Example1.ipynb

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      "name": "python"
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/gnodking7/WDAnepv/blob/main/Example_2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Objective\n",
        "In this example, we consider a couple of positive matrices that examplify the advantage of Acc_SK [1] algorithm over SK [2] algorithm.\n",
        "\n",
        "In particular, these positive matrices are the exponential Euclidean distance matrices that arise from the computation of a regularized Wasserstein distance between data matrices.\n",
        "\n",
        "We will go over the background of the example in the following order:\n",
        "\n",
        "\n",
        "1.   What are Acc_SK and SK?\n",
        "2.   What is regularzied Wasserstein distance?\n",
        "3.   Where do these data matrices come from?\n",
        "\n",
        "### What are Acc_SK and SK?\n",
        "Acc_SK and SK share a common goal:\n",
        "\n",
        "\"Given a positive matrix $\\mathbf{K}\\in\\mathbb{R}_+^{n\\times m}$ obtain a matrix of the form $\\mathbf{T}=\\mathcal{D}(\\mathbf{u})\\mathbf{K}\\mathcal{D}(\\mathbf{v})\\in\\mathbb{R}_+^{n\\times m}$ with desired row and column sums\"\n",
        "\n",
        "$\\mathcal{D}(\\mathbf{u})\\in\\mathbb{R}_+^{n\\times n}$ and $\\mathcal{D}(\\mathbf{v})\\in\\mathbb{R}_+^{m\\times m}$ represent diagonal matrices with diagonal elements $\\mathbf{u}\\in\\mathbb{R}_+^n$ and $\\mathbf{v}\\in\\mathbb{R}_+^m$, respectively.\n",
        "\n",
        "In particular, we consider the resulting matrix $\\mathbf{T}$ to have the row sum $\\mathcal{1}/n$ and the columnn sum $\\mathcal{1}/m$.\n",
        "\n",
        "### What is regularized Wasserstein distance?\n",
        "Wasserstein distance and regularized Wasswerstein distance belong in a family of distances for probability measures [3]. Regularized Wasserstein distance between data matrices $\\mathbf{X}^c\\in\\mathbb{R}^{d\\times n_c}$ and $\\mathbf{X}^{c'}\\in\\mathbb{R}^{d\\times n_{c'}}$ can be defined by associating with these data matrices the uniform probability vectors $\\mathbf{r}=\\frac{1}{n_c}\\mathbf{1}_{n_c}\\in\\mathbb{R}^{n_c}$ and  $\\mathbf{c}=\\frac{1}{n_{c'}}\\mathbf{1}_{n_{c'}}\\in\\mathbb{R}^{n_{c'}}$, respectively [4].\n",
        "\n",
        "Then, the regularized Wasserstein distance between $\\mathbf{X}^c$ and $\\mathbf{X}^{c'}$ is\n",
        "$$W_\\lambda(\\mathbf{X}^c,\\mathbf{X}^{c'}):=\\langle\\mathbf{T}^\\lambda,\\mathbf{M}_{\\mathbf{X}^c,\\mathbf{X}^{c'}}\\rangle$$\n",
        "the Frobenius inner product between $\\mathbf{T}^\\lambda$ and $\\mathbf{M}_{\\mathbf{X}^c,\\mathbf{X}^{c'}}$. $\\mathbf{M}_{\\mathbf{X}^c,\\mathbf{X}^{c'}}$ is defined as the Euclidean distance matrix between data vectors in $\\mathbf{X}^c$ and data vectors in $\\mathbf{X}^{c'}$, i.e.,\n",
        "$$\\mathbf{M}_{\\mathbf{X}^c,\\mathbf{X}^{c'}}:=\\Big( [\\|\\mathbf{x}_i^c-\\mathbf{x}_j^{c'}\\|_2^2]_{ij} \\Big) \\in\\mathbb{R}^{n_c\\times n_{c'}}$$\n",
        "The optimal regularized transport matrix\n",
        "$\\mathbf{T}^\\lambda$ is the solution to\n",
        "an entropy-smoothed optimal transport problem\n",
        "$$\\mathbf{T}^\\lambda:=\\mbox{argmin}_{\\mathbf{T}\\in U_{n_cn_{c'}}}\\, \\Big\\{\\lambda\\langle\\mathbf{T},\\mathbf{M}_{\\mathbf{X}^c,\\mathbf{X}^{c'}}\\rangle-h(\\mathbf{T}) \\Big\\}$$\n",
        "with the regularization parameter $\\lambda>0$ and the entropy $h(\\mathbf{T}):=-\\sum_{ij}T_{ij}\\log(T_{ij})$. \n",
        "\n",
        "$U_{n_c,n_{c'}}$ is the transport polytope of $\\mathbf{r}$ and $\\mathbf{c}$ \n",
        "containing all possible transport matrices between class $c$ and class $c'$, and is defined as\n",
        "$$U_{n_c,n_{c'}}:=\\{\\mathbf{T} \\mid \\mathbf{T}\\in\\mathbb{R}_{+}^{n_c\\times n_{c'}},\\, \n",
        "\\mathbf{T}\\mathbf{1}_{n_{c'}}=\\frac{1}{n_c}\\mathbf{1}_{n_c},\\, \n",
        "\\mathbf{T}^T\\mathbf{1}_{n_c}=\\frac{1}{n_{c'}}\\mathbf{1}_{n_{c'}}\\}$$\n",
        "\n",
        "It can be shown that $\\mathbf{T}^\\lambda$ has the form $\\mathbf{T}^\\lambda=\\mathcal{D}(\\mathbf{u})\\mathbf{K}\\mathcal{D}(\\mathbf{v})$ with $(\\mathbf{K}^{c,c'})_{ij}=e^{-\\lambda\\|\\mathbf{x}_i^c-\\mathbf{x}_j^{c'}\\|_2^2}$. Therefore, computing $\\mathbf{T}^\\lambda$ can be achieved by either Acc_SK or SK on the matrix $\\mathbf{K}$. \n",
        "\n",
        "In this example, we consider two positive matrices $\\mathbf{K}^{1,2}$ and $\\mathbf{K}^{1,1}$ to compare Acc_SK and SK on:\n",
        "\n",
        "\n",
        "*   $\\mathbf{K}^{1,2}$ is formed from the data matrices $\\mathbf{X}^1$ and $\\mathbf{X}^2$\n",
        "*   $\\mathbf{K}^{1,1}$ is formed from the data matrix $\\mathbf{X}^1$\n",
        "\n",
        "### Where do these data matrices come from?\n",
        "The data matrices come from a synthetically generated dataset with three classes. The data matrices are:\n",
        "$$\\mathbf{X}^1\\in\\mathbb{R}^{2\\times 30},\\quad \\mathbf{X}^2\\in\\mathbb{R}^{2\\times 40},\\quad \\mathbf{X}^3\\in\\mathbb{R}^{2\\times 30}$$\n",
        "The dataset is generated such that the data points are centered around the coordinates $(-5,0)$ and $(5,0)$ for Class 1, centered around the coordinates $(-3,3)$ and $(3,-3)$ for Class 2, and centered around the coordinates $(-3,-3)$ and $(3,3)$ for Class 3. These data points are randomly drawn at their corresponding centers using a Guassian distribution with a standard deviation of 0.5, and the number of data points for each class are equally split among its two clusters. Finally, the dataset is standardized.\n",
        "\n",
        "The plot of the dataset is shown below:\n"
      ],
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    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "feaNwpL7RpCA"
      },
      "outputs": [],
      "source": [
        "import sys\n",
        "sys.path.append('/content/drive/My Drive/Colab Notebooks')"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import WDA_subfunc as sub\n",
        "import WDA_datasets as datasets\n",
        "import numpy as np\n",
        "import matplotlib.pylab as pl"
      ],
      "metadata": {
        "id": "R6NNFFb4DHxT"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "TR, TR_L, TST, TST_L = datasets.load_synth(2, 100, 100)\n",
        "\n",
        "pl.figure(1, figsize=(6, 6))\n",
        "pl.scatter(TR[np.where(TR_L==1), 0], TR[np.where(TR_L==1), 1], marker='+', label='Class 1')\n",
        "pl.scatter(TR[np.where(TR_L==2), 0], TR[np.where(TR_L==2), 1], marker='+', label='Class 2')\n",
        "pl.scatter(TR[np.where(TR_L==3), 0], TR[np.where(TR_L==3), 1], marker='+', label='Class 3')\n",
        "pl.legend()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 391
        },
        "id": "63dUQSlBDS0S",
        "outputId": "3f0b8f30-385f-440f-f250-7ae9056692cc"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f6794884990>"
            ]
          },
          "metadata": {},
          "execution_count": 3
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The matrices $\\mathbf{K}^{1,2}\\in\\mathbb{R}^{30\\times40}$ and $\\mathbf{K}^{1,1}\\in\\mathbb{R}^{30\\times 30}$ are formed as\n",
        "$$(\\mathbf{K}^{1,2})_{ij}=e^{-\\lambda\\|\\mathbf{x}_i^{[1]}-\\mathbf{x}_j^{[2]}\\|_2^2},\\qquad(\\mathbf{K}^{1,1})_{ij}=e^{-\\lambda\\|\\mathbf{x}_i^{[1]}-\\mathbf{x}_j^{[1]}\\|_2^2}$$\n",
        "We consider regularization parameter $\\lambda=0.01, 0.1$ for both matrices. "
      ],
      "metadata": {
        "id": "ZrVY5mRaEZ3q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Get data matrices \n",
        "X1 = TR[TR_L == 1, :]\n",
        "X2 = TR[TR_L == 2, :]\n",
        "\n",
        "# Compute matrix K (for lambda=0.1), compute errors of SK and Acc_SK, and plot errors\n",
        "M12 = sub.dist(X1, X2)\n",
        "M11 = sub.dist(X1, X1)\n",
        "lamb = 0.1\n",
        "K12 = np.exp(-lamb * M12)\n",
        "K11 = np.exp(-lamb * M11)\n",
        "\n",
        "K12_u1, K12_v1, Err_K12_1 = sub.SK(K12) # SK K12\n",
        "K12_u2, K12_v2, Err_K12_2 = sub.Acc_SK(K12) # Acc_SK K12\n",
        "K11_u1, K11_v1, Err_K11_1 = sub.SK(K11) # SK K11\n",
        "K11_u2, K11_v2, Err_K11_2 = sub.Acc_SK(K11) # Acc_SK K11\n",
        "\n",
        "pl.figure(1, figsize=(10, 10))\n",
        "\n",
        "pl.subplot(2, 2, 1)\n",
        "pl.semilogy(Err_K12_1, 'bx-', linewidth=3, markersize=12, label='SK')\n",
        "pl.semilogy(Err_K12_2, 'ro-', linewidth=3, markersize=12, label='Acc_SK')\n",
        "pl.legend()\n",
        "pl.xlabel('Iteration')\n",
        "pl.ylabel('Error norm')\n",
        "pl.title('Matrix $\\mathbf{K}^{1,2} (\\lambda = 0.1)$')\n",
        "\n",
        "pl.subplot(2, 2, 2)\n",
        "pl.semilogy(Err_K11_1, 'bx-', linewidth=3, markersize=12, label='SK')\n",
        "pl.semilogy(Err_K11_2, 'ro-', linewidth=3, markersize=12, label='Acc_SK')\n",
        "pl.legend()\n",
        "pl.xlabel('Iteration')\n",
        "pl.ylabel('Error norm')\n",
        "pl.title('Matrix $\\mathbf{K}^{1,1} (\\lambda = 0.1)$')\n",
        "\n",
        "# Compute matrix K (for lambda=0.1), compute errors of SK and Acc_SK, and plot errors\n",
        "M12 = sub.dist(X1, X2)\n",
        "M11 = sub.dist(X1, X1)\n",
        "lamb = 1\n",
        "K12 = np.exp(-lamb * M12)\n",
        "K11 = np.exp(-lamb * M11)\n",
        "\n",
        "K12_u1, K12_v1, Err_K12_1 = sub.SK(K12) # SK K12\n",
        "K12_u2, K12_v2, Err_K12_2 = sub.Acc_SK(K12) # Acc_SK K12\n",
        "K11_u1, K11_v1, Err_K11_1 = sub.SK(K11) # SK K11\n",
        "K11_u2, K11_v2, Err_K11_2 = sub.Acc_SK(K11) # Acc_SK K11\n",
        "\n",
        "pl.subplot(2, 2, 3)\n",
        "pl.semilogy(Err_K12_1, 'bx-', linewidth=3, markersize=12, label='SK')\n",
        "pl.semilogy(Err_K12_2, 'ro-', linewidth=3, markersize=12, label='Acc_SK')\n",
        "pl.legend()\n",
        "pl.xlabel('Iteration')\n",
        "pl.ylabel('Error norm')\n",
        "pl.title('Matrix $\\mathbf{K}^{1,2} (\\lambda = 1)$')\n",
        "\n",
        "pl.subplot(2, 2, 4)\n",
        "pl.semilogy(Err_K11_1, 'bx-', linewidth=3, markersize=12, label='SK')\n",
        "pl.semilogy(Err_K11_2, 'ro-', linewidth=3, markersize=12, label='Acc_SK')\n",
        "pl.legend()\n",
        "pl.xlabel('Iteration')\n",
        "pl.ylabel('Error norm')\n",
        "pl.title('Matrix $\\mathbf{K}^{1,1} (\\lambda = 1)$')\n",
        "\n",
        "pl.tight_layout()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 729
        },
        "id": "NjQkW2NWEOyr",
        "outputId": "18c0c5d8-1c9c-4565-b978-a242f4d6da1f"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x720 with 4 Axes>"
            ],
            "image/png": 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eSq9evWjcuDEA69ev5/jjj2fcuHHsueeeZfmnZpa6dW39x/332/GAATbWFrb7noiEJl3GYY0upeEc3HYbDBwYnPvkEzjqKCtyF5EyNWzYMLp37w5A9+7dGTZsGJ988gkXXHAB5XJ76m633Xb8/PPP1K1bl7Zt2wKwzTbb/Pd4fnvvvTfz5s3juuuuY8WKFbRt25aZM2cCUL58edq3b8+zzz5bBn9dhrv++mDi4YcfbPW9iCSddBmHlSDHw4ABwSwy2FbVRxwBhdwqEEl73m/5061b7DN+WVnWj7Og1ynEihUrGDNmDOeddx4NGjTgnnvuYfjWdsoshmrVqnHiiSfy2GOPccYZZzAqd6FYVlYWw4cPZ8KECdxxxx1xeS8pxA47wGWXBccDBmjDJpGt0ThcKkqQ46VfP7jrruD4iy+ga1f455/wYhJJJtdcA4XcPttCpUp5F8LG4I033qBnz54sXLiQBQsWsGjRIho2bEirVq148skn2ZS7sc+KFSvYY489WLJkCRNzV2ivWrXqv8fzGz9+PH/99RcAGzZsYMaMGXkWgFSpUoX333+foUOHaiY50a69FiIr1mfM2HJ7ahHZOo3DMVOCHE/XX593xedXX0HnzrByZXgxiSSLdu3gmGOKHpwrV7b60tzbbrEaNmwYJ5xwQp5zJ510EkuWLGGXXXahZcuWtGrVildeeYUKFSrw2muvcdlll9GqVSsOP/xw/i2kC83cuXPp0KEDLVq0oHXr1rRp04aTTjopzzXbbbcdH374IYMGDWLkyJHFiluKoXZtuPLK4HjgQO1oKlIcGodj5nwatstp06aNnzRpUngBPPRQ3l7JbdrARx/BttuGF5NIgs2cOZOmTZtu/aKNG635/LvvWseX6NXUWVk2Y3HssfDSS8EOammgoP9tnHOTvfdtQgqpTCRkLP7rL2jQILg799JL0LNnfN9DJEVpHN664ozFmkFOhMsvh0cfDY4nTYJDD4Xly8OLSSQZlC8Pr7wCY8bASSdB1ao2IFetCiefbPX7w4al3aAscbTttnD11cHxLbdoFlmkODQOx0Rt3hLl4ouhXLmgwf1339n+5p98AttvH25sImFyzm7zJVn96OjRo7k+urc50LBhQ0aMGBFSRFKoK6+EBx+02eS5c22m65xzwo5KJHVoHC6SEuRE6t3bkuTzzrNVnz/8YEnyp5/aimyRNOO9xxXRRD5ZdenShS5dusT9ddOxjC10NWrYgr1+/ez4ttvgjDOgQoVw4xJJAhqHC1bcsVglFol2zjnwwgtBW5Xp06FjR/j99zCjEom7SpUqsXz5ciWEUbz3LF++nEqRXeAkfi67DGrVst8XLLBxViTDaRwuWEnGYs0gl4Uzz7SZ5J49rRh+5kxLkseMgZ12Cjs6kbioX78+ixcvZtmyZWGHklQqVapE/fr1ww4j/VSvDn36WPcgsF70vXpB1PazIplG43DhijsWJ32C7JxrBPQDanjvTw47nhI7/XRLkk8/3Zrb//wzdOhgSfLOO4cdnUiplS9fnoYNG4YdhmSSSy6x1pp//AGLFsEzz9g5kQylcTh+Elpi4Zx7zjn3h3Nuer7zXZ1zPzvn5jjn+m7tNbz387z35yYyzjJzyinw2muWKAPMmWNJ8sKF4cYlIlIE51wj59yzzrk3wo7lP1WrQt+oj5A77rC2VSIipZToGuQXgK7RJ5xz2cCjwBFAM+A051wz51wL59x7+X7SbyXbSSfBG28E7VPmz7ckef78cOMSkbSV1pMVF14IO+5ov//2Gzz1VLjxiEhaSGiC7L3/HFiR73Q7YE7uYLsBeBU4zns/zXt/dL6fPxIZX2iOOw7eeitYcb1woSXJc+eGG5eIpKsXSNfJisqV4cYbg+M774S1a8OLR0TSQhhdLOoBi6KOF+eeK5BzrpZz7gmgtXPuhq1c19s5N8k5NyklitOPPhreeSdYULJokSXJs2aFG5eIpJ2ynKwIZSw+/3yILL5ZuhQee6xs3ldE0lbSt3nz3i/33l/ovd/Ne3/nVq57ynvfxnvfZvtU2Yija1fb6jHSduTXX627xU8/hRqWiGSEhExWhDIWV6oU9EQGuPtuWL26bN5bRNJSGAnyr0B024b6uecy0+GHw/vvQ5UqdrxkiSXJP/4YalgiItFinawIzTnnwC672O9//gmPPBJuPCKS0sJIkCcCjZ1zDZ1zFYDuwMgQ4kgehxwCH3xgK7LBbhF26gTTpoUbl4iks/SarKhQAW6+OTi+5x7455/w4hGRlJboNm/DgK+BPZxzi51z53rvNwGXAqOBmcBw772mSw8+GEaPhmrV7HjZMkuSp04NNy4RSVfpN1nRqxc0amS/r1gBDz4YbjwikrIS3cXiNO99Xe99ee99fe/9s7nnR3nvm+Teqrs9kTGklAMPhI8/hm22sePly212ecqUcOMSkZSWMZMV5ctD//7B8X33wcqV4cUjIikr6RfpZZz994dPPoGaNe34r7/g0ENh4sRw4xKRlJVRkxU9ekDjxvb733/D/feHG4+IpCQlyMmobVv49FPYdls7XrkSDjsMvvkm3LhERJJduXIwYEBw/MADdjdORKQYlCAnq332gTFjoFYtO/7nH+jcGcaPDzcuEZFk1707NG1qv69aZaUWIiLFoAQ5me29N4wdC5FeoqtWQZcu8Nln4cYlIpLMsrNh4MDg+KGHbOGziEiMlCAnuxYtYNw4qFPHjtesgSOOsNllEREp2Mkn2/gJNm4OHhxuPCKSUpQgp4JmzSxJrlvXjtetg6OOso4XIiKypawsuOWW4PjRR+H338OLR0RSihLkVLHnnlZaUS93J9h//4VjjoEPPww3LhGRZHX88dC6tf2+bp1tQS0iEgMlyKmkcWNLknfO3fxq/Xo47jh4771w4xIRSUbO5Z1Ffvxx+O238OIRkZShBDnV7LabJckNGtjxhg1w4onwzjuhhiUikpSOPtpaZ4JNKtxxR7jxiEhKUIKciho2tJrkyJaqGzfagpQ33ww1LBGRpOMc3HprcPz00/DLL+HFIyIpQQlyqtp1V5tJ3n13O960CU49FYYPDzcuEZFk06ULHHCA/b5hg2aRRaRISpBTWf36liQ3aWLHmzfDaafBK6+EG5eISDLJP4v87LMwf3548YhI0lOCnOp22smS5MiuUTk50LMnvPRSuHGJiCSTQw+F//s/+33TJhg0KNx4RCSpKUFOBzvuaDXJe+1lxzk5cNZZ8NxzYUYlIpI8nIPbbguOX3wR5swJLx4RSWpKkNPFDjvY7notW9qx93DuufDUU+HGJSKSLDp0gEMOsd83b86bMIuIRFGCnE62396S5EhjfIALLoDHHgsvJhGRZBJdizxkCPz0U3ixiEjSUoKcbmrVgk8/hTZtgnOXXAIPPRReTCIiyeLAA62rBVg5WnTCLCKSSwlyOtp2W/j4Y9hvv+DcFVfA/feHF5OISLKI3l3v1Vfhxx/Di0VEkpIS5HRVsyZ89BG0bx+cu+YauPvu8GISEUkG++0HRx1lv3ufN2EWEUEJcnrbZhv48MOgtRFA375w++3hxSQikgyik+LXX4fvvw8vFhFJOkqQ01316vDBB9CpU3Duppvsw8H78OISEQnTvvvC8ccHxwMHhhaKiCSfjEuQBw+GsWNju3bsWLs+5VWtCu+9B4cdFpwbOBD691eSLCKZKzopfvttmDw5tFBEJLlkXILcti2cckrRSfLYsXZd27ZlE1fCVakCI0cGq7fBdpK64QYlySKSmVq1gpNPDo41iywiuTIuQe7UCYYP33qSHEmOhw/PW5mQ8ipXtlmSyOIUsEV7112nJFlEMtPAgbbLHtidtm+/DTUcEUkOGZcgw5ZJ8vffw++/22NpmxxHVKoEb74Jxx4bnLvvPrjqKiXJIpJ5mjeH7t2D4wEDwotFRJJGRibIkDdJPu00qFfPyimOOw5eeCFNk+OIihVt1faJJwbnHnwQLr3UGueLiGSS/v0hK/fjcPRoGD8+3HhEJHQZmyCDJcH/+x/MnGl54aRJsGoVdOtmEwrvvgsbNoQdZYJUqGAN8rt1C8499hhcdJGSZBHJLHvuCT16BMf9+4cXi4gkhYxOkAGaNYNddsl7bt06eO01q0LYaSe4+GKbUEi7CoTy5eGVV2wKPeKpp+D882Hz5vDiEhEpa/37Q3a2/T5mDIwbF2o4IhKujE+Q//4b1q61nZirVoWGDfM+vnw5PP44HHQQNGoE/frBjBnhxJoQ5crByy9Dz57Bueeeg3POUZIsIplj992hV6/geMCANJwVEZFYZXSCHL0g74EHrKRi1Sp45hm4/nrYeee81y9YAHfcYWs6WreGe++FX38NJfT4ys6G55+Hs84Kzr30Epx5JmzaFFpYIiJl6qabbNIA4PPPbSZZRDJSxibIBXWriCzc69vX2gUvWACffQa9e0PNmnmfP3WqdUfbeWc49FCbdP377zL/M+InOxuefRbOOy8498orVpe3cWN4cYmIlJWGDe3uWcTNN2sWWSRDZWSCvLVWbtHdLT77DA4+GJ580trAjRhhPeUrVgyu994mGc49F+rUscdHjID168v2b4qLrCz7Yy+6KDg3fLjVKKftakURkSj9+tkiZoCvv7auFiKScTIuQY6lz3FBm4lUrAjHH2/d0ZYutRnjQw8N+suDJcVvvmnd03bc0da6jRuXYk0hsrLg0UfhssuCc2++af9jKEkWkXS3yy42eEf0769ZZJEMlHEJ8sSJsW0CEkmSJ07c8rEaNeDss+GTT2DxYttnY5998l6zcqXVMnfqBA0aWE3zDz/E7c9ILOesL/JVVwXn3nkHTjopRafGRUSK4YYbgluFEyfC+++HG4+IlDnn0/CbcZs2bfykSZPK/H1nzoShQ610d/78gq/Zay8r6z399C3byyUd760ge/Dg4FzXrlZDUqlSeHGJpAHn3GTvfZuw40iksMbiuLjySpsoAFuVPXly3luGIpIWChuLM24GOZGaNoVBg2DuXOubfPHFUKtW3mumT7fJiV13tfrmp56CFSvCibdIzsFdd8GNNwbnPvzQGkSvXRteXCKS8gYPDkrYijJ2bN7v6WWib1+oXNl+/+47ePvtMg5ARMKkBDkBnIP27a2Ud8kSeO8925kvMtZGfPEFXHCB1StH6pvXrQsn5kI5Z1n/gAHBuY8/hmOOgTVrwotLRFJa27Z513kUJrJupG3bsonrPzvuCJdcEhwPGJBiC0pEpDSUICdY+fJw1FEwbJgt7nvpJWshlxX1v/zGjVbie8op1gkjUt+cNPt0OAcDB8KttwbnxoyBI4+E1atDC0tEUldBi6Hzi2VRdUL16WM7SAFMmwZvvBFCECISBiXIZah6dduw7sMP4bffrLytXbu816xaBS+8AIcfbj2Wr74apkxJkkXUN98Md94ZHH/+udUk//NPeDGJSMrKnyTPmROMdaEnxwDbb5+3o8/AgUk0cyEiiaQEOSR16sDll8O338KsWTbu7r573muWLIH//Q/23ReaNbNKh3nzQgk30Lcv3HNPcDx+vE2Jp/QuKSISlkiS3K0btGgBBx5onYFCT44jrr3WZjfAVmK/9lq48YhImVCCnAQaN7bytlmzLGG+/HLYYYe81/z0k03g7rZbUN+8bFk48XLttZa5R3zzjU15//VXSAGJSCrr1Mn6yv/7r+3Nce21UK+elaiFrlYt62gRccstsGlTePGISJlQgpxEnLOSiwcfhF9/tVKMnj2DEriIr7+GSy+FnXay+uZXXglhvdyVV8IjjwTHEyfCYYclcUsOEUlmu+6ad23G99/D//2fVXEV1I++TF11lTXAB5vJGDo03HhEJOGUICepcuWscuGll2xx3yuvWDJcrlxwzaZNMGqU9VWuUyeoby6zyY1LLoEnngiOp0yBQw6BP/8sowBEJF0ccQTUrGkth6ONHm0TB8cdZ0lzKLbdFq65Jji+9VZbXS0iaUsJcgqoWhVOO83axS1ZYuUV7dvnvWbNGhgyxD5k6tUL6psTvrjvggtsy8BIA/3vv7ck+Y8/EvzGIpIuIgvy3njDvme//LJtZBe9L8fIkbD33nbdzJkhBHnFFZYogy0GeemlEIIQkbKiBDnF1K5tG5CMH29j9KBBtmlq6q0AACAASURBVEFJtD/+gIcfhv33hyZNbAHg7NkJDOrcc+H554NPs2nTrKjw998T+KYikg4K6lZxxhnwwQc2o9yxY97rX3/ddiTt2dO6XpSZbbaB664Ljm+7DTZsKMMARKQsKUFOYQ0bQr9+8OOPNuty9dVQt27ea+bMsTUlTZoE9c1LlyYgmF69bNonUkQ4Y4Z9sv32WwLeTETSwdZauXXqBG++abuPPv20lVhE5OTYHbM994TzzoOFC8so4Msus1kKsDd97rkyemMRKWtKkNOAc1a3d999sGiRbTJy9tk24RFt4kRbW7fTTkF986pVcQykRw8rls7OtuOff7YkefHiOL6JiKSDWPocR1rA3XCDVThMmGCL9iI2b4Znn7VOQJdcUgbfx6tVg+uvD45vv91ab4hI2lGCnGays61d0nPPWYXD66/bNtbR7ZJycuCjj2zSt04d2wb7vffitObk1FPh1VeD1YSzZ0OHDvDLL3F4cRFJFxMnxtbnOJIkT5xo201/8AF8+WXe523cCI89Zm0wr746wUsgLr7YBk6wL//PPJPANxORsDifFFu0xVebNm38pEmTwg4jqfz1ly2AGTLENsArSK1aNqPTo4ctAoxeIFNsb79tLxbJuhs0sCmjBg1K8aIi6cM5N9l73ybsOBIp0WPxmDHWH/6rr/Ker1LFFipfdx1st10C3viBB6z1G1hd29y5ULlyAt5IRBKtsLFYM8gZYttt4fzz4bPPrHTurrts16poy5fD44/DQQdBo0ZW3zxjRgnf8PjjrYCwQgU7XrDAZpLnzi3NnyEi8p9DDrHZ5A8+sB1HI9autTGuYUNbpBz3jT4vuMBq1cBaC0W3uxSRtKAEOQPtsouV0f3wg/1cfz3svHPeaxYsgDvugObNYZ99rL7511+L+UbHHAMjRli/JrAyi44dE9xSQ0QyiXPBZiJvv533i/8//9gi5YYN4c47YfXqOL1p5cpw443B8V13hbBbk4gkkhLkDNeihY3tCxbAuHE2y1yzZt5rvvvOtn7deeegvjnmGZkjj7QGppUq2fHixTaT/PPPcfwrRCTTOWedLqZOhddesw4XEX/9Zflso0Zw//2wbl0c3vC886B+ffv9jz+sCFpE0oYSZAGsO1uHDvDUU7a4b8QIOPnkYPIXbNORMWOs7XGdOvb4iBGwfn0RL965s60CjNToLVlib1bi+g0RkYJlZdnyh+nTrVNPo0bBY8uW2YZ4u+1mGy4VOXZtTcWKcNNNwfHdd8e5LZCIhEkJsmyhYkUrIX79deuZ/NxzNnMcvWhv/XorMT7xRNhxR+jd2+qbc3IKedFDD7V9satWteOlS63cYvr0RP85IpKBsrNtM5GffrI+ytFlZEuWwKWXWn/4Z54pRQefs88OFh4vX247NIlIWlCCLFtVo4Z9BnzyifVYvvde67kcbeVK+wDq2NE+KyL1zVvo2BE+/NB6iYJN53TqZNtTi4gkQPnyVg0xezY88kjezZR++cXKypo2tX2ONm8u5otXqGBtNCLuvTcBKwJFJAxJnyA755o6555wzr3hnLso7HgyWb16dntyyhSrjujXb8uubYsWweDB0KqV1TfffXe+FsgHHWRNmKtXt+M//7Sl6FOmlNWfISIZqGJF20xk7lxbdBzZEA/s3Jln2pg1fPhW7oQVpGdPq9kAK3Z+8MG4xi0i4Uhoguyce84594dzbnq+812dcz875+Y45/pu7TW89zO99xcCpwAHJjJeiV3TpjBoEMybB+PHW+/8WrXyXjN9OvTtC7vuGtQ3r1gBHHCATUnXqGEXrlhhJRjqXS0iCVa5sm0mMn++derZdtvgsZkzba+j1q3hnXds3UWRypeH/v2D4/vvt0RZRFJaomeQXwC6Rp9wzmUDjwJHAM2A05xzzZxzLZxz7+X72SH3OccC7wOjEhyvFJNztqnIo49aXd+779rOfPl75n/+ubUO3XHH3Prmhe349/1Pg0+nlSvhsMPg22/L/o8QkYxTrZptYT1/PgwYENzUAisRO/54aNfOqsKKTJRPPx322MN+//tvS5JFJKUlfCc951wD4D3v/V65xwcAA733XXKPbwDw3t8Zw2u9770/qpDHegO9AXbZZZd9Fy5cGJf4pWRWrbKepEOHwscfF3zLcptt4MoO39Hvs8Op8M9yO1m9un0itW9ftgGLlLFU20nPOdcUuAKoDXzqvX+8qOek0q6my5dbCfFDD9lGI9EOPNDumHXsuJUXGDbMEmWw7HvBgi1vq4lI0kmmnfTqAYuijhfnniuQc66jc+4h59yTbGUG2Xv/lPe+jfe+zfbbbx+/aKVEqle30rwPP4TffrOyvHbt8l7zzz9w67utafPPGJZn5RYErlqF79IFvvii7IMWSVMqdytarVq2mci8ebaLdHSLy/HjbT3xoYduua31f045BZo1s99Xr4Z77kl4zCKSOEm/SM97P857f7n3/gLv/aNhxyPFV6cOXH65VU/MmmW3M3ffPXh8Gi3pkDOWpewAgFu9mg2HduW3V8aFEq9IGnoBlbvFpE4dq5CYO9fWVpQvHzw2ZozNJh95JEyenO+J2dm2r3XEww/bBiIikpLCSJB/BaI3Nq6fe04yQOPG9hkya5YlzJdfDjvsAD+yFx0ZxxJ2BKDCxrXU7HEkVzT/hMces2YXIlIy3vvPgRX5TrcD5njv53nvNwCvAsd576d574/O9/NH7uuM9N4fAfQo7L2cc72dc5Occ5OWLVuWqD8p4erVs7UVs2bZ5kjZ2cFjH3wAbdrACSfAtGlRTzrpJGjZ0n5fu9Za+ohISgojQZ4INHbONXTOVQC6AyNDiENC5JyVXDz4IPz6q5VitO3ZlCMrj+NXdgKgCuu4a8YxvHPJaOrWhaOPtjK/NWtCDl4kPajcLQYNGthmIjNnwhln5N0w6e23raVl9+62IQlZWXDLLcEFkdXLIpJyEt3mbRjwNbCHc26xc+5c7/0m4FJgNDATGO69/zGRcUhyK1cOunSxbWG/XLYHU+7/jGWV6gNQmX8ZybEcvmkU779va2Dq1AnqmzdtCjl4kQyR6eVujRvbZiLTp0O3bsF57+G116B5c+jVC+budRzss489+O+/cNdd4QQsIqWS0ATZe3+a976u9768976+9/7Z3POjvPdNvPe7ee9vT2QMklqqVoVjrtqd7X/8jM31dwGgIht4m+M5JvdGw5o1MGQIHHGE3Qa94gqYMCHGnqUiEqFytxJo1sw2E/nuOzjmmOB8To59yd+zqePh7W8NHnjySVi8uOwDFZFSSfpFepKhGjUi+4vPoGFDACqwkRFZJ3FpvRF5LvvjD2vLtN9+0KSJ1TfPnh1CvCKpR+VupbD33jBypK2l6Nw5OL9pE1w++kgmuNy2PevXW3sMEUkpSpAleTVoAJ999t82rtk5m3jo927Mvet1rr4a6tbNe/mcOVb+16RJUN+8dGnZhy2SbFTuljjt2sHo0daZskOHyFnHzT6YRd70xNMs/+6XUOITkZJRgizJbeedLUlu0gQAt3kzjfqdxn1thrFoke1YffbZeXfBApg4Ea680kowuna12sFVq0KIXyQJqNwt8Q46CMaOtTFp//3hIzozHtvwqFzORka2G0S/ftqFWiRVKEGW5FevHowbB3vuacebN8MZZ5A9bAiHHgrPPWczxcOHw3HH5e1bunmzze6ceaYt7jvtNHjvPdi4MZS/RETSmHPBZiLvv+94ufFt/z12xqbnGXbHPBo2hFtvtY2SRCR5KUGW1FC3riXJzZvbcU6OZb0vvABA5cq2svztt+H3321dzMEH532Jdevg1VdtYU3durYJwPjxWtwnIvHlnG0m8vhPnVjW3OouyrOJmxjE33/bZkkNG8Ldd6ttpUiyUoIsqaNOHbuH2aKFHXsP55xjTUqjbLcd9O5tlRkLF1qXpchTIpYvh8cft9uiu+0GN91kfU5FROLFZTm2fzToi3wmL7E7top4xQro2xcaNYIHHrCOcCKSPJQgS2rZfnvb73Xvve3Yezj/fHjiiQIv32UXuP56+OEH+P576NMH6tfPe838+XD77da+aZ994L774LffEvx3iEhm6NDB6i6AcmzmwwNujTTnAawTz1VXwe6725f2DRtCilNE8nC+iPvLzrmawJlAA6Bc5Lz3/vKERlYKbdq08ZMmTQo7DEmkFSust9LkycG5hx+GSy8t8qk5ObbifOhQeP11WLlyy2ucg06doEcP2z22Ro04xi4COOcme+/bFON6jcWp6quv4MAD7fesLDZ+N53nv2nKbbdt2SK5QQO4+WarICtXbotXEpE4K2wsjmUGeRQ2IE8DJkf9iIRnu+1suXi7dsG5yy6D//2vyKdmZdmkzlNPWb3yiBFw8slQsWJwjfc2UX3uuVbZEalvXr8+AX+LSGw0Fqeq9u2tnQ5ATg7l77yV3r2tZ/tDD9kYE7FggY07zZrZl/jNm0OJWCTjxTKDPMV7v08ZxRMXmrXIIH//bVvqff11cG7wYLjuuhK91Ftv2S59Y8cWvHivZk1Llnv0gP/7P0u2RUqiBDPIGotT2YQJtqMR2C2qH36AvfYCYO1aeOwxWy+xfHnepzVrZl0vTjhB441IIpRmBvll59z5zrm6zrntIj8JiFGk+GrUsD5uBx0UnOvTB+64o0QvdfbZ8OmnsGgR3HsvtG6d95qVK+Hpp6FjR7sVev31MG1aqf4CkVhpLE5l7doFe1N7b9t+5qpSBa691tZDDBpkX8QjZsywO1z77mstKtV1R6RsxJIgbwDuwXZhitzS05SAJI/q1eGDD6K3sYJ+/WzapYTq1YNrroEpU+wDql8/S4ijLVpkk9UtW9rP3XfDL9osSxJHY3GquyXoaMGbb8LUqXkerl7dxpr5860OuVq14LGpUy2/PuAA+OgjJcoiiRZLgnwNsLv3voH3vmHuT6NEByZSLNWqwfvvwyGHBOcGDID+/Uv9SdK0qc3qzJsHX34JF10EtWrlvWbaNGvZtOuuQX3zihWleluR/DQWp7rWra1WIiJqFjlazZr2/X7+fLshVrly8Ni330KXLjbOfP55YsMVyWSxJMhzgLWJDkSk1KpWtXuQnTsH5267zaZk4jDd4pwtRH/sMWsD9+670L173g8vsA+tCy6AHXeE44+3Thnr1pX67UU0FqeD6KT4nXdgKzXatWvbnal58+CKK6BCheCxL76wJPnww+GbbxIXrkimiiVBXgNMdc496Zx7KPKT6MBESqRyZfvQOeKI4Nydd9o0TBzvSVaoAEcfDcOG2TbXL71kszrRi2g2brRQTjnFkuVzzrH6Zq1KlxLSWJwOWra0QSFiwIAin7LjjraZyNy5cOGFedu/ffKJlV0cfbSVhIlIfMTSxaJXQee99y8mJKI40MppYf16azfx7rvBuSuvhPvvt6ngBPn9d3jtNWvPNHFiwdfstJPNPPfoYXdcExiOJLESdLHQWJwuZsywDhaRz9+vv4b994/56fPn282xF1+0vu7RTjzRSp1zG2SISBEKG4u3miA757KBT7z3nRIZXLxpUBbAtqQ69VRrYBxx6aXWeLQMstJZs+CVVyxZnjOn4Gv23BPOOANOP508u2tJ+itOgqyxOA316GEDBFidxEcfFfslZs2yZHjYsLw3yJyzL+EDB0KTJvEJVyRdlajNm/d+M5DjnNM+YpJ6KlSA4cOtR1LEI4/AxRdvOe2SAE2a2AfUrFm2sOayy2CHHfJe89NPcNNN0KhRUN/8558JD01SjMbiNNS/f1CT9fHHVlRcTE2a2BfwH36wHT8jvLekuWlTa105f36cYhbJILHUIK8GpjnnnlXdm6Sc8uXtk6J79+DcE0/YKroySJLBZnPatbOJ619/tY50Z5xhawqjffUVXHIJ1K0b1Dev1ZIsCWgsTid77AE9ewbHMdQiF2avveCNN6wG+eijg/M5OfDCC5ZIX3jhlttai0jhVIMsmWHTJjjrLJtuiTjrLHjmGcjODiWkNWtg5EgLafRoCzG/qlWtK9QZZ8Chh+ZdnCOpTTXIwty5lihHVu6OGQOdSl9F8803NkH98cd5z1esaHMDN9xgC/9EpIQ1yFFPrgBEKpl+9t5vjHN8caVBWQq0eTOce66tbIk44wx4/vnQM89ly6wd3JAheXfNjrbDDsHivrZttbgv1RU3Qc59jsbidHPeefDss/b7QQdZn8g4/cf9+edWwpW/eqNyZVuO0aePtZITyWQl3mraOdcRmA08CjwGzHLOHRz3CEUSLTsbnnvOkuSIIUPsNmdB07dlaPvtrTT6q69sUum222wBX7Q//rAyjf32s0mngQNh9uxQwpUQaCxOUzfdZKVgYDsRffJJ3F764IPhs89s/d9++wXn162De+6xhcE33wwrV8btLUXSRiw1yPcBnb33Hbz3BwNdgP8lNiyRBMnKsm3uLrggOPfqq3Daada4OAk0amSfmTNmwOTJcPXVVpccbfZsW73epElQ37x0aTjxSpnRWJyOGjTI+6U9Drt/RnPOmmR8/bV1vdx77+Cx1attl9CGDe2fq1bF7W1FUl4sCXJ57/3PkQPv/SygfOJCEkmwrCx4/HFbERfxxhvWEm7DhvDiysc52GcfuO8+WLTI6gnPOguqV8973cSJtstWvXrQtSu8/LI+6NKUxuJ0deONwTZ533wDH34Y97dwzhbwTZ5sw13z5sFjK1faTHLDhjazrMXBIrElyJOcc8845zrm/jwNqKhMUptz8PDDlllGjBhhLeHWrw8vrkJkZ8Nhh1m59NKl1r3uuOOCO7NgJdajR8OZZ0KdOjYp/t57STMxLqWnsThd7bwz9O4dHMd5FjlaVpa1hPv+e1sg3Lhx8Njy5VaX3KiR3ZX699+EhCCSEmLpYlERuAQ4KPfUF8Bj3vvkyyJyaWGIxMx7+0S4997g3JFHwptvQqVK4cUVoxUrbDZo6FBbkFOQWrVscrxHD9uSVov7kkMJulhoLE5nv/0Gu+0WZKXvvAPHHpvwt920ye463XorLFiQ97H69W1m+eyz834ZF0knpepikWo0KEuxeA/9+sGddwbnOne2HfgqVw4vrmJauNB6Jw8dCtOnF3xNw4a2a1+PHraJgISnJF0sUo3G4mK6+mr4X25ZeatW1tg4K5YbvaW3YYOtYR40yPq1R2vY0No09+gResMfkbgrTReLA51zHzvnZjnn5kV+EhOmSAicg9tvt6mSiI8+gmOOSalivF13hb59Ydo0u33ap4/NAEWbP9/+1GbNgvrm334LJ14pHo3FGeD664Mv5d9/b2VfZaRCBdtMZM4ceOABK9OKmD/f1j80b25fwstojyWRUMXy1fRZ4H7stl7bqB+R9OGc3WO85Zbg3KefwlFH2VLvFNOyJdx9t80qjxsH558PNWvmvea77+Daay2JPvRQq2/+++9QwpXYaCxOd3XqWIPiiAEDyjwbrVTJlmbMnWtjyHbbBY/NmmV3oFq1stw9DW9Ai/wnlgT5b+/9B977P7z3yyM/CY9MJAz9+9sUa8S4cXDEESnbFiIrCzp0sM52v/9uH2onnWQ7akV4bxt4nXOOfT5362bVJUm4VjHTaSzOBH36QLVq9vuPP9oOQiGoWtVCmT/f5g5q1Agemz4dTjwR2rSBUaOUKEt6iiVBHuucu8c5d4Bzbp/IT8IjEwnLjTfC4MHB8ZdfQpcu8M8/4cUUBxUrwvHH26K+pUtt865DDsm7aG/9env8hBOs93Lv3rbRgG6pJgWNxZmgdm24/PLgeODAYCvqEGyzjVWfzZ9vSzUiuTtYifRRR0H79ra/iRJlSSexdLEYW8Bp770/JDEhlZ4Whkhc/O9/tmgmol0766OWv1Yhxf36q+2VMnSolV0UZOedg8V9LVqUbXzpqgRdLDQWZ4oVK2xlXORL+csvwxlnhBtTrmXLbP7gkUe2bAPXoYPtAvp//xdObCIloS4WIiXx8MN5Z3P23dcW8EUX5qWRGTMsUX7llS1bPkW0aGGJ8umnW+IsJaMuFrJVAwcGayJ23x1mzkyqFhJLlljjnyef3HJ/pc6dLVFu1y6c2ESKo8RdLEQy2mWXwWOPBceTJ9uKtuXpWfrZrJmVYM+bZ5UlF11kfZSjTZtm3TJ22SWob/7rr3DiFUlbV14Z3K2aMweGDAk3nnzq1rXNRObMsVKs6Nz9o49gv/2sjfPUqeHFKFIaSpBFinLRRZYFRop1p06FTp3sXmOacg4OPNC+G/z2G7z7LnTvvmVb6M8/hwsusMV9J5xg9cvafUskDmrWhGuuCY5vvTUpt8XceWebRf75Z+jVK2/b5nffhdatbeHvjBnhxShSEltNkJ1zWc659mUVjEjSOv98W9UWSZKnTbMkeenScOMqAxUqwNFHW//TpUvhxRftFmr0B+HGjdb5ols3S5bPOce65IW4tiitaCzOUJdfHpRzzZ8PL7wQajhb06iRhffjj/ZlOnrx7xtvwF57WRn17NmhhShSLFtNkL33OcCjZRSLSHI7+2zLDiOZ4Y8/QseOVoyXIapXhzPPtLWKv/5qGwq0zdeJ959/rKfyYYdZGca119rivzRc7lBmNBZnqG22sV5rEYMGJX3/xT33tC/T339vd5UivLf1DU2bwrnnFr7GQSRZxFJi8alz7iTnor8PimSonj2tFjA7245/+smS5Px7s2aAHXe0DQUmTLDbqwMGwG675b3mt99st7599rFduG6/3SbCpEQ0FmeiSy6B7be333/5xfaDTgEtWsBbb8GkSXDkkcH5zZvtT2jSBC6+OCOHTkkRsbR5WwVUBTYD6wCHtRbaJvHhlYxWTkvCvf46nHZaUEOw224wdmzGt3Xw3hLmoUPhtdfgjz8Kvq59e+uEccop1vY1E5WgzZvG4kx13312KwagXj1bGVepUrgxFdPXX1s/5U8/zXu+YkVb5tG3b97trUXKSom7WHjvq3vvs7z35b332+QeJ+2ALFImunWD4cODpdtz51pLh4ULw40rZM7Z6vWHHrKZoQ8+sLrDqlXzXvfVVzYxVrduUN+8dm04MacKjcUZ7KKL7JYN2H9YTz0VbjwlcMABtpnI2LFw0EHB+fXrrVSrUSNLkiMNggYPtmtjMXZs3r2dROIhpi4WzrljnXP35v4cneigRFLCiSfCm29C+fJ2PH++Jcnz5oUbV5IoVw66drU9DpYutd7KRx0VVKcAbNoE779vPZXr1AnqmzdtCi/uZKaxOENVqQI33BAc33lnyn6j7NjRut98+GHe9Qtr18Ldd9v+KAMGWK3yKacUnSSPHWvX5V8LIVJaRSbIzrm7gCuAGbk/Vzjn7kx0YCIp4dhjYcQIa/UANoPcsaPdApX/VK1qFSnvvWdrGh95xGaUoq1ebcl0165Qv35Q36zFfUZjcYbr3Rt22sl+//13eOKJcOMpBeegSxf49lt45x1o1Sp4bNUq62jXqxccd5zdrCssSY4kx8OHW1MhkXiKpQb5B2Dv3FXUOOeyge+89y3LIL4SUd2blLnRo200j6ww32knG72bNAk3riQ3b57NLA8dausdC9K4sdUr9+hhG4qlixLUIGssznSPPWa1SWAL9+bNg2rVwo0pDnJy7GbcgAG2YWC0GjXsjtIbb9iX5wglxxIvpd1Jr2bU7zXiE5JIGunSxaZHIztp/PablVvkH+0lj0aN4KabbBOByZPhqqusLjna7Nm2627jxkF9cwa0ny6MxuJMdu651jsRbKOiR9Oj819Wls0UT5tmd5Giu+H8/TesWWPlWZdfbnealBxLWYglQb4D+M4594Jz7kVgMnB7YsMSSUGHHWYFtVWq2PHvv1u5xY8/hhpWKnDOWsHdfz8sWgQffwxnnWV9l6NNmGClF/XqBfXNq1eHEnIYNBZnuooV7RtlxODB1ng8TWRn26LemTPhmWeC7wJgs8wPP2ytoTt3hv/7P/uivGhRePFKettqiYVzLgs4GfgCiJTAT/De/14GsZWYbutJqD7/3Bp/rlljx7VrW2+jlkl7JzxprVtnE/NDh8KoUQXvtFu5Mhx/vJVgdO4crJlMdsUpsdBYLP/ZuBH22CNoKD5oEPTrF25MCbJ+vW1gevvtdlOuMDvvbK0jDzzQflq2DBoMiRSlsLE4lhrkScWpk0sGGpQldOPHwxFH2IoTsO1iP/kEWrcON64UtmKF1SEOGQJffFHwNbVr263XHj1sEWAyb6lRghpkjcVinn/e9nMHqFnTkuWaNbf+nBS2bh1cc411t4tl+/qqVa0cK5I0H3CA1TKLFKQ0NcifOOeudc7t7JzbLvKTgBhF0seBB8JHH9n9QLDs7tBDrdBWSmS77Wwh/+ef2za1d94Je+2V95o//7R1TAceaHWMN92UVmXgGovF9OwZrFhdudIaCaexb76xvZk+/hj++gvuussq2Vq33rLHOtjNuzFjbHL9iCNg221tZ78LL7SyrLlz1R1HihbLDHJBG8N6732jxIRUepq1kKQxcaLd91+50o5r1LDEuV27cONKIz/8YCUYr7wCixcXfM0++9iscvfuQaessJVgBlljsQSGDLFEGeyL+Pz59i0yzRS2IC9yftgw+7PHjw9+ChsHotWpY1+kI7PMrVtbibdknhKVWOTWvXXz3r+WyODiTYOyJJUpU+Dww20WGezD7MMPt2wELKWSk2Ozy0OHWilG5DtJNOfgkEMsWT7xxHBvu5agBlljsQQ2b4bmzeHnn+34xhutWDeNFNWtorDHFy2yRPmrr+yf339fdGlGxYq22UgkaW7f3kq2JP2pBlkkTN9/b10u/vzTjqtVs32Yo/dclbhZv94W9Q0daov8Iu2po1WsCMccY8nyEUeU/eyRapCl1F591XbgAas1WLAgbbK6WFu5xXLd6tXWASeSNH/9tbWPK8oee+Rd/LfHHsm9rkFKpjQJ8l3An8BrwJrIee/9ingHGS8alCUpTZ9u05fLltlx1arWFq5Dh3Dj+SnhugAAIABJREFUSnMrV8Jbb1myPHZswbWH225rfVh79LDvLFmxdogvhRIkyBqLJa+cHGvZEGkl2aeP7decBgYPthndWPocjx1r1Wx9+sT22jk59j9ZZIZ5/Hjbc6Uo220XzC4feKDFF2l9L6mrNAmy6t5E4mXGDEuSIztdVK4M775rC/gk4X791WoWhw6FqVMLvmaXXWxSrkcPW9gTEe8PbNUgS1y8+SacfLL9XqWKZXp16oQbUwr6/fcgYf7qK1tPXVBbyWjlytn6hsgMc/v2W250JMmvxAlyKtKgLEnt558ty1qyxI4rVYJ33rHFfFJmZswIFvctWFDwNS1aWKJ8+ukwZ078bvlC8RPkVKSxuAzk5FiW9v33dnzVVbbjjpTKunWWJEdmmL/6CpYvL/p5DRvmXfzXvLltgCLJq9gJsnOuj/d+cO7v3bz3r0c9dof3/saERZs3jo7AbcCPwKve+3FFPUeDsiS92bNtJjmy3LpiRRgxwophpUx5bx9+Q4daUlvYh2CHDrDvvvDii9ZyqjiLhgoSa4KcLGNxSWgsLiMjR8Jxx9nvlSpZH7NkadeSJryHWbPyLv776aein7fNNrD//kHSvN9+W+4QKuEqSYI8xXu/T/7fCzreyps+BxwN/OG93yvqfFfgQSAbeMZ7f9dWXqMD0BdYCgzy3s8p6n01KEtKmDfPsqhffrHjChWs/cIxx4QbVwbbsMG68A0ZYjnHunVbXlOunNUo33AD9O1r+QgULzmGYiXIpR6Lw6KxuIx4b/U/kT7rl10GDz0UbkwZYPlyW/AXmWWeOBH+/Xfrz8nKglat8i7+23lnLf4LU0kS5O+8963z/17Q8Vbe9GBgNfBSJEF2zmUDs4DDgcXAROA0LFm+M99LnAP86b3Pcc7VAe733vco6n01KEvKWLDAsqnIPf7y5eG11+CEE8KMSrBNEEeMsJnlTz6xO9n5VakCp55qt1Hvuiv25BiKlSCXeiwOi8biMjRqFBx1lP1eoYLNItevH25MGWbDBvjuu7yL/36PYTP4evXy1jG3amUfBVI2QplBzr22AfBeVIJ8ADDQe98l9/gGAO99/uQ4/+tUAF7x3p9c1HtqUJaU8ssvllVFllGXK2cryU4u8l91KSO//27fW4YMgcKGlkcfhYsvjv01NYMsceW99Vb/9ls7vvBCePzxcGPKcN7b3Ed0HfO0aUXv4leliu0lFUma99/fOu1IYpQkQd6MtRJyQGVgbeQhoJL3PqbvNwUkyCcDXb335+Ue9wT2895fWsjzTwS6ADWBxwurQXbO9QZ6A+yyyy77Lly4MJbwRJLD4sVWkzx7th1nZ9vU5amnhhuXbGHWLPu/ZuhQm6QD+/Bavrx4t0mLkSDHZSwOgxLkMvbxx8Fi3/Ll7V/WBg1CDUny+vtv2zo7Msv8zTe2NXZRmjfPu/hvt91UlhEvoXWxKG2CXBIalCUl/fabJcmRnbGysuCll6yNgiSdMWPgpJOgcWPriPHuu7GXV4C6WEgCeA8HHwxffmnH550HTz8dbkyyVZs22axy9OK/yLKUrdlhhyBZbt/eFhBrq+ySKWwsLoN2+Fv4Fdg56rh+7jmRzLbTTjBuHDRrZsc5OdCzp7VNkKQydqxN7r/1lu3Q9e67tkBv7NiwI0sc51xH59wXzrkncrsLSbJxDm69NTh+/vngNockpXLloHVruPRSazm5cKFtlf3aa3D55Zb4FtQm7o8/4O234brrLEmuUcM2OerTx7qGRvajkpILI0GeCDR2zjXMrSvuDowMIQ6R5LPjjpZlRXao8B7OPhuefTbcuOQ/BXWr6NTJjpM1SXbOPeec+8M5Nz3f+a7OuZ+dc3Occ32LeBmPLbquhC2wlmTUqRN07Gi/b94Mt90WajhSfPXr21jy4IO25uHvv+2O1aBB1gm0Zs0tn7N+vc0+33MPHH+8zTA3aWIfH08/bXe5ClpoLIVLaImFc24Y0BGojbVpG+C9f9Y5dyTwANa54jnv/e3xfF/d1pOU9+efcNhhQfN/gCeegAsuCC8mKbKVWyL6IMeDOgplmC++sFILsFKtmTMtW5K0kJNj/5dGL/6bU2QDXFsrccABweK/tm1tQWCm0056IqlmxQo4/HCYMiU498gjcMkl4cWUwWJNfpN1J72y6iikBdNJonNnW7QHto5hyJBw45GEWrrUEuVIHfPkydZ2bmsi5R3Ri/8ycX8ZJcgiqeivv6BLF+tAH/HAA3DFFeHFlKEGD7YZl1gW4o0da/+X9elT+DVJkCAnpKNQNI3FIfr6a8t6wGqTp08P1jdI2vv332Cr7EjS/OefRT9v113z9mRu0SL9t8pWgiySqv7+G7p2tX5AEffeC9dcE15MUmqpliCXhMbikB15JHzwgf1+yim28ksykvfWRTSSLH/1ldUlF6V6devDHJlh3n//9Nsqu7CxuFwYwYhIMdSoAaNH24fd+PF27tprYeNG2+tYpGTUUSjd3XprkCAPHw433RQsAJaM4pyVoTdpAmedZedWrLAbDZGkecIEWLcu7/NWrbJKnUi1TlaW/SsUXZax667p2ZNZM8giqWL1attK9vPPg3O33go33xxeTFJiSTCDXA5bpHcolhhPBE733v8Yr/fUWJwEjjsORuY2ijrxRHjzzXDjkaS1cSNMnRos/hs/HpYsKfp5O+0UJMsHHgh7751aW2WrxEIkHaxZA8cck7eXWP/+MHBgen6FT2Nl3MVCHYUy1dSpthIrYsqUvMcihfDe+jJHZpjHj7dNTYpqF1e5sm2VHUmaDzgAttuubGIuCSXIIuli7VprdBm55wVw443WJFNJcsrQTnpSZk4+OZg5PuaYYEZZpJj++Qe+/TaoY/7mGyvDKErTpnkX/zVunDwfV0qQRdLJunV2u/TDD4NzffrAXXclz6gjW6UEWcrM9OnQsqVNCYIVm7ZtG25MkhY2b7ZZ5ehZ5lg6O26/vSXKkVnmffeFSpVie8+y6igUxk56IlJalSvDiBFWkxwxeLB1tkjDL70iUgp77WVdLCIGDAgvFkkr2dlWc3zxxTB0KCxYAIsX25rQK6+0RLZcAe0gli2zLbGvv962yK5Rw5Ll666zj7Y//ij8Pdu2jW3X0khP+pJ+F9QMskgq27DBRoB33gnOXXaZ7VGqmeSkphlkKVMzZ1qiHCkg/eorKw4VSbC1a20WN3rnv5Uri37e7rvnXfzXtKl10YCy2dVUCbJIqtu4EU47Le/q9Isusl33snSTKFkpQZYy17NnsKPeYYflXccgUkZycuCnn/JuYjJ7dtHPq1nTvtNFkuZ166BXry2T4OIkx6AEWSS9bdwIZ5xhI0LE+efDE08oSU5SSpClzM2ebdNwmzfb8WefwcEHhxuTCFZyEb2JycSJRW+VnZ0Nu+0Gv/xipRm9e9u/4sVJjkEJskj627TJvk6/8kpw7uyz4emn03+v0BSkBFlCcfbZ8MIL9nuHDjbdpnIsSTLr19tW2dGL/5YtK/p5FSrY2vVYk2PQIj2R9FeuHLz0Epx5ZnDu+eftAzEyYyQime3mm4NVU599VvRKJ5EQVKxopRTXXmuL9pYutdnhF16wmeLmzQt+XuvWxUuOt0YJskg6yc6G556Dc84Jzr38stUebtoUXlwikhwaNbIvzRH9+6vzjSQ952zRXq9e8OST1rlwxQoYNQp69LCd+8qVs7Wo8frOpwRZJN1kZ1tZRe/ewblhw+D0061WWUQyW79+wV7A48drsZ6kpG23td7Jo0fbz9q18PrrsbWAi4USZJF0lJUFjz9uzSkjXn8duncveuWDiKS3XXeF884Ljm++WbPIknLyd6soXx46d7bjeCTJSpBF0lVWlrV6u/zy4Nxbb0G3brYCQkQy1403WqEn2M56o0aFG49IMWytlVunTvFJkpUgi6Qz5+CBB+Dqq4NzI0faNtX//hteXCISrvr14YILgmPVIkuKiKXPcTySZCXIIunOObj3XtvTM2LUKDj+eOu0LiKZqW9fK+IEmDLFvjyLJLmJE2PrcxxJkidOLNn7KEEWyQTOwZ132uKciNGj4dhjbWWDiGSeunXzrlPo3z/YilokSfXpE3srt06d7PqSUIIskimcg9tug4EDg3OffAJHHw1r1oQWloiE6PrroUoV+/2HH2ydgogoQRbJKM7BgAEwaFBwbuxYOOIIWLUqvLhEJBw77ACXXRYcDxigjYVEUIIskpn69YO77gqOv/gCunaFf/4JLyYRCce110K1avb7jBlWuCmS4ZQgi2Sq66+H++4Ljr/6yppI/v3/7N13nFTV+cfxz7NLryKgMYBCROyoEUhiTAQ0igVRUcQSMBLbz5KiscUeSzQhxkQTxRLFghArTYkGCIlRKUYFRSIiCkqkKb3v8/vjzDJ3ly2zO+Xuznzfr9e89p5z23Nnd88+e+bcc1fFF5OI5F67dvCTnyTLN92kJ29KwVOCLFLIfv5zuOeeZPnNN+Goo+DLL+OLSURy7/LLoVWrsPzf/4anb4oUMCXIIoXussvgvvuS5Zkz4cgjYcWK+GISkdxq06bsfOk336xeZCloSpBFJEz19MADyfJ//hOS5GXL4otJRHLrpz8NiTLARx/ByJHxxiMSIyXIIhKcfz48/HCY6QLgnXegb19YujTeuEQkN1q3DjfslfrVr2Dz5vjiEYmREmQRSTr3XHj00WSSPGcO9O4N//tfnFGJSK5ceim0bRuWFy4M7YFIAVKCLCJlDRkCTzwBRYnmYe7ckCR//nmsYYlIDrRsWfbRY7feCps2xRePSEyUIIvIjs48E556CoqLQ3nePDjiCFi8ON64RCT7Lr44PEAEYNEieOiheOMRiYESZBGp2Omnw+jR0KBBKM+fH5LkTz6JNy4Rya7mzeHqq5Pl22+HDRvii0ckBkqQRaRyAwfCM89Aw4ahvGBBSJI//jjeuEQkuy68EL72tbD8+ecwYkS88YjkmBJkEanagAHw3HPQqFEof/JJSJI/+ijeuEQke5o2hWuvTZbvuAPWr48vHpEcU4IsItU74QR48UVo3DiUFy0KSfKHH8Ybl4hkz3nnQceOYfmLL+BPf4o3HpEcUoIsIqnp1w/GjYMmTUL5s89CkvzBB/HGJSLZ0aQJ/PKXyfKdd8LatfHFI5JDSpBFJHU/+AFMmADNmoXykiVhCrj33481LBHJknPPhd13D8vLl8O998Ybj0iOKEEWkZrp2xcmTgx3ukP46LV3b5g9O9awRCQLGjWC669Pln/zG1i9Or54RHJECbKI1NwRR8DLL0OLFqG8bBn06RMeTy0i+WXoUPjGN8LyypVwzz3xxiOSA0qQRaR2Dj8c/vY3aNUqlFesCL3Lb70Vb1wiklkNG8INNyTLw4fDV1/FF49IDihBFpHa+8534JVXYKedQnnlSjjySJgxI964RCSzzjoL9torLK9aBXffHW88IlmmBFlE0tOrF7z6KrRpE8pffQVHHQVvvBFvXCKSOQ0awI03Jst33x0+NRLJU0qQRSR9hx4KkydD27ahvHo1HH00vPZavHGJSOYMHgz77huW16wJQy1E8pQSZBHJjIMPhilToH37UF6zBo45BqZNizcuEcmM4mK46aZk+Q9/CDfoiuQhJcgikjkHHhiS5F13DeV16+DYY0PvsojUf6eeCgccEJbXrYO77oo3HpEsUYIsIpm1//4wdSrstlsor18Pxx8fbuYTkfqtqAhuvjlZvu8++N//4otHJEuUIItI5u2zD/zjH9ChQyhv3Aj9+4e5k0Wkfjv5ZDjkkLC8YUN4BLVInlGCLCLZsddeIUnu1CmUN22CAQPCo6pFpP4yK9uL/Oc/w+efxxePSBYoQRaR7Nlzz5Ak77FHKG/eHHqfXnwx3rhEJD0nnAA9e4blTZvg9tvjjUckw5Qgi0h2dekSkuTSR9Vu2RJu9HnuuXjjEpHaM4NbbkmWH3wQPv00vnhEMkwJsohk3x57hBv3unYN5a1bYdAgGDMm1rBEJA3HHBOepgnh0yH1IkseUYIsIrnRqVNIkrt1C+Vt2+CMM+Cpp2INS0RqqXwv8sMPw8KFsYUjkklKkEUkdzp0CEly6dO4Skrghz+EkSNjDUtEaunII+F73wvLW7fCr34VbzwiGaIEWURya7fdwsNESh82UFIC55wDjzwSa1giUgtmZZPixx6D+fPji0ckQ5Qgi0ju7bpreLpe9+6h7A7DhsGIEfHGJSI1d8QR0LdvWN62Tb3IkhfqfIJsZt8zs/vN7CEz+3fc8YhIhrRvH5Lk0gcOAFxwAfzpT/HFJCK1E50X+Ykn4IMP4otFJAOymiCb2SNmttTM5pSr72dm88xsvpldXdUx3P2f7n4hMB54LJvxikiOtW0Lf/879OiRrLv4YvjDH+KLSURq7vDD4eijw3JJSdmb90TqoWz3ID8K9ItWmFkxcB9wLLAfcIaZ7WdmB5rZ+HKvXSK7ngnodneRfNOmDbzyCnzrW8m6n/wEfve7+GISkZqLJsVPPw3vvRdfLCJpymqC7O7TgJXlqnsB8919gbtvBp4GBrj7bHc/odxrKYCZ7Q6scvc1lZ3LzM43s5lmNnPZsmXZuiQRyYaddoK//Q0OOyxZd/nlcNdd8cUkIjXzrW/B8ceHZfeywy5E6pk4xiB3ABZFyosTdVUZBvylqg3cfYS793D3Hu3bt08zRBHJuVat4OWXk1NGAVx1Fdx2W3wxiUjNRJPiv/4V3nknvlhE0lDnb9IDcPcb3V036Inku5Yt4aWXoHfvZN1116knSqS+OPRQOOmkZPmmm2ILRSQdcSTInwGdIuWOiToREWjeHCZMgKOOStbddBNcf3342FZE6rZoUvzCCzBrVmyhiNRWHAnyDGAvM+tiZo2AwcDYGOIQkbqqWTMYOxaOOSZZd+utcM01SpJF6rqDDoJTT02W1Yss9VC2p3kbBbwO7G1mi81smLtvBS4BJgFzgTHurltdRaSspk1D79NxxyXr7rwTfvELJckx0Jz0UiM33RSesgcwfjy8+Was4YjUVLZnsTjD3Xdz94bu3tHdH07UT3T3bu6+p7vrDhwRqViTJvDcc3Diicm64cPhZz9TklwDmpNecm7//WHw4GT5xhvji0WkFurFTXoiUsAaNw53w598crLunnvgkkvCAwkkFY+iOekl1264AYoSacakSfDaa/HGI1IDSpBFpO5r1AhGj4bTTkvW/elPcNFFSpJToDnpJRb77ANnnZUs33BDfLGI1JASZBGpHxo2hKeeKvux7YgRcN55SpJrR3PSS/bdcAMUF4flyZNh6tRYwxFJlRJkEak/GjSAxx+Hs89O1j3yCPzoR7BtW3xxFQjNSS811rUrDB2aLN94o+4fkHpBCbKI1C8NGsCjj8I55yTrRo6EIUNg69a4oqqPNCe95MZ114XfW4Bp00JPskgdpwRZROqf4mJ4+GH48Y+TdU89FXqWt2yJL676RXPSS2506QLnnpss66E/Ug8oQRaR+qmoCB54INyoV2r0aDjjDCXJ5WhOeondL38ZbrYFeP31MKuFSB2mBFlE6q+iIrjvPrj00mTds8/CoEGweXN8cdUxmpNeYrf77uGG2lI33KBeZKnTlCCLSP1mFuZF/tnPknUvvAADB8KmTfHFJSJlXXNNmNccYMYMmDAh3nhEqqAEWUTqP7PwhL1f/CJZN358eLjIxo3xxSUiSR06wIUXJsvqRZY6TAmyiOQHM7jzTrj22mTdSy+Fx1SvXx9fXCKSdPXV0LRpWP7Pf8KnPSJ1kBJkEckfZnDrrWWf2PXKK9C/P6xbF19cIhJ87Wtw8cXJ8o036kE/UicpQRaR/GIGN98Mt9ySrJs8GY47DtaujS8uEQmuvBKaNw/Ls2fDM8/EG49IBZQgi0h+uv56uP32ZHnaNOjXD9asiS8mEYH27cvOPHPTTXoSptQ5SpBFJH9dcw385jfJ8muvwdFHw6pV8cUkInDFFdCyZVieOzfMYS5ShyhBFpH8dsUVcPfdyfIbb8APfgBffRVfTCKFrm1b+OlPk+Wbb9aj4qVOUYIsIvnvpz+Fe+9NlmfMgCOPhJUr44tJpND97GfQunVY/u9/4ckn441HJEIJsogUhosvhvvvT5bfeiskycuXxxeTSCFr0wYuvzxZvuUWPSZe6gwlyCJSOC64AB56KMx0AfD229C3LyxdGm9cIoXqJz8JiTLAggUwcmS88YgkKEEWkcIybBj85S/JJHn2bOjTB774It64RApRq1Zln4D5q1/B5s3xxSOSoARZRArP0KGhp6oo0QS+/z707g1LlsQalkhBuvRSaNcuLH/yCTzySLzxiKAEWUQK1dlnh5uCiotD+YMP4IgjYPHieOMSKTQtWsBVVyXLt90GGzfGF48ISpBFpJANHgxPPw0NGoTyhx+GJPnTT+ONS6TQ/N//wa67huXFi8O9AiIxUoIsIoXt1FNhzBho2DCUFywISfLChbGGJVJQmjWDq69Olm+/HTZsiC8eKXhKkEVETj4Znn0WGjUK5YULQ5K8YEGsYYkUlAsugK9/PSwvWVJ2WkaRHFOCLCIC0L8/PP88NG4cyp9+GpLkDz+MNy6RQtG0KVx7bbL861/DunXxxSMFTQmyiEip446DsWOhSZNQXrw4zG4xb16sYYkUjB//GDp2DMtLl8Kf/hRvPFKwlCCLiEQdfTSMHx96swA+/zwkye+/H2tYIgWhcWO47rpk+c47Yc2a+OKRgqUEWUSkvCOPhIkToXnzUP7f/8LDRObMiTcukULwox9B585hecUK+OMfYw1HCpMSZBGRivTuDS+9FOZohfBxb58+8M47sYYlkvcaNYLrr0+Wf/tbWLUqvnikIClBFhGpzPe+B5MmQcuWobx8eUiSR46E004LPcxFReHroEEwfTq4xxuzSD744Q9hzz3D8pdfwmGH6fdNckoJsohIVQ47DF55BVq3DuUvvwyPqn72WVi/PvyBXr8+lPv2hTPPhC1b4o1ZpL5r2LDsjBbvv6/fN8kpJcgiItX51rdCklz6MBHYseeqpCRMSfXiizBkiHq2RNLhDn/7G5hVvF6/b5JlSpBFRFJRUgLFxdVvt2EDjBsHM2ZkPyaRfDV9ephNprrEV79vkiVKkEVEUjF8OGzenNq2GzaE7UWkdoYPT/1R0/p9kyxQgiwikooJE0IvcipKSsL2IlI7+n2TmClBFhFJRaq9WbXdXkSS9PsmMVOCLCKSitIn62VrexFJ0u+bxEwJsohIKo4/PszBmoqiorC9iNSOft8kZkqQRURScfnlqfdSNWkStheR2tHvm8RMCbKISCp69YL+/av/o920KZx4IvTsmZu4RPKRft8kZkqQRURSYRYeMT1gQPKRt1FFRdCsWVg/cmTlDzgQkerp901ipgRZRCRVDRvCU0/B5MkwcGDyD3fz5nDqqTB1KowaVfaJeyJSO/p9kxg1iDsAEZF6xSx8/DtmTNyRiOQ//b5JTNSDLCIiIiISoQRZRERERCRCCbKIiIiISIQSZBERERGRCCXIIiIiIiIR5u5xx5BxZrYM+KSGu7UDlmchnLogX69N11W/6LrK2sPd22c6mLqknrfFiqMsxVG3YgDFUV5G2+K8TJBrw8xmunuPuOPIhny9Nl1X/aLrklTUlfdTcSiOuhyD4sh+HBpiISIiIiISoQRZRERERCRCCXLSiLgDyKJ8vTZdV/2i65JU1JX3U3GUpTiS6kIMoDjKy2gcGoMsIiIiIhKhHmQRERERkQglyCIiIiIiEQWXIJtZPzObZ2bzzezqCtY3NrPRifVvmlnn3EdZcylc18/N7H0ze9fM/m5me8QRZ21Ud22R7QaamZtZ7NPNpCKV6zKzQYnv23tm9lSuY6yNFH4WdzezKWb2n8TP43FxxFlTZvaImS01szmVrDcz+0Piut81s2/mOsa6Lp3218yuSdTPM7NjshhDpW2lmW0zs7cTr7G1jSHFOM4xs2WR8/04sm6omX2YeA3Nchx3R2L4r5l9FVmXyfej1r9fmXo/UojhrMS5Z5vZv83soMi6hYn6t81sZm1jSDGO3ma2KvLe3xBZl9LfywzF8YtIDHMSPw87J9Zl8v3olPibUfq38CcVbJP5nw93L5gXUAx8BHwDaAS8A+xXbpv/A+5PLA8GRscdd4auqw/QLLF8UX24rlSvLbFdS2Aa8AbQI+64M/Q92wv4D9AmUd4l7rgzdF0jgIsSy/sBC+OOO8Vr+z7wTWBOJeuPA14CDPg28GbcMdelVzrtb+Ln5B2gMdAlcZziLMVQaVsJrM3he3EOcG8F++4MLEh8bZNYbpOtOMptfynwSKbfj8SxavX7leH3o7oYDou0x8dGf8eBhUC7HL0XvYHx6X4/042j3Lb9gclZej92A76ZWG4J/LeC35eM/3wUWg9yL2C+uy9w983A08CActsMAB5LLD8DHGlmlsMYa6Pa63L3Ke6+PlF8A+iY4xhrK5XvGcCvgDuBjbkMLg2pXNd5wH3u/iWAuy/NcYy1kcp1OdAqsdwa+DyH8dWau08DVlaxyQBgpAdvADuZ2W65ia5eSKf9HQA87e6b3P1jYH7ieBmPIUdtZartWkWOAV5x95WJtuEVoF+O4jgDGFXLc1Upjd+vjL0f1cXg7v8ubY/J4t/RFN6LyqTzc5VuHNn82Vji7m8lltcAc4EO5TbL+M9HoSXIHYBFkfJidnyTt2/j7luBVUDbnERXe6lcV9Qwwn9a9UG115b4KKWTu0/IZWBpSuV71g3oZmavmdkbZlbbP4K5lMp13QScbWaLgYmEXql8UNPfw0KTTvubqfc23bayiZnNTPw+nlSL89c0joGJj4ufMbNONdw3k3GQGGrSBZgcqc7U+5GKymKN6/eu/M+GA38zs1lmdn4Ozv8dM3vHzF4ys/0TdbG8F2bWjJB0Phupzsr7YWHY1SHAm+VWZfzno0Ftg5T6yczOBnoAR8QdSyaYWRHwO8LHkfkjn3BGAAAgAElEQVSmAWGYRW9CT8U0MzvQ3b+qcq+67wzgUXcfbmbfAR43swPcvSTuwERKVdJW7uHun5nZN4DJZjbb3T/KUgjjgFHuvsnMLiD0rPfN0rlSMRh4xt23Repy+X7UGWbWh5AgHx6pPjzxXuwCvGJmHyR6YLPhLcJ7v9bCPRwvEP5WxKU/8Jq7R3ubM/5+mFkLQhL+U3dfnc6xUlFoPcifAZ0i5Y6Jugq3MbMGhI+AV+QkutpL5bows6OAXwInuvumHMWWruqurSVwADDVzBYSxh6Ntbp/o14q37PFwFh335L4WPm/xNsIpiKV6xoGjAFw99eBJkC7nESXXSn9HhawdNrfTL23abWV7v5Z4usCYCqhJ6s2qo3D3VdEzv0QcGhNriFTcUQMptxH6Bl8P1JRWaw5/b0zs+6E78cAd9+eG0Tei6XA89RuCFBK3H21u69NLE8EGppZO+Jrg6r62cjI+2FmDQnJ8ZPu/lwFm2T+56MmA6Xr+4vQI7eA8DFR6QD2/cttczFlbxIZE3fcGbquQwiD9/eKO95MX1u57adSP27SS+V71g94LLHcjvAxUdu4Y8/Adb0EnJNY3pcwBtnijj3F6+tM5TfOHE/Zm0Smxx1vXXql0/4C+1P2Jr0F1O4mvVq3lYQbfBonltsBH1LLG6BSjGO3yPLJwBuJ5Z2BjxPxtEks75ytOBLb7UO46coidRl7PyLHrPHvVybfjxRi2J0w/v2wcvXNgZaR5X8D/bL4Xnyt9HtBSDw/TbwvNfp7mW4cifWtCeOUm2fr/Uhc20jg91Vsk/Gfj1q/afX1RbjT8b+EBvCXibpbCD0FEHqz/pr4JZgOfCPumDN0Xa8CXwBvJ15j4445U9dWbtup1IMEOcXvmRGGj7wPzAYGxx1zhq5rP+C1ROP9NnB03DGneF2jgCXAFkLv/jDgQuDCyPfrvsR1z64vP4d17Gej0vaX0KP7ETAPODaLMVTYVhJmMJid+LmdDQzL8ntxB/Be4nxTgH0i+56beI/mAz/KZhyJ8k3Ar8vtl+n3o9a/X5l6P1KI4SHgy8jPxsxE/TcS78M7ie/ZL7P8XlwS+dl4g0jCXtH3M1txJLY5h3ADbXS/TL8fhxPGNL8bee+Py/bPhx41LSIiIiISUWhjkEVEREREqqQEWUREREQkQgmyiIiIiEiEEmQRERERkQglyCIiIiIiEUqQJS+Z2drE185mdmaGj31tufK/M3l8EZF8oHZY6jMlyJLvOgM1apgTT/CqSpmG2d0Pq2FMIiKFpDNqh6WeUYIs+e7XwPfM7G0z+5mZFZvZb8xshpm9a2YXAJhZbzP7p5mNJTyYAzN7wcxmmdl7ZnZ+ou7XQNPE8Z5M1JX2klji2HPMbLaZnR459lQze8bMPjCzJ83MYngvRETioHZY6p3q/kMTqe+uBq5w9xMAEg3sKnfvaWaNgdfM7G+Jbb8JHODuHyfK57r7SjNrCswws2fd/Wozu8TdD67gXKcABwMHER69OsPMpiXWHUJ4XO7nhKfIfRf4V+YvV0SkzlE7LPWOepCl0BwNDDGzt4E3gbbAXol10yONMsBlZlb6KM9Oke0qczgwyt23ufsXwD+AnpFjL3b3EsJjMjtn5GpEROoftcNS56kHWQqNAZe6+6QylWa9gXXlykcB33H39WY2FWiSxnk3RZa3od89ESlcaoelzlMPsuS7NUDLSHkScJGZNQQws25m1ryC/VoDXyYa5X2Ab0fWbSndv5x/Aqcnxte1B74PTM/IVYiI1F9qh6Xe0X9Pku/eBbYlPqJ7FLiH8LHaW4kbNJYBJ1Ww38vAhWY2F5hH+Hiv1AjgXTN7y93PitQ/D3wHeAdw4Ep3/1+iYRcRKVRqh6XeMXePOwYRERERkTpDQyxERERERCKUIIuIiIiIRChBFhERERGJUIIsIiIiIhKhBFlEREREJEIJsoiIiIhIhBJkEREREZEIJcgiIiIiIhFKkEVEREREIpQgi4iIiIhEKEEWEREREYlQgiwiIiIiEqEEWaQaZtbazKab2VozO6CSbXqZ2etmNs3MRplZw1zHKSKSr1Jsh6vdRiRVSpBFqrceOB54poptFgF93f37wEJgQA7iEhEpFKm0w6lsI5ISJciSF8zsPTPrnY1ju/sWd19WzTZL3H1DorgZKCkX3x1m9tNsxJeqRM/K/nHGICL5qw60w1Vuo3ZYakIJsmSNmS00s81m1q5c/X/MzM2sc4rHOKq67dx9f3efWssY3cxOSpR3NbP3E3XPmFmDGh5vD+BoYFykrj0wBHig3LZzzWxxphpLM7vEzGaa2SYze7SCTX4L3JKJc4lI/VCI7XAl51A7LDWiBFmy7WPgjNKCmR0INMvUwTPRcEaOtQswGdgXeB4Y7O5ba7B/K+Bx4Bx33xJZdQ4wMdLDXOoA4L/AqenEHfE5cCvwSCXrxwJ9zOxrGTqfiNQPBdMOV+Ec1A5LDShBlmx7nPBfe6mhwMjoBmZ2tZl9ZGZrEr0GJyfqHwd2B8Ylbrq4MlG/0MyuMrN3gXVm1qC0h8PM9jSzlWb2zcS2XzezZSl87Nee0CjvR2jATq+uUTazjpHlBsDTwM3uPq/cpscC/yi/v7tvA/4FdK8mtpS4+3Pu/gKwopL1G4FZwDGZOJ+I1BsF0Q5XQ+2w1IgSZMm2N4BWZravmRUDg4Enym3zEfA9oDVwM/CEme3m7j8EPgX6u3sLd78rss8ZhJsxdoo2oO7+EXBV4hjNgL8Aj6Xwsd89wP7AeOC0cj3AmNlEwtCJB83snERCPKpcPN8CrjezqWZ2emTdgUD5pBkza5rY76CKAjKz8Wb2VSWv8dVcT2XmVnY+EclbhdIO77BNZJXaYamRjH0sIlKF0t6LfxAahs+iK939r5HiaDO7BugFvFjFMf/g7osqWuHuD5pZf+BNwIETU4ixaeLrPe6+uYJjHhctm1kvIj0w7v444TorshOwpoL624DFwBFm1sLd15Y75wkpxF1Ta4DdsnBcEanb8r4drmibCLXDUiPqQZZceBw4kzAGbGT5lWY2xMzeLv2vnDAmrF357cqpsFGOeDBxnD+6+6YUYvww8fV5Mzusuo3dfbq7P5jCcQG+BFpGK8zsO8BpwEBgFaF3IxdaAl/l6FwiUneoHVY7LDWgBFmyzt0/IdwkchzwXHSdhVkfHgQuAdq6+07AHMBKd6/ssJWdz8xaAL8HHgZuMrOdUwjzGsJHdS2AlxI9E5nyLtAtEl8TwkeOF7r7SuAdKhj/ZmYvJcb8VfR6qZax7Js4n4gUELXDaoelZpQgS64MIzxIY125+uaERnYZgJn9iNDjUOoL4Bs1PNc9wEx3/zEwAbg/hX22AT8ExgCtgElmdmgNz1uZicARkfItwL/dfUKi/DYVjEdz92MTY/4qeh1bfvvETTJNgGKg2MyaWOTu8sS6Q4FXMnRdIlK/qB1OUjssVVKCLDnh7h+5+8wK6t8HhgOvExrhA4HXIpvcAVyX+NjviurOY2YDgH7ARYmqnwPfNLOzUohxG3AWoXdlJ+AVMzu4uv1SMBI4zsyaJnpETgN+Fln/Npm5g/o6YANwNXB2Yvm6yPr+wFR3/zwD5xKRekbtsNphSZ25V/oJiYhkiJndDix199/HGMObwDB3nxNXDCIicVE7LDWhBFlEREREJEJDLEREREREIpQgi4iIiIhEKEEWEREREYlQgiwiIiIiEqEEWUREREQkokH1m9Q/7dq1886dO8cdhohIpWbNmrXc3dvHHUc2qS0WkbqusrY4LxPkzp07M3PmDnOhi4jUGWb2SdwxZJvaYhGp6yprizXEQkREREQkQgmyiIiIiEiEEmQRERERkYi8HIMsIrm3ZcsWFi9ezMaNG+MOpU5p0qQJHTt2pGHDhnGHIiJ5Tu1w5WraFitBFpGMWLx4MS1btqRz586YWdzh1AnuzooVK1i8eDFdunSJOxwRyXNqhytWm7a4zg+xMLPmZvaYmT1oZmdl7MDu8OabcNpp0Lw5FBWFr4MGwfTpYb2IpGzjxo20bdu20kb5rrtgypTUjjVlSti+vjMz2rZtq96cqqgtFskYtcMVq01bHEuCbGaPmNlSM5tTrr6fmc0zs/lmdnWi+hTgGXc/DzgxIwFs2QJnngl9+8Jzz8H69aERXr8enn021J95ZthORFJWVY9Fz54h56mucZ4yJWzXs2eGg4uJenGqoLZYJOPUDlespm1xXD3IjwL9ohVmVgzcBxwL7AecYWb7AR2BRYnNtqV9ZncYMgTGjg2NcElJ2fUlJbBuHbz4YthOvRciGdGnD4wZU3XjXNoojxkTtpc8prZYJOfUDqculgTZ3acBK8tV9wLmu/sCd98MPA0MABYTkmSoIl4zO9/MZprZzGXLllV+8unTYdy40CBXZcOGsN2MGdVdjoikqKrGORON8m233cb+++9P9+7dOfjgg3nzzTfp3bv39odVfPzxx+y1115MmjQpzSuRtKktFolFttthyI+2uC6NQe5AsqcYQmLcAXgOGGhmfwbGVbazu49w9x7u3qN9+yqe3jp8eGhwU7FhQ9heRDKmosY5E43y66+/zvjx43nrrbd49913efXVV+nUqdP29YsXL6Zfv34MHz6cY445JgNXImlRWywSm2y1w5A/bXGdn8XC3dcBP0plWzPrD/Tv2rVr5RtNmLDjR3mVKSkJ24tIjaQ61Ktv36rLFansk/YlS5bQrl07GjduDEC7du3KrBsyZAi33XYbJ56YmVsZJE1qi0WyKo52GPKnLa5LPcifAZ0i5Y6JupS5+zh3P79169aVb5Rqj0VttxeRWBx99NEsWrSIbt268X//93/84x//2L5u6NChXHLJJZx66qkxRihlqC0WyUv50hbXpQR5BrCXmXUxs0bAYGBsxs/StGl2txeRWLRo0YJZs2YxYsQI2rdvz+mnn86jjz4KwFFHHcUTTzzB+urGu0ruqC0WyUv50hbHNc3bKOB1YG8zW2xmw9x9K3AJMAmYC4xx9/dqeNz+ZjZi1apVlW90/PFhns1UFBWF7UWkRtyrfk2eDO3aha8Vlat6VaW4uJjevXtz8803c++99/Lss88CcOWVV9KzZ09OO+00tm7dmoN3QKqltlgkq+JqhyE/2uK4ZrE4w913c/eG7t7R3R9O1E90927uvqe731aL41Y/xOLyy1PviWjSJGwvIhlT0Y0gqUw9VJ158+bx4Ycfbi+//fbb7LHHHtvLv//972nVqhXDhg3DNWVY/NQWi8QmW+0w5E9bXJeGWORGr17Qv3/1DXPTpnDiifk1S7ZIzKq6Szrdxnnt2rUMHTqU/fbbj+7du/P+++9z0003bV9vZjz22GMsWbKEK6+8Mr0LkfSpLRaJRTbbYcijttjd8+YF9AdGdO3a1au0ebP74MHuzZu7FxWV/eTAzL1Zs7B+8+aqjyMi273//vtVrp882b1du/A1E9vVJxW9N8BMrwPtZjZfhx56aNVvTFVtcVGR2mKRGlI7XLWatMV51YPsqQyxAGjYEJ56Kgy0GTgQiouT6777XZg6FUaNCtuJSEbMmJHa/JqlPRh6LkQBKN8WR518stpikQxTO5y6Oj8PctaYhY/4xoyBM88MjTDABRfoozyRLKjJJ2l9+hT2I04LSrQt7tQJFi8O9cOHQ2TcooikT+1w6vKqBzmlWSwq0qpVcnnNmswGJSIiqYk8UIDly+OLQ0QKXl4lyCkPsSgvmiCvXp3ZoESkLHd480047TRo3jxM4dW8ebgrZPr01OYQkvykBFkkN9QOVyuvEuRaU4IskhtbtoQhTX37wnPPwfr1oSFevx6efTbUn3lm2E4KjxJkkexTO5wSJcigBFkkF9xhyBAYOzY0xCUlZdeXlMC6dfDii2E79WAUHiXIItmldjhleZUg13oMcsuWyWUlyCLZMX06jBsXGuWqbNgQtivk26cLlRJkkexSO5yyvEqQNQZZpA4bPjw0uqnYsCFsXwsvvPACZsYHH3xQq/3LW79+PWeddRYHHnggBxxwAIcffjhr164FoEWLFtu3mzhxIt26deOTTz7JyHkLkhJkkexSO5yyvEqQa00Jskhmme34+utfd/w4rzIlJWHar4qOU41Ro0Zx+OGHM6p06sY03XPPPey6667Mnj2bOXPm8PDDD9Ow3Ly8f//737nssst46aWXyjxSVWpICbJI5qgdTosSZNA0byJ5Yu3atfzrX//i4Ycf5umnnwZg27ZtXHHFFRxwwAF0796dP/7xjwDMmDGDww47jIMOOohevXqxppLf/SVLltChQ4ft5b333pvGjRtvL0+bNo3zzjuP8ePHs+eee2bx6gqAEmSRei9f2uHCfVBIlHqQRfLCiy++SL9+/ejWrRtt27Zl1qxZTJ8+nYULF/L222/ToEEDVq5cyebNmzn99NMZPXo0PXv2ZPXq1TRt2rTCY5577rkcffTRPPPMMxx55JEMHTqUvfbaC4BNmzZx0kknMXXqVPbZZ59cXmp+UoIsUu/lSzucVz3IGXlQiBJkkfS57/g67bQw12YqiorCfJwVHacKo0aNYvDgwQAMHjyYUaNG8eqrr3LBBRfQoEHoD9h5552ZN28eu+22Gz0TT81s1arV9vXlHXzwwSxYsIBf/OIXrFy5kp49ezJ37lwAGjZsyGGHHcbDDz+c2nVJ1ZQgi2SO2uG05FUPsruPA8b16NHjvBrtqARZJPsuvxwmTgxTCFWnSZOwfQ2sXLmSyZMnM3v2bMyMbdu2YWbbG990tGjRglNOOYVTTjmFoqIiJk6cyL777ktRURFjxozhyCOP5Pbbb+faa69N+1wFrW3b5PLy5eEPcQrjHUUkRWqHU5ZXPci11rx5shFetw62bYs3HpF81KsX9O8PlXyEtl3TpnDiiVDDBvWZZ57hhz/8IZ988gkLFy5k0aJFdOnShYMOOogHHniArVu3AqEB33vvvVmyZAkzElMYrVmzZvv68l577TW+/PJLADZv3sz7779f5gaQZs2aMWHCBJ588kn1JKerSRMovSN961Z1WIhkmtrhlClBhvAxQmSaEN2oJ5IFZjByJAwYkHy0aVRRETRrFtaPHFnjnsNRo0Zx8sknl6kbOHAgS5YsYffdd6d79+4cdNBBPPXUUzRq1IjRo0dz6aWXctBBB/GDH/yAjRs3Vnjcjz76iCOOOIIDDzyQQw45hB49ejBw4MAy2+y88868/PLL3HrrrYwdO7ZGcUs5GmYhkj1qh1NmnodPSenRo4fPnDmzZjt17AiffRaWP/kEdt8984GJ5LG5c+ey7777Vr+he5h8/re/DR/1bdgQeiuOPx6uuKLGPRb1QUXvjZnNcvceMYVUY2b2DeCXQGt3PzWVfWrVFvfsCaX7vPlm6PESkZSoHa5aTdrivBqDnJZWrZIJsnqQRbLHLCQ9Y8bEHUnBMLNHgBOApe5+QKS+H3APUAw85O6/ruwY7r4AGGZmz2Q12PLjkEUk89QOVyuvEmQz6w/079q1a8131o16IgVt0qRJXHXVVWXqunTpwvPPPx9TRBn1KHAvMLK0wsyKgfuAHwCLgRlmNpaQLN9Rbv9z3X1pTiLVEAuRglWX2uG8SpBrPYsFKEEWyQB3x+rprAPHHHMMxxxzTMaPWxeGsbn7NDPrXK66FzA/0TOMmT0NDHD3Owi9zbViZucD5wPsXpuhakqQRdKidrhiNW2LdZNeKSXIImlp0qQJK1asqBMJYV3h7qxYsYImTZrEHUpFOgCLIuXFiboKmVlbM7sfOMTMrqlsO3cf4e493L1H+/btax6VEmSRWlM7XLHatMV51YOcFiXIImnp2LEjixcvZtmyZXGHUqc0adKEjh07xh1G2tx9BXBh1k+kBFmk1tQOV66mbbES5FJKkEXS0rBhQ7p06RJ3GJK6z4BOkXLHRF28lCCL1Jra4czREItSLVsml5Ugi0j+mwHsZWZdzKwRMBiIfxJnJcgiUgcoQS6lHmQRyVNmNgp4HdjbzBab2TB33wpcAkwC5gJj3P29OOMElCCLSJ2gIRalogmy5kEWkTzi7mdUUj8RmJjjcKqmBFlE6gD1IJdSD7KISPyiDwpZsQJKSuKLRUQKVl4lyGbW38xGrFq1quY7K0EWEYlfw4bQunVYLimBr76KNx4RKUh5lSC7+zh3P791aeNaE0qQRUTqBg2zEJGY5VWCnBYlyCIidYMSZBGJmRLkUprmTUSkblCCLCIxK7gE+a67YMqUClZU0IM8ZUrYXkREckgJsojErOAS5J49YdCgCpLkaA/ymjVMmewMGhS2FxGRHFKCLCIxK7gEuU8fGDOmgiS5cePwAti6lSGDNjJmTNheRERySAmyiMSs4BJkqCJJjgyzGPXAaiXHIiJxUIIsIjEryAQZyibJDz4IU6fClyXJBPnw7rpRT0QkFtGHhShBFpEYFPSjpvv0gfvvh1NPDeVZtKJN6UrNZCEiEg/1IItIzAq2B7nU8ccnl1ejuZBFRGKnBFlEYlbwCfLrryeX16C5kEVEYhdNkFesiC8OESlYdT5BNrNvmNnDZvZMpo89ZUoYg9wmMa5CPcgiInVAmzZgFpa//BK2bo03HhEpOFlNkM3sETNbamZzytX3M7N5ZjbfzK6u6hjuvsDdh2U6ttLkeMwY2HXXUBdNkOfNWpPpU4qISEKlD20CaNAg2XPhzr/GfamHNolITmW7B/lRoF+0wsyKgfuAY4H9gDPMbD8zO9DMxpd77ZKNoKLJcZ8+sNNOoT6aII95cHXljbeIiKSl0oc2lYoMs7jy3OV6aJOI5FRWE2R3nwasLFfdC5if6BneDDwNDHD32e5+QrnX0lTPZWbnm9lMM5u5bNmySrcrnxxDxQnykJNWV914i4hIrVU6H32pSIJ8703LNS+9iORUHGOQOwCLIuXFiboKmVlbM7sfOMTMrqlsO3cf4e493L1H+/btKz35jBns8IS8ihLkPdqsZsyYsL2IiGReVUnyMpIJ8jd310wWIpJbdX4eZHdfAVyYyrZm1h/o37Vr10q3ufLKHesqSpBZHZ6kp14LEZHsKU2SBw6Ec86B5s3Dc0Laz2rHWaUbaao3EcmxOBLkz4BOkXLHRF3a3H0cMK5Hjx7n1WS/yhJkERHJvj594Nhj4e67Q7lZM3j/5HZhAB4oQRaRnItjiMUMYC8z62JmjYDBwNgY4tiu9GZpzYMsIhKPww9PLnfrBnt8Uw8LEZH4ZHuat1HA68DeZrbYzIa5+1bgEmASMBcY4+7vZeh8/c1sxKpVq2q0X4U9yGs0zZuISK6sjNzO/d57MHeZEmQRiU9Wh1i4+xmV1E8EJmbhfBpiISJSz0yZAr/9bbLcoQPcen87niytUIIsIjlW55+klwtKkEVE4lE69eYjjyTrvvwSfn67epBFJD55lSBndIiFEmQRkayKzkt/0knQqFGoX7UK9v5uMkHesEgJsojkVl4lyO4+zt3Pb926dY32K71Jbx3NKcFCYf162Lo1wxGKiAjs+NAmszC0otTnm5MJ8pb/LddDm0Qkp/IqQa6t0h5kMNaYbtQTEcm2ih7a1LFjcnnR6tZQXAxAK1/NrNc35zhCESlkeZUg13aIRbTDebVrqjcRkWy78sodH8QUTZAXf14EO++8vXzFj1bkKDIRkTxLkGs7xKJRozAxPWiqNxGRuJRJkBcD7XSjnojEI68S5HToRj0RkXgpQRaRukIJcoISZBGReClBFpG6Iq8S5NqOQYbkTBZKkEVE4qEEWUTqirxKkGs7BhnUgywiErfoNG9KkEUkTnmVIKdDCbKISLy+9rXtM7uxfDlsaa0EWUTioQQ5QQmyiEi8iotht92S5S+LlSCLSDyUICeUJshr0DzIIiJxiY5D/qIkkiCv0DzIIpI7eZUgZ/wmPc2DLCKSU9EE+fNN6kEWkXjkVYKsm/REROq3aIK8cK0SZBGJR14lyOlQgiwiEr9ogvzRKiXIIhIPJcgJSpBFROIXTZDnf9ESGjYMhXXrYMOGeIISkYKjBDlBCbKISPyicyF/9rmVnQtZN+qJSI4oQU5QgiwiEj89TU9E6oK8SpD1qGkRkewws33N7H4ze8bMLsrWeb7+9eTykiVQ0lYJsojkXl4lyOnMYtEqkReXmQd5zRpwz1B0IiLxMLNHzGypmc0pV9/PzOaZ2Xwzu7qqY7j7XHe/EBgEfDdbsTZqBLvuWnpO2NhcCbKI5F5eJcjpaNAAWraErTRkA01C5bZtuilERPLBo0C/aIWZFQP3AccC+wFnmNl+ZnagmY0v99olsc+JwARgYjaDjQ6zWN1ICbKI5J4S5AiNQxaRfOTu04CV5ap7AfPdfYG7bwaeBga4+2x3P6Hca2niOGPd/VjgrGzGG02QV1rbZEEJsojkiBLkCCXIIlJAOgCLIuXFiboKmVlvM/uDmT1AFT3IZna+mc00s5nLli2rVWDRBHlpiXqQRST3GsQdQF2iG/VERCrm7lOBqSlsNwIYAdCjR49a3cRRZqq3zUqQRST31IMcoR5kESkgnwGdIuWOibrYRXuQP9HjpkUkBkqQI5Qgi0gBmQHsZWZdzKwRMBgYG3NMgB43LSLxU4IcUZogl5nqTQmyiNRzZjYKeB3Y28wWm9kwd98KXAJMAuYCY9z9vTjjLBVNkD9YrgRZRHIvr8Ygm1l/oH/Xrl1rtX+FPchr1qQfmIhIjNz9jErqJ5LlKdtqIzoGec7/yiXI7mCW+6BEpKDkVQ9yOg8KAQ2xEBGpC5o1g513DsurtzXDmyTmpt+0Cdatiy8wESkYeZUgp0uzWIiI1A3JYRbGllYaZiEiuaUEOUI9yCIidUN0HPJ6PW5aRHJMCXKEEmQRkbohOg55jR43LSI5pgQ5QgmyiEjdUOZx00VKkEUkt5QgRyhBFhGpG6IJ8hfRx02vWJH7YESk4ChBjii9Sa/MPMia5k1EJOeiCfJnm9SDLCK5pQQ5omXLML2meg40CfYAACAASURBVJBFROKlx02LSJyUIEcUFUHr1kqQRUTipsdNi0iclCCXs9NOSpBFROLWqlX4VA/g8y1KkEUkt5Qgl7PTTrCeZmwrfWs2bIAtW+INSkSkAJX2Ii9HCbKI5Fa9SJDN7CQze9DMRpvZ0dk8V5jJwsr2IutGPRGRnAtzITu782mycs4caN4cBg2C6dPBPa7wRCSPZT1BNrNHzGypmc0pV9/PzOaZ2Xwzu7qqY7j7C+5+HnAhcHo249XjpkVE6oY9vr6FJzmTpxlcdsX69fDss9C3L5x5pj7lE5GMy0UP8qNAv2iFmRUD9wHHAvsBZ5jZfmZ2oJmNL/faJbLrdYn9sman1k4v3mQnvkpW7ruveitERHLJnctmDWEAY2nO+h3Xl5TAunXw4oswZIjaZhHJqKwnyO4+DVhZrroXMN/dF7j7ZuBpYIC7z3b3E8q9llpwJ/CSu79V0XnM7Hwzm2lmM5ctW1a7YLds4ZLXz+Tv9KUlkV7jjRvVWyEikkvTp7Pvh+MqTo6jNmyAceNgxozcxCUiBSGuMcgdgEWR8uJEXWUuBY4CTjWzCyvawN1HuHsPd+/Rvn37mkfkDkOGcMCCsbRg/Y5vjHorRERyZ/hwirdsSG3bDRtg+PDsxiMiBaVB3AGkwt3/APyhuu3MrD/Qv2vXrjU/yfTpMG4cjbbUoLeiV6+an0dERKo3YQJFXpLatiUlMGFCduMRkYISVw/yZ0CnSLljoi4t7j7O3c9v3bp1zXcePjwkv6lQb4WISHal2h7XdnsRkSrElSDPAPYysy5m1ggYDIyNKZZgwoTQC5EK9VaIiGRX06bZ3V5EpAq5mOZtFPA6sLeZLTazYe6+FbgEmATMBca4+3sZOFd/MxuxatWqmu+s3goRkbrj+OOhKMU/UUVFYXsRkQzJxSwWZ7j7bu7e0N07uvvDifqJ7t7N3fd099sydK7aD7FQb4WISN1x+eWpt7NNmoTtRUQypF48SS8n1FshIlJ39OoF/fuzqbiaJLlpUzjxROjZMzdxiUhByKsEOa0hFuqtEBGpO8xg5EjmdhvAWppTgpVdX1QEzZrBgAEwcmTYXkQkQ/IqQU5riEWit8KrS5LVWyEikhsNG/Kvi56iL5OZxaHJ+gYN4NRTYepUGDUKGjaMLUQRyU95lSCnJdFbYQMGsI7mbFNvhYhI7Dp2MmbQi99yRbLy5JNh9Gh1VIhI1uRVgpzWEAsIvRBPPcUPO0zmdQ5L1hcXq7dCRCQGHTuGr+tonqxcuzaeYESkYFT7JD0z2wkYAnSObu/ul2UvrNpx93HAuB49epxX64OY8enXenHzZzfyCkeHut69Q2+FiEhM6lNbnEkdOoSva2mRrFSCLCJZlsqjpicCbwCzgRSfpFG/7bQTbCAyFnnjxviCEREJCq4tBthllzDkeO3WSIK8bl18AYlIQUglQW7i7j/PeiR1SJs28DFNkhV6KIiIxK/g2mIII9y+/nVY+6l6kEUkd1IZg/y4mZ1nZruZ2c6lr6xHVgtpj0FO2KEHWQmyiMSv3rTFmdaxo4ZYiEhupZIgbwZ+Q3hc9KzEa2Y2g6qttKZ5i9hpJ9gY7UHWEAsRiV+9aYszTQmyiORaKkMsLge6uvvybAdTV6gHWUTqoIJri0t17FjBLBbumm5TRLImlR7k+cD6bAdSl+gmPRGpgwquLS7VsSNspSEbaRwqSkrULotIVqXSg7wOeNvMpgCbSivzeWqhHYZYqAdZROJXUG3xXXeF54D06VN2LuQmpZe+dm14sikwZQrMmAFXXhlTsCKSd1JJkF9IvOo8M+sP9O/atWtax2nTplyCvGlT6LEoyqvnqohI/VJv2uJM6NkTBg2CMWPKzoXclpWJwlpo354pU5LbiYhkSpUJspkVA+e4e58cxZOWjDwohNCDDMYGmtCUxMd4mzZt760QEcml+tYWZ0KfPiHpHTQI/vjHUFfmRr1168okx30K5p0RkVyoskvU3bcBJWaW3rQQ9UxIkDXMQkTqhkJti0uT5EsvDeVogjzrH2uVHItI1qQyxGItMNvMXiGMgQPyd9wbJBPkDTSlDV8lCkqQRSRWBdcWQzJJPuooWFuSTJBvv3YtY15Qciwi2ZHKoNrngOuBaSTn3pyVzaDiVmEPsu6YFpF4FVxbXKpPH9hrr7I9yH17VT4X8l13hRv3Sk2ZEuoqWl9+XXnVrReR/FRtguzujwGjSDbGTyXq8lbTptCokeZCFpG6oxDb4qhevcomyAvnrGXgwLKJcKnSG/ymTGH7OOWePXdc/7vf7bgOkgl0RftG10PVyXd16ytKvuM6ts5d+foo/cNUQNy9yhfQG/gE+Aeh5+Jj4PvV7RfHC+gPjOjatauna5dd3GdwqHuYjt59xoy0jykiUgqY6TVr3+pNW1z6OvTQQzP2fo0e7T7Czt/eJl/An71BA/dmzdxfeWXH7SdPdm/d2r1Vq7Bc3vDh7mbha033nTzZvV27sG+7dmW3KV03eXLZ5VT2jfPYOnfF6++8M1mu6Nzl1995Z9ljp7M+uq669Tp3xapb7155W5xKozwL2DtS7gbMqm6/OF+1aZTLf0O6dXP/J99NJsjTpm1fl8obLiJSlVokyAXRFlekNDFZOPBn29vky/nN9ua5QQP3Rx7ZcZ9WrUKiW5uEqbJ9S6WTYFe1b5zH1rl3XJ/N5Lu69YX6T0m6567oOFVJJ0F+N5W6uvSqTaNc/o3s1cv9bxyVTJAnTapwOxGR2qhFglwQbXF5Zdrc66/f3ib/se2N25vn0td557kvWOD+1FPuO+8cep3/+tew/Nxz7suXu7/4onvbtu7jx7uvXev+0kvh+JMmuW/Z4v7qq1X/cY7GVJsEOxOJRTaPrXPvuD6biX916wvxn5JMnLsmuVo6CfIjwEOJj/d6Aw8Cj1S3X5yv2jbK0Tf06KPdX6R/suV98UUlxyKSMbVIkGNtixPn/CdwP9A7lX3STZB3aHPvvHN7m7zt51f4j3/sOyTJmXqZuRcVhRe4N2wYhnM0aRLWNW8eEu9WrUK5TRv33XYL8RYVue+6a3gVFbl//evhU8lOndyLi907d3bv3t19zz1D73e3bu49e7rvs08o77+/+/e+F7Zp2ND9kEPcjzrKvUePUP7Wt9y//W33Ro3cv/td95NPDts3auTeu7f7GWe4H3mke+PG4W/ZOee4H3tsiP2EE9wvvNB9wIBQPvlk95/8xP3UU92bNnU//XT3q64Kx2ja1P3ss91vuMF96NBw/eee6z5sWLj+8893/81v3C+6KJQvucT9j38Mx2vRwv1nP3MfMcL9iitC+aqr3EeOdL/2WveWLcP/O6NHu994Y3gfb7kl/ANz662hfMcd7i+/7H7XXSFZGj7c/e67w/If/uD+73+733uv+047uf/5z+6zZoXztWnj/tBD7nPmuP/lL6E8cqT7/PnuTz4Zvm9PP+2+aJH7mDGh/Oyz7suWuT//fPgHauxY99Wr3SdMCN/TO+8MX195xb2kZMef0Xz8x6C+nzvVXK2yttjCusqZWWPgYuDwRNU/gT+5+6bK94pXjx49fObMmbXat/SmjAMOgIumDmIQfwXgveufpvefT9ecmyKSEWY2y9171GD7WrfFZvYIcAKw1N0PiNT3A+4BioGH3P3XVRzjCOBq4AvgVnefX915M9EWl2lz//QnuPjisHzhhfDnP/OXv8D558PWrbU6jUjaiouhQYPwr9XmzdCkSbjRf9s2WL8eWrYMdVu2wKpVsPPO0KxZeP7YsmXwta9B8+ZhsqzPPw+PVm/ZMuz7ySfwjW+AGSxYEGZzadMmHGfePNhvP2jbFr76CubMgYMOgnbt4Msv4T//gR49YJddYMUKePNNOOywcL6lS+G11+D734evfx2++AKmToW+fcP5lyyBV16Bfv3CuV9+GY4/Hjp3hkWLYOxYOPlk6NIFPv0Unn0WTjsN9twTFi6Ep5+Gs84K8S5YAI8/DuecA3vvDR9+CH/5C/z4x7DvvvDf/8IDD8BFF8H++8MHH8B998Fll4UHGP/+93D55dC9O7z3HvzmN3DVVXDwwTB7NtxxB1x3HRxySHj/fv7zms2PXllbXG2CXB+l0yhDaJiPOw7u3ziUoYwE4NIWf+GUsecoORaRjKhpgpzmub5PmEd5ZGmCnHg633+BHwCLgRnAGYRk+Y5yhzgXWO7uJWa2K/A7dz+ruvOm0xbfdVeYPaJMmztyJAwdGpbPPjv81QVefRV++UuYNQtatIA1a0IS0qgRlJSExGPVKmjcOPlQ1OLisK6kJCTXW7aERCAP/ySKFIymTWHChJp1ZFbWFlf7oBAz+y5wE7BHdHt3/0bqp69f+vQJ/xltHJWcB/mSH29kbyXHIhKTdNpid59mZp3LVfcC5rv7gsTxnwYGuPsdhN7mynwJNK4izvOB8wF233336kKr1JVXVlDZIvKo6bXJeZCLi0Mv1SuvhPa7tPf5iSfC+kGD4O9/L7uutIepsvLo0XDEESGBnjw55OPDhsFDD4Xer8MPTybY06aFXuwhQ0IOf9998O1vh3X//nfoCRs8OPSqDR8eevVK950+Ha6+Gk45BZ57Dm65JfSEla5/661Qd8IJMH582PbAA8O6d94JvWlHHw2TJsFPfxp6FEv3fe+9EEvv3uG6zj8funVLrv/gg3Athx0W4jz77NBbWbr+o49CzD16wMyZIcbddw/rPv449CJ27w7vvgvHHgsdOiT3XbQo/OOyzz7hPEccAbvumly/ZEnowdxzz3CeXr1CT2jp+uXLw7V36hSOdcAB0Lp1WLdyZTjmrruGns899ww/GqX7rl4dejXbtAk9qbvtFnpwS9evXx+O36xZWG7dOvQAl67fvDnUN2gQ/nFq2DD881S6vqSk1j/WkmUHHZTBT/krGncRfQEfAMcCuwBtS1/V7RfnKxM3hvztb+5385PtA9LmX/K7tI8pIlKKmo9BTqstBjoDcyLlUwnDKkrLPwTurWL/U4AHgNHkaAzyDiZNSg4SPuood6/6RrpMjGEsf/yalNPZN85j69zVl6+7LjkmedMm9w0b3NetC2OW27Z1/8Uvwtfnn3dfutT9f/9z//zzMOZ6553dL7ssfH3iCfcPP3SfN8997twwG0ubNu4XXBC+PvCA+8yZ7tOnu993XxhvPXRo+Lm++273KVPc//73EMedd4af+cGDw9dbb3V/4YVwg+ozz4Sx5C1bhnHnLVu6X3ON+2OPhXHaDz/sfvnlYaz4cceFr5ddFsZ6//73yXHmRx4Zvg4b5n7bbe6/+pX7zTe7DxkSxqgffngYu37GGe5XXhnGn//85+4DB4Yx7z17hq8nnhiu8bzzwrH69Qtj5rt3D1+PPDJcx6BB7t//fhhf361b+Prtb7sff3wYV3/MMe6HHhrG5u+xR4i7pveJVdYWp9KovlndNnXtlak7p+8sunp7Y/zr1rf7pk1pH1ZExN1rlSCn1RanmyDX5pXxBPm115IJ8re/XeXNOJm4Cz4b08TVhZuXdO7MrC+Ufwzq87lTkU6C/GvgN8B3gG+WvqrbL44XGXpQSOkbPPvUm7Y3xjdzvZ97blqHFRHZrhYJclptcQUJ8neASZHyNcA1NYmpulfGE+S3397eJq/pckCVyXFlf2Cj66uaRzWdBDvd5Dxfp96qr+euan2+/2NQn8+dapKcToI8pYLX5Or2i/OVTqNc5o2NTCl0F1c4uD/+eNX76gEiIpKKWiTIabXFFSTIDYAFwP+3d+dhUpVn3se/dze0rIIaNO+IvBC3cZlRktZoktcLd6IgGHHXZCZGopcmLolIu0aNistoMuqYQWNQ4xIURFBQ1GBwjEZM3INmiFnARNGIyCY03c/7x11lnW66uqu7zuk6dfr3ua66uupU9amnmubUXXf/zvOMAOqAV4DdOjOmji6xF8hLlnx6TF6xxfCib4DlrsTVusAudn93L7CQ5L713OmcJ7mnfigp97k7UyR3uUCuxksc8yCHEDx8kzsY/ydnfjoX5lNPlfC9IiLt6GyBXM4FuA/4O9CIz1hxSm77YfhMFn8ELoz7eWMvkN9999NjchgyJN59R7QusNu7v73iu6P72yq+s7r8b7U+d+v39mL3Z+2DQTU/d1v7aY8K5A60+YOcOvXTg/FtnPLpcbmuruWnlvb+Edr6zygi0p0FcqUusRfIq1cXCuS+fePdt0gbyvmwVO79PfVDSbnPHVVKDVbsWKx5kHPanHPz5z+Hk08G4JntTmC/pfcAPjUM+JQ70MZk9jltTnQvIkL3zoNcKeXOSb+J5ubCigzgExjX1sa3fxHpcYodi2s6+KYaM/tScsNKj0mT2ihi+xTmQd535CcMGeLX16711WHGjoXx4wsF8LXXelEMHRfHCxb440VEOtKTjsXtqqnxJcfy1qyp3FhEJNPaLZBDCM3ALd00lvTp2/fTq70a13H77YW7XnnFj82rVvlE63/6k3egjzkGbrih4+L4mGP88SIiHenxx+KoIouFiIjEqd0COecpMzvKzCzx0aRNpEDmk0844ghfESkqBF/t9HOf89WODjoIvv99aGjYtKsM7XeW1VUWkXb03GNxlApkEekGHS41DXwbOBdoMrN1gAEhhLB5oiNLg0jEgnXrAI9U3H23RywWLSpE4QCeftq/9u4NF1zg933hC4WCGErLK4uItKHnHoujohELFcgikpAOO8ghhIEhhJoQQu8Qwua52z3jgBztIK9b92kRO2MG/OY3MG8ebL45fPGLLb+tsRHWr/dO8gknwKGHwrhxyiuLSNf16GNxlDrIItINSolYYGZHmNn1ucuYpAeVGpECec2Hn2xSxB56KMyaBYsXw8CBcOCBm55QvXw53HOPZ5XXrIHZs2HFCuWVRaTzeuyxOCpaIOskPRFJSIcFsplNAc4Cfp+7nGVmVyc9sMjz72JmPzGzB83s9O56XqBFxOLDd9YVLWLN/HLhhTB/Pgwe7N3irbZq+bimJvjRj2CbbeDWW72rrLyyiJSi0sfi1FAHWUS6QSkZ5MOAPXNnUWNmdwIvAQ0dfaOZ3QGMAZaHEHaPbB8N/BioBW4PIUwpto8QwmLgNDOrAe4Cbi1hzPGIdJC32Xwd2xXJDT/0kN/OF7MzZ/r1SZPgyivhs5+FP/yh8H2NjfDAA359wAC46CIYNKjQVVZeWUTa0OVjcaaoQBaRblBSxAIYHLk+qBP7nwaMjm4ws1p8uqKvArsCx5vZrmb2L2b2SKvL1rnvOQJ4FJjbiecuX6SDXNf0SYu7Wnd399/fry9a5NcbGmDyZLj0UnjrLS+a+/f3k/uiVq/28/++9S2YOBGOPda7z8ori0gbunoszg4VyCLSDUrpIF8FvGRmC/CzpvcDJpey8xDCQjMb3mrz3sCSEMLbAGZ2PzAuhHA13m1uaz+zgdlm9ihwbynPHYtWJ+nlFStS84XyggVw9dVw/fX+deRIOPJImDPHC98BA2D33f1Ev+gsGEuW+AV8saiFC+FLXyp0lhsafH8d5ZXVWRbJpC4fizNFBbKIdIMOV9IDmoF9gJnADGDfEMIvynjObYGlkdvLctuKjWGUmf2nmf037XSQzWyimb1oZi++//77ZQwvondvX7kJfEnTjRsB7xKXUqSee26hq1wYp+/yqqs8r7z55jBqFGy2Wcv9bNwIP/gBDBnis2aceKLyyiI9VULH4uqkAllEukG7HeQQQrOZTQohTAdmd9OYWo/haeDpEh43FZgKUF9fHzp4eGnMPGaxdq3f/uQTGDCASZPafnhbRWq0q9xWXnnWLL9+8cUwZYqf4LdsWWGfq1bBLbn1s7beGi65BIYOVV5ZpCdJw7E4NTQPsoh0g1IyyE+a2ffNbDsz2zJ/KeM53wG2i9wemttWNjMba2ZTV65cGcfuXJGYRVuKdZZLyStffDFcdhksXQp33QX9+nlBHLV8uc9qdOyxfgLgxInKK4v0IHEfi6uTOsgi0g1KySAfm/t6RmRbAD7XxedcBOxoZiPwwvg44IQu7quFEMIcYE59ff2pcewP2GS56fa01VnuSl755JO9Szx+vDdLtt8eXn215X5ffNEv4EmQV1/1qIbyyiKZFfexuDppHmQR6QalZJAnhxBGtLqUdEA2s/uA54CdzWyZmZ0SQtgInAk8DiwGpocQ3ijzdSSnjeWmO6PcvHJtrc+d/OijvhjJyJG+PaqxEc4+G7bd1k/smzhReWWRLCn3WJwp6iCLSDcoJYN8HtClE0FCCMcX2T6XBKZsM7OxwNgddtghvp12ooPcljjzyg8/7NcvvNBX4OvTBz78sLDPv//dT+wD+NznfIq5nXdWXlmk2pV7LM4UFcgi0g0qkUFOTAhhTghh4qBBMU4PWmYHuZhy8spXXglXXAEffAA33eRDjJ63AvD22/7eMWaMP37SJJ9qTnllkapVNcfiRKlAFpFuUIkMcnXpxEl6nRFXXvnMM2G33bzw7dcP/umfCnMp5z31lF/MoK4O/vpX3668skhV6dnH4jwVyCLSDTrsILeReUtt7i3xWSy6ELHojHLzyr16wdSp8OCD3lEeMaLlPkKA9evh3/4NdtkFFi+Gs85SXlmkGlTTsThRKpBFpBsULZDNbFLk+tGt7rsqyUF1VTVFLNoyaVLHxXE0rzxpUsu8cn5O5S239FX7Vq3yYrpPn5Z1PsCbb8IZZ/j0crvv7lPMPfFEoau8YEHHxfExx/jjRSQ51XgsTpTmQRaRbtBeB/m4yPWGVveNTmAs6ZRQxKIzyskr33ijZ5A/+shzy3V1PjNG1Guvwccfw6GH+qIkV1+tvLJIiuhYHNW6gxziWRdKRCSqvQLZilxv63YqVHvEopi2Osvt5ZXzneVoXvnZZ+Gii+Cxx7wB06eP55WjQvBlrU891bvPGzYUZsnId5ZvuKHj4lidZZFYVd2xOFF1dT75O0BTkx+oRERi1l6BHIpcb+t2KlR7xKIzys0r19XBz38Od9zhnwG22qrlPpqb/fPAhAmw777wj3/AeecpryxSAVV3LE6ccsgikrD2ZrHYw8w+xjsUfXPXyd3uU/zbMiYFHeS2xDm/8qOP+vWJE+HOO2HjRm/M5D3/PBx9tBfW++7rUY0999T8yiLdRMfi1gYMgBUr/Prq1Zt+whcRKVPRDnIIoTaEsHkIYWAIoVfuev527+4cZEWltINcTDl55dtug6uu8m7x977ns2JEhQC//rXnmQ85BO691zPLyiuLJEfH4jaogywiCStloZCqkXgGuQoK5Djyyr/7nV+fP9/fhzbbDFqnVpqa4Pbb4dhj/f2psbHQYFdeWUQSpQJZRBKWqQI5kQxySiMWnVFOXrm21gvkGTN8RozNNmvZVAcvltetg8MPh8MO887z5MnKK4tIQlQgi0jCSllJr2ersohFW+LMK8+b53nkI4/0BUkaGwv7C8HvnzcPamrg4IN9irmRI5VXFpEYqUAWkYRlqoOciCqLWHRGV/PKF1wA998PU6bAX/4Cp5yy6dzKzc0e0fjwQ59fed48mDZt07xye88rItImLRYiIglTB7kjGYhYFNNWZ7m9vHK+sxzNK48c6VnkE06AI47wjrKZL2md19gI113nEY38FHPNzX7ftdcWMsgdFccLFniRXqwjLiI9RLSDvGZN5cYhIpmVqQ5yIifpZSBi0RldzSubefa4Tx9f8vrii30uf4ssY7BxoxfLa9b4LBgnngif/Wz7XeXWz60T+kREEQsRSVqmCmSdpFe+tmbBgOJ55fwsGPm88qxZcPLJft/jj8MWW8CYMW1HMO69F77xDV+1r7HRv+ZpqjgRKUoFsogkLFMFciJ6WAe5mK7mlS+80BciueYa+O1vvVsc7SqDF8vr1sG4cf49c+fC5z+vqeJEpAgVyCKSMBXIHcnwSXqdUe78ylOmwMqVMHMmPPYY9OvnkYyaVr+BTz/t08WdfDLstpumihORNqhAFpGE6SS9jvSwiEVnlJpX3n9/P5kv31Xu3dsvvXr50tZPPQU/+YlnlPPefdcvAOefD3/6Exx4oKaKExFUIItI4lQgd0QRi6LinF/5a1+Do47yuZMffbTliekbN8LNN8Ott8I++3imuVcvzzvnO8t77dVy/+0V7poJQ6TKqUAWkYRlKmKhpabToat55RkzPH7Rqxccd5yv2te7d+H7m5rg2Wdh7Vo/oe+mm3xZ7Pp65ZVFehTNgywiCctUgaxZLNKhK3nlPDNfkW/iRF9cZPPN4ZxzYN99W+4vBO9Cf+ELcNZZfr/yyiI9hOZBFpGEKWLREUUsYtFeXhk2jV7kYxAPPODbGxrgzTdh113huecKC40AvP66X8z8cStXwpe+pLyySGYpYiEiCVOB3JFogfzJJ966bD1PmXSovcxvscxy/mtDg3eHr7/eFyh58kmYMMGjEk8/XTi5LwTYsAEuv9z/AnvAAb66X02N8soimaICWUQSlqmIRSJ69fILeNuysbGy48mYUorU6NLWCxbAQQd5p/mFF3y6uLFjW2aVwf/qOmeOv3euXg333APLlnlxrLyySJVTgSwiCVOBXAqdqJeYri5tDYVG/jnn+Kp9W24JX/86jBjRcj/NzfDTn8J228FVV/ky18ori3SOmf0/M/uJmd1uZr+u6GBUIItIwhSxKEXfvoV1kD/5BOI8CbCHi3OquAcf9OuTJ8MVV3ih/PLLLff75JP+ta7OV/mrrS3MgqG8smSVmd0BjAGWhxB2j2wfDfwYqAVuDyFMKbaPEMIzwDNmNh5YVOxx3aJfv8L1tWt9ipvW69mLiJRBHeRS6ES9btfVqeIaGuC88+CSS+Cll3xO5YEDfenqqA0b/LPO2Wf7qn1jxvhS1+PHF/Yd7SyXEgVRZ1lSbBowOrrBzGqBW4CvArsCx5vZrmb2L2b2SKvL1pFvPQG4t7sG3qaampZTva1dW7mxiEgmqYNcCkUsul1bneX2porLd5ajeeWRzkj0zwAAG5lJREFUI+Gww+Dhh73wHTjQu8ULF3rDKe9vf4Np0/x6ba3PxbzXXoW8ckOD76+UKIhIGoUQFprZ8Fab9waWhBDeBjCz+4FxIYSr8W7zJsxsGLAyhLAqweGWpn//whRva9b4f3ARkZhkqoOcyEIhoLmQU6LcvLIZXHwxzJ8Pgwd717h1WqapyTvBn/kM/OxnPluG8sqSUdsCSyO3l+W2tecU4GftPcDMJprZi2b24vvvv1/mENuhHLKIJChTHeQQwhxgTn19/amx7lgRi1SIM688c2ahO3zllbD11vDHPxb2uX493H23Xx882AvrrbcudJWVV5aeKIRwaQmPmQpMBaivrw+JDUYFsogkKFMd5MSog5xq5eSVGxrgBz+AJUv8vv79Yfjwlvv56COPOJ58MnznOz5TxvjxyitL1XsH2C5ye2huW3VQgSwiCcpUBzkx6iCnWlx55aOP9mjF+PH+3rvLLvDii74ASd4bb/gFfO7lRYtgv/2UV5aqtAjY0cxG4IXxcfgJeNVBBbKIJEgd5FLoJL2qU25euaYGrrkG5s2DzTf3pat7tfo42dgI558P22zj8zB/85vKK0s6mdl9wHPAzma2zMxOCSFsBM4EHgcWA9NDCG9UcpydogJZRBKkDnIpFLGoOnHmlWfN8usXXQTXXefvy++9V9jnP/7hxTT4YiSXXgrbb6+8sqRHCOH4ItvnAnO7eTjxUIEsIglSB7kUilhkRjl55csug8svh3ffhdtu889NrWfBWLrU36vHj/ds87nnwpFHKq8sEjsVyCKSIHWQS6GIRWbElVf+1re8Szx+vC/qNWwYvPlmy/0uXOgX8JX73n7b96e8skgMoguF5OdDFhGJiTrIpVDEItPKzSv36gX/9V8ezRgwAHbaadP9bNjgRfWOO8Jrr8F3v6u8skhZ1EEWkQSpg1wKRSwyLc688uzZfv288+Dmm31lvuh795IlcNZZfn233Ty2sfvuyiuLdJoKZBFJkDrIpVAHuUcqJ698/fXwwx/CihUwZQpstplPCxf1xhvw8ccwejTcdJMvWKK8skiJVCCLSIKqokA2s/65pUvHVGQA6iD3SJMmdVwc5+2/vz++dV75mWd8Krh58/xzVt++MHRoy32G4J3ob38bVq3yOMaHH/p9+c7yDTd0XBwfc4w/XqRHUIEsIglKtEA2szvMbLmZvd5q+2gze8vMlpjZ5BJ2dT5QuT8q6yQ9ySk3r9y7N9x1F9x5p5/cN2RIy300N/sfKSZMgH32gQ8+8LiG8soirahAFpEEJZ1BngbcDNyV32BmtcAtwMHAMmCRmc0GaoGrW33/N4E9gN8DfagURSwkJ8688iOP+PXTToOf/QyammDjxsI+f/Mbv98M9t0XrrgC9txTeWURQAWyiCQq0Q5yCGEh8GGrzXsDS0IIb4cQNgD3A+NCCK+FEMa0uiwHRgH74Eugnmpm3R8LUcRCOlBOXvm//xuuusoXHDnvvE2zyiHAr38NH30EhxwC994Lt9yivLL0cCqQRSRBlZjFYltgaeT2MuCLxR4cQrgQwMz+DfgghNDc1uPMbCIwEWDYsGFxjdUpYiEdiGt+5Wuvha9+FcaN8yxynz6wcmXhe5ua4Pbb/VJb6yf/rV/v92l+ZelRNA+yiCSoKk7SAwghTAshPNLO/VNDCPUhhPohrYOd5VLEQrqgnLxyTY0XvzNmwI03+vU+rUJGTU2wdi0cdhiMGeOLkUyerLyy9BDqIItIgirRQX4H2C5ye2huW9nMbCwwdocddohjdwWKWEgXxJlXnjcPjj7aYxUPPgiNjYX9hQCPPuqX2lo49FCfMm7kSOWVJcNUIItIgirRQV4E7GhmI8ysDjgOmB3HjkMIc0IIEwcNGhTH7grUQZYYdTWvfMEFcP/9Pq/yn/8M//7v3mmOamqCxx7zaeIOPRTmz/cZM1rnldt7XpGqoAJZRBKU9DRv9wHPATub2TIzOyWEsBE4E3gcWAxMDyG8keQ4yqYOssQojvmV334b7rgDnnjCo5h1dX6Jamz0Ynr8eI9iNDX5NHJQiF6UUhwreiGpVFfn67yD/7Jv2FDZ8YhIpiQasQghHF9k+1xgbtzPl1jEQifpScJKzSvvv79HJ/JdZTOvEWpr4Re/gP/5Hy9moxGM/PXGRp8F46ST/OuRR3o8Y9as9otjRS8klcy8i/zRR3579WrYcsvKjklEMqNqTtIrhSIWUq3a6ipD8bxyvquczyvPmgUnnwwHHgiPP+51wmGHeeEc1dzsC5WcdJLXE42N3l3O01RxUlUUsxCRhGSqQDazsWY2dWV0Xqw4KGIhFdLVvPKFF/qJfddcA88/D0cc4Q23qKYm/3UeMwYOPhieegq+8AUtbS1VRAWyiCQkUwWyOsiSNeXmladM8Q7xww97wdy3r0cyWhfLTz4JBx3kJ/7tsYemipMqobmQRSQhlZjmrfpEO8iffOLBzdYVhkg36WpeOX8iX+/efoLfk0/Cbbd5Jzlv6VK/AJx/PrzzDowapaniJKXUQRaRhGSqg5wYM1+pIU9dZKmgOPLKp53mt+fPh8GD/YS96B9KADZu9KjFUUfBv/4rjB2rpa0lZVQgi0hCMlUgJ5ZBBsUsJPW6klc+4ACYOdPzx3V1vhhJXV3L+ZUbG+GXv/S/YK9aBVOnwuLFhUVIlFeWilGBLCIJyVSBnFgGGXSinqReV/LKeWaeHDr9dF9oZIst4IwzYM89W+4vBF+sZNddfVnr/fZTXlkqSAWyiCREGeRSaS5kqULt5ZVh06WtFy3ywvmBB3x7QwP85S+w007wwgteIOe98IJfamr8cevXa2lr6WYqkEUkISqQS6WIhVShaJe4tWKZ5fzXhgbvDl9/PZx7rq/aN2GCz3Lx7LOFVfmam30Rswsu8M7zQQf5tHI1NYVFSK691ovn/fcvLa+cL9RF2qUCWUQSkqmIRaIZZEUsJENKKVKjS1svWOBzJc+aBa+84nXJ6NGFlX7zVqzw7vPq1Z5ZnjkTPvhAeWVJiApkEUlIpgrkRDPI6iBLhpQ6Vdy55xZO6MvLz3A4aZLPgrHFFnDssfDZz7bcT1MT3Hyzb7/pJp8FQ3lliZXmQRaRhChiUSp1kCVDisUXisUuotGIfF45/7gZM/z6+efDFVfA0KHw+98X9tnUVPie/v3hootg4EDllSUG6iCLSEIy1UFOlE7Skx6gq0tbNzR40X3ppfDGG75y34ABsMsuLfezZo3/95k4EU491aeVGz9e8ytLF6lAFpGEqEAulSIW0gOUu7R1Pq98xBEwe7avxDdwIHz5yy3nVgb44x/h1lvh4499OeyFC1vOhKG8snRIBbKIJCRTBbJO0hOJX7l5ZTOPXjz+OAwaBAce2PaqfT/4AQwZ4if2nXSS8spSAhXIIpKQTGWQQwhzgDn19fWnxr5zRSykh4ozr/zQQ379oou827zFFrB0aWGfq1b5iX0A22wDl1wCw4YpryxFqEAWkYRkqoOcKEUsRFooJ6980UVw2WXw17/C3XdDv36w9dYt9/Pee55ZPvpoX7Xv9NPhyCOVV5YIFcgikpBMdZATpYiFSAttdZbbyyvnO8vRvPLIkR6n2HZbL3z794ftt4dXX2253/yqfQB1dT5LxqhRhc5yQ4Pvr5QoiGSICmQRSYg6yKVSB1mkQ+XmlWtr4Uc/gkce8dpnjz023c+GDXDmmR69eP557ywrr9xDRQtkzYMsIjFSB7lU6iCLdCjOvPLs2X79ggu8aK6rg48+Kuxz2TK/D2Cnnfwkv112UV65R+nXr3B9zRpf97z1dCkiIl2QqSNJorNY6CQ9kS4rJ6989dU+C8Y//gE33uifVaOfVwH+8Ac/we/wwz2+ccklyiv3CLW1hWNzCDo2i0hsMlUga6lpkXSKY37lX/0Kzj4b5s71bnLfvjBiRMt9huD3f/e7Pr/y+vXw7rt+n+ZXzijlkEUkAZkqkBOliIVIrMrNK/fuDT/9Kdx3n/+lfdttW+4jBC+QTzgBPv95n07u3HOVV84cFcgikgBlkEuliIVIrOLMKz/yiF//znfgttsKxXHeSy/BN77h1+vr4fLL/QRA5ZUzQAWyiCRAHeRSKWIh0i3KySvffDNceSWsWOFzLffu7d3mqBdfhJUr4ZBDYNo0PwFQeeUqpgJZRBKgArlUiliIdIs48srPP19Y3nrAAP/vu9VWLffZ3Ax33eXzMK9eDY2NsHat36e8chVRgSwiCVCBXCp1kEUqppy8ck2Nn9Q3fTrccosXy/37t9xHU5N/7h0zxjvLzc2+ep/yylVAcyGLSAKUQS6VOsgiFRNnXnnuXL/+ta/BL37hneMQCvt84gm/1NTAAQfAD3/oK/4pr5xS0U876iCLSEzUQS6VTtITSZ1y8so//7nHMf72NzjtNJ9SN6q5GZ56yvPMhxziJwLeccemeeX2njdLzGxXM5tuZrea2YRKj+dTiliISAIyVSB320IhiliIpEIceeXFi+HWW2H+fG9G5udYjtq40fPIRx7pOeWmJr+U8rxpYGZ3mNlyM3u91fbRZvaWmS0xs8kd7OarwE0hhNOBryc22M5SgSwiCchUgZzoQiGKWIhUha7mlc2gVy//rz5rFlx2mRfL0ZWLm5o8krFmDRx6KBx/vBfYaS6Oc6YBo6MbzKwWuAUvfHcFjs91if/FzB5pddkauBs4zsyuA1qd8lhBKpBFJAHKIJdKEQuRqhBnXvmxx+Doo+ErX/GIRbRr3NwM99/vl169YOrU1BbHhBAWmtnwVpv3BpaEEN4GMLP7gXEhhKuBMUV2dUausJ5Z7LnMbCIwEWDYsGFljrwEKpBFJAGZ6iAnShELkarW1bzyBRfA7Nk+K8XLL8OECZvOrRyC55KrzLbA0sjtZbltbTKz4WY2FbgLuK7Y40IIU0MI9SGE+iFDhsQ22KJUIItIAtRBLlV+xYEQ/G+sTU2bntUjIqnVVme5vbxyvrMczSuPHAkPPOCzXIwfDxs2eCe5Vy8vntPaQY5DCOHP5DrDqaICWUQSoA5yqczURRbJmK7mlXv18s/M/frBjBk+u8Uxx7ScJ7kKvANsF7k9NLetumgeZBFJgDrIndGnT2GprXXrNl1tQESqSpx55enTU3+iXmuLgB3NbAReGB8HnFDZIXWB5kEWkQSog9wZOlFPpEfoal45XySnrZNsZvcBzwE7m9kyMzslhLAROBN4HFgMTA8hvFHJcXaJIhYikgB1kDtDEQuRHqEreeX89TR2kkMIxxfZPheY283DiZcKZBFJgDrInaG5kEV6rPbyylHRrrJ0AxXIIpIAdZA7QxELkR6rWF65LdGusiRMBbKIJCD1HWQzG2Vmz5jZT8xsVEUHo4iFiEi6qEAWkQQkWiCb2R1mttzMXm+1fbSZvWVmS8xscge7CcBqoA8+kX3lKGIhIpIum21WmJN+wwafp15EpExJRyymATfjKy8BkFum9BbgYLzgXWRms4Fa4OpW3/9N4JkQwq/MbBvgBuDEhMdcnDrIIiLpYuZd5JUr/faaNTB4cGXHJCJVL9ECOYSw0MyGt9q8N7AkhPA2gJndD4wLIVwNjGlndyuAzZIYZ8nUQRYRSZ/+/QsF8urVKpBFpGyVOElvW2Bp5PYy4IvFHmxmXwMOBQbj3ehij5tIbhnUYcOGxTLQTegkPRGR9FEOWURilvpZLEIIM4GZJTxuKjAVoL6+PiQyGEUsRETSRwWyiMSsErNYvANsF7k9NLetbGY21symrsz/qS1uiliIiKSPCmQRiVklCuRFwI5mNsLM6oDjgNlx7DiEMCeEMHHQoEFx7G5T6iCLiKSPCmQRiVnS07zdBzwH7Gxmy8zslBDCRuBM4HFgMTA9hPBGTM+XbAdZGWQRkfRRgSwiMUt6Fovji2yfC8xN4PnmAHPq6+tPjXvfgCIWIiJppAJZRGKW+pX0UkURCxGR9IkWyGvWVG4cIpIZmSqQdZKeiEgP1L9/4bo6yCISg0wVyN16kp4KZBGRdFDEQkRilqkCOXGKWIiIpI8KZBGJmQrkzlDEQkQkfVQgi0jMMlUgd+s0b+ogi4ikgwpkEYlZpgpkZZBFRHogFcgiErNMFciJCgH+938Lt194wc+cPuYYvx5C5cYmItJThQB//Wvh9mOP6dgsImVTgVyKxkY44QSYOLHl9rVrYcYMOOAAv7+xsTLjExHpifLH5nPOabldx2YRKVOmCuREMsghwNe/DrNntx2raG72iekfftgfp26FiEjyosfmts4J0bFZRMqQqQI5kQzyCy/AnDnekWjPunX+uEWL4ntuERFpm47NIpKgTBXIifiP/yj9hLx16/zxIiKSLB2bRSRBKpA78uij/qe6UjQ3++NFRCRZOjaLSIIyVSAnkkHu7HRumv5NRCR5OjaLSIIyVSAnkkGOzn2cxONFRKTzdGwWkQRlqkBOxOGHQ02JP6aaGn+8iIgkS8dmEUmQCuSOfO97pXce+vTxx4uISLJ0bBaRBKlA7sjee8PYsR0fiPv2hSOOgL326p5xiYj0ZDo2i0iCVCB3xAzuugvGjfPlS1v/Sa+mBvr18/vvussfLyIiydKxWUQSpAK5FL17w733wi9/CUcdVTgY9+8PEybA00/Dfff540REpHvo2CwiCelV6QHEyczGAmN32GGHJHbuf9KbPj3+fYuISNfo2CwiCchUBzmRad5EREREpEfJVIEsIiIiIlIuFcgiIiIiIhEqkEVEREREIlQgi4iIiIhEqEAWEREREYmwEEKlxxA7M3sf+Esnv+0zwAcJDCctsvz69NqqV5ZfX0ev7f+GEIZ012AqIYPH4rSOLa3jAo2tq9I6trSOC7o+tjaPxZkskLvCzF4MIdRXehxJyfLr02urXll+fVl+bUlK888trWNL67hAY+uqtI4treOC+MemiIWIiIiISIQKZBERERGRCBXIBVMrPYCEZfn16bVVryy/viy/tiSl+eeW1rGldVygsXVVWseW1nFBzGNTBllEREREJEIdZBERERGRCBXIIiIiIiIRKpABMxttZm+Z2RIzm1zp8ZTLzO4ws+Vm9npk25Zm9oSZ/W/u6xaVHGNXmdl2ZrbAzH5vZm+Y2Vm57VX/+sysj5m9YGav5F7bZbntI8zsN7nfz1+YWV2lx9pVZlZrZi+Z2SO525l4bWb2ZzN7zcxeNrMXc9uq/neyu6X1WNzWv28Fx5La43uRsf3AzN7J/exeNrPDKjCu1L5vtDO2NPzcUvme1M64ppnZnyI/sz3LeZ4eXyCbWS1wC/BVYFfgeDPbtbKjKts0YHSrbZOBp0IIOwJP5W5Xo43A90IIuwL7AGfk/r2y8PrWAweEEPYA9gRGm9k+wDXAjSGEHYAVwCkVHGO5zgIWR25n6bXtH0LYMzIPZxZ+J7tNFRyLW//7Vso00nt8n8amYwP/P75n7jK3m8cE6X7fKDY2qPzPLa3vScXGBXBe5Gf2cjlP0uMLZGBvYEkI4e0QwgbgfmBchcdUlhDCQuDDVpvHAXfmrt8JjO/WQcUkhPD3EMLvctdX4cXWtmTg9QW3Onezd+4SgAOAB3Pbq/K1AZjZUOBw4PbcbSMjr62Iqv+d7GaZOxYnIc3H9yJjq7g0v2+0M7aKS+t7UjvjipUKZP9FXBq5vYyU/HLGbJsQwt9z198FtqnkYOJgZsOBkcBvyMjry0UQXgaWA08AfwQ+CiFszD2kmn8/fwRMAppzt7ciO68tAPPN7LdmNjG3LRO/k90ozcfitv590yTtv2tnmtmruQhGRaNGaX7faDU2SMHPLa3vSa3HFULI/8yuzP3MbjSzzcp5DhXIPVDwuf2qen4/MxsAzADODiF8HL2vml9fCKEphLAnMBTvqP1zhYcUCzMbAywPIfy20mNJyFdCCJ/H4wFnmNl+0Tur+XdSgA7+fdMkhb9rtwLb438K/zvwH5UaSJrfN9oYWyp+bml9T2o9LjPbHWjAx7cXsCVwfjnPoQIZ3gG2i9wemtuWNe+Z2f8ByH1dXuHxdJmZ9cYPJPeEEGbmNmfm9QGEED4CFgD7AoPNrFfurmr9/fwycISZ/Rn/0/kBwI/JxmsjhPBO7uty4CH8jSRTv5PdILXH4iL/vmmS2t+1EMJ7uWKmGbiNCv3s0vy+0dbY0vJzy0vre1JkXKNzcZUQQlgP/Iwyf2YqkGERsGPurMw64DhgdoXHlITZwDdy178BPFzBsXRZLrf6U2BxCOGGyF1V//rMbIiZDc5d7wscjOfRFgATcg+rytcWQmgIIQwNIQzH/4/9MoRwIhl4bWbW38wG5q8DhwCvk4HfyW6WymNxO/++aZLa37V8AZpzJBX42aX5faPY2FLyc0vle1KRcb0Z+bBjeC66rJ+ZVtIDctOn/AioBe4IIVxZ4SGVxczuA0YBnwHeAy4FZgHTgWHAX4BjQgipO5miI2b2FeAZ4DUKWdYL8MxWVb8+M/tX/ISHWvzD6/QQwuVm9jm867ol8BJwUu4TclUys1HA90MIY7Lw2nKv4aHczV7AvSGEK81sK6r8d7K7pfFYXOzft4LjSe3xvcjYRuExgQD8Gfh2JPfbXeNK7ftGO2M7nsr/3FL5ntTOuH4JDAEMeBk4LXIyX+efRwWyiIiIiEiBIhYiIiIiIhEqkEVEREREIlQgi4iIiIhEqEAWEREREYlQgSwiIiIiEqECWTLJzFbnvg43sxNi3vcFrW7/Os79i4hkgY7DUs1UIEvWDQc6dWCOrBBUTIsDcwjhS50ck4hITzIcHYelyqhAlqybAvw/M3vZzM4xs1ozu87MFpnZq2b2bfDFK8zsGTObDfw+t22Wmf3WzN4ws4m5bVOAvrn93ZPblu+SWG7fr5vZa2Z2bGTfT5vZg2b2ppndk1vpR0SkJ9BxWKpOR5/QRKrdZHKrtgHkDrArQwh7mdlmwLNmNj/32M8Du4cQ/pS7/c0Qwoe5pSwXmdmMEMJkMzszhLBnG8/1NXzloz3wlaQWmdnC3H0jgd2AvwHPAl8G/if+lysikjo6DkvVUQdZeppDgK+b2cv4MqNbATvm7nshclAG+K6ZvQI8D2wXeVwxXwHuCyE0hRDeA34F7BXZ97IQQjO+BObwWF6NiEj10XFYUk8dZOlpDPhOCOHxFhvNRgFrWt0+CNg3hLDWzJ4G+pTxvNF16pvQ/z0R6bl0HJbUUwdZsm4VMDBy+3HgdDPrDWBmO5lZ/za+bxCwIndQ/mdgn8h9jfnvb+UZ4Nhcvm4IsB/wQiyvQkSkeuk4LFVHn54k614FmnJ/opsG/Bj/s9rvcidovA+Mb+P7HgNOM7PFwFv4n/fypgKvmtnvQggnRrY/BOwLvAIEYFII4d3cgV1EpKfScViqjoUQKj0GEREREZHUUMRCRERERCRCBbKIiIiISIQKZBERERGRCBXIIiIiIiIRKpBFRERERCJUIIuIiIiIRKhAFhERERGJ+P953LcUVxIcrwAAAABJRU5ErkJggg==\n"
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    {
      "cell_type": "markdown",
      "source": [
        "# References\n",
        "\n",
        "[1] A Aristodemo and L Gemignani. Accelerating the sinkhorn–knopp iteration by arnoldi-type\n",
        "methods. Calcolo, 57(1):1–17, 2020.\n",
        "\n",
        "[2] Richard Sinkhorn. Diagonal equivalence to matrices with prescribed row and column sums.\n",
        "The American Mathematical Monthly, 74(4):402–405, 1967.\n",
        "\n",
        "[3] Marco Cuturi. Sinkhorn distances: lightspeed computation of optimal transport. In NIPS,\n",
        "volume 2, page 4, 2013.\n",
        "\n",
        "[4] R ́emi Flamary, Marco Cuturi, Nicolas Courty, and Alain Rakotomamonjy. Wasserstein dis-\n",
        "criminant analysis. Machine Learning, 107(12):1923–1945, 2018."
      ],
      "metadata": {
        "id": "H2d4QGS2Utmh"
      }
    }
  ]
}