{
    "cells": [
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "# Tutorial 11a - Random Forest Regressor to Predict Optimal Lens Properties\n",
                "### Building a Random Forest Regressor to Predict Optimal Lens Properties\n",
                "\n",
                "This notebook demonstrates how to build and train a random forest regressor to predict the radius of curvature of a plano-convex lens in order to minimize the RMS spot size.\n",
                "\n",
                "#### Steps Included:\n",
                "\n",
                "1. **Data Preparation**: Generate and preprocess a dataset of optimal lens designs.\n",
                "2. **Model Training**: Train the random forest regressor using the prepared dataset.\n",
                "3. **Model Evaluation**: Evaluate the performance of the trained model.\n",
                "4. **Prediction**: Use the trained model to predict the optimal radius of curvature for new lens parameters to minimize the RMS spot size."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 1,
            "metadata": {},
            "outputs": [],
            "source": [
                "import warnings\n",
                "\n",
                "import matplotlib.pyplot as plt\n",
                "import numpy as np\n",
                "import pandas as pd\n",
                "import seaborn as sns\n",
                "from sklearn.ensemble import RandomForestRegressor\n",
                "from sklearn.metrics import mean_squared_error\n",
                "from sklearn.model_selection import train_test_split\n",
                "from tqdm import tqdm\n",
                "\n",
                "from optiland import analysis, materials, optic, optimization"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Build a configurable plano-convex singlet\n",
                "\n",
                "We start by defining a class, which parameterizes a plano-convex lens based on three properties:\n",
                "\n",
                "1. Entrance Pupil Diameter (EPD) in mm\n",
                "2. Index of refraction at 587 nm\n",
                "3. Radius of curvature of the lens front surface"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "metadata": {},
            "outputs": [],
            "source": [
                "class ConfigurableSinglet(optic.Optic):\n",
                "    \"\"\"A class to represent a configurable singlet lens.\n",
                "\n",
                "    This class inherits from the `optic.Optic` class and allows for the creation\n",
                "    of a singlet lens with configurable parameters: entrance pupil diameter (EPD),\n",
                "    refractive index (n), and radius of curvature (R). The lens thickness is fixed\n",
                "    at 1/5 of the entrance pupil diameter to maintain a reasonable aspect ratio.\n",
                "\n",
                "    Attributes:\n",
                "        epd (float): Entrance pupil diameter.\n",
                "        n (float): Refractive index of the lens material.\n",
                "        R (float): Radius of curvature of the lens.\n",
                "\n",
                "    \"\"\"\n",
                "\n",
                "    def __init__(self, epd, n, R):\n",
                "        super().__init__()\n",
                "\n",
                "        mat = materials.IdealMaterial(n=n)\n",
                "\n",
                "        # add surfaces\n",
                "        self.surfaces.add(index=0, radius=np.inf, thickness=np.inf)\n",
                "        self.surfaces.add(\n",
                "            index=1,\n",
                "            radius=R,\n",
                "            thickness=epd / 5,\n",
                "            is_stop=True,\n",
                "            material=mat,\n",
                "        )\n",
                "        self.surfaces.add(index=2, radius=np.inf, thickness=15)\n",
                "        self.surfaces.add(index=3)\n",
                "\n",
                "        # add aperture\n",
                "        self.set_aperture(aperture_type=\"EPD\", value=epd)\n",
                "\n",
                "        # add field\n",
                "        self.fields.set_type(field_type=\"angle\")\n",
                "        self.fields.add(y=0)\n",
                "\n",
                "        # add wavelength\n",
                "        self.wavelengths.add(value=0.587, is_primary=True)\n",
                "\n",
                "        # move image plane to paraxial focus\n",
                "        self.image_solve()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Generate and draw a lens\n",
                "\n",
                "This is an example of one possible lens configuration."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 3,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 1000x400 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "lens = ConfigurableSinglet(epd=25, n=1.5, R=25)\n",
                "lens.draw(num_rays=5)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Data preparation\n",
                "\n",
                "We build a dataset that we will use to train our random forest regressor. The ultimate goal of the predictive model will be to predict the radius of curvature of our plano-convex lens given the lens f-number and the refractive index (at 587 nm). We will run 2500 simulations, each with a different f-number and refractive index. We choose the following ranges of our variables:\n",
                "\n",
                "- F-number: 2 to 10\n",
                "- Refractive Index: 1.4 to 2.0"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 4,
            "metadata": {},
            "outputs": [],
            "source": [
                "fno = np.linspace(2, 10, 50)\n",
                "n = np.linspace(1.4, 2.0, 50)\n",
                "\n",
                "# Total number of simulations = 50^2 = 2500\n",
                "fno, n = np.meshgrid(fno, n)\n",
                "fno = fno.ravel()\n",
                "n = n.ravel()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Generate helper function for optimization\n",
                "\n",
                "This function will identify the optimal singlet, given the f-number and refractive index of the lens."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 5,
            "metadata": {},
            "outputs": [],
            "source": [
                "def optimize_lens(lens):\n",
                "    # Define empty optimization problem\n",
                "    problem = optimization.OptimizationProblem()\n",
                "\n",
                "    # Add target for RMS spot size - use on-axis field and a hexapolar distribution\n",
                "    # Surface number is set to -1 to indicate the image plane\n",
                "    input_data = {\n",
                "        \"optic\": lens,\n",
                "        \"surface_number\": -1,\n",
                "        \"Hx\": 0,\n",
                "        \"Hy\": 0,\n",
                "        \"num_rays\": 5,\n",
                "        \"wavelength\": 0.587,\n",
                "        \"distribution\": \"hexapolar\",\n",
                "    }\n",
                "    problem.add_operand(\n",
                "        operand_type=\"rms_spot_size\",\n",
                "        target=0,\n",
                "        weight=10,\n",
                "        input_data=input_data,\n",
                "    )\n",
                "\n",
                "    # Add target for focal length\n",
                "    problem.add_operand(\n",
                "        operand_type=\"f2\",\n",
                "        target=20,\n",
                "        weight=1,\n",
                "        input_data={\"optic\": lens},\n",
                "    )\n",
                "\n",
                "    # Allow the thickness to image plane and the radius of curvature to vary\n",
                "    problem.add_variable(lens, \"radius\", surface_number=1)  # first lens surface\n",
                "    problem.add_variable(lens, \"thickness\", surface_number=2)\n",
                "\n",
                "    # Define optimizer\n",
                "    optimizer = optimization.OptimizerGeneric(problem)\n",
                "\n",
                "    # Optimize - ignore warnings if ray errors occur\n",
                "    with warnings.catch_warnings():\n",
                "        warnings.simplefilter(\"ignore\")\n",
                "        optimizer.optimize(tol=1e-6)\n",
                "\n",
                "    # Retrieve optimized rms spot size\n",
                "    rms_spot_size = problem.operands[0].value\n",
                "\n",
                "    # Retrieve optimized focal length\n",
                "    f_opt = problem.operands[1].value\n",
                "\n",
                "    return lens, rms_spot_size, f_opt"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Optimize lenses\n",
                "\n",
                "We will record all data in a pandas dataframe. Without loss of generality, we fix the lens focal length to 20 mm. During optimization, we also enforce this."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 6,
            "metadata": {},
            "outputs": [],
            "source": [
                "df = pd.DataFrame({\"FNO\": fno, \"n\": n})\n",
                "\n",
                "df[\"EPD\"] = 20 / df[\"FNO\"]\n",
                "\n",
                "# Variables to store the optimized values\n",
                "df[\"R_opt\"] = np.nan\n",
                "df[\"rms_spot_size\"] = np.nan\n",
                "df[\"f_opt\"] = np.nan"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Run optimization for 2500 systems. This takes 3-4 minutes on the author's machine."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 7,
            "metadata": {},
            "outputs": [
                {
                    "name": "stderr",
                    "output_type": "stream",
                    "text": [
                        "100%|██████████| 2500/2500 [03:38<00:00, 11.44it/s]\n"
                    ]
                }
            ],
            "source": [
                "for k, row in tqdm(df.iterrows(), total=len(df)):\n",
                "    # Generate starting lens\n",
                "    lens = ConfigurableSinglet(epd=row[\"EPD\"], n=row[\"n\"], R=15)\n",
                "\n",
                "    # Optimize lens\n",
                "    lens, rms_spot_size, f_opt = optimize_lens(lens)\n",
                "\n",
                "    # Store optimized values\n",
                "    df.loc[k, \"R_opt\"] = lens.surfaces.radii[1]\n",
                "    df.loc[k, \"rms_spot_size\"] = rms_spot_size\n",
                "    df.loc[k, \"f_opt\"] = f_opt"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Explore the dataset\n",
                "\n",
                "Not all systems may have been fully optimized, so we will exclude these when building the random forest model. We can check for optimization success by comparing the resulting focal length to our target of 20 mm."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 8,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "optimization_success\n",
                            "True     2352\n",
                            "False     148\n",
                            "Name: count, dtype: int64"
                        ]
                    },
                    "execution_count": 8,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "df[\"optimization_success\"] = (\n",
                "    np.abs(df[\"f_opt\"] - 20) < 0.01\n",
                ")  # choose a tolerance of 0.01 mm\n",
                "\n",
                "# View the number of successes and failures\n",
                "df[\"optimization_success\"].value_counts()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Investigate correlations between lens properties and optimized results."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 9,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "<Axes: >"
                        ]
                    },
                    "execution_count": 9,
                    "metadata": {},
                    "output_type": "execute_result"
                },
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 900x700 with 2 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "# Get dataframe of successful optimizations\n",
                "df_success = df[df.optimization_success]\n",
                "\n",
                "# Compute correlation matrix (exclude optimization_success & focal length columns)\n",
                "corr = df_success.drop(columns=[\"optimization_success\", \"f_opt\"]).corr()\n",
                "\n",
                "# Generate a mask for the upper triangle\n",
                "mask = np.triu(np.ones_like(corr, dtype=bool))\n",
                "\n",
                "# Set up the matplotlib figure\n",
                "f, ax = plt.subplots(figsize=(9, 7))\n",
                "\n",
                "# Generate a custom diverging colormap\n",
                "cmap = sns.diverging_palette(230, 20, as_cmap=True)\n",
                "\n",
                "# Draw the heatmap with the mask and correct aspect ratio\n",
                "sns.heatmap(\n",
                "    corr,\n",
                "    mask=mask,\n",
                "    cmap=cmap,\n",
                "    center=0,\n",
                "    square=True,\n",
                "    linewidths=0.5,\n",
                "    cbar_kws={\"shrink\": 0.5},\n",
                ")"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "We identify a few relationships:\n",
                "\n",
                "1. Larger refractive indices generally result in larger optimal radii of curvature.\n",
                "2. Larger f-numbers result in smaller achieved RMS spot sizes."
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Plot relationship between FNO, refractive index, and achieved RMS spot size (mm)"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 10,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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4dROJJGkPM1aIY2MT8ky/dEpVIMDekVG+99Cz9A2NkyuVF+mNBf2cs6CZN66aj8c8sY+0si5KZV30hNpQFEVRlNcbIY9V+ll5RalUimg0SjKZJBKJHPd5vx18mAcGfkPYCOHXj/bcSCkZzI+QKrosERvxi6ltjmayvNA1wBw3zJyKWHktOSmJp/Mks3kuXDaXv1i/bEqVcEVRFOX0eq2/M2ba/p6ufyAcmVo+ZibSqQKL5/yvWbvXP1Uqi/cUs90CAd1LybUouSWgvBZc3i1gChMTnYw9fY2njtEEdsFhYV0N4YAPIQS6plETDVITDbLlQC99Y8lyztNYmt6BxLSVvRVFUZTXJ4k4KS9lqtM+JPfnxJUu8VKc9mAbY8UxxkojpGQRgYZfD9IebqbDiTOSHSOmNWDqOlJKhBAkCwVG0zmafRE8xtQk7kjAx9B4hj++cAgnZdHdG8eyHfw+kyULGjj/3HlUxoIA5LJFEvEMmqZRXRs5rqRwRVEU5cx3MgIeFTBNTwVMp1i55lIKlzQBA6T0AhJd2BTdBHUhH95SgKf7ekiVikgpMTSNan+QOiNAi3f6WkhCCLK5Io8/e4Bq00dNZQjT1MnlSjy1+RB9A+Nc++aV7NvRx44Xukmn8ghNUF0bYc257axa0zaxYO+xFPMlDu3oYWxgHKEJGtpqmLO4EX2aAE5RFEVRXk9UwHQKaUKj0htlb3oLAT1IxKiYyDdypUvGHsdxdYSci6Y5eA0dKUHTBEIX+P0G2Xxp2rZtx2F4LE2jN0hbc+VEu16PQSTs42DnKD/44WM4qSKRqJ+a+iiu4zI2kubX920lncpz4aVLjpn/1HdwiAd//EcGu0bLVcalxPAYtC1t4or3vYFYjRrnVhRFOd3cw68TbUOZSgVMp5iGU16G5PDPR4bcJBJHCjKlAvlcmvOaF6K/ZHZgplRix8AQWatEQzGC3zu5ZEBHfxzXcpnfVjUl6NF1DRyXXR1DXLhqLqHQ0YTAhiYPiXiG5zYdYPHyJmqnmSE3Pprm/h88ykh/gsb2WkxP+WtTyBXZ/3wn0pW8/aOX4/EefxkDRVEU5eRTZQVmj0r6PoXKvUgpmn0tQIl4qYd4qYOx4iFSpSE8eLEtLzVhMSlYAgh5PNRHQmgRje7RcQbiKfJFi3S+SOdQnGyhRL0vSCw4fc2kTCqPi0RMsx5crCJIOl3g4L7p19Hb/dxBhrrHaFlYPxEsAfgCXprm19O5u4+Onb2v/cEoiqIoyhlOBUynmJQSlxw+3cava/h0b/llSDSRByy8xvQdf5WBANWVQS4+ax7hgJexdJZ0vkh7fRVXnb2YWn8A23amPTebK2GaBoY+9SMXQqDpgnSqMHGPju1wpOLE/uc78YW80y6N4vGZOLZL996B1/hEFEVRlJNFzZKbPWpI7hTShEbA8LI/00fYqCDoiU3sk1IyVhrFMIro7vQ1NBzpYho6F69o5/JVi0hkcuiaRlUkQKlk07FvmOGxDI0vG1aTUmK7kpDHxDtNYUspJdKVICWbfr+TXVs7yedKxKpCLD9nLoVsCX2anqmJ96UJbMt+bQ9FURRFOWnKOUwnuviuMh0VMJ1iQtjlhW2liy5LuNJGAEJ40NEwBGSsPP5p0oHGcjlW1tWTy5V4pquH3vg4pq6zsLGaZS31XLB2Pr/+/Xb6BsepqQphGjr5gsXgcIqW5gpkoohVsicNq0G5SJkmBHs2dzA+nCYQ8uL1mfR1jJbXlbMdrFSO2uaqKffkui6u41LTWDlLT0xRFEVRTj8VMJ1CjnSw3AK13gbixW4KTpajyxzq+I0q8FTRn0yQycXJ2za26+AzTIQEj6YTcb1856FnSGYL+D0mjuvyfEc/rdXdvGPDCq558yqe2nyQgaEUjuPi9RosaK/l/DXzeOYPe9i/b5Cq6jDhiB/pShLxDJl0Ac1xGB/OMWd+3USZgIrqMIV8iYM7+7ByFomRFBUvmQ0npWSoa5SKuigLzpp+MWBFURTl1FF1mGaPCphOIYEA6WC7cQK6wJERHFnuPDU0gS4sTK/BoKaxub8fy3XQELhIQqaHixvn8uLePjRNY0FD9cRsOMd16RiO84und/DBN5/HskUN9PQnKJVswiEfjXUxNE1QWxXm8Ud2sW93P90dIwghqKgMctbZbex+5iDRpsopNZV8fg81TTHGhzUy4zlSYxnCFUFcxyWTyBKqCHLpO9cTCPvY+9wB9m05SHY8R6w2wqJz5zNnWcu0uU+KoijKySc5+mf4ibShTKUCplNIExo+3UPeSRA16tE0fSKxWghBwckwXhzFlfPZ0NxC3rKxXRevrqNpgucHB4gUTNY1tUxqV9c0Wqsr6BodZ2//CCvnNDBvTs2U60eifq5+yxrib1jE6EgaXRM0NFXQuXeAbY/tJhCaflgtEg3i2C5v2LicgQOD9B4YxDAN1m6cz/L1C6isi/Bfdz7I7mf2I6XE4zUpbi6x9eEdnH3ZCi577xswTnBRYEVRFEU5ndRvsVNISokrC5jCR94dw3RtJEVAAAHyjqRkQ3XAIKZPLQS5vXsQNHeidtNLeQwd15UMJFKsnNPwivdRWRWisio08bOu6yAE0pUIfWpXrOO4aLrG/BWtrLtsOY7jIgQTPUcP/vMjvPjEbprmNeALeifOSyeyPPvA81TWV7D2irNm8KQURVGU10IiTjjpWw3JTU+NlZxCLg4CiBpeNJnAchNYbgHLzWG7I5hkwDUJmdN/LH7NIO2WKLivPiMtlSkwEs+QL1ivemxjWxXRyiCJscy0+xMjKRpbq6ioKQdZuq5NBEuJ4SS7Nu2jsr5iUrAEEK4I4gt4eeGRFykVX/0+FEVRlBNzpHDlib6UqVQP0ymkoQNFbDlGxKjBAZzDs+QM4SFrpfGbSbCmD5gqgn664uPTji+XbAddE+iu4D9++zz7OkawHYeAz8PKxU2sW9VGJDR9uYJwNMCq8+bz+APbMEydSCxQrkbuuowOpdAMjbPOXzBtLtJw9yjpeIY5S1umaRlitVHigwniAwnq22qP70EpiqIor4lK+p49KmA6hYQQeDSBIx10TUOTOQxRHpLThMDQTAyRpeSUMMSRIpcSDYEQAq/PIGp6iY/n8FdGJoblbMelayRBhd/Hc891kEoXqIoFCfo9ZPNFHn5qD519Y1x/5dlEQtNXAl//xqUU8yW2P3uI+HDqcNuSSEWIi69exaKV0wdEiqIoivLnQAVMp5ArHTTp4tc8FJ0OBBINA4TEdscwhBevFqEvlyRbGma4kMVxXYKGSdTjRzc13rJsGd0dCfYPjOIzDRwpcVyXlqooTtwimSvQ3nJ0Bl3A7yEWCXCwa4SnX+jkzRcsmfbeTI/BZW9Zw8p18+jcN0gxXyIU9TNvSRPRyuAx31NtazXhyhDJ0RQVtdOsQzecpLI+RmVDxcl5iIqiKMoxuSchh+lEz3+9UgHTKSQQuOTxiAK6FqDkuri4IEETPkxNontssk6R50f78WoGpqYzks8C46yta+b61StJLyiyvWuArtFxTF1jSXMtAXT+/dfP01ATmZIQbho60bCfF/f2s2ROLZ0dI/T1JTAMnblza1i0qIFQ2IcQgrqmCuqajj+4qaiNsnT9Qjb9ajP+oG9K0nchV2T1pSvUwryKoiingBqSmz0qYDqFhNAwNQ1HFgkZtThuElfmAQ1D82NLk7QzQtRrsqFhDsO5DJbrEDJjxHw+crbFpsFuqmWA7sQ4A6k0moBIyEfA0cuFKj3TByZBv5fO7lF+/JMnKOYsfF4Dx5W8uL2HxsYY1/zF2TQ2vrZeoIvesZ5MInu0rIDHpFgoYXpN1l55FmdftuIEnpqiKIqinH4qYDqFXOkgpI0poGQfRBMCgYZA4rhpSq7Atn3UB4JoxGiLxiad35Ua5+5tLxBL+hAIogEfluPy+O5DSFti2UVsx512gd3EeJaB/nEqGqpob685WvTScenpHuPXv3qev7rhQny+mfcE+UN+/uLmy1lx4RL2bz1EJpElVhctF65c2qwKVyqKopwikhOf5aZ6mKanAqZTTGDhFTaW1HBe8qUWGOjYeDULx9CYbi1bx3Y5OBbnDZE26kPhie014SAdw3H6nQL9Y0laayf3FEkp6eqN49M1mpsqJg3Z6bpGU3MlfX0JDuwfZPmK15bcbXpMFp07n0Xnzn9N5yuKoignTuUwzR71p/8ppAkdXbiATcSsIqRJQlqOoFYgpBsYIoahWWhy+ppFQ8kMSEk0MLk8gBCCOTUV+EIehrNZhkZT2E55veliyaKrP45rObTUxKbt7TFNHelKBgeTJ/09K4qiKMrrgephOoWkdBDSwaCE4/agCw3wUF65J4lXGycvvGSsEuPFDKOFHJbrEDBMav1hhnNZqj1BfGLqx6ZrGlXRIG0t5dlyPQMJpJTlHqS6GEELjBPspu3vHGHP5kP0HBxG1wXty5pZvGYuldPMjlMURVFOPbWW3OxRAdMppmPh0SS2q+PioosiUkocNEyhEdYlXelRdia60EW5PpMjJS/GB7FxqaV6yiy4I6SQLJvfwIZ5rXT2xSlZNuGgj7amSh55eBdPPrGPmpqpy6rYtoPQBPX1xw58XnhiL4/+x7NkknkCIS+u43JoZx8v/HEvV/7VhbQtaTypz0lRFEWZOTVLbvaogOkUEkLHEDYakrBuAONIaZUDGOFHEqNIFp9hYwgdicQ9/OeCR9MJBEwymRKulGgvC3pyxRJew6CtpoJgwMuyBZPXk1u2rInt27oZGkpSVxedlPTd2xOnsamCOW3V7NvZy4HdA+QyBSqqQixc1oyGyyM/fxaQtC1umDjXdSV9B4f47b89yXv/v6sJRqYviqkoiqIof+pUwHQKudJGw8UUWTRsBH4QYcodoEVsOYiGlznhWsLeOcTzOWwp8ekGtYEgBxJjJO0Ch4bGmFNdgWnoAGQKJfoTSc5qa6S9thIpJalsgWLJJhzw4feZNDVX8ubLV/D73+3g0KERfD4T13GxbJfGxhhvfOMyfveLLex9sQfXlRimgVWy2fLUAXwGZJI52pc2TXo/miZobK+le98g+7d3s/qCRaf+oSqKoigTXClwTzD94kTPf71SAdMpJNAwRAmvAFfqaKTQKSdnO5hIaWJgEzElDj6insnJ3U3hCKbQqcoF6R4bx3VdXCDgMTl7bhNvOXcZfcNJnt7eyf7ul6wlt7CR81a0sXJlKw31MXbv7qe/L4FuaMxtr2Xxogb++NsX2bm1i4bWSnx+z8Q1U+M5XnhiL7VV01f7Li/EKxjqHpu156YoiqIcHzUkN3tUwHRKCXRpY2DjES4SB3k4vc6LhS4ElpAYTD9LThOCoNfDha1tPL2vh46ROIamsaiphsuWz2dkNMO9v3+BRCpHdSxIKOAhmy/x8NP76OpPcP3Gs6ipjVBTG5nUbnw0zZ7tPVTWhicFSwCRWABN0xiLZ3Fdd9pZdlJKhJpvqSiKctqpgGn2qIDpFJLYGMLFQxGJho4fXZNIBI4rMEUWv9DI2NCTHWconz5c6dtLvT9MuljCLrj8cuseXMelNhrCcSVbe/rpio+jp1zy2RLzmquOriXn81AR9nOge4SnX+xk4/qpa8kN9SXIpgu01tVOe9+1zTE6dw+Qz5UIhib3etmWjRCCpva6k//AFEVRFOUMofoFTiGBgYGFIUz8wsYnxjHdcTxuAp8YxydMTCEYzHazLd7HaCFDxi7Sk03w9HAXe8aHycRLRP1e5tVVURsJ0RALs7CumoF4imd7eqmqCE6ZBWcYOrGIn+37+skXpvZeSfnK00ir62J4fCaDPXFc153YblsOPQeGaWyvZd7y11bwUlEURTl5jhSuPNHXTDz++ONcc801NDY2IoTgvvvue9VzvvWtb7FkyRL8fj+LFi3ixz/+8Wt8x6eO6mE6pVx0bDyiiI6OJIAQkvJ/yjPofJqLJTWkBIQAefiFJG8VcaVLZTAwqVUhBBU+H/sdi5RdJIJ3ypWDfg/j6TyZfBH/y5Y/qWuMEQx7SY/niFRMzVUqWg5L1szF79p07R1ENzTk4el7zfPruPKvLsAX8Ew5T1EURTnFZPmP4BNtYyay2SyrVq3i/e9/P29961tf9fhvf/vb3HbbbXzve9/j3HPP5dlnn+Wmm26ioqKCa6655jXe9OxTAdMpZhweHdaw8HA4JqI8g64kBRqSJdEK8qKRwdyRIbkQDYEwz3b1kDaK05YV8JoGAkGqWITw1OuWLAdD1ynkSzx74BCDQ0l0XaO1tYoF8+pYuKyZrU8dwBvw4PUeDajSqTylgsUVbz+XBYsb2L+tm8HuUXRDp3leHfNXtOALesmm8ux59gA7N+0jm8xRURdl2fqFLDqnHY9PBVOKoiivV1dccQVXXHHFcR//k5/8hA9+8INcf/31ALS3t/Pcc8/xpS99SQVMyhEaunAwhEBDw5XuxJ8CmhB4pMCDS9QUtIZjtIZjR0+VENA9ZK0iBWkREJODkFg4gMfUyWSLUD35qlJKRhNZWmqi/Md/bGYsnsHQdVzX5dnNHbQ2V3LZJUvIZYrs39WHAAyvQalgYZg6ay9cxOq17eiGzppLlk55V8nRNL/89u/o2NmL1+/B4/fQ8WI3B57vZMl5C7jqv12KLzC110tRFEU5uU5m0ncqlZq03ev14vWe+P+XF4tFfL7J+bB+v59nn30Wy7IwzZkvAn8qqIDplLIxBUhcDEwMTaBNlBXQKR4uOeBIk3gxy1gxiy1d/LpJjS9EZdDPeDw/bX+rLV1qK8L4CgaDoymqK0IYukahZDMwmsLnMRjtGceQGnPn1KBp5X8Qlu3Q1T3Gw3/YwzvfeS7dB9vYv7OPbKZARXWYxSuamTO/dtrZcVAOxv5w7yYOvdhD6+JGDM+Rr1QFhVyRHU/upbaligvfsnZWnqiiKIpy1MkMmFpaJuemfu5zn+Pzn//8CbUNsHHjRr7//e9z3XXXcfbZZ7Nlyxa+//3vY1kWo6OjNDQ0vHojp4EKmE4hKXUM6aALEw23XMmbcn6Sjotf07FdwVh+gC1jXdhSHt4r6UibGMKg2hNkcCxDa5WJoZeDmHzJomtsnA2L5rAsVs3T27voHkiUM6M0jZa6GBHNZM9IH3PaKiclhZuGTktzBd09Y3T3Jli6upWlq1uP+z2N9iU48HwnNc2VLwmWynwBL+GKIC8+sZdz37wSX9B3jFYURVGUM01PTw+RyNEyNCejdwngM5/5DIODg5x33nlIKamrq+OGG27gy1/+8jH/OD8TqIDpFBKHh+N0IXAJAS7gHA6KPGiU8IoiwwUbUzOIGuVhN+m6jBVzFN08b593Fsleixd6+inYNgKI+nycPaeRd65dSSzg56zFLXT2j1GyHMJBL20NlXz/nx8nFPROuw6daRq4rqR/IMHSGa4JNzaQIJcuUNNSNe3+SGWI0YFxEsMpGuaqgElRFGU2vZZZbtO1ARCJRCYFTCeL3+/nhz/8Id/5zncYGhqioaGB7373u4TDYWpqak769U4WFTCdQlLqGEJD4qEcKOkIPJTTvi0cqSMxafEbPJ60ydvWxOK7Xt2k0hcg4xbQdANXA1eUh+akAYapox+OzIN+Dy31FZQsm5Dfi2HouO7URXdfSojy2nAzpR/u5XJdia5Pbd9xJJomzui/GhRFUV4vpBTIE1za5ETPP16madLc3AzAPffcw9VXX31G/65QAdMpJISDpsVwRAgh/CAzSGkd3hfGkoKim6Y20MI51S2MFrJYrkPA8FAXCJEpFvlj9yHmWHWsam7Ac2QtuWKRLd39SOCN7XN5bncP+7qHsRyXoNfD6oVN1NZHGHwhSe00wbvjlPOoamtn/pdEQ3st0Zow40NJqhorpuxPDI1T31ZLddPUfYqiKMqfvkwmw4EDByZ+7ujo4IUXXqCyspLW1lZuu+02+vr6Jmot7du3j2effZZ169aRSCT46le/yo4dO/iXf/mX0/UWjosKmE4pA01vQ9qDSIqgVXP0IyiAmyXjhslTRZUvgKlrONLFp5sEdA+dYwlylsWcyhgeXZ9oNeT10lIR5dlDPezbPYgsuFRFAwR8HrL5Ir99Zg+1kRCGV2dkJE11dWiit8l1Jb19CerqoixaUD/jdxSKBVl10VIe//nTeHwmocOFM6WUxAeTuI7L2W9chm7or96YoiiKckIkMy6jNG0bM7F582YuueSSiZ9vvfVWAG644QZ+9KMfMTAwQHd398R+x3G444472Lt3L6Zpcskll/DUU0/R1tZ2gnc+u1TAdAoJIZCe89Cdblxp47ojINOAhtCCaFo1Y1aRF5IB9uc6SVl5XCkxNZ0qb4iudIqw7sOvTZ1y6TcNekbGyQsf57e1TgREQZ+HinCAjoE47XMqSPdl6OgaJeD34LqSfKFEbU2Eq65Yid/vKQc6oxlKRYtg2EckOrlIpmM7pMdzCE0QPrzO3IZr1pDPFNj++G5G+uJomobruoQrQlz8jvNYfv6iU/F4FUVR/uyVA6YTnSU3MxdffDHyFapl/uhHP5r085IlS3j++ednfmOnmQqYTjHhPQdpv4Bmd6DpKye+2AKbkJ6lx67iD6NJgqaXkOFDFxol16Y7G2fczbNUb0GbZqXb8UyeQtEmWu2bkqtkGjqxkJ+MY/G2t63h0IERenrj6IbGgvl1LF3cSEVFkO6OEZ59Yh9dB4exbAefz8OiZU2su3AhkWiAF58+wLan9hMfTiE0QUNrNasvWMCi1XPY+L43sPLCxXS82EM+kydUEWL+qjlUN1WekueqKIqigCsF7gnmIJ3o+a9XKmA6xYQWg8BfIfO/AnsfQuYAAVoVJeN8XszbhM0BbNclZ5cmAiZT6AQMk2ypNG27+aKFlJKob/qZaCG/h/FMnmgsyJvfNHWh3EP7B/nlz54lncxRVRsh6jHI5Yo8+8Q+ertHqQx62bO5A4/XIFIRxJWSjj39dO0f4JK/WMPaNy6jsb2ORrUIr6IoivI6pAKm00DodRD8ADi94I6C0EGfy75kkpT9FOfXtjNazDKYT2G5LlW+IA3+CPFcjoNDcUZzWaoDR9d8k1Iymsvh0w2qvP5pr3lkaRSPOTWXyLYcHvvdDrKZAnPm1U70UHl9JpFogJ1buygmsyxd1kQocrT9cDTA2GCSp367nfZlTVTXx07ug1IURVFm5GQWrlQmUwHTaSKEAKMFOFpJNWuPIIGg6UUIMHVwpItXM6n0BAjoJsl8ge6RBHsGRw7XCC/nONWHQlRUeUmniwSrJi+bIqVkNJllzeIWItMUj+ztHmOwL0FdQ2zKcJ6uazgli2S6gMc3NXeqsi5Cx54BDmzvVQGToijKaaYCptmjAqYzSNAoJ13vTfUxXExScm0ABBA0fFSYYcJeL5amkS6VsBynfJ7XQ8Dv4dyWBp55vpOheJrqaBBd1yiWbAbGUlSEA6xbNoeevjg79/SXc5h0jQXz6jAciW27eKcJiACsko3QBKWSg+dl1byFEBiGRmI0PavPRlEURVFOpzOiQtS3vvUt2tra8Pl8rFu3jmefffYVj7/33ntZvHgxPp+PFStW8MADD0zssyyLT37yk6xYsYJgMEhjYyPve9/76O/vn9RGW1sbQohJry9+8Yuz8v6O14JwLZYssT89iCY0YmaQCk+IsBkgZxfZlexlJJ6jOhBi45L5XLlsEVctX8RF8+eSLBTYnxvnzectwusx6BxMcLBvjIF4mqaaGG+7ZCVDfeP89N5neOqZg8QTWQaHk/z2kZ38/ok95IoWlmVPe19CCJBgGNN/XRxH4vWfmYslKoqi/DmR8uS8lKlOew/Tz372M2699Vbuuusu1q1bx9e//nU2btzI3r17qa2tnXL8U089xbve9S5uv/12rr76au6++26uu+46tm7dyvLly8nlcmzdupXPfOYzrFq1ikQiwS233MK1117L5s2bJ7X1v//3/+amm26a+DkcDs/6+30lBdfC1MHUdIpOOdFbR8NyHSzXxXUlFhYNkTBCCCYKawuYU1FBd2KcNy2ax39ffAEHe0fIF20qwgHmNVXR2z/Ow4/vxtA12tuqJ67pupKu7jHixRKD/eO0zKmedE9SSnSvid9rTFvJO58tYnoM5s5wSRVFURTl5DuZS6Mok532gOmrX/0qN910EzfeeCMAd911F7/+9a/54Q9/yN/93d9NOf4b3/gGl19+OZ/4xCcA+MIXvsBDDz3EnXfeyV133UU0GuWhhx6adM6dd97J2rVr6e7uprX16MKy4XCY+vqZF2ucLZ2ZEUxN5+zKOXRn4yRLeRzp4NEMmgMV9BUySMOmhI2XyT06HkPHcV32DIwwPJBm26F+ipZNRcjPeC5P/6Ex8nlrUrAEoGmClpZKxsdzjGeLGL1xqmsjmB6DfK7E8MA4LXNr8DiV9B4cpq6pEn+ovABjOpFjdCjJyvPm0TpfzY5TFEVRXr9Oa8BUKpXYsmULt91228Q2TdO47LLL2LRp07TnbNq0aaKK6BEbN27kvvvuO+Z1kskkQghisdik7V/84hf5whe+QGtrK+9+97v5+Mc/jmFM/0iKxSLFYnHi51Qq9SrvbuYst7wQb9jjocIxKcgMjnTx61Dh8zJEjiI27uF075crlGwe23YIX0kjEvDhMXX6RlMcGthOZiRLS3D6HjRD14hE/bQ1ViCTRQb6EriOxPTozJlXy0VvXk4o6OX3P3+Wrr2DDPcnAAiEfZxz8RIuuW6NquStKIpyBlBJ37PntAZMo6OjOI5DXd3k3om6ujr27Nkz7TmDg4PTHj84ODjt8YVCgU9+8pO8613vmrTq8kc/+lHOPvtsKisreeqpp7jtttsYGBjgq1/96rTt3H777fz93//9TN7ejMU8QUquxbbxQxRdC5/mwYeJJW0OZPopemzcjA/PNB9b0bIZTmSolX6WtzZOLGBYGQ5QKFk83jmC4Qoa66LHvH5bey1vWL+A3u4xigWLUNhPY0vlxAK77/jbN9LfOcrY4DhC02iYUzVpZpzrugx1j1HMlQhG/FQ3Vbzigr+KoijKyaUCptlz2ofkZpNlWbzzne9ESsm3v/3tSfte2ku1cuVKPB4PH/zgB7n99tvxer1T2rrtttsmnZNKpWhpaZly3IloDVSSd/OMl7I0+ComKnp7MSm6JZIiR8gM0TuextQ1craFQBD2eukdHUezYFFj9ZTVnn0ek6pYkP6RNCsdB1Of3BtUsmx0XaOpoQKP16T9GGvKCSFomltD09ypK/gefLGbp3+zjb6DQ1glG6/fw9ylTWy4+mwa2qZZ8VdRFEVR/oSc1oCpuroaXdcZGhqatH1oaOiYuUX19fXHdfyRYKmrq4tHHnlkUu/SdNatW4dt23R2drJo0dS1z7xe77SB1MnUmx8jZHiJeYIkrBw+zZyo9G1Lhzp/jKDHz+59Q4znS+hC4CLREFR4/dSZfiKB6St9z2moJJ7I0tE7xvyWo0GVZTn09CZob6tmXvtrC2z2b+vi/u8/Sj5ToKqxAq/fJJ8psuvZgwz3xnnL315G/RwVNCmKosy2kzHLTc2Sm95pLSvg8XhYs2YNDz/88MQ213V5+OGHWb9+/bTnrF+/ftLxAA899NCk448ES/v37+f3v/89VVVVr3ovL7zwApqmTTsz71QZL2Xx6SYrYi1Ueryk7XHGrFFKMkdTIEp7oJahfJr6WJDVjfW0V1WyqLqa1Y31+D0Gw04e+3BtppfzeA3mNFcSDfvp6Bqjs3uUQ52j9A2MM3dONddcvhqPOfP42bZsnvzlFgq5Is0L6wmEfeiGTigWoHVxIyO9cZ793Ysn+mgURVGU4yImhuVe6ws1JDet0z4kd+utt3LDDTdwzjnnsHbtWr7+9a+TzWYnZs29733vo6mpidtvvx2AW265hYsuuog77riDq666invuuYfNmzfz3e9+FygHS29/+9vZunUr999/P47jTOQ3VVZW4vF42LRpE8888wyXXHIJ4XCYTZs28fGPf5z3vve9VFRUnJ4HAZiaQcm16Mr2kXOzRD0+NCFwpEvCijOUSZK3JOtqavFqk6t5VwYCPDXeSUdinAXVUwPE0VSWlQubeMv6Zew7MMTAcBJD12ltrmRBey1e79FZd4WCRalo4w94MKdZSuWl+g4OM9A5Qk1z5ZR8JU0TVDXEOLi9m/GRFLGaV+7lUxRFUU6MlAJ5govnnuj5r1enPWC6/vrrGRkZ4bOf/SyDg4OsXr2aBx98cCKxu7u7e1JOzoYNG7j77rv59Kc/zac+9SkWLFjAfffdx/LlywHo6+vjl7/8JQCrV6+edK1HH32Uiy++GK/Xyz333MPnP/95isUic+fO5eMf//iU2XenWmugipSVJmmnqfFEJ3KYAIquRb81QkSvwSOmWaIkGCAS8tOfSVPtDRAL+RBC4Lgug/E0PtPgvCVziEYCnHv23GmvPzKc4oXnOti9sw/bdggEvaxY1crqc9oIhqYf6stnCtiWg9fvmXa/N+ghM54jPjhO184ehrpH0DRB47x65q1uw+uf3WFORVEURTkZhJRqtPK1SKVSRKNRksnkq+ZHHa+e3Ahf3vUzxooZAoYPn2YiAEdKsk6BwWySqFvJev/aScHUEXuGR2gwgrgJm3S+hAZIoDoS5E3nLGTNwmagnLeUyhTQNEE07EfTBP29cf7r3ucYGkoSjQXweg1y2RKZdIH5C+u57p1rCYV92JZDKpFFaIJoZZDuvQP821fup6a5ctqgKRXPEB8YJxL2kBxJlsfGJWi6RvPCBq764Juobamecp6iKMrryWz8zpiu/Z/t+TGBcOCE2sqlc1y/+H2zdq9/qk57D5Ny1GgxSYUnRNDw0Z0bIF7KI5Fo6ESMMPVmNalCCQsLL5N7ZhzXRdMEb1wxH4+l8fTuLnIFi+pogEvPWsDcukosy2Hri91s3dFNfDyHJgTNDTHOXtHK808cYGQ4RVt7LZpW7o4Nhf1UVIU4sG+QTX/cS2XYx7anD5IYzSAE1LdUsuLcudTPqWaga5Tm+XWThuWklAx2jpJPZpBFHy2LmibqNVklm+7dffzq27/j3f/rrfinWRRYURRFmRlVVmD2qIDpDCIQFN0iRSeHTwev5qecwOdiaDa6zyJVgK7xcYoWjBfzaEJQ6w/iuJLaYJADHSPs7R6hULLQNI2hZJresRQXrZhLoi/Nlu3d+Hwm0bAP15Uc6Bph554+rHiBBW01E8HSEaapE4n4+N0vnyekCYJBH5GKAK4r6T4wTM/BERYsbSAxnKJ3/yDVjRV4/B7ymQKjfQmElBgatC5untS26TFoWdxI774BDj7fwfILlpzip60oiqIox08FTGeQBl8FaStF3slT5YlN6q2xXZvhUoKgJ8qL3SPYriRgmrhS0p1MEvP6aDCCbOvsp74yQtgfA8q9PCPJLP/+h23oKZeFjVUEA0d7p8IhH3v3DdIbT7GgffrlTUpFm8HeBGevbqWm9mj3bCjiZ2w4RdehES5861r2PneQ/kPDWEULb8DD4jXtjHQNkRrRpgRiAIZpIISga3evCpgURVFOApX0PXtUwHQGKThFTE2QcwSWayOEi8RFCJ2i6yBdge1aLKmrJl9ySBaKaEIwP1hJ3rJ5tq+PcyL1hF+SSC2EoDYWYvehQSg6rPY3TLluVSzAAcdlOJGhrWHqLMGRgXGEgFB46rBZZU2Yjr0DWI7kXf/f1Qx1j1LIFglFA9Q0V/Ivn/sZmfixq1cITeDY0y/1oiiKoszM4TTRE25DmUoFTGeQcStNpSeCrklGioO40qb81RV4ND8+GSIjJfOqo3hEeUhNiHJQ1DuapMMao2hOH3wIBwrSJW/ZBDyTZ9lFY0E8XoPReHpKwCSlZDyRJRLx4/NNnZ0nhMAwdJKJHLqu0Th3ch2r5oWNdO7sQUo5peyA67rYlk3D3NNX+0pRFEVRjsdpLVypTKYLjYLMIskTNX1EzQgRI0LMEyZo6BRlClMv5zpBuc7RkSBE1wRIyNqladv2mDqO4+JOMynS9OjEKoJIWzI6ksJ1y0GXbTn09ybw+syJMgXTcV2Jzz81mAJYun4hoViQ0d74pO1SSgYODlHVUMHCc+Yd3wNSFEVRXtGJFq08GUnjr1eqh+kMUuWNkrfTONKhwhObtE9KyajowxQuBlOn7we9HjRNULKmr/TtC5gYaYGpTY2RM9ki9Q0xVrXX07V3iO6OURDlwKymLsLSRavZ/uR+bMvBeFkhy1ymgOnRmbto6lAfQOO8ei591wU8fPcf6Xixi2A0iJSSbDJHrC7Km//6EqLVatqqoijKyaBymGaPCpjOIBk7g0/3kC7lSVvjuBSRuOiYOOj4dBPLssjaecZyJTJWqbyOnN9P2PAQDfgo5WzsmIuhHw2MsoUSPr+HJU119PYlqK+NEPB7kBKS6TzxRJY1q+Zw7cbVZNIFOg8NUyxYhCJ+5s6rxbEdkiMpuvYNUtMQI3g4lymVyBIfSbNy3Txa5h17WO3sy1ZS21rNzqf20rWzB6EJ1mxcxfINi6htVWvMKYqiKGc+FTCdQQpukagZwHJTpJxUOe8HDUkOQ+jU+qoYKAge6T6AkB40RDnBb1wipOD81lYqcx46huKYuoZhaBQtB00Izl/WxgWL2nj0ib10dI8yNJIGIBTyseHcebzxgsVomiAS9bPyrDkvuzOTa9+7gd//51Y69w0wOpQEIBj2ce7Fi7n4qtXo+iuP7jYvbKR5YeMsPDVFURTlCJX0PXtUwHQG8WleUvYYuiapN+oouRYSiS50DKGRstII3QuuVv5GHynlffh/+/0mly9dxK+f28Pmg70UShaxoJ+LlrWzcc1CogE/77ruXPoGxxmNZ9A1QVNDBVUVwVe9t1hViLd94EIGe+KMDiURQtDYWkVlrRpOUxRFOVOowpWzRwVMZxCvZuBiI6XAEC5oFq500YWBrvnIOyV0TC5rX8BoNk+6VEIX5SG5oMfD/tFRvte7GTtrs7CpBo+hky2WeKFrAEu6vOv81QS8Jh6PjunR0TQN05zcMySlZGQkTbFoEQr5qHhJMCWEoKG1iobWqYv7AsSHknTs6qOQLxGM+Jm3rJnwcQRjiqIoyskhZfl1om0oU6mA6QySdTJEjRBjxUESpVF0oQECF7f8BXY8eHQDj+HSGotNOteVkp6xJBmnyIXNc9AOz2iLBf0ULZsdXYM8FNxHKV5iX8cwuUJ5Nl007Oespc1cvG4BvT1xntl0gO7uMSzLweczWbiwnvXnL6SmJnzM+3Zshyfuf56tj+8hM56dmE0XrQpxwdVns/rCRcecYacoiqIofwpUwHQGEQhcmcOvC0quD0e6E2vJmbqOrZdwXBum6S4dz+bJlUq0R2ITwdIRXtMg4DH5+ePbaCBAQ3WUuuowUkoSyTyPPr2Pru5Rkr1JstkS1dWh8uK7uRKbN3fQ35/g7e9cR3X19EHTs7/fwRO/fp5IRZC2xY0IIXAdl9GBcR762SZ8QS9L1sydjUemKIqivIQakps9KmA6g/h0D5abx6P5CJsGRTeLlC66MPHpIfL2EJYskcjbDGUHSRQL6EKj1h9EliRSQqV/+lWqiwWbsWSO1QvqiQTKs9yEEFRVBDEMweNP76c5FGLRSxbQjUYNwmEfHR2jPPvMQa68avWUdnOZAs8/todAyEdFzdF8Jk3XqG2upPfAEFse3cXC1XNeNTFcURRFOTGqrMDsUQHTGaTkFPDqJll7DFuW6ykJwJFQcBP4dQ851+GZwYNI6cWr67hSMlrIki/aeISg2vRP2/bQWBpD0/CaUz9yx3LJZIuI6uiUoTNN06isDLJndz9nrW5loCvOYH+inDDeVo2wHRIjKZqPUVagsi7KYNco8cFxapoqT+wBKYqiKMppogKmM4gUEo9wKGkSywXQEICLi4bEozlomiyXG5CAPFzz2wXT0PB4dMYyOZpi0cntSkkqX6DC78NnTP3IbdsBJBwjz8jv99DVMcK/fudR8qkCuq4hpeS5J/bh8xrkCxbaMXqPdEPDdVxstV6coijKrFNlBWaPCpjOIIbQsGSeoB5CGDYlJ43ERcODz4gxkh/HZzisa2pnMJ1jvFBA1wTtsQpqgkG29w/Sm0nh1QzCfi+uLK81NzyeIez3UiG80yZflwMggX6MgGk8kWWwN46vPsacebUTwZFtORzY1cdYIk99PEusKjTl3EwyRyjqJ5/O8/C/PUn37n40XdC+spUla+dTrXqdFEVRThqVwzR7VMB0BpHSwRACyx3DEC6GJkAKoEDJKQASrx6iym9S46+bcn51JEhlwMfBzjEGUxmklBi6Rlt1BVees5hd2/rJF0r4fZOXVnGASMjL4W6tl92TpLtzFFMI2ubVTgq4DFNn/pJG4oNJug4OE4760Y2jS6eUihbJeJY5C+q4787fkklkCUT8SCnp3NXLC3/YxZXvv4R5q15eKFNRFEVRziwqYDqDSFx8mosrHSwp0JFolHOYJOXhOkl5f7yYJWuVEEJQ4fETMj3kiyVG8g4Bv4f5gSo0IXBcF6FpjDtFFs2vY/e+AYIBL9GwH9d1iY/nkFLypguX0rd/mN7eODU1ETwenXyuxNBICmk7NNZPzW8CMDwG1U0xKNp07RskGPHj9ZnkMwUKeYvGtiqGDg6h6YK25c0TbUgp6TswyIP/8hh/9b/eQqTq2GULFEVRlOOj6jDNHhUwnUEELq4sEDZCuG4GW2YAF6EZGCJKUgryVp5nhwYZL1m4h7/VHk2n0htkOJmh2Y2wrLluUnBTsh32Dozy5uXzuaJ+KVt39RI/XC+puT7GuSvnsHJRI7t39bPpqf0MDiaxbQev12TBgnpipoFTsI95316fh2XrF1BbFWTnMwco5ktUN1ayYv18RnvH6NvVy9zlLZPuSQhB47w6unb1sW9rB+e8aeWsPVdFUZQ/F2pIbvaogOkMogswNRfHHcMQAkP4AQ2JgySFX4Mxx2QoH6fSW4VHN5BSkrMtdiWG8Ng6i6rnTukJ8hg60YCP7T1DfGTjBiorg3T2xTF0jSXzGmitjyGEYNnyZhYuaqCvL06paBMK+ahviPHI/c/z1CO7p71nx3GRUtK2oJ6zzpvHeRtX4lgOxuFK4v/y9z8nEPZP2zulaRq6oTPQMTIbj1NRFEVRThoVMJ1RXDzCpiTE4SVRcggOd7FioOESMByqvAGSpSIaJSTlgpdVZoBsqUhJn342WtjnpT+e4nv3bWJsLIPjSCSSZ3Z0saS9nisvXErI78U0ddraaiadu2RVK9ue62BkMEl1XWTSsFp/9xg19TEWLC0vrKvr2qR6S7qhId1X6N+VEl1Xf80oiqKcDGpIbvaogOkMImUJDYugpiHJ40oLKUHoAh0vSUcQNFzObZjLcK5IulREFxoVPj+u5fJErouRUpYqc2rxyky+SM9AAs3rMLe+Ap/XREpJJldk865uLMfhLzeeTSqZ51DnyEQP07z2GprmVHPpVat59Ncv0LV/CH/Ii3Ql+WyJqroIG9+yhlBk+vpP7StaObi9u1wK4WW9TLbl4LqSlkWNs/I8FUVR/vyc+JDcdKtJKCpgOqMYwsQQFo5MYeDHo3sBiSsFjrTw6HlsJ4LUbUIeD0IDDQh5TEyvgcfQSeTz8LL1bqWUdAyOodmShfOq0PXyTDYhBOGgD13X2H1wkHt/uYXejlFSqUK5JJOAqsoQl1y0hLPOm0ddY4zd27rpPjSCrgvmLWlk8coWql5S4fvlFq+dz/OP7qR33wCN8+snep9syy5vm1fP/NVts/I8FUVR/tyoOkyzRwVMZxBX5jGFi4GOkAmEtBGUy1dqeLExgCJbRwcZKTg4bvnvCI+uU+cPUxH04aZd9gyMYMvyfo+u47ou+bxFayQ6ESy9VMDnYWA4xXB3gkWNNbTNqUbTBI7jMjSc4te/2YbPZ7Jgfh2NrVUzek+V9TGu/MClPPgvj9G9pw9N00BKJNA4r56rbroUf8h3Mh6foiiKoswaFTCdQXShoVNCFwWE0HE4Gtx4hERQJC6LDOdThM0KTE1HSknBsdk7PkKdP0y9L8yunmGKll1eBFdKIn4vlV4vlf7pA5NSySE5nqU+HKKq8mjxSV3XaGyI0dU9ynNbOpj/sjpML5cYSdO5p59i3iIQ8dG+pJFQNMDc5S381f96C/u2djDYMYymazTNb2DBWXPwBVWwpCiKcrKUc5hOdC25k3QzrzMqYDqDCCHxaDaua2MIiU9YQPnLb0sDDfAKB4+AjGXhNySulORti4BhkskXSFh5LljYRr5kYbsuHl1HCMHuriG6UmnqqqYOn40ncxRLDtUVUyt1A1RWhujpiROPZ6mappq347g89dvtbPnDHjLjucNLrEhiNWEuvHI1K9fPJxQLcvaly0/m41IURVFeRg3JzR4VMJ1BXDeLiYOmOUhZpDy5TCBwDwdSOmFDsriqkZ50iYxVQgCNoQhVZoDnenvRfIJY0E8sODkJezCSZnQ4zXgmTyw0ed/oeAaPrlEXmz5gMg0dx3HJZgsMdI8xOpJGE4KG5gra5tey9bE9PP6rFwhH/bQurJ8YzhsdGOd3P3sGr99k8Vlts/LMFEVRFOVUUAHTGcSjBTBEASFLeISOJgoIJBIdR3qxRAGv5lLpM8g7OlpJoguNan8AWQTHdfF5p/9I2+oqKBRKDCbSJNMFYiEfjpSMp/J4PAZzKmO4tgueqeemMwWk43L/vz/L2HAa6ZZLEhiGTlNzJYnuUfxBD5W1R3uvdF2jrrmSnoPDbH18LwtXtZbzlxRFUZRZI6U4CUNyapbcdFTAdAax3SQmDqawEJQOD21pCFlEE0UCmkFa5tky2kfKMjE0DSklw4U0mqvh4OIT03+kmhA01sZ4U3s7L+zuo3cogaZpLGuv58Kz5vHMkwfYt2+QtjlVkwKbUslmdDSNVrTBMGieU4VxeL24YtFi1/ZuEgPjnLdh/rTXraqN0N85ythgkprGipP+zBRFUZSj1JDc7FEB0xnEIwJ4tSI6DgY6uiyAcMs9TMKPxEKnhOtaVHmPru3mSkl3ehxbd/A503+k8WyeqM9HZ/8Y49k8mlkOinrHkuzsHOSC8xeQSuXp6BwlEvHj8RjkckVy+RLRgJd8zqJ5fnn23BFer0lNbYS+QyOkUgVqaswp19VNHddxsS1nFp6YoiiKopwaKmA6g7iM48XFoIiGDZqBhoHExSCLQODXbFwgWSrgN0zcw0ujRL1eSjgcTMXJ5m1Gs1lKjkPQ4ynvsxxExiGZS9NQFaHFH0NKyXimwBPbDlGybN7x1nPZ9mIPu3b3USrZVFQEufiiJex4+iCJkjMpWDoiFPEjNI2R4RQ1NVMX0M0kcwQiPiKHZ9+5rosQ4hVn2ymKoiivjVpLbvacUMBULBbxer0n617+7BnCi1eUMJDoCHSKAEihYWPg4BAxBEsqatidLJEs5RBCUOsL0x6tojuVYCSdp38wg6FpmLrGUCqLJmBONIonBwubqjEOF48UQlAR9mMaGtsPDHDuklYuu3QpF124CMuy8XpNdF1j1zMHj7l8STDiJxTxkRzL4jjupGVRrKJNcizLBVetYrh7lJ1P76dr7wCaBvNWtLJ8/QIa2+tm/8EqiqL8mVBLo8yeGQVMv/nNb7jnnnv44x//SE9PD67rEgwGOeuss3jzm9/MjTfeSGOjWubitdJkBi8OhrDRAA0DjqR9SwshIEeJlJXGFRq6Wf5W52WeRCnDcCpDwONjZXsjY5kcJdsh6PUQCXjZ2TmIaTARLL1UyO9lYDTNns4hUvEcu/YOkM0WqKoMsXRRIw3NFfR1x6F+6j1LKamqjxLQBF37BglF/Xh9JvlskXy2xIKVzegCfv7N31LMFwnFgkgpeea329n5zAE2vucClq6bPv9JURRFUc4UxxUw/ed//ief/OQnSafTXHnllXzyk5+ksbERv99PPB5nx44d/P73v+cLX/gCf/3Xf80XvvAFampqXr1hZRJdmHg0FxOBLiUa5bwficAVGkJzEdJiuJjGq1cTNstFH/OOxe7xQVK2xQWhelrCMVoqY5Pa3t05xKidx3ZdjGlmqzmuy+NP78coSAxdw2Pq9PTF2b6zlzmNFXh9JvHRNJXVR4fdpJQM9CZoaKnkL96xls7dfeza3EExb1FZG2H5uvlUVAX5r+88jOkzqG+rnji3qiHGYNcov79nEw1za3Bsh47tXRSyRQIRP/NWtxGric7CU1YURXk9O7yu1Qm3cfwef/xx/vEf/5EtW7YwMDDAf/7nf3Lddde94jk//elP+fKXv8z+/fuJRqNcccUV/OM//iNVVTNbTeKV3Hjjjcd13D//8z8f13HHFTB9+ctf5mtf+xpXXHHFtFPD3/nOdwLQ19fHN7/5Tf71X/+Vj3/848d1A8pRgjwe4WJKgS50dCEQgAu40kUg8QsHDwKh6Ydn0YFPNxl2Mrg4xHzTV86uCPgZGE9TcGxC2uTaAY6UDA4nCUmDNQub8JhHvxbZbJGDPWPMm1fN8KFROg8OEQr7ka4kk84TiQV509Vn0dJeS0t7LRs2rsQq2ZiHh/Me+rcnyacLtC1rmvxehaCutZrOnb384s4HGe+Pk45n0HQN13WJVkfY8BfnsvaKs1S+k6IoynE6HUNy2WyWVatW8f73v5+3vvWtr3r8k08+yfve9z6+9rWvcc0119DX18eHPvQhbrrpJn7xi1+8xrueKplMTrnPRx55hGuuuQYopxX95je/ObkB06ZNm46rsaamJr74xS8e17HKVLo08KLhFRoaIHEBgYEEoSOQ+HQDXdMZKKQPnyXR0IkZfmQRxt081UxNvq6OBRkcT5MrlAiZkwOmnoEEVsGmfU7NpGAJIBj04s8UyLku1717Pft29tLdMYqmCVadO5dlq1qpbzpaLkA3dHTj6JIuA4dG8Ienz3PTNEFqLM2WQ4MsXNXK3BWt5eVcXJex/gQP//SPBMJ+Vly45DU9T0VRlD83pyPp+4orruCKK6447uM3bdpEW1sbH/3oRwGYO3cuH/zgB/nSl740o+u+mpcHXx0dHaxcuXJi+8jICPX10+SaHIOaJXcG0WUBr9DQpcQRGuWPRyIPV/s2pU5EE1T6DAYsm7xtoQlBxPTR4o+RK1iM5/MkZYF4rjz85jUMaoIBXA0W1deQShYo5CwCXg+ulGTyRXLZEtU+P7WVUwMtgGjET2I8R6w6xNVvX4s8/OfH8fT86B4dx3an3WeXbOID48SqAlTWxya2a5pGTXMVffsH2Py7F1i6fuGkIExRFEWZfalUatLPXq/3pEz0Wr9+PZ/61Kd44IEHuOKKKxgeHubnP/85V1555Qm3/UoymQy2bU/8XCqVpl2Q/lhmHDBJKfn5z3/Oo48+yvDwMK47+ZfhyexO+3OjCQNDmIf7ldzDPUxQLiNW/qhcqTFSzFLhraLBb+IiydslegsJNI9D72iS4XwBSXkUWh4+vT4c4m8vPJdde4d4bNtBEpk8moDmmhgr2hvo2j2IlBOjfJNIefjvjcM7XylQcg7XXDI9OpqmMX/lHA5u68Z13SnDuYnhFKVCiYa2tmnbqmyoYKhzhOGeURrmqtl0iqIor0ZyEobkDv93S0vLpO2f+9zn+PznP39ijQPnn38+P/3pT7n++uspFArYts0111zDt771rRNu+1iklHzta1+jWCyyY8cOli9fzpYtW2hubj7uNmYcMH3sYx/jO9/5Dpdccgl1dXUqv+Qk0jUN8CKFA2iHO0WPhD0SC7Bcg7DpIS/Lw2o6gpDpY6yQoYRF0A3hSgkShCYmljFxBTyzu5ueviSNNVHmNVUhJWSLJQ6MjGELl2QqR0UsOOW+EuM5GupiCFey6Y976e9NoOsac+bWsHBJA8GQj2Q8y47Nh9i5uZNiwSIY8bPi3Lm0LW2ibk4VPfsGaWqvxfCUv3LFQonBzhF8AQ9VDdMndx8penmsHipFURRl9vT09BCJHF3y6mSVEdq1axe33HILn/3sZ9m4cSMDAwN84hOf4EMf+hA/+MEPTso1jnAch3vvvZf/+3//L+eddx66rvPmN7+ZDRs28Pvf/54PfvCDx93WjAOmn/zkJ/ziF7+Y9a6zP0dCb0ZoFWhuDhcHsOBwX5HAjy0FSSdKsuiSlil0TSBlOWlbugIcQXNNiDlmDWPZHLbr4jMMasJB9gyM8Mj+Ds5vbCEcmJwYPhhP06/lGBhN4/WaBPzlYExKyXgyj+NIqmNB/u1HT5CIZzA9BtKVbNvaRUNTjAsuXMTTD+2gt3OUUNiH12cyNpTkwX9/jgXLm7jsLzfwh58/S9+hYaRbzkjUTZ35q1qJRrzkU3nMqqnDgel4hmAsQKwmMmWfoiiKMrsikcikgOlkuf322zn//PP5xCc+AcDKlSsJBoNceOGF/J//839oaGg4Kdf50pe+xJ133onjOPzDP/wDN954I1deeSVf/vKX6ezs5G//9m9n1GM244ApGo3S3t4+09OU4yCMuWjGPKTdhYYFaDAxT05SdAXDTjuW7iVTzJR7XgR4NZOYESLravgDBjGvn1jAP6ltq+iQsS10c+p4bW1FiPFMniqPn9GxDLbtYhgaluUQCHhYtbSJjp19FIs2bfNqJ3oVHcelt2uUf/5/DxPUBHMXNUwUroxWhigVbfbt6KWuuZL3/t21HHyxh9G+OEIT1LfVMGdxI7/+7kO88OhOApEAxkvurVS0GB9JcuFb1hGaptdLURRFmepPodJ3LpfDMCaHH0dyieRJrJr5ta99jf/5P/8nH/7whyd6x6677rpXLXlwLDMOmD7/+c/z93//9/zwhz/E7/e/+gnK8dMaEd4N6BRwpYt0xykHSyaaiJJyszyaqEYKyZxg1cQ4s0Qyls9g6RaeYyy+my9a6Ho5M2rKZYXANDSWLG1keWMtu/YOkM7kqamOsHRRA/te7COVzE8KlgB0XaOiIsi+F3tZNL9uUpVvAI/XIBoLsGtrJ+suWcLStfOAeZOOufidGxgfStK5q4dgJIDX7yWfKVDIFVi4Zh7rrz3ntT9PRVGUPzOno6xAJpPhwIEDEz93dHTwwgsvUFlZSWtrK7fddht9fX38+Mc/BuCaa67hpptu4tvf/vbEkNzHPvYx1q5de1KLX3d0dOD3+8lkMmzbto1QKMT8+fPxeDyvfvI0ZhwwvfOd7+Tf/u3fqK2tpa2tDdOcvODq1q1bX9ONKIeTqf3XgSyg2ztBC1LuZXJBROh0atiStmnw+TFeltlv6gZoBWzbZdjKMJLNUnJcAqZJXSiELR1MoeHTp//IXVdilRz2dQ6zr3MYy3YYS+Xx+gz27h0gEPROm69mFW0c28Vyp/8XFooGGBtKkoxnCISmjn9X1MV4+/+4hh1P7OHFP+4mn8lT01LJyjcsZfkFi/GHVFCuKIpyJtu8eTOXXHLJxM+33norADfccAM/+tGPGBgYoLu7e2L/X//1X5NOp7nzzjv5H//jfxCLxbj00ktPelkBv9/PZz7zGb7yla9QLJaXGgsEAtx222186lOfmnEO9owDphtuuIEtW7bw3ve+96QlfX/rW9/iH//xHxkcHGTVqlV885vfZO3atcc8/t577+Uzn/kMnZ2dLFiwgC996UsTOVWWZfHpT3+aBx54gEOHDhGNRrnsssv44he/OClyjcfjfOQjH+FXv/oVmqbxtre9jW984xuEQqETfj8nQmgRCP412HuQ1h6QOdCqEeZKdvZtp9LTxWgpBcKZmEUnpI4hPIQMLzvG+vHkQyDKg3mOlByMx3F1lxrHh5gmrsnki7iOZOfOPoqZErGIH7/PJJ0t8OAfdpEezdAQDEx/v3r5Qi+fLXmEYztoujZpuO3lwhUh1l9zDuuuOvvwDDtDTSZQFEV5DU7HkNzFF1/8ikNpP/rRj6Zs+8hHPsJHPvKRmd7ajHzzm9/kO9/5Dt///veZM2cOV155JQ899BDvf//70TSN2267bUbtzThg+vWvf81vf/tbLrjggpmeOq2f/exn3Hrrrdx1112sW7eOr3/962zcuJG9e/dSW1s75finnnqKd73rXdx+++1cffXV3H333Vx33XVs3bqV5cuXk8vl2Lp1K5/5zGdYtWoViUSCW265hWuvvZbNmzdPtPOe97yHgYEBHnroISzL4sYbb+Rv/uZvuPvuu0/K+zoRQnjAXIkwV05sk1JiuS8Q85lkcynyjnW421SiCUHA1JG2wbh00BwHv2miaxpFy6bg2AS8Jo2RCIf6x4iEfBNDc0JCKluEokPJlrS3VqNp5X8s4ZAPK+aweShF90iSpubKKYFMMOTD4zGQljPte4mPpGlur6Gq7tUTBzVNw+OdWkleURRFOU4Spsm8mHkbrwPf/va3+cpXvsJ73vMeDh06hJSSdevW8Y1vfIO/+Zu/mXHAJOQMM6wWL17Mv//7v7Ny5cpXP/g4rFu3jnPPPZc777wTKPdUtLS08JGPfIS/+7u/m3L89ddfTzab5f7775/Ydt5557F69Wruuuuuaa/x3HPPsXbtWrq6umhtbWX37t0sXbqU5557jnPOKefIPPjgg1x55ZX09vYe1xhqKpUiGo2STCZnZRbBdL6y637+OLKDmBnC1Aws10EApqaTKGUYyeaYJ+cTLkUZSKWxXIeAx0NTJEzBcYgaXsYOJekaHseyHaSAgMdkfn0VvrSkoToyMUPupbp6xug4MMzi+iqamismgibXlfR0juKULETeorIqRKwqVK7W7biMDiWxbYdr3ruB1nm1HNjWzXBvOem7cW4N7cta8AVe21iyoijKn5LZ/p1xpP07Nv8Sf+jEJsrkM1n+xznXntLfb7PB5/Oxa9cu2tvbOXToEKtWrSKdTtPZ2cnSpUvJ5XIzam/GPUx33HEH//N//k/uuusu2o5RcPB4lUoltmzZMinK0zSNyy677JjLsWzatGlifPSIjRs3ct999x3zOslkEiEEsVhsoo1YLDYRLAFcdtllaJrGM888w1ve8pbX/qZmkaGVh9gEYLlFbGkjEAhpYtnlQpdVAR/NkUraqytwZTmhG2Ask+WFrn6ajBBnzW8qF6MU5a7XobEUQ6kC7c3TL3pYVxMhkykiNeg4MIzPb07kPNXWR7ny2tV07hlg6xP76Nw/WA6oJMSqQ1zyprPw+0x++pVfM9wTnygrJTRBU3stV77vQmqbK0/dQ1QURXkdUx1MR8VisSnryUF5seBFixbNuL0ZB0zvfe97yeVyzJs3j0AgMCXpOx6PH3dbo6OjOI5DXd3kKs51dXXs2bNn2nMGBwenPX5wcHDa4wuFAp/85Cd517veNREpDw4OThnuMwyDysrKY7ZTLBYnksZgasn42VYekrOp9gYZLo7gSgddaOWilFIiMDClgSMdXClJFgvlOky6QcjjYSyVI5UrsWFOBVHv5DpMjuXw4mCS0WyemtDUXCXLdqiuDvPWjasY6knQ1xtH0wRz59exeGkjkWiAOe21rDhnLh37BinkSoQiftqXNGCXbO75+oMkRlK0LKibWOLEKtn0HBji1z/+I++65XJ8wZNTEE1RFOXPmhTl14m28Tpw9tln8+STT3LWWWcB5Rznm266iZ/+9Kf85Cc/mXF7Mw6Yvv71r8/4IqeLZVm8853vRErJt7/97RNq6/bbb+fv//7vT9KdvTaOdLBlgaBh4rgmtnTLQ3K6Drg4ls1gNkNfpodUsYAjJaamUR0IMjCWImSahKaZTtlYE2XnoUG6huNTAiYpJaOJLEvm17NwQT2LFjbgOC5CiIlcpyMqayNU1k7uvt304DZG+hO0LW6cdLzpMWiZX0ffoSEOvNjD0rXtjPTEKeSKBMJ+qpsqVOK3oijKDKkepqM+9alP0dHRAZSrlJ911lnk83l++9vfcuGFF864vdc0S+5kqa6uRtd1hoaGJm0fGho65grC9fX1x3X8kWCpq6uLRx55ZNI4bH19PcPDw5OOt22beDx+zOvedtttk4YCU6nUlHV2ZpMQAp+uk3PyNHirsLGwXAuBwKN7sV2HVHGMrpE4QUsQ8XrRNY2S49CVHCdZyrMqUIcupiZVm4ZOVSxIPmszMpamqiKIpmlYtsPQSIqAz8Pa1W0cODDEju09dPeMoQnBgoX1rFjRQtMrDKkd3NGLP+CZElwBGKaOQPD847t58fFd9O7rp1Sw8QY8tC1tZsO1a2hsV2vIKYqiKDN3wQUXTExQa2pqmkj1kVLS1dXFnDlzZtTejAOmI4aHh6ddfHcmyeAej4c1a9bw8MMPT1TedF2Xhx9+mJtvvnnac9avX8/DDz/Mxz72sYltDz30EOvXr5/4+UiwtH//fh599FGqqqqmtDE+Ps6WLVtYs2YNAI888giu67Ju3bppr3uyVml+raSU2NLCp5kMl4YQ4iUL8zoarquhoxH0mmBBplRCFwLLdfFpOiXTJGMVj9l2RSzAwnmVZIZzHOgcxZUSQ9doqI1y6fmLGOxN8Phje7Ash3DYh+1KNj11gJ07erniytUsXFhPx/5BDuzqJ5spEKsMsmBZ80RZgWPJpvM8/8hOKioD1DRX4vV7KWQL7Hp6P0NdI7z1o1fQMHfqbElFURRlqtNRuPJPzcjICHPnzj1mOZxjmXHAtGXLFm644QZ27949pe6CEALHmX56+bHceuut3HDDDZxzzjmsXbuWr3/962SzWW688UYA3ve+99HU1MTtt98OwC233MJFF13EHXfcwVVXXcU999zD5s2b+e53vwuUg6W3v/3tbN26lfvvvx/HcSbykiorK/F4PCxZsoTLL7+cm266ibvuugvLsrj55pv5y7/8y5NaZfRkk7j4dEnRtpGOQAit/BkIB4GDJnTmV1fhD1cxlMlSchyCHg/14RAjqSwH+keI5/L4DINssYQGRPw+Epk8saCfN6yex/ZdfQwns5RKDqbPZP68WqTt8sfH9xLwe6hoOjr7oqo6xED/OA8+sI0XntpP575BXMfFMA2sosWWpw7gNzWy6cLhJPPJvUy24zDcM0Y04mPOkqaJ/aFYkGA0QOfOHjbdv5W33LxRDc8piqIcF3H4daJt/OmrrKyctj7Ukd9HNTU1zJs3j69+9ats2LDhVdubccD0/ve/n4ULF/KDH/zgpBSuvP766xkZGeGzn/0sg4ODrF69mgcffHAisbu7uxtNO9pDsWHDBu6++24+/elP86lPfYoFCxZw3333sXz5cgD6+vr45S9/CcDq1asnXevRRx/l4osvBuCnP/0pN998M2984xsnClf+0z/90wm9l9kkhEAXLkW3SLOvlqybwXJLCAx8up+C7VKwk3gNQYM3TMjnxZEuXt0gYJp4dZ2h8TSbO3qwSpOD2ppwkMtXLuTBP+xiJJ6hpiqE1zTI5ks89ux+3KKDkXdobIxNuaf6hhjPPLWfLheWLWvC/5IyAelkjr7OUXBcRvvHqWmqmNgnpaRjRx+u7TBnceOU75EQguqmSjpe7CY+mKSqYfK1FUVRFOWVHCvnOpVK8dGPfpSvfOUrPProo3zoQx9i+/btr9rejOswhcNhnn/+eebPnz+T0153Tksdpj3/yrbEXkzNxsXhSGqeQKNoQ7okqXcWk00GSRQKuIeTvmuDIUKGl+7hBP6khm05SEciBRi6RtDnJSY8+PIwt6V6UvBi2w5/eHIvNQE/5yydmrNVyFv88ZFd1FWHWL2ydcr+wd44Vr6Ex7HIZ0oEwz6klOTSBQSQGh5n+Xnzj7HsisVQ1yh/9Zm30rzg5KxerSiKcjqcqjpMX3rm/pNSh+mT667+k6/DdCzDw8M0NDTgOA4DAwPMmTOHUqn0qufNuIfpjW98I9u2bfuzD5hONSklhgCf7pBzigh0TM3AlRJb2mh6OVfp0OgoWlEQMj0Y4mjSd7ZYotbxs27+HHRNo1CyEQL8HpOekQQv7h9gQ2vLlMDFMHQCXpPRTJ6S5eB52RIn2Uwe23IIhCeXKjgiVhkiMZbmTdeuY7h7lO69/QhNcM6ly4hVhfjNDx6hmCtNW1agkCth+kz8wenbVhRFUZSZikaj/PM//zMAwWCQq6+++rjOm3HA9P3vf58bbriBHTt2sHz58il1mK699tqZNqkcByEErrQQQlLjiZFxUzhuFk0I/HoAr+ZnwEqAcMtr9SIQQiAOF4osHk6+9hjljzzoOzp05hE6Jccl41hMNyetribC3gODFErWlICpVHJAQCx8jEVyD8dfdS2VrFo/Och2bIdtj+6kd38/zQsnD8tJKRntj7N03QIq1XCcoiiKMkOPPfbYMfcdmSEXiUT4xS9+cVztzThg2rRpE08++SS/+c1vpux7LUnfyvGRUqJpLmBRknlMzcWjicODcjlybg4NwfzKGEkCJAtH6zC1RKPoFuSkTcl18GiTgx7D0NGAfMma9tqRmJ9AwMvAYBJ/q4l5OGgqFCySqTyV0QD6MSp3JBNZKqrCVNaEp+zTDZ0N167hV99J0LO3n5rmKrwBD/lMkZHeMSpqo6y/+myV8K0oinLcTnzx3ddL0vell146ZcLRS7OQZjpLbsYrnX7kIx/hve99LwMDA7iuO+mlgqXZpeFiaDYlaeO6GuVCAhqOC460MDWb6kCQ5XW1tFZGaYqFmVddydKaGir9AUqOTdG1p7QbDfkwPTrFwtR9UkrSuRIb1s5jTlMlfX0JOg6NcOjQMCMjKZavaOHSy5aRHMtSLEwOuDLpPIVsiVVr2/F4zSltA8xf3ca1H3oTrUuaSAwl6d7TT2oszYKz2rjuwxtpmj99XSxFURRlGvIkvV4HEokE4+PjJBIJEokEvb29/PKXv2TVqlU88MADM25vxj1MY2NjfPzjH5+yPIkyu4QQCBwMIfAbHkoygyttQODTPWgyQNzJ058dZXhMUnRsECAygp5MsjyUJiGTKzJSyJDKF9E0QWUwgKFpNNfECOY1hkZTVFeE0HWNkmUzOJoiHPRyxSXLaayJsHfvAD09cXRdMK+9jvb2WopFC2k77NvRB4DpNSgVLAxDZ80FCzh7/XyG+xLs3tpBz/4hNENn7uIGFp/VRkVNmHmr5tC2vIXBzhEK2QLBiJ/a1upJsyMVRVEUZSZenrAeiUS4+uqr8fv9fPKTn+Tyyy+fUXszDpje+ta38uijjzJv3ryZnqqcgKP1lgpIJD7NBHxIJOBgu2kMIejPZDBEFZU+/+G8J0myWGSomKE+EOSZ/T0gwGeWF9A9OBTHa+q8e/1q6k0/v3liDy92DOI4Ll6Pzvzmaq69dAUt9TFe2NbN89u6icczCCEYTeSwHJclixv4i/ds4NCeAfbt7CWTzFNRHWbRimbmzK9j95ZOHv6PZ0klsvgDXqSUHHixh+f/uJcr3rOBuYsb0XWNpnkqCFcURVFmV3t7Ozt27JjxeTMOmBYuXMhtt93GE088wYoVK6YkfX/0ox+d8U0ox0cXNqYGtusisNCFRCCwpQZomJqDqUHJcXF1iY7AdspDpZqAomNTFwtRKtkUHQdd14gEguiaRtdYgnE7i6tDTXUIXdNwHJeC67CjY5AD+wZ5/vluTFMnGg0gXcmhQ8N0do7wxkuXsn7dfBavbGHxysmlB4Z64/z+P57FLtm0LWqYGEt2XUl/xwi//benec/HLyccm7ror6IoijIzqtL3q6uoqOB3v/sdjuOg6/qrn3DYa5olFwqFeOyxx6ZkoAshVMA0S4QQaLiYmotXc3BkEZfyF9ura0jXpISkLRak3/KQKORxpItHM6gPhSkVbYaSGS6aOxcTjVzRQghByOfBlS5P7OikQno4q60R0zj6BcoVSjy++QAybbG0tY5Q6OgU/3DYx+homiee3E/73BqsvMWhfYMU8iVCkQDzF9Wze0sH6UR2UrAEoGmCxrZquvYPsX97D2e/YdGpfJyKoiivU6rS9xFdXV3ceuut7N+/nw0bNnDHHXcQDAbp7u6mubl5RsESvIaA6cjKv8qpJaVEYCMoINDwa77D68kJpNTJkcejg9fwEvSbjDt5kKDpEA546Enm0XUNicRjGBPlBQDyOYt0tkBtpX9SsAQQ8HnI50pks0V8fg8vV1UV4sDBYX72r5vIJ7IU8xaaLnAcl02P+SnE0/gCnmlnumm6hm5o9HeNMHe4no6dvRRyJQJhH/NWtBCuCJ3056goiqL8efjABz5AIpHg+uuv50c/+hGf+9zn+MpXvsIzzzzDr3/9a+67774ZtfeaF99VTq0jSd+mpiFkHrBAionJDF7dg+Vo9GQHGcp6CZgedKFRcm32JkdJOQUq8OPVpn7kuUIJx5X4PNPPZMOROEJSsCxC+uQCk0IIxuMZxnrjrFrSRKi5EigHeOPxLHu7E1RFfTRMLQIOlKd1HnqxhwPPHSCdyCG0cq9ZtCrMhqvPYs2ly0iOptj73EF69/UDgtYlTSw6dx6RyqmlChRFUf6snYxZbq+TIbmnn36aJ598klWrVrFixQr+7u/+jq985StccMEFfOYzn5lxe8cVMH3xi1/klltuwe8/RnHCl3jmmWcYHR3lqquumvHNKMcmpUTXLDyigK5puNKDwDn8vTbwICnpJfK2TYXHPzHDzKPreDSdUZHFkS627TCQSZMuFBFCUBHwY9vlGXVh79Rq21Cu0yRdyXTdtMWiRSKeoaEqQihy9PshhKCiKkQ45md4KMniacaKHdshMZgkNZigqa2a1iWNaJrAdVxGB8b5/T1PMdYfZ/+z+xnti2MeLk3w4h938dyDz3PV37yJOUuaT8bjVRRFeV1Q8dJR1dXVE/973rx5DAwMAODxeMhmszNu77jmbe/atYvW1lb++3//7/zmN79hZGRkYp9t22zfvp3/9//+Hxs2bOD6668nHFZ/+c8GXTrowkEjT0DLENByBLU8PpFFUMAUDlGPQbyQJ1UskrWKJAt5UqUSDaEwNi6P7DvEjv4hehJJuuLjvNDTz/aBIUIeE9Odftza9Bp4NA2PPvXrMjqSxrFdWppi057bOq8WqWt07BuaVCTMsV269g9SzJeorItQWR9D08rX13SN2uZKivkSv/ruwyRH0rQtb6VlUSMtixppW9rCWH+CB777e9KJzIk/WEVRFOV155Of/CSf/exnyWQy+P2HOweAH//4xyxZsmTG7R1XD9OPf/xjtm3bxp133sm73/1uUqkUuq7j9XrJ5XIAnHXWWfy3//bf+Ou//mt8PrX218kmhEDXLHyihCYcHOlOTGUQQuLFxdE0mkM+RtMGA7kUjpR4dYO2cAX1vgjPpXopuDZ+DHRDQ0qwXBepSWqqIoynCnjN8vp0juNiGjqW5RCO+GkMB+npjVNfGyUQKOcypVJ5RsYyRP1eYtHpZ7kFw34a51QT8pl07Rss91ZJietKAkEfsZifuqbKac+VtktiJMWSNXMngikoB1QtCxvp3NXDvs0HWfOmVSf5aSuKovyJUl1ME+699162bt1KS0sLbW1tFAoFVqxYwaFDh/jlL3854/aOO4dp1apVfO973+M73/kO27dvp6uri3w+T3V1NatXr57U9aWcfFJKdCwMYWGK8vCcwC1/r6VBUWpYLnQXMuTdErXBEJoQOK7LaDHDUDaDEHDhgjaSmSLJXB5d06gKBYgF/QwkU3hNg817esjkS0gkmhBUhPz8xUUruGT1PH77+50cOjRCT18cBFREA6w7Zy7duwfIpgtEpgmaUuM5muZU8/b3bqBr7wD9nSPlgGdeHQKX/7rrYXRz+pkK6UQGTdMmlbI/QtM1DNOge0+fCpgURVEmqFlyR6xevZrVq1dP/Lxx40ZaW1u59tpraW6eeTrHjJO+NU2bchPK7BNCYAoLn2aDtBBSoolyJ5OLhVcIbKHhyDRV3sCkWWmW67InPUKdGaY6GKQmNHX22Z6+AqmcS2NtFE2Iw+vvaNiuw6GBOOcubWX+/Fr6h5Mkc3mEEEQqg6xY3UpACF54rgN/wINpHv1KFfIlMuk8ay9cSE1DjJqGGHC0G3SkL04g7CMzniNcEZxyT6WChWHq+AJTZ+eVn8lrf56KoijK69tXv/rVk9qemiX3J0JKiSHKPUwe4aKJ0uGgBhA6ltSxNIEhddKlIp4j5QEk5BwbU2ggXGxcdKlRsh2EKCeFu65kZDxDtelnydy6Kdfd3zvKD37+FKRtvF6DOS1VuFIyPJLiF7/ayoZz2pm3qJ5D+4fweAw8XoNCvoR0YcWaNs7dsACAXKZIfDiF0ATV9VGqGyuYt6KV7U/sJRD2ob+kpIFVtBG6hj9gYnqmfk1d18Uq2TQvaJi1Z64oivInRw3JTdHV1cWLL75IPp9n1apVLFy48DW1owKmPxFCCHRK+CihYaMhObLUmiMlYOPXDGqDGtvG8mSLxcPDahox009rKEYinaczkSCeypMplRBARSBAQNMpFC2aaqcudCuEwEBjx8EB1i9opTp2tCcoHPIxOpZhy4vd/OVbzmXZ6jns2tZNJl2gZU41S1e1smBpI9KV/PE323nxuUOkEjmEgIqaCKvXz+P8a9aQGE7RtaefYDSAz+8hny1SyBRYccEikv2j9B8YpHF+/aQq4X37BqhpqmTRufNPwdNXFEX506DipaNKpRIf+tCH+PGPfzwxc9y2bd7xjnfwk5/8BI9n+tGLY1EB058IKSWmsPFoFh5cBKXDX2oJwsAROq50ydsFAh6TiMcDonyeg6QgS+TtEtv7BgmZXnyGgUQymEqTyuUxNY2myPSzG9OpHI4r8Xqnfl2qKoMc6hyluy/OovY6LNuhULAIhnw0t1UjgAd+9gwvPnuIcDRAXVMFrisZH8vwu//YzHmXLuUt//1N7HrmADs27aOQLVJZF2XFW85l2XkL6N3bx4P//CgdL3bjO7wOXTFforq5kitvuoxIlZqRqSiKMkFFTBM+9alP8cgjj/C73/2Oiy66CIDHH3+cG2+8kc985jN86UtfmlF7KmD6E1Hu6cnjFSUMbEzhoovyNH1LSmzXxhY6gjzVL8thclyXg6kxdF3Hpxk4jot1uIaTdCVe08R1HTLFEpWBqbW2kpkCXlOfUgX8yH1pmuDpp/bzzMN7yGYLCCGQLkRjfua0VrFrSyf1LZX4A0frPNU1VZAaz/H8U/tZvLqVDVedxbrLV2GXbEyvMfHXwKJz51PdXMWeZ/bTvacPIaBtWSuL1s6nojZ6kp+yoiiK8npxzz338K1vfYtLL710Ytsll1zCP/3TP3HzzTefuoDpwIEDHDx4kDe84Q34/f7D+TQqC3e2SCkxcdC1EiYOmnQOz2OQ6MLG0Q0c6WIiSZRyICRSysMz5UC4Ao9H59z2ZsZSORK5AroQ1ISDVIcCPLGnk33Do6xpbiSZLWC7Lh5DJ+L3UnJdIl4vPnP6r8vocIrRos3i9npq6moRQuC6krGRNL//zXZCpsGcwNSimJFYgLHhJAd29tE8twZd19CnW36loYLzr1vL+Sf3kSqKorwOqVlyR4yNjbFq1dRZ1CtXrmR4eHjG7c04YBobG+P666/nkUceQQjB/v37aW9v5wMf+AAVFRXccccdM74J5fh4tTzStfAIB0O4iMN9ry4aFi6uZhA0XcasFLZ7uE9VgFfT8WoGHqHh95ksDtZOabuuIkxqJMdDzx8AAZoo5wppQtBYHcafk9i2g/GyXqbxZJ5UMs/8xkpiL5nppmmCmroIe7Z1kyw55ba0qf8IDUMnlcjhui4jfYmJteSqG2IqAFcURVFes9bWVrq6umhra5u0vaOjg9bWY6zX9QpmHDB9/OMfxzAMuru7J1XKvP7667n11ltVwDSLTEoYolSuwyQkOhIpwRGguy6ucNFFgeZgDMeVuEh0BAhJv51GODqZQonuTJLxfAFNCGqCAeojYUq2g6ZpBHwatu1SXrlXYJoaoaif6oiHrp44dbURgoen+SdTebq6xvAbOi0tVdPecyTqZ3ggSS5fIhSc2stkWy6FbIF773yInv2DWCULj89D2+JG1l+xisa2mtl8pIqiKMrr1Kc+9alpe5JGR0e57bbbZtzejAOm3/3ud/z2t7+dUvRpwYIFdHV1zfgGlOPnEzam5mIA5VXVRDmxG4mlgZQOXmHjNzwUXQuJRBcaJjqanqFQLLGtbwDHkXgMHVdKxnI5Do0lyGWKLA3XsHRhDdlCCdtx8ZoGXo/Bwf4xok0hfIbOjj0DJDN5hISayhBzW6uISw1jmmVTAKrrogz1JygWrCkBUyaVxyqW2P98Bzgu1Q0xvIdnye1+7hBDPWO85YNvpK6lkv6DQwz3jAFQ31ZDw9xa1QOlKIrycirpe8INN9ww7fa3v/3tdHd3z7i9GQdM2WyWQGBqRed4PI73GIu3KieHT+QxAa8QaIBO+XvtCIkhQWoSE5uu7DCIw3PoJAgEAd1LSpZIlQo0BKOYenlplIJl0ZdMo9mSlsooCEHQP/lzrI4E2La/n0ppEgx5CYe9E/+e0kULV4dspkAoPDVh3PQaVNdFiQ8m0aQkWhFESkliLFMuMXB4fbnWhUfLBoRjAUJRP517Bnj058+gS5fOXb2U8uWZgf6gl/aVc3jTey8kUjm1CKeiKIqiAPT399PV1UWpVJrYFo/Hedvb3jaRWnRkBt2rmXHAdOGFF/LjH/+YL3zhCwCHE3xdvvzlL3PJJZfMtDllBv5/9t473rKqvvt/r7V2Of32On2GgaEMVUBEBRQpGhHEHhWxPT7GSjRKNKgxPiQaUfPThOQJaIxg4QmiRtQgKipFpIPDML3dXk/fda3fH/vOHa73InNhBgH3m9fhxdll7XX2OYf7Od/1/X6+LuAKcIVECYlEYEiW3iI0CE1WhUnCt07ElBAgJGgdkbEVfS1F6vVgphcdOJZiWUuJkckq05FPkfmi1/djdg9P097XzZGH7TOKNMawe3CK6SiCwWnWrHFRlnzUeSG1ms9LX3kiIgh5+N6d7N42ipCC1vYCR5+4ko2/2UxH7/x8JSEELR0Fbv3BPbS2Zll+aB+5UlJcUK80eejXjxB4IRe+/1wc1z5YtzwlJSUl5RnKZz7zGT7xiU8s2F5LCMGLX/zimd6meoGz57NowfTZz36WF7/4xdx1110EQcBf/dVf8bvf/Y7JyUluvfXWxQ6XsghcoclJC4kksaoEECgkrhAgIS9hdaGTeuwRa42jLLLK4eGpEXJOlpO7l1NueJQ9HyUE7fkcYRgxNl1jstFgWaGUfIBmKuyEEAyMTkFs6OsqzZmPEIKlfa3U6wEZqdi5fYxc3sXNWDQbAYEfcfhRS3j+GevI5V1OPuNwxobKSCnoXtrG4NZRHvzVxsdsfdKoNClP1jjs6GXkStnZaxZacthre9l6/062PbCLdSeuOaj3PSUlJeUZQ7okN8tXvvIVrr76al7+8pej1L6CpbGxMdauXcvU1NSiUjsWLZiOOuooNm3axJe//GWKxSK1Wo1XvvKV/MVf/AV9fWmbioOFMYaMAGUSn28ws4WfmkQ22UJgYxgPpwh0iAGkEdSiRJAIDAO1MiPVBlU/QAgoRz79xSJZx2Gi0mCbnmCkXCOMY7K2TU9rgZGpGj0teVxr/sdFSkkma3PYYUvozme5/dZNTEzWaWvL86KzjuLo41eSydhMjlfZ9NAe9uwYR0rJislu8lkHx7XwmwGZBWwHxgYmUEriLrDPzToYY9j2wM5UMKWkpKSkzGN0dJSXvvSltLW1zdnueYlfYEvL4rz8npAPU0tLCx/72MeeyKkpT5Ck+a6LEAqxgEeGNgZpJEoIKlEDCwslJL6OaBKQd2yatZAHpoaxtE3GUhhgT7nCULWKnVU0xgLuHR2kkHGwbcVoo8ausWkcBO3Z+flJezHaMD5RZWTnBH6sEbak5gXc/+BuWjuLEEb85Lt3MzVew3EtjDY8dM8OuvtayLcXGBucZumauUncxhiqkw1KrTmy+YUjUJZt4TWCBfelpKSkpPxp8+Y3v5nsAn+7stnsYyaE/yEWLZhWr17NaaedxpVXXjknyXt8fJyTTjqJbdu2LXoSKfuHJduJzRQSM7Mmm8SWQCKEIdQxDVOi122hGjWJ0RSFS8HKMOHXiEVIHEFnzp0VJ45UDFWrEBvWFFrIFCym601irSlkXJZ3tTJZaTBarbHWdM4LX4ZhTKXcxJts0NWSZ+nSNixLEQQRIyMVvvPN2xGNAIVg5dqeff3gYs2e7eNYtkQ5Fnu2jNDZ34abtfHqPmOD07R2F7GMXjBkaowh8AI6+loP7k1PSUlJeSZhRPJ4smM8C7j66qsX3F4sFh9z3x9i0YJpx44dWJbFC17wAr7//e/T25s0bI3jOLUVOIgIIZD24Rg9jDExiIi9C80CmSRDx4btXhshTaQKE2GFJsAQ6oisbVFyHSYbzZkolQEEndkcY+U6xY4sR3R00vQjojjGtS0c22LH8CQ7d02wbfcE3R0FPD9CCHAdi+GRCoEX0t1WpPdR4sVxLJYubeOu32zDqzR5walr5wgfqSRLVnWye9soJ5x6GJN7JhjcPkroRzhZmzXrl7HysF5u+c7tlMertHTO7Rk3NVIm35Lj0BNWH/ybn5KSkpLyjOPxCtF+/vOfMz09zQUXXMDPf/7zxx1v0YJJCMGPf/xjPvShD3HCCSdwww03cOKJJy52mJQngMicg4wehriKIZjNYhJAaCRDoc0DjVZqcZOMdJBCEumYclQDAXkny/ql3QxO1plsNpFS0FcoksVivFxHy0RAZV2bvU5PkLiAV+seo6N1Nm4fIYqTigLHtujrLNLiOvT2zF8LFkJAHONHMZ4fkfu9tidKSaSUGCl4/QfPZXjnOF7DJ1/M0r2sHSEEzUqT239wN9WpGi0dRQxQHisjleKFF55Mb2psmZKSkrKPNOl7luOOO+5xj7Fte7+OgycgmIwxFAoFrr/+ei699FJOO+00/u3f/o2XvOQlix0qZZEI5wSk+yIIbscYH6NDwCBljhiLX1aK+LRRsAye9jHaIIWkVeUp6yZh5PPw2ARVLzG1NDE0ylPkpIXGsNcQIIo1sdFYUqKkxAtCpipNOrMOh6zqTsydZkwzq1WP8ZrH4dbCxpVSJdGvOP7DZZtSCvKlLMpS5IqZ2ea7p73qZLqWtHP/LQ8zsmscIWD10Ss49rQjOOzENal5ZUpKSkrKglxxxRWPe0w+n9+v4+AJRpj2cvnll3PkkUfyjne8g9e//vWLHSplkQiZh/ybkaoHgvvBTAMKVC9TwRruqO1AmxApI1wRz/gwGYTwsKSmHgVMew3a3AKWTIRMoGPGGw18ERM2YzZ5YwyXa8Ra49qKvtYSYxM1Ii9i3bpluM5cz6OhkTL3j5QZnqjS11maN+dMzsGMGWxbzdsXx5o41riuxfe/+ku2PTxIGEQ4GZtD1y/jxBcfSVdfK0edehhHnLKWerkJQKE1lwqllJSUlJQnxIYNG7jmmmv4zGc+s6jznlCE6dG88Y1vZM2aNVxwwQWLHSrlCSBkCyL3GkzmTIhHAQXWUqanhrDVLqpxE2UUtnSQAmJj8OIApEEKC8PvRXoMSASOq9g8Oo4TK4pZF0tJmkHE/TuHiPyIQwvt88QSQG93iY0Zm+0DE/R2FOcImTjWSEvR01ViarRC79L2fUnfWjO4Y5x83uHB2zZRm2rS0VOi1JbDqwfc9YuN7Nk2ygVvP52u/jaklBQf1dw3JSUlJWUB0iW5BRkYGOCb3/wm11xzDQ888AAnnnjiwRdMCzlinnLKKdx///1s3LhxscOlPEGEbAfZPvvcGE1MSMnO4ekGoW4CBowkp7LU45i8Kylmckw2GoQ6xhhBzrZY3trK4FQZk9XkQxs/jAjC5DtTyrpMh5pYLvwNEkLQ01MiroVs3z5GSymLZSdVcpWKxyFrezn6iCXc8bMN7Ng8gpuxMcYQ+hGdPS0QhkxO1Fh52L7WKG7GodiWY+cjw9xx00Oc/brnsv13exgbmASgd0UXKw/vn7EV8Hnkzi387vZHqE5UaeksccTzDuOwE9fgZtNWPSkpKSl/qpTLZf7f//t/XHvttdxyyy0cdthhvOENb+D6669n1apVix7vCfkwLURPTw89PT0HariURSIFCDSRaeBKMNKZKYIzCBEiZIQyNtmMYsqHyGiEFMknQBg8P+LQrg4OK3QwUW0kLuGWorOU595H9jBcrRPEMY6au7RmjMFxbY48bClD2yZ44OFBoijGdW2OO2Y557z0GJYubWfNob3cd+dWNm8YQirJkccso6u7yPeu+iVd/fNbo0gp6ehp4cE7tjLwyCATQ1PEkUZgULbF8sP6OO2C5/Dr63/D5ru3oiyLTN5lfGCKTXdv47CTDuG8/30W2cJj+0elpKSkpDx76e3tpaOjg9e97nV8/vOf59hjj31S4+2XYDr++OO5+eabaWtr47jjjvuD+SP33HPPk5pQyhPFYCuNr2MwAlsC0mCMIIjBkhov8BmsVym5ObpyOQzQjEK2Tk9SMz7tmSyFrEvh9yIzS7tamSgPMF1rkLFs6s0ABJTyGXw/RAnB0J4pqg2fQ9f1oqQkimJGxqv89GcbeNk5R/PgPTvY8OAA1XIDhOCBe3fS3V2i2fDpXd6+4CtStmT7hj3UugqsWb90tmec3wzY9tBuNt29Fe35rDxiKU5mXwWe3wzYcPsjdC5p58VveMHBuuEpKSkpTz/SJblZbNsmCAKazSb1ev1Jj7dfgukVr3jFrEnl+eef/6QvmnLgCXSIMJqiJQlIjCcxBoEgY1vISOGJkKy0yFiJ8BBAzraZokmEwRKCquczWWsQaY1rWXQW8xSLGVoKWe7dNIiO4sQKgKTBbzHrsKy1RLXWZNXKztnqNoAwitm8ZYT/e+XNhGWPlrY8fUvb0cYwPVnnrju2UJ9u0u8FZBZYPhvZNYHf8Fl6yJo5DXbdrEP30jZu/+97WHlY/xyxtHd/a2cLD/16Iye/9HgKrWnuU0pKSsqfGsPDw9xwww1cc801nHHGGSxdupTXve51/Pmf/zlHHnnkosfbL8H0iU98YsH/Tnn6kLVspAgJjEdWuiDiRBEhMEAofLJWFl9HDNWrSJlECU1syNs2sa15YHiEbKDwo3g2ipixLTJKkXNsdFYQRTFxlOSx2RmFEYKBsTLHreqfI5YAbEshMGzYOMQpx62kVNq3PNbd24LrWjwwXGbXtjEOPXLpnHONMQztHKNQylJomb+sFngRURATRvGC96PUWWRo2wgTQ1OpYEpJSfkTQsw8nuwYz3xyuRxveMMbeMMb3sD4+Djf+c53+MY3vsE//MM/cNRRR3H//fcvarxF5zDt3r076VK/NPkDd+edd3LttddyxBFH8M53vnOxw6UcIHztYykNMcSmghCJr5IGDAopJFkLtCOZ9AOCMBEaOdumt1AgDDSj5Rr9okBbLouUglhrxip1xsKIJXaBU49aDggaXoAQgnzWYc/QFA9sGCAwCwuXZtVPjC7l/C9gS1ueUkeBRjNgYPsYXf2tOK6N3wwYHZhCWRYdHQtbCAgBQgrixxBMOtZIKVBqYX+olJSUlGcjAhBPcknt2SGX5tLZ2cm73/1u3v3ud7N9+3auueaaRY+xaMH0hje8gXe+85286U1vYnh4mDPPPJOjjjqKa665huHhYS677LJFTyLlyaMAJUKECgFFbGIEBoFECTAqoh74+DpieakFNbOsFuqY4WaNcuSxrFTE9RTTjSbMNE9pL+SYrjQJiFFKIoSgVMjMXreQdTEYxsp1OorzIzmNZoBlJQaYC9HWWaSrs4AKIkb2TBJHGsu26F/Vxcq13Wy+ZzvGmHmiKd+Sw7IVJlxYME2NTNPR30b38s4neEdTUlJSUp4tjI6OUigUyOVyrFq1io9//OOLHmPRP78feughTjrpJAC+853vsH79em677TauueYavva1ry16AikHBikFloiACEcG5K2QnBWStwIsEaJEjBQxBdvBtlQSfZGSjGVjYvCJOLSnk5PXLueo5b0cvqSLo1f2cdLaZZRch0YcUQ/DedctFjO4jsVUpbngvKJYk7EUuex8DyeAONIccuRS3vSX5/LSN57K6a84gZdf9ALe+MFzOO0VJ5AvZZkcLs87b3K0Qt/qHmxHUR6vzvqDGWOYHqvgNXyOP/PoeflNKSkpKSkHll/+8pe8/OUvp7+/HyEEN9xwwx88/i1veQtCiHmPJ5JX9HhcddVVLF26lN7eXgqFAmvXrn1C0SV4AhGmMAxnE8B/+tOfct555wGwbt06hoaGntAkUp48YexhC41UMdpEaJ24fBsEUmhcKYgszW6vSagDYpF0opNGggFHKDyTuIMbAVrONL0miSJN1T20MYk7eBQjSHKULEvS2ppD+TA8UkYqgdYGKQWBH9PRWUTXPHw/JPN74qVWaeJmbFpKGW785m/Y/sgQQRDhZmx2bBnmxNPW8YJXPIdbrv8tOx8epNiWwxioTtXJFTO8+gPnMrFrnHt/9iATg5MoSxJFmnxLludfcBLHv+ToP8I7kZKSkvKnRb1e55hjjuGtb30rr3zlKx/3+C996Uv8/d///ezzKIo45phjePWrX31A5/Wtb32L97///Vx66aWsWbOGt7/97fzd3/0df/mXf0mz2eTtb3/7osZbtGA68sgjufLKK3nZy17GTTfdxKc//WkABgcH6ejoWOxwKQeIrHJQMkToCFsZDFHiwWQEBpu6jnCVC1ZMzYswM/6jSgpKbgY3UOyanGLYq+BFEXuX5PKugyUkjpQMj1bY3PSpNX0E0FrMkbUtlvW302m5/Pau7VRr3uwSWntrnpedczTRVIOH7t1FS3ueltZcEgWarFOrehxyaC+3/c9DlCdqtHe3UGrL4zUC7vnVZvZsH+eCtzyfzv42fnfHZnZuHEQIwfFnHMn6561l+WH9GGM48tTD2Hr/ThrlBvnWHGuOXUnvyu60fUpKSsqfHn8EW4Fzzz2Xc889d7+Pb2lpoaVlX8P2G264gampKS6++OLFXfhx+OxnP8vll1/Oe9/7XrZt24YQgte+9rVkMhkuvfTSgy+Y/uEf/oELLriAz33uc1x00UUcc8wxAHz/+9+fXapLeepp6hq2jNEiBKNRwiBE0ic3JsZVEj/yKbounZkC0Yxjuy0lU4HHhGgQT2lWZFpoz2URQiTl/w2Puh/Qm82yYecISookb8kYtg9OoKTgxLXLmJiosXJFJ0oJjEmSBoMo5pEtI7z87PXk8hnu+PUmtm0ZQQDdPa284MwjGdg0THmyzoq1j3b6tim2ZtmxaYTf/OxhXv7G57H6qGVJgreYm8gthKB/TS/9a3r/CHc9JSUl5dlLpVKZ89x13dkVpgPJVVddxZlnnsmKFSsO6LgPP/ww55xzzrztxx57LNu3b1/0eIvOYTr99NMZHx9nfHycq6++enb7O9/5Tq688spFT+ArX/kKK1euJJPJcPLJJ3PnnXf+weOvu+461q1bRyaTYf369dx4441z9l9//fWcddZZdHR0IITgvvvuW/A1/P7a6bve9a5Fz/3pRFa6KEJcEZFTERnp4wifjArIK40tIywRYwtBYCI8E+KbiNBohAYjoZB18IKYmhfQCEKqTR9jDK5l4emYw1Z00d1WTJbypGRZTysr+jrYsH2YQMcsX9bOkv42li5pY8mSNlYu76BW9/jFrx5h1+4JjBRkCxkyhQwRht/dv5ttm4bp7mtb0Om7s6fElg0DbPjtNn5y7W1c9envcvWnv8tPv3MHQzvHZ4/VWjO4bYStD+xkaPvogu17UlJSUlIWx7Jly2ajQS0tLVx++eUH/BqDg4P86Ec/WnS0Z3/I5/P4vj9v+7333vvUtUZRStHW1jZn28qVKxc9zre//W0uueQSrrzySk4++WS++MUvcvbZZ/PII4/Q3d097/jbbruN17/+9Vx++eX82Z/9Gddeey3nn38+99xzD0cddRSQrKU+//nP5zWveQ3veMc7HvPa73jHO/jbv/3b2ee5XG7R83864es6rgwxJkShsaRGABpBqDWuhJxlM+xNUw1tlEj8mYw22MLCFZLVve20hhmGp6qEWlPKZuhvKzI0VmFoqsqy1W1klY0XRAgBGcdmcrrGth1j6K6FSv8FxXyGO36zlWVtRVav6cayktYqQRDxyEMDTA5NsWzlwpVs2bzLzs3D/Ne/3owwhnwpizGG2390Pw/dsYWzXn8K2azDbd+/mz1bhgi8EDfrsHRtH6e+4jmsOHzJQbzjKSkpKU9DDuCS3O7duymVSrObD0Z06T/+4z9obW09KKbY69ev56677prVB3Ec85nPfIYvfvGLc/7+7y8HrJfcE+GKK67gHe94x+y65ZVXXskPf/hDrr76aj760Y/OO/5LX/oS55xzDh/+8IcB+PSnP81NN93El7/85dno1pve9CYAduzY8Qevncvl6O199izjZJSDLSIsGaKIMMQzlpUSVymascATIY5tkTc2sTZgwLIlsdF4IsaSkoxrk805yDgi69i4ro0fhCgpiLVB2oJcZl/Fm46Tb2cQL1zeX600aDZ8eo5cNiuWABzHon9pK4M7xxkZrbJ0Sdu8c6fGKowNTtGytpvlh+zrU2j6DcO7JvjulTdjGU3kh3Qu7SCTd/BqPlsf2Mn4wCTn/8VZLF+XiqaUlJSUJ0KpVJojmA40xhiuvvpq3vSmN+E4B76i+QMf+MDs0ptSitbWVm688UauuOKKWa2wGP5ogikIAu6++24uvfTS2W1SSs4880xuv/32Bc+5/fbbueSSS+ZsO/vssx+3hHEhrrnmGr7xjW/Q29vLy1/+cv7mb/7mD0aZfN+fE9r7/bXdPzahruPKAGV8lNDYMqlk00YQmRgjFa4M6Mvl8J0czThEiiRZvOYH7PSn2D45yYBXRSBQUjDVaDJYqdLwfTIoMpZFGMc0/RAhBDnXxnGtGQPJhZfBRocr2LZFxp1vK9DWUSSTdRjYPTlPMBlj2LV5FFtJlq7umrNPCEHPsnZ+9b17KBZsjn3ButklvVwpy4rDl7BzwwC3//c9LDusP03+TklJSXkacsstt7Blyxbe9ra3HZTxX/GKV8z+94oVKxgcHHxS4/3RBNP4+DhxHNPT0zNne09PDxs3blzwnOHh4QWPHx4eXtS13/CGN7BixQr6+/t54IEH+MhHPsIjjzzC9ddf/5jnXH755XzqU59a1HWeShwhyQh/JsIUI0TSSw4hsISFIMIVNkONCo3YJzbJkp2SCqEFwggmG03WZgvYj0qqbgQBYzokg2LXyBQj0zW8IAIBhYxDZ6lAPuug/ZggjChXPaJY49iKYt6l7gW0FbO4zvyPmlSSzt4WvHKDgR3jdPW14Lg2XjNgbHCKOI7oW9I6r+UKQL3cxG/6tHbk5wkiIQRdS9vZtXGQsd0TqXllSkrKnwzCHACn70WeX6vV2LJly+zz7du3c99999He3s7y5cu59NJLGRgY4Otf//qc86666ipOPvnk2SWzpzuLFkxf//rXee1rXztvLTMIAr71rW/x5je/+YBN7mDx6BYu69evp6+vjxe/+MVs3bqVNWvWLHjOpZdeOie6ValUWLZs2UGf6/6iTRNHBjgEWCJCknxrDAJtIoRU5KyQiIAgtlAINBDqECkEtiXIZSwqDY+MY6GkJIxigjimq5SnWQ64b/sQrbkM+ayD0YbJapOB8QpHLO3CLsf8/LZNIARCzngxCehsy1EyakG3bq0N2bzLSc9dQ3m4zJ7tY4R+hJu1WX5ID22tWcqj800rAcIgIo5i3MzChphuzmViaJpmfX7CX0pKSkrKgeOuu+7ijDPOmH2+92/lRRddxNe+9jWGhobYtWvXnHPK5TL/9V//xZe+9KWndK5PhkULposvvphzzjlnXlJ2tVrl4osv3m/B1NnZiVKKkZGROdtHRkYeM7eot7d3UcfvLyeffDIAW7ZseUzBdLDKKQ8UljBkRYA9I5iU2Lckp4VCaIknbJYWCkx4GZpRiAAKdoYwihkMq6zubCfbcNg5VSbSmqxtcWhPJyY2PFAZors9T+TFVOs+BnBtRVsxSzOKidG0tOYI/AiSwBa2a5Ev5VDNmInxKp1d+9bCjTEMD07R3llg/fErefjeHQwMTGJijXAUXUtacZe1c+sP7k76wv1eTzipBFJKstmF1729uoebtck+qo1LSkpKSsqB5/TTT5/ttrAQC3UBaWlpodFoHMRZHXgWLZgWihQA7NmzZ44R1ePhOA4nnHACN99882x2vNaam2++mfe85z0LnnPKKadw880384EPfGB220033cQpp5yyqNfw++y1Hujr63tS4/wxkcS40sfBxxERCj3rwxQZhZSSpnAoh01qWs86fZfjiCRf21ANfapehFFJPlkoDIP1KlEzQinJsWuWEPuauhcggFI+Q8ax+Nmdm+nN5Tj5+FX4fjS7JGdZkh27J8kXMtTG6mzfPkY886WylaS/r43jjl/JT2+4m/HRCu2dRdyMTbMZcOcvN9HZU6LUVWT3lhGWrO7GspOk8TCImBqr0ru8g9Dz530mjTGMDUxy+EmH0LW0/Sl/L1JSUlL+aPwRjCv/VNhvwXTcccfNeha9+MUvxrL2nRrHMdu3b1/QIOoPcckll3DRRRfxnOc8h5NOOokvfvGL1Ov12aq5N7/5zSxZsmTW++H9738/p512Gp///Od52ctexre+9S3uuusu/u3f/m12zMnJSXbt2jWb3PXII48ASXSqt7eXrVu3cu211/LSl76Ujo4OHnjgAT74wQ/ywhe+kKOPfua20hD4ZEXysIVO8pgwGAERFkpLGsrHixuEsY0jLcDgxxExGilhd7nMEtpoz2WRQhBrTdUPGK5U6XZyFBwX6QraSvuS4yen6/hBhNueLI25rsWj43Cd7XkGh6axMASxxvdCEIJszkE4it/du4OJsQor1/bMip5MzqGlNcfOLaOsPrSHQrHCwLZRjDZJ3Z8SLDukl6Pf9AJ+ff1v2LlhgK6l7bg5F6/uMTYwSVtPC6f82fFpwndKSkpKygFhvwXT3ijQfffdx9lnn02hUJjd5zgOK1eu5MILL1zUxV/72tcyNjbGZZddxvDwMMceeyw//vGPZxO7d+3aNSfh93nPex7XXnstH//4x/nrv/5r1q5dyw033DAnYez73//+HHv1173udQB84hOf4JOf/CSO4/DTn/50VpwtW7aMCy+88Al1Ln46oYjISZ8cPraIsdn7Q8MQEaOEoilDut0snhYExgcEOdshJ232RBU0BsdSyBmRIWdaohhhiI2h7vmMlutUGl7S+qSQQ+mkv9xCVXAAURiza9cEa3rbOeXUtbMCRmvDpkeG2Lh7kuOOWjrfuFJJ2ruLjI1WeP3bT2fXpkG2bxhECFh7zHKOPHENTsams6+F2//7HnZtHGRiaBo3a7PuxEM49bwTWHJI76PmEQFg2X9UJ42UlJSUlKeIF73oRX9wqfDnP/8509PTXHDBBfz85z9/3PH2+6/HJz7xCSAxqNzbi+VA8J73vOcxl+B+8YtfzNv26le/+g826HvLW97CW97ylsfcv2zZMm655ZbFTvNpjyV8CsInS4QjQAmDhCSx28RYUuNJnyYeQlnYRgAGLUIqUWIx0JXPUi37NOMo6SRnDAXbYWV7OyPjFW7btAu0SVqTGBiZTiwIEIKCnQgmbQw61iglEUIwMDSNjjXLlsx185ZS0NGeZ9sjwzT8kNYFXlMu7zI4UePXP76foe1jVKbqCARjwxWq5SbPPfMolq9bwrLD+hnbPUGz7pMtZOha2o4QImnf8uAuHvjlBnY9vAeAFUcsZf0LjmDV+uVp9CklJeXZhxHJ48mO8Szg2GOPfdxjbNvmuOOO26/xFv1z+6KLLgLg7rvv5uGHHwaShrz7e8GUg4NFRE7E5IXBFqBmmudqIBZgaUNDBMSmiTBFHCUxCPw4wjchUiaGlF5DEMQx2hgspZAZSWc2x8DoNFXPo7tQIOvYGAwNL2Si2iCbVUyO1/AaAaOTNaJI4zqK7vYiwyNlOlryC0agbMdCSpicbtDf2zpvv9cMGN0zSXO8Sk9/K0tXdWGA6fEqt3z/XqrTDU4/73g23buDDb/ZQmWyRktnkSNPPoRDj1/JQ796mJ9989f4jYBSexIRvf8XG9h45xZe/Ocv5DlnHXNQ35OUlJSUlD8eV1xxxeMek8/n9+s4eAKCaXR0lNe97nX84he/oLW1FYDp6WnOOOMMvvWtb9HV1fWHB0g5KCgC8kKTFxJbSCwhEcwkfaOxZERTRrTaNhORT6ATZ25b2bSrLONxk4F6hW7VxvK2VqQQRDM5TA+OjGA7ijUtHZSrHpPVBgLIuDZHruihUmuya7CCvzugkHOwbYvatM/ASBkbSXsxu+Cciy1ZMlmHWqU5b58xhp2bRwgaASvXLyGb3xfR7OxtJZt3ufdXj7Dzd7uZGJjEdi0yOZedGwfZ9uAueld0Mb5jGNux6Dtyn3dXe18bY3smuOU7t7L00D56V85vwZOSkpKSkvL7LFowvfe976VarfK73/2Oww8/HIANGzZw0UUX8b73vY9vfvObB3ySKY+PbQKkkGSFRIoksqRJyvsdFApBU8bEwidjFRHGApHkOAXaAxGjdUzBcdm7UmVJSclxGJiu0OVmOWZVP00/pO4FIKCUy+Daip/fvQWVUaxt72aqXEdrQzHvsnxJOxMTNUanaxxiuuYvgRlo7SziRJqh3RN0dJewbIsgCBkfLuM3A9rbc3PE0l7yxSwP7trC8NaY41+wFvtRESzfC7j/Fw+j/YCTzlo/79zOJe1se3AXG+/cnAqmlJSUZxV/DOPKpyurV6/+gzlMe9um7C+LFkw//vGP+elPfzorlgCOOOIIvvKVr3DWWWctdriUA4RFhCMlEkH0qO2GRDhZQlIQAmKd9JmTiVjSWhKZGMvS5ByboUoVg2Hvep4UgoJKxNV4vU6l7jPd8JBC0B6GFCybWjNgZXsrR6zoIwgiojjGti1sS7E7M8m2raNs3zFOvuDSaAYIBPmcQ63qsfbQXtYf1sfPbnyA2255hCiKcRyLVYf0sHx5BzoIF3y9XiOgXm7Q2lGYI5YA3IwDGJqNgDCIcH5vvxCCTM5lZOfYgXwLUlJSUlKeRjzaggggDEMefPBBfvjDH85rs7Y/LFowaa2x7QXyUWwbrRfuJ5Zy8HEFGGERmsRfaa6RhiA2MZawyLsa3fSJZrw6lJRkpUUcg+sKakQ0wghIvI2KrktHKcf4ZI17dg5iYoMlJQYYqVSRRuBHET0teSBpqus86mPV3VVkbLzKjsFJ6lUfKZNkc2Ogu7PES846iq0PDqCB/uUdKCWJIk0Ya4IgRHgLC6ZmzSP0Ikrt+QX354pZpobLNOv+PMEEEIfzhVRKSkpKyrOH973vfQtuv/LKK/ntb3+76PEWLZhe9KIX8f73v59vfvOb9Pf3AzAwMMAHP/hBXvziFy96AikHBqU6iYWNJE4iRDP/TsSTIDYQGEVsJEUrgybpJSeQ1KMAIWOqgU9fqQ1LSLQxSCHw4oixWp1mHNMIQvpbijOiB2Kt2Tk6TUxMYcYFPQhnjCsthWUpGo2AcrVJT2eRlcs6qdcTS4J8PoMfhPzg+/fihDGrDunBstTs6wmCiIfv301UaSTVb/m5LuvNho9UktbHEEwtnUX2bB5Cx/PDsVEYEcea1cesfNL3PSUlJeVpRWpc+bicddZZ/NVf/RVXXXXVos5btGD68pe/zHnnncfKlStne6nt3r2bo446im984xuLHS7lACHttWjRgqCaZHrPCCJmZJExEeNhgXJs4Znq7D4DWNJGCgMixkYSGYMmiVRllY0fRjiuolW5TNWaM7YCBm0Mfe1FpqYbbBoco2g5jE3XibXGthQ97UUmx6oQGY48rD8571FUKg3uuHUzh63sniOWIIlULVnezu6tEXt2jNHWXqClo4AxhumJGs26T/+KDuLHWLKTStHR18bkwAS5gos700LFbwYMbB5i+RFLOfSE1QfyLUhJSUlJeQZw3XXX0dbWtujzFi2Yli1bxj333MNPf/pTNm7cCMDhhx/OmWeeueiLpxw4hL0eYR+JFTyEFhFmJtIkkEkUycTcU+vDx8URhpik15xCoUWMrTRCwdaJSfSjfl5YQmILQdZxOGJ5L9WKx3i1gZKC7pYCPa1FfrNhJ9uGJ8kbi5Z8Fte2CKKIDdtHiLyQQzrb5oklgDCIkwa/MxV7v0+pLU9HbwuHHdrNxrt2smvbGAjo6mvlRa88EWlifn7dbyiPVyl1FGa9l6bHq8Sx5vz/fSZ7Ht7DrocHiMPkGspWrD5mBS99+4vJFhau3ktJSUlJeeZz/PHHz0n6NsYwPDzM+Pg4//Iv/7Lo8Z6Q7bEQgpe85CW85CUveSKnpxwEhCyisq9BmxrEkxjjk8RVJVK4DESKX1VXIESEozT7Yq4xfiyQ0iAkSEtAnASphAChBEYbYq0ZrdaZrjZphiECQVwxSCXxw4hsxqaIg+eH7K2Fay1mmNaa4DFy24QQSQuWaOH4r441YRgzuHsaLQRuIYsQEGnYvmWUsy98Dl4j4N5fPMzkyEAimLQm35Ln+ecdz/PPew5Ga3Y8tHs2wbtnZRcrj1yWOn6npKQ8O0mX5GbZ26FkL1JKuru7OeOMM1i7du2ix3tCfzVuvvlmvvCFL8waVx5++OF84AMfSKNMf2RE5kVIQPo/w8R7MGiEcBDWWm4ZiRiKGygZY4xGzNSNaiNwlSSONaGIWNXSRqz1rHElwOaJCbzAY2d9ioxlkXNsjIFK02e0Mki94XHK8mX0t5SYKtcJI41rW7S35nh40xDDI+VkWc9ShGEMAmxLkS+4WLaFjhaOMI0MTjM1UkH5EctWd2M7ycc18CN2bhrmx9+5k1e/83SWHNLLnf/zILXpOsX2As8962gOOSZx8p4cqzC6Z5I9m4eTe6QUHX3ttPXsf6PolJSUlGcSzw6f7ifPZZdddkDHW7Rg+ud//mfe//7386pXvYr3v//9ANxxxx289KUv5Qtf+AJ/8Rd/cUAnmLL/CKEQ2Zdg3Ocgoi1gfJAlsA5jMLoayVYcCVLGGDSJe4Ai0AZLaiKjmQwa1MIQbTS2VGSVjQICo8EYipl9yde2kpTrTQKjaStmyWVscpnWOXNa0tvK8GiFjVuHMbGhVvcRAkrFLJaULFnaihsYRoanMQbiWKOUwmhNebKOLQXLD+mZs6TnuBbLVneza9sYN1x9C6M7xqhO1RFSMDFaZWKkzHNHjqa9q8hPvn4LU0PTuLlk3hvv2s7dNz/ISy8+gzXHrHgq3paUlJSUlD8S9Xqda6+9djbAs27dOv78z/+cfH7hgqE/hDB/yNVpAZYuXcpHP/rRef3fvvKVr/B//s//YWBgYNGTeCZSqVRoaWmhXC5TKpX+2NN5XD5y35fZXt+SeDBhmCl0Q5vk4ceS6lQnY6OtKJE03o1MspTmGIUdCPqiAtpP+sSZmaRvS0imKg2OW9JHbzbPRKVBEMZkHIvOljxaG+59cDf+WANpIJd1MAbqDR/XsXj5ucdQG6py+6830Wz4s+7k+WKGrtYcpYzNstULm0ved9tmvGqDQw/vo627hBACrQ1To2Wmx2voICDjKJYc0jtrmmmMYWDLMMW2Am/86/Np7U4jTSkpKQefg/03Y+/4//DDm8g+ATHwaJr1Oh952UueMX/fHos777yTl7/85RhjOProowF44IEHEELwgx/8gJNOOmlR4y06wjQ9Pc0555wzb/tZZ53FRz7ykcUOl/IUIWWEkjGOMBgRJqYDJhFGsVbEJsJWsLRYoh4GxNrgKEXGshisVnBsi9Ud7ewZLzNZbyCFpKdUYHVXG3dv3MMje8YYZJpYa+SMcNk5MgWxwQIOXbcEzwuZnm4gBCxd0oZtW9x7/y7c0HDIob0Yk/h8KUugNezZPoZ6jNcTRTHT41XyOZv2Ry2vSSno6G1lYOsI43smef7Ljp3jMC6EoH9NLzt+t5uNd23juS9NeyCmpKQ8i0hzmGZ517vexdlnn82///u/4zhJpXQQBLz97W/nXe96F/fcc8+ixlu0YDrvvPP47ne/y4c//OE527/3ve/xZ3/2Z4sdLuUpQhLhyAhBhCWYiTAZYmMwUuNIsGSMVobY6OQhQSoLMDTiiC2jE2gNLfksxhgmm0284YgAjd/0yTuK1mI26UMXa6YqDap1nyX5PCuWdwAzjgckCeVhGPOLWx6mp6XA2rW98+Y8NlRmeLTC2sP65lXZVafreA2flas7F3y9JjZEsaZZ97Fbc3PvhRQ4GYc9mwYhFUwpKSkpz0oefvhhrrnmmlmxBOA4DpdeeinHH3/8osdbtGA64ogj+MxnPsMvfvELTjnlFCDJYbr11lv5y7/8S/7pn/5p9tjHctlMeeqxZYwjIyyhMUSzvYIsKbCNxEhBRMhgo4yjFEpIaqHPlN9EWoLQi9HC0JHfJz4KxjBaqVMOfNZ1tSN8TbnqAYkgaivlIDaEIqmyU1Ly6HZytapHFMRYzsJxpBWrO3ngtzUGdk2wfNW+ps7GGCaGK1iWpLN34XCxlEl1n9GP9VPpWfITKiUlJSVlQY444gi2b98+p5UbJD3k1q+f32f08Vi0YLrqqqtoa2tjw4YNbNiwYXZ7a2vrHNdMIUQqmJ5GCAJsGaLQWFIjReK2FBtFpGMcJcgoQ8Fy8HVMqGOkEBRth2YUIWwImjFeGOHMVM95YUQUJX5O/T1FlhRbmKo0iGONY1u0FrPc/9BuRqaqNPyQQsYhnKmIsy2F1gatDc5jCKaW9gJd/a00GwH33L6FWCdmmkoKWjvzLF/dRRwsXGFnZ22kACczv/2J1prQj1i+bsmBuLUpKSkpTx/SJblZ/uZv/oYPfOAD7N69ezbAc/vtt/O5z32Of/zHf2Tnzp2zx65Y8fhFQIsWTIvt7pvy9EAR4coIJWIkGoGe2R5jKYkxCtcyZDMWQRBhSFqj5G2bauDjuhZtIsNIpUZjxoep4Dh0lQrosEI1CKg1fcpNnyCKyDo2tq1ob8szNF5haLxCo+pTa/ggoLWQJec6KCXJPoYnUq3mUShlEEGEN1HFawSJ+3jeJVvKsWp1F9vu30m+lJnjqxQGEUJK+lZ0Mr57nCVre5EyWdLTWjOweYjOJW0c9pw1GGMY2TlGs+aRLWToXt45e2xKSkpKyjOXCy+8EIB3v/vdswaWe3NaL7zwQowxs4bH+9ML90m798VxzIMPPsiKFSuekNV4ylODJX0cEWLLCIVGCkPyjyTUEi0tItNkMqjjSgshFNrEjPg1IqFRsaasA1zXJuvasz9AGiYkEoZdo9OMxrXZpO9YG3aOTpNzLJQUPLxpiHzGJZdNIj6Do2X8IKKrI09QC5iYqDFdbhAEEa5r09qSZWRwirgZ0d6a5eTTD99X2acNAzvGmSx79K/pZdfmESxLoWxFHMXEUczhz1nNMaccwi3X3cHODQNYMx5OURDRtbSdcy8+nfJ4hRv//afsengPgRfiZGyWH76E5513IiuOWPbUv0kpKSkpKQeMe++994COt2jB9IEPfID169fztre9jTiOeeELX8jtt99OLpfjv//7vzn99NMP6ARTDgyWDHFViCsilAhRM5InRmEJBWhcyyCRNONwJtdI4EoFytAMAiyhaCtmZsc0xjDd9GiYCFONWdHSStbNzO6rNQN2jZVpdxzaOrJ4XkSzmfR+cx2bUjFLe2ueynCVTb/ZgrIUypJEYYzWho62PG22Rf/yjjmVblIJlqzsZNfWUdY8dw3NRsCGu7YReCFu1uGok1bz/Jcfz/K1vXQtaeeW6+9kywO7ADj8hNWcdsGJeA2f7/7TjUyPlule1kkm7+I1fDbfvZ2RHWNc8L6XpqIpJSXlGYcwzOaoPpkxng3stRI4UCxaMP2///f/eOMb3wjAD37wA3bs2MHGjRv5z//8Tz72sY9x6623HtAJphwYHCLyIokyKREjZWIrEBuJLRQYm6yKsZzEPDJpqiKwLIWvDVIKIj8iUPGsP5MlBGEYIwS0FLN4fkgQRigpieLkmIxtERvD8UevoF73qdcDEFAsZCjkXX5z93aII1Yd0kNlukEcaeySolDMMjw4Sc6Sc8TSXqSSBEHEL35wL8W8w5Enr8FxLAI/YmKkwo+uvZ1TXnIkd/74foZ3jic2CsDGu7dTnkg8mqZHy6w8ctns+PlSjtwRWXZu2MOtN9zJsnVL0uW5lJSUlGcwQ0NDfOUrX+Gee+6hUChwzDHH8J73vIeWlsV78C1aMI2Pj9Pbm5SA33jjjbz61a/m0EMP5a1vfStf+tKXFj2BlKcGWzZBBTgywCJGJjbfaCMJjQKpEcLHGENBucmymjF4cUhARM5x8BoR41OTaJPID1tKSrZDRlos7Wqhx84zNFGh6Ye0FrP0dZTYtmOU6bpPM4pobcnR2rKvyi7wI2qVJu2lHOsO7yeOdeL0bSmUTNqaTJSbRLHG+v3mvcYwPjiN0DHrj1uBnFmvyxWg1JZj60N7+MY/7qRYdFh6SC+WnSSWR2HMtgd2Mbx9hPUnrZknxoQQdC/rZPcjg4zsHKNvVc9BfV9SUlJSUg4OW7du5dRTT6W9vZ0jjzyS733ve1SrVf7pn/6Jm2++maOOOmpR4y3653NPTw8bNmwgjmN+/OMfzzbgbTQaKPVYNoMpf2wywicnffLCJy89CtIjLz1yyk8e0ienIkJCyrrOlK5S0XUQBksKAhMhLEFHIUdXIU93IU9bLksswSMmNoZpz6cahQRCUw0DKr6PUBKtEyE0PlVn5+AkO4emEo+mqocfRJQKSdsSpSTOTM4TQE9fK41mQL3hz3s91XKTWqVJT3/brFjai5RJVGp49wSdS9pnxRKAZSs6+9uoVz3qdW/he5V38ZsBzerC+1NSUlKetpgD9HgW8JGPfIQXvvCFPPTQQ3z2s5/FcRx+9KMf8c53vpO/+qu/WvR4i44wXXzxxbzmNa+hr68PIcRsw93f/OY3rFu3btETSHlqcKSPMB4ZGWKJGItk2S00kkgoIMZVAbYlUEYlXxgBUhiE1oQGWjNZ8sqZM+50o8mkabBjdIq8sck6No6tCCPNluEJoiDGxIZHto5Qb4YYk6SaKymxZVKr115a2Ma/o6uIs81iaPckXnueRt1HIMgVXMYHprAtSf/ShQsNvJqX2CZE8ysf3KyDZUnGh8osWTW/7YpX93EzDtlCZt6+lJSUlJRnBj//+c/5yU9+gpSSR3eBe/Ob38wXv/jFRY+3aMH0yU9+kqOOOordu3fz6le/GtfdGx1QfPSjH130BFKeGjKyiWV8stLHFjFKJEIiMorQWGA0GeEhMFgSEEniX6QNRmikkkw1mlQJ8HXivZSRFnGkkVJSbQT0txSwrCSa41hgSclgrYKlDcNjVbrb87huUiXXaAaMTdWxlIA4xvNDpqYbRJFO7Ahac4RhzLIVHUzsmGDbpuHZfCJjDMVihs7u4mN25Q7DGCklypofRM235Mi35KlO1WbLSvdijGF0zzhrjllJz8queeempKSkpDwz8H2f9vb2edsbjcYTar77hGwFXvWqV83bdtFFFz2RoVKeIjI0yKgmeRFiE6NmyiBCJCERyJi8CghEgDEaTCIilBQoJZC2oBaHREES5QFDGZ+sZZGxFC0Fh2rTRwiBtTfpW0BbIUvD+PSVCjRqAQ0vqZKzLMWqpR1Uq00e2jKMjSSM9KwAsiyFa0vasi5dfa0sWdFJrdJECMiXsvjNkPpUnaE9U6w6dG5blb2NgR1HkZtZ7puzH0NLVwmhI3Zu2EPXsg4y+Qx+3Wd09zjF9gKnnn9SmvCdkpLyzCM1rpxlxYoVbN68mdWrV89u27NnDx/5yEc466yzFj3ek/ZhSnlmkJceeXzyIsYBlDAzS3KG0GiEiMlKn4LtoE2MMRqBQApFRQdoDB2FLK6xCWbcvR1LUfE8Jv0m67u7sDzJ7olpqn5AzrVZ0dVGeaKOp0LWrumByMzkIwmKBZdSIcOd9+5gwq/jxALXVli2Igxj6nUP31I4sebYY1bMEy9RFPPw/bvxw5htGwdnjSsNEPkR3UvaaW/LMbp7kp5H2RIkRpXj9K3u5vQLnsNDv36Yzfdsx6t5ZPIZ1h6/kudfcHJqKZCSkvKMRMw8nuwYzwbOPfdcvv3tb3P22WcDSWRp+fLlnHHGGXzhC19Y9HipYPoTIS+btJiIrBC4AhTJ0lkoNIHRCKMpKB/fNBAYhBRJo1wjUNKghcSeiRyFIgYBSkgcqdAY9kxXcXyJZVtkMjZhrNk1OY1XD7CkQEpJJGK0nIlPCUEUxVQqTdo7C6zt62R8vILvR2QyNl1dJR7esIeKF8ICtgKWpSi25oiaPkPbxqiWGxidVLmV2nK8+PwTOPSIPn76zVvZeNd2xExiuIkNXUvbeMnrnkehNYe0LKRlISwbYVlIywaRRpZSUlKeoaQRpln+8R//cTZ3qa+vjxtvvJE1a9ZwyCGHPKHxUsH0J0JBeBSFICcsrBlBIBC4xhCKGKEjSsrDkZKYKNkvQCHRxBhLsrs+jYgVaibaM64bKCQSwWS9waGlDqxHRYL8MGYsqpHTis07RynXPOIZ+3lLKXKOouGFrF3SSXd3ie7uuY10c67DZL1GvRFQzM9fWqtM1qhPNzjsmBVIJYjDGMtWRLFm00N76F3WTltfG3t2TFAer2IwtHaWaO9rAwE3fOUnlMeqdC/vJJNz8RoBW+7fyejuCc7/i7NZcXjaay4lJSXlmcqnP/1pPvaxjyGEIJvNzkaaAG655RZOO+20RY2XCqY/EYoipshMy5NZG0eDFOCikBJKMkSpECWSfQBGG6Q2SKnJ2DYYSTyj2HPKxkiohREykjT9kLzrIGXSGsULQrKOQ7PmMzhRpqulgG0pjDGEUczAeJXIxHS1LZx8V2rNMTJaIY41Wmu8ZggCMhmHOI4ZH6nQ1VGgs3e+Adme7WN8999/QSFnc+ixK8jNOJQ3qh47Nw3xyF3bsBWsWb/8UcaVWXKHL2HnwwPc9v27WHZYX5rHlJKSkvIM5V//9V+58cYb+cY3vsGaNWsACMOQv/mbv+ELX/gCvj/fsuYPsd+CKYoi4jierYoDGBkZ4corr6Rer3Peeefx/Oc/f1EXT3nqyAuJQhH+XqxVk0gjWyhKCgwaTIwUYBAgBJYyxDF05rN4NjSiAIGg6DjoyFBpevS2FfCmIoarNbRJvJvaczmWd7aw1RvHMop6I8B1LAzg+yH5jE0jNoxNN2jUA0YnagRBRDZj09VRxM3aZFyL3dvHCCNNc8aPKZdz0WGMjmNWrplvCwCAMYwMTrP81DXkS9l996GUpa2rxG/v28m6o5ctbFy5tIPdm4YY3TVO78rHGD8lJSXl6Ui6JDfLgw8+yLve9S6OO+44rrjiCk499VTe+MY3Mjk5yc9+9rNFj7ffgukd73gHjuPwr//6rwBUq1VOPPFEPM+jr6+PL3zhC3zve9/jpS996aInkXLwcaSD0R4CMe+7sPe5EoqMHWO0wQgQxiCExIs0ltTsqZURxkaJJL+p0QyJ4iQ5vBoEuEpSyLkzNXQQScPAdAXXtVnX10O17FGpeQgB/d0t9HSVuH/DHh7cPEDRclBSopSgWvcYHqtgSUFPTwtDW8fQ2pDLO2BgeGg6cSTPOOQXWKoDqExUk9dkzf+IC8DEmnpt4V8XmbzL2J4JGqlxZUpKSsozlra2Nr797W/zH//xH7z97W8H4MILL+T//t//S7FYXPR4+73ecOutt3LhhRfOPv/6179OHMds3ryZ+++/n0suuYTPfe5zi55AylODku0gFEmHOImY/ScxXdIIpqICEGOpCEdGKBWBiFAyxlIaKZMlOq1N4l+kwZKCWGimPY+2fJaelgLdLQV6WgqUsi5TngcCWotZ3LyDlbOwcxZu3sZ1LZSUhFqj4xhLJb3rLCmJo5imH9Fo+hx17HLWHNpDNuuQzTkcuq6Pw49aSqgNw0PlBV9vvebjOIpM1p63z3IslCXxFnAQh8S40skmxpVRGDG2Z4KxPROEQXjg3pCUlJSUlIPO8PAw3/72tymVSqxcuZKHHnqILVu2PKGx9jvCNDAwwNq1a2ef33zzzVx44YWzDewuuugivvrVrz6hSaQcfJR9HOhRDFGSwWSSXnICgTYGXws2NTvIyJn9ApQBIQzCGGIhac/nKDcjvDhJCs9bDkXlssufRkiRVNBpjTYGJQRxrHGUpBlF3LN5gCiKsZXCYJiuNtk1PMV0tcGa5Z20ZTKMjlaIIo3rWixf3s7wUJnpqTrHH91Cn9WezBlACIwxDO2ZYveuCTIZm/J0gzCIcFyLUkuWONZksw5uZr5gypWyuDmX0AsXNK4cG5hk1VFLGdgyzI/+/aeMD0xijKG9r43jXrSe4150FMpK2wClpKQ8/RAmeTzZMZ4NfPe73+V//a//xfr163nggQdob2/nkksu4ZRTTuFv//ZvF90eZb8FUyaTodlszj6/44475kSUMpkMtVptURdPeepQ2VdAeD/oCTQxSfaSQAiJBgYCl/ubHVgqQgmDwGAQxEYSG7CVZNyvIsmQtRIR4puIatNHKkEx47BnuoIfJWIKAVnLprulwMBImboO6C0V5vghDYyVqUchS3vb6GrJs3xZR9J8V0mkFEwMV4iNoeGFtBTUHHsBIQQ9/a0MbBvlt7duQkqBshRRGGMMLFvZQcESTI9XaekoEPgRQoDtWFQmavSv6cGRsGPDHkodJZQt0aGmPFGh1F7AsiQ/+vefYjsWrd3Jj4LJwSlu/L8/ZWJwkjPf9MK0d2JKSkrK05g3vOENfPrTn+ZDH/rQ7LZ/+Zd/4c/+7M9429vedvAE07HHHst//ud/cvnll/OrX/2KkZERXvSiF83u37p1K/39/Yu6eMpTh3BPQmUvQHg/QusKZsY6QEqXps7xk+kCVWxcGSNEDCRJ35ZRYBl0LBECIq2JZDyTWCiQAkKp8cIoySnCmYleCYyAchigLIlCUqn5ZFwLY8ALQlxLEShJ3Q9wqpLJ6TpBFOPaFh1teaQl9wbCCMOYRsMHIcjnHCxLMTlRQ1mKNUcsoTpdJ/QjHNem0JpNBNXSVrbes53f3b0DHSd2BlJJWjvynPvGU8nnHL73rzdz/683EgYxtqNYekgvh524mgd+9hCtXS20dO5b584Vs1Sn6tx90/2sPX41q49e8VS/jSkpKSkp+8mdd97J+vXr521/2ctexoMPPrjo8fZbMF122WWce+65fOc732FoaIi3vOUt9PX1ze7/7ne/y6mnnrroCaQ8NQjhQuFipLUK6d+CiUdBKIS1il2NJdzj3YsjPaSIUDOdd5MKugiEJFKSjKOomJhIJ21PHKXIK4dGtYFvItaU2uYtb20cHCOfsVnf18eO4Qmm6k1A0F7MsqKnh/s37GHD9mHywiKKNEIkS4S7hqYQUVJtNzw0zdR0Hc9LRF42a9NSzFCeqrNqeQdrDu0Fk+RWSZlU9o0OTrFz+wR6xvf20RFmoSymx2s8tHEA5Vgc8dxDUZYkjmOaVZ9ffvcudBDSt7pn3n0stuWZGJzk4Ts3p4IpJSXl6UdaJTfLQmJpL11di+8Vut+C6bTTTuPuu+/mf/7nf+jt7eXVr371nP3HHnssJ5100qInkPLUIUQWkT0X474QoccBCaqXcvNebHUnkhBb6pkU8OQ7o1EIo4mUwjMBeSuPnKmS00YzHTVBGYSB8UYDL47RRmNJhS0ESgg0hh2TUzTiGGkny1i1KGS4UgMpmJ5uUCgVaWvJAYnQqtQ8qnWfoq3YtGmYQsGlMOOlVKl4DA1M40hYurx974tDqn1iTSnJri0jrDuij6NOWkPgJ2LLcS2mxmvc9J3fUMw7HHb8ykRkzWCM4bbv340wZl5+017crMPU8PQBf39SUlJSUp6+LMq48vDDD+fwww9fcN873/nOAzKhlIOPkHmQ+8wipTA4MsISEYoYJWcEk4GYGKEkoZYIDOXYw8xkBEojsIQiUjHGhtFyA4yZsS4IEEJQyNrUyh5TUZOufB6lksLMMIoZnqxSDnz62oqYEKamG0gp0NpgW4rWUha/FrBkWTuNqketkpT5u45Fvq+FidEKtWaIm3Hmvcap0QpRFFNqzSOEmJP87biK8niNYqlrjliCJDeqpbPA4JYRGlVvjofTXkI/JD8j7lJSUlJS/jTYb8H0y1/+cr+Oe+ELX/iEJ5Pyx0ET4soAWwRYIkaJZMnNmCTpWyIJtMSyDbaWs715hBIIY9ARGGlY1d6GH0XE2mBJiWMphspVImGwEHPEiZKSKEqW99au6qbFcZmcqhOEEa5j0dFeYOeOMXZXmqw6tAcLMeubVChmUErwy59uYPeeSUp5l+mpOmEYY9sWre15psarZDI22dx8MRUFMQZDHMcL3o+eFV3s2TxMbboxTzD5zQBtDIeesOZA3f6UlJSUlGcA+y2YTj/99DkVTgshhHjMP0IpT18UEa4McGUimOzZpG8IjUIJRRhLDDFKgZ7RPdJAEGlQGowhFgafmAiNjcISCj+KcDM2GRyGpqpJLzkBlpDkMw6BHzPd9FAaphsefhiSiW1cz8b3okRkGcgX3HkmlW0deUaHp2lONwiDeCbzChzHol7zaS24OM78j7hlK8TMsuJC5EpZWrtamBicxHYVzkwEK/RCpkamWXfyIaw9ftUBuvspKSkpBw7BAbAVOCAzefax34Kpra2NYrHIW97yFt70pjfR2dl5MOeV8lQiIrIqICt8bBFiCw3CYIwgMgpP2ERKgYhommDfl1EkVWdSQyA0OytlLCmQQhDrgLF6PSnlF5JIGrSEaEalSAucnIOqeewYnGTUWFhKoJSk6TWYmG7gNQJsBHEUs3XHGOVyYmvR1paju7OItBRaG6rlJpmMhW1bhH5EZbqB49rYjkUYRIRhTH3GtTtfzOC4Ntm8i9B6VvzPFPYBMDlc5vgz1+OXa9x/y8PUyw0Mhnwpx9EvOIxz3vriWRGVkpKSkvL0Znx8nPvuu4/x8XGy2SwrVqzg6KOPXnSv0P0WTENDQ3z3u9/l6quv5rOf/SwvfelLedvb3sY555yzYGJsyjMHSUhOBuSlhy1CLKFJ4kmCyFgoHRNYEseG7EzzXSHAQhFojYmT6rSCYxPFiXGlLSV5x6YRhFQbAS3Soae9gJr5gEaxptzwqEYhbl3T3dWOY+/7OHp+xFS5gdGChzYMEMUG20rOna402LVnEq/isWplFx3tBcZHyvheiNtZoKunhWrVY2qozJ2/fASt90VFhUgSwteduBp/usaDt20mjGJ0bJAzTuPd/W3kcjZDmyosPbQPy1IgIApjpsZq/ObGeznzjS+YzcdKSUlJSXl64XkeX/va1/j3f/937r33XgByuRy+7xPHMaVSiVe96lW85z3v4ZhjjtmvMfdbMDmOw2tf+1pe+9rXsmvXLr72ta/xnve8B9/3ueiii/jUpz6FtUDfrpSnP1LEFFSTvPBwZIglYiQQA5G2sLEJpYURPgE2UiZl+p6JkvYqwqAsKOWzlP0mRhtsJWlxMzT8gBhDTiVtUPYKF0tJhAaNob01T70R0JQhllJEUbK81t1RYHK0SqXq0daSI5tNojqNps/ERB1iTU9/K22tebp6W+a8pkzeZWD7GGFokEbPRo9iA0JKSp0laloz/dAeAi9MlJQx2BmH9t5Wtt6/k7buEqWOuf2GatN17vnZ71h7/CpWr19+cN+YlJSUlMWS2grwy1/+kje/+c309/fz1re+lec///kcccQRsxplbGyMu+66ix/84AeceeaZnHvuuXz9619/3HGfkMJZvnw5l112GW9605t429vext///d/zl3/5l7S3tz+R4VL+yCh88rJJQTZxRYgtYiQGjSAQFpaICIzCUaCkwcy4hNtCYoRAaE0zDhlqVFFSIoWgGUdUa1UiNK6tqIQBE+NNIpMYSFpIXKXIWBa9/a20CoddQ1N4YUQmY7Oiv51mzWN6qsHy/jZq5SblShMBuBmbVSs72bljnErDp601P+811ctNahWPE05aRca1qFeS5bx8KYvj2jxw+xYcCc895xi8hk8YRFi2RbaQ4b5bHkYHISvWLZk3bqE1z/jgFBt/uzUVTCkpKSlPQ6rVKt/+9rc5+eSTF9zf1dXFueeey7nnnsvnP/95vvSlL+3XuIsWTL7v81//9V9cffXV3H777bzsZS/jhz/8YSqWnsFIPIrCo6Q8MiLAEXFS/YbER+LgEiqFEiFK7f3pYTDEmBiEBGUnnZxjrdmbfm0LSSxjjEpyhHRkklwhYzCWwVhgJExUGpTDBr6JwZI045ido1MEtQBLSVas6MS1FbWqB0JQLGQIw4ihgSnGxmvkHZuJsSq+H+FmLDo7SwzunkApQbGUJZt1KD1KVPnNgPJknc7uAm7Wwc3OzUeybMn0tI/XDMhk5+cquVmHqZGk6W95vEKj0iRTyNDaVUqXp1NSUlL+yLzsZS/b72Oz2Swf/ehH9+vY/U7CuPPOO/nf//t/09vby+c+9znOO+88du/ezXe+8x3OOeec/Z7c7/OVr3yFlStXkslkOPnkk7nzzjv/4PHXXXcd69atI5PJsH79em688cY5+6+//nrOOussOjo6EEJw3333zRvD8zz+4i/+go6ODgqFAhdeeCEjIyNP+DU807HxKFp1WmWdNuHRKgNaVUib8mmTHq2qSVF6uCoCGSFUiFAhUsYoyyBV0mQ3k7WJlSZUBm0ZslkbpQTNOKboOKzqaWd1bzur+zpY0dVGxrWpxyGjkzUE0FbM0l7K0lbMEGvNWK2BkUnu0I7dE2zZOcaWnWPsHJgg0ppc3mVoYIrfPbiH4ZEylUqT4aEyDz24m4HBMqUZsfT7NBs+Oo4fsxdcoSVH4Ed49WDB/aEfoeOYH/zLT7jq0mv42mXf4uq/vobv/n83MrBl6EC+NSkpKSmLwxygR8o89lswPfe5z+VHP/oR73vf+/jUpz7FypUr+fWvf833v//9OY/F8O1vf5tLLrmET3ziE9xzzz0cc8wxnH322YyOji54/G233cbrX/963va2t3Hvvfdy/vnnc/755/PQQw/NHlOv13n+85/PP/zDPzzmdT/4wQ/ygx/8gOuuu45bbrmFwcFBXvnKVy5q7s8mLHxaZZNWGdKqNK0S2iS0SGgTmlbl06rq2CrCkWDNPGxlUDJGKY1HQD0Kydg2BcfBtRTl0MMjRghDgKbmB0w3PaaaHo0gwsxYDBgMUkj2FbMKpJBIJfGCiAcf3sPA0DRhFBOGEbsGpnhgwwBeGCMRhEGEYylc18KxFVEQJb3sZr70nhcwMVZlYqyK5wWJU7kGJ7NwgLWls4SUksAPAYijmDiKMcbgNwO8epNdG/Zw900PYDs2nUs6cLMuD97yMNd/8YfsfmTg4L9pKSkpKU8TfvnLX/Lyl7+c/v5+hBDccMMNj3uO7/t87GMfY8WKFbiuy8qVK7n66qsP6LxWr17NqlWrHvOxWBa1JLdr1y4+/elPP+b+xfowXXHFFbzjHe/g4osvBuDKK6/khz/8IVdfffWCIbIvfelLnHPOOXz4wx8G4NOf/jQ33XQTX/7yl7nyyisBeNOb3gTAjh07FrxmuVzmqquu4tprr51tHvzVr36Vww8/nDvuuIPnPve5+z3/ZwuO9GiTIe1S4gqJhZzxKTKESuOYiFAFuMpHqpC9fVMMAoVI8pokGKOpRzHJHoGFSLqvOJKJWoMo1MiZJSttDI5UZG2LjmIerxEyUaljSNqRFDMOK/vb2bptlHLDZ0lXy6zxZcbVDI9W8JsBxx7Wi4VkbKRMGMRYtmT1ob0EfsSebaM8cPd2GnUff6Y1iuva5AsObs5BiUQMlSf3ml4qWtrzGAy9yzsY2jbKwNaRWeHkuDZKgpux8Oseq49ZMVuW6mYdiu0Fdm7Yza/+6w5e99ELFl2ympKSkvJkETx5H6XFnl+v1znmmGN461vfut/Bh9e85jWMjIxw1VVXccghhzA0NITWevGT/QN84AMfmPM8DEMefPBBfvjDH3LJJZcserz9FkwH+oUEQcDdd9/NpZdeOrtNSsmZZ57J7bffvuA5t99++7wXefbZZ++Xmt3L3XffTRiGnHnmmbPb1q1bx/Lly7n99tsfUzD5vo/v+7PPK5XKfl/z6U6GBgUpyAsLISQajcYghcBFYSEIZUROhdjq0fFaSSQ0lhFgGbQFWptE9DBTCWcSj6asa2E7iiBMBLVrK/woph4GWI5Eh5o4nPFDkmAcSaQ1jqMoudnZhG9mrl4quEwFESrjsGpZB8tXdRKFMZatUJbCa/rs2DLCzh3jFHIuhZbEsbtWbjI1UWXp8g4alQZ3/OxhdKxnfZiUlBRbs6x/3qHc87OHmBouz1wxqQwstObQcczKw/rmCSIhBN3Luti9cZCRHWMLNu9NSUlJOaj8Eark9iZQ7y8//vGPueWWW9i2bdts/vPKlSsXd9H94H3ve9+C26+88kp++9vfLnq8A/oTuNls7vex4+PjxHFMT8/cPyo9PT0MDw8veM7w8PCijn+sMRzHobW1dVHjXH755bS0tMw+li1btt/XfLrjGI+8sJBCEM1UxxkEMRCSuHKXhCIrA6QIUTJCyRApAmwZYylNJCIsISm4DgXXpeDYGAyRMGgMrfkspXyGllI2eRSytOUzhDpmeKqGZUmWdJVY1tNKf0cJgJ1jU1iu4rj1y1ixopN8KUO+lGXVqk7WHdqHbSmqDY9azWNgaJo9Q9MMDpep132mJuoYYzjk8H5aO/IEfkjgh7R2FDjiuBUIS9IMNF7DJwojMJoojGk2A3w/YutDu1mxbgnPf8VzOPa0Izj2tMN5/nknsGRND2OD08SP8fshW8zgNXxq0/Wn7P1LSUlJeSbx/e9/n+c85zl89rOfZcmSJRx66KF86EMfWpSGeDKcddZZXHfddYs+74AYJ/m+z5e//GU+97nPLUq8PJO49NJL50S3KpXKs0Y0ZaXBEpJoJjL0+8SALRR5pclY8UysBQySSBu00WgFdQKiKFESArBRSCHQ0jBQrqJmz9xr3y8QAqI4JuvasxVmUgryGYdIayIh2T04yUS5QRhpwOCNRLS15JBKMjJaoTpRJwjjvSuFuLaFX/OwLMmaw/tRUuA1kwTuTNZBCMGvfvwAGVtyytlHMzVWJQoiLFvR1l1i4z072LNzglVH9KOUIlPY15KlvbcFbQyjeyZp7y7Nu1dBM8B2LdycO29fSkpKyjOJ319JcV0X133y/2/btm0bv/71r8lkMnz3u99lfHycd7/73UxMTPDVr371SY//eFx33XW0tbUt+rz9Fky+7/PJT36Sm266Ccdx+Ku/+ivOP/98vvrVr/Kxj30MpRQf/OAH9/vCnZ2dKKXmVaeNjIzQ29u74Dm9vb2LOv6xxgiCgOnp6TlRpscb50B9UJ6OuKoHjQIiZhOUZhFoYzBIjBQ4MkSKZIkqNgKJxChBICNcS2EbhTHJch4SmjoCCbHQiHhfQFNjMIC0JDnLYXiySmT0zOKXwBaCjmKOqak6u0amaS1kyc9UvPlBxNBYmXoUoRoh2bYCbS252byratVjstyktyOPbSeVcLlCZvba1ekGgRdQKrWQK2Tm7IPECTwMYupVn1Jrbs6+QkueUnuRscFJDjtuBTrWRFGMZSVLgaO7J+hb08OSQ/b/M5mSkpJywDiAS3K/HxT4xCc+wSc/+cknOXiS4iOE4JprrqGlJTEdvuKKK3jVq17FP//zP5PNZh9nhP3j+OOPn9P71hjD8PAw4+Pj/Mu//Muix9tvwXTZZZfxr//6r5x55pncdtttvPrVr+biiy/mjjvu4IorruDVr371Y5ZpL4TjOJxwwgncfPPNnH/++UByE2+++Wbe8573LHjOKaecws033zwnkeumm27ilFNO2e/rnnDCCdi2zc0338yFF14IwCOPPMKuXbsWNc6zCWUfg5ZZpGmgzd4WtnsRGDS12GFaZ8hYEWJvMzkjCLUEoWioiEDEGGlmm+CiwQiDEYb+tiKBr2mGEQLIOw7CGHZPVlCOIgo1XhDDTC6RdB1yroWeNBhjsC01G4GybYWuaWJj6GgvYCJDebqBVBIda6QSlFqy+KGmUm4wOVFjeqoBQGtbjoytiCJNvrBwPzjHtdGxJo4WWHcT0N7bytTQJPf87HeEYTyTeAW2bdG1tI3nnfcclLX/34WUlJSUpyO7d++mVNoXST9QQYO+vj6WLFkyK5YADj/8cIwx7Nmzh7Vr1x6Q6+zVFnuRUtLd3c0ZZ5zxhK6x34Lpuuuu4+tf/zrnnXceDz30EEcffTRRFHH//fc/YbO+Sy65hIsuuojnPOc5nHTSSXzxi1+kXq/PVs29+c1vZsmSJVx++eUAvP/97+e0007j85//PC972cv41re+xV133cW//du/zY45OTnJrl27GBwcBBIxBElkqbe3l5aWFt72trdxySWX0N7eTqlU4r3vfS+nnHLKn2SFHIB0T0Bah0L0MBDPOHnvlU2SUBt+1+ygiSKj9kaYIDYCJSRgsK2YWCR95PbGqKRMksFNZBiu15F6pjWKSHrFCQ3aaCpNj0Pa22dapySCKYw1u4YmsTIWbbk80+UG4UzikG0pCrkMXiOkq7+FJW0lJsYT48pMxqa9s4DfDLjrjq389s5tKCFmI03TU3XQBiMgl3UI/IjpydpMhZ2irSNPtuAiVfIqpsaq+1zCi0kOlVSStp5WBjcPEQVRkqSuDcqy6FvTS0d/x1P47qWkpKQcHEql0hzBdKA49dRTue6666jVahQKBQA2bdqElJKlS5cesOtcdtllB2wsWIRg2rNnDyeccAIARx11FK7r8sEPfvBJORu/9rWvZWxsjMsuu4zh4WGOPfZYfvzjH88mdu/atWtOJdLznvc8rr32Wj7+8Y/z13/916xdu5YbbriBo446avaY73//+7OCC+B1r3sdMDeU+IUvfAEpJRdeeCG+73P22Wfzz//8z0/4dTzTEbKAlbuYuP7/IeIJNHurAQUSlz2R5Be1fjIqQokYJZKqstgoIpE0UbFkjGNJQmIMBoXAQlLXIcICP45wtYU9E3kJojhpk6IE6KTCrBmGxNqgpMRVMrEesC1a23PUgoDAS6wBbMemUMowNVkjiDTNIKLmh/hBRCQMuSDCdW20NjTrAW2tWTIZO3lJxlCteDi5DHt2jDO4YwLPC2fvhZu1UVLQs6SNB27dhJBi9jOudSIG2zryuLbi1PNPpFFpEPoRlmORb80xsGmIX17/G1753rQpdUpKylOPMMnjyY6xGGq1Glu2bJl9vn37du677z7a29tZvnw5l156KQMDA7P92t7whjfw6U9/mosvvphPfepTjI+P8+EPf5i3vvWtB2Q5bmJigo6O/f/hur/HC/PoBb4/gFKK4eFhurq6ACgWizzwwANPyPzp2UClUqGlpYVyuXxQFPhTjTExxvsfTPMH6HgPEIHIIK1D+KfdZX7nebgywhLRoyJMkkgrmrHFYLmNLUP9SCGQJDlKINCxQQewOuig2QxpRok4ydsOWWUxWqnRGjtQ1xixdy6ghCAjLLxGQIdyKWZcMq4FBrwgpOmFVKYatFg2GWkhlZht3Ku1IQoj4kbAutXdTI1Uac4kfWdzDj39rQzunmRy9wRKG0qtOWzXJgwiKlN1HNemf0kLI1tH5thpmJnJSWDdsSvoWjI/abA6VadRbfLmv7mQ7mUdhEGIMWA7ViqgUlL+hDnYfzP2jv+Fb95ENje/v+ZiaDbqfPD1L9nvuf7iF7/gjDPOmLf9oosu4mtf+xpvectb2LFjB7/4xS9m923cuJH3vve93HrrrXR0dPCa17yGv/u7vzsggukf//Ef+a//+i/e9773cf755z/mmBs2bOBrX/sa//Ef/7Ff3T72O8JkjOEtb3nL7Bqm53m8613vIp+f+8Zcf/31+ztkytMIIRQiey7GfS4y2gzGA1EC+zCGdl5GTlXIyBBLRKgZwRQZSSgthIhxVYg7E2GKMciZXnKe1qCgHHgoIcm4NsJAiMYLPTQGrSCfdYgiPZs9pSyFiTV+HONk1GzCN0A+66JjQ6gNtbpPe08Ox9n3UQ6CiJ07K7QXMqw+pJd4ZReNmTYnuXxSJbf9kWHybQWW9JQYH5rGbwYoJVl9eD/1qsfg7ilOfslReHWfermBMUnLFK01v73pQfwgWvA+FlpzTAxOsvHOzfzmv+9i+0O7MMawdG0f6194BGuPX50Kp5SUlGcVp59+On8o9vK1r31t3rZ169Zx0003HZT5fOhDH2LZsmV86lOf4u1vfzsnnHACRx11FO3t7TSbTQYHB7nzzjsZHBzkz//8z7n33nv3a9z9FkwXXXTRnOdvfOMbF/cKUp4RCNkGzklzttnCRyqfnAywRYglkvhRbBSBsZL2vFaUeDFJiQC0gVBHoEBoCExExjhJ5EmAiZN8Jy0gjjX9HaVkmU5rLCWxpWTb4CTSTkwtJ6brCJUsz5pYw8xyXS4jqdd9fC9EWZIo0ujYUMi5aGBqqk55usHUVOKL1NaWJ+PaNBsBff1trDlyKcsO6Zk1vXRcm9/9diuBHxEEMW1dJdq69v3Cqk3XkUoyOVJm6aquefcvDCIqkzVuvuZXKCUodZQQAjbcsZlN92znBReezKmvOCkVTSkpKQcHY2D/Fo7+8BjPcF772tfy2te+lttuu42f/OQn3Hvvvdx7773kcjlWrFjBxz/+cS644IJ5nox/iP0WTE+FN0LK05OM9JA0ycsA51GCKTKKwNhINFkVIpVBEyaLcUKgZLIkZ2JBxrXwvIg4Tr6IlpTkbQsviIgwDExXCHTSr00IgassYmNwXQtpW0xNzfgwCXAsRXsxi9MI6e1to9Vx2D0whecFuK7NyhWdmCjmwft3c98DuxCxmU36Lk83wWi8MKKtfV90dE4lrkn+W8fz/6eRa8mRL2apTtWplRtMjVYIvBDLsWjvLjE+OEl5rEJnz9I5Tt9tPa1MDk9z63fvZPm6pSxft+SgvFcpKSkpKft43vOex/Oe97wDMtYBMa5MeXaTkU0yoklBejgimiOYfGMjiMhZPlLpGcuBpMLMaIM0Gi0VnokoOPv8jgyGWhhirKTCrNr0kSKpuotMjB9GKFviNyOaRPR3t8wu12lgutqkFkdUah6N2CPCIB2L0Bj2jExTyrsEYUS9ounvb0XNFA/EWjM8ME1sBH4zYPPGQSbGqsSRRilJR1eR2BiESAwVhnZNUJ5MolOlthztXSUKbXkmByf5zf88iLIVSkniWLP1wV0IoFR06V3VPe8+tve2sv2hXWz8zaZUMKWkpKQ8w0gFU8rjkpcNCrJBXnpkZYQ1YzAZIWnqJMJUUE2EjGf7yBkAlSSAS5X0pqtof8auMjGntKREC420bZbmSlSaPrHW2MqhmHUYnqrRJCbv2riONbtGLoSgmHWYnKozNlmjv7VAW0t21riy6YVs3TmOk3HoKmWpTDeZXQEz0NVTojLd4OENAxRzLtm8QyZrE0Uxe3ZNEHghmazNg3duQ2uDVAIBjAxMIeUguaxNviWHX2sSRzEmTprJOBkbr+GDJR9zyS1byDC4bfTgvmEpKSl/svwxquT+VEgFU8rjUlR1WkSDFtUkI0LsmQq4AEFT2FhCU7I8bMsgxL6qMq0FAaAsgbBFstSlE/EhpMAIMKEgig3Tvo+nIwyGQGsi3xBGMZYlqTR8KnU/sSEg6W2nhMBWkljrxFV8Nv4kEAiiMMLNOBx9wkrGhitMTNQA6Ogo0NPXwm9v3UxDCIzR6EijhUBHGoyeWb7TNCtN3IyN4ySWBHEjoFkP8Bs+hxzeR//KLqZHy4RBhGVbtHaX+N1tjzA5NE0YRNjO/K9XHMa4ey0OUlJSUlKeMaSCKeVxKckanbJOiwrJYLBmtElooCk0SmharAZSRnMEkxQSAwSxQBuNazuEM6LHRuKHEUZBGMSUmx5Zx0YJSRjHlBseWpqk8i7SBM19VWmBELi2heUo2osZms2Q8ek6eqYlSz7n0NGax/NCtuwYp1pu4vuJnUEziql7AY2aR++ydno6CowOTidJ347FqhUdeI2AnZuHOfK5a6hP1ilP1DBAz7J2csUMG+7cjkZguxZdy+Z6d/St7mZk5ziTI2VsW1GbqbDLF7OUOgv4XsDaE9Yc1PcrJSUlJeXAkwqmlMelRdboVD4tUuEKhSJx944weDpGEdCmalgqnrEcSBbmkh50Am3FxFJTDwP2RoJ8IqQSiUO2I2kRLrUgJDYaJSSt+QzVpk+jGdKfy1NqbyGIkga7tm0xVakzWvfoKmQxkcREAqPBCIGxJPmsw/hklT0DE5TyWUrFxIfD80N27pqg5oWs62th2bIOWjuLeF5AJuNQbMmy8e4dMyInx9IVXcQzDuNKSSqTNaQSVKcbC96rjv423JzLA79+ZNZ7SYgkT8sYw/pTD+WwE1PBlJKScpA4gL3kUuaSCqaUx6VDNehQioywEYhZU0oXcKREiZBOq4Gj9ppaJkLJGIlAYLRA2gKNIjQxAK6QaC0Io5hYazxijAXSSIyAJjGhiTEiadRSCwK8MIkyZbWeaaNiGJuqs6y1REspM5vD5PkRw5M1YgPSCDIZe2bZDjIZm2q5gRZQq/s8dP8uKtNN4jhJ+i61ZPHqSQK6VILKdIN61QMgV3DJ5Fxsx6JZ8xnZM8nY4BR+I8DJ2HT1tyWCzrUhipK8qb3lucIgpEQo9Wyo2E1JSUn5kyMVTCmPS5uIyQqbGNDsW3KLAQtBXth0qRBHRSipZ5O+Yy0RQmK0oKFDNImDN4BHkihtJERCE0QxrpU4dps4KfuPBFhKMVKrQwyWFBhgMm5iKZlUp0Uax04+xns7YLuOReBHOFmb1pYc5ak6sUm8ApQUtHcU0LFh86ZhWgtZ8nkHy05cwqcm61TLDWxg99ZRylON2Sa8ypK0tOWxMw7T4xUerjWxbIVlK7xmwORIhcALyGUsnveK59CoNKlN1cAkdgSljgJ7Ng3zyF3beM5L1jO2Z4J6uUEm59KzsmtOG6CUlJSUJ0Ka9H3wSAVTyuOSVwpB9CiptBdBJAwOgqIUZK0QJQxCGIwRxFIgI4VWAstOEsADkmU1ZUQS9dEGy1aISFCOfHSU5CHlLAvLCMJI0+7aWDrJbQJwXEWkDbUwIue4DIyVCeOYvYYGjrLIZhJH8UJnIclbqiVRomI2Q/eSNsrTdZpVg8SglJzxjZIIAVJJgiBk9/ZxunpbsG2FEIIgiBjYMY4U4GTtxJ1zxiQuWXLTREGMyDu4meTR1t0y5445GZt7bn6Q7Q9sZ8fvduM3AmzXYunaPk4570TWHLPyoL6XKSkpKSlPjFQwpTwujsxgdG0m++j3y+WTqE+MQ84KkSKJHGkE2kikiNEGYhkhlMKaOd8AodYYbZKGvcoip/ZVj2kMYWTQaFoLWbQ2NIIkcTvnOBAbyrUmOCIp4zcmETACjCWQQlKbarJ7zwSubdPZVQTA8yI2bR2h2gjoX9qGq6FW8WYMMyFXyNDeUWDH5hEKBYd6pYk10zA4imIKLYlp5fI1fbS1ZRkbnMKr+xRac3QtaWdg6zBTw2WaDZ9szp13L30v4MFfP0xXbytdyzroWtKB3wzY8dBuRnaN84p3n8Mhx/1p9mdMSUlJeTqTCqaUx0XJpRizCWHMrI/SozEIRsMCOeUjZRK10UYQGYUUgtgIpNJJFEgkI0gjEEpgtEYLQxxrIrVPkpk4EUtYgj3lChYyyVvCUPMDtE7mUmuGHNrVjpQCY0CIxJxy9+AUvo5xLEWpuM8w07EtJidr+FFMV28Leddhz84JPC8kk7HpX97B9GgFZUkOOXo5UTOYrZJraS+Qydrcd+tmwljTvayD7t+rkgu9kJFdk0yOlImCiKmxKkYbWjoLdPa1MrRlBKVg5VHLZr2acsUsy9YtYc8jg/zq+jtYtX45akakpaSkpCyKNOn7oJEKppTHRWXORTd2IfDn9BgSM9ElX0se9NrJWQGWSNy+E8EksbQi1hKpNNJidtkMkh5ySMA2hMoQ6zgZXoClJAJJrOMkAVuDnqlWkwBSYCyBCQ1eGOKFEbExWFLiWoo41khLEkYxlUpzTh86HRtsS7Fjxzi2EQghsCxJ0wvZ9MgQQSNASInrWmAMdiEDxmBlbJStEDJp8FuZqjMxWiXwQmzXor2rSGtnMekd99ttOK41WylX3Vxn++8GCGoNjj710HnGlkIIupd3MrRthD2bh1hx+NKD/K6mpKSkpCyGVDClPC4qdyEEv8aONhITznHr1sZik59hV1ygaHlYIkaSJIRHxsaKJbElUUqjoxhmzhYIpCXRRhNjyNkWEWbWS0kiqcYeRkB7a56mF9AI9y3JZaVi0A9QjmTXeDmJWgmB1snSmmNJ8kphZWwmJuqEYZL/ZNuKvp4WgiBkcqrB6qXt2I+K5oRRzOR4FcvA1keGaNSDRNwIGB6cJptzMQimR6s8WG4QhTFKCWJtGNw5juMobNdG+yHo5LUwY5AZhREaQSafYSHcnEvoRzSrzYP3ZqakpKSkPCFSwZTyuEirH0ofR9T+BRltxOgGCIGQJQbDbn5Uq5GRPhnl4xIjBWgj8I3CFi7aSJQKsSwHI/aKLdBxDApQmmkdzGxPrAEEJE7gAoarVTLKwp2phvOjiGroYwTEGDpb8/h+iNYGJSWOa1GuetQaAVmh6OwqMbPaR2yg2vCpBxFZx6Je8cgVXCwrqZJr1HwKhQyVyTpTk3W6elqQcibvyhgmRqt4kUY0PWwrT2tHIfFZMlCvNBjeNUmh4PCc09cxvmeKyZFpjIG+Vd2U2gs88KuNjOyeoNiaSxr3+hGWrWjtKiaWBI5FdsYzKiUlJWWxpFVyB49UMKXsF9JZj2i9HBPcD/FWwALrcDZN7ESL/6RNNcjKAFeGiRhC4GkLJ46JjcCxIupRPNOcF8xMDpM0ICyDa1kEOgIMEoEtVdIqRRuEFEmO08ySnECgpCCQoDUUCxksRxEbgxKCnGNTqXoE2lDIOuRzzpzXEkcxkdYsXdVFWPUZGa8RxTGWUnR25ukutrCp6qEsSXW6QSabnO97AZaV2BmUelqwtGZ6vDormGzHotCaxcSGbDHHmmNLrDbLkzmLpDXMro0D7No8Qm2yRrOeiESMwcnauBmbo55/GEvX9j0Vb2lKSkpKyiJIBVPKfiNkCyLzQuCF+7aJHbRYddpUlZwIcUSIFIbISEJhkREhkVE4lkapJL8JkfSU00YgEWhl8EU082kUGAy+iYilRkiDk1GEfpI0jgBbKrKWRSMMCOOYnWNTs8tmxgDGoHWMsgVTdY+6FxLpGS8lKYmDCKUkE9MNbCPIFJx9jXsjTX24jJ2xWH1YH9PjVaYn6xgDLa052rsKbH5wN8XOImvX9jA5XMbzAhzXpr2nhYEtw+zYOER5soaONZXJOmAotOTo6GnBzWfxm2NMjca0dpdwMg5REDI9VqUGdPS3pwnfKSkpKU9DUsGU8qSwRJM2VaND1clLn6yIZpO+G8bG1SGhkbgqwLL39YNDgdYSbQRGqhlrgpiZGjkUEqPAaGg0Q4q2S85NbAe0NlT9AC0AJRBx0mJFzogeIZP2KBaCMNY06sE+w20BuYyDUpKpcoNVfXNzmKIoZtd4FRtoeiHNIMZYCgR4Ucx0xUNriCPN5HiN0bEaYRhjWT4oRbaUJY40m+7fjY6i5PUIMDsn2JMfpTJSpndFJ/mCS3msglf3UErRvbyDfEuOoe1jjO2ZYMdDu9j+4C50rFlyaD+Hn3wInUvmVuSlpKSkzCOtkjtopIIp5UlhiwYdskq3VaMgYrJCzyZ9N01IRQRERpG1fZxIzzbn1UaiZWJwGVoarL31cwax16spmqmiU4JK6M+2ZJGAYymCEKQl6CwVKNc9wjjGURat+Qyj41WaUUhPoUShw5mT9N3wQsqVJjmRVN6FIhFmQibPlZI0mwGDA1MUixnaOvIABH7E1GSNZhAzMVKmNlnHcSwsWxEGETs2j6CEIIo15YkqvcvbsawZF/JYM7xzDL8RcMSJq+ld0UGj0iDwQizbIt+aQ8eazffu4Kq/vhav5uFkbISUbLxzC3f95D7Ouuh0jnzeYU/l25uSkpKSMkMqmFKeFA41uu06PTKkKCW2sJJlNgy+0WSFT2CqFC0fxwoTF3CSHKZYS0ASWzGR0BgBe3/aaJO0TUEBlkAhUHt/9cy0SDEKvCBmpFKbbXLr6ZjhSo1QJ87fUgmCOMafcQk3kmTdTkCxNc/4VI2Gty/ylc1YdHQVGdw5gTYG17VnfRBc16bZCNAYGvWAtqX5ZD/gYmM7EYM7xrGzLt2dWerTDfaebIyh1F5gOq7ieUnEK4oMsQZijTGJzcLg1mHCJW0cefJa5F4rBGMY3j7KT772czr62+hd2X2w3s6UlJRnOmmE6aCRCqaUJ0VW1GiXAZ3KRomZP/AkHyxHKFwhCI1HXjVxrZC93dI0gihOFFFgaeKZT2ISQ9r7bwMxxEYnVWwz32ILQfj/s/fmcZZdZb3+86619t5nqLnnOZ15TkgCIQFkigaISASVyQsXUPQKCMQJEAmI1yBeFLhwiYjKDxSDoCCiRGKQBEgISUgg89jpeajqms+0915r/f5Y+5yqSldnIN2pJOzn86l0ao/rDH3Ot9/h+2Y5rhBUPiW0dYT2PLwHpwQVKfZONsDT63RzziMujENp5zlJJWIgifBd10sRZlopUTUiSSJG903Pe7SeaiWmUo2J+4R2I6XdSNEmzLTzeOp9FWxuOfaMI2lNN5kcm8XjGRzpY2Ckjx/854/Ycf8+pvfPMjPZwNlgg9A3WENJML7ceNzanliCUDC+evNKtty6jduvvasUTCUlJQdFOHAew09yjZIDKQVTyWOiJjMMa40RRT7PB7xbjZSIYYXOGTHNYnRKN4IkpKIR5ejomJZyRS9rEEriBa8BA1Z5mvlcFKiDxWjB52EgbmIMM60O1nq0EgaqCb7haWeWpGJQtjDJBHSsQQkzUy2anYz165YvMJH03rPl/lGUEupDVVr7cjqtDA9UKhG6GqGnNctW9TM8UGXn1v00mh2SSsy6jSO0Z9tsv28f+/dN05rtMD3ZBA+5BZNEJH0Je7aM4jJL/1ANE2lsbpmdbjK+a5J6PWJgpO+A51lEqPVXeeDW7YfldSwpKXmKUMy3fMzXKDmAUjCVPCb6pUkiBrvI0BQPOKAimmVxh7pNUVh8MWcuUhqVRzRNjhiP8y5EeehWMzmwCqUFoxSZD6InRuG9x2no5JaWz6lV42Bc6YO46vgch2doqIrLoZWGFv5aEmNEMTnVQkSYnmmTWUfuLEZpIqNQCjqtnImJJiPL+oiiUBSeZZapySaz7ZRkskVjqoUHqgNVXO7YtWsSo4ROO2XLXXuIjCKpRggwsX+Wif2zzE60qFRjvLW0Gx2i2JDnFpdZosSADn5QsxMNZiaa4D21/ipDKwfC86LKf/uVlJSULAWlYCp5TFT1UCFuFscRvJGqxlPXbYwKR+ZeyFyECMyYHC8OUYA48KHbDQ1eO9o+xziNClZGtL0N+4uCcNtxNJzrqiy0D7VK3sCO8RlipegGmRtphs1cEGFas3dihu6lHMEtvFaLaLcylNHE8dxfkTg21PsS9o/OMDnRZP36oQX7s8yyd8cEae5xWc7AiuGu/iOuxIztmaTZSDn5zE3UqhF7t42RFcaVa49cj80td15/Hzd9+3Y6zQxfWCGICPXBGnHF8IyXPO3QvXglJSUlJY+YUjCVPCaS+BRs68sI+aL7PcGTadbFDERtoqJLLvOa1OUIlmkTo4zHyZwxpXjBWR8KvmONzyDt1jCJoL3CWhusByIht0FEiQhidHAMt0XAyvq5pLwPtU5WQ+oda1cNkmeWPHcYozCRZv/+WSRSpJ2cnbsnccWpSiBSiiQ2YC1ZJycyOtgYeE/WyfHeEddiagMVJsdmQnRKhCzNiWNDXIlwwMCKAXIHzdk2STVmcOUAlUrELd+7m73b9rPmiJXESfjrmeeWsR3j1AaqrD92LdZadt27h9nJJpVazLpj1xIXxeclJSU/5ZRF34eNUjCVPCZ05QXYmY+h/RjWuwV/zwRQXrE3T5j1mpGoiS7kR4am7QwijlpUBW1RyveMBSgCRjhFhiUyGu1DIbQTj7UOp4MfUmQUcRSurADvwkBeLzA8VA9+Sp2QkqsmMSPVmG27JnBeiGITUn2i8Cr8bq1DjIJY0W5keFuMc1ECFYVODAP1Op12yti22VBIroT+voThkT5mppqsPXIV4/umGNs7DR6GlvexZsMI9/zwAXbeP8r4nkny1KKUwjvHnm1jRJHGxIaBgT4akw1aOgwGtrllYFkftYEad1x3L9d+7Xp23L2btJ2hjWLlxhWc+wtncdKzjj9gqG9JSUlJyaGhFEwljwmlV2Fqr8A1v4CnGeqOuvtQtJxwU3uEwSiMTokI7f4phraN0TgmohraFEXfRVrNKwmz4jxgHHmucCpYAyivUDp0vHmjmG1lWO97I0q0CKIEpzyjM7Mk2lCphAhMZi27J2fxKsyh27ZnAqUVSoXBvWNTTURB2raoumbTpuVzBeNaMTnZZHSySTUxGKOp9FWK+3owmo73dNKcbVvH8Hlw+AZot3N2bhsntY7mRJP+gRHq/dWewMk6GTvu3Usca55x/mns3z3BxL4pvPMMLutn+foRdt63l8s/+21WrR9h1aYVVPsqpJ2Mse37+fqnr8B7OOU5Jzxur31JSckTj7JL7vBRCqaSx4zu+1/gO0Sdb+HdFKEaSKPUMq6a7bAzF1aYGSqFYAIh9YqmitHi2B/VUcailOtFmJwrHLJdsAgwOtQXQdBVuXN4DVYcSRSRe4crnAW0KFo+C112OeTWkRcF49KNXGkBUcSisbkDF2bYmUiRS7inVkI7zekUppex0USxxnnP1HSLIzaMYOa5hFvr2L19nHYnFHEPL+vrCSLvPdNTLRrNjFpfTHu2gwAmNtjc0pxpEyUGpRWN2TbtTk6rHdKMcTun3czYv2uc1nSLTSeu7103TiLWHr2aXfft4ZqvXc9xTz+KuLJwdl5JSclPEWVK7rBRCqaSx4yoPvTA76OyC6DzHbybRPRqiJ/D7aPvZmW0I4xOkYxIhVqnjoto+giDY2/URxKFkSrdAnLvhEwJ3gtOObIH5fq6HXFooZ1ZimwdFsi8xQt4gahqijl0QTBFWlGtRLSmckTB8HCdyZl2b/juUF+FsdFpdKSYmG5iXSi6FkJESysJdUnW4ayjlTuccyhRaBVGtIgOw4LTNMdEBsGT54602UFEWHf0aiLx7Nm+n2yiiTGKFWuGWL1pOXf/8AFuufZeAOKKQUTYs20/e7aNMbVnkk3Hrlo07bZi/TJ2b9nL9rt2cdRpRxyul7qkpKTkp5ZSMJUcEkRiJH4axAu7uIbMNGv0FMt1hz5lSYrv+rbKmPWqEEz9xN0Ik/dFhEkhDpwT0qhItxXnqqIg3CuPVaGmyfm50SpKgoeTs9BMcwaTuGdXgPfMtjOcgjSz7J2YRYpoUuoseyZnQwE5nqiaUPVCXkSYdKRwHpq5pVqJ2LVnmjy3xeBeMFqoVgyQkPRVGB2dpdPJAIgjw+BglVqWMz3ZIokVYgxGGUSg0c6JqjFpmtOYabH2iBU9s81aH4zumqCT5vSP9NOcaTO+d4q0nWIizdCKAfqH6zjraDc6h/mVLikpKfnppBRMJYeVlWaSdVGL5UqoSNRLq+XeM+AthgZ7ohkqUYouuuQ84JxGWcF5IROLVQpfmF56PxdhcdojkZozaxMVCqVdjtehUHsyTXsuUYIQaSlsBxQ+88HTqRfaArQizxwDg1WMKFqF6KnEEeCZmmqSa03/QAXvfIgqqeAS3mmnZLkjtY6knlDpS4o1e5xRpNYzuneKVav6GVrejyo67FqNlC137kFFhoHBKlNjMySVCERI2ylRZEhqMTvu28ueB0bptLNCqHlMtIeRVYPU+xPqRc1USUnJTyllSu6wUQqmksPKKj3Daq1IxISRJT1rAEW/KLTkrNZT1EyGEYuIxyFYp9GicF7RjPy84qOiwNp158mFyJAXX7T3O6wTnC4snYygi1ooCALKi8KpkNaLkyhEnJxDaUU9ifCtjCwV9o5No/VcjdJUo423QXplmWXZmiGsCx17SglGK7Y/sJ925oiMZmD5QvHSanbopBbtPEkl6kWQRISkEoWIURJx3NOPZvs9u9m/ZxLvQ9H3puPWcu9NW9i7bZQ1G5YxtKK/J5jSdsbWO3Zy7JlHMLi8nx984ybu/9ED5Lll/bFrOOHsY1m1acXhfqlLSkpKntKUgqnksLJa51TEkFNEcQococi6JoZ1UYf+qI0RhxKH9YrcG4worFcQBXfw3iBbPGGQHHilECOh9857RIFC8LnHKbDeoozu9e5pQorNKehklra31CoRWgnWedLc0rIWFDiv0MWsNyiiRIBECu88u0enyazrRZgiHQrClYJ2JyNqpmR56AqMtKI120G0YnCkxtREk06a000jRkYxMNJHY7rFvbfvJEszKgNVBKGTWrbft49WKyWKIzqtDloLURKRZ5bmTItqf4W0Y/ncB77ExN5JkkqM0op7f7iFG6/4Mee99mc47XknPT4veklJyZJRdskdPkrBVHJY6VcKFpgNzOHwGIRBpeg3bRKdB8NJoG01sYpwXlDaopwJISMITuDi8XicEXIVRqr4Iq2We4dTIAasBpvnvQ+AjGAP4BV4DXnu6HTsnEs4gmiwCpYNVul0XC8lV40N1diwe/cUXmsazeDtpJTgMk+HHG2EuJbQyR3TuybCcgmpwDjWIc2mNUSC64SCcVFCFEXU+hP275tmdrrJijVDKFWIQu+ZHJ1hZqrN5hPWUk0Me7aOMj0ZCsaXrR1h9eYV3Pbdu8jbKSeec8yCc/dtG+OKz1/FsnUjrD9mzWF4lUtKSp4wlLPkDhulYCo5rESS4Gk/5DEezXDcIpYwnNd6RU0bGnlO7oUoduTY+XXbIcIkgPF4U3TM4UEEXaSqvAvDeUUFGwIAo4picg3iQ90RNtQxSfAkwKcKpxxj0y2M0igTbtzKLY1OFubmCazbMEKzEaJIxijqtZi9e6ZpZin1vgoDA1Xy3IaC8CjMiBvfN42dbLJu3TDLVw30noMszdm7axKHoHzotpur2fLYPIg666DVzhEToQmDhDuZY2znJK3ZNsvXL+uJJQjpvpUbl7Pl1m3cfs1dpWAqKflpoNQ7h4VSMJUcVpTeiNh7irhRbz4J3ZCOByZswvJomopKi5luQsvFJCoh90JiMlKrw6y54h9PTnlA4YzHKtfroMOHyJM34dhO26IcPRGRuuADhQqjVvq1QhsdUoQiiPe0OsHDyWagcos3RbTGBq8nbwRnHVONDu00D07fzpECtkjb1foSKklEmllCyk2Dh9E9U2gfhFya5lgX7msiRZ7mxNWY+kiNvTsnQuQLTxQZBkdq1DoVdt6/j5Hl/QyM1MO6raM522HLtv04D31DVabHZ5mZaOA91PorDC3vp2+wzgO3bntcXvOSkpKSpyKlYCo5rES1X8LOfARFZ15aTgrpJOResSWrsronmCzOa5o+piZVrBcqJqXtIkTNdck568mKlJzXwVogXJHe8F4xApHgXVcoBWsA7SGzoAzMdrIiOhVQImAEbz3VekS7Y8my4B0VGU01NnTSnFw8k9Mt4lgTGU1uHdPTLbx3KKMYG2uEDrgi1SeAtxatNXGi2bljAuvmnM2VQFSJyNrQyTymmmAq83yptMYh5KmlWo/RhWGm0opaX8Lojhyc54HbdzE1NhMiUgSh2D9SZ3CkzuCKfgCstXSaKVFiiOJyBl1JSUnJI6EUTCWHFV37ZXznKqL8h+Q+g7lRtuAVWzJDJhlr9Qw11cGIJ/OKpouZVCmZF/qSDi3iuZScg1xrEI01Cqd9sP+mEBc+xK7EQ4YlFo0uokR4SAku4bmFgSTqiSmAWGma7RSnYbaT0hfH1CvFEFzraKQZViCJFIN9FWabHdJOhhZhYKBCs5nSzl0QYTakCQUh3EEgUlggqcaoLO8NDNZREEDtqRb1WsTKtUMLDCpnJpu0mhmDy/uZmWiS5Tb4TXlQCoZXDTC2Y4JdW0YZWTVAFJveHLqpsRn2757g5Occzw++cRM/uuo2ZidmiZOIE845ltOedzLL1gwfpndASUnJ40ppK3DYKAVTyWFF6UHM0Idxsx9FOtfj/Uzo4lAjbM0GuTu9i/XxFMOSUleh6NrimXUpfS4IpnrUZsZW0EWEyTohdw7BYY0m08HEsot4jy/qmCRSZPncUGCR0EUXjC9hNgt+Rt05dJnLcBJqlFDCTJr2uvsUoQbKK8gdtJ3FRxrlQ2qx7T2Z9+SeUJ/koVkUhleSiFo14r679yLOsenIZVjrQv2TUmij2LV1f7iXs3Q6lizNQ4ed0eRpDiIk/VVsJyNtZjhrEaWo9VfoG+ln3/YJnHOYSPfEVndOXpZabvnOXdxy1e1U6hVqAzXazZSrv/R97rr+Pi5824tZs3nV4/COKCkpKXlyUgqmksOOMmuQwT9F5fdAvgVQYI5h2+iXWBldz0ad0aciIpkrVh5Qln6XkvlJRuJZZl1tnmBSpC5HJCKNDWlk55y8CUXSXhQ4yMURad2rcRIP1vmQxtOgnJA7Szd3ZpTGm+Aw7kWB9Ygr5JYSnBJcKmTe00ktlUQjyuBcGIWSOYdo2D/ZLMa3hFPbuWW60Q7eSSKMjc3QTm2wJBAhiQ1ZZomSiE4OU9vGw7F48JAkmrgSMb5vmlVrhhheObDAh2nP9nFMYugf6WPfzokwH48QfeofqjMw0scDt+/kWS992oJZc8vWDrP19h1c+Q/f4TXvefmCgvGSkpInH6WtwOGjFEwljwsiGomOh+j43rY+P8EakzGkIkSEvCgCV0AkmiGl2GTarIhnmXQDPSfw3CvSPEIBbWNoaQ/a0SsIsgI4MAqnPHm3iAiCgJHCTTwPogldVJOjcBSZNAU2dySJ6XXYRaLIshyniu47hKlOhvdFFCkyxLGmbR2dzBIrFebOSTC67OQOHytwnqmpdhgUrBW5c7TbKVorXGpRScxIf4W0cPM2scY5YbKV4a2jWo9x1mOtRSkhroQBvihFXA9pQW9zwCPGIHFEY2KGJImIKzF5lpN1crQJImz1ESvZfudOdty9m43Hrzvcb4WSkpLDSZmSO2yUgqlkyRjS4wwS0kfZvL+hjuDRFIswojRr4mlG3RBRIZgyq+noDK0SGknEVORCQXihl7ySUEUNeKPnzZkD8IiTotsNbO6D6aX4woeJMMhXQ64deZr2StQ75KFuSIXRLihFxahgT1CsuZNbnMDgSJ20ndFoh0dWiQ0jQzX27p4iUorV6weYnemEqJJR9PclTIw3aDU61PtjatWENC2KzSONzR37905S76uyc+t+bBGZ8j4IzKQaM9NKmdo/y4p1I2hddPY5z8ToDNMTLdYf2ccDd+xkdMc4WZqjlGJk1SBrNq8gbWdMjU5DKZhKSkpKFqUUTCVLxrDKiZxeIJbmk+OJlWatabMzapCoUDrdcZqWjVDimIlixoxF9LyOMitYUcF+IFJgwRdiS7wgyod9ueAK+4FQxASuiD4FDyeN0pAWXXSRqFBInjucg9xZvFKEYS4CLhR7eyVMN9sYbUhqYZac846pZgcvHuthppWTOoeTkCKcbeVY6xCtmNjfYNK06FlLKfB5GN2CVggGyfKu7RTKaCQ2wcNJCSJC2smLOXOauGJwzjO+b5rWTJukGpFUIqx17H5glIl9U/QP1ZidbPCdf/4+d99wH3mWs/64tZx4znEccdKGBQXoJSUlT2TKENPh4glRsPDJT36SI444gkqlwtlnn80PfvCDhzz+S1/6EscffzyVSoVTTjmF//iP/1iw33vP+973PtasWUO1WuW8887jnnvuWXDMEUccURT7zv186EMfOuSPreTgVOMNC2qPHkz3r2ykPWviKdZEE6yOJlgTTbEynmYkajAQd9CRJYospvhTRxYTOcQ4vHahi04DOgzrddrjTPh/Kw6rizEqxe+ucAHveEubUJMkGjo42hT7DWQCHWtJc0vHWjIJY1OckkJUOSzhxztPluV4o7ECM9MtBEhig1aK2UabjvWoSJOLYDOLzy3eOmzmcAheK9rtnLVHLGftkStZtXEZazavZN2RK8g6ORIFe4Nt9+5j17b97N4+zvb7giN4Uo1oTLcZXNZHrb9KlERUaglDK/qZmWgwtnuS7/3r9Vz5D99h/+4JZiea3PCfP+KfPvyvXPu1G8L8vpKSkic+/hD9lBzAkgumL37xi1x00UVcfPHF/PCHP+S0007j/PPPZ9++fYsef8011/DqV7+aN73pTdx0001ceOGFXHjhhdx66629Yz784Q/z8Y9/nEsvvZTrrruOer3O+eefT7u90HH6j//4j9m9e3fv521ve9thfawlC6kkLyD0xR1YZCiEN6dFsN6yPhpnfTzBhniC9fE466JJVsfTDMUNkiQniXMqcUYS5ySJJYozdGTxkccbH8SQDv/vij+9IXgu6SCWvA6/26IgnCik31JcsCJQoIwK41YE4kpEXDHoiiGqaCqViMyH6yT1hI53NNOcZprTdo6oFodglgneSe3MMt3s0EwzKvWEODbkzrN8ZT/DqwZJ+qvEfRUGl/exesMw1od04eREk9HRWcb2NxgdnWFivElugyGnRBFxNUZrjdKKqGJQUYTXGmU00+OzTE82mBxvMDXRYGaiAQoaU03275pg8ykbWX3ESlZsWMbmkzeS1BKu/udr2XJLaXpZUlLy082Sp+T+4i/+gl//9V/nDW94AwCXXnop//7v/87f/u3f8q53veuA4z/2sY/xohe9iN/7vd8D4IMf/CBXXHEFn/jEJ7j00kvx3vPRj36U9773vbzsZS8D4HOf+xyrVq3iq1/9Kq961at61+rv72f16tWPw6MsWQyVnIPozRh7H7l3zHcAFwQFjOWKoWiKIZ1RK9JqDaeY1AmR5OyPa9SiDK1s4RIO1mk6KqTkrI7C3LnCpwkvFKZIWAO5+F5bifeElJoOF8qLobhqnpzLnMVrwVmYzVKQwobTQ9s6MOAstPKc/lqMLXyWRKDTscVA4BCdksSgu9eV8OOVYnyq1fNYQiBrpsw0UkQJojT7xxpoJWijcC44fWttcKQklZih9X3kmcV7TxQb2s0O0/tn6B+uMT3dJu1kYWaf9+hIMzBcJ22lDK0cJM8ss5NNvPdU6wkjq4d44LZt3Pa9Ozny1E2H/01RUlLymJA5W7rHdI2SA1lSwZSmKTfeeCPvfve7e9uUUpx33nlce+21i55z7bXXctFFFy3Ydv755/PVr34VgC1btrBnzx7OO++83v7BwUHOPvtsrr322gWC6UMf+hAf/OAH2bhxI695zWt45zvfiTGLPyWdTodOp9P7fXp6+lE/3pKFKBUT9f8B+fR7idx+LGHuWvBKMsxax7jrcExkqStFVLxdM+2YdS0SsYymfdTjDrEKhd/eCR2r0MrgvdCJLM4qpDeXLYxFQRQuB0yhn3rDd8Hb0E3nDKTezYWnJcTDnAqiKlKG1Fms9yggNoZOx+GMQO6ZTrOFj9d5vBZsHtJzcRKFocHeY1NL5sJcvDSzxFphjEYEsiwnzz1OhxqqFev6acx0yLKcKI4Y7q8wM9Wi3VA0G21y5+i0Q8G4iXR4TAKtZs6KNcMIHpuHob/aaCb3TdNJLRN7p9hxzx7ajQ7ee+IkYmTNEH2DVbbduRPnHHu3jjIzPktciVl79OrwGEpKSkp+ClhSwTQ2Noa1llWrFhrmrVq1ijvvvHPRc/bs2bPo8Xv27Ont72472DEAv/3bv80ZZ5zByMgI11xzDe9+97vZvXs3f/EXf7HofS+55BI+8IEPPLoHWPKwqMrzidSHsY3PobLb8D5FpILEp3H3xJUcFTsGVATFNDqACopEeSKTsTcZYyhuEescJeC8kDpNIw/pr9kowSvd+yeTFBEmL+BTRW7CWJWucaX3YZyJ9mG+r0Ho2l4qBCseHFgb6pdES9GQJ3ScxSoKXwSFcuBs1w9JIUbhcksUKZxXTLVTukot0hodhwG9A0NVOu2cRicIrigyDA4ljO6exHpIrccqwUcGJ0LH+tA1pzWdzNNuNdFREFudVrAmUMaQ55Zaf5W0k4EKgqlSifDek6WOPVvHqPZV6B+uI0rotDJ2bxklrhiOOGEdX/rI13jg1u20Gx1MpFm5cTlnX3AmpzznhLIovKTkiUL4IHvs1yg5gCVPyS0V86NUp556KnEc8xu/8RtccsklJElywPHvfve7F5wzPT3Nhg0bHpe1PpURESR5NhI/A59vAT8LMoiYIxiZPoYBZfAEj6b5GGBAGY6MG4wkTSo6I/SrKdrWkOgM54XxOMflGlUIJucl2A4IYARnQkrOSeEsULh2Wx9qm3Lne6aXzhchKBcW4HzofusOZdGFnYHTnizzRJHG6a5NuOAzhxch91CLNfVYh3MF8J5WM8UrYaadEWlNra/Su+9MIw3nimdyokmlGpHEBmsdMzNt8tziRegfrhFFisZ0G+89fYMxUWzYs20/ysCO+/eBUj2BiPc4Gx6DaE2tv4K1DnJPUo0wsWb3fXvRSmjNtli1cQWrj1hJ1skY2znOv3/6CmxuedoLTjmcb5OSkpKSJWdJBdPy5cvRWrN3794F2/fu3XvQ2qLVq1c/5PHdP/fu3cuaNWsWHHP66acfdC1nn302eZ7zwAMPcNxxxx2wP0mSRYVUyaFBJEaihc/7Mu0R1KK2A7lAjLBSO1Ym09RVBy0e64WGqzCdxVin2Bf3i/thPQAAYkVJREFU4VWOKlzCnROs1TjlcZng0jlTS9/9TyGerBaUppeS8wLiwLnwp3cARbrPB1du6wEXapzSYgAuAjYHUYIzgss87SzDK9UTS8qDFwEtWOtQIqHIWwTxHmctaIVSnmpiaLVzXCcvOu00SgnN1JJZR+7B6SDGOhZcFuwOjAkmmjhXNMJ4RBQqihCT0pxtkVtLltqQnjQqiFDnmJlsctbPnQpAlgbTy7VHrWbPln1c86/Xc/zZx1CtVw7dG6KkpKTkCcaSdsnFccyZZ57JlVde2dvmnOPKK6/knHPOWfScc845Z8HxAFdccUXv+M2bN7N69eoFx0xPT3Pdddcd9JoAN998M0opVq5c+VgeUskhJBbzsN2tkQgbkv1sisfYlIyxMR5jQzLG2mSK5cks1aRNklgqcRa66BJLEqfo2ELkQtdcFH66HXWu2OZ1SMvZKPy4onvOmbA9F0+mHFnxZy5dewLwRiBRuFhwkeAThUQqRKsiwRuFK6I7zhfnFJYEqhqRAu3c0c4sHedR1TiMZRHBao2KDTqJUEmEjwxWBK8Us42UTjvDGE0ca/LMMjnVwmuNBdYcuYL+ZQNUBmrUh/tZdcQKTKxRWmMdzE61yNoZWZrRnG3TaKZ4pTGxZtf9+7j5qjv54bdu48Yrb+O+W7ZRG6yxf/cEW2/bTp7l7LpvD9vv2snsZOPwv0FKSkoOpLQVOGwseUruoosu4vWvfz1nnXUWz3jGM/joRz9Ko9Hodc297nWvY926dVxyySUAvP3tb+e5z30uH/nIR7jgggu47LLLuOGGG/j0pz8NhBTPO97xDv7kT/6EY445hs2bN/NHf/RHrF27lgsvvBAIhePXXXcdz3/+8+nv7+faa6/lne98J7/6q7/K8HA5tf2JgtbD4PY/5DG5F46K9jGoUzQOi2LKJoyqNg7hnngZXhs0oZbIosi0RpTHRSoIo6JTzvtQ4+SLSSk28igncxGooiDdFwXh3flzXrolUgpX3Ce3IWokRRucdx5LKAjPM0810kGc+VA/pZWi08xwCjLrqPfFWBs+tbQSOu0MrwTrIE9zTMUUfYQem+VkuQOt6KtHZGnObDM0KBij6B+oMplZnM3Zu2uKMOnFA452Z5q0lWO9p3/ZANVaRHOmg/eOpBqjjWbnvXuZnepw/y3bMZEhSgzOOnbcs5fxPVPU+mNu+e4dfPcrP2B0+xjOefqGapx0znGc8wtnUR+sH7o3RUlJyROOq6++mj//8z/nxhtvZPfu3XzlK1/pfd8uxre//W2e//znH7B99+7dT+jO9SUXTK985SsZHR3lfe97H3v27OH000/n8ssv7xVtb9u2bcFA0HPPPZcvfOELvPe97+U973kPxxxzDF/96lc5+eSTe8f8/u//Po1Ggze/+c1MTk7y7Gc/m8svv5xKJaQMkiThsssu4/3vfz+dTofNmzfzzne+84Duu5KlJaq8CN/8R6TwAZjXrNb7PfWOE+ImdRXa/y2Ohm4wZFtYDyPJaiTTmMIlPHeajjYoMWSxphMX+bXuWBWvIAfvVDC8VLJgcC+uEE0W8rwQS1LUM+HwJlwOLWHESzF9V4ygUThr0V5oF+k6kZDay50NnlBOcE6YbgYbAQh1VQpwIuhIsCK0m1nvOTBaYRJDlls6HiSK0Cr4W6GETMJjEGXIOjlKK4xRWOvIU4crolNpmpNbF1JyQO4y4sRhnaPTTlk7vBxRCmcdJjZU6gmTozPs3zWOd56RVUMsWzuCNpqZ/TN851+uY9+O/fzi215Mta96eN4kJSUlC1gKW4FGo8Fpp53GG9/4Rl7+8pc/4vPuuusuBgYGer8/0TM84ksL35+I6elpBgcHmZqaWvCClxw6XL6DdP9r8HZXcMsutgdTSyF1HoelovQB57ac5e5M8Y9jT2NfPkwsQQSkXtPOIqazhNGZOjNTdVBzkSMc+FxBqlBTGu3VQoXmQHJBdyBOmVe0XfxhgQySdvjXiC9EjzgfolaZx6SeOprMuVBHBGilcanFppY6Ci1CXnTY6eIanWaGzj39iZm3oHDfdisjb2fE3lOrRogqCsq9o93MSNspkcDwUI2ZqRZ57lBKqPcl2DRjev8skXi0USSVMAw5TTPy1JJ3MnCWlWuGaDUznHWIQKWekLU6zE7McvrPnMARJ66nMdPCO0+lnoCHnffu5ud/42c582dPO1Rvi5KSJyWH+zuje/1L/++/U60+tqhuq9XgN992wU+0VhF5xBGmiYkJhoaGHtNaH0+WPMJUUnIwlFlPPPQXZNMfQNmteJ8CoUB8xkYIY9SUJscXibDiPKCmNJujnA2VcSTTJMriEVKnaJgErTzNNKYRO7Se+zeDtRJGnwAuVkHoPFgwSRBNTofuut59/dxx3kDuAPFFBxrBZkCHYvI0d4gBEYX3ntyGkStoIbM+XDcKkVULuDw4jXsNnTyfVzAO4n3hAi5oY2ikFufy4rkS4kQjmSK3jmYrI65GJEqB96S5p9PJ8SLUh2q4PKfdseCDeOofqTA5OoPPYGzvNHFsMLHGWsfkaPAiE63ptFJ+/N27aEy3eh5Oy9cPY7Tmx1ffznFPP5r7bn6A6f0zmNhwxEkbWL15ZWlHUFLyBObBfoOHuvnp9NNPp9PpcPLJJ/P+97+fZz3rWYfs2oeDUjCVPKFRyVnEyz6Pa1+Fz24GFBKdwcTU37PGjQcx8aBzXPHTJ5pj4nGU0lRVSGG1XMSMrRKJZTaNmEpqaGXDgFsH1ilyrci8wRvV82WCwnbAFoIpCx13Xub8yYsgEqrwcFKK3rm+GGviAO0IBdzOhxltAjoO3XPY4HPuCtfxcF+PaAnGlcWoX+dcuCEgSkGs8dZiBaq1OFybEJ3KrccpAa+w1mK96noo4F2wOsCEiJdog45ViHxpRe7COnWkGRqq0pxp02nniAi1gSp5amlMN9lx3z5qfRWq9QRRQtrO2H7Xbmp9VTrtlL/9wy8wsXeqeDKg0pdw8rOP57xf/RmSatl9WlJyyDgURdvF+Q+2zrn44ot5//vf/xgvDmvWrOHSSy/lrLPOotPp8JnPfIbnPe95XHfddZxxxhmP+fqHi1IwlTzhETWErr0MeFlv29DsP6O9kB7kkyHHE4uw1rRRei91aeMRmj5hIq8Sq4ypNGE06SfSthusIbOaVBu8E7JI41BFUVLhEm4FMnAROFsIpqLou/CvDONZoqI4fJ7YUi5syzUY7/FRt1pccDa4gPtI8LmE83p2BhKK0XOL82Genfehy04QtBKydoYzCueglc+LilkPNtQpRUYg0mRpjvchVGa0JtKKLLW0Wzm1WkRUDe7d3jlajRSvNd47rCgkjlCuMPrUEU4s1nq00SS1mFYrA4KFQd9Qnb1bR5ncN0l9oMrGE9ajdYiozU40uP7ym9FG86I3vOBQvl1KSkoOEdu3b1+QkjtU0aXjjjtugX3Pueeey3333cdf/uVf8vnPf/6Q3ONwUAqmkicl9eQ0yL/NPF2xgK5eGDQdVkqTatE40HItRs00lTRjf1JjVzJEYmxheimkuaalY3CeLAm+RVLk2rwTyEOBtMsVzoJTc3dXTuYiTIV/k+/2K7gQdXKA2GCg6Yp0HXiUCT5O4grPJkL6rXuu0B2N4unY8E9IEcF7RycHdFgXWvA2eCcBKBGU0WCCi3g9Uui4gvc+zKbz0Jhp47UiqcS0OjmuE5yvtECUREgWRFFrtkNSi4omDE/azul0LChFs5nSaud45ygG7BFFmlYjRfUnVPurbLltB62ZNibSjKweZGDZALd9706e/qKn0T9cZ/f9e7G5Y3jVIMOrhg7F26SkpOQxMDAw8LjV6D7jGc/gu9/97uNyr5+UUjCVPCmp1F9Ou/kptO+QL7JfA9Z7VhuIJO5t71cw5C01GWc072NrawVVk6LF473QzGNmszDTrlWJcC4MzoXCBdyAVx6fgbMqzJWjEGiuK5AEb4I46skpFYSUR3COsOZ59Tu2e6AT8giMzI1kERXyfl3DTBUprPXFfkErhc0sTgcX8ahq8EXBuBcJA4WVoIyimbpgviAh7Sfeg1agFbmDpJYEMVVEvrwHpxTKa1SkmW1kvakJkRHiakyeW1qtlCQ2RJUIJUKe5cxONUOAy3pu+/69WOuIouBOPrpznMHl/VSqEd/6h+8wvmeCsZ3jWOuoD9Q49qyj+JlfeiaDy8uGipKSR8WTdDTKzTffvMBs+olIKZhKnpQoswEVPw/f+S8Uodust6/rUCSg0WTz9iogEc16YzkxGeWu2iR9uoPGYxEaNmE6S3A4JqNuJCac6x1YGwwgfSzkuQvKjKIe3PqeuLHZ3Bq6B/jCvcDZ4lqFJQF+LqXno5D6ywChaytQiC0dRFPmPZjiZD83vsUZwebgM4sUdgiuiPh4E4YNm0iR21A7JUBkNGlq8ZkULuUOj+AJ0SdsqHHySiFRRKw1qttRKELWyfAoagMJWSdjdjYU5islVAdqzEzM0mplLI8Nldhgc4cRwtDf0RnajRatmRarj1jJqk0r0ZFmdnyWG7/5I8Z3T/CKd/48fUOlj1NJySPmENYwPVJmZ2e59957e79v2bKFm2++mZGRETZu3Mi73/1udu7cyec+9zkAPvrRj7J582ZOOukk2u02n/nMZ/jWt77FN7/5zce48MNLKZhKnrTEQ/+bdGKGKLsZT4r3DhGFENOxLWLFATVOjrAtFs3mqM1RySgDuolRDusUU7bGmO7Hes1opY7FoAufJusUWa7ppBF5HDybJJ7n4ZQqSAWHwqWF2JnXBCa2iETZEFFy8+wMlAdUEFm20GG2e54vCtl9GHoXisJ9z9JAmZAi806QONywG7EK/k+QW4t4ReYFMWquZssXHYZagZLQ2ee60akwHgVjcHkeZswZTe4lpCmdw7oQoUozR1RJiKqEYnK63lSC4Jmd7dBpzWKdC517sUErmB5vsO6oVejIsPWOnUWEqcry9cvYcss2bv3unZx9wRns2zbG1Ng0UWxYd8wa4spc1LCkpGQOYa4k4bFc49Fwww03LDCi7Hoavv71r+ezn/0su3fvZtu2bb39aZryO7/zO+zcuZNarcapp57Kf/3Xfy1qZvlEovRh+gkpfZieGDg7i+/8F7b17+DHQS1HV17K1PjbqKqDF4XHCA1nuamTsFy3MeLJvbDfVtiVD3Bnaw3XjW0idTGxDqIotYqOjWh1DI3ZCs7qnlgKfwqk4Gc0ZkajROFVt9NNgmDKQXUgyhZaEogP+yTzRG1CVGtedEoc+NwF/ycnvdooT1FMbi0+gygrhgDPq3/CemxuUZkj8YUQK9athFDz1MmJgSjW8/yfQs1Uc6aNcQ7T6+wrPpQLZ4N0toURiGMTfKeCARQus3TaHSR3VGsRcRL1zDhtZmk12rg0Y+2RK3E2tBgqFWbpJdWYgZEaazavYM2Rq3jg1u20ZlroSLNi/TKe/qKncfoLTl5galtS8kTm8fJh+quPfv2Q+DD9xjt+vvx+exBlhKnkSY3SfVC7EF27sKi9CV/IavJ38GQHPc8TslqnJS2qoouaHs8602K1buO8cH9lORkZsQ5DblNraGQRU5KQZppOS4WU2rwaJxJBvMWmxZiUrvCxHqWLeihb2AZ0z+2m5Iosm7VCT3d0L+9Cis670J3nZG4ki9eAKMQ7pEhQdqefiIBEEuwRXKhVEucLw0zBK8F1crxWWOdwmUUVoibLbdCCRpHnUKtF5M5jbYgSJZGmOdMGE6EjIcssPg9iS0RQxiA6J2T2PI1m2ksjSlG07lDMTjZZtmaYPA9Df2OjyDsZux8YY+/WUfbvnmDVxpWs2LAcm+Xs3z3JN/7mSrJOxtkXnHno3kwlJU8FnqQ1TE8GSsFU8pRhvgmi1kcj9o5Fu+i6OiUWTSK6KM72KFH0i6ISWXJGua22n4yEqi48nGzEdF4h0n20M4O1BqUdqjsaxSpspvCJ4GNHqPQubmpC8bOIQA6aOYPM3igDAeUFa4pU3jxLgqCAgmeBklDMjcyd7/EoL2QelMxFXbyAWIfTCpwj88G+oHtxcT501hkFPghA64ouPK3RQnAFN9BKgwmVUqFwvdHJwSh8LljvqfRXwrgYwGgB5+i0FaJAxQaf2Z7vlDIGrxUuzXEIY3umQsqveB2TasTseAOlPPWhPrbeuYvmTAutNcvXDaOV4vv//kOOe8bRjO+eZOvtO8iznOFVQxx75pEMLOs/NG+qkpKSkoJSMJU8JUn634qdejvaZ6FIu9guhGxVsID0dBbIqfD/sWg2GMtx1d3kRNRV6MNrOMN+209F5TSyiMwakqh7dSHNFamJSNsRtuKKwugif1VYEiDgcshFQM1bl5uXhus6cc5LyVGUSklRLN4VVL36p6KjTblwq266T3lQSuF82OFFzRsyE2qUbLBOwmUueAl0a5y8J8s9FAXjyoQoVOZBtGCUYNMcdBjD0uwE8SgC7dSHDjyj8VlwA9fG4AoPJyVCp9lGlKbZSKn1JcH+oCjqasy0aacZSaS594dbQQlxYkjzjAdu30G9v0qyz/D/ve+LzE42yNK8sFnwjKwe4oWv/RlOOnfO56WkpKTksVIKppKnJFH1fOj8ErS+giLtiYQglAL5QeqbLJ6q0pxeGcUDAyoYW055xZ68Rk06TKcxqTNUTYYWj/VCJ49oGMu0B5t0i4SKizrACj4tPJwIFgU98lC/E8IzLKjcDN1qRUddMZoF1TW0DBGhbm2Qch4lczVO1hUDgIvBvrnv5unCdXNXRJyc4EQXbuVF3ZUIKla94b85oCKDKZZpXfCG8kaDClEz68IzrUxhqJk7xIRRMN1be1/UXpkItMMCzVYOIsV+j7cOjyIthFqWO6anWyilqFRjZqfb7H5gmnazwzFnHEnaynDOE1cMjakWl//tlfSP9LHx+HXMTjaYHA0F48vXj6D1gbMHS0qeMixBl9xPC6VgKnlKIqKIhv4YHZ9G3vonVF50aJiNNPM2FXdHrwvtwVhCFGpz5IhEMBKcr9d4xwbTYEBtZyKrk/qIvijF4MgRGlnCdBaD94y1NUq5XtTIO3BZaM/3ucGKhILwrijSwe1bI2CDcJjvEi6q+MnBdQVRd78TsD5009miLqkYNy7FflV00YFgoScbFSqIE69w1hViay70ZZ3HmTA3RktI+XX3STFSxVsXuvK0oKLwkeKdJ3MeIo3HYSox1lK4k4eUnW1noDXaBBXlitkyIkGYkVmcc0xONAt7B4X3Oa1GiuBpzoYxLXdev4W0nfbShf1DdaJE84P/+CF3Xnc3t197dy+dt/rIVTz9RadzwtnHlHPsSp6alDVMh41SMJU8ZREx6PorUbWXg9sfNqpluNkv4mfe95Au4QqhpgzO+14kSotiUBQnxTn7qttJJWJYN4jEkXth0tYZ7dRxXmi0I5QWjA75NWuFNDJk7QiXWZwUnWzdgvHcIzZ4IUl3NMq8TjdtgTx02mGZKyYn/N7tWLMuFIy7QgwIwc7ARYJ2oVsv6Kaw3xXF5BKBQwehNV+oSahvsj7UMyFSRLbCc+JSC0YHwSO98XZF0bfgrSAY0qLoXYnCQ5hvpxVojcUTxdG82XiED2wd7NKtC+18Ng/F5kYLzdk21gszE00Glvdjkqj3+k3un0GAKz5/NSs3Lmdw+QD1oT6cdWy/cye77ttDu9HhjBeeAkCWZuSZJanGZdddSUnJQSkFU8lTHpEI9Ore70ntF2nOXIKhRbaIZIoQlAiZd9h5QYickJqqKc0plWmcbGWlmSUWS+qF0byfHXoYgKl2BaMhLubUdayinUc0laORVYIC0n7OlsAKPhO8V1grQTTMH6tii5SdhaI+u1fDJIVpk0KQYgTLfDUohd8TXpBiYLATUPgQnRIJdVDOo5Tq1UdJsc17QXlF7j2+q8wQxDuIgvWAsx5twv8jwXLTOYfXOhSqGxXSf8XSVBQW5Z3DOxf2KSk6AYv6p0IwtTvBiFMpwXlHJ+1WyCsy65maaIbOPUJkLkoMrekm5BkrNq5g6x27SDsZooSB4TpJNeI7/3wtwysHuPemB7jz+nuwmWV41RCnPvdETnrW8cTzBFhJSUkJlIKp5KcQpetEfW/Ezf4VhmxBaq5bEO68XzRl5wh/aZZrz7OqY9SVCh1veBrxfrZH03jxjLZrJBqqJlgStK1mJksYUzXSVGHzCDVPMDkrRerL43LpLqR3U7GhSFyshNTWvAiTcoSCcu+xjlDP1E3J+XAdJaHDrmtn4CWYSipHL9pEsT3UkIcokhRpPO9DZMh37cvFgzd4caFgXYK49PMiNIKCyBR6sIg4FUVMnuCMjjaI8aBCF18QchLSZUW3noo01vmQ9hOFMkWXoHV0UosYHdzIi4fSaqW0mika2HnfXkxsUFrjvWf/nilMpBnfM8lnL/4i3nv6Buoordh+1y623rGDrbfv4CW/fh5xEuG9p9NK0UaFKFhJyROdMiV32CgFU8lPJXH/O8h8G1r/jHKzBCmkQPWRuSnUQ1Q9eqBPaWpFzqxbpx2Lph5bPDvY0RmmX6cM6BTwzNqE8bxOoodoZ5p26omjvGdJkOeGTmbIvcZbNU8wefBF9EkJkhUDduel85wFVaTvxHVTfWGn96AdYf6dI1yra2dQ7BcVokJBj4QIlBDSd1gfhE/P/bsrlorRKSLBjkCFqJif02phtp4H8RrnQ1rNF1EgfLe+CVzh60QcPo6cJ9RVRSYUtYug43mviA9pOtEGiyfN3MJXqxjvkuPJc0+z1S6GAkMUGyTNmB2bJcssy9YM88Cdu3HOkVQiBlf0c9OVP2btUatIagm3XH07YzvHUUZz3FlHcepzT2TN5lWP5q1WUlLyFKEUTCU/lYhoooH3YOq/im1dDm40uIRXX8Tkvl+iyvhBz9VFbU/Kwi9qIcypOzrKOLP2AMtNixHTQYAJG7ErG6Km1zLbMczEOTWTYVTosGtmEc0sYsZXyXIJfzO7XfYWiBS+HQwktVO4edEpKQrKdQgbBaE13+nbFQXaxfBeV6T0uv5OSkmvsaYXnSqsCrBhakpXZXkVIl3hvh4pCsatBNHT9YfCg3JhGrEqbDKDjUKx04NXQVF5LT3B1kUpFTRaFJaRMe++AkRSpAsdmQV0N51XDGMxBrGOZisNaUbCujodi81y2mnOzHiDPHMooxGB2ekWM5NN4sTwzx/7d+oDNZz1xNUYbx3X/OsN3HHdPbz0N3+Oo047Au8943smydOcvuE69YHaY3tTlpSUPKEpBVPJTy0igphNqP7fWLC9Un8NvvEJFHOWSF1UcZ7FHxCDCt3/nppSPLc2Sl0pYgnKJTMdpuLdDOlZprKYibSfwahFpCw5ium0wv60Bt4zaWsoIxgdhs85q8hTjVMK7wy2iBh1FxiiSh7xIcQjqkjZUdg65cHsEktw/DbzxJYFn3fX362dKgrGi9qq0OXncUgRJSqeCweiVOEtrvC6EEwQ6ppcECq+CGe5IjolheOmFK7fzhbu4t10nisKvWONx+N111FdirEsHp9ZcAa8Q7Qu0nyCaB1cxF1IS+TO96JLxYteGGQKndRCO8fmwY1LiRDFmtmpJvt37ueIUzbSnG73PJ7qg1Vas22++f99m+e98lx+fNXtbL9zJ3lmqQ1UOfHc4zj7JWfQP9z36N6IJSWHktJW4LBRCqaSkgdR6ftNWu3LMfY+HK5Xy6QBTSh6Tg+S47dARYQVJu4Gd8I1RZOgeWZ1lrH8Afbmw6yOpkgkI/OGvdkAOztDiPekVpFEjsSEgvHMalqpoaVjchuKotG+cKwUfAYYRe7BoPHaL4gwSa/mp6gd0nOV7KooyvJFAKebVuvtt+AlFH6Ll2BsWUR6vC0EF93I0pzdgThBFSNYusPnvOoWjBfRKXFB3ChwonrXRfswO48g2npdfcW5tvvc+xDhckoVkbFuEbkHE4GHzApSRLDC8+FCaZTRpA4ks73vBuc9WTOj00why9i3YwKlCz8HHOm+GbQWJv/7NnbcvRuUYKIIpYTW7CRXffEadt27h5e//QIq9YQHbt3OxN5JtNGsP3YNKzYsL60MSg474n2vi/WxXKPkQErBVFLyIJSuUV3296STf4DKb0C7TvjiVwmW5Xi37aCWBKG5TZHjFnTgBW8nYUAZnlnbR8ONscZkxAK5h1G7j7uTQRSO1CkG4pS6zkCgbSOmOlXGdYWJHPAaFbl5BeMK11F4X/g7FYLJS1G0nXVNMVUQC936KF/UP+VzD8Z303ndiJQrxJYP9gN+nudj8H+SoM2KYXheF7VQ3odUonSflVAb1TXUDM7mOixDJNROKek9r2Id3UShEISa745z8R4ntuikC2LJdvfp0KnXXQNaishWKKgPBp9FITue1PZ8EHrFss6BR9Hu5CEaVWQolQru5o2JGdqtlPpAjU47C+lHJVT7Kvz46jsYWD7AxO4Jdt63B5vleOepD9U58ZnH8oLXPodqvRKeax+GImujSyFVUvIkoBRMJSWLoMxKkmV/i8/vxaU3Erq1Tge1hsa+Z2DID2pJgGfRfZZgTLnReBQeJVHPSmlYeVabccQ7Uq9ZkcyyTLcAz7StsCcdYJseoWODMKpEGbqof+pkhjQypPjgoxTNRZi69U9WS896wBvm0nm2qH+iiALpeaKmK6gkDAvWgJsnmJQPas/7IoKjwfXSeYK1Hi1BhHgJgqgXYbI+FJvTLRiXuXMBrEJJMVtPCIKp17nne6k/rAOl5oktHyJphfjxSvUiTOIp1mLDY/M2GEV0nc8J6TtfOIF3Uhuu7cJzoxykaU6ae2YnW6A0WRbqsJRWdDqziHd87ZOXM7xmGKU0rUYbpRSdVs53v/IDrLU8++XP5Lbv3slt19xF2k4ZWT3EKc85kRPOOba0MygpeQJTCqaSkoMgIkh0DCo6ZsF2XXkJ0v43DAutB0J0KVgMHCygLUBFDBl+gajSIgyK5pzaFDl3cWQ8y3Kdo4App7g37edms5Gm1eA1g5U2EY4cxUwWM9muMuFrpAIq8igTkoHOCS7VoFWwI5AH1zAJKg1ixEsoNvfz0nnKFvVSfp6ZZhGdsnm37EjIVRHNmSe2lIXeHJdCUHVtBcQJyvqQCux26eniGfIe0YIXXYxTkTnBBEVboQtNhNoF93SZKyhX2hdpxW7nnppLMxZRJu9BnMJrFbylevuK+ieRUCsmc+k864LfFEqTeWG2kXbfKJCFGFfe7mA7GShNbn0oqPcwtX82+D/9yw+458b72b97Eu9AacWu+/Zy701buf+WrVzw6+cBcN+PtjK+ewJtNOuOWc26Y9aUppolj4zSVuCwUQqmkpJHSWXoz2iPz6Cy76J8XrToexBD5h1yQKn4HKoIsTx4jp0tUk9DSjivPkFNNLooGF/lPRvMFKvN3cxkMSKaNckkFZWR+oh9WR+7WoPc55czoRyVig31TwJpLrQ7ER0d42wQD0Su5/HkM7BREA1eKYgKgQRBMOWCUr0ypBCd6oqtqBj30q3X1hQdbyGC5JxCKVdYCci86JSEyFHmMF6F+xXn9aJIuUcKISMPik7hCMcTBB+6EExdB3I799yGdJ+ae7zWh1CRJ1TG6xCdCjs9UkSnJBNyUaAUIkWfn/Ohs8+E1Ge3zmruUXmyLNg3NBop1oe6KACjhE4nZ9/2MfZuG6M2UKPdDFOPlVJU6wnX/OsNxEnErvv3svPuXXTaGYLQN1znuLOO5Pw3vIC+oTrWWvZtHaPTSukf6WNk9VCZ0ispeRwoBVNJyaNEqYTqsk/j0uvJG5fh3T6QEaL6L9No/BtR518WrXHShPRW6hcXVDmeqmhiUWRAWlxBC9RFc0qSMjl4BxVl2RR3qIgn88LOLOG2ZAWCY1s0wnDSpD8q6p9yw3i7xlhUY9pVUVqhY4eIAy/kmcJ1NA4T0nHddF5Rw+RyQekwuFeUzAkmQHJQJkRztA77uuk8XDDFVErhvQvn6mBLIN5jLahC9Ki8OLdbjO4EbTySFfVMUqTrCisEcYRJwH6eYOoKKOdDBEoJqhjC57WaJ7Y8PndFpCoYWM0JJnCmmG4shQosxFioXS/a/RC8d0FQSbcmyiO+62zuaad2gYmn9eDznLRjYbJF7hS5tb1uwXY7Y3Jshi9/7N/pG+zDWkee2Z7dweiOcax1nPKcE/jBN25m1727yToZ1f4qRz9tM8/+xbNZsX5ZuJe1NKdbKK2o9VdLMfXTSBkgOiyUgqmk5CdARKOTZ6KTZy7YXjen0By9kshPkc9LzYVsVihjfnB0qUvwmxRy77HzjrGAw5OI4pm1BokIRnRPA6zUKUfEOzBk3BxtZFN1gpVmBi2e8bzK9s4y7opWcp9dRmSgHqdE2oaZd52IRjuhLQk+0hC7uU8FB76jsErhvUa0xxnfS8mpXFBZKPoOYmsunSc26BEtYeiv6KI7r0jhqdyH6FRxrJi5+iflPTYXdOGijgBGemm1INQIdUkumHz2xEkxpiUUdwfhFARTcS/nEV2k86zCGzVnZ9CNTnUFkxDGswj0Kr91ESP0Dqd173cPkNlQPyYhOtVL9fXeAwJak1lotrOQBi1sElQGeSfFdjp0OiGc13VDUNNtokjxrcu+x83fuo3GTJs8DcYWSil23buX3ffv5RXv/Hl237eXH111WzDbVMLG49dx+gtO4chTN/WEU1ls/lSn9BU4XJSCqaTkEKLNCLWRL9Ce+A2M2w29KieFk0EyN0kxEu7Ac4uCcbvIh5UH8J4BFWHxC8RYJIrlGn62by9HxpMcFbfpK4qg296zPd/Jt6NNZDn0xZaVlRnqOiP1mtFOH3tb/eyQQdI4Ik5y4tiFspxM6HQM1piQZNRAXNgZeLC5wnYEj0JlIUrkonnpvMKdXOERU6TkekXfgso8TsJQYKcETBHBKWqn6DqHi2ALA0uKjJpkCiMOsYLvjlwRwjw8G6wKPCYUk/eEWiHOCi8pVcyv86ZI/XkPuQ/6SSSILdX1SejWNs15RXml5nXv+ZC+UyEF2B0s7FXRfedcKDqPIpx4snmdg3iP8mCtx3tFq5MV1+wVXqE7sH/3JBN7p4mqFdy8uXzaKGauvJXp/TNM7Z+lMdnEWo8IPHD7Tm7/fjDbPPLUTdzynTu47Xt30m52GFw+wCk/cyInnXssSTXpvdecCyakpZgqKVlIKZhKSg4xOjmB6sorsO0rcenV4B0qfjq6+vNM7zufxO04oDC8F4ESH1r/F0GJQhCyB9VIZXgihOVaGK52iCX8tfZADRhUjuWD95FaWJfMcHwyyYDK6Xjh3nSAW1vruc5vYiKtM1JpMBi1EQXNLGK83cf+uEqbMGjXJLZXl2RThWuFcS5iVUjnRX4unZeGVJkmFJO7bncewcpAFd153obaKGe6oqcQU0pCqVIxCsZpKdzFuxEmFXygzFx9lPKCzT1aFSJKFYXs3S45F8SbV4JzDrRa0J0n1hU16oIU+7zu1kaBMjYIORcsDYINOkEUmcIWXYqolg6CCk/RzVcs0nmsNkh30LHz4B0+Ch1ymQOUCnYI3iNeyK0ltzDbzEkkx3WNOvGoVJiZzBj795sZXDlIltmiZjekU6cnGvzzX36d5etH2Hr7TtJ2Huq0lHDbtXdx5nmn8tLfOp9d9+7h1u/eyfY7dyJacewZmzn52Sew9qi5wdU2t2RpTlyJyiL0JyplgOmwUQqmkpLDgFIJqvYSqL1kwfb+kc/Q3P8rRH4Gj8cVsQSFYGFuDtuDEIr2/m5q6EFkRf2Tw9N50AERsForXjV4L8ORUBPVix4cFU9yemWSRNps6yzn2OooG+IJFJ4xW+ee1gpuj9bwgBuiWnEMVNokxmK9MN1JmGlWaUsFnymoWlTkETwuV/hUkUcah4bYh+hTN9KThu68CAnpu5gFtVMqF5wu3MWjufooQSAH1W1Q80FoeV3UO3U7+3QhtowEIdb9bs89unA2F1cMPDbFM+x8EH6FzQFaFanAboG5w2cKJRL+P9JzxegOlNV4ZVHCnGDq2R94fFTMzHPdc1XP/8nmNtRmiWC1Ced3BYl1SA7EEU6E1BfeUj48H+I8Nvf41CHTHbwUHY2E7st223HrtfdSqcfoJCHLQnxTBOKJJt/64jVM7Jti5717GN8zRZ4Gh/k7f3AfN3zzx/zib7+ENUeu5EdX3c5t37mTVqNF/7J+TnvuSZzynBOo9VfDU5vlTI3NIAKDKwbQep4HRcnjR9kld9goBVNJyeOIjo+lvuLf6Ex9CJ99F+U7gMGbp+H0Caj2Z9AcmLKb+75f/IPMhK/ORdN5mUCMsCEJf90t3a48qIhig/H80tA9TNitHBF1qPfSeePsq+/ging//yknsLbWYHN1H/0mJXOGB9pDPNBYzv0sI8sN9WqHWiVDgE5umG0ltHWM8wYSgWo+5w+ZKWxT40WhrOASP1dQbkGlglZFv2EMLmJe7RSoWHqDfl0kc2LLgc5CA5wVFWqjosKBvDjXZeBQocstCim9nugpUnJKAKPCvm5azSpU5FAqpO+8nldQ7j0qC35MXgSJisiVLloMnUfldq543Oi5QnUf7hVSegoX6VA71a3DskU0K+RlybUpIlsSopfO4Y0FF5F6WVBsnvuQhrSppeNSEqsKp/Rw7U5qmZ5s8s3PfYfqYJ08t4VxZyjknxpv0PzTf2F41QAP3LKDZiOdi05dczdPu+4efvFtL+KeHz7AD6/4Ebu3jqJE2Hj8Ws782dM48dzjUEphc8vOe/fQbrSpDdRYe9SqMkJV8qSjFEwlJY8zymyguuyTONcANw3Sh9L9OGeZHf0+kb0NxVzhd8/fyfuDOjx1/y1/sP0KQSE050kxT+jEi4ANRlhvMoyYXkS/X6BPwS8PbSWhxZn1CdZHwZ3cAWNWuL65nK+pU5nNKmzqm2BtZQojjomsxgONEbbEyxjXVSpVT63WIdYuDBtuR7QqMU7HOBuiU8RFqjFX2I7CGoXWGok9Ni669zxIBrqtiESCfUFXUHXFViYY7UMGzAgunhdhykCnYEShXIhsufmCKQOjVHBGj8BFqjeoWHLfK3IXQuTKF9Ep8R6XhfSYEvBG443C60IQOYdOFap7rNFhoDKCOIfkGtFhpp43Cm/M3KgY55AspGPB4yNDT9V5j81s2Ccp1hgwpjcPEGsRFMTh3dTxgle6CHx5cuvxucd3cqxJg6dV8VSJ9aSp5cffu4ekYpDIhDqr4qmenWnz7S99n93372XP1jGm98+S2/Aabrl9F7d87y5+4X/9HKs2reTqL1/LfT/aStrOqNQTjjtzM8/9lWdxxEkbyNKMLbdsY9+2MUSE1ZtXcsRJG9CmjFD9ZJQ5ucNFKZhKSpYIpeqg6vN+1/St+Cfak3+Ia38TQwsAJxHOnEUzu5UaU4saY3Y7tRYrJu/tl4Ok8wSqLJ7O0wgjWvMrw3upKo0KnuAIMKBgdf8ofXIjMz7i6bX9LFPhy7vl4c6BPv6jcjzfNxtZ3z/DkbVRBk2niE4Ns3VmhB16GG8V1f4OfXGOUpZWaphtVsijGKs81DxULaJ9iE51NK6lwhe/F2zicPFcsbnpKJwpbAtimUv3eZBMcOmcU7iLCCk/KdJ5KcW5hHOj+ek80KnQzfDZqFtwHs7VmUfp4FtFpIpzC+GSK1zk0IWtgouKCJMCnEYyhzaFJ1QUokxduwOVOyRzQUw5j4/NXLrPhdop0UHk+cgUgqr7hvBIlvfGxfg4wneFiAexWTGoGFLRyDybBXGOzFp85si9xXgVZv4VpB1Lc7bDNV+/iaSvGqwTikJ1RcbMVIu//9OvUO+vsn/3FPk8f6wd9+1ly207edlvnc/1l9/EXTfcx+x0Czz0D9c58eyjedlbX0zfUI27rr+PW75zBxN7p1i2ZohTnnMCx551FHElBqDT6rB/1wQAy9YOLyhg/6mk1EuHjVIwlZQ8gVCqQm3kIzg7jc9uAnLEnIwyq4jbN9Iefy0RKQ6PY75dgRRbFrkmof4pP8j+bjrPLfIpaUOvGf0qIsf3vKG6160pzfP6JtAiVETT/UgZBJbrBhvjHzJsJjhvcAdHxB2S4jt+1Gm+O7uaf1GnAoZj+vdxZG0MLZ7RtI+7Gqu4d/8ypqIqlT7LYF+HikmxTjPdTpidqZBLHJ6BqkWqwVvJ5ZC3DHms0Mrgaw6X+NCB50PtlG6HgmrBYxMJdgiqsCtIBRMVYisBGzNnkpkJpu3xhYJylaJ7j65gAmN08KRKQmTLFvpCZ6DTcF/lwcWCi7oF46Ayh+uEIm0iXYitYn/uUJnDqHAfl+hQe9VLI1pUW4cxLrHBR93oEyE6lYZUn3SjU920IR6faUTCfh8bXDd6JeG+kuZQDWaeqYnnUoF4JLeQObwXXO7xen5ky6Fyx+z9o2it0UlcvEfDA1YtuOXae9l61w7SVk6WOTIX5Nb4/ln2bN3P5NgM/SN9/Oiq25kam+3aa3HNv93I2S9+Gr/w1hdx63fu4Nqv3cDebWMgsGrjCs79hbN4+otOx0SGsZ37ue/mB2jNtqn2VTjytCNYvm5kgcVCu9EGoFKvPDU6Az2HoIbpkKzkKUcpmEpKnoAoPQD6uQu2RZUzkZHLaE+9F3F3o32QTFatRVVfg539MBGe7EGf+b3MzkE+RLsxg4N9RkpI6hzgH+UIgqpfRXjCqJf5kixC2GQ8/2v5ffRr1XMuBxjUsHZwJ8tUi0TlnFadYUB5lAgd59k+HPGl6rFcHR/NScOjnDGwjTVmlpY3/Lixhlum13GXXo0IjAw0WFZrECnHdFphbLaPmfEK1lioe3R/jjEW74W0ZchnDY4QhXE1C8lcZ5+0FHZGoTW4quAqHnR43NKBvCJERXAnr4CPpfdk6I7gjEeMgkTIKxRdcsFnSXUgUsHXyRWRLy+haFunGtMqBFOssUlhh0AQWipzvXl5Li6iV0WESWUKbRTKFOdGuifyyB06NSidIp5CFKnefVVmEa1RWuOTCB+rIrzmIXNIpELdGR5ficEUxWI+RL0oGghsnPTEGADW4tIcjA01c8osKHIX50g7HRpbJzG1BK9NIWJDyrXVybj6qzegI41DYbv/OvDQaE7wjc9dzf23bmXbnbuZmW5ji+jV1rv3csf197L7vr0MrOjjvy+7ht1bxsjSnCg2rD5iOS949bN43ivP5f4fbeW6b9zEfTdvBe854qT1nH3BmRz/jKMRERrTTbb8eCuN6RaVesKRp26if7jvIH9LSn4aKAVTScmTCFM5nb7K13F2Fz7fhcgIEm1GRGiK4GY+TDwvVlTEAmj5YD2wmCxSxb/8FysY73bn+YN051Hsz/yB8a1MoIJixMii0am60pzXP04kQiRztTMVDQPasXLl7Rxf2cPzB8YZ1hAVRo8vrI9x7/DdfEI/g2pkecHQPZxSncTgGLMxV01v4r/rx7EtGWDlSIujBsdYFs+QuZitjSG2TQ0zo+tghKg/o6/WRilIM83sTIWsEpHHBt+fQ81CTFCHLUXWVDgxoD226rEVF2yaLOiWIo8FHYGvQl4titG9ICnoFlgdnu+sCj4p/KCsoDqeKFLBVb0qQTBFhY1CJpi2EAmhi64ivUJ2sUFQ6UjQRkL0KZlzPleZx6YOXczpc7GGWOaES6oxUai3chUTxJYJheqSO1Rq0IUdgq+Y0N0n3XVZJNIo0xVbek4w5Q6J8qK2CnwSB2PU7n2z0ACAF/IoDmnGnu2CRdKcvJEFm4fEhCL5YvRNZi2tqTbXfvNWTKWCmzcrUHJPc1+DL/7lv2MiQ7OVF6lCEDImJ7eza8tXue/mLdxyzT2M7pzopQpvv+F+fvDNH/Pyt72IweUDfONvrmTbXbvpdILYWn/0Sn7ufzyXc1/29LJg/aeUUjCVlDwJUXot6LULttUG3oxNnkFz+i+Q/MeAx6v1JP2/hdhp8un3EuPJZU77mCIVJwdRQ91g1WJiCkI68GBWCN0rCAemA8N0E0+/CqaYnQftNwgrjOIVQ/uJlcYXgkxEGNSa01XKH2z4HkPasUyHAnCAzaSclNzJM/t28YX6Cbxqxe2cWJmlokKEbcxqrphezz/qM6lVLGcOP8A5/duoimN71sdVk8dw6961zFQS6stS1gxOMVLpkDthx+wA45P9pKoCEchATrWvgxJPlmnSmQQ7oZHY4Acsvu6CL5UTaAuqoYI7uIG86rBVV6S+wLQUeUVQkUANsmooOscLKvWYlmC1RhTktSCoQtjPoztCNCsYo3A1Fc41FClIj2mrILYU2IrGVYq6Kws69dhIoSKFr2pcrPBRkYJMPbptez5VrmZwcYgSifNI6jCxxmuFq0a4WId0oA91V6qT94SFr0a4uPt141GdQmxpg68UgqlbW5VbpJMVLlPgqwnE3TZID6lFtRQ4IdMRPo4WnptlTM22EDKoVkK3o9KIs2TW0Rpt8LW/uRoVRzilcYVQU5mjtXWcv7v4S5hIMzXdCQOYESBlfOwBtt+9B2U05770rId60y8tpa3AYaMUTCUlTyF0cjr9Kz636L4WGdnMnxPRpNtPZ4nw5gX47ApicWQPKijXFG3wD4GHReufoBudYtHoVAiYCG6R2Xo5ngoKowwdXM9XqHuhSBTHxb5w3pbeujXQpzTn1GY4fv11LDMKPa9QeUjDumXbWBdNckSlzeaoQ12FDrTcT/OSgV1cPrSOLw+cwGvW3soz63vp08FMdEee8NX9R/L16GnUKylPW7Gdnxm8j7qybE37+e/9x3LHnrWkYxHJ8ow1yyZZUWmQO8X26SEmJvpo60pwSx/KqfZ3UNqRdQzpdEI+btCxxg5afH8R2QJoCWpGE2uFaMj6PLbmwoPNwcwq4kQwsSLvE/K64KNgaykdIWp68qLrLq8LtkIvnWdaQhwLOhZsXZNXQ00XBMEUNRWRDpGyvKqxlbkid9Puii3B1yLyZE5s6cyjWhpT2C7YrthS4b667dBNjTYGV4uwSVScW9gztOMQ2VIeV4vxielFp1Q7x0caZUyxL4JoXhqxk/Xed75WCZEvpYLPVpojTYVvtrFxgkvintiyuUWlGfsnGmHgc7Wy4L55lrN3rMVlf/5vnPWzp/aKzkt+eigFU0nJTwnV/teR1F9N3v4GLrsbpZZTqV6IMkO0m1fSmfwtYjKgm8IAi9CgjwozB/WH8viDdufBwa0OuqNgHoogqA7cnuOpKk3u3YJUX9djKhHF6ij4Uj04FVgVxYv7p1Ei6MLs0+Ixolhp4JeGd/Ks+k42xoIRKdr5YYXJOHbN7RxTGeeE2hTHJm3qIoiA9RO8fGgb/7ZsPV/aeSJv3nQTz6iPUVcOh7A3i/naxBFcFp/JYF+H5666k/NHtlERy56sylfGTuT6bUfQGUuorWlx/Iq9bKxNkDrFHVOr2L5vBW1TgcSjl2UsG57FaE+ro5ka7yMfjVAVg1uW4wdzdDU8Zjuj6EwaYq2RCNJBh+tzoD2SC2pakVQVelpjB4W0z/eEmrQgbgixNhAHsZXVgniSHEzTE1cEMyPk/ZqsHord8YQUY1MRmWACmvVpbDW4skvm0S2IZhU6Vrh+Q17TvXow6XhM02JMeP1tPcJWC4sGC7plMIlBxQZfj8lqBgqhRuqJWhm66CK09QRXCZ1/4jyqbdGJQUUGV6/gq3Gv+F7lDtdKg6WEFGIriUKa0TmkneNaHe6/d5Q7rruH05570kO/eUuecpSCqaTkpwilIuLaLxywvVJ7IXF8Lc2Zj2M73wJylD6O2uDvUVUbmNr3PCpMoLwPEQa65pZhvEkkFFJrjm506uGC+w8bnVqErth6qEL1xcbIdFOBFaWxDxJbXdf1miiOSsK1sweJrT6l+eXhvUQCWhSuOK8rtl6zbAcv6N/JhhiMCF2HrBGds3n13RxbHeWk6iwb44yKdLvt2jyn77t8b/ntfHbHCfzB5hs5Mm5RLWbeTa2F6zct54O157JhcJI3bLiZUysTROJpOM1/T63h/9tyFqM7B9mweZxXrPsRp9TGyYCrJjZy+c4TmLh3BOqO4dWTnLZqJ0OmzZ72AD/es47mrjqMxrA6pbKiyXB/G+uFiak6jdGENIrxscMuy5Dh4OaedwTZb4j2G/SEJl8O+WCGrxXGAg1FPGFITBAznSHI+13oVswgmlFUJg0mUWQjmqwfbLV4bZtCPCMkkYAR0v4QOfNGkNxjZhXJtEZPaeygIe1XwWsLUKknntFERiMGsv6IvKbwpivyHPFMEFtuICHr19hCMOnMEc1GREbhlSLvj3GV0LEYhFqOmYnxo55bv/8EFkxlSu6wUQqmkpISAJQZoW/4/cD7D9g3tOo7NKf/D3nrX9A08RiIz6Te/z5mZz+Paf99YWgZBJLygAgtL8Tigt3Qg65Z2DAexOwgcHAjzrn6qkX3F8GrxaynVCGmghfTwr2exU0+YU5s1dWBnlVdsVUVxZFJqJdaLLL1C4MTxUxAhe2mEQUGRPHC/nGecex3GTEamed3VTHwov79rD3t39iYpAwrQYtAYSWxcfkOnjuwm39dv5HXr7qfISWFWINzarfxP1fdwR/2P5PnrtjBS4Z2MGIcBiHzjt2bIj6z62T+475j+Y1TrudFQ9sZ0qEfcl8ec9m+Y/niTWfQN5jyiqNv4ueXPUBVOaat4R/3nsjl955Ma3tC7chZXnbEbZw7vB2L8J+jR3L1A8czc08f1CzRhhZnrt/KiniWXc0Bbt25iantFXQtxq5Lida0GRmaBWD/eD+tPQlJHEMFOitSWJ5jEkfeUTAaUdkXYapCvkrRGcnwA8GeXGYUyXhEJQ6pxc4yRTps8VHovosnNZX9QlxRpMsM7RHB1sLrpJuGZEpTjQWMoj2syQZCN6PKwUxrqvsNVe/Z/sD+h3j3lTxVEf9wBQolizI9Pc3g4CBTU1MMDAws9XJKSh43vPcH+NW0Z79Oa/bDGLcbwZNRJar+InH1t5kZfyFVZuBB0ams+OSJhAXiAsK/5AwKz4FmmhBGvRgUbeyigqsmGo+ntUh9VIQQochwCyJIXaph+i5tf2CpuwFi9EHPraAWFVsQRFNCGE2SLlIpn/QK5P0BFg4xEmrJiqjb/P2RBy+QOU+i5qJeUDgiiDBpLTUlJN2oFnOCc9Y5trQjTqjmRQpyjrZ3XDE1xEm1WTZEtldc74HUO+5sV/j0thN5z1E3s0K7Xrdj6h27MsNFtz+b563azi+t2MJy7bplV+zLNZ/dfQKX/fgk/uCZ3+O8od0MqPCcTVrNNyY38pffew6DQy1++5Tv8eyBvSTiaXvh21Nr+PiPn03zngGWnbqXdxz/fU6uTeCBW5sjfOzOZzJ+8yqoW1Yft5ffPOZ6VkYtRvMqn7rnLPbcvRq1tYI7qs2Go3byonX3osTzzd1Hs+XedcT3VPGJJ9vYZt3mUVb1zTDa7GP7AyuItlYYudfxgpERLvnbNx/wGj4Uh/s7o3v9T//xF6lWao/pWq12kze/75Xl99uDKAXTT0gpmEpKDsT7DO8tIklPVNm8QXP6YvL2NzB08F5h9bH0Df4xaX4v+fS7iaU79kW6foy0/ABVmS4E2ByakJJTIuT+QHEBQfR4oL2InDIIMYoUt+i5NVGFFcOBoqcrtnLcASKve9+HE1sHO7dSxL5aB6kIq6EOsGfokhRRsQ7ugEdsEEywqTxAfKpiPxyYgpTi8VrviqjYnLBVhNfAeUfHQ7XohrMPEmrj1lJXMpd+JMzhExGa3rGtbTi6YnsRsS6Z91zfjNmcdFipWVC4b71nt4XL9mzi19Y+QL90I25h37T3/NXOYzlrcJSz+yaK2Yjh8Tec5/rGIO+98Rz++pn/zRFxu7f2tvdsS2N+87qf5Wlr9vC2TT9iTZRjChG7Lzd8dtfxfPkr5/K8PcN85nP/a9HX6WCUgunJT5mSKykpOWSIRIhEC7ZpU6d/5P8A/wfvc0D3xFTEGeTJM5idvBif34DgsDJCve+3Wdb3K+wf+18k6TeJ532feqBBnczVGZR9RMUXWrdLTiOk3qFFDl6oLgfv/vP+4KnA7taDpRHlIevYH9pFWor/KH/g9YOokcVzjMxF7Ra7t8OjRZEt8ngdB09BeoJAqoo+wPqhG8VKRBHLgULNFc4GK7Q5UKhJSCbWRHF8NSQzHywCYxHOqaVFRG3hfiPCOgNvX/cAkSjcPBFpBIZF8c71d6FRGAmpz27KtF8pfqZviv949uUMmiD7ulK9KorjkpwvP+vr1JRQFQU+pG4jD5six+9vvJXhX+nw7b++YJFnuuSpTimYSkpKHjdEDvzIMfERDK38/xY9fvmKS8nTrcxM/THO3odQpVZ/AyP1V4D37B97FXH+Q+LubDigQY2k78+Znv09+qV5QKF65qHhoK6CxOjKBCHUJFs8UtgcHVB35T1ePbzYeqiw/cOF9H/ikL/IQWu2fLcg6uBV8osKNU3oVPO4g1tDHEQIOjxKQgrywXRjifogEbUg1NSiHl05npgwiufBQi0HFJ6qBCOq9oMWbfHEolgWBbPV+RHGMAYIVhYiL8MXdha+ULNhTa9ffQ+fWzex6GN+QlAWfR82SsFUUlLyhMbEmxhe8TeL7lux6svYfJq0+c84P0WUPJN65ZkA1OovYHry93Gdy4l9sM7syGr6h/6EanQS46MvpE8aPbujbm1QS78Yya+gX+XBMLPQAxrBCsxaR/VBYguCz2QvJcWBkS3xHi8P0zV4kK5CX3xpL2axAN3Y1cNd+6F2Huy6IWR28BFr0gt8PZheYf4jEGqLRQFDFHJxodZd28GWpSRYShz0XC+LJC+D4IqKdS32XIdRQIq3/Py3D3Lnpcd7/7DeaY/kGiUH8oTwd//kJz/JEUccQaVS4eyzz+YHP/jBQx7/pS99ieOPP55KpcIpp5zCf/zHfyzY773nfe97H2vWrKFarXLeeedxzz33LDhmfHyc1772tQwMDDA0NMSb3vQmZmdnD/ljKykpObxoM0B14A3UB99BXIilsD1hePnHWLbuLvrW3sPA2ntZufZ7VOvPJ4pXsnLtj1GDn2JWn8qsOpJO/PPUVt7AqtWfZHjl95lWJ5L2vpaFGZ+Q195G34prmfIVBCGe95N7YVzOYcJFKITYB+Fkiv0OmHS6VxvURRGKujNvsfgF+3qPpVtLdJDnwBG+4A+Wkgu65+Bfgl0n9cXOlYcQavPvv+h1+ckiZnNdkItLou7IlcX3zTvmIc5dbO+cUFv8XEvowHzawNjBlr70+EP0U3IASy6YvvjFL3LRRRdx8cUX88Mf/pDTTjuN888/n3379i16/DXXXMOrX/1q3vSmN3HTTTdx4YUXcuGFF3Lrrbf2jvnwhz/Mxz/+cS699FKuu+466vU6559/Pu12u3fMa1/7Wm677TauuOIKvv71r3P11Vfz5jc/uq6HkpKSJwdSDIlduE2o1s9nxaqvsmL1fzG8/OOYaBkAUTzCqtVfZ2DN3VRXXkNt1Q9Zue4OhobeSZysYtXa22DgY0yrY5hmLbPRc6it/B7r1vwDK1f9iBl1Lg00eMF6mHJVbP0PWbb6Nvb7tVjve0JLI7Q9zMS/yj5/BJ4goKJ5Yiz1nn1uE3lxnmauYDsuCtTb3hIjCz7Uu4It9RZ50L7u/q61g+ZAQmG3Rw6WguTgXlsWujnKxV+T4gKLlbh3BdjBIh1SRI8Wj8Z1r3GwNT/GlJUH7xd7tkqe6ix5l9zZZ5/N05/+dD7xiU8A4Jxjw4YNvO1tb+Nd73rXAce/8pWvpNFo8PWvf7237ZnPfCann346l156Kd571q5dy+/8zu/wu7/7uwBMTU2xatUqPvvZz/KqV72KO+64gxNPPJHrr7+es84KM4Euv/xyXvKSl7Bjxw7Wrl17wH0fTNklV1JS8lCE1EgKaJRaWP2QpTuYmv4Q1u4nTp7GYP87UToUy89M/zPTMx8k8bPB+0kfxfKRTxAnx7B3/5/hW5+hX1mEbldYHwMjn6bduRNpfpDavOiJA6acoVb5KGn7rfQ/SDF5YL8N8/xW6DC/zRUVRt0arklrGNJ5GF03T1xphNyHcupIpLcP5sSc8z50M7IwghUEX7iHhQO6FaNCSM4v6J5PBUFE6PgDE2td+wbnPZ2D2DcohNZB4mJVFq+dYt5j2hNfzDEr/uei5x+Mx6tL7q8u/sIh6ZL7jQ+8pvx+exBLGmFK05Qbb7yR8847r7dNKcV5553Htddeu+g511577YLjAc4///ze8Vu2bGHPnj0LjhkcHOTss8/uHXPttdcyNDTUE0sA5513HkoprrvuukXv2+l0mJ6eXvBTUlJScjBEBKWSA8QSQBSvZ/nyT7Bq1T8yPPT7PbEE0D/wCtatu5nl6+9l5fp7WbvmP4mTYwBYtewPWL3+HpLl38aMfJHaqh+ybv0t9NfOYcXwGxhZcy/tylsZl2OZUCfj+v8fa9ffzdDylzCy6hYmzc8y4QzTThizFZqVt7Bu3Z2sX3M7Y3Ims8WwWec9k04xFb2CdRvuZq96Ng3n0UVESxBmHEzHb6RR+T0afm5fN2o24zyz5k+YcCzYFxeCZcxqtmbhyzj4akkvYua9Z3taJS0iaqYQV939be+ZsrZ3TjeJ1v294SxOOCC9GRWp0dS74nHMe72KdQQR6A+IuKniZ7+VRy2WHle6Rd+P9afkAJa06HtsbAxrLatWrVqwfdWqVdx5552LnrNnz55Fj9+zZ09vf3fbQx2zcuXKBfuNMYyMjPSOeTCXXHIJH/jABx7hIyspKSk5fJh4I7DxgO1KKUZGLgIuOvCcqM6alX+1+AWVYuOaLwPgbBtE06/mRNyRqz+Hs5bZ2X8gze+lEj+dlf0v7e23+a+zb+IPSTvfxoumWvklVgy/E6UUNv8Vdo//Ab7zdYxYMh8RVX+V9SPvQSnFjn3vgvTL9EtIzk27CF15HUevey97xi9luvF/GFIWJUHI7XcRcf8fMRA9hz3j57NcpT0fJ+s9+1zC6mVXsGXslazTu3sdlB7IvWeHXUEl/nmG7d9ReVCatuM9O92LGeBylmlZIJo8MGk9y4e/8dAvTslTlrJL7hHy7ne/m4sumvsQmp6eZsOGDUu4opKSkpJDj9KVg2zXDAy+btF92kSsWfHhg+5bv/IvgL9YdP/6lR8CPtT7fXDevtUjvwkjv0mejWLzrWizmf6izgxgc/0u2q07GJ/9DAAjfb/O5urxAJy48RrarR3snPgtvN2LqFWsG/kkJ1bD53baeQdbx15H5O4EPClHs2nF5zmpMoLNc7aOvRWd/RcVsXS8pqPP4YhVf00UL/78PGE4FEXbZYBpUZZUMC1fvhytNXv37l2wfe/evaxevXrRc1avXv2Qx3f/3Lt3L2vWrFlwzOmnn9475sFF5XmeMz4+ftD7JklCkiSP/MGVlJSUlBwSTLQCE61YdF+legJrqx85yL71HFX92qL74mSAY9Z9ddF92hiOXH3pT7TWJaf0YTpsLGkNUxzHnHnmmVx55ZW9bc45rrzySs4555xFzznnnHMWHA9wxRVX9I7fvHkzq1evXnDM9PQ01113Xe+Yc845h8nJSW688cbeMd/61rdwznH22WcfssdXUlJSUlJS8tRgyVNyF110Ea9//es566yzeMYznsFHP/pRGo0Gb3jDGwB43etex7p167jkkksAePvb385zn/tcPvKRj3DBBRdw2WWXccMNN/DpT38aCIWW73jHO/iTP/kTjjnmGDZv3swf/dEfsXbtWi688EIATjjhBF70ohfx67/+61x66aVkWcZb3/pWXvWqVz2iDrmSkpKSkpInJmVO7nCx5ILpla98JaOjo7zvfe9jz549nH766Vx++eW9ou1t27ah1Fwg7Nxzz+ULX/gC733ve3nPe97DMcccw1e/+lVOPvnk3jG///u/T6PR4M1vfjOTk5M8+9nP5vLLL6dSmcs9/8M//ANvfetbeeELX4hSile84hV8/OMff/weeElJSUlJyaGm1EuHjSX3YXqyUvowlZSUlJQ8Uh43H6Y//Pyh8WH63/+j/H57EEseYSopKSkpKSk5RJRF34eNUjCVlJSUlJQ8RSiH7x4+SsFUUlJSUlLylKEsYjpcLPnw3ZKSkpKSkpInL1dffTUvfelLWbt2LSLCV7/61Ud87ve+9z2MMT2fxCcypWAqKSkpKSl5quAP0c+joNFocNppp/HJT37yUZ03OTnJ6173Ol74whc+uhsuEWVKrqSkpKSk5CnDoRie++jOf/GLX8yLX/ziR32X3/zN3+Q1r3kNWutHFZVaKkrB9BPSLYqbnp5e4pWUlJSUlDzR6X5XHO6C6landciu8eDvt0M5Iuzv/u7vuP/++/n7v/97/uRP/uSQXPNwUwqmn5CZmRmAcgBvSUlJSckjZmZmhsHBwYc/8FESxzGrV6/mnX/5W4fken19fQd8v1188cW8//3vf8zXvueee3jXu97Fd77zHYx58siQJ89Kn2CsXbuW7du309/fj4gc9Ljp6Wk2bNjA9u3bn1QGYOW6H1/KdT++lOt+/Hmyrv1Qrdt7z8zMzGEbv1WpVNiyZQtpmh6S63nvD/huOxTRJWstr3nNa/jABz7Ascce+5iv93hSCqafEKUU69evf8THDwwMPKk+JLqU6358Kdf9+FKu+/Hnybr2Q7HuwxFZmk+lUlkwAuyJyMzMDDfccAM33XQTb33rWwFwzuG9xxjDN7/5TV7wghcs8SoXpxRMJSUlJSUlJY8LAwMD3HLLLQu2/b//9//41re+xZe//GU2b968RCt7eErBVFJSUlJSUvITMzs7y7333tv7fcuWLdx8882MjIywceNG3v3ud7Nz504+97nPoZTi5JNPXnD+ypUrqVQqB2x/olEKpsNMkiRcfPHFh6yz4PGiXPfjS7nux5dy3Y8/T9a1P1nX/Xhyww038PznP7/3+0UXXQTA61//ej772c+ye/dutm3btlTLO2SIL4fGlJSUlJSUlJQ8JKXTd0lJSUlJSUnJw1AKppKSkpKSkpKSh6EUTCUlJSUlJSUlD0MpmEpKSkpKSkpKHoZSMB0mLrnkEp7+9KfT39/PypUrufDCC7nrrruWelkPy6c+9SlOPfXUnknbOeecwze+8Y2lXtaj5kMf+hAiwjve8Y6lXspD8v73vx8RWfBz/PHHL/WyHhE7d+7kV3/1V1m2bBnVapVTTjmFG264YamX9ZAcccQRBzzfIsJb3vKWpV7aQ2Kt5Y/+6I/YvHkz1WqVo446ig9+8IOHfS7ZoWBmZoZ3vOMdbNq0iWq1yrnnnsv111+/1MtawNVXX81LX/pS1q5di4gcMAjWe8/73vc+1qxZQ7Va5bzzzuOee+5ZmsWWLBmlYDpMXHXVVbzlLW/h+9//PldccQVZlvFzP/dzNBqNpV7aQ7J+/Xo+9KEPceONN3LDDTfwghe8gJe97GXcdtttS720R8z111/PX/3VX3Hqqacu9VIeESeddBK7d+/u/Xz3u99d6iU9LBMTEzzrWc8iiiK+8Y1vcPvtt/ORj3yE4eHhpV7aQ3L99dcveK6vuOIKAH75l395iVf20PzZn/0Zn/rUp/jEJz7BHXfcwZ/92Z/x4Q9/mP/7f//vUi/tYfm1X/s1rrjiCj7/+c9zyy238HM/93Ocd9557Ny5c6mX1qPRaHDaaafxyU9+ctH9H/7wh/n4xz/OpZdeynXXXUe9Xuf888+n3W4/zistWVJ8yePCvn37POCvuuqqpV7Ko2Z4eNh/5jOfWeplPCJmZmb8Mccc46+44gr/3Oc+17/97W9f6iU9JBdffLE/7bTTlnoZj5o/+IM/8M9+9rOXehmPmbe//e3+qKOO8s65pV7KQ3LBBRf4N77xjQu2vfzlL/evfe1rl2hFj4xms+m11v7rX//6gu1nnHGG/8M//MMlWtVDA/ivfOUrvd+dc3716tX+z//8z3vbJicnfZIk/h//8R+XYIUlS0UZYXqcmJqaAmBkZGSJV/LIsdZy2WWX0Wg0OOecc5Z6OY+It7zlLVxwwQWcd955S72UR8w999zD2rVrOfLII3nta1/7pDB4+9rXvsZZZ53FL//yL7Ny5Uqe9rSn8dd//ddLvaxHRZqm/P3f/z1vfOMbH3KA9hOBc889lyuvvJK7774bgB/96Ed897vf5cUvfvESr+yhyfMca+0B882q1eqTIpIKwbV6z549Cz5TBgcHOfvss7n22muXcGUljzel0/fjgHOOd7zjHTzrWc96wlu/A9xyyy2cc845tNtt+vr6+MpXvsKJJ5641Mt6WC677DJ++MMfPuHqIx6Ks88+m89+9rMcd9xx7N69mw984AM85znP4dZbb6W/v3+pl3dQ7r//fj71qU9x0UUX8Z73vIfrr7+e3/7t3yaOY17/+tcv9fIeEV/96leZnJzkf/7P/7nUS3lY3vWudzE9Pc3xxx+P1hprLf/7f/9vXvva1y710h6S/v5+zjnnHD74wQ9ywgknsGrVKv7xH/+Ra6+9lqOPPnqpl/eI2LNnDwCrVq1asH3VqlW9fSU/HZSC6XHgLW95C7feeuuT5l9Uxx13HDfffDNTU1N8+ctf5vWvfz1XXXXVE1o0bd++nbe//e1cccUVT/hp3fOZHyE49dRTOfvss9m0aRP/9E//xJve9KYlXNlD45zjrLPO4k//9E8BeNrTnsatt97KpZde+qQRTH/zN3/Di1/8YtauXbvUS3lY/umf/ol/+Id/4Atf+AInnXQSN998M+94xztYu3btE/75/vznP88b3/hG1q1bh9aaM844g1e/+tXceOONS720kpJHRZmSO8y89a1v5etf/zr//d//zfr165d6OY+IOI45+uijOfPMM7nkkks47bTT+NjHPrbUy3pIbrzxRvbt28cZZ5yBMQZjDFdddRUf//jHMcZgrV3qJT4ihoaGOPbYYxcMsnwismbNmgME9AknnPCkSCcCbN26lf/6r//i137t15Z6KY+I3/u93+Nd73oXr3rVqzjllFP4H//jf/DOd76TSy65ZKmX9rAcddRRXHXVVczOzrJ9+3Z+8IMfkGUZRx555FIv7RGxevVqAPbu3btg+969e3v7Sn46KAXTYcJ7z1vf+la+8pWv8K1vfYvNmzcv9ZJ+YpxzdDqdpV7GQ/LCF76QW265hZtvvrn3c9ZZZ/Ha176Wm2++Ga31Ui/xETE7O8t9993HmjVrlnopD8mznvWsA2wy7r77bjZt2rREK3p0/N3f/R0rV67kggsuWOqlPCKazSZKLfy41lrjnFuiFT166vU6a9asYWJigv/8z//kZS972VIv6RGxefNmVq9ezZVXXtnbNj09zXXXXfekqe0sOTSUKbnDxFve8ha+8IUv8K//+q/09/f3ct2Dg4NUq9UlXt3Befe7382LX/xiNm7cyMzMDF/4whf49re/zX/+538u9dIekv7+/gPqw+r1OsuWLXtC14397u/+Li996UvZtGkTu3bt4uKLL0Zrzatf/eqlXtpD8s53vpNzzz2XP/3TP+VXfuVX+MEPfsCnP/1pPv3pTy/10h6W/7+9uw+KqnrjAP5dXnYXlkVe3BYClnjZAAkySEdFQ6NaG6MlLQmDRcEhlJCl0B21ZRTBlQjMyumFKQjGEnMay9CBsdFw1jcciAFhMBLBjMxxeImIRdjz+8PhjiuLS6Wu/ub5zOzMnnPPPee55zLMM+fevddoNKKsrAzJycmws3sw/gXGxsaioKAAMpkMoaGhaGxsRElJCVJSUqwdmkU1NTVgjCEoKAgdHR1Yv349goODsWrVKmuHxhkcHDRZ1e3s7MRPP/0ENzc3yGQyqNVq5OfnQy6Xw8/PD1qtFg8//DDi4uKsFzS596z9M73/VwDMfsrKyqwd2m2lpKQwX19fxufzmUQiYTExMay2ttbaYf0rD8JjBeLj45mnpyfj8/nMy8uLxcfHs46ODmuHNSUHDx5kjz32GBMIBCw4OJh9+umn1g5pSmpqahgA1t7ebu1QpmxgYIBlZWUxmUzGhEIh8/f3Z5s3b2YGg8HaoVlUVVXF/P39GZ/PZx4eHiwjI4P19fVZOywTR48eNfv/Ojk5mTF249ECWq2WSaVSJhAIWExMzAP190PuDB5jD8CjYgkhhBBCrIjuYSKEEEIIsYASJkIIIYQQCyhhIoQQQgixgBImQgghhBALKGEihBBCCLGAEiZCCCGEEAsoYSKEEEIIsYASJkII+RfKy8vh4uJi7TAIIfcIJUyEmLFy5Up67cE9dvHiRfB4vAmfxMREa4dGCCH0LjlCyP3lyJEjCA0N5cr387sX74br16/D3t7e2mEQQm5BK0yETMHChQuRmZkJtVoNV1dXSKVSlJaW4q+//sKqVasgFosRGBiIw4cPc/uMjY0hNTUVfn5+cHBwQFBQEHbt2mXS7+joKNatWwcXFxe4u7tDo9EgOTnZZHXLaDRCp9Nx/Tz++OPYv3//bePt6upCbGwsXF1dIRKJEBoaikOHDgEAjh07Bh6Ph+rqaoSHh0MoFGLOnDloaWnh9r927RoSEhLg5eUFR0dHhIWF4auvvjIZw2g04p133kFgYCAEAgFkMhkKCgq47ZcuXcLy5cvh4uICNzc3KJVKXLx40eJcu7u7w8PDg/tMmzZt0rbjl8VqamoQEhICJycnLF68GD09PVybhQsXQq1Wm+wXFxeHlStXcuVHHnkE+fn5UKlUcHJygq+vL7777jtcvXoVSqUSTk5OCA8Px9mzZyfEcODAAcjlcgiFQigUCly6dMlk+7fffouIiAgIhUL4+/tj69atGB0d5bbzeDx89NFHePHFFyESiUzmkBBy/6CEiZAp+uKLLzB9+nScOXMGmZmZWLNmDV555RXMmzcPDQ0NeO6555CUlIShoSEANxIKb29vfP3112htbUVubi42bdqEffv2cX0WFhZiz549KCsrg16vx8DAAA4cOGAyrk6nQ0VFBT7++GOcO3cO2dnZSExMxI8//jhprBkZGTAYDKirq0NzczMKCwvh5ORk0mb9+vUoLi5GfX09JBIJYmNjcf36dQDA8PAwIiMjUV1djZaWFqSlpSEpKQlnzpzh9t+4cSN27NgBrVaL1tZWfPnll5BKpQBurJIoFAqIxWIcP34cer2eS2ZGRkb+03m41dDQEN59911UVlairq4O3d3dyMnJ+cf97Ny5E1FRUWhsbMSSJUuQlJQElUqFxMRENDQ0ICAgACqVCje/fnNoaAgFBQWoqKiAXq9HX18fXn31VW778ePHoVKpkJWVhdbWVnzyyScoLy+fkBRt2bIFL730Epqbm5GSkvLvJ4MQcvdY+eW/hNyXkpOTmVKp5MrR0dFs/vz5XHl0dJSJRCKWlJTE1fX09DAA7OTJk5P2m5GRwZYtW8aVpVIpKyoqMulXJpNxYw8PDzNHR0d24sQJk35SU1NZQkLCpOOEhYWxLVu2mN02/mb2vXv3cnXXrl1jDg4OrKqqatI+lyxZwt566y3GGGMDAwNMIBCw0tJSs20rKytZUFAQMxqNXJ3BYGAODg6spqbG7D6dnZ0MAHNwcGAikYj7NDQ0TBpTWVkZA8A6Ojq4ut27dzOpVMqVo6OjWVZWlsl+SqWSexM9Y4z5+vqyxMRErjx+LrVaLVd38uRJBoD19PSYjH3q1CmuTVtbGwPATp8+zRhjLCYmhm3fvn3C3Hh6enJlAEytVk96jISQ+wPdw0TIFIWHh3PfbW1t4e7ujrCwMK5ufHXljz/+4Op2796Nzz//HN3d3fj7778xMjKCmTNnAgD6+/tx5coVzJ4926TfyMhIGI1GAEBHRweGhobw7LPPmsQyMjKCJ554AgAQGhqKrq4uAMCCBQtw+PBhrFu3DmvWrEFtbS2eeeYZLFu2zCR+AJg7dy733c3NDUFBQWhrawNw43Li9u3bsW/fPly+fBkjIyMwGAxwdHQEALS1tcFgMCAmJsbsXDU1NaGjowNisdikfnh4GL/88ovZfcZVVVUhJCSEK/v4+Ex6nADg6OiIgIAArr2np6fJOZiqm+dn/FxOdn49PDwAAHZ2dpg1axbXJjg4GC4uLmhra8Ps2bPR1NQEvV5vsqI0NjaG4eFhDA0NcfP55JNP/uN4CSH3FiVMhEzRrTfi8ng8kzoejwcAXLKzd+9e5OTkoLi4GHPnzoVYLEZRURFOnz495TEHBwcBANXV1fDy8jLZJhAIAACHDh3iLqWN3yC9evVqKBQKVFdXo7a2FjqdDsXFxcjMzJzSuEVFRdi1axfee+89hIWFQSQSQa1Wc5fTLN2IPTg4iMjISOzZs2fCNolEctt9fXx8EBgYOKHe3HEC5s8Lu+mymY2NjUkZANfPzcydy9ud36kYHBzE1q1bsXTp0gnbhEIh910kEk25T0KIdVDCRMhdotfrMW/ePKxdu5aru3l1Zdq0aZBKpaivr8dTTz0F4MbqQ0NDA7cKNWPGDAgEAnR3dyM6OtrsOL6+vmbrfXx8kJ6ejvT0dGzcuBGlpaUmCdOpU6cgk8kAAL29vTh//jy3sqPX66FUKrmf9BuNRpw/fx4zZswAAMjlcjg4OOCHH37A6tWrJ4wdERGBqqoqPPTQQ3B2dp7SfFky2XFaIpFITG4CHxsbQ0tLCxYtWvSfYxodHcXZs2e5VcL29nb09fVx8xgREYH29nazCSAh5MFCCRMhd4lcLkdFRQVqamrg5+eHyspK1NfXw8/Pj2uTmZkJnU6HwMBABAcH44MPPkBvby+3miEWi5GTk4Ps7GwYjUbMnz8f/f390Ov1cHZ2RnJystmx1Wo1nn/+eTz66KPo7e3F0aNHTS5zAUBeXh7c3d0hlUqxefNmTJ8+nft1nlwux/79+3HixAm4urqipKQEV65c4RImoVAIjUaDDRs2gM/nIyoqClevXsW5c+eQmpqK1157DUVFRVAqlcjLy4O3tze6urrwzTffYMOGDfD29r4LM27e008/jTfffBPV1dUICAhASUkJ+vr67kjf9vb2yMzMxPvvvw87Ozu88cYbmDNnDpdA5ebm4oUXXoBMJsPLL78MGxsbNDU1oaWlBfn5+XckBkLIvUEJEyF3yeuvv47GxkbEx8eDx+MhISEBa9euNXn0gEajwe+//w6VSgVbW1ukpaVBoVDA1taWa7Nt2zZIJBLodDpcuHABLi4uiIiIwKZNmyYde2xsDBkZGfj111/h7OyMxYsXY+fOnSZtduzYgaysLPz888+YOXMmDh48CD6fDwB4++23ceHCBSgUCjg6OiItLQ1xcXHo7+/n9tdqtbCzs0Nubi5+++03eHp6Ij09HcCN+4rq6uqg0WiwdOlS/Pnnn/Dy8kJMTMwdW3GaqpSUFDQ1NUGlUsHOzg7Z2dl3ZHUJuHGcGo0GK1aswOXLl7FgwQJ89tln3HaFQoHvv/8eeXl5KCwshL29PYKDg82uyhFC7m88duvFfUKI1RiNRoSEhGD58uXYtm3bXRnj2LFjWLRoEXp7e+nVHoQQMkW0wkSIFXV1daG2thbR0dEwGAz48MMP0dnZiRUrVlg7NEIIITehB1cSYkU2NjYoLy/HrFmzEBUVhebmZhw5cmTC/UaEEEKsiy7JEUIIIYRYQCtMhBBCCCEWUMJECCGEEGIBJUyEEEIIIRZQwkQIIYQQYgElTIQQQgghFlDCRAghhBBiASVMhBBCCCEWUMJECCGEEGIBJUyEEEIIIRb8D57rs7Dtn0LpAAAAAElFTkSuQmCC",
                        "text/plain": [
                            "<Figure size 640x480 with 2 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plt.scatter(df_success.FNO, df_success.rms_spot_size, c=df_success.n, alpha=0.5)\n",
                "plt.xlabel(\"Image-space F-number\")\n",
                "plt.ylabel(\"RMS spot size (mm)\")\n",
                "cbar = plt.colorbar()\n",
                "cbar.set_label(\"Refractive index (n)\", rotation=270, labelpad=20)\n",
                "plt.show()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "This plot shows that there appears to be an RMS spot size minimum, which varies with f-number. We also see that larger refractive indices appear to result in smaller RMS spot sizes, which appears as a gradient-like effect that can especially be seen at smaller f-numbers."
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Build Predictive Model"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Split data into features and target variable"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 11,
            "metadata": {},
            "outputs": [],
            "source": [
                "X = df_success[[\"n\", \"FNO\"]]\n",
                "y = df_success[\"R_opt\"]"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Split the data into training and testing sets"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 12,
            "metadata": {},
            "outputs": [],
            "source": [
                "X_train, X_test, y_train, y_test = train_test_split(\n",
                "    X,\n",
                "    y,\n",
                "    test_size=0.2,\n",
                "    random_state=42,\n",
                ")"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Train regression model"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 13,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/html": [
                            "<style>#sk-container-id-1 {\n",
                            "  /* Definition of color scheme common for light and dark mode */\n",
                            "  --sklearn-color-text: black;\n",
                            "  --sklearn-color-line: gray;\n",
                            "  /* Definition of color scheme for unfitted estimators */\n",
                            "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
                            "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
                            "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
                            "  --sklearn-color-unfitted-level-3: chocolate;\n",
                            "  /* Definition of color scheme for fitted estimators */\n",
                            "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
                            "  --sklearn-color-fitted-level-1: #d4ebff;\n",
                            "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
                            "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
                            "\n",
                            "  /* Specific color for light theme */\n",
                            "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
                            "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
                            "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
                            "  --sklearn-color-icon: #696969;\n",
                            "\n",
                            "  @media (prefers-color-scheme: dark) {\n",
                            "    /* Redefinition of color scheme for dark theme */\n",
                            "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
                            "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
                            "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
                            "    --sklearn-color-icon: #878787;\n",
                            "  }\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 {\n",
                            "  color: var(--sklearn-color-text);\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 pre {\n",
                            "  padding: 0;\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 input.sk-hidden--visually {\n",
                            "  border: 0;\n",
                            "  clip: rect(1px 1px 1px 1px);\n",
                            "  clip: rect(1px, 1px, 1px, 1px);\n",
                            "  height: 1px;\n",
                            "  margin: -1px;\n",
                            "  overflow: hidden;\n",
                            "  padding: 0;\n",
                            "  position: absolute;\n",
                            "  width: 1px;\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-dashed-wrapped {\n",
                            "  border: 1px dashed var(--sklearn-color-line);\n",
                            "  margin: 0 0.4em 0.5em 0.4em;\n",
                            "  box-sizing: border-box;\n",
                            "  padding-bottom: 0.4em;\n",
                            "  background-color: var(--sklearn-color-background);\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-container {\n",
                            "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
                            "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
                            "     so we also need the `!important` here to be able to override the\n",
                            "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
                            "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
                            "  display: inline-block !important;\n",
                            "  position: relative;\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-text-repr-fallback {\n",
                            "  display: none;\n",
                            "}\n",
                            "\n",
                            "div.sk-parallel-item,\n",
                            "div.sk-serial,\n",
                            "div.sk-item {\n",
                            "  /* draw centered vertical line to link estimators */\n",
                            "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
                            "  background-size: 2px 100%;\n",
                            "  background-repeat: no-repeat;\n",
                            "  background-position: center center;\n",
                            "}\n",
                            "\n",
                            "/* Parallel-specific style estimator block */\n",
                            "\n",
                            "#sk-container-id-1 div.sk-parallel-item::after {\n",
                            "  content: \"\";\n",
                            "  width: 100%;\n",
                            "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
                            "  flex-grow: 1;\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-parallel {\n",
                            "  display: flex;\n",
                            "  align-items: stretch;\n",
                            "  justify-content: center;\n",
                            "  background-color: var(--sklearn-color-background);\n",
                            "  position: relative;\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-parallel-item {\n",
                            "  display: flex;\n",
                            "  flex-direction: column;\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
                            "  align-self: flex-end;\n",
                            "  width: 50%;\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
                            "  align-self: flex-start;\n",
                            "  width: 50%;\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
                            "  width: 0;\n",
                            "}\n",
                            "\n",
                            "/* Serial-specific style estimator block */\n",
                            "\n",
                            "#sk-container-id-1 div.sk-serial {\n",
                            "  display: flex;\n",
                            "  flex-direction: column;\n",
                            "  align-items: center;\n",
                            "  background-color: var(--sklearn-color-background);\n",
                            "  padding-right: 1em;\n",
                            "  padding-left: 1em;\n",
                            "}\n",
                            "\n",
                            "\n",
                            "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
                            "clickable and can be expanded/collapsed.\n",
                            "- Pipeline and ColumnTransformer use this feature and define the default style\n",
                            "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
                            "*/\n",
                            "\n",
                            "/* Pipeline and ColumnTransformer style (default) */\n",
                            "\n",
                            "#sk-container-id-1 div.sk-toggleable {\n",
                            "  /* Default theme specific background. It is overwritten whether we have a\n",
                            "  specific estimator or a Pipeline/ColumnTransformer */\n",
                            "  background-color: var(--sklearn-color-background);\n",
                            "}\n",
                            "\n",
                            "/* Toggleable label */\n",
                            "#sk-container-id-1 label.sk-toggleable__label {\n",
                            "  cursor: pointer;\n",
                            "  display: block;\n",
                            "  width: 100%;\n",
                            "  margin-bottom: 0;\n",
                            "  padding: 0.5em;\n",
                            "  box-sizing: border-box;\n",
                            "  text-align: center;\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
                            "  /* Arrow on the left of the label */\n",
                            "  content: \"▸\";\n",
                            "  float: left;\n",
                            "  margin-right: 0.25em;\n",
                            "  color: var(--sklearn-color-icon);\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
                            "  color: var(--sklearn-color-text);\n",
                            "}\n",
                            "\n",
                            "/* Toggleable content - dropdown */\n",
                            "\n",
                            "#sk-container-id-1 div.sk-toggleable__content {\n",
                            "  max-height: 0;\n",
                            "  max-width: 0;\n",
                            "  overflow: hidden;\n",
                            "  text-align: left;\n",
                            "  /* unfitted */\n",
                            "  background-color: var(--sklearn-color-unfitted-level-0);\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
                            "  /* fitted */\n",
                            "  background-color: var(--sklearn-color-fitted-level-0);\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-toggleable__content pre {\n",
                            "  margin: 0.2em;\n",
                            "  border-radius: 0.25em;\n",
                            "  color: var(--sklearn-color-text);\n",
                            "  /* unfitted */\n",
                            "  background-color: var(--sklearn-color-unfitted-level-0);\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
                            "  /* unfitted */\n",
                            "  background-color: var(--sklearn-color-fitted-level-0);\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
                            "  /* Expand drop-down */\n",
                            "  max-height: 200px;\n",
                            "  max-width: 100%;\n",
                            "  overflow: auto;\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
                            "  content: \"▾\";\n",
                            "}\n",
                            "\n",
                            "/* Pipeline/ColumnTransformer-specific style */\n",
                            "\n",
                            "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
                            "  color: var(--sklearn-color-text);\n",
                            "  background-color: var(--sklearn-color-unfitted-level-2);\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
                            "  background-color: var(--sklearn-color-fitted-level-2);\n",
                            "}\n",
                            "\n",
                            "/* Estimator-specific style */\n",
                            "\n",
                            "/* Colorize estimator box */\n",
                            "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
                            "  /* unfitted */\n",
                            "  background-color: var(--sklearn-color-unfitted-level-2);\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
                            "  /* fitted */\n",
                            "  background-color: var(--sklearn-color-fitted-level-2);\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
                            "#sk-container-id-1 div.sk-label label {\n",
                            "  /* The background is the default theme color */\n",
                            "  color: var(--sklearn-color-text-on-default-background);\n",
                            "}\n",
                            "\n",
                            "/* On hover, darken the color of the background */\n",
                            "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
                            "  color: var(--sklearn-color-text);\n",
                            "  background-color: var(--sklearn-color-unfitted-level-2);\n",
                            "}\n",
                            "\n",
                            "/* Label box, darken color on hover, fitted */\n",
                            "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
                            "  color: var(--sklearn-color-text);\n",
                            "  background-color: var(--sklearn-color-fitted-level-2);\n",
                            "}\n",
                            "\n",
                            "/* Estimator label */\n",
                            "\n",
                            "#sk-container-id-1 div.sk-label label {\n",
                            "  font-family: monospace;\n",
                            "  font-weight: bold;\n",
                            "  display: inline-block;\n",
                            "  line-height: 1.2em;\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-label-container {\n",
                            "  text-align: center;\n",
                            "}\n",
                            "\n",
                            "/* Estimator-specific */\n",
                            "#sk-container-id-1 div.sk-estimator {\n",
                            "  font-family: monospace;\n",
                            "  border: 1px dotted var(--sklearn-color-border-box);\n",
                            "  border-radius: 0.25em;\n",
                            "  box-sizing: border-box;\n",
                            "  margin-bottom: 0.5em;\n",
                            "  /* unfitted */\n",
                            "  background-color: var(--sklearn-color-unfitted-level-0);\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-estimator.fitted {\n",
                            "  /* fitted */\n",
                            "  background-color: var(--sklearn-color-fitted-level-0);\n",
                            "}\n",
                            "\n",
                            "/* on hover */\n",
                            "#sk-container-id-1 div.sk-estimator:hover {\n",
                            "  /* unfitted */\n",
                            "  background-color: var(--sklearn-color-unfitted-level-2);\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
                            "  /* fitted */\n",
                            "  background-color: var(--sklearn-color-fitted-level-2);\n",
                            "}\n",
                            "\n",
                            "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
                            "\n",
                            "/* Common style for \"i\" and \"?\" */\n",
                            "\n",
                            ".sk-estimator-doc-link,\n",
                            "a:link.sk-estimator-doc-link,\n",
                            "a:visited.sk-estimator-doc-link {\n",
                            "  float: right;\n",
                            "  font-size: smaller;\n",
                            "  line-height: 1em;\n",
                            "  font-family: monospace;\n",
                            "  background-color: var(--sklearn-color-background);\n",
                            "  border-radius: 1em;\n",
                            "  height: 1em;\n",
                            "  width: 1em;\n",
                            "  text-decoration: none !important;\n",
                            "  margin-left: 1ex;\n",
                            "  /* unfitted */\n",
                            "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
                            "  color: var(--sklearn-color-unfitted-level-1);\n",
                            "}\n",
                            "\n",
                            ".sk-estimator-doc-link.fitted,\n",
                            "a:link.sk-estimator-doc-link.fitted,\n",
                            "a:visited.sk-estimator-doc-link.fitted {\n",
                            "  /* fitted */\n",
                            "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
                            "  color: var(--sklearn-color-fitted-level-1);\n",
                            "}\n",
                            "\n",
                            "/* On hover */\n",
                            "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
                            ".sk-estimator-doc-link:hover,\n",
                            "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
                            ".sk-estimator-doc-link:hover {\n",
                            "  /* unfitted */\n",
                            "  background-color: var(--sklearn-color-unfitted-level-3);\n",
                            "  color: var(--sklearn-color-background);\n",
                            "  text-decoration: none;\n",
                            "}\n",
                            "\n",
                            "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
                            ".sk-estimator-doc-link.fitted:hover,\n",
                            "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
                            ".sk-estimator-doc-link.fitted:hover {\n",
                            "  /* fitted */\n",
                            "  background-color: var(--sklearn-color-fitted-level-3);\n",
                            "  color: var(--sklearn-color-background);\n",
                            "  text-decoration: none;\n",
                            "}\n",
                            "\n",
                            "/* Span, style for the box shown on hovering the info icon */\n",
                            ".sk-estimator-doc-link span {\n",
                            "  display: none;\n",
                            "  z-index: 9999;\n",
                            "  position: relative;\n",
                            "  font-weight: normal;\n",
                            "  right: .2ex;\n",
                            "  padding: .5ex;\n",
                            "  margin: .5ex;\n",
                            "  width: min-content;\n",
                            "  min-width: 20ex;\n",
                            "  max-width: 50ex;\n",
                            "  color: var(--sklearn-color-text);\n",
                            "  box-shadow: 2pt 2pt 4pt #999;\n",
                            "  /* unfitted */\n",
                            "  background: var(--sklearn-color-unfitted-level-0);\n",
                            "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
                            "}\n",
                            "\n",
                            ".sk-estimator-doc-link.fitted span {\n",
                            "  /* fitted */\n",
                            "  background: var(--sklearn-color-fitted-level-0);\n",
                            "  border: var(--sklearn-color-fitted-level-3);\n",
                            "}\n",
                            "\n",
                            ".sk-estimator-doc-link:hover span {\n",
                            "  display: block;\n",
                            "}\n",
                            "\n",
                            "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
                            "\n",
                            "#sk-container-id-1 a.estimator_doc_link {\n",
                            "  float: right;\n",
                            "  font-size: 1rem;\n",
                            "  line-height: 1em;\n",
                            "  font-family: monospace;\n",
                            "  background-color: var(--sklearn-color-background);\n",
                            "  border-radius: 1rem;\n",
                            "  height: 1rem;\n",
                            "  width: 1rem;\n",
                            "  text-decoration: none;\n",
                            "  /* unfitted */\n",
                            "  color: var(--sklearn-color-unfitted-level-1);\n",
                            "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
                            "  /* fitted */\n",
                            "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
                            "  color: var(--sklearn-color-fitted-level-1);\n",
                            "}\n",
                            "\n",
                            "/* On hover */\n",
                            "#sk-container-id-1 a.estimator_doc_link:hover {\n",
                            "  /* unfitted */\n",
                            "  background-color: var(--sklearn-color-unfitted-level-3);\n",
                            "  color: var(--sklearn-color-background);\n",
                            "  text-decoration: none;\n",
                            "}\n",
                            "\n",
                            "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
                            "  /* fitted */\n",
                            "  background-color: var(--sklearn-color-fitted-level-3);\n",
                            "}\n",
                            "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>RandomForestRegressor(random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;RandomForestRegressor<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.ensemble.RandomForestRegressor.html\">?<span>Documentation for RandomForestRegressor</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>RandomForestRegressor(random_state=42)</pre></div> </div></div></div></div>"
                        ],
                        "text/plain": [
                            "RandomForestRegressor(random_state=42)"
                        ]
                    },
                    "execution_count": 13,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "model = RandomForestRegressor(n_estimators=100, random_state=42)\n",
                "model.fit(X_train, y_train)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Evaluate the model"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 14,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Mean Squared Error: 2.457e-07\n"
                    ]
                }
            ],
            "source": [
                "y_pred = model.predict(X_test)\n",
                "mse = mean_squared_error(y_test, y_pred)\n",
                "print(f\"Mean Squared Error: {mse:.3e}\")"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Based on the resulting mean squared error on the test dataset, we can see that the model has successfully captured the relationships in the dataset."
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Prediction\n",
                "\n",
                "We now choose new parameters for the refractive index and f-number and use our random forest model to predict the radius of curvature. We compute the RMS spot size and plot the spot diagram to confirm the resulting lens indeed reaches a minimal spot size."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 35,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Predicted Radius of Curvature: 17.31 mm\n"
                    ]
                }
            ],
            "source": [
                "new_data = pd.DataFrame({\"n\": [1.864], \"FNO\": [5.45]})  # Example new data\n",
                "prediction = model.predict(new_data)\n",
                "print(f\"Predicted Radius of Curvature: {prediction[0]:.2f} mm\")"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 36,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 1000x400 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "lens = ConfigurableSinglet(epd=20 / 5.45, n=1.864, R=prediction[0])\n",
                "lens.draw(num_rays=5)"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 37,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "RMS Spot Size: 0.0052 mm\n"
                    ]
                }
            ],
            "source": [
                "spot = analysis.SpotDiagram(lens)\n",
                "print(\n",
                "    f\"RMS Spot Size: {spot.rms_spot_radius()[0][0]:.4f} mm\",\n",
                ")  # field index 0 and wavelength index 0"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 38,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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oE6OhRU6sA33OhJgOjX43Ahr5qo5GRVsH+pz/Qt8BxFho9Dsxun6erlb/JW8N6HMmxPio+50QQgixEBTUCSGEEAtBQZ0QQgixEBTUCSGEEAtBA+WI1mg0MzE2OucI0Q0FdaIVWsubGBudc4TojrrfSYdoLW9ibHTOEdI5FNRJh2gtb2JsdM4R0jkU1EmHaC1vYmx0zhHSORTUSYdoLW9ibHTOEdI5vAvqGzZsgJ+fHxwdHREWFobc3Nx20+/duxcBAQFwdHTEsGHDcOjQIbX9jDEsXboU3t7ecHJyQnh4OM6fP9/qOAcPHkRYWBicnJzg7u6OqKgofVbL7E0J9cWamCC8HzUUa2KCaMASMTg65wjRHa+C+p49e5CYmIhly5bh5MmTGDFiBCIiIlBaWqoxfVZWFl544QXExcXh1KlTiIqKQlRUFH7//XcuzcqVK7Fu3TqkpKQgJycHLi4uiIiIQH39X/fu/v3vf2P69OmYNWsWTp8+jczMTPztb38zeH3NTT9PV4zu50FXS8Ro6JwjRDe8ekpbWFgYHnzwQXz66acAAJVKBV9fX8yfPx+LFy9ulT4mJga1tbU4cOAAt23UqFEICgpCSkoKGGPw8fHBwoUL8frrrwMAqqqqIJFIsH37dkydOhVNTU3w8/PDu+++i7i4uE6Vm57QRIh1o+8AYiy8uVJvbGxEXl4ewsPDuW1CoRDh4eHIzs7WmCc7O1stPQBERERw6S9fvgy5XK6Wxs3NDWFhYVyakydP4saNGxAKhQgODoa3tzeeeuoptav9+zU0NKC6ulrtRQghhBgab4J6eXk5mpubIZFI1LZLJBLI5XKNeeRyebvpW/7bXppLly4BAP75z38iKSkJBw4cgLu7O8aOHYuKigqN75ucnAw3Nzfu5etL9wIJIYQYHm+CuqmoVCoAwNtvv43o6GiEhIRg27ZtEAgE2Lt3r8Y8S5YsQVVVFfe6du2aMYtMCCHESvEmqHt4eMDGxgYKhUJtu0KhgFQq1ZhHKpW2m77lv+2l8fb2BgAEBgZy+x0cHNC3b18UFxdrfF8HBweIRCK1FyGEEGJovAnq9vb2CAkJQUZGBrdNpVIhIyMDMplMYx6ZTKaWHgDS09O59P7+/pBKpWppqqurkZOTw6UJCQmBg4MDioqKuDRKpRJXrlxBnz599FY/QgghpKt49UCXxMREzJgxA6GhoRg5ciTWrl2L2tpazJo1CwAQGxuLnj17Ijk5GQDw6quvYsyYMfj4448RGRmJ1NRUnDhxAps3bwYACAQCvPbaa/jggw8wYMAA+Pv745133oGPjw83D10kEmHOnDlYtmwZfH190adPH6xatQoA8Nxzzxm/EQghhJA28Cqox8TEoKysDEuXLoVcLkdQUBDS0tK4gW7FxcUQCv/qfBg9ejR2796NpKQkvPXWWxgwYAD279+PoUOHcmneeOMN1NbWIj4+HpWVlXj44YeRlpYGR8e/lqNctWoVbG1tMX36dNy5cwdhYWE4fPgw3N3djVd5PaFHWRJrQec6sUa8mqfOV+YyR5UeZUmshbmd6+byHUAsH2/uqZOuoUdZEmtB5zqxZhTUrQQ9ypJYCzrXiTWjoG4l6FGWxFrQuU6sGQV1K0GPsiTWgs51Ys1ooJwRmNMgGRoRTKyFOZ3r5vQdQCwbr6a0ka7r5+lq8i84QoyBznVijaj7nRBCCLEQdKVOiB50pavXnLqJCSH8RkGdkC7qykIn5rZICiGE36j7nZAu6MpCJ7RICiFE3yioE3KPi2U1yLpYrnVg7cpCJ11dJEXXshJCLB91vxPyP53pCr93oRMPFwedFjrpSl7qtieEaEJX6oSg813hXVnopLN5qdueENIWulInBH91hfd2d+a6wotv1UFRXd9hkJ0S6ovgPu6dGsHembxdKSshxLJRUCcEXesKB7q20ImuebtaVkKI5aLud0LAr/XC+VRWQohx0drvRmDIdZ9p4RLNOtsufGpPa6ijMRmyXWjtd2Is1P3OYzQCWrOutAuf1gvvTFnpnNGM2oVYCt51v2/YsAF+fn5wdHREWFgYcnNz202/d+9eBAQEwNHREcOGDcOhQ4fU9jPGsHTpUnh7e8PJyQnh4eE4f/68xmM1NDQgKCgIAoEA+fn5+qpSp9AIaM2oXdpGbaMZtQuxJLwK6nv27EFiYiKWLVuGkydPYsSIEYiIiEBpaanG9FlZWXjhhRcQFxeHU6dOISoqClFRUfj999+5NCtXrsS6deuQkpKCnJwcuLi4ICIiAvX1rRcAeeONN+Dj42Ow+umiqwuXWCpql7ZR22hG7UIsCa+C+ieffILZs2dj1qxZCAwMREpKCpydnbF161aN6f/1r39h/PjxWLRoEQYPHoz3338fDzzwAD799FMAd6/S165di6SkJDzzzDMYPnw4du7ciZs3b2L//v1qx/r+++/x448/YvXq1YauplbuHQGtUjEaAf0/1C5to7bRjNqFWBLeBPXGxkbk5eUhPDyc2yYUChEeHo7s7GyNebKzs9XSA0BERASX/vLly5DL5Wpp3NzcEBYWpnZMhUKB2bNn44svvoCzs3OHZW1oaEB1dbXaS99oBLRm1C5to7bRjNqFWBLeDJQrLy9Hc3MzJBKJ2naJRIJz585pzCOXyzWml8vl3P6WbW2lYYxh5syZmDNnDkJDQ3HlypUOy5qcnIx3331Xq3p1RVcWPbFk1C5to7bRjNqFWAreBHVTWb9+PW7fvo0lS5ZonWfJkiVITEzk/l1dXQ1fX8OMpOXTaG1jonZpG7WNZtQuxBLwpvvdw8MDNjY2UCgUatsVCgWkUqnGPFKptN30Lf9tL83hw4eRnZ0NBwcH2Nraon///gCA0NBQzJgxQ+P7Ojg4QCQSqb1I19ATyUyH2p4Q/uBNULe3t0dISAgyMjK4bSqVChkZGZDJZBrzyGQytfQAkJ6ezqX39/eHVCpVS1NdXY2cnBwuzbp163D69Gnk5+cjPz+fmxK3Z88efPjhh3qtI9Fs34lrWLAnH+/s/x0L9uRj34lrpi6S1aC2J4RfeNX9npiYiBkzZiA0NBQjR47E2rVrUVtbi1mzZgEAYmNj0bNnTyQnJwMAXn31VYwZMwYff/wxIiMjkZqaihMnTmDz5s0AAIFAgNdeew0ffPABBgwYAH9/f7zzzjvw8fFBVFQUAKB3795qZXB1vds9169fP/Tq1ctINbde988hLq9twM5jVxHcx526Sg2M2p4Q/uFVUI+JiUFZWRmWLl0KuVyOoKAgpKWlcQPdiouLIRT+1fkwevRo7N69G0lJSXjrrbcwYMAA7N+/H0OHDuXSvPHGG6itrUV8fDwqKyvx8MMPIy0tDY6ONJ3FHNATyUyH2p4Q/qG1342A1n3uvItlNViwJx+MMe6JZAKBAGtigiiwGBi1vf7QdwAxFt7cUyfWieYQmw61PSH8Q1fqRkC/0ruOnixmOtT2XUffAcRYeHVPnVgvmkNsOtT2hPAHdb8TQgghFoKCOiGEEGIhKKgTQgghFoLuqZsxaxmgZC31tGTW8hlaSz0Jf1FQN1P7TlzDzmNXUdvQBBcHW8SO6oMpoYZ5KIwpWUs9LZm1fIbWUk/Cb9T9bobuX56TMYadx65a3AM1rKWelsxaPkNrqSfhPwrqZqhleU4PFwduec7ahiYoqutNXTS9spZ6WjJr+QytpZ6E/yiomyGJyBEuDrYor22ASsVQXtsAFwdbSESWtR69tdTTklnLZ2gt9ST8R0HdDFnL8pzWUk9LZi2fobXUk/AfLRNrBJ1dItJaRtpaQz0tvY6WXr8Wna0nLRNLjIWCuhHQH7Tl0uZLXttR09YSGK0RfQcQY6EpbYR0kjbB+v5R0+W1Ddh57CqC+7irBW6aLkUI0Qe6p05IJ2g7xUmbUdM0XYoQoi8U1AnpBG2nOGkzapqmSxFC9IWCOiHtuFhWg6yL5a2umrWd4qTNqGltj9VWWQghpAXvgvqGDRvg5+cHR0dHhIWFITc3t930e/fuRUBAABwdHTFs2DAcOnRIbT9jDEuXLoW3tzecnJwQHh6O8+fPc/uvXLmCuLg4+Pv7w8nJCf369cOyZcvQ2NhokPoR87HvxDUs2JOPd/b/jgV78rHvxDVuny5TnKaE+mJNTBDejxqKNTFBre6Va3Os9spCCCEteDVQbs+ePUhMTERKSgrCwsKwdu1aREREoKioCF5eXq3SZ2Vl4YUXXkBycjImTpyI3bt3IyoqCidPnsTQoUMBACtXrsS6deuwY8cO+Pv745133kFERAQKCgrg6OiIc+fOQaVSYdOmTejfvz9+//13zJ49G7W1tVi9erWxm4CX+DiqW5sBblNCfRHcx12ruvXzdG13f3vH0nawnTnj4zlACB/xakpbWFgYHnzwQXz66acAAJVKBV9fX8yfPx+LFy9ulT4mJga1tbU4cOAAt23UqFEICgpCSkoKGGPw8fHBwoUL8frrrwMAqqqqIJFIsH37dkydOlVjOVatWoWNGzfi0qVLWpXbmqez8HVUd9bFcryz/3f0dneGUCiASsVQfKsO70cNxeh+HlZbls7g6zmgT9b8HUCMizfd742NjcjLy0N4eDi3TSgUIjw8HNnZ2RrzZGdnq6UHgIiICC795cuXIZfL1dK4ubkhLCyszWMCdwN/9+7d29zf0NCA6upqtZc14vOobnNaFtScyqIrPp8DhPARb4J6eXk5mpubIZFI1LZLJBLI5XKNeeRyebvpW/6ryzEvXLiA9evX46WXXmqzrMnJyXBzc+Nevr7WdVXSgg+jutsafGZOy4JqWxZzHEjHh3OAEEvCq3vqpnbjxg2MHz8ezz33HGbPnt1muiVLliAxMZH7d3V1tVUG9nuvMD1cHMzuCrOjbmFd7pkbWkdlMdcubnM/BwixNLy5Uvfw8ICNjQ0UCoXadoVCAalUqjGPVCptN33Lf7U55s2bN/HYY49h9OjR2Lx5c7tldXBwgEgkUntZI3O62r2ftt3C/TxdMbqfh1mUua2ymHMXtzmfA4RYIt5cqdvb2yMkJAQZGRmIiooCcHegXEZGBhISEjTmkclkyMjIwGuvvcZtS09Ph0wmAwD4+/tDKpUiIyMDQUFBAO5eVefk5GDu3Llcnhs3buCxxx5DSEgItm3bBqGQN7+FTM6crnbv1dIt3DL4zMPFAcW36qCorjebMmrL3OtirucAIZaIN0EdABITEzFjxgyEhoZi5MiRWLt2LWprazFr1iwAQGxsLHr27Ink5GQAwKuvvooxY8bg448/RmRkJFJTU3HixAnuSlsgEOC1117DBx98gAEDBnBT2nx8fLgfDjdu3MDYsWPRp08frF69GmVlZVx52uoh0JWlT/fpaDqXKVhStzAf6mKO54A+WfrfMOEPXgX1mJgYlJWVYenSpZDL5QgKCkJaWho30K24uFjtKnr06NHYvXs3kpKS8NZbb2HAgAHYv38/N0cdAN544w3U1tYiPj4elZWVePjhh5GWlgZHx7tfiOnp6bhw4QIuXLiAXr16qZVHH7MBzfVeqKVr6Rbeeewqim/VcW3Pxy9kS6oLH9HfMDEnOs9Tb2hoQE5ODq5evYq6ujp4enoiODgY/v7+hioj77U1R/ViWQ0W7MkHY4y7whIIBFgTE0RfyEZiSVdYllQXvtD2b5jmqRNj0fpKPTMzE//617/w3//+F0qlEm5ubnByckJFRQUaGhrQt29fxMfHY86cOejWrZshy2wxzP1eqDWwpG5hS6oLX9DfMDE3Wo34evrppxETEwM/Pz/8+OOPuH37Nv78809cv34ddXV1OH/+PJKSkpCRkYGBAwciPT3d0OW2CHxeVIRvzHEOt7FYc90Njf6GibnR6ko9MjIS//73v2FnZ6dxf9++fdG3b1/MmDEDBQUFKCkp0WshLRXdCzUOa77nac11Nwb6Gybmhldrv/NVR/fT6F6o4VjzuAVrrruxdfQ3TPfUibF0afR7TU0NVCqV2jY6YXVnafdCzelHiinveWpqB2O2jTnf7zWnc0QfLO1vmPCXzkH98uXLSEhIwNGjR1Ff/9f6zYwxCAQCNDc367WAhF/MrbvXVHO4NbUDAKO2jbnOXze3c4QQS6JzUH/xxRfBGMPWrVshkUggEAgMUS7CQ+b43G9j3fO898oTQKt22PLLJTAADrbCVm0DwCBXreZ4v9cczxFCLInOQf306dPIy8vDoEGDDFEewmPm2t1r6GVK77/ylPXt3qodihS3AQA9Jd3U2mbv8WvIuvSnwa5azW2JVnM9RwixFDoH9QcffBDXrl2joE5aMdfuXsBw9zw1XXkeLSqDjVCg1g7dHG3BALVttkIBDheVarx61/cVu7kETHM+R/ioubkZSqXS1MUgBmRnZwcbGxut0+sc1P/v//4Pc+bMwY0bNzB06NBW09yGDx+u6yGJhTC37l5DDsZqOfbNyjsarzyfGCxB1qU/uXaY/UhfAFBrm7GDPPFTYanas8aLb9XhVPEtg5fbVFft5naO8BVjDHK5HJWVlaYuCjECsVgMqVSq1e1unae0HTt2DH/7299w5cqVvw4iENBAuXZY23QWUwcOwLCDse49tq1QgNqGJri72LeaNga0vld+/733+6ecVdYp4WRvg2YVM2i5TT1AzRzOEWPS93dASUkJKisr4eXlBWdnZxrbZKEYY6irq0NpaSnEYjG8vb07zKPzlfrf//53BAcH46uvvqKBckQjU3f3GnIwlqZj1zUK0NCk0njlef/73d8291612grv/jh2sBVyQd6Q5TblADVTnyN81tzczAX0Hj16mLo4xMCcnJwAAKWlpfDy8uqwK17noH716lV899136N+/f+dKSIiBGXIwlqZj1zU2I/7RvvARO+l85XnvQLablXew8ejFVt3xhio3DVDjp5Z76M7OziYuCTGWls9aqVR2GNS1Wvv9Xo8//jhOnz7duZIRYgSGWo/7YlkNblbe4QbB3Xvs4N7uGN3Po1MBsp+nK0b380Bwb/dW5bYVCnCz8k6X122nNcotD/WSWg9dPmudr9QnTZqEBQsW4MyZMxg2bFirgXJPP/20rockRK8MMRjr3vvRjU0q1DU0oa6xWetja3MP+f5yNzapwBjDxqMXu3wPnAaoEWIddB4oJxS2fXFPA+U0s7aBcuZCX4OxNK2h3tikwuxH+yK4d9v3pFveP7/4FtLOKriBdWMHeeL5B3u3m+9U8S1s/vmS2v11fazbbm0D1MyFPr8D6uvrcfnyZfj7+8PRkXparIEun7nO3e8qlarNFwV0Yk5aurX1dT/63nvdTSoGH7FTm8f+7Mh5zN5xAolf52P94Qv4s6YBtjYCXK2ow9bMK5jxeS4+O3K+zXL7iJ3QrGJq71nb0ARFdb3GPNrSV5sQ0lkbNmyAn58fHB0dERYWhtzc3HbTb9++HQKBQO11f2CrqalBQkICevXqBScnJwQGBiIlJYXbf+XKlVbHaHnt3buXS1dcXIzIyEg4OzvDy8sLixYtQlNTk34bwMC69EAXQqyBrgumfHbkPNYfvgAVA4QCoLFJhco6JSrrlGAqhqZmBnl1PdYfvgAAePmxAV1+T0L4YM+ePUhMTERKSgrCwsKwdu1aREREoKioCF5eXm3mE4lEKCoq4v59/z3mxMREHD58GF9++SX8/Pzw448/4uWXX4aPjw+efvpp+Pr6tnok+ObNm7Fq1So89dRTAO7OKoiMjIRUKkVWVhZKSkoQGxsLOzs7LF++XI+tYFg6X6kDwPHjx7Fy5Uq8/vrrSExMVHsZmq6/8vbu3YuAgAA4Ojpi2LBhOHTokNp+xhiWLl0Kb29vODk5ITw8HOfPq19BVVRUYNq0aRCJRBCLxYiLi0NNTdcGLhH+aLkfLRAIUHyrDgKBoM370RfLarAv7waaGeBibwOBQAAVA+40NuOOshmNzQwCwd19Kgbsy7uhcRCcLu9JCF988sknmD17NmbNmsVdTTs7O2Pr1q3t5hMIBJBKpdxLIpGo7c/KysKMGTMwduxY+Pn5IT4+HiNGjODig42NjVp+qVSK//znP3j++efh6nr3b+rHH39EQUEBvvzySwQFBeGpp57C+++/jw0bNqCxsVFjuY4ePQqBQKC2CFB+fj4EAgG3lsv27dshFotx4MABDBo0CM7OzpgyZQrq6uqwY8cO+Pn5wd3dHa+88opeert1DurLly9HWFgYtm3bhhMnTuDUqVPcKz8/v8sFak/Lr7xly5bh5MmTGDFiBCIiIlBaWqoxfVZWFl544QXExcXh1KlTiIqKQlRUFH7//XcuzcqVK7Fu3TqkpKQgJycHLi4uiIiIUHsC3bRp03D27Fmkp6fjwIED+PnnnxEfH6+XOl0sq0HWxfIuj242B+ZUF32XJbiPO2JlfTB3bD+siQlqc8Caoroed5TNsAHQ0KQCwMAAqACoGMAA2AgBpYpBKADqlG13qU8J9cWamCDMHdsPsbI+3MNfusqSPydT42N9jFXmxsZG5OXlITw8nNsmFAoRHh6O7OzsdvPW1NSgT58+8PX1xTPPPIOzZ8+q7R89ejS+++473LhxA4wxHDlyBH/88QeefPJJjcfLy8tDfn4+4uLiuG3Z2dkYNmyY2g+GiIgIVFdXt3o/XdXV1WHdunVITU1FWloajh49imeffRaHDh3CoUOH8MUXX2DTpk3Yt29fl94H6ET3+7/+9S9s3boVM2fO7PKb6+reX3kAkJKSgoMHD2Lr1q1YvHhxq/T/+te/MH78eCxatAgA8P777yM9PR2ffvopUlJSwBjD2rVrkZSUhGeeeQYAsHPnTkgkEuzfvx9Tp05FYWEh0tLScPz4cYSGhgIA1q9fjwkTJmD16tXw8fHpdH3MaYWvrjKnuui7LPcfD6z1ojIt8otvobKuEUqVCs1Nd4P4/ZTNQFNzM4QCoKpOifziWxjdz0Pj8U5dvWXQuljS52RqfKyPMctcXl6O5ubmVlfZEokE586dazPfoEGDsHXrVgwfPhxVVVVYvXo1Ro8ejbNnz6JXr14A7n4nx8fHo1evXrC1tYVQKMSWLVvw6KOPajzm559/jsGDB2P06NHcNrlcrrFsLfu6QqlUYuPGjejXrx8AYMqUKfjiiy+gUCjg6uqKwMBAPPbYYzhy5AhiYmK69F46X6kLhUI89NBDXXrTzujMr7zs7Gy19MDdX14t6S9fvgy5XK6Wxs3NDWFhYVya7OxsiMViLqADQHh4OIRCIXJycjS+b0NDA6qrq9Ve97t/hS/GGHYeu8qrX/gtzKku+i6LLse7WFaDtLMKdHexh4OtDTqaWupoZ4PuLvZIO6to83imqouhmVNZ9IGP9eFLmWUyGWJjYxEUFIQxY8bgm2++gaenJzZt2sSlWb9+PY4dO4bvvvsOeXl5+PjjjzFv3jz89NNPrY53584d7N69W+0q3dCcnZ25gA7c/bHg5+fHdf23bGur11kXOgf1BQsWYMOGDV1+Y1219yuvrV9Rbf3yaknf8t+O0tw/gMPW1hbdu3dv832Tk5Ph5ubGvXx9W//y1TSiWh+jm03BnOqi77LocryWtN0c/tcB1s5k0ZZdro62HR7PFHUxNHMqiz7wsT7GLrOHhwdsbGygUCjUy6FQQCqVan0cOzs7BAcH48KFuwNN79y5g7feeguffPIJJk2ahOHDhyMhIQExMTFYvXp1q/z79u1DXV0dYmNj1bZLpVKNZWvZpy1N98XvX89FIBBo3KZSqbR+n7boHNRff/11FBUVoV+/fpg0aRImT56s9iLAkiVLUFVVxb2uXbvWKo0lrfBlTnXRd1l0OZ5E5Agb4d1pa8pmVXsxHQIATc0qXP3z7prvbR3PVHUxNHMqiz7wsT7GLrO9vT1CQkKQkZHBbVOpVMjIyIBMJtP6OM3NzThz5gz3cBOlUgmlUtlqDRUbGxuNQfLzzz/H008/DU9PT7XtMpkMZ86cUbtaTk9Ph0gkQmBgYLtluvfHwKVLl7SuiyHoHNRfeeUVHDlyBAMHDkSPHj3Urkjd3NwMUUYAnfuV19Yvr5b0Lf/tKM39XSJNTU2oqKho830dHBwgEonUXvezpNHN5lQXfZfl3uNdKKtBbUMzxg+RaDxeP09XPD7IC00qBuX/RrnbtNEFLxAAjc0MzSqGsYM82zze+CES1DY040J5jV7rYmmfk6nxsT6mKHNiYiK2bNmCHTt2oLCwEHPnzkVtbS03TgoAYmNjsWTJEu7f7733Hn788UdcunQJJ0+exIsvvoirV6/iH//4B4C7093GjBmDRYsW4ejRo7h8+TK2b9+OnTt34tlnn1V7/wsXLuDnn3/m8t7rySefRGBgIKZPn47Tp0/jhx9+QFJSEubNmwcHB4d267V48WKcO3cO2dnZePfddwEAJ06caHPUvCHpPFBux44d+Pe//43IyEhDlKdN9/7Ki4qKAvDXr7yEhASNeWQyGTIyMvDaa69x29LT07lfhf7+/pBKpcjIyEBQUBCAuys/5eTkYO7cudwxKisrkZeXh5CQEADA4cOHoVKpEBYW1qU63fswD76v8GVOddF3WaaE+qL0dj325d2AUqVC2lkFvLo5ahxQ9NyDvjh45ibkVQ1wtrdBk4qhrrGZu2oX4G5Ad7azQX2TCpJujnj+wd4a33ffiWtIO6uAslkFOxshxg+RdHkQkyV/TqbGx/oYu8wxMTEoKyvD0qVLIZfLERQUhLS0NLVboMXFxWpX3bdu3cLs2bMhl8vh7u6OkJAQZGVlqV09p6amYsmSJZg2bRoqKirQp08ffPjhh5gzZ47a+2/duhW9evXSOCrexsYGBw4cwNy5cyGTyeDi4oIZM2bgvffe67Bew4cPh0wmg729PT766COsW7cOr776apuj7w1J52Vi+/Tpgx9++AEBAQGGKlOb9uzZgxkzZmDTpk0YOXIk1q5di6+//hrnzp2DRCJBbGwsevbsieTkZAB3p7SNGTMGK1asQGRkJFJTU7F8+XKcPHkSQ4cOBQB89NFHWLFiBXbs2AF/f3+88847+O2331BQUMCtWvTUU09BoVAgJSUFSqUSs2bNQmhoKHbv3q1VuWmZWH7TtExse0u2tiw+0/y/xWeamhnsbe6uXqVsVkHZzGArFMDWRoD5j/fXuPiMru9JzBstE2uZjh49isceewy3bt2CWCw22Pvo8pnrfKX+z3/+E8uWLcO2bduM/ui/jn7l3f8Lb/To0di9ezeSkpLw1ltvYcCAAdi/fz8X0AHgjTfeQG1tLeLj41FZWYmHH34YaWlpag23a9cuJCQkYNy4cRAKhYiOjsa6deuMV3FiUro+trQlSO/Lu4E6ZROq6pRwd7FHNwdbXK2oAwMgFTnghZG9NQb0zrwnIYQAnbhSDw4OxsWLF8EYg5+fX6sRfCdPntRrAS0BXambhiEf6NLQpEJ8Jx7oYiMU4PFBXnjuQd8OH+iy5edLsKcHulgEulK3TBZxpd5yP5sQc6bPRTXuf2xpg7IZAoGgw0ei9vN05R6gEjHUW6tgem+5G5TNqGsU6PSI1/bwcXEUQszZ2LFjoeN1scHpHNSXLVtmiHIQojf3L6pRXtuAnceuIrhP21fVHWkZUKTpClqbY7cEeF3LrU2PgDYM0SaEEPOj1ZQ2c/slQkh7DLWoRssjUZsM8EjUtsrd3MEjXrtybHNfHIW0j76XrYcun7VWQX3IkCFITU3tcM7d+fPnMXfuXKxYsULrAhCib4ZcVKOtYzc2qTr9UIyWB2o0NqmMXm5zXhyFaNYyjqmurs7EJSHG0vJZ3z+GTROtBsplZGTgzTffxKVLl/DEE08gNDQUPj4+cHR0xK1bt1BQUIBff/0VZ8+eRUJCAt566y2DLkTDN9Y2UM4cBmMZ8v7x/cceLO2GQvntVu+lqR3u36btsQxRblPeUzeHc8SY9P0dUFJSgsrKSnh5ecHZ2bnV88WJZWCMoa6uDqWlpRCLxdwqeu3RafT7r7/+ij179uCXX37B1atXcefOHXh4eCA4OBgRERGYNm0a3N3183hIS2JNQd1aAkfLsRubVPgk/Y9W88nHD5FwI95b2gGAWtu0pLk/b+ITA2FvKzRouS31B5e50vd3AGMMcrlc7TnexHKJxWJIpVKtfrzpPKWN6M5agro1LpiSdbEc7+z/nZtPrlIxXCirgZ2NEC4ONmpT4ASA2gC72oZmKFUq9Pdw5fIW36rD+1FD23wUK99Z4zkCGO47oLm5GUqlUm/HI+bHzs4ONjY2WqfXefQ7IW2xxgVT7r1X3RKk7GyEUKpU8HD5qx2KFLcBAIMk3bhtlXV3g/+9eS39Prc1niOGZGNjo9MXPrF8Oj/QhZC2mPNgrJbBaPp+VrSmh2JMCekJd2d7tXZwdbRFN0f1tnF3sceUkJ4Gf6CGoereGeZ8jhBiCehKnejN/Yu06GPBFH0w9D1cTQ/F8OrmqNYO8Y/0BYBWbTMl1FfrhWk6w9zuX5vrOUKIpdD6nvrNmzfh4+Nj6PJYJGu5p97CHAZj3VsWU93D1Wb0u6Hf31zvX5vTOWIM1vYdQExH6+73IUOGaP1UMqIbc+oe1YeWpVHN4cvalIuuaGoHY7aNOS84Y07niD5Y2t8w4S+tu98//PBDvPTSS/jPf/6DTZs2oXv37oYsl9Uwt+5RS6NpIJu13MO15robE/0NE3Oi9ZX6yy+/jN9++w1//vknAgMD8d///teQ5bIK96/HzRjDzmNX6de+HmkayGYt93Ctue7GQn/DxNzoNFDO398fhw8fxqefforJkydj8ODBsLVVPwQ9elV7NL3HODQNZLMW1lx3Y6C/YWJudB79fvXqVXzzzTdwd3fHM8880yqoE+1R96jxtPWUNEsasNVWXbR5QhzpHPobJuZGp4i8ZcsWLFy4EOHh4Th79iw8PT0NVS6rQNN7TMuS7oVaUl34hP6GibnROqiPHz8eubm5+PTTTxEbG2vIMlkV6h41DUt6vrgl1YWP6G+YmBOtB8o1Nzfjt99+M1lAr6iowLRp0yASiSAWixEXF4eamvYHo9TX12PevHno0aMHXF1dER0dDYVCoZamuLgYkZGRcHZ2hpeXFxYtWoSmpiZu/zfffIMnnngCnp6eEIlEkMlk+OGHH/RaN0ub3nM/c5zuY87TvXTFh7qY4zmgT5b+N0z4Q+sr9fT0dEOWo0PTpk1DSUkJ0tPToVQqMWvWLMTHx7c7d37BggU4ePAg9u7dCzc3NyQkJGDy5MnIzMwEcPeHSmRkJKRSKbKyslBSUoLY2FjY2dlh+fLlAICff/4ZTzzxBJYvXw6xWIxt27Zh0qRJyMnJQXBwsFHqzmfm2i1sSfdCzb0u5noOEGKJePGUtsLCQgQGBuL48eMIDQ0FAKSlpWHChAm4fv26xpXuqqqq4Onpid27d2PKlCkAgHPnzmHw4MHIzs7GqFGj8P3332PixIm4efMmJBIJACAlJQVvvvkmysrKYG9vr7E8Q4YMQUxMDJYuXapxf0NDAxoaGrh/V1dXw9fX1+pWkzLnFc0Aywo25loXcz8HjIVWlCPGwouh69nZ2RCLxVxAB4Dw8HAIhULk5OTg2WefbZUnLy8PSqUS4eHh3LaAgAD07t2bC+rZ2dkYNmwYF9ABICIiAnPnzsXZs2c1XomrVCrcvn273cV3kpOT8e6773a2uhbD3Kf7aHMv1JxGx7dXFnO9r2vu5wAhloYXQV0ul8PLy0ttm62tLbp37w65XN5mHnt7e4jFYrXtEomEyyOXy9UCesv+ln2arF69GjU1NXj++efbLO+SJUuQmJjI/bvlSt3amHu3MND+dC9zuvrVpizmOHWND+cAIZbEpI9eXbx4MQQCQbuvc+fOmbKIanbv3o13330XX3/9dasfGfdycHCASCRSe1kjPq9oZk4rhZlTWXTF53OAED4y6ZX6woULMXPmzHbT9O3bF1KpFKWlpWrbm5qaUFFRAalUqjGfVCpFY2MjKisr1a7WFQoFl0cqlSI3N1ctX8vo+PuPm5qain/84x/Yu3evWpc+aZ+5dgt3RNtuY312z7d1LL53YfP1HCCEj0wa1D09PbVawEYmk6GyshJ5eXkICQkBABw+fBgqlQphYWEa84SEhMDOzg4ZGRmIjo4GABQVFaG4uBgymYw77ocffojS0lLuyjs9PR0ikQiBgYHcsb766iv8/e9/R2pqKiIjI7tUZ2tkjt3CHdGm21if3fPtHcsSurD5eA4Qwkcm7X7X1uDBgzF+/HjMnj0bubm5yMzMREJCAqZOncqNfL9x4wYCAgK4K283NzfExcUhMTERR44cQV5eHmbNmgWZTIZRo0YBAJ588kkEBgZi+vTpOH36NH744QckJSVh3rx5cHBwAHC3yz02NhYff/wxwsLCIJfLIZfLUVVVZZrGIEbRUbexrl3i7c3T7uhY1IVNCNEWLwbKAcCuXbuQkJCAcePGQSgUIjo6GuvWreP2K5VKFBUVoa6ujtu2Zs0aLm1DQwMiIiLw2WefcfttbGxw4MABzJ07FzKZDC4uLpgxYwbee+89Ls3mzZvR1NSEefPmYd68edz2GTNmYPv27YatNDGp9rqNdekS7+iKXptjURc2IUQbvJinznc0R9XyaDv/Wpt0NJfb8tF3ADEWXnS/E2JutO0S12YJV+peJ4ToC2+63wkxN9p0iWs7yI261wkh+kBB3YyZ02pmhsTnenY0qluXR3PyeYQ4nz9DXVhLPQl/UVA3U+a0mpkhWUM9Lf0q3Bo+Q8B66kn4je6pmyE+ryCmC2upJ2C5j+a0ls/QWupJ+I+Cuhniw/Ox9cFa6mnJrOUztJZ6Ev6joG6G7h1cpVIxXq4gpg1rqacls5bP0FrqSfiPgroZspYpTtZST0tmLZ+htdST8B8tPmMEnV14wlpG2lpLPS2ZtXyGna0nLT5DjIWCuhHQHzQh1o2+A4ixUPc7IYQQYiEoqBNCCCEWgoI6IYQQYiFoRTnCC9YyEMscUdsTwh8U1InZo+U5TYfanhB+oe53YtZoeU7TobYnhH8oqBOzRstzmg61PSH8Q0GdmDVantN0qO0J4R/eBPWKigpMmzYNIpEIYrEYcXFxqKlpvxuwvr4e8+bNQ48ePeDq6oro6GgoFAq1NMXFxYiMjISzszO8vLywaNEiNDU1aTxeZmYmbG1tERQUpK9qkQ7Q8pymQ21PCP/wZkW5p556CiUlJdi0aROUSiVmzZqFBx98ELt3724zz9y5c3Hw4EFs374dbm5uSEhIgFAoRGZmJgCgubkZQUFBkEqlWLVqFUpKShAbG4vZs2dj+fLlaseqrKxESEgI+vfvD4VCgfz8fK3LTqtJdR2NwDYdavuuo+8AYiy8COqFhYUIDAzE8ePHERoaCgBIS0vDhAkTcP36dfj4+LTKU1VVBU9PT+zevRtTpkwBAJw7dw6DBw9GdnY2Ro0ahe+//x4TJ07EzZs3IZFIAAApKSl48803UVZWBnt7e+54U6dOxYABA2BjY4P9+/e3G9QbGhrQ0NDA/bu6uhq+vr70B02IlaKgToyFF93v2dnZEIvFXEAHgPDwcAiFQuTk5GjMk5eXB6VSifDwcG5bQEAAevfujezsbO64w4YN4wI6AERERKC6uhpnz57ltm3btg2XLl3CsmXLtCpvcnIy3NzcuJevL00BIoQQYni8COpyuRxeXl5q22xtbdG9e3fI5fI289jb20MsFqttl0gkXB65XK4W0Fv2t+wDgPPnz2Px4sX48ssvYWur3bT+JUuWoKqqintdu3ZNq3ydcbGsBlkXy2ma0X2oXdpGbaMZtQuxBCZdfGbx4sX46KOP2k1TWFhopNK01tzcjL/97W949913MXDgQK3zOTg4wMHBwYAlu4sWBtGM2qVt1DaaUbsQS2HSoL5w4ULMnDmz3TR9+/aFVCpFaWmp2vampiZUVFRAKpVqzCeVStHY2IjKykq1q3WFQsHlkUqlyM3NVcvXMjpeKpXi9u3bOHHiBE6dOoWEhAQAgEqlAmMMtra2+PHHH/H444/rUmW9uX9hkPLaBuw8dhXBfdytejATtUvbqG00o3YhlsSkQd3T0xOenp4dppPJZKisrEReXh5CQkIAAIcPH4ZKpUJYWJjGPCEhIbCzs0NGRgaio6MBAEVFRSguLoZMJuOO++GHH6K0tJTr3k9PT4dIJEJgYCDs7Oxw5swZteN+9tlnOHz4MPbt2wd/f/9O172rWhYG6e3uzC0MUnyrDorqeqv+IqJ2aRu1jWbULsSS8GLt98GDB2P8+PGYPXs2UlJSoFQqkZCQgKlTp3Ij32/cuIFx48Zh586dGDlyJNzc3BAXF4fExER0794dIpEI8+fPh0wmw6hRowAATz75JAIDAzF9+nSsXLkScrkcSUlJmDdvHtd9PnToULWyeHl5wdHRsdV2Y7t3YRAPFwdaGOR/qF3aRm2jGbULsSS8GCgHALt27UJAQADGjRuHCRMm4OGHH8bmzZu5/UqlEkVFRairq+O2rVmzBhMnTkR0dDQeffRRSKVSfPPNN9x+GxsbHDhwADY2NpDJZHjxxRcRGxuL9957z6h16wxaGESzrrYLnwZL6VpWOmc0o3YhloQX89T5zpBzVGlhEM060y58GizVlbLSOaOZIduF5qkTY6GgbgT0B23+LpbVYMGefDDGuC5YgUCANTFBZhf4+FRWchd9BxBj4U33OyGGxKcnkvGprIQQ46KgTgi6/kSyrtyL1zUvPT2NENIWXox+J8TQWgZL7Tx2FcW36rj71Np0Z3fl/nZn8nalrIQQy0ZBnZD/mRLqi+A+7joNlurKwiVdyduZshJCLB91vxNyj36erhjdz0PrINmV+9tdvTeua1kJIZaPgjohXdCV+9t0b5wQom8U1Anpgq4sXEKLnhBC9I3mqRsBzVG1fF1ZuIQWg7F89B1AjIUGyhGiB/08XTsdkLuSlxBC7kVB3crQVSGxFnSuE2tEQd2K8Gltc0K6gs51Yq1ooJyVuH9ONGMMO49d5cXTyAjRBZ3rxJpRULcStF44sRZ0rhNrRkHdStCcaGIt6Fwn1oyCupWgOdHEWtC5TqwZzVM3AnOao0ojgom1MKdz3Zy+A4hlo9HvVobmRBNrQec6sUa86X6vqKjAtGnTIBKJIBaLERcXh5qa9kez1tfXY968eejRowdcXV0RHR0NhUKhlqa4uBiRkZFwdnaGl5cXFi1ahKamJrU0DQ0NePvtt9GnTx84ODjAz88PW7du1XsdCSGEkK7gzZX6tGnTUFJSgvT0dCiVSsyaNQvx8fHYvXt3m3kWLFiAgwcPYu/evXBzc0NCQgImT56MzMxMAEBzczMiIyMhlUqRlZWFkpISxMbGws7ODsuXL+eO8/zzz0OhUODzzz9H//79UVJSApVKZfA6E0IIITphPFBQUMAAsOPHj3Pbvv/+eyYQCNiNGzc05qmsrGR2dnZs79693LbCwkIGgGVnZzPGGDt06BATCoVMLpdzaTZu3MhEIhFraGjg3sfNzY39+eefWpe3vr6eVVVVca9r164xAKyqqkqnehNCLENVVRV9BxCj4EX3e3Z2NsRiMUJDQ7lt4eHhEAqFyMnJ0ZgnLy8PSqUS4eHh3LaAgAD07t0b2dnZ3HGHDRsGiUTCpYmIiEB1dTXOnj0LAPjuu+8QGhqKlStXomfPnhg4cCBef/113Llzp83yJicnw83NjXv5+tJKVoQQQgyPF93vcrkcXl5eattsbW3RvXt3yOXyNvPY29tDLBarbZdIJFweuVyuFtBb9rfsA4BLly7h119/haOjI/7zn/+gvLwcL7/8Mv78809s27ZN43svWbIEiYmJ3L+rq6spsBNCCDE4k16pL168GAKBoN3XuXPnTFlEqFQqCAQC7Nq1CyNHjsSECRPwySefYMeOHW1erTs4OEAkEqm9CCGEEEMz6ZX6woULMXPmzHbT9O3bF1KpFKWlpWrbm5qaUFFRAalUqjGfVCpFY2MjKisr1a7WFQoFl0cqlSI3N1ctX8vo+JY03t7e6NmzJ9zc3Lg0gwcPBmMM169fx4ABA7SqKyGEEGJoJg3qnp6e8PT07DCdTCZDZWUl8vLyEBISAgA4fPgwVCoVwsLCNOYJCQmBnZ0dMjIyEB0dDQAoKipCcXExZDIZd9wPP/wQpaWlXPd+eno6RCIRAgMDAQAPPfQQ9u7di5qaGri63p3z+scff0AoFKJXr15dawCeMafFPIh1oHOOEN3wZkW5p556CgqFAikpKdyUttDQUG5K240bNzBu3Djs3LkTI0eOBADMnTsXhw4dwvbt2yESiTB//nwAQFZWFoC7U9qCgoLg4+ODlStXQi6XY/r06fjHP/7BTWmrqanB4MGDMWrUKLz77rsoLy/HP/7xD4wZMwZbtmzRquyWsJoUPcqSGJslnXOW8B1A+IEXo98BYNeuXQgICMC4ceMwYcIEPPzww9i8eTO3X6lUoqioCHV1ddy2NWvWYOLEiYiOjsajjz4KqVSKb775httvY2ODAwcOwMbGBjKZDC+++CJiY2Px3nvvcWlcXV2Rnp6OyspKhIaGYtq0aZg0aRLWrVtnnIqbAXqUJTE2OucI6RzeXKnzGd9/pWddLMc7+39Hb3dnCIUCqFQMxbfq8H7UUIzu52Hq4hELZGnnHN+/Awh/8OZKnZgOPcqSGBudc4R0DgV10iF6lCUxNjrnCOkc6n43AkvpeqORyMTYLOWcs5TvAGL+eLGiHDEP9ChLYmx0zhGiG+p+J4QQQiwEBXVCCCHEQlBQJ4QQQiwEBXVCCCHEQtBAOWJ0ljKimbSPPmdCjI+COjEqS1rPm7SNPmdCTIO634nR0Hre1oE+Z0JMh4I6MRpFdT1qG5rg4eIAoVAADxcH1DY0QVFdb+qiET2iz5kQ06GgToyG1vO2DvQ5E2I6FNSJ0dB63taBPmdCTIfWfjcCWvdZHY2Ktg70Of+FvgOIsdDod2J0tJ63daDPmRDjo+53QgghxELwJqhXVFRg2rRpEIlEEIvFiIuLQ01N+1Nk6uvrMW/ePPTo0QOurq6Ijo6GQqFQS1NcXIzIyEg4OzvDy8sLixYtQlNTk1qaXbt2YcSIEXB2doa3tzf+/ve/488//9R7HYnuLpbVIOtiOU2X0gNqS0L4jzfd79OmTUNJSQnS09OhVCoxa9YsxMfHY/fu3W3mWbBgAQ4ePIi9e/fCzc0NCQkJmDx5MjIzMwEAzc3NiIyMhFQqRVZWFkpKShAbGws7OzssX74cAJCZmYnY2FisWbMGkyZNwo0bNzBnzhzMnj0b33zzjVHqTjSjBU70h9qSEMvAi4FyhYWFCAwMxPHjxxEaGgoASEtLw4QJE3D9+nX4+Pi0ylNVVQVPT0/s3r0bU6ZMAQCcO3cOgwcPRnZ2NkaNGoXvv/8eEydOxM2bNyGRSAAAKSkpePPNN1FWVgZ7e3usXr0aGzduxMWLF7ljr1+/Hh999BGuX7+uVflpkIz+XSyrwYI9+WCMwcPFAeW1DRAIBFgTE0T3cXVEbWl49B1AjIUX3e/Z2dkQi8VcQAeA8PBwCIVC5OTkaMyTl5cHpVKJ8PBwbltAQAB69+6N7Oxs7rjDhg3jAjoAREREoLq6GmfPngUAyGQyXLt2DYcOHQJjDAqFAvv27cOECRPaLG9DQwOqq6vVXkS/aIET/aG2JMRy8CKoy+VyeHl5qW2ztbVF9+7dIZfL28xjb28PsVistl0ikXB55HK5WkBv2d+yDwAeeugh7Nq1CzExMbC3t4dUKoWbmxs2bNjQZnmTk5Ph5ubGvXx9qRtT32iBE/2htiTEcpg0qC9evBgCgaDd17lz50xZRBQUFODVV1/F0qVLkZeXh7S0NFy5cgVz5sxpM8+SJUtQVVXFva5du2bEElsHWuBEf6gtCbEcJh0ot3DhQsycObPdNH379oVUKkVpaana9qamJlRUVEAqlWrMJ5VK0djYiMrKSrWrdYVCweWRSqXIzc1Vy9cyOr4lTXJyMh566CEsWrQIADB8+HC4uLjgkUcewQcffABvb+9W7+3g4AAHB4d260W6bkqoL4L7uOt1gRM+LZiiz7Iaoi0JIcZn0qDu6ekJT0/PDtPJZDJUVlYiLy8PISEhAIDDhw9DpVIhLCxMY56QkBDY2dkhIyMD0dHRAICioiIUFxdDJpNxx/3www9RWlrKde+np6dDJBIhMDAQAFBXVwdbW/VmsrGxAQDwYIyhxdPnAid8GgFuiLLSYjGE8B8v7qkPHjwY48ePx+zZs5Gbm4vMzEwkJCRg6tSp3Mj3GzduICAggLvydnNzQ1xcHBITE3HkyBHk5eVh1qxZkMlkGDVqFADgySefRGBgIKZPn47Tp0/jhx9+QFJSEubNm8ddaU+aNAnffPMNNm7ciEuXLiEzMxOvvPIKRo4cqXHUPeEnQz8uVJ9zwOnRpoSQtvBmnvquXbuQkJCAcePGQSgUIjo6GuvWreP2K5VKFBUVoa6ujtu2Zs0aLm1DQwMiIiLw2WefcfttbGxw4MABzJ07FzKZDC4uLpgxYwbee+89Ls3MmTNx+/ZtfPrpp1i4cCHEYjEef/xxfPTRR8apODGKlhHgvd2duRHgxbfqoKiu7/LVq76vqg1ZVkIIv/Finjrf0RxV82eoudqGOC7NK+cf+g4gxsKL7ndCDM1QI8ANMQecRqsTQtrCm+53QgzNECPA750D3nJVrY854DRanRCiCQV1Qu6h7xHgLVfVO49dRfGtOu6euj7eg0arE0LuR0GdEAOjq2pCiLFQUCfECOiqmhBiDBTUjaBlggE92IUQ69Tyt0+TjYihUVA3gtu3bwMAPdiFECt3+/ZtuLm5mboYxILRPHUjUKlUuHnzJrp16waBQGDq4uhddXU1fH19ce3aNZqD2wZqo/ZZevswxnD79m34+PhAKKSZxMRw6ErdCIRCIXr16mXqYhicSCSyyC9kfaI2ap8ltw9doRNjoJ+MhBBCiIWgoE4IIYRYCArqpMscHBywbNkyeoZ8O6iN2kftQ4h+0EA5QgghxELQlTohhBBiISioE0IIIRaCgjohhBBiISioE0IIIRaCgjpppaKiAtOmTYNIJIJYLEZcXBxqamrazVNfX4958+ahR48ecHV1RXR0NBQKhVqa4uJiREZGwtnZGV5eXli0aBGampq4/UePHoVAIGj1ksvlBqmnLjZs2AA/Pz84OjoiLCwMubm57abfu3cvAgIC4OjoiGHDhuHQoUNq+xljWLp0Kby9veHk5ITw8HCcP39eLU1nPgdTMUX7+Pn5tTpXVqxYofe6EcIrjJD7jB8/no0YMYIdO3aM/fLLL6x///7shRdeaDfPnDlzmK+vL8vIyGAnTpxgo0aNYqNHj+b2NzU1saFDh7Lw8HB26tQpdujQIebh4cGWLFnCpTly5AgDwIqKilhJSQn3am5uNlhdtZGamsrs7e3Z1q1b2dmzZ9ns2bOZWCxmCoVCY/rMzExmY2PDVq5cyQoKClhSUhKzs7NjZ86c4dKsWLGCubm5sf3797PTp0+zp59+mvn7+7M7d+5waTrzOZiCqdqnT58+7L333lM7V2pqagxeX0LMGQV1oqagoIABYMePH+e2ff/990wgELAbN25ozFNZWcns7OzY3r17uW2FhYUMAMvOzmaMMXbo0CEmFAqZXC7n0mzcuJGJRCLW0NDAGPsrqN+6dcsANeu8kSNHsnnz5nH/bm5uZj4+Piw5OVlj+ueff55FRkaqbQsLC2MvvfQSY4wxlUrFpFIpW7VqFbe/srKSOTg4sK+++oox1rnPwVRM0T6M3Q3qa9as0WNNCOE/6n4narKzsyEWixEaGsptCw8Ph1AoRE5OjsY8eXl5UCqVCA8P57YFBASgd+/eyM7O5o47bNgwSCQSLk1ERASqq6tx9uxZteMFBQXB29sbTzzxBDIzM/VZPZ01NjYiLy9PrW5CoRDh4eFc3e6XnZ2tlh64W9eW9JcvX4ZcLldL4+bmhrCwMLX20vVzMAVTtU+LFStWoEePHggODsaqVavUbucQYo3ogS5EjVwuh5eXl9o2W1tbdO/evc1723K5HPb29hCLxWrbJRIJl0cul6sF9Jb9LfsAwNvbGykpKQgNDUVDQwP+7//+D2PHjkVOTg4eeOABfVRPZ+Xl5WhubtZY9nPnzmnM01Zd722Llm3tpdH1czAFU7UPALzyyit44IEH0L17d2RlZWHJkiUoKSnBJ5980uV6EcJXFNStxOLFi/HRRx+1m6awsNBIpdFs0KBBGDRoEPfv0aNH4+LFi1izZg2++OILE5aMmKPExETu/4cPHw57e3u89NJLSE5OpuVmidWioG4lFi5ciJkzZ7abpm/fvpBKpSgtLVXb3tTUhIqKCkilUo35pFIpGhsbUVlZqXa1rlAouDxSqbTViOiW0fFtHRcARo4ciV9//bXdchuSh4cHbGxsWo3kv7du95NKpe2mb/mvQqGAt7e3WpqgoCAuja6fgymYqn00CQsLQ1NTE65cuaL245AQa0L31K2Ep6cnAgIC2n3Z29tDJpOhsrISeXl5XN7Dhw9DpVIhLCxM47FDQkJgZ2eHjIwMbltRURGKi4shk8kAADKZDGfOnFELVOnp6RCJRAgMDGyz3Pn5+Wpf7MZmb2+PkJAQtbqpVCpkZGRwdbufTCZTSw/crWtLen9/f0ilUrU01dXVyMnJUWsvXT8HUzBV+2iSn58PoVDY6rYFIVbF1CP1iPkZP348Cw4OZjk5OezXX39lAwYMUJtKdf36dTZo0CCWk5PDbZszZw7r3bs3O3z4MDtx4gSTyWRMJpNx+1umtD355JMsPz+fpaWlMU9PT7UpbWvWrGH79+9n58+fZ2fOnGGvvvoqEwqF7KeffjJOxduQmprKHBwc2Pbt21lBQQGLj49nYrGYG8k/ffp0tnjxYi59ZmYms7W1ZatXr2aFhYVs2bJlGqdsicVi9u2337LffvuNPfPMMxqntLX3OZgLU7RPVlYWW7NmDcvPz2cXL15kX375JfP09GSxsbHGrTwhZoaCOmnlzz//ZC+88AJzdXVlIpGIzZo1i92+fZvbf/nyZQaAHTlyhNt2584d9vLLLzN3d3fm7OzMnn32WVZSUqJ23CtXrrCnnnqKOTk5MQ8PD7Zw4UKmVCq5/R999BHr168fc3R0ZN27d2djx45lhw8fNnh9tbF+/XrWu3dvZm9vz0aOHMmOHTvG7RszZgybMWOGWvqvv/6aDRw4kNnb27MhQ4awgwcPqu1XqVTsnXfeYRKJhDk4OLBx48axoqIitTQdfQ7mxNjtk5eXx8LCwpibmxtzdHRkgwcPZsuXL2f19fUGrSch5o4evUoIIYRYCLqnTgghhFgICuqEEEKIhaCgTgghhFgICuqEEEKIhaCgTgghhFgICuqEEEKIhaCgTgghhFgICuqEEEKIhaCgTkgXFRUVQSqV4vbt20Z/77S0NAQFBUGlUhn9vQkh5oeCOrF6zc3NGD16NCZPnqy2vaqqCr6+vnj77bfbzb9kyRLMnz8f3bp1M2QxNRo/fjzs7Oywa9cuo783IcT80DKxhAD4448/EBQUhC1btmDatGkAgNjYWJw+fRrHjx+Hvb29xnzFxcXo378/Ll++jJ49exqzyJwNGzZg+/btOH78uEnenxBiPuhKnRAAAwcOxIoVKzB//nyUlJTg22+/RWpqKnbu3NlmQAeAr7/+GiNGjFAL6Nu3b4dYLMaBAwcwaNAgODs7Y8qUKairq8OOHTvg5+cHd3d3vPLKK2hububy+fn54YMPPkBsbCxcXV3Rp08ffPfddygrK8MzzzwDV1dXDB8+HCdOnFArw6RJk3DixAlcvHhR/w1DCOEVCuqE/M/8+fMxYsQITJ8+HfHx8Vi6dClGjBjRbp5ffvkFoaGhrbbX1dVh3bp1SE1NRVpaGo4ePYpnn30Whw4dwqFDh/DFF19g06ZN2Ldvn1q+NWvW4KGHHsKpU6cQGRmJ6dOnIzY2Fi+++CJOnjyJfv36ITY2Fvd2sPXu3RsSiQS//PKLfhqCEMJbtqYuACHmQiAQYOPGjRg8eDCGDRuGxYsXd5jn6tWrGoO6UqnExo0b0a9fPwDAlClT8MUXX0ChUMDV1RWBgYF47LHHcOTIEcTExHD5JkyYgJdeegkAsHTpUmzcuBEPPvggnnvuOQDAm2++CZlMBoVCAalUyuXz8fHB1atXu1R/Qgj/0ZU6IffYunUrnJ2dcfnyZVy/fr3D9Hfu3IGjo2Or7c7OzlxABwCJRAI/Pz+4urqqbSstLVXLN3z4cLX9ADBs2LBW2+7P5+TkhLq6ug7LSwixbBTUCfmfrKwsrFmzBgcOHMDIkSMRFxeHjsaRenh44NatW62229nZqf1bIBBo3Hb/VLR70wgEgja33Z+voqICnp6e7ZaVEGL5KKgTgrv3wGfOnIm5c+fisccew+eff47c3FykpKS0my84OBgFBQVGKqVm9fX1uHjxIoKDg01aDkKI6VFQJwR355ozxrBixQoAd0eir169Gm+88QauXLnSZr6IiAhkZ2erjWI3tmPHjsHBwQEymcxkZSCEmAcK6sTq/b//9/+wYcMGbNu2Dc7Oztz2l156CaNHj263G/6pp56Cra0tfvrpJ2MVt5WvvvoK06ZNUys7IcQ60eIzhHTRhg0b8N133+GHH34w+nuXl5dj0KBBOHHiBPz9/Y3+/oQQ80JT2gjpopdeegmVlZW4ffu20ZeKvXLlCj777DMK6IQQAHSlTgghhFgMuqdOCCGEWAgK6oQQQoiFoKBOCCGEWAgK6oQQQoiFoKBOCCGEWAgK6oQQQoiFoKBOCCGEWAgK6oQQQoiFoKBOCCGEWIj/D4bVubL07bwMAAAAAElFTkSuQmCC",
                        "text/plain": [
                            "<Figure size 1200x400 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "spot.view()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Conclusions\n",
                "\n",
                "- This notebook demonstrated how a random forest regressor can be trained to predict optimal lens parameters to achieve a minimal RMS spot size.\n",
                "- Although we chose a random forest model, other (likely simpler) models could also have been used.\n",
                "- Additional hyperparameter tuning or an expanded dataset would likely improve the model performance further."
            ]
        }
    ],
    "metadata": {
        "kernelspec": {
            "display_name": ".venv",
            "language": "python",
            "name": "python3"
        },
        "language_info": {
            "codemirror_mode": {
                "name": "ipython",
                "version": 3
            },
            "file_extension": ".py",
            "mimetype": "text/x-python",
            "name": "python",
            "nbconvert_exporter": "python",
            "pygments_lexer": "ipython3",
            "version": "3.11.1"
        }
    },
    "nbformat": 4,
    "nbformat_minor": 2
}