{ "cells": [ { "cell_type": "markdown", "id": "8fd75052", "metadata": {}, "source": [ "# Tutorial 3: Halo mass functions and collapse thresholds\n", "\n", "The halo mass function $\\mathrm{d}n/\\mathrm{d}M$ — the comoving number\n", "density of dark matter halos per unit mass — is the backbone of any\n", "semi-analytic model. Its ingredients are all objects from Tutorial 2 plus\n", "two collapse-threshold classes:\n", "\n", "* `criticalOverdensity` — the linearly-extrapolated collapse threshold\n", " $\\delta_\\mathrm{c}(t)$ from spherical-collapse theory\n", " ($\\simeq 1.686$ for Einstein-de Sitter);\n", "* `virialDensityContrast` — the mean density contrast $\\Delta_\\mathrm{vir}(t)$\n", " of a just-virialized halo ($\\simeq 178$ for Einstein-de Sitter, higher in\n", " $\\Lambda$CDM today).\n", "\n", "We compare the Sheth & Tormen (1999) and Tinker et al. (2008) mass\n", "functions and follow their evolution to high redshift." ] }, { "cell_type": "code", "execution_count": 1, "id": "c128e14f", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:39:56.235471Z", "iopub.status.busy": "2026-07-05T19:39:56.235274Z", "iopub.status.idle": "2026-07-05T19:39:56.426285Z", "shell.execute_reply": "2026-07-05T19:39:56.424124Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Galacticus library interface loaded.\n" ] } ], "source": [ "import os, sys\n", "\n", "# Locate the Galacticus library interface. Two supported layouts:\n", "# * a Galacticus source tree built with\n", "# make GALACTICUS_BUILD_OPTION=lib libgalacticus.so\n", "# (galacticus.py at the tree root, the library under galacticus/lib/);\n", "# * an unpacked binary distribution (the `galacticus/` folder from\n", "# libgalacticus.tar.bz2, with python/ and lib/ inside it).\n", "# Set GALACTICUS_LIBRARY_PATH to the directory CONTAINING the `galacticus/`\n", "# folder if the auto-detection below does not fit your setup.\n", "root = os.environ.get('GALACTICUS_LIBRARY_PATH',\n", " os.path.abspath(os.path.join(os.getcwd(), os.pardir)))\n", "os.chdir(root) # galacticus.py loads galacticus/lib/libgalacticus.so relative to here\n", "for candidate in (root, os.path.join(root, 'galacticus', 'python')):\n", " if os.path.exists(os.path.join(candidate, 'galacticus.py')):\n", " sys.path.insert(0, candidate)\n", " break\n", "else:\n", " raise RuntimeError(f\"galacticus.py not found under {root} - build the library \"\n", " \"(make GALACTICUS_BUILD_OPTION=lib libgalacticus.so) or set \"\n", " \"GALACTICUS_LIBRARY_PATH\")\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import galacticus\n", "print(\"Galacticus library interface loaded.\")" ] }, { "cell_type": "code", "execution_count": 2, "id": "3e9e8a1a", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:39:56.430525Z", "iopub.status.busy": "2026-07-05T19:39:56.430364Z", "iopub.status.idle": "2026-07-05T19:39:56.432220Z", "shell.execute_reply": "2026-07-05T19:39:56.431995Z" } }, "outputs": [], "source": [ "plt.rcParams.update({'figure.figsize': (7.0, 4.5), 'font.size': 11,\n", " 'axes.grid': True, 'grid.alpha': 0.3})" ] }, { "cell_type": "code", "execution_count": 3, "id": "4bd715c0", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:39:56.432933Z", "iopub.status.busy": "2026-07-05T19:39:56.432852Z", "iopub.status.idle": "2026-07-05T19:39:56.439035Z", "shell.execute_reply": "2026-07-05T19:39:56.438873Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigma(M) chain ready.\n" ] } ], "source": [ "# Assemble the sigma(M) chain (see Tutorial 2 for a walk-through).\n", "cosmologyParameters = galacticus.cosmologyParametersSimple(0.3, 0.045, 0.7, 2.78, 70.0)\n", "cosmologyFunctions = galacticus.cosmologyFunctionsMatterLambda(cosmologyParameters)\n", "darkMatterParticle = galacticus.darkMatterParticleCDM()\n", "transferFunction = galacticus.transferFunctionEisensteinHu1999(\n", " 3.046, 0.0, darkMatterParticle, cosmologyParameters, cosmologyFunctions)\n", "linearGrowth = galacticus.linearGrowthCollisionlessMatter(cosmologyParameters, cosmologyFunctions)\n", "powerSpectrumPrimordial = galacticus.powerSpectrumPrimordialPowerLaw(0.965, 0.0, 0.0, 1.0, False)\n", "powerSpectrum = galacticus.powerSpectrumPrimordialTransferredSimple(\n", " powerSpectrumPrimordial, transferFunction, linearGrowth)\n", "powerSpectrumWindowFunction = galacticus.powerSpectrumWindowFunctionTopHat(cosmologyParameters)\n", "cosmologicalMassVariance = galacticus.cosmologicalMassVarianceFilteredPower(\n", " sigma8=0.8, tolerance=1.0e-4, toleranceTopHat=1.0e-4, nonMonotonicIsFatal=True,\n", " integrationFailureIsFatal=True, monotonicInterpolation=False,\n", " rootVarianceLogarithmicGradientTolerance=1.0e-4, truncateAtParticleHorizon=False,\n", " storeTabulations=True, cosmologyParameters_=cosmologyParameters,\n", " cosmologyFunctions_=cosmologyFunctions, linearGrowth_=linearGrowth,\n", " powerSpectrumPrimordialTransferred_=powerSpectrum,\n", " powerSpectrumWindowFunction_=powerSpectrumWindowFunction)\n", "ageToday = cosmologyFunctions.cosmicTime(1.0)\n", "def timeOf(z):\n", " return cosmologyFunctions.cosmicTime(cosmologyFunctions.expansionFactorFromRedshift(z))\n", "print(\"sigma(M) chain ready.\")" ] }, { "cell_type": "markdown", "id": "19aedfaf", "metadata": {}, "source": [ "## Collapse thresholds\n", "\n", "$\\delta_\\mathrm{c}$ and $\\Delta_\\mathrm{vir}$ are computed here from full\n", "spherical-collapse solutions (not fits), tabulated on first use." ] }, { "cell_type": "code", "execution_count": 4, "id": "3bca66e5", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:39:56.440810Z", "iopub.status.busy": "2026-07-05T19:39:56.440728Z", "iopub.status.idle": "2026-07-05T19:39:56.612406Z", "shell.execute_reply": "2026-07-05T19:39:56.611397Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "delta_c(z=0) = 1.6756, Delta_vir(z=0) = 339.8\n" ] } ], "source": [ "criticalOverdensity = galacticus.criticalOverdensitySphericalCollapseClsnlssMttrCsmlgclCnstnt(\n", " linearGrowth, cosmologyFunctions, cosmologicalMassVariance, darkMatterParticle, True)\n", "virialDensityContrast = galacticus.virialDensityContrastSphericalCollapseClsnlssMttrCsmlgclCnstnt(\n", " True, cosmologyFunctions)\n", "\n", "zGrid = np.linspace(0.0, 6.0, 60)\n", "deltaC = np.array([criticalOverdensity.value(time=timeOf(z), mass=1.0e12) for z in zGrid])\n", "DeltaV = np.array([virialDensityContrast.densityContrast(1.0e12, time=timeOf(z)) for z in zGrid])\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(11, 4))\n", "axes[0].plot(zGrid, deltaC); axes[0].axhline(1.686, color='gray', ls=':', label='EdS value 1.686')\n", "axes[0].set_xlabel('$z$'); axes[0].set_ylabel('$\\\\delta_\\\\mathrm{c}(z)$'); axes[0].legend()\n", "axes[1].plot(zGrid, DeltaV); axes[1].axhline(177.65, color='gray', ls=':', label='EdS value 178')\n", "axes[1].set_xlabel('$z$'); axes[1].set_ylabel('$\\\\Delta_\\\\mathrm{vir}(z)$'); axes[1].legend()\n", "fig.suptitle('Spherical-collapse thresholds approach Einstein-de Sitter values at high $z$')\n", "fig.tight_layout(); plt.show()\n", "print(f\"delta_c(z=0) = {deltaC[0]:.4f}, Delta_vir(z=0) = {DeltaV[0]:.1f}\")" ] }, { "cell_type": "markdown", "id": "5d904b76", "metadata": {}, "source": [ "## The mass function today: Sheth-Tormen vs. Tinker et al.\n", "\n", "`differential(time, mass)` returns $\\mathrm{d}n/\\mathrm{d}M$ in units of\n", "Mpc$^{-3} M_\\odot^{-1}$; we plot $\\mathrm{d}n/\\mathrm{d}\\ln M = M\\,\n", "\\mathrm{d}n/\\mathrm{d}M$. The two calibrations agree to tens of percent\n", "over the well-resolved range — differences of exactly the size that matter\n", "when you fit galaxy surveys." ] }, { "cell_type": "code", "execution_count": 5, "id": "922244bb", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:39:56.614955Z", "iopub.status.busy": "2026-07-05T19:39:56.614754Z", "iopub.status.idle": "2026-07-05T19:39:56.829890Z", "shell.execute_reply": "2026-07-05T19:39:56.829102Z" } }, "outputs": [ { "data": { "image/png": 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QIDZt2pRumxkzZhAdHc2CBQvw9/cHICkpiSeeeIIxY8ZQpkyZfK1ZRETEXorSSJ4UHrn1uSv0wTUz37pbsmQJHTp0SA2tAH369CE8PJylS5cyaNCgLB83Pj6e+Pj41NfR0dEANx31zU1WqzV1Arekp/7Ypv7Ypv7Ypv7YVpD7c6O2Gw97uXFsfQk6Y0W1Pzc+dzfLSZn9O1Pog2tm7Nu3j8GDB6dZ5uvrS1BQEPv27cvWPidMmMBrr72Wbvn58+eJi4vL1j4zy2q1EhUVhWmaRepyGblF/bFN/bFN/bFN/bGtIPcnMTERq9VKUlJSvl8G64Ybl+ECjfxmpCj3JykpCavVysWLF3Fyckq3PiYmJlP7KRbBNTIyEl9f33TL/fz8uHTpUurrQYMGsXz5cgDKlStHu3bt+PrrrzPc5+jRoxk2bFjq6+joaIKDgwkICMDb2zt3T+A/rFYrhmEQEBBQ4P7DWBCoP7apP7apP7apP7YV5P7ExcURExODo6Mjjo72/d9/RsElq7799lsmT57M/v37MU2TsmXL0qJFC8aPH09gYCAAFStWpGvXrrnyfZaZM2fi7OxMv3790ixv164dnp6e/Pzzz5nez38H0zJSEEftc8LR0RGLxUKJEiVwdXVNtz6jZRnuJ7cLK8xmzpyZ6W1dXFxwcXFJt9xiseT9f6zio7EkXMFiKVXg/sNYUBiGkT8/i0JK/bFN/bFN/bGtoPbHYrFgGEbqwx5M00w9dk5qePvttxk1ahTPPfccr7/+OqZpsmvXLr799lvOnDlDqVKlUrfNrfOdNWsWnp6e9O/fP8P1mT1Gt27dWLduXerrxYsX8+abb/Lrr7/i7e1NcnIyDg4ORW7E9cbP4WZ/NzL796VYBFc/Pz+ioqLSLY+MjEwz77WwMNZOImDj59DiKWgWDi5e9i5JREQk30yePJlBgwbx3nvvpS7r0qULw4cPL/AjlQEBAQQEBKS+vjFlsWHDhpQoUSL1clhZFR8fj5OTU4H7B1NuK9pnd12NGjXSzWWNiorizJkz1KhRw05VZZPVCv+sxhIfhWXVm/BhXVjzISRctXdlIiIi+SIyMvKmF7LPKLh99NFHVKhQAR8fH3r27Mn58+fTrL98+TJPPPEEQUFBuLi40LBhQ5YuXZq6vm3btvz+++8sXrw4deRw7NixafYxd+5cqlevjqenJ+3bt+fw4cPZPr9jx45x77334uPjg4eHB507d2bnzp1ptgkJCWHo0KG8/fbbVKhQATc3Ny5dukTbtm3p1q0b3333HVWrVsXd3Z3u3bsTGRnJsWPH6Ny5M56entSuXZvVq1enO/bMmTOpW7curq6ulC1blhdffDHNXdZmzpyJYRhs3bqVLl264OHhQdWqVfnqq6+yfb5ZUSyCa5cuXVi+fDmXL19OXTZnzhwsFgudOnWyX2HZYbFwvOeP7Go4DrNEFbh2CZa/mhJg/5oCCbH2rlBERAoR0zSJTUiy6yOr36Bv2LAhM2bM4LPPPuPs2bM2t124cCELFy7ko48+YtKkSfz+++889dRTqesTEhLo2LEjixYtYty4cSxcuJBatWrRtWvX1LA4bdo06tevT8uWLVm3bh3r1q1jyJAhqfvYtm0b77zzDhMnTmTmzJkcOnSIAQMGZOmcboiJiaFdu3Zs3bqVGTNm8M0333Dx4kVat27NiRMn0mw7b948Fi1axKRJk/jpp59Sr9G7detWJk2axLvvvsuMGTP4888/eeSRR7j33nvp1q0b8+fPJzAwkF69enHlypXU/b3//vsMGTKEzp078/PPPzNy5EgmT57Miy++mK7O/v3706lTJ3788Ufq16/PoEGD2Lt3b7bOOSsK/VSB2NhYfvnlFyDlXyjR0dHMnTsXgDZt2hAQEEB4eDhTpkyhZ8+ejBkzhlOnTjF8+HDCw8ML5TVcP1z1Dwu2VqRd1Sm8UmsPFXdNhcgjsPQlWDsZbhsGDR8Cp8xNdBYRkeLrWmIytV75za417Hm9M+7OmY8k06ZN4+677+aRRx4BUr6E1b17d5577jlCQkLSbGuaJgsXLkz9XsrRo0cZP348VqsVi8XCt99+y7Zt29i+fTu1atUCoHPnzhw8eJA33niDH374gVq1auHt7Y2npyfNmjVLV8/ly5fZunVr6hSAK1eu8NBDD3Hy5EnKlSuXpV7MmjWLY8eOsXv3bmrWrAmk5Jny5cvz4YcfppkekZiYyJIlS9LdVCIqKort27en3iFtx44dvPfee0yfPp3w8HAAypQpQ506dVixYgU9evQgJiaGV199lREjRjB+/HgAOnbsiLOzM8OGDWP48OGUKFEi9RhDhw7liSeeAKBFixYsXryYefPm8dJLL2XpfLOq0I+4RkRE0Lt3b3r37s3q1as5ceJE6uvdu3cDKXNcV6xYgaOjIz179mTUqFEMGTKE999/387VZ51pmjg5WHAwYNXBSNotC2KQx0ccafk2+JaHqxHw6yiYHAZ/fwpJ8bfcp4iISGESGhqaeufMZ555Bh8fHyZPnkzdunXZtm1bmm3btGmT5svUtWrVIjExkYiICACWLl1KnTp1qFatWuqlwpKSkujYsSMbN27MVD1hYWFp5q3eCMAnT54EUm63++992xphXrNmDaGhoamhFcDf35+OHTuyZs2aNNu2bds2wzuhhYWFpbmtb7Vq1QDo0KFDumU3RnH/+usvrly5Qu/evdPU2qFDB65du8auXbvSHOPfv7H28PCgQoUKqeeblwr9iGtISEimfsVQs2bN1EtdFWaGYTCxVx36hPryw67LzN9yitWHLrP6UDluqzSN12rsoNLe6RB1An55AdZ8ALc9D/UfAEdne5cvIiIFjJuTA3te75wvxzJNM/XLR//+1rybU9ZvAers7Mydd97JnXfeCcBvv/1G165def3115k/f37qdv+9HKazc8r/C29cc/3ChQts3bo1w0t0ZfbWpLc6xu23387vv/+eun7VqlW0bds2w31dvnw5zVURbihVqlS68JjRdrbq+ffyjPoA0KBBgwz3+d9pChkdI6+vYw9FILgWV+V8XZjYqw5Pta/KtNWHmbv5BH/+E037f0JoEfIRb1TfTqW90zGiT8HiYSkBtvULENYfHHJ+/TwRESkaDMPI0q/pc8I0TZIspAuuuaFz587Uq1cvy/Ms/f39qVu3Lp9//nmu1vNvH3/8cZoL7FevXv2m2/r5+XHw4MF0y8+dO5fuSki52cMb+54/fz7BwcHp1lesWDHXjpUTCq6FXLC/OxN61WFo+ypMX32IHzae5K+jV7j9aGWal5/OG9U2U3n/JxhRJ+DnZ+DP96H1cKjXVwFWREQKpXPnzqUbbbx27RonTpygdu3aWdpXhw4d+OWXXyhTpozN773kZETRVlD9r5YtWzJ//nz279+f+r7IyEiWL1/Oo48+mq3jZ0bz5s1xd3fn5MmT3H333Xl2nJxScC0iyvq68WbPOjzZrgozVh/mu40nWHf8Kh2O16Bp8HTerLaJKvs/xbh8DBYOhT/fgzYjoE4fcNDHQERECo86derQvXt3OnfuTFBQEKdOnWLq1KlcuHCBZ555Jkv7GjhwIB9//DFt27blhRdeoFq1aqlftkpISGDChAlAypTDWbNm8fPPPxMUFHTLoJtdDz74IJMnT6Zr1668+eabuLq6Mm7cOBwdHXn22Wdz/Xg3+Pr68vrrrzNixAhOnjxJ27ZtcXBw4J9//uGnn35i3rx5uLu759nxM6vQfzlL0gryceO1HqH8OaIdD7UMwcXRwoYT1+j4V216u07nQL2RmO4lU65C8OPj8FET2D4brMm33rmIiEgBMHbsWE6fPs2wYcPo0KEDzz//PF5eXqxYsYKePXtmaV8uLi6sXLmSbt26MW7cODp16sQTTzzBpk2baNWqVep2I0aMoGXLlgwcOJDGjRvzySef5PJZpfDy8mLVqlXUq1ePRx99lP79++Pn58cff/yR4a/wc9Pzzz/Pl19+yapVq7jnnnvo3bs3n3zyCY0bN06dE2tvhpnVi6dJhqKjo/Hx8SEqKgpvb+88PZbVaiUiIoLAwMBb3iEjIiaOT//4h2/WH+daYko4bRDkzIRy66l26AuMa5dSNixZDdqMhNp3gyXrk+QLkqz0pzhSf2xTf2xTf2wryP2Ji4vjyJEjVKxYMdP3hc9tN/tylqQoyv251ecvszmqYP2tklwX6OXKi11r8efIdoS3qYy7swNbziTQeWMDejlPZ3/tZzFdfeHCAZj3MExvAbsXpNyhS0RERKQAUXAtJkp6ujCqSw3WjGzPk+0q4+niyNZzyXTe3IS7nWewt+bTmK4+cH4fzBkEM1rBnoUKsCIiIlJgKLgWM/4ezgzvXIM1I9vx9O1V8XJxZFuElS5bm3GX4zT2Vn8S08ULInbDDw/Ax61h32LQjBIRERGxMwXXYsrX3ZlhHauxZlR7nutQDW9XR3ZeMOiyvSXdHaazp2o4prMXnNsJ3/eDT9rA/iUKsCIiImI3Cq7FnI+bE890qMraUe0Z3rk6vu5O7Lpk4c6drenu8BF7Kj+C6eQBZ7bDd33h03ZwYKkCrIiIiOQ7BVcBwMvViSfbVWHNyPaM6lKDEh7O7Ip05M7d7ehqmcauioMxndzh9Fb4X2/4rAMcXK4AKyIiIvlGwVXS8HRxJLxNZf4c2Y6XutakpKcLe6Kc6La3A12NqewOeRDT0Q1ObYJv74HPO8KhFQqwIiIikucUXCVD7s6ODLmtEmtGtuOVbrUo5e3CnmhXuu7rTBemsqv8A5iOrnByI3zTC764A/5ZrQArIiIieUbBVWxydXJgcKuK/D68HW/0qE2Qjyv7rrjR7UAX7jCnsrPc/ZgOLnBiPXzVA768E478Ye+yRUREpAhScJVMcXVy4IHmIawe3pbxd9ehrK8b+6+60/1QdzqbU9hR9r6UAHv8L5jVHb7sCkfX2LtsERERKUIUXCVLXBwd6Ne0PKuHt+Xte+tSoYQ7B2I9uetwDzpbJ7EjqDemgzMcWwMzu6aE2GPr7F22iIgUEYZh3PIxc+ZM2rZtS7du3bK8/5CQEIYOHZoHlWdPcnIyb7/9Nq1bt6ZkyZL4+/vTrl07/vzzz3TbJiQkMHz4cEqXLo2HhwcdO3Zk//796bbbt28fHTt2xMPDg9KlSzNixAgSEhLSbBMbG8vo0aOpVKkS7u7uVKtWjfHjx5OUlJRn55oZjnY9uhRaTg4W+jQKplf9sizcfpqpKw9x4ALcdeRuqri2473SK6gbsRDjyB8pUwcqtYW2Y6B8U3uXLiIihdi6dWkHQ5o3b85TTz1Fv379UpdVrlyZJk2a4ODgkN/l5bpr164xYcIEBg0axMiRI3FwcOCTTz6hXbt2LF26lPbt26du+/TTT/P999/z/vvvU7ZsWcaNG8ftt9/O7t278fHxASAyMpL27dtTtWpV5s+fz6lTpxg2bBixsbFMnTo1dV9Dhw5l3rx5jB8/nlq1arFu3TpeeeUVrl69yrhx4/K9DzcouEqOODpY6NWgHD3CyrJox2mmrDzEoQjocfQeqrq0591Sy6h7YRHGP6tTvrxVuX1KgA1ubO/SRUSkEGrWrFm6ZeXLl0+3PCAgIL9KypRr167h5uaWbvnq1atp164d5k2+3Ozm5sY///yDn59f6rKOHTsSGhrKBx98kBpcT548yWeffca0adMYPHgwAI0bN6Z8+fJ8/PHHjBgxAoAZM2YQHR3NggUL8Pf3ByApKYknnniCMWPGUKZMGaxWK7Nnz2b48OE8+eSTALRr1479+/fz/fff2zW4aqqA5AoHi0GPsLIsfbY1H/VrQI3SXhyM96PH8T50TPqAbQF3YVoc4fBK+LwDfHMPnNxs77JFRMQ0IeGqfR95cEWa/04VGDt2LJ6enuzcuZNWrVrh7u5OaGgov/32m839XLx4kcaNG9OwYUMuXLgAwN69e+nRowc+Pj54eHjQtWtXDh8+nOZ9hmEwceJERo4cSenSpQkMDMzWeTg4OKQJrTeW1a1bl9OnT6cuW7p0KVarld69e6cu8/f3p1OnTvzyyy+py5YsWUKHDh1SQytAnz59sFqtLF26FADTNElKSkodpb3Bx8fnpgE7v2jEVXKVxWLQtW4QXUJLs2zvOaasPMiuU9DzRF+qON3OO4HLCLu0BOPQcji0HKp2grajoGxDe5cuIlI8JcbC+DL5cigDcMpoxZjT4OyR58dPTEykf//+PP3007z88su89dZb3HPPPRw7dowSJUqk2/7s2bN07NgRHx8fFi9ejI+PD//88w8tWrQgNDSUmTNnYrFYUn8lv3//flxcXFLfP2nSJJo1a8bnn3+eq3NDk5KSWL9+Pbfddlvqsn379hEYGJgu5NasWZPPP/88zXY3RmRv8PX1JSgoiH379gEpwXjQoEFMnTqVVq1aUbNmTdavX8/XX3/Nyy+/nGvnkR0KrpInLBaDzrVL06lWKVbtj2DSikNsPwF3n+pHZccOvBu4lLDI3zAOLoWDS6HaHSkBtkx9e5cuIiJFVEJCAhMnTuTOO+8EoHr16lSsWJElS5YwYMCANNseP36c22+/nZCQEH788Uc8PFKC9WuvvYa/vz/Lli3D1dUVgBYtWlCpUiU+//xznnjiidR9+Pv7M3/+fAzDSF1mmibJycmpr288T0pKSh3pBHByyjDiA/D2229z6tQpnnvuudRlkZGR+Pr6ptvWz8+PS5cuZXm7adOmER4eTpMmTVKXjR49mmHDht20rvyg4Cp5yjAM2tcoRbvqgfxx8AKTVxxk8zG4+/QAqjh04u3AX6l/eSnGgV/hwK9Qrcv1ABtm79JFRIoHJ/eUEc98cCOYOTo6pglzOLnny/EtFgsdOnRIfR0SEoKbmxsnT55Ms93hw4e57bbbCAsL44cffkgzirp06VL69u2Lo6Njasj08/Ojfv36bNy4Mc1+unTpkvY8gVmzZvHQQw+lq+2/QfXIkSOEhISk227ZsmW8+uqrvPLKKzRsmHe/rRw1ahSLFy/ms88+o2rVqqxfv57XXnsNPz8/hg8fnmfHvRUFV8kXhmHQploArauWZN3hi0xacZANR6DXmYFUsXTi7YBfqR+9HOPAEjiwBKp3TQmwQXXtXbqISNFmGPnya3ogZS6rJQkcHVOOm8/c3NxwdnZOs8zZ2Zm4uLg0y/7++28uXbrE5MmT04RWgAsXLvDhhx/y4Ycfptv/f/ddqlSpdNt07949TcDdvHkz4eHhbNy4MXU01sHBgTJl0k/f2LJlC/fccw/9+vXjlVdeSbPOz8+PqKiodO+JjIxMM581M9vt2rWLd999l4ULF9K9e3cAWrduTWJiIi+//DLh4eF4eXml20d+UHCVfGUYBi2qlKRFlZJs+OciU1YeYs0h6HVuEFUsnXmr5BIaRK/A2L8Y9i+GGt1SAmzpOvYuXUREion7778fR0dH+vbty6JFi7j99ttT1/n7+9O1a9c0UwJu+G+Y++9oK0CJEiXSzKe9cuUKAI0aNbr5iDRw6NAhunTpQosWLfjss8/S7bdGjRqcO3eOyMjINPNc9+3bR40aNdJsd2Mu6w1RUVGcOXMmdbs9e/YAEBYWlma7+vXrEx8fz8mTJ6lZs2a6GvKDriogdtO0Ugm+GdKUeY+3oG31AA5Zg7gnYjCdEt5mk9ftmBiwbxHMaAWzB8C53fYuWUREiokPP/yQBx98kB49erB27drU5R06dGDXrl3Ur1+fRo0apXlUr149T2o5c+YMnTp1onz58sydOzfD+a+dOnXCYrEwb9681GWRkZEsXbo0dU4vpExfWL58OZcvX05dNmfOHCwWC506dQKgQoUKQMoI779t3rwZwzBS19uDRlzF7hpW8GPmQ03YfuIyU1YeZPleuPf8w1QxOjOhxBIaXVmNsfdn2Psz1OoBbUZBqVr2LltERIq46dOnc+3aNe68806WL19O48aNee2112jcuDGdO3fm0UcfpVSpUpw9e5bff/+d2267jfvvvz9Xa7h27RpdunThwoULTJo0iV27dqWuc3FxoX79lC81lytXjiFDhjB8+HAcHBwoW7Ys48ePx8fHh8ceeyz1PeHh4UyZMoWePXsyZswYTp06xfDhwwkPD0+dnnAjiD/22GOcO3eOKlWqsGHDBiZMmMDgwYNxd8+fOckZUXCVAqNesC+fPdiYXaeimLryEL/uht4XHqGq0YXx/r/Q6OrvGHt+gj0LoXZPaDMSAu3zqwoRESn6DMPgiy++ID4+ns6dO7N69Wrq1q3L33//zUsvvcQTTzzBlStXCAoKonXr1tStm/vfyzh37hzbt28H4K677kqzrkKFChw9ejT19aRJk/D09GTUqFHExMTQsmVLli9fnuZ6rH5+fqxYsYKnnnqKnj174uXlxZAhQ9LcVMDBwYGff/6Zl19+mfHjxxMREUFwcDAjRoxg5MiRuX6OWWGY9r6SbBERHR2Nj48PUVFReHt75+mxrFYrERERBAYGYrEU3dke+8/GMHXVIRbtOI1pQjXjBG/6LaZJ7B/XtzCg9t3XA+z/z98pLv3JLvXHNvXHNvXHtoLcn7i4OI4cOULFihVTL+OU32zN4ZSi3Z9bff4ym6MK1t8qkX+pXtqLKffXZ9lzbehVvyyHjfL0uRRO5/iJbHC7DTBh93yY1gzmDoaIfbfcp4iIiBReCq5S4FUJ9OT9+8JYMawNfRqV47BRgfsiH+eO+Imsd20FmLBr3vUA+zCc32/vkkVERCQPKLhKoRFS0oO3763Hqhfa0r9peQ5bKtD38hN0iZ/AepcWpATYuRjTm+Oz/Hm4cMDeJYuIiEguUnCVQifY351xd9fhjxHtGNQihMMOFekbNZQ748ezzrk5BiZuhxZhTGsG84bAhYP2LllERERygYKrFFpBPm6Mvas2a0a0Y0irihxxrMz90U/RNX48ax2aYGDCzjnwUROY94gCrIgIKV8AEslvufW5U3CVQi/Q25WXutVizch2PN62MkedKtP/6rN0jR/HX45NwLTCzh9SAuz8R+HCIXuXLCKS75ycnDAMg6tXr9q7FCmGYmNjATK8eUJW6DquUmSU8HRh5B01eKRVCB8t28MP2x3pd+VZQo1/GO2+kJbJf8OO2SmjsHX6QOvhULKKvcsWEckXDg4O+Pj4cP78eeLj4/H29s73yy4V5cs95Yai2B/TNImNjSUiIgJfX18cHBxytD8FVylyfN2deaR5GZ7qVJuv1x/n87VO9L+aEmBHuf9Eq+SNsOP7lFHYOn2gzQgoUdneZYuI5LnSpUvj5uZGREQE0dHR+X580zSxWq1YLJYiE8xyU1Huj6+vL6VLl87xfhRcpcjydnPiqdur8lCrinyz/hif/uHMgKuVUgKs24+0sm76/wBb976UEVgFWBEpwgzDwNfXFx8fH5KTk0lKSsrX41utVi5evEiJEiUK3A0aCoKi2h8nJ6ccj7TeoOAqRZ6niyPhbSrzYPMQ/vf3cT7+3YUBMZWoY/zDSNcFtDI3w/bvUqYRKMCKSDFgGAaOjo44OuZvDLBarTg5OeHq6lqkglluUX9uTV2RYsPN2YGHW1XkjxHteKNHbS5612LAtee5K/4N/qRBype4tn8HUxvDgsfh4mF7lywiIiL/ouAqxY6rkwMPNA9h9fB2TOxVh8t+dXgg7gXuin+DP2gAZjJs/58CrIiISAGj4CrFlrOjhb5NyrPy+Ta817seV0rUZeD1APu7qQArIiJS0Ci4SrHn6GDhnoblWDasDZPvr09cYD0ejE8JsKsVYEVERAoMBVeR6xwsBnfVK8Ovz7RmxoAGJJWuz6DUAFtfAVZERMTOdFUBkf+wWAzuCA2ic+3SrNwXweSVvgw6UZm6xmGec5pPO8vWlACbehWCF3QVAhERkXyg4CpyE4ZhcHvNUrSvEcifBy8wZaUfDx1NCbDPOs2nfWqA/V6X0RIREckHCq4it2AYBq2rBdC6WgDr/7nIlJUlGHzoeoB1nE97h626DqyIiEg+UHAVyYJmlUrQrFIJNh+LZOrKAAbvr0zdpMM84zif2/8dYOv0SQmwJavYu2QREZEiQ1/OEsmGhhX8+PKhJvw8tBWla7bg4cThdI9/k+XJ9VNuZLDje/ioMcx/DC4csne5IiIiRYKCq0gO1CnnwycDG/Hrs7dRoU5LHklKCbDLkhv8J8A+ChcO2rtcERGRQk3BVSQX1CjtzdR+DVj2XBuq1r+N8OThdIt/k2XJDa8H2NmYHzWBeY8owIqIiGSTgqtILqoS6Mn7fcJY+XwbQhu14QnrC6kB1jCtsPOH6wF2CJw/YO9yRUREChUFV5E8UKGEBxPvqcvq4e1o0KwdT5rD6Ro/jqWpAXZOSoCd+zCc32/vckVERAoFBVeRPFTW143Xe4SyZkQ7mrdszzOMoGv8eH5LboSBCbvmYn7UFOYOhoh99i5XRESkQFNwFckHgd6uvNStFmtGtqNNm9t53vLfADsPc1ozmPMQROy1d7kiIiIFkoKrSD4q4enCiDtqsGZkOzre3pHhDiO4M348vyY3Tgmwu+djTmsOcwbBuT32LldERKRAUXAVsQNfd2ee7VCNtaPa061zZ8Y4j6RL/ASWpAbYBTC9OfzwIJzbbe9yRURECgQFVxE78nJ14om2VVgzsh333HkHr7qO4o74ifyS3CRlgz0/wvQWMPsBOLvLrrWKiIjYm4KrSAHg7uzIkNsq8ceIdvS/qwtvuo+ic/xEFiU3Tdlg70KY0RJmD4CzO+1brIiIiJ0ouIoUIK5ODjzQPITVw9vxcK9uvOM9mk7xb7EouRlWDNj7M8xoBd/3hzPb7V2uiIhIvlJwFSmAnB0t9GkczIphbXiiT3c+9BtD5/i3WJjcHKtpwL5F8HFr+O5+OL3N3uWKiIjkC0d7FyAiN+foYKFn/bLcVa8Mv+6uxpSVtZh0di9POS7gLss6LPt/gf2/QLU7oM1IKNvA3iWLiIjkGQVXkULAYjG4s04QXUJLs2JvNaasqs2Uk7sZ6vgjd1n+wuHAr3DgV6jaCdqMgnIN7V2yiIhIrlNwFSlEDMOgQ61S3F4zkDWHqjFlZR0mH93NUMcF9LSsxeHgUji4FKp0SAmwwY3tXbKIiEiu0RzXf3nssccoW7YshmHYuxQRmwzD4LaqAfzwWHMmPnI3P4a8wu0J7zI3uTVJpgUOLYfPO8DXd8PxDfYuV0REJFcouP5L//792bJli73LEMmSppVK8PXDTfng8Xv4tcortE94jx+S2qQE2MMr4YtO8FUPOLbO3qWKiIjkSIEOrocOHSI8PJywsDAcHR0JDQ3NcLt9+/bRsWNHPDw8KF26NCNGjCAhISHLx2vdujWlSpXKadkidlG/vB+fPdiY6U/dw+81x9I+4T2+S2pHoukA/6yGL++Amd3g6Fp7lyoiIpItBXqO6+7du1m8eDFNmzbFarVitVrTbRMZGUn79u2pWrUq8+fP59SpUwwbNozY2FimTp1qh6pF7Kt2GR8+6t+AQxFVmbaqAdO3byfc8iP3OvyO89E/sRz9E7+gxtDhZajUGjQ1RkRECokCHVy7d+9Ojx49ABg0aBCbNm1Kt82MGTOIjo5mwYIF+Pv7A5CUlMQTTzzBmDFjKFOmDAANGjTg+PHj6d7fqFEjfv311zw8CxH7qBLoxfv3hXGsQ1Vm/F6fGZu38YjxE30cVuNyZiN8fRdm+eYYbUdBxTYKsCIiUuAV6OBqsdx6JsOSJUvo0KFDamgF6NOnD+Hh4SxdupRBgwYB5Prc1fj4eOLj41NfR0dHA9x0ZDg3Wa1WTNPM8+MUVupPWsF+bozrGcrptpX59M8GdNq4lcH8RF+HVbgcXwdf9cAs1xSzzQio1K7YB1h9fmxTf2xTf2xTf2wrzv3J7DkX6OCaGfv27WPw4MFplvn6+hIUFMS+ffvy7LgTJkzgtddeS7f8/PnzxMXF5dlxIeWHGxUVhWmamQr3xY36kzFH4PGmJbm3Vmtmrq/IFwfuZpD5E/0cVuJycgPGt/cQH1iPq42eJCG4+E4h0OfHNvXHNvXHNvXHtuLcn5iYmExtV+iDa2RkJL6+vumW+/n5cenSpSzta9CgQSxfvhyAcuXK0a5dO77++usMtx09ejTDhg1LfR0dHU1wcDABAQF4e3tn6bhZZbVaMQyDgICAYvfBzgz1x7aSJa284OmMw10N+Gp9Q+74624GJP1Ef4fluEZsx+WXR7GWaQCtR6Tc0KCYBVh9fmxTf2xTf2xTf2wrzv1xdXXN1HaFPrjmppkzZ2Z6WxcXF1xcXNItt1gs+fJhMwwj345VGKk/thmGQUkvV17oXINHWlfm63WN6Pbn3dyX+CMDHJbjdnoLfN8Xa+kwLG1HQvUuxSrA6vNjm/pjm/pjm/pjW3HtT2bPt9B3xc/Pj6ioqHTLIyMj08x7FZGM+bg5MbR9VX4adQ90GkcPpxnMSOpGrOmC5ew2+P5+rDNug70/QzGcdyUiIgVHoQ+uNWrUSDeXNSoqijNnzlCjRg07VSVS+Hi4OPJI60osHNkT967juNdlBtOS7uKK6Yrl3E6YPYDk6a1g948KsCIiYheFPrh26dKF5cuXc/ny5dRlc+bMwWKx0KlTJ/sVJlJIuTo5MLB5CD+O6EnJHuO53+MTpiT1JMZ0w+H8bpjzIEnTmsOueWBNtne5IiJSjBTo4BobG8vcuXOZO3cux44dIzo6OvX1+fPnAQgPD8fLy4uePXuydOlSvvzyS4YPH054eHjqNVxFJOucHS30aRzMgue7U/7e8Tzo/RmTknoRbbrjeGEfzB1M0tRmsGOOAqyIiOSLAv3lrIiICHr37p1m2Y3Xq1atom3btvj5+bFixQqeeuopevbsiZeXF0OGDGHcuHH2KFmkyHF0sNAjrCzd65Zh6Z6GPLKiD00j5vKw4y/4XDoA84eQuGoCTm1HQOi94FCg/7MiIiKFWIH+P0xISAimad5yu5o1a6ZexkpE8obFYnBHaBCda5dm9YGGPLGsL2FnfmCI4y/4RR6GBY+RuHICTm2HQ937wMHJ3iWLiEgRU6CnCohIwWMYBu2qB/LNkx1oOXgCz5f5mrcS+3LR9MIp6ij89CQJHzaAzbMgKcHe5YqISBGi4Coi2WIYBi0ql+SLx9rT4dGJvFThf4xL7Md50xvnmOPw89MkfBgGGz+HpPhb7k9ERORWFFxFJMcaVvBj+uDW9HhiIm9U/p7Xkx4gwvTF+copWDyMhPfrwoZPIDFvb4csIiJFm4KriOSa0LI+TB7YkvufmsC7NX7g1cQHOWP64xx7FpYMJ/79OpjrPoKEWHuXKiIihZCCq4jkuqqlvHj7/qY89NwEpobO4ZXkwZw0S+JyLQLjtzEkvBeKuXYyJFy1d6kiIlKIKLiKSJ4JKenBuN6NCH9+PF+EzeXF5Ec5YQ3AOf4ixrKXiX+3NtY/3of4GHuXKiIihYCCq4jkuTK+brxyd32eHfEm/2u6gBet4Ry1lsIlIRLLyteIf7c2yavfhrgoe5cqIiIFmIKriOSbAC8XRnatwwsj32BBqx8ZzVAOW4NwSYzCYfU4Et6tTdKKcXAt0t6liohIAaTgKiL5zs/Dmec61WLMqLEsa7eQ0cazHLCWxTkpBsc/3ybh3dokLn0dYi/Zu1QRESlAFFxFxG68XJ0Ib1eNV0a/wtpOPzPG8QX2WsvjnHwVp7/eI/HdWsQveQmunLd3qSIiUgAouIqI3bk5O/BQq8q8OmoM27r+zBjnUey0huBkvYbLhikkvl+buJ9HQsxZe5cqIiJ2pOAqIgWGi6MD9zcN4fWRIznYYxFj3F5mm7UyTtZ4XDfPIOn9OsT+NAyiTtm7VBERsQMFVxEpcBwdLPRqGMybw5/n9L2LeMnzNTZZq+FoJuC+9XOSPqzHlXlPweXj9i5VRETykYKriBRYFovBnXXL8MbzzxB9/8+84jueDdYaOJqJeO78iuQPw4j5IRwu/WPvUkVEJB8ouIpIgWcYBu1rlua1Z54geeBiXi/5DmuSa+NAMl57viN5ckOi/vcwXDhk71JFRCQPKbiKSKFhGAYtqpTklaGP4jZkEeNKfcjq5Ho4YMXnwFysUxtz+euBELHX3qWKiEgeUHAVkUKpYQV/Xnz8IUqG/8zEctNYntwAC1Z8D/+EdVpzLn3ZF87usneZIiKSixRcRaRQCy3rw6gh/akwdCHvVvyUX61NsGDif2wJzGjJhc/uwTy11d5liohILlBwFZEioWopL154sA81n/mRD6vOZJG1OVbToOTJ5RiftuX8x3dhPf63vcsUEZEcUHAVkSKlQgkPnu1/Nw2GLWBarW/5ydqKZNMg4MzvWL7oSMS0LiQfWWvvMkVEJBsUXEWkSCrj68bQ+7rScsR8Pqs/h/lmOxJNBwIj/sJh1p1ETL6dpEOrwTTtXaqIiGSSgquIFGklPV14rGdHbh85h68bL2AOHUkwHQi8tAnHb3oQMaktCft+U4AVESkEFFxFpFjwcXdicLc2dBn9PXNa/sxsowvxphOBl7fh/H0fIt5vSdyuRQqwIiIFmKO9CxARyU+eLo7079SSuHbNWLh2C8l/TqJH0m8ExuyGuf0571ENs/HjEDAQ/dteRKRg0X+VRaRYcnVyoHfbxvQa/RVLOy7jf069uGK6EnD1AEGrn+Piu42J2fQ9WJPtXaqIiFyn4CoixZqzo4UercLoM+pz/ui6km9c7iPadCfg2j94LXqMC2+HEbX+K0hOsnepIiLFnoKriAjg6GDhzia16Tt8OsvbLuQbtwFEmp6UjDuOz69PcfGtOlz641NISrB3qSIixZaCq4jIv1gsBi1qBnP/C5PZ3WcN33g+xAXTmxIJp/Ff+QKX3golYuVUSIyzd6kiIsWOgquISAYMw6BV7YoMeOFDjvT7i299H+Oc6Yt/4jkC/3iRyxNrc+a39yAh1t6liogUGwquIiK30Lh6MP2ffZtzgzbwbYmnOGWWwDf5AkHrXidqYk1OLpoA8VfsXaaISJGn4Coikkl1K5am/1NvEvPo33xX6gWOmwH4WC9TbtNEYibW4PiCsZjXLtu7TBGRIkvBVUQki2qULcn9j79M8hObmF12NEfM0niZMZTf/gGxb9fiyJwxmLGX7F2miEiRo+AqIpJNFUv5ct8jo3B6ehNzKozloFkOD/MqFXd/xLW3a3H4fy9gjYmwd5kiIkVGtu6cddddd2XrYB9++CGVKlXK1ntFRAqqciW86P3Qc0REPca8n7+k9sGPqWEco/KBT4l7bxYnKt1HxbtG4+hb1t6liogUatkacV20aBGnTp0iJiYmU4/o6GgWL17M5cuXc7l8EZGCI9DHnXsGPEmp4Rv5scZ77KQyriRQ9Z+vSf6wHge+eJT4i8fsXaaISKGVrRFXgOnTp9OkSZNMbZuUlISzs3N2DyUiUqj4ebrQs+8Qoq8NZOEv3xO88yPqs49qx2eTOGUe+8t0p0KPl3EtVdnepYqIFCrZGnEdOXIkZctm/ldeDg4OjBw5kqCgoOwcTkSkUPJ2c+auewZSffQaFjf4lI1GHZxIovrpBThOb8S+6f24cmqPvcsUESk0shVcJ0yYkKXgahgGEyZMUHAVkWLJ3cWJrnf1oe6Lv/Nbs69Yb6mPI1ZqnFuM+6ct2Df1XqKObrd3mSIiBZ6uKiAikk9cHB3ofEcPGr64kpW3fc8ax6ZYMKlxYRk+M1uzf9JdXDr0t73LFBEpsBRcRUTymZODhfa3d6H5mN/4o/2P/OHUCqtpUD3yd/y/6cj+97twfu8ae5cpIlLgZCm4XrlyhVdffZWxY8cSGxvLO++8Q506dejXrx8XLlzIqxpFRIokB4tB69btuG3MIv7uspjVLu1INg2qR/9FwOyuHHz3ds7uWGHvMkVECowsBdeHH36YK1eucPbsWbp168b58+f5/vvvqV69Ok8//XRe1SgiUqQZhkGzZi1pM2oB23osY5V7JxJNB6pe2UTp+b04/NZtnNq0GEzT3qWKiNhVli6HtXfvXmbPno3VaqVUqVKsWLECwzCoXbs29erVy6saRUSKBcMwaNigMTSYw46dO7jw21u0jPmVytd2wKJ+/LOsJpa2IwhpdjcYhr3LFRHJd1kacXV0TMm5FouFsLAwjH/9h9PQf0RFRHJN3Tp1af/Ctxzp/xcrfHoRZzpRKX4vIb89xNEJjTn8+//AarV3mSIi+SpLwdXV1ZUrV64AsGzZstTlFy9eTA21IiKSe2pUq87tz33JqUF/s8K/L1dNF0ISDlJ51eMcH1+f/cu/xExOsneZIiL5IkvBde3atXh6ema47quvvsqVgkREJL3KFStx+9Mfc3HIZlYEPEiM6Ub5pKNUX/Msp8fXZe+SGZhJCfYuU0QkT2UpuN5sOkCJEiWoVatWrhQkIiI3Vz44mNufnEzM49tYGTSESNOTssmnqLlhJOfGh7Jr4YdYE+LsXaaISJ7I0XVc77zzztyqQ0REsqBM6dK0f+w9kp7ezsrgJ7lg+lDaeo7QLa9yYUJtdsx7i6S4q/YuU0QkV+UouG7atCm36hARkWwIKFGS9g+Px+G5HawKeY4I/Ag0L1B353ii3qrNttlvkBAbY+8yRURyhe6cJSJSBPj5+tJu0FhcX9jJ6qqjOENJSpiRhO19l6tv12LLty8TdyXS3mWKiOSIgquISBHi7elF2/6j8Rm5kz9qvsIJSuNHNA0OTibh3dpsnjmCq5d1p0MRKZwUXEVEiiB3N3da3/c8AaN3sKbOOI4aZfHmKg2Pfoz5YSibPn+WmEtn7F2miEiWKLiKiBRhri4utLpnKGVGb+evBu9xyBKCJ9dodOJLHCbXY9PHj3P53HF7lykikik5Cq7BwcG5VYeIiOQhZ2cnWtw1hJAxm9nQdAoHLFVwJ55GZ/6H27QGbJr2MBdOHbZ3mSIiNuUouG7evDm36hARkXzg6OhI0y4DqfLiRja2/IQ9jjVxMRJpFDEX708as2nqQM4d22fvMkVEMpTjqQIrVqzgyy+/zHDdzJkzWbVqVU4PISIiucziYKFxx/uoOeYvtrabxU6nujgbyTS68BMlvmjOpkn3c/rQTnuXKSKSRo6D60svvcS5c+cyXHf+/HleeumlnB5CRETyiGGxUL9NT0LH/MGOTrPZ7twAR8NKo8hfKPX1bWx5vxfH92+xd5kiIkAuBNfdu3fTqFGjDNc1aNCA3bt35/QQIiKSxwzDoG6LO6g3ZhW771zAFrdmOBgmDaJXUO5/7dny7l0c2bXe3mWKSDGX4+BqGAZRUVEZrouMjCQ5OTmnhxARkXxUu0l7Goz8jf09f2GT+21YDJMGV36n4tzO7Hi3K6f2b7R3iSJSTOU4uDZt2pSPPvoI0zTTLDdNk2nTptG0adOcHkJEROygelhLGo1YxOF7l7PRsz3JpkFY7F80XDWAXW93Yv/G5fYuUUSKGcec7uC1116jXbt21K1bl0GDBhEUFMTp06f56quvOHDgAKtXr86FMkVExF4qhzamcugCju7fzrnF42gYtYy6cRth8T3sWh6Gpc0IajW/EwzD3qWKSBGX4+DavHlzVqxYwYgRIxg5ciRWqxWLxZK6vFmzZrlRp4iI2FlI9XqUr/o9u7b8xbU106kfuYTQ+G2wtB97V9Um6bYXCG3VE8Oie9uISN7IcXAFaNmyJWvXruXatWtERkbi6+uLu7t7buxaREQKmMByVQh8+mvOnjjE8Z/H0+D8z9RM3A0rH2L/HxOJazGMum37KMCKSK7L1f+quLm5UaZMGYVWEZFioEyFajQbOpPLj25mfeB9XDOdqZ60n3p/PMbhcY3Y8tvXWPUFXRHJRbkSXC9cuMCLL75Ihw4dqF27Nh06dOCll17i/PnzubH7fGG1WmnevDlhYWHUqVOH3r17Ex0dbe+yREQKvMCyITR74hOuPr6F9aX7E2u6UCX5MA3WDeXYuAZs/uVzkpOS7F2miBQBOQ6uGzZsoGrVqkydOhUfHx/atGmDj48PU6ZMoUqVKmzYsCE36sxzFouF3377jW3btrFz506Cg4N555137F2WiEihUbJ0MM3CpxE/dDvryj7EFdONitajNPx7GCfH12PTwukkJSbYu0wRKcRyHFyffPJJateuzYkTJ5g3bx7Tpk1j3rx5HD9+nNq1azN06NBs7/vQoUOEh4cTFhaGo6MjoaGhGW63b98+OnbsiIeHB6VLl2bEiBEkJGT9P47e3t5Ayujr1atXMfQNWRGRLPMLCKL5Ix+S/MxO1pV/lGg8qGA9SaMtozg7vi5/L5hCYkK8vcsUkUIoV+6cNWrUqNTQd4OPjw+jRo1i165dOdr34sWLqVKlCrVq1cpwm8jISNq3b09CQgLz589n/PjxfPLJJwwbNixbx+zQoQOBgYHs37+fESNGZLt2EZHizsc/gOaD38F4bhfrQ54kEi/KmWdosv0lzk+ow4Z5H5AQH2fvMkWkEMlxcK1SpQqXL1/OcF1UVBSVKlXK9r67d+/OiRMnmDt3Lg0aNMhwmxkzZhAdHc2CBQvo3LkzgwcP5u2332bGjBmcPn06dbsGDRpQsmTJdI877rgjzf6WL1/OuXPnaNSoEdOmTct27SIiksLLx59mg8bj/Pwu1ld+hov4UMY8R9OdY7k0oTYbfnib+LhYe5cpIoVAji+H9c477/Dkk08SHBxMmzZtUpevXr2asWPHMnXq1Gzv25KJS6ksWbKEDh064O/vn7qsT58+hIeHs3TpUgYNGgTAli1bMn1cBwcHBg0aRN++fW866hofH098/P//quvGF7msVitWqzXTx8oOq9WKaZp5fpzCSv2xTf2xTf2xLSf9cfPwpkn/sVy7+jzrFk6i6sHPKc0FSu8ZR8Se6RyuNoR6dz2Fq7tnHlSeP/T5sU39sa049yez55zj4Dp8+HCioqJo3749Pj4+BAQEcP78eaKiovDz82PkyJGMHDkSAMMw2L59e04Pmca+ffsYPHhwmmW+vr4EBQWxb9++TO/nwoULAJQsWRLTNJk7d+5N59QCTJgwgddeey3d8vPnzxMXl7e/+rJarURFRWGaZqbCfXGj/tim/tim/tiWW/2pePujXG05gN2rZ1Hj6NeU4iKBB97m/Luf8Hf5AYS0ewhXt8IXYPX5sU39sa049ycmJiZT2+U4uDZs2NCuX2K6ccOD//Lz8+PSpUuZ3s+5c+cYOHAgiYmJmKZJ7dq1mTx58k23Hz16dJp5tNHR0QQHBxMQEJBuvm9us1qtGIZBQEBAsftgZ4b6Y5v6Y5v6Y1tu9yd44KvExw1nw6LplN/zMUGcp+3xqVyc9TUHKg0itMezeHj55rzwfKLPj23qj23FuT+urq6Z2i7HwXXmzJk53UWBULt2bTZv3pzp7V1cXHBxcUm33GKx5MuHzTCMfDtWYaT+2Kb+2Kb+2Jbb/XFz96Rpn+EkxD/F34tmUG7XNMqY52j+zyQiP/iSDRUHUufuF/D09suV4+U1fX5sU39sK679yez5Fvqu+Pn5ERUVlW55ZGRkmnmvIiJSsDm7uNLknmcJGL2Tv+uN46QRhB/RND8ylaT3Q1k3cxTRly/au0wRsaNsjbj+d07prXzxxRfZOUym1KhRI91c1qioKM6cOUONGjXy7LgiIpI3nJxdaHL3UJK6PcrGXz6n1LYplDdP0fzodKI//Ir15ftT8+6R+PiVtHepIpLPshVcZ86ciZeXF5UrV8Y0TZvb5vX81y5dujB+/HguX76cOtd1zpw5WCwWOnXqlKfHFhGRvOPo5EzjHo+T3PURNv36BQFbJlPBeoJmxz8hZtLXrC/Xj1q9RuHtH2jvUkUkn2QruDZv3pz169eTnJxMv3796Nu3LxUqVMjt2oiNjeWXX34B4NixY0RHRzN37lwA2rRpQ0BAAOHh4UyZMoWePXsyZswYTp06xfDhwwkPD6dMmTK5XpOIiOQvB0dHGnV7lOQuD7P5t1n4b/qQitZjNDv5OVcm/Y/1wX2pdfdovEuUsnepIpLHsjXHde3atRw5coT+/fvz3XffUalSJVq1asW0adNSLyuVGyIiIujduze9e/dm9erVnDhxIvX17t27gZQ5ritWrMDR0ZGePXsyatQohgwZwvvvv59rdYiIiP05ODjQ8M7BVHhxK1uaTeIfSwiexjWanfwSh8l12fDpM0RdOGPvMkUkDxnmrX7Xnwl79uzhu+++Y/bs2Rw9epTbb7+dp59+mi5duuRGjYVCdHQ0Pj4+REVF5cvlsCIiIggMDCx23zrMDPXHNvXHNvXHtoLUH2tyMtuWfYv3xg+okvwPALGmCzvL3kf1u0fjG5D/v3UrSP0piNQf24pzfzKbo3KlK7Vq1eKNN95gx44dPPvssyxbtoxPP/00N3YtIiKSIYuDAw3uGEilMZvZ0uIjDjlUxt2Ip+npr3CeGsaGT4Zy+fzpW+9IRAqNHAfX5ORklixZwoMPPkjp0qX54osvePjhhxk9enRu1CciImKTxcFCg04DqDRmE1taTuegQ5XrAfbr1AAbdUEBVqQoyHZw/eOPP3j88ccpVaoUffr0ITk5mW+//ZazZ8/y8ccf07hx49ysU0RExCaLg4UGHftR5cWNbGn1MQccqqYGWKcpYfytACtS6GXrqgLBwcFcuHCBLl26MH36dLp3757pW3WJiIjkJcNioUGHvpjt+7B55Q94rXuXaskHaXL6a2Kn/MDfZftQvdcYfErqyjMihU22guupU6dwcnJi2bJlLF++3Oa2hmFkeGcrERGRvGRYLDTs0Bdruz5sXqUAK1IUZCu4vvrqq7ldh4iISJ6wOPwrwK78Aa/171At+VBqgN1Y7j6q93oR7xKl7V2qiNyCgquIiBQLFgcLDTv2xdq+D5tW/oD39QDb+NRXxE6ZzaZy91P9njF4+elGBiIFVfG6SJiIiBR7FgcLjTr2pcqYjWxqMZ2Dlsq4E0+jkzOxTKrLpi+GceXyeXuXKSIZyFZwHT9+PGfOZO3uJOPHj+fcuXPZOZyIiEiuszhYaNSpH5Vf3MTfTady0FIRD+JodPxzzA/rsOnLF7h6OffuBikiOZet4Pryyy9z8uTJTG+fnJzMyy+/zKlTp7JzOBERkTxjcbDQpMsDVHpxC383mcxhSwheXKPRsU+xfliHzTOHcy060t5ligjZnONqmibPP/88vr6+md5eRESkIHNwsNDkzgdJ6tSf9b9+ReDmD6hkHqfh0U+Ifv9b9lQeRO27R+Dq6WvvUkWKrWwF19atW2MYBjExMVl6j5eXV3YOJyIikm8cHR1p1m0wSXcM5K9fviRo64dUNE/S8PBHRL77NXuqP0xozxdwdvO0d6kixU62guvq1atzuQwREZGCxdHRkRZ3PULCHYNYu+hTgndOprx5Br/9H3DxrS85Xusx6vR4FkcXd3uXKlJs6KoCIiIiNjg7O9Gy1xMEjtrOmtqvcYpASnCZ+nveInJibbbNf4fkhDh7lylSLCi4ioiIZIKriwutej+L/8id/FH9Zc5QkgDzEmE73uTChFB2LJyCNSnR3mWKFGkKriIiIlng5uZK6/tfwHv4Dn6vMpII/Chlnqfulpc4N7Eex9fOxkxOsneZIkWSgquIiEg2eHh40GbAGFyf38HqkOe4aHpT1nqGJjtf4dTERuxb9S3oqjoiuUrBVUREJAe8vbxpO2gsxrPbWVX2MaJMD8onH6PG70/wz/jGHF47XwFWJJdkK7j269ePiRMn8ssvv+imAiIiIoC/nz9tHp7Iqb7LWF3qQa6YrlRKPEjlZQ9xcGJLjm76zd4lihR62boc1vfff8/s2bNTX/v5+VGnTh3q1atH3bp1qVu3LqGhobi6uuZaoSIiIoWBv18Jajz2IWdOv8DmBW/S9MJ8qsbvhkV92LuyET5d36BM7Rb2LlOkUMrWiGtoaCju7u7079+fTz/9lEcffRQPDw/mz5/PkCFDaNq0KV5eXtSsWZO+ffvmds0iIiIFXtly5Wnz1Cece2g9f/j2JMF0oGbsJsrM6cLOD3pw/p8d9i5RpNDJVnDdvn0706ZNY82aNbzyyitUqFCBn376iePHj3Pp0iVWrVrFBx98QKtWrTh69GgulywiIlJ4VAipQutnZ3Hs/t/5y6MDVtOgTtRq/Ge1ZvvUfkSdPmzvEkUKDcM0sz9jPDExkenTpzNu3Dh8fHx488036dOnT27WV2hER0fj4+NDVFQU3t7eeXosq9VKREQEgYGBWCz6ft1/qT+2qT+2qT+2qT+2ZaY/O7eu59qvY2kSvw6ABNORPWXvpeq9r+LhXyY/y813+vzYVpz7k9kclaOuODk58fTTT3P48GH69evHI488QsOGDVm6dGlOdisiIlJk1anfjMajlrC54xy2OdbF2Ugi7PT3GJPrs23m88RfibR3iSIFVq7EeU9PT8aOHcvhw4dp2LAhXbp04dlnn82NXYuIiBQ5hmHQsGUn6o75g79afsEeS1XciSPs6GfEvRvKjjlvkpxwzd5lihQ42bqqAEBUVBR79+5N9zh69CgWi4X4+PjcrFNERKTIsVgMWnS8h8R2Pflj8VcEb32Xipyk7u53OLdnJpeavECNTkMwHLL9v2uRIiVbfxPKlCnDuXPnAAgODqZ27dqEhoZy3333ERoaSs2aNXFxccnVQkVERIoqJ0cHWvd4iGud+7FqwVRq7Z9KKfM8pTaM5Pjm6SS0fZkqLe8Bw7B3qSJ2la3gevbsWby9venZsyetWrWibt261KlTBzc3t9yuT0REpNhwc3Wh3f3PczlqCCvnvk3D419SPukoLH+Yg2s+xK3LG5Sr187eZYrYTbaC64svvsiOHTv4/fff+eqrrzAMA8MwqFSpUuoNCG48KlWqlNs1i4iIFGm+Pj60f3gcZ84OZcuc12h+YS5V43bCgp7sXtGKUr0mUjKkjr3LFMl32Qqub7zxRurz6OhoduzYkfrYvn07v/32G1evXsUwDDw9PYmKisq1gkVERIqLoNJBBD01g38OP8epBa/SIuZXakevIenL1mwr3ZOq940r8pfQEvm3HM/29vb2plWrVrRq1SrN8sOHD7Nt2zZ27tyZ00OIiIgUa5UqV6fSC9+za9vfxP7yMk0S1hN2bj5XJ//CtiqDqX3PGJzcvOxdpkiey7OvKVauXJnKlStzzz335NUhREREipXQsCaY9X5lw+qFeP/5BjWtBwk7NI0Lb3/H2QbPU/vOx3UFAinSitdtGURERAo5wzBo2q4HVcas54+6EzlFICXNSEI3v8SJCQ04tHY+ZP+mmCIFmoKriIhIIeTk6EjrXo/j/cJWVlV4hsumB+WTjlFl2UPse7sdp/dusHeJIrkuV36fkJyczIYNGzh58iRxcXHp1g8cODA3DiMiIiL/4eXpSbuHXufsucf5/YdXaXZhHjWubcX6fWe2BXSlUp+JeAcG27tMkVyR4+C6ZcsWevXqxYkTJzAz+NWEYRgKriIiInmsdKkgSj/1CYcPPE3Ejy/SPHY1YRcWETttGVuqPEqde0fj5Oph7zJFciTHUwUef/xxfHx8WLlyJefOnSMyMjLN49KlS7lRp4iIiGRC5WqhNB/xE1s6/sBeh2q4E0+DQ1O49FY9dv32OabVau8SRbItxyOuu3fvZs6cObRp0yY36hEREZFc0KBlZ5Ka3s6ahZ9QZce7lDbPU2rdMA5s/gynOydSMUz/35bCJ8cjrtWqVSM6Ojo3ahEREZFc5OjoSKteT+D+/Fb+KPcosaYL1RL2UPHHu9j6wb1cOHXY3iWKZEmOg+sHH3zAhAkT2LdvX27UIyIiIrnM28uH1kPeIfLh9azzvgOA+lHL8PikGX/PGk183FU7VyiSOTmeKjB06FDOnj1LaGgoZcqUwdfXN816wzDYvn17Tg8jIiIiOVS2fCXKDpvNnk2/Y/46mtpJu2lyZBqn35rH+ZavUrf9/RgWXSlTCq4cB9eGDRtiGEZu1CIiIiL5oFajNljrr2H9ok+puHUiZcxzlFnzBDs2fYHP3e9RoXqYvUsUyVCOg+vMmTNzoQwRERHJTxYHC816PEZMuz789f2rNDr1LXXjNpH4v/asK92HWvePx8fX395liqSh3weIiIgUY17efrR4dDLnHvidbe7NcTKSaX7uOxI/rM/6+VNITk62d4kiqbI14lqnTp0sTQ/YsWNHdg4jIiIi+SS4SijBI35l5+q5+P7+MsHmaUrueIm9e76Bru9Rs34re5cokr3gqnmtIiIiRVOdtveS2KIbf/8wgdqHZlAzaR/JP3bjzzX3UrvfRPxLlLR3iVKMZSu4al6riIhI0eXk7EqTAa9x6cxDHPzuWcKiV3HbxTlETFnOH/XG0PKuITg4aLah5D996kRERCRD/kEhhA37kQMdZ3HKEkQgkbTePpztE29nz66t9i5PiqFsjbh+9dVXWdp+4MCB2TmMiIiIFADVWvYkqVEntv3wOjUPf0aDxC3Ez+nI8j8G0KD/6/j7eNu7RCkmshVcBw0alOb1jfmupmmmWwYKriIiIoWdo4s7YQ9M5OLxBzky+2lqXP2bDhFfcvyDX9jeaCxt7rwfi0Xff5G8la2pApGRkamPjRs3UqFCBV566SW2b9/O2bNn2b59Oy+++CIVKlRgw4YNuV2ziIiI2EmJ8jWp8cJSDrWdygXDn/Kco92mx/nz7bs5dOSovcuTIi5bI64+Pj6pz0eNGsWjjz7KqFGjUpcFBgZSp04d3NzcGDlyJCtWrMh5pSIiIlIwGAZV2j5AUpPu7PpuDDWP/482cau4NLMli6q8QIf7nsLVOcf3OBJJJ8dfzvrrr79o2LBhhusaNmzI+vXrc3oIERERKYAc3X0JfXgakf0Wc9K5Iv7GFbodHsu2iR3ZsHWbvcuTIijHwTUwMJDZs2dnuO77778nICAgp4cQERGRAqxk9ZaUG7mRg6HPEY8TzaxbCP2xE/Onvcj5qFh7lydFSI7H8ceMGcNjjz3G4cOH6dmzJ4GBgURERLBgwQL++OMPPv7449yoU0RERAoyByeq3juWqy3u4+z/wqlwZRu9Iqay44Pf2HjbW9zRrr29K5QiIMfB9ZFHHiEoKIhx48YxfPhwkpKScHR0pEGDBvz000907949N+oUERGRQsCjTE08hq3i1Irp+P71JnXNg9T4ozfzt/QhrN8beDrYu0IpzLI1VSAhISHN627durFu3Tri4uI4c+YMcXFxrF+/XqFVRESkOLJYKNvxSVye3sixgLY4G8nce/U7kj5pz5Lf15CUbLV3hVJIZSu4+vv7c/fdd/P5559z7ty5/9+ZxUKpUqWwWHRDLhERkeLO0a8cFZ74kYtdPyXa4ksN4zj99zzK7PefYe+pS/YuTwqhbCXM+fPnExwczPjx4ylbtixNmjTh9ddfZ+tW3f5NRERE/sUwKNG4D17DNnKydAecjWQeuPYNCR93YNZPv5GQpNFXybxsBddOnToxefJkDh8+zPbt27nnnntYtmwZTZo0ITg4mMcee4zFixcTFxeX2/WKiIhIIWR4BlLmkR840XIiVy2e1LMcpu+W/sx893l2HL9o7/KkkMjx7/Rr167NyJEj+fPPPzl37hzjx48nKiqKAQMGUKJECbp166YrC4iIiAgYBk517sb1qfVElLoNFyORR+O+IOGzO5ixYClxicn2rlAKuFydjOrv788DDzzA999/z/nz5/n555+pVq0aH3zwQW4eRkRERAoxw6csgeE/c6XT+8QZbjSyHGDgtgF8/M4othzT6KvcXJ59i8rR0ZH27dvz/vvvs2/fvrw6jIiIiBRGhoFni4dxfXoDlwKa4m7E80zCJ0R/djfTfv5Lc18lQzm+juu1a9eYPn06Bw4coGTJktSpU4d69epRvXp1DMPIjRrzTUhICO7u7jg7OwPwv//9j1q1atm5KhERkSLMrwL+j//KtbUzcFj5Km0dtlN7U1/ePDCMBwY8TNVSXvauUAqQHAfXBx54gJ9++okmTZpw6dIl3nrrLaxWK66uroSGhlK/fn1mzJiRG7Xmi19++YWQkBB7lyEiIlJ8WCy43fYEVGtL9LcPEBB9iNdjXuWLj/5mTYdXebBVNSyWwjUYJnkjx1MFfvvtNyZPnszatWvZu3cvMTExbNiwgUmTJtG4cWN2796d7X0fOnSI8PBwwsLCcHR0JDQ0NMPt9u3bR8eOHfHw8KB06dKMGDEi3U0SREREpIArVQvvp9YQW28wAIMti2m0vA/DZ8zl1OVrdi5OCoIcj7gGBARQpUqV1Neurq40atSIRo0a5XTX7N69m8WLF9O0aVOsVitWa/r5LpGRkbRv356qVasyf/58Tp06xbBhw4iNjWXq1KlZPubdd9+N1Wrlzjvv5PXXX8fJySnH5yEiIiKZ5OSG+90fYNbsQPy8J6iTeJQ3zj3JhA82Uf+uodzdoFyhm4oouSfHI66PPvooP/30U27Ukk737t05ceIEc+fOpUGDBhluM2PGDKKjo1mwYAGdO3dm8ODBvP3228yYMYPTp0+nbtegQQNKliyZ7nHHHXekbrNmzRq2bt3K2rVr2bdvH2+//XaenJeIiIjYZtToiutT67hWtiXuRjxvGDNw/nEIz3/1B5FX9VvV4irHI64uLi789ttvvPHGGzz//PO4u7vnRl0Ambp17JIlS+jQoQP+/v6py/r06UN4eDhLly5l0KBBAGzZsuWW+ypXrhwAnp6ePPzwwzavPxsfH098fHzq6+joaICbjgznJqvVimmaeX6cwkr9sU39sU39sU39sU39sS3L/fEsjctDP5G0dhLG6vF0c1hP2D+DeeGD53nk/j40qeh/630UIsX585PZc85xcH3zzTeJjIzk1VdfZeLEiTRt2pSwsLDUR61atXB0zPFhbmrfvn0MHjw4zTJfX1+CgoKydBmuq1evkpycjLe3N0lJScybN4+6devedPsJEybw2muvpVt+/vz5PL9jmNVqJSoqCtM0MxXuixv1xzb1xzb1xzb1xzb1x7Zs96f6AJx86+K+9DnKXT3J9MSXGPfFPlY0epBBTcvgUES+uFWcPz8xMTGZ2i7HifLixYucOHGCHTt2pD5+/fVXpkyZQnJyMs7Oznka5CIjI/H19U233M/Pj0uXLmV6P+fOnaNXr15YrVaSkpJo0aIFL7744k23Hz16NMOGDUt9HR0dTXBwMAEBAXh7e2fpHLLKarViGAYBAQHF7oOdGeqPbeqPbeqPbeqPbeqPbTnqT2AHqLaWxB+H4rz/Z15zmsWCLYcYfXY4E/s2pbSPa94UnY+K8+fH1TVzP79cGQoNDg4mODiYrl27pi6Lj49n9+7d7NixIzcOkecqVarEtm3bMr29i4sLLi4u6ZZbLJZ8+bAZhpFvxyqM1B/b1B/b1B/b1B/b1B/bctQfN18sfb+GdR9hXfYKdzuspeaZ4zwxZThP97mD9jVK5X7B+ay4fn4ye77ZCq5fffVVrheSXX5+fkRFRaVbHhkZmWbeq4iIiBQBhgEthmIpU5+kHwZRI/YEXyWPZPhXR/irRR9G3FEDZ8fiFfqKk2wF1xtfeLrhxmUpTNNMtwxg4MCB2TlMptSoUSPdXNaoqCjOnDlDjRo18uy4IiIiYkchLXF8/E+sPzyI94n1fOz8ATPWH6LPkUeY1K8RFUp42LtCyQPZ+idJZGRk6mPjxo1UqFCBl156ie3bt3P27Fm2b9/Oiy++SIUKFdiwYUNu15xGly5dWL58OZcvX05dNmfOHCwWC506dcrTY4uIiIgdeZXGMmgRNHsSgHDHnxkRMYqBkxexaMfpW7xZCqNsjbj6+PikPh81ahSPPvooo0aNSl0WGBhInTp1cHNzY+TIkaxYsSJbxcXGxvLLL78AcOzYMaKjo5k7dy4Abdq0ISAggPDwcKZMmULPnj0ZM2YMp06dYvjw4YSHh1OmTJlsHVdEREQKCQcnuGM8BDfG+uOTtGAPs82RPPHdM2w/0ZmRd9TA0UFTB4qKHP8k//rrLxo2bJjhuoYNG7J+/fps7zsiIoLevXvTu3dvVq9ezYkTJ1Jf37iVrJ+fHytWrMDR0ZGePXsyatQohgwZwvvvv5/t44qIiEghU/tuLI+uwixZndJGJN85j+Pc2m8Y8PkGLlyJv/X7pVDI8VUFAgMDmT17Nh07dky37vvvvycgICDb+w4JCUkzb/ZmatasyfLly7N9HBERESkCAqpjPLICFoTjsm8Rk50/YtLx09w1uT8fDWhE/fJ+9q5QcijHwXXMmDE89thjHD58mJ49exIYGEhERAQLFizgjz/+sHn3KREREZFc5eIFfb6GFWNh7SSecVxA5WtnGPjxE4zpUZ/7m5S3d4WSAzkOro888ghBQUGMGzeO4cOHk5SUhKOjIw0aNOCnn36ie/fuuVGniIiISOZYLNDxdShZDfPnZ+nGesoZ53lk/vNsP1GHsXfVxtXJwd5VSjbkyg0IunXrRrdu3bBarZw/f75Y3vFBRERECpj6AzD8QjBnDyDs2mF+cnmZhze9wH1nopk+oCFlfN3sXaFkUa6mS4vFQqlSpRRaRUREpGAIaYUxZAWUqEoZ4yLzXMZS8vRKuk1Zw1+HL9i7OskiJUwREREp2kpUhiHLoGIb3InnU+f36RW3gIGfb+C7v4/buzrJAgVXERERKfrc/GDAPGj4EBZMXnL6ltctn/Hi/O1M+GUvVuutr2Ik9qfgKiIiIsWDgxN0+wDumIhpWOjnuJKPnCbx5R/7efzbzVxLSLZ3hXILCq4iIiJSfBgGNHsco/cscHCmi8NGZjq/w5rdR7nvk3VERMfZu0KxQcFVREREip9ad0H/OeDsSQvLLma7jufEyRP0+Ggte05H27s6uQkFVxERESmeKrWFBxeCmz+hHGaB+5uYUafoPeMvVu2LsHd1kgEFVxERESm+yjaEwb+Cd1lCrCf52eMNAhNP8vCsjcxce8Te1cl/KLiKiIhI8RZQHQb/BiWqEJAcwc/ub1CTI4z9eQ9jF+7WFQcKEAVXEREREd/glPAaVA/P5MsscB9PU2MvM/86yrOzt5GYbLV3hYKCq4iIiEgKj5Lw4CIIuQ3n5Kv8z+0tOjtsZuH20zz61SZdLqsAUHAVERERucHVG/rPhepdcbAmMN15Enc6bWbV/vM8+MXfRMcl2rvCYk3BVUREROTfnFyhz1dQpw8WM4mpTpO502UHfx+9RN+P13PhSry9Kyy2FFxFRERE/svBEXpOh9q9sFgTmerwPt3c97DnTDR9Zqzj1OVr9q6wWFJwFREREcmIgyP0+gRqdsdiTWCy8S7dvQ7yz4Wr3Dv9Lw5FXLF3hcWOgquIiIjIzTg4wT1fQLUuWJLjmGROpKffUc5ExdHn43XsPBll7wqLFQVXEREREVscnaHPLKjSAUvSNT5IepPegae4dDWB+z9dz/p/Ltq7wmJDwVVERETkVhxd4L5voGIbjMRY3o5/nf7lznMlPokHv/ibtYcu2LvCYkHBVURERCQznNzg/u+hQiuM+BjevPIKD1WMIj7JysOzNrJBI695TsFVREREJLOc3aHfbAhuhhEXxSuXxzCgYgxxiVYemrmRzccu2bvCIk3BVURERCQrXDyh/xwo2wjjWiRvRL3IPSHxxCYkM+iLjWw/cdneFRZZCq4iIiIiWeXqDQPmQVA9jNgLvBP/Bh0qOBATn8QDn29g1yldbSAvKLiKiIiIZIebL/SbAz7lsUT+w8eO79K8vDvRcSnhdd/ZaHtXWOQouIqIiIhkl1cpGDAXXH1wOLWRr/w+J6ycN5GxifT/dAOHImLsXWGRouAqIiIikhMB1aHv/8DBGaf9PzO74i/ULuPNxasJ3P/pBv45rzts5RYFVxEREZGcCmkFPaYB4LJxGnPq76RGaS/Ox8TT79MNHL8Ya+cCiwYFVxEREZHcULc33P4KAO4rX+SHtpFUDfTkbHQc93+6njNR1+xcYOGn4CoiIiKSW1oNgwYPgmnFe9FjzO7mTKWSHpy6fI2HvtxIdFyivSss1BRcRURERHKLYUDX96FKB0i6hv9PD/DtvaUJ8HJh39kYnvhmC4nJVntXWWgpuIqIiIjkJgdH6D0TSteFq+cJ+nkAs+6riruzA2sOXWD0/J2YpmnvKgslBVcRERGR3ObiBf1+AO9ycPEgtf4IZ9p9tbEYMHfzSSavOGTvCgslBVcRERGRvOAdlHJrWBdvOP4XbY+8z5s96wDwwfIDzN180s4FFj4KriIiIiJ5pVQtuPdLwIBNX9DPdR2Pt60MwKh5O1hz8IJ96ytkFFxFRERE8lLVDtBmZMrzn59heL0k7qpXhiSryePfbNatYbNAwVVEREQkr7UZAZXbQ9I1LHMG8s5dITSt6E9MfBIPfbmRs1Fx9q6wUFBwFREREclrFgfo9VnKl7UuHcZl0dN8MqAhVQI9ORMVx0MzNxKja7zekoKriIiISH7wKAF9ZoHFCfYuxGfHp3w5qDElPV3Yeyaaod9tIylZl8myRcFVREREJL+UawR3TEh5vvRlgmO288WgRrg5OfDnwQtM+vOEfesr4BRcRURERPJT4yEQei+YyTBnEHV9E5h8f30A5mw7z8Ltp+1cYMGl4CoiIiKSnwwDuk+CgBpw5SzMHUzH6iV48vplskbP38WBczF2LrJgUnAVERERyW8untDna3D2hKN/wqo3ebZDVRqX9+JaYjLhX2/Wl7UyoOAqIiIiYg8B1eCuKSnP13yAw8ElvH5HRYJ8XPnnwlVGzN2BaerLWv+m4CoiIiJiL6G9oGk4AMaPj1My6Swf9auPk4PBkl1n+ezPI3YusGBRcBURERGxp45vQLkmGPHR+KwcSVg5b17pVguAib/uY8M/F+1cYMGh4CoiIiJiT47OcM9nmM6eOJ/dDBtmMKBZBe6uX5Zkq8nQ77YSEa07a4GCq4iIiIj9+VXA7PgGAMbKNzAuHmLc3aFUL+XF+Zh4nvzfFhKTrXYu0v4UXEVEREQKggYPEl+uFUZSHPz4OO6OBjMeaIiXiyMbj0by1pJ99q7Q7hRcRURERAoCwyCq7ZuYLl5wciP8NYWKJT14p3c9AD5bc4TFO87YuUj7UnAVERERKSCsnkGYna/fEnbVOIjYyx2hpXmsTSUARszdzqGIK3as0L4UXEVEREQKknr9oGpnSE6ABeGQnMjwTtVpVsmfqwnJPPP91mI731XBVURERKQguXFLWFdfOLMN1nyIo4OFyffXx9fdid2no5my8pC9q7QLBVcRERGRgsY7CO58J+X572/B2Z0EernyZs9QAD5adYgdJy/brz47UXAVERERKYjq9IYa3cCaCAseh6QEutUtQ7e6QSRbTYb9sJ24xGR7V5mvFFxFRERECiLDgG4fgJs/nNsJf74LwBs9QgnwcuFQxBXeW7rfzkXmLwVXERERkYLKMxC6vpfy/I934fRW/DycmdirDpByiay/j1yyY4H5S8FVREREpCAL7QW17wYz+fqUgXhur1mKPo3KYZrwwpztXI1PsneV+ULBVURERKSgu/M98AiA83vhj5Qvbb3crRZlfd04fimW8b/stXOB+UPBVURERKSg8yjx/1MG1k6GS0fwcnXinXvrAvDthuP8fuC8HQvMHwquIiIiIoVBzbugUltIjoelLwHQokpJBrUIAWDk3B1EXUu0X335QMFVREREpDAwDLjjLTAcYN8iOLwSgJF31KBiSQ/ORsfx2sLddi4ybym4ioiIiBQWgTWgySMpz5eMguRE3JwdeLd3PSwGzN96il93nbVvjXlIwfW6iIgIwsLCUh/lypWjfv369i5LREREJK22o8C9BFzYDxs/A6BhBT8ea1MZgBcX7OTilXh7VphnFFyvCwwMZNu2bamPNm3a0LdvX3uXJSIiIpKWmx+0fznl+aoJcPUCAM92qEqN0l5cvJrAK0V0ykCBDq6HDh0iPDycsLAwHB0dCQ0NzXC7ffv20bFjRzw8PChdujQjRowgISEh28eNiYlh4cKFDBgwINv7EBEREckzDQZC6boQHwUr3wDAxfH/pwws3nGGtYcu2LnI3Fegg+vu3btZvHgxVapUoVatWhluExkZSfv27UlISGD+/PmMHz+eTz75hGHDhmX7uHPnzqV58+aULVs22/sQERERyTMWB+jyVsrzzbPg9DYAQsv68ECzCgCMXbibxGSrnQrMGwU6uHbv3p0TJ04wd+5cGjRokOE2M2bMIDo6mgULFtC5c2cGDx7M22+/zYwZMzh9+nTqdg0aNKBkyZLpHnfccUe6fX711Vc8+OCDeXZeIiIiIjlWoQWE3guYsGQkmCYAwzpWx9/DmYMRV5j111G7lpjbHO1dgC0Wy61z9ZIlS+jQoQP+/v6py/r06UN4eDhLly5l0KBBAGzZsiVTxzx+/Dhbt27l7rvvtrldfHw88fH/P/E5OjoaAKvVitWat/+6sVqtmKaZ58cprNQf29Qf29Qf29Qf29Qf29Qf27LVnw5jMfb/gnFiPdadcyD0XrxcHRjeqRqjF+ziw+UH6V43iAAvl7wrPBdk9pwLdHDNjH379jF48OA0y3x9fQkKCmLfvn1Z3t/XX3/NPffcg7u7u83tJkyYwGuvvZZu+fnz54mLi8vycbPCarUSFRWFaZqZCvfFjfpjm/pjm/pjm/pjm/pjm/pjW/b644RH2CN4bZyE+dtLXPBrhOnkTpvyztQq5c6ec7G8/tN2Xu4Ukpel51hMTEymtiv0wTUyMhJfX990y/38/Lh06VKW9/f111/z8ccf33K70aNHp5lHGx0dTXBwMAEBAXh7e2f5uFlhtVoxDIOAgAD9xc+A+mOb+mOb+mOb+mOb+mOb+mNbtvvTcRTmwR9xuHyMwP3fYLZPuavWm71c6DV9HYv3XOSh1lVpUN4vjyrPOVdX10xtV+iDa27L7Citi4sLLi7ph90tFku+/GU0DCPfjlUYqT+2qT+2qT+2qT+2qT+2qT+2Zas/zu7QeRzMHoCxbipGgwfAvyINKvjTp1E5fth0ktd+3suPT7bEwWLkXfE5kNnzLfSfGj8/P6KiotItj4yMTDPvVURERKTIqtENKraB5HhY+lLq4hF31MDL1ZGdp6KYvfGEHQvMHYU+uNaoUSPdKGlUVBRnzpyhRo0adqpKREREJB8ZRsrlsQwH2LcIDq8CoKSnC891qAbAO7/t43Js9q9zXxAU+uDapUsXli9fzuXLl1OXzZkzB4vFQqdOnexXmIiIiEh+CqwJTR5Jeb70Jbj+Tf2BzStQvZQXkbGJvLf0gB0LzLkCHVxjY2OZO3cuc+fO5dixY0RHR6e+Pn/+PADh4eF4eXnRs2dPli5dypdffsnw4cMJDw+nTJkydj4DERERkXzUZiQ4e8G5XbB/MQCODhbG3lUbgG83HGPP6Wh7VpgjBTq4RkRE0Lt3b3r37s3q1as5ceJE6uvdu1Puwevn58eKFStwdHSkZ8+ejBo1iiFDhvD+++/buXoRERGRfObuD00fS3m++q3UUdfmlUvQrW4QVhNeXbgL8/rNCgqbAn1VgZCQkEw1tmbNmixfvjwfKhIREREp4Jo/CRs+hnM7U0Zda3YH4MWuNVmxN4KNRyP5adtpetYvfLe2L9AjriIiIiKSRf8edf39rdRbwQb5uDG0fRUAxv+ylyvxSfaqMNsUXEVERESKmuZPpsx1PbsT9i1OXTzktoqElHAnIiaeKSsO2rHA7FFwFRERESlq3P2h6aMpz3+fmDrq6uLowCvdawHw5dqjnIm6Zq8Ks0XBVURERKQoaj4UnD3Tjbq2r1GKZpX8SUi2MnXlITsWmHUKriIiIiJFUZq5rv8/6gqk3pTgh00nOHEp1h7VZYuCq4iIiEhRdZNR16aVStCqSkkSk00+WlV4Rl0VXEVERESKKlujrh2rAjBn80mOXbxqj+qyTMFVREREpCj796jr/l9SFzes4E+bagEkW02mFJK5rgquIiIiIkWZuz80uX6FgdUT/jPqmjLXdf6Wkxy5UPBHXRVcRURERIq6m4y6hgX7cnuNQKwmTFp+wI4FZo6Cq4iIiEhR51HilqOuP20/zaGIGHtUl2kKriIiIiLFwU1GXUPL+tC5dilMEz5cXrDvpqXgKiIiIlIceJSAJo+kPF+d9goDz16/ruvinWfYdzbaHtVlioKriIiISHHR/Clw8oCzO2D/ktTFNYO86VonCNOESQV41FXBVURERKS48CgBTa/Pdf39rTSjrs90qIphwJJdZ9l9OspOBdqm4CoiIiJSnDR/Chxd4cw2OLEhdXG1Ul50r1sGKLhzXRVcRURERIoTjxJQ596U539/kmbV07dXxWLAsj3n2HHycv7XdgsKriIiIiLFzY1LY+35CaLPpC6uEuhJz7CyAHywrOBd11XBVURERKS4CaoHwc3AmgSbZ6ZZ9fTtVXGwGKzaf54txyPtU99NKLiKiIiIFEc3Lo21+UtISkhdHFLSg3saFMxRVwVXERERkeKo5l3gWRqunIO9C9Oseqp9VRwtBn8evMC2E5ftU18GFFxFREREiiNHZ2j0UMrz/3xJK9jfnec6VmN6/wbULetjh+IypuAqIiIiUlw1fAgsTimXxTq9Lc2qJ9tVoUudICwWwz61ZUDBVURERKS48ioFtXqkPP/7U/vWkgkKriIiIiLFWdPHUv7cOQeuXrRvLbeg4CoiIiJSnJVrnHJ5rOR42PqVvauxScFVREREpDgzDGhyfdR14+eQnGTfemxQcBUREREp7kJ7gZs/RJ2AA7/au5qbUnAVERERKe6c3KDhgynP/3NprIJEwVVEREREoNFgMCxw5HeI2GfvajKk4CoiIiIi4Fseqt+Z8nxjwbw0loKriIiIiKRo8mjKn9u+g7go+9aSAQVXEREREUlRsTUE1IDEqynhtYBRcBURERGRFIYBTR5Jeb7xU7Ba7VvPfyi4ioiIiMj/q9sXXLzh4iH4Z6W9q0lDwVVERERE/p+LJ4T1T3n+d8H6kpaCq4iIiIik1XhIyp8HfoNLR+xby7842rsAERERESlgSlaB+gPALwRcfexdTSoFVxERERFJr8dH9q4gHU0VEBEREZFCQcFVRERERAoFBVcRERERKRQUXEVERESkUFBwFREREZFCQcFVRERERAoFBVcRERERKRQUXEVERESkUFBwFREREZFCQcFVRERERAoFBVcRERERKRQUXEVERESkUFBwFREREZFCQcFVRERERAoFR3sXUFSYpglAdHR0nh/LarUSExODq6srFov+7fFf6o9t6o9t6o9t6o9t6o9t6o9txbk/N/LTjTx1MwquuSQmJgaA4OBgO1ciIiIiUjjFxMTg4+Nz0/WGeatoK5litVo5ffo0Xl5eGIaRZl3jxo3ZuHFjlpfd7HV0dDTBwcGcOHECb2/vXD2PjOrKjffY2kb9UX/Un5y9R/25+Xuy2pubLS+M/cmLz87Nlqs/tperP7aXN27cmL///puYmBjKlCljc7RZI665xGKxUK5cuQzXOTg4pPsAZmbZrV57e3vn+gc7o7py4z22tlF/1B/1J2fvUX9u/p6s9uZmywtjf/Lis3Oz5eqP7eXqj+3lDg4O+Pj42BxpvaF4TaCwkyeffDJby271Oi9k5xiZeY+tbdQf9Scn26g/6k92199sXVHpT158dm62XP2xvVz9sb08K7VpqkAhFB0djY+PD1FRUbn+L7KiQP2xTf2xTf2xTf2xTf2xTf2xTf25NY24FkIuLi68+uqruLi42LuUAkn9sU39sU39sU39sU39sU39sU39uTWNuIqIiIhIoaARVxEREREpFBRcRURERKRQUHAVERERkUJBwVVERERECgUFVxEREREpFBRcRURERKRQUHAVERERkUJBwVVERERECgUFVxEREREpFBRcRURERKRQUHAVERERkUJBwVVERERECgUFVxEREREpFBRcRURERKRQcLR3AUWF1Wrl9OnTeHl5YRiGvcsRERERKTRM0yQmJoYyZcpgsdx8XFXBNZecPn2a4OBge5chIiIiUmidOHGCcuXK3XS9gmsu8fLyAlIa7u3tnafHslqtnD9/noCAAJv/Kimu1B/b1B/b1B/b1B/b1B/b1B/binN/oqOjCQ4OTs1TN6PgmktuTA/w9vbOl+AaFxeHt7d3sftgZ4b6Y5v6Y5v6Y5v6Y5v6Y5v6Y5v6wy2nWxbProiIiIhIoaMR10Jo2Z5zHDx1ntAKBiElPSnr54aTg/4NIiIiIkWbgmsh9MOmk6zYFwGcAMDBYlDW140KJdwp7+9OSAkPypdwT33t7qwfs4iIiBR+SjSFUJOKfiQmxHP2SjLHI2OJS7Ry/FIsxy/FZrh9oJfL9RDrQYV/BdoKJTzwc3fS5btERESkUFBwLYQeua0SPap7EhgYCBhExMRz7OJVjl2KTfnzYizHLsZy9OJVYuKSiIiJJyImno1HI9Pty8vV8XqI/f9gW94/5VHG1w0Hi0KtiIiIFAwKroWcxWJQ2seV0j6uNK1UIt36y7EJHL2YEmiPX4zl2KXY639e5Vx0PDFxSew+Hc3u09Hp3uvkYFDOz51gf3cqXA+z5a8H22B/dzxd9PERERGR/KPkUcT5ujsT5u5MWLBvunXXEpI5EZkyOnv8UizHr4/aHr8Uy8lL10hItnLkwlWOXLia4b5LeDinhNp/hdkbo7WlvF01WisiIiK5SsG1GHNzdqBaKS+qlUp/sd9kq8nZ6DiOX4zl+KWr1+fQXuP4xZTnkbGJXLyawMWrCWw7cTnd+/89Wlve341gv/8Pt8H+7vi4OeXDGYqIiEhRouAqGbpxpYKyvm40r5x+CkJ0XCLHL8Zy4voI7bFLKc9PXIrlZOQ1EpNNm6O13q6OlC/hTrDf/4fZYD83yvu7U9bPDRdHh7w+RRERESlkFFwlW7xdnQgt60NoWZ9065KtJmeirqVOObhxxYPjl2I5GRnLhSsJRMclsetUNLtOpZ9baxhQysuVcn5uqYG2nJ875a6P3Ab5uOKo69aKiIgUOwqukuscLCnTBMr5uUPl9OuvxidxMjIl0J64FMuJyFhOXLqW+jw2IZmz0XGcjY5j07H0V0JwsBgE+bgS7OdOuRuh9nrILefnRoCncz6cpYiIiOQ3BVfJdx4ujlQv7UX10unn1pqmyaWrCZyIvJY67SAl2MZyKvIaJyNTvjR28vrzjDhaDEp5OVGhpFdqsC3r60Y5PzfK+rlR2lsjtiIiIoWRgqsUKIZhUMLThRKeLhleCcFqNYmIiedE5I0gmzJae/JySsg9FXmNJKvJqagETkVdzPAYDhaD0t6uqUG2nG/Kn2V9U+bXBvm44uqkObYiIiIFjYKrFCr/vm5t45D065OtJmcux7LryGmumK6cjopLCbjXg+3pyylfHDt1+RqnLl+DIxkfJ8DLJeXLaX5uqV9SK+vrRpnrf3q7OeqOYyIiIvlMwVWKFAeLQRlfNxzLehEYGIjFknZKwI0R21PXg+yNx6nL1zgVGcupy9eIS7RyPiae8zHxGV7qC8DTxZEyvq6U+VeYLeubMlpbxteNUt6uODtqOoKIiEhuUnCVYuXfI7YNK6Rfb5omkbGJnIq8lhpuT11OGak9fTmO05evcfFqAlfikzhw7goHzl3J8DiGAQGeLteDrStBPikBt4yPK0HX/yzp6YJFN2kQERHJNAVXkX8xDAN/D2f8PZypUy79pb4g5Y5jp6NuhNlrnLqcMh3hzI1lUXEkJFmJiIknIiaebScyPpajxaCUt2tqsA3ycU15XB+5Le3jSkkPhVsREZEbFFxFssjN2YHKAZ5UDvDMcL1pmly8msCZy3GcuvyvQHs5jtNR1zgbFce56LiUL5HdmGtL+st+wf+H2xujxEH/el7a25VS3q4Eervohg0iIlIsKLiK5DLDMCjp6UJJT5ebjtomJaeMyJ6JusaZqDjO/CvUno6K41xUHBEx/w23N+fv4ZwScL1dKO3jev35/wfb0t6u+Lk7a/RWREQKNQVXETtwdLCkfrHrZpKSrZy/Es+Z60H2TFTKTRnORMVxNuoaZ6PjOBcdT0KSlUtXE7h0NYG9Z25+TCcHg0AvVwK9XPBxgfIlL1DKJ+V1oLcrAZ4uBHq74K+AKyIiBZSCq0gB5ehguT739ebh9saXyW5MPzgbHZfmeUR0PBExcVy4kpD2MmAAhy5nfFxLyohxoLcLgV4uBFwPuwH/fnim/Knr3YqISH5ScBUpxP79ZbJaZbxvul1CkpULV+JTAm3UNQ6fvkCs6cy568H2xuW/Ll5NIMlqpt5y91a8XB1Tg2xJLxdKejinTJPwSpkqUcLTOWWdpwtuzgq5IiKSMwquIsWAs+P/T02wWn2ICLBkeJ3bxOSUgJsyUpsSaiOi4zl/JT413F64krIuIclKTFwSMXFJ/HP+6i1r8HB2uH5XNGdKeDhTwsMF/xvPPVNe3/jTz8NJXzgTEZF0ci24Ojg4sG7dOpo0aZJbuxSRfOaUiekJkDJFISY+KTXMRsTEcyEmnotX47kQk8CFK/HXHynP45OsXE1I5uqlWI5fis1ULZ4ujvh5OOHvnjKi7OfhnPLcM+VPX3dn/Nyd8PNwxtfdCV83Z930QUSkiMu14GqaZm7tKkOHDh3i3XffZf369ezatYsaNWqwa9euTNX11ltvMW3aNM6fP09YWBgffPABzZo1S7Pd6dOneeqpp1i6dClOTk706tWL999/H2/vm//6VaS4MgwDb1cnvF2dbnpZsBtM0+RKfBIXr4fYi1cTuHglgUtXU4Ltxaspz1PWJxAZm0CyNeU9V+KTOHHJ9hUV/s3D2SEl0Ho44efujI+bE77uTil/ujnjk/rcCd/r633cnHB1sugWviIihUChmSqwe/duFi9eTNOmTbFarVit1ky976233uLVV19l4sSJ1K1bl48++ohOnTqxbds2KlWqBEBiYiKdO3cG4H//+x+xsbG88MIL9OvXj0WLFuXZOYkUB4Zh4OXqhJerEyEl/6+9+46PoswfOP6Z7UlIJ5AAQUqA0ELoIApIFVAOFSl2xIL1RJQD9Px5J8p5Ap4NK6eHAnIUxUJTBLGEQ6QJJigdQgikbkhIsrszvz+WrIQkSwJbsuT7fr3ygn3m2Wee+c7s5JvZZ54JuWB9VdUoKLaTU1Tqmi0ht7CUnKKz/5aVFZWSV2Qjt6iU/DM2VA3nVd3SC08fdj6j/mwiHmQkzGLAotOoH55OWJCJsCADYRYjoRYDoRYD9cx//D/07P/rWQwY9XK1VwghvM2jiavVaiUnJ6dadaOiomrU9vXXX8+f/vQnAO666y62bt16wfcUFxcza9YspkyZwuTJkwG4+uqrad26NbNnz2bevHkALFu2jD179pCamkqbNm0AiIyMZOjQoWzZskWGPwjhQzqd4rwyGmykeTUSXXAmu9ZiG7lnE9m8olJyC23kn7GRd8aG9YyNvKJS8s44y/KL/ljmUDVsDudDI7ILS89p1VqjfluMOuqZDYSYDYSYDGf/ryfE7ExyQ0zOZcEm/dmfs/8/ryzEpMdi0hNk1EsyLIQQ5/Fo4lp21bI6HA5Hjdo+/yaS6vjxxx+xWq2MGTPGVWYymbjxxhtZsWKFq2z16tUkJSW5klaAwYMHExUVxapVq2qUuJaWlqJpmutrR4fDgcPhQKfTYTAYytUDMBqNF123tLQUg8FQrq7NZkPTNAwGgytmqqpit9tRFAWj0Vir6trtdlRVRa/Xo9fra1xX0zRsNhvg3LdlyuJjNBovWPdC7Va2j2pS1xv7vrK6lcXdXd3S0lJMJlPAHifn78+Is+Ne4+3mah8nNpuN08U2Cm0qp0tVrGfs5BUWc/TEKTBaKLTryD9jo6DYRsGZEgqLbVhLVKwlDk4X2ykotrnaLbZpFNtUsk6XokNFh4aKgsof5y4DzvOeHR3g3J/u6up1zjhYjAaCTDqCDQrBRh0mox6zyYTZoHP+6DTMRh1mowmLSY/ZoMOkUzDqNUx6PRazEaNeh8mgQ6c5MBl0WIxGTEYDRr2C7mw/jAYFi8mMQa9g0OnQVDtGRcFkNmLU69HpQDv72bLZbJjNZr/se3d1nce7HnQ6HKqGQ1UpLilFVTV0BqOzTNMoKbVhdzjQ0IGiw65q2B0qJaU2HKoKOgMOVcOuathsdmwOByqg4mzXZlex251/+DgUPerZuna7jfz8AoJCctEUAw5Vxa6qOOwOVE1DRYcKaBqoDgeq6nDte1XT0DRAtTs3SNFD2RAWTXX+oIBOj0GvoFMUDJrz86036DHo9eh1oAMMiobJoCfIbMRsdB4TRkXDbFAIMpkIMhswG/QEGSDYpCMsyESIxeQ6z3jzc2+z2VBV1efnCH/Xre45v2y7y9SG3yW+OOdXl0cT16eeeoqWLVt6sslLkpaWBkBiYmK58rZt23LkyBHOnDlDUFAQaWlpFeooikJiYqKrjfOVlJRQUlLiem21Oq/OzJkzhxkzZhAS4rxS9P3337Nx40Y6d+7Mdddd56o/e/ZsbDYbjzzyCBEREQBs2bKFdevW0aFDB2644QZX3VdeeYWioiLuv/9+GjRogKqq7N27l++++47WrVszduxYV9033niD/Px8Jk6cSKNGjQD45Zdf+PTTT2nevDm33Xabq+4777xDVlYWt99+O82aNXPFbOnSpTRp0oQJEya46r7//vtkZGQwbtw4WrVqBcCBAwdYuHAhDRs25L777nPVXbhwIYcPH+amm26iXbt2ABw9epQPPviAqKgoHnroIVfdJUuWsG/fPkaOHEmnTp0AOHHiBO+++y6hoaE89thjrrorVqwgNTWVa6+9lu7duwOQnZ3NvHnzMJvNTJ06FXB+EDZt2sRvv/3GwIEDufLKK1376JVXXkGn0/HUU0+52l27di1bt26lb9++9OvXD3BerX/ppZcAmDFjhusktH79elJSUujduzeDBg0CnB/+WbNmAfDkk09isVgA2LRpE5s2baJbt24MGzbMtb4XX3wRVVX585//7BpDnZKSwvr160lKSnJ9swAwd+5cSkpKePDBB4mOjgZg69atrFmzhrZt2zJ69GhX3ddee42CggLuvfdeYmNjAdi1axefffYZCQkJjB8/3hWfZcuWYbVaueuuu4iPjwfg119/Zfny5VxxxRXccccdrnbnz59PZmYmt956q2t4ze+//87HH39MXFwc99xzj6vuggULOHbsGDfffLPrM3Xo0CE+/PBD6tevzwMPPOCqu3jxYg4ePMioUaPo2LEj4BxrPn/+fMLDw3n00UdddZcuXcpvv/3GiBEj6NKlCwAnT57k7bffJjg4mClTprjqrly5kt27dzNkyBB69uwJQF5eHq+99hpGo5Fp06a56q5evZrt27fTv39/rr76agAKCgpIWf4uAH/961/LHSdbtmyhT58+DBgwAHD+MnjxxRcBuO3+RylRdRSW2Nn90w8cSd1O5BVtCWnZjcISO6dL7dh+WgpA5hWDOO0wUFTqIMK6j/jigxxRGvI/RzOKSh2oGoyz7MSoqCwt7khWiTNBbKfPJNl0lP32KDbZWrj6Nt6yA7Ni55Pi9uRpzhvrWutP0cd0mMOOCL4pTXDVHW3eRaiulM+L25KlOc9TLfTZ9DMdJN0RyrrSP/6AH2XeTaSumNUlrTmhOo/VprpcBpr3c1INYZ29HTpFQa9TGKzbTZRSyI8kclKJRAEakE9v7VfyCeEHYzIKznNrD9suojQr2w2JZOrqAxChWull30UhFjYZu6JqoAHd7XtoSB7baMkRpQGqBmHaaQYpv1CkGVnp6IyqOa+6X23YRzN9LimlTUlzNAAgTCnmJstuSjQ9i4o7u7btKuNBWhmy+cnWhN125+clmFLGBu1C1RT+U9zVVbeX8TBtDafYbotjh70xACbs3Bq0A4APznRxJsBAN8NROhoz+cnWkK1252dLQeWuoG0ALDyTTOnZX73JhnQ6GzNItcew2XaFa313Wn5Gp2gsOZNEEc7EqIPhBN2Nx/jdHs33tuauurdYtmNWHPy3uANWzXnuSdSfpLfpCAcdkWws/eN38hjLTkIUGyuL25GjBQOQoM/iatMhjjrC+dbRmlCzgVCLkStLfsKinuFUXG+CoxoSU89McFEGWb9sIrJBI0bcNI6YUDMhJn2NzhEfffQRx44dY/To0bRt2xao3eeIVatWVThHFBYWMnfuXKD8OeKrr75ye474y1/+4kp0N2zYwA8//ECPHj3KXfQrq/vYY48RGhoKeCePANi+fTtffvllrckjxo0bR3V4NHG97rrratXX6rm5uZjNZlciUSYyMtI5cXtuLkFBQeTm5rp2+vn1qhr6MGvWLP72t79VuiwrK4vCQuf0QGX/njlzhpMnT7rqlP01lZ2d7fpLqKCgAHAmTefWLRvPW9YXVVUpKnLemV1aWlqubtmV7JycHNdfUGVJdVV18/LyXOX5+fmA8y+jc+va7fYKdfPy8lzLzq1btj35+fmu8tzcXLd1rVarq7xsOx0OR7m6ZX8oFBQUVOivpmmuMlVVXe2ePn3aVV62L4By7ZbFsrCw0FV+7h8lJ0+edCWu5+7Xsrrnfntw6tQp11WosrpFRUXl1lcmOzub4uJiVz+h4r4vO05ycnJc6yk7TkpKSqrc92V/zVa2788dI172GTk3lucfJzXZ92VXFs7d92V1z9+fNdn3535Gzq+rqmq5umUxPbduWczOPU7A+bmE8vvzQsfJufuzbHsBTLbThBiNRAVBhgWOAI1D9fRpFeyq8/ZPzn+f7NeIoCBngrltWx4//XSQIW0ieb5fsvMKjUNjwX924LCrvDG6NTpTMCV2lcO/OziWepROjetxTZtmlNhVSuwaedt2gR3+1KE+JYYQSuwqutwiyIaYECN9Godjd2jYVBVTjgIaNA43EYQZu6oRZteD5nz4RLBJh8OhYb/ADbeaBjaHhjO9BIdZAwUKS+zkqs64WHQ2MINdVcm0/vGZKjGpoIe8wlIyVOf+cuhKwAwOVePEOXVLTRroneOXcx3OdvWKAyzONRfb/rjfoTq3COsUzibbztdmvUKE0YBegWBFhbMXNa+INKPXOa9qRpYawAYNQ010Dq6HXqdgwg5Zzjb6t4xAp9Oj1ymE550CK7SsH0R8TH1nG2jwm7Pu2M4N0BlMKAoomVY4mUG7hiF0atrIeR1eUTiz7WcA7uwei2JyHie2zCLs6ZDYIJiOVzTCoTljpe7eASpc374+DmMwqga6nCI4BXGhJgZFR1J69jgxZjn3fZMIMyGamRK7itn2x1V+m0Mjp8hGTpGNbmYViw62HMrh5AFn3JvpcrjGDL9mWJk7d5NzHxt0jDAWEAa8/nUaDeIKaBxuJqj4FHB5niPKyqBm54hTp065rkBWVvdcWVlZ5dZdtl5P5RHn1q0tecSpU6cqxKEyiuah6QB0Oh2bN2/2SeJaNsb1QrMKPP/88zz33HOug7TMsmXLuPnmm0lPT6dRo0a0atWKgQMH8tZbb5Wrd91111FaWsq6desqtF3ZFdf4+HgyMzOJjo726tfFqqqSmZlJZGSkDBWo5CsbVVU5ceIEUVFRMlSgkrqqqpKRkUF0dPRlNVTAU3UdDgcZGRnUr1+/3B+9nvoa0N91axL30tJSbA4VRadHQ8GhaZSW2sjIzCQyKhq9wYiqcvar91I0DRRFh6Jzfu3tcKhnf1kpKHq9K7F02O1omoZOr3f1QVNV5y9BBUxGIwoKiuL8Oh1NQ2/QYdAbUABNU9E0Fb2iYDY5k0CdoqCpDkDFaDBgNBjOJqmgOuzoFYUgi9kVH299BWyz2cjMzKRhw4auWNaW46Sqc4TNZueMXeWMHefczCV28k4XUVBsp9CmkVdkd87lbD3jnBnkdAknT9spLHUmLXpUFDQc6NDODoFR0NCjEmIxEh9Vj6ZRwTSrH0LrGAsNTTa6tG7qik+gnSO8OVSguLiYrKws4uLiyp2T/H2c+OKcf+bMGSIjI8nPz3c7o1PAzCpwMSIjIykpKaG4uLjcL6Dc3FwURSEyMtJVr+wvhHPl5ua6vkY9n9lsLje+q4zFYnEdbOBM6M/dcefWO19N6ur1eiwWS4Wxv5X16fyDsjbVPfdDfzF1gXLxLmMwGCqNT2V1a9JuVfuoJnUvdd9XVbequFdW12g0VohPoB0ncOn7s6q6JpOpQnw8cZx4a9974jipLO4Wi4XzW1YtRtTiEBpEh13UvQf+UXGbvXVMGY1GTCYTRqOxXHxqw3Hi7hwRXGFJdIWS8xWV2skqKOVkQTHH84s5kl3I4ewiDucUcSS7iBPWYvKLVfKPW9l9vPzNjvXMB2jXKIwOjcJp3yiM9o3DSIipVy5mtfkc4a3fJRaLBZPJhP6cP+pqy3Hi7XP+uRcD3fFY4vr+++/XqvGt8MfY1r1797rGT4Jz/EXTpk1dX9UlJibyyy+/lHuvpmns3buXwYMH+67DQgghRIAINhloGm2gaXTFtBeg2ObgaE4Rh7OLOJRdyP5Tp9mdbmXvCSunS+xsOZjDloN/fHVtNuhIjAujV/MorkyoT49mUfKoaFGBxxLXW265pdy4jzInTpxg9uzZpKamEhcXx6RJk+jWrZunVuvWlVdeSVhYGEuXLnUlrjabjRUrVjB8+HBXvWHDhvHRRx/x+++/uwYMr1+/nuzs7HL1hBBCCFE9FqOeVg1DadUw1FWmqirHMzKxKsH8mlHAnuP57Dlu5dfjzmR259E8dh7N4+1NBzDqFTo3jaRPy/r0SYimU3yETBEnPJe4Pv7446xbt469e/e6yrKzs+nSpYtrvGF+fj4LFy4kJSWF5OTkGrVfVFTEqlWrADh8+DBWq5Vly5YB0K9fP2JiYhg4cCCHDx9m3759gPPS+PTp03n22WeJiYmhY8eOzJs3j+zsbJ544glX26NHj+aFF17gpptu4oUXXnA9gGDEiBG16mYzIYQQItAZ9AqJDUJp1yic0V2bAM5ZIY7kFLH9aC4/7svmx/3ZpOedcV2Vfflr55PxejSPok9CfYa0i63ySq+4vHkscf3uu++4/fbby5XNmTPHNbXRxIkTOXnyJIMGDWLWrFksWbKkRu2fPHmSm2++uVxZ2esNGzbQv39/HA6H6661Mn/5y1/QNI3Zs2e7Hvm6du1a15Qd4ByTtGbNGh599FHGjx+PwWDgxhtv5OWXX65RH4UQQghRczqdQrP6ITSrH8INnZugaRqHs4v4YX/W2UQ2i9wiGxv2nmLD3lPM/DKV5PgIRnZqxIikOBqGVRzDKS5PHptVICoqigULFpSbY6x9+/aoqkpqaqqr7D//+Q/PPvssBw8e9MRqaw2r1Up4ePgF74bzhLKpPRo0aBBAN0f4jsTHPYmPexIf9yQ+7kl83LvY+KiqRuoJKz/uy2bD3pNsPpCNejZ7URTo1Tya6zs1YliHWCJDKr9JKhDU5eOnunmUx6642mw2goP/uGyfl5dHWloakyZNKlevRYsWZGZmemq1QgghhLjM6XQK7RuF075ROPf2bcHJgmJW7crgs53H2XYkj5QD2aQcyOaZlbu5ulV9RiY3Ymj7WIJNl/XkSXWSx/Zoy5YtSUlJcT0tYu3atQAMHDiwXL2cnBzXNFRCCCGEEDXVINTCXX2ac1ef5hzNKeKLXRl8vvM4v2ZYXcMJwoN+5daeTbnzymYylOAy4rHEdeLEia7HpMXGxvLcc8/RsGHDco+6BOd41PMfryqEEEIIcTHio4J5oH9LHujfkn0nC/h8ZwafbE/nSE4R8zbu593vDnB9p0bcc1UL2jXy7lA+4X0eS1wffPBBUlNT+fvf/47NZqNp06YsXrzYNVcqOIcPLFiwgOnTp3tqtUIIIYQQACQ0CGXy4FAeHdiKr1Mzmf/dQbYcymHFtnRWbEunT0I091zVgn6tY9DpFH93V1wEjyWuer2eefPmMWfOHAoLC6lfv36FOvXq1eP333/3+s1LQgghhKi79DqFoe1jGdo+lh1H83jvuwOs3n2CH/Zl88O+bBIa1GPiVc25oXNjLEZ5yEEg8fgta0FBQZUmreB8DGd0dHSljxgTQgghhPC05PgIXr+lC98+2Z97r25OPbOBfSdPM33FL1wzeyOfbk9HVT0ywZLwgbo114IQQggh6qQmkcE8NaIdKdMH8PSItjQKt5CRX8xjS3Zww5s/svVQzoUbEX4niasQQggh6oxQi5F7rm7BN0/058mhbQgx6dl5NI/Rb6Xw0KJtHM0p8ncXhRuSuAohhBCizrEY9Tx0TQIbn7yG8T3i0Snw5a4MBs79ln+sTqOg2ObvLopKSOIqhBBCiDorJtTMrBuT+PLRq+mTEE2pXeWtb/dzzeyNLPrfERwy/rVW8VjimpCQwOTJk/nmm2+w2+2ealYIIYQQwuvaxoXx0cSezL+zGy1iQsg6XcqMT37h+te+J+2E1d/dE2d5LHGdOnUq+/fvZ+TIkdSvX58xY8awYMECsrOzPbUKIYQQQgivURSFgW0bsvaxvjx7fTsigo38mmFl5Os/8N53B2T2gVrAY4nrfffdx2effUZ2djYLFy4kOjqap59+mtjYWPr06cOsWbPYvXu3p1YnhBBCCOEVRr2Ou/o056vJ/RiQ2IBSu8rML1O5/d//IyP/jL+7V6d5fIyr2WxmxIgRvPnmmxw5coSffvqJYcOGsXLlSjp16kTz5s15+OGHWbt2radXLYQQQgjhMTGhZubf2Y2ZozpgMer4YV82Q1/exBe7jvu7a3WW12/OSk5O5umnn2bz5s1kZGTwzDPPkJGRwZgxY7y9aiGEEEKIS6IoCrf1uoIvH72apCbhWIvtPLxoO5OX7MAqMw/4nE9nFWjQoAETJkxg+fLlZGVl+XLVQgghhBAXrWVMPZY/cCWPDkhAp8An29MZ9q/v2HxA7uXxJb9NhyWPfRVCCCFEIDHqdTw+pA1LJ/WmaVQw6XlnGP/uZv6xOg27Q/V39+oEmcdVCCGEEKIGul4Rxao/X83YbvFoGrz17X7uWbBVHlrgA5K4CiGEEELUUD2zgRdHJ/HGLV2wGHVs3HuKm99KIT1PZh3wJklchRBCCCEu0oikOP57f29iQs2knSjgT6//wI6jef7u1mXL44lrcXEx4eHhfP75555uWgghhBCi1klqEsHKh/qQGBtK1ukSxr6dwqpfMvzdrcuSxxNXi8VCcHAwBoPB000LIYQQQtRKjSKCWPbAlQxIbECJXeXBhdt4Y8M+NE2etuVJXhkqcOedd/Lee+95o2khhBBCiFqpntnAu3d0Y0KfZgC8tHYvTy7bRaldZhzwFK9cFo2MjGTz5s0kJSVx7bXX0rBhQxRFcS1XFIXJkyd7Y9VCCCGEEH6j1yn83/XtaV4/hGc/28Oyn49xNKeIt2/vSkSwyd/dC3heSVynT58OQEZGBrt3766wXBJXIYQQQlzO7ujdjKZRwTy8aDv/O5jDDfN+5MOJPWgSGezvrgU0rwwVUFXV7Y/D4ahxm2lpaQwePJiQkBBiY2OZOnUqpaWlbt+zceNGFEWp9CcxMfGC9caNG1fjfgohhBBCAPRv04DlD1xJ44ggDmYVMv7dzTJd1iUKiDuocnNzGTBgAK1atWLFihWkp6fz+OOPU1RUxOuvv17l+7p06UJKSkq5MqvVyrBhwxg2bFiF+u+//365hLZ+/fqe2wghhBBC1DltYkNZ/sCVjHsnhUPZRYx/ZzMf39eLRhFB/u5aQPJa4mqz2Zg/fz4//fQTR48e5Y033qBVq1YsWbKEpKQk2rZtW+223nrrLaxWK5988glRUVEA2O12HnzwQWbMmEGjRo0qfV9YWBi9evUqV/bBBx+gqiq33HJLhfodOnSgW7duNdhKIYQQQgj3YsMtLL6vF2Pf3syRnCLGv7uZJff1Jjbc4u+uBRyvDBU4cOAAbdq0YerUqezbt4/169dTUFAAwKZNm/jnP/9Zo/ZWr17NoEGDXEkrwJgxY1BVlXXr1tWorUWLFtGqVSu6d+9eo/cJIYQQQlysuPAgFt/Xi/ioIA5nO5PXTGuxv7sVcLxyxfXRRx8lJiaGLVu2EBERgcn0x110/fr1c928VV1paWncfffd5coiIiKIi4sjLS2t2u1kZmbyzTff8PTTT1e6fPjw4WRnZxMXF8f48eP5+9//TlBQ5ZfyS0pKKCkpcb22Wq3AH+N7vUlVVTRN8/p6ApXExz2Jj3sSH/ckPu5JfNyr6/GJCzOzaGJPxr/3Pw5mFTLunc0svqcHDcKcV17rcnyqu81eSVw3btzI4sWLqV+/foUbsWJjY8nIqNnTJHJzc4mIiKhQHhkZSU5OTrXbWbJkCQ6Ho8IwgfDwcKZOnUrfvn0JCgrim2++Yfbs2aSmpvLFF19U2tasWbP429/+VqH81KlTFBd79y8oVVXJz89H0zR0Onlq7/kkPu5JfNyT+Lgn8XFP4uOexAeMwKujWvLgst84mFXI2LdTmDe6NdEhxjodn7Jv5i/EK4mrwWCo8kkRmZmZ1KtXzxurvaCFCxfStWtXWrduXa68c+fOdO7c2fV6wIABxMXF8fDDD7NlyxZ69OhRoa3p06fz+OOPu15brVbi4+OJiYkhLCzMexuB84OvKAoxMTF17sCuDomPexIf9yQ+7kl83JP4uCfxcWrQAD6+P5rx7/6Pw7nF/PnT/Sy8pycNQox1Nj4WS/XG+3olce3Xrx9z5sxh2LBhrsArioKmabzzzjsMHDiwRu1FRkaSn59foTw3N7fcuFd39u/fz5YtW5g7d2616o8ZM4aHH36Yn3/+udLE1Ww2YzabK5TrdDqfHGyKovhsXYFI4uOexMc9iY97Eh/3JD7uSXycmtWvx8f39WLcO5vZd6qQ2/+9hY8m9qiz8anu9nolKv/4xz/45ZdfaNeuHVOnTkVRFN544w169+7Ntm3bmDlzZo3aS0xMrDCWNT8/n4yMjHLTV7mzaNEidDqdzM0qhBBCiFrhiugQFt/bi4ZhZn7LPM1t87eQd8bu727Val5JXNu2bcvPP//MlVdeyeLFi9Hr9XzxxRckJCSwZcsWWrZsWaP2hg0bxtdff01eXp6rbOnSpeh0OoYMGVKtNhYvXkz//v2Ji4urVv2PP/4YQGYfEEIIIYTXNKsfwsf39aZBqDN5ffKzfZTYav6gprrCK0MFcnJyaN68Of/5z38qXb579246dOhQ7fYmTZrEa6+9xqhRo5gxYwbp6ek8+eSTTJo0qdwcrgMHDuTw4cPs27ev3Pu3b99OamoqU6ZMqbT92267jYSEBLp06YLFYuGbb77h5ZdfZtSoUTKvqxBCCCG8qnn9EBbd25Mb5v3ILxmFTF3+C6+O74yiKP7uWq3jlSuuQ4cO5fTp05Uu27p1K/37969Re5GRkaxfvx6DwcCoUaOYNm0a99xzT4Xxqg6HA7u94iX2RYsWYTabuemmmyptv3379ixbtoxbb72V6667jk8++YQZM2awZMmSGvVTCCGEEOJiJDQI5c1bu6DXwee7Mnj569/93aVaSdGquv3/EnTv3p3g4GDWrFlTbh7UH3/8keHDhzNs2DAWL17s6dX6ldVqJTw8nPz8fJ/MKnDy5EkaNGhQ5wZvV4fExz2Jj3sSH/ckPu5JfNyT+LinqirzN/zK818dBmDumE7c2KWJn3vlG9XNo7xy1KxZs4acnBxuuOEGbDYbABs2bGDo0KGMGjWKhQsXemO1QgghhBAB7fr29ZnUrwUAf1m+i/8dyPZzj2oXrySu0dHRfPXVVxw4cICxY8fy+eefM2LECG677TY++OAD+StLCCGEEKIKTwxuzfCOsdgcGvd/9DMHswr93aVaw2sZZGxsLOvXr2fbtm2MGjWKSZMm8eabb3prdUIIIYQQlwWdTmHumGQ6xUeQV2RjwvtbyC0s9Xe3agWPzSrw6KOPVlrerl07CgsLsdvtrjqKovDKK694atVCCCGEEJcVi1HPe3d0Y9QbP3Aou4j7P/yZD+/pgdmg93fX/Mpjievnn39e5bJ69eqVWy6JqxBCCCGEezGhZt6f0J2b5v3IlkM5TF/+C3PGdKrT02R5LHE9ePCgp5oSQgghhBBA64ahzLutC3e9/xMrtqfTrH4Ijw5s5e9u+Y3cJSWEEEIIUYtd3SqG5/7kfHDT3K9+4/Odx/3cI//xypOzAHJzc1m9ejXHjh2juLi4wvJnnnnGW6sWQgghhLis3NKzKQezTvPudwf5y/JdtI0LI6FBPX93y+e8kriuW7eO0aNHc/r0aYKCgjCZTOWWK4oiiasQQgghRA1MG9aW3elWUg5k8+DCn1n50FUEmerWzVpeGSowZcoUunfvzsGDByksLCQ3N7fcT05OjjdWK4QQQghx2dLrFF4Zn0xMqJnfMk/z9Ke78cIDUGs1rySuBw4cYNq0aVxxxRXeaF4IIYQQok5qEGrh1XGd0SmwfNsxlm495u8u+ZRXEtcuXbpw9OhRbzQthBBCCFGn9W4ZzZQhbQD468rdpGZY/dwj3/FK4vrmm2/y6quvsnbtWux2uzdWIYQQQghRZz3QryX928RQYld5cOE2Copt/u6ST3glce3duzdpaWkMHz6coKAgwsLCyv2Eh4d7Y7VCCCGEEHWCTqfw8phkGoVbOJhVyLTlv9SJ8a5emVVgypQpdfqpDkIIIYQQ3hYZYuK1W7ow9u0Uvvwlg56bo7ijdzN/d8urvJK4Pvvss95oVgghhBBCnKPrFZFMG5bIzC9Tee6LX+nUJIJO8RH+7pbXyJOzhBBCCCEC2MSrmjO0fUNsDo0HF24jv+jyHe/qsSuuI0eOZM6cObRq1YqRI0e6rasoCitXrvTUqoUQQggh6ixFUfjn6E6kZnzPkZwipizdwbt3dLssh2167IprQUEBDocDAKvVSkFBQZU/VmvdmbZBCCGEEMLbwoOMzLu1Cya9jq9TT/Ludwf83SWv8NgV1wkTJhATEwPAxo0bPdWsEEIIIYSohg6Nw3nm+nY8/eluXlq7lz4J9Wnf6PKaycljV1wnTJjA/v37PdWcEEIIIYSooVt7NmVIO+d418lLdlBsc/i7Sx7lscS1LswdJoQQQghRmymKwqwbO1K/nonfMk/z0tq9/u6SR8msAkIIIYQQl5Hoemb+OToJgPnfH+SHfVl+7pHneHQe18WLF/P9999fsJ6iKEyePNmTqxZCCCGEEGcNSGzILT2bsuh/R3hi6U7W/Lkv4cFGf3frknk0cX3llVeqVe9iEte0tDQeeeQRfvzxR0JDQ7njjjuYOXMmJpPJ7fuaNWvG4cOHK5SfOXMGi8Xien38+HEeeeQR1q1bh9Fo5MYbb2Tu3LmEhYXVqJ9CCCGEELXBU8Pb8uO+LA5lF/HMZ7t5ZVxnf3fpknk0cd28eTM9evTwZJMA5ObmMmDAAFq1asWKFStIT0/n8ccfp6ioiNdff/2C7x89ejRTpkwpV2Y2m13/t9lsDB06FIBFixZRVFTEE088wS233MIXX3zh2Y0RQgghhPCBELOBl8cmM/qtFFbuOM7Atg0Z2amRv7t1SbzyyFdPe+utt7BarXzyySdERUUBYLfbefDBB5kxYwaNGrnfCQ0bNqRXr15VLl+2bBl79uwhNTWVNm3aABAZGcnQoUPZsmWLV5JxIYQQQghv69w0koeuSeDV9b/z9Ce/0L1ZJHHhQf7u1kULiJuzVq9ezaBBg1xJK8CYMWNQVZV169Z5pP2kpCRX0gowePBgoqKiWLVq1SW3L4QQQgjhL48MSKBTk3CsxXaeWLoTVQ3cmaAC4oprWload999d7myiIgI4uLiSEtLu+D7Fy5cyLvvvovRaKRv3768+OKLdOzYsVz7iYmJ5d6jKAqJiYlVtl9SUkJJSYnrddnTwFRVRVXVam/bxVBVFU3TvL6eQCXxcU/i457Exz2Jj3sSH/ckPu55Kz56BebcnMR1r//AD/uyef+Hg0zo08yj67hU1d1mjyWu3jwIc3NziYiIqFAeGRlJTk6O2/eOHDmSnj170rRpUw4cOMDzzz/PVVddxfbt22nRosVFtz9r1iz+9re/VSg/deoUxcXFF96oS6CqKvn5+Wiahk4XEBfNfUri457Exz2Jj3sSH/ckPu5JfNzzZnzqAQ9f1ZjZG47y4po02kYptIiuPUMGCgoKqlUvIK64XopXX33V9f+rr76aIUOGkJiYyOzZs5k3b95Ftzt9+nQef/xx12ur1Up8fDwxMTFen4lAVVUURSEmJkY++JWQ+Lgn8XFP4uOexMc9iY97Eh/3vB2fBwbF8FP6Gb79LYuZXx9lxQNXYjLUjv1w7kxP7gRE4hoZGUl+fn6F8tzc3HLjXqsjLi6Oq666ip9//rla7cfHx1fajtlsLjczQRmdTueTD6OiKD5bVyCS+Lgn8XFP4uOexMc9iY97Eh/3vB2fl0Z3Yui/NvFrRgGvfLOPv1ybeOE3+UB1tzcgjprKxprm5+eTkZFRYWyqp9rXNI29e/d6pH0hhBBCiNqgQZiFWTc67/N5+9v9bDuS6+ce1UxAJK7Dhg3j66+/Ji8vz1W2dOlSdDodQ4YMqVFbx48f5/vvv6d79+7l2t+5cye///67q2z9+vVkZ2czfPjwS+6/EEIIIURtcW2HOEYlN0LV4MmlOym2OfzdpWoLiMR10qRJhIaGMmrUKNatW8f777/Pk08+yaRJk8rN4Tpw4EASEhJcrxcvXsytt97KwoUL2bBhA/Pnz6dv377o9fpyDyQYPXo07du356abbuKLL77gv//9L3fffTcjRoyQOVyFEEIIcdl5dmR76tczs/9UIS9//Zu/u1NtAZG4RkZGsn79egwGA6NGjWLatGncc889zJ07t1w9h8OB3W53vW7evDnHjx/nscceY8iQIUybNo2uXbuSkpJC8+bNXfWMRiNr1qyhVatWjB8/nvvvv5/BgwezaNEin22jEEIIIYSvRASbeOGGDgC8u+lAwAwZCIibswDatm3L119/7bbOxo0by73u1asXGzZsqFb7jRs3Zvny5RfbPSGEEEKIgDKkfSyjkhvx6Y7jPLl0J18+ejUWo97f3XIrIK64CiGEEEIIzwu0IQOSuAohhBBC1FGBNmRAElchhBBCiDqsbMhAIMwyIImrEEIIIUQd9+zI9sSE1v4hA5K4CiGEEELUcc4hA84HE9TmIQOSuAohhBBCCAa3a1jrhwxI4iqEEEIIIYDaP2RAElchhBBCCAHU/iEDkrgKIYQQQgiX2jxkQBJXIYQQQghRTtmQgazTpfyeedrf3XEJmEe+CiGEEEII34gINvHWbV2JjwyiQZjF391xkcRVCCGEEEJU0PWKSH93oQIZKiCEEEIIIQKCJK5CCCGEECIgyFABD9E0DQCr1er1damqSkFBARaLBZ1O/vY4n8THPYmPexIf9yQ+7kl83JP4uFeX41OWP5XlU1WRxNVDCgoKAIiPj/dzT4QQQgghAlNBQQHh4eFVLle0C6W2olpUVeX48eOEhoaiKEq5Zd27d+enn36qcVlVr61WK/Hx8Rw9epSwsDCPbkdl/fLEe9zVkfhIfCQ+l/YeiU/V76lpbKoqD8T4eOPYqapc4uO+XOLjvrx79+5s2bKFgoICGjVq5PZqs1xx9RCdTkeTJk0qXabX6yscgNUpu9DrsLAwjx/YlfXLE+9xV0fiI/GR+FzaeyQ+Vb+nprGpqjwQ4+ONY6eqcomP+3KJj/tyvV5PeHi42yutZerWAAo/eeihhy6q7EKvveFi1lGd97irI/GR+FxKHYmPxOdil1e17HKJjzeOnarKJT7uyyU+7str0jcZKhCArFYr4eHh5Ofne/wvssuBxMc9iY97Eh/3JD7uSXzck/i4J/G5MLniGoDMZjP/93//h9ls9ndXaiWJj3sSH/ckPu5JfNyT+Lgn8XFP4nNhcsVVCCGEEEIEBLniKoQQQgghAoIkrkIIIYQQIiBI4iqEEEIIIQKCJK5CCCGEECIgSOJ6mVq9ejWdO3cmOTmZbt26kZKS4u8u1SrvvfceSUlJtG3blltuuYUzZ874u0t+df/999O4ceMKT30DSE1NpXv37rRu3ZoBAwaQkZHhhx76l7v4uFtWV1QVg+zsbIYNG0abNm3o2LEjd999NyUlJX7qpf9UFR9VVenduzfJycl07NiRm2++2fW89rqkOp+he++9t85+xtzFp1mzZrRr147k5GSSk5P59ddf/dBDH9PEZSkuLk7bs2ePpmma9vnnn2vdunXzc49qjz179mjNmzfXcnNzNU3TtAcffFCbOXOmfzvlZ99++6124sQJrbJTQt++fbVPP/1U0zRN+9e//qXdcccdvu6e37mLj7tldUVVMcjOzta+/fZbTdM0zeFwaOPGjdNmz57tjy76lbtjJD8/3/X/yZMna08//bQvu1YrXOgz9NVXX2l33nlnnf2MuYvPFVdcoR08eND3nfIjueJai+zbt49JkyaRnJyMwWCgQ4cOldZLS0tj8ODBhISEEBsby9SpUyktLS1XR6fTkZ+fD0B+fj6NGzf2ev+9zVPx2bNnD927dyciIgKAoUOHsnjxYl9sgkd58njp27cvDRs2rPDezMxMfv/9d/70pz8BMHHiRD755BPPb4wX+CI+F1pWm/kiPlFRUfTt2xdwnpO6devGkSNHPL8xXuCr46dsknlVVSksLAyYq4q+ik9hYSFPPfUUc+bM8fg2eJOv4lMXGfzdAfGHPXv28OWXX9KzZ09UVUVV1Qp1cnNzGTBgAK1atWLFihWkp6fz+OOPU1RUxOuvv+6q99FHHzFy5EiCgoLQNI0ffvjBl5viFZ6KT1JSEpMnTyY9PZ3Y2FiWLVsWML9Mz+XJ46Uqx44dIz4+3vW6Xr16WCwWsrOziY6O9uj2eJov4hPIfB2f4uJiPvjgA1566SVPbYJX+TI+gwYNYseOHXTo0CFgEjRfxWf69On8+c9/rvXnm/P58vi54YYbUFWV4cOH8/e//x2j0ejJTal9/H3JV/zB4XC4/n/nnXdq7du3r1DnhRde0EJCQrTs7GxX2dtvv63p9XotPT1d0zRNs9ls2tChQ7UdO3ZomqZp77zzjjZ48GAv9977PBUfTdO0Dz/8UOvatavWq1cvbcaMGVpkZKR3O+8FnoxHmfNPCVu3btV69OhRriwmJkbLysq61O57nS/iU91ltZEv4+NwOLQxY8ZojzzyiAd67hu+Pn7sdrs2ZcoU7cUXX7zEnvuGL+Lz/fffa8OHD69yeW3mq+Pn6NGjmqZpWkFBgTZq1Kg6MexNhgrUIjrdhXfH6tWrGTRoEFFRUa6yMWPGoKoq69atA2DHjh3k5OTQqVMnAG699Va+//5773TahzwVH4DbbruNrVu3kpKSQnJyMomJiV7pszd5Mh5VadKkCUePHnW9Pn36NMXFxQFx9cMX8QlkvozPQw89hE6n41//+tfFdNUvfH386PV67rrrLhYsWFDjvvqDL+Lz3XffsX37dpo1a0azZs0A581IJ06cuOh++4qvjp8mTZoAzm/DJk6cyObNmy+uwwFEEtcAk5aWViHJioiIIC4ujrS0NMB5IO/bt8+VcKxZs4b27dv7vK/+UJ34gHPsJjjH//7zn//kscce82U3faa68ahKw4YNSUhIYOXKlQDMnz+fUaNGeaOrfnGp8bnceSI+U6dO5ejRoyxYsKBav8wDyaXGJysri6ysLAA0TWPZsmVVjoUMRJcan2nTpnH8+HEOHTrEoUOHADh06BCxsbHe6K7PXWp8CgsLXbNQ2O12li9fTlJSklf6WptcXmeROiA3N9d1U9G5IiMjycnJASA2NpY5c+Zw7bXX0qlTJ2bPns38+fN93FP/qE58wHnFtX379nTt2pUxY8YwZswYH/bSd6obj7vuusv1l3uTJk24/fbbXcvefPNNnnvuOVq1asWnn37KP/7xD6/321c8ER93ywLdpcZnz549vPTSS+zfv5/u3buTnJzMk08+6ZO++8KlxiczM5OhQ4eSlJREUlISaWlpvPrqqz7puy944vN1OfPE8dO3b1/X8aPX63nqqad80nd/kpuzLlMTJkxgwoQJ/u5GrfXVV1/5uwu1ygcffFDlsvbt27N161bfdaYWchcfd8vqiqpi0L59ezRN821naiF38fn5559925laqLqfobp6LFUVnxYtWrBjxw6f9qU2kCuuASYyMtI1zdW5cnNzy42TqaskPuVJPNyT+Lgn8XFP4uOexMc9ic/FkcQ1wCQmJlYY+5Kfn09GRkZA3mDkaRKf8iQe7kl83JP4uCfxcU/i457E5+JI4hpghg0bxtdff01eXp6rbOnSpeh0OoYMGeK/jtUSEp/yJB7uSXzck/i4J/FxT+LjnsTnIvl5Oi5xjsLCQm3p0qXa0qVLtf79+2vx8fGu1ydPntQ0TdNycnK0uLg4rV+/ftratWu1f//731pERIT20EMP+bn33ifxKU/i4Z7Exz2Jj3sSH/ckPu5JfLxHEtda5ODBgxpQ6c+GDRtc9X799Vdt4MCBWlBQkNagQQPtiSee0EpKSvzXcR+R+JQn8XBP4uOexMc9iY97Eh/3JD7eo2haHb1NTwghhBBCBBQZ4yqEEEIIIQKCJK5CCCGEECIgSOIqhBBCCCECgiSuQgghhBAiIEjiKoQQQgghAoIkrkIIIYQQIiBI4iqEEEIIIQKCJK5CCCGEECIgSOIqhBBCCCECgiSuQgghhBAiIEjiKoQQQgghAoIkrkII4Wd//etfURSF2NjYCstUVSUpKQlFURg3blyVbfTv3x9FUVAUhZkzZ3q07eqYNm2aa/3XXXfdJbUlhBBVkcRVCCH8bOfOnYSGhpKZmUlubm65ZQsXLuTAgQMAJCUluW2nT58+pKSkMGHCBI+3fSEPPfQQKSkpdO7c+ZLaEUIIdyRxFUIIP9u1axejRo0CIDU11VVeWlrKM88841p2oeQyIiKCXr160bhxY4+3fSHx8fH06tWLsLCwS2pHCCHckcRVCCH8KD8/n8OHD3PVVVcRHx9fLrl86623KCkp4ZprrgGgU6dOtaZtIYTwB0lchRDCj3bt2gU4r3h26NDBlVwWFBQwc+ZM/vrXv7Jv3z4iIyOJj4+vNW0LIYQ/SOIqhBB+tGvXLhRFoWPHjuWSyzlz5hAWFsY999zDrl276NixY61qWwgh/EESVyGE8KNdu3bRokULQkJC6NixI6mpqZw6dYq5c+fy3HPPYTQa2bVr10V9le/NtoUQwh8kcRVCCD/auXOn68aoDh06cPjwYWbMmEHLli0ZN24cubm5HDt27KJunvJE2x9++CFJSUm0a9eO7t27s2bNmovbUCGE8ACDvzsghBB1laZp7N69m2uvvRaAtm3boigK7733HqtWrUJRlHLjVH3d9rJly1i6dCmbNm0iIiKC48ePM3bsWCIjI+nZs+fFbrYQQlw0SVyFEMJP9u/fT2FhoStxtFgsTJw4EZPJxLBhwwDn1/06nY4OHTr4vO3nn3+eTZs2ERwczKFDh2jWrBkLFixg4sSJfPPNNxe72UIIcdEkcRVCCD/ZuXMnUP6K59tvv12uzq5du0hISCA4ONinbauqisFgIDQ0lBMnTtC8eXM0TaN58+YVHmQghBC+ImNchRDCT3bt2kVISAgtW7Z0W+dixrdeats6nQ6Hw0FBQQHR0dF89913ABw6dIioqKga90cIITxB0TRN83cnhBBCXJr+/fsTEhLCypUr0ev1KIpyyW0uW7aMDz74gI8++oiIiAjS09MZO3Ysc+bMqTDGVVVVVFVl4MCBhIaG8sUXX1zy+oUQ4nxyxVUIIS4Tq1atwmg08vzzz3ukvdGjR3PzzTfTp08f2rRpw/XXX89TTz1V6Y1ZM2bMwGg0smnTJo+sWwghKiNXXIUQ4jKwd+9eCgoKAGjcuDFxcXE+XX96ejoZGRkAREREkJCQ4NP1CyHqBklchRBCCCFEQJChAkIIIYQQIiBI4iqEEEIIIQKCJK5CCCGEECIgSOIqhBBCCCECgiSuQgghhBAiIEjiKoQQQgghAoIkrkIIIYQQIiBI4iqEEEIIIQKCJK5CCCGEECIg/D+J+SpaFsljLwAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "haloMassFunctionST = galacticus.haloMassFunctionShethTormen(\n", " cosmologyParameters, cosmologicalMassVariance, criticalOverdensity,\n", " 0.707, 0.3, 0.322183) # a, p, normalization (Sheth & Tormen 1999)\n", "haloMassFunctionTinker = galacticus.haloMassFunctionTinker2008(\n", " cosmologyParameters, cosmologicalMassVariance, linearGrowth,\n", " cosmologyFunctions, virialDensityContrast)\n", "\n", "masses = np.logspace(8, 15.5, 60)\n", "fig, (axF, axR) = plt.subplots(2, 1, figsize=(7, 6.5), sharex=True,\n", " gridspec_kw={'height_ratios': (3, 1)})\n", "dndlnM = {}\n", "for label, hmf in (('Sheth-Tormen', haloMassFunctionST), ('Tinker+2008', haloMassFunctionTinker)):\n", " dndlnM[label] = np.array([M*hmf.differential(ageToday, M) for M in masses])\n", " axF.loglog(masses, dndlnM[label], label=label)\n", "axF.set_ylabel('$\\\\mathrm{d}n/\\\\mathrm{d}\\\\ln M$ [Mpc$^{-3}$]'); axF.legend()\n", "axF.set_title('Halo mass function at $z=0$')\n", "axR.semilogx(masses, dndlnM['Tinker+2008']/dndlnM['Sheth-Tormen'])\n", "axR.axhline(1.0, color='gray', ls=':')\n", "axR.set_xlabel('$M$ [$M_\\\\odot$]'); axR.set_ylabel('Tinker / ST')\n", "fig.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "660e556f", "metadata": {}, "source": [ "## Evolution with redshift\n", "\n", "The exponential high-mass cut-off tracks $\\delta_\\mathrm{c}/\\sigma(M,t)$:\n", "cluster-mass halos are exponentially rare at $z=4$, while the dwarf-scale\n", "mass function barely moves." ] }, { "cell_type": "code", "execution_count": 6, "id": "70f75dda", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:39:56.832082Z", "iopub.status.busy": "2026-07-05T19:39:56.831995Z", "iopub.status.idle": "2026-07-05T19:39:56.991041Z", "shell.execute_reply": "2026-07-05T19:39:56.990607Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for z, color in ((0.0, 'C0'), (1.0, 'C1'), (2.0, 'C2'), (4.0, 'C3')):\n", " t = timeOf(z)\n", " plt.loglog(masses, [M*haloMassFunctionST.differential(t, M) for M in masses],\n", " color=color, label=f'$z={z:.0f}$')\n", "plt.ylim(1.0e-12, 1.0e2)\n", "plt.xlabel('$M$ [$M_\\\\odot$]'); plt.ylabel('$\\\\mathrm{d}n/\\\\mathrm{d}\\\\ln M$ [Mpc$^{-3}$]')\n", "plt.legend(); plt.title('Sheth-Tormen mass function through cosmic time')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "e863ab92", "metadata": {}, "source": [ "## How much matter lives in halos?\n", "\n", "`massFraction(time, massLow, massHigh)` integrates the mass-weighted mass\n", "function — the collapsed fraction. Watching it grow with cosmic time is\n", "hierarchical structure formation in a single number." ] }, { "cell_type": "code", "execution_count": 7, "id": "fea0a8b7", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:39:56.993296Z", "iopub.status.busy": "2026-07-05T19:39:56.993085Z", "iopub.status.idle": "2026-07-05T19:39:57.039011Z", "shell.execute_reply": "2026-07-05T19:39:57.037762Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " z = 6.0: fraction of matter in halos above 1e8 Msun = 0.094\n", " z = 4.0: fraction of matter in halos above 1e8 Msun = 0.190\n", " z = 3.0: fraction of matter in halos above 1e8 Msun = 0.260\n", " z = 2.0: fraction of matter in halos above 1e8 Msun = 0.348\n", " z = 1.0: fraction of matter in halos above 1e8 Msun = 0.454\n", " z = 0.5: fraction of matter in halos above 1e8 Msun = 0.512\n", " z = 0.0: fraction of matter in halos above 1e8 Msun = 0.570\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "zGrid = np.array([6.0, 4.0, 3.0, 2.0, 1.0, 0.5, 0.0])\n", "fractions = [haloMassFunctionST.massFraction(timeOf(z), 1.0e8, 1.0e16) for z in zGrid]\n", "for z, f in zip(zGrid, fractions):\n", " print(f\" z = {z:3.1f}: fraction of matter in halos above 1e8 Msun = {f:.3f}\")\n", "plt.plot(zGrid, fractions, 'o-')\n", "plt.gca().invert_xaxis()\n", "plt.xlabel('redshift $z$'); plt.ylabel('collapsed mass fraction ($M > 10^8\\\\,M_\\\\odot$)')\n", "plt.title('Hierarchical growth of structure')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "96bc22fe", "metadata": {}, "source": [ "**Try it yourself:** swap the transfer function for one of the WDM variants\n", "from Tutorial 2 and re-run — the low-mass slope of the mass function\n", "flattens and turns over below the half-mode mass." ] } ], "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": "3.14.4" } }, "nbformat": 4, "nbformat_minor": 5 }