Skip to content

Instantly share code, notes, and snippets.

@zonca
Last active December 11, 2025 18:18
Show Gist options
  • Select an option

  • Save zonca/c34c46224fed1205b6853df93c56d017 to your computer and use it in GitHub Desktop.

Select an option

Save zonca/c34c46224fed1205b6853df93c56d017 to your computer and use it in GitHub Desktop.
Healpy blm_gauss breaking change comparison
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "markdown",
"id": "1571d3a1",
"metadata": {},
"source": [
"# blm_gauss breaking change (healpy 1.18.1 → 1.19.0)\n",
"\n",
"healpy 1.19.0 changed the Gaussian beam spherical-harmonic coefficients from\n",
"`exp(-0.5 * l**2 * sigma^2)` to `exp(-0.5 * l*(l+1) * sigma^2)` to align with\n",
"`gauss_beam` and Challinor et al. 2000. This notebook visualizes the difference,\n",
"shows percent impacts at representative multipoles, and illustrates how beam\n",
"window functions shift for different smoothing scales. The goal: make it easy to\n",
"judge whether a pipeline that relied on the old convention needs reprocessing."
]
},
{
"cell_type": "markdown",
"id": "b6bd7205",
"metadata": {},
"source": [
"## Imports and helpers\n",
"We replicate the two formulas directly to avoid any dependency on the installed\n",
"healpy version. All arrays are `m=0` (temperature) coefficients; polarization\n",
"scaling follows the same exponential factor."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "917458dd",
"metadata": {
"execution": {
"iopub.execute_input": "2025-12-11T18:18:28.073414Z",
"iopub.status.busy": "2025-12-11T18:18:28.072964Z",
"iopub.status.idle": "2025-12-11T18:18:28.798855Z",
"shell.execute_reply": "2025-12-11T18:18:28.797204Z"
},
"lines_to_next_cell": 1
},
"outputs": [],
"source": [
"from __future__ import annotations\n",
"\n",
"import math\n",
"from dataclasses import dataclass\n",
"from typing import Tuple\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"CURRENT_RELEASE = \"1.19.0 (l(l+1))\"\n",
"PREVIOUS_RELEASE = \"1.18.1 (l²)\"\n",
"\n",
"\n",
"@dataclass\n",
"class BeamComparison:\n",
" ell: np.ndarray\n",
" blm_old: np.ndarray\n",
" blm_new: np.ndarray\n",
" pct_diff: np.ndarray\n",
" ell_half_power: int\n",
" pct_half_power: float\n",
" pct_extreme: float\n",
" ell_extreme: int\n",
"\n",
"\n",
"def beam_coefficients(fwhm_rad: float, lmax: int, use_l_lplus1: bool) -> Tuple[np.ndarray, np.ndarray]:\n",
" \"\"\"Compute m=0 Gaussian beam coefficients using either l^2 or l(l+1).\"\"\"\n",
" ell = np.arange(lmax + 1, dtype=float)\n",
" sigma_sq = fwhm_rad * fwhm_rad / (8.0 * math.log(2.0))\n",
" exponent = ell * (ell + 1.0 if use_l_lplus1 else ell)\n",
" prefactor = np.sqrt((2.0 * ell + 1.0) / (4.0 * math.pi))\n",
" bl = prefactor * np.exp(-0.5 * sigma_sq * exponent)\n",
" return ell, bl\n",
"\n",
"\n",
"def half_power_ell(fwhm_rad: float, lmax: int) -> int:\n",
" \"\"\"Multipole where the Gaussian damping term drops to 50% of its peak.\"\"\"\n",
" sigma = fwhm_rad / math.sqrt(8.0 * math.log(2.0))\n",
" target = 2.0 * math.log(2.0) / (sigma * sigma) # l(l+1) = 2 ln 2 / sigma^2\n",
" ell = int(math.ceil(0.5 * (-1.0 + math.sqrt(1.0 + 4.0 * target))))\n",
" return min(ell, lmax)\n",
"\n",
"\n",
"def compare_beams(fwhm_rad: float, lmax: int) -> BeamComparison:\n",
" ell, bl_old = beam_coefficients(fwhm_rad, lmax, use_l_lplus1=False)\n",
" _, bl_new = beam_coefficients(fwhm_rad, lmax, use_l_lplus1=True)\n",
" pct_diff = 100.0 * (bl_new - bl_old) / bl_old\n",
" ell_hp = half_power_ell(fwhm_rad, lmax)\n",
" pct_hp = pct_diff[ell_hp]\n",
" extreme_idx = int(np.argmin(pct_diff))\n",
" return BeamComparison(\n",
" ell=ell,\n",
" blm_old=bl_old,\n",
" blm_new=bl_new,\n",
" pct_diff=pct_diff,\n",
" ell_half_power=ell_hp,\n",
" pct_half_power=pct_hp,\n",
" pct_extreme=float(pct_diff[extreme_idx]),\n",
" ell_extreme=int(ell[extreme_idx]),\n",
" )\n",
"\n",
"\n",
"def beam_window(bl: np.ndarray) -> np.ndarray:\n",
" \"\"\"Return the usual beam window function B_ell^2.\"\"\"\n",
" return bl * bl"
]
},
{
"cell_type": "markdown",
"id": "548330d4",
"metadata": {},
"source": [
"## Single-beam comparison: 1° FWHM (typical CMB smoothing)\n",
"The plots below overlay the old vs new coefficients and show the percent shift.\n",
"The marker highlights the half-power multipole: where the Gaussian damping term\n",
"reduces the beam to 50% of its zero-mode amplitude. This is a simple, common\n",
"way to describe beam width in harmonic space."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "51765912",
"metadata": {
"execution": {
"iopub.execute_input": "2025-12-11T18:18:28.803666Z",
"iopub.status.busy": "2025-12-11T18:18:28.803278Z",
"iopub.status.idle": "2025-12-11T18:18:29.845290Z",
"shell.execute_reply": "2025-12-11T18:18:29.843504Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"FWHM = 60.0 arcmin; ell_half_power = 159; percent change there = -0.436%\n",
"Most negative percent change within [0, 2000] = -5.345% at ell = 2000\n"
]
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 900x700 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fwhm_arcmin = 60.0\n",
"lmax = 2000\n",
"fwhm_rad = math.radians(fwhm_arcmin / 60.0)\n",
"comparison = compare_beams(fwhm_rad, lmax)\n",
"\n",
"print(\n",
" f\"FWHM = {fwhm_arcmin:.1f} arcmin; ell_half_power = {comparison.ell_half_power}; \"\n",
" f\"percent change there = {comparison.pct_half_power:.3f}%\"\n",
")\n",
"print(\n",
" f\"Most negative percent change within [0, {lmax}] = \"\n",
" f\"{comparison.pct_extreme:.3f}% at ell = {comparison.ell_extreme}\"\n",
")\n",
"\n",
"fig, (ax_top, ax_bottom) = plt.subplots(\n",
" 2,\n",
" 1,\n",
" figsize=(9, 7),\n",
" sharex=True,\n",
" gridspec_kw={\"height_ratios\": [3, 1]},\n",
")\n",
"\n",
"ax_top.semilogy(\n",
" comparison.ell,\n",
" comparison.blm_old,\n",
" label=PREVIOUS_RELEASE,\n",
" color=\"#1b9e77\",\n",
" linewidth=1.6,\n",
")\n",
"ax_top.semilogy(\n",
" comparison.ell,\n",
" comparison.blm_new,\n",
" label=CURRENT_RELEASE,\n",
" color=\"#d95f02\",\n",
" linewidth=1.6,\n",
")\n",
"ax_top.set_ylabel(r\"$|b_\\ell|$\")\n",
"ax_top.set_title(rf\"blm_gauss change at FWHM = {fwhm_arcmin:.1f} arcmin, $\\ell_{{\\max}}$ = {lmax}\")\n",
"ax_top.legend(loc=\"upper right\", frameon=False)\n",
"ax_top.grid(alpha=0.3)\n",
"\n",
"ax_bottom.plot(\n",
" comparison.ell,\n",
" comparison.pct_diff,\n",
" color=\"#7570b3\",\n",
" linewidth=1.5,\n",
")\n",
"ax_bottom.axhline(0.0, color=\"black\", linestyle=\"--\", linewidth=0.9)\n",
"ax_bottom.plot(\n",
" [comparison.ell_half_power],\n",
" [comparison.pct_half_power],\n",
" marker=\"o\",\n",
" color=\"#e7298a\",\n",
" label=f\"Half-power ℓ={comparison.ell_half_power}\",\n",
")\n",
"ax_bottom.set_ylabel(\"Percent diff\\n(new - old)/old\")\n",
"ax_bottom.set_xlabel(r\"Multipole $\\ell$\")\n",
"ax_bottom.grid(alpha=0.3)\n",
"ax_bottom.legend(loc=\"lower left\", frameon=False)\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "26fbeff6",
"metadata": {},
"source": [
"## How the window function shifts for different beams\n",
"The beam window function is $B_\\ell^2$. Here we plot the fractional change of\n",
"$B_\\ell^2$ for three beam sizes to see how the impact grows with narrowing beams."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "3ad1392e",
"metadata": {
"execution": {
"iopub.execute_input": "2025-12-11T18:18:29.849487Z",
"iopub.status.busy": "2025-12-11T18:18:29.849169Z",
"iopub.status.idle": "2025-12-11T18:18:30.226273Z",
"shell.execute_reply": "2025-12-11T18:18:30.224469Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/tmp/ipykernel_3614767/797072927.py:10: RuntimeWarning: invalid value encountered in divide\n",
" frac = (beam_window(comp.blm_new) - beam_window(comp.blm_old)) / beam_window(comp.blm_old)\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAA3kAAAHWCAYAAADKJUDHAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjcsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvTLEjVAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAxYlJREFUeJzs3Xd0FFUfxvHvbnohCYSE3qW3QJCOFAsqRVBAAZFmAUWl+YqihCIgCAiCAoqKoqICCkgVFaX3Ir1Ih1BDAiGk7rx/rERCQgtJZrN5Pufs0czOzjyzN1nyy71zr8UwDAMRERERERFxClazA4iIiIiIiEjGUZEnIiIiIiLiRFTkiYiIiIiIOBEVeSIiIiIiIk5ERZ6IiIiIiIgTUZEnIiIiIiLiRFTkiYiIiIiIOBEVeSIiIiIiIk5ERZ6IiIiIiIgTUZEnInIHBg8ejMViMTsGAEeOHMFisTB9+vR7Ptaff/6JxWJh9uzZ9x7MgVksFgYPHpxhx2vUqBGVKlXKsONlV126dKF48eIOf8z0iI6O5vnnnyd//vxYLBZ69+5tdqQ0OdJnk4g4DhV5ImK66dOnY7FY0nwMGDAgy3LExMQwePBg/vzzzyw7p4g4phEjRjB9+nR69uzJjBkz6NSpk2lZ9NkkInfL1ewAIiLXDB06lBIlSqTYlpW9JTExMQwZMgSw99Rc75133snSglMy1tWrV3F11T95Ge2zzz7DZrOZHSNT/PHHH9SuXZuwsDCzo+izSUTumv7FExGH8dhjj1GjRo072jc2NhZ3d3es1qwZkODq6qoiIRvz9PQ0O4JTcnNzMztCpjl79iwVKlQwO8Zt6bNJRNKi4Zoi4vCu3Tf2/fff884771CoUCG8vb25dOkSERER9O/fn8qVK+Pr64ufnx+PPfYY27dvT3Wc2NhYBg8eTJkyZfD09KRAgQI8+eST/PPPPxw5coSgoCAAhgwZkjxc9Np9XGnd95KYmMiwYcMoVaoUHh4eFC9enLfffpu4uLgU+xUvXpzmzZuzatUqatasiaenJyVLluTrr79Osd/dXMudioyMpE+fPhQvXhwPDw8KFy7Mc889x/nz51PsZ7PZGD58OIULF8bT05MHH3yQgwcPpthn5cqVtG3blqJFi+Lh4UGRIkXo06cPV69eTbFfly5d8PX15eTJk7Rq1QpfX1+CgoLo378/SUlJKfa9cOECnTp1ws/Pj4CAADp37sz27dvTvOdw7969tGnThjx58uDp6UmNGjWYP3/+Hb0PN96Td609Dx48SJcuXQgICMDf35+uXbsSExNzR8cE2Lx5M3Xr1sXLy4sSJUowZcqUVPvExcURFhbGfffdl/y+/e9//0v1ffLll1/SpEkTgoOD8fDwoEKFCkyePDnV8a59P/3555/UqFEDLy8vKleunDyU76effqJy5cp4enoSGhrK1q1bb3kNkZGRuLi48NFHHyVvO3/+PFarlcDAQAzDSN7es2dP8ufPn/z1jffPXbtfdMyYMXz66afJPxv3338/GzduTHXuuXPnUqlSJTw9PalUqRI///xzmhmvXLlCv379KFKkCB4eHpQtW5YxY8akyPbkk09SvXr1FK9r0aIFFoslxffJ+vXrsVgsLF68OM1zXfu8OXz4MAsXLkz+LDhy5Ejy0PIjR46k+Zrrh1Neu29z9+7dNG7cGG9vbwoVKsTo0aNTndPRP5tEJPvRn35ExGFERUWlKj7y5s2b/P/Dhg3D3d2d/v37ExcXh7u7O7t372bu3Lm0bduWEiVKcObMGaZOnUrDhg3ZvXs3BQsWBCApKYnmzZvz+++/88wzz/D6669z+fJlli1bxs6dO3nooYeYPHkyPXv2pHXr1jz55JMAVKlS5aZ5n3/+eb766ivatGlDv379WL9+PSNHjmTPnj2pflk9ePAgbdq0oXv37nTu3JkvvviCLl26EBoaSsWKFQE4dOjQHV3LnYqOjqZBgwbs2bOHbt26Ub16dc6fP8/8+fM5ceJEivf2/fffx2q10r9/f6Kiohg9ejQdO3Zk/fr1yfvMmjWLmJgYevbsSWBgIBs2bGDixImcOHGCWbNmpTh3UlISTZs2pVatWowZM4bffvuNsWPHUqpUKXr27AnYC8sWLVqwYcMGevbsSbly5Zg3bx6dO3dOdS27du2iXr16FCpUiAEDBuDj48OPP/5Iq1atmDNnDq1bt76r9+aadu3aUaJECUaOHMmWLVuYNm0awcHBjBo16ravvXjxIo8//jjt2rWjffv2/Pjjj/Ts2RN3d3e6deuWfI0tW7Zk1apVvPjii5QvX54dO3bw4Ycfsn//fubOnZt8vMmTJ1OxYkVatmyJq6srv/zyCy+//DI2m41XXnklxbkPHjxIhw4deOmll3j22WcZM2YMLVq0YMqUKbz99tu8/PLLAIwcOZJ27dqxb9++m/Z6BwQEUKlSJVasWMFrr70GwKpVq7BYLERERLB79+7k79GVK1fSoEGD27433333HZcvX+all17CYrEwevRonnzySQ4dOpTc+/frr7/y1FNPUaFCBUaOHMmFCxfo2rUrhQsXTnEswzBo2bIly5cvp3v37oSEhLB06VLeeOMNTp48yYcffghAgwYNmDdvHpcuXcLPzw/DMFi9ejVWq5WVK1fSsmXL5GuwWq3Uq1cvzezly5dnxowZ9OnTh8KFC9OvXz+A5ELrbly8eJFHH32UJ598knbt2jF79mzefPNNKleuzGOPPQZkj88mEcmGDBERk3355ZcGkObDMAxj+fLlBmCULFnSiImJSfHa2NhYIykpKcW2w4cPGx4eHsbQoUOTt33xxRcGYIwbNy7V+W02m2EYhnHu3DkDMMLCwlLtExYWZlz/kblt2zYDMJ5//vkU+/Xv398AjD/++CN5W7FixQzAWLFiRfK2s2fPGh4eHka/fv3u+loOHz5sAMaXX36ZKuf1Bg0aZADGTz/9dNNrvvbeli9f3oiLi0t+fsKECQZg7NixI3nbje+9YRjGyJEjDYvFYhw9ejR5W+fOnQ0gRWbDMIxq1aoZoaGhyV/PmTPHAIzx48cnb0tKSjKaNGmS6voefPBBo3LlykZsbGyKa6hbt65RunTpW74PhmGkatdr7dmtW7cU+7Vu3doIDAy87fEaNmxoAMbYsWOTt8XFxRkhISFGcHCwER8fbxiGYcyYMcOwWq3GypUrU7x+ypQpBmCsXr06eVta72/Tpk2NkiVLpth27ftpzZo1yduWLl1qAIaXl1eKtpg6daoBGMuXL7/l9bzyyitGvnz5kr/u27ev8cADDxjBwcHG5MmTDcMwjAsXLhgWi8WYMGFC8n6dO3c2ihUrlvz1te/NwMBAIyIiInn7vHnzDMD45ZdfkreFhIQYBQoUMCIjI5O3/frrrwaQ4phz5841AOO9995LkblNmzaGxWIxDh48aBiGYWzcuNEAjEWLFhmGYRh///23ARht27Y1atWqlfy6li1bGtWqVbvl+2EY9ve5WbNmKbZd+6w6fPhwiu3Xfo6uf5+vfY98/fXXydvi4uKM/PnzG0899VTytuzw2SQi2Y+Ga4qIw/j4449ZtmxZisf1OnfujJeXV4ptHh4eyT0USUlJXLhwAV9fX8qWLcuWLVuS95szZw558+bl1VdfTXXe9Ew/vmjRIgD69u2bYvu1v/ovXLgwxfYKFSqk6AEJCgqibNmyHDp06K6v5U7NmTOHqlWrptnLdeM1d+3aFXd39+Svr2W9Pt/17/2VK1c4f/48devWxTCMNIcE9ujRI8XXDRo0SHG8JUuW4ObmxgsvvJC8zWq1puq1ioiI4I8//qBdu3ZcvnyZ8+fPc/78eS5cuEDTpk05cOAAJ0+evOV7cTNpZbxw4QKXLl267WtdXV156aWXkr92d3fnpZde4uzZs2zevBmw936WL1+ecuXKJec+f/48TZo0AWD58uXJr7/+/b3Wq92wYUMOHTpEVFRUinNXqFCBOnXqJH9dq1YtAJo0aULRokVTbb/+fU9LgwYNOHPmDPv27QPsvV0PPPAADRo0YOXKlYC9d88wjDvqyXv66afJnTt3iuNfnyM8PJxt27bRuXNn/P39k/d7+OGHU90Ht2jRIlxcXJJ7Ga/p168fhmEkD7usVq0avr6+rFixIvkarg1P3rJlCzExMRiGwapVq+7oGjKCr68vzz77bPLX7u7u1KxZM0V7ZIfPJhHJfjRcU0QcRs2aNW858cqNM2+CfTjchAkT+OSTTzh8+HCKe74CAwOT//+ff/6hbNmyGTZBwdGjR7Fardx3330ptufPn5+AgACOHj2aYvv1v3hfkzt3bi5evHjX13Kn/vnnH5566qk72vfGfNd+Qb8+37Fjxxg0aBDz589PsR1IVYR4enqmGt524/UePXqUAgUK4O3tnWK/G9/TgwcPYhgG7777Lu+++26a+c+ePUuhQoVudYlputV1+/n53fK1BQsWxMfHJ8W2MmXKAPZ702rXrs2BAwfYs2fPTYf6nT17Nvn/V69eTVhYGGvXrk11X2BUVFSKYujG3NeeK1KkSJrbb2yvG137Jf9aYbR161bee+89goKCGDNmTPJzfn5+VK1a9ZbHSivfjd9P134+Spcuneq1N/5R4+jRoxQsWJBcuXKl2K98+fIpjuXi4kKdOnWSi9JrQ0vr169PUlIS69atI1++fERERGRZkVe4cOFUhVru3Ln5+++/k7/ODp9NIpL9qMgTkWzjxl48sK9l9e6779KtWzeGDRtGnjx5sFqt9O7dO0umdr/Tv7S7uLikud24buIIM6/ldvmSkpJ4+OGHiYiI4M0336RcuXL4+Phw8uRJunTpkirfzY6XHteO3b9/f5o2bZrmPjf+Qnun7qRd7oXNZqNy5cqMGzcuzeevFWX//PMPDz74IOXKlWPcuHEUKVIEd3d3Fi1axIcffnjH7296r6dgwYKUKFGCFStWULx4cQzDoE6dOgQFBfH6669z9OhRVq5cSd26de9oRtvMfl9vpn79+gwfPpzY2FhWrlzJwIEDk+85XLlyJfny5QNId5F3s5/3GycUusas9wEy9rNJRLIfFXkikq3Nnj2bxo0b8/nnn6fYHhkZmWJikVKlSrF+/XoSEhJuOu373QyNKlasGDabjQMHDiT3KACcOXOGyMhIihUrdpdXcufXcqdKlSrFzp077/p1admxYwf79+/nq6++4rnnnkvefuOQ2rtRrFgxli9fTkxMTIrevBtn9SxZsiRgn67/oYceSvf5MtqpU6e4cuVKit68/fv3AyTPOFmqVCm2b9/Ogw8+eMvvr19++YW4uDjmz5+fomfl+uGcma1BgwasWLGCEiVKEBISQq5cuahatSr+/v4sWbKELVu2JK/Vdq+u/XwcOHAg1XPXhoxev+9vv/3G5cuXU/Tm7d27N8Wxrl1DfHw8M2fO5OTJk8nF3AMPPJBc5JUpUya52Ltb13okIyMjU2y/sXfsbmSHzyYRyX50T56IZGsuLi6p/uI8a9asVPdoPfXUU5w/f55JkyalOsa1118rNG78BS4tjz/+OADjx49Psf1aj02zZs3uKP/17vRa7tRTTz3F9u3b05yW/m7/Sn/tr/3Xv84wDCZMmJCubABNmzYlISGBzz77LHmbzWbj448/TrFfcHAwjRo1YurUqYSHh6c6zrlz59Kd4V4kJiYyderU5K/j4+OZOnUqQUFBhIaGAvbZO0+ePJniGq+5evUqV65cAdJ+f6Oiovjyyy8z8xJSaNCgAUeOHOGHH35ILo6sVit169Zl3LhxJCQkZNgwxwIFChASEsJXX32VYqjvsmXL2L17d4p9H3/8cZKSklL97H744YdYLJbkWSrBfg+im5sbo0aNIk+ePMmzQzZo0IB169bx119/3dM1lCpVCiD5vj+w9+J9+umn6T5mdvhsEpHsRz15IpKtNW/enKFDh9K1a1fq1q3Ljh07+Pbbb5N7f6557rnn+Prrr+nbty8bNmygQYMGXLlyhd9++42XX36ZJ554Ai8vLypUqMAPP/xAmTJlyJMnD5UqVaJSpUqpzlu1alU6d+7Mp59+SmRkJA0bNmTDhg189dVXtGrVisaNG2fatdypN954g9mzZ9O2bVu6detGaGgoERERzJ8/nylTptzRvVXXlCtXjlKlStG/f39OnjyJn58fc+bMuaf7dlq1akXNmjXp168fBw8epFy5csyfP5+IiAggZe/Fxx9/TP369alcuTIvvPACJUuW5MyZM6xdu5YTJ07c01qC6VWwYEFGjRrFkSNHKFOmDD/88APbtm3j008/Te6R6dSpEz/++CM9evRg+fLl1KtXj6SkJPbu3cuPP/7I0qVLqVGjBo888gju7u60aNGCl156iejoaD777DOCg4PTLGwzw7XiZ9++fYwYMSJ5+wMPPMDixYuT17vLKCNHjqRZs2bUr1+fbt26ERERwcSJE6lYsSLR0dHJ+7Vo0YLGjRszcOBAjhw5QtWqVfn111+ZN28evXv3Ti68wF4MhYaGsm7duuQ18q5dw5UrV7hy5co9FXkVK1akdu3avPXWW0RERJAnTx6+//57EhMT033M7PDZJCLZj3ryRCRbe/vtt+nXrx9Lly7l9ddfZ8uWLSxcuDDVBBQuLi4sWrSIgQMHsn79enr37s24cePw8/OjcuXKyftNmzaNQoUK0adPH9q3b8/s2bNveu5p06YxZMgQNm7cSO/evfnjjz946623+P777zP1Wu6Ur68vK1eupGfPnixatIjXXnuNTz75hLJly6Zai+x23Nzc+OWXXwgJCWHkyJEMGTKE0qVL39OiyS4uLixcuJCnn36ar776ioEDB1KwYMHknjxPT8/kfStUqMCmTZto1qwZ06dP55VXXmHKlClYrVYGDRqU7gz3Infu3CxatIhNmzbxxhtvcPz4cSZNmpRqttC5c+fy/vvvs2PHDvr375/8PfP6668nT9RStmxZZs+ejcVioX///kyZMoUXX3yR119/Pcuup2zZsgQHBwP2e9uuuVYU1axZEw8Pjww736OPPsqsWbNISkrirbfe4qeffuLLL79MNfmS1Wpl/vz59O7dmwULFtC7d292797NBx98kOa9jtfyXn8N+fPnT75v8157I7/99lvq1q3L+++/z4gRI2jcuDHvv/9+uo+XHT6bRCT7sRi6s1ZERBzI3Llzad26NatWrbrpgtUiIiJycyryRETENFevXk0xa2pSUhKPPPIImzZt4vTp02nOqCoiIiK3pnvyRETENK+++ipXr16lTp06xMXF8dNPP7FmzRpGjBihAk9ERCSd1JMnIiKm+e677xg7diwHDx4kNjaW++67j549e9KrVy+zo4mIiGRbKvJERERERESciGbXFBERERERcSIq8kRERERERJyIJl65SzabjVOnTpErV64UC/WKiIiIiIjcjGEYXL58mYIFC2K1Zm5fm4q8u3Tq1Kl0L0wsIiIiIiI52/HjxylcuHCmnkNF3l3KlSsXAEePHiUgIMDcMDmYzWbj3LlzBAUFZfpfQuTm1A6OQ23hGNQOjkHt4BjUDo5B7eA4IiMjKVasWHI9kZlU5N2la0M0/fz88PPzMzlNzmWz2YiNjcXPz08fWCZSOzgOtYVjUDs4BrWDY1A7OAa1g+Ow2WwAWXLLl1paRERERETEiajIExERERERcSIq8kRERERERJyIijwREREREREnoiJPRERERETEiajIExERERERcSIq8kRERERERJyIijwREREREREnoiJPRERERETEiajIExERERERcSIq8kRERERERJyIijwREREREREnoiJPRERERETEiajIExERERERcSIq8kRERERERJyIijwREREREREnoiJPRERERETEiajIExERERERcSIq8kRERERERJyIijwREREREREnoiJPRERERETEiajIExERERERcSI5tsj7+OOPKV68OJ6entSqVYsNGzaYHUlEREREROSe5cgi74cffqBv376EhYWxZcsWqlatStOmTTl79qzZ0URERERERO5Jjizyxo0bxwsvvEDXrl2pUKECU6ZMwdvbmy+++MLsaCIiIiIiIvfE1ewAWS0+Pp7Nmzfz1ltvJW+zWq089NBDrF279o6P893qvXgH5MPFasFqteBi+e+/KbZZSHu7lTT2/Xf7rY5nBavluufTOJ7FYsmMt05ERERERLKBHFfknT9/nqSkJPLly5die758+di7d2+q/ePi4oiLi0v++tKlSwBYl7XiXGIoPyfV4xj5ccmVF4vVhcRL58FISt7f4uKOi29ujMR4kq5cTHFsq5cfVncvkmKiMBJiUzzn6m/Plxh1JsV2i5snLt7+2OKvYrt6KcVzLj65sbi6k3TlItakBKxWe5Hp4uKCR0AwVpuNpOjz/xaMYLFa8PDKhbtPLmyxV7DFRqcoIr3zBOPm6kZs1DmsRtK/RagFN3cPfALyYiTFER8V8e957M/5+OfGy8uH2OiL2OKuYrmuWM2TvxAuVguXzp767zUW8PL2wT93HuJjY7h6ORIr/xWtAXmD8fL05PLFcyQmxCcXzi4urnj6+OJ3MpbI82evK6Yhl38AAf4BxERfIvpylL0QxoLFaqFgwUK4u7txLvwkhi0pOYeXpxf5C+QjIS6O8+fO/ls829+j4LxB+Pn5cvHCBa7GXElRRBcvXhyAI0eOpGgLX19f8ubNS3R0NOfPn0/xXP78+fH09OT06dPExv7X7q6urhQuXJjExEROnDiR4jUBAQEEBAQQGRlJZGRkiucKFy6Mq6srJ06cIDExMXm7p6cn+fPnJzY2ltOnT6d4Td68efH19eX8+fNER0eneO5urslmsxEREYGvry/e3t5OcU3XZLd2utYWAMHBwU5xTddkp3a6dOkSERERREdHY7VaneKasmM7xcTEcOzYseR2cIZryo7tVLBgQQzD4NixY9hsNqe4puzYTjabjcTERPLmzes01wTZs52ioqLIMkYOc/LkSQMw1qxZk2L7G2+8YdSsWTPV/mFhYQZw28fgd/sZnT753fDOkz/F9sD7qhrNxy83ar48LtVryrTpb9QbucwIqvZwqueqhC02Kg1anGq7T6UHjWJvLjACH++d6rl87UcYxd5cYHgUqZRiu4tfsFHszQVGoR6fp3qNf732RrE3Fxj+9dqneq5Qj8+NYm8uMFz8glNs9yhSySj25gIjX/sRqV4T+Hhvo9ibCwyfSg+meq7YmwuMYm8ucKprKjNwoVH+nUWpX1PtYaPWe78aJZ/qn+q56j3GGo+M/cPIU6pqiu3eefIZT036y2g29IdUrwlp0c14/vPVRvUnuqV6rtv4n41+3603/PIWSPl+V6huDPlps9Ft2NRUr2nfe4gxYfF2o+ZDLVM998UfO42vlu9Ktb3R462Mn9fuNV59Z2Sq58ZMnWEs33bQCKlRK8X2AgULGZv2HjEW/L4y1Wt6vd7HOHj0hPF6776pntuwYYMRHh5uFC5cOMX2OnXqGOHh4cacOXNSvWb8+PFGeHi40a5du1TPhYeHG+Hh4am2t2vXzggPDzfGjx+f6rk5c+YY4eHhRp06dVJsL1y4sBEeHm5s2LAh1Wv69etnhIeHG/369TPtmtq2bet01+SM7aRrytxrmjVrltNdU3Zsp3Xr1hm7d+92qmvKru308ssvGydPnnSqa8qu7QQYUVFRmV7zWAzDMMhB4uPj8fb2Zvbs2bRq1Sp5e+fOnYmMjGTevHkp9k+rJ69IkSKUGlaKDt5BdD22CwsGhf0suPgGcaJwSxLKPwn+hYDM+YtBYGAgly5Hc/bsOWyGQZJhYDMM8gblw83dg9OnTxNzNZYkw8AwDCxWF4ILFCI+PoFTJ09gMyDJZn+NTy4/vHP5ExUZyaWoyOTtNgPyBBfAYnXhTPhJEhISk8/j6uaBX54grsZe5eL5cyTZDIx/j+nlF4C7pzdRkRe4euUKNgNsNvvx/IMLkmQYXAg/ac9ms2d38fDC0zeA2KsxXIm6aL+mf3N45MqD1c2DyxfPkRAfl3wsw2LF6h2AxQJXLp7D9u+xbDYDq5cvLh6+xF65TELM5X/fI+zZffNis1iJjTxLUlLiv+8FGC6uuPjkJiE+jsToiyne80zrcY2+iJEUf92LXHD1y4thSyLpcsq/Blk9fLB6+mKLjcYWdyXl8RypFzmDrsndPwhXFxeSoi9gNWz2nl0suLp74O6XB0tSAolXLtqHKFvsvbSevv64e3nbryk+FovFgsu/PdO5ggriYrEQE3E6eZvVCp6ePnj75yYp7irx0VHJPdlWiwW/PHnx8PAkJuoCRmI8VgtYLBbc3FzJHVQAjCSiz5/57zVWC75+/uTK5U/slUvEXrmcvN3FAnnzFcDd3Y3Is6cxrvWMWyx4enmSNyiYxPg4oiLOYcGS3JOcOzCQXLlyceliBLFXY+w91v9eV9GixbFaLYSfOIbVYgEMLkVFUrRIYfLly0fMlStcjDifoie7UIECeHt7Of1fSs28pms9eXny5FFPnonXFBMTw+7du5PbwRmuKTu2U8GCBbl48SJxcXHqyXOAnrz77ruPS5cuOcU1QfZsp6ioKKpXr05UVBR+fn5kphxX5AHUqlWLmjVrMnHiRMD+zV+0aFF69erFgAEDbvnaS5cu4e/vT/nJ5fHw8WBO408oeeBP2PIVXA7/dy8L3PcQ1OgGpR8Blxw3KjbT2Ww2zp49S3BwcPI/4BnF+LfIvVZoJl1XQF77/2tF7fX72P+b+nXGTbbbbClfZzOue/7646Xa154v9b7XH5cUuf7bl1tkuNVxSbHv9fskJCaCxeWG9yH18a4/h5jrxnt5k4vRf4cvu1zbnuK+X8t1Reb1+153rOu2XStiXW7Yfv39xslDyq9/Pq0Myfv+V7inneG/56/P4WK94XUprpc09r35td3qml3+LbYz67NJ7lxm/hshd07t4BjUDo4jMjKS3LlzZ0mRlyOrj759+9K5c2dq1KhBzZo1GT9+PFeuXKFr1653fIx6BeqxLnId7+36jM8f+RzLA2/A/sWw6Qv45w84uMz+8CsEoV2gWifwK5B5FyUZxmKx96K4WDWBze2k5x+OWxXRqbbfooi+XXFtu0Wheasi+vqi+3ZFdOrj3qyIvlWG/4rotAritN8HI7mXPCkdRXSSzSAJA5Juv6/cPZd/7xFOu6hMWcD+V2DerNi9YdIt640FbOpC05LG9psV0ZY0tt8sg+XfjGkfN2W+m21P/fq7/cMBmlxMROQO5Mgi7+mnn+bcuXMMGjSI06dPExISwpIlS1JNxnIrfUL70PnPzmw8vZEFhxbQolQLKP/v48I/sHk6bP0GLp2E5cPhz/eh3OP23r0SjUB/SZEcSkV05rhWcAcFBYHFmqowtP1b0N6uiE5dTN68iL6xKL9ZEW2ksf1mRfTNe8lTF9FGGttvVkSnznCzIvq6Y6W3iDYgKenarReS0VIVxDcU0deeN2w23N1ccLFab1pE36q4vr6Itlium+36NkW0xcIN+968iP7vuGkXuymKYeuNGdIuom88z9394UBFtIizyJHDNe/FteGaFy9eZPbx2UzYMoE8nnmY32o+/h7+KXdOiIU9v8Cmz+HYdcsz5CkJoV0hpCP4BGbtBTgJDT1wDGoHx6G2yBo39kT/VxDaC9qExCTOnjtH7jyBGFhuOxQ6rSL6+h7lWxXRN+/5Tn2uWxXXNxbRtyqu7zxD6iI61R8S0llES+ZKq4i+dS9uymI5+Xmr/Q96SYmJeHq437IXN3UBe/Ph32kXuymL29THTV1EpyqGb1FE367nOs0CP43jmVVE698Hx5GVwzVV5N2l64s8n1w+tP2lLf9E/UPbMm0ZVGfQzV94Zjds/hK2fw9x/05a4eIBFVvZe/eK1AL99eyO6QPLMagdHIfawjGoHe6Nca0398bi7yY90Wntm2QzSEyycf5CBP4BARhY/t33xqLy5kX0zY6bVo/3f8XqrYvomw2xvlkP+u1737llhhvPdW1/Mde1gjhl7/Cti+i0eoevFdGpiuE0t0NCfBzeXl64WK3/Fa9pFNc3K07T3H5DEX2r4vrG1yf/YeAOeqhvtca0IxTRd0P35GUTbi5uvFP7Hbou7crs/bNpdV8rqgRVSXvnfBXg8Q/gwTDYOcfeuxe+Hf7+wf4Irgg1ukKVp8EzcxtdRETEEVn+7TWyYsHNJf3HsdlsnHWPIzg4t4rtG6TZg3pDQXm74tqWRvGY+riQmJTExcgofHP5YcB/RXKaxW7KIvr6WbNvXUSTxr43L6Lv9NpSFPq3KaKv3/e2778BNtOGc1+8/S7Z3LWCOGURmHYRnTz52E0L2DSK4bSK6GtF6I3FcBpFdNzV6NtfRAZRkXePauSvQctSLZn/z3yGrRvGzGYzcbXe4m318IXQzvbHyc32iVp2zIGzu2BRf1gWBpXbwP3doUDVrLsQERERcXpWq+Wei+g7Ze/Ztuaonu1bFdG2GwvRWxSaNw6FTquITlW43qSITkyyEXXpMt4+Psk927crov/r+b59EZ26l/z2ve8p34e0i2ibce28d15EGwYkGgaOOvbbFheTZedSkZcB+tXox5/H/2RvxF5m7p1Jpwqd7uyFhULtj0eG23vzNn4O5/fZl2PY8pX9uRrdoOKT4O6dqdcgIiIiIvcmK4voO+VMw8hvdi9vmoVoGoXmzYZCp1VEpyrKb9ETnWo49k2K6OjLlxiZRe+VirwMkMczD71DezN07VAmbZ3EI8UeIZ/Pnc/UiVcA1HoJar4IR9fYe/d2z7P39J3cDEvfhqod7MM5g8pm2nWIiIiIiDgqRyyi70ZkZGSWFXnZu5x3IE+VfooqQVWISYxh9MbR6TuIxQLF60Gbz6HvHnhoMAQUg9goWD8ZPq4J05vb7+lLjM/Q/CIiIiIi4hxU5GUQq8XKoNqDcLG48OvRX1l1ctW9HdA3COr3gde2Qcc5ULYZWKxwZCXM7gYfVoDfBsPFIxmQXkREREREnIWKvAxUNk9ZOpTvAMDwdcOJTYy994NarVD6IWj/HfTeCQ0HQK4CcOUcrPoQJoTAN21g7yKwJd37+UREREREJFtTkZfBXgl5hWDvYE5En2DajmkZe3D/QtD4Lei9A57+Bko2Bgw4uAy+bw/jq8Bfo+FSeMaeV0REREREsg0VeRnMx82HATUHAPD5zs85HHU440/i4gblW8Bzc+HVLVD3NfDKA5dOwPLh8GFF+KET/LMcbLaMP7+IiIiIiDgsFXmZ4KGiD1G/UH0SbYkMXzccw8jEtToCS8Ejw+wTtTz5GRStA0YS7JkPM1rBpFBY/RHERGReBhERERERcRgq8jKBxWLh7Vpv4+HiwfrT61l0eFHmn9TNE6q0g25LoOdauP8FcM8FEYdg2bswthz89CIcW2dfKVJERERERJySirxMUiRXEV6s8iIAozeO5lL8paw7eb4K0GwM9NsLLT6CAlUhKc6+4PoXTWFyPdjwGcRmYSYREREREckSKvIyUZeKXSjuV5yI2Ag+2vJR1gfw8IXQzvDSCnjhD6j2LLh6wdldsKi/vXfvl9chfHvWZxMRERERkUyhIi8Tubu4807tdwD4cd+P7Dy/07wwhULhiY/tvXuPjoK8ZSHhCmyeDlMfgM+awNZvIT7GvIwiIiIiInLPVORlsloFatG8ZHMMDIauHUqS2WvZeQVA7R7wynrosggqtQGrG5zcDPNehnHlYPEAOLff3JwiIiIiIpIuKvKyQL8a/cjlnos9EXv4ft/3Zsexs1igeD1o87l9Zs6HBkNAMYiNgvWT4eP7YXpz2DkHEuPNTisiIiIiIndIRV4WyOuVl9ervQ7AxK0TORtz1uREN/ANgvp94LVt0HEOlG0GFiscWQmzu8GHFeC3IXDxiNlJRURERETkNlTkZZE2ZdpQOW9lriRc4YONH5gdJ21WK5R+CNp/B713QMM3wTc/XDkHq8bBhBD4pg3sWwxmDzsVEREREZE0qcjLIi5WF96t/S5Wi5UlR5aw5tQasyPdmn9haPw29NkJT38DJRsDBhxcBjOfgfFV4M9RcOmU2UlFREREROQ6KvKyUPnA8rQv1x6A4euGE5cUZ3KiO+DiBuVbwHNz4dUtUPc18MoDl07AnyPgw0rwfUc48BvYbGanFRERERHJ8VTkZbFeIb0I8gri2OVjfL7jc7Pj3J3AUvDIMPtELU9Og6J1wUiCvQvg26fgo6qwcixEO9g9hyIiIiIiOYiKvCzm6+7L/2r+D4BpO6Zx9NJRkxOlg5snVGkL3RbDy+uhVk/w9IfIY/D7UBhXHn7sDIf+VO+eiIiIiEgWU5FngqbFmlK3YF0SbAkMXzccwzDMjpR+weXgsfeh715oNRkK1wRbIuyeC18/AZNCYfVHcOWC2UlFRERERHIEFXkmsFgsDKw1EHerO2vD17L0yFKzI907d28I6QDPL4Meq+H+58E9F0QcgmXv2hdZn90djqyG7FzUioiIiIg4OBV5JinqV5TnqzwPwKiNo7gcf9nkRBkofyVoNhb67YUWH0HBapAUDztnw/TH4eNasG4yXL1odlIREREREaejIs9E3St1p5hfMc5fPc+krZPMjpPxPHwhtDO8+Kf9Ub0zuPnA+X2wZACMLQc/94DjG9S7JyIiIiKSQVTkmcjdxZ2BtQYC8P2+79l1YZfJiTJRwWrQ8iN7716zsZCvMiTGwvaZ8PnDMLkebPgMYqPMTioiIiIikq2pyDNZnYJ1eKz4Y9gMG8PWDiPJlmR2pMzl6We/X6/HSuj+G4R0BFcvOLsLFvW39+7N6wUnt5idVEREREQkW1KR5wDeuP8NfN182XVhF9/v+97sOFnDYoEi90OrT6DfHnh0FASVg4QY2DoDPmsMUx+ATV9CXLTZaUVEREREsg0VeQ4gyDuI16u/DsDErRM5c+WMyYmymFduqN0DXl4HXZdA5Xbg4gHh22FBb3vv3oI+EP632UlFRERERByeijwH0bZMW6rkrcKVhCuM2jjK7DjmsFigWB146jP7vXuPDIfA+yD+Mmz6AqY2gM8ehK3f2Hv8REREREQkFRV5DsLF6sKgOoNwsbiw7OgyVpxYYXYkc3nngbq9oNcm6PwLVGwNVjc4uQnmvYJlXHlyrXoPzu4xO6mIiIiIiENRkedAyuYpy7PlnwVg+LrhxKi3yt67V+IBaDsd+u6BhwZDQDEscZfw2TkD65S68MWjsP0HSIg1O62IiIiIiOlU5DmYl0NeJr9Pfk5dOcWUv6eYHcex+AZB/T7w2jZsHecQW+JhDIsLHFsLP78I48rB0oFw/oDZSUVERERETKMiz8F4u3nzds23AZixawb7L+43OZEDslqhVBMim07C6L0DGg8Ev8Jw9SKsnQSTasD05rBzDiTGm51WRERERCRLqchzQI2LNubBog+SaCQydO1QbIbN7EiOK1cBaPg/6P03dPgRyjwKFiscWQmzu8G48rAsDCIOmZ1URERERCRLqMhzUANqDsDb1Zvt57Yz58Acs+M4PqsLlGkKHX6A1/+Ghm/aC8CY87B6PHxUDb5uBbvnQ1KC2WlFRERERDKNijwHld8nP72q9QLgw80fcv7qeZMTZSMBRaDx29B7Jzz9LZR6ELDAoeXwYyf4sCL8Pgwij5mdVEREREQkw6nIc2Dty7WnfJ7yXI6/zAcbPzA7Tvbj4grlm0Onn+D1bVC/L/gEQfQZWDkGxleBb9vC3kWQlGh2WhERERGRDKEiz4G5Wl0JqxOG1WJl0eFFrDm1xuxI2Vfu4vBQGPTZbV+OoURDwIADv8L37WFCFfjzfbh0yuSgIiIiIiL3RkWeg6uYtyLPlH0GsK+dF5cUZ3KibM7V3b6weuf58OoWqPsqeOWBSyfhz5HwYSWY2QEOLANbktlpRURERETumoq8bODVaq8S7BXMscvH+Ozvz8yO4zwCS8Ej79kXWX9yGhSrB0YS7FsI37aBj0JgxRi4fMbspCIiIiIid0xFXjbg6+7LmzXfBODznZ9zKErLAWQoN0+o0ha6LoKX10OtnuDpb5+Y5Y9h8GEF+PE5+Gc52LSchYiIiIg4NhV52cTDxR6mQaEGJNoSGbZ2GIZhmB3JOQWXg8feh377oNVkKFwTbImwex7MaAWTQmH1BLii2U5FRERExDGpyMsmLBYLA2sPxNPFk01nNjHvn3lmR3Jubl4Q0gGeXwY9VsP9z4N7Lvui6ssG2RdZn90NDq8EFdwiIiIi4kBU5GUjhXwL0TOkJwBjN43lYuxFkxPlEPkrQbOx0G8vtPgIClaDpHjYOQe+ag6TasCaiXDlgtlJRURERERU5GU3nSp0onTu0kTGRTJu8ziz4+QsHr4Q2hle/NP+CO0C7r5w4SD8+g6MKwezu8ORVerdExERERHT5Jgi78iRI3Tv3p0SJUrg5eVFqVKlCAsLIz4+3uxod8XN6sag2oMAmHtwLhtPbzQ5UQ5VsBq0mGDv3Ws+HgqE/Nu7NxumN1PvnoiIiIiYJscUeXv37sVmszF16lR27drFhx9+yJQpU3j77bfNjnbXQoJDaFumLQDD1g0jPil7FapOxSMX1OgKL/2l3j0RERERcQg5psh79NFH+fLLL3nkkUcoWbIkLVu2pH///vz0009mR0uX16u/Th7PPByOOsyXO780O45AGr17VdW7JyIiIiJZztXsAGaKiooiT548t9wnLi6OuLi45K8vXboEgM1mw2bimmm53HLxRo03eGvVW3z696c0LdaUon5FTcuT1Ww2G4ZhmNoGN+XmA9U72x+ntmHZMh12zsHyb++e8ftQKN8So3oXKFYXLBazE6ebQ7dDDqO2cAxqB8egdnAMagfHoHZwHFnZBjm2yDt48CATJ05kzJgxt9xv5MiRDBkyJNX2c+fOmX4/X6h3KNUDq7PlwhbCVoXxfuj7WLJxwXA3bDYbUVFRGIaB1erAHdKuBaHm21hCXsPz4EK8d/+A2/ldsHM2lp2zSQwoQUz5p7la5gkMr1v/wcERZZt2yAHUFo5B7eAY1A6OQe3gGNQOjiMqKirLzmUxsvmq2gMGDGDUqFG33GfPnj2UK1cu+euTJ0/SsGFDGjVqxLRp02752rR68ooUKcKFCxcICAi4p+wZ4dilYzz1y1PE2+IZWX8kj5d43OxIWcJms3Hu3DmCgoKy3wfW9b178dEAGC7u2bJ3L1u3g5NRWzgGtYNjUDs4BrWDY1A7OI7IyEgCAwOJiorCz88vU8+V7Yu8c+fOceHCre9xKlmyJO7u7gCcOnWKRo0aUbt2baZPn37X3+yXLl3C39+fixcvOkSRBzB1+1QmbZtEHs88zG81H38Pf7MjZTqbzcbZs2cJDg7Ovh9YcZdhx2zY/CWEb/9ve2Bp+wQuVduDT6Bp8e6EU7SDk1BbOAa1g2NQOzgGtYNjUDs4jsjISHLnzp0lRV62H64ZFBREUFDQHe178uRJGjduTGhoKF9++aXTfKN3rdSVhYcXcjjqMBO2TGBQnUFmR5I7cW1mzhpd4dRW2PSlvei7cAB+HQi/D4EKT9gLvmL1sk3vnoiIiIiYyzmqnDtw8uRJGjVqRNGiRRkzZgznzp3j9OnTnD592uxo98zdxZ13a78LwKz9s9h2dpu5geTuFawGLT+C/vug+YeQv4p9Zs4ds/6dmfN+WDMJYiLMTioiIiIiDi7HFHnLli3j4MGD/P777xQuXJgCBQokP5zB/fnv54lSTwAwdN1QEmwJJieSdPHIBTW6QY+V9nX3qne2z9Z5rXdvbFmY87zW3RMRERGRm8oxRV6XLl0wDCPNh7PoV6MfAR4BHLh4gBm7Z5gdR+6VevdEREREJB1yTJGXE+T2zE2/Gv0AmLxtMiejT5qcSDLEHffurVbvnoiIiIioyHM2T5R6ghr5ahCbFMuI9SOcqqdSuE3v3uPwcU1Y+7F690RERERyMBV5TsZisfBunXdxtbqy4sQKfjv2m9mRJDPcrHfv/H5Y+rZ690RERERyMBV5Tqikf0m6V+oOwPvr3yf63wW3xUld693rt1e9eyIiIiKiIs9ZvVDlBYrmKsrZq2f5aOtHZseRrODp91/v3gvL1bsnIiIikkOpyHNSHi4evFvHvnbe93u/5+9zf5ucSLJUoerq3RMRERHJoVTkObHaBWrTomQLDAyGrB2itfNyotv27pWDOS+od09ERETEiajIc3L97+9PgEcA+y/u19p5OV2avXtxsONH9e6JiIiIOBEVeU4uj2eeFGvnnbh8wuREYjr17omIiIg4NRV5OcATpZ6gZv6axCbF8t6697R2nvxHvXsiIiIiTkdFXg5gsVh4t/a7uFvdWX1qNYsPLzY7kjiaa717L634t3fvOfXuiYiIiGRTKvJyiOL+xXmxyosAjNo4iqi4KJMTiUOyWP7t3Zuo3j0RERGRbEpFXg7SrVI3SvmXIiI2gnGbx5kdRxzdHfTuWX5+EbdTG9W7JyIiIuJAVOTlIG4ubgyqMwiAnw78xKbTm0xOJNnCLXr3LDtmETj/WSyf1II1E+HKebPTioiIiOR4KvJymOr5qtOmTBsAhqwdQnxSvMmJJFtJ0bv3B0b1zthcvbFcOAC/vmO/d29WVzj0J9hsZqcVERERyZFU5OVAvav3JtAzkCOXjvD5js/NjiPZkcUChUIxmo/n3HMrsTUfDwWrgS0Bdv0EXz8BE6vDynFw+YzZaUVERERyFBV5OZC/hz8Dag4A4LMdn3Eo6pDJiSQ7M9x97WvtvfinvYevRnfw8IOLh+H3IfBhBfjhWTj4m3r3RERERLKAirwcqmnxptQvVJ8EWwLD1g7T2nmSMQpUhebj7PfuPfExFK4JtkTY8wt88xRMqAp/fQCXTpmdVERERMRpqcjLoSwWC+/UfgcvVy82ndnE3INzzY4kzsTdB6o9C88vg55roVYP8PSHqGOw/D34sCLMbA/7loAtyey0IiIiIk5FRV4OVsi3EC9XfRmAMZvGcOHqBZMTiVPKVwEeGwX99kHrT6FoXTBssG8RzHwaxleG5SMg8rjZSUVEREScgoq8HO7ZCs9SLk85LsVfYvTG0WbHEWfm5gVVn4Zui+GVDVCnF3jlgUsn4a9R9mLvmzawZwEkJZidVkRERCTbUpGXw7laXRlcZzBWi5VFhxex+uRqsyNJThBUFpoOt9+799TnUOIBwICDy+CHjvbhnL8PhYtHzE4qIiIiku2oyBMq5q1Ih3IdABi2bhhXE6+anEhyDFcPqNwGOv8Cr26Ber3BJwiiz8DKsfaJWr5uBbt+hkSt6SgiIiJyJ1TkCQC9qvUin3c+TkafZMr2KWbHkZwosBQ8PAT67IZ2X0OpJoAFDi2HWV1gXHn49V248I/ZSUVEREQcmoo8AcDHzYeBtQYC8NWur9gXsc/kRJJjubpDhSeg08/w+jZo0B9880PMeVjzkX2R9enNYcdsSIg1O62IiIiIw1GRJ8kaF23MQ0UfIslIYujaoSRpansxW+7i8OC70GcXPPMdlG4KFiscWQlzusO4crDkbTinP0qIiIiIXKMiT1IYUHMAPm4+/H3+b37c/6PZcUTsXFyhXDPo+CP03gGN3gK/QnD1Iqz7GD6uCV88CttmQoLuKRUREZGcTUWepJDPJx+vV38dgAlbJnDmyhmTE4ncwL8wNBpgL/Y6zIKyzcDiAsfWwtweMLYsLHoDzuwyO6mIiIiIKVTkSSrtyrSjSlAVriRcYeSGkWbHEUmb1QXKPALtv7MP52zyDgQUhdgo2PApTK4Lnz0IW2ZA/BWz04qIiIhkGRV5koqL1YWwOmG4Wlz5/djv/HHsD7MjidyaXwF44A14bTs8+5N94harK5zcBPN7wZiysKAPnNpmdlIRERGRTKciT9JUJncZOlfsDMCI9SO4kqCeEMkGrFa470H7Egx998BDQyBPSYi/DJu+gE8bwtSG9v+PvWR2WhEREZFMoSJPbqpH1R4U9i3MmZgzTNw60ew4InfHNxjq94Zem+G5+VDpKXBxh/Bt9l69seVgXi84sRkMw+y0IiIiIhlGRZ7clKerJ+/WeReA7/Z8x87zO01OJJIOViuUbAhtvoC+e+GR4RBYGhKuwNYZMK0JTKkPGz6Dq5FmpxURERG5Zyry5JbqFqxLs5LNMDAYsnYIibZEsyOJpJ9PINTtBb02QtfFUOVpcPGAMzthUX97797PPeHYOvXuiYiISLalIk9u640ab+Dv4c/eiL18s/sbs+OI3DuLBYrVhSc/hX574dFREFwBEq/C9u/gi6bwSW1Y+wnERJidVkREROSuqMiT2wr0CqRfaD8APt72MScunzA5kUgG8s4DtXtAzzXQ/TcIeRZcveDcXlj6lr13b87zcGSVevdEREQkW1CRJ3ek1X2tuD///cQmxfLe+vcw9MuuOBuLBYrcD60+hv77oNlYyF8ZkuJgxyyY3gwm1YDVH8GV82anFREREbkpFXlyRywWC+/Wfhc3qxurT65myZElZkcSyTye/nD/8/DSSnhhOVTvDO6+cOEgLHvX3rs3qwv8sxxsNrPTioiIiKSgIk/uWAn/ErxQ5QUA3t/wPlFxUSYnEslkFgsUqg4tP7Lfu9diAhSsDrYE2PUzzGgFE6vByrFw+bTZaUVEREQAFXlyl7pX6k5J/5JExEYwdtNYs+OIZB2PXBDaBV5cbu/hu/958PCDi0fg96EwrgLM7AD7l4Ityey0IiIikoOpyJO74u7iTlidMAB+PvgzG8I3mJxIxAQFqtjv2eu3F574BIrUAiMJ9i2E79rBh5Xgj+Fw8ajZSUVERCQHUpEnd616vuq0K9MOgCFrhxCbGGtyIhGTuPtAtY7Q/Vd4eT3UfgW88sDlU7BiNEyoCjNaw665kBhvdloRERHJIVTkSbr0Du1NsFcwxy4fY+rfU82OI2K+4HLw6Ah7716bL6BkI8CAf/6AWZ1hXHn49R04f8DspCIiIuLkVORJuuRyz8Xbtd8GYPrO6eyL2GdyIhEH4eoBlZ6C5+bBa9ugQT/wzQ8x52HNRPsyDF88Btu/h/gYs9OKiIiIE1KRJ+n2YNEHeajoQyQaiQxeM5gkTTYhklKeEvDgIOizC56ZCWUeA4sVjq2Bn1+yL8WwsD+E/212UhEREXEiKvLknrxV6y1yueVi54WdzNw70+w4Io7JxRXKPQ4dvrcXfE3egYCiEBcFGz+DqQ3g00aw6QuIvWR2WhEREcnmVOTJPQn2DqZ3aG8APtr6EaeiT5kbSMTR+RWEB96A17ZDp5+hYmuwusGprbCgD4wtC/NegeMbwDDMTisiIiLZUI4s8uLi4ggJCcFisbBt2zaz42R7bcq0oXpwda4mXmXYumEY+sVU5PasVijVBNpOt0/W8shwyFsGEmJg6zfw+cPwSR1Y+wnERJidVkRERLKRHFnk/e9//6NgwYJmx3AaVouVsLphuFndWHVyFYsPLzY7kkj24pMX6vaCVzZAt6VQtQO4esG5PbD0LXvv3uxucOgvsNnMTisiIiIOLscVeYsXL+bXX39lzJgxZkdxKiX9S/JClRcAGLVxFJGxkeYGEsmOLBYoWhtaT7b37jUbC/mrQFI87JwDX7eEidVh5Vi4fNrstCIiIuKgclSRd+bMGV544QVmzJiBt7e32XGczvOVnqeUfykiYiMYs0lFtMg98QqA+5+HHivhxb+gRjdwzwUXD8PvQ2FcBZjZAfYvhaREs9OKiIiIA3E1O0BWMQyDLl260KNHD2rUqMGRI0fu6HVxcXHExcUlf33pkn3mO5vNhk3DplJwsbgQVieMzks6M++feTQr0YxaBWplyrlsNhuGYagNTKZ2yCL5q8DjY+GhobB7HpatX2M5vh72LYR9CzFyFYSqHbAWfRRb3rxmp83R9DPhGNQOjkHt4BjUDo4jK9sg2xd5AwYMYNSoUbfcZ8+ePfz6669cvnyZt956666OP3LkSIYMGZJq+7lz54iPj7+rY+UEBShAiyItmH98PoNXD+bTep/i4eKR4eex2WxERUVhGAZWa47qkHYoagcTFHwICj6ES8RBvPfOwmv/XKyXT2FZNYYgxhJXuC5Xy7clrviD4OJudtocRz8TjkHt4BjUDo5B7eA4oqKisuxcFiObT4V47tw5Lly4cMt9SpYsSbt27fjll1+wWCzJ25OSknBxcaFjx4589dVXab42rZ68IkWKcOHCBQICAjLkGpxNdHw0rX9pzdmYs3St2JXe1Xtn+DlsNhvnzp0jKChIH1gmUjs4gMQ4e4/elq+xHv4rebPhnReqPoNRrZN91k7JEvqZcAxqB8egdnAMagfHERkZSWBgIFFRUfj5+WXqubJ9kXenjh07ljzUEuDUqVM0bdqU2bNnU6tWLQoXLnxHx7l06RL+/v5cvHhRRd4tLD+2nNeWv4aLxYXvm39PuTzlMvT4NpuNs2fPEhwcrA8sE6kdHIfNZuPCwc3kPbYYy7ZvIfq6iVmK1oXqz0GFJ8Bd9yNnJv1MOAa1g2NQOzgGtYPjiIyMJHfu3FlS5OWYli5atCiVKlVKfpQpY//LdqlSpe64wJM717hoYx4u9jBJRhKD1wwm0aaJIUQyW5JfEYwm70CfXfDMTCjzGFiscGwNzO0BY8vBwn4Q/rfZUUVERCQT5ZgiT7LeWzXfIpdbLnZd2MW3e741O45IzuHiCuUehw7f2wu+Ju9AQFGIi4KN02BqA/i0EWz6AmIv3fZwIiIikr3k2CKvePHiGIZBSEiI2VGcVpB3EH1r9AXg420fc+LyCZMTieRAfgXhgTfgte3QaS5UbA1WNzi1FRb0sS+0PvcVOL4BcsbofREREaeXIUVeQkICx48fZ9++fURERGTEIcVJPFn6SULzhXI18SrvrXuPHHILqIjjsVqhVGNoO92+0Pojw+0TsiTEwLZv4POH4ZM6sPYTiNHnuIiISHaW7iLv8uXLTJ48mYYNG+Ln50fx4sUpX748QUFBFCtWjBdeeIGNGzdmZFbJhqwWK2F1wnC3urP61GoWHl5odiQR8ckLdXvBKxug21Ko2gFcveDcHlj6lr13b3Y3OPQXaF0lERGRbCddRd64ceMoXrw4X375JQ899BBz585l27Zt7N+/n7Vr1xIWFkZiYiKPPPIIjz76KAcOHMjo3JKNlPAvwUtVXwJg9IbRXIy9aHIiEQHAYoGitaH1ZOi/D5qNtS+8nhQPO+fA1y1hYnVYORYun7798URERMQhpGsJhfbt2/POO+9QsWLFW+4XFxfHl19+ibu7O926dUt3SEeiJRTSJyEpgXYL2nEw8iAtS7VkeP3h93Q8TQfsGNQOjiND2+LUNtjyFfw9C+Iv27dZXKDMo/alGO57yD65i6SinwnHoHZwDGoHx6B2cBxZuYRCjlknL6OoyEu/v8/9zbOLnsXAYOrDU6lbsG66j6UPLMegdnAcmdIW8Vdg11zY8jUcX/ff9lwFoVpHqNYJchfLmHM5Cf1MOAa1g2NQOzgGtYPjyLbr5J0/f56FCxcyf/58wsPDM/LQ4gSqBFWhfbn2AAxbO4yriVdNTiQit+TuYy/mui+Fl9dD7VfAKw9cPgUrPoAJVWFGa9j1MyTGm51WRERE/pVhRd6cOXO47777GDJkCGFhYZQqVYovv/wyow4vTuK16q+R3yc/J6JPMHnbZLPjiMidCi4Hj46wz8zZ5gso2Qgw4J8/YFYXGFcOlg6Ec/tMDioiIiLpLvKio6NTfD1kyBA2bNjAhg0b2Lp1K7NmzWLgwIH3HFCci4+bD+/UegeAr3Z/xe4Lu01OJCJ3xdUDKj0Fz82D17ZBg/7gmx9iLsDaSfBxTfj8Edj6jX24p4iIiGS5dBd5oaGhzJs3L/lrV1dXzp49m/z1mTNncHd3v7d04pQaFmlI0+JNsRk2Bq8ZTKIt0exIIpIeeUrAg+9Cn13wzEwo+7h9gpbj62HeKzCmLMx/DU5s1kLrIiIiWSjdRd7SpUv59NNPad26NadOnWLChAk8/fTT5M+fn7x58zJgwAA++eSTjMwqTmRAzQHkcs/Fnog9fLP7G7PjiMi9cHGFco9D+5nQdzc8GAa5S9hn5tzyFUxrApPrwbrJWmhdREQkC6S7yCtevDgLFy6kXbt2NGzYkG3btnHw4EGWLVvGb7/9xrFjx3j88cczMqs4kbxeeXmjxhsAfLztY45fPm5yIhHJELnyQ4O+8NpW6LwAqjwNrp5wdhcsGfDfQuv/LNdC6yIiIpnknidead++PRs3bmT79u00atQIm81GSEgInp6eGZFPnFir+1pRM39NYpNiGbZ2GFrNQ8SJWCxQogE8+al9spbHx0D+yv8ttD6jFXxUFf76AKJOmp1WRETEqdxTkbdo0SLGjh3Lpk2bmDZtGqNHj6Zjx4688cYbXL2q6fHl1iwWC4PqDMLd6s7a8LUsOLTA7Egikhm8ckPNF6DHKnjxL7j/efDwh8hjsPw9GF8Jvm0Le36BpASz04qIiGR76S7y+vXrR9euXdm4cSMvvfQSw4YNo2HDhmzZsgVPT0+qVavG4sWLMzKrOKFifsXoGdITgNEbRxMRq/t1RJxawRBoNtbeu9d6KhSrB4YNDvwKPzwL48rDr+/C+QNmJxUREcm20l3kTZ8+nUWLFvH999+zceNGZsyYAYC7uzvDhg3jp59+YsSIERkWVJxX54qdKZO7DJFxkYzeONrsOCKSFdy9oeoz0HUR9NoM9XqDTzBcOQdrPoJJNeCLR2Hbd1qKQURE5C6lu8jz8fHh8OHDABw/fjzVPXgVKlRg5cqV95ZOcgQ3qxtD6g7BarGy8NBCVp7Q941IjpL3Pnh4iH1mzme+gzKPgsUKx9bC3J72pRh+6Q0nt2gpBhERkTuQ7iJv5MiRPPfccxQsWJCGDRsybNiwjMwlOUylvJV4tvyzAAxdN5QrCfrLvUiO4+IG5ZpBhx/sa+81eRdyF7cvxbD5S/isMUxpAOunaikGERGRW0h3kdexY0eOHz/OvHnzOHLkCE888URG5pIc6JWQVyjkW4jTV04zYcsEs+OIiJn8CsID/eHVrdD5F6jcFlw84MwOWPw/GFsOZneHQ39pKQYREZEb3NPsmoGBgdx///0EBARkUBzJybzdvAmrEwbA93u/Z+vZrSYnEhHTWa1Q4gF4app9spbHPoB8lSEpDnbOhq9bwsRqsOIDuHTK7LQiIiIOIV1F3rFjx+5q/5MntQaS3Jk6BevQ6r5WGBiErQkjLinO7Egi4ii880CtF6HHSnjxT6jRDTz84OIR+OM9+LAifPc07FmgpRhERCRHS1eRd//99/PSSy+xcePGm+4TFRXFZ599RqVKlZgzZ066A0rO079GfwI9AzkcdZhP//7U7Dgi4mgsFihYDZp/CP32QaspULSufSmG/Uvgh44wrgIsC4ML/5idVkREJMu5pudFu3fvZvjw4Tz88MN4enoSGhpKwYIF8fT05OLFi+zevZtdu3ZRvXp1Ro8ezeOPP57RucWJ+Xv483att+n3Vz++2PEFjxR7hLJ5ypodS0Qckbs3hLS3P84fgK0z7MsuXDkLq8fbH8XqQfXnoHxL+/4iIiJOLl09eYGBgYwbN47w8HAmTZpE6dKlOX/+PAcO2Bev7dixI5s3b2bt2rUq8CRdHi72ME2KNCHRSGTwmsEk2ZLMjiQiji5vaXh4KPTdA09/A6Wb2pdiOLoafn4JxpaFBX3h1Dazk4qIiGSqdPXkXePl5UWbNm1o06ZNRuURAcBisTCw9kA2nt7Izgs7+WbPN3Su2NnsWCKSHbi4QfkW9kfUSXvP3tYZEHkUNn1uf+SvDNU7Q+U24JXb7MQiIiIZ6p5m1xTJTMHewfSt0ReASVsncfzycZMTiUi2418IGr4Br22D5+ZBpafAxR1O74BF/e1LMcx5AQ6v1ELrIiLiNFTkiUN7qvRT1Mxfk9ikWIauHYqhX8JEJD2sVijZCNp8YZ+s5dFREFwREmNhx4/wVXP4qBqsHAuXws1OKyIick9U5IlDs1gshNUJw8PFg3Xh65h7cK7ZkUQku/POA7V7QM/V8MIfENoF3HPBxcPw+9B/l2J4BvYugqREs9OKiIjcNRV54vCK+hXllZBXAPhg0wecv3re5EQi4hQsFigUCi0mQP998MQnUKQ2GEmwfzF8395e8P02WEsxiIhItqIiT7KFThU6USGwApfjLzNi/Qiz44iIs3H3gWodoftSeGUj1H0VvPNC9GlY9SFMrA7Tm8P2HyDhqtlpRUREbumui7yrV69y8uTJVNt37dqVIYFE0uJqdWVI3SG4WFxYdnQZvx/73exIIuKsgsrAI+/Zl2JoNwPuexiwwJGV8POLMKYsLOwP4dvNTioiIpKmuyryZs+eTenSpWnWrBlVqlRh/fr1yc916tQpw8OJXK9cnnJ0rdQVgJEbRhKdEG1yIhFxaq7uUKElPDsb+uyExgPBvyjERcHGz2DqA/bHxmlwNdLstCIiIsnuqsh777332Lx5M9u2bePLL7+ke/fufPfddwCa9VCyRI+qPSjuV5xzV8/x6b5PzY4jIjmFf2Fo+D94fTt0+hkqPmlfiiF8OyzsZ19o/aeX4MhqLcUgIiKmu6vF0BMSEsiXLx8AoaGhrFixgtatW3Pw4EEsFgsAO3fuZMOGDYSEhFC9evXk10ZHR+Pu7o67u3sGxpecxsPFg7A6YXRd2pXFJxfz5OknqV2wttmxRCSnsFqhVBP7IyYC/v4BNn8F5/bA399j/ft78voVgxrPQUhH8CtgdmIREcmB7qonLzg4mL///jv56zx58rBs2TL27NmTvH3y5MmsXbuWxYsX07FjR8aNG8fVq1eJi4ujW7duGZtecqQa+WvQtkxbAIauG8rVRE2CICIm8M4DtXvCy2vh+d+hemcMd19cLx3F+sewf5dieBr2LICkBLPTiohIDnJXRd6MGTMIDg5Osc3d3Z2ZM2fy119/ATBq1CjKlCnDqlWriIyMZP78+ZQrV44RI0YQHx+fccklR+tdrTd5PfJy/PJxJm+bbHYcEcnJLBYoXANafoTRdw9RjUZgFKn171IMS+CHjjCuPPz6Dpzbb3ZaERHJASxGJt5MFxcXx4EDBzh37hzh4eFs2bKFMWPGZNbpssSlS5fw9/fn4sWLBAQEmB0nx7LZbMzbOY9BWwdhtVj5rtl3VAysaHasHMdms3H27FmCg4OxWrUii5nUFo4hRTtE/ANbZ8C2mXDl7H87FakF1Z6139fn4WteWCemnwfHoHZwDGoHxxEZGUnu3LmJiorCz88vU8+V7iLvwoULjBw5kpiYGHr06EGVKlUAOHHiBAEBAfj6pv6Hy2azZftvLhV5juHaB9bYfWNZcmQJZXOXZWbzmbhZ3cyOlqPoHw7HobZwDGm2Q1ICHPgVtsyw/9dIsm9384FKraHac1Ckpr1HUDKEfh4cg9rBMagdHEdWFnnpbunnn3+eTz/9lHXr1tGgQQPWr19PSEgIxYoVIzAwkD59+qQ+mb6xJIP9r8b/8PfwZ9/FfUzfOd3sOCIiqbm4Qblm0OF76LsbHhoMgfdBwhXY+g188Qh8XBNWT4Dos7c9nIiIyO2ku+pasWIFc+bMSR6C2bp1awICAvj5558ZOXIk06dPZ8aMGRmZVSSVQK9A3rz/TQCmbJ/C4ajDJicSEbmFXPmhfh/otQm6LrHPwOnmDef3w7JB9nv3vu8I+xZDUqLZaUVEJJtKd5F38eJFKleuDEDnzp05c+YMo0aNomXLlvTt25dx48bxySefZFhQkZtpXrI59QrWI94Wz+A1g7EZNrMjiYjcmsUCxepAq0+g3z5o8REUvh9sibB3Acx8xj4752+D4cI/ZqcVEZFs5p7GT14bfunu7o63tzdBQUHJzzVs2JADBw7cWzqRO2CxWBhUZxBerl5sObuFWftmmR1JROTOefpBaGd4/jd4eR3U6QXegRB9GlZ9CBOrwxePwbbvIP6K2WlFRCQbuKci77vvvmPbtm0kJqYeUuLj48PFixfv5fAid6ygb0Fer/46AB9u+ZDTV06bnEhEJB2Cy0PT4dB3L7SbAaUfAYsVjq2BuT1hTFmY/xqc2ASZNzm2iIhkc+ku8ho0aEBYWBihoaHkypWLmJgYwsLCmDp1Khs3biQmJiYjc4rc1jNln6FKUBWuJFzhvXXvkYmrg4iIZC5Xd6jQEjrOgt47ocm7kLsExF+GLV/BtAfhkzqw9mO4ct7stCIi4mDueZ28AwcOsHnzZrZs2ZL8iIyMxGq1YhgGSUlJGZXVIWgJBcdws+mAD148SNsFbUm0JTL6gdE8VuIxE1M6P03L7DjUFo4hU9vBZoOjq+1r7+2eB4mx9u1WNyj7GFR/Dko1AatLxp43G9LPg2NQOzgGtYPjyMolFFzv9QClS5emdOnSPPPMM8nbDh8+zKZNm9i6deu9Hl7krtyX+z5erPwin2z/hPc3vE+dAnUI8AwwO5aIyL2zWqFEA/vj8Q9gx2x7wXdqK+yZb3/kKgghHeyLrecpYXZiERExSbrL+UGDBrF58+Y0nytRogRt27ZlxIgR6Q4mkl7PV36e+wLuIyI2gtEbR5sdR0Qk43n6w/3d4cU/ocdqqNUTvHLD5VOwcgx8FALTm8PfP0LCVbPTiohIFkt3kXfixAkee+wxChcuTM+ePVm8eDHx8fEZmU0kXdxc3BhSdwgWLPxy6BdWnVxldiQRkcyTvxI89r59KYY2X9qHbGKBIyvhpxfsk7Us6Gvv8dO9yiIiOUK6i7wvvviC06dPM3PmTHLlykXv3r3JmzcvTz31FF9//TUREREZmVPkrlQJqkLH8h0BGLp2KFcSNO24iDg5Vw+o9CR0+hl674BGb4N/UYiLgk2fw6eNYEp9WDcFYvRvtIiIM7vndfIaNGjA6NGj2bdvH+vXr6dWrVpMnTqVggUL8sADDzBmzBhOnjyZUXnv2cKFC6lVqxZeXl7kzp2bVq1amR1JMsmr1V6lkG8hwq+EM2HLBLPjiIhknYAi0OhNeH07dJoLldqAiwec2QlL3oSxZWFWV/jnD/uELiIi4lQydIqd8uXL87///Y/Vq1dz/PhxOnfuzMqVK5k5c2ZGnibd5syZQ6dOnejatSvbt29n9erVdOjQwexYkkm83bwZVGcQADP3zmTzmbTvIRURcVpWK5RqDG0+h3574bEPIH9lSIqHXT/BjNYwoQosHwmRx8xOKyIiGeSel1DILhITEylevDhDhgyhe/fu6T6OllBwDHczHfCg1YP4+eDPFPMrxuwWs/F09cyilM5P0zI7DrWFY8g27RC+HbbMgB0/QmzUvxstULIhVOsE5ZqDW/b9rMw27eDk1A6OQe3gOBx6CYWrV68SERFBoUKFUmzftWsXFStWzLBgGW3Lli2cPHkSq9VKtWrVOH36NCEhIXzwwQdUqlTppq+Li4sjLi4u+etLly4B9h8Ym4a4mMZms2EYxh21Qd/Qvqw6uYqjl47y8baP6VO9TxYkzBnuph0kc6ktHEO2aYd8leGx0fDQENi7AMu2b7Ec/gsO/QmH/sTwDIAq7TBCnrX3/GUz2aYdnJzawTGoHRxHVrbBXfXkzZ49O3mCFZvNxmeffUatWrUAqF69Olu2bMm0oPfq+++/p3379hQtWpRx48ZRvHhxxo4dy6+//sr+/fvJkydPmq8bPHgwQ4YMSbV97969+Pv7Z3ZsuQmbzUZUVBT+/v539FepNWfXELY1DCtWPqr9EWX9y2ZBSud3t+0gmUdt4Riyczu4XDqO176f8Nr7Ey5XTidvT8hbkZhyTxFbugWGR+b+5TmjZOd2cCZqB8egdnAcUVFRlCtXLkt68u6qyAsJCWHp0qXky5ePzZs307lzZ95++206dOhAtWrV2Lp1Kzt37mTDhg2EhIRQvXr15NdGR0fj7u6Ou7t7hl7AgAEDGDVq1C332bNnD1u2bKFjx45MnTqVF198EbD30hUuXJj33nuPl156Kc3XptWTV6RIES5cuKDhmiay2WycO3eOoKCgO/7AenPlmyw5soTSAaWZ+fhM3FzcMjml80tPO0jmUFs4BqdoB1sSHPoTy7ZvYO9CLLYEAAxXTyjXHKNaJyheHyyOe31O0Q5OQO3gGNQOjiMyMpLAwEDHG66ZkJBAvnz5AAgNDWXFihW0bt2agwcPYrFYAJg8eTLx8fGEh4czduxYQkND6dmzJ3FxcfTo0YNvvvkmQy+gX79+dOnS5Zb7lCxZkvDwcAAqVKiQvN3Dw4OSJUty7NjNbzb38PDAw8Mj1Xar1aofFJNZLJa7aoe3ar3F+vD1HIg8wBe7v6Bn1Z6ZnDBnuNt2kMyjtnAM2b4drFYo87D9ceWC/b69LTOwnN0FO2dj2TkbAopBtWchpAP4FzY7cZqyfTs4CbWDY1A7OIasfP/v6kzBwcH8/fffyV/nyZOHZcuWsWfPnuTto0aNokyZMqxatYrIyEjmz59PuXLlGDFiRKYslh4UFES5cuVu+XB3dyc0NBQPDw/27duX/NqEhASOHDlCsWLFMjyXOJ48nnkYUHMAAJ/+/SkHLh4wOZGIiIPzCYTaPaHnanjhDwjtCh5+EHkUlg+HDyvBN0/BrrmQmPH/xouISPrcVU/ejBkzcHVN+RJ3d3dmzpxJr169APD19eWNN97gjTfeIC4ujgMHDnDu3DnCw8OTe/vM4OfnR48ePQgLC6NIkSIUK1aMDz74AIC2bdualkuy1mMlHmPx4cX8eeJPwtaEMeOxGbhYXcyOJSLi2CwWKBRqfzQdAXvm22fnPLoKDv5mf3gHQpWn7bNz5qtw+2OKiEimuasir3Dhmw/JqFevXqptHh4eKWaufOaZZ+7mdBnugw8+wNXVlU6dOnH16lVq1arFH3/8Qe7cuU3NJVnHYrHwTu132DRvEzvO7+CbPd/QuWJns2OJiGQf7t5Q9Rn748I/sO1b2PYdXA6HdZ/YH4VC7cM5Kz0FnpqkTEQkq6V7YOiFCxfo378/L7/8coohnCdOnCA6Ojrtk5k8DtjNzY0xY8Zw5swZLl26xLJlyxx62QfJHPl88tG/Rn8AJm6dyNFLR01OJCKSTQWWggcHQe+d0OFHKN8CrK5wcjMs6ANjysJPL8LhFaDp20VEsky6q67nn3+eTz/9lHXr1tGgQQPWr19PSEgIxYoVIzAwkD59tBaZOK4nSz9JrQK1iEuKI2xNGDZDv3yIiKSbiyuUaQpPfwN998Ij70FQOUi8Cn//AF+1gI9C4K/REHnc7LQiIk4v3UXeihUrmDNnDlu2bGHMmDG0bt2agIAAfv75Z0aOHMn06dOZMWNGRmYVyTAWi4XBdQbj5erF5jObmbVvltmRREScg28Q1H0VXl4Hz/+eerKW8ZXh61awYzYkxJqdVkTEKaW7yLt48SKVK1cGoHPnzpw5c4ZRo0bRsmVL+vbty7hx4/jkk08yLKhIRiucqzCvV38dgHGbxxEeHW5yIhERJ2KxQOEa0GI89NsHrT+F4g0AAw4thzndYWwZWNgfTm2FO1+2V0REbuOebpK7do+du7s73t7eBAUFJT/XsGFDDhzQFPXi2NqXa09IUAgxiTEMWTcEQ79kiIhkPHdvqPo0dFkAr22DB/4HfoUhNgo2fgafNoIp9WHdZPvafCIick/uqcj77rvv2LZtG4mJiame8/Hx4eLFi/dyeJFMZ7VYGVJvCO5Wd1afXM0vh34xO5KIiHPLUwKaDITef0Onn+0zcLp4wJmdsGQAjC0LPz4H+3+FpNS/X4iIyO3d1RIK12vQoAFhYWFER0fj7u5OfHw8YWFh1K9fn+rVq5M3b96MzCmSaUr6l6RnSE8mbJnAqA2jqFuwLnm99P0rIpKprC5Qqon9ERMBO+fA1m8gfBvsnmd/5CoAVdvbl2MILGV2YhGRbCPdRd5ff/0FwIEDB9i8eTNbtmxhy5YtvPXWW0RGRpq68LnI3epcsTO/HvmVPRF7GLF+BOMajTM7kohIzuGdB2q+YH+c3gFbv7XPynk5HFaNsz+K1rUXexWeAA9fsxOLiDi0dBd515QuXZrSpUunWOj88OHDbN68mZkzZ97r4UWyhJvVjaH1htJ+QXuWHV3GsqPLeLjYw2bHEhHJefJXhsfeh4eHwL7F9sXWD/4Gx9bYH4vegEqtoVonKFLLPsGLiIikkOGrk1++fJlly5YxevRo5s6dm9GHF8k05fKUo2ulrgAMXzecyNhIcwOJiORkrh5QsRV0nAV9dtkXXc9TEhKu2Id1ftEUJtWAVR/CJc2OLCJyvQwr8lasWEHnzp3Jnz8/77zzDkWKFMmoQ4tkmR5Ve1DSvyQXYi8weuNos+OIiAiAX0Fo0A9e3QJdF0NIR3DzgQsH4bfB8GEF+LYd7J4PifFmpxURMd09FXmnT5/m/fffp3Tp0jz++OMkJiYya9YsTp06xZAhQzIqo0iWcXdxZ0jdIViw8MuhX1hxYoXZkURE5BqLBYrVhVafQP990HISFKkNhg0OLIUfO8G4cliWDsT1wj6z04qImCbdRV6LFi0oWbIkK1euZPDgwZw5c4Zvv/2Wxx9/HFdXV028ItlWSHAIz1Z4FoCha4cSHR9tciIREUnFIxdU7wTdl0KvTVCvN/jmh5gLWNZ/Qt5ZLbFMawIbp8HVSLPTiohkqXQXeQsXLuTJJ59kyJAhdOzYER8fn4zMJWKqV6u9SmHfwpyJOcOHmz80O46IiNxK3tL2iVr67IIOP2KUa4FhdcVyaiss7Gdfe2/O83DoT7DZzE4rIpLp0l3krVmzBi8vL5o0aULZsmUZOnQo//zzT0ZmEzGNl6sXQ+rahxz/uP9HNp7eaHIiERG5LRdXKNMUo93XnO20EtsjwyG4AiTGwo5Z8PUTMKEqLB8JF4+anVZEJNOku8irXbs2n332GeHh4bz55pv8+uuvlClThtq1azNx4kTOnDmTkTlFslzNAjVpU6YNAGFrwriaeNXkRCIicqcMrzxQ+2XouQZeWA41uoOHP0Qdg7/ehwlV4KuW8PcsSNDnu4g4l3ueXdPHx4du3bqxatUqdu/ezQMPPMCIESN46KGHMiKfiKn6hvYl2DuY45eP8/HWj82OIyIid8tigULVofk4+2QtT06DEg3tzx3+C356HsaUhQV94ORmMAxz84qIZIAMXSevbNmyjB49mhMnTvDTTz/RrFmzjDy8SJbL5Z6LsDphAMzYM4Md53aYnEhERNLNzQuqtIXO8+H1v6HRW+BfFOKiYNMX8FkTmFwX1n4MV86bnVZEJN0yfDF0ABcXF1q1asX8+fMz4/AiWeqBwg/QrGQzbIaNQWsGEZ+kNZhERLK93MWg0QB4fTs8Nw8qtwVXTzi7G5a+bZ+s5fuOsG8JJCWanVZE5K5kSpEn4mzevP9N8njm4WDkQT7b8ZnZcUREJKNYrVCyETw1Dfrtg2bjoGB1sCXC3gUw82n7YuvLwuD8AbPTiojcERV5Incgt2du3qr1FgDT/p7Gvggtsisi4nS8AuD+7vDicvuELbVfAe9AiD4Dq8fDpBrw+SOw5WuIu2x2WhGRm1KRJ3KHmhZrSpMiTUg0Ehm0ZhCJNg3fERFxWvkqwqMjoO9eePobKPMoWKxwfD3MfxXGlIGfe8KR1ZqsRUQcjoo8kTtksVh4p/Y75HLPxe4Lu/lq11dmRxIRkczm6g7lW0CHH6DPbnhoMATeBwkxsP07mP44TKwOK8ZA1Emz04qIACryRO5KkHcQ/7v/fwB8su0TDkcdNjmRiIhkGb8CUL8P9NoE3X6Fap3A3RciDsEfw2B8JfimDez6GRLjzE4rIjmYijyRu/REqSeoV7Ae8bZ4Bq0eRJItyexIIiKSlSwWKFoLnphkn6zliU+gaF0wbHBwGczqYp+dc/GbcFpL74hI1lORJ3KXLBYLYXXC8HHzYdu5bXy751uzI4mIiFk8fKFaR+i2GF7dAg36Qa4CcPUirJ8CU+rDlAawfirERJidVkRyCBV5IulQwLcAfUP7AjBx60SOXTpmciIRETFdYCl4cBD02QUdZ0OFJ8DqBqf/hsX/s/fu/fgc7P9Va++JSKZSkSeSTm3LtKVW/lrEJsUyaM0gbIbN7EgiIuIIrC5Q+mFo97V9OOejoyB/ZUiKh93z4Lu28GFF+9p75/abnVZEnJCKPJF0slgsDKk3BC9XLzaf2cz3e783O5KIiDgan0Co3QN6rIKXVkKtHuCVB6JP29fe+/h+mPYQbPoSYqPMTisiTkJFnsg9KORbiD6hfQAYv2U8xy8fNzmRiIg4rAJV4LFR9t69dl//u/aeC5zYCAt6w5iyMOcFOPQn2DQ6RETST0WeyD16uuzT1MhXg6uJVxm8ZrCGbYqIyK25utvv1+vwA/TdDQ8PhbxlIfEq7PgRvn4CJlSF5SPg4hGz04pINqQiT+QeWS1WhtQdgqeLJxtOb2D2/tlmRxIRkewiV36o9zq8sh6e/x1Cu4KHP0Qdg79G2Yu96c1h20yIv2J2WhHJJlTkiWSAon5Feb366wCM3TSWU9GnTE4kIiLZisUChWtAi/HQfx88OQ1KNgIscGQlzO0BY8rAvFfg6FowDJMDi4gjU5EnkkE6lO9AteBqxCTGMHjNYAz9AywiIunh5gVV2sJz86D3Dmj8DuQuAfHRsPUb+PJRmBgKK8ZA1Emz04qIA1KRJ5JBrBYrQ+sOxcPFg7Xha/n54M9mRxIRkewuoAg0fANe2wpdFkFIR3DzgYh/4I9hML4SzHgSds6BhFiz04qIg1CRJ5KBivsXp1dILwA+2PgBp6+cNjmRiIg4BYsFiteDVp9A//3wxMdQtC4YNvjnd5jdDcaWgYX94OQWDecUyeFU5IlksE4VOlElbxWiE6IZsnaIhm2KiEjG8vCFas9Ct8Xw6hZ44A3wK2xfZ2/jNPisMUyuC2smQvRZs9OKiAlU5IlkMBerC8PqDcPd6s6qk6uY/898syOJiIizCiwFTd6B3n9Dp5+hUhtw8YCzu+HXd2BceZjZHvYsgKQEs9OKSBZRkSeSCUoGlKRnSE8ARm0cxdkY/SVVREQykdUFSjWBNp/bh3M2GweFQsGWCPsWwQ8dYWw5WPI2nNlldloRyWQq8kQySZeKXagYWJHL8ZcZtnaYhm2KiEjW8AqA+7vDC3/Ay+ug7qvgEwwx52Hdx/ahnFMbwobPICbC7LQikglU5IlkElerK8PqDcPV6sqfJ/5k4eGFZkcSEZGcJrg8PPIe9N0N7X+A8i3A6gbh22BRfxhbFmZ1gQPLwJZkdloRySAq8kQyUencpXmpyksAvL/hfc5fPW9yIhERyZFc3KDso/D0N9BvLzz6PuSrDEnxsOtn+LYNfFgRfhsM5w+anVZE7pGKPJFM1r1yd8rlKUdUXBTD1w3XsE0RETGXT16o3RN6roKXVkDNl8ArN1wOh1UfwqRQ+PwR2PwVxF4yO62IpIOKPJFM5mZ1sw/btLjy27HfWHp0qdmRRERE7ApUhcdHQ7990PYrKP0IWKxwfD388hqMKQM/vQSHV4DNZnZaEblDKvJEskC5POV4vsrzAIxYN4KIWN3oLiIiDsTVAyq2go6zoM9ueGgwBJaGxKvw9/fwVQv4qCr8+T5cPGp2WhG5DRV5IlnkxcovUjp3aS7GXWTE+hFmxxEREUmbXwGo3wd6bYTuv0FoF/Dwg8hj8OdImFAFpjeH7d9DfIzZaUUkDSryRLKIm4t92KaLxYWlR5by29HfzI4kIiJycxYLFLkfWkywD+d88jMo0RCwwJGV8PNL9uGc81+FY+tB95yLOAwVeSJZqGJgRbpW6grAsHXDiIyNNDeQiIjInXD3hirtoPN86P03NHobAopB/GXY8jV88QhMuh9WjoNL4WanFcnxclSRt3//fp544gny5s2Ln58f9evXZ/ny5WbHkhymZ9WelPIvRURsBO9vfN/sOCIiIncnoCg0ehNe2wZdFkLVDuDmDRcOwO9D4MMK8E0b2D3XvkSDiGS5HFXkNW/enMTERP744w82b95M1apVad68OadPnzY7muQg7i7uDKs3DKvFysJDC/nz+J9mRxIREbl7VisUrw+tJ0P//dByEhStA4YNDi7DOrsrwV/Xx7L4DTi1VcM5RbJQjinyzp8/z4EDBxgwYABVqlShdOnSvP/++8TExLBz506z40kOUzmoMp0rdAZg6NqhRMVFmZxIRETkHnjkguqdoNsSeHULNOiHkasg1rgoLBunwaeNYHI9WPsxRJ8zO62I08sxRV5gYCBly5bl66+/5sqVKyQmJjJ16lSCg4MJDQ01O57kQC+HvExxv+Kcu3qO0RtHmx1HREQkYwSWggcHYbz+NxHNpmFUfBJcPODsLlj6NowrBzPbw54FkKjhnCKZwdXsAFnFYrHw22+/0apVK3LlyoXVaiU4OJglS5aQO3fum74uLi6OuLi45K8vXboEgM1mw6ZFQU1js9kwDCNbt4G71Z0hdYbQZWkX5v8zn6bFmlK/UH2zY90VZ2gHZ6G2cAxqB8egdnAMNizEFa5PUrXWWOMuwa45WLbNxHJqM+xbBPsWYXgHQuW2GFU7QP7KZkd2Svp5cBxZ2QYWw8jeA6QHDBjAqFGjbrnPnj17KFu2LK1atSIhIYGBAwfi5eXFtGnTmD9/Phs3bqRAgQJpvnbw4MEMGTIk1fa9e/fi7++fIdcgd89msxEVFYW/vz9Wa/bukJ6ydwpzjs4hr0deptWbho+bj9mR7pgztUN2p7ZwDGoHx6B2cAw3aweXiIN47f8Zr/3zcIn5b+hmQmBZrpZ5ktgyLbB5BZoR2Snp58FxREVFUa5cOaKiovDz88vUc2X7Iu/cuXNcuHDhlvuULFmSlStX8sgjj3Dx4sUUb2rp0qXp3r07AwYMSPO1afXkFSlShAsXLhAQEJAh1yB3z2azce7cOYKCgrL9B9bVxKu0W9COY5eP8eR9TxJWJ8zsSHfMmdohu1NbOAa1g2NQOziG27aDLRH+WY5l+0zYtxDLvzNxGlZXuO9hjJCOUPphcHHP4uTORT8PjiMyMpLAwMAsKfKy/XDNoKAggoKCbrtfTEwMQKpvbqvVesuuUw8PDzw8PFJtt1qt+kExmcVicYp28HH3YUjdIXRd2pWfDv5E0+JNqVuortmx7piztIMzUFs4BrWDY1A7OIZbtoPVHco2tT9iImDXT7DtOywnN8P+xVj2LwbvQKjcDkI6QIEqWX8BTkI/D44hK9//HNPSderUIXfu3HTu3Jnt27ezf/9+3njjDQ4fPkyzZs3Mjic5XI38NWhfrj0Ag9cOJjo+2uREIiIiWcg7D9z/PLzwB7y8Huq9Dr75IeYCrJ8MUxtodk6Ru5Bjiry8efOyZMkSoqOjadKkCTVq1GDVqlXMmzePqlWrmh1PhN7Ve1PItxDhV8IZu3ms2XFERETMEVwOHh4KfXZBx9lQsbV9yOaZnZqdU+QOZfvhmnejRo0aLF261OwYImnydvNmWL1hdFvajdn7Z/NwsYepWzD7DNsUERHJUC6u9nvySj+cYjgnJ/+bnVPDOUXSlmN68kSyg/vz3588bDNsTZiGbYqIiICGc4rcJRV5Ig6md/XeFPYtzOkrpxmzaYzZcURERByLhnOK3JaKPBEH4+3mzdB6QwGYc2AOq0+uNjmRiIiIA7o2nLPtdOi3D5qNhUKh9qUZ9i2CHzraC77FAyD8b7PTimQpFXkiDuj+/PfToVwHwD5s83L8ZZMTiYiIODAN5xRJQUWeiIN6vfrrFMlVhDMxZzRsU0RE5E7d8XDOXzScU5yWijwRB3Vttk0LFn468BMrT6w0O5KIiEj2cdvhnM/C2LKw+E0I3252WpEMpSJPxIGF5gulY/mOgH2R9Evxl0xOJCIikg3dbDjn1QhYPwWmPqDhnOJUVOSJOLjXqr9G0VxFORtzlg82fmB2HBERkexNwzklB1CRJ+LgvFy9kodtzj04lxUnVpgdSUREJPvTcE5xYiryRLKB6vmq82yFZwEYsmYIUXFRJicSERFxIhrOKU5GRZ5INvFqtVcp5leMs1fPMnrjaLPjiIiIOCcN5xQnoCJPJJvwcvXivXrvYcHC/H/m89fxv8yOJCIi4ryuH87Zf7+Gc0q2oiJPJBsJCQ7huQrPATBkrYZtioiIZAmv3BrOKdmKijyRbKZXtV4U9yvOuavnGLVhlNlxREREchYN55RsQEWeSDbj6erJsHrDsFqs/HLoF5YfW252JBERkZwn1XDOcVCohoZzikNQkSeSDYUEh9C5QmcAhq4bqmGbIiIiZvLKDfd3hxd+h1c2aDinmE5Fnkg29Uq1VyjhX4LzV88zcsNIs+OIiIgIQFBZDecU06nIE8mmPFw8eK/ee1gtVhYeWsgfx/4wO5KIiIhcc6fDORe9ASe3gGGYnViciIo8kWysSlAVulTsAsDQtUOJjI00NY+IiIikIa3hnLkK2IdzbvgUPmsMn9SGVePhUrjZacUJqMgTyeZeDnmZUv6luBB7gREbRpgdR0RERG7l+uGcz86BSm3A1RPO7YXfwuDDCvDNU7BjNiRcNTutZFMq8kSyOQ8Xj+TZNhcfXszvR383O5KIiIjcjtUF7nsI2nxuH87ZYgIUqQ2GDQ7+BnO6w5iyMP81OLZOwznlrqjIE3EClYMq07ViV8A+2+bF2IsmJxIREZE75ukPoV2g+1J4dQs88D/wLwpxUbDlK/iiKUysDn+NhshjZqeVbEBFnoiTeDnkZe4LuI+I2AhGrNewTRERkWwpsBQ0GQivb4fOCyCkI7j5QMQhWD4cxleG6c1h67cQF212WnFQKvJEnIS7izvv1XsPF4sLS44sYdnRZWZHEhERkfSyWqFEA2j1iX04Z6spUOIBwAJHVsK8l2FMafi5Bxz6C2w2sxOLA1GRJ+JEKuatSLdK3QB4b917RMRGmJxIRERE7pmHL4S0h86/QO8d0OQdyFMKEmJg+0z4uiVMqAK/D4PzB81OKw5ARZ6Ik+lRtYeGbYqIiDirgCLwwBvw6mbovgxCu4KHP0Qdh5VjYFIoTHsYNn0BVyPNTismUZEn4mTcXdx5r7592ObSI0tZemSp2ZFEREQko1ksUKQmtBhvH87Z5gu472GwWOHEBljQB8aUwTK7G+5H/7Ivwi45hoo8ESdUMbAi3St3B2D4uuFcuHrB5EQiIiKSadw8odJT8Oxs6LsHHh4GwRUgKQ7L7p/Js/hFLOMrwdKBcGaX2WklC6jIE3FSPar0oHTu0lyMu8jw9cMxtL6OiIiI88uVH+q9Bj3XwIt/YdR8CZtnbizRZ2DtJJhcF6Y+AOumwJXzZqeVTKIiT8RJubm48V6993C1uLLs6DIN2xQREclJLBYoGILx6Puc7bQC29PfQrnmYHWD8O2w5E0YWxZmdoA9v0BivNmJJQOpyBNxYhUCK/B8lecBGL5+OOev6i92IiIiOY6LO5R9HJ75Fvrtg8c+gAIh9vv09i2EH561F3yL3oCTW0Cjf7I9FXkiTu7Fyi9SNndZIuMiGbZ2mIZtioiI5GQ+gVDrRXjpL3h5HdR9DXzzw9UI2PApfNYYPqkNq8bDpXCz00o6qcgTcXJuLm4Mrz8cV6srfxz/gwWHFpgdSURERBxBcHl4ZBj02QUd59gnb3H1hHN74bcw+LACfPMU7JgNCVfNTit3QUWeSA5QNk9ZelbtCcDI9SM5feW0yYlERETEYbi4QumH7Msw9NsHLSZAkdpg2ODgbzCnO4wpC/Nfg2PrNJwzG1CRJ5JDdKvUjUqBlbiccJnBawZr2KaIiIik5hUAoV2g+1J4dYt94XX/IhAXBVu+gi+awsTq8NdoiDxmdlq5CRV5IjmEq9WV4fWH4251Z/Wp1cw5MMfsSCIiIuLIAktBk3fg9b+h8y9QtQO4+UDEIVg+HMZXhunNYeu3EBdtdlq5joo8kRykZEBJXqv+GgAfbPyAk9EnTU4kIiIiDs9qhRIPQOvJ0H8/tJpi/xrgyEqY9zKMKQ0/94BDf4HNZm5eUZEnktM8W/5ZqgVXIyYxhndXv4vN0AexiIiI3CEPXwhpb+/Z670DGr8DeUpCQgxsnwlft4QJVeD3YXD+oNlpcywVeSI5jIvVhffqvYeXqxcbT29k5t6ZZkcSERGR7CigKDR8w37vXrdf7ffyefhD1HFYOQYmhcK0h2HTF3A10uy0OYqKPJEcqKhfUfqE9gFg/ObxHL101OREIiIikm1ZLFC0ln1Wzv777LN03vcwWKxwYgMs6ANjysCsLrD/V0hKNDux01ORJ5JDPV32aWoVqEVsUiwDVw0kyZZkdiQRERHJ7ty87OvtPTsb+u6Bh4dBcAVIioNdP8N3be3r7y0dCGd2mZ3WaanIE8mhrBYrw+oOw8fNh+3ntvP17q/NjiQiIiLOJFd+qPca9FwDL/4FNV8CrzwQfQbWToLJdWHqA7BuClw5b3Zap6IiTyQHK+BbgP/d/z8AJm6dyMGLukFaREREMpjFAgVD4PHR9sXWn/4WyjUHqyuEb4clb8LYsjCzPeyeB4lxZifO9lTkieRwre9rTYNCDUiwJTBw9UASbAlmR5IcZvDgwYSEhGTIsR544AG+++675K8tFgtz587NkGNL1smo74np06cTEBBwz8fJyPPcyb4DBgzg1VdfvfdgIo7I1R3KN4dnvoV+++Gx0VAgBGyJsG8R/Pic/f69BX3h+EYwDLMTZ0sq8kRyOIvFwuC6g/Fz92P3hd18vuNzsyPJdVasWEGLFi0oWLDgTQsWwzAICwujatWq+Pj48NBDD3HgwIGsD5tO/fv35/fff7/n48yfP58zZ87wzDPPJG8LDw/nscceu+djA/z5559YLBYiIyMz5HhmysjC2lEUL16c8ePHp9j29NNPs3///kw/d0afp3///nz11VccOnQow44p4pB8AqHWS/DSX/DyOqjXG3IVgNhI2PQ5fP4QTKoBKz6AyGNmp81WVOSJCMHewbxd620Apm6fyp4Le0xOJNdcuXKFqlWr8vHHH990n9GjRzNx4kRGjRrF2rVr8fHxoWnTpsTGxmZoloSEzOnl9fX1JTAw8J6P89FHH9G1a1es1v/+acufPz8eHh73fOy7ER8fn6Xny2qZ9X2QGby8vAgODs5258mbNy9NmzZl8uTJGXZMEYcXXB4eHgJ9dkGnn6HK0+DmDRcOwh/vwfjKML05bP0W4i6bndbhqcgTEQAeL/E4DxV9iEQjkYGrBxKf5Ny/qBqGQUx8YpY/jLscdvLYY4/x3nvv0bp165tex/jx4xk4cCCPPvooVapU4euvv+bUqVO3HKa4ZMkS6tevT0BAAIGBgTRv3px//vkn+fkjR45gsVj44YcfaNiwIZ6ennz77bcAfPHFF1SsWBEPDw8KFChAr169kl9nsViYOnUqzZs3x9vbm/Lly7N27VoOHjxIo0aN8PHxoW7duinOdWOvUpcuXWjVqhVjxoyhQIECBAYG8sorr9yyuDh37hx//PEHLVq0SLH9+t7Pa9f0008/0bhxY7y9valatSpr165N3v/o0aO0aNGC3Llz4+PjQ8WKFVm0aBFHjhyhcePGAOTOnRuLxUKXLl0AaNSoEb169aJ3794EBwfTvn375HNt27Yt+diRkZFYLBb+/PNP4L+ewaVLl1KtWjW8vLxo0qQJZ8+eZfHixZQvXx4/Pz86dOhATExM8nFsNhsjR46kRIkSeHl5UbVqVWbPnp38/LXj/v7779SoUQNvb2/q1q3Lvn37APtwwSFDhrB9+3YsFgsWi4Xp06en+b7e6vtg2rRplC9fHk9PT8qVK8cnn3yS/Lr4+Hh69epFgQIF8PT0pFixYowcOTL5+WPHjvHEE0/g6+uLn58f7dq148yZMzdt30aNGtG7d+8U21q1apWiDY4ePUqfPn2wWCy4uLgkX+uNQyMnT55MqVKlcHd3p2zZssyYMSPF8xaLhWnTptG6dWu8vb0pXbo08+fPv2m2tM6zfft2GjduTK5cufDz8yM0NJRNmzaleM3SpUspX748vr6+PProo4SHh6d4vkWLFnz//fe3PK+IU7K6QKkm8OSn0H8/PPEJFG9gf+7ISpj3MnxQGua8AAd/B80OniZXswOIiGOwWCy8U/sdNp/ZzIGLB5iyfQqvVX/N7FiZ5mpCEhUGLc3y8+4e2hRv94z76D18+DCnT5/mwQcfTN7m7+9PrVq1WLt2bYqhi9e7cuUKffv2pUqVKkRHRzNo0CBat27Ntm3bUvSEDRgwgLFjx1KtWjU8PT2ZPHkyffv25f333+exxx4jKiqK1atXpzj2sGHDGDduHOPGjePNN9+kQ4cOlCxZkrfeeouiRYvSrVs3evXqxeLFi296XcuXL6dAgQIsX76cgwcP8vTTTxMSEsILL7yQ5v6rVq1KLipvZ+DAgYwZM4bSpUszcOBA2rdvz8GDB3F1deWVV14hPj6eFStW4OPjw+7du/H19aVIkSLMmTOHp556in379uHn54eXl1fyMb/66it69uzJypUruXDhwm0zXG/w4MFMmjQJb29v2rVrR7t27fDw8OC7774jOjqa1q1bM3HiRN58800ARo4cyTfffMOUKVMoXbo0K1as4NlnnyUoKIiGDRumuM6xY8cSFBREjx496NatG6tXr+bpp59m586dLFmyhN9++w2wf8/cyo3fB99++y2DBg1i0qRJVKtWja1bt/LCCy/g4+ND586d+eijj5g/fz4//vgjRYsW5fjx4xw/fpz/t3ffUVFc7//A30tZepWuFBGliQgWxBKJYsAWe8UgNoyRr1hDrKCIHWuMMX4UjD0maIwdC0YRFUFUlKASEAuIIh2Rsvf3Bz8mjixNgV3xeZ2z5zAzd+48c+/O7j7MnRmgPEmtSPAuXbqE0tJSTJ8+HaNGjeIS4LoKCwuDvb09vL29MWXKFIhEIrHljhw5Al9fX2zcuBGurq44fvw4JkyYgBYtWnBJPAAsXboUa9aswdq1a7FlyxZ4eHjg8ePH0NbWrlU8Hh4ecHBwwLZt2yArK4u4uDjIy8tzywsLC7Fu3Trs2bMHMjIyGDduHObOncsl0ADQuXNnPH36FCkpKTAzM/ugdiHkk6egBjh4lL+yU4E7vwG3D5Sf3bv7W/lLzRBoNxKwH1N+NpAAaGJJXlBQEE6cOIG4uDgIhUKx102kpqZi2rRpuHjxIlRVVTF+/HisXLkScnJNqikI+SDNlJphifMSzIqYhZ3xO+Fi7IJ2uu0kHRapRnp6OgBAX1+fN19fX59bJs6wYcN407t27YKuri7u37+Ptm3bcvNnzpyJoUOHctPLly/HnDlz4Ovry83r1KkTr64JEyZg5MiRAAA/Pz84Oztj8eLFcHNzAwD4+vpiwoQJ1e6XlpYWfvzxR8jKysLKygr9+/fH+fPnq0zyHj9+DH19fV6CWpW5c+eif//+AMp/zNva2uLRo0ewsrJCamoqhg0bBjs7OwCAubk5t17FD3w9Pb1KZ4dat26NNWvWQCQSISMjg3fmrSbLly9Ht27dAACTJk3C/PnzkZSUxG17+PDhuHjxIvz8/PD27VusWLEC586dg7OzMxfjlStXsH37dl6SFxQUxE3/8MMP6N+/P4qKiqCkpARVVVXIycnBwMCgVjG+/z7w9/dHcHAwN69ly5a4f/8+tm/fjvHjxyM1NRWtW7dG9+7dIRAIYGpqyq17/vx53L17F8nJyTA2NgYA/Prrr7C1tUV0dHSl91NtaGtrQ1ZWFmpqajAwMOD64X3r1q2Dl5cXvvvuOwDA7Nmzce3aNaxbt46X5Hl5eWHMmDEAgBUrVmDz5s24ceMG3N3daxVPamoq5s2bBysrKwDl7493lZSU4Oeff0arVq0AAD4+Pli2bBmvjJGREYDy9zYleYQA0DQBvpgL9JgDPIspT/bu/g7kpQGRm8pfhvaA/VjAbjigoiPpiCWqSWU2xcXFGDFiBJydnbFzZ+WbR5SVlaF///4wMDDA1atXkZaWBk9PT8jLy2PFihUSiJgQ6eNq6op+LfvhZPJJLLyyEIcHHoainKKkw6p3SvKyuL/MTSLblQYPHz7EkiVLcP36dbx69Yo785GamspL8jp27Mj9nZGRgefPn/POGorTrt1//xioSD4rkqaKeUVFRcjNzYW6urrYOmxtbbkhdwBgaGiIu3fvVrnNN2/eQFGxdu/Td+MzNDQEUL5vVlZWmDFjBqZNm4azZ8/C1dUVw4YN45WvSocOHWq17Zri0dfXh7KyMi+51NfXx40bNwAAjx49QmFhIfr06cOro7i4GA4ODlXW++5+mpiYiI3j22+/xd69e7np/Px87u933wcFBQVISkrCpEmTeEl3aWkpd0bQy8sLffr0gaWlJdzd3TFgwAB89dVXAICEhAQYGxtzCR4A2NjYQFNTEwkJCR+U5NVWQkICvL29efO6deuGTZs28ea923YqKipQV1fnkkZbW1s8fvwYANCjRw+xZ6Rnz56NyZMnY8+ePXB1dcWIESO4hA4AlJWVedOGhoaVktKKM8V1+YcBIZ8FgQBo0bH85bYCeHAGuH0QeHim/HEMabeBswsBiz6A/WjAsi8g17jXZkuDJpXkLV26FACqvLbg7NmzuH//Ps6dOwd9fX20b98egYGB8PPzQ0BAAIRCYSNGS4j0WuC0ANHp0UjJTcHmW5u5Z+k1JQKBoF6HTUpKxZmYFy9ecP/5r5iu7u6JAwcOhKmpKXbs2AEjIyOIRCK0bdu20k1DVFRUuL/fHZ5YnXeHpQkEgirnVTWk7v3yFetUV15HRwdZWVkfHF9F3ZMnT4abmxtOnDiBs2fPYuXKlQgODq7xdvbvthMA7oziu9dgVnVN4fvxVLfvFYnXiRMn0Lx5c165928wU9c2X7ZsGebOnSt22bv7VxHDjh074OTkxCtXkZg7OjoiOTkZp06dwrlz5zBy5Ei4urryrh2sCxkZmUrXszbkDWCq64OTJ09y267qmAgICMDYsWNx4sQJnDp1Cv7+/jh48CB3ba24+t/fv9evXwMAdHV1P36HCGmq5BQAm6/LXwWvgPgw4PZ+4Pkt4MGp8peiJtB2aPlwzhadypPEz8Cn/wunDqKiomBnZ8cb1uTm5oZp06bh3r17lf4LCgBv377F27f/PZAxNzcXQPkXZXVflqRhiUQiMMaoDxqImrwa/J394XPBB3vv70WvFr3gqO9YqRz1Q+N7/7PH1NQUBgYGOH/+PMaNGweRSITc3Fxcv34dU6dOFds3mZmZSExMxPbt29GjR/nF7FeuXOHVX7Heu3+rqKjAzMwM586d4w0LrC5GcfW8P6/ix23FfMZYpffV+2XeZ29vj/T0dGRmZkJLS0tsPLWJBQCaN28Ob29veHt7Y8GCBdixYwemT5/ODesvKSmpFEdFvBX7U3G30GfPnsHe3h4AEBsbW6d4xO27lZUVFBQUkJKSwvVddW1f1X7Ky8ujrKyMtx0dHR3o6OjUWJeuri6MjIyQlJTEDWl8Pwag/K6pI0aMwIgRIzB06FD069cPr169gqWlJZ48eYLHjx9zZ/Pu37+P7OxsWFlZiX1P6Ojo4Pnz59x0WVkZ4uPj4eLiws0TCoUoLS3l9cP79VhbW+PKlSv45ptvuHivXLkCa2trXluI+46vmPfuGciq2hkALCws4OvrC19fX4wdOxa7du3CoEGDxJYVN+/OnTuQl5evFNunhL4jpMNn0w9K2kCnyeWvl/9AcOcQcOc3CPKeAzd3ATd3gWm3Ams3uvwaPk3xoxoaUmP2wWeV5KWnp4u9bqVimTgrV67kzhC+6+XLl03+NtnSTCQSIScnB4yxWl2DQ+rOUt4S7s3dcfrZaSy4vADbu26Hkhz/v9bUDw2voKAAycnJ3PTdu3ehrq4OTU1NtGjRAkD5dVxBQUFQVlaGlZUV1q5dC319fXTt2lXsdUkikQhaWlrYsmULhEIhnj17hqCgIABATk4OMjIyuJuHvH79mlfHrFmz4Ofnx90JMj8/H9HR0Zg0aRJXpqIOAGLrqbheuuJztKCgAKWlpdzyoqIivH37lrfdwsJCFBcXi90foDwx09bWxsmTJysNZaxun3JycriYMjIysHjxYvTq1QutWrVCdnY2wsPD0bJlS2RkZEBFRQUCgQAHDhxAr169oKSkBBUVFRQXF6OwsBAZGRm8Y6JDhw5Yvnw51NXV8erVKyxfvpy3rffbAQDy8vLAGOPt5/vt8+2332LWrFnIyclB586dkZubi+joaKipqWHkyJFi6604K5SZmQllZWVoaWnh33//xYULF2BoaAhVVVWxj5qo6n0we/ZsLFq0CDIyMvjyyy9RXFyM27dvIzs7G99++y1+/vln6Ovro23btpCRkcHevXuhp6eH4uJitGvXDtbW1hg1ahSWLVuGsrIy/PDDD3B2doaJiQkyMjIq7XPHjh0REBCA/fv3w9TUFNu3b0dWVhaKioq4MoaGhjh37hx69+4NeXl5yMrKIjc3l9eekydPxtSpU2FhYYEePXrg7NmzOHLkCH777Tfe/r37HgbKE+28vLwq33/v9tubN28QGBiIAQMGwNjYGGlpabh+/Tr69++PjIwMsX1c8T58d96ZM2fg5OSEvLw85OV9mreLp+8I6fB59oM2YDcNsPWG8Pl1KD04CoV/z0LmdRIEEUFARBDeGnVGUZvBKDJ3AxOqNkpUFcd6Y5D6JO+HH37A6tWrqy2TkJDAXdxc3+bPn4/Zs2dz07m5uTA2Noaurm6lC+9J4xGJRBAIBNDV1f2MPrAa3+Lui3H7+G2kFaRh75O9WOi0kLec+qHhRURE8JKWgIAAAICnpydCQkIA/DdUfenSpcjNzUX37t1x5syZKq+9AoCDBw9i5syZ+PLLL2FpaYmNGzeiV69e0NDQgJ6eHncdkLa2Nu/5Xz4+PpCXl8emTZuwbNky6OjoYNiwYbwyFXUAEFtPxWdnxeeoiooK5OTkuOWKioooKiri1amsrAyhUFjts8gmTpyIEydOwMPDgze/un2qGKavqakJPT09KCgoYPHixXj69CnU1dXh5uaG9evXo1mzZtDT00NAQABWrlyJmTNn4ptvvkFISAiEQiGUlZWhp6fHOyZ2796NKVOmwN3dHZaWlli1ahXc3d25bb3fDgCgpqYGgUDA28/32yc4OBhmZmb46aefMHfuXGhqasLBwQHz58+vst6Km8ZU7MeECRNw/vx5jBgxAtnZ2di5cyf3OIJ3VfU+mDVrFvT19REcHIzAwECoqKjAzs4OM2bMgJ6eHgwNDfHzzz/j4cOHkJWVRadOnXDy5EluePFff/2FGTNmYOjQoZCRkYGbmxs2b97MbeP9ffb19UVycjJ8fX0hJyeHmTNnIi8vD4qKilyZlStXYtq0aXB2dsbbt2/x/PlzqKur89pz/PjxKCwsxPr167F48WK0bNkSO3fuxODBg8W+ZyoIBAKoqalV+f57t98qkv6ZM2fixYsX0NHRwZAhQ7BmzRooKiqK7eOKaxnfnXf8+HEsWbKkUZ7z11DoO0I6fPb9YDAYcBwMFOdDlHAcgtsHgJTLUHh+AwrPb0D9SiBg1R/MfgzQsmf5IxwaSGNeGiZgdX1oUyN7+fJljbejNjc35zVaaGgoZs6cWenumkuWLMGxY8d4zy1KTk6Gubk5YmNjxQ7XfF9ubi40NDSQlZVFSZ4EVdw5TU9P7/P8wGpE19KuYcrZ8psr/NLnFzgbOXPLqB+kB/VF+YgMW1tbxMbG8u7m2JioH6TDp94Pp06dwpw5c3Dnzp1P+u7fn3o/NBXUD2JkPyl//ELcASDz4X/zVQ3+exyDvk39bzY7G1paWsjJyanyxmP1Reo/OXR1devtomNnZ2cEBQVxb3QACA8Ph7q6Omxs6r8jCWkKuhh2wWjL0TiYeBBLri5B2NdhUBOqSTosQioxMDDAzp07kZqaKrEkj5D6UFBQgJCQkE86wSNEqmkalz+Kofts4Fls+eMY4n8H8tOBq5vLX4b25cle2+GA6qd3A6Qm9emRmpqK169fIzU1FWVlZdwZOwsLC6iqquKrr76CjY0NvvnmG6xZswbp6elYtGgRpk+fLvZaBEJIuVkdZiHyeSSe5D3Bmug1COwWKOmQCBHr/WF3hHyKhg8fLukQCPk8CARAiw7lL7cV5Y9huH2w/LEMFY9jOLMQaN2nPOFr4w7IfxqPlWpS52yXLFkCBwcH+Pv7Iz8/Hw4ODnBwcMDNmzcBlN/a+fjx45CVlYWzszPGjRsHT0/PSg8gJYTwKcsrY3m35RBAgKOPjuLSk0uSDokQQgghpP7ICQHrgcDofcCcRKDfOsDIEWBlwIPTwOHxQHAb4K+ZwJMbgHRf8Sb91+RJG7omTzrQ+HLJWBe9Drvv74aOkg6OfH0E6kJ16gcpQceEdKB+kA7UD9KB+kE6UD98pJeJ5Wf37hwCcp/9N1/bvPzsXrtRgFbtLhFozGvyqKcJIbXm4+CDlhot8erNK6y4sULS4RBCCCGENCxdS8DVH5h5F/D8szyxk1cBXv8LXAwCNrUDQvoDsXuAolxJR8uhJI8QUmuKcooI6hYEWYEsTiWfQvjjcEmHRAghhBDS8GRkAXMXYMjPwNwHwJDt5Y9cgAB4fAU45gOsaw38Pgl4dA4QlUk2XIlunRDyybHTtcPEthMBAEHXg5D1NkvCERFCCCGENCIFVcB+NDD+GDArHujtD+i0AUqLyu/SuXcYsN4GOLsIeHFfIiFSkkcIqbNp9tPQRqsNst5mYdP9TaBLewkhhBDyWdJoAfSYDUy/AUy5AHT2BpS0///jGLYA25yBn3sAUT8B+S8bLSxK8gghdSYvK48V3VdATkYOkRmROJ58XNIhkU9YQEAA2rdvXy91ffHFF9i/f3+91FWd0NDQer35VkREBAQCAbKzs+utTlKuNu8vFxcXzJw5s163e//+fbRo0QIFBQX1Wi8hREoJBEDzDkC/teV35xy9H7AaAMjIA+l3gDPzIdjaudHCoSSPEPJBLLUt8W27bwEAq2+sRnpBuoQjarqePXuGcePGoVmzZlBSUoKdnR33aBgAYIzB398f9vb2UFFRgaurKx4+fCjBiOtm7ty5OH/+/EfXc+zYMbx48QKjR4/m5gkEAhw9evSj637fqFGj8ODBg3qvl3ycD+3vsLAwBAbW7/M/bWxs0KVLF6xfv75e6yWEfALkhIBV//LHMcx9UP44huYdIUDjXadHSR4h5INNsJ0AKw0r5JXkYXHkYoiYSNIhNTlZWVno1q0b5OXlcerUKdy/fx/BwcHQ0tLiyqxZswZbtmzB6tWrERUVBRUVFbi5uaGoqKheYykpKanX+iqoqqqiWbNmH13P5s2bMWHChEa5RbiSkhL09PQafDukcWhra0NNTa3e650wYQK2bduG0tLSeq+bEPKJUNYGOk8BppyHaPKFRtssJXmEkA8mJyMHPzs/KMoq4lraNRxKPCTpkJqc1atXw9jYGCEhIejcuTNatmyJr776Cq1atQJQfhZv48aNWLhwIdzd3dGuXTv8+uuveP78ebVnNE6fPo3u3btDU1MTzZo1w4ABA5CUlMQtT0lJgUAgwKFDh9CzZ08oKipi3759AIBdu3bB1tYWCgoKMDQ0hI+PD7eeQCDA9u3bMWDAACgrK8Pa2hpRUVF49OgRXFxcoKKigq5du/K29f5wOi8vLwwePBjr1q2DoaEhmjVrhunTp1ebZL58+RIXLlzAwIEDuXlmZmYAgCFDhkAgEMDMzAwpKSmQkZHhnQkFgI0bN8LU1BQikYgbOnnixAm0a9cOioqK6NKlC+Lj47ny4oZr/vXXX3BycoKZmRn09PQwZMgQbtmePXvQsWNHqKmpwcDAAGPHjkVGRkaV+yPOh7RtUlISBg0aBH19faiqqqJTp044d+4cr14zMzMEBgZizJgxUFFRQfPmzbF169ZqY4mIiEDnzp2hoqICTU1NdOvWDY8fPwbwX3/u2rULJiYmUFVVxXfffYeysjKsWbMGBgYG0NPTQ1BQEK/O1NRUDBo0CKqqqlBXV8fIkSPx4sULXplt27ahVatWEAqFsLS0xJ49e3j7AZT3t6ysLDp16sRbd8+ePTAzM4OGhgZGjx6NvLw8btn7wzXNzMywYsUKTJw4EWpqajAxMcEvv/zCq+/q1ato3749FBUV0bFjRxw9ehQCgQBxcXFcmT59+uD169e4dOlSte1JCPlMNLNotE1RkkcI+SgtVFpgpuNMAMD6m+uRkpMi0XhqjTGguKDxX3W8Sc2xY8fQsWNHjBgxAnp6enBwcMCOHTu45cnJyUhPT0fv3r25eRoaGnByckJUVFSV9RYUFGD27Nm4efMmzp8/DxkZGQwZMgQiEf9s7A8//ABfX18kJCTAzc0N27Ztw/Tp0+Ht7Y27d+/i2LFjsLDgf2kFBgbC09MTcXFxsLKywtixYzF16lTMnz8fN2/eBGOMlxiKc/HiRSQlJeHixYvYvXs3QkNDERoaWmX5K1eucIlPhejoaABASEgI0tLSEB0dDTMzM7i6uiIkJIS3fkhICLy8vHhnAefNm4fg4GBER0dDV1cXAwcOrDLRPHHiBIYMGYK+ffvi7NmzCA8PR+fO/117UVJSgsDAQNy+fRtHjx5FSkoKvLy8qm0Dceratvn5+ejXrx/Onz+PW7duwd3dHQMHDkRqaiqv3rVr18Le3h63bt3i+jw8XPwjUkpLSzF48GD07NkTd+7cQVRUFLy9vSEQCLgySUlJOHXqFE6fPo0DBw5g586d6N+/P54+fYpLly5h9erVWLRoEa5fvw6g/GHNgwYN4hKi8PBw/Pvvvxg1ahRX55EjR+Dr64s5c+YgPj4eU6dOxYQJE3Dx4kUA/P5+9uwZTp06xYvn6NGjOH78OI4fP45Lly5h1apV1bZ1cHAwOnbsiFu3buG7777DtGnTkJiYCADIzc3FwIEDYWdnh9jYWAQGBsLPz69SHUKhEO3bt8fly5er3RYhhNQ7RuokJyeHAWBZWVmSDuWzVlZWxtLS0lhZWZmkQ/msVfRDSWkJm3xmMmsb2paNPTGWlZSVSDq0mr3NZ8xfvfFfb/PrFKaCggJTUFBg8+fPZ7GxsWz79u1MUVGRhYaGMsYYi4yMZADY06dPecfEiBEj2MiRI2u9nZcvXzIA7O7du4wxxpKTkxkAtnHjRl45IyMjtnDhwirrAcAWLVrETUdFRTEAbOfOndy8AwcOMEVFRW7a39+f2dvbc9Pjx49npqamrLS0lJs3YsQINmrUqCq3u2HDBmZubi42niNHjvDmHTp0iGlpabGioiLGGGMxMTFMIBCw5ORkxhhjFy9eZADYwYMHuXUyMzOZkpISO3ToEGOMsZCQEKahocEtd3Z2Zh4eHrX+bIqOjmYAWF5eHm+b1X23fEjbimNra8u2bNnCTZuamjJ3d3demVGjRrG+ffuKXT8zM5MBYBEREWKX+/v7M2VlZZabm8vNc3NzY2ZmZrx2sbS0ZCtXrmSMMXb27FkmKyvLUlNTueX37t1jANiNGzcYY4x17dqVTZkyhbetESNGsH79+nHTFf39bj+Ii2fevHnMycmJm+7Zsyfz9fXltcm4ceO4aZFIxPT09Ni2bdsYY4xt27aNNWvWjL1584Yrs2PHDgaA3bp1ixfjkCFDmJeXl9i2aurou1o6UD9Ij6ysLAaA5eTkNPi26EweIeSjyQhkENgtEGryarjz8g5C4kNqXonUikgkgqOjI1asWAEHBwd4e3tjypQp+Pnnnz+q3ocPH2LMmDEwNzeHuro6N9Tt/TM8HTt25P7OyMjA8+fPeWcNxWnXrh33t76+PgDAzs6ON6+oqAi5ublV1mFrawtZWVlu2tDQsNrhjW/evIGiomK1cVUYPHgwZGVlceTIEQDlQy+//PJLrg0qODs7c39ra2vD0tISCQkJYuuMi4urtl1iYmIwcOBAmJiYQE1NDT179gRQub1rUte2zc/Px9y5c2FtbQ1NTU2oqqoiISGh0nbf3deK6ar2VVtbG15eXnBzc8PAgQOxadMmpKWl8cqYmZnxrnHT19eHjY0N70ypvr4+16cJCQkwNjaGsbExt9zGxgaamppcHAkJCejWrRtvO926dasyzuriqen9BPDbWiAQwMDAgFsnMTGRG8pb4d0zt+9SUlJCYWFhjTESQkh9kpN0AISQpsFAxQDzneZjwZUF+On2T+jRogestK0kHVbV5JWBBc8ls906MDQ0hI2NDW+etbU1/vjjDwCAgYEBAODFixcwMjLiyrx48aLa28YPHDgQpqam2LFjB4yMjCASidC2bVsUFxfzyqmoqHB/Kykp1SpmeXl57u+KIXzi5r0/NLSqOirWqa68jo4OsrKyahWfUCiEp6cnQkJCMHToUOzfvx+bNm2q1bpVqa5tCgoK4ObmBjc3N+zbtw+6urpITU2Fm5tbpfauSV3bdu7cuQgPD8e6detgYWEBJSUlDB8+vM7bfV9ISAhmzJiB06dP49ChQ1i0aBHCw8PRpUuXSjFVxFXXPq1PH7Lt+or39evX3DW0hBDSWOhMHiGk3gwwH4DeJr1RKirF/MvzUVz2cT8kG5RAAAhVGv/1znVLtdGtWzfuOqAKDx48gKmpKQCgZcuWMDAwwIUL/92xKzc3F9evX690dqZCZmYmEhMTsWjRIvTu3RvW1ta1SpDU1NRgZmZWL487qG8ODg5IT0+vtB/y8vIoK6t8y+rJkyfj3Llz+Omnn1BaWoqhQ4dWKnPt2jXu76ysLDx48IB3zd+72rVrV2W7/PPPP8jMzMSqVavQo0cPWFlZ1fmmKx8qMjISXl5eGDJkCOzs7GBgYICUlJRK5d7d14rpqva1goODA+bPn4+rV6+ibdu2H/V8Qmtrazx58gRPnjzh5t2/fx/Z2dncPzmsra0RGRnJWy8yMpL3T5Cq+ru+WVpa4u7du3j79i03r+KawPfFx8fDwcGhwWMihJB3UZJHCKk3AoEAS5yXQFtRG4+yH+HHuB8lHdInb9asWbh27RpWrFiBR48eYf/+/fjll18wffp0AOVtPnPmTAQFBeHMmTO4e/cuPD09YWRkhMGDB4utU0tLC82aNcMvv/yCR48e4cKFC5g9e3at4gkICEBwcDA2b96Mhw8fIjY2Flu2bKmv3f1gDg4O0NHRqZQEVCSl7yeA1tbW6NKlC/z8/DBmzBixZ+KWLVuG8+fPIz4+Hl5eXtDR0amyTf39/XHgwAEEBATgwYMHuHv3LlavXg0AMDExgVAoxJYtW/Dvv//i2LFj9f5Mtqq0bt0aYWFhiIuLw+3btzF27FixZ6MiIyOxZs0aPHjwAFu3bsXhw4fh6+srts7k5GTMnz8fUVFRePz4Mc6ePYuHDx/WmBRWx9XVFXZ2dvDw8EBsbCxu3LgBT09P9OzZkxsyPG/ePISGhmLbtm14+PAh1q9fj7CwMMydO5er593+bsgHy1e0o7e3NxISEnDmzBmsW7cOAHg3oElJScGzZ8/g6uraYLEQQog4lOQRQuqVtqI2/J39AQCh8aGIfREr4Yg+bZ06dcKRI0dw4MABtG3bFoGBgdi4cSM8PDy4Mt9//z18fHwwb948ODk5IT8/H6dPn67yGjUZGRkcPHgQMTExaNu2LWbNmoW1a9fWKp7x48dj48aN+Omnn2Bra4sBAwZIxYPXZWVlMWHCBO4xDxWCg4MRHh4OY2PjSmdTJk2ahOLiYkycOFFsnatWrYKvry86dOiA9PR0/PXXXxAKhWLLuri44PDhw/jrr7/Qp08fuLq64saNGwAAXV1dhIaG4vDhw7CxscGqVau4hKChrV+/HlpaWujatSsGDhwINzc3ODo6Vio3Z84c3Lx5Ew4ODli+fDnWr18PNzc3sXUqKyvjn3/+wbBhw9CmTRt4e3tj+vTpmDp16gfHKRAI8Oeff0JLSwtffPEFXF1dYW5ujkOH/nssy+DBg7Fp0yasW7cOtra22L59O0JCQuDi4sKVqehvU1NT9OnT54PjqYm6ujr++usvxMXFoX379li4cCGWLFkCALzj7sCBA/jqq6+4M++EENJYBIzV8X7en7nc3FxoaGggKyur0jOSSOMRiUTIyMiAnp5eozz4mIhXXT8surIIfyb9iRaqLfDH139AuY7XopG6oWMCSE9Ph62tLWJjY2v1ozowMBCHDx/GnTt3ePMjIiLw5ZdfftDn/KfYD2ZmZpg5cybvOXGfOkn0w759+zBhwgTk5ORASUkJxcXFaN26Nfbv31/phjGfi0/xeGiKqB+kR3Z2NrS0tJCTkwN1dfUG3Rb1NCGkQfh19oOhiiGe5j9F8M1gSYdDPgMGBgbYuXNnjXeszM/PR3x8PH788Uf83//9XyNFR5qaX3/9FVeuXEFycjKOHj0KPz8/jBw5khv6m5qaigULFny2CR4hRLIoySOENAg1oRoCu5Vfd/Tbg99w5dkVCUdEPgeDBw9Gjx49qi3j4+ODDh06wMXFpcqhmoTUJD09HePGjYO1tTVmzZqFESNG4JdffuGWW1hYfNQQVkII+Rg0XLOOaLimdKChB9KhNv2w6sYq7EvYBz0lPYQNCoOGgkYjR/l5oGNCOlA/SAfqB+lA/SAdqB+kBw3XJIQ0Gb6OvjBTN0PGmwwEXQ+SdDiEEEIIIU0eJXmEkAalJKeEFd1XQFYgi1PJp3A65bSkQyKEEEIIadIoySOENDg7XTtMtpsMAFh+bTleFr6UcESEEEIIIU0XJXmEkEYxtd1UWGtbI+dtDvyv+oMuByaEEEIIaRiU5BFCGoW8rDxWdF8BoYwQl59dRtjDMEmHRAghhBDSJFGSRwhpNBZaFpjhOAMAsCZ6DZ7mPZVwRIQQQgghTQ8leYSQRjXOehwc9RxRWFqIhVcWokxUJumQyCfAxcUFM2fO/Oh6MjMzoaenh5SUFABAREQEBAIBsrOzP7puUrXQ0NAaHzvk5eWFwYMH1+t2X716BT09PTx9Sv9QIoR8XijJI4Q0KlkZWSzvvhzKcsqIzYjF3oS9kg5Jqv39998YOHAgjIyMIBAIcPToUd7ykpIS+Pn5wd7eHubm5mjRogU8PT3x/PlzXrnXr1/Dw8MD6urq0NTUxKRJk5Cfn9+Ie/JxwsLCEBgY+NH1BAUFYdCgQTAzM/v4oIhYZmZm2LhxY53X27RpE0JDQ+s1Fh0dHXh6esLf379e6yWEEGlHSR4hpNEZqxljXqd5AIDNsZvxKOuRhCOSXgUFBbC3t8fWrVvFLi8sLERsbCwWLlyIs2fP4vfff0diYiK+/vprXjkPDw/cu3cP4eHhOH78OP7++294e3vXa6xlZWUQiUT1WmcFbW1tqKmpfVQdhYWF2LlzJyZNmlRPUZH6pKGhUePZvg8xYcIE7Nu3D69fv673ugkhRFpRkkcIkYhhrYehR/MeKBYVY8GVBSgRlUg6JKnUt29fLF++HEOGDBG7XENDA+Hh4Rg5ciQsLCzQpUsX/Pjjj4iJiUFqaioAICEhAadPn8b//vc/ODk5oXv37tiyZQsOHjxY6Yzfu9avXw87OzuoqKjA2NgY3333He/sX8UQvGPHjsHGxgYKCgpITU3F27dv4efnB2NjYygoKMDCwgI7d+4E8N/wyDNnzsDBwQFKSkro1asXMjIycOrUKVhbW0NdXR1jx45FYWEht633h2uamZlhxYoVmDhxItTU1GBiYoJffvml2rY8efIkFBQU0KVLl0rLYmJi0LFjRygrK6Nr165ITEzkLf/zzz/h6OgIRUVFmJubY+nSpSgtLa3UVmpqaujQoQOmT5/OtVVubi6UlJRw6tQpXp1HjhyBmpoaCgsL0atXL/j4+PCWv3z5EkKhEOfPnxe7P7dv38aXX34JNTU1qKuro0OHDrh58yavb44fPw5LS0soKytj+PDhKCwsxO7du2FmZgYtLS3MmDEDZWX/DZnOysqCp6cntLS0oKysjL59++Lhw4e87f7xxx+wtbWFgoICzMzMEBwczC1zcXHB48ePMWvWLAgEAggEAt66Z86cgbW1NVRVVeHu7o60tDRu2fvDNV1cXDBjxgx8//330NbWhoGBAQICAnj1/fPPP+jevTsUFRVhY2ODc+fOVTrjbWtrCyMjIxw5ckRsOxJCSFNESR4hRCIEAgGWdl0KDQUNJLxOwC93qv+BXt8YYygsKWz0V2M8OiInJwcCgYA7KxIVFQVNTU107NiRK+Pq6goZGRlcv369ynpkZGSwefNm3Lt3D7t378aFCxfw/fff88oUFhZi9erV+N///od79+5BT08Pnp6eOHDgADZv3oyEhARs374dqqqqvPUCAgLw448/4urVq3jy5AlGjhyJjRs3Yv/+/Thx4gTOnj2LLVu2VLufwcHB6NixI27duoXvvvsO06ZNq5Scvevy5cvo0KGD2GULFy5EcHAwbt68CTk5OUycOJG3nqenJ3x9fXH//n1s374doaGhCAoKqtRWd+/exaZNm3Dx4kWurdTV1TFgwADs37+ft819+/Zh8ODBUFZWxuTJk7F//368ffuWW7537140b94cvXr1Ehuzh4cHWrRogejoaMTExOCHH36AvLw8t7ywsBCbN2/GwYMHcfr0aURERGDIkCE4efIkTp48iT179mD79u34/fffuXW8vLxw8+ZNHDt2DFFRUWCMoV+/figpKf8nTExMDEaOHInRo0fj7t27CAgIwOLFi7lhlmFhYWjRogWWLVuGtLQ0XhJXWFiIdevWYc+ePfj777+RmpqKuXPnVtlfALB7926oqKjg+vXrWLNmDZYtW4bw8HAA5WeOK9rv+vXr+OWXX7Bw4UKx9XTu3BmXL1+udluEENKkMFInOTk5DADLysqSdCiftbKyMpaWlsbKysokHcpnrT764VTyKdY2tC2z323P7r68W4/RVa+guIC1DW3b6K+C4oIPjhkAO3LkiNhlFX1RUFDAHB0d2dixY7llQUFBrE2bNpXW0dXVZT/99FOtt3/48GHWrFkzbjokJIQBYHFxcdy8xMREBoCFh4eLrePixYsMADt37hw3b+XKlQwAS0pK4uZNnTqVubm5cdM9e/Zkvr6+3LSpqSkbN24cNy0SiZienh7btm1blfEPGjSITZw4scZ4Tpw4wQCwN2/eMMYY6927N1uxYgVvvT179jBDQ8NK26joh0OHDvHa6siRI0xVVZUVFJT3f05ODlNUVGSnTp1ijDH25s0bpqWlxQ4dOsSt065dOxYQEFDl/qipqbHQ0FCxyyr65tGjR9y8qVOnMmVlZZaXl8fNc3NzY1OnTmWMMfbgwQMGgEVGRnLLX716xZSUlNhvv/3GGGNs7NixrE+fPrxtzZs3j9nY2HDTpqambMOGDTXGs3XrVqavr89Njx8/ng0aNIib7tmzJ+vevTuvnk6dOjE/Pz/GGGOnTp1icnJyLC0tjVseHh7OALA//viD99k0a9Ys5uLiIratSMOh72rpQP0gPbKyshgAlpOT0+DbojN5hBCJcjdzR1+zvihjZZh/eT6KSoskHdInq6SkBKNGjQJjDNu2bfvo+s6dO4fevXujefPmUFNTwzfffIPMzEzeMEqhUIh27dpx03FxcZCVlUXPnj2rrfvddfT19aGsrAxzc3PevIyMjFrXIRAIYGBgUO06b968gaKiYo11GRoaAgBX1+3bt7Fs2TKoqqpyrylTpiAtLY1ri4q2MjY2hoWFBcaPH89rq379+kFeXh7Hjh0DUD7kUV1dHa6urgAARUVFfPPNN9i1axcAIDY2FvHx8fDy8qpyf2bPno3JkyfD1dUVq1atQlJSEm+5srIyWrVqxU3r6+vDzMyMd1b13XZOSEiAnJwcnJycuOXNmjWDpaUlEhISuDLdunXjbadbt254+PAhb9inOO/HY2hoWKc+fn+dxMREGBsbw8DAgFveuXNnsfUoKSnx3reEENLUyUk6AEIIWdhlIW6+uImU3BRsit0Ev85+Db5NJTklXB9b9VDFhtxuQygpKYG3tzeeP3+OCxcuQF1dnVsmLvkpLS3F69eveT+Q35WSkoIBAwZg2rRpCAoKgra2Nq5cuYJJkyahuLgYysrK5fujpMS77kpJqXb79+6wQoFAwJuumFfTTVzquo6Ojg6ysrJqFQ8Arq78/HwsXboUQ4cOrbSeoqIir60CAwPBGENCQgKmTJnCtZVQKMTw4cOxf/9+jB49Gvv378eoUaMgJ/ff1/DkyZPRvn17PH36FCEhIejVqxdMTU2r3J+AgACMHTsWJ06cwKlTp+Dv74+DBw9y12+Ka58Paef6Im7brIbhy/UV7+vXr6Grq1vn9Qgh5FNFZ/IIIRKnoaCBpV2XAgD2JuzFjbQbDb5NgUAAZXnlRn+9fyOK+lBxBi85ORlnz55Fs2bNeMudnZ2RnZ2NmJgYbt6FCxcgEol4Z23eFRMTA5FIhODgYHTp0gVt2rSp9iYtFezs7CASiXDp0qWP26kG4ODggPv379d5PUdHRyQmJsLCwqLSS0ZGplJbtWrVinctWgUPDw+cPn0a9+7dw4ULF+Dh4cFbbmdnh44dO2LHjh3Yv38/77rAqrRp0wazZs3C2bNnMXToUISEhNR5/ypYW1ujtLSUd51mZmYmEhMTYWNjw5WJjIzkrRcZGYk2bdpAVlYWQPnZ3ZrO6tUHS0tLPHnyBC9evODmRUdHiy0bHx8PBweHBo+JEEKkBSV5hBCp0KNFD4xoMwIAsChyEfKK8yQckXTIz89HXFwc4uLiAADJycmIi4vj7pxZUlKC4cOHIyYmBlu3bkVZWRnS09ORnp6O4uJiAOU/zN3d3TFlyhTcuHEDkZGR8PHxwejRo2FkZCR2uxYWFigpKcGWLVvw77//Ys+ePfj5559rjNfMzAzjx4/HxIkTcfToUSQnJyMiIgK//fZb/TTIR3Bzc8O9e/eqPJtXlSVLluDXX3/F0qVLce/ePSQkJODgwYNYtGgRgMptdfjwYWzfvr1SPV988QUMDAzg4eGBli1bik2wJ0+ejFWrVoExVuUdVYHyoac+Pj6IiIjA48ePERkZiejoaFhbW9dp397VunVrDBo0CFOmTMGVK1dw+/ZtjBs3Ds2bN8egQYMAAHPmzMH58+cRGBiIBw8eYPfu3fjxxx95N1AxMzPD33//jWfPnuHVq1cfHE9N+vTpg1atWmH8+PG4c+cOIiMjuT55958phYWFiImJwVdffdVgsRBCiLShJI8QIjXmdpyLFqotkFaQhtU3Vks6HKlw8+ZNODg4cGchZs+eDQcHByxZsgQA8OzZMxw7dgxPnz6Fq6srmjdvDkNDQxgaGuLq1atcPfv27YOVlRV69+6Nfv36oXv37tU+csDe3h7r16/H6tWr0bZtW+zbtw8rV66sVczbtm3D8OHD8d1338HKygpTpkxBQUHBR7RC/bCzs4Ojo2OdE043NzccP34cZ8+eRadOndClSxds2LCBG0r5blu1a9cOYWFhvDtvVhAIBBgzZgxu375d6SxehTFjxkBOTg5jxoyp8vpBAJCVlUVmZiY8PT3Rpk0bjBw5En379sXSpUvrtG/vCwkJQYcOHTBgwAA4OzuDMYaTJ09ywyYr2u/gwYNo27YtlixZgmXLlvGuHVy2bBlSUlLQqlWrBh0iKSsri6NHjyI/Px+dOnXC5MmTubtrvtt2f/75J0xMTNCjR48Gi4UQQqSNgNU0IJ7w5ObmQkNDA1lZWQ3y0FZSOyKRCBkZGdDT04OMDP2vQlIaoh9iX8TC67QXGBg2frkRvU1610u9TR0dE7Vz4sQJzJs3D/Hx8Q3STh/bDxXJUXR0NBwdHes9vqYuMjIS3bt3x4MHD6CmpgY9PT107doVM2bMwNixYyUd3meHPpekA/WD9MjOzoaWlhZycnJ41843BOppQohUcdR3hFdbLwDA0qtL8epNww33Ip+f/v37w9vbG8+ePZN0KDwlJSVIT0/HokWL0KVLF0rwaunIkSMIDw9HSkoKzp07B29vb3Tr1o27i+erV68wdOhQjBkzRsKREkJI46IkjxAidXza+6CNVhtkvc1CwNWARnmAOPl8zJw5E8bGxpIOgycyMhKGhoaIjo6u1bWPpFxeXh6mT58OKysreHl5oVOnTvjzzz+55To6Ovj+++8b5IZHhBAizegRCoQQqSOUFWJlj5UYfXw0Lj29hLCHYRjWZpikwyKkwbi4uNA/Mz6Ap6cnPD09K81vrMdCEEKItKIzeYQQqdRGqw1mOMwAAKyOXo0nuU8kHBEhhBBCyKeBkjxCiNT6xuYbdNTviDelb7DgygKUiRr+2VuEEEIIIZ86SvIIIVJLVkYWQd2DoCKvgriXcQi59+EPeiaEEEII+VxQkkcIkWpGqkZY4LQAALD11lYkZCZIOCJCCCGEEOlGSR4hROoNNB8IVxNXlLJSzL88H0WlRZIOiRBCCCFEalGSRwiRegKBAEucl6CZYjMk5SRhU+wmSYdECCGEECK1KMkjhHwStBS1sKzbMgDA3oS9uJZ2TcIREUIIIYRIpyaV5AUFBaFr165QVlaGpqZmpeW3b9/GmDFjYGxsDCUlJVhbW2PTJjojQMin4osWX2Bkm5EAgEVXFiG3OFfCERFCCCGESJ8mleQVFxdjxIgRmDZtmtjlMTEx0NPTw969e3Hv3j0sXLgQ8+fPx48//tjIkRJCPtScjnNgomaCF4UvsOL6CkmHQwghhBAideQkHUB9Wrp0KQAgNDRU7PKJEyfyps3NzREVFYWwsDD4+Pg0dHiEkHqgLK+MFT1WwPOUJ078ewIuxi5wN3OXdFiEEEIIIVKjSZ3J+xA5OTnQ1taWdBiEkDqw17XHFLspAIDAqEC8KHgh4YgIIYQQQqRHkzqTV1dXr17FoUOHcOLEiSrLvH37Fm/fvuWmc3JyAADZ2dkNHR6phkgkQm5uLoRCIWRkPvv/VUiMJPthlOkoXHhwAf9k/QO/s37Y4LIBAoGgUWOQJnRMSAfqB+lA/SAdqB+kA/WD9KjIHxhjDb8xJuX8/PwYgGpfCQkJvHVCQkKYhoZGtfXevXuX6ejosMDAwGrL+fv717h9etGLXvSiF73oRS960Yte9KrNKykp6WNTpBoJGGuMVPLDvXz5EpmZmdWWMTc3h1Ao5KZDQ0Mxc+bMKs+23b9/H19++SUmT56MoKCgaut+/0xednY2TE1NkZqaCg0NjdrvCKlXubm5MDY2xpMnT6Curi7pcD5b1A/Sg/pCOlA/SAfqB+lA/SAdqB+kR05ODkxMTJCVlSX2SQD1SeqHa+rq6kJXV7fe6rt37x569eqF8ePH15jgAYCCggIUFBQqzdfQ0KADRQqoq6tTP0gB6gfpQX0hHagfpAP1g3SgfpAO1A/SozGGzUp9klcXqampeP36NVJTU1FWVoa4uDgAgIWFBVRVVREfH49evXrBzc0Ns2fPRnp6OgBAVla2XhNJQgghhBBCCJGUJpXkLVmyBLt37+amHRwcAAAXL16Ei4sLfv/9d7x8+RJ79+7F3r17uXKmpqZISUlp7HAJIYQQQgghpN41qVvshIaGgjFW6eXi4gIACAgIELu8LgmegoIC/P39xQ7hJI2H+kE6UD9ID+oL6UD9IB2oH6QD9YN0oH6QHo3ZF1J/4xVCCCGEEEIIIbXXpM7kEUIIIYQQQsjnjpI8QgghhBBCCGlCKMkjhBBCCCGEkCaEkrw62rp1K8zMzKCoqAgnJyfcuHFD0iE1GStXrkSnTp2gpqYGPT09DB48GImJibwyLi4uEAgEvNe3337LK5Oamor+/ftDWVkZenp6mDdvHkpLSxtzVz5pAQEBldrYysqKW15UVITp06ejWbNmUFVVxbBhw/DixQteHdQH9cPMzKxSXwgEAkyfPh0AHQ8N5e+//8bAgQNhZGQEgUCAo0eP8pYzxrBkyRIYGhpCSUkJrq6uePjwIa/M69ev4eHhAXV1dWhqamLSpEnIz8/nlblz5w569OgBRUVFGBsbY82aNQ29a5+U6vqhpKQEfn5+sLOzg4qKCoyMjODp6Ynnz5/z6hB3DK1atYpXhvqhejUdD15eXpXa2N3dnVeGjoePV1M/iPuuEAgEWLt2LVeGjoePV5vfqvX1OykiIgKOjo5QUFCAhYUFQkND6xYsI7V28OBBJhQK2a5du9i9e/fYlClTmKamJnvx4oWkQ2sS3NzcWEhICIuPj2dxcXGsX79+zMTEhOXn53NlevbsyaZMmcLS0tK4V05ODre8tLSUtW3blrm6urJbt26xkydPMh0dHTZ//nxJ7NInyd/fn9na2vLa+OXLl9zyb7/9lhkbG7Pz58+zmzdvsi5durCuXbtyy6kP6k9GRgavH8LDwxkAdvHiRcYYHQ8N5eTJk2zhwoUsLCyMAWBHjhzhLV+1ahXT0NBgR48eZbdv32Zff/01a9myJXvz5g1Xxt3dndnb27Nr166xy5cvMwsLCzZmzBhueU5ODtPX12ceHh4sPj6eHThwgCkpKbHt27c31m5Kver6ITs7m7m6urJDhw6xf/75h0VFRbHOnTuzDh068OowNTVly5Yt4x0j736nUD/UrKbjYfz48czd3Z3Xxq9fv+aVoePh49XUD++2f1paGtu1axcTCAQsKSmJK0PHw8erzW/V+vid9O+//zJlZWU2e/Zsdv/+fbZlyxYmKyvLTp8+XetYKcmrg86dO7Pp06dz02VlZczIyIitXLlSglE1XRkZGQwAu3TpEjevZ8+ezNfXt8p1Tp48yWRkZFh6ejo3b9u2bUxdXZ29ffu2IcNtMvz9/Zm9vb3YZdnZ2UxeXp4dPnyYm5eQkMAAsKioKMYY9UFD8vX1Za1atWIikYgxRsdDY3j/x5RIJGIGBgZs7dq13Lzs7GymoKDADhw4wBhj7P79+wwAi46O5sqcOnWKCQQC9uzZM8YYYz/99BPT0tLi9YOfnx+ztLRs4D36NIn7Ufu+GzduMADs8ePH3DxTU1O2YcOGKtehfqibqpK8QYMGVbkOHQ/1rzbHw6BBg1ivXr148+h4qH/v/1atr99J33//PbO1teVta9SoUczNza3WsdFwzVoqLi5GTEwMXF1duXkyMjJwdXVFVFSUBCNrunJycgAA2travPn79u2Djo4O2rZti/nz56OwsJBbFhUVBTs7O+jr63Pz3NzckJubi3v37jVO4E3Aw4cPYWRkBHNzc3h4eCA1NRUAEBMTg5KSEt5xYGVlBRMTE+44oD5oGMXFxdi7dy8mTpwIgUDAzafjoXElJycjPT2ddwxoaGjAycmJdwxoamqiY8eOXBlXV1fIyMjg+vXrXJkvvvgCQqGQK+Pm5obExERkZWU10t40LTk5ORAIBNDU1OTNX7VqFZo1awYHBwesXbuWNySK+qF+REREQE9PD5aWlpg2bRoyMzO5ZXQ8NL4XL17gxIkTmDRpUqVldDzUr/d/q9bX76SoqCheHRVl6pJzyH3YLn1+Xr16hbKyMl6HAIC+vj7++ecfCUXVdIlEIsycORPdunVD27Ztufljx46FqakpjIyMcOfOHfj5+SExMRFhYWEAgPT0dLF9VLGM1MzJyQmhoaGwtLREWloali5dih49eiA+Ph7p6ekQCoWVfkTp6+tz7Ut90DCOHj2K7OxseHl5cfPoeGh8Fe0mrl3fPQb09PR4y+Xk5KCtrc0r07Jly0p1VCzT0tJqkPibqqKiIvj5+WHMmDFQV1fn5s+YMQOOjo7Q1tbG1atXMX/+fKSlpWH9+vUAqB/qg7u7O4YOHYqWLVsiKSkJCxYsQN++fREVFQVZWVk6HiRg9+7dUFNTw9ChQ3nz6XioX+J+q9bX76SqyuTm5uLNmzdQUlKqMT5K8ohUmj59OuLj43HlyhXefG9vb+5vOzs7GBoaonfv3khKSkKrVq0aO8wmqW/fvtzf7dq1g5OTE0xNTfHbb7/V6kOFNIydO3eib9++MDIy4ubR8UBI+U1YRo4cCcYYtm3bxls2e/Zs7u927dpBKBRi6tSpWLlyJRQUFBo71CZp9OjR3N92dnZo164dWrVqhYiICPTu3VuCkX2+du3aBQ8PDygqKvLm0/FQv6r6rSotaLhmLeno6EBWVrbS3XFevHgBAwMDCUXVNPn4+OD48eO4ePEiWrRoUW1ZJycnAMCjR48AAAYGBmL7qGIZqTtNTU20adMGjx49goGBAYqLi5Gdnc0r8+5xQH1Q/x4/foxz585h8uTJ1Zaj46HhVbRbdd8FBgYGyMjI4C0vLS3F69ev6TipZxUJ3uPHjxEeHs47iyeOk5MTSktLkZKSAoD6oSGYm5tDR0eH9zlEx0PjuXz5MhITE2v8vgDoePgYVf1Wra/fSVWVUVdXr/U/3CnJqyWhUIgOHTrg/Pnz3DyRSITz58/D2dlZgpE1HYwx+Pj44MiRI7hw4UKlIQPixMXFAQAMDQ0BAM7Ozrh79y7vC6Xii9/GxqZB4m7q8vPzkZSUBENDQ3To0AHy8vK84yAxMRGpqanccUB9UP9CQkKgp6eH/v37V1uOjoeG17JlSxgYGPCOgdzcXFy/fp13DGRnZyMmJoYrc+HCBYhEIi4Rd3Z2xt9//42SkhKuTHh4OCwtLWlIVC1VJHgPHz7EuXPn0KxZsxrXiYuLg4yMDDd8kPqh/j19+hSZmZm8zyE6HhrPzp070aFDB9jb29dYlo6Huqvpt2p9/U5ydnbm1VFRpk45x4fdS+bzdPDgQaagoMBCQ0PZ/fv3mbe3N9PU1OTdHYd8uGnTpjENDQ0WERHBu71vYWEhY4yxR48esWXLlrGbN2+y5ORk9ueffzJzc3P2xRdfcHVU3Jb2q6++YnFxcez06dNMV1eXbhlfB3PmzGEREREsOTmZRUZGMldXV6ajo8MyMjIYY+W3BjYxMWEXLlxgN2/eZM7OzszZ2Zlbn/qgfpWVlTETExPm5+fHm0/HQ8PJy8tjt27dYrdu3WIA2Pr169mtW7e4uzauWrWKaWpqsj///JPduXOHDRo0SOwjFBwcHNj169fZlStXWOvWrXm3jM/Ozmb6+vrsm2++YfHx8ezgwYNMWVmZblX+jur6obi4mH399desRYsWLC4ujvedUXF3uqtXr7INGzawuLg4lpSUxPbu3ct0dXWZp6cntw3qh5pV1w95eXls7ty5LCoqiiUnJ7Nz584xR0dH1rp1a1ZUVMTVQcfDx6vpc4mx8kcgKCsrs23btlVan46H+lHTb1XG6ud3UsUjFObNm8cSEhLY1q1b6REKDW3Lli3MxMSECYVC1rlzZ3bt2jVJh9RkABD7CgkJYYwxlpqayr744gumra3NFBQUmIWFBZs3bx7vuWCMMZaSksL69u3LlJSUmI6ODpszZw4rKSmRwB59mkaNGsUMDQ2ZUChkzZs3Z6NGjWKPHj3ilr9584Z99913TEtLiykrK7MhQ4awtLQ0Xh3UB/XnzJkzDABLTEzkzafjoeFcvHhR7GfR+PHjGWPlj1FYvHgx09fXZwoKCqx3796V+iczM5ONGTOGqaqqMnV1dTZhwgSWl5fHK3P79m3WvXt3pqCgwJo3b85WrVrVWLv4SaiuH5KTk6v8zqh4jmRMTAxzcnJiGhoaTFFRkVlbW7MVK1bwkg/GqB9qUl0/FBYWsq+++orp6uoyeXl5ZmpqyqZMmVLpn990PHy8mj6XGGNs+/btTElJiWVnZ1dan46H+lHTb1XG6u930sWLF1n79u2ZUChk5ubmvG3UhuD/B0wIIYQQQgghpAmga/IIIYQQQgghpAmhJI8QQgghhBBCmhBK8gghhBBCCCGkCaEkjxBCCCGEEEKaEEryCCGEEEIIIaQJoSSPEEIIIYQQQpoQSvIIIYQQQgghpAmhJI8QQgghhBBCmhBK8gghhBBCCCGkCaEkjxBCCCGEEEKaEEryCCGEkHe4uLhg5syZ9VauIbZdk6dPn2L48OFYvHjxxwdFCCHkk0NJHiGEkE+al5cXBAIBvv3220rLpk+fDoFAAC8vrw+uv6rEKywsDIGBgR9cb0OaNWsWWrdujcOHD0s6FEIIIRJASR4hhJBPnrGxMQ4ePIg3b95w84qKirB//36YmJg0yDa1tbWhpqbWIHV/jJycHERERKB79+4wMjKSdDiEEEIkgJI8QgghnzxHR0cYGxsjLCyMmxcWFgYTExM4ODhw88zMzLBx40beuu3bt0dAQIDYer28vHDp0iVs2rQJAoEAAoEAKSkpAPhn+FxcXODj4wMfHx9oaGhAR0cHixcvBmOMq+vt27eYMWMG9PT0oKioiO7duyM6Orra/RKJRFi5ciVatmwJJSUl2Nvb4/fff692nQsXLqBHjx64dOkSunXrVm1ZQgghTRMleYQQQpqEiRMnIiQkhJvetWsXJkyY8FF1btq0Cc7OzpgyZQrS0tKQlpYGY2NjsWV3794NOTk53LhxA5s2bcL69evxv//9j1v+/fff448//sDu3bsRGxsLCwsLuLm54fXr11Vuf+XKlfj111/x888/4969e5g1axbGjRuHS5cuVbnO5cuX0aVLFxw/fhxDhgz58J0nhBDyyaIkjxBCSJMwbtw4XLlyBY8fP8bjx48RGRmJcePGfVSdGhoaEAqFUFZWhoGBAQwMDCArKyu2rLGxMTZs2ABLS0t4eHjg//7v/7BhwwYAQEFBAbZt24a1a9eib9++sLGxwY4dO6CkpISdO3eKre/t27dYsWIFdu3aBTc3N5ibm8PLywvjxo3D9u3bq4z55s2byMrKgqKiIhwdHT9q/wkhhHya5CQdACGEEFIfdHV10b9/f4SGhoIxhv79+0NHR6fRtt+lSxcIBAJu2tnZGcHBwSgrK0NSUhJKSkp4wyfl5eXRuXNnJCQkiK3v0aNHKCwsRJ8+fXjzi4uLeUNQ35eSkoKXL19i6dKlH7lHhBBCPlWU5BFCCGkyJk6cCB8fHwDA1q1bKy2XkZHhXScHACUlJY0SW13l5+cDAE6cOIHmzZvzlikoKFS53osXL2BlZYXhw4c3aHyEEEKkFyV5hBBCmgx3d3cUFxdDIBDAzc2t0nJdXV2kpaVx07m5uUhOTq62TqFQiLKyshq3ff36dd70tWvX0Lp1a8jKyqJVq1YQCoWIjIyEqakpgPLkMjo6usrn4tnY2EBBQQGpqano2bNnjduvIC8vj+DgYMjI0BUZhBDyuaIkjxBCSJMhKyvLDX8Ud+1cr169EBoaioEDB0JTUxNLliyp8hq7CmZmZrh+/TpSUlKgqqoKbW1tsQlUamoqZs+ejalTpyI2NhZbtmxBcHAwAEBFRQXTpk3DvHnzoK2tDRMTE6xZswaFhYWYNGmS2O2qqalh7ty5mDVrFkQiEbp3746cnBxERkZCXV0d48ePr7TO7t27UVBQAAUFBVy7dg2vXr3CgAEDamw3QgghTQsleYQQQpoUdXX1KpfNnz8fycnJGDBgADQ0NBAYGFjjmby5c+di/PjxsLGxwZs3b5CcnAwzM7NK5Tw9PfHmzRt07twZsrKy8PX1hbe3N7d81apVEIlE+Oabb5CXl4eOHTvizJkz0NLSqnLbgYGB0NXVxcqVK/Hvv/9CU1MTjo6OWLBgQaWyRUVFCAsLw+7du+Ht7Q0zMzP8+uuv1e4bIYSQpknA3r84gRBCCCF14uLigvbt21d6Bh8hhBAiCTRgnxBCCCGEEEKaEEryCCGEEEIIIaQJoeGahBBCCCGEENKE0Jk8QgghhBBCCGlCKMkjhBBCCCGEkCaEkjxCCCGEEEIIaUIoySOEEEIIIYSQJoSSPEIIIYQQQghpQijJI4QQQgghhJAmhJI8QgghhBBCCGlCKMkjhBBCCCGEkCaEkjxCCCGEEEIIaUIoySOEEEIIIYSQJoSSPEIIIYQQQghpQv4fQJ2HzLaFntAAAAAASUVORK5CYII=",
"text/plain": [
"<Figure size 900x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"beam_cases = [\n",
" (\"10 arcmin (instrument-resolution-ish)\", 10.0),\n",
" (\"60 arcmin (typical map smoothing)\", 60.0),\n",
" (\"120 arcmin (heavy smoothing)\", 120.0),\n",
"]\n",
"\n",
"plt.figure(figsize=(9, 4.8))\n",
"for label, fwhm in beam_cases:\n",
" comp = compare_beams(math.radians(fwhm / 60.0), lmax)\n",
" frac = (beam_window(comp.blm_new) - beam_window(comp.blm_old)) / beam_window(comp.blm_old)\n",
" plt.plot(comp.ell, 100.0 * frac, label=label, linewidth=1.5)\n",
"\n",
"plt.axhline(0, color=\"black\", linestyle=\"--\", linewidth=0.9)\n",
"plt.xlim(0, lmax)\n",
"plt.ylim(-12, 1)\n",
"plt.xlabel(r\"Multipole $\\ell$\")\n",
"plt.ylabel(r\"$\\Delta B_\\ell^2 / B_\\ell^2$ (%)\")\n",
"plt.title(\"Fractional change in beam window function\")\n",
"plt.grid(alpha=0.3)\n",
"plt.legend(frameon=False)\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "5863c723",
"metadata": {},
"source": [
"## Effect on a toy power spectrum\n",
"To get an intuition for spectra-level impacts, take a simple toy model\n",
"$C_\\ell = 1/(\\ell+1)$: a smooth, monotonically decaying spectrum that avoids\n",
"divergence at $\\ell=0$ and mimics high-$\\ell$ damping without acoustic\n",
"features. Applying the two beam windows shows how the change redistributes\n",
"power."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "0612d7a0",
"metadata": {
"execution": {
"iopub.execute_input": "2025-12-11T18:18:30.230356Z",
"iopub.status.busy": "2025-12-11T18:18:30.230076Z",
"iopub.status.idle": "2025-12-11T18:18:31.410595Z",
"shell.execute_reply": "2025-12-11T18:18:31.408823Z"
}
},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 900x700 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ell = np.arange(lmax + 1, dtype=float)\n",
"cl_toy = 1.0 / (ell + 1.0) # avoids divide-by-zero at ell=0\n",
"\n",
"_, bl_old = beam_coefficients(fwhm_rad, lmax, use_l_lplus1=False)\n",
"_, bl_new = beam_coefficients(fwhm_rad, lmax, use_l_lplus1=True)\n",
"\n",
"cl_old_beamed = cl_toy * beam_window(bl_old)\n",
"cl_new_beamed = cl_toy * beam_window(bl_new)\n",
"\n",
"ratio = (cl_new_beamed - cl_old_beamed) / cl_old_beamed\n",
"\n",
"fig, (ax0, ax1) = plt.subplots(2, 1, figsize=(9, 7), sharex=True)\n",
"\n",
"ax0.loglog(ell[1:], cl_old_beamed[1:], label=PREVIOUS_RELEASE, color=\"#1b9e77\")\n",
"ax0.loglog(ell[1:], cl_new_beamed[1:], label=CURRENT_RELEASE, color=\"#d95f02\")\n",
"ax0.set_ylabel(r\"$C_\\ell B_\\ell^2$ (toy model)\")\n",
"ax0.set_title(\"Toy spectrum with beam applied (FWHM = 1°)\")\n",
"ax0.grid(alpha=0.3)\n",
"ax0.legend(frameon=False)\n",
"\n",
"ax1.plot(ell, 100.0 * ratio, color=\"#7570b3\")\n",
"ax1.axhline(0, color=\"black\", linestyle=\"--\", linewidth=0.9)\n",
"ax1.set_xlabel(r\"Multipole $\\ell$\")\n",
"ax1.set_ylabel(\"Percent diff (%)\")\n",
"ax1.grid(alpha=0.3)\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "ca21bcdf",
"metadata": {},
"source": [
"## Where else is `blm_gauss` used?\n",
"A quick ripgrep scan in the repository (tests and docs only) shows no other\n",
"functions call `blm_gauss` internally; it is exposed as a user-facing helper.\n",
"Downstream impacts occur when these coefficients are injected into custom\n",
"pipelines (e.g., multiplying custom $C_\\ell$ or $a_{\\ell m}$ by `blm_gauss`\n",
"to apply a Gaussian beam). Those pipelines should regenerate coefficients\n",
"under 1.19.0 to stay consistent."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "3553f24c",
"metadata": {
"execution": {
"iopub.execute_input": "2025-12-11T18:18:31.414640Z",
"iopub.status.busy": "2025-12-11T18:18:31.414345Z",
"iopub.status.idle": "2025-12-11T18:18:31.426707Z",
"shell.execute_reply": "2025-12-11T18:18:31.425178Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
}
],
"source": [
"import shutil, subprocess, textwrap\n",
"\n",
"if shutil.which(\"rg\") is None:\n",
" print(\"ripgrep (rg) is not available in this environment.\")\n",
"else:\n",
" scan = subprocess.run(\n",
" [\"rg\", \"blm_gauss\"],\n",
" cwd=\"..\",\n",
" capture_output=True,\n",
" text=True,\n",
" check=False,\n",
" )\n",
" if scan.returncode not in (0, 1): # 1 means no matches\n",
" print(f\"rg failed with code {scan.returncode}: {scan.stderr}\")\n",
" else:\n",
" print(textwrap.dedent(scan.stdout))"
]
},
{
"cell_type": "markdown",
"id": "12204bc6",
"metadata": {},
"source": [
"## Takeaways\n",
"- The new convention damps high-$\\ell$ modes more strongly. For a 1° beam,\n",
" the percent change at the half-power multipole is modest (~0.5%), but reaches\n",
" several percent near $\\ell_{\\max}=2000$.\n",
"- Narrow beams (e.g., 10 arcmin) see the largest fractional changes because\n",
" the $\\ell(\\ell+1)$ factor grows faster than $\\ell^2$ at moderate $\\ell$.\n",
"- Pipelines that multiply custom $C_\\ell$ or $a_{\\ell m}$ by `blm_gauss`\n",
" should regenerate those coefficients with 1.19.0 to stay consistent with\n",
" `gauss_beam` and the Challinor et al. convention."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.12.9"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment