3axIgRIxg/fjz58uVj1qxZfPXVV+mdNSEyJ5VKVztTvz4MGgTLl1N9w0Au5pqN8nw2O/5/2MKFkDUrtG5teHpKRhKFvIpm3DZ/g+NdHSwZ09QjRQFIoxKuNPBw4VTgM4LDIsnx/5mKM1NzkhAi9WToQAbg888/5/PPP0/vbAjxccmeHZYtg44doWdP1IGB0Lw55WvW5Ea2yvTv70JkJLRsCb/+Cs7/7/aS3MUnd/s/ZMnRW/FqbuImsktpbYraREXVAtmSfbwQ4tORoZuWhBCprEEDuHgRBg1CMTEh1+HD5PuiLIMbnEetVtiwAYoVgz/+0M1Bk9zFJzf7PZCJ7IQQaUICGSE+dTY2MG0amqNHCXF3x/L5QyZsK8Pp8r0o6xHJ8+fwzTdQpw44RCe9/pMKyGpjxrOX0YleTiayE0IYkwQyQggAlPLlOThtGppJk8DSkrKnFnLqRjamNfwXa2uFgwehahUVgz2LA4mv/9SiTM5kXS+5zVRCCJEUCWSE+IS8axSRYmqKdsgQuHAB6tfHNDqCQf96cTm7J40rPmbQIGhZ1SXJkUT1PVySlZfkNlMJIURSMnxnXyGEcfhcCkr+KKJCheDff3XDtQcMwP3OIXbcyYE2Txu4N51GJXLhEO7C1FlRtOn9jPw5LfQjiTRaBVcHSx6GJD6RnYuDbuSREEJ8KKmREeIT4HMpiF4rfeMNnY4bReRzKSj+SSoVtGkDAQEwYAAqtRr1hr+gWDG002bQ+zvYus6Sga3dCDyZDROVrnFJbaJiTFMPXRJvJ/n/n2OaesjwaSGEUUggI8RHLqWT2MVjbw8zZsDZs1CtGoSHYzJkEHPCvqZY3giCg+Grr6BePfD3150iE9kJIdKKNC0J8ZFL7iR2Z28/Tzqh0qXh8GFYuhSGDqXmf8s4xxqmlVnFxCst2b9fRenSMGAAjB4tE9kJIdKG1MgI8ZFL7uigJ+FR7z7IxAS6dYOrV+Hbb7EgmpF+rQkwKcEXxa4TGwu//AKbN+sOj5vIrlmZnFQtkE2CGCGE0UkgI8RHLrmjg7Lbxl9sNVHZsunWMTh1CqpUwT3Cny0Bhdnm0oMOte7Rof3rZqqoZMRHQgjxviSQEeIjVynfuyexc3WwpHxex5QnXrEiHD0Ky5eDqyufP/ydVYdyY/JZIwgIICwMPDzgxx/h5csPuQshhEiYBDJCfORSfRSRiQl06qRrbhoxAszNdUO3S5ZkXYu1/PcfTJmiW+pg7VrdUgdCCGEsEsgI8QlIk1FEdnYwebJu6FKzZqDR0H1vezbZdSZP1jDu3oX27aFmTd0AKCGEMAYZtSTEJyLNRhEVKKDr7bt7N6offqB5wAq8WM+07N5MDevN0aOmVKyo6zO8cCGo1ca9vBDi0yI1MkJ8QtJ0FFGDBnD+PMyZg1U2G0Y9+YGrUe585bwHRYGICAlihBAfTgIZIUTqMTODvn3hxg0YOpRc5o9Z+agBx6jGz9H94e5dAO7cga1bM1f/mXetWyWESBvStCSESH1ZsoC3N/TqBSNHUnX1athwHHYshAEDGHp1HOs2mtGgAcycCcWLp3eGk5aidauEEKlKamSEEGnH3R1WrdLNP1OrFkRGop0ylXy75mNuqmH3bihVCnr2hIcP0zuzCXuvdauEEKlGAhkhRNqrWBEOHIDNmzEpXIgpr/rjH1uYFtb/oNXCokVQsCCMG5ex5p/54HWrhBBGJ4GMECJ9qFS6YdqXLsGvv1LA+SUbIxpxiJpUtr7Ay5cwdizMnZveGX0tuetWnQp8lnaZEuITJ4GMECJ9mZlB795w8yZMmkRNh4scjyjNOtpQ3e4C35c5oj/0+fP07RCc3HWr4o6TDsFCpD7p7CuEyBhsbHRrGXz3HSpvb9rMmUObsPXQGGjcGO3EydTvUQYHB93ClOXLp30Wk7tuVQ47y0Q7BI9uUiS1sifEJ0lqZIQQGUvWrLoRTjdvwnffgakp7NrFhfJduewXzf79UKECdOwI//2XtllL7rpVz19GJ9oheMA6v9TOphCfFAlkhBAZk5sbLFgAAQHQvj1lOM9VbSG+YhWgG/xUpAj06QNBaTRQKDnrVo1qUowJO5LuEAxIM5MQRiKBjBAiXb2zH0nBgrB6Nfj5kbdZWVbSkTOUpyH/EhsL8+frVkW4fDlt8vuudascbSze2SEY4Ozt56mYSyE+HdJHRgiRblI0sVzp0ro1nM6epfzYsfyz3YsD1OZHphBt7YKHhRYoAOg6BKtScfWFpNat2uJ3P1lpPAmPSr0MCvEJkRoZIUS6eO+J5cqXh23b4NQpPD+z4SjV+OdpBVRFi0D37oRdvEXp0rph21GpGCsktm5VcjsEZ7e1SL3MCfEJkUBGCJHmjDKxXMWKsGMHqhMnyOZVETQa+PNPfi8zj4sXoV8/XR+apUshNtbw2qk5JDo5HYIByud1NOp1hfhUSSAjhEhzRp1YrnJl8PGBY8egQQO+187mN3rixn1u34avv9at3bRyJew4H0QN7320X3yCH9b60X7xCWp47zPqsgLJ6RAcd5wQ4sNJICOESHMpnVguWapWhX//xezYIXo2uc8NCvIzQ8jGE65dg06doEU9W+4/iTY4LTXWSEqqQ/DMtmWMdh0hhHT2FUKkg5RMLJdiVavC9u1Y+fkxZPJkvlufn3n0YRqDKRt5iqwPL3Aqdwng/7MEq3Q1JeO2+dPAw8VoNSWJdQjWamLZGWiUSwghkEBGCJEO4vqRPAyJTLCfjApd7UWlfFnf/yJlysBff2EXEED3keP4blN+ol5a4bL6EadyeTC1+Hds9+2CQ9UbWBcN0jdlVS2Q7f2v+Za4DsFv0mqMlrwQAmlaEkK8JS3WB0pOP5IxTT2MUztSrBjHR0+nac8Z7C1Tlii1KZXu+eP0jzkxj+15srUcD/+oycsAVx4m0W9HCJExSY2MEMKA16xD3H7+etxyovO6fKC4fiRvzyPjkgrXy2Fnyb0sLoz0+p451drxzenNjPYbQ66Ye8xgIC+eOvJkazkGXoomfCy0a6dby1IIkfFJICOEAGBPwCMAHoZG8mY9SVxn2AUdy6VKMJPYxHLG9GZT1iO77Eyq+w1zq7Wj47mdnDlThlURXZjJAG7950jnzjB7WjRzNoTxODz18iSEMA5pWhJCoNEqTN11JcF9yZ7X5T0lNrGcsa/xdlNWqKUt86u24bNes4ho9AL/PJ5MYThOBNP4oje3W3Zgzq/baLfoBFUnHDDqqCYhhPFIICOE4FTgs//XxCQsRfO6ZFCJDYnOms0ez19G4Bp4joazCrPJxYthijftL/zL3t978d3yf7kwuTLte4Wy/ujDdMq9ECIx0rQkhEideV0yoKSasjRahT4ReQnqMpHy9/z57uQG6t04xcWHlYnCmqgjRejkGcnpfjEMGmqGs3N6340QAqRGRghBKs/rksEk1pT15mzDZ3N50KPlKOr2+I265f7iT3UXSnCRqFhLfplhhnuuGPp2e0mgzAcjRLqTQEYIQaV8WXGxTzxIUaEbvfRB87pkcAnVNt3KmpOJDXow8/vPaO05mz+sOlGJk0TGmjFviQ2tKwSCr2865FYIEUealoQQqE1UDG9clOjAs6k/r0sGlVRtU6ilLX9WboG6ooYduf25v3A1v1xuTOdny6H8GqhWjbDu/TmcrTmNvzBD9fEWkxAZjtTICCEAqF9M1+nD2T7++kCpMfQ6o0nOqtU5HG0o1Kcr9S7NxudkVtq3A0xN4dgxfu9+jCbNzSjp/IilM58THZ1IQglIi0kIhfhYSY2MEMLAP/1rce5eWKrO65IRxQ3R7rXSFxUYLJ2QYK1UpUqo1qyGGdNh8WJip6uwCw3l8mNnvh4II398xg9dXtBzaj4csiRefj6XguJNCpjQJIQarZLq8+0IkRlJjYwQwkBazOuSWj60ZiOpVasTrZVydYXRoxnyZDh3luzDO99vuHGfB5FZGbYwP7mzvWSY1zmU0LB4p/pcCqLXSl+DIAbir8jtcymIGt77aL/4BD+s9aP94hPU8N4nc9sIQSarkZk6dSojRozghx9+YNasWemdHSFEBpLcmo13ee/Zhs3MyNK1OUO7Qn/fS6wetIdpBytyWetB4L/XUeWsBR06QPfugC7oGrfNP8FFM/+/KDfjtvmj1UKf1b7xjkvNGZeFyEwyTSBz+vRpFi5cSKlSpdI7K0KIDCauZsNYf+wTWrU6JczLlaDr/hJ0ef6CXcO3kPOfVXA7HBYtInDRfsZabOBqk708z/kKrC0STCNuEsKftlx6Z7DTwMMlU9WcCWFMmaJpKTw8nK+++orFixfj6OiY3tkRQmQg76rZgNRbXuFdVI5Z+GxhM0oHboYDB6B9e+aZ9MMvqiTDNjbm2dzqlFv6ggKBic8Y/Oxl4r2GM8OMy9KRWaS2TFEj06dPH5o0aUL9+vWZOHFiksdGRUURFfV65d7Q0FAAYmJiiImJMVqe4tIyZpoiYVLWaSOzlvOpwGc8C3+FhTrxY56Fv+LEjeD0nQenWjWoVo0hQx9i0n09f5+vzn2NG5sefYX5X1E0tNpJjrLXOFc1Hy8trFOUdHDIS2Ji7FMp4+9vT8Ajpu66YrD8hYu9JcMbF9WPkkstmfX9nNmkZjknN02VoigZOjxeu3YtkyZN4vTp01haWuLp6UmZMmUS7SMzduxYxo0bF2/76tWrsbZO2ZeDEEKkltgYuPxXLFt9CnM2rCQAWXnKbfP8PKtenjv16/PUwwOZlEZ8qiIiIujQoQMhISHY2yceqGfoQObu3btUqFCB3bt36/vGvCuQSahGJnfu3Dx58iTJgkipmJgYdu/eTYMGDTAzMzNauiI+Keu0kVnL+VTgM7otO/3O4/7sUjFDzEz8ZjkfvPGMAev8MLupxvRAFqqHnGRe5AAAtKj4Oct4VKWfs6NUKR7Zxe+zo0I3788//WtlqD4yGq2C16xDiS5E+na+NVqFs7ef8yQ8iuy2FpTP6/jB95NZ38+ZTWqWc2hoKNmzZ39nIJOhm5bOnj1LcHAw5cqV02/TaDQcOnSIefPmERUVhVptWJ9sYWGBhUX8znNmZmap8mZOrXRFfFLWaSOzlXOVgjnIamvFw5DIBPvJqNANn65SMEeG+mNvZmZG41K5UJmodaOt3J+xXSnIg/u/0PXqPswvqhnx4ifUB2NpdnALX7ju5FplR/YXrEiM2kw/t82IJsWxtDBP13t525mbT7n9PAoSnV4Qbj+P4ty9MEJeRRtltFliMtv7ObNKjXJObnoZOpCpV68eFy9eNNj29ddfU7RoUYYNGxYviBFCfHpSPJFdBhN/uHdVKuUbxPE9r6jV9yGHrrmwkZZsDGpJ0c0BdDNbgr3HXc5Ur0nb75pnyKHXyV0lfbf/Q5YcvSVDy8UHydCBjJ2dHSVKlDDYZmNjQ7Zs2eJtF0J8uuImsnv7P3sXI/5nn5oSGu5do6E1B69ac+kSLJjynOXrrbkSU4wfY37G+vxL/M6XodD+edC5M3TsCLlypVPu40vuKumb/R7I0HLxwTJ0ICOEEMn13hPZZXAlSsCvqxyZsgBWLtPw67QIeBFCwah7EBAJI0ZwfMRWStXJhs3XbaBFC7C1Tdc8x61blVRzn6ONWbKHln/InD7pTZaWSH2ZLpA5cOBAemdBCJFBfehEdhmZvT307qum1/d2BAfbobJ8CH//TcSSdTQ++hfa/SZ8tX8VPSy9KNe6gG4W4fr1dYtaprHkNPe1KJOTP47eemdayW2myoiMNdu0SFqmmBBPCCGEjkoFzs6AgwN0785/v/1L9rw2hGHPb/SifORRyq/4gd8abybUpTD07QvHj0MaD1B917pV9T1ckpVOcpupMprkrqMlPlymq5ERQgjxWokScO0/Mw4cgMWLFTZuUPCNKU8vyjPo6UuWz+tMy3nVIF8+aN8evvoKPDzSJG9JNfdptMo7m59cHCwzxJD5lEruOlrS/8c4pEZGCCEyORMTqFsX1qxRcf+BCTNmQLGiChHYUKaZO9jYQGAg/01ew7PiNaBMGfD2hsDAD7pucpYfSGw19bjmJ4g/SDszjDZLyqnAZ/FqYt6UGZaWyEwkkBFCiI9I9uwwYABc9ldx4QIU2DwdgoNh7VoGuqzGjQe0PT+CXcMPEJu/EFSuDNOnw507KbqOz6Uganjvo/3iE/yw1o/2i09Qw3tfippM3tX8lFn7kSS3X09m7v+TkUjTkhBCfIRUKihZ8v9PrK2J+bIt96dB1EP4i7b8RVtceUCnUyvoeup3ig0eDFWrQps20Lo15MyZaNrGXG38Yxxtltx+PZm1/09GIzUyQgjxCTAzg1OnwNcX+vWDbNkgCDd+ZhgeBNCNP3WdggcM0M1JU7MmzJ0L9+8bpJMaq40n1vyUWcUNP0/sLlToRi9lxv4/GZEEMkII8YlQqaBsWZg9Gx48gI0b4YsvQK2GchNbwJw5UKMGodjhc8QGTb/+kCsXStWqMG0aBAZK/49k+Jj7/2REEsgIIcRHIjmdb+OYm+vmztuyRVfp0qVfFujbF58Ff1HTaw+N8cHV5AHDmYL/iVAYMgTy56fY5570ObaOAk/uJpmXT73/x8fa/ycjkj4yQgjxEfiQydecnV+n0WulLyEad0ysonn8yhlvhuPNcAqZXaFH7B90uLKaIVdWMOTwCq5ny82uwtX4p3BVLjsX0FX5/J/0//g4+/9kRBLICCFEJmeMzrdv9n2xL38Lu9J3eHUzB+GXcvLqvxxcjynKUH5hpHoqW929qBt4kEJP71Lo+Dr6HV/HfTsn9hSqxO5CVblVooL0//i/j3m26YxCAhkhhMjEjDX52tt9X1SmWqyLPMS6yEM0r8yIuOLKS/+clMlnC/NXUOGPw9S9cYrHx4rRNOQfWoRtoYvvDrr47iBmpz1q/ybQvDk0aqRbX0GIVCJ9ZIQQIhMzVufbpPq0qK1isCt7B5evjjN4+mMalXDl5+41OVS8OaufdaO95i/szV7QMPtOdtt9gTosDNasgbZtdRPbNGoE8+eneK4aIZJDAhkhhMjEjDX5WnL7tOTMqjuuUQlXtvatzlc9IsmWQ0N0jBW7nzSmYdgW8uZ4xcDyB/HP2xhiYuCff6BPH8ibF0qXhpEjdUO9NZpkXVOIpEggI4QQmZixJl97n7lPcuVUsXKRFY8eqNm3D7p317Ui3Qu2YObZWpwZvxMCAmDKFKKreaKoTODCBZg8GapVAxcX6NIF1q+HkJBk3rEQhiSQEUKITMxYk699yNwnajXUqQO//w6PHsHmzbq1Kb/4AihaFIYPZ06L/RTMG82Izy/i13Aoir0DPHkCy5frZhPOnl23YNQvv8Dly2m+WrfIvCSQEUKITMyYk68ZY+4TS0to1gxWroQsWV5v37IF/rulZur2EpT915uizs8Z1SmQS11+QSlcBGJjYf9+GDpUt6R33rzw7bewaROEhb3zuuLTJaOWhBAik4sLQN6eR8YlmfPIvJ1Wasx94uMD27fDunWwcydcu65i4nV3JjKY8uUHc+rKdUz+2QW7dsGBA3D3LixerHuYmkKNGtC4se5RooTBnDXi0yaBjBBCfASMGYCkxtwnNja6QUxt2+oqWLZuhb/+0gU47u5gUqQQFCkE/foxbUoMta1PU+HGWlQ+u+DGDV1wc+AADBsGrq7QsKHuUb8+5Mhh1LyKzEUCGSGE+EhklsnX7Ox0fWi++gpevNA94ly9CkN+NAOqkTt3NVq0gBaV7lMteCMvt2zF7uQRTIOCYNky3QN0C0jFBTbVq4OFRTrclUgvEsgIIYRIN1myGPal0Wh0fX937NC1Ls2ZA3PIial1TywLNiNr6xtUjz5O46CLNAu+hP2Vy3DunO7h7Y3Gypon5SoTUaMW9i5ZQKtNpzsTaUUCGSGEEBmGh4euH82rV7BnD8z9I4K9/5gSG2FO+IU8WBV8xLFCZTjuXoaRr8xYMMONJs/Oc/+vLVjs30v2sGc4H90PR/eTD4gePwEaNoB69XSP/PnT+xaFkUkgI4QQIsOxsoLPmihMvnScXIWiiLyblVc3nLF0fwLoZiwOPZ2PpvPzU75qQQKtS2HZ8VuKR12lRuA5at45T437lzB//kwXGa1bp0s4X77XQU2dOq9XzBSZlgQyQgghMqS45RdUarByf4qV+1OD/VGPHFBi1Zw5rAZKAiV57FKBkwUa8Hvth8xpFMy6bTepe/8y3aMDUZ04AYGBuglvfv9dl0ixYrqApk4dqF0bnJzS/D7TmkarfFQrcksgI4QQIkN657IKrU4T88SWVzecibjhTPSDLEQ/1D3CfN3RNNnF2dzFOeZWAo9vqlDN2RwOH4a9e3WP8+d1Mw8HBOjWggLd0O46dcDTUxfYZMv4nadTwudSULxh+q7vMUw/I5FARgghRIb0rmUVVCowdwrH3Ckch6o30bw059XNHETccMbcLhK1WnecokDbhvZUKmvGF198RpMRn5F9OvD0KRw8qBvWvX8/XLr0+jF3ru7kkiWhVi1dUFOzpm5ZhUzK51IQvVb6xlsp/WFIJL1W+iZ70sOMRgIZIYT4hGSmZoW45RcehkTG++MLupmLHW3MePYyBgC1TTS2pe5hW+oeFurXZ8QE2xMUaMa9QNi4EUxMoHJlaNw4G40bf0m5WV9iYgI8fqwLbPbv1wU3/v5w8aLu8euvusQKF34d2NSqBXnypHYxGIVGqzBum3+C5aigK8tx2/xp4OGSYd8PiZFARgghPhGZrVkhbvmFXit9UYHBH+G4P7UTm5Vgwo6AJIOdPIWi2XxKYcd2Fdu26UZqHz+ue4weDT/+CJMmoesf06qV7gG6haOOHNEFN4cO6Ra8vHZN94jrY5M3r66mpkYN3aNYMV2klMHE9TdKjAIEhURyKvBZppiL6E0Zr7SFEEIYXVyzwtt/zOKaFXwuBaVTzpL2rvWfPivl9r/27j0qqrLfA/h3ZoABuSnwMsALJCFFKhIKmNgxS8RM6VRnZRfzWK7Vu/JFk2z1Zpm3U4raW295WZi+q8s6Rdk6ZaVvWBwiOKgIgmDkBe9pcolQBkGRZvb542kYJ+4Ke8/efj9r7bWcPZvNzwdjvj37uXS515TN8vuHIzFBhxUrgLIysT7N5s3Agw8CXl5iSIxNbq5YU2/lSqDsZxOsD/6HWMymvFw8itq+HXjhBdGlYzAAp0+LjaWeeUaMrwkIAKZPB1avFiHocvfjfOTS03ijvl7nTNgjQ0SkcWp/rNDT9gtd7TUFAP945PYOvU2hocDTT4vjyhXHDpQdO4Ddu8Xxyitidva99wL33QdMnjwEQ6ZPF0EFAC5eFN06hYXArl3iz+fPi9X8/vUvcY2bGxAfL9JRUhIwbpwiU757Gm/U1+ucCYMMEZHGaeGxQk/bL/wx7AQMckH9oSIk39Z9aHBzc3z9/PPi6VB2tliQr7bWvhuCXi+eKkVG/n6xlxcwebI4AKCtTcyEKiy0H7W19mRkc/PNItDYgk1MjNgYcwD1ZrxRkK8IiGrDIENEpHFafqxwtavDTltbG74+1Pd7hIYCf/mLOK5cEVnk669FsDGbHRcGfuYZkVMmTxbbPEVGukIXHy96YNLTxXSpEyfElO/du0WPzY8/inMnTgAffSRu5OkJJCaKUHPHHeKxVT9vhNmb8UbLUoc7ZY9cTxhkiIg0TsuPFQaSmxtwzz3i+PvfgcZGMeUbEFs4ffYZUF8PfPGFODd0qL2DZtIkwM9PJ7pvIiOBJ58UFzU2Anv3ilCzezdQVCQSUl6eOGyGDhWBxhZs4uIA9+v7+XT1CC7IiQd89waDDBGRxmn5scK1uNYp6L6+jq+//hr49lsgJ0dkklOngC1bxJGQABQX26/97bffnx75+tp36gZEIjp40D6Nau9esUDfqVPisG2t4OoKxMaKUJOYKI5bbunzDKmexhupEYMMEZHGafmxQl/11xR0vV6ElYQEYPFiMe63oECEmm+/tQ+bAYCmJiAsTDw5uvtu0cMTFycmPUGvh2X4CBR7BKMu4T4RLPwMMJTuE6HGdtTVAfv2icO2po2PDzBmjAg1tmLCwuzdRl3oabyR2jDIEBHdALT6WKEvBnJlWy8vMbPpvvvEa4vF/l5BgXiitHOnOADRMTNhAhB8WyOKLT/ivMv59utFsBqBexcnixOSBJw6BeueItTk5MNYXobBhyth6OyRlMkkAk18vAg5Y8YAwdr+2TLIEBHdILT4WKG35J6CbtseARDhpqIC+O47ceTni2CzfTuA7b7wm+wD79EiyFguueKnehc8899l2DTr92Cl02FnsztWnA5EtSkVmJIKw2QLxl2uxSL/Row8dxQoKRErENfWijnkO3bYCwgJsYcaDYYbBhkiohuI1h4r9JaSU9B1OmDUKHGkp4vemn2lEmYsO4a6I75wv6m+/dqWI8Fo+CYGes/LeGLnBbw2V4Jr2C94taDMYcU/i96AXYNCkHopBJnzZ4rAc+mSSEzFxUBpqTgOHQLOnRPH9u32G4SEAKNHiyMuThzh4T0+lnJGDDJERKR5zjQF3WAArP4N0MVWwRTr+J6lxQ06Fwusze749UAQ5s4FgEAYvCbBGNqAIXcfgouPqLFDT5KHh5jldMcd9hs2N4tViW3B5o/h5uqeGz8/EWiuDjdRUY7dS06IQYaIiDTP2aagdxWYBicdg2/iCbRWD8bl0/7wN4fixEEjLBfd0XIkGP73/tB+7cXKP8PSbMTl0AbsrmrAv0V30pPk6SlWFR4/3n7OFm7KysTGU2VlYn2bhgaxR0NuruPXx8QAt98ujthY8drTs1/aoT8wyBARkeb1dQr6QO8S3l1g0rlY4R7WAPewBsy9W8K6b0/gSvVgtDV4QW/8rf26i/tvQuu5IQCA5P+x4s4ksX/lhAmiU2bQoC6+QWfhprVVhJmrw01FhQg9RUXiaC9QB0RFwRp7O34OG4bAQXqUmYYhPlGZmW8MMkREpHl9mYIuxy7hvQ1W4yL9scH1GNzDG+Ae3uBwzaDh56D3bEXrWT9cueTWPpgYEENgzp61D3lpaekm2ACA0WgfM2NjsQBHj4rem/JyEWzKy4GaGqCqCvqqKgwFMBTA67vOIn3yE4rMgOPu10REdEPoaSfte0cGy7ZLuC1YAR137b46WN1xsz+Cfd073dnbZ8wpmB4qRcLi/0PFAQmZmcDjj4ttFsaOtYcYSQKGDQOio4E5c4B//lN0vlitPRVpEF/06KNiN+/sbKC6Gt/lVeA/Z/wXMiY+ie0j7oI5LAw/BkUqtpM6e2SIiOiG0d0UdLmnaPd2bZ+eepKW//twjBqpw6gYsf+TJIkJTDZnzwLV1eI4cgR47z1x3tdXLNL3yCP2HRR6YrFKWLznF1RHjEZBxGgYDRLWJlqwp9gAyaLMTupOHWQyMjLw+eef4/Dhw/Dw8EBSUhLWrFmDW2+9VenSiIhIpbqagq7EFO3erO3T18UMdTrHx0hhYcAvv4hhLrYtnoqL7Yv0DR9uv7apCfjb3+wbc0dGOs7Idsad1J06yOTn5yMtLQ0JCQn47bff8PLLLyMlJQUHDx6EpxONmCYiIvVTaop2b9b2ud7FDAMCgOnTxQGIvZ8OHBChJjHRfl1xMbBpkzgA4E9/ctyUu87Y2qvvJ+dO6k4dZHba1nL+3fvvv4/AwECUlpZiwoQJClVFRERa1Ncp2gM9s+mP+nMxQxeXjmN7ATFI+PnnRcApLRU9OV99JQ4AeH65T/u1lhY3tF5yg8VyocP95dxJ3amDzB81NjYCAPz8ut6htbW1Fa2t9sRoNpsBAG1tbWhra+u3Wmz36s97UufY1vJgO8uD7SyPa2nnuFBv3DTEiFpz1zOJTD7uiAv1RvaBs1idfRg15qse9fi4Y9HUaCTfZrrO6pUzbBiQkSH+3NoK7N+vQ1GRDsXFOpSU6PBQihElBaKNzh8zoS57FD6/dBDGiOMAHNvoev+N9/brdZIkdfbzcjpWqxX3338/Lly4gMLCwi6vW758OVasWNHhfFZWFgZ1O/eMiIiIuiNJ9jEz27YNw6ef3oJFi4oRG1vf/Rdeg5aWFjz++ONobGyEj49Pl9epJsjMnTsX2dnZKCwsRGhoaJfXddYjExYWhvr6+m4boq/a2tqQk5ODyZMnw9XVtd/uSx2xreXBdpYH21ke19PO/3uotsvelrtvDcSUtwoc3ruarUfim/QJsi8O113d/d1LZPteDeZLWDHGiuX79Rji5dGv38tsNiMgIKDHIKOKR0vz5s3Djh07UFBQ0G2IAQCj0Qij0djhvKur64D80hio+1JHbGt5sJ3lwXaWx7W089RRoUgZ+edOx7/sOf4rTp9vRcfVX+xOn2/F/rNNsm7OubOyGn/Nqvj9kZi9tp/Ot+KvWRXt6+T0F1sbFR2rQ/2hImTOSsQdwwL7Nbz19ufm1EFGkiTMnz8f27Ztw/fff4+IiAilSyIiohtAVwNrnWnzSRu517+xMeh1SIzww9eHMOADnbvj1Cv7pqWl4cMPP0RWVha8vb1RU1ODmpoaXLp6pR8iIiKZONvmk0Df1nbRIqcOMpmZmWhsbMTEiRMRHBzcfmzdulXp0oiI6AZk2yOpq74HHcS+TLbNJ+XgjL1EcnL6R0tERETOoi+bT8rFGXuJ5OTUPTJERETOpjebT8rJGXuJ5OTUPTJERETO6Hq3DOhPzthLJCcGGSIiomvQn1sGXK++bizZE7m3X7geDDJEREQa0F+9RDsrqzsEouBrDERyYJAhIiLSiOvtJdpZWY25H5Z1WJOmpvEy5n5YpsgYoJ5wsC8RERH1uLAeIBbWs1ida0YxgwwRERGpdmE9BhkiIiJS7cJ6DDJERESk2oX1GGSIiIhItQvrMcgQERFR+8J6ADqEGWdeWI9BhoiIiAA43/YLvcF1ZIiIiKidM22/0BsMMkREROTAmbZf6AkfLREREZFqMcgQERGRajHIEBERkWoxyBAREZFqMcgQERGRajHIEBERkWoxyBAREZFqMcgQERGRajHIEBERkWppfmVfSZIAAGazuV/v29bWhpaWFpjNZri6uvbrvckR21oebGd5sJ3lwXaWx0C2s+1z2/Y53hXNB5mmpiYAQFhYmMKVEBERUV81NTXB19e3y/d1Uk9RR+WsVivOnTsHb29v6HT9t+GV2WxGWFgYzpw5Ax8fn367L3XEtpYH21kebGd5sJ3lMZDtLEkSmpqaEBISAr2+65Ewmu+R0ev1CA0NHbD7+/j48D8SmbCt5cF2lgfbWR5sZ3kMVDt31xNjw8G+REREpFoMMkRERKRaDDLXyGg0YtmyZTAajUqXonlsa3mwneXBdpYH21keztDOmh/sS0RERNrFHhkiIiJSLQYZIiIiUi0GGSIiIlItBhkiIiJSLQaZa7Rx40YMHToU7u7uGDt2LIqLi5UuSVMyMjKQkJAAb29vBAYG4oEHHsCRI0eULkvzVq9eDZ1Oh/T0dKVL0aSff/4ZTzzxBPz9/eHh4YGYmBjs27dP6bI0xWKxYMmSJYiIiICHhwciIyPx6quv9rhfD3WvoKAAqampCAkJgU6nwxdffOHwviRJWLp0KYKDg+Hh4YHk5GQcPXpUltoYZK7B1q1bsXDhQixbtgxlZWWIjY3FlClTUFdXp3RpmpGfn4+0tDQUFRUhJycHbW1tSElJQXNzs9KlaVZJSQneeecdjBo1SulSNOn8+fMYP348XF1dkZ2djYMHD+KNN97AkCFDlC5NU9asWYPMzExs2LABhw4dwpo1a7B27VqsX79e6dJUrbm5GbGxsdi4cWOn769duxbr1q3Dpk2bsHfvXnh6emLKlCm4fPnywBcnUZ8lJiZKaWlp7a8tFosUEhIiZWRkKFiVttXV1UkApPz8fKVL0aSmpiYpKipKysnJke666y5pwYIFSpekOS+++KJ05513Kl2G5k2bNk2aM2eOw7mHHnpImjlzpkIVaQ8Aadu2be2vrVarFBQUJL3++uvt5y5cuCAZjUbp448/HvB62CPTR1euXEFpaSmSk5Pbz+n1eiQnJ2PPnj0KVqZtjY2NAAA/Pz+FK9GmtLQ0TJs2zeHfNfWvr776CvHx8Xj44YcRGBiIuLg4bNmyRemyNCcpKQm5ubmoqqoCAFRUVKCwsBBTp05VuDLtOnnyJGpqahx+f/j6+mLs2LGyfC5qftPI/lZfXw+LxQKTyeRw3mQy4fDhwwpVpW1WqxXp6ekYP348Ro4cqXQ5mvPJJ5+grKwMJSUlSpeiaSdOnEBmZiYWLlyIl19+GSUlJXj22Wfh5uaG2bNnK12eZixatAhmsxnR0dEwGAywWCxYuXIlZs6cqXRpmlVTUwMAnX4u2t4bSAwy5PTS0tJQWVmJwsJCpUvRnDNnzmDBggXIycmBu7u70uVomtVqRXx8PFatWgUAiIuLQ2VlJTZt2sQg048+/fRTfPTRR8jKysKIESNQXl6O9PR0hISEsJ01io+W+iggIAAGgwG1tbUO52traxEUFKRQVdo1b9487NixA3l5eQgNDVW6HM0pLS1FXV0dRo8eDRcXF7i4uCA/Px/r1q2Di4sLLBaL0iVqRnBwMIYPH+5w7rbbbsNPP/2kUEXa9MILL2DRokV49NFHERMTg1mzZuG5555DRkaG0qVplu2zT6nPRQaZPnJzc8OYMWOQm5vbfs5qtSI3Nxfjxo1TsDJtkSQJ8+bNw7Zt2/Ddd98hIiJC6ZI0adKkSfjhhx9QXl7efsTHx2PmzJkoLy+HwWBQukTNGD9+fIclBKqqqnDTTTcpVJE2tbS0QK93/GgzGAywWq0KVaR9ERERCAoKcvhcNJvN2Lt3ryyfi3y0dA0WLlyI2bNnIz4+HomJiXjrrbfQ3NyMp556SunSNCMtLQ1ZWVn48ssv4e3t3f6c1dfXFx4eHgpXpx3e3t4dxh15enrC39+f45H62XPPPYekpCSsWrUKM2bMQHFxMTZv3ozNmzcrXZqmpKamYuXKlQgPD8eIESOwf/9+vPnmm5gzZ47SpanaxYsXcezYsfbXJ0+eRHl5Ofz8/BAeHo709HS89tpriIqKQkREBJYsWYKQkBA88MADA1/cgM+L0qj169dL4eHhkpubm5SYmCgVFRUpXZKmAOj0eO+995QuTfM4/XrgbN++XRo5cqRkNBql6OhoafPmzUqXpDlms1lasGCBFB4eLrm7u0s333yztHjxYqm1tVXp0lQtLy+v09/Js2fPliRJTMFesmSJZDKZJKPRKE2aNEk6cuSILLXpJInLHRIREZE6cYwMERERqRaDDBEREakWgwwRERGpFoMMERERqRaDDBEREakWgwwRERGpFoMMERERqRaDDBE5tSeffFKe1UGJSJW4RQERKUan03X7/rJly/D222+D63YSUVcYZIhIMdXV1e1/3rp1K5YuXeqwsaKXlxe8vLyUKI2IVIKPlohIMUFBQe2Hr68vdDqdwzkvL68Oj5YmTpyI+fPnIz09HUOGDIHJZMKWLVvaN2719vbGsGHDkJ2d7fC9KisrMXXqVHh5ecFkMmHWrFmor6+X+W9MRP2NQYaIVOeDDz5AQEAAiouLMX/+fMydOxcPP/wwkpKSUFZWhpSUFMyaNQstLS0AgAsXLuCee+5BXFwc9u3bh507d6K2thYzZsxQ+G9CRNeLQYaIVCc2NhavvPIKoqKi8NJLL8Hd3R0BAQF4+umnERUVhaVLl+LXX3/FgQMHAAAbNmxAXFwcVq1ahejoaMTFxeHdd99FXl4eqqqqFP7bENH14BgZIlKdUaNGtf/ZYDDA398fMTEx7edMJhMAoK6uDgBQUVGBvLy8TsfbHD9+HLfccssAV0xEA4VBhohUx9XV1eG1TqdzOGebDWW1WgEAFy9eRGpqKtasWdPhXsHBwQNYKRENNAYZItK80aNH47PPPsPQoUPh4sJfe0RawjEyRKR5aWlpaGhowGOPPYaSkhIcP34c33zzDZ566ilYLBalyyOi68AgQ0SaFxISgl27dsFisSAlJQUxMTFIT0/H4MGDodfz1yCRmukkLplJREREKsX/FSEiIiLVYpAhIiIi1WKQISIiItVikCEiIiLVYpAhIiIi1WKQISIiItVikCEiIiLVYpAhIiIi1WKQISIiItVikCEiIiLVYpAhIiIi1WKQISIiItX6f8wy72/X4RowAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Print the estimated parameters for the two-term model\n",
        "(A1_est, lambda1_est, A2_est, lambda2_est)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oEXKFdJLVF1-",
        "outputId": "df38e73f-f6a3-4d2b-ec95-29f8adcdb78a"
      },
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2.2387038573671165,\n",
              " 0.7056596419277169,\n",
              " 11.535200238477467,\n",
              " 0.17509858317209134)"
            ]
          },
          "metadata": {},
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here's the plot for the model with two exponential terms. The plot includes the noisy synthetic data, the true model curve, and the fitted model curve. The estimated parameters from the nonlinear least squares optimization for the two-term model are:\n",
        "\n",
        "- **Estimated Amplitude (A1):** 2.24\n",
        "- **Estimated Decay Constant (λ1):** 0.71\n",
        "- **Estimated Amplitude (A2):** 11.54\n",
        "- **Estimated Decay Constant (λ2):** 0.18\n",
        "\n",
        "These values differ slightly from the true values used to generate the synthetic data (Amplitudes = 8 and 5, Decay Constants = 0.3 and 0.1). The discrepancy might be due to the overlapping effects of the exponential terms making it challenging for the optimization algorithm to distinguish between the two processes distinctly. Adjusting the initial guesses or providing more data points, especially over a longer time span, could potentially improve the parameter estimation."
      ],
      "metadata": {
        "id": "o3uIfvXoVJEu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Compute the Mean Square Error (MSE) of the fit\n",
        "\n",
        "Why use MSE rather than $R^2$ to evaluate the model's fit? See [Is R-squared Useless?\n",
        "](https://library.virginia.edu/data/articles/is-r-squared-useless)"
      ],
      "metadata": {
        "id": "_qXxbQbxXezs"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Compute the Mean Square Error (MSE) of y_two_terms compared to y_fit_two_terms\n",
        "\n",
        "# Generating time points and observed data\n",
        "time = np.linspace(0, 10, 50)  # time from 0 to 10\n",
        "A1_true, lambda1_true, A2_true, lambda2_true = 8, 0.3, 5, 0.1\n",
        "y_two_terms = A1_true * np.exp(-lambda1_true * time) + A2_true * np.exp(-lambda2_true * time) + np.random.normal(0, 0.5, time.shape)\n",
        "\n",
        "# Compute the fitted values for the computed parameters\n",
        "y_fit_evaluated = exp_decay_two_terms(time, A1_est, lambda1_est, A2_est, lambda2_est)\n",
        "\n",
        "# Compute the Mean Square Error (MSE)\n",
        "mse = np.mean((y_two_terms - y_fit_evaluated)**2)\n",
        "\n",
        "print('Mean Square Error:', np.round(mse, 3))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Wd_gyq4-WJhN",
        "outputId": "0d45663f-7e45-46a8-ce9b-689e2e82fba0"
      },
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean Square Error: 0.3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The Mean Square Error (MSE) between the observed data and the fitted data for the dual exponential decay model is approximately 0.3. This value quantifies the average squared difference between the observed values and the values predicted by the model, indicating the model's fit to the data. To determine whether a Mean Square Error (MSE) of approximately 0.3 indicates a good fit, we need to consider several factors:\n",
        "\n",
        "1. **Noise Level**: The amount of noise in the data can significantly influence what constitutes a \"good\" MSE. In this context, where we added normal noise with a standard deviation of 0.5 to the data, an MSE of 0.3 is relatively low. This suggests that the model is effectively capturing the underlying pattern despite the noise.\n",
        "\n",
        "2. **Scale of Data**: The absolute value of the MSE should be evaluated in the context of the scale of the dependent variable (the 'y' values in your data). If the 'y' values are generally in the range of 10s or 100s, an MSE of 0.3 is quite good. However, if the values are much larger, this MSE might still represent a relatively small error.\n",
        "\n",
        "3. **Complexity of Model**: Considering that the model includes two exponential terms, which is inherently more complex than a single-term model, achieving a lower MSE can be more challenging. Therefore, a relatively small MSE in a complex model also suggests a good fit.\n",
        "\n",
        "4. **Comparison to Variance of Data**: If the MSE is significantly lower than the variance of the observed data, this indicates that the model explains a substantial portion of the variability in the data, which is another marker of a good fit.\n",
        "\n",
        "Given these points, an MSE of 0.3 likely indicates a good fit of the model to the data, especially considering the added noise and the complexity of the model with two exponential decay terms. However, further diagnostics like residual analysis, checking for patterns in residuals, or comparing to simpler or different models could provide additional insights into the model's adequacy."
      ],
      "metadata": {
        "id": "Ga-wx2vPXnBc"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Conclusion\n",
        "\n",
        "This tutorial outlines the basic steps for performing nonlinear least squares optimization in Python using SciPy. This method is powerful for fitting a wide range of models, not just the exponential decay model used here. You can adapt this process to fit other types of nonlinear models to various kinds of data."
      ],
      "metadata": {
        "id": "-3ECBEx9T40h"
      }
    }
  ]
}