{ "cells": [ { "cell_type": "markdown", "id": "dfeaab9e", "metadata": {}, "source": [ "# Tutorial 5: Merger-tree building blocks\n", "\n", "Galacticus grows galaxies inside dark-matter-halo *merger trees*. When\n", "trees are not read from an N-body simulation they are built with the\n", "extended Press-Schechter (EPS) formalism, where the linear collapse\n", "threshold $\\delta_\\mathrm{c}(t)$ from Tutorial 3 plays the role of a\n", "\"time\" variable: walking backwards to higher $\\delta_\\mathrm{c}$ (earlier\n", "epochs), a halo's mass splits into progenitors at rates given by a\n", "*branching probability* algorithm.\n", "\n", "Building full trees is the job of a Galacticus run, but every ingredient\n", "is a `functionClass` you can drive directly from Python:\n", "\n", "* `criticalOverdensity.collapsingMass` — the characteristic collapsing\n", " mass $M_*(t)$, hierarchical growth in a single curve;\n", "* `mergerTreeBranchingProbability` — the Parkinson, Cole & Helly (2008)\n", " branching rates that decide how trees fragment;\n", "* `mergerTreeBuildMasses` — the sampler that decides which root halo\n", " masses a suite of trees should have (returning its results through the\n", " library's output-array interface)." ] }, { "cell_type": "code", "execution_count": 1, "id": "3972a752", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:40:00.699982Z", "iopub.status.busy": "2026-07-05T19:40:00.699805Z", "iopub.status.idle": "2026-07-05T19:40:00.890300Z", "shell.execute_reply": "2026-07-05T19:40:00.890016Z" } }, "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": "2bfd82b8", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:40:00.891255Z", "iopub.status.busy": "2026-07-05T19:40:00.891136Z", "iopub.status.idle": "2026-07-05T19:40:00.892707Z", "shell.execute_reply": "2026-07-05T19:40:00.892469Z" } }, "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": "47c26b10", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:40:00.893807Z", "iopub.status.busy": "2026-07-05T19:40:00.893726Z", "iopub.status.idle": "2026-07-05T19:40:00.901546Z", "shell.execute_reply": "2026-07-05T19:40:00.901323Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "chain ready.\n" ] } ], "source": [ "# The sigma(M) chain from Tutorials 2 and 3, condensed.\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", "criticalOverdensity = galacticus.criticalOverdensitySphericalCollapseClsnlssMttrCsmlgclCnstnt(\n", " linearGrowth, cosmologyFunctions, cosmologicalMassVariance, darkMatterParticle, True)\n", "ageToday = cosmologyFunctions.cosmicTime(1.0)\n", "def timeOf(z):\n", " return cosmologyFunctions.cosmicTime(cosmologyFunctions.expansionFactorFromRedshift(z))\n", "print(\"chain ready.\")" ] }, { "cell_type": "markdown", "id": "5b295f9d", "metadata": {}, "source": [ "## The characteristic collapsing mass $M_*(t)$\n", "\n", "$M_*(t)$ is defined by $\\sigma(M_*, t) = \\delta_\\mathrm{c}(t)$ — the mass\n", "scale just going non-linear. Its rise by eight orders of magnitude from\n", "$z=6$ to today *is* hierarchical structure formation: the halos collapsing\n", "\"now\" grow from sub-galactic clumps to cluster scales." ] }, { "cell_type": "code", "execution_count": 4, "id": "da9d3d06", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:40:00.902866Z", "iopub.status.busy": "2026-07-05T19:40:00.902716Z", "iopub.status.idle": "2026-07-05T19:40:01.081973Z", "shell.execute_reply": "2026-07-05T19:40:01.080817Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "M*(z=0) = 5.175e+12 Msun, M*(z=6) = 5.989e+04 Msun\n", "sigma(M*) = 1.6756 vs delta_c = 1.6756\n" ] } ], "source": [ "zGrid = np.linspace(0.0, 6.0, 60)\n", "massCollapsing = np.array([criticalOverdensity.collapsingMass(time=timeOf(z)) for z in zGrid])\n", "plt.semilogy(zGrid, massCollapsing)\n", "plt.xlabel('redshift $z$'); plt.ylabel('$M_*(z)$ [$M_\\\\odot$]')\n", "plt.title('The characteristic collapsing mass')\n", "plt.show()\n", "print(f\"M*(z=0) = {massCollapsing[0]:.3e} Msun, M*(z=6) = {massCollapsing[-1]:.3e} Msun\")\n", "\n", "# Verify the defining relation sigma(M*, t) = delta_c(t) at z=0.\n", "sigmaAtMStar = cosmologicalMassVariance.rootVariance(massCollapsing[0], ageToday)\n", "deltaC = criticalOverdensity.value(time=ageToday, mass=massCollapsing[0])\n", "print(f\"sigma(M*) = {sigmaAtMStar:.4f} vs delta_c = {deltaC:.4f}\")\n", "assert np.isclose(sigmaAtMStar, deltaC, rtol=1.0e-3)" ] }, { "cell_type": "markdown", "id": "74efbb65", "metadata": {}, "source": [ "## Branching rates: how trees fragment\n", "\n", "The Parkinson, Cole & Helly (2008) algorithm — the default tree builder in\n", "Galacticus — gives the probability per unit $\\delta_\\mathrm{c}$ (the EPS\n", "\"time\" step) that a halo of mass $M$ splits off a progenitor of mass\n", "$M_\\mathrm{branch}$. Its empirical parameters $(G_0, \\gamma_1, \\gamma_2)$\n", "were calibrated against the Millennium simulation.\n", "\n", "The `node` argument allows environment-dependent variants; the standard\n", "algorithm ignores it, so we pass a null handle as in Tutorial 4." ] }, { "cell_type": "code", "execution_count": 5, "id": "9fba0751", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:40:01.084565Z", "iopub.status.busy": "2026-07-05T19:40:01.084364Z", "iopub.status.idle": "2026-07-05T19:40:01.169954Z", "shell.execute_reply": "2026-07-05T19:40:01.168916Z" } }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAApIAAAG1CAYAAABKyRR1AAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjksIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvJkbTWQAAAAlwSFlzAAAPYQAAD2EBqD+naQAAqi5JREFUeJzs3XdcVfX/wPHXvey9BAFBEVBBhgNn4sxZ7jRNKy1HNmz+WlaWmba+2bQ0G44sS9OsXKmZew9QFAeKICIoICBDxj2/P05cJUAZFy7g+/l43Me9nPV533su+PYzNYqiKAghhBBCCFFBWmMHIIQQQggh6iZJJIUQQgghRKVIIimEEEIIISpFEkkhhBBCCFEpkkgKIYQQQohKkURSCCGEEEJUiiSSQgghhBCiUiSRFEIIIYQQlSKJpBBCCCGEqBRJJIWogxYuXIhGo+Gff/657bHjx49Ho9FUf1D1lI+PDz169DB2GJWm0WgYP358sW3V8Z5iY2PRaDS89dZbBr2uMVXkc6qP71+I8pBEUogq+ueff9BoNMUeNjY2hIaG8s4775Cbm2vsEO8Iu3bt4qGHHqJp06ZYWVlhbW1NYGAgjz/+OAcPHjR2eKXy8fHB39+/zP1vvfUWGo2GHTt21GBUQtzw1ltv8dtvvxk7DFGLmRo7ACHqixEjRjBkyBAAkpKSWLZsGW+88QY7d+5k3bp1RotrwYIFzJs3z2jlVzdFUXj++ef55JNP8PT0ZNSoUbRo0QKAEydOsHLlSubNm0dUVBQtW7Y0crSivmrSpAk5OTmYmtavf1ZnzJjBuHHjGDp0qLFDEbVU/frGC2FErVq14sEHH9T//PTTT9O+fXvWr1/P/v37ad++fZXLyMjIwN7evkLnmJmZYWZmVuWya6t3332XTz75hOHDh/PDDz9gZWVVbP+HH37IJ598YpzgRIUUFhZy/fp1rK2tjR1KhWk0GiwtLY0dRpkq87dDiPKQpm0hqomZmRm9e/cG4MyZM+h0OmbPnk2PHj3w8PDA3NycRo0aMW7cOOLi4kqcX9S37Z9//qFHjx7Y29vTqlWrW5b51VdfYWpqyn333UdOTg5Qeh/Jom0ZGRlMnToVDw8PLCwsaNu2LRs2bChx3fXr19OrVy/c3NywtLTEy8uLAQMGsH379mLHJSQkMHHiRBo1aoS5uTleXl5MnjyZxMTEYscVdQdYuHAhS5YsITQ0FEtLSxo1asS0adMoLCy8/QcMXLlyhVmzZuHt7c2SJUtKJJGg3ocXX3yxWG1kbm4uM2bMICAgAEtLS5ydnRk0aBAHDhwoV7kAhw8fZsSIEbi5uWFubo6vry+vvPIK2dnZ5b5GZeXl5fHBBx8QGhqKlZUV9vb29O7dm23btlXqegMHDsTKyoq0tLQS+5KSkjA3N2fEiBHlvt6KFSto27YtVlZWeHh48Oyzz3Lt2rVixxQ12x8/fpyXXnqJJk2aYGFhwS+//ALAX3/9xQMPPICfn5/+PXbr1o0//vijRHkV/T4DbN++nSFDhuDq6oqFhQWNGzdmzJgxxMTElDj21KlTDBkyBAcHB2xtbbnnnns4c+ZMsWNK6yN587Z169bRqVMnrKyscHV15bHHHiMrK6vMsuzt7bG3t6d///4cO3aMHj164OPjc7uPHrj1347MzEzeeOMNOnXqhKurK+bm5vj4+PDUU0+Rmpqqv0bR7yjAokWLinXduVl5fw8uXLjA5MmTadq0KZaWljRo0ICwsDBmz55drvckai+pkRSiGp06dQoAV1dX8vLyeP/99xk+fDj33nsvDg4OREZG8t1337F582YiIyNxdnYudv6BAwdYsWIFjz76KGPGjCEzM7PUchRF4ZVXXuGDDz7gmWeeYc6cOWi1t/9/Yr9+/XB0dOTVV18lOzubTz75hMGDB3P69GkaN24MwLZt2xg4cCAtW7bkxRdfxMXFhUuXLrFr1y4OHz5M165dATWJbN++PcnJyUycOJFWrVoRERHBggUL9LWyDRs2LFb+/Pnz9cmnq6srK1eu5N1338Xe3p5XXnnltvGvWbOG7OxsnnvuuXLXYhUWFnLPPfewZcsW7rnnHp566ikuXbrEV199RXh4OOvWraNnz563vMb69esZOnQo3t7eTJ06lYYNGxIREcGcOXPYuXMnW7ZsKXcTp06n48qVK6XuKy0pLSgo4J577mHr1q088MADTJkyhezsbH744Qd69erFb7/9xsCBA8tVdpHHHnuMNWvWsGTJEp5++uli+xYuXEh+fj6TJ08u17X+/PNP5syZwxNPPMGECRPYvHkzn376KUeOHGHz5s2YmJgUO37s2LGYmpry5JNPYmtrq++WsHDhQpKSknjwwQfx8vLi8uXLLFq0iMGDB7Ns2TJGjRpVouzyfJ8BvvnmGx577DFcXV2ZOHEiTZs25dKlS6xfv55jx47h5+enPzYhIYFu3boxePBg3n//fU6fPs3nn3/OkCFDOHr0aLl+z9atW8cXX3zBY489xvjx49m8eTNff/01Go2mWLeT8+fPc9ddd3Ht2jWmTJlCixYt2L9/P927dy/xt+F2yvrbkZCQwNdff83w4cMZNWoUlpaW7Nu3j/nz57Njxw7279+PmZkZgYGBLFmyhIceeoiuXbuWev/L+3tQUFBAnz59iI+P5/HHHycgIIBr164RHR3N33//zbRp0yr03kQtowghqmTLli0KoLz66qvK5cuXlcuXLytRUVHKyy+/rABK06ZNldzcXEWn0ylZWVklzt+4caMCKB988EGx7YACKOvWrStxzvfff68AypYtW5Tc3Fxl9OjRilarVT7++OMSx44bN07576960bbJkycX27579279eyny3HPPKYBy6dKlW34ODz30kAIoS5cuLbZ90aJFCqBMmDBBv63oM3N3d1dSU1P12wsLC5XAwEDFw8PjlmUVeeGFFxRA+fXXX8t1vKIoyrfffqsAyqRJk4ptP3nypGJhYaE0a9ZMKSws1G9v0qSJ0r17d/3POTk5iru7u9KhQwclNze32DVWrFihAMrChQvLFUuTJk309/lWj+3bt+vP+eSTTxRAWblyZbFr5eXlKW3atFGaNm1abDugjBs3rkS5N7+ngoICxdvbWwkODi52nE6nU/z9/ZWmTZsqOp3ulu/l3LlzCqBoNBpl7969xfY9/fTTCqB8//33+m1vvvmmAijh4eFKXl5eietdu3atxLasrCylWbNmSsuWLYttr8j3+cKFC4qFhYXStGlT5fLlyyXK+O+9B5Qff/yx2DHvvvuuAigbNmwo8f7ffPPNEtusrKyUmJiYYtfo16+fYmZmVux9jhkzRgGUNWvWFDt2zpw5CqA0adKkRLyludXfjuvXr5f6eS9YsEABlF9++aXEtf77/VGUiv0eREREKIDy3nvvlSt+UbdI07YQBvLuu+/i6uqKq6srQUFBvP/++/Ts2ZO//voLCwsLNBqNvtZMp9Nx9epVrly5QuvWrXFwcGDv3r0lrtmqVSv69+9fZplpaWn07duX3377jeXLl/Pss89WKOb/+7//K/Zzp06dsLW11dekAjg6OgKwfPly8vPzS72OTqfjt99+o0WLFowZM6bYvoceegg/Pz9WrlyJoijF9j366KM4OTnpf9Zqtdx9990kJiaWaAotTXp6OkCF+n79+uuvgDqI4GbNmzdnzJgxnD59mqNHj5Z5/qZNm7h06RLjx48nMzOTK1eu6B/dunXD2tq6zObU0nh6erJx48ZSHw899FCJ45csWYKPjw9du3YtVnZ6ejqDBw/m3Llzxe5feZiYmDBp0iSOHTvGnj179Nv/+ecfzpw5w8SJE8s9hVSfPn3o0KFDsW2vvfYacOOzv9kLL7xQah9eGxsb/eusrCxSUlLIzs6mV69eHD9+vNTa+fJ8n5cvX87169eZPn06DRo0KHGN/9Ywenp68sADD5R4j0C5P+dhw4bh6+tb4hr5+fmcO3cOUH+Hfv/9d4KDg7nnnnuKHfvEE09gZ2dXrrKKlPW3w9zcXP95FxQU6P8O9erVC6DUv0OlqcjvgYODAwBbtmzh0qVLFXofovaTpm0hDGT8+PGMHTsWjUaDlZUVzZo1w9XVtdgxv/32Gx988AEHDx4kLy+v2L6b+ycVad68+W3LzMjIYOPGjfr+mBXx33/cAFxcXEhJSdH//NRTT/HHH38wdepUXnnlFTp37kyPHj0YM2YMTZs2BeDy5ctkZmYSHBxc4noajYagoCB+//130tLSijXRlVU+QEpKCra2tuTk5OgTxiK2trbY2trq/4HKyMgo93s+e/YsLi4ueHh4lNgXEhICQExMTJn9UU+cOAGo/7g/8cQTpR6TlJQEcMvYi1hZWZV570qb9ufEiRNkZ2eX+G79t/zbfXf+a+LEibz99tssWLCATp06AeqIf1NTUx599NFyX6e0kfFubm64uLiU6FcIZX/HY2NjeeONN1i7dm2pvxtpaWklkqvyfJ+Lkr+2bdve+o3c5ppAsetW9RrJyclcu3aNgICAEsdaWFjg6+vL1atXy1Ue3Ppvx4IFC/jyyy85duwYBQUFxfaV9lmXpiK/B02aNOHNN99k5syZeHp6EhISQnh4OEOHDtUn5aLukkRSCAPx8/O7ZTK3evVqhg0bRrt27ZgzZw6NGzfWDw4ZPXo0Op2uxDm36/c3atQovvvuO95++206duxY4VqL//ZXK3JzzaGzszN79+5l165dbNq0ie3btzNjxgxmzJjBkiVLSu2rVtXyb47h559/5pFHHim278033+Stt97SJ36HDh1i+PDhlY6jIoru06xZs0rUvBUpqmW9VexVKb9FixZ88cUXZR5TWkJ/Ox4eHgwePJiff/6ZTz75hLy8PFauXMngwYNxd3evdLy3U9p3/Nq1a3Tr1o309HSeeeYZQkNDsbe3R6vV8t133/HTTz+V+vtSnu9zRZXnO1oT16iosv52fPrppzz77LP07t2bL7/8Ek9PTywsLCgoKGDAgAGlfq6lqcjvAaiDqx555BHWrVvH9u3b+fXXX/nyyy8ZMmQIq1atkkUT6jBJJIWoIYsWLcLS0pKtW7cW+yOflZVV6mjZ8hgzZgz9+/fngQceoHfv3qxfv77YH29D0Wq1hIeHEx4eDkB8fDxt27bl5ZdfZtSoUbi6umJnZ0dUVFSJcxVFISoqCicnp0rF1q9fPzZu3FhsW1ENz7333ou1tTVLlizhtddeK3XU9n/5+fkRHR1NUlJSicE/x44d0x9TlqKaHktLy9vWAt8q9spq3rw58fHx9OjRw+BzFk6ZMoWVK1fy448/kpOTw/Xr18s9yKbI8ePHS2xLTk4mJSWFzp07l+saf//9N/Hx8Xz77bclakMXLFhQoXj+q+j+HT58mNDQ0Cpdy5Dc3NywtbUlOjq6xL68vDzOnj1b4QE3pVm0aBE+Pj5s2LChWDN+UQ1jeVXk96BIkyZNmDJlClOmTKGgoIDx48ezdOlStm7dWqdXj7rTSR9JIWqIiYkJGo2mxP/4Z86cWe5agNIMHz6cVatWERkZSY8ePUhOTq5qqMVcvny5xDZvb28aNmyob5bTarUMHTqU6OhoVqxYUezYpUuXEhMTw/DhwytV6+Dh4UHv3r2LPYqSsQYNGvDaa68RFxfHuHHjSl1FqKCggP/973/6BKeo5nLmzJnFjjtz5gw//vgjzZo1u2WC0a9fPxo2bMiHH35Yan+vgoICffPgrWKvrIcffpi0tDRmzZpV6v6i5sTK6N27N35+fixYsIBvvvkGHx8f+vbtW6FrbNy4kX379hXbVhRreWuNi2rw/ltbFxkZWeVVVkaOHImFhQUzZ84stRm3Kr+LVaHVahk0aBDHjh1j7dq1xfbNnTu3zBkbKqros735fSqKwttvv13q8ba2tqV+ThX5PUhPTy/Rv9rU1FTffaS8XQRE7SQ1kkLUkJEjR7JixQq6d+/O+PHjURSFDRs2cPz48VI7/VfEPffcw9q1axk0aBDdu3dn8+bNeHp6GiTuyZMnExcXR9++ffHx8aGgoIA///yTqKgonnrqKf1xs2fPZtOmTTzwwANs2bKFkJAQ/fQ/3t7eZSY+VfXqq6+SnJzMp59+yq5duxg1ahQBAQEoisLJkyf59ddfiYuL0w9gePjhh/nhhx+YO3cucXFx9OvXTz/9j6IozJ8//5YJb1EN6JAhQwgMDOSRRx4hICCAzMxMYmJiWLlyJe+9916J9a0N5ZlnnmHz5s289dZbbNu2jb59++Ls7Ex8fDy7du3i7NmznD17tlLX1mg0TJ48mZdffhmAd955p8LJf5s2bejduzdPPPEEjRs3ZtOmTaxatYrw8HAefvjhcl2jS5cueHh48MILL3D27Fl8fHw4ceIECxYsICQkpEpLXjZq1IjPPvuMKVOmEBQUxCOPPELTpk1JTk5m/fr1/N///Z9+haqaNmvWLDZs2MDw4cOZMmUKAQEB7Nu3j9WrV+Pv71+iP2NljBw5kpdffpl+/foxYsQIsrOzWbVqVYk+20U6derEpk2beP/992ncuDEajYbRo0dX6Pdgy5YtTJo0iWHDhtGiRQscHR05fvw48+bNo1GjRpXq3y1qEeMMFhei/iiaymbmzJm3Pfbbb79VgoODFUtLS8XV1VUZM2aMEh8fX2I6FkUpe9oNRSk+/c/Ndu7cqTg4OCi+vr7KuXPnFEW59fQ/pflvLL/++qsyZMgQxdvbW7GwsFCcnJyUDh06KPPmzSs2VYqiKEp8fLwyYcIExcPDQzE1NVU8PT2VSZMmKRcvXix2XNFndvN0MEWKpoUpir+8duzYoTz44INKkyZNFAsLC8XS0lIJDAxUnnjiCeXIkSPFjs3JyVHefPNNpXnz5oq5ubni6OioDBw4UNm3b99tP48iJ06cUMaNG6d4eXkpZmZmSoMGDZSwsDDl1VdfVeLi4soVc5MmTRQ/P78y9xd9FjdP/6Mo6nQ9X375pdKxY0fF1tZWsbS0VHx8fJThw4crP//8c7FjS/selfWeFEVRkpOTFXNzc8XU1LTEfbuVm6e/+eWXX5TWrVsrFhYWSsOGDZWpU6cqGRkZpb63su7z0aNHlXvuuUdxcnJSrK2tlU6dOimrV68u9byKfJ+LbN68Wenfv7/i5OSkmJubK40bN1bGjh1bbJqess691VQ/t9tWpKzf4RMnTigDBw5UbG1tFVtbW6Vfv37K0aNHlbZt2yqBgYGlvsf/utXfjsLCQuX9999XmjVrplhYWCienp7K448/rqSmppZ63qlTp5Q+ffoodnZ2+mmF/hvv7X4Pzp49q0yZMkVp2bKlYm9vr1hZWSn+/v7K1KlTlfj4+HK9J1F7aRSlmnr6CiGEqHPS0tLw9PRkwIABrFy50tjhCNRm4gYNGtC5c2fWrVtn7HCEKEb6SAohhNBbsGABubm5TJkyxdih3JFKW83o888/Jz09nX79+hkhIiFuTWokhRBCsGzZMhISEnjrrbcIDAwsMWBG1IyAgADCw8Np1aoVOp2OHTt2sGLFCgIDA9m/f3+xidqFqA0kkRRCCIFGo8HCwoLOnTvzzTff3HIKJFF9pk2bxu+//05cXBy5ubk0atSIwYMHM336dP0k5kLUJpJICiGEEEKISpE+kkIIIYQQolIkkRRCCCGEEJUiE5LXATqdjosXL2JnZyfrkQohhBCi2imKQmZmJp6ensWW0/wvSSTrgIsXL+Lt7W3sMIQQQghxh4mPj8fLy6vM/ZJI1gF2dnaAejPt7e0BtZby8uXLuLq63vJ/CqJmyX2pveTe1F5yb2onuS+1V03cm4yMDLy9vfU5SFkkkawDipqz7e3tiyWSubm52Nvbyy94LSL3pfaSe1N7yb2pneS+1F41eW9u16VOvhlCCCGEEKJSJJEUQgghhBCVIomkEEIIIYSoFOkjKYQQQtQxhYWF5OfnV2sZOp2O/Px8cnNzpY9kLVPVe2NmZoaJiYlBYpFEUgghhKgjFEXh0qVLXL16tUbK0ul0ZGZmyhzGtYwh7o2joyPu7u5VvreSSAohhBB1RFES6ebmhrW1dbUmeIqiUFBQgKmpqSSStUxV7o2iKGRnZ5OcnAyAh4dHlWKRRFIIIYSoAwoLC/VJpIuLS7WXJ4lk7VXVe2NlZQVAcnIybm5uVWrmlk4PQgghRB1Q1CfS2trayJGI+qDoe1TVvraSSAohhBB1iNQOCkMw1PdIEkkhhBBCCFEpkkgKIYQQQohKkURSkJGXwTN/P8OgVYMo0BUYOxwhhBBC1BGSSApszWzZk7iH2IxYzqWfM3Y4QgghhKgjJJEUaDVaApwDADiectzI0QghhBB1y2OPPUajRo1KHcByq331gSSSAoCWLi0BOJF6wsiRCCGEEHXL2LFjOXToUIX31QeSSArgRiIpNZJCCCFqyhtvvIFGo8Hd3b3EPp1OR2hoKBqNhtGjRxu03DNnzjBlyhRat26NqakpwcHBZR4bHR1Nnz59sLGxwd3dnZdeeom8vLxix3Tr1o2GDRuWev6t9t3MWJ9FVcnKNgK4kUhGp0ZTqCvERGuYxdyFEEKIskRERGBnZ0dSUhJpaWk4OTnp9y1dupSzZ88CEBoaatByo6KiWLNmDR07dkSn06HT6Uo9Li0tjV69etGsWTNWrlxJQkICzz//PNnZ2XzxxRcGjclYn0VVSY2kAMDH3gcrUytyCnKIzYg1djhCCCHuAJGRkQwdOhSAEydudK3Ky8tj+vTp+n2GTp4GDRpEfHw8K1asoG3btmUeN2/ePDIyMli1ahX9+vXj0Ucf5YMPPmDevHlcvHjRoDEZ67OoKkkkBQAmWhMZcCOEEKLGpKenc/78ecLDw/H29i6WPM2bN4/r16/Ts2dPAFq1amXQsrXa8qU/69ato3fv3jg7O+u33X///eh0Ov766y+DxWPMz6KqpGlb6LV0acnh5MMcTznOIL9Bxg5HCCHEbSiKQk5+YbVdu6CgAFPd7ZfTszIzqfCo5MjISECtYQsODtYnT5mZmbzzzjvMmDGDM2fO4OTkhLe3d6nxFRbe/r2bmlY+1YmOjubRRx8tts3R0REPDw+io6Mrfd3/quhnoSiKwcquKkkkhZ4MuBFCiLolJ7+QltM3GDsMjr/dD2vziqUUkZGRaDQaQkJCCA4OJioqCoCPPvoIe3t7Jk6cyNChQwkJCSn1/EWLFvHII4/ctpxz587h4+NTodiKpKWl4ejoWGK7k5MTqamp+p/Hjx/Ppk2bAPDy8qJnz54sWbLktvuKVPWzMCZJJIVeoHMgoA640Sk6tBrp+SCEEKJ6REZG4uvri42NDSEhIaxYsYLLly8zZ84c5s+fj5mZGZGRkQwbNqzU8wcNGsT+/ftvW46np6ehQy9h4cKFldpXpKqfhTFJIin0mjo0xdLEkuyCbGIzYvF18DV2SEIIIW7BysyE42/3q5Zr65u2TU3L1bRdUREREfqBI8HBwZw/f55p06bh5+fH6NGjSUtL48KFC2UOLnF2dsbBweG25VSladvJyYn09PQS29PS0or1m6yqqn4WxiRVTkLPVGtKC+cWgDRvCyFEXaDRaLA2NzX6o6L9IxVF4dixY/rEKDAwEI1GwzfffMPs2bPRaDTF+g2WZtGiRZiZmd32ERsbW+nPNyAgoERfyPT0dBITEwkICKj0dW9miM8CYMmSJYSGhtKyZUvat2/P+vXrDRLf7UiNpCimpUtLIi5HcDzlOAN9Bxo7HCGEEPVQTEwMWVlZ+sTI0tKSCRMmYG5uzoABAwC1uVer1ZY5WXhNNG0PGDCA2bNnc/XqVX1fyeXLl6PVaunbt2+lr3szQ3wWK1asYPny5Wzbtg1HR0cuXrzIqFGjcHJyomPHjgaJsyySSIpi9EslpshSiUIIIapHREQEULyGbf78+cWOiYyMxN/fH2tr61Kv4eLigouLS6XKz87OZu3atQCcP3+ejIwMVqxYAUD37t1xdXUFYMqUKXz++ecMHTqUadOmkZCQwIsvvsiUKVMM1vfSEJ/FrFmz2LZtG9bW1sTGxuLj48PixYuZMGECf//9t0HiLIskkqKYm9fclgE3QgghqkNkZCQ2Njb4+fnd8pjq6hOYnJzMyJEji20r+nnLli306NEDUPtIbt68malTpzJ06FDs7OyYOHEis2bNMlgsVf0sdDodpqam2NnZcenSJZo2bYqiKDRt2pS0tDSDxVkWSSRFMb4OvliYWJCVn0VcRhw+Dj7GDkkIIUQ9M2PGDGbMmHHLY/bu3Vtt5fv4+JR7LsbAwED99D3VoaqfhVarpbCwkMzMTFxcXNi+fTsAsbGxBh0QVGb51V6CqFNMtaa0cJIBN0IIIURdMW3aNB544AGysrIIDw8nISGBBx98kNmzZ1d72VIjKUoIdAkk8kokx1OOc4/vPcYORwghhBC3MGLECLKysujSpQsFBQXY2Ngwa9asah9oA5JIilIEuQQBcDxVaiSFEEKIumDcuHGMGzeuxsuVpm1Rws0jt3WKzsjRCCGEEKK2kkRSlODr6Iu51pxr+de4kHnB2OEIIYQQopaSRFKUYKY1o7lTc0AG3AghhBCibJJIilIVNW9LIimEEEKIskgiKUoliaQQQgghbkcSSVEqfSKZerzck7YKIYQQ4s4iiaQolb+jP2ZaMzLzMrlwTQbcCCGEEKIkSSRr2IkTJ2jfvj3NmzenV69eJCYmGjukUpmZmNHMqRkgzdtCCCGEKJ0kkjVsypQpvP7665w6dYohQ4bwyiuvGDukMkk/SSGEEELcSp1MJJcvX86QIUPw8vLCxsaG1q1b891331VbX74zZ84wZcoUWrdujampKcHBwWUeGx0dTZ8+fbCxscHd3Z2XXnqJvLw8AJKSkjh9+jRDhgwBYMKECaxatapaYjYESSSFEEIIcSt1MpGcM2cO1tbWfPTRR/zxxx8MGDCASZMm8fbbb1dLeVFRUaxZswZ/f39atmxZ5nFpaWn06tWLvLw8Vq5cyezZs/n66695/vnnAbhw4QLe3t76421tbbG0tCQlJaVa4q6qmxNJGXAjhBBClO6xxx6jUaNGaDSaYttTUlIYMGAALVq0ICQkhEcffZTr168bKcrqUScTyT/++IOffvqJUaNG0atXL959910mTJjAnDlz0OlKX9IvKiqKmJiYUvdt3bqVq1evllneoEGDiI+PZ8WKFbRt27bM4+bNm0dGRgarVq2iX79+PProo3zwwQfMmzePixcvVug91gbNHJthqjUlIy+Di1l1L34hhBCiJowdO5ZDhw6V2K7RaHj11Vc5efIkERER5OTk8MUXXxghwupTJxPJBg0alNjWpk0bMjIyyMrKKvWcmTNncvfddxMfH19s+9atWxkwYAALFy4sszyttnwf07p16+jduzfOzs76bffffz86nY6//voLLy+vYuVfu3aN3NxcXFxcynX9mmZuYk4zRxlwI4QQonq88cYbaDQa3N3dS+zT6XSEhoai0WgYPXq0Qcs1VJe1It26daNhw4YlznV2dqZbt26Amku0a9eOuLi4Ussx1mdRVXUykSzNjh07aNSoEXZ2dqXuX7BgAa6urvTu3Zvk5GQA9u3bx6BBgxg9ejTPPPNMlWOIjo4mICCg2DZHR0c8PDyIjo6mYcOG+Pv7s3r1agC+/fZbhg4dWuVyq5P0kxRCCFFdIiIisLOzIykpibS0tGL7li5dytmzZwEIDQ01aLmG6rJWEbm5uSxcuJABAwaUut9Yn0VV1YtEcseOHSxbtoz/+7//K/MYOzs71q9fj5mZGX379mXbtm0MGDCAfv36sWDBghL9GiojLS0NR0fHEtudnJxITU0F4KuvvmLmzJk0a9aM3377jffee6/M682dO5eWLVvSvn37KsdWWZJICiGEqC6RkZH6CpUTJ07ot+fl5TF9+nT9PkMnTzXdZU2n0zFu3Dh69uxJ//79Sz3GWJ9FVdX5RPLChQuMGjWKnj178vTTT9/yWBcXFzZu3Mi1a9fo3r07HTp04Mcff8TExKSGooWgoCAOHDjA6dOn2bJlC56enmUe++STT3L8+HH2799fY/H9lwy4EUIIUR3S09M5f/484eHheHt7F0ue5s2bx/Xr1+nZsycArVq1MmjZhuqyVl5PPvkkWq2WTz75pNT9xvwsqsrU2AFUxdWrVxkwYAAuLi78+uuv5fpiXL9+ndzcXLRaLdnZ2RQUFGBmZmaQeJycnEhPTy+xPS0trdiXsC5p5tQMU40pV69fJTErEU/bshNfIYQQNUxRID+7+q5dUAA6U7hdq52Z9e2P+Y/IyEhArWELDg7WJ0+ZmZm88847zJgxgzNnzuDk5FRsxpMb4SkUFhbethxT08qnOtHR0Tz66KPFtt3cZa08XnrpJeLj41m1alWZeUpFP4vaVLFTZxPJnJwcBg4cSHp6Ort378bBweG25yQmJtK7d28aN27MH3/8wT333MPw4cNZvXo15ubmVY4pICCgxBcrPT2dxMTEEn0n6woLEwv8HP04mXaSEyknJJEUQojaJD8bZlfP32UNUO5qlmkXwdymQtePjIxEo9EQEhJCcHAwUVFRAHz00UfY29szceJEhg4dSkhISKnnL1q0iEceeeS25Zw7dw4fH58KxVakPF3WAMaPH8+mTZsA8PLyomfPnixZsoSoqCg+/PBDAgIC9N3U+vTpw4cffljselX9LIypTiaSBQUF3H///Zw4cYLt27fTqFGj256TkpJCnz59sLe3Z+3atTg6OrJp0ya6d+/O2LFjWbZsWZWbuAcMGMDs2bO5evWq/ou3fPlytFotffv2rdK1jamlS0tOpp0kKiWKu5vcbexwhBBC1AORkZH4+vpiY2NDSEgIK1as4PLly8yZM4f58+djZmZGZGQkw4YNK/X8QYMGlavr1626kBlKWTO/BAUFlav2sKqfhTHVyUTyiSee4M8//+Sjjz4iIyODPXv26Pe1adMGCwuLEudMmTJF36ehKMkLCgpiw4YN3H333Xz66adljsLKzs5m7dq1AJw/f56MjAxWrFgBQPfu3XF1ddWX8fnnnzN06FCmTZtGQkICL774IlOmTKmRL3J1aenSklVnVnE8VQbcCCFErWJmrdYGVgNFUSgoKMDU1PT2A1LNrCt8/YiICP3AkeDgYM6fP8+0adPw8/Nj9OjRpKWlceHChTIHlzg7O5erNbIqTds11WWtqp+FMdXJRLKog+sLL7xQYl9ZVdgffPABFhYWJeagDAsLY8uWLbRo0aLM8pKTkxk5cmSxbUU/b9myhR49egDqF27z5s1MnTqVoUOHYmdnx8SJE5k1a1ZF3l6tUzTg5kTKCRRFMcgIdyGEEAag0VS4SbncFAW0BWBajj6SFb60wrFjx/QjmAMDA9FoNHzzzTesXbsWjUZTrN9gaWqiabsmuqwZ4rMAWLJkCR9++CEFBQXY2Ngwc+bMMkeIG1KdTCRjY2MrfE7Tpk3L3NemTZtbnuvj41Pujq2BgYH6fhL1RXOn5phoTEjNTSUpOwl3m5KTpQohhBDlFRMTQ1ZWlj4xsrS0ZMKECZibm+vnWYyMjESr1ZY5WXhNNG3XRJc1Q3wWK1asYPny5Wzbtg1HR0cuXrzIqFGjcHJyomPHjgaJsyx1MpEUNcvS1BJfR19Op50mKiVKEkkhhBBVEhERARSvYZs/f36xYyIjI/H398fauvRmcxcXl0qvDFebuqwZ4rOYNWsW27Ztw9ramtjYWHx8fFi8eDETJkzg77//NkicZZFEUpRLsEswp9NOE5Ecwd2NZcCNEEKIyouMjMTGxgY/P79bHlNdfQJrU5e1qn4WOp0OU1NT7OzsuHTpEk2bNkVRFJo2bVpihZzqIImkKJeOHh1ZdWYVOy/u5HkqvjSUEEIIUWTGjBnMmDHjlsfs3bu32sqvTV3WqvpZaLVaCgsLyczMxMXFhe3btwNqN8CamMO6zq9sI2pGZ8/OaNBwKu0UydnJxg5HCCGEEP+aNm0aDzzwAFlZWYSHh5OQkMCDDz7I7Nmzq71sqZEU5eJs6UyQSxDHUo6xM2Enw5rVvrmshBBCiDvRiBEjyMrKokuXLvpR27Nmzar2gTYgiaSogLsa3cWxlGPsurhLEkkhhBCiFhk3bhzjxo2r8XKlaVuUW3ijcAB2XdxFoe7265sKIYQQon6TRFKUW0iDEOzM7MjIyyAqJcrY4QghhBDCyCSRFOVmqjWlk2cnAHYm7DRyNEIIIYQwNkkkRYV08ewCwI6LO4wciRBCCCGMTRJJUSFdGqmJ5LErx0i/XnIheyGEEELcOSSRFBXibuOOn4MfOkXH7sTdxg5HCCGEEEYkiaSosKJaSeknKYQQQtzZJJEUFVaUSO5K2FXuJaaEEEIIUf9IIikqLKxhGJYmliTnJHP66mljhyOEEEIII5FEUlSYhYkF7dzbAWqtpBBCCCHuTJJICshNh7UvweIhoNOV6xSZBkgIIYRQPfbYYzRq1AiNRlNsu06no3PnzrRu3ZqQkBBGjhxJRkaGkaKsHpJICjCzgUOL4Ow/kHq2XKcU9ZM8lHSI7PzsagxOCCGEqN3Gjh3LoUOHSmzXarVs2LCBI0eOcPToUby9vfnwww+NEGH1kURSgIkpNAxWXyceKdcpPvY+NLJtRL4unwNJB6ovNiGEEPXWG2+8gUajwd3dvcQ+nU5HaGgoGo2G0aNHG7TcM2fOMGXKFFq3bo2pqSnBwcFlHhsdHU2fPn2wsbHB3d2dl156iby8vGLHdOvWjYYNG5Z6vr29PaC+n6ysrBK1lkWM9VlUlSSSQuXZRn2+eLhch2s0Gu7yvAuAHQnSvC2EEKLiIiIisLOzIykpibS0tGL7li5dytmzaitZaGioQcuNiopizZo1+Pv707JlyzKPS0tLo1evXuTl5bFy5Upmz57N119/zfPPP1+h8nr37o2bmxsnT57kpZdeKvUYY30WVSWJpFB5tlafEyPKfYrMJymEEKIqIiMjGTp0KAAnTpzQb8/Ly2P69On6fYZOngYNGkR8fDwrVqygbdu2ZR43b948MjIyWLVqFf369ePRRx/lgw8+YN68eVy8eLHc5W3atImkpCTatWvHl19+WeoxxvosqkoSSaHyaK0+XzxS7gE3Hd07YqoxJS4zjviM+GoLTQghRP2Tnp7O+fPnCQ8Px9vbu1jyNG/ePK5fv07Pnj0BaNWqlUHL1mrLl/6sW7eO3r174+zsrN92//33o9Pp+OuvvypUpomJCePHj2fx4sUl9hnzs6gqSSSFyjUATC0hL7PcA25szW1p5aZ+oXdelFpJIYQQ5RcZGQmoNWzBwcH65CkzM5N33nmHN954gzNnzuDk5IS3t3eJ8xVFoaCg4LaPqoiOjiYgIKDYNkdHRzw8PIiOjr7t+VeuXOHKlSv6eFesWFFqf8yqfhbGJImkUJmYgnuI+rqcA24AwhuFA9K8LYQQxqAoCtn52dX2yCnIKddxlVnlLDIyEo1GQ0hISLHk6aOPPsLe3p6JEycSGRlJSEhIqecvWrQIMzOz2z5iY2Mr/fmmpaXh6OhYYruTkxOpqan6n8ePH4+XlxcAXl5ePPTQQwAkJSXRr18/QkNDCQ0NJTo6ms8++8zgn4UxmRo7AFGLeLSGC/vVATchI8p1ShfPLnx66FP2XtpLfmE+ZiZm1RujEEIIvZyCHDr+2NHYYbB3zF6szawrdE5kZCS+vr7Y2NgQEhLCihUruHz5MnPmzGH+/PmYmZkRGRnJsGHDSj1/0KBB7N+//7bleHp6Viiuyli4cGGp24OCgjh48OBtz6/qZ2FMkkiKG4oG3Fw8Uu5TWji3wNnSmdTcVA4nH6aDR4dqCU0IIUT9EhERoR84EhwczPnz55k2bRp+fn6MHj2atLQ0Lly4UObgEmdnZxwcHG5bjqlp5VMdJycn0tPTS2xPS0sr1m+yqqr6WRiTJJLihqIBN4kR6oCbcnRG1mq0dPHswh9n/2DnxZ2SSAohRA2yMrVi75i91XJtRVEoLCzExMSkzLkPb46jotc+duwY/fv3ByAwMBCNRsM333zD2rVr0Wg0xfoNlmbRokU88sgjty3r3Llz+Pj4VCi+IgEBASX6Qqanp5OYmFii72RlGeKzAFiyZAkffvghBQUF2NjYMHPmTP01q5MkkuKG/w64aeBfrtO6NPo3kUzYyXNhz1VzkEIIIYpoNJoKNymXl6IoFGgKMDU1vW0iWVExMTFkZWXpEyNLS0smTJiAubk5AwYMANTmXq1WW+Zk4TXRtD1gwABmz57N1atX9X0lly9fjlarpW/fvpW+7s0M8VmsWLGC5cuXs23bNhwdHbl48SKjRo3CycmJjh2rt+uDJJLihqIBNxf2qwNuyplIdvbsjAYNJ9NOcjn7Mq7WrtUbpxBCiDotIkKds/jmGrb58+cXOyYyMhJ/f3+srUtPlF1cXHBxcalU+dnZ2axduxaA8+fPk5GRwYoVKwDo3r07rq7qv2NTpkzh888/Z+jQoUybNo2EhARefPFFpkyZYrC+l4b4LGbNmsW2bduwtrYmNjYWHx8fFi9ezIQJE/j7778NEmdZZNS2KE4/n2T5VrgBcLZ0pqWLujLArou7qiEoIYQQ9UlkZCQ2Njb4+fnd8pjq6hOYnJzMyJEjGTlyJP/88w/x8fH6n6OiovTHOTk5sXnzZkxNTRk6dCivvPIKEydOZM6cOQaLpaqfhU6nw9TUFDs7Oy5fvkzTpk0BaNq0aYkVcqqD1EiK4iox4AbU5u2olCh2JOxgiP8Qg4clhBCi/pgxYwYzZsy45TF791ZP308AHx+fck9ZFBgYyKZNm6otlqp+FlqtlsLCQjIzM3FxcWH79u0AxMbGGnRAUJnlV3sJom4pWnO7aMBNOXVt1BWA7QnbySnIqY7IhBBCCFGKadOm8cADD5CVlUV4eDgJCQk8+OCDzJ49u9rLlhpJUVyDFmBqVeEBN6GuoTSybUTCtQS2xG3hHt97qjlQIYQQQgCMGDGCrKwsunTpoh+1PWvWrGofaANSIyn+y8QU3P8dFVaBfpJajZZBfoMA+P3s79URmRBCCCHKMG7cOKKiojh58iSHDh3Sj/iubpJIipL080keqdBpg3zVRHL3xd1czr5s2JiEEEIIUetIIilKKuonWcEBN43tG9PatTU6Rcfac2sNH5cQQgghahVJJEVJRSO3KzjgBrjRvB0jzdtCCCFEfSeJpCjpvwNuKqCfTz/MtGacSjvFydST1RSgEEIIIWoDSSRFSZUccAPgYOFAD+8eAKyOWW3gwIQQQpR3/kMhbsVQ3yNJJEXp9PNJHqnwqYP9BgOw5uwaCnQFBgxKCCHuXGZmZoC6vJ8QVVX0PSr6XlWWzCMpSqdfKvFIhU/t0qgLThZOpOamsuviLrp5dTNoaEIIcScyMTHB0dGR5ORkAKytrdFoNNVWnqIoFBQUYGpqWq3liIqryr1RFIXs7GySk5NxdHTExMSkSrFIIilK998BN9ryV16bac24x/celp5Yyh8xf0giKYQQBuLu7g6gTyark6Io6HQ6tFqtJJK1jCHujaOjo/77VBWSSIrSFRtwEwMNmlXo9EF+g1h6Yil/x/1NRl4G9ub21RSoEELcOTQaDR4eHri5uZGfn1+tZel0OlJSUnBxcUFbgcoEUf2qem/MzMyqXBNZRBJJUToTU3APgQv71ObtCiaSLZ1b4ufgR0x6DBtjN3Jf8/uqJ04hhLgDmZiYGCwRKItOp8PMzAxLS0tJJGuZ2nRv5JshyqZv3j5S4VM1Gg2D/dVBNzKnpBBCCFE/SSIpylaFATcA9za9Fw0aDiUfIj4z3mBhCSGEEKJ2kERSlE0/BVDFV7gBaGjTkE4enQD48+yfhoxMCCGEELWAJJKibA2aFx9wUwlFSyb+EfOHTKIrhBBC1DMVSiTHjBnDe++9x9q1a0lISKiumERtUTTgBirdvH1347uxMrUiPjOeiMsRhotNCCGEEEZXoVHby5Yt4+eff9b/7OTkREhICK1atSI0NJTQ0FCCg4OxtLQ0eKDCSDxbqyO3E49A6MgKn25tZk2fJn34PeZ3fo/5ndZurQ0doRBCCCGMpEI1ksHBwVhbWzN27FgWLFjA5MmTsbGxYeXKlUycOJGOHTtiZ2dHYGAgo0ePrq6YRU0q6idZwTW3b1a0ZOL62PVcL7xuiKiEEEIIUQtUKJGMiIjgyy+/ZMeOHUyfPp0mTZqwevVq4uLiSE1NZcuWLXz88ceEh4cTGxtbTSGLGlU0cjsxslIDbgDau7fH3cadzLxMtsZvNVxsQgghhDCqCiWSGo2Ghx56iJMnT/LSSy8xffp0AgMD+eWXX3B0dKRbt2489dRTLFiwgD179lRXzKImGWDAjVajZaDvQEAddCOEEEKI+qFSo7bNzMx4+umniYmJYcyYMUyaNImwsDD++usvQ8cnjM0AA24ABvmqo7d3JOzgSs4VAwQmhBBCCGOr0vQ/tra2vPXWW8TExBAWFsaAAQN49tlnDRSaqDUM0E/S19GXVq6tKFAK+PHEjwYKTAghhBDGVOG1ttPT0zlx4kSJR2xsLFqtluvXZTBFvVOFpRJv9kjQIzz7z7MsO7mMCSETsDGzqXJoQgghhDCeCiWSnp6eJCUlAeDt7U1QUBDBwcGMGjWK4OBgAgMDsbCwqJZAhRH9d8BNJReI7+HdAx97H2IzYvn11K88HPSw4WIUQgghRI2rUCJ56dIl7O3tGTp0KOHh4YSGhhISEoKVlVV1xSdqg/8OuGnQrFKXMdGaMC5oHDN2z2Dx8cU8EPgAZlozAwcrhBBCiJpSoUTytddeIzIykq1bt7J48WI0Gg0ajQZfX1/9hORFD19f3+qKWdQ0E1PwCIX4vWo/yUomkqAumTj3yFySspNYf269fglFIYQQQtQ9FUokZ86cqX+dkZFBZGSk/hEREcGGDRvIyspCo9Fga2tLenq6wQMWRtKonZpIxu6A0PsrfRkLEwvGBo7l00Of8t2x7xjoOxCNRmPAQIUQQghRUyo82KaIvb094eHhhIeHF9seExPDkSNHOHr0aJWDE7WIfy/YMxfObAJFgSokf/e3uJ8FkQs4c/UM2xO2082rmwEDFUIIIURNqdL0P6Xx8/Pjvvvu46233jL0pYUxNekCppaQkQCXo6t0KXtze0Y2V9ft/v7Y94aITgghhBBGYPBEUtRTZlbg01V9fWZTlS/3YMsHMdWaciDpAJGXI6t8PSGEEELUPEkkBYqikJiew9ZTl299oH9v9fn0xiqX6W7jzr1N7wWkVlIIIYSoqyrdRxKgsLCQvXv3cuHCBXJzc0vsf/hhmSewLkjPyafzu38DEPFmXxysypiSpyiRjNsN16+BhW2Vyn0k+BFWx6xmc9xmYtNj8XHwqdL1hBBCCFGzKp1IHjp0iOHDhxMfH4+iKCX2azQaSSTrCEdrc7ycrLiQlkNUQjp3+Tco/UAXP3DygbRYiN0OLQZUqVw/Rz96ePXgnwv/sOj4It7s/GaVrieEEEKImlXppu3HH38cBwcH/v77b5KSkkhLSyv2SE1NNWScopqFejkAEJlwiymbNJobtZIG6CcJaq0kwO9nfudKzhWDXFMIIYQQNaPSiWRUVBTvvfce3bt3x9XVFQcHhxIPUXeENHIE4OitEkko3k+ylJroimrj1oZWrq3I0+Wx9MTSKl9PCCGEEDWn0olk8+bNycjIMGQswohCGqmJ/9ELt0kkfbqCiTlcPQ8pMVUuV6PR6Gslf47+maz8rCpfUwghhBA1o9KJ5Mcff8y7775LdHTV5hQUtUNRIhmXms3V7LyyD7Swhcad1dcGat7u6d0TH3sfMvMzWXFqhUGuKYQQQojqV+lE8qmnniIhIYHg4GAaN25cYq3tVq1aGTJOUc0crM1o4mINwLGE29Q06/tJVn0aIACtRquvlVx8fDH5hfkGua4QQgghqlelR22HhYXJGsn1THAjB86nZBOZcJXwZmWM3AZo1gc2vqGuu52fo05WXkUDfQfyxeEvSM5O5s+zfzKs2bAqX1MIIYQQ1avSieTChQsNGIaoDUIbObAmMpFjtxtw4xoA9o3U5RLP77xRQ1kF5ibmPNzyYT46+BFzj8ylf9P+WJlWPUEVQgghRPWRlW2EXkjRFEC3G3Cj0YD/3err04bpJwnwQOADeNp4kpSdxKKoRQa7rhBCCCGqR4VqJENCQirUnB0ZKWso1yXB/w64uZCWQ1pWHk425mUf7N8HDi022IAbAAsTC54Le44Xt73Id8e+Y3iz4bhZuxns+kIIIYQwrAolktIvsn6ztzSjaQMbzl3J4mhCOt2au5Z9sG930JhAyml1pRsnH4PE0M+nH0tOLCHyciSfH/6cmV1mGuS6QgghhDC8CiWS0i+y/gtu5FC+RNLSAbw7QtwutVay/USDlK/RaHip/Us8uPZBVp9ZzZiAMQS6BBrk2kIIIYQwLOkjKYoJbVTUT/Lq7Q9uVjQN0GaDxtDKtRUDmg5AQeF/B/5X6lruQgghhDC+CtVILl68uEIXf/jhhyt0vDC+ogE3t51LEtTR2pvfhrNboeA6mFoYLI5n2z7L33F/s+/SPrbEb6FX414Gu7YQQgghDKNCieT48eOL/VzUX/LmGqOb+1BKIln3BHnaA5BwNYeUa9dxsb1FctgwBGzcICsZ4vao/SYNxNPWk4dbPsyCowuYc3AOXRt1xczEzGDXF0IIIUTVVahpOy0tTf/Yv38/TZo04fXXXyciIoJLly4RERHBa6+9RpMmTdi7d291xSyqkZ2lGb6uNgAcvd18klrtTavcGG70dpEJIRNwtnTmfMZ5lp1cZvDrCyGEEKJqKpRIOjg46B+vvPIKkydPZsaMGYSEhODm5kZISAhvv/02kyZN4uWXX66umEU1K+onefR280nCjfkkqyGRtDGzYWqbqQDMi5hH+vVyxCOEEEKIGlPpwTa7du0iLCys1H1hYWHs2bOn0kEJ4yqaTzLydjWSAH69QKOF5OOQnmDwWIb5D6OZUzMy8jL4KuIrg19fCCGEEJVX6UTSzc2Nn3/+udR9y5Ytw9X1FlPHiFot1MsR4PZLJQJYO0Ojf/9DUQ21kiZaE15s9yIAP0f/zLn0cwYvQwghhBCVU+m1tqdNm8Zjjz1GTEwMQ4cOxc3NjeTkZFatWsW2bduYP3++IeMUNSjI0x6NBhLTc0nOzMXNzvLWJ/j3hgv71UQybJzB4+ns2ZnuXt3ZemErcw7M4fO7Pzd4GUIIIYSouErXSE6aNInff/+d3NxcXnzxRcaOHcuLL75Ibm4uq1evZtKkSYaMU9QgGwtT/FxtgXLWSvr3UZ/P/gOF+dUS0/PtnsdUY8o/F/5hT6J0mxBCCCFqgypNSD5w4EB2795Nbm4uiYmJ5ObmsmfPHgYNGmSo+ISR3BhwU475JD1bg5UzXM9Qayarga+DL/e3uB+A9/e9T341JaxCCCGEKD+DrGyj1Wpp2LAh586dIycnR789OzubmJgYQxQhaljRxORHE67e/mCtiTroBqqln2SRx1s9jpOFE2eunmFe5LxqK0cIIYQQ5WPQJRJHjRqFiYmJ/mcTExNGjx5tyCJEDQkpqpEsT9M2QLN/m7dPrqumiMDR0pHXOr0GwLdHv+XYlWPVVpYQQgghbs+giWRBQQHm5ub6ny0sLMjLyzNkEaKGtPS0R6uBpIzrJGXk3v6EZn3BxFydBigxstri6ufTj/4+/SlUCnl9x+tcL7xebWUJIYQQ4tYMmkhaWloSFRWl//nYsWNYWt5mxK+olazNTWnmZgeUc2Jya2doMUB9HfFTNUYGr3V8DRdLF2LSY5h7ZG61liWEEEKIshk0kXz//ffp27cvQ4cOZciQIfTv35///e9/hixC1KDgijZvtxqjPkf+Um2jt0Ft4p7eeToAi6IWcST5SLWVJYQQQoiyGTSR7N69O0ePHmXSpElMnjyZyMhIunbtasgiRA0K9apgIul/N9i4QvaVah10A9CrcS8G+Q5Cp+h4Y+cb5BTk3P4kIYQQQhiUQRNJAGdnZ+69917uvfdenJ2dDX15UYP0SyVeSEdRlNufYGIGIeoUPRz5sRojU73c4WXcrNyIzYjls0OfVXt5QgghhCiuQonktm3b2LFjh/5nRVHYtWsXv//+O0eOHDF0bMLIWnrYY6LVcOXadZIyyjmopfUD6vOp9ZCdWn3BAQ4WDrx515sALD2xlAOXDlRreUIIIYQorkKJ5LPPPsuxY+qUK9evX6dr16507dqVoUOHEhYWRuPGjXnvvffKV3slaj0rcxOauakr3EReuFq+k9xD1EdhHhz7tfqC+1c3r24M8x+GgsIbO98gOz+72ssUQgghhKpCieTp06dp2bIlAJ9++inHjh3ju+++IyIigg0bNjBixAhmzZrF3XffzfXrMi1LfVA0n2S5lkosUjTopgaatwFebP8i7jbuXLh2gTkH59RImUIIIYSoYCKp1WrRatVTli9fzqxZsxg3bhwhISH07t2bOXPmEBERwcmTJ5k5c2a1BCxqVtGAm8iKJJIhI0FrChcPweWT1RTZDXbmdrx919sA/HzyZ1mLWwghhKghFUok/f39OXjwIHFxcRw5coTu3buXOMbX15e3336bpUuXGixIYTwhXo6AOpdkubss2LqC/78r3dRQrWRnz87c31wd6DN953Qy8zJrpFwhhBDiTlahRPKxxx7j5ZdfpnPnzpiZmfHNN9+UepyHhweJiYkGCVAYV4C7HaZaDSlZeSSml2OFmyJFg24ifwZdYfUE9x8vtHuBRraNSMxKZNr2aegUXY2UK4QQQtypKpRITp48mYULF3LvvfeydetWLl26RL9+/di0aRP5+eoE1MnJyfzvf//D19e3WgIWNcvSzITmDdUVbiLLs8JNkeb9wcoJMhPh7JZqiq44azNrPur+EeZac/658A/zI+fXSLlCCCHEnarC80iOHj2ar7/+mvbt2/PDDz/QsmVL+vfvj5WVFc7Oznh4eLB9+3bpI1mP3JiY/Gr5TzK1gOAR6usj1btk4s2CGgTxeqfXAfjyyJdsjd9aY2ULIYQQd5oqTUhuamrKxx9/THx8PHPnzmXy5MnMnDmTI0eOcN999xkqRmFkN5ZKzKjYiUXN29F/Qm4FajOraFizYYxqMQqAV7e/yvmM8zVWthBCCHEnMa3IwYsXLy5zn5WVlX5qoIMHD3Lw4EEefvjhqkUnagV9jeSFqyiKgkajKd+Jnm2hQQu4chKifoOwcdUX5H+83P5lTqWd4nDyYZ75+xl+vPdHrM2sa6x8IYQQ4k5QoURy/PjxxX4uSihuHs17c5IhiWT90MLdDjMTDWnZ+SRczcHLqZwJmUaj1kpuegsifqrRRNLMxIyPun/EqD9HEZMew+s7X+ej7h+VPwkWQgghxG1VqGk7LS1N/9i/fz9NmjTh9ddfJyIigkuXLhEREcFrr71GkyZN2Lt3b3XFLGqYhakJLdzVATdHKzLgBiB0FGi0ELcbUmKqIbqyuVq7MqfHHEy1pmw8v5Hvjn1Xo+ULIYQQ9V2FEkkHBwf945VXXmHy5MnMmDGDkJAQ3NzcCAkJ4e2332bSpEm8/PLL1RWzMIJW/84nufdcBdfPtvcE357q64hlhg2qHFq7tebVDq8C8Nnhz9h1cVeNxyCEEELUV5UebLNr1y7CwsJK3RcWFsaePbK6SH3StZkrAFtPXa74ya3/XTIxYhnoan5ux5HNRzLMfxg6RcdL217iQuaFGo9BCCGEqI8qnUi6ubnx888/l7pv2bJluLq6VjooUft08XfBVKvh3JUszqdkVezkgHvBwh7S4+D8zuoJ8BY0Gg2vdXqNYJdg0q+n89w/z5FTkFPjcQghhBD1TaUTyWnTpvHdd9/Rs2dPPv30U3766Sc+/fRTevTowcKFC3nttdcMGacwMjtLM9r5OAHwz8kK1kqaWUHQUPV1RM3NKXkzCxMLPu75Mc6WzkSnRjNt+zQKa2jFHSGEEKK+qnQiOWnSJH7//Xdyc3N58cUXGTt2LC+++CK5ubmsXr2aSZMmGTJOUQv0aOEGwD8nkyt+cuux6nPUb3D9muGCqgB3G3c+6v4RZlozNsVt4u09b5d//XAhhBBClFChRDIvL6/YzwMHDmT37t3k5uaSmJhIbm4ue/bsYdCgQQYNUtQOPVqo3RV2n00hN7+CtXneHcHFH/Kz4PCSaoiufNq5t+ODbh+g1WhZeXolnxz6xGixCCGEEHVdhRJJZ2dnhg0bxrfffktSUtKNi2i1NGzYEK22SgvliFquRUM73O0tyc3XVXz0tkYDnZ9SX+/6Agrybn18NerdpDdvdn4TgO+Ofcf3x743WixCCCFEXVahzG/lypV4e3sze/ZsGjVqRIcOHXj77bc5fPhwdcUnahGNRqOvlaxU83arB8DGDTIuwLEVBo6uYoY3G85zYc8BMOfgHFaeXmnUeIQQQoi6qEKJZN++ffnss8+IiYkhIiKC++67j40bN9KhQwe8vb157LHHWLNmDbm5udUVrzCyokRya0UH3ACYWULnJ9TXOz81ylRAN3s0+FEeCX4EgBm7Z7Dp/CajxiOEEELUNZVuiw4KCuLll19m+/btJCUlMXv2bNLT03nwwQdxcXFh4MCBzJ8/35Cx1mknTpygffv2NG/enF69epGYmGjskCqli38DTLUazl7JIi4lu+IXaPeoOhXQ5Wg4td7wAVbQc22fY3iz4fo5JvcmyopMQgghRHkZpFOjs7MzDz30EMuWLePy5cv88ccfNG/enI8//tgQl68XpkyZwuuvv86pU6cYMmQIr7zyirFDqhQ7SzPCmvw7DdCpSjRvWzpA+wnq6x1zwMijpjUaDW90eoPejXuTr8vn6b+f5tiVY0aNSQghhKgrKpVIJicnc/78+VL3mZqa0qtXL+bMmUN0dHSVgjO2M2fOMGXKFFq3bo2pqSnBwcGlHhcdHU2fPn2wsbHB3d2dl156qdgI96SkJE6fPs2QIUMAmDBhAqtWraqR91AdbkwDVInmbYCOj4OJBVzYD+eNv2ShqdaU97u9T0ePjmQXZPP4psc5m37W2GEJIYQQtV6FEskzZ87Qpk0bPDw88PX1xdXVlU8++aSaQjO+qKgo1qxZg7+/Py1btiz1mLS0NHr16kVeXh4rV65k9uzZfP311zz//PP6Yy5cuIC3t7f+Z1tbWywtLUlJSan291AdivpJ7oq5UvFpgADsGkKbf+eV3FE7aq3NTcz5tOenBLsEc/X6VSZtmETM1RhjhyWEEELUahVKJJ955hnOnTvHSy+9xMyZM2nXrh0vvPACn332WXXFZ1SDBg0iPj6eFStW0LZt21KPmTdvHhkZGaxatYp+/frx6KOP8sEHHzBv3jwuXrxYwxHXjAD3G9MA7avoNEBF7poKGi2c2QiXjho2wEqyMbPhy95f4u/oT3JOMuPXjycqJcrYYQkhhBC1lmlFDt69ezeffPIJ48eP12978803mT17Nk8//bShYzO68syLuW7dOnr37o2zs7N+2/3338+UKVP466+/GD9+PF5eXsTHx+v3X7t2jdzcXFxcXEq95vXr17l+/br+54yMDAB0Oh26f0c663Q6FEXR/1zTujVvwC8HLrDlZDLh/qW/j1ty9EHTcgiaqFUoOz5GGf6N4YOsBAdzB77t+y1PbH6CqJQoJmyYwOc9PyesYVi5zjf2fRFlk3tTe8m9qZ3kvtReNXFvynvtCiWSV69eLdHEO3nyZGbOnMnZs2fx9fWtyOXqhejoaB599NFi2xwdHfHw8ND3EW3YsCH+/v6sXr2aIUOG8O233zJ06NAyr/nuu+8yY8aMEtsvX76sn1pJp9ORnp6OoihGmQi+dUNzfgH+Pp7IY+0rkUgCpoEP0yBqFUStIiX0cQrtvW9/Ug2Z3Xo20w9NJyItgimbpjC99XQ6una87XnGvi+ibHJvai+5N7WT3JfaqybuTWZmZrmOq1AiCeoo15u5u7sDkJ6eXtFL1QtpaWk4OjqW2O7k5ERq6o1m36+++opx48bxf//3f3h5ebF06dIyr/nqq68W62OZkZGBt7c3rq6u2NvbA+qXSKPR4OrqapRf8HvsnZi+7hzn066Ta2pLY2fril/EzQ3F7240MZtpcOonlHv+Z/hAq+Brt695aftLbL2wlbcOv8Ws8Fn09+l/y3OMfV9E2eTe1F5yb2onuS+1V03cG0tLy3IdV+FEcuLEiYSFhREUFERQUBDNmzevcHB3oqCgIA4cOFCuYy0sLLCwsCixXavVFvvCaDSaEttqiqO1BW2bOLHvXCrbTl/h4c4+lbtQ+HMQsxnNkaVoerwCtm6GDLNKrM2t+bjnx7y24zXWnVvHK9tfIbsgmxHNR9zyPGPeF3Frcm9qL7k3tZPcl9qruu9Nea9bodJfe+01fHx82LJlCy+++CL33HMPzZo1A+Cpp57ihRdeYPHixURERJCfn1/xqOsgJyenUmtj09LSivWbrI9uLJdYyWmAAHzCoVE7KMiFvfMMFJnhmGnNeDf8Xe5vfj8KCjN2z2DhsYXGDksIIcQd6krOFRZFLeKJ3U+QkZdh7HAqViM5c+ZM/euMjAwiIyP1j4iICL7++muysrIAMDMzKzZgpL4KCAgoMV9meno6iYmJBAQEGCmqmtGjuRsfrD+pnwbI0syk4hfRaNRayZ/Hwr5voMuzYGlv8FirwkRrwuudXsfW3Jbvjn3HRwc/IiMvg6ltppbo6iGEEEIYWn5hPlsvbOW3M7+xI2EHhYo69d6G2A2MChhl1Ngq3LRdxN7envDwcMLDw4ttL1qHOzIyssrB1QUDBgxg9uzZXL16Vd9Xcvny5Wi1Wvr27Wvc4KpZoIcdDe0tSMq4zr5zqXRr7lq5C7W4Bxo0hyun4OD30OUZwwZqABqNhufCnsPO3I5PD33KgqMLSMxK5M3Ob2JpWr5+JEIIIURFRKdG89uZ31hzdg1Xr1/Vb2/l2oqerj1v22+/JlQokVy8eHG5j60PI7izs7NZu3YtAOfPnycjI4MVK1YA0L17d1xdXZkyZQqff/45Q4cOZdq0aSQkJPDiiy8yZcoUPD09jRl+tdNoNHRv7sovBy7wz8nLlU8ktVo1eVz9JOyeCx0eA7PamZxNDJmIg4UDs/bM4s+zfxKbHssnPT+hoU1DY4cmhBCiHkjJSWHduXWsjllNdOqNFk83KzcG+Q1isP9gfOx8SE5Oxs7czoiRqjSKUv7Fjv/b8bKoWe/mS9zc1FdYWIlVT2qR2NhYmjZtWuq+LVu20KNHDwBOnDjB1KlT2bVrF3Z2djz88MPMmjULc3Nzg8SRkZGBg4MD6enpxUZtJycn4+bmZtRO0GuPJvLE0kP4utrw9ws9Kn+hgjz4tBVkXoR759xYj7uW2pu4lxe2vkD69XRcrVz5pOcnhLqG1pr7IkqSe1N7yb2pneS+1JzrhdfZEr+FP2L+YGfCTn3TtZnWjF6NezHEbwidPTtjqlXr/2ri3pSWe5SmQjWSaWlp+tdnzpxh5MiRPPTQQ4wYMYKGDRuSlJTE8uXL+eGHH/jll18qH30t4ePjQ3ny7MDAQDZt2lQDEdU+XfwbYKLVcPZyFvGp2XhXZhogAFNztVZy/cvwz7sQMrLW9ZW8WUePjvx07088/ffTnLl6hkfWP8Kbd73JwKYDjR2aEEKIOkCn6DicfJg/Yv7gr9i/yMy/MW9jSIMQBvkN4p6m9+Bg4WDEKG+vQomkg8ONN/PKK68wefJkXnnlFf02Nzc3QkJCsLKy4uWXX2bz5s2Gi1TUSg5WZoQ1dmJfbCr/nEzmocpOAwTQ7lHY9zWkxsD2j6BPyUnZaxNvO29+uOcHXt3+Klvit/DajteITolmrNdYY4cmhBCiljqXfo41Z9fw59k/SbiWoN/uYePBQN+BDPIbRFOH0ltDa6NK14fu2rWLsLDSl40LCwtjz549lQ5K1C3dDTENEKi1kv1mqa/3fAmpZ6sYWfWzMbPhk56fMDl0MgBLTizh9UOvk3Hd+FMyCCGEqB2Ss5NZFLWIUX+OYvBvg5kfOZ+EawnYmNkwzH8Y3/X7jvX3refptk/XqSQSqjBq283NjZ9//pk+ffqU2Lds2TJcXSs58ELUOT1auPLhhpPsikmp/DRARZr3B9+ecHYLbJwOo34wXKDVRKvRMrXNVJo7Nef1Ha9zIOUAY9eN5fNen+PrWPcHnQkhhKi4zLxMNp3fxJqza9h3aR8Kalc5E40Jd3nexSC/QfTw7oGVqZWRI62aSieS06ZN47HHHiMmJoahQ4fi5uZGcnIyq1atYtu2bcyfP9+QcYparKWHPW52FiRnXmd/bCpdm1XhPxEaDfSbDfO6wIk/4Nx2aNrVcMFWo34+/fCy9WLq5qnEZcYx6s9RvNThJUY0GyHzTQohxB0gtyCX7QnbWXt2LdsubCNPl6ff19q1Nff63ktfn744W9afBUsqnUhOmjQJDw8PZs2axYsvvkhBQQGmpqa0bduW1atXM2jQIEPGKWqxommAlh9UpwGqUiIJ0LCl2l9y/zew/lV4bCtoq1DLWYMCnQOZ22kuc6LnsOfSHt7e/TY7E3byVue3cLR0NHZ4QgghDCyvMI9dF3exPnY9W+K2kF2Qrd/n5+DHvb73MqDpALzsvIwYZfWpdCIJMHDgQAYOHIhOp+Py5cuysPsdrGeAG8sPXmDj8SRevzew6jVwPabB0eWQdBQOL4Gw8QaJsyY4WTjxVe+v+OHED3x6+FM2x23m6JWjvBv+Lh08Ohg7PCGEEFVUoCtgX+I+1sWuY3PcZjLzboy49rDxoL9Pf+71vZfmTs3rfYtUlRLJIlqtloYNZULmO1mPFq7YmJsQl5rN/tg0OjStYrW9jQt0fwU2vAqbZ0LQMLCs3VMg3Eyr0TI+eDwdPDrw8raXic2IZeJfE3k0+FGebPMkZlozY4cohBCiAgp0BRxMOshfsX+x8fxG0q7fmBLR1cqVfj796OfTj1aurep98ngzgySSQlibm3JvqAe/HLjAioPxVU8kATpMggPfQcpp2PY/6Dvz9ufUMi1dWvLzwJ/5YP8H/Hr6V7499i17E/fyfrf3aWzf2NjhCSGEuIUCXQH7L+3nr/N/8Xfc36Tmpur3OVk40adJH/o37U9bt7aY1JEuWIYmiaQwmBFh3vxy4AJrIhN5a3AQ1uZV/HqZmKnTAf14P+z5Sm3edvEzSKw1ydrMmrfueosujbrw1q63OJZyjBF/jODVDq8y1H/oHfU/VyGEqO3ydfnsS9zHxvMb2Ry3udga1w4WDtzd+G76NulLR4+O+pVm7mTyCQiDae/jRGNna+JSs1l/7BLD2xqgY3GzvuB3N8RsVqcDGr206tc0kj5N+hDSIIRXt7/KgaQDTN81nTXn1jC903SpnRRCCCPKLchl98XdbI7bzD8X/iH9erp+n5OFE3c3uZs+TfrQ3r29dE36D4Mmkvv37+f111/n3LlzFBQUoCgKGo2Gs2dr/8TSouo0Gg0jwryYs/EUKw5eMEwiWTQd0Fd3QfSfcHYr+Hav+nWNxN3GnW/6fsPCqIV8FfEVexP3Mvz34UxpNYVxQePkD5QQQtSQa3nX2HZhG5vjNrM9YTs5BTn6fc6WzvRu3Js+Pn1o17Cd1DzegkE/mXHjxjF9+nQ6dOiAicmd2VfAkObOncvcuXMpLCw0dijldl+YFx9vOsWumJSqrb19M7cAaD9BXT5x/aswZXudmQ6oNCZaEyaETKBPkz68vedt9ibu5dNDn7L23Fre6vwWoa6hxg5RCCHqpZScFP6J/4fNcZvZk7iHfF2+fl9D64b0btKbuxvffUf3eawojaIoiqEu1q5dOw4cOGCoy4l/ZWRk4ODgQHp6Ovb29gDodDqSk5Nxc3OrdVMujf1mDzvPpPBc7+Y807uZYS6anQqftYHcqzDwY3WeyVqoovdFURT+OPsHH+7/kKvXr6JBw+iA0Tzd5mlszW1rIOI7R23+nbnTyb2pnerLfTmXfo4t8VvYEreFiMsR+hVmAHzsfejdpDe9G/empUvLOtNnvSbuTWm5R2kMWiM5cuRIfvjhB+6//37Mzc0NeWlRh4wI82LnmRRWHIpnai9/tFoD/GJaO0OPV2H9y7D5bWhxD9i5V/26RqbRaBjsN5iujbryvwP/4/eY3/kp+ic2x21mWsdp3N34bmOHKIQQdUqhrpDIK5FsidvClvgtxGbEFtsf6ByoTx5lGduqM9g8khqNhqLKzXHjxgHo+0jWpaZZUXX9gtyxtYgiPjWH/bGpdPR1McyF20+AI0vhUiT8PhXG/KL2oawHnCydmBU+i4G+A5m5ZybxmfE8u+VZ7vK8i+fDnqeFcwtjhyiEELVWVn4Wey7uYeuFrWy9sLXYND2mWlM6uHegp3dPenj3wN2m7ldC1CYGSSR1Op0hLiPqCWtzU+4N8eDnA/EsP3jBcImkiRkM/xrmd4fTf8GhxRA2zjDXriU6e3Zm5eCVzI+cz8Kohey6uIs9iXsY6j+UJ1s/iZu1m7FDFEKIWiE+M55tF7axNX4rB5IOFOvvaGdmR1evrvT07kmXRl2wM7czYqT1m0GbtmNiYvD09MTKygqAnJwcLl68iJ9f3Zv7T1TNyHZe/HwgnrVHE5kxOAgbCwN91dwC4e434K/XYcM0dQS3k49hrl1LWJpa8kzbZxjebDifHPyEv87/xcrTK1l3bh2PBD3CuKBxWJsZYBCTEELUIfm6fCKSI9Tk8cJWzqYXnxHG286b7l7d6e7dnbCGYTILRg0xaCI5atQodu3apf9Zq9UyevRo9u/fb8hiRB0Q1sQJHxdrYlOyWXfsEiPCDLhYfacnIHotxO2CVY/D+D/r9CjusnjbefNRj484knyEDw98SOTlSL6M+JLlp5Yztc1UBvsNllGFQoh6LSkriZ0Xd7IjYQd7Lu4hM//GmtYmGhPaNmxLd6/udPPqho+9T50ZLFOfGDSRLCgoKDbIxsLCgry8PEMWIeqIojkl//fXKVYcjDdsIqk1gaFfwrxwNZnc8yXcNdVw169lWru15ocBP7Dh/AY+OfgJCdcSmL5rOj+c+IFn2j5D10Zd5Y+nEKJeyNflcyT5CDsSdrAjYQen0k4V2+9o4UjXRl3p5t2Nuzzvwt687NHEomYYNJG0tLQkKiqKoKAgAI4dO4alpaUhixB1yLC2Xny08RR7zqYSl5JNYxcDNsc6N1WXT/zjGdg8E/x7q83e9ZRGo6G/T396effip+ifmB85n1Npp3hy85MEuQQxpdUUunt1l4RSCFHnXMi8wK6Lu9h9cTd7EvdwLf+afp8GDSENQujSqAvhjcIJcgmSlphaxqCJ5Pvvv0/fvn1p3749iqJw8OBBfvrpJ0MWIeqQRo5WdPFrwI4zV/j10AWe69PcsAW0HQfRa9SBNysnw8TNYFq/p50yNzFnXNA4hvgN4Zuj3/DLqV+ISoli6t9TCXAOYEroFHo27olWU3fnfBNC1G/X8q6x79I+ffIYlxlXbL+zpTN3ed5FeKNw7vK8CydLJyNFKsrDoBOSA6SmprJ7924AOnfujLOzsyEvf0eqaxOS32z1kQSeWXYELycrtr3Y0zBzSt4s8xJ82Qly0qDbS9DrNcNev4Jq+r6k5KSw+Phifor+Sb+8VzOnZjwW+hh9mvSRhPImdeV35k4k96Z2MtR9ydflc+zKMfYk7mH3xd1EXo6kULkxLaCpxpRWbq24y/Mu7vK8i5YuLeVv123U2wnJAZydnbn33nsNfVlRR/Vt6Y6dhSkX0nLYey6Vzn4GmgqoiJ073DsHVjwC2z+C5v3BK8ywZdRiLlYuPBf2HOODxrPk+BJ+jP6R02mn+b+t/4efgx8TQyfSz6efjF4UQtQYnaLjdNpp9iTuYW/iXg4mHSS7ILvYMT72PnT27MxdnnfR3r09NmY2RopWVJVBE8n9+/fz+uuvc+7cOQoKCvQTkp89e/b2J4t6ycrchIGtPPhpXzzLD8YbPpEECB4O0X/CsV9h1WPqWtxmVoYvpxZzsnTi6bZPMy5oHEtPLOWH4z8Qkx7Dq9tf5eODHzO6xWhGNB8hTURCCINTFIULmRfYe2kvexP3su/SvmITgoM6SKa9e3vu8ryLzp6daWTbyEjRCkMzaNN2y5YtmT59Oh06dMDE5EZn2CZNmhiqiDtSXW7aBjh4PpX7vtqNlZkJ+1/vja2h5pS8WXYqfNkZrl2Cjo/DgPcMX0Y51Jb7kpmXyU/RP/HjiR9JyU0BwMLEgnt972Vs4FiaOxm4v2odUFvujShJ7k3tVNZ9KUoc9yftZ/8l9ZGUnVTsXCtTK9o2bEsn90509OhIC+cW0lxtQPW2adva2prRo0cb8pKiHmjb2AnfBjacvZLF2qOJ3N/O2/CFWDvDkLmw9D7Y+xX49oAW/Q1fTh1hZ27H5NDJjA8az4bYDfxw4geOpxxn5emVrDy9ko7uHRkbOJZuXt1kBKQQ4pYURSE+I54DSQfUxDFpP5eyLhU7xlRrSkiDEDp5qIljaINQzEykS82dwKCJ5MiRI/nhhx+4//77i80nKe5sGo2G+8K8+HDDSVYcvFA9iSRAs97QYTLs+xpWTlJHcbveeTVvNzM3MWeQ3yAG+g7kyOUjLDm+hM1xm9UmqEt78bL14r7m9zHYb7AsvyiEAG70cTyYdJDdcbuJSo/ics7lYseYak0JbRBKO/d2tHdvTyvXVliZ3lldioTKoE3bpVWvajQaCgsLSzlalFddb9oGSEzP4a73/kZRYPML3fFzta2eggryYPFgiNsNLs1g0mawdKieskpRF+5L4rVEfjr5E7+e+pWMvAwAtBotXRt1ZZj/MLp5dauXNQl14d7cqeTeGFdeYR7HU45zKPkQh5IOcTj5sP5vQxFTrSnBLsG0d2+vTxxlqVbjqU1N2waf/kcYXn1IJAEmLtrPphPJ3N/Oiw9GtKq+gq4lw9c9ICMBmvWDB36qsSUU69J9yc7PZkPsBn478xuHkg/ptztbOjPQdyDD/Ifh7+RvxAgNqy7dmzuN3JualZqbypHkIxy5fISI5AiOXTlGnq74KnRWpla0cm1FC5sWdG3alVZurbA0lQVGaot6nUiuW7eOo0ePkpubq982ffp0QxZxx6kvieTB82nc99UuzEw0bH2xJ56O1dgMcvEwfNcfCnKh6wtwd818B+vifQE4l36O3878xu8xv3Ml54p+e2iDUAb6DaRPkz40sGpgxAirrq7emzuB3JvqU6grJCY9hsjLkRxOPkzE5QjOZ5wvcZyThRNt3NrQtmFb2jVspw6OQSv3pZaqTYmkQftIPvvss8TGxrJv3z7GjBnDr7/+So8ePQxZhKjDwpo40bGpM3vPpbJg+1neHBRUfYV5toHBn6t9Jbd/BO4hEDSs+sqr45o6NOW5sOeY2mYqOxN2surMKrbGbyXySiSRVyJ5b997tG/Ynr4+fendpDfOlrLQgBC10ZWcK0RejiTyciRHrxzl2JVjJeZwBPB39KeVayvauLWhtVtrGts1LrHEqk6nq6mwRR1m0BrJ4OBgjh49SqtWrYiMjCQlJYVRo0axadMmQxVxR6ovNZIAW09dZtx3+7AyM2HnK71wtqnmQVkbXoPdX4CZNUz4S00oq1FdvS+lSclJYc3ZNWyI3UDklUj9dhONCR3cO9DPpx93N74bR0tH4wVZAfXp3tQ3cm8qJys/ixMpJ4hKieLolaNEXo4kMSuxxHHWptYENwimtVtrWru2JtQ1FAeL2/cdl/tSe9XbGklra2s0Gg2mpqZcu3YNFxcXEhISDFmEqOO6NWtAkKc9URczWLjzHM/3bVG9BfaeAUlRcHYLLBsDk/4Bm2qYFL0ecrFy4eGgh3k46GESriXwV+xfrI9dz/GU4+xO3M3uxN28s+cdOnp0pLt3d7p5dZNJhoWoJrkFuUSnRhOVEsXxlOMcu3KMc+nnUCheF6RBg7+TP6ENQglpEEKoayi+Dr4yzZeoNgZNJH19fUlLS2PkyJF069YNR0dHAgICDFnEHWXu3LnMnTu3Xo1612g0PNnTnyeWHmLhrlgmd/erngnKi5iYwojvYEFPSIuFFePhwVXqdlFujWwb8UjwIzwS/AjxGfFsOL+BDbEbiE6NZufFney8uJPZe2fj7+hPN69udPfqTqhrKKZa+ZyFqKis/CxOpp7kROoJTqScIDo1mjNXzxRbn7qIu407QS5BBDcIJrRBKEENgmS5QVGjqm3U9rZt20hPT6d///6YmdW/qURqUn1q2gYo1Cn0mbOVs1eyeHVAAI9196v+QpOOwze9IT8LOj0B/d+tlmLq8n2pjNj0WLbEb2Hrha0cST5S7B86BwsHwhuF061RNzp5djJ6v8o77d7UJXfyvUnNTSU6NZro1Gh90ng+43yJmkZQZ1QIbhCsTxxburSs1kFwd/J9qe1qU9O2wRLJwsJCFixYwJQpUwxxOXGT+pZIAvyyP56Xfo3E1c6C7S/1xNKsBppdjv8Ovzykvh78ObR92OBF1PX7UhXp19PZmbCTbQnb2H5he4l56Jo7NaeDewc6eXQirGEYtubVNJdoGe7ke1Pb3Qn3Jr8wn7PpZzmVdorTaac5lXaKk2kni82ScDM3azcCnQMJcA4g0DmQoAZBNLRuWGJATHW6E+5LXVUvE0mAdu3aceDAAUNdTvyrPiaSeQU6un+4hcT0XGYNC2Zsxxpaj/3vWbDtA9BoYcT3EDTUoJev6/fFUAp0BURejmTrha1sT9jO6bTTxfabaEwIcgmig0cHOnp0rJFVMeTe1F716d7oFB0J1xKIuRrDmatnOHP1DKfTTnM2/SwFuoISx2vQ4G3nTaDLjaQxwDkAFyvj9+WuT/elvqm3ieTMmTNxc3PjoYcewtpaZrw3lPqYSAJ8t+Mcb/95nMbO1vz9QndMTWrgfSgK/D4VDi8BrRk8sExdWtFA6sN9qQ4pOSnsT9rPvsR97E3cS1xmXLH9phpTWji3oJVrK1q7taaVays8bDwMWvsi96b2qov3plBXSGJWImfTz3Lm6hl94ngu/Rw5BTmlnmNnZkczp2Y0d2pOC+cWNHdqjr+jf61dIaYu3pc7Rb1NJIveTNEff0VRZIlEA6iviWR2XgFd3vubtOx8Ph3dmiGta2jEr64Qfp0AUavA1AoeWglN7jLMpevBfakJidcS2XdpH/suqYllUnZSiWPcrNxo5daKVq6tCHUNpYVTiyr9gyv3pvaqzfcmOz+b2IxYzqWfu/HIOMf59PMlVoMpYq41p6lDU/wc/fB39KeZUzNaOLXA3ca9Rpumq6o235c7XW1KJA06pFKn05GXl8fJkycBCAgIkIE2okzW5qY80qUpczae4qt/YhjcyrNm/shqTWDY15CXBaf/gqX3w/g/1EnMRY3wsPVgiP8QhvgPQVEULmVdUpdruxzBkeQjnEw9SXJOMhvPb2Tj+Y2A2gTo4+BDgHMALZ1bEuCiNgOWZz48IW4lpyCH+Mx44jPiOZ95nriMOOIy4zifcZ7k7OQyzzPXmtPYvjH+jv76h5+jH152XjJjgbhjGPSbvmPHDsaOHUuDBg1QFIXU1FSWLl1Kly5dDFmMqEfGdfZh/tYYoi9l8nd0MncHNqyZgk3N4f7F8MMIOL8DlgyHR9aBm0xXVdM0Gg0eth542HowoOkAQP2H/XjKcY4kq8nlsSvHuJxzWV8jtO7cOv35njaeBDgH4O/kj5+DH36Ofvg4+GBhYmGstyRqGUVRSMlN4ULmBRKuJdx4vnaBuIy4UmvEb+Zs6YyPvQ9NHZoWe3jaeMr8jOKOZ9BE8oknnuDXX3+lXbt2ABw8eJBHHnmEyMjI25wp7lQO1mY82KkJ87edZe6WM/QKcKu5ph8zK3jgJ1g8BC4eUp8fXQ/OTWumfFEmK1MrwhqGEdYwTL/tSs4V/fQoRfPrXbh2gYtZF7mYdZG/4//WH6vVaPGy9cLX0VefXHrbemOdZ42r4mqMtySqUaGukMs5l7mUdYnErET1cU19vpCpfkfK6rdYxM7Mjsb2jdWHXWOa2DehsX1jmtg1qTOrNwlhDAZNJDUajT6JBAgLC5N+FeK2JoQ35ftdsRyKu8rec6l08q3B0YqW9vDgr7DwXkg+fiOZtPesuRhEuTSwakBXr6509eqq35aRl8HJ1JNEp0YTczVGP/AhMy+TuEy1efKf+H+KXcfOzA4vOy+87byLPbzsvHC1dsVMK91xapPrhde5nH2Z5OxkknOSSc5K5nLOZZKyk0jKSuJS1iWSspNKnaz7Zho0NLRpiJetF41sG9HIrhFetur3oIl9ExwtHOtU/0UhaguDJpL33Xcfn376KRMmTEBRFL7//nvuu+8+QxYh6iE3e0tGhnmxdG8cX/4TU7OJJIC1Mzy0Cr7rD2nnYPFQeGQt2FTfRL/CMOzN7Wnv3p727u3124qaMWOuxuiTy5irMZzPOM/lnMtk5meqNZqpJ0pcT6vR0sCyAQ1tGuJu405D63+fbRribu2Oi5ULLpYutXaUbV2RV5hHWm4aKbkppOSkcCXnCucvn+d63HVSc1NJzU0lJTeF5Oxk0q+nl+uaphpT/X3zsPHAw8YDdxt3vGy98LLzwsPGAzMT+U+CEIZmkFHbWq0WjUbDzZcq+llGbVddfR21fbO4lGx6/G8LOgX+nBpOcCMjDKBIOw/fD4CMBHAPUZdStK1YM2h9uy/1iU6nIy4xjjyrPBKuJaiDKzLjib8Wr+8zV9o8f6WxMrXC2dIZFysX9dlSfXa2dMbO3A57c3vsLezV539fW5pY1qsarwJdAdfyrpGZl0lmfqb6Oj+TzDz1dXpeOldzr5J+PZ2r169y9br6Ou162m2bmf/LwsQCVytX3Kzdij2KEn0PGw8aWDWQ/ooGJn/Paq96N2pbp9MZ4jLiDtbYxZpBrTxZfeQi76+PZvGjHWr+H12nJvDQb7DwHrh0FL7rq/7sVEOTpYtqZ2liSWPHxjR3bl5in07RkZqbqm8uvZR9SX1d9Jx1iZTcFK4XXienIIeEawkkXEsod9lmWjPszO2wNrXG2swaK1MrrE3/fb7pZ3MTc8xMzDDXmquvtWb6ZzMTM8w0Zmg0GrQaLRo0+tda1P/QazQadDodhUohOkV9VhSl2M/5unzyCvP0z3mFeeTp8sgvzCdPl0duQS45BTlkF2STU5Cjvs6/8broURUmGpNiybgNNng6etLAqoG+5tfVWk0e7c3t61USLoQhmKTFgJubscOoWCI5ZswYQkNDCQ0NpVWrVjRqVEPz/ok7wnO9m7Pu6CW2n77C5hPJ9G5ZQyO4b+baHB5ZD0uGQepZ+K4fPLgSGras+VhEjdJqtDSwakADqwYENQgq9RhFUcguyCYlJ0Vtfs1JUZtn/22iTb+eTkZeBhnXM9TnvAwy8zL1yVtqbiqppNbwO6teVqZW2JnZYWtui625LXbmdtiZqbWyDhYOOFk64WjhiIOFA44WjurD0hFbM1u0GrUmRWq+hCin7FQ4uhzN4SW4XjqK7vE90DDQqCFVKJFctmwZP//8s/5nJycnQkJCaNWqlT7BDA4OxtLS0uCBivrPp4ENj4Y3Zd7WGN5Zc5yuzRtgYWqEpqoG/jBhgzol0OUTanP3mF+gcceaj0XUKhqNBhszG2zMbGhs37hc5yiKQlZ+lj6pvLl2r6jGLzs/W//6euH1YjWG+YX56vO/2wp0BSgoKIqCTtGhUPxZp+gw0Zig1WjVZ61aW6nVaDHRqtvNtDdqPG+u9bx5m7WpNVZmVsVqTm+uPbUzs8PG3EYGJwlR3XSFcPYfOPwDRP8JhXloAEVrBolH6lYiGRwczLlz5xg2bBg9evTgzJkzREZGsnLlSj777DO1iUWrxd/fn1atWrFs2bLqilvUU0/18ufXQxeITcnm+52xTOnuZ5xA7D3VATc/jYb4vepo7lFLoFkf48Qj6iyNRqOvrRNCiHJLi4UjP6qP9Pgb291D0LV+kMvuPXBtXLKbTk2rUBtCREQEX375JTt27GD69Ok0adKE1atXExcXR2pqKlu2bOHjjz8mPDyc2NjYagpZ1Ge2Fqa83F+dFPzzzadJzsw1XjDWzmofSf8+UJCjJpWRvxgvHiGEEPVbXhZELINFg+HTVrD1fTWJtHSA9pPgsW0wZQd0mIxSS+Y3rdSo7fz8fL766itmzZqFg4MD77zzDvfff391xCe4M0Zt30ynUxj21S4i4q8yIsyL/41sZdyACvPhtyfg6L9JZP/3odOUUg+tz/elrpN7U3vJvamd5L7UEJ0Ozu+EiJ/g+GrIu3Zjn28PaPMQBAwEM8ubTqk9o7YrVbqZmRlPP/00MTExjBkzhkmTJhEWFsZff/1V6YCFKKLVanhzkDq4ZcXBC0TEXzVuQCZmMGw+dHxc/Xn9y/D3O1D1mbOEEELcqVLPwpbZ8FkrWDQQjixVk0gnH+gxDZ6JhIdXQ8iIYklkbVOlNNbW1pa33nqLmJgYwsLCGDBgAM8++6yBQhN3sraNnRjeRp0V4K0/otDpjJy0abXQ/13o9br687YPYcWjajOEEEIIUR45aXBwoboAxmdt1Kbrq3FgbgdtH1ZnDXn6CPR4uc5MPVfheSTT09M5ceJEiUdsbCxarZbr169XR5ziDvTygADWR13icNxVVkckMKyNl3ED0mig24tg4wZrnoeolXDlFIz6QdbnFkIIUbqC63B6I0Qug1MboDDv3x0a8OsJrcZAwL1gXjdXzKpQIunp6UlSUhIA3t7eBAUFERwczKhRowgODiYwMBALC4tqCVTceRraW/JUL38+WH+S99ZF07elOzYWBl3Vs3LCxkGD5vDLw5B0DL7uASO+A/+7jR2ZEEKI2kBR1Bk/In+GYysh9+qNfW4tIfR+CLkfHOr+fNwV+lf50qVL2NvbM3ToUMLDwwkNDSUkJAQrK6vqik/c4R7t0pRl++KJS83my3/O8GK/AGOHpGrSGSb/A788BAkHYekIuPtN6DzV2JEJIYQwluRoOLZCneHj6vkb2+081L6OoaOgYbDawlVPVCiRfO2114iMjGTr1q0sXrxYvxyXr6+vfkLyooevr291xSzuIJZmJrx+byCTlxxkwfZzjGrXmMYutaT636ERjF8La19QJ4rd9Caai0fQdJ5u7MiEEELUlKtxcOxXOLpCbaUqYm4LgYPV2sem3aCergVfoURy5syZ+tcZGRlERkbqHxEREWzYsIGsrCx1Al5bW9LT0w0esLjz9GnZkHD/Buw4c4VZa48z/6F2xg7pBjNLGPwFeLaBdS+jOb4K50tRMGYZNDDSZOpCCCGq17XLELVKrX2M33tju9ZM7eYUMhJa3FNn+z1WRKU7nNnb2xMeHk54eHix7TExMRw5coSjR49WObg73dy5c5k7dy6FhYXGDsWoNBoN0we1ZMCn29kQlcTOM1fo4t/A2GHdoNFA+4ngFoTyy8OYpZ5C+aYXDP8amvczdnRCCCEMITsVoteoAy3PbgWl6N9mDfiEq03XgYPVxSzuIJWakFzUrDttQvKyvPV7FAt3xeLnasOap7tiaVb7mgl0Vy9Q8OMYzJMj1A3tHoW+74C5jXEDE3fk70xdIfemdpL7AuRchZNr1drHmL9BV3Bjn2dbNXkMGqYuq1uDatOE5LVgCKwQ5fNc7+b8GZlIzOUsPlh/kun/Tlpeq9h7kjrkBxpGzkWzdx4c+A7ObVNrJxuFGTs6IYQQt5ObASfX/Zs8br5puh7UgTJBQyFoOLhI9yWQRFLUIQ7WZnw4IpRHFu7nu53nuDvQrXY1cRcxMUfp9y6a5v3UpRVTzsC3faH7yxD+PJjIr50QQtQqOVfV5PHE73BmMxTeNCe2a6Ba6xg0DFybGy3E2kr+RRN1Ss8AN8Z2bMzSvXH83/II1j/TDQdrM2OHVTq/XvD4rn8nL18FW2apk9IOnw/OMquBEEIYVVYKnFyjrm99divo8m/sc2kGwcPV5NEt0Hgx1gGSSIo657V7A9l55gqxKdlM//0Yn45uY+yQymbtDCO+h+YDYO3/wYV98FW4utxi24fr1VxiQghR62UmQfSfavIYu+OmATOoNY8th0DLweqk4fL3uVwkkRR1jrW5KR+Pas2IebtZfeQidwc2ZHCrmu3oXCEaDbQapU5ivupxOL8D/nhabUa550Nw9DZ2hEIIUX+lxKjJY/QaiN8H3DTG2D1UTRwDh0izdSVJIinqpDaNnXiypz+fbT7N66uO0sHHGXcHS2OHdWuOjWHc77D7C9g8E06tUwfi9HgFOj0OJrW0iV4IIeoSRYHEI2rieOJPuHyi+P5GYeo0PS0HSzcjA5BEUtRZU3v5s/VkMhEX0nlxRQSLHumAVlvLmyK0JtDlGWjWF/58DuJ2w8Y3IOInGPgxNO5k7AiFEKLuKciD8zvVlp7oNZBx4cY+rak6z2PAQHWS8HqwvnVtIomkqLPMTLTMGdWaez/bzvbTV1i8O5bxXZoaO6zycQtUl1eM+BH+egOSj8N3/aDNg9D7bbBxMXaEQghRu2WnwplNavJ4ZhNcz7ixz8wa/HuryWPzvmDlZLw46zlJJEWd5udqy2v3BPLG6ijeXRdNeLMG+LvZGTus8tFq1cSxxT2w6U04tFhdszt6LfR5G1qPVY8RQgihSolRE8dT6+H8ruKDZWxc1dXEWtwLfj3BzMp4cd5BJJEUdd6DnZqw8UQy205d5tmfj7Dy8S6Ym9ahBMzaGQZ/riaOfz4PyVHw+1NqUtn/XWjU1tgRCiGEcRTkQdwudeq0Uxsg5XTx/W4tocUAdWaMRmHyn28jkERS1HkajYYPR4TS75NtHEvI4PO/T/NC3xbGDqviGneCx7bC3nmw5V2I3wMLeqrzmPV6Q1ZREELcGTIvqYnj6Q0Q8w/kZd7YpzWFJl3UlpwW/cHJx1hRin9JIinqhYb2lsweFsITSw8xd8sZOvu6cFdtXPXmdkzM4K6pavL49zsQsUydzPzEHxD2CHR/CWzdjB2lEEIYTmEBJBxQV5Q5vQESI4rvt3GDZn3UQYp+PcHSwThxilJJIinqjXtCPBgZ5sXygxd44sdDrH6yC01cbIwdVuU4eMGwedD5Kdj0FpzZCPsXqKO775oKnZ8EizrSF1QIIf4rPUFdx/rMJrXW8Xr6TTs1apeeZn3Vh0drabKuxSSRFPXKzKHBnEq+RkT8VSYuOsDKJ+7CzrIOz8/oHgwPrlDnm9z4Jlw8BP+8C/u/UdfubjsOTM2NHaUQQtxafq463VnMZrXmMfl48f1WTuqysv69wb8P2LoaJ05RYZJIinrF0syErx8KY/AXOzidfI1nlx3h64fbYVLb55e8nabdYNLfcPw32Pw2pJ5Vl1zc+ak6L2WbB2WEohCi9tDp1IGDMVvg7BZ1hHVB7o39Gq06OMa/t/rwbKPOsyvqHEkkRb3T0N6Srx9qx/3zd7M5OpmP/jrJS/0DjB1W1Wk0at/JgIFwcCFs/QDS49WEcuv70OkJaD9B+g8JIYwj4+KNxPHsP5B1ufh+W/d/E8e7wbeHOmOFqPMkkRT1UitvRz4YEcozy47w5T8xtHC3Y0jrerKagYkZdJik1kIe/gF2fgbpcbB5Buz4RN3X6XGwqYODjYQQdUd2KsRuV7venNsGV04V329mAz5dwLenOkjGNUD9D7GoVySRFPXWkNaNiL6UyVf/xPDSikh8XGxo5e1o7LAMx8xKTRrDxsPRFbBjjvqHfPv/YPdcdftdT6kDd4QQoqpyM9R+jue2wbmtcOlo8f0ardpEXZQ4enWQPtx3AEkkRb32f31bcOpSJpujk5m85AB/PBWOm72lscMyLBMzaP0AhI6Ck2tg2/8g8Qjs/Qr2fQ2BA6HDZHXuNakNEEKU1/UMzOO2oomMUtexvni4+EoyAK6Bah/upt3U2kdZivCOI4mkqNdMtBo+Gd2a4V/u4nTyNSYvOciyyZ2wNKuHnbq1WggcpPahPLsFts9Rm52Or1YfroFqDWboKLCwNXa0QojaJucqxO2B8zsgdgeaxAicFV3xY5ya3kgcm3aTeW2FJJKi/rOzNOObce0Y/MVOjsRfZdrKo3x0fys09bV2TqNRp9Hw6wVJUbBvAUT+DJdPwJrn1XkpWz2gJpUNmhk7WiGEsWReUhPHuN3qqOpLRwFFv1sDFNh7Y+LbDY1POPiEg2Njo4UraidJJGvYY489xp9//snFixdRFOX2JwiDaOJiw5dj2/Lwd/tYeTiBpg1smHr3HZBENQyCQZ9A77fUycz3fwMpZ2DffPXh2wPaPAQB98r0QULUZ4qi/u7H7Ybzu9XntHMlj3P2UxNGn3B0jTtzJdcMNzc3NDIhuCiDJJI1bOzYsbz99tu4u7sbO5Q7Thf/Brw5qCXTV0fx0cZT2FiY8mh4U2OHVTOsHNWR3B0eg3P/qLWUp9arU3Sc/Qcs7CFoqFpT2biz9KUUoq7Lz1H7NMbvhfj96nP2lf8cpIGGwdCkM3h3VPtR23vc2K3TQW5yjYYt6p5am0guWrSITz75hBMnTmBra0v79u1ZuXIlVlaGrTU5c+YM//vf/9izZw/Hjh0jICCAY8eOlXpsdHQ0U6dOZdeuXdjZ2fHwww/zzjvvYG5e/lFp3bp1M1ToohIe7uxDalYen2w6zdt/HsfK3IQHOtxBTTVa7Y1m77Tz6vRBEcvU6YMOLVYfjk3UhLLVKHD2NXbEQojbURRIv6Amixf+TRovHQVdQfHjTCzAqx007gSN7wLv9jLvrKiyWplIzpo1i/fff59p06bRuXNnrly5wubNmyksLLz9yRUUFRXFmjVr6NixIzqdDp1OV+pxaWlp9OrVi2bNmrFy5UoSEhJ4/vnnyc7O5osvvjB4XKL6PHN3M3LyCpm/7SzTVh3F0kzLsDZ34BQ5Tk2g12vQ41WI26U2fUethqvnYet76sO7E4SMUAfx2EktuhC1Qm6GWtuYcPDGIzOx5HG27mqy6N1RnYrHszWYWtR4uKJ+0yi1rKPeyZMnCQ4O5vfff2fAgAHlOicqKgpLS0v8/PxK7Nu6dSutWrXC0dGx1HN1Oh3af/t+jB8/ngMHDpRaI/nuu+8ya9Ys4uLicHZWZ+P/+uuveeKJJ4iLi8PT05O2bdsSFxdX4tx27dqxfv36Yts0Gk25+0hmZGTg4OBAeno69vb2+riTk5Nxc3PTxy/KT1EU3vw9isW7z6PVwNwxbRkQ4nH7E2+jzt+XvGyIXgMRP6pN3voRmxr1H6OWg9VR4U5NjBllpdT5e1OPyb25hYI8dV3qhAOQcEhNGi+f5OZBMQBoTMAjVE0Yvf99OHhXqZuK3JfaqybuTWm5R2lqXY3k999/T9OmTcudRALMnDmTPXv2sH37dry9vfXbt27dyoABA5g9ezbPPvtsqeeW9wasW7eO3r1765NIgPvvv58pU6bw119/MX78eA4dOlTumIVxaTQa3hoURG5+Ib8cuMDTyw4z30xLr4CGxg7NuMytIXSk+si4qE50fny1+o9Y/B71sWEaeLRWk8rAwTLyWwhDKcxXk8aLR9Qax8Qj6swLhXklj3VsrK5V3SgMGrUDj1bq768QNazWJZJ79uwhJCSEd955h88++4yrV6/Svn175syZQ8eOHUs9Z8GCBfTq1YvevXuzfft23Nzc2LdvH4MGDWL06NE888wzVY4rOjqaRx99tNg2R0dHPDw8iI6OrvL1SzN37lzmzp1bLU36ArRaDe8ODyU3X8fvEReZ8sMhvh/fni7+srQgAPae0OVp9ZGeANF/wvHf1WbwxCPqY/Pb0KAFNOujrqHb5C5pOhOiPPJz1aTx0lH1d+nikX+Txuslj7V0hEZt1YSxUZj6WuZvvOOlZOVTG74FtS6RvHTpEgcPHuTo0aN8+eWXWFtbM3v2bPr27cvp06dxcyv5sdnZ2bF+/Xq6d+9O3759+eyzzxg2bBj9+vVjwYIFBpkvMC0trdTmcScnJ1JTU8t9nfHjx7Np0yYAvLy86NmzJ0uWLCn12CeffJInn3xSX70sDM9Eq+Gj+1uRm1/IX8eTmLjoAIsndKC9j/PtT76TODSCjo+pj2uX1RV0jv+uLpN25aT62P0FmFmrkxT791YfznfIqHghbiU7VU0YL0X++3xUbZ7+7yoxABYOal9Gz9bqcoMercHJR2ZSEABcLyjkr6gklu2PY3dMCn+/4IRPA+MuMFHrEkmdTse1a9dYsWIFoaGhAHTq1AkfHx+++OIL3n777VLPc3FxYePGjXTt2pXu3bvTv39/fvzxR0xMatcKJgsXLjR2COI/zEy0fD6mDZMXH2Trqcs88v1+lk7sWL/W5TYkW1d1He+w8ZCTBjF/w5nNcGYTXEtSpxU69W+fYGc/NaFs2k2trbSWBF3UYwV5kHIako5DcpT6nBQFGRdKP97KWe3X6B6iJo2ebdSVYyRpFP8RfSmDn/fHs+pwAlez8/Xbd59NkUTyv5ycnHBxcdEnkQDOzs60adOGqKioW557/fp1cnNz0Wq1ZGdnU1BQgJmZmcHiSk9PL7E9LS2tWL9JUTdZmJow78EwHlm4jz1nU3nw271883A7Ovq6GDu02s3KCYLvUx+Kota0nNmkJpbxeyA1BvbFqJOfA7i1VOeq8+miPkvznKiLdDp1doPLJ9UVo5L+TRqvnAJdfunnOPmAe+i/jxD1Ye8pSaMo07XrBfwRcZFl++OJiL+q3+5ub8nIsEb09LGidTPvsi9QQ2pdIhkUFERMTEyp+3Jzc8s8LzExkd69e9O4cWP++OMP7rnnHoYPH87q1asrNM9jWQICAkr0hUxPTycxMZGAgIAqX18Yn5W5Cd+Oa88j3+9nX2wqD323j89Gt6Z/cNVHc98RNBq1dsUjFLo+D7npcG6bWmMZu1Nt/k4+rj72L1DPadBcrals3Fnt++Xsp851KURtUFgAabFwOfrfx0n1+cppKMgp/RwLe/U/TA1bqitLuQWpr2W+RlEOiqKwPzaN5QfiWXM0kew8tfuDqVZD78CGjOrgTbdmrmhQSE6uHZPF17pEcuDAgXz//fccOXKE1q1bA5CSksKhQ4d47rnnSj0nJSWFPn36YG9vz9q1a3F0dGTTpk10796dsWPHsmzZsio3cReN/r569aq+r+Ty5cvRarX07du3StcWtYeNhSmLJ3Tg6Z8O89fxJB5feoi3hwTzUKe6N92N0Vk6qPNPBg5Sf752Gc7vVNf0Pb8Tko6pNThXTsHBheoxFg7QqM2NkaiN2sr8laL6ZaWoTdJXTqvPKTHq69SzZdcwmlio/xFybaEmim5BauLo4CW1jKLCEq7msPLgBVYcusD5lGz9dl9XG0a392ZYGy9c7W4MZNTpas/MjbVuHkmdTkenTp1ITU1l1qxZWFlZ8e6773L69GmOHTtW6tKCI0eOJCoqim3bttGgwY0RtwcPHuTuu+9m+vTpPP/886WWl52dzdq1awF1lHRMTAxz5swBoHv37ri6ugJqE3ZQUBDNmzdn2rRp+gnJx44dW+0Tkss8kjWvUKfwxupj/LhXnRf06V7+PNen+W0Hbsl9qYDs1H/X/d2lrsaRGAEFpbQ62HupAw/cQ9R/qBsGgaNPhWsu5d7UXtV+bxRF/b6lnVOTw9SzkPrv65TTal/fsphagWtzcA1Qk0bXQPXZyQe0tasPvqHJ70z1ys0vZEPUJZYfuMDOmCsUZWM25ibcG+rByHbetGviVOq/O7VpHslal0gCXLlyheeee44//viDvLw8unbtyscff0zLli1LPf7cuXNYWFjg6elZYt/hw4dp0aIF1talz68VGxtL06aljyzdsmULPXr00P984sSJEkskzpo1yyBN57ciiaRxKIrCp5tP88mm0wCMbu/NO0ODMTUp+/OW+1IFRXPo6VfrOATJJygx8TKAue2/zYdBNx4NWoBN2X1a5d7UXga5N/m5kB6v9l28GqcuAXr1/L9JYyxcL9nHvRh7L2jgDy7N1LlRXfzVZ3uvO7a7hfzOGJ6iKByKu8qvhy7wR8RFMnNvLGPZydeZkWHeDAhxx9r81g3GkkiKCpFE0riW7j3PG78dQ6dA78CGfP5AG6zMS6+JkPtiYNcz1ZrKojn2ko6pfdRKm6AZ1ME/+kTA78ZrZ190WjO5N7XUbX9vFEWtNUy/ABkJ/z5fVBPHtH8Tx2uXbl+Qnae6fryzj/rs1FRNGF38wNzG4O+rrpO/Z4YTl5LNqsMJrDp8gdibmq4bOVoxIsyL+9p60dil/BPK16ZEstb1kRSithnbsQkNbC2Y+tNhNp1I4sFv9/LtuHY4WldvTbQALOzAJ1x9FCnMV/uwJR27kVwmHVenWMlJgwv71MfNNFo09o1wtvZA4+YHjk3UlUGKHvaNwET+HBpFfg5kJGKWeAKuXIdryWpSmJmk3tP0BDVpLGtwy83MbNTlOx0b37jHzr7qfKZOPmBmVe1vR4gi6Tn5rD2ayKpDCeyLvTHftLW5Cf2D3BkR5kUnXxe02rrdp1ZqJOsAqZGsHfbHpjJh4X4ycgvwd7Pl23HtaOJSvBZD7osR5WWpCWbKabhyBlLO3Hidl3nrczUmYOehDuyxc//3dUP12db9xnYr5zu2mbPcCgvUEfvZKZB1GbKvqM9Z//6cdVndV5Qw5t6myflmNq5q0u/gpU6d4+B1I2F08lFrpGWgi8HI37OKyyvQsf30ZVYeTuD/27vz8Kbq/F/g75M0SZs0W5um+wKl0EJpkR1kkUVEEHHEi8t1dB6VmZ/P+HOuy3if0YsLzijz+zlzmXHkunsvj4pOR3F+gCiKyCYidIACpYWWbrSlS5KmS5qmSc79IyU0lDVN2rR5v57nPCc5ySnfw6dp3/2e7znfb4ob4HC6AXi+LWeNMuDOicm4ZdzVT11fDXskiYagKRkxKPi3mXjw/Z9Q1tiOZa/vxbp7JnB+7lAhV124/VBvogi0N8BtrkBr9XFo3C2QWGs8p0PPr10OT+/X5W4cfZ4g8UxXp4ztWWJ6llhPyIzSe3pRFZqe9UVLqF+c4XZ7ev4cHZ5hBX2W1gvrzhbA3uLpBfYu1quPRbwEMSISrigDpLpkCOqEnvAe7wmNmmTPzErqJEAWGfBDJuovt1tEYbUFXxyuxZfH6mHpdcPw0fHRWDExBcsnJCNBOzy/fxkkia7DmAQ1vvj1jXj0o0Icrm7BQ//3EH6zIAu/WZA15E9PDFuC4OlNVBlhV4yAxmj07VV0u4GORqClpueUau+l3jNbT1u9pxdNdAOdZs9iOn39bZEpgYhIzylW71rhuTJYFunZJpUBkoieRepZC9IL2873uIkiAPHSa3e3ZwiAq9sTkt1O38dOu+eUcretZ92zXGqeZ38ptIDK4OlFVBk8i7L38zhPXaLjIcrVaG5qgtFohMCeLxoiSs+14YsjtfivI3Wobbkw9CJOrcCyvCTcOTEZ45I0AZmmOZQxSBJdpwRtJD795Qz8fmsxNuyvwl92nMbRsy1Yd/cEaCL5kRpyJJILp66vxOnwBEib2RMqO3vWtl7b7NaLeu56lvMBrdvmWa5huN+gk/fuTY3u9VjjuWo+Sn/RorvwOFLrCcTXyu0O2mEQBVKN2YYtRfX455FalJy7MGQmWhGBxbkJuGNCMmZkxkIaRh0L/K1H5Ad5hARrluciP0WHZzcdw/elTVj2t734P/dNhIGfquEpQn5tgfNSnF0XQuX53kBnl+c0crfds+38drcTcLt61r0ei64LzwUBgHD5tVTuuXhIIrv04/O9oTJlT69oVK/nkZ7n7BkkAgA0tNqxtagem4vqcLi6xbtdJhUwb4wRyyckY0GOEZGyEB+6EiT8lUfUDysmpSA7UY1HP/wXqs02rHhzP/7n/DT8wsg5pKmXCIVnURmu/l4iGnSm9i5sO34Om4/W4adKs/dm4YIATB8Ri9snJGFJbiK0yuvoeR+mGCSJ+mlckhabH5uF//HpYewsbcKa7ZU4Y3Xj+WXjII9grw4R0VBg6XBge/E5bD12DvvKmuHqNQ3hpHQ9luUlYsn4RBg1w/OiGX8xSBIFgFYpw3sPTsFfdpzCX3eU4cMD1Thc04I/r5yAMQnqwW4eERFdgrnDge0nzmHrsXrsLzfB2Ss8jk/WYll+IpbmJSFZx3uQXg6DJFGASCQCfrMgC+nRwMvfVOFEXSuWvb4XTy0ajUdmjwyrwddERKHK1N6Fr0804Mtj9dh/xuTT85iTqMHS8Qm4LS8JGQbOdnQtGCSJAmzmCC2++s1sPLvpOHaUNOLVbSX49mQD/vTfJlzXFFhERBQYDa12bD9xDtuOn8OBCrNPeBybqMHSntPWIxgerxuDJFEQxKkVePfBySg4dBYvbT6Bg5UWLP7Lbjy3NAf3TU0b9vcVIyIabFWmDnzdEx57X20NAOOSNFgyPhFLxyey57GfGCSJgkQQBKyckooZmbF4uuAoDlSY8dym49h+ogF/XJE3bGc5ICIaDKIoorShDV8fb8BXJ87hZH2rz+sT03RYnJuAW8Yl9JnelvzHIEkUZKkxSmxcNR0f/FCJ//iqBLtONeGWdbvx4u1jcceEZPZOEhH5yely41CVBd8UN+Cb4gZUm23e16QSAdNHxmDxuATcPDaBf7wHCYMk0QCQSAQ8PGsE5o424Mm/H0XRWSue+PQo/n7wLNYsH4eseF7ZTUR0LTq6nNhzugnbixvwXUkjWnrNbS2PkGD2KAMW5yZgYU489Cr5ILY0PDBIEg2gUUY1Pnt0Jt7aVY7XvyvD/jMm3PqXPXho1gg8viAL0Qp+JImILnbOasd3JY349mQD9pY1w+G8MK2mTinD/GwjFo2Nx+ysOKj4c3RA8X+baIDJpBI8Nj8LyyckY82WYnxT3IC3d5/BP4/U4rmlY7EsL5Gnu4korLndIo7VWrGjpBE7TjbgRJ3veMe0GCVuHhuPm8fGY3K6HhFSTv4wWBgkiQZJaowS7zwwGTtLGvHi5hOoMtnw+MbD2HigGi8tH4fRPN1NRGGko8uJvWXN+O5kI74rbURTW5f3NUEAJqTqMH+MEYvGJWB0fDT/4A4RDJJEg2xethEzMmPxzu4z+NtOz+nuJX/Zg1/MzMC/L8iCNopzuRLR8COKIsqbOvB9aSO+L23CTxVmOFwXTlmr5FLMGR2HBTnxuGlMHAzRikFsLV0OgyRRCIiUSfHvC7Jwxw3JeHlLMbYXN+DdvRUoKDyLf5ubiV/MzECUXDrYzSQi6hebw4n95Sbs7AmPZy2dPq+nxSixIMeIBdnxmDoiBvIInrIOdQySRCEkNUaJtx+YjJ2ljXj1y5M41dCOP35Vgvf3VeDx+aNw95Q0/mAloiFDFEWcamjHntNN2HWqCQcqzD4XysilEkwbGYObxhhx05g4jDSoeMp6iGGQJApB88YYMScrDv88Uos/f3MKZy2dWP3PE3hnTwWeuDkLt+cnc+5uIgpJ5g4H9pY1Y/epJuw53YSG1i6f11P0UbhpTBzmjfEM61HKGUWGMlaPKERJJQLunJiC2/KS8MnBavx1RxmqzTY88elRvPn9GTx9yxgszDHyr3ciGlRdThcOV7dg7+lm7D7dhGO1VogXprJGpEyCaSNiMTvLgJvGxCEzjhfKDCcMkkQhTh4hwQMzMnDXpBR8sK8Sb+0qR2lDG1ZtOITxyVr8au5I3JqbyB5KIhoQbreI4vpW7Ctrxr5yE36qMMHe7fZ5T3aCGnNHx2F2VhwmZ+gRKeMY7+GKQZJoiFDKI/DreaNw/7R0vLW7HB/sq8SxWise+/gw0mNLsWr2SNw1KYU/sIkooERRRGVzB34oN2FfWTN+KG+GpddsMgBgiFbgxlGxmJMVh9lZBhg1nI4wXDBIhrA33ngDb7zxBlwu12A3hUKIVinDM4uz8cjskfh/P1Riw/5KVJls+F9fHMe6b0/hFzMzcP/0dOiUnBqMiPxTY7bhh/JmfF9ciyN1J1Bvtfu8rpJLMX1kLG4cZcCNowy8r2MYE0Sx90gGCkWtra3QarWwWq3QaDQAALfbjcbGRhiNRkgkvIo3VAxGXWwOJ/5+sAbv7KlAbYvnVhpKuRT3Tk3DQ7NGIFkXNSDtCHX8zIQu1mbw1bV0Yn+5CfvPmPDjGVOf2/LIpAImpOowa1QcbhwVi/xUHWScTWbQDMRn5lLZ41LYI0k0xCnlEfjFjSNw//R0bD1Wjzd3ncHJ+la8t7cCH+yrwIKcePz3aWmYkxUHCcdREoU9URRRabLhpwoTfqqw4KdKE2rMvsExQiIgL0WL8fGRmJ+biikjYnh1NV0SvyuIhokIqQTLJyTj9vwk7DndjLd2l2NfmQnfFDfgm+IGpMZE4d6paVg5OZUzRBCFEbdbxKnGNvxUYcaBCjN+qjD7TD8IABIBGJ+iw/SRMZgxMhZTMmIQJZP09HoZ2FNMl8UgSTTMCIKAOaPjMGd0HMoa2/DxgRr8o7AGNeZO/MdXpfjf35zCLeMScP/0dEwbEcNxTUTDTKfDhSM1LSisMuNQlQX/qrKg1e70eY9cKsGEVB2mjNBj6ohYTErXI1rhGwncbt8rsYkuhUGSaBgbZVTj+WVj8dtbxmDrsXp8dKAKh6tbsKWoHluK6pEZp8KdE1OwfEISUvTKwW4uEfmhsdWOQ1UWHKq0oLDKjBN1rXC6fS9/UMqlmJSux9SMGEwdEYP8VB3v8EABwSBJFAai5FLcNSkFd01KwYk6Kz4+UI0vDteivKkD//l1Kf7z61JMzYjB8huSsHR8Iq/4JgpR9m4XTtS14nC1BYdrWnCkusV7kV1vCZpITMrQY3K6HpPTY5CTqEYEL46hIGCQJAoz45K0+MPPxuN3S3KwtagOXxyuw48VJvxUacZPlWa8+F8ncNMYI+6YkIwFOUb2WhANElEUUW224UhNCw5Xt+BwTQuK66zodvn2NkoEYHS8GlMyYjA5Q49J6Xok66I4bIUGBIMkUZiKVkTg7ilpuHtKGuqtndh8tA6bDtfhZH2r9wIdtSICC8fGY9HYeMwZHQeVgj8yiIKlodWOozUtKDprxdGzLThWa0XLRTf+BoBYlRw3pOlxQ5oON6TpkJei6zO+kWig8DuPiJCojcIv52Til3MycaqhDV8crsU/j9ShtqUTmw7XYtPhWsgjJJg1yoBFY+OxICcecWpe+U3kr8Y2O07UtuJ4rRVFtVYUnW1BQ2tXn/fJpRLkJKovBMdUPVJj2NtIoYNBkoh8jI5X45nF2Xh60RgUVluw/cQ5bC9uQJXJhu9KGvFdSSME4RgmpumxaGw8Fo6Nx0iDir/YiC5BFEXUW+04XmvF8bpWnKi14litFY1tfUOjRACyjGrkpWiRl6pDfooW2QkayCM4tpFCF4MkEV2SRCJgSkYMpmTE4NklOTjV0I5vij2hsuisFYVVFhRWWfDqthIk66IwO8uA2VmeWS94sQ6FI4fTjdONbThZ34aT9a3e5eJ5qQFAEIDMuGjkJmmQm6xFXooOucka3vSbhhx+xxLRVQmCgDEJaoxJUOOx+Vmot3bi2+IGbC9uwIEzZtS2dOKTgzX45GANBAEYn6zF7CwDZo2Kw6R0PXtUaFgRRRENrV0obWhD6blWb3Asa2zvc9sdwDNLTFa82hsac5M1yE7QcMwxDQv8Liai65aojcLPZ2Tg5zMyYHM4caDCjL2nm7HndBNONbSj6KwVRWeteGNnOaJknvvXTc7w3IbkhjQdf4HSkGHucKD0XBtONbShtKENp3oeX3yD7/M0kRHISdQgJ1GDsT3rrPho3v2Ahi3+NCeiflHKIzBvjBHzxhgBeK48PR8q95Y1o7ndgb1lzdhb1gwAkEoEjE3UYHKG3nu7EqM6cjAPgcKc2y2ivtWOssZ2lDW2o7ypZ93YDlOH45L7SCUCRhhUGB0fjZwET2DMSdIgSRvJ8cIUVhgkiSig4jWRWDEpBSsmpXjn+D1UacGhSjMOVlpQ29KJYz0XHHywrxIAkKyLQl6KtmesmBbjk7UcZ0kB12rvRmVzByp6lsrmDpQ1teNMUwdsDtdl90uLUWJ0vBpjEqIxOl6N0fFqjIxTQRHBXkYiBkkiChqJREB2gmc82P3T0wEAdS2dPdO5eYJlyblW1LZ0oralE9uOn/Pum6K/EC5zk7TITlAjTq1gbw9dkdXWjWqzDVXmDlSZbN7gWGnqQHP7pXsXAc84xgyDCqPiojHKGI1Mowqj4tTINKp4AQzRFfDTQUQDKkkXhdt1Ubg9PwmAp5foeK3Vcz+9s551pcmGs5ZOnLV04stjF8KlNkqGMfFqZMVHY0yCGllGNUbHRyM2mve0DBedDhfqrJ2otXSixmJDtdmGGrNnXW2yXXbs4nmGaAVGGlTIMCiRYVAhsyc4psUoIeMUgkTXjUGSiAaVJlKGmZkGzMw0eLdZO7u999s7VmtFcV0rKk0dsHZ2e6dy7M0QLccIgwrpsSpkxCqRHqvCCIMKabFKaCJlA31I5CeXW0RTux3nrHbUW+2o6+mprrV0esPj5cYs9hanViAtRom0GCUyYlUYEafCiFhPeFTz+4EooBgkiSjkaKNkmDnKgJmjLoRLe7cLZ5o6cKqhrdfSjmqzDc3tDjS3O3Cw0tLna8Wq5EiPVSJFHwWdTERmUieSdUok6aKQpIuENkrG0+VB5nKLMHV0obnNgab2LjS3daGxrQsNredDYyfqWmww25xwXeL2ORdTyaVI1kchRa/0Bsa0GCXSeurMU9FEA4efNiIaEiJlUoxN0mBsksZnu83hRFljOypNNlQ1d3jWJs+6ub0Lpg4HTB0O/Ku6pWePcz77K+VSJGojkaiNQpxaAUO0HIZoBQzRip7nChjUcsSqFJBKGDgBz423W2wOmG0OWDq6YbE5YO5wwNLhgMXmed7c3oWmti40t3fB3OHANeRDAJ6roeOiFYjXRiJZF4lkXRSSdVFI0kV5wqNOCU1UBMM/UYhgkCSiIU0pj0Beig55Kbo+r7XZuz0XXJg6cNZsQ/k5M6wOCeqsnahvscPU4YDN4UJ5UwfKmzqu+O8Iguc0vDbKs+iUMmjOP+5ZqyNlUCmkUMojoJRLoZRLoVKcf+xZy6USSAYwkIqiiG6XCIfLja5uF7qcbnR2u2DrcsHmcMLmcKHD4fQ+73C40NHlRKu9G62d59fdaLNf2NbZffkrnC9HEIBYlSeox6k9IT1BE4kEbSSMagXkThtyMhJh1EQxsBMNIQySRDRsqSNlPTOJaOF2u9HYGA2j0QiJxHNRhb3b5R2LV2+1o7nntGtze1fP6fIub6+mKHrGblo7+053d70iJAJkUgnkERLIpBIoIiSQST3bpBIBgiBAInjCl0QQIMAzu9D5Tji3W4RLFOFyAy63Gy63CLfoOYXscovocrrhcHpCo8PlhniNvYHXQyIAeqUcOqUMMSo59Eq5Z62SQ6+UIVZ1oUc3Tq1AjEp+2YDoqU0jjJrIAQ3ZRNR/DJJEFLYiZVKMMHguzLkSp8sNs82B1s5utNi6vYHSZ7F1o63L6e3ls3X19PT19PB1Od0Xvp5bhNPt8qtnr79kUgFRsp4eUoUUKnkEouRSqORSKBURnrU8ApooGTSR59cyaKIivD2y6kjPY4Y+ImKQJCK6igipBEZ1ZL9m4HG5RdgcTs9pZqcb3S5Pb6H3sdOzuEVAhKeH0S2KQM9aPP8cnnGEEokAqSB4HvespRJPD6YiQgqFTAK5VAKFTOJ5HiEZ8NPqRDT8MUgSEQ0AqUTgrWeIaNjh3VeJiIiIyC8MkkRERETkFwZJIiIiIvILgyQRERER+YVBkoiIiIj8wiBJRERERH5hkCQiIiIivzBIEhEREZFfGCSJiIiIyC8MkkRERETkFwZJIiIiIvILgyQRERER+SVisBtAVyeKIgCgtbXVu83tdqOtrQ2RkZGQSPj3QKhgXUIXaxO6WJvQxLqEroGozfnMcT6DXA6D5BDQ1tYGAEhNTR3klhAREVE4aWtrg1arvezrgni1qEmDzu12o66uDmq1GoIgAPD8pZCamoqamhpoNJpBbiGdx7qELtYmdLE2oYl1CV0DURtRFNHW1oakpKQr9nqyR3IIkEgkSElJueRrGo2GH/AQxLqELtYmdLE2oYl1CV3Brs2VeiLP46AHIiIiIvILgyQRERER+YVBcohSKBR44YUXoFAoBrsp1AvrErpYm9DF2oQm1iV0hVJteLENEREREfmFPZJERERE5BcGSSIiIiLyC4MkEREREfmFQZKIiIiI/MIgGWJKSkpw8803Q6VSISEhAc888wwcDsdV9xNFEWvXrkVaWhqioqIwY8YM/PjjjwPQ4vDhb23Wr1+P2267DXFxcRAEAf/4xz8GoLXhxZ/a1NfX45lnnsGECROgVquRkpKC++67D1VVVQPU6vDg7+fm/vvvR1ZWFlQqFfR6PebMmYPt27cPQIvDg7916W3dunUQBAG33XZbkFoZnvytTUZGBgRB6LPY7fagtpcz24QQi8WC+fPnIysrC59//jlqa2vx5JNPwmaz4W9/+9sV9/3jH/+IF154AWvXrkVeXh7eeOMNLFq0CEeOHMHIkSMH6AiGr/7UZsOGDQCAJUuWeB9T4Phbm8LCQnz++ed46KGHMH36dDQ3N+Pll1/G1KlTcfz4ccTFxQ3gUQxP/fncOBwOPPnkk8jKyoLdbsd7772HJUuWYOfOnZg9e/YAHcHw1J+6nHfu3Dm89NJLMBqNQW5teOlvbe666y489dRTPtuCfosgkULGK6+8IqpUKtFkMnm3vfXWW6JUKhVra2svu19nZ6eo0WjE3/3ud95tXV1dYnp6uvjoo48Gtc3hwt/aiKIoulwuURRFsaKiQgQgFhQUBLWt4cbf2lgsFrG7u9tnW01NjSgIgvjaa68Frb3hpD+fm4s5nU4xNTVVXLVqVaCbGXYCUZef//zn4gMPPCDOnTtXXLp0abCaGnb6U5v09HTx17/+dbCb2AdPbYeQbdu2YeHChYiJifFuW7lyJdxu9xVP6fzwww9obW3FypUrvdvkcjnuvPNOfPnll0Ftc7jwtzYArjjZPfWfv7XR6XSIiPA9KZOSkoK4uDjU1dUFrb3hpD+fm4tJpVLodLrrPv1KffW3Lnv37sUXX3yBtWvXBrOZYSmQn5mBwt9wIaSkpATZ2dk+23Q6HRITE1FSUnLF/QD02TcnJwfV1dXo7OwMfGPDjL+1oeALZG1OnTqFxsZG5OTkBLKJYau/tRFFEU6nEyaTCa+99hpOnz6NX/3qV8FqbtjoT11cLhcee+wxPPfcc0hMTAxmM8NSfz8zH330ERQKBaKjo7FkyRIcO3YsWE314hjJEGKxWKDT6fps1+v1MJvNV9xPoVAgMjKyz36iKMJisSAqKirQzQ0r/taGgi9QtRFFEY8//jiSkpJw7733BrCF4au/tXnvvfewatUqAEB0dDQ+/fRTzJgxI9DNDDv9qcv69evR0dGBJ554IkitC2/9qc3tt9+OadOmIS0tDWfOnMEf/vAHzJo1C4cPHw7qtRIMkkREAF588UXs2LEDX331FVQq1WA3hwDccccdmDBhApqbm1FQUICVK1di06ZNuPXWWwe7aWGpsbERzz//PDZs2AC5XD7YzaGL/PWvf/U+nj17NhYtWoTs7Gy89tprWL9+fdD+XQbJEKLX62G1Wvtst1gsPuMlLrVfV1cX7Ha7T6+kxWKBIAjQ6/VBaW848bc2FHyBqM0777yDNWvW4L333sOCBQsC3cSw1d/aGAwGGAwGAMDixYthNpvx29/+lkGyn/yty/PPP4+8vDzMnj0bLS0tAACn0wmn04mWlhZER0f3GXdM1yeQv2sSExMxa9YsFBYWBqp5l8SKh5Ds7Ow+YyCsVivq6+v7jJm4eD8AKC0tRX5+vnd7SUmJ976S1D/+1oaCr7+12bRpEx599FGsWbMGDz30ULCaGZYC/bmZNGkStm3bFqjmhS1/61JSUoLdu3dfsnNCr9dj27ZtWLx4ccDbG06G4u8aXmwTQm699VZ8++233r/0AKCgoAASiQSLFi267H4zZ86ERqNBQUGBd1t3dzc+//xzLFmyJJhNDhv+1oaCrz+1+f7773Hvvfdi1apVWL16dZBbGn4C/bnZu3cv74sbAP7WZd26ddi5c6fPkp+fj+nTp2Pnzp2YOnXqALR+eAvkZ6aurg579+7FlClTAtzKiwz4DYfossxms5iYmCjOnTtX/Prrr8X3339f1Ol0fe4LNX/+fDEzM9Nn26uvvioqFApx3bp14o4dO8QVK1aIarVaLC8vH8hDGLb6U5uDBw+KBQUF4vr160UA4lNPPSUWFBSI33///UAewrDlb22Ki4tFrVYr5ubmivv27RP379/vXcrKygb6MIYlf2uzZcsWceXKleKGDRvEnTt3ip999pm4YsUKEYC4cePGgT6MYac/P88uxvtIBpa/tfn444/F++67T/zwww/F7777Tnz33XfFzMxMUa/Xi2fOnAlqmxkkQ0xxcbG4YMECMSoqSjQajeLTTz8tdnV1+bxn7ty5Ynp6us82t9stvvLKK2JKSoqoUCjEadOmiT/88MMAtnz487c2Dz74oAigzzJ37tyBa/ww509tPvjgg0vWBYD44IMPDuwBDGP+1ObkyZPi8uXLxaSkJFEul4tJSUni4sWL+cdXAPn78+xiDJKB509t9u/fL950002iwWAQIyIiRIPBIK5cuVIsKSkJensFURTF4PZ5EhEREdFwxDGSREREROQXBkkiIiIi8guDJBERERH5hUGSiIiIiPzCIElEREREfmGQJCIiIiK/MEgSERERkV8YJImIiIjILwySREREROQXBkkioiBYvXo1BEFAQkJCn9fcbjfy8vIgCALuueeeQWid/7Zv3w6VSgW73e6zfbgeLxFdGYMkEVEQHD16FGq1Gg0NDbBYLD6vffTRRzhz5gwAIC8vbzCa57fNmzdj4cKFiIyM9Nk+XI+XiK6MQZKIKAiKiopwxx13AABOnjzp3e5wOPD88897XxtqwWrr1q247bbb+mwfrsdLRFfGIElEFGBWqxVVVVWYNWsWUlNTfYLVm2++ia6uLsybNw8AkJ+fP1jNvG4nTpxAZWVlnyA5XI+XiK6OQZKIKMCKiooAeHrfcnNzvcGqra0Nv//977F69WqUlZVBr9cjNTV1MJt6XTZv3oyJEyciMTHRZ/twPV4iujoGSSKiACsqKoIgCBg/frxPsPrTn/4EjUaDRx55BEVFRRg/fvwgt/T6bNmy5bKntYfj8RLR1TFIEhEFWFFREUaOHAmVSoXx48fj5MmTaGpqwp///Ge8/PLLkMlkKCoq8jnNKwjCoLT1Wv9dk8mEH3/8EcuWLevzmj/HS0TDA4MkEVGAHT161HtRSW5uLqqqqvDss88iMzMT99xzDywWC86ePXvdF544nc5gNPeafPnll4iPj8fEiRP7vBas4yWi0McgSUQUQKIo4vjx497QlJOTA0EQ8O677+KVV16BIAg+Ywp7e+mll7zjDHfv3g3A02O4Zs0aTJo0CW+//TYA4O6778bkyZMxduxYPP744979BUHA2rVrMWnSJGRnZ+PAgQPe13bt2oVp06YhPz8fEydOxOnTp72vXW6f3rZs2YIlS5b06cHsz/ES0dAXMdgNICIaTsrLy9HR0eENTZGRkXj44Ychl8tx6623AvCcCpZIJMjNzfXZV61Wo6ioCAcPHsSdd96JsrIyAIDBYEBhYaH3fevXr0dsbCzcbjd+9rOfYevWrVi6dCkAIDExEYWFhdi4cSNWr16N7du3w2Qy4d5778VXX32FvLw82O12uFwu79e71D69dXd34+uvv8aGDRsCerxENPSxR5KIKICOHj0KwLf37a233sLrr7/ufV5UVIRRo0ZBqVT67Pvwww8DAKZMmQKDwYDS0lIAwAMPPODzvrfffhs33HAD8vPzceDAARw7dsz72t133w0AmDp1qvcm4Pv378fkyZN9wp5KpbriPr3t2bMHXV1dWLhwYUCPl4iGPvZIEhEFUFFREVQqFTIzM6/4nus5zRsdHe19vGvXLnz66afYtWsXtFotnnrqKZ/pCs/POCOVSq95TOXV9tmyZQvmzZt3ySAYjOMloqGDPZJERAH00ksvob29/YpXQx84cAAFBQV9tn/wwQcAgMLCQphMJmRnZ/d5j9VqhU6ng0ajgclkwmeffXbVNs2YMQOHDh3yjlW02+3o6Oi41kO67G1/gP4dLxENfeyRJCIKEVarFfn5+XC5XPjwww8hl8v7vGfx4sV4//33kZ2djeTkZMydO/eqXzc2NhYbN27EI488ArvdDplMhk8++QRZWVnX1K5Tp05d97EQUXgQRFEUB7sRRERERDT08NQ2EREREfmFQZKIiIiI/MIgSURERER+YZAkIiIiIr8wSBIRERGRXxgkiYiIiMgvDJJERERE5BcGSSIiIiLyC4MkEREREfmFQZKIiIiI/MIgSURERER++f+4//yC9ILQeQAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import ctypes\n", "nodeNull = ctypes.c_void_p(0)\n", "branching = galacticus.mergerTreeBranchingProbabilityParkinsonColeHelly(\n", " 0.57, 0.38, -0.01, # G0, gamma1, gamma2 (Parkinson et al. 2008)\n", " 0.1, # accuracy of first-order expansion\n", " 1.0e-6, True, # hypergeometric-function precision, tabulation\n", " True, False, # CDM assumptions; do not tolerate round-off errors\n", " cosmologicalMassVariance, criticalOverdensity)\n", "\n", "deltaCToday = criticalOverdensity.value(time=ageToday, mass=1.0e12)\n", "fig, ax = plt.subplots()\n", "for massParent, color in ((1.0e11, 'C0'), (1.0e12, 'C1'), (1.0e13, 'C2')):\n", " ratios = np.linspace(0.02, 0.5, 60) # branch masses up to M/2\n", " rate = np.array([branching.rate(massParent, deltaCToday, ageToday,\n", " x*massParent, nodeNull) for x in ratios])\n", " ax.semilogy(ratios, ratios*massParent*rate, color=color,\n", " label=f'$M = 10^{{{np.log10(massParent):.0f}}}\\\\,M_\\\\odot$')\n", "ax.set_xlabel('$M_\\\\mathrm{branch}\\\\,/\\\\,M$')\n", "ax.set_ylabel('$M_\\\\mathrm{branch}\\\\,\\\\mathrm{d}P/\\\\mathrm{d}\\\\delta_\\\\mathrm{c}\\\\mathrm{d}\\\\ln M$')\n", "ax.legend(); ax.set_title('Parkinson-Cole-Helly branching rates')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d0e6e9f8", "metadata": {}, "source": [ "Small progenitors split off far more frequently (the rise toward small\n", "mass ratios), and more massive halos — rarer, higher-$\\sigma$ peaks —\n", "branch faster: they assembled more recently.\n", "\n", "## What tree building costs\n", "\n", "Two more methods expose the mechanics of the tree-build loop:\n", "`probability` is the *total* branching rate above the mass resolution, and\n", "`stepMaximum` the largest $\\delta_\\mathrm{c}$ step the algorithm permits.\n", "Resolving smaller progenitors makes branchings more frequent and steps\n", "smaller — the classic resolution/cost trade-off of EPS trees." ] }, { "cell_type": "code", "execution_count": 6, "id": "165b1574", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:40:01.171712Z", "iopub.status.busy": "2026-07-05T19:40:01.171621Z", "iopub.status.idle": "2026-07-05T19:40:01.398693Z", "shell.execute_reply": "2026-07-05T19:40:01.397767Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "resolutions = np.logspace(6, 10, 24)\n", "massParent = 1.0e12\n", "total = np.array([branching.probability(massParent, deltaCToday, ageToday, r, nodeNull)\n", " for r in resolutions])\n", "steps = np.array([branching.stepMaximum(massParent, deltaCToday, ageToday, r)\n", " for r in resolutions])\n", "fig, axes = plt.subplots(1, 2, figsize=(11, 4))\n", "axes[0].loglog(resolutions, total)\n", "axes[0].set_xlabel('mass resolution [$M_\\\\odot$]')\n", "axes[0].set_ylabel('branching rate d$P$/d$\\\\delta_\\\\mathrm{c}$')\n", "axes[1].loglog(resolutions, steps)\n", "axes[1].set_xlabel('mass resolution [$M_\\\\odot$]')\n", "axes[1].set_ylabel('maximum $\\\\delta_\\\\mathrm{c}$ step')\n", "fig.suptitle(f'Cost of resolving a $10^{{12}}\\\\,M_\\\\odot$ tree')\n", "fig.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "696ae842", "metadata": {}, "source": [ "## Sampling root halo masses for a tree suite\n", "\n", "A Galacticus run needs a *set* of trees whose root masses sample the halo\n", "population. `mergerTreeBuildMasses` implementations decide that sampling;\n", "`construct(time)` returns four arrays at once through the library's\n", "output-array interface — the sampled masses, the mass interval each\n", "represents, and (for weighted samplers) per-tree weights.\n", "\n", "Here: masses uniform in $\\log M$ over $10^{10}$–$10^{14} M_\\odot$ at five\n", "trees per decade." ] }, { "cell_type": "code", "execution_count": 7, "id": "ce2ad2fe", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:40:01.400748Z", "iopub.status.busy": "2026-07-05T19:40:01.400661Z", "iopub.status.idle": "2026-07-05T19:40:01.475968Z", "shell.execute_reply": "2026-07-05T19:40:01.475124Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sampled 20 tree root masses from 1.26e+10 to 7.94e+13 Msun\n", "weight array size: 0\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "distribution = galacticus.mergerTreeBuildMassDistributionPowerLaw(0.0) # uniform in log M\n", "buildMasses = galacticus.mergerTreeBuildMassesSampledDistributionUniform(\n", " 1.0e10, 1.0e14, 5.0, distribution)\n", "mass, massMinimum, massMaximum, weight = buildMasses.construct(ageToday)\n", "\n", "print(f\"sampled {mass.size} tree root masses from \"\n", " f\"{mass.min():.2e} to {mass.max():.2e} Msun\")\n", "# This sampler assigns no per-tree weights: the weight array comes back\n", "# empty (each tree instead represents its [massMinimum, massMaximum]\n", "# interval of the mass function).\n", "print(f\"weight array size: {weight.size}\")\n", "\n", "fig, ax = plt.subplots(figsize=(8, 2.8))\n", "ax.hlines(np.ones_like(mass), massMinimum, massMaximum, color='C0', alpha=0.5,\n", " label='interval represented')\n", "ax.plot(mass, np.ones_like(mass), 'o', color='C1', ms=5, label='sampled root mass')\n", "ax.set_xscale('log'); ax.set_yticks([])\n", "ax.set_xlabel('tree root mass [$M_\\\\odot$]'); ax.legend(loc='upper left')\n", "ax.set_title('A tree suite: 5 trees per decade, uniform in $\\\\log M$')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "7dd75077", "metadata": {}, "source": [ "## From building blocks to trees\n", "\n", "These are the exact objects a full Galacticus run assembles from a\n", "parameter file to build its trees — the same branching rates, the same\n", "mass samplers. To *grow and evolve* the trees (and the galaxies inside\n", "them) you hand these ingredients to `Galacticus.exe`; see the\n", "`user guide `_ for tree-building\n", "parameter files." ] } ], "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 }