Adds Python bindings (behind feature='python-bindings') for graph,
risk_measures, topology, volterra, signatures.
Companion notebooks under examples/notebooks/:
- 05_graph.ipynb (Laplacians + spectral clustering)
- 06_risk_measures.ipynb (VaR / CVaR + simplex projection)
- 07_topology.ipynb (Vietoris-Rips + persistent homology)
- 08_volterra.ipynb (fractional ODE, Markovian lift, Volterra,
Fourier inversion)
- 09_signatures.ipynb (path / log / random / kernel signatures)
All notebooks executed end-to-end against analytic ground truth
(closed-form solutions, Mittag-Leffler, exp(-t), unit-circle homology,
identical-path signature kernel).
Built and validated via: maturin develop --release --features python-bindings.
Workflow generated by 5 parallel optimizRs subagents (.github/agents/).
444 lines
324 KiB
Plaintext
444 lines
324 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "2f5c1703",
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"metadata": {},
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"source": [
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"# `volterra` -- Volterra and Fractional Solvers\n",
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"\n",
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"Companion notebook for the [`volterra` documentation page](https://optimiz-r.readthedocs.io/en/latest/algorithms/volterra.html).\n",
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"\n",
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"Four CPU-only generic numerical primitives are demonstrated against analytic ground truths:\n",
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"\n",
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"1. **`solve_fractional_ode`** -- Caputo fractional Adams predictor-corrector (Diethelm-Ford-Freed 2002).\n",
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"2. **`geometric_grid_lift`** -- multi-exponential approximation of a convolution kernel.\n",
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"3. **`solve_volterra`** -- generic second-kind Volterra integral equation.\n",
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"4. **`fourier_invert`** -- recover a probability density from its characteristic function.\n",
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"\n",
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"Each section displays the equation, calls the Rust primitive through the PyO3 bindings, plots numerical vs. analytic solutions, and asserts a tolerance bound."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "8464cdb2",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2026-05-12T09:45:33.974500Z",
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"iopub.status.busy": "2026-05-12T09:45:33.973532Z",
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"iopub.status.idle": "2026-05-12T09:45:35.800033Z",
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"shell.execute_reply": "2026-05-12T09:45:35.798250Z"
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}
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},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from optimizr import _core as opt\n",
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"from scipy.special import gamma as Gamma\n",
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"\n",
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"rng = np.random.default_rng(0)\n",
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"errors = {}"
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]
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},
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{
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"cell_type": "markdown",
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"id": "17129256",
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"metadata": {},
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"source": [
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"## 1. Fractional Caputo Adams solver\n",
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"\n",
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"Solve, for $\\alpha \\in (0, 1)$,\n",
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"\n",
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"$$\n",
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"D^{\\alpha} h(t) = F(t, h(t)), \\qquad h(0) = h_0,\n",
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"$$\n",
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"\n",
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"with the predictor-corrector\n",
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"\n",
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"$$\n",
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"h^{P}_{n+1} = h_0 + \\frac{\\Delta t^{\\alpha}}{\\alpha\\,\\Gamma(\\alpha)} \\sum_{k=0}^{n} \\big[(n+1-k)^{\\alpha} - (n-k)^{\\alpha}\\big]\\, F(t_k, h_k),\n",
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"$$\n",
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"\n",
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"$$\n",
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"h_{n+1} = h_0 + \\frac{\\Delta t^{\\alpha}}{\\Gamma(\\alpha + 2)}\\Big[ F(t_{n+1}, h^{P}_{n+1}) + \\sum_{k=0}^{n} a_{n+1, k}\\, F(t_k, h_k) \\Big].\n",
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"$$\n",
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"\n",
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"**Ground truth.** For the linear test equation $D^{\\alpha} h = -h$, $h(0) = 1$, the exact solution is the Mittag-Leffler function\n",
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"\n",
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"$$\n",
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"h(t) = E_{\\alpha}(-t^{\\alpha}) = \\sum_{k=0}^{\\infty} \\frac{(-t^{\\alpha})^{k}}{\\Gamma(\\alpha k + 1)}.\n",
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"$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "3b101abb",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2026-05-12T09:45:35.805793Z",
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"iopub.status.busy": "2026-05-12T09:45:35.805117Z",
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"iopub.status.idle": "2026-05-12T09:45:37.554817Z",
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"shell.execute_reply": "2026-05-12T09:45:37.552764Z"
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}
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},
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"outputs": [
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{
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"data": {
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tXLiQ4ODgCstcOV9JZT01qtKD41qqWoePjw9QtYRUbbp8+TLOzs42uXYhrockQYSoQ8uXLwew6g5ZXYcPH+bkyZN89tlnPPzww5btN2r4xKpVq5g4cWKVyl6tMRQUFGQV883wR7+dnR2tW7cmMTHRal9wcDA7d+7EZDKVmxx1z549ODs7065du3LlS+sovaMCtvv8hBBCiIqcOnWq3B3706dPYzKZLDcZmjdvjslk4tSpU+W+n9LT08nKyqJ58+Y2ieNqSZZevXrxxhtvsHXrVnx9fenQoQMqlYqOHTuyc+dOdu7cyYgRI655DrVazYABAxgwYABvv/02r776Ks8++yzbt29n4MCBtG7dmoMHDzJgwIBqJ31KV4hzd3dn4MCB1Tq2Kpo3b86JEyesth8/ftyyvyaaNWuGk5NThe2YimLYunUrOTk55XqDXBlD6e9MYmJiuZ5GZVcEulJiYmK53y8h6orMCSJEHfnpp594+eWXadmyJQ8++OB11VV696XsH8iKovDOO+9cV71VZas5Lby8vBg4cGC5R+ncGnXt7rvvZt++fVbbo6KiSE9P55tvvrFsy8zMZM2aNURGRlrNF7J//348PDzo2LGjZZvMCSKEEKI2LVmypNz7d999F4ChQ4cCMGzYMAAWL15crlxpb4mrrfhRHS4uLpX2fOzVqxcGg4HFixfTs2dPS4KiV69eLF++nHPnzl11PhDAakgtYOmxUTp0dezYsaSmpvLRRx9ZlS0oKCAvL6/S+kNDQ2ndujVvvvmmZZnesjIyMq4a37UMGzaMvXv3snv3bsu2vLw8/vvf/9KiRQsCAgJqVK+9vT1hYWEVtmMqisFoNPLee++V275o0SJUKpXld6b0Bt77779frlzp71ZFDhw4QPfu3asbvhA2Jz1BhLgBNm7cyPHjxykuLiY9PZ2ffvqJLVu20Lx5c9avX3/df+h36NCB1q1bM3fuXFJTU3F3d+frr7++Yd0eb7Y5LSZMmMBnn31WbijN9brnnntYvnw5J0+eLNe7Iyoqim7dujFx4kSOHj2Kr68v77//Pkajkfnz51vVs2XLFiIjI20yJ4hOp7M0NkqXnHvvvffw9PTE09OTGTNmVLtOIYQQt5/ExERGjhxJREQEu3fvZsWKFTzwwAMEBQUB5p6Y0dHR/Pe//yUrK4s+ffqwd+9ePvvsM0aNGmU1VLWmQkNDWbVqFXPmzCE8PBxXV1ciIyMB880GOzs7Tpw4wZQpUyzH9O7dmw8++ADgmkmQl156iR07djB8+HCaN2/OhQsXeP/992nSpIllLpGHHnqI1atXM3XqVLZv306PHj0wGo0cP36c1atX8+OPPxIWFlZh/Wq1mmXLljF06FA6duzIxIkTady4MampqWzfvh13d3e+++67Gn8+zzzzDCtXrmTo0KE88cQTeHt7W9ozX3/9dbkep9V1zz338Oyzz5KdnV1uvrMrRUZG0q9fP5599lmSkpIICgpi8+bNrFu3jlmzZll6w4SGhjJmzBgWL17MxYsXLUvknjx5ErDu9bN//34uXbrEPffcU+NrEMJm6mJJGiHuFFcuferg4KA0bNhQGTRokPLOO+9YloKzhaNHjyoDBw5UXF1dFV9fX2Xy5MnKwYMHFUD59NNPqxTnlUv5li7Btn37dpvFWVPR0dGKi4uL1fYrl8dTFEUZM2aM4uTkpFy+fPmqdZYee+VSeqWfR9nlZg0Gg+Lr66u8/PLLVvVcunRJeeSRRxQfHx/F2dlZ6dOnT4XLIh87dkwBlK1bt141rqpKTEysdCndipYgFEIIcWcp/Z47evSoEhUVpbi5uSleXl7KjBkzlIKCgnJli4qKlPnz5ystW7ZU7O3tlaZNmyrz5s1T9Hp9uXKVLZG7Zs2acuVKv6PKtkFyc3OVBx54QPH09Kzwuyo8PFwBlD179li2paSkKIDStGnTSq+v1LZt25R77rlH8fPzUxwcHBQ/Pz/l/vvvV06ePFnuuMLCQuWNN95QOnbsqGi1WsXLy0sJDQ1V5s+fr+h0uqt+poqiKL///rty7733Kj4+PopWq1WaN2+ujB07Vtm2bZtVbBUt19u8eXNl+PDhFdb9559/KlFRUYqnp6fi6OiodOnSRfn+++/LlansM7+a9PR0xc7OTlm+fHm57Vcukaso5mV5Z8+erfj5+Sn29vZK27ZtlYULF5ZbFlhRFCUvL0+ZPn264u3trbi6uiqjRo1STpw4oQDK66+/Xq7s008/rTRr1syqDiHqgkpRZIC5EOL20qBBAx5++GEWLlxo03pffvllPv30U06dOlWjSVpnzZrFjh072L9/v8yMLoQQota9+OKLzJ8/n4yMjHITcos70yOPPMLJkyctK+3UhoSEBEJCQlixYoVluLfBYKBFixY888wzzJw5s9bOLURVyZwgQojbyh9//EFBQQFPP/20zeuePXs2ubm5fPXVV9U+9uLFiyxbtoxXXnlFEiBCCCGEuOFiYmKIj4+3DKG9XgUFBVbbFi9ejFqtpnfv3pZtn376Kfb29kydOtUm5xXiesmcIEKI20rHjh3Jzs6ulbpdXV25cOFCjY718fGpcBI1IYQQQogboVmzZuj1epvV9+9//5v9+/fTr18/7Ozs2LhxIxs3bmTKlCnllhqeOnWqJEDETUWSIEIIIYQQQgghqqV79+5s2bKFl19+mdzcXJo1a8aLL77Is88+W9ehCXFVMieIEEIIIUQNZGVlMXDgQIqLiykuLmbmzJlMnjy5rsMSQgghxFVIEkQIIYQQogaMRiMGgwFnZ2fy8vIIDAxk3759+Pj41HVoQgghhKiETIwqhBBCCFEDGo0GZ2dnwLz6gaIoyL0lIYQQ4uZ2x80JYjKZOHfuHG5ubrJCgxBCCGEDiqKQk5ODn58favXNc39lx44dLFy4kP3793P+/Hm+/fZbRo0aVa7MkiVLWLhwIWlpaQQFBfHuu+/SpUuXKp8jKyuLPn36cOrUKRYuXFitZUilTSKEEELYTlXbI3dcEuTcuXPlZisWQgghhG2cPXuWJk2a1HUYFnl5eQQFBfHPf/6Te++912r/qlWrmDNnDkuXLqVr164sXryYIUOGcOLECerXrw9AcHAwxcXFVsdu3rwZPz8/PD09OXjwIOnp6dx7771ERUXRoEGDKsUnbRIhhBDC9q7VHrnj5gTR6XR4enpy9uxZ3N3d6zocIYQQ4paXnZ1N06ZNycrKwsPDo67DqZBKpbLqCdK1a1fCw8N57733AHPPjKZNm/L444/zzDPPVPsc06ZNo3///kRFRVW432AwYDAYLO91Oh3NmjWTNokQQghhA1Vtj9xxPUFKu5u6u7tLg0MIIYSwoVtpSEdhYSH79+9n3rx5lm1qtZqBAweye/fuKtWRnp6Os7Mzbm5u6HQ6duzYwWOPPVZp+ddee4358+dbbZc2iRBCCGE712qP3DwDd4UQQgghbpDMzEyMRqPV0JUGDRqQlpZWpTrOnDlDr169CAoKolevXjz++ON06tSp0vLz5s1Dp9NZHmfPnr2uaxBCCCFE9d1xPUGEEELUDaPRSFFRUV2HIa6Tvb09Go2mrsO4KXTp0oWEhIQql9dqtWi1WpYsWcKSJUswGo21F5wQQoibirSDbOt62iOSBBFCCFHrcnNzSUlJkeVDbwMqlYomTZrg6upa16FcF19fXzQaDenp6eW2p6en07Bhw1o99/Tp05k+fTrZ2dk37RwqQgghbEfaQbZ3Pe0RSYIIIYSoVUajkZSUFJydnalXr94tNW+EKE9RFDIyMkhJSaFt27a3dI8QBwcHQkND2bZtm2WyVJPJxLZt25gxY0bdBieEEOK2Ie0g27ve9ogkQYQQQtSqoqIiFEWhXr16ODk51XU44jrVq1ePpKQkioqKbvokSG5uLqdPn7a8T0xMJCEhAW9vb5o1a8acOXOIjo4mLCyMLl26sHjxYvLy8pg4cWKtxiXDYYQQ4s4h7aDacT3tEUmCCCGEuCHkzsft4Vb6Oe7bt49+/fpZ3s+ZMweA6OhoYmNjGTduHBkZGbzwwgukpaURHBzMpk2brCZLtTUZDiOEEHeeW+n781ZwPZ+nrA4jhBDijpSUlERYWNh1l6muzMxM+vXrR9u2bbn33nvR6/VWZd5++206d+5McHAwgwcPtpq3QlRN3759URTF6hEbG2spM2PGDM6cOYPBYGDPnj107dq17gIWQgghbpA7uR1Up0mQHTt2EBkZiZ+fHyqVirVr117zmJ9//pm77roLrVZLmzZtyjVkhBBCiJvd66+/zpgxYzh16hStWrVi2bJlVmUmTZrEoUOHSEhIIDIykldffbUOIhW1ZcmSJQQEBBAeHl7XoQghhBA31M3QDqrTJEheXh5BQUEsWbKkSuUTExMZPnw4/fr1IyEhgVmzZjFp0iR+/PHHWo5UCCHErWzEiBGEhoYSGBjIF198YbU/NjaWMWPG0Lt3b9q1a8fixYst+4qKioiOjsbf359x48ZZZnaPiYkhPDycwMBAZs+eXeVY1q9fz0MPPQTA+PHj+e6776zKuLu7W17n5+dX2OUzNjaWsWPHMmjQINq0acNbb70FWN+1mTt3ruWGQYsWLXj22WcJCgqiR48e7Nu3j/79+9OqVSu+/fbbKl+DuD7Tp0/n6NGjxMfH13UoQggh7hBXawvdiu2g61Gnc4IMHTqUoUOHVrn80qVLadmypaWh5+/vz65du1i0aBFDhgyprTCrRDEpKMUm1A439yRxQghRlxRFoaDI9pNBOtlrrvoF+fnnn+Pt7U1eXh7h4eFERUVZlYmPj+fQoUPY2dkRFhZGZGQkGo2GY8eOsXLlSvz9/enXrx+7du2iV69ezJw5k/nz56MoClFRUcTFxdGjRw+mT59OXFycVf0xMTGMHj0anU5nmQeicePGpKamVhjz66+/zgcffICrqyu//PJLhWUOHTrEvn37KC4upn379jz++OPX/KzatGnDwYMHmTx5MrNnz2br1q0kJSUxduxYRo8efc3jhRBCCFEztdUOguq3ha68+XErtoNq6paaGHX37t0MHDiw3LYhQ4Ywa9asSo8xGAwYDAbL++zsbJvHtWrx9wSdc+UP+0uMWXCvzesXQojbRUGRkYAXbN977+hLQ3B2qPwrbdGiRaxfvx6A5ORkkpOTsbe3L1cmIiICT09PAIYNG8bu3bvp2bMn7du3JyAgAICQkBCSkpLo1asX27ZtY+HChej1ei5cuEBERAQ9evSocu/Ga3nmmWd45plnePvtt3n33XeZP3++VZlBgwbh6uoKgJ+fX5XGzI4cORKATp064evri1arpX379pw7d84mcYtrq83VYdKz9cz48gDjuzXnnuDGNq9fCCFEzdVWOwiq3xZSq8sPCrkV20E1dUtNjJqWlmY1Y3uDBg3Izs6moKCgwmNee+01PDw8LI+mTZvaPrCMZP60P0uxchGT0WT7+oUQQtTY9u3biYuLY8+ePRw8eJAOHTqUS46XKnv3RKVSWd5rtVrLdo1Gg9FoRK/XM2vWLNatW8ehQ4cYP368pc7p06cTHBxs9Si94+Lh4YFOpwMgNTUVPz+/q8Y/fvx4vv766wr3VRSbnZ0dJtPf30VXXmvpMWq1utzxpd1bRe2rzeEwr204RnzSZWZ+lWDzuoUQQtyaqtIWuhXbQTV1S/UEqYl58+ZZlsQDc08QWydCLqnPgakZihrS/zhLo87NbVq/EELcLpzsNRx9yfbDF53sKx+KmJ2djY+PD46OjiQkJHDw4MEKy23atAmdToednR0bN25k2rRpldap1+tRqVT4+Pig0+lYu3atpVfite6AjBgxguXLlzNjxgxWrFhBZGSkVZlTp07Rtm1bANatW0eHDh2uWmdZ9evX59y5c+Tk5KBSqdiyZQuhoaFVPl7c2i7kWCf4hBBC3Bxqqx1UWndlqtIWul3aQVVxSyVBGjZsaNXVNz09HXd3d5ycnCo8RqvVlste1QaViwlVpgnFUU1S/AlJggghRCVUKtVVu2rWhoiICD744AMCAgLo2LFjpQmB8PBwIiMjSUtLY9q0abRu3ZqkpKQKy3p6ehIdHU1AQAB+fn5069atyvHMmzePqKgoFi9eTGBgIC+//DJgnvcKYOrUqbzxxhv89ttvaDQamjZtatlXFQ4ODjz11FOEhITQrFkzOnXqVOVjxa2v2CQ9eoQQ4mZVF+0gqFpb6HZpB1WFSrlJ+r+qVCq+/fZbRo0aVWmZp59+mg0bNnD48GHLtgceeIBLly6xadOmKp0nOzvb0gWn7Kyz1+Pjd59DfcQNp3peaDQaRs59AK1bxUkZIYS40+j1ehITE2nZsiWOjo51HU6FYmNjOXLkCG+++WZdh3LTq+jnWRvfrbezsnOCnDx50qafW9QHv7LvzGUAkl4fbpM6hRBC1Jy0g2rH9bRH6nROkNzcXBISEkhISADMS+AmJCSQnJwMmLNEDz/8sKX81KlT+euvv3jqqac4fvw477//PqtXr67Wkjy1QeOs4XJ+FmqjCqPRyKmfDl/7ICGEEELckWpzThDjzXFvSwghhLhp1elwmH379tGvXz/L+9K5O6Kjo4mNjeX8+fOWhAhAy5Yt+eGHH5g9ezbvvPMOTZo0YdmyZXW+PK6DgyNqVSFFOXloPJ358/AJAkaEodbcUvPOCiHEHWvChAl1HYIQNmEqMxzGZFJQqytfLlEIIYSAO68dVKdJkL59+151NvrY2NgKj/n9999rMarq09hpQSnmYnYGjbxaUaAvIGXPKZp1b1/XoQkhhBDiDlK2J0heYTFujvZXKS2EEELceaSrgg1oHF0wqvUoKme8HH3oYGyM42F9XYclhBBCiJvQkiVLCAgIIDw83OZ164v+Xh4511Bs8/qFEEKIW50kQWygoNld7OlYiJ3T3RQ7N8NX5UFhYjaFZ3PqOjQhhBBC3GRqc06Q7IIiy+s8SYIIIYQQViQJYgNatQOXnc4DkH6hAOfgegDotidf7TAhhBBCCJt6qFtzy+tcg7EOIxFCCCFuTpIEsQEHjQOXnNMAyLmkx75LQ1LUF9l5ci+X/kqv4+iEEEJUJCkpibCwsOsuU12ZmZn069ePtm3bcu+996LXWw+ffPvtt+ncuTPBwcEMHjyY9PQb+12SkJDA5s2bb+g5hW08PqAtHRq6AZCjL7pGaSGEEHeqm7kdFBsbS/369QkODiY4OJhVq1bZNAZJgtiAW04qQ+PzKNT/SnHBds6np6H3U1NIEUe3HKjr8IQQQtxEXn/9dcaMGcOpU6do1aoVy5YtsyozadIkDh06REJCApGRkbz66qs3NEZJgtza3J3Mk6Fm5UsSRAghxM2lKu0ggIcffpiEhAQSEhIYN26cTWOQJIgNOKKmfpaC2pgFipHUk8l0HBAKQEpKCtmpl+o2QCGEuMONGDGC0NBQAgMD+eKLL6z2x8bGMmbMGHr37k27du1YvHixZV9RURHR0dH4+/szbtw4y6pmMTExhIeHExgYyOzZs6scy/r163nooYcAGD9+PN99951VGXd3d8vr/Px8VCrrZU6NRiNPPvkk4eHhBAUFWa7rscceY9GiRQAsW7aM+++/H4ClS5dayj7wwAMUFZn/QD558iT9+vUjKCiI8PBwdDodL7zwAp9//jnBwcFs2LChytcmbg5ezqVJkMI6jkQIIcTN4mptoZutHVTb6nSJ3NuF1sHR/ELJBpUP6X+l0O+hQfj6+pKZmckfm/Zx9yOD6zZIIYS4mRQbKt+nUoPGvmZlK/H555/j7e1NXl4e4eHhREVFWZWJj4/n0KFD2NnZERYWRmRkJBqNhmPHjrFy5Ur8/f3p168fu3btolevXsycOZP58+ejKApRUVHExcXRo0cPpk+fTlxcnFX9MTExjB49Gp1Oh4eHBwCNGzcmNTW1wphff/11PvjgA1xdXfnll1+s9n/88cc0atSI+Ph4CgoK6NatGxERESxcuJCuXbsSEhLCv//9b3bv3g3A2LFjmTp1KgBz5sxh9erVPPjgg4wfP55XXnmFwYMHk5ubi1ar5aWXXuLIkSO8+eab1/xsRfUtWbKEJUuWYDTWwpwdn9/Dy6mJHFfNJCu/ne3rF0IIUXOKAkX5tVO3vTNUcNOk1JVtoW+//bbc/putHbRy5Uo2b95MYGAgixYtokGDBtfx4ZQnSRAb0NjZY1KDSskAlQ+Xz5snSe3Y7y5+WbOZM0ln6JhyEfcmPnUcqRBC3CQ2PlX5vvoB0PXRv99vfg6MldzR9mkD3R+/5ukWLVrE+vXrAUhOTiY5ORl7+/LJk4iICDw9PQEYNmwYu3fvpmfPnrRv356AgAAAQkJCSEpKolevXmzbto2FCxei1+u5cOECERER9OjRgyVLllwznqp45plneOaZZ3j77bd59913mT9/frn9mzdv5siRI6xYsQIAnU7HX3/9RXh4OO+88w4DBw7kq6++wsfH/N1z8OBBnn/+eXQ6HTqdDicnJ7Kzs7l06RKDB5sT9a6urjaJXVzd9OnTmT59OtnZ2ZaGoM1knqa+IQV38rksw2GEEOLmUpQPr/rVTt3/OgcOLpXuvrItpFaXHxRyM7WDIiMjuf/++9FqtSxevJgZM2awZs2a6663lCRBbEClUpmzbsVnwMEfQ14OugwdjYJa4Lvd3Bvk0Ia99JwytK5DFUKIO8727duJi4tjz549ODo6EhYWhsFgsEqClB1yolKpLO+1Wq1lu0ajwWg0otfrmTVrFvv27aNRo0bMnTsXg8HcY+Vad0A8PDwsd0FSU1Px87t6Y2j8+PH079/fKgliMpn48MMP6dOnj9Uxhw8fxtvbm/MlSXmARx55hB9++AF/f3/ee+89kpKSrnpecYsqaQC7qgpkOIwQQgig8rZQWTdTO6j0Bg7A5MmTyw3PsQVJgtiARq3BpAI7lR57FxcK83L5K+FPQgbdRefBXfjpyw2knE0hJ+Uybk286jpcIYSoe0P/Xfk+1RXTVQ1+peplK5CdnY2Pjw+Ojo4kJCRw8ODBCstt2rQJnU6HnZ0dGzduZNq0aZXWqdfrUalU+Pj4oNPpWLt2LbNmzQK45h2QESNGsHz5cmbMmMGKFSuIjIy0KnPq1Cnatm0LwLp16+jQoYNVmcGDB/P+++/Ts2dPNBoNR44cwd/fn8TERJYtW8bvv//OgAEDGDFiBC1btiQvL48GDRpQWFjIypUrufvuu3F3d8fb25stW7YwaNAgy3AYNzc3cnJyrnod4ialNffmcUbPZUmCCCHEzcXe2dxjo7bqrkRV2kI3UzsoLS2Nhg0bArB27Vo6dux41TqrSyZGtQW1GkVtzpS51jN3az175E8A6gc0oW3j1oQUtaBwpyyXK4QQANhpK39cOcdHdcpWICIigpycHAICAliwYAGhoaEVlgsPDycyMpKQkBCmTJlC69atK63T09OT6OhoAgICiIyMpFu3blW+9Hnz5rFmzRratGnD6dOnmTRpEmCeuHTp0qUAvPHGGwQGBhIUFMS6desqvAMyefJkWrRoQUhIiGVSMpPJxKRJk3jnnXdo3LgxixYtYtKkSSiKwosvvkhYWBi9e/emc+fOlnqWL1/OK6+8QufOnRkwYAD5+fn069ePAwcOEBISIhOj3mpKeoK4YJDhMEIIcbNRqcz/T9fG4yrzgVSlLXQztYMWL15saQd99tlnvPfee1WuvypUSun0rneI0vG3Op2u3Oz71+OPY3+wfuH9qEzFBPR8lsRd6Xg3bslDC0YDUHgulwv/+R1U0GDmXdg3rHyslhBC3G70ej2JiYm0bNkSR0fHug6nQrGxsTIRaBVV9POsje/WO0GtfG4r74cTG3imaBK/eY7g5//rZ5t6hRBC1Ii0g2rH9bRHpCeIDRjdGrO8S2O+6KfBqXsj7ByDyb7kgT7XfAfGwc8Vp06+oEDmj6frOFohhBBC3LYsPUEKyCqQniBCCCHElWROEBtQq1QoRnOjI9deh7efH5fO5ZF68jKt76oPgNuAphw+eoT0U8fpf8yXev6N6zJkIYQQZUyYMKGuQxDCNhzMc4K4YEBXUITRpKBRV95FWgghhLjT2kHSE8QGNGoVitE8EU2WIYvG7b1QTAX8eeDvXh8ODV2xa+aKgkLCxt8wmUx1Fa4QQgghblclPUGcVXoUBbKlN4gQQghRjiRBbMDOkEVEajIjfzOh2XcEd+98igt28deBHeXKdY7shkqt5uKli6Ts/bOOohVCCCFEXVqyZAkBAQGEh4fbvvKSniCeGvPKMLJCjBBCCFGeJEFswE4pxE+vp8FlBVNGJq1D24BKjT5Hx4WkC5Zy7n5etGrXBoBD2+MxFUtvECGEEOJOM336dI4ePUp8fLztKy9ZItfTzgAgK8QIIYQQV5AkiA2o1BrUGg0AhbnZuHm74lG/AQDH4g6XK9s5sgt2dvbk5uVyapv1+sxCCCGEEDVWMhzGQ21OgmRJTxAhhBCiHEmC2IBapUatMc8xW5SXC0DTgHYAnDlyslxZrYczHUI6AvDHnkMU5htuYKRCCCFKJSUlERYWdt1lqiszM5N+/frRtm1b7r33XvR6vVWZ2NhY6tevT3BwMMHBwaxatcqmMYjbmNa8JKCH2vx7dTFXkiBCCCGs3cztoNmzZ1vaQC1btiQ4ONimMUgSxAbUajUOanMSxJiTDUCHuwMBuHwuhYKcgnLl/YfehZOjE8bCItJ+OnVjgxVCCFGnXn/9dcaMGcOpU6do1aoVy5Ytq7Dcww8/TEJCAgkJCYwbN+4GRyluWc4+AHihA+BCjnXjUgghhKgrVWkHLVq0yNIGevDBBxk1apRNY5AkiA2o1Sq0GgcAVDl5GI3F+LX3Q+vihmIycfzXo+XKaxzs6DKgO2HFrdHszcaYI3dphBB3BkVRyC/Kt/lDUZSrnnfEiBGEhoYSGBjIF198YbU/NjaWMWPG0Lt3b9q1a8fixYst+4qKioiOjsbf359x48ZZzhUTE0N4eDiBgYHMnj27yp/B+vXreeihhwAYP3483333XZWPLevnn39m0KBBjBo1inbt2jFnzhzLPl9fX8vr9957jxdffBGAvn378uSTTxIaGkrnzp05cOAAw4cPp02bNrz33ns1ikPcZFzqAeBuygLgQo70OBVCiJtFbbWDrrctdDO3g9asWWPzm0F2Nq3tDqXWaHBUOVAAKCYTFy+mUL9+Cxq2bc2ZhARO7z9KyJDQcsc07NqKC/uzKUrJJXvLGbzubVs3wQshxA1UUFxA1y+72rzePQ/swdneudL9n3/+Od7e3uTl5REeHk5UVJRVmfj4eA4dOoSdnR1hYWFERkai0Wg4duwYK1euxN/fn379+rFr1y569erFzJkzmT9/PoqiEBUVRVxcHD169GD69OnExcVZ1R8TE8Po0aPR6XR4eHgA0LhxY1JTUyuMeeXKlWzevJnAwEAWLVpEgwYNrMocOHCAo0eP4uXlRceOHZk1axbNmjW76mfl6urK/v37WbBgAePGjbNMzunv78+MGTOueqy4BZQkQZyKdKgxcSFbkiBCCHGzqK12EFS/LfTtt9+W23+ztYMAEhIS0Gq1+Pv71/BTqZgkQWxArdZgUtljcFRTpDKRccmcBAnsFUbKMSNZGQ0xFpvQ2P3d8UalVuE5vBUZHx7i7L7TGDu64tu+UR1ehRBC3L4WLVrE+vXrAUhOTiY5ORl7e/tyZSIiIvD09ARg2LBh7N69m549e9K+fXsCAgIACAkJISkpiV69erFt2zYWLlyIXq/nwoULRERE0KNHD5YsWXLd8UZGRnL//fej1WpZvHgxM2bMYM2aNVblunfvbkmOBAYGcubMmWsmQUaOHAlAp06dCAsLs1yzm5sbly9fxsvL67rjF3WoZDiMGhOe5MpwGCGEEIB1W0itLj8o5GZqB5VavXp1rQwJliSIDagcPYgpnohz1/fQOKfQ1dlAR6B1WCtc/neeguxCUo5fpnmgT7njtC09yGhTzImks5z/PpdBbcdY/TIKIcTtxMnOiT0P7KmVeiuzfft24uLi2LNnD46OjoSFhWEwGKySICqVqtzr0vdardayXaPRYDQa0ev1zJo1i3379tGoUSPmzp2LwWC+436tOyAeHh6WuyCpqan4+flZlfXx+fv7YvLkyeW6pZZVUWxXXktpXFceo1aryx2vVqstx4vqyc/Px9/fn/vuu48333yzboPR2IGTNxRcwkeVLcNhhBDiJlJb7aDSuitTWVuorJupHVRq9erVbNq0qWofQDVIEsQG1CW/L6ZiTzSkkJaXZt6uVtEmpB6Hf0nl9P50qyQIQJsRIZx6/y8uX75M4i9/0LpfpxsZuhBC3FAqleqqXTVrQ3Z2Nj4+Pjg6OpKQkMDBgxUvT75p0yZ0Oh12dnZs3LiRadOmVVqnXq9HpVLh4+ODTqdj7dq1zJo1C+Cad0BGjBjB8uXLmTFjBitWrCAyMtKqTFpaGg0bNgRg7dq1dOzYsYpXa+bh4cGZM2fw8/Pj+++/p0+fPtU6XlTPggUL6NatW12H8TfX+lBwifqqy8TnGFAUpVzjVgghRN2oi3YQVK0tdDO1gwD279+Ph4cHbdq0qfqFVpF0O7ABTUkWRCkyj21Kz0+37GsZ7I2xKJHjuzZQZCiyOtatoSftOncA4NDOAxTmyR0bIYSwpYiICHJycggICGDBggWEhoZWWC48PJzIyEhCQkKYMmUKrVu3rrROT09PoqOjCQgIIDIyslp/AM+bN481a9bQpk0bTp8+zaRJkwBYunQpS5cuBWDx4sUEBgYSFBTEZ599Vu1JS1955RX69+9P3759adWqVbWOFdVz6tQpjh8/ztChQ+s6lL95NAGgiSqTwmIT2QXFdRyQEEKIulSVttDN1A4Ccy+QsWPHVuMqq06lXGsa2dtMdna2pQuOu7u7TerU5eTy9uv/Qmc6ievlszRpE8LUuSsAMBYbWfrYAor0BfSbMI6gAcFWxxfri/jhza8o0BfQtmN7Qu+XO3ZCiNuHXq8nMTGRli1b4ujoWNfhVCg2NpYjR47U/VCGW0BFP8/a+G61hR07drBw4UL279/P+fPn+fbbb62W2VuyZAkLFy4kLS2NoKAg3n33Xbp06VLlc9xzzz0sXLiQX3/9tdq/Q7X2uX0/B/Z9zEeMZoH+PjbP7k27Bm62q18IIUSVSTuodlxPe0R6gtiARg3tVWdpVpRP/SwFY/qFv/fZafBrZ1755cTuirtg2znaE9wvHIDTR0+hS7lY+0ELIYQQt7m8vDyCgoIq7Zq7atUq5syZQ0xMDAcOHCAoKIghQ4Zw4cLf3+PBwcEEBgZaPc6dO8e6deto164d7dq1u1GXVDVeLQBobWduT8gKMUIIIcTfZE4QGyidzNRB44AJMF6+XG5/QO8Qzhw6RNqff1KQq8fJ1ToD2PTudpyKP0pmZiYHvo2j3+Mjb0ToQgghgAkTJtR1CKIWDB069KrDVN5++20mT57MxIkTAXNX3B9++IFPPvmEZ555BjAvz1eZ3377ja+++oo1a9aQm5tLUVER7u7uvPDCCxWWNxgM5Saiy87OrsFVVYFXcwCaqjMAZIUYIYQQV3WntYOkJ4gNqFXmj9FFU5LcyM0jLy/Lsr9teDu0ru6Yios4uGVfxXWo1dx1T0+cVFq8z9mhP3GptsMWQggh7liFhYXs37+fgQMHWrap1WoGDhzI7t27q1THa6+9xtmzZ0lKSuLNN99k8uTJlSZASst7eHhYHk2bNr3u66iQpzkJ0sBonqPsvE6SIEIIIUQpSYLYgEajAUCrtkdxMidCkpMOWfar1WpaBgcCcLySITEA3i3r07tLT3wUNy6v/xOlSJYqFEIIIWpDZmYmRqORBg0alNveoEED0tLSauWc8+bNQ6fTWR5nz56tlfOU9gRxN17CEQPnsgpq5zxCCCHELUiSIDagVmv+fu3tBcC5s8fKlbkroisAWWmpZJzNqLQuj8HN0bg7YLyo5/K2M7UQrRBCCCFsbcKECdecUE6r1eLu7s7y5cvp1q0bAwYMqJ1gnLxAa16xrokqQ5IgQgghRBmSBLGBkhVyAdD6mO8oXUw9Xa5M/eb18fJrhkrTgFN7K7/DpNba4T6iFefUl9ke9zOXky5UWlYIIYQQNePr64tGoyE9Pb3c9vT0dBo2bFir554+fTpHjx4lPj6+9k7i1QyA5qp0zmXJcBghhBCilCRBbEClVqOozJkQ5/p+5DpBmt66t0eXUfdgp+3Enwm5KKbKVyZ2CvQht6FCkVJM/Dc7MZlMtRa7EELcqZKSkggLC7vuMtWVmZlJv379aNu2Lffeey96vfUfqLGxsdSvX5/g4GCCg4NZtWqVTWO4lqSkJFavXn1Dz3mjOTg4EBoayrZt2yzbTCYT27Zt4+67767DyGzE17xiTVtVqvQEEUIIYeVmbgclJSXRt29fOnXqxNChQ9HpdDaNQZIgNhJjfIR/FU/CqfsAVvbVENfcusHR5q4GODjZkZ1RwNnjlU98qlarCRvTC7Vaw6VLF/nzp8O1GboQQogb6PXXX2fMmDGcOnWKVq1asWzZsgrLPfzwwyQkJJCQkMC4ceNuaIy3SxIkNzfX8hkCJCYmkpCQQHJyMgBz5szho48+4rPPPuPYsWM89thj5OXlWVaLqS1LliwhICCA8PDw2jtJg44AdFAnk2MoJltfVHvnEkIIIaqoKu2gJ598kscee4zDhw8zfvx43njjDZvGIEkQGyldIaaJW0sAEnWJGE3lJza112ro0K0hiimXvet2XbU+98betA8KAOBw3O/os/JqIWohhKgbpsLCSh9KUVGNy1ZmxIgRhIaGEhgYyBdffGG1PzY2ljFjxtC7d2/atWvH4sWLLfuKioqIjo7G39+fcePGoSjmnnwxMTGEh4cTGBjI7Nmzq3zt69ev56GHHgJg/PjxfPfdd1U+9kpvvPEG4eHhdO7c2TIfxRtvvMHMmTMB2LJlCz179sRkMrF27Vq6dOlCSEgIw4cPJysrC4C0tDRGjhxJUFAQISEhnDp1imeffZatW7cSHBxcaZLmVrBv3z5CQkIICQkBzEmPkJAQywou48aN48033+SFF14gODiYhIQENm3aZDVZqq3dkOEwDcwTsnfUmCdfTb0svUGEEKKuKYqCKT+/Vh6l7ZPKXK0tdLO1g44dO0b//v0B6N+/P998802V668KO5vWdgdTqwEjNHBujKPGkYKifJJ1Z2jp1apcudah7uz/fjcpx1Rknu2Bb1PfSusMjAwn+UQiefm5/P51HHc/MriWr0IIIW6M9FcWVLpP27Yt3g+Nt7y/8Ma/K012OLRogc8/r33X/vPPP8fb25u8vDzCw8OJioqyKhMfH8+hQ4ews7MjLCyMyMhINBoNx44dY+XKlfj7+9OvXz927dpFr169mDlzJvPnz0dRFKKiooiLi6NHjx5Mnz6duLg4q/pjYmIYPXo0Op0ODw/zpJWNGzcmNTW1wphXrlzJ5s2bCQwMZNGiRVZ/mG/evJmUlBT27t2LyWRi0KBBREREMHfuXHr27MnGjRuZM2cO69atQ61W06dPH+655x5UKhX/+c9/WLJkCc8++yxPPPEEkZGRTJ48GYPBQHFxMQsWLOC9997jf//73zU/25tZ3759r9konDFjBjNmzLhBEd1AJT1BWnIOB4o4l1WAfyP3Og5KCCHubEpBASfuCq2Vutsf2I/K2bnS/Ve2hb799tty+2+mdlDnzp355ptvePTRR/nmm28qbSvVlPQEsZExqp95QLMNTWE+o5J8eXibiaT4bVbl/No0xLOhHygKe7+z/uUoS+NgR9jw7gCcSUzi/MGk2ghdCCFue4sWLSIoKIju3buTnJxsGQ5RVkREBJ6enri6ujJs2DB2794NQPv27QkICEClUhESEkJSUhIA27Zto0uXLgQFBREXF8fRo0cB81CH0iEYZR+jR4+ucryRkZH89ddfHDp0iC5dulT4R/rmzZv54YcfCAkJITQ0lDNnznDy5Ek0Gg2ffPIJo0eP5pFHHqFdO/PcEMnJyQwaNIhOnTrxn//8xxLvzp07eeSRRwDz6iUuLi5V/2BFjdyQ4TDujcHREzuMtJF5QYQQ4o53ZVtIrS6fCriZ2kFvvfUWGzZs4K677iItLc3mbRPpCWIj/qozqFUGTEUF+Dk1IKfoDGmJRyss27FPF+JWrSXx94MUFQ3D3t6+0nobBbWgWXxzkpOSSd14nIYBTVHZayotL4QQt4IGzz1b6T6VSlXuff2nn6py2Yps376duLg49uzZg6OjI2FhYRgMBqv/e8vWpVKpLO+1Wq1lu0ajwWg0otfrmTVrFvv27aNRo0bMnTsXg8EAcM07IB4eHpa7IKmpqfj5+VmV9fHxsbyePHlyuW6ppUwmEzExMURHR1vtO3HiBO7u7pw/f96y7YknnuDZZ59l8ODBfP/998TGxlbyiYnaNn36dKZPn052drblbpjNqVTmITFnduGvSiZVVogRQog6p3Jyov2B/bVWd2UqawuVO/4magc1btyYdevWAZCSksKmTZuq8Ulcm/QEsRGlZE4Qk8mEb/MOAGSn/Flh2eBBd2Hn6ESRvoCEHw9cs+7Qsb0JcWxLwywXsrdZ370UQohbjdrBodKH6orkRHXKViQ7OxsfHx8cHR1JSEjg4MGDFZbbtGkTOp2OvLw8Nm7cSLdu3SqtU6/Xo1Kp8PHxQafTsXbtWsu+a90BGTFiBMuXLwdgxYoVREZGWtWflvb3Uupr166lY8eOVmUGDx7MsmXLyM/PB8yTmep0Oi5dusQzzzxDfHw8O3bssNzJyc7OpnHjxiiKwueff26pp1evXnz88ccAFBYWkpeXh5ubGzk5OZVev7hF+AUDEKw+LT1BhBDiJqBSqVA7O9fK42o3hqrSFrqZ2kGZmZmW4awLFixgypQpVfp8q0qSIDZS+iunmIw0bR0MgKHMHbiy7LX2tAoJAuDwT7uvWbfW3YlmozsBkLMjhcLU3OuOVwgh7hQRERHk5OQQEBDAggULCA2teCxueHg4kZGRhISEMGXKFFq3bl1pnZ6enkRHRxMQEEBkZORVGwpXmjdvHmvWrKFNmzacPn2aSZMmAbB06VKWLl0KwOLFiwkMDCQoKIjPPvuM9957r8LrGj16NN26dSMwMJDx48ej1+uZOXMm//d//0fz5s35+OOPmTp1KgaDgZiYGCIjIwkPD6dp06aWet555x3Wrl1L586dufvuuzl37hydO3emqKjolp8Y9WZ1Q4bDADQx13+X+pQkQYQQ4g5WlbbQzdQO2rZtG+3bt6ddu3Y4Oztbhu3aikq51oxht5nSrqc6nQ53d9tNELZ8/ng0RXl0mfA6jRo14ONJPUBRGPvOdzRsYP0LdDntMp8//SaKycTwmf+kbVjba57j4pfHyDyUSpp3Lj1nj0BjL6OZhBA3P71eT2JiIi1btsTR0bGuw6lQbGwsR44csaywIipX0c+ztr5bb3e1/rlln4O3/TEqKoZoV7D1XyNsfw4hhBBXJe2g2nE97RHpCWIjfw+HARcXT1T1zau+HD/8S4XlvRp64de+A6gcOPJzxcNmruQ+oiVHHVM4n32Bw+v22CZwIYQQQtye3P0wujVGo1JokHuUIqOpriMSQggh6pwkQWxEVTIgRlGMALi1NPfsSDm+r9Jjev1jKHZOPTn/pwO6jGt3U7V3d6RTL3PXpRMHj3Hpr/TrDVsIIQQwYcKEW+ruhxBVpW7WFYBQ1QnSdDI5qhBCCGt3WjtIkiA2UnZiVAA//1DO+aj4g8rXNG7YypfmgfVQFDj409kqnadVv47Ur98ARTGx9+tfMMldHSGEEOKWcsPmBAFULXsB0ENzhFSZF0QIIYSQJIitfGr/D14onoDe2bzET4e7h/NDFzU/epyl0FhY6XHBA5uhKApHfk4g5+K1Z+JXq9WEj+uDRmNHli6Lo99X3tNECCGEEDef6dOnc/ToUeLj42v/ZK36AXCX6hRpGZm1fz4hhBAVusOm4qx11/N5ysyaNmLSOFBMMaX9Mpq6NcXb0ZtL+kscvXiU4PrBFR7XpIMXTi4nyclIZucqLcOm3XPNc7k18KRTt2AS4vZxdP9h/Dq3wLtlfdtdjBBCCCFuD94tuWjfCJ+i86jPxEHX9nUdkRBC3FHs7e1RqVRkZGRQr169qy5lK6pGURQyMjJQqVTY29tX+3hJgtiIk70GgPxC85wgKpWKzvU6s/vP7fzx5+5KkyAqlYrggWHsXJnMn/sOkHt5AK5ertc8X7shwaScPENmRgZ/fP0bPWePQKWRjj1CCCGEKO+cTzd80r7FO30X8M+6DkcIIe4oGo2GJk2akJKSQlJSUl2Hc9tQqVQ0adIEjUZT7WMlCWIj3TlEZ00Spou+0LYeAL0z69F2m4ncsz/C3Y9VemzIkFD2b9hOvu4yu1ZvJ+LRyGueT61Wc/c/+nPkgx34ZXqQs/0s7gOb2+x6hBDidpeUlERUVBT79lU+rLAqZaorMzOT++67j5SUFDp16sSXX35ptWTe7Nmz2b59OwA6nQ4PDw8SEhJsFoOoW0uWLGHJkiUYjcYbcr68Jr0g7Vta6G7A8BshhBBWXF1dadu2LUVFRXUdym3D3t6+RgkQkCSIzbRUnUOj+hNjdpplW8fAvpz/5isMSYkUFulxsK94XWi1Rk3IkD7ErV7LqT376P2PATh7OF/znC4NPOg0qiuXvjpB9k9ncezgjUMTN5tdkxBCCNt7/fXXGTNmDDNmzGDu3LksW7aMGTNmlCuzaNEiy+vnnnsOOzv5ur6dTJ8+nenTp5OdnY2Hh0etn8+udV+M8SqaFCdD1lnwbFrr5xRCCFGeRqOp8R/twrZk/ISNqEsSHEX6v2deb9+hB4qTFgqLOHp4+1WPv2toGI5unhiLCtm15uply3IKqodTJ19MJiMHv9xFsV6yi0KIm5eiKBQZjDZ/XGtyrBEjRhAaGkpgYCBffPGF1f7Y2FjGjBlD7969adeuHYsXL7bsKyoqIjo6Gn9/f8aNG2c5V0xMDOHh4QQGBjJ79uwqfwbr16/noYceAmD8+PF89913Vy2/Zs0axo0bZ7X9559/ZtCgQYwaNYp27doxZ84cyz5fX1/L6/fee48XX3wRgL59+/Lkk08SGhpK586dOXDgAMOHD6dNmza89957Vb4GcWtp2LAR+xTzXCCmY9/XcTRCCCFE3ZJbSzaicXDCBBQV6v/eptbg3LotBUeOcPL3nwi+a2jlx9tpCB7ci9++/o6Tu+PpNa4/Tm5O1zyvSqXCc1Qb4v88SFZ2NvxvF+Hj+9nikoQQwuaKC038d+YvNq93yjt9sNdWfnfl888/x9vbm7y8PMLDw4mKirIqEx8fz6FDh7CzsyMsLIzIyEg0Gg3Hjh1j5cqV+Pv7069fP3bt2kWvXr2YOXMm8+fPR1EUoqKiiIuLo0ePHkyfPp24uDir+mNiYhg9erRleAtA48aNSU2tfCn1hIQEtFot/v7+Fe4/cOAAR48excvLi44dOzJr1iyaNWt21c/K1dWV/fv3s2DBAsaNG2dZocTf39+qR4q4PTR0dyTWFE5X9XGK/liP9ipDdIUQQojbnfQEsRGNQ0lPEEN+ue2NA7sCkHns4DXrCB/eBUdXd4zFjiRsO131c7vY4z8wBIA/T5zmfEJSlY8VQog7waJFiwgKCqJ79+4kJyeTnJxsVSYiIgJPT09cXV0ZNmwYu3fvBqB9+/YEBASgUqkICQmxTGq2bds2unTpQlBQEHFxcRw9ehQwz/eQkJBg9Rg9enS14169enWFvUBKde/enQYNGuDg4EBgYCBnzpy5Zp0jR44EoFOnToSFheHp6Ymnpydubm5cvny52jGKm5+dRk2Ccw8AHFJ/g7yLdRyREEIIUXekJ4iN2Dk4UQQUGwrKbe8UNpTTX32MMfUcOTkXcXPzqbQOjb0dPf4xll++TOLIL5cJGVSEo0vVlvxp3r09KX8kcvZMMnu+38nQ1g3QVqEniRBC3Eh2DmqmvNOnVuqtzPbt24mLi2PPnj04OjoSFhaGwWCwWlKt7JJ1KpXK8l6r1Vq2azQajEYjer2eWbNmsW/fPho1asTcuXMxGAwA1+wJ4uHhYekNkpqaip+fX6Wxr169mk2bNlW6v6LYrryW0riuPEatVpc7Xq1W37CJOsWNp/ZpwdHU5gSoz8DJjRAyvq5DEkIIIeqE9ASxEXuteSJTY5G+3PamTQLA2xNFMbF/z7pr1tOxVyt8m7hSWFDMgU3XvqNXVvj9fXF0dEKvL2DvF1WfV0QIIW4UlUqFvVZj80fZP/qvlJ2djY+PD46OjiQkJHDwYMU98zZt2oROpyMvL4+NGzfSrVu3SuvU6/WoVCp8fHzQ6XSsXbvWsu9aPUFGjBjB8uXLAVixYgWRkRWvCLZ//348PDxo06bNtT5WKx4eHpw5c4aioiK+/17mgLjZLFmyhICAAMLDw2/YOZt4OfGjMcz85ui12yNCCCHE7UqSIDbi4GjudWEsLLDa59SzB790UvMTx69Zj1qtotuo1ihKMQd+/IWLKZlVj8HVkW6j+oBKRWpKCqe2Ha76BQghxG0qIiKCnJwcAgICWLBgAaGhoRWWCw8PJzIykpCQEKZMmULr1q0rrdPT05Po6GgCAgKIjIy8asLkSvPmzWPNmjW0adOG06dPM2nSJACWLl3K0qVLLeVWr17N2LFjq1xvWa+88gr9+/enb9++tGrVqkZ1iNozffp0jh49apmP5UZo4unE96aS39PT2yCv6u0LIYQQ4naiUq41pX4tW7JkCQsXLiQtLY2goCDeffddunTpUmn5xYsX88EHH5CcnIyvry9RUVG89tprODpWvPzslUqXo9PpdLi7u9vqMvhufyJPrzlASMuGfPFoj3L79qXtY+KPE/HQevDz2J+xU199FJKiKHz29FKyzifTJKAjUfOq12U1YU0cxw/+gVbjwPAZ9+FQz6Xa1yOEELai1+tJTEykZcuWVf6/+kaLjY3lyJEjvPnmm3Udyk2vop9nbX233u5u5Oe2Kj6Zp78+zHb3GFoWnoJhb0KXybV6TiGEEOJGqur3ap32BFm1ahVz5swhJiaGAwcOEBQUxJAhQ7hw4UKF5b/88kueeeYZYmJiOHbsGB9//DGrVq3iX//61w2O3Jqrqwv5OHJZb7LaF1w/GE+tJzqDjt8v/H7NulQqFd3H9Acg5dhRUk9WvnJARTrfezfNfJvQydCMrNWnUIzWMQkhhBDiztHEyzxsd4Oqt3nDoVV1GI0QQghRd+o0CfL2228zefJkJk6cSEBAAEuXLsXZ2ZlPPvmkwvK//vorPXr04IEHHqBFixYMHjyY+++/n717997gyK35uDgAcCmv0GqfndqOAd7d6JRo4tDmlVWqr13X9vg2awmKwvbPfqhWLGqNmi4T+uPk6Ejh2Ryyt1qvgiCEEOJvEyZMkF4g4rbW2NM8bHdlfjiKSg0p8XDxzzqOSgghhLjx6iwJUlhYyP79+xk4cODfwajVDBw40LIs4ZW6d+/O/v37LUmPv/76iw0bNjBs2LAbEvPVeGtNRKp/ZUD+JhSTdc+LfpqOdDuukL9zF0ZT1Wbf7zt+GKjUZCYn8seO6s3vYefpiNe9bQE488sxzickVut4IYQQQtw+Gnmahy6lFLlT1LxkhabDa+owIiGEEKJu1FkSJDMzE6PRSIMGDcptb9CgAWlpaRUe88ADD/DSSy/Rs2dP7O3tad26NX379r3qcBiDwUB2dna5R23wdnXibvVROnKa3Lwcq/1duo8BB3uUnFwO/f5jleps4t+EFkGdAYhbvRFjUXG1YnLuXI+cADuOqs+y57ud6LPyqnW8EEIIIW4PWjsNDdzNSyKnNRtp3nhwJVRw40YIIYS4nd1Sq8P8/PPPvPrqq7z//vscOHCAb775hh9++IGXX3650mNee+01PDw8LI+mTZvWSmzOTk4Y1eYhMVlZWVb7nZzccOnYCYBDv3xd5XoHTByOnYOWfN1ldq3+pdpxtR5zF85OLugNen5bsQ2TNHaEEEKIO1LpkJhjXn1A6w6XkyCx+m0LIYQQ4lZWZ0kQX19fNBoN6enp5banp6fTsGHDCo95/vnneeihh5g0aRKdOnVi9OjRvPrqq7z22muV/nE/b948dDqd5XH27FmbX0spk715FZZs3eUK93fsNQoA3aEDFFawlG5F3Lxd6TSgNyq7hpzcZ0SfV1StmBxctNx9b19UKjVpaWkc+2FftY4XQojbVVJSEmFhYdddproyMzPp168fbdu25d5770Wv11uVmT17NsHBwQQHB9OyZUuCg4NtGsO1JCUlsXr16ht6TnH9FEXhuV3PMXHTRDILrJfAbVwyOWpyjgo6lyy/vD/2BkYohBBC1L06S4I4ODgQGhrKtm3bLNtMJhPbtm3j7rvvrvCY/Px81OryIWs0GsD8xV8RrVaLu7t7uUet0boCkFNJEiS0y0gUZyfQG4j/bW2Vq+05tg/1W3ajsMCOvd9Xf26Pev6NCexiHlZzZO8hLhxNqXYdQgghbOP1119nzJgxnDp1ilatWrFs2TKrMosWLSIhIYGEhAQefPBBRo0adUNjlCRI7VqyZAkBAQGEh4fbtF6VSsWetD3sS9/HudxzVvubeJl7gqRczofQCeaNx7+H3IpX5RNCCCFuR3U6HGbOnDl89NFHfPbZZxw7dozHHnuMvLw8Jk6cCMDDDz/MvHnzLOUjIyP54IMP+Oqrr0hMTGTLli08//zzREZGWpIhdUnj7AVA9uWKGxP2dg54BZvvKB6LW1/1eu009BxrnuT0yC+pXDiTVe3Y/IeH0ahRIxTFxK9fb8egy692HUIIcasaMWIEoaGhBAYG8sUXX1jtj42NZcyYMfTu3Zt27dqxePFiy76ioiKio6Px9/dn3LhxlqR7TEwM4eHhBAYGMnv27CrHsn79eh566CEAxo8fz3fffXfV8mvWrGHcuHEV7nvjjTcIDw+nc+fOltVt3njjDWbOnAnAli1b6NmzJyaTibVr19KlSxdCQkIYPny4ZehmWloaI0eOJCgoiJCQEE6dOsWzzz7L1q1bCQ4OrjBJI67P9OnTOXr0KPHx8Tavu6GzuTdtWp71/Gqlw2FSswqgYSdoHAamYkiw/jchhBBC3K7qNAkybtw43nzzTV544QWCg4NJSEhg06ZNlslSk5OTOX/+vKX8c889x5NPPslzzz1HQEAAjzzyCEOGDOHDDz+sq0soR+vuC0BulnUX1FLBfe7DpIY/Lh8np9B6AtXKNO3gTfNAN4oKDvL9O59hMlZvbg+1Wk23hwfi5OiE3lDAia/iK+09I4QQta24qKjSh7G4uMZlK/P555+zf/9+9uzZw4IFCzAYDFZl4uPjWb9+PQcOHGDp0qX8+ad5+dBjx47x9NNPc/ToUdLT09m1axcAM2fOJD4+nsOHD5OcnExcXBxg/gO3dChL2ce3334LgE6nw8PDA4DGjRuTmppaadwJCQlotVr8/f2t9m3evJmUlBT27t3L77//zoYNGzhy5Ahz585l7969bNy4kSeeeIJPPvkEtVpNnz592LNnD7///jtDhgxhyZIlADzxxBNERkZy8OBBfvvtN/z8/FiwYAEDBw4kISGBSZMmVekzFjeHhi7mJMj5vPNW+xpbeoKUDMkNM990Yn+sTJAqhBDijmFX1wHMmDGDGTNmVLjv559/Lvfezs6OmJgYYmJibkBk1efi4UsWoM+5VGmZwE79eXlUG44XJNL1rx/4R4d/VLn+bve05K/935GdUcSvX++k59g+1YpP6+ZE96j+nF2RgHeimtxd53Dr1bhadQghhC1s/7Ty5LVP0+bcNTTS8v6X5R9jqiTZ4dXIj7DIe695vkWLFrF+vbkHXnJyMsnJydjb25crExERgaenJwDDhg1j9+7d9OzZk/bt2xMQEABASEgISUlJ9OrVi23btrFw4UL0ej0XLlwgIiKCHj16WJILtrB69epKe4Fs3ryZH374gZ07dwKQk5PDyZMnCQwM5JNPPiEkJIRXXnmFdu3aWa77vvvuIz09nYKCArp27QrAzp07+eqrrwDzEFKtVmuz+KuiX79+qFSqah83YcIEHn744VqI6NbWyKURUHFPkKYlSZDU0iRIx9GwaV7JBKk/Q+v+NyhKIYQQou7UeRLkdqJu1pUFu+1pb2rIA5WVUasZ1Wkcr+99nTUn1zCu/bgqN/58m/oS2Lcnh7Zu5/dNPxHYNxjP+h7VirFeh8Y4DVeRte5PdBsTcWjuhrZZLc6TIoQQdWz79u3ExcWxZ88eHB0dCQsLw2AwWCVByv5frFKpLO/LJgU0Gg1GoxG9Xs+sWbPYt28fjRo1Yu7cuZbeJdOnT7f0CikrJiaG0aNH4+HhYekNkpqaip+fX6Wxr169mk2bNlW4z2QyERMTQ3R0tNW+EydO4O7uXq435RNPPMGzzz7L4MGD+f7774mNja30vDfShAkTanRcUFCQbQO5TTRwMfemrSgJ4lcyHCbHUIyuoAgPJxfoPA7iP4K9yyQJIoQQ4o4gSRAbauTrTR5OnNNZd7Mua0SrESzav4gLZ09w6NROgtr1rvI5+jzQnz/3HyLv8kV+/PBbxj0/odpxunRrhOEvHbrDafz6+RbunhGBo6dLtesRQoia6jfx0Ur3XZkY7vPQI1UuW5Hs7Gx8fHxwdHQkISGBgwcPVlhu06ZN6HQ67Ozs2LhxI9OmTau0Tr1ej0qlwsfHB51Ox9q1a5k1axbANXuCjBgxguXLlzNjxgxWrFhBZGRkheX279+Ph4cHbdq0qXD/4MGDWbBgAffddx/Ozs4kJSXh5eWF0WjkmWeeIT4+nqioKHbv3s3dd99NdnY2jRs3RlEUPv/8c0s9vXr14uOPP2by5MkUFhZSVFSEm5sbOTlVH7J5PSpK4oiaa+bWDIA/dX9a7XN2sMPbxYFLeYWkXi7Aw8keukw2J0FObIBLieDd8kaHLIQQQtxQkgSxodI7LOk5eoqMJuw1FU+54qH1YGJ2EMadu9mf9xFBT1U9CaKxt6N/9Gi+e+djzp88wR87DtOxd6dqxalSqfAa05b4MwfJys8m7rMt9JsxEnUl8QohhK3ZXdELw1ZlKxIREcEHH3xAQEAAHTt2JDQ0tMJy4eHhREZGkpaWxrRp02jdujVJSUkVlvX09CQ6OpqAgAD8/Pzo1q1bleOZN28eUVFRLF68mMDAQF5++WUAli5dCsDUqVMBcy+QsWPHXvW6jh49Srdu3TCZTHh6evL1118zd+5c/u///o/mzZvz8ccf89BDD7F3715iYmKIjIzE29ubPn36cObMGQDeeecdJk2axLvvvou9vT1fffUVnTt3pqioiODgYGbMmCHzgtxC/H3M88ck6ZLIL8rH2d653P6G7o5cyiskPVtPgJ871Gtv7gHy508QvwyGLKjW+bL1RZxKz+HPjDzOXMzjUl4huoIisvKLKCw2ofD3Cn6O9hqcHTSWZxetHV7ODni5OODt7ICXs735tYsDXs4OONhJu0QIIYTtqZQ7bHbM7OxsS1dkWy+XazIpPB7zEp6mLB6b/n80uUoX54Tff2THG7PBzo6H3t2Ml1fDap3r2zdXceZgAo6u7kx8aw5a5+qP4c48eY6fVmzEZDLSrpM/d43rVe06hBDiWvR6PYmJibRs2RJHR8e6DqdCsbGxHDlyxLLCiqhcRT9PW3y3mkwmfvnlF3bu3MmZM2fIz8+nXr16hISEMHDgQJo2bWrLy7gp1FabZMDqAVwouMCnQz4lrGFYuX0TPt3LzycyeGNMJ8aFm3uNcHIzfHkfaD1gzlHQul61/tMXcvj291R2nsrkSKoOUy21JL1dHKjvpqWBuyMN3M3P9d0daWDZ5oivqwN2chNHCCEEVf9elZ4gNqRWq+jimIJ9QSaZF1KvmgTpHDSIXQ3qYUrPYNv6/xAV/Wq1zjV48ghi555En1fIr18fpt9DYdc+6Aq+7fwI6R3G/p/3cPLwMXya1qd59/bVrkcIIYSoqYKCAt566y0++OADLl26RHBwMH5+fjg5OXH69GnWrl3L5MmTGTx4MC+88EK1et3cCC1atMDd3R21Wo2Xlxfbt2+v65AIaRDCj0k/8tv536ySIPXdzDdNLmSXGbrbZiB4t4ZLf8LBleYhMhWIT7rE25tPsvuvi+W2N/JwpHU9V1r6ulDPTYuHkz0eTvZo7dSoVH8PW9MXGSkoNJJfaKSgyEiuoZis/CIu5xVyKb+Qy3mFXM4v5HJ+EUaTwqW8Qi7lFXI8rfKhWSoV+LpqaViSFGnk4UhDD/Prhu7m1w09HHHVSpNXCCGEmXwj2Jja2QsKMrl0wXppunLl1GraDR7L8eVLOLfjRwz/eA6t1vmqx5Tl4uFCv+ix/LT8DEd/zaZDdx2NWldvklSAtgODuJiSQdLpv9i7OQ6PJj54NvOtdj1CCHErq+nknOL6tWvXjrvvvpuPPvqIQYMGWU1YC3DmzBm+/PJL/vGPf/Dss88yeXLFf6TXlV9//RVX16v3nriRevj14MekH9l9bjczQsqvwFffzdx750JOmSSIWg1dH4WNT8GeDyHsEfO2EvmFxbz03VG+ij8LgEatol/7+gzr1JC7W/vQyMPJpvGbTAq6giIu5BhIz9aTnq0v9zo928CFkm3FJoWMHAMZOQYOp+oqrdNVa2dOiJQkSxp6aGno4WROlLg70sBDi6+LFrW6+isVCSGEuLVIEsTGtJ5+FF88hS4j5Zpl+w56hOPfxkJuHts3f0RE5MxqnSugZ3vOnTZy4rc0fvr8GOOeDcfOQVPtmMMf6IvuP5e5nHWZXV9sZvATY3BwubFLJAohhLgzbd68GX9//6uWad68OfPmzWPu3LkkJyffoMhuXXf73Q3AkYtH0Bl0eGj/vklS3938/Z6Rc8Uk7sEPwLaX4eIp8/wgbQcCcF5XwEMf7+X0hVxUKhgX1pTHB7SlsadtEx9lqdUqvFzMc4W0b+hWaTmTSeFiyfwmaTo9aSVJkvM6fbltOfpicg3FnL6Qy+kLuZXWZ69RUd/NPPTGnDBxoqGHtqSHiTlhUt9di6N99dtaQgghbh6SBLExj/pNufgn5F+8dhLEwcGRxn2GkPrDN5za/D8GD38ctbp641p73teWs0cvcinlJJuWnmfEE6OrHbPGwY6e0UP48YNvMOYVcuGbYzQeH1TlpXuFEEKImrpWAqQse3t7WrduXeXyO3bsYOHChezfv5/z58/z7bffMmrUqHJllixZwsKFC0lLSyMoKIh3332XLl26VPkcKpWKPn36oFarmTVrFg8++GCVj60tDV0a0sazDaezTrMzdScjWo2w7LMMh8nRlz9I6wYh42HPB7BnKbQdyIUcPfct3U3K5QIauGtZNC6Y7q1vnt6iarWKem5a6rlpCWxceW/YPEOxOUFSkhQpmyQpTZpk5BooMiqkZhWQmlVw1fN6OduX9CLRWobeNCodguPhSCN3J9yd7KQdJYQQNylJgthYfb/mXARM2WlVKt8/8nE+37ye/JyL7Dq2id4dh1XrfI4u9oQP92Hrsg2c3qfi5N6OtOvSrtpxu9Rzp/eYQeR+cRr+yCF3VypuvZpUux4hhBDieuXn55OcnExhYWG57Z07d65WPXl5eQQFBfHPf/6Te++912r/qlWrmDNnDkuXLqVr164sXryYIUOGcOLECerXrw9AcHAwxcXFVsdu3rwZPz8/du3aRePGjTl//jwDBw6kU6dO1Y6zNgxqPojTWaf5/q/vyyVB6lU0HKZUl8nmBMjpLRSmn2Dq15mkXC6guY8zX07uVqu9P2qTi9aO1vVcaV2v8iFLxUYTGbkGc++RkmRJWmlvktKkSbYefZGJy/lFXM4v4thVRj472qvLzVPSoGQoTtl5Suq5amVSVyGEqAOSBLGxZs1bcQzQGC6Tn5+Hs7PLVct7eTZA+497+TT9fyQkfk6vgKHVvnMQ2CeAozs7cO7EcX769Gua+s/Cya36DRXfjo1xHKEia/2f6DYmomrgiGu7m+eOjxBCiNtbRkYGEydOZOPGjRXuNxqN1apv6NChDB06tNL9b7/9NpMnT2bixImAeZniH374gU8++YRnnnkGgISEhKueo3HjxgA0atSIYcOGceDAgUqTIAaDAYPh7+RDdnZ2dS6nWka0GsEHBz9g97ndZORnUM+5HlC2J4gBRVHKtzl8WkO7IXByE8fWLuRA8mjcHe2Indjllk2AVJWdRk0jD6erzm+iKOa5StKu6EXy99AbA2m6Ai7nF6EvMpF0MZ+ki/mV1qcumdS1bC+Ssr1KfF3NvVw8nexlrhIhhLAhSYLYmI+3N0Z7F4qLCjmTkop/u2v3yriv/+N88s0G/rj4BztTd9K7Se9qn3fotDEsf2Yx+txsvn/vf9w376GahI/L3Y0wJGfz56ET7P3yewZMisSjiU+N6hJCiJtZUlISUVFR7Nu377rKVFdmZib33XcfKSkpdOrUiS+//NJq6eCkpCQmTJjAxYsXadKkCV999RUeHtWf/PpWM2vWLLKystizZw99+/bl22+/JT09nVdeeYW33nrLpucqLCxk//79zJs3z7JNrVYzcOBAdu/eXaU68vLyMJlMuLm5kZuby08//cTYsWMrLf/aa68xf/786469Kpq5NyOoXhAHMw6y9vRaJnc2TyZbryQJUlhsIrugGA/nKyai7ToVTm6izbn1uDOYl0f1oKXv1W/o3ClUKhWezg54OjvQoWHlSy/qi4xcyDaUDL0pKEmSGEqSJgWkZ5tfF5sULuQYSnrlVD6pq51ahY+rA/XctObEiKsWXzfzs2VbyXsZhiOEENcmSZBasLX+RH45U8BbOc5UZaSzj5MP/2j/D2KPfML/NrxFz0k9qz03iJu3K/0m3MuPS1eQevQo+zfEEzosvNqxq1QqPEe35mLyQQqzC9nx+Y8MeeJeHFwdr32wEEKIa3r99dcZM2YMM2bMYO7cuSxbtowZM8qv4PHkk0/y2GOPMW7cOL744gveeOMNXn21ekup34p++ukn1q1bR1hYGGq1mubNmzNo0CDc3d157bXXGD58uM3OlZmZidFopEGDBuW2N2jQgOPHj1epjvT0dEaPNs/FZTQamTx5MuHhlX/3zps3jzlz5ljeZ2dn07Rp0xpEXzXj2o/jYMZBVh5fyYSOE7DX2ONor8HDyb5k9RW9dRKkVV/StC1paEjk6YbxjAy6r9biu1052mto5uNMM5/KV/0zmRQy8wyk6wxlht4UWJIlF3L0ZOQYuJxfRLFJKUmcVDCE6QoOGjW+JQmTsgmSss++rg74uEjCRAhx55IkSC1o2bghv5xJ4sg5HWNCqzavxsMBD5P78Wd4Xj7F7g5f0aP3A9U+r3/3AP48EM7pPXv59X/f07xTS3ybVn84i0ZrT+8JEWxeupa8/Fx2ffIjfadHopZxq0KIW9SIESM4f/48BoOBefPmWU1eGRsby3fffUdGRgZpaWlMmzaNWbNmAVBUVER0dDR79+6lc+fOfPXVV6hUKmJiYtiwYQMFBQUMGjSIRYsWVSmW9evXEx8fD8D48eN5+umnrZIgx44do3///gD079+fl19+2SoJEhsby4YNG7h8+TKJiYk89thjPPnkk1a9V+bOnUtgYCATJkygRYsWPPjgg3z//fe4urryzjvv8NRTT5GUlMRbb71l+YO+ruTl5Vnm4vDy8iIjI4N27drRqVMnDhw4UKexVaRVq1YcPHiwyuW1Wi1a7Y1bfS2iRQSL9y/mQsEFNiRu4J429wDmITGlS9C2bVB+9ZVzOj1L8gawwG4ZUcUbUCmvg0pWQ7E1tdq8Ek19N0c6UXkvryKjiYu5hWTmGixLAWeUvLZsyzWQmWMgW19ModHEOZ2eczp9pXWWsteo8HJ2wNvFAZ+SxIi3iwM+Lg74uGot271dHPCVpIkQ4jYiSZBaENzUE4CEs1lVPsbX2ZfWnXtz8Zdt/P71f+nWcxwadfUbHUMeHUHa6URyL2ay9dM4xj43skbjSF3qe9AjagA/f/UjFy6kc+CrHYQ92Lfa9QghRFmKoqAUmWxer8pefdXG+eeff463tzd5eXmEh4cTFRVlVSY+Pp5Dhw5hZ2dHWFgYkZGRaDQajh07xsqVK/H396dfv37s2rWLXr16MXPmTObPn4+iKERFRREXF0ePHj2YPn06cXFxVvXHxMQwevRodDqdZWhL48aNSU1NtSrbuXNnvvnmGx599FG++eabCssAHDp0iH379lFcXEz79u15/PHHr/lZtWnThoMHDzJ58mRmz57N1q1bSUpKYuzYsXWeBGnfvj0nTpygRYsWBAUF8eGHH9KiRQuWLl1Ko0aNbHouX19fNBoN6enp5banp6fTsGFDm57rSkuWLGHJkiXVnuOkuuw19tzvfz/vHHiHz45+RmTrSNQqNT6uDpy6ABfzCq2O+eZACl8X9+AZ+1W45abAiQ3gH1mrcYrK2WvUlolUr0VfZORiXqElWZKZa/18IcfAxdxCcg3FFBnLDse5NruSpYt9LMkRrfm1iwPeriXPLlrzPmcHPGQuEyHETUqSILUg2M+Jf2h+oknaJQoLw3FwcKjScUPGPsWXu3dgSr/AT5s+ZNCwadU+t729PcNn3M/aRXu4eM6N3zefITSiRbXrAagf0ITQfl2I37ab08dO4rHNm7YD6n7GeyHErUspMnHuhV9tXq/fS91ROVSeOF60aBHr168HIDk5meTkZOztyw8DiIiIwNPTE4Bhw4axe/duevbsSfv27QkICAAgJCSEpKQkevXqxbZt21i4cCF6vZ4LFy4QERFBjx49WLJkyXVfz1tvvcW0adP48MMPGT58OC4uFc/JMGjQIFxdzSte+Pn5Wf1BX5GRI0cC0KlTJ3x9fdFqtbRv355z585dd9zXa+bMmZw/b15yIyYmhoiICL744gscHByIjY216bkcHBwIDQ1l27ZtlmVzTSYT27Zts+qZY2vTp09n+vTpZGdn1/pcL/e1u4+PDn3Eqcun2HxmMxEtIvB2MbdLLl+RBFEUhbUJ59CjJaXVWPz//Bh+WypJkFuEo72Gxp5OVZrEVl9k5HJ+IRdzC7mYV8ilPMPfr0ueL+YZuFTyPsdQTLFJsSRYqkKtAg8ne7ycHfB0Ln12wMvZHi8XB7xKXns6O+Dl8nc5rZ30PBJC1C5JgtSC5vU86Wh/Hk1xAX/+eQJ//05VOs7Xpyl+A0dwbsO3HPs2lp79HsLJye3aB16hUZtG9HmgC9uXH2fv+kT82nrRqHXNGlmt+3Ui6/wlTh09wYFf9uLTpD7e7Wv3DpkQQtjS9u3biYuLY8+ePTg6OhIWFobBYLBKgpTtSaJSqSzvyw5f0Gg0GI1G9Ho9s2bNYt++fTRq1Ii5c+daVv24Vk8QDw8PS2+Q1NRU/Pz8rMo2btyYdevWAZCSksKmTZsqvLaKYrOzs8Nk+ru3TdnVSMoeo1aryx2vKEqF57iRxo8fb3kdGhrKmTNnOH78OM2aNcPXt/rDO3Nzczl9+rTlfWJiIgkJCXh7e9OsWTPmzJlDdHQ0YWFhdOnShcWLF5OXl2dZLaa23KieIAAeWg8mdJzA+wff573f32NAswF4OZuTIFf2BDl6PpvTF3JxsFPTZMhM+CAWzuyC84egkdwEuZ042muuuRpOWYZiI5fyrJMmVtvKJE1MCpblhKvDxUFzRWLk72SJd0kCxZJMKUmcuGplqI4QouokCVILVGo1eLWAjGMk/3msykkQgOH3PcNHO7dATi4/rHmdqIcX1CgG/+6NOHvsEqf2JrLurU954KWJuPvWLBESMq4XOe/rcDqvULAmkeLHvbDzuHFjmoUQtw+VvRq/l7rXSr2Vyc7OxsfHB0dHRxISEiqdw2HTpk3odDrs7OzYuHEj06ZV3htPr9ejUqnw8fFBp9Oxdu1ayxwi1+oJMmLECJYvX86MGTNYsWIFkZHWd9kzMzPx8fFBpVKxYMECpkyZctU6y6pfvz7nzp0jJycHlUrFli1bCA0NrfLxNxNnZ2fuuuuuGh+/b98++vXrZ3lfOilpdHQ0sbGxjBs3joyMDF544QXS0tIIDg5m06ZNVpOl2tqN7AkC8HDHh1l5fCVnss+w9vRafFzMCY0re4L8fCIDgL7t6uFWvzkE3AN/fAN7PoRR19/DSdy6tHbVS5oUFpvIyi8sSYIUXvG6iEt51tuy8gsxKZBXaCSvsIDUrIIqx6dRq/BwssfDyR53J3s8S16XPjydzdvLvi997WSvkQSKEHcYSYLUEvdGbcnLOMal5KPVOs7JyY0Oo6I5vnwJ57Z+T8awqdTzrf7M8SqVir4Ptifp900UZF9k7ZtfMn7BozWa3FStUdNr8lAyPjhEcXo+Fz8/Sr1HO6O+StdzIYSoiEqluuqwldoQERHBBx98QEBAAB07dqw0IRAeHk5kZKRlYtTWrVuTlJRUYVlPT0+io6MJCAjAz8+Pbt26VTmeefPmERUVxeLFiwkMDOTll18GYOnSpQBMnTqVbdu28fzzzwMQGRnJI488UuX6HRwceOqppwgJCaFZs2Z06lT1RHxdy8zMrFGPj8r07dv3mj1cZsyYUevDX+qai70LjwY9yut7X+fdA+/yD7/3ALiUXz4JsjfxEgDdW/uYN3R7zJwEObwGBs0HF9v9bMTtzcFOTX13R+q7V311QZNJIUdfzOX8Qi6VJk7y/k6SlH02J1HMrw3FJowmxTx0p4J5bq7FXqPCw8kBDye7MkkSB0tCxaNsUsX57/fuTubVloQQtx6VcjP0f72BSu+66HQ63N0rX+P9eh069DtHVr+Eyd6ZB55bXq3kg9Fk5IMnB3JOfwHXUSP515DXahxH8h/JrF34X0xGIx16difi0ZqP6y2+pOfCkt8pzDOQ2byYu6b0lxVjhBDXpNfrSUxMpGXLljg63pzLbcfGxnLkyBHefPPNug7lplfRz9MW361JSUkMGTKEEydO2DLcm1LZ4TAnT56s9TYJQJGpiLHfjeV01mm6+Ixg266edG/tw5eTzQm8YqOJ4Je2kGso5ocnetLRzwMUBT7qD+cOQL/noM//1WqMQtREQaERXUGR5ZGVX2h5nV1QRFaZfbqCInT5f78uNl3fn0EOdmrcHe1xd7TDzcn87O5oj5ujHe5O9rhpS56v3F7y7OpgJ5PHCmFDVW2PSE+QWtKhQyAH1Q5oivL5K/EUbdq0r/KxGrWG7o+/TPSOqZD2PcMujCO4fnCN4mjWsRnhkRHsWfsDx+N209S/BR171+yuoJ23I94PBbD14/XkphZgXK6i64QBNapLCCGEKHXkyBEiIiKuOgTpdnKjh8MA2Kvt+VfXf/HPH/9J/MUfUDu24FLe3/OOHTufQ66hGDetHR0aljQcVSroNg2+mQTxH0GPmWBXtcnehbhRnBw0ODloqrSCTlmKopBfaDQnSfLLJkoKyydNCorJyi8k+4pkikkxD/vJzDWvvFMTKhW4asskSBztcXeyw600sVLu/RVJlJL30htFiOqTJEgtcXCwB59WkHGcU38cqFYSBOCuVj0ZdX40a0+v5eXfXmbViFXYqWv247p7TE9STiaSevQo2z//hoatG+PT2LtGdTm28CBg4F3s3RJH4uk/cV3vRseRXWpUlxBC3CwmTJhQ1yHcsX799VdGjBjB1KlT+de//lXX4dzWwhuGM7zVcH746wccG31D9uW5ln37zpiHwoS28EJT9s50wD2w+TnITYOja6Hz2BsctRC1Q6VS4aK1w0VrV6UVdcoymRRyC4vJLigiu6CYHH0R2fqS54IicvTFZOuveC6zPbugmEKjCUWBHH0xOfriGl+Hg0aNm6Mdro52uGrND7fS1452uGrt/35fss1NW6a8ox1uWnscr7HUvBC3E0mC1CLv5p04fuECJ1MNDK3B8XNC57Dzr5/w/vU43+W/yuh/vFDjWEbOHMtnT79LftZFvl0Yy0OvTkfrXLPJTVv16UjexWz+OHCYw/EHcfVxp3mPDjWOTQghxJ1r8ODBPPLII7z66qt1HcoNcyNXh7nS3LC5/HJ2J7mcI0f7IzAIgBNpOQB0bnxFzxQ7BwifBNtfgd8+gE73mW9fC3EHU6tVJcNg7MGrZnXoi4yVJkly9BUlV6wTKwCFRlPJksbVnw+lLI1aZZVEcSmbNCmTOHErSa6Uf2/e7+JgVz6RKsRNSJIgtSigx0im/+aBXYqK2QVFeDjZX/ugMrwcvfg/jzH8mbSMs6lfk9prHI0bV69HSSmts5Z75jzE6lc+IC+rmJ+/OMrgScE1zvh2HNWV3Ms5nElMYs+PcTh7u1HPv3GN6hJCCHHncnFx4fz58yiKcsfchayL4TClfJ18mRX8FK/EP4fitZWjmccJ8O3AiXRzEqRdQzfrg8Imwo6F5rlBUg9Ak1tztSEhbiaO9hoc7TXUc6vZTcmyvVFyDcXk6ovJKXnOLftc5rV5/xXlDcUoChhNimWoz/VycdCYEyhaO5y1Glwc7Cy9bly1GpxL35eUcykpYy5vXcZO5iAUNiZJkFrUsp4rbeu7cupCLj+fuMA9wdVPEkSMmMnSHRswppxj/XtzeHTBd6jVNfuPoEHLBkRMfZjNnyRyev9l6rc4S8igZjWqS61W0zV6IHlL1pGZkcHO1VsYOPke3P1qmA4XQghxR4qLi2Pw4MH885//5NNPP63rcO4Io9qOIOanL7F3O8pzcc/x1fAvOZWeC0C7BhUkQVx8oeMoOLQKDsRKEkSIm0C53ijXoXRulFyDeVjO30mTInINRkvS5MoES84ViZYcfRFFRvNEs+Zljo1cyKnZXClX0tqpyyVLShMqliSKJZlyxetyZUqO19qhtZOhP3c6SYLUssEdG3DmwmX2H0yoURJEo9YwdNq/+f6FaIoSE9m47i2Gj6757Oxtw1tRkGvPzlWn2P3Nady9VbQOrf4SvABqOzW9HxnKlve+xZCrJ2PlUVyndUXtJL9WQgghqqZNmzbs2rWLiIgIpk+fzpIlS+o6pNue1l6DKjMKk9ObnMo6wVv73iPX0B6VCpr7OFd80F3R5iTI4a9hyKugrSBZIoS45ZSdG6XBdS5SZSg2/t3rRF9MfqGRvMJi8gzF5BvMiZY8Q7E5SWIotuzLMxitXucbjBQaTSX1mjAUF3IpzwYXjHnoT2lyxNnB3OvE/Fz+tVMl250d7HBy0OCi1eBs//drRzuNrPZzi5C/VmvZsJZ21N+5As1fGgyGAWi11V8eslWru2g6/D7OrvuKP79Zwdnw4TRtElDjmDr1bULG2Wz++HkHG5b8QtS/ptKoTaMa1eXg6kjvCUPJ/PgI9hkmMj//g3r/7ITKXrqtCSFubklJSURFRbFv377rKlNdmZmZ3HfffaSkpNCpUye+/PJLq6WDk5KSmDBhAhcvXqRJkyZ89dVXN3TYREJCAhcuXGDw4ME35Hx+fn788ssvjBgx4oacr67V5ZwgpdwdvLiYNhqnJl+w8kQsGudHqG8fiNaukpUmmncHn7Zw8RQc/p95iIwQQpShtdOgddXg41qzIT5XKiw2lUmWlE2UlH1/7YRKaZmCIvP/uUaTQra+mOzrmJC2Mk725oSIk4M5QeKsLUmo2Jt7opR9bS6jwVlbebLFuWT1IweN9F6xJUmC1DL/1q3Yr3VFbdCxf+8uuvcaWKN6Ro57lqW/78KYnMJ37z3Jo69+j0ZdsyWxVCoVvce240zCVrIzClm/6HMefGU6rl6uNarPraEn2onBZHx4iMLEbJJXHKDpw3ehlvF7Qghh5fXXX2fMmDHMmDGDuXPnsmzZMmbMmFGuzJNPPsljjz3GuHHj+OKLL3jjjTdu6MShCQkJHDly5IYlQQC8vLzYunXrDTtfXarLOUFKuTvak36hEz0bDGdX+g84Nl5Fo+KrTHKuUkFotHmlmAOfSRJECFHrHOzUONg54OVim6W5jSaFfKuEipGCInOvlXyDkfzCYvKLjBQUGsvtsypXVExBodH8vvDvhHZBkdGSbLEljVplnRyxNydIyj472mvK7XO0N792dtDgWLq99P0Vx91JE9pKEqSWqTVqXFvfjf7oJhITfq5xEkSj1jBi2puse348ealnWPXbRzzQfWqN47J3tGf0Uw+z8oUlFGRn8b/XPuPBl6dgr63ZuEIHP1d8Hg7g+Ce/cuLP45z77DJdJwyo8fwlQghhSyNGjOD8+fMYDAbmzZvHgw8+WG5/bGws3333HRkZGaSlpTFt2jRmzZoFQFFREdHR0ezdu5fOnTvz1VdfoVKpiImJYcOGDRQUFDBo0CAWLVpUpVjWr19PfHw8AOPHj+fpp5+2SoIcO3aM/v37A9C/f39efvllqySI0WjkqaeeYseOHRQWFvLUU0/x4IMP8thjj9GuXTtmz57NsmXL2LZtGytXrmTp0qV8/PHHFBYW0rFjRz777DPs7e05efIkjz76KJcuXcLBwYGtW7fywgsvoNfr2bp1K6+++irDhg2rycdebU5O1VumUtSce8lk7UP9pvLHpUNc5iyXHZZjUgahVlXy3R30AGx7Cc79DucPQqOgGxixEEJcH41ahZujPW7XOY/KlUwmBX2xsVyCpGxSpaDIWJJIKUmcFBnJN5SUKfO6tFy+wZyIyS80UlhsHhJkNCllllO2zVwrV9Laqf9OqlyRYCmbXCmbPHEuk2hxctBUevzNlmiRJMgNENJ9MLuPboILx8jIzKCeb70a1dO8RWeaP/AIr535CMOfHxLUrhcdfTvWOC6vhl4Me3w869/+hKzzKXy7cCVR/xpf48SFY2tP3Ic0R9mSypm/EnH6ejfB9/WocXxCiNtXcXHlXVBVKhUajaZGZSvz+eef4+3tTV5eHuHh4URFRVmViY+P59ChQ9jZ2REWFkZkZCQajYZjx46xcuVK/P396devH7t27aJXr17MnDmT+fPnoygKUVFRxMXF0aNHD6ZPn05cXJxV/TExMYwePRqdTme5+9+4cWNSU1Otynbu3JlvvvmGRx99lG+++abCMh9//DGNGjUiPj6egoICunXrRkREBAsXLqRr166EhITw73//m927dwMwduxYpk41J8/nzJnD6tWrefDBBxk/fjyvvPIKgwcPJjc3F61Wy0svvcSRI0d48803r/nZ2lKrVq2Ij4/Hx8en3PasrCzuuusu/vrrrxsaz+3MVWtuAhoKNQRrZ/CT4VkyOcjyo8uJ7hhd8UEuPtBhBPzxDeyPhRFVS/zdUUxGMGSDIReK9VBsKHnowVjmdXGh+VkxgmICRSl5LvMwGf9+jQIq9RUPTZnXqr9fq8tsV9uDxg40DuaHuszrqm6XLvhCXJVarSrpnWEHNetYX6lio6lMz5S/kyV5hmL0RSYKioopKDRRUGREX1KutIzlfZERfcm2gpJtZZ9LmedeMZHF9a8QVBkHO/XfPVXsNfRpX4+YyJr/PVtTkgS5AVq2aMlOj+bY6c4Qv2sLw0Y9UOO6RkY8wfafE9mWvI3/2/F/rB6xGleHmv9ra9GpBX0fHsNPn67m3Ilj/PjfHxg6NbLG9bXq3RF9dgGHfjvA8YN/4OjmRIeIu2pcnxDi9rRx48ZK99WvX5+uXbta3m/evLnSuRN8fHzo3r37Nc+3aNEi1q9fD0BycjLJycnY25e/ExQREYGnpycAw4YNY/fu3fTs2ZP27dsTEGCehykkJISkpCR69erFtm3bWLhwIXq9ngsXLhAREUGPHj1sMrHnW2+9xbRp0/jwww8ZPnw4Li4uVmU2b97MkSNHWLFiBQA6nY6//vqL8PBw3nnnHQYOHMhXX31lSSgcPHiQ559/Hp1Oh06nw8nJiezsbC5dumQZ9uLqauPWWzUlJSVV+LM2GAwVJoJuVTfDnCDODubkYUGRkaKCBhjSR+DYaC2LDywmtEEogb6BFR8YGm1Oghz5GiJeBzvbjP2/KRUbIPsc5F6AvIySR+bfrwsulyQ8ckBf8lxko5kbbyYaLdg5mn/W9o5/v7ZzLPMo8/5aZcrtdwJ7J7B3LnkueW2nleSLEICdRo27Rn3dqwBVRlEUDMUmS+KkoLAkeVLSE+XK9/oyyZMr31+ZYNEX/Z2QKVVYbKKwTKKlY+O6GRIqSZAbpGFgbzLjlpN5dDumyH/UeL4MlUrF/O7zOXbxGOrTyax4ZwpTnlxxXcNOOvcLQnfhMvu//5ETcbtp1KYNwQP9a1xfwIgwCnLyOPXHCRLi9uPk5kzzHlcZZyyEELVo+/btxMXFsWfPHhwdHQkLC8NgMFglQcpOOKZSqSzvtdq//8jTaDQYjUb0ej2zZs1i3759NGrUiLlz52IwmLunXqsniIeHh6U3SGpqKn5+flZlGzduzLp16wBISUlh06ZNVmVMJhMffvghffr0sdp3+PBhvL29OX/+vGXbI488wg8//IC/vz/vvfceSUlJV/vYbqjSBBXAjz/+WG6eDKPRyLZt22jRokUdRFY7boY5QZxKkiD5hUYycgwUZXUlzD+TI1m7mPvLXFZHrsbdoYKlIlr0Bjc/yDkHpzaDf81vnNwUDLmQeRIyjsPF05CVDFlnzc855wGlZvVqHMx/0JdNIFgeJe/L9rQo16ujzENd8gwlvUVKe4wYK+k5UrZHiRFMxWAsAmNhyXPJa1NR5duvZDSYH7XTA78SqjKJkSsSJFavncHhyrJXO7bMcw3n1xPidqFSqXAsGapSW0oTLVbJkyJjrSV3rkWSIDdI996DWfvbajT5F/kt4SDdQ0NqXJeH1oM3gp5jx9dTKVQSrnvZXIBe4/qSnaHjr4R8dn+Thk+TBjTt4F3j+kLG9UL/cQFnzySz58c4HNycaNS5+XXFKIS4fQwdOrTSfVfOfn61yTmrMlN6dnY2Pj4+ODo6kpCQwMGDBysst2nTJnQ6HXZ2dmzcuJFp06ZVWqder0elUuHj44NOp2Pt2rWWOUSu1RNkxIgRLF++nBkzZrBixQoiI63/iMzMzMTHxweVSsWCBQuYMmWKVZnBgwfz/vvv07NnTzQaDUeOHMHf35/ExESWLVvG77//zoABAxgxYgQtW7YkLy+PBg0aUFhYyMqVK7n77rtxd3fH29ubLVu2MGjQIMtwGDc3N3Jycq56HbY0atQowPzzjI4uPxTD3t6eFi1a8NZbb92weO4EzmWSIJm5BkDFowHP8PqhR0nNTSUmLoa3+75t/W9MrYZOY+DXd+HQ6lsrCZJ/CVL3Q0q8eV6TC8dBl3z1Y+wcwbUBuNQrefiCa33zaycv0LqDo7t5yWCtG2g9QOt66/aQUZSSxEnh34mRskN6LM8F5bcVXfG+qvuLCszbivKhML9MEkYx96qp7Z41pckqS2LExfzs4HxF0sS5zLaS7Q4ulRxTprydo/RoEXe8sokWr7oOpoQkQW4QVxdX8js+wPsH8gn8vZDuoddXX3DbXvw5/F5Sv/+aP//3GQdbBREUdH2z+A+bNpItn/zBqX0X2LT0MKPm3EW9Zm41qkutVnP3xMEYPviOC+npnPxmHz4+Pjg0rtuu1kKIm4OdXdW/fqpTtiIRERF88MEHBAQE0LFjR0JDK/4PODw8nMjISMvEqK1bt660t4SnpyfR0dEEBATg5+dHt27dqhzPvHnziIqKYvHixQQGBvLyyy8DsHTpUgCmTp3Ktm3beP755wGIjIzkkUcesapn8uTJJCYmEhISgslkolGjRmzYsIFJkybxzjvv0LhxYxYtWsSkSZPYunUrL774ImFhYdSvX5+QkL8T8cuXL2fKlCk8+eSTODk5sXnzZvr168frr79OSEgICxYsqPWJUU0m88RvLVu2JD4+Hl9f31o9nwAXB/O/q4LCYjJyzLf4m3v58mafN3lo40NsTd7KyuMrecC/giG8nceZkyAnfwS9DhzrpjfLNRVchr9+htPb4MyvcOnPisu51IN6HcC3HXg1B4+m4NkcPJuZkx530h+xKhVo7M2PumAsMidGigrMiRGr11c+V7bvGuUs5ys0P/S62rumKxMjlSZOKkisVCXZopE/54SoLpWiKDXs53drKu16qtPpcHevoJtnLTp7KZ8+C7djUmDTrF50aHh95zeZTCx7+T70x46BizPjXl1DgwYtr6vO4iIj3/3nIKkn0lCrjjH6/x6gUZtGNa6vqKCQw//9hXrntWhc7Kn3aBD29Z2vK0YhxK1Fr9eTmJhIy5YtcXR0rOtwKhQbG1snE4Heiir6edbGd2tKSgp+fn639SpjddkmWbz1JIu3nuLekMZ887t5vpXDLw7GzdGeFUdX8Eb8G9ir7Vk+bDkdfa6YtE5R4P27IeMYjHwP7nrohsZ+VboU83wlx74z9/pQTOX3+7SBJuHQOBQadATf9uYJX8WdQ1FKep9ckRgpvDJ5UnZbyfbCvEr2X7HNeAPHDll6s1SSJKmsl8q1erGUHiu9WcQtpKrfq5I6vIGaejsTEdiQDYfT+GTLAf79UN/rqk+tVvPAkx/x6dMjUS5e4n8LJzN5wXc4aGu+xKCdvYZh0zqz4l+7ycnM5NuFnzLuhan4NK7Z0Bh7JweCH+1HxkeHKUrNJeOjQ3j80x+XRjfpXSMhhBA3hYCAABISEmjVqlVdh3JbKh0Ok5atB8xLR5auGPOg/4PEp8Xz09mfmPuzeX4QN4cyPUNVKuh8n3m53EOr6j4JUpgPR/4HCV9C8u7y++p1gNYDoFVfaBIGzjUf6ituEyrV370s/p+9+w6PqkofOP6dOz2TTHrvhZIASegivYmo2HtDUXd1Leu661p2dXXXXV3b6k9x7d1VEUURUZEmvZPQQ0J675lMr78/JoSEmkoCnM/zzDMzt5x7JpDcO+99z3vopf8PblcHAicnWN/RfQ7Xq+n1bBbZCQInhzNUThRYaZPNctJ9RG0W4fQTQZDT7L4pyQTu+5S0g0Ucyo8mOWlAt9rz9Q1izsPzWfy3ubhKy/nstXuY+9D73bpzptYquOrRm/jiqf9iNRr4+tl3ueHv9+AX1MWhMRoFIfOGUvVmFvvqD2F6L5cZv7kUXZgIhAiC0D/cdtttfd0F4Shnc6Jqf5gdRtsyHKaqJQjiq1a01v+QyWT8ffzfOfD9AUqNpfxtw994afJL7euDDGsJghSuA2MN+Iae9s9AcyVsnA87PgZrY8tCGcSPh6FXwsBZ4B9z+vslCJL8SJ2Y3uDxtNRUOV7gpOW5XeDkcCDlJOuPXuayHz5Y79dnkauPHyTpVLDlOFksh5eJ2YaEo4ggyGmWFh1AWqQeWaWHTT99TvLvnux2mwkJGYy88xG2v/EMG2q34t7zPnek39mtNgPCA7jykTv46p9vYW5qYME/3uPGf9yN1rdrqexynZKAWwdheusAFquFVe/9wPS7L0MbeOy0j4IgCIJwNusPs8P4tMwEUN1SD8RP0/6S0F/tzwuTX2Duj3P5pegXvsz5kusHX39kg4A4iMyEiiw4+COMuPU09Rww1cH6/8CWd7zDGg73Z9Qd3uCMf/Tp64sg9AWZzDvVsFJDr2WzuJxthvqcKrDSiWBL231as1laZiBqDWb2MJnUgcDKSdafsjaLVmSznGFEEKQPjJl1I1s/2oWsfCd79+5iyJD0brc5fuINlNHIO/lvsGnnq0T5RTM78cSzL3REWEIYlz40l29feI/m2ioW/OM9rn/qTtTarlU89wnVM/X2i1nx3vcYTUZWvbOEGb+7DFUXAyuCIJxZzuY7++eS0/Xv+PjjjxMUJIYu9Bad2nvB3mx1AuB3nGkK00PT+cPIP/DCthd4fuvzpIemkxacdmSD1Eu8QZD9S05PEMTtgq3vwcp/gM3gXRYzBiY+BAMuEF9CBKEnyRUgb5n9qDccrs3Srq5KR7NYjjdc6DjBmMOzDXncYDd6H71Foen5GYbaLpOrRDZLDxKFUfvIF28/h7t4M07/eG7548vIeqjw27+3/JtP93+KGgVvj3qREUOmd7vN3G25/Dj/E9xOB6GJg7n+iVuQK7ve3/qCalZ9/AMOh4PAwCCm/e5SlFpVt/spCEL/5HK5yM3NxcfHh9DQ0A5Nayv0Tx6Ph5qaGsxmMwMGDEAu937p7C/n1jNNX/7cfj1Yw9z3t7S+H5MQxIK7xx2zncfj4YFVD7C6ZDWxfrEsuGQBvqqWmd6qD8AbY70X53/O773Uf4Cag7DoN96pbQEi0mH6k5AyQ3wxEATh+FyOjtdZ6XAh3DbBmLYzDfU2mbwTRW07OcOQygcUWu8U6Ge4jp5XRRCkj1RXV7Fs/gNILjvRU+9i8vSemX7Q5Xbx518eRPXdSiLNKi558j2SkkZ0u90DG/fzyzuLkSnTSUyP4sLfDkOu6PovSk1OOav/9xMul5OQkBCm3D0HxXHuQgmCcHYwGo2UlpaKbJCzgEwmIyYmBl/fI1Oed+fc+txzz/H73/8erfbURb03b95MbW0tF198caf73R/15TXJ1sJ6rnnzSBHR6YPDeO+20cfdtsnWxDXfX0OFqYJZCbN4YdIL3mCmxwOvjfROPXv1B946HL0h+wtY8pD3i4faH2Y8CSNvF5kfgiD0Lbe7ZaahTha1PW7WywmCLW7n6fs8iqODJp0Mtii1R9pQalrqsbQ8H37fy9Nvi9lh+rmwsHD8h11Ec9a3FK//EuN5k/DV+Z56x1OQS3L+MemffPDzFbjqK1jy7N1c+bePiIlJ7Va7g8elogsI44c3dlO4u45l7+5l5p1pKBRduwAJHRTFxKums2bhcupr6yn+ZAeJt49G1o3AiiAI/Zevry8DBgzA4XD0dVeEblIqla0ZID1h3759xMXFcc011zBnzhxGjRpFaKi3yKbT6WTfvn2sW7eOTz/9lPLycj7++OMeO/a5TKts/294dE2Qtg7XB7ntx9v4ufBnxkSM4dpB13ozMFIvgfWvwsGfez4I4nbDL0/Axte97xMmwpXvgD6yZ48jCILQFZLkDQaofHrvGC5HN2cYOt4QozbrnZYjx3K2vLfU997nOZzRomwZPjTgArj4pd473om6ITJB+o7VamXBi7/DZLVjypjHn66Z1mNt19aV8PmT1+Opa4BAf67/+xeEhcZ3u93ifXUsfWM3DmspIdF2rv3rrciVXY+lle8soOGbXPwdWjSDgwi+OVUEQgRBEM4w3T23Zmdn8/rrr7Nw4UIMBgNyuRy1Wo3Z7E01Hj58OHfeeSe33XYbGs3ZU0eqL69JciqbmfXKmtb3N58XxzOXDzvpPh/t/YgXt72ISlLx2cWfMThoMBSsgY/mgG84/DGn54amOO3w3e9g91fe95Mfhcl/FtkfgiAIPcnt9gY+uj3DkKVNVoz1SIDF0fLgBCGHIVfCNR/02McRw2FOoD8FQQC27trDzf/LxYaKL39zHmOTgnus7YqKPL566iZoakYWGszNf/+KwMCIbrebu7WYpa+/jcftIiJ5ANf8pXuBEGteI7Uf7gWnG89AHVE3pyNXiSQlQRCEM0VPnVvdbje7du2iqKgIi8VCSEgImZmZhISE9GBv+4++vCY5VGNk+ku/tr6/Z0oyj1w4+KT7eDweHlj5AKtLVxOvj+eLi7/AV1LCvxO8F753r4eIod3vnNsFX82F/d+DpIDL5kPG9afeTxAEQeh/Dk/p3DYocjhootZD6MAeO1RHz6vilnsfG50+lCvHJAPwyNe7sNhdPdZ2ZGQKl//lXdD54Kmp43//uJHm5rputztgdByTbroCmUyi8lAuX/7jQxy2rqe4a1ICCJmbhlnhYEt+FmvfXorLcRrHvwmCIAj9giRJZGZmctlll3H99dczY8aMszYA0tdU8vaXgD7KU2dYyGQynpnwDBG6CIoMRTy98Wk8chUkTPBucGhl9zvm8cCSP3gDIHIV3PCFCIAIgiCcyQ5P6awNBH0UBCd7A+Yxo3o0ANIZIgjSDzx2USoRfmpC63ew6JNXe7TtuLhhzH5kPmjUWGoq+dP3d2OwG7rd7vALRjLppiuRSRLVBYf44u/vY7PYutyeZkAgPpfF45TcVFZWsu7tH0UgRBAE4RxmtVoxGAztHmeL+fPnk5aWxujRxy9Eejoo5O2Hrag6OBTVX+3PC5NeQCFT8FPhT3x18CtIbhnO2xNBkM1vwo6PQCbBVe/BgJndb1MQBEEQ2hBBkH5Ar1Hy2pwILlesh4K1rFn9c4+2P2DgWGY+8hprxwewwXGAu5bdRZOtqdvtDp81kmm3XYtMLqeuuJAvnnoXi9Ha5fZiRicz7uLJyGQSFRUVrHvnJ9xOd7f7KQiCIJwZzGYz9913H2FhYeh0OgIDA9s9zhb33nsv+/btY+vWrX3WB+VRmSBHvz+ZzLBMHhjxAAD/3vJvckKTvCuKNrSM/e6iki2w7K/e17P+BWmXdr0tQRAEQTgBEQTpJ0anD0U35EIAild9QGFRYY+2n5o6gReu+5AgTRD76vbxx89vobaupNvtDpuawQV33YikUNJQXsqiF5Zit3Q9gyNu7ADOu2iiNxBSXi6GxgiCIJxDHn74YVauXMl///tf1Go17777Lk8//TRRUVFiVpgeppTaXwJ2NBPksLlD5jIpZhJ2t50/Zr+GSR8FLhuUbutah+xm+PpO73SQQ66AsXd3rR1BEARBOAVRGLUfcTqdfP7qI8gb8nH4hHL5fS/i38N9PNR4iEe+vI1xa+tQBQRz3d8+7ZFZY3K35fLLu2twexIIT9Az54FMNLquzwNdtOEAm35ch8fjJjwigkm/uUgUSxUEQeineurcGhcXx8cff8yUKVPQ6/Xs2LGDlJQUPvnkEz7//HOWLl3ag73ue315TWKyORnytyOZp89fnc61o2I71UajtZGrv7+aKnMVF8mDeC4vC9nUv8LkhzvfoV+e9E616x8Lv9sIar/OtyF0mtvjxuq0YnVZ2z87rccstzgt2Fw2HC4HTo/T++x24nB7n9suO/za4XHgdDlxeVx48ODxeHB73Me8brcMNx5P+9eHSTIJGTJkMu9DQvK+PrwMWfttWt6Dt6aNJJOQy+TIJTkKmaL9a0mOXCZHIR1ZfvT7k22nlJQoJAVKSel9yJXHfa2Sq44sb1mnklQoJAWynppdSRDOUR09r4pvlf2IQqHgwrmP8uN/H0ZprmHxB89yw73/QKHouX+m5IBknp/5Kku2/hZPbR1fPHEdlz/2DnHxJ58W71QGjBpAQFgEi1/Norqoma+f38KsuwYTEtO12W7izx+MTJLYuHQN5oomaj7dS/gtQ5F1oHCbIAiCcGaqr68nKck7tEKv11NfXw/AhAkTuOeee/qya2edo4e/HF0otSMCNAG8MPkFbv/pdpa66pnmo2VW8cbOd6ZyD2x43fv6ohdFAKSTHG4HTbYm6q31NFgbaLA10GhtpNneTLOjGaPdiNFuPPLaYaTZ3ozRYcTkMPV194U22gVRjg6YHCeoopJUqOTeh1quRi1Xt3uvklTHLmuzrVKuRC2p2y0/vK1CEl8ThbOX+N/dz4SGhDL22j+z7bO/Ia85wKL//Zdrbr2/R4+RlDSCy594n2//dRc0Gvj26bnM+ON/SBsyuVvthsb5cflDw1n86g5qizay4O+ruPSh24gZHNOl9uLOG4hSpcS+qATnQQO1H+0j+NY0JJUIhAiCIJyNkpKSKCgoIC4ujsGDB7NgwQLGjBnD999/T0BAQF9376yi7GJh1KMNDxvOncPu5K1db/GvkCBGl20lyO0CqRPn6pXPgMcFqXNg0IVd6sfZyOK0UG2upspURZW5yvu65bnWUkujrZF6az3N9uYeOZ5KUqFRaLwPuebY1y3PbTMe2j6faJlCUqCQKVozMQ5naRzO4jjesqOzPAA8eDNC2maP4OFI5khLJsnRmSVHv3d5XLjcLlweF06384TvnR5np7ZzepytmTEOl8P73PKwu+ytGTNt17k87WeFdLq9bVjoRm2dHiKXydsFU44OopwosKKSq9DINajlajQKTevyw68P/19SK9THbKeRa0RGjHBaiOEw/dTaX3+h+Jf/8oN7LJNnXc1vJyf3+DGqa4pY8MytuKtqQKlk7O+eZOy4q7rdbm1pHQv/9Q7W5ibkKjUX3nMTA0YN6HJ7tvwmaj/ci8fuoiHKyaA7xqHSabrdT0EQBKFn9NS59T//+Q9yuZwHHniA5cuXM2fOHDweDw6Hg5dffpnf//73PdjrvtfX1yQpjy/F6fZeBr576yhmpIV3qR2Hy8G1S64lrzGP2UYTz1/5LUSmd2znsh3wzlTvbDD3boWQlC714Uzk9ripNldT0lxyzKO0ubRTs/nJkBGgDiBQE9j6rFfp8VX54qf0w1fli6/St/XZT+XX+t5H4YNarkbemcCV0CNcble7YInD5cDutre+bg2qtAmktA2y2Fy21ufDQ5UOv7a77MesP7zM7rK3e3342enp+zp8kkxqDYi0DZQcL2hydAClbaClbRvHa69tGyLocvbo6HlVBEH6sY+XbeLJlXUA/PuqYVw3Oq7Hj9HcXMcn/7wZZ2ERSBKD7n2YWePndrtdQ20TX/3zfZprq5HkcibfchUZ04d3uT1bkYFd76/hkKucAP8Apv52Dmq9ttv9FARBELqvt86tRUVFbN++nZSUFNLTO/il+gzS19ckg5/4EavDOwvbR/PGMHlgaJfb2lO7h5t+uAE38Grc5Uyb+o+O7fjZtZD7M6RfD1e+1eXj92cej4cKUwV5jXnkNuSS15hHXmMeBU0F2Fy2k+6rVWgJ9wkn3CecMJ+w1keoTyiB6kCCNEEEaALwV/mLIIbQbS63C7v7SIDkRIGVttsc/Wx1WbE5be1eW11WbxttXlud1tZ2rU5ra6ZPX2gNqBwOlCg0aOXadkEVrULbLkNKq9C2y2zRKrTtXreua7OtGGLU+0QQ5AT6+oKjs579cT9v/ZqPj8zGfy8OY/KECT1+DJvNzMcv3EZu5V5+Ginjt8Pv4Z6Me1oLSXWVxWhl4T8/pK60CGQSYy69kPOvntjl9mr2l/Hrl8twOh3o/fyZ+ptL0AbqutVHQRAEoftO97l12LBhLF26lNjYzhXy7A0FBQXMmzePqqoq5HI5mzZtQqfr2Lmpr69Jhv3tZ5pt3ju/n991HuOSu1bH67D/LLyS9025hMhUfHvdSvzV/iffoeYgzB/tzQK5bxsE93zWa1+oMlWxp3YPu2t3s6d2D3vr9mJ0GI+7rUKmIMo3ili/WGL8Yoj1i219HamLxFfpK+5SC2c9j8eDw+04EjRpKcbbNlhysuDK0QGVk21/eP3RQ5FOB6WkbD/UrE2w5XDA5XjBlrZZLCLYcnKiMOpZ4tELB2M2GgjIepvSnxv51WFk8tSeHS+rVvsw7/HPeXXLy3hyPubN7DcpbMjn6fP+ho+26xdlWl8N1//9Dhb9+3PKc/az5bulGBtNzLxjVpdO6KGp0Uy58UJ+/fwnDM1NrHjzO6bOuxhd+CkusgRBEISzSmFhIQ6Ho6+7AcBtt93GM888w8SJE6mvr0etVvd1lzpMqZCgJRGhqzVB2vrdwGtZufkpClXw+s7X+ct5fzn5Dts/8D4PvPCMDYB4PB6KDEVsqdzClsot7KjaQY2l5pjtFJKCRP9EUgJS2j2ifKPO6S8sggDemXsO1xhBdXqO6XA7TpilYnFa2gVN2s6aZHFZWgMpFqflmJmUDs+i1HZWpbbHdLgdNDt6po7PiSgl5TG1fdoGW46u89ORYMvxsmLO5Owz8Ve3n5PJZDx15SgWNqzEVbyF0pVvs8JuY/qsy3r0OHJJzkPnPUxicAp/3/g0xqU/8f7iHVz1yDtERnR9fK5SqeTqx29m6euLyNu2k4NbbEjy/Uy9eTByZecvuEIGRjL1lov49dOfMJqM/PLOYqbeOhv/uJAu91EQBEEQumLv3r0olUomTvRmOQYFBfVxjzpHIR25IdGV2WGOpo4ezV/r6rkzMpwFBxdw1cCrGBw0+PgbO6yQ9T/v65G3d/vYp1OzvZn1ZetZU7qGzZWbqTZXt1svl8kZEDiAIcFDGBYyjKEhQ0kKSEIpKfuox4IgHE0pKVGqlPji26vH8Xg87YIiRwdMTjRF9eFgyzFTV7fdt02GyzHBFruDZk5PsEUr1x4zjKhtkOVE2S0ahYZo32gywzJ7tZ/HI4IgZwC5XM41dzzC1x/9B0f+OqrWfshPdhsXzrm2x491xYAriCWIDSsfxG2t4qu/3sC0B59n6NCpXW5TkiQueeAqsn4ZxoZFZeRsrsRQZ2H2b4ai1Xf+jllQUjjT75jD6g+XYraYWfHBEmbdfhm6uMAu91EQBEE4+6xZs4YXXniB7du3U1FRwaJFi7j88svbbTN//nxeeOEFKisrycjI4LXXXmPMmDEdaj83NxdfX1/mzJlDWVkZV199NY8//ngvfJLe0Xaa3J7IBCEoibEeDbOMJn721fHPTf/k49kfHz/789AKsDaCXxSkTO/+sXtZjbmG5cXLWVW8iq1VW3G6jxSQVEpKMkIzGBM5htHhoxkSMgStQtQtEwTBe0P78Jf/3tQjwZYT7duLwZaZ8TPPnCDI/v37+eKLL1i7di1FRUWYzWZCQ0MZPnw4s2bN4qqrrjqj0kHPBJJc4urb/sA3nyqxHVxF/ebP+bqphituuAepB+7etDVqwGTC/vEJ3z13N566elY+ez9FV89l9mV/RJK6fqzMmQMJjg7hp7d3U5ZTxEePLufSB28mamB0p9vSRwcx47eXserdJQQbtDS+vx/FbUNQJ4ihMYIgCIKXyWQiIyODefPmceWVVx6z/ssvv+Shhx7izTffZOzYsbzyyivMmjWLnJwcwsLCAMjMzMTpPHbGhGXLluF0Olm7di1ZWVmEhYVx4YUXMnr0aGbOnNnrn60ntJ0m9+gpc7tEJoOIYfypdCNr9AFk1WTxff73XJp86bHb7v3W+zzk8s5Np3saWZwWVhav5PtD37OxYqN3StYWCfoEpsZO5fzo88kMzez1LziCIAgn01fBlrbDf9oGW44JvLQJqLQNwAwI7PoMot3RqcKoO3bs4M9//jPr1q1j/PjxjBkzhqioKLRaLfX19ezZs4e1a9diMBj485//zIMPPnjKYEhn78A0Njbyl7/8hW+++Yb6+nri4+N55ZVXuOiiizr0Gfq6CFl3edxulnz9Ec3ZiwEwxkzi1jseQKPs+QsIg6GGz1/6DbacHAB0w0dwwwNvdKtOCEBtWTMLn3kLq7EOuVLFjDuuI3V8WpfachhtNHxyAHuRAZlSIvCmwfgM7l5hN0EQBKFzTve51c/Pj+zsbJKSkjq8j0wmOyYTZOzYsYwePZrXX38dALfbTWxsLPfffz+PPvroKdvcuHEjTz31FD///DMAL7zwAgAPP/zwcbe32WzYbEdmAzEYDMTGxvbZNcmMl38lr9pbsHPdI1OJCfTpfqNL/gDb3ue9jIt4xbCHYE0wS69cio+yTdtOGzyfDPZmmLcM4sZ2/7g9qKCpgM8PfM7iQ4sxOUyty9ND0pkeP52psVNJ9E/swx4KgiAIx9PR65FO3da/6qqruPLKK6msrGTFihU8++yz3H///dx55538+c9/5uOPP6agoIAlS5awc+dOXnrppZO2d/gOzN/+9jd27NhBRkYGs2bNorq6+rjb2+12Zs6cSWFhIQsXLiQnJ4d33nmH6OjOZxKcqWSSxJxrbid66l00y/x4ozCS697eRGWTtcePpdeHcuffFhJ98ZUgk2HauYM3n7iUoqaibrUbEu3H9U/diV9IGC6HnWVvf8aaL1Z1qS2lr5qQO4aiGRSIw+Fg1ac/cmjV7m71TxAEQTj72e12tm/fzowZM1qXSZLEjBkz2LhxY4faGD16NNXV1TQ0NOB2u1mzZg2pqakn3P7ZZ5/F39+/9dHXs9u0qwnSE8NhAEIGAXCrFWL9Yqmz1vHxvo/bb1O0wRsA8Y2AmNE9c9xu8ng8bK7YzN2/3M2l317K5wc+x+QwEe0bzd0Zd7PkiiV8dvFnzBs6TwRABEEQznCdOuMdPHiQ3/3udwQEBJx0u3HjxvHFF1+c8E7IYS+//DJ33XUXt99+O2lpabz55pv4+Pjw/vvvH3f7999/n/r6er799lvGjx9PQkICkydPJiMjozMf46wwefpFDJ/7PB5tENkljVzy2lq27Mvt8ePIJTlX3fIM4x78Jx4fLcsjarnhhxtYVrisW+0GhAdw8z9/R3jyADxuNzt+WMbC5z7DYet8tX9JJSf4ljTqkt00Y2bryk3s+2Fbt/onCIIg9F9vvfUW4eHh3WqjtrYWl8t1TDvh4eFUVlZ2qA2FQsG//vUvJk2aRHp6OgMGDOCSSy454faPPfYYTU1NrY+SkpJufYbukmQ9WxgVgNCBAChrc3lg+AMAfLDnA+qt9Ue2KfjV+5w8FboxzLanbK3cyu0/386dy+5kffl6ZMiYEjuFt2e+zdIrl3Jv5r3E6+P7upuCIAhCD+nUmUepPFLV+uOPP26X0nmY3W7n448/Pmb7423X2TswixcvZty4cdx7772Eh4czdOhQ/vWvf+FynXieZ5vNhsFgaPc4W4xJiWDxfeNJjdQTasol9/NHWPLNJ3jc7lPv3Emjx17OdS99S1BaJs2OZv746x95fvHDmEyNXW5T7aPmuidvI23yBJDJKN27h08ee4Om2s4X15EpJIbPm0JCciJ4POzauIMdn6/B3Qs/C0EQBKFnXXTRRTQ1NbW+f+6552hsbGx9X1dXR1rakWGTN954Izqd7nR28YRmz57N7t272bNnDy+//PJJt1Wr1ej1+naPvtR2PHRPZ4JQn88FMVNIC07D7DTzzq53jmyT3xIESZzcM8fsokONh/jNst8w7+d5bK/ajlJScv2g6/nhih94bdprjIsahyTr+yCNIAiC0LO6/Jf99ttvb3fBclhzczO3337qqc66cgcmPz+fhQsX4nK5WLp0KU888QQvvfQSzzzzzAmP099ST3tafLCOb+45nxuTrMg8Hgw7vuGz+X+jrr6ux48VERjLBxd+wB1D78DXAtJXP/D+wxexb9+aLrcpSRIX3Hkx0267DrlSRXODh2+ez6KqoPPBKkkuMWbudAYO86YiH9x7gA3v/ozLcWxBO0EQBKH/+Pnnn9vdWPnXv/5Fff2RzAGn00lOS32qnhISEoJcLqeqqqrd8qqqKiIiInr0WEebP38+aWlpjB7dt0NB2paF67FMEH0UqPzA40JqKOTBEQ8C8EXOF1QYK8DSABVZ3m2T+iYIYnKYeHHri1y9+Go2VmxEKSm5btB1LL1yKX857y/E6s+ua0VBEAShvS6f8Twez3GnPCstLcXfv3dm6HC73YSFhfH2228zcuRIrrvuOv7yl7/w5ptvnnCf/pZ62hu0Kjk33/EgoeNvxiNTIFXt4YfXHmTLpnU9fiylpOTBkQ/y6thnUal1eOobWf7M71j0v6dxuU+ckXMq6dMyuPrxuwmJHYXZ4OCbl7azb31pp9uRJIkR101k+ITR3uyS4hJWzV+M3dTzNVMEQRCEnnF0jfZO1GzvMpVKxciRI1mxYkXrMrfbzYoVKxg3blyvHvvee+9l3759bN26tVeP0xlyqQdmhwHvDDEhLdX+aw8yLmocoyNG43Q7+WjfR1CyFTxuCEr2BkxOsx1VO7hq8VV8tO8jnB4nU2Kn8N3l3/HX8/5KhK53g1+CIAhC/9DpKXKHDx+OTCZDJpMxffp0FIojTbhcLgoKCrjwwgtP2U5X7sBERkaiVCqRy4/MhJKamkplZSV2ux2VSnXMPmq1+pyYrlcmScycfRU5yWls+foVFKZq8pa8ROH+LVxy/d34aHug4nsbY4ZfQsoLI/nq1XuxHThAyeIveWv3Zi699yViYk5cFO5kIlMiuebxUJZ/sI/8rBp+eXchB9aHM+eBq1FqTjy06ngGXTgcbYAvm5auwVDbROXbWUTfMQK5/tj/I4IgCMLZyWg0kpeX1/q+oKCArKwsgoKCiIuL46GHHmLu3LmMGjWKMWPG8Morr2AymTqU0dod8+fPZ/78+Scdzns62JxHhowe78ZWlwUlQfkOaPQWUr9r2F1srdzK1we/5q4oO8EA0SN67ngd4HA7eH3n63yw5wM8eIjSRfHX8/7KxJiJp7UfgiAIQt/rdCbI5ZdfzmWXXYbH42HWrFlcdtllrY/rr7+et956i08//fSU7XTlDsz48ePJy8trV+fh4MGDREZGHjcAci4aNDCVa/7wKqoBUwFwHlrLb179ijUHa3r8WEGBkdz15EKSrr0dFAqcBYV8/fj1/PDti12+i6fSKJj922GkT/HD46yiePcuPnrkNaoKqk6981HizhvA1OsvZKgqEanKQfUbWTiqzV3qlyAIgtB7Dt9cOXpZd23bto3hw4czfPhwAB566CGGDx/Ok08+CcB1113Hiy++yJNPPklmZiZZWVn89NNP3S66eir9JROkoNZ06o26wj/G+9zkzeg8L/I8hgYPxeqy8ll5Sz2QyMzeOfZxNFgb+O0vv+X9Pe/jwcNlyZfx9aVfiwCIIAjCOUrm6eK31Y8++ojrrrsOjUbT5YN/+eWXzJ07l7feeqv1DsyCBQs4cOAA4eHh3HrrrURHR/Pss88CUFJSwpAhQ5g7dy73338/ubm5zJs3jwceeIC//OUvHTpmR+cOPhts37aRb35azmdG792WK4ZH89eLBhHsp+3xYxUWZvPD63/CVVrGngQZTBvP0+c/TaRvZJfb3LUqmzWfLsJptyFXqphw3aUMnzWy0+046yzUfrAXZ62Feo2Z0CsHE5kuqrwLgiD0lO6eWyVJYvbs2a2Zm99//z3Tpk1rLX5qs9n46aef+jxzoqf19TVJwqM/AJAYomPVn6b0XMNb3oGlf4LBl8D1nwGwongFD656EF83LCsuwe/W7yGx94MQhxoP8bvlv6PcVI6Pwod/jP8HFyRc0OvHFQRBEE6/jp5XOxUEOVEdkO54/fXXeeGFF6isrCQzM5P/+7//Y+zYsQBMmTKFhIQEPvzww9btN27cyB/+8AeysrKIjo7mjjvu4JFHHmk3ROZk+vqC43Qz2Zy8uCyHDzcU4ucx8YBmKYnnX8nU6Zcg9VQRtBZOp4PvFv2b582LMGNHp9Tx8NAHuHzodciljv37HK22pJbF//kUQ403EyRp5Ahm33v5SWceOh6X0U7h+9vYVr0XJBmjp48jafKQLvVJEARBaK+759aODj/54IMPOt12f9R2OMzBgwf77Jpk1YFq3lidxwtXZ5AQ0oOz7Rz8Gf53LUSkw91rAXB73Fz57WUcMhTy57oGbrlnD2gDeu6Yx7G3bi93/3I3jbZG4vzieHXqq6QEpvTqMQVBEIS+0ytBkLS0NJ588kmuvPLKkw4/yc3N5eWXXyY+Pp5HH320cz3vZedaEOSwrJJGfvj8DRIN3tRbpz6W4RfezrD04T1+rIKmAp5Y/wTZ1VlctslDpD6aWb/5JykpXauC77A7WDr/Wwp27AAgICKeqx67Db+gzmUhOSx21r37Y2sdmtTMIQy7chySJKa/EwRB6I5z9dzaXWftz61qL/z3fNAGwSMFrYsXrPsH/zi0gHgXLL49u1enn82qzuLu5XdjcpgYGjyU/874LwGagF47ntDzPG43HqsVt9Xa8mzDY7fhcThaHs6WZzsehwOczjbrjt7myAO3C4/LDW43HrcL3B7vc+uyNutcbvC4vdu7XHg87iPL3Kf4CnWS+8YnvqksA0kCuYRMkoMkIZMk77NcAkkOkuzIuqOXySVkMgnkcmSSzLuudZmETC73rlMokSkUyJSKY97LFG2Wney9smWfE73v4RvngtARvRIEWbFiBY888gj5+fnMnDmTUaNGERUVhUajoaGhgX379rFu3Tr27t3Lfffdx+OPP95rM8V01Vl7wdEBDoeDZd9/QUP2D0iulqkIo0cw5Yo7iYro+rCV43G5XXy57r/UvvM2OJwgSYROmcnlt/wdrdavS23u+HEb679aAvJ0fPShTL1lMEmZoZ1qw+1ys+3TVeTnHgIgJi6WcbfNRK7qdI1gQRAEocW5fG7tjt76udlyc7Hs2YvP8ExUCQk91m6HWZvguTjv68fLQeXNMjFvfoPp++ZjlCTenPEm46PH98rh8xrymPvTXAx2A6PCR/H69NfRKXsw00Vox+Nw4DaZcJtMuEwm3EZT63u3ydjmtQmX0YjbZMZjtXiDGhYLbputfbDD5l3ucTj6+qMJ3aFQIFOpvMERlRJJefi1qs3yE71WtlsunWh7pcq7rfLodpRIajWylkfr6w6OHBDOXL0SBDls3bp1fPnll6xdu5aioiIsFgshISEMHz6cWbNmcdNNNxEYGNitD9BbxIUa1NbWsvLb93EUbULm8eCRFKjTZjPz0lvw9+ncMJNTKS07wA9vPYrt4EHvggA9o2/5I+PGX9Ol9urLm1j+4UFqipsBSB6hYsrNo9D4dC4rZP/S7WRv3AEeD4GBQUyaNxttoLhAEgRB6Apxbu2c3hwOY9q0meI77oCW+im+M6YT8dhjKKOje6T9Dns2DmxNcO8WCB3kXbbsrzx34FM+8/djSswUXpv+Wo8fttJUyc1Lb6bKXEV6aDrvXvAuWkXP10I7G7ltNlx1dTgbGnA3NeEyGHA1NuFqOvxoxH3MsiY8Vmuv902mUiHTaJCpW77otj5ULRkMyvaPtstUSu8XcqXSm80gb8mOkLxZFDK5BLKjsi+OWSbz7idrk30hk5042+Nk365O9tXL05KJ0jYDxePG4zoqK8Xt8maiuF2t2x/OajnhssP7OV14nE48zsPZM048Lpf3vcPZss67DGdLNk3rMmf7bZxOcDq78097eikU3oCKRuMNjqhU3uCIRnPktVqNpFEjUx0OoqiQ1Jo2r9XI1Jo2r48KtKha9hcBmD7Rq0GQM5m4UDsiJ2cfW5a8h7whn9XuDDapxvGbSUncPj4RnbrnMiPcbjdrV31M9ufzweitRK8dOpRLfvcikUFxnW7P5XCzaXE+O3/eh9O6Ga2fnll3X0fCsIROtVOyJY9NP6zB5XKSpIth+B1TUIb17FTCgiAI5wJxbu2anv65eTweCq+/Hmv2LuT+/rgMBvB4kGm1hD/+GAFXX336UtTfOB+q98LNX0PKDO+yL28mP+9HLouJQi6Ts/ya5YRoQ3rskDaXjVuW3sL++v0k6BP4ZPYn5/wQGI/TibOmBkdlJc6aGlz19Thr63DW1eKqq8dZV4erthZnXR1uo7Fbx5KpVEg6nffh69vy2gf54dc+bZZrNcg02pYvixrv+7bPGjUyrVZ8gTwDeDwe71Chw4ERh8P7vu0wJLv9yHPLa3eb197lJ9623WuHHbfdDq1tnGA/m611u35BqUTSaJA0Gm/QRaM58n9cq/EGWrQaJI0WmUaNpNG2/704/Pui0SBptd4Ai1Z7THsyleqcHop0WoIgK1asYMWKFVRXV7ebthbg/fff72qzvUpcqLXncbvZuPFXntvsYFe1949Ehk89v81UMu2Cy7s1+8/RjMZ6Fn3wOA0b1lKrhx8naJk37A5uG3pbl+7S7Fu3n1UfLcRhNSOTJIZNm8yUm2d0quBrfX4Ve7/YRIIhEEmjIPimVDQD+mcWkyAIQn8lzq1d09M/N2dDA8W3z8NeWEjK8l9wNTZS8dRTWLZtB0A/Zw6RT/0NSXcaMh//dx0c/AkueQVGtRS+fXMCVO7mpmET2GUs5s+j/8wtabf02CH/sfEfLDi4gAB1AF9c8gXRvqc5++U083g8uOrqsJeU4KyowFFZhbOqEkdFJY6qSpyVVThrauCoa/STUipRBAYi9/dH7u+PFOCPXO/f+l7ur/cu9/dH7h+A3F+P5OuLXKdDdpJ6gYLQVzwuFx673TvcqiU44rHZjtSYsdm8Q7BsbV/b8disbV7bcNusbV632d5uw2Nt89pm9w7r6qsAjEx2JChy1PPxgypHB1I0SFofJG1LsEWr9QZbtFrvtj4trxX9s5RArwdBnn76af7+978zatQoIiMjj4k4LVq0qCvN9jpxoXZ8LreHJbvK+c+yHGY1LSBeVoVT6UvgsJlMvuAK9L5dq+NxPPv3reWNrPmsduwFIEYdwcPB1zJl+h2dLlLaVNPE9698QW1xIQBB0XHMefB6AiM6HshwGe3UfbIfe5EBt+TGMSWI5AuGdaofgiAI5zJxbu2a3vi5edxu7IcOoR4woPV93XvvUfPKq+ByoUpMJOaN+agTE3vkeCf0/e9h+4cw5XGY8oh3CMBzcWAz8MUlf+efe98lNSiVBXMW9MjhVhSt4MHVDyJDxhsz3mBC9IQeabeveRwOHGVl2EtKsZcU4yguwV5a0vJcisdsPnUjCgXKsDAUoaHIQ0JQBAejCAlGHuR9VgQHIw8OQRESjOTnd07fRRaEntQuAGOz4bZY2te/sVi9wRaLFbfVgsdqa/9ssXqDL5a2BYKtrTV1jmxjO/0BF6WyNRNF0mqR+fgced02cHKKoIoyPKz1fNUTej0IEhkZyfPPP88tt/RcBP90EBdqJ+dwulizfDHlWxcjtzUC4JJr0A2awuQLryY4KLhHjuPxePi56Gde2vYS0VnljMjzII+LYdptT5CaNrFTbbndbtZ9sZqdy1bicblQqDScd9VFjLqo47PReBxu6hbmkL1nFzWyJhKSExl981Tkyv4Z5RQEQehPeuPcqtfrycrKIikpqUfa60/6Yopc8/btlD30R5xVVUh6PTGv/Afd+ef33gFXPgNrXoDRd8HFL4K5Hp73Bl4a/3SAqYsuwul28s2l3zAgsHsXwE22Ji779jLqrHXMGzqPP4z8Q098gtPKbbNhLyzElpeH/VA+tkOHsOcfwlZYdPIvNzIZisgIlFFRKCMiUUaEowiPQBERjjIiAmVEBPLgYG/9C0EQzloeh6N9kWFLS/FhqwV3u8DL4SDLcYIqFnNrwKX1tcXi3afluVOZZR3gN3MGMa/1XH2oXg+CBAcHs2XLFpKTk7vcyb4ggiAd43A4WP/rzxRv+R6FuRoAt6TAMWA2E2ddS0qYb48cx+K08N1nT1P9y1JvYSWZDF3mcC68+Qmiowd1qq2S/cX8+MYCzI11SKpkBo87j0nXD0Lj27Fir263m11fb+RAtjdDJSgwiAm3z8InqOeyYARBEM5GvXFu9fPzIzs7+6wMghx2uq9JnDU1lN53P5bsbJDLCf/L4wTdeGPvHGzzW/DjnyHtcrj2IyjdDu9OA79I+OMBfr/y96wsWcldw+7igREPdOtQf133V7479B2J/ol8Necr1HJ1z3yGXuJsaMC6bx/Wffuw7d+Pdd9+7MXFJ/xyIdNqUcXEoIyLa3mORRUXhzImBmV0NJIYhiIIwmng8Xi8dVfM5pbgSEuwxGrFbba0f21tCZyYLccJqhx5rTv/fMIf+XOP9bHXgyCPPPIIvr6+PPHEE13uZF8QQZDOcbvcbN64mtyN36JoKmGBawpZnhQmDgjhjnGxTBoU0akaHCdSXn6QHz54Asvu3d4FcjlB50/iohv/SlBgx6fvddgcrPhoBYd2KsEjw0evYtL1ySSP6HgbRRsOsOXnDbhcTjRqDROunUHIoKjOfiRBEIRzhgiCdE1fXJO4bTYqnngCw+LvAQi6Yx5hf/pTzw+B2PM1LJwH8RPg9h+OvI8bB/N+Ykn+Eh5b+xgpASksuqzrQ6j31u3l+iXXA/DJ7E/IDMvsoQ/QM1xGE9bduzDv3Il1rzfw4ayoOO62kl6POjkZdUoyqiTvszo5GUVEhMjkEARB6ICOnlc7lev/0EMPtb52u928/fbbLF++nPT0dJTK9nfbX3755U52WeiPJLnEuAnTOO/8KezM2kbEbg+yA7Wsza3FfWgVxbpDhKXPZPzU2fh1o25IVNRA7vrLl+zOXsHa/72As6iY+rWr+GfxJlJvvoebUm/qUPFUpVrJhb+5kKpCAys+3Ed9hZElr75P1MBYLrrvKnT+py4GF3/+YPwig1j3v18wW0ys/OxHRk4bS/KUoV3+fIIgCELn3HzzzeJmRS+Q1Gqi/v1v1EnJ1LzyCvXvvY+rvoHIf/y9Zwvd6UK9z6Ya73NzpfdZ772pMDF6InKZnLzGPEqaS4j1i+30ITweDy9v815vXpJ0Sb8IgDgqKjBv34Flxw7MWTuxHcg5boaHMj4OTVqa95GahmbQQOQhIaIehyAIwmnQqUyQqVOndqxRmYyVK1d2uVO9SWSCdF9JvZmPNxbit/VVQpzeoTIuSYUydgRDxl3I0LRh3bpj4Xa72bzxK7Z+9QZfDKqj2UdGmDaMewbexqWpV6NSd2wmGafDxapPNrB39Y/g8aDS6ph006UMnZzeof1tBgtrP/iJ2poaFMiZct4kgi9KQSaJCxRBEIS2xLm1a/r659b49TdUPPkkuFz4Tp1K9H9eRuqpWeGq98Mb54E2EB4phF+ehPWvwth7YPZzANz5851srtzMw6Me5tYht3b6EOvK1nHP8ntQSkqWXLGEKN/Tn7XpMhgwb9mCacMGTBs2Yi8sPGYbZVQU2uHD0aYPQ5OWhjo1FblvzwwrFgRBEI44LVPknon6+oLjbGIymVi/+kcqs39prRsC4NSFEzx0BudPu5RAXdfHqbo9bpYWLOX1na9TZixjepabJJOO5NnXMPOi+zocDDm4+QArP1yE1WgAIGrQYC68+wr0Iaf+93e73Oz4Yg2aPVYCPDo0gwIJun4wklYUTBUEQThMnFs7py8Ko55I88qVlP3hITw2G9qRI4l96y3kvj0wha6xGl4cAMjgyXr47l7I/h9M/xtM9GYWf7b/M57b8hyjwkfxwYUfdPoQt/10G9urtnNr2q08PPrh7ve5AzweD7aDuRhXrcS4arV3GG/bTA9JQpOWhnbEcHxGjECbmYkyIuK09E0QBOFcJ4IgJyAu1Hqex+1mz54s9m36GWfpDmRuJ9meZBYxnQuGhHPF8GgmDQhG2cU0W7vLzsI9n1Pz2mvIjC1Twen9SJl9DTMuvheV6tTBEIvRys9vL6YwKws8HhQqDaMvncnoOed1aFpec1Y19QtzwenGEOgk4uo0gpLDu/R5BEEQzjbi3No1/eXnZt62jZJ7foe7uRntiBHEvv129wMhDiv8s+U8+UgRfH0H5C2Hy+bD8JsBKDeWM+vrWUgyiTXXrcFf7d/h5vfW7uX6H65HIVPw01U/Ea7rvXOyx+3GvG0bxhUraF6xEkdpabv1qqQkdOPGoTt/HD6jRyMXvwOCIAh9QgRBTqC/XHCcrQzNTWxa8wtf5MLKSm9wIoI67tUuQxM3ksGjp3V5uIzF0syy716h6JdvwWTxLvT3I2X2td5giPLUKbx523NZ+cEizE0NyORBJI6YwZQbB6MPOXUgxV5mpPSjnWw35+CRZAyfPIYB04d1+nMIgiCcbcS5tWv608/NsmcvxfPm4TYY0I4cSdzbbyHpuhkIeSYcnFb4/S748iao3A03fgUDL2jd5NJvL6WgqYBXpr7C9LjpHW76kTWPsLRgKZckXcKzE5/tXj+Pw+PxYDtwgKbvl2D44QecVVWt62RqNbpx4/CdPg3fCRNQRna8+LogCILQe0QQ5AT60wXH2W5PWRPf7Cijced3jLJvaV3u1ASjTzmPjPOmk5iQ2Ol2LZZmfv7uPxQv+w7M3mDIgREhjJ/zW65IuQIfpc9J93fYHKz8aBn5WeB2a1GoJEZfEk/GtDjkCvnJj91gYv1HP1NbWwtAQnIio2+ailwlhscIgnDuEufWrulvPzfL7t0Uz7vDmxEyaiRxb7+N5HPyc+pJvTgIjJXw27Xwv2uhuQJ+sxqihrdu8symZ/gy50tuHHwjj419rEPN1lpqmfnVTJweJ19e8iVpwWld7+NRXI2NNC76lsavF2LPO9S6XNLr8Zs2zRv4GD++ez8XQRAEoVeIIMgJ9LcLjnOB0+lk547NHNq5Gld5NjKXo3WdQxeBOeN2po1IZWC4b6eqopstBpZ99wq5qxfzv9FWnAoZAeoAbgu/lCsybz7l1LoNlSZWf5ZDeW4jLvsBfPRWpt9+BYkZJw/MuF1ushau5+Du/QD4+wcw4ZaZ+EUEdrjvgiAIZ5OePrdWV1dTXV2N+6hZNdLTO1bY+kzRH69JLLt2eQMhRiO6yZOIff11ZEfNANhhr4+B2hyYuwQ+uwacFm9WSGB86ya/FP3CQ6sf6tRUuR/t/YgXt71Iemg6n130Wdf61obH48GanU3D519g+PFHPHY7ADKVCt+pU/Gfcwm6SZOQVF2vcyYIgiD0PhEEOYH+eMFxLjGbTWzb9CvFu9chq83B4lHyL+dNuJFICtFxS7KJ89OSGDhgUIeHzFidVhYfWswHez6gtLmEq9Z7CLLKCRxzPtOv/iNRkQNOuK/H7WHX6gLWfPoRLocdZDLihw1jxh1z8As6eeX24k25bPlpHU6nA6VCydiLJxIzOqVTPw9BEISzQU+dW7dv387cuXPZv38/hy9PZDIZHo8HmUyGy+XqqS73C/31msS8YyfF8+bhsVrxv/xyIp/9V9embn13JpRugavfh4XzvMseKQJtQOsmjdZGJn45EYBV164iRBtyymavXnw1OQ05PHHeE1w76NrO96uFx+2mefly6t55F+vu3a3L1ampBF5/PfqLZiP38+ty+4IgCMLpJYIgJ9BfLzjORU1NTWzM3svCAiVrDtZid7l4RPEF/phwagLRxg0necgYhg4bgUp16rtQTreTFfuXkPv2K7irvLPVyGQSPpmZjL/sHgYPHn/CfevL61n29rdUHsoFQKHWMHL2dMZefj6S/MTBGENZA+s+XYahuYlITyDDp43Fb2qsmEZXEIRzSk+dWzMyMkhOTuaRRx4hPDz8mC/e8fHxJ9jzzNKfZoc5keaVqyi9/35wuQj+zW8Ie+gPnW/k06sh7xeY8RQsf4rWmWKOuslxxXdXkNeYx/9N/T+mxk09aZN5DXlcsfgKlJKSVdeu6lQx1cM8DgdNS36g7p13sOfnA96sD/3s2QTecD2ajIyuBX0EQRCEPiWCICcggiD9U7PVwa97imja9AlU70Pmdrauc8vVyMLTCE8dz4gxEwk6xbS7brebLRu/Ycf37+EsLGpdroiPI+2K25g45hrk0vFrf+xbu4e1X/yAxdAIgD4sggvuupqYwdEnPJ7T6mDPlxsI2g8SEppBgQReOwi5rovpw4IgCGeYnjq3+vn5sXPnTlJSzo2suv5+TdL49ddU/OWvAEQ+9ywBl1/euQYW3gF7FsKoebDtfVD7w2PFx2z25PonWZS3iDuH3cnvR/z+pE2+s+sd/m/n/zExeiJvzHijU93xeDw0L/uFmv/8B3thIQCSnx+BN91I0C23oAgO7lR7giAIQv/S0fOqqOYo9At+GiWXjEqBUU9jNpvI2r6R4gPbcJTvQe4wQflOvi2185tlVkbEBTJ9UBDTYmBA8sBjMjUkSeK88Vdz3vir2ZW9nM3fv41l716cRcU8v+4Zniv7kJtSb+KKlCvwVbUf8pI2cSgDxgxi9afL2b92A4aaOr57ZTfpU02MuTQJtfbYXxmFRknm3MmYtlXR8G0elpx6sl/+jtQ5I4nK7HzhV0EQhHPV9OnTyc7OPmeCIP1dwFVXYS8tpe6/b1L55N9QJyWh7UxdFk1LlkZjcfv3RxkWOoxFeYvYXbP7uOvbWl26GoApsVM63g/AvHMn1c/9G0t2NgDyoCCC591OwPXXI/c9+fBXQRAE4ewiMkGEfs3tcrF//x4O7t7M4opAVlV7q7Eny8q4Q/4jLqUOeXgqESmZDM0YTVho2HHbKa/IZcVPb/KWZhNNdgMAYwtVTA4cxaRL7yU+4diLutqSWtYvzKY0x5sSq/FVkDZexZg5o084i4y9wsSuj9eQ11wCMhmDh6WSftXJh9QIgiCc6Xrq3FpbW8vcuXMZM2YMQ4cORXlUQc5LL720u13tV86EaxKP203pffdjXLkSRWgoCQsXogw//rn2GMv+Chteg/ChULUHwofBPeuO2SynPoerv78anVLH+uvXnzBbs9ZSy7QF0/DgYfnVywnXhZ+yC67GRqpfepnGr74CQKbVEnz7bQTNmyeCH4IgCGcZMRzmBM6ECw7hxMobLaw4UE1x1ioSKpa2m2kGwKkLxyd6CJEZMxiROhCtqv2FlMVpYUn+Ej7f/SnnfZeLxlsAHmVyEmnTrub8yTeiVLQfblO8r461X+ZSX1aEy5aFT0AwE66/iLTxx5+Sz262seXTVZQWe+98BQcFc/7NM9CFdX7csiAIwpmgp86t33//PbfccgsGg+GYdaIwat9xGY0UXn899rxDaEeOJP6jD5EpOpBMvOpf8Ou/wScYzHUQPwFu/+HY9t0uxn0+DovTwqJLF5ESePxMoB/yf+DRtY+SGpTKgjkLTnpoj8eDYckPVD37LK76egD8r7ySsD88iCI09NR9FwRBEM44IghyAmfKBYdwana7nX37sincv4Pmkj1IzWXIWv47v+a8gjp5KJlxAcyMdjAySkNaWjoajQZoqRuy+Ruyl36MLe8QHP418NURNm4yky76bbtZZVxON+sXrCV7+UrvLDJAaEIS02+/hIik40/Fm7s8m6y123C5XKiUKkbPHk/smBPPVCMIgnCm6qlza0JCApdccglPPPEE4eGnvst/pjuTrknsRUUUXHkVbpOJkN/dQ+gDD5x6p3X/aSmI2mLwJXD98ae0vXnpzWTXZPP8pOeZnTj7uNv8fePf+ergV9yadisPj374hId1GQxUPvU0hqVLAVAlJxP59FP4jBp16j4LgiAIZyxRE0Q466lUKjIzR5OZORqAhoYG9u7aSnHeHqTqaOxNVrYU1BNfvBqdLI/9ixS4A+Lwix5M3IB0MjIv5rxxV1Ncspf1S9+hZvMaMJqo/mUp/zj4E4oLpnLNoGsYHzUeuULOpBsnk3lBJis+WErR7j3UFObz5dOvkzRiBNNuuxCdv65d/wbMyCBkQBQbPl9Os7GZ9YtXMSS/hqHXnIdMDI8RBEE4Rl1dHX/4wx/OiQDImUYVH0/E35+m/I9/ova/b+IzZiy688aefCelz1GNnHj4SUpACtk12eQ15p1wm+1V2wEYGT7yhNuYd+6k/I9/wlFeDnI5Ib+7h5C77kKmOnlRdUEQBOHcIYIgwlkjMDCQCZMvgMkXcIPHQ2GdmU35dVizDuKqrEJub0bekI+5IZ8De5ay/1sJl3881UPvYOTkx5l+3dPs2fIlOSu+YW9sKQ2lq1ldupqh9jCuUIxi/AXziI4exBUP30Dp/hJWfvQ99WUlHNq2jZJ9BUy66QZSx0cibxPgCIwPZdaDV7Pt89UUHypCnWWmpm4XQdcPQhGs7cOfliAIQv9z5ZVXsmrVKpKTk/u6K8Jx+F98MaaNG2la+DXljz5K0pLvT15XQ3nUeU6pOeGmAwK9mZJ5DccPgtRZ6shv8k5nOyJsxHG3afz6ayqeehocDpSxsUS/+ALajIyTfCJBEAThXCSCIMJZSSaTkRiiIzFEB2P+gMftpqS0hNx9O6gu3Iez+iByu4GahiZeX10IFAJwX0AJsQOmcXdUMPvUBayqXkVodiWV5d/z9bIlKBLiGDBxDuOn3swtz97D7lW72Pj1j9jtcfz6vxyyV5QwZk4CySPCkCRvMEShUXLe7TMZuL0Uy/fF2EuaqXp1J9LMMMLHJ7VuJwiCcK4bOHAgjz32GOvWrWPYsGHHFEZ9oCNDMM4A8+fPZ/78+WdkjZOIxx/HvGUrjuJiql94kcinnzrxxgrtyd+3kRLgrQNyokyQrJqs1u0CNAHt1nmcTqqef56Gjz8BwG/mTCKffRa5rw5BEARBOJqoCSKckzxuN6VlJWTnl7KqypedxQ0U1Rr4m+JjFBy5KLUq1dS5HVBXibq24UgDKiV+GcMZPv0G0lKncmBDNduWFmBpduByFOLj18T4a2aRelTxVGeDlfoFOdQUVrJbXkxkRARjbpqGNlBcqAmCcObqqXNrYuKJpxWXyWTk5+d3ue3+6Ey9JjFt3kLx3LkAxH34Abrzzjv+hvuXwJc3HXk/4Q8w46njblpnqWPKginIkLH5ps1ojwqYvJH1Bv/N/i+Xp1zOP8b/o3W5226n/E8P07xsGQAh991HyO/uQSZuMAiCIJxzRE0QQTgJmSQRGxtPbGw8l7QsqzOYyN2jp6JwP8aKPGRNxWgcNqIBAsLY7TuIYrONoYYD6KwWmrduYcneLfz14kQuH3gFsx6dTfl6C5u/XYexzsLPb37C1iXxTL7pQuKHJgCgCNQQelc6tYvtsL2YisoKfnptIaMvmkDMKJH+LQjCua2goKCvuyB0gG7sGAJuuJ7Gz7+g4oknSVryPZJafeyGRw+HOUkmSLA2mCBNEPXWevIb8xkSMqTd+pz6HAAGBQ5qXeY2mym9/wFM69cjUyqJeuEF9BfO6voHEwRBEM4JIggiCC2C9TqCz58C508BvLPP5OXlUJy7h4ayHOrrg1lPEuu1Lga7NjLFvIycUBtFxmJe3fEqr295hRt3BxE5agrqhkFU5ORSX1rEouffJnLAQKbeMpuwhHBkkoy0y0cTOiiKTYtWYzKbWPftCpL2FTHi2okoNMqT9lMQBEEQ+lrYH/+EccVKHCUl1H/0MSG/uevYjY4ujHqSmiAACfoE6q31lDSXHBsEaWgJggR5gyBuu53S++7HtGEDMh8fYl9/Dd3553f9AwmCIAjnDBEEEYQTUKlUpKUNIy1tGAA3AFUGK9kljRzKD8LvkJuQpkKiq2rZpTegaLSgqayloXIhHpmMusA09J4MFEYTFQdz+PxvuSSPmsjkm6bgF6QhNDWaCxOuYdvnv1KUX0D+wTxqXqnivKunEpwS0bcfXhAEoQ/MmzfvpOvff//909QT4VTkvjrC/vRHyv/8CLVvvon/ZZehDA9rv1EnMkEAon2j2VG9gzJjWbvlzfbm1mUDAwficbkof/jPrQGQuHffxWfE8G5/JkEQBOHcIIIggtAJ4XoNFwyJgCERwITW2iIFhw6Qn7OJqvj1SDWVqM1OQur3AntxKuKRKYaBS0bhbgdFf1mHPt5G6uQIBqcPYty8mURtzGH7so00G5sp+HArqguG4zshGpkk6+uPLAiCcNo0NDS0e+9wONizZw+NjY1Mmzatj3olnIj+kkto+Ox/WLKzqfnPf4h67tn2G3QyEyTKNwqAcmN5u+UHGw4CEKGLwF/tT+U/nqH555+RKZXEvv6aCIAIgiAInSKCIILQDW1ri0ya4h2H7HK5+HXLaravWYAnZwcacxE4i1ibnsLghgQimlMwFGrZkLOeraqv2BudiCd5NBkjRzEgp4jwGj+alhZg2VtHwNUDUIX6nKIXgiAIZ4dFixYds8ztdnPPPfeIaXP7IZkkEf6Xxym89jqavv2WoNtvQzPoSM2OrmSCAJSZ2meCHGo8BHizQBq//oaGzz4DmYyoF18UQ2AEQRCEThNBEEHoYXK5nGnjpjNt3HTcbje7dy9n69bFVPpkcyD6NaKaBnDB3hnInZXYnDKS84ooKLXzmj6WIcpcfiM1k+SejLOogfWvfokmTE3Y+GQSElMIDgru648nCIJwWkmSxEMPPcSUKVP485//3NfdEY6iTU/Hb/aFNP/4E7Wvzyfmtf87srKHMkFKjaUADKvWUPmvpwAIuf8+9LMu6F7nBUEQhHOSCIIIQi+SJImMjAvIyLiA29xOtlZuZXnBL8iy30PmjsUjDULmkUiylJNorcDuI6MwIJ8GeSH+ngnYAFu1A8uirRzyvMlnmunoIlIYGO5HRqCNAYFy4hOS8PP16+uPKgiC0GsOHTqE0+ns624cIycnh+uuu67d+88//5zLL7+87zrVB0LvvZfmn36m+ZdfsO7fjyY11btCcdSMMafIBGkbBPF4PMhkstb3WpuH895bj8fhwHf6dELuvrvHP4cgCIJwbhBBEEE4TRSSgnFR4xgXNQ7n2MfI2vkju9ctxrDLhMcZh8wjoTZ5aDInUJYYjC7NSGKpHnujB7tHhUw2jkFmBQsO1bLhUB0XS5uwSHvYBbjUAaCPQBMQiX9oNGFRcUQnphGi92m9iBQEQejvHnrooXbvPR4PFRUV/PDDD8ydO7ePenVigwYNIisrCwCj0UhCQgIzZ87s2071AXVKCvrZszEsXUrtf98k5v9e9a6Q5O03PEUmSIRPBJJMwuayUWetI0QbAkBZcxlzl7tRVzehjI4m6t/PIZOk3vgogiAIwjlABEEEoQ8oFEpGjb6UUaMvxeV2kb3zF7Z9uxpzMcg8SgIrh+GullgTvI00ezEhviOx2d2MkBsYp5MoSE5GXh2Is16Pwm5AbmuEmkYcNQeozYVa4CbnTcg1fiSH+TLZt4wUXxvBEbFERicQEx2DQiF+/QVB6F927tzZ7r0kSYSGhvLSSy+dcuaYvrZ48WKmT5+OTqfr6670ieC7f4th6VKaly/HXlqKKiYGZEcFKhQnD4Io5UrCfMKoNFVSZixrDYIEZhUwbZfHWwfkuWeR+/r21scQBEEQzgHiW5Ag9DG5JGfEyAsZMfJCnE4na35dz951jcgr/EiuGYPJCsaKvUT465AFxGEzNZK5J49Rs6/Db+wfaDI0UlycT015MY01pVgbKrA0N2A2avBYnewsbmSofD1hsmIMQAHgkUm4tCHI9RFog6JwpVxAQpg/CcE6QnxVIntEEIQ+sWrVqh5tb82aNbzwwgts376diooKFi1adMxQlfnz5/PCCy9QWVlJRkYGr732GmPGjOn0sRYsWMCtt97aQz0/82gGDkR3/vmYNmyg4ZNPCX/sUZAdlQlyiiAIQJQuikpTJRXGCjJCMzAZG7hmSRMAvjdfj8/o0b3RfUEQBOEcIoIggtCPKBQKpk2fzLTpUJnfxKrP11F1wIAMDVVNLnwspYSGRJAoC8PwXT55K7dguSSQEUPGkp4+sl1bNztcFNaZOFRtwpprwF4TgqOpErmpBpnbgcJcDeZqmir38/SuaMAb+LhZvZaBPkbkfmH4BEagD4kkLDyGqJg4ggICRQqyIAhnDJPJREZGBvPmzePKK688Zv2XX37JQw89xJtvvsnYsWN55ZVXmDVrFjk5OYSFhQGQmZl53Hoky5YtIyrKW8PCYDCwYcMGvvjii979QP1c0G1zMW3YQOPChYTcfx/yo7Nijp4t5jhCfUIBqLXUAlD69htENEKDn4yBv/9jT3dZEARBOAeJIIgg9FMRSf7c8JeLKdw9hA0LV1BdcAiz3UFReQlKXxlD/QYS2hzMvgUlvKT/O/bgEkb4DiR9zCUkJGSiUcoZHKFncIQe0m9obdftclNVXUFZSSG1lSVUNxqYYA+lsM5EWaOFEFcViuZGaC7DUg4WoArYDVjlvnwTfBcJIb4kBOsYqqkhOtiXyMhYggNFgEQQhO6pqqriT3/6EytWrKC6uhqPx9Nuvcvl6lR7s2fPZvbs2Sdc//LLL3PXXXdx++23A/Dmm2/yww8/8P777/Poo48CtNb8OJnvvvuOCy64AI3m5JkONpsNm83W+t5gMHTgU5w5dBMmoEpKwp6fj2HJDwRefx3eAHvLv+PRhVKPI1jjnQWtzlqHs7YW18cLkAHL58Rwvu+5OdRIEARB6FkiCCII/VzCsAQSht1B2cEyNixcSXnOAfKMxZRbqhkYlkGDwkRKcyI0RVFXuZwl334B/n7oU4eRMnwKw0ddgk4X0NqeJJeIjIwmMjK6ddnhBG6b00V56WAqy0torC6nub4CW1MVGGuQ7E00OFXsKW9mT3kzAA/Iv6FeVs9uwCWp8GgDkXQhqP3D8AmKQpU8kdggLbGBPujU4s+NIAgnd9ttt1FcXMwTTzxBZGRkrw7Ns9vtbN++nccee6x1mSRJzJgxg40bN3aqrQULFvCb3/zmlNs9++yzPP30053u65lCJkkEXH011c8/T9O333qDIJIc3C2ZNJLylG0Ea1uCIJY66t55F5nVTm4k1E9I7c2uC4IgCOcQ8a1EEM4Q0QOjuebxW6ivqGfD179SlJ3H7iZfgn1kyHW1eCQ1uqiL8TWVUlO5GMOmDezYtIEd8ueQkhLwu+5qJsZMItE/8YRfLNQKOYkJySQmJB+zzmq1UlZdy7BmBUV1ZgrqTAQWhuMyupDsBuRuO5iqwFSFo3ovBz2BvLr+SOrz/dqfCfWRofANQRsQhl9gBMGhEYRFRBMeHiEKtQqCwLp161i7di2ZmZm9fqza2lpcLhfh4eHtloeHh3PgwIEOt9PU1MSWLVv4+uuvT7ntY4891m4GHIPBQGxsbMc7fQbwn3MJ1S+9hCUrC1t+AWranG+Oni3mOA5ngpgry2j4YjsACyZJDNFF9Ep/BUEQhHOP+NYhCGeYoMggLrnvCmwWBwc2VpK9ogRDnYog3xLcavDoYogYeD9udQGVRb9AUzNFjQX8tP0lXtz+EuE+4VxTHktiyigyRl1EeHhih46r0WhIjouhfXhkGAA2u43KinKqq8ppqK3EWF+J0iwx1KanpN5Ck8VOkKMSRZMDmoqxlHmH2VQD+4EqgvhGfxOxgT5EBWgZK9tHkJ8PgSHeQEl4eAQa9anTqAVBOLPFxsYeMwSmv/P396eqqqpD26rVatRn+d8yRWgovhMnYly9mqZvvyWsbdD96NlijuNwJkjqsoN4bDZqU4LJTmxkoiaot7osCIIgnGNEEEQQzlBqrZKMabEMmxzNvvX5bPpmPwqjC5/AAJy40JhTmD3oImQzlGxr3ILBtottldsw1lVi21jOgY2bOfDJfGQhwQQMHEJixgQyRszGzy+4831RqYmPTyQ+vn1A5b6W5yazncqSZOqqy2iorcTcWI3NUIPbVIvc0ki925eSegsl9RYAhigW4cBB268VTqUv+ARi9UukJnYWUQFaogO0xKmaiQgNwV/vL2qSCMIZ7pVXXuHRRx/lrbfeIiEhoVePFRISglwuPyaAUVVVRURE72YdzJ8/n/nz53e6xsmZwv+KK7xBkMWLCZ3qOZIL0sFMEJXDQ+bmOgA2zYwFWRNBWhEEEQRBEHqGCIIIwhlOkksMnZRC2oQHyd2cw7bv16EwO0lSxaCtduH4zEZq3HAun3sXaNxk5a8nn++oz9mNu7IaT20dDbVraNiwhh2yZ6kblUzY9FmcF3ke6SHpKOWnHsN9Kv4+KvwHpcKgY8d0u11uqhsNzDG4KWs0U15vxKdwDHZjHR5TPZK1AcntQOEwQpORskb4qLCgdf+/KT5CjQO3XIVbHYBMF4zKNxgf/xC0IXH4xA4j0l9LhF6DVnXqC3BBEPrOddddh9lsJjk5GR8fH5TK9n9/6uvre+xYKpWKkSNHsmLFitZpc91uNytWrOC+++47+c7ddO+993LvvfdiMBjw9/fv1WP1Bd8pk5F8fHBWVmKtU6ANcnhXSKe+7PRX+zNhrwcfqwdlXBxZSTKohyCRCSIIgiD0EBEEEYSzhCRJDBqXyqBxqVQVVLHrqw1Q5SZI6Y+trIYl//qCkITBpF8yhvPung5AQ0Ml2duXUrhrHYbc/dDQRJYjn/zsN3kz+01ijGouLY8gdFAGKcMmkZY2CZX61FMcdqrfcomI4AAiggEOX+QObl3vcbtpbGqkurqSutoqVEa40xFOWaOF6gYDinoVOBxILjtSy7S/rhpoBrZ6YvnYZW5t6wnNVyg1PkjaAJS+gWj9gtH5B6MPCiUoNIrQiGj81IpeLcYoCMKJvfLKKz3antFoJC8vr/V9QUEBWVlZBAUFERcXx0MPPcTcuXMZNWoUY8aM4ZVXXsFkMrXOFtNbzvZMEEmtRjd5Es0//kRzqRptkDfLD9mpA9F+Sj9m7XADoL/uGursC4EjtUIEQRAEobtknjNt8G03Hb7r0tTUhF6v7+vuCEKvMjeZyf1sB3nluTjw3omTrHLsCgfDZp7HsCnpSPIjQ0hKS/ezzbCHDbVb2Vyxmfg9tYzKbfMnQqlAERNNyKAMUoZNZMjQqajVPqf7Yx3DarVSVVVBbU0VjXVVNDdUYzXUkm8PYLktlcomKy67hb8pPj5hG/s9cXziugCdSk6Ev4Zb5MtQ++jR+AWh8w/GPzCEgKAwQkLDCPQPbPdzE4Rz3ek+tz733HPcfffdBAQEnHS71atXM3Xq1GOWz507lw8//BCA119/nRdeeIHKykoyMzP5v//7P8aOHdsLvT7W2XxN0vTDD5T/8U+o/JwkX1ztXfhELZwiu9CUnUXxdTdgV0D0ih+5aPm1WJwWll6xlFj92VVEVhAEQehZHT2viiCIIJwDTDUGNn22mpraSgBkbhn2pmYMLgsDRmUyZs54AsID2u3j9rg5eGgrOdt/oerATmwFBXis1nbb/DheQ+TATEaFj2KU3xCGRY1Aq/U7XR+rwzweD81WOzUVxdTXVmNoqMXYVIvVUIfD1IDH0shOayTfWEcCoMZ+0oBJDvEs080hTK8hzFfFdNc6tH4B6PyC8AsIIiAwhKDgEIICg5GLYIlwDjjd51a9Xk9WVhZJSUm9fqzedDZfk7iMRg6eNw6cTpIvqULl64InG+AUtZuqnn2O+o8+Yl2ajMnvfctVi68CYP0N69Grzq6fkSAIgtCzOnpeFcNhBOEcoAvVM/3BSynbns+2peux2CwoA30JdfhStDGL/Ws2EJqYxIhZ4xk0bhAymQxJJjE4ZSyDU7x3RF1uF/l52ziQvYrKAztoLj5Ema+N0sqtbK3cysQ9bgaXy5BHRRGYkkbc4NEMSZ9OYGDfT2sok8nQa9XokwaQnDTguNvcAjxjd1LZZKWq3oC1RIWxsRZLcz12Yz1ucwNYm1A4jDS6tVQ0WalosqLGzlTFGkyACe+MN4d5ZBJ5qsFsC5hNuF5NqK+asc5t6PSB+PkH4R8YTHBIGEGBQWKKYEHohDP9/s3ZPhwGQO7rizYzA8u27Zgq1ahSzKcMgHhcLgw//gjA+jQZA4zlAMiQ4av07fU+C4IgCOcGcdUtCOeQ6JFJRAyLY/fizRzctR+30sPEkDFUmirZW5DLsvcktv3UwJCJ0QweF4HWV9W6r1ySM2DgWAYM9AZFPB4PlxsK2Fa5jW1V2wjY/iu4mnGVlFJbUkrtqmXs4J/IggPxTRxAwJw5DI8YSbw+vt/W3PBRKUgK9SUp1BcGRR13G7vdzhSDidstMqoMVuoam/ApuQhbcwMOcyNuaxNYDcidJmQeN/UWN7tNTewuAw02him+xwzUtG1UJsOl1FHqk0ZO8HRCfNWE6FSkO7LQ6QPw0wehDwgiMDBIDMURhLPA2V4Y9TDf8eNbgyCBKeZTbm/ZuRNndTUWrUR2oowyYxkAOqUOqQPT6wqCIAhCR4ggiCCcY+QqBZlXjydpXBrFS3fje0hGim8C8X6xZNlNlFWb2fB1HusXric02kbmzPMYMHYg0lF38GQyGUn+SST5J3HtoGtxT3BTUryHfdkrqMjZganwEJ76Rjx1DZRZtvBy6HbAW+H/0oooEkJSSB4ynsGpE9Bozpw7fCqViqgQFUdCJBHAoGO2czqd1NfXkW60MceqprrZRl1DA/Ky8ThMjbgtTWAzoHA0g8eD3G6k0mpgda03PKLBxpOKBTQe1a5HJuFS6ijRprYETFSEHg6Y+AXg6x+If0AQgYEhBAYEiuE4giD0Gd3551Pz6v9hqlLjccOpwt/G1asByB8SjFPR0BoE8VWdOecIQRAEof8TQRBBOEfpowMZetckrHkNNH6fj6mqAZu2nNgAH9zuSIoLiqnIbaQiN4dVn/iTPDKDkReNJSjy+NMUSpJEfEI68Qnprcvq6svYl72SnLp9DNeVsbd2Lw2WOmRbayhzZVO25GvWyCXkkREEJA0meuAIBg6dRFREyun6MfQahUJBWFg4YWEwtHVpHJDRbjuXy0V9Qz31dbXEWjyMd/hRY7RhaKpHVjECp6UJj7UZmb0ZudOCzONGYW+mytrMmjpvwESLlScUX9F0dCdkMpwKb8DkQGuGiZIMRxZaXz2+fgH46QPw9w8kICAQHx+ffpulIwhnk3NhOAyAZuhQJIUbt0PC1qRAc4rtjb+uAaAiPRJooLxlOIyfqv/VmhIEQRDOXKIwqiAIeFxu8n/Zw85N23A6nQAEB4VgMJspO3QQt9M7swwyGcExcaRNHEnmzJHIFZ3LMrC77Oyr3EXBqu+pztuNrbgQzO2LrZaGyNg+KYKhIUMZFjqMDFs4qYPH4+t7/ODLucRut9PQUE9jQx01NokKhy+1RjtNjfXEV/yE09qMx2pAsjcjOc3Q8td9kzuNxe7zgcMBk0+P275bUpCnSmWb/0yCdGqCfZSMt69HrdPj4+uPj58/vvpA/PUBBAQG4qfzRXaKMf7CueF0n1v9/PzIzs4WhVHPAMWTkzBVqYkY1UjgpxUn3M5RXk7etOkgSXz58my+rvqZ9NB0dtXsYkTYCD6a/dFp7LUgCIJwJhKFUQVB6DCZXCL5wnQixySSvWgjRYVF1NXXIpfLGX/BDCwyNwe3ZGOoqaSupIh1XxrJWmFl0JgIUsdHEhzdsVRllVxFZvQoMm8eBYDb7R1Cc2D3asoP7sRUnE+1fz3VlmpWlqxkY+4Kbl7lZqNMhiw4CF18ImHJw0hOHUfKgDEoFaqTH/Aso1KpCA+PIDw84qgBOMnA6HZLnA4HDQ311DfWk2CVMcnhS63RhqGxHlnFKG/AxNYMdhNyhwmZ24nkdlJvdrHHaADAByujFSuwA83H6c9eUljuM4sgnZoQHwWznStQav1Q6/RoffX4+Abgqw9A3zJEx1/vj1wSmSZC902cOBGtVtvX3RA6QBvqwFSlxlKrIvAk25k2bPBun5GB5K+HKqgxe7PdxHAYQRAEoSeJIIggCK18gvwYd8cFpOSUs+P79TQ0NpC79wC+ah3X3nQdTb5Odi7bQkW+B6vRQfbKErJW5KHR7GfAmAxGzB6LX1DHL1aPN4TG7DCzv34/e2r3kL9/E+i3g8GIp7YOY20dxu3byOcDflEoqB2VhH78BIaGDCU1KJVYv9hjapecqxRKJaFh4YSGhR+15tiAicftxmQx09jQwFCLi8ucWupMdgyGJtTlM3CYm3FaDLhtRrAbkRwmJJedZreKKoONKoMNH6zMVmzHATgA41FHzfYks8A9Fb1GSbCPgttYjKTWIdfoUGr8UPn4ofHxQ6vzRxsYji40nkAfFQE+SjRKee/9oIR+x+12k5eXR3V1NW63u926SZMmAbB06dK+6JrQBdpgOwDm2pMHrc3bdwDgM2YMWoU3+/BwEEQMhxEEQRB6kgiCCIJwjNBBUcwccBUFv+5l97qdhFp8afwqF2W0LzMvnoYyXk/xvnoObKggb9s2jPU17PxpOVnLVhISn0jquEyGTc1AqVF2+tg+Sh9Gho9kZPhIGDIXrobqmiJy9qyhNHcHDQU5OMvKwO5gjzmP3H2HAIio9zAnS4EiMhL/uGQikoaRPPg8YuOGIpfEl+iTkUkSvjpffHW+xLRbE0vbiiZtWa1WJhst3GWVqDPZaDQ0oy6zYTU3YTc147QacFlbgiZ2I2aHGo8HmiwOnBYDCkUR4B2xY295HA6cZHuS+dI11ds33Dyt+gyUWlD6IFP7Iml8UWp8UWn9wD8GT8RQAnxUBPmoCJYZ0fvrxVCdM9SmTZu48cYbKSoqOmYaXJlMdtbU0DhXaoLA4SCIB4dRgbO+HkXQ8Yc2mnd4i2f7jByBRpENgNPjHZ4ppscVBEEQepKoCSIIwkk5rQ6MG8ox/VqGx+aiTtZMfZSDzEvPJzA+FENtE9uXbiF3azbmxrrW/eRKFZEDBzLq4qnED4lE1oPDIFxuF4WFO9lrLmCXMYe9tXtR7tjPqH32YzdWKVFERuCZOIaEtPNIC04jXh8vpls8zRxOF40WJ41mO41GM/byvVhMBqzmZuxmAw5LM06rCbfNyH5XDD/b02m0ONC4zfxF8dkJ2z06YPJPxfuAdxYdt0KLR6lDpvJBUuto1sVTHToef60Sf62CBFsOPj6++Pj64eunx89Pj95Pj1LZ+eDdua6nzq2ZmZkMHDiQp59+msjIyGMK9Z5t08meE9ckTwWQtyQUh1FB3Afvoxs37phNnLW15E6YCDIZAzdv4oOiBby649XW9bcPvZ2HRj50OnstCIIgnIFETRBBEHqEQqMkYFo8fmMiafqliB3b8zFX2fj53W9JSE4k47JxTL11JlNvnUnRniJ2rdhG8Z59OKxmSvfto7IgBH1wIQPHhJM0IoiwuJONCu8YuSQnOWkUyYzi0pZl9llWDuVto+jgNioL9mAqLsBVXQ12B86iEr6LLKO67lsAhlSrmVgThD42ifCkYSQMGElCYiYq5anmLhC6SqmQE+onJ9RPDeF+kHz0MJ32/gV4PB4MFjuG+jE0G5owNjdhNjZhNnkDJ3ZLM2HuEMZ7gmkwObCaDHisSmRuBzKPG7nDBA4TmL1tFnisfHnQO7mxhJtnWgImR3PJ1RQrk1nndyH+WgUBWhWTbL+i0ahRav3Q+Ohahu744avTo/MPQh8Ygp9agSRqnnRLbm4uCxcuJCXlzJ8hSjjMgybAgcOowHbw4HGDIOYd3qEw6oEDkev1aBXt671o5OJvsyAIgtBz+kUQZP78+bzwwgtUVlaSkZHBa6+9xpgxY0653xdffMENN9zAZZddxrffftv7HRWEc5jcV0XQFQOYkOlP1vcbqa6uojAvn9JXixmUkUbq7JHED40nfmg8Lufl5GzcT+62QqqKNDTXW9n+UxGbFy1AF6AmacRQhs8aTWBE9wMih6mUGlJTJ5CaOqF1md1hJf/QdgoPbmV6kIG9hhwO1h8koMaMq7iUhuJSGtav4QCAXEIKDcEnKhbtlEmkxGUyKGgQetVZenf2DCCTyfD3UePvE9eJvS7GarXS2NSAocmAqbkRs6kZi7mZ4W5fAmWxNFkcmExGXLUDwG7C47Agc1qQO70zFcldNpqcNva3FIiVcDNJsRYrYOXYIrE5nlg+cs1CkoGfRskDim9QKlWtGSgKtQ8qrS8qjQ7JLxx32FD0WgV+GiUBHgN+vjr8fP1Qqc6tQr/HM3bsWPLy8kQQ5Cyj9nfSXArWgwePu966dx8A2nRvfaijgyAqufjdEARBEHpOnwdBvvzySx566CHefPNNxo4dyyuvvMKsWbPIyckhLCzshPsVFhbypz/9iYkTJ57G3gqCEJQYxrQHLqNsez7Zv2zBYDSwd/suDu05SMb5I0iYMgS5Qk7axKGkTRyK0+6iYFct+zcUUrDNiLHewK7lq9i1YjUBEVEkjRhCxvQR+If2fJq7Sqlh8ODxDB48ngtbljndTvLH7aRg30aq8vfQXHIkY8RdWY2xspr/BuzEut97R39KRSBDLEEExCQTkTiEpAGjiY5NE3VG+jGNRkOEJpKI8MhTbNn+jrTT6aS5uZnmZgPDbG4u9vjSaLbTbDLjV3EpdrMRh82Ey2rCbTeDwwx2MzanDlzg9kCzxYZWUQWWI+268L61cDhgcmTY1t8UH6HGWwTSLSnxKDR4FFpkSi0GbTQHgmeg1yjQa5UMtmTjo1Gg1vqh9dHho/PDR+eHr68vfn56NGp1j/z8Trddu3a1vr7//vv54x//SGVlJcOGDTtmaFJ6evrRuwtnAHWA9/+4Lef4QRBbS3BEPdg779XRmR9q+Zn5f1sQBEHon/q8JsjYsWMZPXo0r7/+OuCtCh8bG8v999/Po48+etx9XC4XkyZNYt68eaxdu5bGxsYOZ4KcE+NvBeE0cbvc5K3czb5N2VhtVtJcsYSFhOI/KwHNkOBjxvMbapvY+fM28rbtprm26sgKmUR4UjoZMyeSlBmKRnd6azK43C7KSvZRkLeN8pL9bIyzklOfQ7mpnNlb3cTUHvVnUqlEHh6KLiYB35nTGRCWRkpACjql7rT2W+g/bE4XTRYHBrMNS9UhzKZmzCajt+aJxYjDYsRhN1PhCmKTlIHB4sBosXO39V0kl+24bR7OMDmsbcDkaMWeMN6XXY5eo0SvVXCd5yd8lDIkpRaFWodCo0Wl8UWl1eEIS2dCWjwBPj13d70751ZJkpDJZMcUQj3s8LqztTDqwYMHz+5rkqf8sRnk5C8NR6bRMGj7NmTy9kHkvGnTcZSXE//Jx/iMHs2q4lU8sOqB1vVPnPcE1w669nT3XBAEQTjDnBE1Qex2O9u3b+exxx5rXSZJEjNmzGDjxo0n3O/vf/87YWFh3HHHHaxdu/Z0dFUQhOOQ5BIDZ2aQNDGN/OW70W234qyxUPfpfuojnARPjCd6ZFLr9voQfybfNJ3JN02nurCa7BXbKdq1H2N9DbWlHlZ9coBfP8shMkVNeLyb9OmZ6AJ6f1YAuSQnLn4YcfHDALihZbnBbiA3fR2lB3dQV3wQc1kx7po6cDhwlZZTW1nOSwGboCXYc0meP/EEo4+OJyR2ELFJGSQmZqLRiJkNznZqhZwwPzlhfhoIH9GJPWfgcrkwGo0YjQaMJiNmkxGL2UigQ0GcIgaDxYHBYkdbOQKXzYTbbgGHGY/TiuS0ILmsWD0q7E43tUYbtUYbKkU+8paAiavlcTjU8qLzWj77fXiPBkG6o6CgoK+7cNrde++93Hvvva0Xa2c7la8LmdyNx2rFUVKCKiGhdZ2ruRlHeTngrQkCoFGITBBBEASh9/RpEKS2thaXy0V4ePsCeeHh4Rw4cOC4+6xbt4733nuPrKysDh3DZrNhsx25y2YwGLrcX0EQjk+hUTLwkhG4ZzhpXlNK47piDtbm41yUS8jaEDJmjSU0NbrdPmEJYcy8YzYwm4pDFZQcMJO/s466UiPFe/ZSuDOfLYt/JDgmjpTRw0ifmomPv89p/Vx6lZ6Rwy9i5PCLWpc5nHYK83dSdGgHpbWHOD+imdyGXGosNejK6rGb66nNzaWW5d5aIzIZskB/lNHRuC+eSkpACimBKcT6xqKUi1lIBJDL5fj7+3fgy/Dxpyt2u1wYrVbutMswWJwYrA7cFTqsFhN2ixG7xYTdasJpM+GyWRimiCRY1z8CIADx8fF93QWhl8kkUPm5sDVK2IuK2gVBbLm5ACgiI5G3/A4cXRNEBEEEQRCEntTnNUE6o7m5mVtuuYV33nmHkJCQDu3z7LPP8vTTT/dyzwRBAJA0CvwvSEA1KoTYxXYKDxVSW1vLis9+IDIqivSLxxIYH3rMfpHJkUQmw5iLk2moNLF9qYtD2xuwGBqoLS6ktriQzYt+ICg6lqThaWTMGIVv4OkNiBymVKgYMHAsAwaOBeC2luWN1kYODVlPecFu6ktzMVWU4qyqApsdT30j5c4mFmUfCe5etRFCVIFoIqMJiE4iIj6NuKQMoiIHoVCI4IjQcZJcjl6nQ68DDtcaTppywu1vOh2dEoSjqHyd2BqV2IuK2i235eQAoB44oHWZCIIIgiAIvalPgyAhISHI5XKqqqraLa+qqiIiIuKY7Q8dOkRhYSFz5sxpXeZ2uwFQKBTk5OSQnJzcbp/HHnuMhx46Mre8wWAgNja2Jz+GIAhH0Qb5Mva2GaSW1bNryWZKS0upKC+n4t1viYmNIePisfhFBx1338AIHTPmzWTGvJmU7C9m96qdFO/Zj7W5ibqSIupKy8laYSdqQBBJmaHEDw0gINzvNH/CYwVoAhg56mJGjrq4dZnb7aamppCCQzsoaSoCfRN5jXkcqs8lwGDC7a7FXF2LOTubchaxA0AhxxwXSt2skST5J5EYkEiiK4j4mCFo1KLmiHD2SUxMPKZ+UEc8+OCDPPDAA6feUOgXVH5OAOxFxe2W2wu9QRF10pHrNzEcRhAEQehNfRoEUalUjBw5khUrVnD55ZcD3i8NK1as4L777jtm+8GDB7N79+52y/7617/S3NzMq6++etzghlqtRn2GVswXhDOdPjqICb+dTV1eJbt+3ExVVRWlxaWEzVfiGB6HflosimDtCfePTY0jNjUOt3sOZTml7Fu7i4pDDZiaJMpzGyk72MCqj9fjG+BL7NBBDJmYQczgmNP4CU9OkiTCw5MID0/iPOCaluUut4uyKQcozt9JZdF+GksPYakow1PfCE4XleYqVhT+5N3Y42HeMjdyjwwC9KhCw/CLjCM4OpnI+DQSE4ej1x+bXSMIZ4oPP/ywS/sltBlSIfR/Sl9vUVt7cfsgiKO8zLs++siQSbmsfeFUMUWuIAiC0JP6fDjMQw89xNy5cxk1ahRjxozhlVdewWQycfvttwNw6623Eh0dzbPPPotGo2Ho0PZjogMCAgCOWS4IQv8RnBLB1Psvo3pfKWWrc/ApVmHeXoV5ZzVNg2XETk9DHx14wv0lSWoNiAAYai3kZ9WQu7WAsv1WjPUW9q+pYf+adWj8/IlJG0Tq+ekkZiQiyaXT9TE7TC7JiYsdQlzskHbLnU4HZaX7KTIUkSHVkt+UT2lVLnLlAbDZoaEJe0MTdQdzqWMFB4GPw2TsmBDmzRrRJ5BeqiAibjAxcUMJD08SU/kK/d7kyZP7ugunXdvZYc4VSp33szorK9ott5cdDoJEtS5TSO0vT4/ODBEEQRCE7ujzIMh1111HTU0NTz75JJWVlWRmZvLTTz+1FkstLi5GkvrflxhBEDovLC2GsLQYbMUGDMuLaThYye6DBezO3Ud8QjxDLx6NX8SJgyGH6UO0ZM6II3NGHI1VGexenUVB1gEaykuwNjeRt3kLeZu3oPVPYeDY80lIDyEmNQilqn8HBBQKJfEJ6cSTzqQ2y92Xu6mtK6EoP4vK4v3Ulx/CVFmKs6aWBj8ztZZaai217CncjH6Vm8IjDSILCkAdEoZfeCz+A9OIGjKaBH0CAZqA0/75BEHwOtdmhwFQ+niHwzjKylunPAZwlnlnhmmbCSLJ2l/3iUwQQRAEoSfJPB6Pp687cTp1dO5gQRB6X93+cnb+vIna2loAZDKJuKR4hl40Gr/wgE63Z2oysffXXeRt20ttSTEyxTAkeXBL2034BVQRnzGItPHDCIntWHHl/q7Z1kyhoZD8pnxKSvaiXL0Ve3UVNBrweNzttt2VKGPzYO+XizD0XLFLgzY0An1Ey/Ca2MHExQ5Fpwvog08inMnEubVrzomf21PeII/bKSNnYSQAA7dsRq7X4zIaOThqtHfZtm3Ifb11j+osdUxZMKW1iSVXLCFeL2YREgRBEE6uo+fVPs8EEQTh3BWcGsWM1Cup2FXEnhXbqKuro+hQAcWvFxGXEEfGRWPxiez4XVKdv44xl45jzKXjcFgdlB9qpGh3A4W7ammsPEhdaRF1pUXs+GEZusBgogcPYNDYoSRm9s9hMx3hp/ZjWOgwhoUOg5TLYKp3ucNho7wsh9LivdSU5dJUUURIkJkIXS2Vpkpk9U24yxowlVVgYicVwJ6WNj1+Ohoy4pFGphOvjyfeJ4ZYlz/RMYPRaHz76qMKgnAGkxQe5IGBuBoacFRUINfrcbRkgcgDAloDIHBsTRBRGFUQBEHoSSIIIghCn4tMjycyPZ6KrEJ2r9xOfX0dZQUlRL2mxi8jAr8pMSjDOzczilKjJH5IKPFDQpl43QBKD8Sxf302pfvyMNRWYWqo4+DGOg5u3IRCo2Xg2ItJGRlHzOBAVNoz/0+jUqn2Dq1JSD9mncVpoagyh4qh26krP0RTZTHW6kpcdXVgtSFrNrGv4QD7D3qnrgxv8HDpJjfIZODrgyIoCG1IBH7hMQRFxBM+IJ3Y6DT0qrP0TrYgCD1CERGBq6EBZ2UlDBqE43A9kKiodtsdXctIBEEEQRCEnnTmX+kLgnDWiMxMIDIzgYpdRdStL0JeJMO8sxpTVhXlcRaSpg4ldHD0qRs6ikwmIzY1hthU78wxTTVN7Fu3m4KdB6gtKcZpc3NwayO525qQJBn64GpC4/0YODaNuCFxZ11dIq1Cy+CYTAbHZB6zrr6hgpLi3STRQL6riiJDETbrQVAVg90BzSaczSaai0poZivlwNtpMvbGSwSoA0h1RzC6QMIvLJrAiATColKIikklNDT+rPs5CoLQOYqQEGyAs7YO4EgQJLr933WRCSIIgiD0JhEEEQSh3zmcGWIvbaZ5VQll+4ooKCuh4NMiQkJDGTJ1OJHpCV1u3z/Un3FXTGDcFRNw2BwUZJdQVeCkaG8djVVmaor2UVNoZ9+va1FqtITGJ5CQPpDU8UPwC/bruQ/aDwUFRhIUGElG24VTwH2Xm/qGMspK91NVmktjZRHNNWVYa6vwBFuBJhptjdSUNWDZ7cbCbqqBnMNtKBVIAf7UjR6ALjWNWL9YYpShRMoCiIoaKIbZCMI5QBHsrdHkrGsJgpS3FEU9RSaIKIwqCIIg9CQRBBEEod9SxfgRfEsaUkEITcs8lJWWUVtTw68LlhH4SxBpEzOJHpXUrQwDpVrJwDFJDBwDE4GGymZ2rYCSfXnUl5fhsFooz9lPec5+NixcTEBEImkTpxM3JJiwBD2SJOu5D9yPSZJESHAsIcGxkHFBu3X3AiaHidLmUsoK99AYl42hqgRzbSXO+nowGMHhxF1Tx+aqBko8WwFILvcwLbuleKvOB3lgAOrgUHxDIvEPiyUoNYPoyIGE68JRSsrT/IkFQehpilBvQWpnbY33uc5bFFsRFtpuu6Nnhzk6M0QQBEEQukMEQQRB6PcCE8OY+NuLaCqtY9/P2ykuLKahoZ71i1eiX7mNcdMmEDAyClkPFDcNjPBj8k3Tgek4rA5yt+ZwaEcOFXn5mBvrMdS62fpDIVt/KESlleHrX0BsWjIDx6QSlhDW/Q97htIpdQwKGsSgoEEw4qp26+w2C+XlOVSU5RCms1DkqKK0uRRFYy4oK8DhAJMZl8mMubQcM9lUAz+PlCgOkyGXyck0BDKmRI06KBS/0EgCwuMIiUgkImog4eFJx9w5FoT+bP78+cyfPx+Xy9XXXTmtFCHeIIirZTiMq64eAHlQcLvtjg56HJ5OVxAEQRB6ggiCCIJwxvCPCWbcHReQXtXE3p+2UXioEFezHeM3+VhXluM7Phqf0WHINT2TNaDUKEmbOJS0iUMBqCurpzSnnoo8K6UH6rE0V2KqzaXqUC7bvv8Jtc6P0IR4EoYNYODYQehDOj6zzdlMpdaSkJhJQmIm49qumA5ut5uGxgoqynKoqThEfXUxzdVlWOqr8YtwoaIau9uOq7oaZ5EHZ1ExJqCybTuSxI5JkaiSEon2iybB4U+0SU1wWDzhkSmEhiWgVIh0eqH/uPfee7n33ntbp/I7V8hDDmeCeDNAnPXeIIgipH0Q5OhMEEEQBEHoSSIIIgjCGUcX7s+YudMZ1mCifmMxsh1NuBpt1P+Qx4oVy4kZEE/qzOHownr2y0VwdBDB0UFkTAO3y03RnlL2b1BTmVuIobYam6mZ0r17KN27h3VfyAiKG0XyiHRiBwcSmRKAUi2yFY4mSRLBQdEEB0XDsGnt1t0DuD1u6ix1lJXso+bQXhqrSzDWlGOpq8bZ0IDMYMTjdpPvrKChohIqIOOQmzEHPUcaksnAT4fcPwB1YDCOcekERyUToYsgUhFCpG8Evr5Bp/eDC8I5SBEYCICrsdH73FIbRB4kfv8EQRCE00cEQQRBOGNpA3VEX5SKZ6Yb084qclftxtpsI2//QQ4dyCMmLobU6cMJSgrv8WNLconEjDgSM+IAMBvM5G7NoTA7l6r8IsxN9RhqFGT9UkzWL8V43BXo9PVEDUwkacQgkjISkSvFn+BTkWQSoT6hhA6aDIMmH7Pe4bRTVXmIcTIDZZYKyo3l2Dy7UNgKcTY2QrMR3G4wGHEZjJhLSlmo301DsTe9/nDAxKNWIfnrUQUEoQkKwTckkoCQGIJTM4gMSSREGyKG3AhCN0l6b2Da1dSEx+M5kgkSHHyy3QRBEAShR4krcEEQzngypYTvmEgyRoYTtPkgBzbupqGhgZKiYkreLyY0NIzBE9OJzEzotWlaffQ+ZEwfTsb04QA0VDZQXWSlLKeRkgP1NFbU0FRVRVNVOfvXrkdSKAmMiCJyQAKJGQNISI8XQZEuUCpUxMSkEgOMPrww88h6p9NBbV0xVZWHqKsqpLG6lIsSlJTZq6k0VRKUWwiYkNnseKprsVXXYuMgTUAZsHCCRIOfDIVMwbhqf4ZWq1EHhaANDMUvKIKA0GiCw+IJDUskOChaTAMsCCch99cD4DIYcBsM4HR6l4tMEEEQBOE0ElfcgiCcNSS5RPz5g4k/fzCVe4o5sDqLyqoqamqqqflmBeNWDyNkYgI+maHIlL17Vz8wIpDACBg0NhKPx0NlfjK5W/dTuu8QdWUluOx26kqLqCstYs+qNWgDpxE1IISoAQGExqqIHBiKUilmROkuhUJJRHgyEeHJx99gDhiN9VRWHqKmMp+66iKaayow11dhbajFLxgMjmqcHifu6hqcxR6cxSWYgNqjmvp2khp1eAThunAG12mINSjxDY4gIDia4LA4b6AkOAaFQvy7Cucmud4bBPFYLK11QWQ+PkgqUbNHEARBOH1EEEQQhLNSxNA4IobG0Vhcy/4VO7EUNCCvdtDwdS5NPxZgSFMQO3EguvDeL0ook8mITI4gMjkCmIrb6aJobzEFWbmU5xbSVG3EaZco3ltP8d56nNYtyGRm/MMiiEiJJzE9hcTMJJRq8eW5N/j6BpGSEkRKyuhj1t0LuNwuaiw1VIzeR13xQZpqSjHWV2FtqMPR1IDbYEBmstKocuAwllJqLEWz141PsYc6oKhNezKZhMfPhz0zktCHxxDuE06sUU2Y04eg0FjCwpMIDY0XhVyFs5Lk5+et0ePx4CgvB0Du69vHvRIEQRDONSIIIgjCWS0gLoRxt8/EZbJj3laNcWM5psZmsrLyycrOIioqioEThxExNO60Mba43gAAMT9JREFU9UlSyEnMSCQxIxEAj9tDXbmRsoONlOXUk7/NjtPuoKG8hIbyEvavWYckl+MfHknUwBTSJo4hPEGPQiVqVJwOcklOhC6CiLQISJt23G3sNgtX2uuptlRTZaqiOSgba2EBloZaHE0NuAwGMJrxeLz1SbYZ9uCw7AVgwh43qSVHFXLV+SDX+6HwD6Rx0lCCgmMI8wkjzKEhRB5ASFgC/vpQMfxGOKPIJAnJzw+3wYCjtBRoCYwIgiAIwmkkgiCCIJwT5DoVfpNj8J0QTfX2IgLXNtDQUE95WRnlX5Th7x/AwJGpJExIRa46vX8aZZKMkBg/QmL8yJgWi9s1jNIDpeTvzKX8YAH1ZWU47VYayktprLZzcKsSSS4jJNYXjU8p0YPiSB6Rgn/ouTPVZn+jUmuJVkcT7RftXZB44THbOJx2amuLqakqJNXfTZW5mipzFXLzbuSU4zI0QbPJW8jVaMJlNOEqr+TL6BwcLYVc2wVMFHLw1SHX61HpA9AEBOMZN4LgwCjCfMIIkfkR5huBThdwmn4K56b//Oc/vPvuu3g8HmbMmMGrr76KTCbr6271H0ofcJhb38r1em8QpKzM+15kggiCIAinmQiCCIJwTpHJZYSPSWDWmARqc8rJWbOL0uJSmpoa2bpyI9nrdjBmxCgiJ6Ug16v7pI+SXCJuSBxxQ7zZKW63m7KcUvJ35NJQ5aGhSoW5yU5VfhVOyxYObd3Cmk9B4+dPcEw0UQPiScpMITw5QmQK9CNKhYrIiBQiI1Larxh15KXL7aKurpSa6gJqq4sw1FVwW6KWGmst1eZqwgrzQFMPVhs4XdBowNVowEIpFuBD7VociqMCJiolMj9f5H561P6BmMcN5epRtxPpG3n6PvxZqqbm/9u78+g2yzP//2/Jtixvsi1v8u7E2WPihCQ2oWUrISHQlkzPtMB3gJQWyvQXZoaTYabhjyHN9DAEwoFMwaeZ6SmEzgxbp6V8v6UNS4pJCwmBLJCdOPFuy4tsLZY32Xp+f5i4cfYE27Klz+scn0SPbj26L92WnsuX7ud+2njuuec4ePAgMTExXHvttezcuZMlS5aEumsTxz3/F/7fP8DNjwNDRZAA0N8wVATRTBARERlvKoKISMRKn5lD+swcujt8fL7tM04crmKwP8Dgn9tp/rCDuDlpRF1pxzYrM6TFBLPZTP7sAvJnDxVFDMPA5+ql5rN6ju3y0N7QSI+nk16fh8bDHhoPH+Lj/wtW2zQKShaTPS0Fx5Qk0vMTta7IBBdljiIzo5DMjEKYe5YGNw3909vbRWtbLa7WWjpdDXg7nPg721g2PZ7WnjbauttIGqwH+qE/gOHqZMDVyQC1vJzyGTeXfns8wwprAwMD9Pb2AhAIBMjMzAxxjyaY/MXw/304fNP8xcyPgZaWodtJmgkiIiLjS0UQEYl48fYk5n/7K1zRX07rJ7VEfdZFf42X7gPt7D38Mab4aKaUTGf69SXEJseHuruYTCZs6XHM+9oM5n1tBgC+Dh8n9lRRf7ia1pp6fO1tBPoSqP60nepP2wkOuggGPsWWlkl6QS45MwoomldMWq4uTTkZWa2JFOTPpSD/bJWSL/zV0JVvWltrcLXV09negK/TyV8Vx+NIcIxfZ0No+/btbNy4kd27d9Pc3Mzrr7/OypUrR7SpqKhg48aNOJ1OSktLefbZZykrK7uo/WdkZPDwww9TUFBAdHQ0f/u3f0tx8TmuRCQAmOKsAAy0tgIQlaiZICIiMr5UBBER+UKUJZrsq4vhagg4/bT9uZq+/VUM9vRx4ON9HNq9n9z8XKZ/pYTMOXmh7u4ISfYkSpcuoHTpAgACvQHa6n04q300V3moP1BHb+8gntZmPK3NHP/kE/70EljiEkhxOJhy5WKKSgrJKEjSgqthJDHRTmKinalTrwx1V0LC7/dTWlrK9773Pb71rW+dcf+rr77KmjVr2Lx5M+Xl5WzatInly5dz9OjR4Rkd8+fPZ2Bg4IzHvv3228TFxfG73/2Ompoa4uLiWLFiBdu3b+faa68d89gmK3PcUCH5ZBFEp8OIiMh4UxFEROQsYhwJ5Px1CbetmMbx7Qc58enn+Lp81NfWUV9bhy0pmZLF88j76gzME7BoEGONIWe6nZzpdlgGwWAJzVXN1H52gubj9XQ0NuF3d9Df46e1+jgdzgz2bHVhNpuwpfmIT+4he1o+RfOmklkU2tOBRC7XihUrWLFixTnvf/rpp7n//vu59957Adi8eTNvvvkmzz//PGvXrgVg375953z8r371K6ZNm4bdPjSj6tZbb2Xnzp0qgpyHOS4OACMQACBKp8OIiMg4UxFEROQ8LAlWZq9YyMzlC2g91MCxDw7Q1NCE1+fB804NUe93Er8gk7grM7DkJU3YYoHZbCZ3Ri65M3KHt/X4eqjZX03D4Vr6+7Jpremi29tPe0MtRk0TtZ/uY+evIdpiJTkri8yiPHJnFjB1wQzibdYQRiPy5fX397N7924eeeSR4W1ms5mlS5eyY8eOi9pHfn4+H374Ib29vcTExFBZWckPfvCDc7bv6+ujr69v+LbX6738ACYpc9zIzw5zfOhPMRQRkciiIoiIyEUwm804SgpwlBTQ0+mn+v2DpByFYGcf/p3NHNj1KV5bP1NKplN8zZwJsXbIhcQlxTH76jnMvnoOMLTgaldnH5/vSqHhUBWuhiZ8rjYG+ntx1dfiqq/l8J8+JDr+epIzEskstJGQ3ENabgKFJUXET4KYRU5qb29ncHCQrKysEduzsrI4cuTIRe3jqquu4pZbbmHBggWYzWZuvPFGvvnNb56z/eOPP8769eu/VL8nO9MXM0GGb8eG5ipcIiISuVQEERG5RHGpCcxZWYYRNOg74aFrVzPtR47T19XPZzv3sH/XPnJycphaNovs+UUTdnbI6UwmE0l2KwtvvpKFNw+tIRHoDVB3sI76wydwHm/A2+4jEIjG296Lt72Xgd5PMAY7wQRxScmkOBxkFuaSO6uQgpICrPGaMSLh7bHHHuOxxx67qLaPPPIIa9asGb7t9XrJz88fq65NSGbr6UUQfUaIiMj4UhFEROQymcwmrNNSsE5LYYW7gBN/OkT1wSp8XT4aGxpobGgg7g/xFM+ezuyl84myTb5vPGOsMRQvLKZ44V+ueNHrH1p0ta3Wx9EddXQ2D9Df7aPH66HH66H586N8+g6YzLFkTVtBRqGNrMIkktIMcqY5iLHqMr0Seunp6URFRdHyxaVaT2ppacHhGJur58TGxhIbG0tFRQUVFRUMDg6OyfNMZOb4kUUQc6wlRD0REZFIpSKIiMgosKYkMOcbi5l160LajzRxfOchGmob6OnpxvVJHc2f9GOdaSduQSbWWalEWSbvx681IYb8WXbyZ9m5cvl3AfC0eajdX0PTsTra65rwtLYwEEjE1ejH1ejnyIfNBLq3YzIFiLOlkurIJL0gm5xp+eTPKdCpNDLuLBYLCxcuZNu2bcOXzQ0Gg2zbto0HH3xwTJ979erVrF69Gq/XS3Jy8pg+10Sj02FERCTUJm8WLiIyAZnNZjLn5JE5J4/+7j5qPjiC5fNeqO+n93AHziP1HIltJrcwj6lls8iYnTtpTpc5n+SMZOZ9rZR5XysFhtYX8bn8uBp7aK314TzRTv1+GOgP0u120e120XjkMJ++PfT4+NR8CkquJaMgkfT8JFIyY0jOsIUwIgkHXV1dVFVVDd+urq5m37592O12CgoKWLNmDatWrWLRokWUlZWxadMm/H7/8NVixkpEzwTR6TAiIhJiKoKIiIwRS3wsM24qhZsg0NpN954Wqj/+lIG+ALXHq6k9Xk1CXAIFM4uY+tU5JDlSQ93lUWMymbClJ2JLT2RKaQYwlWBwEe317TQcqcd5ooGOBifetjb6e/z0dpk4vqeV43taMYwBBrrfI8Yajy09A3ueA8eUXPJm55NRqMv1ysX75JNPuOGGG4Zvn1yPY9WqVWzZsoXbb7+dtrY2Hn30UZxOJ/Pnz2fr1q1nLJY62iJ5JohOhxERkVAzGYZhhLoT4+lkwuHxeLDZ9C2jiIyv4GCQpr3VVO8+SnNjM8HgyW+CTaTZ7Sy6upzkBQ7MsZFTo/a2eWir9+FpG6S93vdFgWQ7nOXwFBVtwZ43h4KSBaTlJWLPjifFYdUCrCGmY+vlicTXzVdZScPf/nD4dtFrrxI3b94Z7a548Yrh/+9ftX9c+iYiIpPbxR5XIyfLFhGZAMxRZvIWFZO3qJh+fy81Hx6ldn8Vrg4X/g4fXb89QfebtcSVpBOcnYB9Tg7m6PCe+WDLSMaWceq34SX0+K6j/nA9zcfqaa1rwuNsxe/uYHCgH1dTD+62BgCMoI+B3o+wJtqwpadjz80iqyiHnBl5ZBRkYI4K79dOJqeIPh0mbuT6Pxc6HcaEaSy7IyIiEUgzQUREJgBvUyedexuIPdzHQHsPQYJ8FF1FVEwUOYV5FC2cQebcvIg+FSQQCNB0tBFPWxBv+yCuxi6cxz+nx73vrO3N0TGk5S8gd+Zs0nITScmykuqwkpiaOL4djwA6tl6eSHzduvfspfb//J/h28Vb/4ClqOiMdidngphNZj6959Px6p6IiEximgkiIjKJ2HJSseWkYtxi0F/vo2VnNeZDZvoD/dRUnaCm6gRWaxz5U/MpKpuFvTgLkymyviGNiYmhsKRoxLZgsBRP6zKajjbgPNGEq9GJp7WNbk8nwYEAHc0B3K1NQ20HWhjs+wxLfCK29HRSszPJKMjGUZxNdnGOLt0rMg5M0VEjb1/g6jCaCSIiIqNNRRARkQnEZDIRW2CjoKCU3MBcGvdUU7vvGM4mJ729PRw79DnHDn3OtOQCZiycQ3xpBtFpcRfecZgym82kOlJJdaQy97q/rCEQCARoqWqhyw2dLX10NHbRdKwRfx/0d3fRXtdFe10Nxz764gEmMyk5V5E1pQh7dgJJqSYS7VFkF2erOCKjLpJPh8F8WhHEqtNhRERkfKkIIiIyQUXFRFNQPp2C8ukEevqp23WMuv3HaW1pxeaKxvt2Ld63a+nONtE/xcKUJbNI0GVlgaFZI3mz807bWkpXZxeNRxpwnmikvaEFT0vb0FojgX66OsDvbuPE3jYGA9UE+6vAZCYuKYnEtHRSHRlkFDjImpJN9vRsYiwqjsjlieSrw5w+E8RsucDVYVQDERGRUaYiiIjIJBATZ6H4urkUXzeXfl8vgaNuuj9to6/KTV1rA+1tXg58/CmpKankzyyisGw6CZmR9cfVxUhMTWTmklnMXDJreFswGMTtdNPVGaTT2UNHUxcNh524nRYGA/30eD30eD20VR/n8x1Dj4mJX0Jqdib27ASsSd0k2MAxNRvHVM0cETmv09Y1utDpMCIiIqNNRRARkUnGkmTFsshBwiIHg75+ut7/jIHDJ3B73HR2dtC5s4PPPtpDanIquTMKmXnNPGJSdQnZczGbzdhz7NhzoGDuya2zCQaDdDa7aa5qoLXGSUdTK962dvzuTgzi6XR20+nsZrDvEMGBxqGHmUxYE5JItNuxZaRhz8mgcN4c0vOSiUu8wDfeIhHAFHXKTJDoaEzR509FdTqMiIiMNhVBREQmsagkC7O+vohZX1+Ez9lJ7UfHaDxWS6e7k053J/0f9ZDyYR+WgiTirkgnaoaN+CydMnMxzGYzabl20nLtcN284e3BYJBuT4CO5i46mvzUfOqho3EAf2cHgwMBeru89HZ5aa+r4cRu2LetH5MpCmtCDNa4ZiwJfaRmZZCRn0XmVAeZBRlExehwHEkieU2QU4sgFzwVBhVBRERk9OkSuSIiYcjX4qZu1+cEq/2kNkeDAQMM8lH0MWw2G3nTCiksm44tLy3UXQ0bwWAQd4ublhNO2upa6Ghqpauji6AxG19HLwADvZ9gDHaOeJzJbCYuKZlEu50pC67Dnp1IiiOB5IxYrAmT41QBHVsvTyS+bv319Ry/aRkAUSkpzNi546ztnj/wPM/sfoYnr32SFVNWjGcXRURkkrrY46qKICIiYW7Q20fPQReNe06w13kYTvnYT0pMIntKHgULirFPc2A+7Xx9GR2B/kHcLd3UfnaUtrpGPC0ufB0d9HjdBE/OBjDFEhN/7fBjBnr3EB3TTbwthcS0VFKy0rHnpJNRkEXWlCxi4ydOgUTH1ssTia9boKmJqq/dCEBURjoz/vSnc7b1B/wkxCSMV9dERGSSu9jjqubfioiEuShbLIlLcpi5JIf89lJqd31Ow9FaXB0ufF0+fPsP8/n+w8yIL2BqyXSsc9OILUrGFKVp6KMlxhJFRn4SGfmLgEXD24ODQdob2mk50Yy7xcdgMAO300+nsxtPt59Aby+e3h48rc00Hj5lhyYLqbnLSM6MJyUzDrO5naS0ODIKHWQVZmpxVpm4TjkdxhR1/jRUBRARERkLKoKIiESQ+PQkZt+ykNm3LKSn00/9J1U0Hq2lrbUNm9dC14dNdH3YRHtcF10OyJtTRM7CqVgm0KyDcGKOMpNZmElmYeYZ93W5F9BaffLUmna8bS58He6h2SPBeLo6++jq7KPxaCeBnj9DsGfogSYTsfGJxKekYEtLxZ6TTeG8ElKy4rGlWTFHabaPhM6pa4JcaFFUERGRsaCjj4hIhIpLTWDGTaXMuKmUgd4AgRNeeg666D3ioqW3k876Lhrq6zG/8yHp6enkziwgf/E04u1Joe56REhMSSBxQTFTFxSP2B4MBun29tDVMYC7tRt3SzfVe2vo6uigx+clOBCgz++jz++js7GeuoO1HPhTEACz2USi3czNP7iSjAKNY6hE8sKop84EOf1yuSIiIuNBa4KIiMgIRtCgZX8ddZ8ep7mukZ7enr/caTKRakvhqgVlxM1OIyYnAZNJp81MFCcXZ22raaG9oY3O5jZ6u6MYCGTjbu1hoH8AGOSex67Flh43as+rY+vlicTXbdDj4fPyqwCIKSxg2ltvhbhHIiISLrQmiIiIXBaT2YSjtBBHaeHQH9XVbdTtqaLpRANen4dBdx++d+vwvVuH2WbBmd2DfUYWOfOnYpkkVzMJV2azGXu2HXu2nZnMHnGfETTwdfTgbe8l0W4NUQ8l4l1gHRAREZGxpiORiIick9lsxl6chb04i/mAv8WD90grMbUB+qo66fV283l3FRz/HNPWD0hLs+OYmkf+/KkkF6SHuvtyCpPZhC09Hlt6fKi7IhHMdMqaNCaTTocREZHxpyKIiIhctISsZBKykgEwBoJ4jrQy5ZMgzoYmenp7aG9vp729nQO79pEQn8C0qdOYsmgmsUU2TNH6g0ck0p26MCo6lU5EREJARRAREbkspmgzKSUOykscBINBPHXtNOw7gfNEI67ODvzdfro/baV9Xz8mSxTBIiu+zCDZ84pIzrNj1qKIIpHn1CKIiIhICKgIIiIiX5rZbCa1KJPUokyuAPp8PTTurSa+ySBY5SPYFaCpqp7qEy18tnMPVmscWTlZZE/PJ3t+EbFJo7dIp8hEF9FXhzm1+KmZICIiEgK6OoyIiIwpI2gQaPZTu+cYNcdO0NHZiWEE/9LAZCI1OYX5JaWkzs0mJjcRk1l/HE0mOrZenkh93Q7PGlq01zJ1KsW/fzPEvRERkXChq8OIiMiEYDKbsOQmMj13AdNZQL+/j+bPanAerae1sQV/jx+P20NfZTOtlS2Y46PpzB0kOi+BnNIikhypoQ5BRMaCip0iIhICKoKIiMi4siTEUrhkJoVLZgLgbezEdaiRBKeZ3uNugt0DHD9xgu7qPvb+6WPi4+LJcGSSOS2X7CsKiLcnhTgCERkNJp0OIyIiIaAiiIiIhJQtNxVb7tBsD2PQoK/eS95H0FrXjNvrobunm9rqGmqra+CdD0hLsrN4zgJip6UQOyUZs1WHMhERERG5OMocRURkwjBFmbAWJXNl0TUA9Hf10ry/lpZjjbQ1teDr8hHlHaTrgya6PmjCMBscsbdhz03HMSOfrLn5RFtjQhyFiFwczQQREZHxpyKIiIhMWJZE64hTZ7o7fPQcd2Ou76XvuBu3y43L7cLldnHs4FFMb5ixp6aSkZtF5oxcMmflqSgiMlHpdBgREQkBFUFERGTSiLcnDa0Jsnjotq3Ni3lvJq3VTbS1tNLX34fL5cLlcnHks0Pkk8H0vKnETkkmpiiJ6LxELAmxoQ1CRIaoCCIiIiGgIoiIiExa8Rk2ZiwrZQalBINBPHXtNB+so63Wiau9HVtPHP01XvprvLhMPg5HN5JiSyYtO5OsaTlkzc0nNiku1GFIhKmoqKCiooLBwcFQd0VERCTiqAgiIiJhwWw2k1qUSWpRJgDBYJABVy+BGi99JzzUV7mhx8DtceP2uDl+5HN404QtMYl0RwbTSmaQPMtBVIJOn5GxtXr1alavXo3X6yU5OTnU3QkdzQQREZEQUBFERETCktlsxpIRjyUjnoTFDpYwk7lNnbQcqqO1uhlXq4vuHj9enxevz0vqYeimhuj0OHxZBsGMaDJm5pJSkI45yhzqcETCj4ogIiISAiqCiIhIxLDlpGLLSWU6pQD4Wz04DzXgqmkh0WVjsK2HgfYeajobcB31wZ8/JiY6hlS7nbScDDKn5ZA+M4eYOEuIIxEJA6qBiIhICEyIIkhFRQUbN27E6XRSWlrKs88+S1lZ2Vnb/vznP+eXv/wlBw4cAGDhwoX827/92znbi4iInEtCZjLFmckUMxeAYHeAvjofWZ+aMRqcuD1uAgMBWltbaG1t4fC+A5hNUVyTtYC4ohQshV8stpqqdUVELpVJVRAREQmBkBdBXn31VdasWcPmzZspLy9n06ZNLF++nKNHj5KZmXlG+8rKSu68806uvvpqrFYrTzzxBMuWLePgwYPk5uaGIAIREQkX5vgY4mbZmTfrK8wDBgMDuI45aa1qwtXQgqu9g9g+M4MNfroa/PBn2BtVTTDORGq6nbTcDNKnZpM+PZsoS8gPsSIiIiJyGpNhGEYoO1BeXs7ixYt57rnngKGF7PLz8/m7v/s71q5de8HHDw4OkpqaynPPPcc999xzwfYnFyHzeDzYbLYv3X8REYkcwWCQvnY/RmMPfbVeeqrd/KljL6cfSk0mMzabDYfDwcySWVjyk4hKs2IK0zUQdGy9PJH6uh2eNRsA69y5TPn1/4a4NyIiEi4u9rga0q+p+vv72b17N4888sjwNrPZzNKlS9mxY8dF7aO7u5tAIIDdbh+rboqIiABDx6i4zCTITCJ+QSapwF91ldB6uIH2aicdze10dnYSGAjg8biJcQfpODhU+DDFRXEstY0URxppRVlkzMjBmpIQ2oBEREREIkxIiyDt7e0MDg6SlZU1YntWVhZHjhy5qH386Ec/Iicnh6VLl571/r6+Pvr6+oZve73ey++wiIjIaSyJVvIWTyNv8TRgaLZIV1MnbceaMLcNYGkz0d/Uhb+nG2egBWdrC3x2CID4uARS01NJy80ka1oO9uIsTDFRoQxHLtFTTz3FCy+8gMlkYu3atdx1112h7tLkYdZVl0REZPxN6hOWN2zYwCuvvEJlZSVWq/WsbR5//HHWr18/zj0TEZFIZTabseWlYctLG95mDATpqu1k3qFkXI1tdLo66O7pprvHT3e9n8b6BvI/rKOQDGIyEyDHiiuhm/QpDuxTs4i2xoQwIjmX/fv389JLL7F7924Mw+CGG27g61//OikpKaHu2uQQpqeHiYjIxBbSIkh6ejpRUVG0tLSM2N7S0oLD4TjvY5966ik2bNjAu+++y7x5887Z7pFHHmHNmjXDt71eL/n5+V+u4yIiIpfAFG0mqTiNOcV/KYz0dPpp+7yJ9honnU4XKd5E8EPA6cfV4uRwVAPsAEwmkhISSUlLxZ6bTlqRCiMTxeHDh1myZMnwFzGlpaVs3bqVO+64I8Q9ExERkXMJaRHEYrGwcOFCtm3bxsqVK4GhacTbtm3jwQcfPOfjnnzySR577DHeeustFi1adN7niI2NJTY2djS7LSIi8qXFpSZQUD6dgvLpABiGwaC3n0CDj0BVI+k1fXjdHvoD/fi6fPi6fNTX1sGHMN3IIS8zB0teEoOZMQTTokmb5tAVaU6zfft2Nm7cyO7du2lubub1118fzjdOqqioYOPGjTidTkpLS3n22WcpKyu7qP2XlJSwfv163G43hmFQWVnJjBkzxiCSMKWJICIiEgIhz5bWrFnDqlWrWLRoEWVlZWzatAm/38+9994LwD333ENubi6PP/44AE888QSPPvooL730EkVFRTidTgASExNJTEwMWRwiIiJfhslkIjo5lujkWKbMTWcKpQSDQfytHlzHnHQ0tNHR6sLjdpPYYyXQ7CfQ7KfR3EG1uWV4xkiyPYUURxr2ggzSpjqItcWFOrSQ8fv9lJaW8r3vfY9vfetbZ9z/6quvsmbNGjZv3kx5eTmbNm1i+fLlHD16lMzMTADmz5/PwMDAGY99++23mTNnDn//93/P1772NZKTk7nqqquIitKaLiIiIhNZyIsgt99+O21tbTz66KM4nU7mz5/P1q1bhxdLraurw3zKwlk/+9nP6O/v56//+q9H7GfdunX8+Mc/Hs+ui4iIjCmz2UySI5UkRypFDF1WNBgMMujuY6DJT39DF9FVvcS0xxAYCAzPGGmoq4ddQ/u4MnEmabkZxOQkMpgeRXxeChZ7fNhervdUK1asYMWKFee8/+mnn+b+++8f/uJl8+bNvPnmmzz//POsXbsWgH379p33OR544AEeeOABAO677z6mT58+Op2PACZNBRERkRAIeREE4MEHHzzn6S+VlZUjbtfU1Ix9h0RERCYos9mM2R5HjD2OuJJ0FlLEgi9mjHQcb6GzsZ3Olg48bg+9fb3EuqHH7aLnoIvjZieZwWSm3FeGdVpKqEMJqf7+fnbv3s0jjzwyvM1sNrN06VJ27Nhx0ftpbW0lMzOTo0ePsmvXLjZv3nzOtrpi3UhmzeAVEZEQmBBFEBEREbl8p84YKTxle5+nG6Otn0BTF4FmP0aNiwRPLDHZCSHr60TR3t7O4ODg8MzTk7Kysjhy5MhF7+e2227D4/GQkJDACy+8QHT0uVMrXbFuSM6TT+D6xfM4frwu1F0REZEIpCKIiIhImIpNjofk+OFZH9czEyMQxBRjPv8D5aJdyqwRXbFuSPI3v0nyN78Z6m6IiEiEUhFEREQkgqgAMiQ9PZ2oqChaWlpGbG9pacHhcIzJc568Yl1FRQUVFRUMDg6OyfOIiIjIuSkTEhERkYhjsVhYuHAh27ZtG94WDAbZtm0bS5YsGdPnXr16NYcOHeLjjz8e0+cRERGRM2kmiIiIiISlrq4uqqqqhm9XV1ezb98+7HY7BQUFrFmzhlWrVrFo0SLKysrYtGkTfr9/+GoxY0UzQURERELHZBiGEepOjCev10tycjIejwebzRbq7oiIiEx6E/XYWllZyQ033HDG9lWrVrFlyxYAnnvuOTZu3IjT6WT+/Pn89Kc/pby8fFz6N1FfNxERkcnoYo+rKoKIiIjIl6Jj6+XR6yYiIjJ6Lva4qjVBRERERMZRRUUFc+bMYfHixaHuioiISMRREURERERkHGlhVBERkdBREUREREREREREIoKKICIiIiLjSKfDiIiIhI6KICIiIiLjSKfDiIiIhI6KICIiIiIiIiISEaJD3YHxdvKKwF6vN8Q9ERERCQ8nj6knj7FycZSTiIiIjJ6LzUcirgji8/kAyM/PD3FPREREwovP5yM5OTnU3Zg0lJOIiIiMvgvlIyYjwr62CQaDNDU1kZSUhMlkGrX9er1e8vPzqa+vx2azjdp+QykcY4LwjEsxTR7hGFc4xgThGddYxWQYBj6fj5ycHMxmnWl7scYiJ9Hv7eQRjnGFY0wQnnGFY0wQnnGFY0wwNnFdbD4ScTNBzGYzeXl5Y7Z/m80WVr+cEJ4xQXjGpZgmj3CMKxxjgvCMayxi0gyQSzeWOYl+byePcIwrHGOC8IwrHGOC8IwrHGOC0Y/rYvIRfV0jIiIiIiIiIhFBRRARERERERERiQgqgoyS2NhY1q1bR2xsbKi7MmrCMSYIz7gU0+QRjnGFY0wQnnGFY0wyUjiOcTjGBOEZVzjGBOEZVzjGBOEZVzjGBKGNK+IWRhURERERERGRyKSZICIiIiIiIiISEVQEEREREREREZGIoCKIiIiIiIiIiEQEFUHOoaKigqKiIqxWK+Xl5ezateu87X/1q18xa9YsrFYrV1xxBb///e9H3G8YBo8++ijZ2dnExcWxdOlSjh07NpYhnNWlxPXzn/+ca665htTUVFJTU1m6dOkZ7b/73e9iMplG/Nx8881jHcYIlxLTli1bzuiv1Wod0WYyjtX1119/Rlwmk4lbb711uE2ox2r79u184xvfICcnB5PJxG9/+9sLPqayspIrr7yS2NhYpk2bxpYtW85oc6nv1dF0qTH95je/4aabbiIjIwObzcaSJUt46623RrT58Y9/fMY4zZo1awyjGOlSY6qsrDzr757T6RzRLpTjBJce19neLyaTiblz5w63CfVYPf744yxevJikpCQyMzNZuXIlR48eveDjJsvxSoYoH1E+MpnGSvmI8pHRFI45ifKRvwjl8UpFkLN49dVXWbNmDevWrWPPnj2UlpayfPlyWltbz9r+ww8/5M477+T73/8+e/fuZeXKlaxcuZIDBw4Mt3nyySf56U9/yubNm/noo49ISEhg+fLl9Pb2jldYlxxXZWUld955J++99x47duwgPz+fZcuW0djYOKLdzTffTHNz8/DPyy+/PB7hAJceE4DNZhvR39ra2hH3T8ax+s1vfjMipgMHDhAVFcW3v/3tEe1COVZ+v5/S0lIqKiouqn11dTW33norN9xwA/v27eOhhx7ivvvuG3GQvpzxH02XGtP27du56aab+P3vf8/u3bu54YYb+MY3vsHevXtHtJs7d+6Icfrzn/88Ft0/q0uN6aSjR4+O6HNmZubwfaEeJ7j0uP793/99RDz19fXY7fYz3lOhHKv333+f1atXs3PnTt555x0CgQDLli3D7/ef8zGT5XglQ5SPDFE+MnnGSvmI8pHRFI45ifKRISE/XhlyhrKyMmP16tXDtwcHB42cnBzj8ccfP2v773znO8att946Ylt5ebnxwAMPGIZhGMFg0HA4HMbGjRuH73e73UZsbKzx8ssvj0EEZ3epcZ1uYGDASEpKMl588cXhbatWrTJuu+220e7qRbvUmF544QUjOTn5nPsLl7F65plnjKSkJKOrq2t4W6jH6lSA8frrr5+3zT//8z8bc+fOHbHt9ttvN5YvXz58+8u+TqPpYmI6mzlz5hjr168fvr1u3TqjtLR09Dr2JVxMTO+9954BGJ2dnedsM5HGyTAub6xef/11w2QyGTU1NcPbJtJYGYZhtLa2GoDx/vvvn7PNZDleyRDlI2enfGTyjJXyEeUjoyUccxLlI6E7XmkmyGn6+/vZvXs3S5cuHd5mNptZunQpO3bsOOtjduzYMaI9wPLly4fbV1dX43Q6R7RJTk6mvLz8nPscbZcT1+m6u7sJBALY7fYR2ysrK8nMzGTmzJn88Ic/xOVyjWrfz+VyY+rq6qKwsJD8/Hxuu+02Dh48OHxfuIzVL37xC+644w4SEhJGbA/VWF2OC72vRuN1CrVgMIjP5zvjPXXs2DFycnKYOnUqf/M3f0NdXV2Ienjx5s+fT3Z2NjfddBMffPDB8PZwGCcYek8tXbqUwsLCEdsn0lh5PB6AM36fTjUZjlcyRPnIuSkfmTxjpXxkcnxuhlM+AuGdkygfGZ3PQBVBTtPe3s7g4CBZWVkjtmdlZZ1xPtlJTqfzvO1P/nsp+xxtlxPX6X70ox+Rk5Mz4pfx5ptv5pe//CXbtm3jiSee4P3332fFihUMDg6Oav/P5nJimjlzJs8//zxvvPEG//3f/00wGOTqq6+moaEBCI+x2rVrFwcOHOC+++4bsT2UY3U5zvW+8nq99PT0jMrvdKg99dRTdHV18Z3vfGd4W3l5OVu2bGHr1q387Gc/o7q6mmuuuQafzxfCnp5bdnY2mzdv5te//jW//vWvyc/P5/rrr2fPnj3A6Hz2hFpTUxN/+MMfznhPTaSxCgaDPPTQQ3zlK1+hpKTknO0mw/FKhigfOTflI5NjrJSPTJ7PzXDIRyD8cxLlI6M3VtFfeg8SETZs2MArr7xCZWXliIW77rjjjuH/X3HFFcybN4/i4mIqKyu58cYbQ9HV81qyZAlLliwZvn311Vcze/Zs/uM//oOf/OQnIezZ6PnFL37BFVdcQVlZ2Yjtk22swt1LL73E+vXreeONN0acq7pixYrh/8+bN4/y8nIKCwt57bXX+P73vx+Krp7XzJkzmTlz5vDtq6++muPHj/PMM8/wX//1XyHs2eh58cUXSUlJYeXKlSO2T6SxWr16NQcOHBj387VFxpvykclD+cjkEC75CIR/TqJ8ZPRoJshp0tPTiYqKoqWlZcT2lpYWHA7HWR/jcDjO2/7kv5eyz9F2OXGd9NRTT7Fhwwbefvtt5s2bd962U6dOJT09naqqqi/d5wv5MjGdFBMTw4IFC4b7O9nHyu/388orr1zUB954jtXlONf7ymazERcXNyrjHyqvvPIK9913H6+99toZUwFPl5KSwowZMybsOJ1NWVnZcH8n8zjB0Mrkzz//PHfffTcWi+W8bUM1Vg8++CC/+93veO+998jLyztv28lwvJIhykfOpHxk8oyV8pHJ8bkZ7vkIhE9OonzkzDZfhoogp7FYLCxcuJBt27YNbwsGg2zbtm1Exf5US5YsGdEe4J133hluP2XKFBwOx4g2Xq+Xjz766Jz7HG2XExcMrcr7k5/8hK1bt7Jo0aILPk9DQwMul4vs7OxR6ff5XG5MpxocHGT//v3D/Z3MYwVDl5rq6+vjrrvuuuDzjOdYXY4Lva9GY/xD4eWXX+bee+/l5ZdfHnHJwHPp6uri+PHjE3aczmbfvn3D/Z2s43TS+++/T1VV1UUl8uM9VoZh8OCDD/L666/zxz/+kSlTplzwMZPheCVDlI+MpHxk8owVKB+ZDMe5SMhHIHxyEuUjo/wZ+KWXVg1Dr7zyihEbG2ts2bLFOHTokPGDH/zASElJMZxOp2EYhnH33Xcba9euHW7/wQcfGNHR0cZTTz1lHD582Fi3bp0RExNj7N+/f7jNhg0bjJSUFOONN94wPvvsM+O2224zpkyZYvT09EzYuDZs2GBYLBbjf//3f43m5ubhH5/PZxiGYfh8PuPhhx82duzYYVRXVxvvvvuuceWVVxrTp083ent7J2RM69evN9566y3j+PHjxu7du4077rjDsFqtxsGDB0fEPdnG6qSvfvWrxu23337G9okwVj6fz9i7d6+xd+9eAzCefvppY+/evUZtba1hGIaxdu1a4+677x5uf+LECSM+Pt74p3/6J+Pw4cNGRUWFERUVZWzdunW4zYVep4kW0//8z/8Y0dHRRkVFxYj3lNvtHm7zj//4j0ZlZaVRXV1tfPDBB8bSpUuN9PR0o7W1dULG9Mwzzxi//e1vjWPHjhn79+83/uEf/sEwm83Gu+++O9wm1ON0OXGddNdddxnl5eVn3Weox+qHP/yhkZycbFRWVo74feru7h5uM1mPVzJE+chf+qx8ZHKM1UnKR5SPhCKuyZCTKB8ZEurjlYog5/Dss88aBQUFhsViMcrKyoydO3cO33fdddcZq1atGtH+tddeM2bMmGFYLBZj7ty5xptvvjni/mAwaPzLv/yLkZWVZcTGxho33nijcfTo0fEIZYRLiauwsNAAzvhZt26dYRiG0d3dbSxbtszIyMgwYmJijMLCQuP+++8f1z9sLjWmhx56aLhtVlaWccsttxh79uwZsb/JOFaGYRhHjhwxAOPtt98+Y18TYaxOXrbs9J+Tcaxatcq47rrrznjM/PnzDYvFYkydOtV44YUXztjv+V6nsXapMV133XXnbW8YQ5fdy87ONiwWi5Gbm2vcfvvtRlVV1YSN6YknnjCKi4sNq9Vq2O124/rrrzf++Mc/nrHfUI6TYVze75/b7Tbi4uKM//zP/zzrPkM9VmeLBxjxPpnMxysZonxE+chkGivDUD6ifCR0cU2GnET5yF+E8nhl+qLjIiIiIiIiIiJhTWuCiIiIiIiIiEhEUBFERERERERERCKCiiAiIiIiIiIiEhFUBBERERERERGRiKAiiIiIiIiIiIhEBBVBRERERERERCQiqAgiIiIiIiIiIhFBRRARERERERERiQgqgoiIiIiIiIhIRFARREQmpOuvv56HHnoo1N0QERGRCKecRCS8qAgiIiIiIiIiIhHBZBiGEepOiIic6rvf/S4vvvjiiG3V1dUUFRWFpkMiIiISkZSTiIQfFUFEZMLxeDysWLGCkpIS/vVf/xWAjIwMoqKiQtwzERERiSTKSUTCT3SoOyAicrrk5GQsFgvx8fE4HI5Qd0dEREQilHISkfCjNUFEREREREREJCKoCCIiIiIiIiIiEUFFEBGZkCwWC4ODg6HuhoiIiEQ45SQi4UVFEBGZkIqKivjoo4+oqamhvb2dYDAY6i6JiIhIBFJOIhJeVAQRkQnp4YcfJioqijlz5pCRkUFdXV2ouyQiIiIRSDmJSHjRJXJFREREREREJCJoJoiIiIiIiIiIRAQVQUREREREREQkIqgIIiIiIiIiIiIRQUUQEREREREREYkIKoKIiIiIiIiISERQEUREREREREREIoKKICIiIiIiIiISEVQEEREREREREZGIoCKIiIiIiIiIiEQEFUFEREREREREJCKoCCIiIiIiIiIiEUFFEBERERERERGJCP8//mu+DAgBfqoAAAAASUVORK5CYII=",
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"text/plain": [
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"<Figure size 1100x400 with 2 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"max error vs Mittag-Leffler = 5.625e-04\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"def mittag_leffler(alpha, z, n_terms=200):\n",
|
|
" z = np.asarray(z, dtype=float)\n",
|
|
" out = np.zeros_like(z)\n",
|
|
" term = np.ones_like(z)\n",
|
|
" for k in range(n_terms):\n",
|
|
" out = out + term / Gamma(alpha * k + 1.0)\n",
|
|
" term = term * z\n",
|
|
" return out\n",
|
|
"\n",
|
|
"T, N = 2.0, 800\n",
|
|
"alphas = [0.3, 0.5, 0.7, 0.9]\n",
|
|
"fig, ax = plt.subplots(1, 2, figsize=(11, 4))\n",
|
|
"max_err = 0.0\n",
|
|
"for a in alphas:\n",
|
|
" res = opt.solve_fractional_ode(1.0, a, T, N, lambda t, h: -h)\n",
|
|
" t = np.asarray(res[\"t_grid\"]) ; h_num = np.asarray(res[\"h\"])\n",
|
|
" h_exact = mittag_leffler(a, -t**a)\n",
|
|
" err = np.max(np.abs(h_num - h_exact))\n",
|
|
" max_err = max(max_err, err)\n",
|
|
" ax[0].plot(t, h_num, label=f\"alpha={a} num\")\n",
|
|
" ax[0].plot(t, h_exact, '--', alpha=0.6, label=f\"alpha={a} exact\")\n",
|
|
" ax[1].semilogy(t[1:], np.abs(h_num - h_exact)[1:], label=f\"alpha={a}\")\n",
|
|
"ax[0].set_xlabel(\"t\"); ax[0].set_ylabel(\"h(t)\"); ax[0].legend(fontsize=7); ax[0].set_title(\"D^a h = -h, h(0)=1\")\n",
|
|
"ax[1].set_xlabel(\"t\"); ax[1].set_ylabel(\"|h_num - E_a(-t^a)|\"); ax[1].legend(fontsize=7); ax[1].set_title(\"pointwise error (log)\")\n",
|
|
"plt.tight_layout(); plt.show()\n",
|
|
"errors['solve_fractional_ode'] = max_err\n",
|
|
"assert max_err < 5e-2, f\"max err = {max_err}\"\n",
|
|
"print(f\"max error vs Mittag-Leffler = {max_err:.3e}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "3ec2f158",
|
|
"metadata": {},
|
|
"source": [
|
|
"## 2. Markovian lift on a geometric grid\n",
|
|
"\n",
|
|
"Approximate a convolution kernel admitting the integral representation\n",
|
|
"\n",
|
|
"$$\n",
|
|
"K(t) = \\int_{0}^{\\infty} e^{-\\gamma t}\\, \\nu(d\\gamma)\n",
|
|
"$$\n",
|
|
"\n",
|
|
"by\n",
|
|
"\n",
|
|
"$$\n",
|
|
"K(t) \\;\\approx\\; \\sum_{j=1}^{N} c_j\\, e^{-\\gamma_j t},\n",
|
|
"\\qquad c_j \\ge 0,\n",
|
|
"$$\n",
|
|
"\n",
|
|
"with rates on a geometric grid and weights fitted by non-negative least squares.\n",
|
|
"\n",
|
|
"**Target.** The rough kernel\n",
|
|
"\n",
|
|
"$$\n",
|
|
"K(t) = \\frac{t^{H - 1/2}}{\\Gamma(H + 1/2)}, \\qquad H \\in (0, 1/2],\n",
|
|
"$$\n",
|
|
"\n",
|
|
"with $H = 0.1$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 3,
|
|
"id": "d1ce930a",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-05-12T09:45:37.562632Z",
|
|
"iopub.status.busy": "2026-05-12T09:45:37.561864Z",
|
|
"iopub.status.idle": "2026-05-12T09:45:39.631556Z",
|
|
"shell.execute_reply": "2026-05-12T09:45:39.630065Z"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 1100x400 with 2 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"max relative error on rough kernel = 1.688e-02\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"H = 0.1\n",
|
|
"rough_kernel = lambda t: t ** (H - 0.5) / Gamma(H + 0.5)\n",
|
|
"t_samples = np.geomspace(1e-3, 1.0, 200).tolist()\n",
|
|
"lift = opt.geometric_grid_lift(rough_kernel, t_samples, 12, 1e-2, 1e4, 20000)\n",
|
|
"gammas = np.asarray(lift[\"gammas\"]) ; weights = np.asarray(lift[\"weights\"])\n",
|
|
"\n",
|
|
"t_eval = np.geomspace(1e-3, 1.0, 400)\n",
|
|
"k_target = np.array([rough_kernel(tt) for tt in t_eval])\n",
|
|
"k_lift = np.array([np.sum(weights * np.exp(-gammas * tt)) for tt in t_eval])\n",
|
|
"rel_err = np.max(np.abs(k_lift - k_target) / np.abs(k_target))\n",
|
|
"\n",
|
|
"fig, ax = plt.subplots(1, 2, figsize=(11, 4))\n",
|
|
"ax[0].loglog(t_eval, k_target, label='target K(t)')\n",
|
|
"ax[0].loglog(t_eval, k_lift, '--', label='lift sum c_j exp(-g_j t)')\n",
|
|
"ax[0].set_xlabel('t'); ax[0].set_ylabel('K(t)'); ax[0].legend(); ax[0].set_title(f'Rough kernel H={H}')\n",
|
|
"ax[1].loglog(t_eval, np.abs(k_lift - k_target) / np.abs(k_target))\n",
|
|
"ax[1].set_xlabel('t'); ax[1].set_ylabel('relative error'); ax[1].set_title('lift relative error')\n",
|
|
"plt.tight_layout(); plt.show()\n",
|
|
"errors['geometric_grid_lift'] = rel_err\n",
|
|
"assert rel_err < 0.5, f'relative err = {rel_err}'\n",
|
|
"print(f'max relative error on rough kernel = {rel_err:.3e}')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "7b414887",
|
|
"metadata": {},
|
|
"source": [
|
|
"## 3. Generic second-kind Volterra equation\n",
|
|
"\n",
|
|
"Solve\n",
|
|
"\n",
|
|
"$$\n",
|
|
"y(t) = g(t) + \\int_{0}^{t} K(t - s,\\, y(s))\\, ds\n",
|
|
"$$\n",
|
|
"\n",
|
|
"by trapezoidal product integration,\n",
|
|
"\n",
|
|
"$$\n",
|
|
"y_n = g_n + \\Delta t\\,\\Big[ \\tfrac{1}{2} K(t_n, y_0) + \\sum_{k=1}^{n-1} K(t_n - t_k, y_k) + \\tfrac{1}{2} K(0, y_n) \\Big],\n",
|
|
"$$\n",
|
|
"\n",
|
|
"with the implicit step solved by fixed-point iteration.\n",
|
|
"\n",
|
|
"**Ground truth.** Take $g(t) = 1$ and $K(t, y) = y$. Then $y(t) = 1 + \\int_0^t y(s)\\, ds$ is equivalent to $y' = y,\\, y(0) = 1$, with exact solution\n",
|
|
"\n",
|
|
"$$\n",
|
|
"y(t) = e^{t}.\n",
|
|
"$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 4,
|
|
"id": "f0dcd786",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-05-12T09:45:39.636022Z",
|
|
"iopub.status.busy": "2026-05-12T09:45:39.635722Z",
|
|
"iopub.status.idle": "2026-05-12T09:45:40.961468Z",
|
|
"shell.execute_reply": "2026-05-12T09:45:40.959903Z"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
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"<Figure size 1100x400 with 2 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"max error vs exp(t) = 1.232e-06\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"T, N = 2.0, 2000\n",
|
|
"res = opt.solve_volterra(lambda t: 1.0, lambda dt, y: y, T, N, 100, 1e-13)\n",
|
|
"t = np.asarray(res[\"t_grid\"]) ; y_num = np.asarray(res[\"y\"])\n",
|
|
"y_exact = np.exp(t)\n",
|
|
"err = np.abs(y_num - y_exact)\n",
|
|
"max_err = float(err.max())\n",
|
|
"\n",
|
|
"fig, ax = plt.subplots(1, 2, figsize=(11, 4))\n",
|
|
"ax[0].plot(t, y_num, label='numerical')\n",
|
|
"ax[0].plot(t, y_exact, '--', label='exp(t)')\n",
|
|
"ax[0].set_xlabel('t'); ax[0].set_ylabel('y(t)'); ax[0].legend(); ax[0].set_title('Volterra: y = 1 + int_0^t y(s) ds')\n",
|
|
"ax[1].semilogy(t[1:], err[1:])\n",
|
|
"ax[1].set_xlabel('t'); ax[1].set_ylabel('|y_num - exp(t)|'); ax[1].set_title('pointwise error (log)')\n",
|
|
"plt.tight_layout(); plt.show()\n",
|
|
"errors['solve_volterra'] = max_err\n",
|
|
"assert max_err < 1e-2, f'max err = {max_err}'\n",
|
|
"print(f'max error vs exp(t) = {max_err:.3e}')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "19a8f090",
|
|
"metadata": {},
|
|
"source": [
|
|
"## 4. Fourier inversion of a characteristic function\n",
|
|
"\n",
|
|
"Recover a density from $\\varphi(u) = \\mathbb{E}[e^{i u X}]$ via\n",
|
|
"\n",
|
|
"$$\n",
|
|
"f(x) \\;\\approx\\; \\frac{\\Delta u}{\\pi}\\, \\sum_{k=0}^{N_u - 1} w_k \\big[\\,\\Re\\varphi(u_k)\\,\\cos(u_k x) + \\Im\\varphi(u_k)\\,\\sin(u_k x)\\,\\big].\n",
|
|
"$$\n",
|
|
"\n",
|
|
"**Ground truth.** Standard normal $X \\sim \\mathcal{N}(0, 1)$ has\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\varphi(u) = e^{-u^2 / 2}, \\qquad f(x) = \\frac{1}{\\sqrt{2\\pi}}\\, e^{-x^2 / 2}.\n",
|
|
"$$\n",
|
|
"\n",
|
|
"We supply $\\varphi$ in the trigonometric form $\\varphi(u) = \\cos(-u^2/2) + i \\sin(-u^2/2)$ rescaled by $e^{-u^2/2}$ -- equivalently, real part $e^{-u^2/2}$ and imaginary part $0$, which matches $\\cos(-u^2/2) e^{-u^2/2}$ and $\\sin(-u^2/2) e^{-u^2/2}$ when one writes the Gaussian characteristic function in polar form with phase $-u^2/2$ collapsing to $0$ for a real symmetric law."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"id": "bf8f64a8",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-05-12T09:45:40.965231Z",
|
|
"iopub.status.busy": "2026-05-12T09:45:40.964938Z",
|
|
"iopub.status.idle": "2026-05-12T09:45:41.737924Z",
|
|
"shell.execute_reply": "2026-05-12T09:45:41.736418Z"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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jjEH4GhI7P3WHIeSAPEEIohpz69Yt5OTkmD9k2A/2qVOnShqMCj+QVCqV6Djuh9Mvv/yCf//9F3/++Se2b9+OV155BZ9//jn+/fdfu0y1hMTFxaFBgwZYt24dHn30Uaxbtw7BwcFmwcIWYnc6jEYj+vXrh3feeUf0GPYLjSPY88H8+OOPw8vLCxs3bsQjjzyCjRs3QqlU4plnnuHFplAo8Pfff4s+38LnUOpOTlRUFDp06IB169Zh1KhRWLduHdRqNUaMGOHglREEQRCECanPuvIsTm19t7CGu7s7unTpgv379+PatWtIT09Hz5490aBBA5SUlODo0aM4cOAAWrVqhXr16knO4+npif3792Pv3r3YsmULtm3bhg0bNuCxxx7Djh07oFKpYDQa0bZtWyxevFh0jrCwMMn52e9cn332GWJiYkTH2Pv5bk8Ghy3snaNu3boA7BOkKpIHDx7Ay8vLJddOEI5CIghBVGO+//57ADALHmynEnd3d7sFBXvp2rUrunbtio8++gg//vgjXnjhBaxfvx6vvfaa6HhrX55UKhWef/55rF69GgsXLsQff/yBsWPHSn5psofIyEjk5+fbvO7IyEhs374dWVlZktkgTZo0gdFoxNWrV813OwAgIyMD2dnZaNKkiXmbt7c3hgwZgp9//hmLFy/Ghg0b0LNnT4SEhPDOyTAMIiIinBJjuIwaNQpTpkzBnTt38OOPP2Lw4MF2pbQSBEEQBGDKYODesb927RqMRiPCw8MBOPYZWB6sfU/o2bMnFi5ciF27diEoKAitWrWCQqHAQw89hAMHDuDAgQM8k3AplEol+vbti759+2Lx4sX4+OOP8cEHH2Dv3r2IjY1FZGQkTp8+jb59+zos+kRGRgIwlca6+jsXYPo9XL582WL7pUuXzPudoXHjxvD09ERSUpJdMezatQt5eXm8bBBhDOxrJikpiZdpxO0IJCQpKYn3+iKIyoTKYQiimrJnzx7MmzcPEREReOGFFwAA9evXR+/evfHNN9/gzp07FscIW9/aw4MHDyzu3LB3PKyVxLDeHtx2dlxeeuklPHjwAK+//jry8/Px4osvOhwblxEjRuDIkSPYvn27xb7s7Gzo9XoAwPDhw8EwDObMmWMxjr3OQYMGAQCvowwA850iodv5yJEjcfv2bXz77bc4ffo0rxQGMHXLUalUmDNnjsVzyTCMuT7XHp577jkoFApMmjQJN27cKPfzRhAEQdQu4uPjeT9/9dVXAICBAwcCcPwz0Fm8vb0tykVYevbsCa1WiyVLlqBHjx5mgaJnz574/vvvcfv2bat+IIDJJ02I8PvLiBEjkJaWhhUrVliMLSoqQkFBgeT8HTp0QGRkJBYtWmRu08vFme9cXAYNGoRjx46Zy20BU7va//3vfwgPD0dUVJRT87q7u6Njx444ceKEXTEYDAb83//9H2/7F198AYVCYX7NsDfjvv76a9449rUlxsmTJ/HII484Gj5BuATKBCGIasDff/+NS5cuQa/XIyMjA3v27MHOnTvRpEkTbN68GR4eHuax8fHx6NGjB9q2bYuxY8eiadOmyMjIwJEjR3Dr1i2cPn3aoXOvWbMGX3/9NZ588klERkYiLy8PK1asgJ+fn/mLkhgdOnQAYGqD9+yzz8Ld3R2PP/64WRxp37492rRpYzYle/jhh514ZsqYNm0aNm/ejCFDhuDll19Ghw4dUFBQgLNnz+KXX35BcnIygoKC0KdPH7z00ktYunQprl69igEDBsBoNOLAgQPo06cPJkyYgOjoaIwePRr/+9//kJ2djV69euHYsWNYs2YNhg0bhj59+vDOPWjQIPj6+mLq1KlQqVQYPnw4b39kZCTmz5+P6dOnIzk5GcOGDYOvry+SkpLw+++/Y9y4cZg6dapd11mvXj0MGDAAP//8MwICAlz2ZZQgCIKoHSQlJWHo0KEYMGAAjhw5gnXr1uH5559HdHQ0ADj8GegsHTp0wIYNGzBlyhR06tQJPj4+ePzxxwEA3bp1g5ubGy5fvoxx48aZj3n00UexbNkyALApgsydOxf79+/H4MGD0aRJE2RmZuLrr79Go0aNzF4iL730EjZu3Ig33ngDe/fuRffu3WEwGHDp0iVs3LgR27dvR8eOHUXnVyqV+PbbbzFw4EA89NBDGDNmDEJDQ5GWloa9e/fCz88Pf/75p9PPz3vvvYeffvoJAwcOxMSJExEYGIg1a9YgKSkJv/76K5RK5+9lP/HEE/jggw+Qm5sLPz8/yXGPP/44+vTpgw8++ADJycmIjo7Gjh07sGnTJkyePNmcDdOhQwcMHz4cS5Yswf37980tcq9cuQLAMusnISEBWVlZeOKJJ5y+BoIoFzJ0pCEIwk7YNrbsQ61WM8HBwUy/fv2YL7/80tw+Tsj169eZUaNGMcHBwYy7uzsTGhrKDBkyhPnll18s5ha2vmVbre3du5dhGIY5efIk89xzzzGNGzdmNBoNU79+fWbIkCHMiRMneMdBpAXavHnzmNDQUEapVIq2y/30008ZAMzHH39s93PSpEkTZvDgwaL78vLymOnTpzPNmjVj1Go1ExQUxDzyyCPMokWLGJ1OZx6n1+uZzz77jGnVqhWjVquZevXqMQMHDmQSEhLMY0pKSpg5c+YwERERjLu7OxMWFsZMnz6d13qYywsvvGBuOSzFr7/+yvTo0YPx9vZmvL29mVatWjHjx49nLl++bB7Tq1cv5qGHHrL6HGzcuJEBwIwbN87qOIIgCIJgYdu0XrhwgXn66acZX19fpk6dOsyECROYoqIi3lh7PwOlWuT+/PPPvHFJSUkMAGbVqlXmbfn5+czzzz/PBAQEMAAs2uV26tSJAcAcPXrUvO3WrVsMACYsLEzy+lh2797NPPHEE0xISAijVquZkJAQ5rnnnmOuXLnCO06n0zELFy5kHnroIUaj0TB16tRhOnTowMyZM4fJycmx+pwyDMOcOnWKeeqpp5i6desyGo2GadKkCTNixAhm9+7dFrGJteu19r3m+vXrzNNPP80EBAQwHh4eTOfOnZm//vqLN0bqObdGRkYG4+bmxnz//fe87cIWuQxj+m711ltvMSEhIYy7uzvTvHlz5rPPPuO1BWYYhikoKGDGjx/PBAYGMj4+PsywYcOYy5cvMwCYTz75hDf23XffZRo3bmwxB0FUFgqGscOhiCAIogL48ssv8dZbbyE5OdnCSZ6QZtOmTRg2bBj2799v804YQRAEQQDA7NmzMWfOHNy9exdBQUFyh0PIzKuvvoorV66YO+1UBImJiWjfvj3WrVtnLt3WarUIDw/He++9h0mTJlXYuQnCGuQJQhCELDAMg++++w69evUiAcRBVqxYgaZNm1ptDUgQBEEQBCHFrFmzcPz4cRw6dMgl8xUVFVlsW7JkCZRKJR599FHztlWrVsHd3R1vvPGGS85LEM5AniAEQVQqBQUF2Lx5M/bu3YuzZ89i06ZNcodUbVi/fj3OnDmDLVu24MsvvyxX+0KCIAiCIGovjRs3RnFxscvm+/TTT5GQkIA+ffrAzc0Nf//9N/7++2+MGzeO12r4jTfeIAGEkB0SQQiCqFTu3r2L559/HgEBAXj//fcxdOhQuUOqNjz33HPw8fHBq6++ijfffFPucAiCIAiCIAAAjzzyCHbu3Il58+YhPz8fjRs3xuzZs/HBBx/IHRpBWECeIARBEARBEARBEARB1ArIE4QgCIIgCIIgCIIgiFoBiSAEQRAEQRAEQRAEQdQKyBNEBKPRiNu3b8PX15eMBwmCIAjCDhiGQV5eHkJCQqBU0j2W8kLfRQiCIAjCMez9LkIiiAi3b9/muRgTBEEQBGEfN2/eRKNGjeQOo9pD30UIgiAIwjlsfRchEUQEX19fAKYnz8/PT+ZoCIIgCKLqk5ubi7CwMPNnKFE+6LsIQRAEQTiGvd9FSAQRgU079fPzoy8eBEEQBOEAVLrhGui7CEEQBEE4h63vIlS0SxAEQRAEQRAEQRBErYBEEIIgCIIgCIIgCIIgagUkghAEQRAEQRAEQRAEUSsgTxCCIIgqjMFgQElJidxhEATc3d2hUqnkDoMgCIIgCKJckAhCEARRBWEYBunp6cjOzpY7FIIwExAQgODgYDI/rUDi4+MRHx8Pg8EgdygEQRAEUSMhEYQgCKIKwgog9evXh5eXFy06CVlhGAaFhYXIzMwEADRs2FDmiGou48ePx/jx45Gbmwt/f3+5wyEIgiCIGkeVEEHi4+Px2WefIT09HdHR0fjqq6/QuXNnm8etX78ezz33HJ544gn88ccf5u0Mw2DWrFlYsWIFsrOz0b17dyxbtgzNmzevwKsgCIJwDQaDwSyA1K1bV+5wCAIA4OnpCQDIzMxE/fr1qTSGIAiCIIhqiezGqBs2bMCUKVMwa9YsnDx5EtHR0YiLizPfbZIiOTkZU6dORc+ePS32ffrpp1i6dCmWL1+Oo0ePwtvbG3FxcSguLq6oyyAIgnAZrAeIl5eXzJEQBB/2NUk+NQRBEARBVFdkF0EWL16MsWPHYsyYMYiKisLy5cvh5eWFlStXSh5jMBjwwgsvYM6cOWjatClvH8MwWLJkCT788EM88cQTaNeuHdauXYvbt2/zskUIgiCqOlQCQ1Q16DVJEARBEER1R1YRRKfTISEhAbGxseZtSqUSsbGxOHLkiORxc+fORf369fHqq69a7EtKSkJ6ejpvTn9/f3Tp0kVyTq1Wi9zcXN6DIAiCIAiCIAiCIIiahawiyL1792AwGNCgQQPe9gYNGiA9PV30mIMHD+K7777DihUrRPezxzky54IFC+Dv729+hIWFOXopBEFUEEYjg3+u3MV7v57B418dxOKP38Hl+V3w79djcfnEHjBGo9whElWAffv2QaFQVEg3nd69e2Py5Mkun9fVzJ49GzExMXKHQRAEIQubEtMwYvkRZObVjPJ3o5HB69+fwKLtl+UOhSBqHLKXwzhCXl4eXnrpJaxYsQJBQUEum3f69OnIyckxP27evOmyuQmCcJ5Lx3bizMePYtLK3Vh//CbOpuUgoDAFLfWX0DVzI1r+9STOLXwMN6+eljtUopSXX34ZCoXC4nHt2rUKPe8jjzyCO3fuVEg3jd9++w3z5s1z+byuZurUqdi9e7fcYRAEQcjCpPWJOJachU/+viQ5hmEYbDieikvpVT/r+9+k+9h+PgP/t7diPz8JojYia3eYoKAgqFQqZGRk8LZnZGQgODjYYvz169eRnJyMxx9/3LzNWHoX2M3NDZcvXzYfl5GRwWvhl5GRIXmHTKPRQKPRlPdyCIJwEYzRiH/XzULn619BpWDwluZPXH94Oro3C0JDQzBO3IwFc2UHorP3oK32FArX9cOJzh+h4+CxcodOABgwYABWrVrF21avXr0KO19JSQnUarXo54Yj6HQ6qNVqi+2BgYHlmtcVGAwGKBQKKJXS9y58fHzg4+NTiVERBEFUPfKK9ZL7/jxzB+/+ehYAkPzJ4MoKSZTiEgM83KW7bJUYmEqMhiBqF7JmgqjVanTo0IF358poNGL37t3o1q2bxfhWrVrh7NmzSExMND+GDh2KPn36IDExEWFhYYiIiEBwcDBvztzcXBw9elR0ToIgqhaM0Yhjy8ai242lUCkYnPDrh6ETFmHuE20Q91Aw2rXrgI6Dx6LTWz/j7uiDOKeJgZdCi47Hp+Lfnz6SO3wCJmE5ODiY92Dbqf7zzz/o3LkzNBoNGjZsiPfeew96fdkX1vDwcCxZsoQ3X0xMDGbPnm3+WaFQYNmyZRg6dCi8vb3x0UcfiZbDHDx4ED179oSnpyfCwsIwceJEFBQU8M41b948jBo1Cn5+fhg3bpzo9QjLYcLDw/Hxxx/jlVdega+vLxo3boz//e9/5v2PPPII3n33Xd4cd+/ehbu7O/bv3w/A5EU1depUhIaGwtvbG126dMG+ffvM41evXo2AgABs3rwZUVFR0Gg0SE1Nxb59+9C5c2d4e3sjICAA3bt3R0pKCgDLchij0Yi5c+eiUaNG0Gg0iImJwbZt28z7k5OToVAo8Ntvv6FPnz7w8vJCdHS0VU8ugiCIqo7KioHzqdQHlRiJNCsPJqHVjG3Ydu6O5Bgl+VATRIUheznMlClTsGLFCqxZswYXL17Ef/7zHxQUFGDMmDEAgFGjRmH69OkAAA8PD7Rp04b3CAgIgK+vL9q0aQO1Wg2FQoHJkydj/vz52Lx5M86ePYtRo0YhJCQEw4YNk/FKCYKwh3/XTEeXu7/AyChwtNV76DjlF9Sp11B0bGjT1mg9bTf+rT8CWsYNK8+WYP2x1EqOuHJgGAaFOr0sD4Zxzd2otLQ0DBo0CJ06dcLp06exbNkyfPfdd5g/f77Dc82ePRtPPvkkzp49i1deecVi//Xr1zFgwAAMHz4cZ86cwYYNG3Dw4EFMmDCBN27RokWIjo7GqVOnMGPGDLvP//nnn6Njx444deoU3nzzTfznP//B5cumuu0XXngB69ev5z1vGzZsQEhIiLmt+4QJE3DkyBGsX78eZ86cwTPPPIMBAwbg6tWr5mMKCwuxcOFCfPvttzh//jwCAwMxbNgw9OrVC2fOnMGRI0cwbtw4yY4tX375JT7//HMsWrQIZ86cQVxcHIYOHco7BwB88MEHmDp1KhITE9GiRQs899xzPGGKIAiiOmElYQ5afdXwEZv71wUAphIeKRQoe2931ecwQRAmZC2HAYCRI0fi7t27mDlzJtLT0813qlhj09TUVKvpv2K88847KCgowLhx45CdnY0ePXpg27Zt8PDwqIhLIAjCRRz/4//QLWW56f8PvY8uI96xeYzKzQ1d3vgG/9v0DHYcLcGeP86heQMfdGgifwmDKykqMSBq5nZZzn1hbhy81PZ/XPz111+8soyBAwfi559/xtdff42wsDD83//9HxQKBVq1aoXbt2/j3XffxcyZMx16r3/++efNYjkA3Lhxg7d/wYIFeOGFF8wZHM2bN8fSpUvRq1cvLFu2zPx58Nhjj+Htt9+2+7wsgwYNwptvvgkAePfdd/HFF19g7969aNmyJUaMGIHJkyebM1EA4Mcff8Rzzz0HhUKB1NRUrFq1CqmpqQgJCQFg8vPYtm0bVq1ahY8//hiAqczn66+/RnR0NAAgKysLOTk5GDJkCCIjIwEArVu3loxx0aJFePfdd/Hss88CABYuXIi9e/diyZIliI+PN4+bOnUqBg82pYXPmTMHDz30EK5du4ZWrVo5/LwQBEHIjdJKJoi2pGqIICzWRBluJojeyMBdRakhBOEqZBdBANMdMeHdORZuerAYq1evttimUCgwd+5czJ071wXREQRRGVxMSUf4qU8BBXCk4Sh0s0MAYVEolRg3rB/OFJ3CljN38OG6PVj3WlfUbdCoAiMmpOjTpw+WLVtm/tnb2xsAcPHiRXTr1o2XudC9e3fk5+fj1q1baNy4sd3n6Nixo9X9p0+fxpkzZ/DDDz+YtzEMA6PRiKSkJLN4YGseKdq1a2f+v0KhQHBwMDIzMwGY/E/69++PH374AT179kRSUhKOHDmCb775BgBw9uxZGAwGtGjRgjenVqtF3bp1zT+r1WreeQIDA/Hyyy8jLi4O/fr1Q2xsLEaMGMHzv2LJzc3F7du30b17d9727t274/RpvpEw9xzsXJmZmSSCEARRLbEmgugMVUsEsQpXBDEwsGIfQhCEg1QJEYQgiNpNcYkBk3+7ghztfLwXnIChry12eA6FQoGFw9uBuXUCMws+xp2VTRD47l4oHMwkq6p4uqtwYW6cbOd2BG9vbzRr1sypcymVSou035KSEtFzWCM/Px+vv/46Jk6caLGPK7bYmkcKd3d33s8KhcJs1A2YSmImTpyIr776Cj/++CPatm2Ltm3bmmNTqVRISEgwe6WwcDNoPD09LUpdVq1ahYkTJ2Lbtm3YsGEDPvzwQ+zcuRNdu3Z16jqE18Kez0itpwmCqKaorJhpaEsMlRhJ+eCKOXqjEQCpIAThKkgEIQhCdj7fcRmXM/IQ5NMQPV77FEqVcx/0Pho3vDu0I/x/KkCwNhHHNv0fOj9puQiujigUCodKUqoirVu3xq+//gqGYcyL7UOHDsHX1xeNGpmydurVq4c7d8qM4nJzc5GUlOTwuR5++GFcuHDBaTGmvDzxxBMYN24ctm3bhh9//BGjRo0y72vfvj0MBgMyMzPN5TKO0L59e7Rv3x7Tp09Ht27d8OOPP1qIIH5+fggJCcGhQ4fQq1cv8/ZDhw6hc+fOzl8YQRBEFcdKIkiV8QSxB54IQp1iCMKl1IxbpARBVFuunD6MC4f+BAB88lQ7BPmUr111k1YP43Sz/wAAWpxeiKzMtHLHSLiGN998Ezdv3sR///tfXLp0CZs2bcKsWbMwZcoUsx/IY489hu+//x4HDhzA2bNnMXr0aItsCXt49913cfjwYUyYMAGJiYm4evUqNm3aJFl66Wq8vb0xbNgwzJgxAxcvXsRzzz1n3teiRQu88MILGDVqFH777TckJSXh2LFjWLBgAbZs2SI5Z1JSEqZPn44jR44gJSUFO3bswNWrVyV9QaZNm4aFCxdiw4YNuHz5Mt577z0kJiZi0qRJLr9egiCIqoK17jC6aiSCcNEbSQQhCFdSvW8rEgRRrWGMRhj+ehs/qC/g9/rjERs12CXzdhj5Aa4v3IxIQxJOrJuEwCm/uGReonyEhoZi69atmDZtGqKjoxEYGIhXX30VH374oXnM9OnTkZSUhCFDhsDf3x/z5s1zKhOkXbt2+Oeff/DBBx+gZ8+eYBgGkZGRGDlypCsvySovvPACBg0ahEcffdTC72TVqlWYP38+3n77baSlpSEoKAhdu3bFkCFDJOfz8vLCpUuXsGbNGty/fx8NGzbE+PHj8frrr4uOnzhxInJycvD2228jMzMTUVFR2Lx5M5o3b+7S6yQIgqhKWC2H0VefchgDR/jQU4kiQbgUBUM9lyzIzc2Fv78/cnJy4OfnJ3c4BFFjObFlBToen4pCRoP8cUdRPzTCZXNfObkPzTYNg1LB4MrQzWjxcC/bB1URiouLkZSUhIiICOpqRVQprL026bPTtdDzSRCOEf6eKZPu+S6N8fGTbUXHDPnqAM6l5QIAkj9xzY0XZ2j54d/m0hypOA5du4cXvj0KADjwTh+EBXpVWnwEUV2x97OTymEIgpCF4sJ8NDr+CQDgdPgYlwogANDi4d5ICDAZieq2z3Tp3ARBEARBVE2slcNUlRa5GjfbSzB+JgjdsyYIV0IiCEEQspD4xxcIxj2kIwjtR86okHOEPjkXWsYdyYUaHL54q0LOQRAEQRBE1cFKNUyVMUb1sKPrmoGTrK+vTq19CaIaQCIIQRCVTnFhPppd+RYAkNpmPDy8fGwc4Rwh4S3xf+1+wYSSSViwK9mi9SpBEARBENUf7ue70ooKUlWMUe0RQYyc7I8S6g5DEC6FRBCCICqdxE1LEYRspKMeYh5/s0LPNTquG7zVKpxNy8G+y3cr9FwEQdROnnzySdSpUwdPP/20xb7w8HC0a9cOMTEx6NOnjwzREUTNh1suorRWDlNFjFE93B0rhzFQOQxBuBQSQQiCqFSKSwz447oBycYGSIl6HWpNxRp/Bvlo8HyXxmikyETqls8q9FwEQdROJk2ahLVr10ruP3z4MBITE7F3795KjIogag4Mw2DJriv4/ZR4aauekylhvTtMNcoE4WS3lEh0hzmRnIVZm84hX6t3WWwEURugFrkEQVQqf5xKw/r8h3HQrwt2P/FopZzz1Y6BePvYNHjkleDyiYFo2fGxSjkvQRC1g969e2Pfvn1yh0EQNZaTqQ+wZNdVAMCT7RtZ7OeKBFYSQapMOYx9xqhl/9dLlMM8vfwIAEClVGLm41EuiY0gagOUCUIQRKXBMAxWHkoCAIzu0QyaCs4CYQluEIyzdfoCAAr2Lq6UcxIEUTXYv38/Hn/8cYSEhEChUOCPP/6wGBMfH4/w8HB4eHigS5cuOHbsmMvOr1Ao0KtXL3Tq1Ak//PCDy+YliNpEeo7W6v4SjrhhrRymMrqsrPs3Bb+dtG7G7rAxqkQmCMvljFz7giMIAgCJIARBVCJn/t2F9vf+RB21ASM6hVXquevFTQMAxOQfxM1rZyv13ARByEdBQQGio6MRHx8vun/Dhg2YMmUKZs2ahZMnTyI6OhpxcXHIzMw0j4mJiUGbNm0sHrdv37Z5/oMHDyIhIQGbN2/Gxx9/jDNnzrjs2giitqAzWPfyqCotZDPzivHhH+cwZeNpqx1dNG5lIoiU3wfXGFUqE4SFjFMJwjGoHIYgiEqD2b8IC93/xdB6efD3HFqp5w5v3RGnPTohuvg40nbGI6zZ8ko9P0EQ8jBw4EAMHDhQcv/ixYsxduxYjBkzBgCwfPlybNmyBStXrsR7770HAEhMTHT6/KGhoQCAhg0bYtCgQTh58iTatWvn9HwEURvRlpQJCkYjY9EBpsTA38+luMSAP0/fRq8W9ew+3427+TibloOh0aYMMnsp0pWJNQU6A/w9xe83c41RtXoDvNSWSzJHjFHJOJUgHIMyQQiCqBRuXTuHdoVHAQCN+1dsRxhJOr8GAGidsRnFhfnyxEBUS+7fv4/69esjOTm5Qs9z4cIFNGrUCAUFBRV6HsKETqdDQkICYmNjzduUSiViY2Nx5MiRcs9fUFCAvLw8AEB+fj727NmDhx56SHSsVqtFbm4u70EQhAmuoamYSSg3U4JrKAoAi3dewbRfzuDJrw/bfb7HPv8Hk9YnYuvZdIfi5J66UCdtVsothykuEc8Y4ZbDlFjJKgFgNeuEIAhLSAQhCKJSuLXz/6BUMDjt2RlhzaNliaHNo0/jDurBHwU4s32VLDEQFY+U74PYOA8PD6SkpPC2Dxs2DC+//DJv20cffYQnnngC4eHh5m2pqakYPHgwvLy8UL9+fUybNg16vXWH/o8++giPPPIIvLy8EBAQYLE/KioKXbt2xeLF5F1TGdy7dw8GgwENGjTgbW/QoAHS0+1f/MTGxuKZZ57B1q1b0ahRI7OAkpGRgR49eiA6Ohpdu3bFqFGj0KlTJ9E5FixYAH9/f/MjLKxySwYJoirDbW0rVvrB9cwQ6gE7zpv+ltOyixw+b0LKA4fGc8WaAq10CQ83kaW4xIDM3GIwAvGGVw5jI9ODymEIwjFIBCEIosLRFRehZcYWAADT4RXZ4lC5uSE5YiRyGS8kXrduWkbUDhQKBWbOnGl1TGFhIb777ju8+uqr5m0GgwGDBw+GTqfD4cOHsWbNGqxevdrmXDqdDs888wz+85//SI4ZM2YMli1bZlNQIaoOu3btwt27d1FYWIhbt26hW7duAICmTZvi9OnTOH36NM6dO4dJkyZJzjF9+nTk5OSYHzdv3qys8AmiysPt6iKW9VBiJROkPJUiVrrtisIVawrsbFu7/lgqOn+8G3P+vMDbzjdGtX4RtoxTy4tQoCGI6g6JIARBVDhn96xHHeQiE4Fo02u4rLE0f3wKeuq/xsf3HsW5tBxZY6mJGI1GLFiwABEREfD09ER0dDR++eUXAKYvUbGxsYiLizN/ocrKykKjRo3M4oHBYMCrr75qPr5ly5b48ssvLc6zcuVKPPTQQ9BoNGjYsCEmTJgAAOZMjSeffBIKhYKXuSHGhAkTsG7dOpw7d05yzNatW6HRaNC1a1fzth07duDChQtYt24dYmJiMHDgQMybNw/x8fHQ6XSSc82ZMwdvvfUW2rZtKzmmX79+yMrKwj///GM1dqL8BAUFQaVSISMjg7c9IyMDwcHBlRqLRqOBn58f70EQhImikjJxQSciglgrhxHzy3BX2aduCL1HbMHLBLFSDsNl6Z5rAIDVh5N52/nGqLbKYSpOpDiWlIXOH+/G1rN3KuwcBFHZkAhCEESF437mewDA9dAn4OauljWWoMC66NUmHACw8UQ1vNOqK5B+lBQ7MLbIvrEOsmDBAqxduxbLly/H+fPn8dZbb+HFF1/EP//8A4VCgTVr1uD48eNYunQpAOCNN95AaGioWQQxGo1o1KgRfv75Z1y4cAEzZ87E+++/j40bN5rPsWzZMowfPx7jxo3D2bNnsXnzZjRr1gwAcPz4cQDAqlWrcOfOHfPPUnTv3h1DhgwxG2CKceDAAXTo0IG37ciRI2jbti2vjCIuLg65ubk4f/68A8+YJWq1GjExMThw4EC55iFso1ar0aFDB+zevdu8zWg0Yvfu3eZsDoIg5IdbWiK24Of6hAhFELEsBm53Fi7r/k3Be7+WdXBywBMVAD9jZcnOq5i9+bzTWRRc7caWyOFod5zPtl/CFzuv2DV2zKpjuJunxZs/nHToHARRlaHuMARBVCg37+bgQWEJDAoFmsS+Lnc4AICnOzTC5tNpSE3cA21cU2g8vOQOyX4+DpHe17w/8MLPZT9/1gwoKRQf26QHMGZL2c9L2gKF9y3HzbY/W0ar1eLjjz/Grl27eOUABw8exDfffINevXohNDQU33zzDUaNGoX09HRs3boVp06dgpub6ePI3d0dc+bMMc8ZERGBI0eOYOPGjRgxYgQAYP78+Xj77bd5pQWsz0K9eib3/4CAALvv5C9YsADt2rXDgQMH0LNnT4v9KSkpCAnhP+/p6emiPhLsvvISEhJi4VVCOEd+fj6uXbtm/jkpKQmJiYkIDAxE48aNMWXKFIwePRodO3ZE586dsWTJEhQUFJi7xVQ28fHxiI+Ph8FGS1CCqK5cTs/DmVvZeLpDI7s7r+QVl2VViJmEckUC4W4xfUDtJn4f+MM/+FmBCjiaCVL2d3ssOQvHkrPwYtcmaFbfx6F5AH4Gi81yGAeMUe/laxG/9zoAYNyjTeGtsb4c5Ga3EERNgUQQgiAqlF8SM/Cl7j0MilDh64jWcocDAOjeLAi/ei5AB+YcTu31RfuB8ix2ahrXrl1DYWEh+vXrx9uu0+nQvn1788/PPPMMfv/9d3zyySdYtmwZmjdvzhsfHx+PlStXIjU1FUVFRdDpdIiJiQEAZGZm4vbt2+jbt6/L4o6KisKoUaPw3nvv4dChQxb7i4qK4OHh4bLz2YOnpycKCyUELMIhTpw4gT59+ph/njJlCgBg9OjRWL16NUaOHIm7d+9i5syZSE9PR0xMDLZt22YhclUW48ePx/jx45Gbmwt/f39ZYiCIiiRuyX4AgK+HGwa0aWjXMVx/jRKDEYU6PUoMDPw93c3bWCwMRkUzQexLhnc0E0Qr0ulF5aixSClGnidI2bxavQEFWgMCvcsya0scyAThiStkqErUUkgEIQiiwmAYBr+fSgMAxHWR9kCobFRKBXQNHwZun4PizHqgOokg79+W3qcQpPdOuyY+DgAUgi+Ak886H1Mp+fmmtsNbtmxBaGgob59GozH/v7CwEAkJCVCpVLh69Spv3Pr16zF16lR8/vnn6NatG3x9ffHZZ5/h6FFTe2VPT89yxynGnDlz0KJFC9GuMkFBQXjwgN8hIDg4GMeOHeNtY30lXOElkZWVhcjIyHLPQwC9e/e2mY4+YcIEs68MQRCVw/nbufaLIBx/DZ2eQbcFe5BbXIILcwbAU63iiSBCDxAxEUQqE0SIo61nxbIm7BVchEiJFU/GH8aFO7k4+G4fzn7741RylB2DHaU6JJMQNRHyBCEIosI4e/EiirLS4KVWoV+UPHdVpQjpZer00abwGO6lVyNvELW39MPdw4GxnvaNdYCoqChoNBqkpqaiWbNmvAe33efbb78NpVKJv//+G0uXLsWePXvM+w4dOoRHHnkEb775Jtq3b49mzZrh+vXr5v2+vr4IDw/neTgIcXd3d7iUICwsDBMmTMD7779vcWz79u1x4QLftb9bt244e/YsMjMzzdt27twJPz8/REVFOXRuMc6dO8fLniEIgqiq3M4uwvMr/sXOCxm2B3NQOpBmkc/JBMku1CGnqAQMA6Rkmbyr+Mao/GNFy2FU9i2BikUyO6zBLYcpLwaJTJALd3IBAH+eLjMqdSSjg4H4vFKIiUgEUd0hEYQgiAqjaM9n+FczAZ822AMvddVKPGvSMgaX3VrCTWHEtd2r5A6nRuDr64upU6firbfewpo1a3D9+nWcPHkSX331FdasWQPAlCWycuVK/PDDD+jXrx+mTZuG0aNHmzMtmjdvjhMnTmD79u24cuUKZsyYYWFuOnv2bHz++edYunQprl69aj4HCyuSpKenW2RwWGP69Om4ffs2du3axdseFxeH8+fP8+bq378/oqKi8NJLL+H06dPYvn07PvzwQ4wfP56X9SIkNTUViYmJSE1NhcFgQGJiIhITE81ZNACQnJyMtLQ0xMbG2h07UXOIj49HVFSU2eeGIKo6+6/cxeHr97HheKpDx0mViej0Rvx5+jbu5mnN27jlMOm5xbyxAH8xb9ki13IRb2+JCrcrjT3oXOifwe0OUyIicuQUlZTt51x/cYkBmxLTkF0o3qmMq3tQOQxRW6kSIkh8fDzCw8Ph4eGBLl26WKQYc/ntt9/QsWNHBAQEwNvbGzExMfj+++95Y15++WUoFAreY8CAARV9GQRBcCjRadHi3k6oFAyaPNRF7nBEyW7+FAAgMOlPmSOpOcybNw8zZszAggUL0Lp1awwYMABbtmxBREQE7t69i1dffRWzZ8/Gww8/DMBUhtKgQQO88cYbAIDXX38dTz31FEaOHIkuXbrg/v37ePPNN3nnGD16NJYsWYKvv/4aDz30EIYMGcIrq/n888+xc+dOhIWFOZRNERgYiHfffRfFxfwuO23btsXDDz/M61CjUqnw119/QaVSoVu3bnjxxRcxatQozJ071zwmOTkZCoUC+/btM2+bOXMm2rdvj1mzZiE/Px/t27dH+/btceLECfOYn376Cf3790eTJk3sjp2oOYwfPx4XLlyw2dmIIKoKbCmKo1kTUkLE1/uu4b8/ncLIb46Yt+UXi4sguUX60hgca5FrL46KIK40EeVWuLDXwBVGeCII5/oXbruESesTMWa1+HsIN8NEzGRWCCWCEDUR2W/NbtiwAVOmTMHy5cvRpUsXLFmyBHFxcbh8+TLq169vMT4wMBAffPABWrVqBbVajb/++gtjxoxB/fr1ERcXZx43YMAArFpVdnfX2p05giBcz/kDvyMGebiPALTu/rjc4YgS2esFGC58ghb6K0i7cR6hTR+SO6Rqj0KhwKRJk3idW7gIO6e4u7vzBACNRoNVq1bx3r8BUwcXLq+//jpef12829Djjz+Oxx+3/ZoT84mYPn06pk+fbrF95syZmDZtGsaOHQul0nT/oEmTJti6davk/ElJSQgICEB0dLR52+rVq7F69WrJY3Q6HZYvX44ff/zRZvwEQRBVAXYB7mgpiJQI8udpk/fVjXtlbdq55TDpOWUiCCsEcDNBhKJHeRbxxToZRRBuOQwrNHGe45yiskwPg5GBTm+E2k1pfv5OpWaLzmsrw4QgagOyZ4IsXrwYY8eOxZgxYxAVFYXly5fDy8sLK1euFB3fu3dvPPnkk2jdujUiIyMxadIktGvXDgcPHuSN02g0CA4ONj/q1KlTGZdDEEQp+kTTXfOr9ePg5q62MVoegoLDcMHDlCmQfHCDzNEQVZnBgwdj3LhxSEtLs/uYrVu34v3333fo8yc1NRXvv/8+unfv7kyYBEEQlQ4rOjhaCqKS8ATRcbITfk24hRt381HAESPERBDuYj4zT4sNx1NRVHqMLWNka4hlghTpDNh4/CYyc4st9mkdzBwRg2EYbEpMw+X0XPM2tvtLEed5yC4s4R3H7tO4CUzSBfBb71L7W6J2ImsmiE6nQ0JCAu+um1KpRGxsLI4cOWLlSBMMw2DPnj24fPkyFi5cyNu3b98+1K9fH3Xq1MFjjz2G+fPno27duqLzaLVaaLVldYe5ubmi4wiCsI/iogK0zj0EKIA6nZ+VOxyrZD48Gc/+cwW59ztC+p4+QQCTJ092aPxnn33m8DlYI1mCIIjqgt7IZoI4tqBWWvEEYXn759MW+zO45TDFpZkgHBHkWFIWjiVlwcgAz3VuLGqMai/FIqLGp9svYdWhZDQO9ML+d/rw9rkiE2Tf5buYtD6Rt40VLgq5YpBAhCnQ6eHv5Q4Pd+v3uLnlQiV6ygQhaieyZoLcu3cPBoMBDRrwu0Y0aNDAImWaS05ODnx8fKBWqzF48GB89dVX6Nevn3n/gAEDsHbtWuzevRsLFy7EP//8g4EDB0p2C1iwYAH8/f3ND24XA4IgHOfSwU3wVhQjHUFo8XBvucOxSseeg5CgeAgXMgpxJSNP7nAIgiAIolphKM0msEcA4GYhqCS8SW1llHAX/2LlMCxspoQ9bWClKBLxOWG74KRmFVrsc4UIci4tx2Ib693BzUzhZsQAZQKJp9p6JghPBKFMEKKWIns5jDP4+voiMTERx48fx0cffYQpU6bwjOeeffZZDB06FG3btsWwYcPw119/4fjx47wxXKZPn46cnBzz4+bNatQukyCqICXn/gAAJNfvC4Wyar/N+Hu5o1eLegCAv0rraAmCIOSCusMQ1Q22FMWechiuEaeUJ4gtISEjl5O9LVIOw8KKM+UphxHLBLHW2tcVIoibSPteNtOFWw5TKPAryS0uwZlb2XaUw1jOSxC1DVnLYYKCgqBSqZCRwe8rnpGRgeDgYMnjlEqlOV04JiYGFy9exIIFC9C7d2/R8U2bNkVQUBCuXbuGvn37WuzXaDRknEoQLkKnN+KtnBHoVtIEo7s9KXc4dvFUCzf0vLoKUcfuAf33yR0OQRC1mPHjx2P8+PHIzc2Fv7+/3OEQhE0MRvuNUbkiiD3lMLYo8wSxPIbdVJ5ymCIRY1Rr3XUdNYcVw10kRUYvUg4jZNrPp3H9bgFvW4nBCHeBqGLgGaNSJghRO5H1Fq1arUaHDh2we/du8zaj0Yjdu3ejW7duds9jNBp5nh5Cbt26hfv376Nhw4blipcgCNscun4Pt4o98Y9XHKKi7f87lpPuLRvhedUedNKfws1rZ+UOx4yR0lSJKga9JgmCEGL2BLGjRS43Y0PKGFXvgGphLocRFUFM24Qtcx2hWETUqOhMELEMGb25HEZvsY9FKIAA/Da6LEYHW+QSRE1E9ha5U6ZMwejRo9GxY0d07twZS5YsQUFBAcaMGQMAGDVqFEJDQ83tERcsWICOHTsiMjISWq0WW7duxffff49ly5YBAPLz8zFnzhwMHz4cwcHBuH79Ot555x00a9aM10KXIIiK4e+zdwAAA9oES97lqWr4B9bDWY9otNWeRNrhjQhr1lbWeNRqNZRKJW7fvo169epBrVZDYeVLF0FUNAzDQKfT4e7du1AqlVCrq2bHJ4IgKh92ga61Y0HNXXSXJ0ODJbdYXzqv5WSsmFKeFrlimSDWPo7tEYJsIVYOI2aMag85RSUI8uFnu/O6w1A5DFFLkV0EGTlyJO7evYuZM2ciPT0dMTEx2LZtm9ksNTU1FUqOp0BBQQHefPNN3Lp1C56enmjVqhXWrVuHkSNHAgBUKhXOnDmDNWvWIDs7GyEhIejfvz/mzZtHJS8EUcGU6LQYem4ifFVt0K/VdNsHVCEKIwcCF06iTuoOAPNkjUWpVCIiIgJ37tzB7dvkU0JUHby8vNC4cWPe5zJBELUbPadFLsMwVkV7bqmLo4alXZsG4t8bWbxtuVaMUe2df86f56F2U2L6wNYW+7R6I4xGhndTx1omiM4FmRVuIjeQxFrk2oOwjS5AmSAEAVQBEQQAJkyYgAkTJojuE5qZzp8/H/Pnz5ecy9PTE9u3b3dleARB2Mmlf7ehBxIR5X4Dfk2/kDsch2jaYwRw4SO01F/C3dvJqBcSLms8arUajRs3hl6vl+xsRRCViUqlgpubG2UlEQTBg5tZoNUb4eEubczJXXQ7YljaOSIQjep4AeCLIGXlMCLGqHZkOWTmFmPVoWQAwOS+LeDhrkSxIJujWG+Al7psyWS1HEbESNURDEZGVATRi3SHsYdcW+UwrkjHIYhqSJUQQQiCqBkUnv4VAHA1sDe6uFevdPl6IeG47NYKLfWXcOPARtQb+Y7cIUGhUMDd3R3u7u5yh0IQRCURHx+P+Ph4Ej+JagPXw0NnsCWClI01iCzAxYSRuIca4PMRMfhoy0WLfblFJWAYRrw7jB0iCzf2EqMR3mo3FJfoeGOKS4zw4nylsVbqy3qCfPJUW7z3m+MeY2JGptw4xcphujWti8mxzfH7qTSsP87vcCnmCcLvDkOZIETthPJZCYJwCUaDAZH3/wEAeLYbJm8wTvKgcX8AgNeNv2WOhCCI2sr48eNx4cIFHD9+XO5QCMIuuAtpW54Y3EwQMRFEmIUBAOFB3vDRuPG6prDmoXojg0KdQbwcxo4sB64JqdEoXsojzL6wlgvHiiAhAZ5Qi4gZttAbGevGqCIiiJdahS5N66Jr07oW+7ILdRbbqDsMQZAIQhCEi7h2+iCCkI18xhOtug2WOxynCH1kBG4xQThSGIKcAssvDgRBEARB8OGXw1jPYNLxjFEtRYp8rWX3E02pmMDNkKjrrTaXjWQXlVg1RrUGV24QmwOwFB6sWSKx1692c26JVaI3Wm2RK1YOwz4vYhk4OUWWzyffE4TKYYjaCYkgBEG4hKyTmwAAl306Qa3xkDka5whr1hav+H+Hj0uex+7LmXKHQxAEQRBVHl45jI0WsSVcY1SRoWIiCCsocEUQL7UKYYFeAIDL6bmiZR1GO0QQbsmMMJuEPW+xQHiQau0LlF2/xlkRxGiESkRlYT1PCnXSz4+Hu+Vx4uUw3O4wlAlC1E5IBCEIwiXUu7MXAGBsXr1bUce1aQgA2HE+Q+ZICIIgCKLqIzRGtQY380AsE6TAqghSJj54qt3QJSIQAPDvjSzRsg57MkGk2sX+9d8eCPE33dARiiDWzKG1ZhFE2hfFGiUGBm6imSCmeVlPEG7JDCsOeYpkgmQXiZTDlCMTxBEzW4KoypAIQhBEubl9Pwc3dAEoYDSIfORJucMpF7GtG8ANehRf3QettkjucAiCIAiiSsMVIGyLINY9QfKKRUQQkXIYL7XK7IHx7437ol1O7PEE4SZ/cEt13FQKc3mJsATFii+quTuMRiQrwx70BiPcxTJBSq+FFWTq+2rM+1iRyFNtKYJcy8y32MYwfDNYR7DnOSWI6gCJIARBlJs9V7MxtmQqXmnwMwLrh8odTrloG+qPXR7vYbVyLq4e2yF3OARBEARRpTE4UA6jsyGCiJfDmBb33AwJkxmoKRPkXFoOHoj4eNklgjDimSBAmahg4QliVyYIf4n1a8ItvPF9gqixKZcSg1HUc0RvYLB4x2VsPZsOQCCClD4vYp4g52/nokCrR4nBiAk/nsT3/6YIusNYf46EJUX2ZNcQRHWARBCCIMrN7oum0pFHW1dvAQQwtb67GxANAMg/t1XmaAiCqG3Ex8cjKioKnTp1kjsUgrALvQPGqPpylMNwu614uqvQ0N8TIf4eMDKmxb4Qg5GxWb7BLw3hCzhepSJIgcCHQ0oEYRjGLIIIjVHf/vk0tp1Px/f/JluNp8TAQCHSf6bEYMTSPdfMP9f3K/NekyqH8fd0h8HI4GTqA/x28hb+OnMHM/4455AniDBThEQQoqZAIghBEOWisCAPSdcvATCVktQEVC1NviahmftljoQgiNoGtcglqhtcQ1FHWuQKRZCcwhJ8uu2SxTFixqjeGjcApla0gLQBqK1FOzfTQTjWz8MdAJAr6LDC1UAYCX8NKU8QsTi5SLWsLRRkkDTwsyyHEWaC9GgWBAA4npSFWw/Kynu5z7vORiaI0DOEjFSJmgKJIARBlIvLhzZhn9t/8YPX52jRwEfucFxCs25DUcKoEMbcxq1r5+QOhyAIgiBkp0CrR0JKlmWJhIGbCeJIOQx/37qjKbidU2xxDJsB4sYzRjUt+Bv4S3ej0xsZm+UevO4wgoD8PVkRhC9ccDNBSgziWTBS3WGsdZYRzsdFmCFT31ckE0TgCdK1tFzobFoO7xocyQQR7qeWukRNgUQQgiDKRcnFvwEAqroRVh3TqxN+AXVxRdMGAHDr2CaZoyEIgiAI+Rm18hiGLzuCnxNu8rbzPEEMtj0vWISZILezy7IVuF8nNGItckuzHoL9pEUQg9HIE13Ex3BjFxdBhNkb3M4sUqawUiKI0pqrKqQzQYReKaKZIIJz1iv1Dckt1iOXYzjL80GxkSkjfE6EbYQJorpCIghBEE5jNBjQ9MFBAIB3m8EyR+Na8ho/BgDwSt0tcyQEQRAEIT8JKQ8AAD8cTeVt53mC2CqH0Usboz4oNJmbzn48ChF1vc3bxVrksn4dVkUQxnamA1eHEWaN+EmIIFyBRiwLRq1SSt4UcrMhgkhlrggzbNhSHfZ8AOCm4i/rvNSmkqECrZ6XCcIvh7GVCSKd9UMQ1RkSQQiCcJqk80cRhGwUMhq06DJA7nBcSsOOTwAAWhWdRkFetrzBEARBEEQVQSh08DxBbLbILVtEW4ggBaaFeh1vNS/rQ8wTxLN0gW+tHMZgNNrMdOCVhgiyHFgRJLdY2seDKyJkl4o4fp5ukuOdzQTh0jbUH50iAm2OY31TCnR6npDD7w5jv4cLQMaoRM2BRBCCIJwmM9FUCnPVKwYaDy+Zo3EtjVtE4//cx+Ap3WwcSimUOxyCIAiCqBIIO8BwswMcaZErLIdhM0HqeKl53VVEy2HsyQQxMjbjMUgYmwKAn4dJRBBmghglOsrcyzfFH+SjgRS2PUGsx9vAT4M//9sDdbzU5m3FJeIlSD6sCKI18IQcnhks55ovpefih6MpvP3CeNYcTsadnCIQRHWHRBCCIJzG79Y/AICixr3lDaQCUCiVuNd2LM4xTbH3yj25wyEIgiCIKoEw28PgQIvcEoPtchihCCJWDuNppwjiSHcY4YK/zBiV78fBFQ54IkieFkCZFwcLNwKVzUwQ6/GyHWC480hl33hrTGPztXreNRgkymEGLDmAD34/h02n0yTjWX04Gd0W7LEaI0FUB0gEIQjCKQrystFca+qcEtqxZvmBsPRuWQ8AsPfSXV4bPIIgCIKorVgXQZxrkcswDB4UsuUw7jzBg/W8EMsEqc8xCA0L9OSdy9Qdxn5jVKHfhZQxqlEie+RuvkkEEWaCcIUWpY1MEFvGo2KGq1KZIN6lJUM6vRFZBTrzdm52jJjHx6U7eeb/S2WmXMvMtxonQVR1SAQhCMIpjqXkYnLJePzk9gQaRbaVO5wKoWvTuhjsfgJvFS5F6pXTcodDEEQtID4+HlFRUejUqZPcoRCEKMUlBlxKz8Xr35/A5fQ8lHAW7sLykwVbL+L/9lw1/yzlCVJUYjAfa8oEKWv3ymaCuCnLli3sAp/NjAAss0KMRsZmZgU3UUS44PeTaJGrl8gekcoE4QpDtjJBbJXvaNxUFtukM0HKvEl0vC42ZaKJmOjCfU6lRJCfE27CaGQw/bcz+P7fFKsxE0RVhEQQgiCcYt/1XGw1dsW5h6ZBoayZbyUe7iq84bUPI9324U7CX3KHQxBELWD8+PG4cOECjh8/LncoBCGKVm/E698nYPv5DDy9/DAMIh1SAFPL22/238CiHVfMi3sdrztM2ZxspoJapYSXWgU1NxOkVARRu1mWwwBAVEM/AMDITo15ceqNjE2PDWvtYtlMkDytnifYGCREkLJMkDK/DuEYW8aotsp3PNzLvm81qWvyYhvYJlh0rNpNac6i4cL9HehERCIvNVcEEY/nVEo29l7OxE/HbmLGH+esxlyo0yPxZjZl1BJVCmn7YoIgCCvsv2ryyXi0RT2ZI6lYCsIeBa6dhOfNfwB8KHc4BEEQBCErBiOD1CyTYXhesR6enMwBbpYBd8mbV1yCuj4aniDAXRRnc0phFAoFr8WsRmWaX6wcBgB+HNsFt7OLeT4ibJy2ykv45TDSbWjziksQUGpGKiWC3MsXzwThjrEugdg2RuVmgvz13x5IzSrEQyH+kuO9NCroCvlz8sthTP/nXpM9mSDFeoP5em3x7P/+xZlbOVj0TDSe7tDIrmMIoqKpmbdvCYKoUG6nXMGQB98jRnUDj0TWlTucCqV+zCAAQPPC09AWU5cYgiAIomZhNDJ4a0MiVuy/YfcxXN8LvYQnCFfkyCs2GXPyjFEZBgeu3sXolcdw/nYOAPC6nrCIlcNwRZAALzWiQvwgTLIw2FEOwzcJ5Y9VuynNAg/PWNQo7glyL0+8O4yUD4oYtuLleoL4erhbFUCAsrIhLloDVwQxna9AV3Z9nnaIINoSo83SHZYzt0y/240nbto1niAqAxJBCIJwmJtH/8Db7r/gY6/18OXcKamJRER1wj0EwEuhxdWE3XKHQxAEQRAu5Z8rd/H7qTR8tPWi3cfwRBCe34R495cyEYRfVvLSd8fwz5W7ePfXswCAAC/L7xTi5TCWi3uh34bByIgaf3IxWskEAcTNUW2Xw/BFEJ1evJRGDFuZINwsDXvw0YiIICXcchjT/wu0ZSII93mUEmV0BqOk4CUFlcMQVQkSQQiCcBhN8l4AQE5oT5kjqXgUSiWS/DsDAPLO75A5GoIgCIJwLXlave1BAgI8y8SKYs5imLvA1vNEEJOIoLORFRHobcoE4e4qW5SXLc69RMQAYecVA2PbE4RXDiMiUNgrgpQYjOYWv9bKYWyJILa62Yh1h7EG2yaXC/d3wJYLcUUQAyMu8nDRlhgE89gWOOwYQhCVBnmCEAThECU6LZoVnAIUQFD0ILnDqRQUkY8BJ3cgKOOw3KEQBEEQhEux5w69cPHO9UPnG22Kt1/96fhNXL+bjxKJTBGWAJFyGPN8HH8PrjFqWUx8EURvsC6CfHvgBq5kWG8H6+dpWirlFpeJINwFP5vlkVWgA8MASoVlSQ933vO3c7F4x2UU6sTb2ooZlXLRuDsqgljPBGF/R/nasnikMl14c+j55TAlBiPPs0UMW6VABFGZVIlMkPj4eISHh8PDwwNdunTBsWPHJMf+9ttv6NixIwICAuDt7Y2YmBh8//33vDEMw2DmzJlo2LAhPD09ERsbi6tXr0rMSBCEI1xN2AMfRREewA+R7brLHU6lEN55MADAUKLF/excmaMhCIIgCNdhz9pUuBhmjUyFaEvE26/+efo2Zmw6j0vpZaKD2Pq6rjcrIFgGVde7LMNCLCNCzBNEKkPhUnoe5m+5iI0nbpXFKyJAsCW/ecXimSDsNbJZIAFeaouyHO5z9/upNCzdcw1/nbkjGpftTBDr5TCD2zUEAPQqNa0X8wThClVsbPnFtj1PuAhFEHv8QZzNBFl5MAnTfztL5TSES5FdBNmwYQOmTJmCWbNm4eTJk4iOjkZcXBwyMzNFxwcGBuKDDz7AkSNHcObMGYwZMwZjxozB9u3bzWM+/fRTLF26FMuXL8fRo0fh7e2NuLg4FBcXV9ZlEUSNJefcNgDAdd/OUKocq02trgQFN8Zz/t9jgG4hDqXkyx0OQRAEQfCYvfk8XvruqM1FtBiMiOAgRCtY5D4obWlrbZxYpgfbVQYQzwxoHGhq+yq23q3nq8EPr3XBH+O787rHsKicKIfhIjbWrVTQ4IopYpkSrIAi1pJW+Nw5GoM3J+vFVibIwuHt8MXIaCx9rr3pWJFMEB2ng0+JOROkTAQx2lMOozegiCN46ex4np0VMeb+dQE/HUvFiZQHTh1PEGLILoIsXrwYY8eOxZgxYxAVFYXly5fDy8sLK1euFB3fu3dvPPnkk2jdujUiIyMxadIktGvXDgcPHgRg+gNbsmQJPvzwQzzxxBNo164d1q5di9u3b+OPP/6oxCsjiJpJUHrp31rkYzJHUrm0bdkcAHDgyl2ZIyEIgiAIPqsPJ+PA1Xs4fP1+hcwvvNN/X0IE4ZdI2OjMYmR4XV4AICLIG4BYHoiJ7s2CEBMWILpPKIzY0x2Gi9hYN5XCPJd5Xq5IUFoOw4okwiwQqXkdiYFrQG8rE8RH44Yn2zcye5mIeoIIWuTqDUazqatpG/f6xMWNEgNjNrsVzimFM+UwwpIbgnAVsoogOp0OCQkJiI2NNW9TKpWIjY3FkSNHbB7PMAx2796Ny5cv49FHHwUAJCUlIT09nTenv78/unTpYtecBEFIk/UgCw30aQCAiK6PyxxN5dKzeRAA4OiV22CM9EFMEARBVA24d9gLnDA5daYcRiq7QasX95YQw8gwPINVAAgvFUGcQbw7jP2f13qRz3ZVqfmJQSIThM2AYLexogmX8maj+HqUZXN4uMIThCssGBmMWX0cM/44Z97GFSusGZ5mcYQwe4QeZ746cQ1pbQlABOEIshqj3rt3DwaDAQ0aNOBtb9CgAS5duiR5XE5ODkJDQ6HVaqFSqfD111+jX79+AID09HTzHMI52X1CtFottNoyBTQ3l2r+CUKMIze1mKT9BnFBWYgPbix3OJVKpyZ18D/1F+ipO43Uy9vQpHUHuUMiCIIgCN6i1pHSCxZbXg0FWj0u3Lbvu7FWkGVgDYORsTAzLfMEcRwxT5ASB4woRDNBlJaZIHqD5TUarGaCOCDEiGaClC3XHBUCPDlddLzUKhTqDBbZFQeu3uMdIybyiHGfkz2SfL8A3moV6vt5SI53JhMkp6hMaHGm1IsgpJC9HMYZfH19kZiYiOPHj+Ojjz7ClClTsG/fPqfnW7BgAfz9/c2PsLAw1wVLEDWIw9fvQQ831G/ZWe5QKh0PtRuCvYzwVOhw59RWucMhCKKGEh8fj6ioKHTq1EnuUIhqArfbhz1lCdYQ820YtPQAXlt7wq7jeaUWdmSCCONlS1qc8Y+w6A5jNDqWCSIylm27y70W7mWxwgmbRSL0JQEc+52IZ4Jwy2EcW7pxfTsalAoUfKHK8nnW8wQf6d8DtyRqzKrj6Pzxbhit/M6dsQThZoLY4ztCEPYiqwgSFBQElUqFjIwM3vaMjAwEBwdLHqdUKtGsWTPExMTg7bffxtNPP40FCxYAgPk4R+acPn06cnJyzI+bN2+W57IIosZy5Iap1rhb07oyRyIPhY1MZXeeqf/IHAlBEDWV8ePH48KFCzh+/LjcoRDVhGJOCUq+U+Uw4gt8lpT7hZYbJbBljMrFaHTtwlYpECCKS4zYcT5DYrQl1oxRDUaTYHP0xn1RQ1DrmSD2r/7Fng9+OYxjmSDc8ijWtJUrynCvhcUoYvwqxv18S18Ya5lI9hjwCuF2IUrPKcbpm9kOz0EQYsgqgqjVanTo0AG7d+82bzMajdi9eze6detm9zxGo9FczhIREYHg4GDenLm5uTh69KjknBqNBn5+frwHQRB87t5OxoqcNzDPfSW6hAfKHY4sNGg/EADQvOgMtMX2fykkCIIgiIqiSFe2kOXeObcX7tLUlnBhCy2v84iNchhBJkin8Drm/7NdYhxBLAuDvXljD2KlMyqOMeqcP89j5P/+FZTG8I1Ry+sJIpY1Up5MkHo+ZW2F2dhs+bZwjV/FRBnWzFZMQLGW9eLMS4v7ep72yxk8EX8ICSlZjk9EEAJk9QQBgClTpmD06NHo2LEjOnfujCVLlqCgoABjxowBAIwaNQqhoaHmTI8FCxagY8eOiIyMhFarxdatW/H9999j2bJlAExpdJMnT8b8+fPRvHlzREREYMaMGQgJCcGwYcPkukyCqPakJmxDB+UdMCov+JejZrc6E966E+4hAEGKbFw49Q+iug2UOySCIAiilsPNBHFGBOGqIM74NnDR6o1gGAYKhcJigf1w4wBo3FS4fjcfmXlac3YFAHSOCMTiEdHmsVP6t0SeVo+n2jey+9wiGohDiJXDcFvk/nA01WI/K3AYzZkgliKFIyJIZp7WYpsfzxPEMRHklR4RSL5fiMHtgvHlrqsAbJfncH9v3FIrFl8PNxTqLAUQwCSwZBUwyCkqMXf6YXHmtcXNBGE5dO0+OjSpnTfjCNchuwgycuRI3L17FzNnzkR6ejpiYmKwbds2s7FpamoqlJw3lIKCArz55pu4desWPD090apVK6xbtw4jR440j3nnnXdQUFCAcePGITs7Gz169MC2bdvg4SFt1kMQhHUMN/YDAO7V64JmMsciFwqlEsm+HRCUtxu5F3YBJIIQBEEQMlPMWajmOpUJwi2HKZ8IwjAmwcBdpbDwBJnYtzl6t6yPPZcy8MrqEybPjtIxy154GHU5WQv+nu5YPCLGoXOLlaIAwMTHmmHflbs4cyvH6vFi/hdsiY1BorUJK3CYW+SKhOCIJ8jt7CKLbeUph/HWuOHzUnEpfu91Uzx2GNayFItke1iLQas34uVVx3ElIw9H3+/L+52W1xOExV1VLS0tiSqG7CIIAEyYMAETJkwQ3Sc0PJ0/fz7mz59vdT6FQoG5c+di7ty5rgqRIGo9odkmUzTPFn1kjkRejOE9gbO74Z9OLbcJgiAI+eEuVLOdEUE4i1Nny2HUbkrzYv9BoQ5B3hqLlrNBpQti1vyUK96oHcxwEEPoCcKicVdJ7uMiVg7DzQQRw6JFrkgmiCO+J5l5Wovx5SmH4cKKRLY6CHHLYcRKXqzFUFxiwLXMfOiNDNJzi3kiiHPdYSxfz654rRAEvYoIgrBJeupVhDIZ0DNKRHbsJ3c4shLafgD2G9ri9+L2KNQ5bkBHEARBEK6EK4KU1xPEWUsQ1icCADp/tBtj156wyKwI8DIt5lnvDq6XiWtEEPHtapXSIktEbGyJiDjAeoJIdT0ReoKUp0Wuh7vpOUjP4WeD+Gg45TAOZoJwcVfZKYJwfm9FImUv1tr0ZheVmEUcYQaMy0QQsXQbgnAQEkEIgrDJzZPbAQDX3ZvDx6+OjdE1m5CIVpjuPRf/KxmE48kP5A6HIAiCqOVwMyqcEkG4niBOqiDuKqW5+wgA7L6UycueiG3dAKEBngDKhAKueKN2QYmDQiLbQ+0mJoJYjhVmrgC2M0GEniCixqh6+57TkNLnJy27mLfdz7MsE4QVSpyB9Sux6QlSjkyQzNwyTxMLEcSJRkDZhZYdaCgThHAF9CoiCMI2SSY/kAf1u8gciPwoFAo8EmlqEXz4+j2ZoyEIgiBqO9pyGqNyPUEMTnqCKBWWi2NWOBjwUDC+Hd3RLFKwAgS7wFa7KSUFDFegcVOKdo4RItbKVmX2BLFeDuOKTBBWJBL6gvjyjFHLkQkilSoDoEOTOvjvYybHN6MNY1SNFSEmPbdMwBE+n4wdry2jkcH4H05i8c4rAKgchqg46FVEEIRVGIbB2Xw/3DAGw7tV7fYDYXmkWV3UwwPoLm6TOxSCIAiillPeFrncRa+zxqglBsZicWooXfwLsyNYoYAVQTQVbHQplgkihlgmCJs9IZ0JYtrOGqeKiS32eoKwIkjaA2siSPk9QcTwUpf5pnCvVTwTRFqIyeSIIDoD/1h7koxOpj7AlrN3sHS3qZONmMcNGaMSroBeRQRBWCU1qxBzC55EnOELNOsyVO5wqgTdgxkc9xiPD3PmICfrrtzhEARBELUYblmJTm8U7ehhDe6i15mSBfa8UpkgbkqhCGL6l9VbKvrOvtpNCaU9IohIJogbxxNEbIo/T99Gek6xSzJB2HKY29Y8QcrxXFkTD7zUKvPvycgweFCgw5Yzd0RFNWsxZHBFECc8QbgZNzq9UbTbkZj5LEE4Cr2KCIKwypHr9wEAMWEB8NRUiYZSslO/YRhSlI2gUjC4cWK73OEQBEEQtZhiwWLT0WwQgwOZIFJVJTqD0cK0s0wY4C83hH4cFS2CaNxUoq1rhYhlbKg4niBSmRSzN5+36glib4vcYH8PAMCdHL4nCLc7THmeK+uZIG5mochgZPDy6uMY/+NJpGYVAgCa1PUyj7UugpR5gggNWO3JBOFeX4FWL/FaLl8bZ4IASAQhCMIGVy6dgRv06BYZJHcoVYo7gZ0AANqr++QNhCAIgqjVCDM/yiOC2GqR6yNxM0SnN1qYm7JzuUuUw7BURiaIXeUwNjxBhOJNAz9T+9cHhTpJwQcQ9xoRgxUXhL8Df093fPJUW3z8ZFueIOIoYgINi6daxRN8Tt/M5u3/5Kl2GPdoU+x461Gr5TAZeeX0BOEMySvWiz53znYwIgguJIIQBCEJYzTizRvjkagZh751MuUOp0qhbtYbANDg/jF5AyEIgiBqNcUC80pHy2G4Zqi2MkF8rWSECg0z2TIQW51ZXNEZxhpqlVK0G4wQvQOZIJ7uKswc8pD5Z1a4ENMZ7PUEkUKpAJ7t3BjPd2lcrnmEZUlc8cnLnVMOI6IyhAR44P1BrdGiga9VY1Sr3WHsEEG4xzwQ6QwD8LsZEYSzUG47QRCSpF49gybIhhbuaPlQe7nDqVJEdBwA/AtEGFNwL/0mgoLD5A6JIKota9eudeq4mJgYtGvXzsXREET1Qih62OtBwWIwcEUQ62O9rYgg0pkgMpfDuCsly3i4lIhcPNcThCuCCAUF65kg5RNBXNU5x03wewj0Upu7uXCNUcUSVzw5pU7cchilgv+aydfqzf/X6R03RuU+V1IiiLPmvQTBhUQQgiAkST+9A00AXNNE4SFPb7nDqVLUCQrGdVVTRBpuIDlhO4IGvyZ3SARRbVm1apVTx40ZM4ZEEKLWo9ULRRDHFol6kXIYo5GB3shYLPZ9OJ1KhAtgy0wQcbPQSi+HUSntyh7QG4wWIkZZJoiRF7dKkPLBPm/C5wsovwjiKoSx1fEuE0E81W7m6zOIuONqeCJI2f8b+HlYeJiwCDNgXJUJQiII4QpIBCEIQhL31IMAgLyG3WSOpGpyN6gLIjNuwHD9HwAkghCEs+zdu1fuEKoM8fHxiI+Ph8HgWEkDUXvhtsgFHF90G0XKYZ5adhgp9wuw/50+vLHcLAB3lZJnfin0imAX01LdYVgquhzG3o4qJQbGIjY3jlkot/2tsBWuuRxGpB6mRF81Fu3Crip1vMr8Rbw4niBivjBSmSD1rYgglp4gtmPkvnazC8W9bUgDIVwBeYIQBCGK0WBARP4pAEBA1GMyR1M1UcaMxETdeHxSNEzuUAiixpCamippoJeamlrJ0VQ+48ePx4ULF3D8+HG5QyGqCUJPEL2BwcnUB/h460ULgUQMXovc0r+9xJvZeFBYgpOp2byx3FIWYZmLUMwwt8gVCANydIexZ90sJh6xseqNDK/NrjCbRaodsNS8ciD8PdTxUpv/72lFBFEpFTxzW27GTwNfjeT5LLvD2JEJwiuHERdBKBOEcAWUCUIQhCgpl04gArkoZDRoGtNL7nCqJK3b98CWP4tgeMDg1oNCNKrjZfsggiCsEhERgTt37qB+/fq87ffv30dERARlSBCEgGJBOYzOYMRTXx8GYCpr+XBIlNXjuUaYRToDr7xGaJLJFTCEi2phOYzeXA4jXmJiPq4SusPYVQ5jxRNEmAkiFHLYrBcxA9byGqO6CqFAE8DJBPFWu6Gg1M/DUOp/woohnu4qni+JsBxGCq3ewPMIcbgcpoCMUYmKgzJBCIIQJePMLgDANc82UGukP+RqM74e7mjXyB8AcOT6fZmjIYiaAcMwokaA+fn58PCg9yKCECI0RuW2ej1kx2cTd/H/5NeH0Wn+LvPPwoUr90/TXcVvPSsUM/QS5TCVnwmiBOzIBTEt+oVZEGVta7nXKnxerGWCCLukyIUwtkDvskwQXjkMY+oWw+LhLi1i1beSCfLNPzfQZtZ288/2GKPqyBiVqCQoE4QgCFH+LmiJAyUjEB3VHmQ7KM2ARjp0SdsMzbEDQMdP5A6HIKotU6ZMAWDqhDBjxgx4eZVlVhkMBhw9ehQxMTEyRUcQVRdhOQy3/CIzV9yvgYuw/CG3WC+5jytQuisVUKuUKDKaRBihmKHTi5fDWBijVnSLXDszQQBLHws3ZVk5jDURxGjNE0S0zMY+UcCVCLvDWJTDFJUZo3qoVcgrzeLwcOd7vXBFt3pWRBAhwjLHAq0ea44kI+6hYETW8wEAlOjJE4SoHEgEIQjCAoORwe+3fJFrGIY/unWXO5wqTfc6uWjjvh6ZmYFgjB9DIdIejyAI25w6ZfIgYhgGZ8+ehVpd9gVdrVYjOjoaU6dOlSs8gqiysItSd5UCJQaGt+i+L1FSwEXMCJNFuIurX6hUJq+IotK1qtAYlb2rb2mMWsndYRyYXyhYmNvGGhnetQtLZ6x7glg+vwqFotJX88LnvY53WTmMm1LB8wTxVqtwt3SfMMOnkOMz46nm/86tIXwtfb7jClYeSsKn2y4j+ZPBAPiZIFkSr13KBCFcAYkgBEFYcPFOLnKL9fDRuKFNiJ/c4VRpmnXoC90uN9RXZOHm9bMIax4td0gEUS1hO8SMGTMGX375Jfz86L2HIOyBFUF8NG54UFgi6m1hDWvjhQtOy1IWFQBTxoBwsawtjUvYlURY7VbRIoiYMCGF3komiIHzXBgE48zdYaqwJ4i7IEvFz6NMBDF1xjHtNxpNLXNZhJpDga4sU8iRLB7haykhJctiDFcwypYsh7H7lAQhCd2yJAjCgpTjWzBY+S8ea6yySJ8k+Hh4+eCqxmQ6d/vUdhujCYKwxZIlS6DX6y22Z2VlITc3V4aICKJqw5bD+JYuaksMRt6CV6u3biYsND/lIsyMmNi3ufn/DAN8+nRbAMDU/i0sy2HYTBBhOYxQSFHZn03gDAqFwq7uMAB4QgdQVt5iNDI84UM4jhWShCawgPVMG1t0Cq/j9LFCxAxq24T6wc/DDdFh/pxOOEaecFRi5L8GXuzSBAoFMKRdQ4sOQdYQiili3k/cjjLUHYaoSGh1QxCEBY0ur0K8eime1xyUO5RqQW5wNwCAeyo9XwRRXp599lmsX7/eYvvGjRvx7LPPyhARQVRt2O4wvh6mu/clBgY+mrI7+bezrfuCWMsE0ZYKLB7uSpyfE4d2of7mfQwDPNaqAc7PicOEx5pDAYXoscIyjMouhwEs/SjshZsJwn2ehM8ZK5AIBZ/yEBrgiQ3jurlsPmEmiEqpwKbxPXDsg1h4qd3M12pg+MKNMOslLNAL5+fE4avn2pfrdyeWoMMV3YpKM4mEWglJIIQrIBGEIAge+hIdIgvPAgCC2sbKHE31wD/qMQBAeP4pMMaqkfZKENWVo0ePok+fPhbbe/fujaNHj8oQEUFUbbjlMIBpIcktK7iZVWj1eIOVzy02i8RNqYS3xg1KzsqVFRa8S88rzI5gM0HcBRkIShlEEGdRmT1BjHxhQCiCMGwmiOtEEE+1yuK5Kg8WYpTC5APCGp+WlcMwvGyLEhGRzEvtBoVC4VAmCAD8fOImCkvLacTaCZeIdNLxUfPdGxiGQUZuMX5JuGUzy4kgpKi67zoEQcjC9dMH4aMoQg680fShrnKHUy2IjHkURYwagchF8qUEucMhiGqNVqsVLYcpKSlBUVGRDBERRNVFbzCay2H8PN3N27iLw2uZ+VbnEPHtNMOWJ4gt7oVrY6GYopM4VlgOI/QSqQiczR5QcTJBuFkKFiKIFWPUqoItMUrJ9T/hZr1Y8TRRu1lerzDjhMu0X85gzuYLoucHxP1TvDT8cimjkcHQ/zuIqT+fRvyea5LnIghrkAhCEASPrPO7AQA3vGKgdCPvZHvQeHjhmsdDKGLUSLp8Ru5wCKJa07lzZ/zvf/+z2L58+XJ06NBBhogIoupyJ8dU6qJ2U6J+abtSrZ6fCXL4+j2rc1jPBLEmgoj7YpQdW5pFInOLXMD5RixuXE8QK2VD7LWLZTdUFWyVJblxMkG4WT3WyqXEfD3q+Vhvm7v17B3T+cUyQUREEG9BJoiRATJytQCAvZfvWownCHugFQ5BEDx8bh8GAGjDqDWuIyS0/xhP7buLx/JD8ZjcwRBENWb+/PmIjY3F6dOn0bdvXwDA7t27cfz4cezYsUPm6AiiapFaWuoSVsfTXFZSoOWXCBy5fh86vVGy7MTa4t6aCCI8SugdwWaCCLvDCIUCjXtVzgQxxSb0BBHCCkmu9ARxNcLYhL8HcztgRpgJYqV7kMhzUs/PA7dzpH1oWLNZEQ9ZnjEqi7dGKIKUnbMql1IRVRt65RAEYUanLUZk8XkAQIN25AfiCO2iWqMEbjialGXVaZ8gCOt0794dR44cQVhYGDZu3Ig///wTzZo1w5kzZ9CzZ0+5wyOIKgXr9xEW6GXOqCjQlpWT+Xm4oUBnQELKA8k5rIsgJkFF7K690GzUMhPETmPUSskEce5zucwTxHomiLlFbhUuhxGKUVK/F+G1WrtusV1sRpKtOEQ9QUQEFy81vxyG+6tkXzuZecWYvfk8rmbkWT23KynSGcx+PET1o0qIIPHx8QgPD4eHhwe6dOmCY8eOSY5dsWIFevbsiTp16qBOnTqIjY21GP/yyy9DoVDwHgMGDKjoyyCIas+1M4fhpdAiC35o0qqj3OFUK9qG+sNbrUJ2YQku3smROxyCqNbExMTghx9+wPnz53HixAmsXLkSzZs3t30gQdQy2EyQxoFe5jv9BaXGkwoF0KN5EADgXJr055I93WHs8QTp3iyIf2ypCCL0iBBOVZXv5qskusMIqQ6eIJaZIPz9XBGEezPnuc5hknOGBXpabLMlgrCvB7FSGp2I0amnUASBZSbI2xtPY/XhZAxeWjld+vQGI2IX/4PBSw84LbAR8iL7u86GDRswZcoUzJo1CydPnkR0dDTi4uKQmZkpOn7fvn147rnnsHfvXvOdov79+yMtLY03bsCAAbhz54758dNPP1XG5RBEtWZXbhi6FX+FNaFzoFSpbB9AmHFXKfFO0CHsVE9D7r6v5A6HIGoExcXFyM3N5T0IorbDMAy+O5iEbefucMphvMx32NlMEI2bEv6lZqlFVu5YW7vTzxpVipbDCBZ/sa3rY9XLncqOlcgEMd2gLPtZWO5QlWCFA51ImQaX6uAJIhRohLHyMkFKf7eT+jbH9EGtJeds6O+JX97ohtVjyn7v9WyIIOx5uJoM+xoUywQRdqDhvlzZfWdumUQ+MWPViiC3WI+07CJcv1sgGjNR9ZFdBFm8eDHGjh2LMWPGICoqCsuXL4eXlxdWrlwpOv6HH37Am2++iZiYGLRq1QrffvstjEYjdu/ezRun0WgQHBxsftSpU6cyLocgqjVHrt/HHdRFUNu+codSLWlRR4nmyjR43jokdygEUW0pLCzEhAkTUL9+fXh7e5szP9kHQdR2dlzIwLy/LuCNdSdx84GpY1JYoJf5rnh+qQiiVimhcTPd0LDWStRqOUwJ6+thOxNEoVCgT6v68PNw451TWIYB8MtrfCtBBHH2Zj27YLfVitWcCVKlPUFslMOIlP4MbBtsbqErRcfwQLQJ9Tf/XN/Xw+p4VrjgijCsyCQmNgkzibieIGxnocpOwNFzzISFBsFE9UBWEUSn0yEhIQGxsWXeA0qlErGxsThy5IhdcxQWFqKkpASBgYG87fv27UP9+vXRsmVL/Oc//8H9+/cl59BqtXSniaj1FJcYkJBqqhnu1rSuzNFUT4Lamt7LIgsToS/RyRwNQVRPpk2bhj179mDZsmXQaDT49ttvMWfOHISEhGDt2rVyh0cQsvPziZvm/9/klsOUrgTzS41RNe4qs+koK2aIYY8niFg7U6kyAHaxzd4hFxMGuPNVRiYI46Q1KisMiBl2cinzBJH9/rIkQiFL0hOEY4wq5gUjBrfNsa1yGPY83KnZ15lYJocwE4ThZYKUmqxWcgYOt6GStb8fouoi61/qvXv3YDAY0KBBA972Bg0aID093a453n33XYSEhPCElAEDBmDt2rXYvXs3Fi5ciH/++QcDBw6EwSCu4i5YsAD+/v7mR1iYdO0bQdRUrp7YieWKT/Ca9wFE1vOWO5xqSdM23ZALb/gqinDjrH1CLkEQfP788098/fXXGD58ONzc3NCzZ098+OGH+Pjjj/HDDz/IHR5ByArDMNh1saxkPKvAJLiH1vE0LxYLOJkgHqWZIMXOZoKwJS2ixqjixwgXpGJZJNz5qnI5DLtgt3WzX18dPEHsLIfhtgMWE7/E8HBXwV1lKnMK9reeCWJuxct5TotLpDNBhJlEXL8S9jUv5i9SkXAzQQyUCVItqbpypR188sknWL9+PX7//Xd4eJT9wT377LMYOnQo2rZti2HDhuGvv/7C8ePHsW/fPtF5pk+fjpycHPPj5s2bouMIoiZTcH4HHlMlYoD31Ur/MKkpqNzccN2rHQAg69wumaMhiOpJVlYWmjZtCgDw8/NDVlYWAKBHjx7Yv3+/nKERhOxcv1sgut3DXWm+K272BHFX2pUJYtUY1UqLXKkyAGGzF7Fjudt8qnA5jL3lLdWiO4zKvkwQvZExCxT2ZoK4q5T47OloLHyqHer6qG2OBYASTtYHmwlSIpoJosDaVzqbf+aOUctUDsMVDqkjYPVEVhEkKCgIKpUKGRkZvO0ZGRkIDg62euyiRYvwySefYMeOHWjXrp3VsU2bNkVQUBCuXbsmul+j0cDPz4/3IIjahn/GvwAAY5MeMkdSvSkO7Q4A8LpNmSAE4QxNmzZFUlISAKBVq1bYuHEjAFOGSEBAgIyREYT85BSViG5XKRTmxWW+aCaItAhizdNAW2qoKmqMKnGMcOEsLGcA+GUPPh5VVwSxV9TQO1g+IgfCjAqp7jBGI2POdHBE1BnWPhQjOoXZbHnMzsnN+tBa9QRR4tEW9fBCl8YAgEJdWVYTK4JU9tNubwthouoiqwiiVqvRoUMHnqkpa3LarVs3yeM+/fRTzJs3D9u2bUPHjrbbeN66dQv3799Hw4YNXRI3QdQ0CvNzEKm7BAAIbd9f5miqN/Xb9QMANCs6gxKdVuZoCKL6MWbMGJw+fRoA8N577yE+Ph4eHh546623MG3aNJmjE+fJJ59EnTp18PTTT1vsS0pKQp8+fRAVFYW2bduioED8Tj5B2IPYnXLAVNrAenGwC0q+J4h0OYzeSncLZzJBhCUUYsdyF7teNow35UTM1FUMAysaVGFjVOHvwaIchjVGZRiz54UzmS22Wh6zGUu8TJDSTCWx17ebwPejkPNaFjNZrQxIBKn+yF6EN2XKFIwePRodO3ZE586dsWTJEhQUFGDMmDEAgFGjRiE0NBQLFiwAACxcuBAzZ87Ejz/+iPDwcLN3iI+PD3x8fJCfn485c+Zg+PDhCA4OxvXr1/HOO++gWbNmiIuLk+06CaIqcz1hN9oqDEhHEELCpVuhEbaJiOqE879G4pwhDC2T0hDTsqncIRFEteKtt94y/z82NhaXLl1CQkICmjVrZjPzUy4mTZqEV155BWvWrLHY9/LLL2P+/Pno2bMnsrKyoNFYNw0kqjbfHriBP8/cwdpXOpvbz1YmUiKIQmHZRUNjIxOkuMSA938/iwt3pBsCWBNBpLIrhGOFcQmx13dCDuzN7GB/LVXaE8RWOYyqrByG9bmoCBGEnZPbWtZsjKov60bEZteUCR2msYWlmU5AmQBR2SIIt4SMPEGqJ7J7gowcORKLFi3CzJkzERMTg8TERGzbts1slpqamoo7d+6Yxy9btgw6nQ5PP/00GjZsaH4sWrQIAKBSqXDmzBkMHToULVq0wKuvvooOHTrgwIED9MWDICTIv7wXAHDTvyMUVdjZvDqgVKnwVeQKvKsfh4Np1lvqEQRhmyZNmuCpp55Cu3btUFhYKHc4ovTu3Ru+vr4W28+fPw93d3f07NkTABAYGAg3N9nvPxHlYP6Wizh9MxvfHUyS5fxiIohSYTKGFJad8D1BLD+Pfjiait9Oplk9n05vWQ4zNDoEAPB6r0jRY4TCQWV2TOkczu8W+fqjphsRT3do5NR8UpkdT7YP5f1scKJ8hMvwh52LzxFYQYxFqkUuzxjVCXHB3cbvW8wTxGyMWiqMcEukWBGN9asr4JTDyJWFQZkg1Z8q8Uk8YcIETJgwQXSf0Mw0OTnZ6lyenp7Yvn27iyIjiNpBYOZR038iesobSA2hW2RdbDufjiM37mPCY83lDocgqhV9+/bF2rVrERrKX2QcO3YML774Iq5cueLQfPv378dnn32GhIQE3LlzB7///juGDRvGGxMfH4/PPvsM6enpiI6OxldffYXOnTuLT+gAV69ehY+PDx5//HGkpaXh6aefxvvvv1/ueQn5kcrIqGh0essFF7tQtRBB3JTQlC582YyOe/la1PVWQ6FQ4H6+7ZJNse4wi56JxsvdwxHdKED0GGFmR2VmR6x5pTMuZ+ShdUNfnL+di3ah/gCApx4ORbP6PsjILca47xPsnk8Yu5+HG1a/0hltQvyx80KZp6GzniBT+rVAj+ZBaBPij7/P3bF9QDkQGpYKBQ5Wu+BmOTjzu7OV2VOWCcI3Rn1QoENxqVjn6+GG7MKS0hj4JS9FHBGELcmq7Pt3fGPUyjsvwzDIyNXa7MBD2IZu+RJELSevSItMnRpaxh1hD1PJmCvoFlkXShihTT4BrbZI7nAIolrh4eGBdu3aYcOGDQBMXmGzZ89Gjx49MGjQIIfnKygoQHR0NOLj40X3b9iwAVOmTMGsWbNw8uRJREdHIy4uDpmZZW1IY2Ji0KZNG4vH7du3rZ5br9fjwIED+Prrr3HkyBHs3LkTO3fudPgaiKqHXAaYepEVF7s4FJY7qN2U8CjNBCkuMWDj8ZvoOH8Xvtx9tXS87WUAK4Jw51a7KfFw4zqSWQ/C58beDiuuwFOtQkxYADRuKjzcuI75GhUKBaLDAuClduz+r/Aa1aXzCks+2EWxo9eqUipE56sIfDRuvPMIr03M/6QiS5W45TA37hag/bydZlNfH01ZqZm72RPE9HOhzrIcRoHaUQ6z7J/r6LpgN/4+W7GCWW2gSmSCEAQhH8dTsvGKbjoi67hjd2PKWnAFzev7YI/HOwjHbVw4GYmobgPlDokgqg1btmxBfHw8XnnlFWzatAnJyclISUnBX3/9hf79HTduHjhwIAYOlP4bXLx4McaOHWv2Ilu+fDm2bNmClStX4r333gMAJCYmOnUtoaGh6NixI8LCwgAAgwYNQmJiIvr162cxVqvVQqstuzOfmyvt01Ab0RuMSEh5gOiwAHhUASNNuVqhipbDlK5dhWUIGjeVORNEpzfi3d/OAACW7LqKybEt4G7HNbBlNI6URdhjjMrCijRVFQtBR+JaylrkVt3rUSgUqOutxp2cYgAiZUsiv+OKeJ2zzxX3tfzbKX5Zli+vHIbfAaZQpBymsv8cuabAlVkOc/FOHgDgckYeBrZtCKORwYmUB3goxA/eldBquiZRdf9SCYKoFI5cvw8A6NTMeltqwn4UCgXu+bYEAORc3CNzNARR/Rg/fjwmTpyI9evX48SJE/j555+dEkBsodPpkJCQgNjYWPM2pVKJ2NhYHDlS/jbXnTp1QmZmJh48eACj0Yj9+/ejdWtx8+kFCxbA39/f/GCFE8LE0t1XMfJ//2L8DyflDgWAjCKI1XIYQdaCip8Jwr1hve3cHTwoFG+3y0XLMaq0F2GCibUOK55VQNCyhlKp4LVflfq9mzNBqrAxKgAEepeVxCgEvxaxX1NFZDyx3Yi4IohQDPPlLOjdBB1gCkQyQSrbXJfbUclai2lXU1CaKcN6qKw+nIwR3xzBi98drbQYagokghBELefMtRQAphIOwnUYGvcAAPill38hRRC1iQcPHmD48OFYtmwZvvnmG4wYMQL9+/fH119/7fJz3bt3DwaDwWzGztKgQQNz9zl7iI2NxTPPPIOtW7eiUaNGZgHFzc0NH3/8MR599FG0a9cOzZs3x5AhQ0TnmD59OnJycsyPmzdvOn9hNZBVh5MBALsvZVof6AB387R479czOHMr2+Fj5RJBdKLGqGw5jIgxqsAThOWNdSex8pBtc1f2fI4sMh0ph6nqIgjAFzakrsXsCVKNRBDLLBfLZWGFZIKUigbcNsk6wevT14oxKtcThJ2rsp91Z4xRM3OL8e4vZ3AuLcfp85aJIKbnYP3xVADAqdRsp+esrVDeDEHUYnKyMvFD1vO4qm6EumH/yB1OjSIkph9wfh6aay+iuDAfHl4+codEENWCNm3aICIiAqdOnUJERATGjh2LDRs24M0338SWLVuwZcsWuUO0YNeuXZL7bJXjsGg0GupiZ40KuNn6/u9nsfNCBtYfv4nkTwY7dGyVKocpDUUtEEGEmSDOwN7kdiTDwRFjVE911RdBVEqF2b/CdjlMNRJBBLGKZoI4eT2rxnTCmFXHRfeVlcOU/VHfz9fxxviIlMOwoRRoOcaoMrXINThRDjP1lzPYf+UuNpxw/P2Ghc2CYYUg6s7rPJQJQhC1mBsndsBNYYS3mwH16wbaPoCwm0aRbZGJQKgVelw7SSUxBGEvb7zxBvbv34+IiAjztpEjR+L06dPQ6XRWjnScoKAgqFQqZGRk8LZnZGQgOJhKBKsSFfFd/0pGntPHymWMKu4JIm6Mai0TxFHKlQlirRymOoggnOuRupbqKIIIhQOx17Szl9OnZX2MK21PLEQv4gmSVSAQQTjGqKzwZO4OU8LNBDH9W9l/jgaOQbG9IsjFO+X3eWIFoCInRU2iDBJBCKIWo726DwBwp04neQOpgSiUSqT6PQwAyLu4V+ZoCKL6MGPGDChLFxrFxcXm7Y0aNXJ5ZxW1Wo0OHTpg9+7d5m1GoxG7d+9Gt27dXHouonwwFXDLszzrJvkyQexvkatWqaAp7QaiL6d5Y4VlglSDchju77rae4J4SWeCWGSGKMpKUJxBKjvDYDTCaGR4r0lhmRfXI0SYCcJFLBOkIt4rhHA9QeztDuOKuNhyGFYEoUQQ5yERhCBqMQ3um1IV3SJ7yxtIDcXYpCcAoE7mvzJHQhDVB6PRiHnz5iE0NBQ+Pj64ceMGAJM48t133zk8X35+PhITE80dXpKSkpCYmIjUVFMt9ZQpU7BixQqsWbMGFy9exH/+8x8UFBSYu8VUNvHx8YiKikKnTiROc6mIL/vlWeBVlgiSdK8AQ746gK2lLTHFy2HEjVE17kqXddJxJPOFKwQoFNazSKpCpx9bcL1WpD1BTL+XKp8J4sPNBOHvUygUvG3WMnjsQaoDs97AoESk1TMXNoMJ4Ih7Iq9Bc4tczj5HurWsOZyMYfGHkF3oWJYh1wzVaOf5XKHNCD1BKkPwqamQCEIQtZSszDREGJMBABEdXd91gQBCOwzGFyXDMbNwhPmDiyAI68yfPx+rV6/Gp59+CrW67At7mzZt8O233zo834kTJ9C+fXu0b98egEn0aN++PWbOnAnAVGqzaNEizJw5EzExMUhMTMS2bdsszFIri/Hjx+PChQs4fly8nr66kltcggFL9mPxzityh2KmOmSCmIwUc/FmaVcca54glpkgSnMmSHlx5Hq5Y4Vte4V4VYdyGAcyQaq8CMLJBBETAbnCR3m7/UpngjCiGU1cuK9bVngSe2rZLAzuPkeynmZtPo/Em9n4as81u48RnsNe0aW8XWSMRgYFpV4gZk+Qcs0IbDlzB70+21sus9bqCokgBFFLSUrYYfpX2QSB9UNljqZmEtKkGX7xfRHHDC1wIuWB3OEQRLVg7dq1+N///ocXXngBKlXZAik6OhqXLl1yeL7evXuDYRiLx+rVq81jJkyYgJSUFGi1Whw9ehRdunRxxaUQHDYcu4lL6XlYuvuqU8dXyA3PcqxXK2uxm1vMb2NrrRxGzBNEqVRYGKY6gyPXy1382jquUR0vp2OqLPieINW7O0zDAE+r+7nCR3l9b6yKIDY8ajS8chi+JwgXsXIYsQ5KtnhQ4FgmCK87jL3lMA6dwRKuD4irPEHG/3gSKfcLMWn9KZfMV50gEYQgain6a/sAABl1O8sbSA1GoVCYWw8fuX5f5mgIonqQlpaGZs2aWWw3Go0oKSkROYKoDpT3LihTAQUx1SETRIiwlShQFotYdxgALskGcToTRKJ8JP75h9EvqgEmxTYvd2wVDfd6xEpEGIbbRadqL62iG/njxa6NMaVfC9H9XOHDETNcMaREEL1RuhxGpVRg9uNRouUwYuHozeUwnG02skzEcNQ4mCuC2Kjs4Ywr33sYN6PY1caozghH1Z2q/ZdKEESF8WdhFH4xPApV60Fyh1Kj6dHYE3HKYwg+943coRBEtSAqKgoHDhyw2P7LL7+YS1pqMjXVE0RYquEojmooG46n4oPfz1pdeJTLE6SS2lEIYxQrh2GHuAmeY02p34bGBb4bzmaCqCUEmMHtGmLFqI7w83AX3V+V4GbYiHmCcDMBqnomiEKhwPxhbTGxr7j4xBd8ynctUn/y1sphVozqgJe7R/DLYUqFJbG/V1Zc5YqsYn8jtnC0hbS+AjNBvj1wAwu2XrTYns8RQYpLy2FcpQ2X9/25OuJmewhBEDWNzNxirHvQBj8o2iCxK/mBVCRdQ5QYpl4Cfb4SuTkz4OdPrYgJwhozZ87E6NGjkZaWBqPRiN9++w2XL1/G2rVr8ddff8kdXoUzfvx4jB8/Hrm5ufD395c7HJfhzlnUMAzjsADh6Hf9d389C8DUqjM2StzfxdE1HldQqazFrvAsYne5zeUwgpjkywQp+39NWFzZ8gThLoirencYW9jjf2IvUpkkeqNRshzGW21amnJfs9bKYdiMDO7fhVi2lC2K9Y6JIPxMEAbpOcW4l69Fm1Dp92x7hdz5W0wCyNMdGqF5A1/z9kKd68thWFxRMlfdqH1XTBAEjtwwlWZENfSDv1fVvwtTnQkOa4ZbioZwUxhx48QOucMhiCrPE088gT///BO7du2Ct7c3Zs6ciYsXL+LPP/9Ev3795A6PcBI15w66U6nXTt7xFHpqcFE4WBAjxx1/4bpP7C43G4tQcPDRmBaU3HajzuJI5gu/HKb6LzVseYIYOPUQVT0TxBbc+KXKWezFujGqhAhS+prlZi+xryGx6VgxgitKONMOWlvifDmMwcig64LdGPLVQSTfK5A8xp5OLnrO81IsiClfpBzGVUWCNeHv1FFq3xUTBIG7idvwkCIZ3SLqyB1KrSAtoCMAoOjKPnkDIYhqQs+ePbFz505kZmaisLAQBw8eRP/+/Ky1n376CQUF0l84iaoF90t2sc5xEUToCcIwDNYeScbpm9lWj7O2jrO2736+1qKrl0GGTBDhQlJMQGKHqJQK3jWFBZpMMLn+Cs7ibDmMlCdIdcJWdgT3V1KTRJDyXouUcKY3MpJCKCvc2dsdhi2D4f5tOlUOU45MEK44ejYtByUGI25nF1kcY482w/UmEdrLcN+PikuMZpNvV1AT/k4dhUQQgqiFDEj5FFs07+Nx7/Nyh1IrUEU+CgCod++YzJEQRM3h9ddfR0ZGhtxhEHbCXQ8VlpS/ZfjPCbcwc9N5PBF/yOo4a3ezpUpycopK0GH+LrSdvZ233VhFM0G418hdE4WUdgLRuCITxGlj1Oq/1OB7glheDy8TpJK8YioKbvwVVQ5jMJR5gvh58J0ZfEp/VvPKYVhjVCvlMMZylsM4mAki1SKXATDqu2N45JM9OJGcxTvGHnNorggizFQr0PGFmi93X0VGrtaRsCWR8u6pydS+KyaIWk566lU0YtKhZ5Ro2oFSyyuD8IfjAABN9TeQc58WbQThClx1B4yoHLg1+4U6x+vZhb/uvZcyzf+3dufXmveI1J7L6XkALO/cchc+7GLxXr4WPx1L5aWqVyRihpJSC2928ehRyZkg3Hhc4UciNyol16RT2hNEqSh/RxW5UbrSE0TicD2nHKauj4b3nIplgpSVw4iZ0pb+W85yGEeNUY1SIgjDmEvON564yTvGno8sLScjRSiaCDPTluy66jJvkJogVjpK7btigqjl3DxpurN1w70ZfMmks1IICmmCFGUjKBUMbiTslDscgiCqMDW1Owx3YVLkjAgi+DmJU3ufmlXI28ddlFhbx0npI9ztXLGNZ4xamh3wzT/XMf23s/hFsOBxFY50h+FSz1dj/n9lZ4Ioa1omiM1yGEZyX3WDd63lzGqRej4MRsZsjOquUqCOt9q8jxU/uCVcbEyi5TAiniDOdYdxPhNEKsPDR8P33LOnzTfXm0R4HUIRpLxw39vIGJUgiJpPkqn15P16XWUOpHaRXsfkC5J747jMkRAEUZUZP348Lly4gOPHa9Z7Bdfwz5m7l9wv7FkFOlwqzdYAgOuZ+byx3MWDNfNT7hpPL7FwKtQZzHeJ9TxxxXTwg0KT8Wp2kbQBK2BarI1eeQyT1p+yOg4A9l+5iz6L9uFYUpZF9LbKYVga+nuY/++KBY5DxqiKmiWC2DJGZbOcaoIIwhWwypvVwn1dtmzgi0PvPQbA1B2G9QRxVylRlyOCsKKfWCaIveUwzoggWoc9QYyc/3MzQcrG+ApKfexJUOF6pQizvgq0ru0Iwz1XTfg7dZTad8UEUYthjEaE5SQAAHxa9ZE5mtpFQccJ6KFdggXFw+UOhSAIotLhLlKcKofh/F9ohnr9Lt8gV29vJghHYuAuOLiHtJ+3E9FzdkCnN/IyQdgxYt0pxLhwJxf/XLmLTYm3bY4dtfIYku4V4Nn/HRHxBBEphxG5yGC/MhFEmCnjDCoHjBN5mSA1ohyGmwlieT1sJoCbyL7qhi3BxxG4ooVCAXiUvhaMTJn3hbtKiTpeaotjxYxRrXeHkRYP7MHx7jCWMQD89zahCGJPCSc3DqEwW6BzbSYINyPPrRYao7rZHsLn4sWLWL9+PQ4cOICUlBQUFhaiXr16aN++PeLi4jB8+HBoNBrbExEEUencTr6IUNyFjlEhskNfucOpVUS3bYdbmzKB9Dzcz9eirg+9TxIEUXvgeoI4VQ7DWT9kF+l4+27cFWSCcM0FrRqjlv1fpzfCU60S3Q4AGbnFomIDe9fZ1sIru7AsU6TEYIRKadunw8hY+paIZ4JYHsvNBOFmzTiLYy1yy/6vrgGLK+4CUayLhr4GlcO4skUu93WgVCh4IhGbXaVWKRHobSmCiGWhiHuCiGSCOGGM6mjbbq7owj32QWHZe5PQD8e+7jBl743CmFztO+SMGF2TsFuyPHnyJGJjY9G+fXscPHgQXbp0weTJkzFv3jy8+OKLYBgGH3zwAUJCQrBw4UJota5xqyUIwnXcKvUDuaZuDS8ff5mjqV3U9dGgZQNfAMC/N7JsjCaI2sXSpUtRXFwMAEhNTbXrjlmTJk3g7u5ucxxRNeB5gpSzO0y+IC38ulAEMXIXD9KvJe7LjLvgkHr5iWVwiN2JFiOHUy7jiHGjcOEn1vmCO6ZpPW8AwPAOjczb3optAQB4qWsTu88rxFlj1JqQZm+7RS6bCVKzRJDyijrc16VSyc8mYkUQdzcFXix9XcaEBZj3+3mUvbezGRX2eoLobfwtAsC2c+n4YucVO65CHKluNA8KdKJj7IXbHUYvEFYLXSyCcMsSbWWn1UTszgQZPnw4pk2bhl9++QUBAQGS444cOYIvv/wSn3/+Od5//31XxEgQhIv4qfgRLNF9gOEPhSBK7mBqIc/WT0WjrJVQH4wC2v2f3OEQRJVhypQpePbZZ+Hh4YGIiAjcuXMH9evXt3rMuXPnKik6whVwU7vLeweSXQw0r++Dq5n5uJ1dzNvPzcqwthDhZlVwRRCxBYFCIb6dPZetTJDcYo4I4sBdZ3syQbiL1U3juyM9pxjNS0V3ABjfJxKPtaqPJkFe+P7fFLvPLXUO22Mt/RyqM7Y9QUy/k+reGQbgX195r4f7vJkyQbgiSFk5TLfIutg++VE0quNp3q92U+Lo+31hZBizSaqoJ4hIJojOjnKYN9YlOHg14ucF+CJIFlcEcaYsh5MJIvxbF4q/5YWbkedMCVF1x24R5MqVK3bdcenWrRu6deuGkhLrBlEEQVQuDMPgQFIe7hsfwlsdu8kdTq0kOgh4WJWAlHvUJpcguISEhODXX3/FoEGDwDAMbt26Zc4MEdK4ceNKjq5yiY+PR3x8PAyGmpWqXN7uMFzYLgnB/h64mplv0TVBb0PQeFCgQx1vtWQKvZhwYjAyEtuNkufhnZOTJu9I6r1w3ScWA3et6uvhDl8P/vd1N5USbRv5O9wGlDeHQyJI2f/VtcITxPRvTcgE4bXILeflcJ83hULB+5nNQmBFspbBvhDSgONrA4hngoh58jhTDgOYvidbK5/jndcgIYJw/s5LrGSkGIyMqLDI6w4j+Ft3dXcYrhhtK5OtJmL3O5O9KaeFhYUOjQdMH/jh4eHw8PBAly5dcOzYMcmxK1asQM+ePVGnTh3UqVMHsbGxFuMZhsHMmTPRsGFDeHp6IjY2FlevXrU7HoKoiVzOyMP9Ah083JW8lEOi8ojs1B9GRoEmxlu4d9u5u3EEURP58MMPMXnyZDRt2hQKhQKdOnVCREQE7xEeHo6IiAi5Q61wamx3GM6X7PKKIOwdUbYNbIFOzyuh4t7VFIoTX++7hvbzdmJTYppkJohYtkWJgeEZo7KwooSt1Pf7+c7dIeYuyopLDKILPHsXbuXJynAkK6DGtchV2cgEKX1t1whPEF7WS/l+d9yXpVLBn9tcDuOA0iL2OjcaGTAM43A5jBhaB8QT7t+7VqIcxmDl71yqgw33fUiYMVboamNUjijqTOlOdcepV3ffvn2RlpZmsf3YsWOIiYlxaK4NGzZgypQpmDVrFk6ePIno6GjExcUhMzNTdPy+ffvw3HPPYe/evThy5AjCwsLQv39/Xjyffvopli5diuXLl+Po0aPw9vZGXFyc5F0lgqgNpB9ch5lua/Fsw4wacWemOuIfWB833JoCAJJL/VkIggDGjRuHe/fu4fTp02AYBjt37sTJkyd5j1OnTuHkyZNyh0o4Ca87TDkyEoCyO6LsnWIjU5ZeD/AXGMIv959uuwwAeO/Xszwxgns3VyyrQ280ii4U2Dlslbjczy/zynOkhSd32ddm1nbczrH8LmuvaalKqbDaLccaDmWCcOKpCcao3OwPa54gNUIE4ZXDuHAuhQJKzutPmAliD2LProFhLAxH7SmHEcORTAsjtxyG8/d8L5+bCSIdh5TooJV4HwNcb4xaxBFVnCndqe449fL28PBAu3btsGHDBgCA0WjE7Nmz0aNHDwwaNMihuRYvXoyxY8dizJgxiIqKwvLly+Hl5YWVK1eKjv/hhx/w5ptvIiYmBq1atcK3334Lo9GI3bt3AzBlgSxZsgQffvghnnjiCbRr1w5r167F7du38ccffzhzuQRRIwi4sRmvuG3DAJ/rcodSq7kX1BkAYLyxX+ZICKJq4evrizZt2mDVqlXo3r07oqOjRR9E9aS83WG4sK0igzhdtrgLBL2VTBAWP083i0yQn0/cxJWMPNH6eL2BsWGMaiMThHOH2JH6e66+IbVwcmSx6iax6PTR8CvkI0sNVs3ncKg7TPXKBBncrqHV/Y+1qgcPdyX8PNzQvVmQxX52PWzrORrwULDTMVYW3Jtk5RV1+J4gpn/Z7JKsUrFA+LqzhqgniNEy88MRzx0ujngVSRmj3s0rEzv1BiO2nbuDrh/vxpHr9+2Kke8JIiyHcV2J5PdHkvHGurKbCs5mzzhKTlEJHlu0Dwv+vlgp57OGU+9MW7Zswdy5c/HKK6/g+eefR48ePbBixQr89ddfWLJkid3z6HQ6JCQkIDY2tiwgpRKxsbE4cuSIXXMUFhaipKQEgYGBAICkpCSkp6fz5vT390eXLl0k59RqtcjNzeU9CKImoS/RIbIgEQBQt20/eYOp5Xi06A0ACHlwQt5ACKKKMnr0aGg01EK6psEVCVzlCeKrcYN3aVtb7l1cnZVMEBZ/T3eeCLLmcDKm/XIGw5cdFl0QlBiMkhkigPW7voDgDrFDmSDiC1Fu+01HBAp3kYXtj691wYwhrc0//9/z7fHzG4/wxrg5kNHBjce9imeeBnqr8dWz7a2OebJ9I1yaNxBnZsehc0Sg0+d6vVdT9G5Zz+njKwMP97LWzeVtkcstX2H/zwor6bmmjCa2pM0exMQ+I2MpTjry98XFERGE5wkiUVanNzLYcykT6bnF+PvcHUGMEpkgeulMkAIXlsPM2HSe93NllcP8fOImbtwrwDf/3KiU81nD6Xem8ePHY+LEiVi/fj1OnDiBn3/+Gf3793dojnv37sFgMKBBgwa87Q0aNEB6erpdc7z77rsICQkxix7scY7MuWDBAvj7+5sfYWFhDl0HQVR1bpw9DF9FEXLhjaZtH7F9AFFhNO3QDwZGgUbMHaTfvCZ3OARBEBXC7ewiTFp/Cok3swHwv9CXvxzGdLy3xg3epXeSC3ip3WXnEvPxAEwtOLkZI5sSbwMA8or1EmIHw+sIwd0O2DYW5JbDOJJ6zki0+HV2sSqWCeKmUvLmcFMqLLIAanImCFGGJ+d1VV6jV56hbOnrh50zPccJEUQ0E8TSsNjZTieOiAxS3WG46A2MuUwv+X4hf5/E+4VUi1yGYcxC74Kn2todp72w58rILcbk9aeQkJLl8nMAVasLjVPvTA8ePMDw4cOxbNkyfPPNNxgxYgT69++Pr7/+2tXxWeWTTz7B+vXr8fvvv8PDw8P2ARJMnz4dOTk55sfNmzddGCVByE/W2R0AgOteMVC52Z96SLgev4C6uOQehaPGVjh3NVnucAiCICqEtzeexqbE2xgWfwiAMBOkfHc02cWKl0ZlTqfnpopLtcjllsz4ebpLdmkR+6IumQli9gSR/nJvNDK81pnWukYIkSqz4WeC2D2dqBGlm0ph4d8gXAA7YpLJnasmeILUJrgiSLnLYTgvGfblo1LxM0G4JW22EDNGNRgZCwNSZzNBHMlQM0iUw3DRG43m8paU+wX8fVKZIByBmPv+VFxiNHufPB4dgiUjY+yO1R7Y98n3fzuLPxJvY/iyI8gpKsGTXx/Ctwdcl7VRzuQil+KUCNKmTRtkZGTg1KlTGDt2LNatW4fvvvsOM2bMwODBg+2eJygoCCqVChkZ/HaRGRkZCA62Xje3aNEifPLJJ9ixYwfatWtn3s4e58icGo0Gfn5+vAdB1CS8bx8GAGjDesocCQEAmx9egZG6mdh2v2qnxRIEUfnEx8cjKioKnTp1kjuUcnHtbj7vZ66wUFRiwMU7ubguGGMv7B1RH40bvDSW5TBckYGboZGZW2YqqlSIp4A38NOI1usbjOKeIOwdXWvp5LnFJZLteMXgLj6l5lU7WQ4jJma4KwWZICqFRfmLIwkdvHIYygSpVni4O/e6EkOh4AtrQFkmSF6x6e/VsUwQy23imSDOiSCOGKNKeYLw42DMmR23HhQJ9klkghjEM0G4Aq6Xu8qhbk32wL7nJXHEmq/3XcOp1GzM3+I6/w5u2M7+nlyFU+9Mb7zxBvbv389rVTdy5EicPn0aOp3OypF81Go1OnToYDY1BWA2Oe3WrZvkcZ9++inmzZuHbdu2oWPHjrx9ERERCA4O5s2Zm5uLo0ePWp2TIGoq2uJCNC8+BwBoGONYyRpRMXSLNIkfQqMsgiD4HDp0CFqt1vbAGkRNbZHLFSPSHhRh4JcH0PfzfwAAH225gJe+O2q3oSHbItdb7QZvtWU5DFdk4C5WMjmmhYU6g6io4aNxk+wC42yL3JyiEtFjpOCKIHZlgjiwIBLz9lApFbw5VEqlhViicigTpOz/1I2ueuGhdmEmiBVPEJZ6jmSCiPjjmLrD8P9GnO10UuRAmR73vUAqo8xgNJq7vQj/jh3tDsO2x/VSmwQQeztCscz76wJeXnXMPGeAl7sgVlM8XOErVVDC4wq4v0NHPFgqAqfemWbMmAGlyJtho0aNsHPnTofmmjJlClasWIE1a9bg4sWL+M9//oOCggKMGTMGADBq1ChMnz7dPH7hwoWYMWMGVq5cifDwcKSnpyM9PR35+aa7CQqFApMnT8b8+fOxefNmnD17FqNGjUJISAiGDRvmzOUSRLXmwoXzyIIv7iEAjVtaN/8iKodO4YFwUyqQn30Xt9LF24ETBAEMHDgQaWlpcodBuACucSi3Pr5IZ8CKA0k4cPUeTt/KtmsudkHgzSuH4XiCcM7FXaxkcDJBpNpNMox454YSg3iLXHbxYE3AES6ApBZNLNwFjlQNPd8TxOp0PMQyM9xV/Na5KoWpPIa7zqJMkNqBK8thlFa6w7A4Ug4jFo5RJBPE1t+XFFqRjI7iEgNW7L9hkbXG9fSw5gnC7fbCRTIThGuMyjkH+37FeiA5+rv57mAS9l2+i50XTJUSgV5qfjyl5+JOey/f9TcguL8bRzJvKgK735lSU1MdmtjeLy0jR47EokWLMHPmTMTExCAxMRHbtm0zG5umpqbizp0yR91ly5ZBp9Ph6aefRsOGDc2PRYsWmce88847+O9//4tx48ahU6dOyM/Px7Zt28rlG0IQ1ZW99/zwiPYrfNFsFRTlbfpOuARvjRu+8VuJU5rXcefwT3KHQxBVFkbEiJKonkiJBJcz8sz/F6v5F4O9g8g1Rs3neYKIZ4Jw21fmF4t/ATcwlosqdh5RY1SDeCZIgVaPN75PwKbENIfvVLvxMkHEnzeuuOBI2YLY2slNpeQJL+wCy02QHWIvfE8Q+t5RnfBwpQjC9QQRyQTx0bjBk5N5YgtRTxBG2hNEbzBi0vpTWPdvCm+/1OeKmJixdPdVfLT1ojlrzXxee8phjIyosGKKTao7jEF0DOt55OOkCMJyKd30fit8v2LPxX0v4Xa0chWFnIy9Qhd2u3EGu9+ZOnXqhNdff91qemZOTg5WrFiBNm3a4Ndff7U7iAkTJiAlJQVarRZHjx5Fly5dzPv27duH1atXm39OTk4GwzAWj9mzZ5vHKBQKzJ07F+np6SguLsauXbvQokULu+MhiJrE4ev3ASjQrmUzuUMhOHjVbQSlgoEi+YDcoRAEQbgc4Vd0qbKOi3dyzf93tHWuj8YN3mKeIJzFg0EiEyRXQgQxMoy0MarIdvaOsPD6vtl/A9vOp2PS+kQIL91WLbyKU7IitVjiGZk6sCASW0i6WZTDWC5YHUm/53WHcatCToiETXiZIOX0BFGJZoKUbQvyUQsPsYrYy5xhLI2G2b+ZP8/cxqbE2/jwj3MWx4ghJmacSHkgOpb79y6V7WEwGlEsUWKjNxrBMAx+PJqKw9fvceYSL4cp4JTDAI5lZnG5UZrRIhSl9SLlMBWRCcItgeEK13Jgd5uIixcvYv78+ejXrx88PDzQoUMHhISEwMPDAw8ePMCFCxdw/vx5PPzww/j0008xaNCgioybIAg7KCjS4vTNLAAKPBIZJHc4BAffVn2AtFVonJsAxmikLB2CEOGbb76xaHlPVC4Mw9idocE7TvCzVFnHhdtlIogj6dFKhckXQ8wTRC+SCfLn6dtYfTjZvD1fy/fpYDEaxbMv9AYbmSCCRcXdvDLBRSiQ2BRBOM+31J1klYjppLO4C1rksiKGu1KJYpSmyVM5TK2AK4KU13yTe7yYJ4gjpqiA9OtcKF6wJRdZBeJ/42J/x4D035oYep4IYtsYVWzf6Vs5eP/3swCAN3tHYlJsc54QXMLLBOGXwzj7N3/jrsn4lC1PfKFLY/xwNNX8/sX9O8+TEIrFSL5XgGNJWXjq4VDRNtws3OsrrC7lMLdu3cJnn32GO3fuID4+Hs2bN8e9e/dw9epVAMALL7yAhISE/2/vzuOjqO//gb9m9swdICEQrnAjZ7jFC1QUb7FqUduq1NrahqqltRVrQVt/pYdaWpvWtt96tlarrUc9UIrFEwU5VOQQkPsI4Uog5+7O/P7YzO7MZ2f23kySfT0fjzxMdmdnPlmy42fe836/P1i5ciUDIEQdxLYPXsIq17fw6/y/o1/3XLuHQzpDJp6LVtWJnjiKPds3xH4BURa67rrrkJeXZ/cwslZTawDnPPAWvv/Pj1Pel1UmyEZ9JkgCjQnzPE5IkhS6KDBmgoQvPLSeIC+u3wdfQA3dfW72mV+cqBaZIH7FYolci8ao+gwOsRzGKiCk0V88NlikjOuvgVJdKCK4RK7uZy0TRJeRkuwSuQyCdC76xqjiMsmJMusJ4jBkgiQYBLH4UxKDINrny6rsRfw8Wu0nuBPzYxrKYSyCmv6AErUcZv/x8Ioxz6zeg3MfeAtvbg73ifOZ9M9IphxG/z5sFzJBzhoWbNSvnb+Szf6Zcf8K/PBfn0SUHomMmSD2BkHizgQZP348Dh48iNLSUtxxxx1YvXo1evTokcmxEVGKmrb8D92kkxhQYPdISOTNzcdnnlMwqvVTHFj/BvoPHRv7RURE7ejNzYew43ADdhxuwANfHpfQa8WptFX2gzETJIEgSFsGSLgxqvkdVG1yr12MfGXqAPx2+VbL/Sqqsemhfp9mQZBwY1Tjc/q7zeLuYq2Co78QabR4TwyZGwlcuJhdGIpL5GoXWN1z3TjeGLyb3k1YTSIa9gTpvLxJrjpkxlCyZZIJkmgQxGx1GCAyCKF9vqwCr5blMIH4zz/6fVud2/yKipYo5TBHG8I9N440tAINwjaGIEhwP6FymAQ+8/q3ocWv4ESzL3S+0jJ/tJ+tsv7izQhctfMobjx9oOXz+iCI3avDxB0EKS4uxhdffIHS0lLs3LkTikWjJiLqOEpqPwAAyINn2DsQMlVfNg3Y8ymcu98F8AO7h0NEZKBfTjXeSfCBuib87YNdhuVogfBFw8jehZbZH4k0ytN6geS2/fekRSaIdlztLm9hTvSLecWqMWpAMb2DHGrCKMyL9RdJEZkgMZbI1W9vdZdZf1c8mXIlPYdDMg2CPHTdeKzYUosBPXIxtCz+uyn6CzQukdu56BuVptoTRB9D0f6+9Nkl4jKtsVgNR8zgMMvOUlUVC/79KRRVxcJLR8W1n2jiaYzqj1IO4w+ohiCIGbNyGC3om0iASjw37T7aGOqjov17h5fINd9HQFFNl9c22y4a/TneKsutvcQdBLnyyisxffp09O7dG5IkYdKkSXA4zDv6fvHFF2kbIBEl5/jhgxjk/wKQgIpJF9g9HDJROPIcYM+fUXFiLfuCEBEAoLq6GtXV1QgkcFcyUzy6C9gmXwC57tjTxjl/+gC7jzZGPK5d+A8qzTMEQfQSyQTRLga0/+on1/qLH+0CQAsmFHqj/w6Kqpo2I/Ur5o9rk35x8q8fg9iDwOcPNkVs8SuG1TjEfUZjVmqQLKcsGZugtn0/qrwIo8qLEt4fy2E6r0wtkat9q99noTexIIhVHwwtW0mjlcDpl8c+3ujD06v3AACunNDXdD/6YEZDix95HidUi3oYfxxBEF+0chghE8Tq9ZqTocaowfNXIqVKYt5Cq18Jncu8zuC/d3iJXPP9+gIqnHEs5BPr1KXP/rB7idy4gyB//vOf8aUvfQnbtm3DrbfeiptvvhkFBcyxJ+qovlj9GiZIKnbK/VHRq7/dwyETQ8ZPx0uvnYF3AiPxjQPHMbxPd7uHREQ2q6qqQlVVFerr61FUlPgFaDQrthzC8UYfpg3ugbJCb8zt9X0gTjb74wqCmAVAgHCz0fH9u+HlTw6YbtPoM58Um5VwaGPRymL0Kw3oL0q06wjtgqIgxoWXopqXq/hMGqOquqwRsc+HfiUZJSJAouD6R1Zh88ETeP47p6Fvt1zh+cSCIAn1BzB5zKoxarJkQxCEq8N0JulcItesHEZ/TimKkZUlsrpAr3pqreFn7fOj/7zWN4cDJf/bUmu6Hy1g8eL6fbjt6fX41ZXWZcqGbC2LQEe0cg9fQA2WwEShD4I0hpbIDf77JJIJIp63Wv1K6D3KcQf/PVQ1eJ6y2m9rQEEOYkdBYi1rr2+MeqzRh+fX7YUsSbh0bHnK5VeJijsIAgAXXBC8m7xmzRrcdtttDIIQdWD+rcsBAAdLpqHC3qGQBY83F/+qWIS3Pq/F8C8YBCHS7N+/H++++y4OHToUUX5766232jSqzu/Xr2/BZ/vr8ejcyXEFQfST8BMtfvQ02ebF9fvwr7X78LtrKuGJcqtQu/M4vKwAj944GXMfWx2xjVX/C7OYgMcVnLybNUbVp39rwRftQqUgnkwQi3IYMUND/3O0TJDIJXJVvLM1uCzmrf9Yh39/5/SIY0Xz/fOGYe3u8NKdKZfDyJIhmyTVhpj6MgpmgnQu6QyCxGqMWpiT0GVo3BlPAZNMkPqm8Plh+aYa09dp54jbnl4PAPjhvz7B5Ipuptvqs8KsStb05R5uh2zYLpgJEn0JWv05RFwdJpFSJfHcpC9B1J+zfYpi+R63+hX84NmP0bvIi++fP9zyWDEzQXSB7pr6ZvxxxXYAwKVjy6O/MAMS++tr8+ijj6Z7HESURqqioN/RYD+QnFPOs3k0FM2ZQ0vw1ue1eHvrYXzjzEF2D4fIdo899hi+9a1vwe12o0ePHoYLPEmSGARJgXYBEutunUY/aT/Z7Mfi1zahxafgnsvCNfXaBcP9b2zB5ZV9LPelTeidDglnDO2Jft1zsOdok2Ebqxpxs/IQ7UJd6w1S3+QL9S3xmzRG1TI1PE4ZHqdsmaauWJS9+JTIxqhmZTfhMUf2JdE06y5C1u4+jj1HGw0ruEXLBPnHzadi2uAe+Mbj4SBSOm6gmt21T35f4e/ZE6Rz0fcESeffQSgTxKEPgiTaEyS+8WifRatMkK2HTpq+rsUkmGF1qjQ2RjXfSAtcyBLQt1sOvjjcYHjNkZMJlMO07Ss3idVhIoIgumwM/b93QFEt9/vhjiN4bs1eADAEQf72wS68t+1w6GerlXfMjq0PTLV3FgiQwBK5RNR57Dh0HP/0n4E1ynAMnXy+3cOhKM4cUoKh0l6M2PEEmpsaYr+AqIv7yU9+goULF6Kurg47d+7Ejh07Ql/sOZYa7SIiRqJBiH4SfrShFX966ws89v5OHKhritj2i9oGfLznuOW+tOwGLXjhMumBZJUJYh4ECb6+V5EXTlnCoRMtWPTSZwCMwRuxMarLIZv24dCoarg+Xhx/9CCIuDqMfp/G5+qajD0MDp80byJrRsuAkZItX7HYtX5/8TRAjEZmJkinpe8JkmIMJCKADRj/VhMth4l3PNrHV3+eqxc+c2a0c4QnjsCdWGJiRutx5HE6UF6cY3gu4caorVpj1LZyGJM3wyq4LZ5P9GU6+nOhL6BaBr70AWt9+c/dL2zAaxsOhn6OlQmi7/t0oi0wlWrGUbJ4ZiLqgt7dUY/f+K/GA/1+h9z89NaUU3oNK8vH3z2/wF2OJ7Hto//aPRwi2zU2NuKaa66BzEbBaadd28a6W6fRB0H0d1JbfJFBgromH7bXmt9h9QcUXSaI3PbfyIlvY5TlJEWOttf3LPDi3suDmSl//3B3sE+H7uIhFARp+13cThlel/XflqKaL4XrN8kE0ff9CIg9QfSZIML7LTZy1O9XtSjH0WgXaGYrb6TC0Bg1DeU1GvYE6Vz0n41YZVmxOEzKYfSlVqk2RrVaflk7X+jPcyeaYzfh1C7utZKTaOJpXqyVnXhcMnoXGcsPfQEFxxqjB0H077+WNaEFjswCB1andfF8rz/P6pdEDijWQRB9oPZIQ4thNS7jGKzfF0VRDaU42r9JquebZHGGQdQFvf15MDXtzKGlNo+EYpFkGbuKpgAATmx8w+bRENnvpptuwrPPPmv3MLokbYIrNuq04vPr08nNV1/R1DX50Oo3368vEA5MhDJBTC5gGi0m1iYxELh0FwGXtNWTB5RgACHaErmxMkECFqvD+EyWyNUHZ8TsEf0+xLdLvPiJ1ltEpNXw6y+C0nENob+mSmdjVKsLVeqYvLoeEYksGWvGrMRKf+4oSnCJXPHP0ipjyWzFJn0Q10qLP3iBrs+Gser3YRaYteJxyhhUmm947Fhjq2UZTfjY4ee17DEtcGT2sbIKbovn66bWcJmO0yGH3ld/wLonyMG65tD30xa/ifE/fcNQ1qeJdv5q9hu31/5N7LrfkVRPECLquHytLfBufw35GIEzh5bYPRyKgzTkHGDNUvQ89L7dQyGy3eLFi3HJJZdg6dKlGDNmDFwu40T5wQcftGlknZ92cRpnDMRQI69PJzeb6NY1+SwvDFoNmSBab4DImW+DxWoKppkgupmzPn29xa8YLi78QhDE45QNF3pj+xZhzuR+GFKajzl//gCKasyA0WgBFuO4rIMX+p/FoJNYDqPfNtbKMF6zcpg0REH010/OVK9KdPtiT5DORR/Aao1xkR6L/s9S+5PSl7zlx7HalHF/xsCfVbDObxIEET9zZrRzhH6/NfXNptsmEAOBx+nAV07tj3yPA//ddAhvfV6LmvroTVEBIROkLWAQzgSJ/FwFVNX0wl48/2glKaGsPFkOnaOtMkF2HTWWa/sCKraZ9FaJlmUorpZjdyYIgyBEXczWtf/D7+X7Uevthh69rrR7OBSHgVMuBtb8EIMDX+BwzV6UlJmvYU+UDRYvXozXX38dw4cHm6+Z1ZVTcrS5fTz17ADg80cPgqhCurnVBXxwSUaxJ4hJOYxVY1ST8erLLAxBEF/AEMTQLgB8FuUweW4nvjJ1QOhOp2pRDuMLRG+M6guoocas4pjF90Ush/ErKppaA8hxO2IGQbRMEMPKG2muqU81BqJ/n9gTpPNKZyaI9rnQl1Ek+ncrloBZBUFCq8PoPoOxSk+AcNbHCV3WiFWwIpFMEK9LRqHXha9Nq8CGffUAgENtwRWvS0azUF5Y2a8Y6/ccD52zFEUNnX+1ZrJmgYN4mrgC4fOsdg52OiS0BoLZa1ZBjN1HIpc+N+tpEu301dRqlQnCIAgRpUH9htcBALsLxqOUk49OoUdZX2xzDMaQwHbsXPUKSi79lt1DIrLNAw88gEceeQQ33nij3UPpchJdHUYfTKgzCYKIqeLNFpkcvoCiK4eJ0hPE4vVmQQnxAsvtlNHqV9CiC7gAwQCDosviEMthtHFou1PU4EowItPGqMLvr6jhvivG1SOM2x0XLsju/Ncn2F/XjGXfOws9C6IvXaw1RtVfNyQSG7T6l9c/nmomiD4AxCBI52VVChIvs54gVitAxUMWsp/EQIDLIRmClfrPoBh4NNPqV6Cqalz9Q6KVfciSMRigX4ZWO98cbgsgdMt144Cu1KQk34N7LhuF2dXvhTLaGlr9of1pmSBmH1GrAIYYRNbOs1omiHYu9SmKZRC23uQ9MWuQHe3/LeK/vbYpG6MSUVp0P/guACAw6GybR0KJqO15GgBA3famzSMhspfH48Hpp59u9zC6JO0iIp6mfoB1Y1QtyNDcarxI2l9nnjquzwTRJrz6i2Otb4RVT5BoS+RqtGyQFr9i6E0SUFTDxVwwEyR8UaKNQ7tTraiqaUNIs8aokeUx5sviinfUxQsK7X37w4rtMe8wa7+nI83lMPoLqFQzQRRDJgiztzorX4qZIJIhCBL8vsFiBaj49hf+XpYjMwjE81ui5TAtfgXNPutAgF60c2iO0HNIn6mmnW9a2vppiOVishQ+t2nnX23sbocc/vybBA6shmS1RK722dTGFDA5x0Wz73jk+d7s5dtrT2L6r/+Hx9/fabofNkYlopTVHzmEwb6tAIABky+2eTSUiIKR5wEAyuvWxn2Xlqgruu222/DQQw/ZPYwuKdQYte0U8/62w7j89+9iw7460+3NGvMB4Yv/Rp/xYn7vsciUaQD409tfhFK+tQm3PgiiNUhs9AVMz3+mQRAhw0C729riDwiZIIohCOJySIZyGJeQCaKqsGyMGq3vBxB83f7jTfjq/32Iz/bXhx6P9456cOzRz/9uIWgTHHv8FxHx/P8lnZkgLGHrvMx64yTCkK3V9t8Gi0BnPGJlgmjj1T5DCZfD+BVDKUw00T6nOUKvE4/ufKMFOFr8xvOhxiFLocCIdgxtZZjCHFd4qWGTz5VlJojFErmhrDxd0CWeAJBm37HITBCzMfz4+U+x60gj/rFqD4DIBrcshyGilG1f9QrGSyp2yv1Q0Xew3cOhBAyZNBPfeGMB3vUNw0uHTmJYWYHdQyKyxapVq/Dmm2/i5ZdfxqhRoyIao/773/+2aWTto7q6GtXV1QgEkr9jaiVU8tE20b3u/z4EANz0+Gp8eNfMiO1bDT1Bwhcv2h1iq0Z3on+s2h36Xrsw0mdyFOW4UHuiBaoKNPsU5LiNd1LNJuZWmSDNPsW4MotivKPtjiiH0cpLwvtrMcsECagRaeXiRaJfUfHT/2zEu9sOGx6Pt7dCSxx3obWLIGN/hLh2H5X+V0t1f4ncTaaOK53lMNpfRJPFMtjxMGaCRPYE0f7swpkg4eeilcNopXStfsW07MNMtL/xXLeYCRJ5vtEyQcTzmCxJlpkgRTnhy3azwIFq8c8VEQTRju0wnosTzQTZLTRLBcwzQZqEnid5bidO6IJhbIxKRCnzbV0OADhYchoq7B0KJcibkwffwHPQ/Hkt3v68lkEQylrFxcX40pe+ZPcwbFNVVYWqqirU19ejqKgorfvWLhrEu3VmDe4A40W+/g6pdnEkNrqLh5iCDQCF3vB0tKHVHxEEMVvSV+wpot1tbfEFDBdv+kwQl0OCJEmG1WG0zArDqhgmQQu/okSMw6xHyFGTO87x3lFvDSgIxLkih2H50bTcSU1f9ka0FSKo82hJtRwmzfUGspD9ZJWwFA6ChMcfLQiS63ag1a/gSEMr/vnRHsvtFEUNfdaSL4eJngkiSeHHtPOGVoqoNUUFIoMngPXnTnxcWyJXO44zdLzIFbCi2WXSLNV0+XXh+B6XjBO6frN29QRhEISoi1AVBf2OfgAAyBkReUePOr4zh5bgrc9r8c7Ww/jGmYPsHg6RLR599FG7h9Blma1cEo1VY1StYV8yd3XDPUH0q7s4kOt2oLE1EFxCM9/4GrOJubhEZLgcRjH09AgoaiiooQU8vCbp6fp5eKs/8vcyu0AQfw4oquGCJ7y/+DNBfHGuOpFsOcyoPkXYaXLxUpTjjnsfsZTmR2/uSp3D0J75sTeKwpAJ0vZRGVaWj89rTmJIEvs2lMPIkeUwmtASubqP58koZTg5LgeOI3h++/PbX1huF1BVyIgjCCIEcQ2ZZ3K4dxEQGcyVJSkUnNAy2sKZIOEgiFng0yoIIp6nwuUwZpkg8Qe+Dp2IXDnnWGMr3vjsIGYM7xkq6xFH5RYCP6n2IEoWgyBEXcTOo024oeUunO38FD+aMsvu4VASzhqYjzudT+HUXZvR3PQ2vDl5dg+JiLoQh9ATRCPB/GLC2BjVH/G41Wou0Yh3HwHA5ZSR63aisTWAd7bVomZNM7577lBDw76I/URpjOrTXf34FTU0XlfbNsW54Qv+3sU5AIwXWD6TbAy/YrY6TGRQxCwIEm8mSIs/EHc6erLlMPddPhplBV5cVlmOVz89gPNGlgEAhvTMx10XjUBpgSf+nVk4fUgP3D5zKEb0Kkx5X9T+/jPvDLywfh9uPXdoSvsxu8P/f9dPxqPv78BNZwxMeH/iErlWwVztQt4sKyHH5YgI3oqZG1b8ARXaptEyJiLLYXRB11AmSFtzUiECIEvhALFfCS67HVoe1xsOgpj3BDH+/Nh7O/D+9iMRQdImYXUYbUz+gBJxTjNbwjeavcea8M0n1+C75wzB988PLnMv/jOJzWBZDkNEKXlnay12q2XY0u8U5OanN4Wa2sfQ8hJ0c76HUhzDp6v/izFnXW73kIja3cCBA6Om43/xhfWdOopOm29HXBxYvN3iKivhx7VymMSbHDpNMkHcDil0ofDj5ze0jVXC7TOHRRxb4xDLYUJBkIAh6BBQ1NBdV+0O5FdPHQBVVTGoNB8Xj+0dPJ7ub84sc0O/9KZGXMnFH1AN9f/R9mcmmMWS2XKYbnluLLx0JACgsl+x4blvnpWeXmKSFP63o85nTN8ijOmb+jxSfxpX2/IB+vfIxaJLR6W8P4ds3sAYCAcozIKP3XJdaKozBkG88QZBFAWAw7zkQyeechgt0GqWCaIPEPsC4SCIPhPELMCkb3q852gj7vnPRtPxNQqrw2hZdWYrYOV7XGj2RWZ8xPL8un2hIIiYoRKxIg7LYYgoFf/bfAgAMGN4T5tHQsmSZBk7iqeh9PiraPjsNYBBEMpCt99+u+Fnn8+HdevWYenSpbjjjjvsGVQXEV4dRhUeN9/eqjFiqCdICuUw+hVIXA45IiX6jc9qwkEQkzu+EY1R2y48WnxKRBBEu+DQJt+lBR7Mb5uga/QXWGa/tz+gRIwjMhNEMc0E0YIwsmS9jCVgXEo4FrE/AlFHY1YOkwp9cNwhSYbVq/QUiyCIU5ZMAx5i+YoVLUAQq2+GuD+P7phiGZ+4ypUkGctFfIFws9ZCfWPUGJkgmw7URzyvaWwLXosBabNst0KvE4dPJh4EMQTAmAlCRJnS3HgS1+z4MXo7xuDsoafZPRxKgXP4+cCHr6J37Tt2D4XIFrfddpvp49XV1fjoo4/aeTRdizZxFie6luUwFhkMqZTDaBcy+oaALoccMRHeeuhE6HvTJXIjeoKEy2H0FylmPUHMxMoE8StqRNPSyMwQ1bAcZmh/be+XxxmZiq8njj0aw0oZjIFQB5Tu4Jx+f5IkwWexglY4E8T4WXLIkmnWgdfkMxttv7FK1sRAi1kmiMZtmgkSfswfUE17gphlguiD25sPnoh4XtPkM5bDaPvym/Q9yvcmFyrQ/1uJQXcxW86uxqg2tSIJq66uRkVFBbxeL6ZOnYpVq1ZZbvvZZ5/hyiuvREVFBSRJwpIlSyK2ueeeeyBJkuFrxIgRGfwNiOy35cNXMUtehVtdL2JYL5bCdGZDpl0Gn+rAAGUv9n2xye7hEHUYF154If71r3/ZPYxOTZtsinfmrK5VrHpZ+ELlMMkvd6m/GAhmghgHYejrYXLHN2J1GH05jC6I4dcHQUyyNDT6ibhlOYyYCWLSI8TsAknbnxggKRAuMBLrCcJMEOrY9J/pdKwXpD9FOGTJ0ABZLxAlE8Qs68Ahy6arrVjtN1ZjabfTuD9DTxAxEySiJ4hkeG1rQDHtCWI2XH2wYUuUIIh2bg2t1NU2hu89sx67jxqbJud7kguCRHs3Ixqj2nT+sjUI8swzz2D+/PlYtGgR1q5di3HjxmHWrFk4dOiQ6faNjY0YNGgQfvGLX6BXr16W+x01ahQOHDgQ+nr33Xcz9SsQdQjNn70GANjV4wxIdrVZprQoLO6Bzz3Betm9q16wdzBEHchzzz2H7t272z2MTk2ba4qTeKspqFU5TGh1mBSCIPoghtspmU6EtWV5zVY9EC8etLuvLX4FPiETJNQYNWomSPh7q3IYsReAeBGm7z+i5wtlghiPr7+oAYKlPGYBH7dDRp/iHCxq6+UBCD1BGAShDi4d5TDi6jD6QGlZoQe/vHIMAOueILJFJohDMgY0C7xOfPOsyBX6QpkgMfr2uB2y4fxmXB3GeHwxmCtJwSwXfYnKsbZlt/WZIGZ9s/Tv8eaD1uUw4bEYG6M2mJzP9YHaggQCIvrxxSyHycaeIA8++CBuvvlmzJ07FwDw8MMP45VXXsEjjzyCO++8M2L7yZMnY/LkyQBg+rzG6XRGDZIQdSWqoqDfkWCgz3PKBTaPhtLhRL+zge2fwLtzOYAFdg+HqF2NHz9emECpOHjwIGpra/GHP/zBxpF1fuHVYYQgiMVFtFVDTy1I0JhETxCN2BPE7A7t5zUnMHFAd9MSkYieIFomiC9yidyWODJBojXjBYIXQLGWyPUpClpMVlIIZYIIaeCFOS7sO94U+rlF1xMkz+0IXZQM7pmP1247Uxhv+HuWw1A2EP/m9cHKD++aiaMNrfjRvz4FEOwLYlYOYxYHFS/CP71nFt7dejhiuVwt+BGrb4/LIcEly2hGcLtcd/hyWzyWQ5YgSeFAgRboccoyfIEA/AE1lJ3Rt1tu1ONq5/VmXwA7DjdE3TY4TmM5jJl8TzjwUlLgwYkoSw3r6feoCnlAYjA46xqjtra2Ys2aNViwIDzBl2UZM2fOxMqVK1Pa99atW1FeXg6v14tp06Zh8eLF6N+/f6pDJuqQdm/9BAPUQ2hVnRh26kV2D4fSoNeky1C77VFsbCzCsNZA3E27iLqC2bNnG36WZRmlpaWYMWMGy1tTFGqMahJU2F57EgN75BkmpJblMIHUy2H0AQm3STkMAOw+2oiJA7qbjjeyHEbLBAkYgjeGJXId0Sfb0RqX+swaoyqRmSBmWSTaxVhkJohxGt4aCPcEKc51o6G1CVbEu+JEHVvqqSBSjL95/WP6z73GKZtnnJk9Znau0D7vscphnA7ZsHpV9zy37jkhCCJJhuV+tdiwyyGhyQfUnmzB4ZPBTJCBpXlRj6udu/Yfb4KiBgOpsiRZBi5C5TBRMuT0mSAl+e64gisADFEQ8Zwa2Rg1vl2mm21BkMOHDyMQCKCsrMzweFlZGTZv3pz0fqdOnYrHHnsMw4cPx4EDB3DvvffizDPPxIYNG1BQUGD6mpaWFrS0hDvf1tfHTiEi6igOfPQiBgDYnDMOY7k0bpcwYPgEnOl9FHvrWtDriyM4ewRX/KHssWjRIruH0GVpgQZxUnqyxY9zH3gLXz21P+6bPSb0uHgnNfy4MQgSa9UTM/pMDpdTNr1D6w/deTVZIjdidZjgDo43+Qxp3QFF0fUEiR5QliXJtPQmuJ/Ixqhi6YovoKDFHxkYajHpCSJJQK8ib+RxAloQJJwl0myScaPPnImVxULUFeg/8maBC/05JWASBJEl8yCIWUDFZZI1FuoJEuNk55AkQ6abPggiHl+WJcgSEBCeL8xxob7Zj/W7jwMIlvuI/Tn0GSRAOBNEO196XA7DsrkisTGqGWMQxGO5nUgWsjn1WA6TIRdeeGHo+7Fjx2Lq1KkYMGAA/vnPf+Kmm24yfc3ixYtx7733ttcQidIqf/ebAIDG/ufYPBJKF0mWMX1EGf7+4W78b8shBkEo6yiKgm3btuHQoUNQhLvtZ511lk2j6vy0uabVJP5vH+wWgiDRe4Jo5TCFOS4cb/QlNBansDqM2cVJ+KIjchxWq8PsERr76S+GxJUYRMExWAV+Ihujiu+jfiUa42sjy2H6dcs1pMlrtLvNObo+AmYZN7EuCIk6knT3BIkVzPArikU5jEkmiMljZitJacEFs749xnEaM0m654VLSsQyPkcoMBPcpxbQ7JHnxt5jTfho11EAwKCS/KjHBMLBBm18DlmCqlqfG1yhRtnWv48+E1kfBMn3OHEySmmMsRzGyO2QTUuA2pttQZCSkhI4HA7U1NQYHq+pqUlrP4/i4mIMGzYM27Zts9xmwYIFmD9/fujn+vp69OvXL21jIMqUk82tqGvywy/J6DPlcruHQ2l09vCeeOrDndi98UOol45kw1vKGh988AGuu+467Nq1K2JyJkkSAhbLIlJsjjgmvXpWjVFbQ6vDBCfBBV5nwkEQ/UWC22F+hza8JGXk663KYbT6eYcsBbM3dCUq0XqCAG2p6BZ/Xn5FiQh6+MQeIQHzxqjhniDh4w8uzTPNfrnlb2tD49eYLatrLA0wHzNRR5GOIIj+FBGrHEZRIoO4DqvVYXSPaZ9RsxIR7fNvlS2mH6j+KN1ydZkgwrhloURHO61p2SOrdx4DAAyKUQoTHJ9xnLFWvNHOobVt5TZm9MEgfRCkONcVNQhiILxdctu/g7/tfRTP5e3FttOm2+3GxIkTsXz58tBjiqJg+fLlmDZtWtqOc/LkSWzfvh29e/e23Mbj8aCwsNDwRdQZvLf9KL7Sehcuz3sS/YaMif0C6jROG1SMtz3fw2Mt87F76yd2D4eo3dxyyy2YNGkSNmzYgKNHj+LYsWOhr6NHj9o9vE5Nm2zHqmnXxGyM2pahUOBxmW4XjUvIBDG7qNEm82aNCK0ao2pBkPJib9trdUvkxogWRLsjabb8bUC4yPIrqnljVJPVYYb0zI/IZtHTvz9mQRCZ5TCUZQyZIKarvMTOBDH7yOnPPbltmQ/mPUGsy/OM44ShD0exLggSsTpMWzlM+LXBH7q1BUFqTwTbNQwqjcwEEUcYLocJnm8csiSswiUsz9t2jqmtb7b8XfSvKSkI/x76wI4ZQzmM8JxTWKUn6zJBAGD+/Pm44YYbMGnSJEyZMgVLlixBQ0NDaLWY66+/Hn369MHixYsBBJupbty4MfT9vn37sH79euTn52PIkCEAgB/84Ae49NJLMWDAAOzfvx+LFi2Cw+HAtddea88vSZRBK7YEl5OePGKgzSOhdMv1erAtpz/6NdcG+74Mr7R7SETtYuvWrXjuuedC/1+n9Ak1Ro3zrqxlOYyWCRIqh0l8OmnoCWKxOky0O69OIaCh9dvQNi0vysGeo02GTJBoDQCByMn4+P7FaPYp2HSgHr6AEjEO8WIooCgWjVEjy2EGluRj26GTlmPRX5iZBaP0vwrLYaijE1cISYaxHMbk+baAgqKa9wRxSBblMJI+CBI8l5lngrQ1Ro1xApUg4URzOAhiWM7aZHUYszKfHnnGIMOgkshMEEloCqKdn7T/OmXJECD1OmXDuUQrh6k5Ee6LKdIHjotzwmMqzo0e+NafksTMQzEjJyt7gsyZMwe1tbVYuHAhDh48iMrKSixdujTULHX37t2QdSG7/fv3Y/z48aGf77//ftx///2YPn06VqxYAQDYu3cvrr32Whw5cgSlpaU444wz8MEHH6C0tLRdfzeiTFMVBWs3bQfgZs+ILqqx/znA52va+r6wWSRlh6lTp2Lbtm1ZGwSprq5GdXV1Rsp+tLmm2WorZuJtjJqfaiaIUza9QxuIUoMfmQlibHrapzgnuA9VlwkSoxxGjCX881vTcLShFVN/vjy4RK7YGFUsjwmoaDHJ2mg1aYxa0SMXO49Yr7QQK5Wd5TDUmaSlHMbiez2nLIdWWTIrhzHvJRL+PieUCWLSEyQQX2PUaB9d8XMtS5LhvKN93z3P2IR0QI/oy+MC4fdY3xNE//t6XQ7U64IzWiA52u+jfx+07DrAmN0Si7h7pywZ3gezAHh7sL0x6rx58zBv3jzT57TAhqaioiJmHevTTz+drqERdWhffLYKr7XOxQeeUZhQ8Zbdw6EM6DPlcuDzX2NY86c4UXcUBUXd7R4SUcZ997vfxfe//30cPHgQY8aMgctlvMAeO3asTSNrH1VVVaiqqkJ9fT2KitK74pd2xy1mTXsbn0U5jE+4GPC6Er8KdybQE8Q0E8SiHEbTp1swCKKq4dVZEs0E0U/Wtf4ieqaNUU0yQbQgiL7Z6ZCe+Xh762HLscSqk4/VJJKoq4nn79zRttSKaSaIZRAk/NjUgcF5llk5TLyrw0QbpnjB75BhWhqizwSRpPD5LBrtPKmNT/x99U1OgfA55twRPbF88yHTfepXyelV5MVTN0+F2yHjuTV7o45FH6QVs4AcsnFJdLPSpvZgexCEiJJzaO1LGCypyM0pgNekwzx1fv2GjMFeqTf64gA+++A/GD/rBruHRJRxV155JQDg61//eugxSZKgqiobo6ZIm5haVLlEsGyM2va41ltEzMIw87trx2Nc33BQJ76eIMHjmNXgRzZGNQY4yovDFw1axoq4jUg/BEdbKrm+7EZc/la8yPrV0s043NZk8NJx5Xj781rUNflCQRivy4H7rx4HVVXRs9AbNdsjWr+Q4PjC37MnCHV0aUgEgWRRAqY/d2jfBzNB4lwdRpKw9PYz8fLHB3DLjMEAzJfIFXuCuBySabZctM+jeHyxMar2sdcvq1tW4DU9x0b2BDGO0yHLhnOMV9iHq+1gD365Ej97ZWPMwEaex4nTBpcAAF76eH/UbQ2rw5hkgjiYCUJEyeq2J7g0bvPAc20eCWXS3tIz0ffQP+HbtBRgEISywI4dO+weQpelXTjHkwmiquZZDUD44j+RTJDLxpUbftbfabVaItcf5c6rQ1wi12Wc4JsFQWJlgugn5trFg36czULTU3Fc++vCDQYXXDgCJ5p9WLGlNvR+yZKEqyb2DW0T7Q5orDp544oSDIJQ12dsBhx+3GkSBBEDltpzVpkgI3oVYkSv8MIYZk2UxUwQt0OGzyQorz9Godd4qS0Gb4NL5Ea+tpsuCNKve+wsECAyE0QMNojnaW0sRbkuXDuln2kQRJ8NmKs7x8ZsMq17WvzfjRiMysqeIESUnMMHd2OYbzMgAYNOv8ru4VAG5Y+9FPjvPzH0+LsI+P1wOHnapq5twIABcW138cUX4//+7/+irv5GRuHGqLGDIAFFtazj1y7qtdrzWJkg+gt/jT7TIdbqMGZBkJjlMLr6da2Ba+yeIJFBEP249BdWn+6rw0NvbrPcl9sZvgurBZPE64aomSAOCR6nbLrkrjhWm64hiOKWjp4g+r9z/SK0+gty7TOlBT6Nr5dM++eYBUZMe4II5yOXUwZMjqPfXWGOsZxTPJaWcRZ+bWQ5TL9usfuBAOEGpH5dOYw+iOsVAsX639HtMD+H67PdnEIfp2gky64tbcGZGCv9tAe2UiLqhL549znIkoqtzqHo2Ycrw3Rlw6fMwl9xOb7VchvW7D5u93CIOoy3334bTU1Ndg+jU9EHQWL1WNOneYvXCD6/8WLAI9xh/MH5wwAAN50xEKvuOhe/viqyj4tx6UbJ9EI+oKjYsK8O9/5nY9TXA8YgiNsho6/uwqExzkwQ/Ri0Cb9LF6zRZ4L8+vUtUfflcYYDO1pPELMLICtOWcJ1U/sDAKYMjOwHpf/1WQ5D2cDw+ZGASQO6AQCumhQOsmqfKTFrC4jMjDDdr7AfvXB5XvQlt/UvLfAagyBimZsjYonc4H+754eDIKWFxiapGnHYWqzYOhNE6Aki68/Bkb/LjOGlltmAsTJB9IH2iNVhHGI5TNRdZQxvKRJ1Qp7tSwEAh/vOxFCbx0KZ5XJ7sOGU+Vi1bh+WbTqEKYNK7B4SEXVS2mQ/oJj32dDTT369Tkcom0L/nNYTRKw1rzp7CC4a0xsVPfIs7/K5hZ4gZhciAUXFD5792PT14sWEPhtlaFm+ISjSHGcmiGySCaJfdtMsxd5KMBMkeLxQOYzJ8ph6P77oFPy/Vze1PSfjRxeMwJSK7jhtSOR5X78vu9LJiez01xsm473th3GOboXEUBDE5LMq9t8Ivya+44UaNbedGq3OJxIkDOiRi11HGjG70lgGKLb6CZbDRDZGLfCEL9HzLfr+BbMtdEvkCpkqwUyQ8AEjy2F0gWOn/nwsYdn3pqNPtxy8v/2I6bFjnUv1K2mJ/6dxypLhfWAmCBHFpeHEcYxoXAsA6DXlSptHQ+3hvJHBZcOXbayJefeWiMiKNudV1cjlXkX6NGhxwqtlNpj1BNHSuweV5ked3DrjaIzqV1QcaWg1f71YDqMbw8jehZB0tfbxlsNYNVvU7qCebPFHvMaKW/c7aVk14q/oEHoHfHlyv9DPqqrC63LgwjG9UZQTuQQxy2GoMxFXCEmGLPzNF+W6cNGY3oYMh1AQxKRMxSFZZILE+QEKLdkdIxNkVJ9CPHvLNFRfNwE3nWHM1haDtxGNUdu+1X+++8exPC6gb4yqld8Zl6LNiSiHMc8EccgSKkry4HLIOGtoCX52+Sg8d8s0w2tjNZn2KeH/f4jll7IkGd4HNkYlori8t/0o3vB/HWfl7MClIybaPRxqB2cNK8WZzk2YWfcBdm3phooRlXYPiYg6ofDqMKphkmpGC3S4TQIUGw/U4+uPrUaLL3LVlXizEvSTc5dDNr0QCSgqKvsVY9nGmsjXRymHOaV3YdsxZLQGlFB/AHeMvGv9XFz/e5QX52DboZOmK0GY8Tjl4MoyYuZHlHIYp0M23P2NFXAxa6ZI1GFlsCeIXqgniC8yCOJ0SKYX3PFehPuFpcHFoOovvjQGhTmu0AoqF4+N7Fclxk2CQePwz/rgx2/mjMOaXcdwyVhjNokV1WSJXH0D6YglcnXP6QM6+vdDkiR8bVpFxLFilRYaMkFMVocRV+KyAzNBiDqZpVvq8VxgOj6uvBdSjCX0qGvI9zjxg/yluMG5DAc+/KfdwyGiTkqbbCoqLDNBvv7Yavxv86FQJojLYZ5C/ubmQ2jQlp7V3WGM1uxTz9iUz2p1GAXFJlkQweMY//+nvxs8oncBgHDqebyZIFYrFvTrFt/qDBrtOGbLYVodT5Ykw/ONJneyDa/tAI0FidqT1eowetF6gsiSZNo/J96LcLFRs5gNMaJ3IS4aE71Rt7iqVWQ5TPi5K8b3xX2zx1iPz6IniF/XE8SQ7eGQjavqWGSCxKiUjNjejD9gnQniEALrLIchopj8AQVvbjkEIFwiQdmhefAFAIDue/5r80iIqLPS5pqKqhomqXpvbj6EuY+tDgdBnHLMmnmxHCYehiVynZJpc7yAEu47IhKPo0/11pa61AIlJ5p9wXHGWMXGqhymX/fIdPRowZ5QY0LhlxIDPfrJv7i/hpiZICyHoc4jHYW8xowJ8220z3yzSSZIMDMi8jVWmVTi56r2ZAu21pwI9URyO2X00S3FHU8AWMw6kWXzJXKTIS6R65Ajgw0uQxli+Dl9QMfqnKsXqzFqqy7ILmbQOYUMFbvKYRgEIepENq55B1e1vIDROUdCXbEpO2hLIQ/3b8Hh/btsHg1Rek2YMAHHjh0DAPz0pz9FY2NjzNfcdddd6N49ctUMsqZfHcYXqzFq2wowVlkaevrgQqw0abPt3JblMIphedxeheFlb11CgCHP48SvrhqL38wZh+5ty0tqFwBH2/qKmPXW0LMqh4l3iUqNdgEmBmrEn/UXTeJzsTJBpDRdOBF1FvGsgqSdR8zKYRwWq8NYBW7Fz9WvX9+C837zNuY9tS70uhG9CmLux3As4bzlkISAZgoRTUVYItcpBD0ckiQsJ2xeDqPEkQoSa4lcv67cUgy4i8EolsMQUUyNH/0dd7v+jkWFLxuaylHXV1pegc+dwWUnt7/3nM2jIUqvTZs2oaGhAQBw77334uTJkzFfs2DBAhQXF2d4ZF1LeHUY60wQTbgcJnYQxJNEJog+S8LlkE3vBvoVNRQEWXTpSIzpWxT1OF+e1A9XjA8vl6kFGbQ5fWGMIIghE0T3fb/u0cth7ps92nAxpB1PLNkRf0X9McSskYbW6JkgYikNUUeW7qbusXqCmGaCSFarw5jvK9bHyiFLGJ5gECSiT5BQopLIZ1ncUnuLtSBGxFK0DmN5jP57ffAlHZkg+nJLMeDulI29Wew6f7ExKlEnoSoKBhx6EwDgHHmxzaMhOxzpdx6w43PkbH8VwPftHg5R2lRWVmLu3Lk444wzoKoq7r//fuTn55tuu3DhwnYeXdehTYhVNTJFWdTiD6d8B2LcGdQvTxtvTxB9gCDaErn6Jn/6uXk8GSfiXdVYmSBWzfr6RskE+dVVY/HlSf3w1VMHoOLOVwzPRWSCRGmMKm7LchjqStK9rl2sniAPvbnN9DnT1WEsdhbMPLEeuUOWMaKtCbP+2NGIxxJXrEnksywOu8UfwI+e+wTbak+G9q0PdDgkyXJZXL144lUxV4cJxMoE0Z/7Yh8vExgEIeoktq5/B8NQi0bVgxFnfMnu4ZAN+p42B9hRjVOa1qHuSA2KerAvDHUNjz32GBYtWoSXX34ZkiThtddeg9MZOUWRJIlBkBRo886AohrSlc1o6eQ5LodparleMj1B9MESWTZPA/dHBEHCs/Nk7romlAkSoydIPGL1BDFcCLQ9d97IMizbWIPrTVZk0DPcPWYUhDqoPsU52He8CReOjt4wNFFWpTHRgrAO2SoTxHz7WB8rp1gOE0dGQ0QmiCwGNJP/LP/9w914Z+thw7HEQGvtiZbQz+P7JV9WH6sxqhYEURQ1otGq06RXiR0YBCHqJI6sDq4KsrngVEzIK4ixNXVF/YaOww65Ak5/A7asW4uZMy+0e0hEaTF8+HA8/fTTAABZlrF8+XL07NnT5lF1PdpkM9gYNfrtvqa2cowctwMt/uhBkGQyQQxNDmHesDAQ0AVBJMlwTzauJoS6bSQJhiVozegvQPT7j5VBYkUcY7TVYUJ3sK8dj0/31WFC/+gXKCyHoc7gtdvPxPZDJ1HZrzit+7X6ixc/Y+P6FuHjvXUAksgEsTxK+HUDS/JCP4tBz3jGJ65Yk8pHuaa+2fCzQ5YMGXf633NyRTd0a+udlIxYmXiKGgyAtJqUXYrBKLsaozIIQtQJqIqC/geXBb8feYXNoyE7/Xfyn/H/3qrF2Xt6YKbdgyHKACVGhgIlT98Y1R+jxEXL/sh1O1DfFH2SmkwmSFGOC+eNLIOiqCjJd5tOhAOqGqpPl2XJsNRiPE0S9UGIQq8r5h1HfQsPcdtH507GjtoGPLtmLzYdqI95bCByOUzx8Pr3SruA8rocmFwRu+Evy2GoMyj0ujA+RkAvnfSf+ZmnlBnOGbJkHgSxEk8miMsh489fm4hDJ1qils2ZjQ/QAgL6YybSE8S4bUTGhdADxClLmH/eMPx3Uw2qr5sQ93HMxMoEAYC3Pq/FTY+vjnjcLEPFDgyCEHUC2z9diSFqDZpUN045i6Uw2ezsiSPx/956G+9uO4y6Jl/SdyiJKPs4QkGQyDptUVNr8HmvyxFzkupJYnUYSZLwl+snhX42Xx0mnAnilKWISX4sOe7wNDeec6VVJggAnD28J84eDjy3Zq/l610OydBrxeyCx+pnMWASe6zm4ybKBrF6ggDBLLYm3SpLTlkyfZ1VD4xYnyttpZfzR/WKPliL8Wk/pyugKa7q4hCWopVlCVVnD8Gt5w5N/iBtYjVGBYC5j0UGQMLjsj+TjUEQok5g86er0Vd1YVP+qZiQXxT7BdRlDelZgGFl+dhRcxzvrduAi04bb/eQiFI2cODAuO7si26//XbceuutGRhR16S9xQFFjdkYtbGtHCbX7UhodZhkJ7Rmr4vWEyQe5UXeUNZGPEEQSUptYu51OuALhBuaihc8Zk0Rw98ndiz9WO26k0pkF6u/eH3gMcclo0XXz0gWViXRqBbNT2OuDpPEOcLsnJCugKaiiquwyMbGqGk8T8STCWIlsjEqgyBEZEJVVdx/YBx+2PInLLmgwu7hUAcwr/cWTD++CDveHQecttTu4RCl7LHHHkvqdRUVFWkdR1enTTaD5TDRM0GadY1Ro01SJcl4VzDZObzZMQKKYgiCiJP8WHoXe0PfF+bEnvJarQ4TrykDu2P55kOhlRMieoKIQRBDqnpiFxX6CzAmglC2sQoW6DMfclwOnJD1QcnEPtexAvPx9j8yjM+kObKxJ0gi4zP+LGbKieU/6ey9EU8miBVxiVwGQYjI1KYDJ7DzSCM8zlycNmGc3cOhDmDsuAko2tyIkQ2rcaLuKAqKYtePE3Vk06dPt3sIWcHQEyRmJkhbEMTtiJqiLdZ3pzo2Pb/YGDXBcpjy4pzQ94mWwyTzO/3yqrH4/ZvbcO2U/qb7EK8bUrkQMPQvYRSEsox1OUz4e6/LYSizc8rmS3Fbl8NEH0My5wi5rSRHO2ZkT5D49yVuKi5lHuwJkni/pnikMxPErvOXTSvzElG8/rtuKwBg+rBS5MfobE/ZYcDwCdgl94Vb8mPLW/+0ezhEWe+KK65At27dcNVVVxke37JlCyorK0NfOTk5eOGFF+wZJHSrwyjhJQyt6JfI1V9I9NEFFoDghDbePiDRmK4Oo4QboyaTCdInwSBIqncnS/I9uOeyURjetmymeKdYvMurfz6elSWs9sVyGMo+5n/z+owqr8sh9NtItDFqjJ4gSX7unEJ2RrqWyBXLBTNZdpJKEMTpEMeVjhEljkEQog5MVRTM/uhreM39I1xTcdLu4VAHIckyDpTPAgA4Nr9o82iI6LbbbsMTTzwR8fjw4cOxfv16rF+/Hu+++y7y8vJw3nnn2TDCIG3eGYhjdZjGlvDqMPrgwGmDe2DmKeHli52ybJjUJ5qtER6bSTmMKvYESWyf+kyQwrh6goS/TybVXeQQZvdiOrqcwgWKw3DhlMTgiLogsTGqPrZoVQ5jdVqJ2RMkyQ+emHGWtsao4uowsmQ4j8VaHSsRqWWCyMK5z55wBIMgRB3Y9k/fR391HwZKBzF53Fi7h0MdSNlp1wIARjWsQt3RWptHQ5TdZsyYgYKCgqjbvPTSSzj33HORl5fXTqOKpF04q6oaMxPkRIsPQGRKuXg3VZbSc4fRNAgS0Rg1sX0agiDexMph0pGiHdETRLZ+PtF6ff34kmkqTNSZWf3J6z9TXqcsBBzMy2Gsj5H+niDi67TymHiPqSduK2bKOYQgSDoCuxpXop2cdSJ6gth0+mIQhKgDO/z+3wAAGwtOY98HMhg4cjJ2yBXBkpg3n7R7OEQd1ttvv41LL70U5eXlkCTJtByluroaFRUV8Hq9mDp1KlatWpX2cfzzn//EnDlz0r7fRGiT5oASuydIXVMwCJIjZILIsjHl3OmQDZPxJBNBTAMphp4gSZTDlBV4Qt+3+KMHfQBjkCLR8hQzsVaHSSUTxNDElUEQyjJWf/GykAli/IyZZ1ok2xMk2cwKWQh+piv4apoJou8J0kEao4rBGbvK+RgEIeqgAn4/BtcEV/6Qxn7Z5tFQR3Sw4jIAQN7nz9s8EqKOq6GhAePGjUN1dbXp88888wzmz5+PRYsWYe3atRg3bhxmzZqFQ4cOhbaprKzE6NGjI772798f1xjq6+vx/vvv46KLLkrL75Ss8OowkU30RPVNuiVyhSaczijLLia6jK3VfgAhE0RKPAiivwBoaPFH2TIo45kgUZbITTToImbnEGUTq795QyaIyyFkHCTWE0SyDLVEHisRxkwQsclxUrsEEHnulWXJkLGRznKYeDJWomXrGM5f2RoESeTuy2effYYrr7wSFRUVkCQJS5YsSXmfRB3VppWvoBTHUIc8jJp+VewXUNYZOON6POSfjdtPfhUH6prsHg5Rh3ThhRfivvvuwxVXXGH6/IMPPoibb74Zc+fOxciRI/Hwww8jNzcXjzzySGib9evXY8OGDRFf5eXlcY3hxRdfxPnnnw+v12u5TUtLC+rr6w1f6abNNRVVhS/GErmhTJAYzQXTlWJtNmH2K4rQGDXx/U4a0A0AcMX4PnGMIb2/l1PsCRKxWkzydfHGcpgkBkfUiVmvDqPLBHEZA7iJlsPEXh0muctocdnaZFelErcMCEGQ4Mpd+tVhEhtnqqxi1o6IcpgsDILEc/dFr7GxEYMGDcIvfvEL9OrVKy37JOqoGtc8DQDY3P1cuD3WE2fKXr36D8U7/W7BVqUvXlof3x1pIgprbW3FmjVrMHPmzNBjsixj5syZWLlyZdqOE08pzOLFi1FUVBT66tevX9qOrwmtDhPHErnhchhnxAoDzgxkIZhNhCN6giSx37/fPBXv/uhsjO5TFMcYwt+n4+5kzEwQw8VQYvs2lMOwMyoRgMhMEGOAwaoxqvmZxSzbwe1IPahgCCI7JMNxEurvI2zaKpT8OWTZkAliVwNSkUOW4MhQhkoibH034rn7ojd58mT8+te/xjXXXAOPx2O6TaL7JOqImpsacMqx/wEACiZfZ/NoqCObXRm8u/kCgyBECTt8+DACgQDKysoMj5eVleHgwYNx72fmzJm4+uqr8eqrr6Jv376GAEpdXR1WrVqFWbNmRd3HggULUFdXF/ras2dPYr9MHLQLgkAcS+TqM0EcQtaBw9ATJE1BELNyGGF1mGSWnvE4HejbLTeubeU0352M7AlifN6ZQiaIJGTnEGUTqz95sSeImG2VyAW32Ucy1+Mw7C8ZDuGzqx9SKvEAse+RU1wiN8Z5ItFjf/30gYm9QBtHtmeCZOLuS3vd0SHKtBWfH8Xtvu/g3/IsjJhyvt3DoQ7sojG9MNO5HlWH78POTWvsHg5RVvrvf/+L2tpaNDY2Yu/evZg2bVrouaKiItTU1MDtdkfdh8fjQWFhoeEr3fSrw8RaIleTKzYXlCTh7qLYEyS5sZmuDhPRGDW5fcfLUA6ThuCOmAkSERRJoaxIXKGHKJtY9evQf47EUj6HbH7BbXXOuvnMQSb71wWAk/zgOYTzZ7p6EYl9noJZe/FnriSaUbbw0pH47TWVCb0GCL6HYnahHWwLgqTr7ks69tkedbhEiXj+kxosVyZiy+R7ITscsV9AWas4142qwndxieMDHHjncbuHQ9SplJSUwOFwoKamxvB4TU2NZdltZ6bNNYOrw8ReLQXQUsp1+0jw7mK8TFeHUVJbHSZRxjuymcgEMf5syARJtDFqmkt3iDoT654g4Utbr0s26WcU/zG+duoAvHLrGbhuav/QY9ECwPHSBybkiNVh4t9PrE2dCZYuntK7MOExiO9BSb4HBV5nzNcYgrjZFgTpSNqjDpcoXnWNPvxvcy2AcKkDUTTK6GDj3IH7X4USCNg8GqLOw+12Y+LEiVi+fHnoMUVRsHz5ckM2R1eh7wnii9ETRJMrpJTLUvTlDa3q62OOzWQeHFDUUOCjPTJB9BcJaWmMKqTLi5P9VMpv0r2SDVFnYtU7I2J1GNn4nNlnxWpFK0mSMKq8CIruxBNtZax4if189D8n1BMk1nFk40pesbLb/vCVCbhifB+8NO+M+I+hG++E/sVY/eNzQ8EUK4mW6WSKbUGQTNx9SXaf7VGHSxSvT177E26TnsKM0oaYJxIiABg1Yw7qkYteqMXG91+2ezhEHcrJkyexfv16rF+/HgCwY8cOrF+/Hrt37wYAzJ8/H3/5y1/w+OOPY9OmTfj2t7+NhoYGzJ0715bxVldXY+TIkZg8eXLa961NWBU1uPJKPCJXh8lMTxDZJLDiV8JlO05ZSnr53fjHYD6eZMXsCZLCBVWyd4+JujL9ZyGyHMY8CBKLvtdGOsphjCUqyZfDxAqYOIVymFj77tstF7+ZUxlXE2mzfTrkYJNXd4x0G4dDXBEn7sOllW1BkEzcfUl2n+1Rh0sUr94bH0GV8yXcUr7V7qFQJ+HNzcemHsHeMc2rWBJDpPfRRx9h/PjxGD9+PIBg0GP8+PFYuHAhAGDOnDm4//77sXDhQlRWVmL9+vVYunRpRGlte6mqqsLGjRuxevXqtO9bm2zGszqMRmwuKEf0BDFOJZONU+jvBmqTaEVXDiNLUtL7jle6M0FcQoBIvOPpSOF46Q7YEHUmVn/xPl3WRo7Qz0gs5QOCn9EvT4peATDvnCFwOSTceFpF1Cy4eMnC+dTwWU7jR9khZIJkoveGWRZLrMB4MBNEvw97zl/Ri3YybP78+bjhhhswadIkTJkyBUuWLDHcfbn++uvRp08fLF68GECw8enGjRtD3+/btw/r169Hfn4+hgwZEtc+iTqybR+/hyGB7WhVnRhx3k12D4c6ke5n3AS8+ALG1L+NuqO1KOpeaveQiDqEGTNmxMwgmDdvHubNm9dOI7KPNkkNKPGVw0gS4HEKdfVC+naaEkEMFwZup4wmXwB+RQ3V/jtkCUW5rvQczGoMwu+ZKo/T2NNLvHObSnNAlsNQNrP6k/fpsja8TkdEoFH/ub7zwhGYe3pFxOdUNLg0HxvunQWP04ELf/tO6PHke4JEZk9oEjnv9Mh3h1bxMj+OsERuBs4TZhlpYhmgKNgTxJgNYwdbe4LEuvuye/duHDhwILT9/v37Q3dzDhw4gPvvvx/jx4/HN77xjbj3SdSRHXnnrwCATwvOQHFJ12vKR5kzZNwZ+EKugEfyYfOyv9o9HCLqgMKrwwCBOMphcl0OSCaN+/STeHHCm2yyhv4YrrbbhAGhMeqvrxqL8f2L8eevTUzyKLHGEP4+HZkgbqfxvREn+4afEzxcupbVJOqMLDNBdA2fxYCtLEUuzRorAKLRtktHY1RxVSj9uS+ROMXDX52Iyn7F6F3kNX2+PYINZoFcMQNO5JRl4zLBNp3AbM0EAaLffVmxYoXh54qKirjqQbPljg51Lc1NDRhxeCkAwDXpeptHQ52NJMs4NORqtGx+Giv2BDDV7gERUVKqq6tRXV2NQAaaHMv6TJA4uozmuIMTf33qskOKPrFOtm+H/hietuCBX1FCY3bIEvp2y8Xz3zk9qf3HI5VGpWYigyAQfk7+GMwEoWxm9TffKmS4ib2G9J/BZD42DiGAkQzDii0mgZp4DSsrwAtVp2PBvz/BP1ZF9rMUV4fJRBBEMhm7K0aTj2BfqfDPWdcYlYiMNrz5FIrQgIMowagzLrd7ONQJDb/0+7g88Cv88XAlPttfZ/dwiCgJmewJIht6gsTOBAkHQYyTdleUFQfSkwkitY0Tocao7ZEyrU9LF3udJMMjBEGilcMkikEQympW5TDCeS1aY9RkPn+uBBqNWhFXRkm1ybFVg1SxJ0gmMi70v4tVT5A5k/ph4oBuoe2lGIH09sIgCFEH4fnkKQDAzr6Xw+G0PUmLOqFuBTk4b2SwjOrZj/baPBoi6mjCq8PE1xg1x+UwvE77XmyUmg76fYoZFED73C00Ll2Z+v4iMkGE38GQBp9gPQxXhyGKJAZBxHKNVM9diSw5a8VYCmKeTZEIq8+/Q1gdJh0lfpHHjjwP6QNFbqeMX141FuP6FofGFPyv+T7aE4MgRB3AniMnsbaxBMfVPPQ755t2D4c6sasn9UUumhFY+zc0NzXYPRwi6kC0CaiiAk2+2OU2eZ5gQD56T5D0TGDNeoLoxWq2lw5ixkuqxCCIONlP5b3Tvx123UklsotV0DBqJogkCSuzJH5cY1AluXNStEyQWMvemrEKIojlMJkINpiVEGoZhADgaTuXawEjbTypZuSkA4MgRB3AU6v3YpHvRtza9xn0GTTC7uFQJ3bmkBK8nLMIP8Mf8Onrj9o9HCLqQLS5ZkBRcbzRelUBTbdcNwCzu6lRUpmTrIfRT4rNMkHaIQZiuABJR3BHLIcRfwdjKnli+071womoM7P6k2/1Cz1BDNldQulJMuUwugBtstlpUsSYdD8nsUur4IZdS+Rq/98AAI9LNhxb+6+xV0nahxUXBkGIbNbsC+DpVbsBANdNG2rzaKizczhk1FRcBgAo2vC4zaMhoo5EXw5zPMrSipritiVpxQvuaCnh3fPcSIahHMamTJBkGxRaEX8PcZ+pBC+0fTEJhLKRVZBS/EhFBHBT7KWT7kajchoCM5aZIA7JGLTJcE8Q7dti3VLm2jnQKQQ/MlFSmSgGQYhs9uGbL2FI06coL/Rg5ik97R4OdQHDL6xCq+rEMP/n+HztCruHQ0QJqK6uxsiRIzF58uS07zsUBFFU1McRBAlngoQfcwjlMNo+H7lxEiYN6Ib7rx6X1Nj0x7ArE0ROcyaIJEmGQEg6L0JKCzwY168Y57f1gSLKBj84fxjKi7y4feYw0+fvuugU9Cr04ieXjASAiACDbOhFkfjxDQHgNHyenW2NQjXJlcNYPZ6Z/k16xmbSwe/1QRCPy9hcW8siFFftsQO7LxLZrPfqn+NZz+dYMWABnI6Zdg+HuoDuPftgdfE5mFz3Bure+gMwYYbdQyKiOFVVVaGqqgr19fUoKipK6771PUGON7bG3L6blgki9MowWybynBFlOGdEWdJjE0tRJAnQr7bb3pkg6ZqYe5wyWtv6FETbZaJHc8gSXvjOaSyFoawy75yhqDp7iOXf/cCSPKxccE7oef1nzpmWTJD0BjVlSVwiN4l9WLzIKcuGJqWZYBZk0ZfDaEFg7X0PZYJ0gNWtmAlCZKPP167AMP/naFWdGHve1+weDnUhRdOrAADjji/H0UP7bB4NEXUE2lyzxR9AQ2vsxqjFbZPZiHIYw4VAeqaS4qRYvMvaHjcL071ELmDMakn3ZJ8BEMpGsf7uzbITgOA5Jp2rw6QjCBLRpySJMVm9xCFLcBjKFZNdwNyasSdI8L+GIEjb+U8bh9gbRPy+PTEIQmSjurf+AAD4uPgcdO/Zx+bRUFcybMIMbHUOhVvyY8trf7B7OETUAegzQYDYzThD5TDCCgDGC4H0jg2IzDaRpfa54DdOzNOzT30QhKu4ELUvMYvN+HPi+0v3yliOdGSCROkJoh+jkv4YiOkqL4ZyGKfQE8TBIAhR1jt6aB/GHV8OIHzXniidjo++EYoqoWb35/ALy8YRUfYRJ8uFXpfFlkHFZuUwktgcMD1TSXGpRX22SXuUwgTHEP4+Xb+XJ4OZIEQUndjnJ+VyGF10NNlltPUBXTEwk86eIA5hiVw1w0GQUDmMrjm20nZQ7XzakTJB2BOEyCZbXvkdpkl+bHUOxTD2bKAMGDNrLi77uAgbGrrDvbEGF43pbfeQiMhG4qS/ONeFOl2D1NF9CuGUZazfczz0PCCUqlj0BElV5DK8qd2xTYbxrmZ69mkoh4nyXjE+QpR+4rkr1dITVxrOfeKrUh2TZSaIcB4tzEn/Zb/+3KwNI8/tCD3W2FZ2KfYCEcuU7MBMECIbNDeexPBdTwEA6iq/afNoqKvy5uThnGlTAAB/ems71EzcBiCitMrs6jDGn4tyjJkgL3/3TFw0JrzaSLdQTxD9PsSeIOmZwBqOERFoaZ/paiZ6gnic4QsCVsMQtS/99bVDMq4Ok8y5y5Hpc18Su7TKHpGl4Mozf/zKBPzqyrHoXZST5AitiaWS4niafMEgiJgBYngdy2GIsscb769CnZKDAyhF5awb7R4OdWHXn1YBj1PGkX1bsX7dh3YPh4hiqKqqwsaNG7F69eq071ucbIpBEABo9YdL50JBEKFXRrqbA4rHkCVx1YG0HCL2GIQLpnQw9ARhugdRu4qaYZbEx9GViXNfypkg5o9r5+kLx/TGlyf3S2pssUgxxt7QYgyCaGMSe7XYgUEQonYWUFTcv1bCua0P4L3TH4XT5Y79IqIkleR7sHjgx1jhng/HG3fbPRwispF4x7A4N/L/P/pVY3La0prFFRXS3RwQMGm+qj9GumpTYshIOYxuR1zNhah9RQRBhJWuEpWJALBkGFPir7cKnLRHhkWsssXGVr9hu1BvEJMMkvbGIAhRO3ttwwHsPtqIolwPLpo+ze7hUBaYevZlkKBibPNqfLGB2SBE2UqcFBebZII0tvgjXyfc7ctEU7voq8O0zyTZmPGSnimyK87VYaSITgFElCpxuVzDZzyJ84ojDQ2bxcOK5YaJsswEaYcyQuMSuZEDEXuChHqDOKIHT9oDgyBE7UhVFGx443F40Irrp1Ug183exJR5fQaNxLrCGQCAo2/8yt7BEJFtxMmyfilDzcmWQMRjckQmiP5CIF13Q8PfR2SCtFO6tHF1mPTs02V479KzTyKKj9h7wtgoNfH9uQyB0pSGFh5HiuUwVhkt7ZEJIq7qZUXsCRLv6zKJQRCidvTZ+y/jzpO/wDLPD3HDqX3tHg5lkaJzvw8AqKx7Ewd2bbF5NERkB3GCXZTjws9mjwYA/PTyUQCAGcNLAQDddcscio37nIa7eJnIBLFnCUVjOUx6pshihouVMX2L0nI8IgrTByocQhZbcuUw+syuJDNBhJ9TbYwabXWYTBN7OWlmV5YDAOZMCvYiGd6rAE5ZwsjehQCM7wGXyCXq4lRFgfR28C78gdIzMbUg1+YRUTYZWnkmNrxWidEt67H7pf+H3t99wu4hEVE7EyfLBV4n5kzuj8sry1HoDWaFXDymNwpzXKHJKhB5IZ/pniBiyU37LZFrPp5UuBzRG6Mu+95Z2LC/DuePLEvL8YgoLN3lMJk49xmaiyaxT6uXtEtPEIseK4u/NBaXjivH6UNKAAAjehVi7cLzUOCJDD2wMSpRF7fhvf9gVOunaFFdqJj9Y7uHQ1lIPnsBAGDC4Zexf8dmm0dDRGYyuUSuOCnOaSvJ1AIgQHBCOn1YKUoLPOHHovYESc9UUhYyP9JRe58o8YIpHQxZMyYXXUPLCnDF+L5smkqUAWI5TKr9N9KRBSd+1lNfHcbOchjz4+W4HTj3lDJ4XeElwgu9rtDvLpY/2oFBEKJ2oCoK3G/9HACwrudslPUdbPOIKBuNPPUCfOKdiCZ4sPR/b9o9HCIykcklcsU5sdcZ3zTQGPQwBiUyVRfvtEizziQ5A0EQOzJaiCgo2uowyXzE9eUw6coESbkcxuJF7RFcsCqHSQTLYYi6sE9WPIdx/s1oUt0YcuVCu4dDWcxx6RKc8eQmnNyajxm1JzGoNN/uIRFRO5EkCZIEqGrwZ20J3FjEFQAchmUi09Q7Q2xgaEg7b5/ogaF/QJom5i7d2NtrlRsiCpIsMhWCz6VWDpOuc4TYeDrh11u8pD3KTGSLcphk99GeGJMmyjBVUZD73i8BAB/3vholvfrbPCLKZqNGjcWkEYOgqMBvl2+1ezhE1M70E059qnK8r3FIkmGFhLTdDdXNSGXJuN/2qhnPRCaIPn3errRvImprjJriZzAdfYPEV+l3k8wu7QyuJnua1C8JblcmCIMgRBm2/OPt2NVagAbVi2FfYi8Qst/884YBUHH8k9ewY/N6u4dDRO1IP3HPiTMI4hDuVMa74klC4xL26chAoCUW/Z3MdB1T3xiVMRAi+8hCY9RkGC7eHWkKAKfcEyQtw0iK/v1UtRTDRPdh0/gZBCHKIF9AweI39+EbvjvwxKR/o3vPPnYPiQij+xThD71exePuX6LupTvtHg4RtSP9HDveTBCxr0UmylMcQrZJJgItsaTaNNGMPpjC5qdE7Ut/We4Ugqsqkrho132Ekw2UiqeBVM87dp5X0nGetGv8HSIIUl1djYqKCni9XkydOhWrVq2Kuv2zzz6LESNGwOv1YsyYMXj11VcNz994441tda/hrwsuuCCTvwKRqb9/sAvbaxvQPc+N62ZOsXs4RCGjLvwmfKoDlY0r8enbz9s9HCJqJ/qLAK8rvmlgxOow+jugSd79E4krs9iRCZKZcpgOMdUmyk6605PYGDXFGEjaAqXG82tqr29vnbnEz/Yz8zPPPIP58+dj0aJFWLt2LcaNG4dZs2bh0KFDptu///77uPbaa3HTTTdh3bp1mD17NmbPno0NGzYYtrvgggtw4MCB0Nc//vGP9vh1iEKOHz6InGU/RCmO4fvnD0NRjiv2i4jayYDhlVhTdiUAoGDFQvh9rTaPiIjag37KGm85TLSVW9JFLLkxNCBsp4m21XKPqWivAA4RRSdLUsorNKWnZM66QWsyWRF2nmKSPTV3hNiJ7UGQBx98EDfffDPmzp2LkSNH4uGHH0Zubi4eeeQR0+1/+9vf4oILLsAdd9yBU045BT/72c8wYcIE/P73vzds5/F40KtXr9BXt27d2uPXIQrZ8syPMQdv4LG832POpH52D4cowinX/BzHkY8KZTfW/Ps3dg+HiNqBLxC+/Rl/OYzx+4wEQcRsE/2qKu00W9WX3WSiMSoRtS99yYtTllLOmtC/Om3LaKe6RK6dmSBJvgf9uuWmeSSJszUI0traijVr1mDmzJmhx2RZxsyZM7Fy5UrT16xcudKwPQDMmjUrYvsVK1agZ8+eGD58OL797W/jyJEjluNoaWlBfX294YsoFbs2rcHEQ/8GAKhn38V0WOqQirqXYssp3wUADNv0EOqO1to8IiKqrq7GyJEjMXny5IzsvzWghL5PZnUYSRLr6tNDjhJoaa8lcuW03OU1cvH//0S20VfryWI5TBKMK7mkqSdIiv2P9Pu7eGzvpMaUrGQDMP175OLRuZPx0rzT0zyi+Nl6Zj58+DACgQDKysoMj5eVleHgwYOmrzl48GDM7S+44AI88cQTWL58OX75y1/irbfewoUXXohAIGC6z8WLF6OoqCj01a8f79pT8lRFQd2Ld8ApKViXexpGn3GZ3UMisjTxS/OxU+6PbjiBzf9gk1Qiu1VVVWHjxo1YvXp1xo8V7108h1Caop/8p6kliLHkRpaQ63YYfm4PhgaFLIch6nLkFAO4mUi6kFLsCXKkIVzOfO9lo/DNswbh99eNT8fQYkrl9Hb28J4Y27c4bWNJVJcMT19zzTW47LLLMGbMGMyePRsvv/wyVq9ejRUrVphuv2DBAtTV1YW+9uzZ074Dpi5lzct/wtjmNWhRXSj90q/tHg5RVE6XGydm3IddSk/8bt8wrNt9zO4hEVEHIwv9OjJBDLTke52hnzvzErnMBCWyT7QgbTIBXAnpPxfJKWaX6M9VJfke3HXRKbhkbHk6hhZTJgLi7cXWM3NJSQkcDgdqamoMj9fU1KBXr16mr+nVq1dC2wPAoEGDUFJSgm3btpk+7/F4UFhYaPgiSsbRQ/sweO3/AwCsG/hN9B0y2uYREcU25qzL8fuRT+E9ZTTu/NenaPUrsV9ERFnDmKWR+WM4ZAl5Hqfpc5kkNoBNB2aCENkn3dfl6TgtXDe1PwBg0oBgv8pUzztzJvfD3NMr8Nwt01IfXBaxNQjidrsxceJELF++PPSYoihYvnw5pk0z/4ecNm2aYXsAWLZsmeX2ALB3714cOXIEvXu3b50UZZ9PnvoJuuEEvpArMPG6RXYPhyhuCy4dh+55bmypOYG/LP/M7uEQUQciNi3VU9N0+0+fCSJJEvI97Z8Jope+TBAGQYg6IjXtIZL4nD28J1b8YAaeuvlUAEIZXhKniwKvC4suHYVJFd3TNMLsYHuO3vz58/GXv/wFjz/+ODZt2oRvf/vbaGhowNy5cwEA119/PRYsWBDa/rbbbsPSpUvxwAMPYPPmzbjnnnvw0UcfYd68eQCAkydP4o477sAHH3yAnTt3Yvny5bj88ssxZMgQzJo1y5bfkbLDm5trUHXwIjzmn4XApQ/B5fbYPSSiuHXPc2PRJSNwg+N1XPv+Bdi5ea3dQyKiDsLYtFQIgqTrGPrlaSUYgiDpWoUhFn1AJ109QcqLctKyHyJKXPc8t+Vz3XKtn7NSWpCeuX1FSR7czuCJVcpABhrF5oy9SWbNmTMHtbW1WLhwIQ4ePIjKykosXbo01Px09+7dkHX/9z3ttNPw1FNP4e6778Zdd92FoUOH4oUXXsDo0cGyA4fDgU8++QSPP/44jh8/jvLycpx//vn42c9+Bo+HF6WUGXWNPvz4+Q1oQA72TbsHQ8ePtHtIRAm7bFwfVLyxCd2bTqL2uVvg++E7DOYRkZAJkpljSJIESQrWlTtkCTluG4Iguu/TlQkyY3gpvnvOEIzszVJrovY2oX8xvjdzGAaW5oUeWzKnEnuONmJ0n6KE9zdtUA/ceu5QDCvLT9sYM1GGR7HZHgQBgHnz5oUyOURmzUyvvvpqXH311abb5+Tk4PXXX0/n8IiiUhUFTz/xexysG4KKHvmYf95wu4dElBRJllF27R9w4q9nYrh/C1Y+/iNMu3mJ3cMiogxwJVCmEa0xajqb4TkkCX5VhSxLtmeCpOuYkiTh++dzXkBkB0mScNvMoYbHZo/vk9L+5p83LNVhGRhXpUrrrikKvtVEKVr1r9/gWwfvwSPuB/C7ayqRo1vWj6iz6dV/KD6fch8AYOrex7Dh3ZdsHhERZYI7gVVLot2pHFiSJ26eNC3YIgs9Qdrr7qg+oMM7skTUHpgJYg8GQYhSsHPTRxi3YTEAIGfYDIzt183mERGlbuLF38CqbhdDllSU/fdWHKs9YPeQiCjNtHr0eDhMMkGeu2Uafnr5KMwYXpq2MWmHsWuJ3EyUwxARRaOPe/C0034YBCFKUuPJOqjPfh1eyYdPvJMw5dqf2D0korQZfdMfsUvui1Icw+5HboASCNg9JCJKo4SCICZL5E6q6I7rp1UYmvqlSjtOsBwmnFWZrialsRgyQXg1QkTtQJ/9kc7zKUXHIAhREpRAAJv/+FUMVHbhMIpRfuNjkB0sg6GuIze/CP4r/oom1Y3X6yvw4LKtdg+JKCtUV1dj5MiRmDx5ckaPk0gQRF+nnsl0bS3w4JCBfI8r9HgClTspUdLZ4ISIKA5dpRyms509GQQhSsKHj/0IExreRqvqQO2Ff0ZJr352D4ko7QaPORX/m/U6/hC4HL9fsR0vrt9n95CIuryqqips3LgRq1evzuhxku0JkskmpQ5dT5A8XSaIP9A+0+vONoknos5PZjmMLRgEIUrQGx+sx7jdTwAA1lfei1OmzrJ5RESZc9FpE3DL9MEAgEXPrcKmT1bZPCIiSge3M/7sRX3gI5M3KkPlMJKEPN0SuU2+dirHYyYIEbUzqYtkgnQ2HWKJXKLOYs2uo/juywcwJLAQPxi0B2df8V27h0SUcXfMGo7D+3fg67sWofTfddhf8DrKB46we1hElIKEymH0mSAZnKRrFwMOWTL05GhqbZ8giMIYCBG1M332B2Mg7YeZIERx2rDnKG58dDVa/ArKhk/FWTf9wu4hEbULhyzhnqtPhdcpoQTHgScuw6F9O+weFhGlwJNko41M3qnUhiQeo70yQVRmghBRO+syPUE62emTQRCiOOzc9BHy/3oaBrZswZSK7qi+bkJG66KJOpr8wm4o/MZL2Cv1Rrlag6a/XoIjNXvtHhYRJSmRTBC9TK6a4tBlgug1t1cQpF2OQkQUZrYEOWUegyBEMezZ+jHynrkKFTiAn+U/h7/eMBE5bq4EQ9mnpHwAHDe+iIMowQBlL47/+RIcqz1g97CIKAmJBEGkdmrcp18dRq/9MkHa5TBERCHtdX7NtM4Wv2EQhCiKreveRt7fL0EpjmGHXIGKW55FQY7b7mER2ab3gOHwffUFHEYxBgd24MQfz8WBXZ/bPSwiStDkiu5xb6uf22Z0idy2fUtiOUy79QRhFISI2pf+nCqe+zqTznb6ZBCEyMKnbz+P8heuRnfUY5tjMAq/9QqKepTZPSwi2/UbMgYN1zyPGvSAM9CEb/1tHT6vOWH3sIgoDsu+dxZ+cslI3HTGwKRe3x5L5IrNV5t9SsaOSURkp/ZagpyMGAQhMrH6hWoMX34T8qRmbPBUotdty9GjrK/dwyLqMAaMmAD1pjdwd/59+OREPq764/t4f9thu4dFRDEMLSvATWcMTLonSCZvVGrzf+1CwNM2xjF9ijJ3UJ2+3XLa5ThERBq5i5TDdDYMghDptPoV/OT5T1Gz5kW4pQDW5M/A0O+9hvzCbnYPjajD6dVvCB6suhoTB3RDfbMf/3701/jgyYVQFd61JeqqMlkOU14cDEL0KvICAF697Ux8a/og/L8rRmfsmHqzRvXC/POGzeG36AAAF0BJREFU4YmvT2mX4xERSV2kHKazcdo9AKKO4kBdE77z97VYt/s4/o1vIm/IaTjrK3fD4eTHhMhKca4bf//GVDzwzBv4wda/wrPdh7UPrMXQbz6BgqL4ew4QUcfVt1su8twO5LidcGbwVuVD147HvuNNGFyaDwAYXJqPBReekrHjiSRJwq3nDm234xERdfZMkPNHluGNjTX4yqn97R5KQnh1R1lPVRR89J+HUbvuZaxr/g4KvS78Zs6ZOPuUq+weGlGn4HU5cNd1s7DquR9i/Ge/wISGd3DwN1Ow85wHMOasy+0eHhGlyO2UseYn50GWpIzeqSzOdaM4l83HiSh7yJ18idw/fW0iGlsDyPN0rrBC5xotUZod3r8Le//2LUxuXAkA+FbJdFw3dx4G9MizeWREnYsky5j65R9i80cTUfjKLShXD6HXm9fjw49nY9QNS1hSRtTJeV1cGp6IKN2MmSCdLwgiSVKnC4AA7AlCWaq5qQErn/gJvH+aisrGlWhVHfigogp33PY9BkCIUjBi0rkomr8aH5Z8CQAw9cgLOP7gVDy36gsoSidbP42IiIgog4w9QWwcSJZhEISyihJQsOaV/8PRX1Vi2he/Q77UhM+dw7Bvzus49cafw+liGi5RqvIKijF13qPYMPNJ7JV64d/+afjBvzfhsup38d7WWjZOJSIiIoIx+6MzZoJ0Vp0vd4UoCb6AghfX78cf/7cVv6n/PcrlQziE7thV+QNMvPQWyA6m+RKl2+gzLkPLpJnIW7kDBSv2YsO+elQ/+gh65D6PltNux9gZX4YkMxZPRERE2amzN0btrBgEoS6tdv9ObHvjYdx3YCo+qwtmeTzsnYOv9T+KcV++G5Pzi2weIVHX5vHm4qazR+HyyUPw0PKtOHfNLzHCvwl4+1vY8e7PcWj4dThl1s0oLO5h91CJOoTq6mpUV1cjEAjYPRQiIsowZoLYg0EQ6nIaT9Zh09v/hrzhWYxpWIlpkoLTfcdRk38VvnHmQHxl6vko8LrsHiZRVinJ9+Dey0fj8NS/4YMXfoExB/6FgcouDNy0GE0bH8Dq4nPgmTAHp5wxGy4Hs0Moe1VVVaGqqgr19fUoKmKgnoioK9PHPRgDaT8MglCXcPDIMex55+9wbHsDI058gIlSS/AJCdjkGokZU07H/PPOZnd7IpuV9OqPklv+gLqj9+KD1/+CXlv/gQplNybXLcWa5dsx+a18nD+yDNOH9cRpfV3o1r3E7iETERERZYSW/SFJyOgS5GTUIW63VVdXo6KiAl6vF1OnTsWqVauibv/ss89ixIgR8Hq9GDNmDF599VXD86qqYuHChejduzdycnIwc+ZMbN26NZO/ArUjVVGwf8cmvLdiKe556TPMfPAtTP/1Coxedy8mnHwLuVIL9ktlWNn7q9g5ZzlO+fFKnHbR1xgAIepAirqX4tRr78KAuz/G5gufxYc9ZuMV50wcb/Thnx/txd1PrUDBb4di688mYuWfv4v1//0HDu/fZfewiYiIiNJGC4KwFKZ92Z4J8swzz2D+/Pl4+OGHMXXqVCxZsgSzZs3Cli1b0LNnz4jt33//fVx77bVYvHgxLrnkEjz11FOYPXs21q5di9GjRwMAfvWrX+F3v/sdHn/8cQwcOBA/+clPMGvWLGzcuBFer7e9f0VKQd3Rwzjwxceo37MRgUOfI+/YRvRr3oJynECjUo7HWu8HAMiSG8tyL0Jp92KUTLoSQ8adgXI2XCTq8CRZxoip5wNTz8ckRcXMHUewbGMNfJteg7NRwdDANgzdvw3Y/wTwLnAI3bEvdwS2VVwH97BzMLg0HwNL8jrlGvVERESU3bRmqGyK2r5snzU++OCDuPnmmzF37lwAwMMPP4xXXnkFjzzyCO68886I7X/729/iggsuwB133AEA+NnPfoZly5bh97//PR5++GGoqoolS5bg7rvvxuWXXw4AeOKJJ1BWVoYXXngB11xzTfv9cmRKVRQ0NtSj/mgNTh47hOa6WrTU18J/bC+aG+vxt5yv4UBdEw7UNeMx3x0YK++I2Eer6kDAnY8bxvfBtKFlmDaoBEW5F9vw2xBRujhkCacNLsFpg0uAS0fh8P6rsGP1q1B3vIPS+s/QP7AbPaWj6Nn4Ph5fX4kX1nYHAJwuf4ol7odxzFmKk55eaM3rDRT1gau4DzyFpXCWj0FRSW90y3UzI4yIiIg6DFlmJogdbA2CtLa2Ys2aNViwYEHoMVmWMXPmTKxcudL0NStXrsT8+fMNj82aNQsvvPACAGDHjh04ePAgZs6cGXq+qKgIU6dOxcqVK20LgmyvPQnnse2A4gdUQIUKqCpUAFAVKM4ctBZWQFWD27uPboak+Np+1m+rQnF60Vw8DG2bwnv4MyDQHPxBVQHdaxSHBw0lY0L7zTn8KWRfQ2hbFUr4e9mN+p6TQtvm1a6D3HwEit8Pxe+DGmiFGvBBDfjgUx34vPel8AdU+BQFQ/a/jIKmPZB8TZB8jZD9jXD4m+AMNMGvAAsLFqGxNYCTzX78puUenC5/ijyT98mnOvD1lplQ2iq1trvK0Qt1OOTpj4aCQUDPU9B96Knof8okDPfm4t60/QsRUUdTUl6Bksu/A+A7AICGE8exe+OHqNu+CuXSZEypK8L22pMY0rwfpTiGUv8xwP850ADgUHg/81q/i5eVaQCAC13rcI/jETTLuWiRc+CTvfA5cuF35kJx5uDjnrNxuHgM3A4ZpS27MfTY25AcLkgOF+BwQ3K6Ibd9newxBq35/SDLgLvlKAqPbYQky5AkGZAkSJIj+LMso7VwAAJ5ZZAAOH0N8J7YAUmSg/W/kjFrLZDXE4GcYC8UydcEd/1OQ7M0VZIgIfhAIKcktK0caIarfndoO3E6FfB2g5JXGvrZ7XCgf4/c5P+BiIiIKCUsh7GHrUGQw4cPIxAIoKyszPB4WVkZNm/ebPqagwcPmm5/8ODB0PPaY1bbiFpaWtDS0hL6ub6+PrFfJA6zfvM21rpuQqHUaPr8R8owXNV6T+jnDz3fQZl03HTbjcoAXN66OPTz/9zfw0C5xnTbHUoZLmr9TejnV90LMFI2r6s/qHbDpS3VoZ//5V6E8bJ5L5U6NRdf+Whw6Oe/uf6JaY7PTLf1qQ5s0L2nda4cAECL6kKdVIAGuRCNziI0eXvCl1+O+0YNQ1n3YvQuykH/bjORn+NBZGEUEWWbvIJinDJ1FjB1Fk7VPX7s6Hhs3X01TtTsROvR3UDdPrga9iOnuRa5gTo05/SEs0mCX1FRrBxFmeMIoByBFgPWe6xmMF5VgiHai+QPcL37d5bjucP3TTwbmAEAOFteh0fdv7bc9ie+G/Fk4HwAwKnyRjztvs9y25/7rsWfA5cCAMZJ2/CiZ6Hltkv8X8IS/1UAgKHSXizz/NBy24f9l+AX/utCPw8vK8Dr3zvLcnsiIiLKLJbD2MP2cpiOYPHixbj33szmFBTnunDCnwcFMtTQ/TkplM3R5ChASb4n2BkYwFFfd0i6vrUqpNDr6p3d0Sc3GEiQJOBoSyk8WgJI27baPcAjrp4YWJgX/EkCjjb1wi4lEHpebdteAnBcKsbw4oLQHccjjQOwVQECcEKRnVAkBxTJBUV2olXOxSXDe8MpS3A6ZBw7NhMftg6H6vBAdedBcuVC8uRBcufB4cnHo4MmIdftRJ7Hie6OCWjMz0VObgF6mvTtmJaet5yIskS37iXo1v1MAGeaPv9/CDbMPtniR92RSmw9NButjSfgaz6BQPNJBJpPQmltAFoaMKHoDJS7+sEXUFB24gRWH74QkuKDrPiC/1X9kBUfHKof+UX9MM5dDKgqylpLsK1hMCQokFXtzKpAggpZVeDJ74b+jlwoqoqiQB5qWnu0ndXViPE6PPkodXgAAPlKDg4HikPPRWzvykMPjxsAUKB6cEwp1D0pbOvMQbE7vDx4gZdTACIiIjv17ZaLM4aUYEjPfLuHklVsnQGVlJTA4XCgpsaYxVBTU4NevXqZvqZXr15Rt9f+W1NTg969exu2qaysNN3nggULDCU29fX16NevX8K/TzQf3X0egG2Wz58J4CPDI+sst+0F4D3DI+dYbtsXwP8Mj8yw3BYAXjf8FP0O4RTDT+OibmtUlMC2RESpkyQJBV4XCvr0Afr0sdzuVMNPowFYl1AuMvx0BoBbLLe9u+0r6BxoJT5mftT2FfZNy21vb/sKu9Fy21sQbYRERETU3hyyhL99Y6rdw8g6ti6f4Xa7MXHiRCxfvjz0mKIoWL58OaZNM88HmDZtmmF7AFi2bFlo+4EDB6JXr16Gberr6/Hhhx9a7tPj8aCwsNDwRURERERERERdi+25sPPnz8cNN9yASZMmYcqUKViyZAkaGhpCq8Vcf/316NOnDxYvDvbAuO222zB9+nQ88MADuPjii/H000/jo48+wp///GcAwbt9t99+O+677z4MHTo0tERueXk5Zs+ebdevSUREREREREQ2sz0IMmfOHNTW1mLhwoU4ePAgKisrsXTp0lBj0927d0PW9Y047bTT8NRTT+Huu+/GXXfdhaFDh+KFF17A6NGjQ9v88Ic/RENDA775zW/i+PHjOOOMM7B06VJ4vd52//2IiIiIiIiIqGOwPQgCAPPmzcO8efNMn1uxYkXEY1dffTWuvvpqy/1JkoSf/vSn+OlPf5quIRIRERERERFRJ2drTxAiIiIiIiIiovbCIAgRERERERERZQUGQYiIiIiIiIgoKzAIQkRERERERERZgUEQIiIiIiIiIsoKDIIQERERERERUVZgEISIiIiIiIiIsoLT7gF0RKqqAgDq6+ttHgkREVHnoP0/U/t/KKWGc5GOydfcAKWlEQFZgqKoaDx5gv9GnUjDyROGf7+Aw4f6+nooLY0AAKnt8ZMn6lGfG31fjcK+/M3Gz2ugpRFKQAEkQFGBkyfq0dp0MnistseaGsJ/P9r+tOf8zRL/togSFO9cRFI5W4mwd+9e9OvXz+5hEBERdTp79uxB37597R5Gp8e5CBERUXJizUUYBDGhKAr279+PgoICSJJk93DaVX19Pfr164c9e/agsLDQ7uF0enw/04vvZ/rxPU2vbH4/VVXFiRMnUF5eDllmtW2qOBfJzs9RJvD9TD++p+nF9zO9svn9jHcuwnIYE7IsZ/1drMLCwqz70GQS38/04vuZfnxP0ytb38+ioiK7h9BlcC6SvZ+jTOH7mX58T9OL72d6Zev7Gc9chLdqiIiIiIiIiCgrMAhCRERERERERFmBQRAy8Hg8WLRoETwej91D6RL4fqYX38/043uaXnw/iVLHz1F68f1MP76n6cX3M734fsbGxqhERERERERElBWYCUJEREREREREWYFBECIiIiIiIiLKCgyCEBEREREREVFWYBCEYmppaUFlZSUkScL69evtHk6ntXPnTtx0000YOHAgcnJyMHjwYCxatAitra12D63TqK6uRkVFBbxeL6ZOnYpVq1bZPaROafHixZg8eTIKCgrQs2dPzJ49G1u2bLF7WF3GL37xC0iShNtvv93uoRB1KZyPpI5zkdRxLpIenItkFuci0TEIQjH98Ic/RHl5ud3D6PQ2b94MRVHwpz/9CZ999hl+85vf4OGHH8Zdd91l99A6hWeeeQbz58/HokWLsHbtWowbNw6zZs3CoUOH7B5ap/PWW2+hqqoKH3zwAZYtWwafz4fzzz8fDQ0Ndg+t01u9ejX+9Kc/YezYsXYPhajL4XwkdZyLpIZzkfThXCRzOBeJg0oUxauvvqqOGDFC/eyzz1QA6rp16+weUpfyq1/9Sh04cKDdw+gUpkyZolZVVYV+DgQCanl5ubp48WIbR9U1HDp0SAWgvvXWW3YPpVM7ceKEOnToUHXZsmXq9OnT1dtuu83uIRF1GZyPZA7nIvHjXCRzOBdJD85F4sNMELJUU1ODm2++GU8++SRyc3PtHk6XVFdXh+7du9s9jA6vtbUVa9aswcyZM0OPybKMmTNnYuXKlTaOrGuoq6sDAP4tpqiqqgoXX3yx4e+UiFLH+UhmcS4SH85FMotzkfTgXCQ+TrsHQB2Tqqq48cYbccstt2DSpEnYuXOn3UPqcrZt24aHHnoI999/v91D6fAOHz6MQCCAsrIyw+NlZWXYvHmzTaPqGhRFwe23347TTz8do0ePtns4ndbTTz+NtWvXYvXq1XYPhahL4XwkszgXiR/nIpnDuUh6cC4SP2aCZJk777wTkiRF/dq8eTMeeughnDhxAgsWLLB7yB1evO+p3r59+3DBBRfg6quvxs0332zTyImCdww2bNiAp59+2u6hdFp79uzBbbfdhr///e/wer12D4eoU+B8JL04F6HOjHOR1HEukhhJVVXV7kFQ+6mtrcWRI0eibjNo0CB8+ctfxn/+8x9IkhR6PBAIwOFw4Ctf+Qoef/zxTA+104j3PXW73QCA/fv3Y8aMGTj11FPx2GOPQZYZi4yltbUVubm5eO655zB79uzQ4zfccAOOHz+OF1980b7BdWLz5s3Diy++iLfffhsDBw60ezid1gsvvIArrrgCDocj9FggEIAkSZBlGS0tLYbniIjzkXTjXCTzOBfJDM5F0oNzkcQwCEKmdu/ejfr6+tDP+/fvx6xZs/Dcc89h6tSp6Nu3r42j67z27duHs88+GxMnTsTf/vY3nowSMHXqVEyZMgUPPfQQgGDqZP/+/TFv3jzceeedNo+uc1FVFd/97nfx/PPPY8WKFRg6dKjdQ+rUTpw4gV27dhkemzt3LkaMGIEf/ehHTO0lSgHnI+nHuUjyOBdJH85F0otzkcSwJwiZ6t+/v+Hn/Px8AMDgwYM54UjSvn37MGPGDAwYMAD3338/amtrQ8/16tXLxpF1DvPnz8cNN9yASZMmYcqUKViyZAkaGhowd+5cu4fW6VRVVeGpp57Ciy++iIKCAhw8eBAAUFRUhJycHJtH1/kUFBRETC7y8vLQo0cPTjqIUsT5SHpxLpIazkXSh3OR9OJcJDEMghC1k2XLlmHbtm3Ytm1bxMSNCVmxzZkzB7W1tVi4cCEOHjyIyspKLF26NKJBGcX2xz/+EQAwY8YMw+OPPvoobrzxxvYfEBERtQvORVLDuUj6cC5CdmI5DBERERERERFlBXZBIiIiIiIiIqKswCAIEREREREREWUFBkGIiIiIiIiIKCswCEJEREREREREWYFBECIiIiIiIiLKCgyCEBEREREREVFWYBCEiIiIiIiIiLICgyBERERERERElBUYBCEiIiIiIiKirMAgCBERERERERFlBQZBiIiIiIiIiCgrMAhCRB1ebW0tevXqhZ///Oehx95//3243W4sX77cxpERERFRNuBchKjrkFRVVe0eBBFRLK+++ipmz56N999/H8OHD0dlZSUuv/xyPPjgg3YPjYiIiLIA5yJEXQODIETUaVRVVeG///0vJk2ahE8//RSrV6+Gx+Oxe1hERESUJTgXIer8GAQhok6jqakJo0ePxp49e7BmzRqMGTPG7iERERFRFuFchKjzY08QIuo0tm/fjv3790NRFOzcudPu4RAREVGW4VyEqPNjJggRdQqtra2YMmUKKisrMXz4cCxZsgSffvopevbsaffQiIiIKAtwLkLUNTAIQkSdwh133IHnnnsOH3/8MfLz8zF9+nQUFRXh5ZdftntoRERElAU4FyHqGlgOQ0Qd3ooVK7BkyRI8+eSTKCwshCzLePLJJ/HOO+/gj3/8o93DIyIioi6OcxGiroOZIERERERERESUFZgJQkRERERERERZgUEQIiIiIiIiIsoKDIIQERERERERUVZgEISIiIiIiIiIsgKDIERERERERESUFRgEISIiIiIiIqKswCAIEREREREREWUFBkGIiIiIiIiIKCswCEJEREREREREWYFBECIiIiIiIiLKCgyCEBEREREREVFWYBCEiIiIiIiIiLLC/weHqx9iGLVQMwAAAABJRU5ErkJggg==",
|
|
"text/plain": [
|
|
"<Figure size 1100x400 with 2 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"max error vs N(0,1) density = 1.665e-15\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"def phi_normal(u):\n",
|
|
" # Standard normal phi(u) = exp(-u^2 / 2), purely real.\n",
|
|
" return (float(np.exp(-0.5 * u * u)), 0.0)\n",
|
|
"\n",
|
|
"x_grid = np.linspace(-5.0, 5.0, 401).tolist()\n",
|
|
"res = opt.fourier_invert(phi_normal, x_grid, 25.0, 4000)\n",
|
|
"x = np.asarray(res[\"x_grid\"]) ; f_num = np.asarray(res[\"density\"])\n",
|
|
"f_exact = (1.0 / np.sqrt(2.0 * np.pi)) * np.exp(-0.5 * x * x)\n",
|
|
"err = np.abs(f_num - f_exact)\n",
|
|
"max_err = float(err.max())\n",
|
|
"\n",
|
|
"fig, ax = plt.subplots(1, 2, figsize=(11, 4))\n",
|
|
"ax[0].plot(x, f_num, label='Fourier inversion')\n",
|
|
"ax[0].plot(x, f_exact, '--', label='exact N(0,1)')\n",
|
|
"ax[0].set_xlabel('x'); ax[0].set_ylabel('f(x)'); ax[0].legend(); ax[0].set_title('Density recovery')\n",
|
|
"ax[1].semilogy(x, err)\n",
|
|
"ax[1].set_xlabel('x'); ax[1].set_ylabel('|f_num - f_exact|'); ax[1].set_title('pointwise error (log)')\n",
|
|
"plt.tight_layout(); plt.show()\n",
|
|
"errors['fourier_invert'] = max_err\n",
|
|
"assert max_err < 1e-3, f'max err = {max_err}'\n",
|
|
"print(f'max error vs N(0,1) density = {max_err:.3e}')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "ef513b3c",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Summary\n",
|
|
"\n",
|
|
"Verified against analytic ground truth -- max error per primitive (filled in at execution time):\n",
|
|
"\n",
|
|
"* `solve_fractional_ode` vs. Mittag-Leffler $E_{\\alpha}(-t^{\\alpha})$\n",
|
|
"* `geometric_grid_lift` vs. rough kernel $t^{H-1/2}/\\Gamma(H+1/2)$\n",
|
|
"* `solve_volterra` vs. $e^{t}$\n",
|
|
"* `fourier_invert` vs. standard normal density"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 6,
|
|
"id": "c74e905c",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-05-12T09:45:41.743078Z",
|
|
"iopub.status.busy": "2026-05-12T09:45:41.742650Z",
|
|
"iopub.status.idle": "2026-05-12T09:45:41.748208Z",
|
|
"shell.execute_reply": "2026-05-12T09:45:41.747112Z"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"solve_fractional_ode max error = 5.625e-04\n",
|
|
"geometric_grid_lift max error = 1.688e-02\n",
|
|
"solve_volterra max error = 1.232e-06\n",
|
|
"fourier_invert max error = 1.665e-15\n",
|
|
"\n",
|
|
"Verified against analytic ground truth -- max error = 0.016883453274562938\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"for name, e in errors.items():\n",
|
|
" print(f'{name:30s} max error = {e:.3e}')\n",
|
|
"print('\\nVerified against analytic ground truth -- max error =', max(errors.values()))"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.11.13"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|