{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Merger rate density model comparision" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "Here is a summary comparing the binary black hole (BBH) merger density distribution between BBH from Population I/II (Pop I/II) stars, BBH from Pop III stars, and primordial black holes (PBHs):\n", "\n", "| BBH type | Merger rate density distribution | Peak value |\n", "|-------------------------|---------------------------------------------------------------------|------------------------------------------|\n", "| Pop I/II stars | Peaks at redshift $z \\sim 1-2$, and declines ever since | $\\sim 150–300 \\, \\text{Gpc}^{-3} \\, \\text{yr}^{-1}$ |\n", "| Pop III stars | Peaks at redshift $z \\sim 8–16$, and declines rapidly at higher redshifts | $\\sim 2–30 \\, \\text{Gpc}^{-3} \\, \\text{yr}^{-1}$ |\n", "| Primordial black holes | Unknown, expected to have a power-law dependence on the age of the Universe | Expected to be higher at high redshifts |\n", "\n", "* The BBH merger density distribution from Pop I/II stars is well-studied, while the BBH merger density distribution from Pop III stars and PBHs is much less well-studied.\n", "\n", "* Astronomers are interested in studying the BBH merger density distribution from Pop III stars and PBHs, as they would provide important information about the early Universe.\n", "\n", "* The next generation of gravitational wave observatories, such as the Einstein Telescope and the Cosmic Explorer, are expected to be able to detect BBHs formed from Pop III stars." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## BBH/BNS merger rate at source redshift $z_s$ (in small dz)\n", "\n", "* $R(z_s)$: Source frame merger rate density at source redshift $z_s$.\n", "\n", "$$ R(z_s) = \\frac{\\mathcal{R}_m(z_s)}{1+z_s} \\frac{dV_c}{dz_s} $$\n", "\n", "* $\\mathcal{R}_m(z_s)$: Source frame merger rate density at source redshift $z_s$.\n", "* Differential co-moving volume : $\\frac{dV_c}{dz_s}$.\n", "* $\\frac{1}{1+z_s}$: this factor takes care of the time dilation effect." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# calling necessary class from ler package\n", "from ler.gw_source_population import CBCSourceRedshiftDistribution" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "z_min = 0.0\n", "z_max = 40.0\n", "z = np.geomspace(0.01, 40.0, 500)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## BBH/BNS pop I/II Oguri et al. 2018 model\n", "\n", "* LeR default meerger rate density distribution follows [WIERDA et al. 2021](https://arxiv.org/pdf/2106.06303.pdf).\n", "* It is a functional fit to the population I/II star merger-rate density normalized to the local merger- rate density following Oguri (2018). \n", "* This model follows from the M10 model to the Belczynski et al. (2017), which is arrived from Madau & Dickinson (2014) with the inclusion of the metallicity dependence of the star formation rate, which is bassically the effect related to pair-instability supernova (PSN) and pair-instability pulsation supernova (PPSN). \n", "\n", "\\begin{equation}\n", "\\mathcal{R}_m(z_s) = \\frac{\\mathcal{R}_O(b_4+1)e^{b_2 z_s}}{b_4+e^{b_3 z_s}} \\text{Gpc}^{-3}\\text{yr}^{-1} \\tag{1}\n", "\\end{equation}\n", "* $z_s$: redshift of source\n", "* $\\mathcal{R}_O$: local merger rate density. $\\mathcal{R}_O=23.9^{+14.3}_{-8.6}\\text{Gpc}^{-3}\\text{yr}^{-1}=23.9^{+14.3}_{-8.6} \\times 10^{-9}\\text{Mpc}^{-3}\\text{yr}^{-1}$\n", "* fitting parameters: $b_2=1.6$, $b_3=2.1$, $b_4=30$\n", "\n", "* with results from [GWTC-3 Section IV.A](https://journals.aps.org/prx/pdf/10.1103/PhysRevX.13.011048):\n", "\n", "| Model | $\\mathcal{R}_O$ |\n", "|-------|---------------------|\n", "| BNS | $105.5^{+190.2}_{-83.9}$ |\n", "| BBH | $23.9^{+14.9}_{-8.6}$ |\n", "| NSBH | $45^{+75}_{-33}$ |\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "z_to_luminosity_distance interpolator will be loaded from ./interpolator_pickle/z_to_luminosity_distance/z_to_luminosity_distance_2.pickle\n", "differential_comoving_volume interpolator will be loaded from ./interpolator_pickle/differential_comoving_volume/differential_comoving_volume_2.pickle\n", "merger_rate_density interpolator will be loaded from ./interpolator_pickle/merger_rate_density/merger_rate_density_0.pickle\n" ] } ], "source": [ "# initializing the class\n", "# BBH pop I/II Oguri et al. 2018 model\n", "cbc = CBCSourceRedshiftDistribution(\n", " z_min=z_min,\n", " z_max=z_max,\n", " merger_rate_density=\"merger_rate_density_bbh_popI_II_oguri2018\",\n", " merger_rate_density_param=dict(R0=25.*1e-9, b2=1.6, b3=2.0, b4=30),\n", " )\n", "\n", "# source frame\n", "rate1_src = cbc.merger_rate_density(z)\n", "# detector frame\n", "# normalised to 1\n", "rate1_det = cbc.pdf_z(z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Star formation rate\n", "\n", "* Madau and Dickinson's 2014 paper, titled [\"Cosmic Star-Formation History\"](https://www.annualreviews.org/doi/pdf/10.1146/annurev-astro-081811-125615) provides a comprehensive overview of the star formation rate in the universe\n", "* Madau and Dickinson identify a peak in the star formation rate around redshifts of 1 to 2, corresponding to a critical period in the universe's history when galaxies were forming stars at a significantly higher rate.\n", "* Extinction-corrected cosmic star formation rate is given below. Extinction refers to the process by which starlight is absorbed and scattered by dust and gas in galaxies, making it appear fainter and altering the observed spectrum. This is also Eqn. 1 in [Belczynski et al. 2016](https://arxiv.org/pdf/1602.04531.pdf). Also refer to [Belczynski et al. 2017](https://arxiv.org/pdf/1612.01524.pdf) for the metallicity dependence of the star formation rate.\n", "\n", "\\begin{equation}\n", "\\psi(z) = 0.015 \\frac{(1+z)^{2.7}}{1+[(1+z)/2.9]^{5.6}} \\text{M}_\\odot \\text{yr}^{-1} \\text{Mpc}^{-3} \\tag{2}\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "z_to_luminosity_distance interpolator will be loaded from ./interpolator_pickle/z_to_luminosity_distance/z_to_luminosity_distance_2.pickle\n", "differential_comoving_volume interpolator will be loaded from ./interpolator_pickle/differential_comoving_volume/differential_comoving_volume_2.pickle\n", "merger_rate_density interpolator will be loaded from ./interpolator_pickle/merger_rate_density/merger_rate_density_1.pickle\n" ] } ], "source": [ "# Star formation rate Madau & Dickinson 2014\n", "cbc = CBCSourceRedshiftDistribution(\n", " z_min=z_min,\n", " z_max=z_max,\n", " merger_rate_density=\"sfr_madau_dickinson2014\",\n", " merger_rate_density_param=dict(af=2.7, bf=5.6, cf=2.9),\n", " )\n", "\n", "# source frame\n", "rate2_src = cbc.merger_rate_density(z)\n", "# detector frame\n", "# normalised to 1\n", "rate2_det = cbc.pdf_z(z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## BBH pop III model, Ng et al. 2022\n", "\n", "* This model is based on the section II B [Ng et al. 2022](https://arxiv.org/pdf/2204.11864.pdf) paper.\n", "* Its a phenomenological model for the volumetric merger rate density of Pop III BBHs.\n", "* This model is a simple fit to the merger rate density predicted from population synthesis studies.\n", "\n", "\\begin{equation}\n", "\\dot{n}_{III} = n_o \\frac{e^{a_{III}(z_s-z_{III})}}{a_{III}+b_{III} e^{(a_{III}+b_{III})(z_s-z_{III})}} \\text{Mpc}^{-3}\\text{yr}^{-1} \\tag{3}\n", "\\end{equation}\n", "\n", "* $z_s$: redshift of source\n", "* $n_o$: Normalization factor. $a_{III}$, $b_{III}$, $z_{III}$ are fitting parameters.\n", "* $n_o=19.2\\times 10^{-9}$, $a_{III}=0.66$, $b_{III}=0.3$, $z_{III}=11.6$\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "z_to_luminosity_distance interpolator will be loaded from ./interpolator_pickle/z_to_luminosity_distance/z_to_luminosity_distance_2.pickle\n", "differential_comoving_volume interpolator will be loaded from ./interpolator_pickle/differential_comoving_volume/differential_comoving_volume_2.pickle\n", "merger_rate_density interpolator will be loaded from ./interpolator_pickle/merger_rate_density/merger_rate_density_2.pickle\n" ] } ], "source": [ "# pop III Ng et al. 2022\n", "cbc = CBCSourceRedshiftDistribution(\n", " z_min=z_min,\n", " z_max=z_max,\n", " merger_rate_density=\"merger_rate_density_bbh_popIII_ken2022\"\n", " )\n", "\n", "# source frame\n", "rate3_src = cbc.merger_rate_density(z)\n", "# detector frame\n", "# normalised to 1\n", "rate3_det = cbc.pdf_z(z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Primordial BBH model, Ng et al. 2022\n", "\n", "* This model is based on the section II A [Ng et al. 2022](https://arxiv.org/pdf/2204.11864.pdf) paper.\n", "* the volumetric merger rate density of PBHs has a power-law dependence on the age of the Universe $t(z)$ extending up to $z \\gtrsim 10^3$.\n", "\n", "\\begin{equation}\n", "\\dot{n}_{PBH} = n_o \\left(\\frac{t(z)}{t_o}\\right)^{-34/37} \\text{Mpc}^{-3}\\text{yr}^{-1} \\tag{4}\n", "\\end{equation}\n", "\n", "* $z_s$: redshift of source\n", "* $n_o$: Normalization factor. $t_o$ is the present age of the Universe.\n", "* $n_o=0.044\\times 10^{-9}$, $t_o=13.786885302009708$" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "z_to_luminosity_distance interpolator will be loaded from ./interpolator_pickle/z_to_luminosity_distance/z_to_luminosity_distance_2.pickle\n", "differential_comoving_volume interpolator will be loaded from ./interpolator_pickle/differential_comoving_volume/differential_comoving_volume_2.pickle\n", "merger_rate_density interpolator will be loaded from ./interpolator_pickle/merger_rate_density/merger_rate_density_3.pickle\n" ] } ], "source": [ "# primordial black holes Ng et al. 2022\n", "cbc = CBCSourceRedshiftDistribution(\n", " z_min=z_min,\n", " z_max=z_max,\n", " merger_rate_density=\"merger_rate_density_bbh_primordial_ken2022\")\n", "\n", "# source frame\n", "rate4_src = cbc.merger_rate_density(z)\n", "# source frame\n", "# normalised to 1\n", "rate4_det = cbc.pdf_z(z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plots and comparison" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### reproduction of Ng et al. 2022 [Fig. 3](https://arxiv.org/pdf/2204.11864.pdf)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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99lkApk2b5tjWp08fvvvuO6f9Xn755QZbbM40adIkvLy8ePLJJ7FYLE6P1b2OXPFabuzruKWa+p6QmJgIwIUXXtiqcYi2Iy02otM6V/9/nXHjxnHHHXfw5JNPkpSUxKRJkzAYDCQnJ7N+/Xqee+65Bsfn1Lnjjjt44YUXmD9/PkuXLiU0NNQx7gL+9+1fq9Xy6quvMnXqVAYPHszNN99MeHg4GRkZfP3113h7e/Ppp5+2/Bc/w/Tp03nrrbfw8fFh0KBB/Pzzz2zbts3RNVInLi4OnU7HP/7xD0pKSjCZTFx22WUEBQXx4osvcuONNzJixAiuu+46evTowalTp/jss8+46KKLeOGFFxo8//333+9YMn/p0qWO6d7R0dHs3bvXsZ+3t3eLznM2t912G4WFhVx22WVERERw8uRJnn/+eeLi4s75DTs+Pp61a9eybNkyRo0ahaenp1OCvGDBAu6//342bNjA73//e6fpv+cya9YsHnroIUpLSx1jhr766ivuuusu5s6dS79+/aitreWtt95Cp9Nx9dVXAxAbG8vChQt5+eWXKS4uZty4cfz666+88cYbzJ49mwkTJjj9zr/73e+4+uqrueKKK9izZw9ffPFFo7tKvL29+de//sVtt93GqFGjHOso7dmzh8rKSt544w2XvJYb+zpuqaa+J2zdupWoqCiZ6t2ZuGo6lhBNcfp073M5c7p3nZdfflmJj49X3NzcFC8vL2Xo0KHK/fffr2RmZp73uYqiKMePH1emTZumuLm5KT169FDuu+8+5cMPP1QA5ZdffnHad/fu3cpVV12lBAQEKCaTSYmOjlbmzZunbN++3bFP3XTvvLy8Fv/+RUVFys0336wEBgYqnp6eyuTJk5XDhw/Xm/6rKIryyiuvKL1791Z0Ol29KdBff/21MnnyZMXHx0cxm81Knz59lEWLFikJCQnnjW/v3r3KuHHjFLPZrISHhyuPPfaY8tprrzlN927KeRYuXKh4eHjUO0/ddavzwQcfKJMmTVKCgoIUo9GoREVFKXfccYeSlZXldL4zf9fy8nJlwYIFiq+vrwKcder3lVdeqQDKTz/9dN7fv05OTo6i1+uVt956y7Ht+PHjyi233KL06dNHMZvNir+/vzJhwgRl27ZtTs+1Wq3Ko48+qvTq1UsxGAxKZGSksnz5csVisTjtZ7PZlAceeEAJDAxU3N3dlcmTJyspKSkNTvdu6G/mk08+US688ELFzc1N8fb2VkaPHq289957Tvs05rXcEM4x3bslr+OGjtHQ31RDr6XGvCfYbDYlNDRU+ctf/nLe31d0HBpFkXWihWiOlStX8oc//IH09HTCw8NdHY5oZXPmzGHfvn31xlKdz6233srRo0f5/vvv2ygy0V42btzIggULOHbsGKGhoa4ORzSSJDZCNEJVVZXTQEOLxcLw4cOx2WwcPXrUhZGJtpCVlUV0dDQPPfQQjzzySJOee+rUKfr168f27du7fYXvzm7s2LFccskl/POf/3R1KKIJJLH5TVpaGjfeeCO5ubno9Xr++te/NnrdCtH1TZ06laioKOLi4igpKeHtt9/mwIEDvPPOOw0uDig6n9TUVH788UdeffVVdu7cybFjx1q1sKoQou3J4OHf6PV6Vq5cSVxcHNnZ2cTHx3PllVc6ZpKI7m3y5Mm8+uqrvPPOO9hsNgYNGsT777/Ptdde6+rQRCv69ttvufnmm4mKiuKNN96QpEaITkhabBoQGxvLpk2b6q1iKYQQQoiOq8usY/Pdd98xY8YMwsLC0Gg0bNy4sd4+q1atomfPnpjNZsaMGeO07sbpEhMTsdlsktQIIYQQnUyXSWwqKiqIjY1l1apVZ328bs2KRx55hF27dhEbG8vkyZPr1QUpLCzkpptu4uWXX26PsIUQQgjRirpkV5RGo2HDhg3Mnj3bsW3MmDGMGjXKsQCY3W4nMjKSu+++mwcffBBQVyq94oorWLx4MTfeeOM5z1FdXe20sqndbqewsJCAgAApliaEEEI0gaIolJWVERYWhlbbsjaXbjF4uKamhsTERJYvX+7YptVqmThxIj///DOgXtRFixZx2WWXnTepAXjyySd59NFH2yxmIYQQortJS0tzKgzbHN0iscnPz8dmsxEcHOy0PTg4mMOHDwPw448/snbtWoYNG+YYn/PWW28xdOjQsx5z+fLlLFu2zHG/pKSEqKgoTpw44VhKva3ZbDaOHz9O7969G1UJuTuSa3Rucn3OT67Rucn1OT+5RudXXFxM79698fLyavGxukVi0xgXX3wxdru90fubTCZMJlO97X5+fu2a2Hh7e+Pn5yd/LA2Qa3Rucn3OT67Rucn1OT+5Ro3XGkM5uszg4XMJDAxEp9ORk5PjtD0nJ6fF61SsWrWKQYMGMWrUqBYdRwghhBAt1y0SG6PRSHx8PNu3b3dss9vtbN++nbFjx7bo2EuWLOHgwYPs3LmzpWEKIYQQooW6TFdUeXm5U7G61NRUkpKS8Pf3JyoqimXLlrFw4UJGjhzJ6NGjWblyJRUVFdx8880ujFoIIYQQranLJDYJCQlMmDDBcb9uYO/ChQtZs2YN1157LXl5eTz88MNkZ2cTFxfHli1b6g0oFkJ0P4qiUFtbi81mq/eYzWbDbrdjsVhkfMRZyPU5P7lGoNPp0Ov17bIcSpdJbMaPH8/5luS56667uOuuu1r1vKtWrWLVqlVnfUMUQnR8NTU1ZGVlUVlZedbH65KekydPyhpVZyHX5/zkGqnc3d0JDQ3FaDS26Xm6TGLjKkuWLGHJkiWUlpbi4+Pj6nCEEE1gt9tJTU1Fp9MRFhaG0Wis98GjKArV1dWYTKZu/aHUELk+59fdr5GiKNTU1JCXl0dqaip9+/Zt8SJ85yKJjRCi26qpqXGsQu7u7n7Wfepags1mc7f8UDofuT7nJ9cI3NzcMBgMnDx5kpqaGsxmc5udq1vMihJCiHNpy2+PQghVe/2dyV+zEEIIIboMSWxaSBboE0IIIToOSWxaSBboE0II0RLffPMNGo2G4uJiV4fSJUhiI4QQndCiRYvQaDSOW0BAAFOmTGHv3r1O+52+j16vdyxYWl1d7dhnzZo1+Pr6nvU8Go3GURjYlRqK8Y033uDiiy8G1GU/7r33XsdjZ94/m6qqKh555BH69euHyWQiMDCQuXPncuDAgVaM/twuvPBCsrKyZGZtK5HERgghOqkpU6aQlZVFVlYW27dvR6/XM3369Hr7rV69mqysLFJTU/nPf/7DW2+9xd///ncXRNz6Pv74Y2bOnNms51ZXVzNx4kRef/11/v73v3P06FE2b95MbW0tY8aM4ZdffmnlaOuzWq0YjUZCQkK67Yyp1iaJjRBCnEZRFGpq7c43m73+tja4nW+R0TOZTCZCQkIICQkhLi6OBx98kLS0NPLy8pz28/X1JSQkhMjISKZPn86sWbPYtWtXq1yvCRMm8Ic//IG77roLHx8fAgMD+etf/+r0uxQVFXHTTTfh5+eHu7s7U6dOJTk52fF4XWvMxo0b6du3L2azmcmTJ5OWlnbOc1ssFr788stmJzYrV67k559/ZtOmTcybN4/o6GhGjx7Nhx9+yMCBA7n11lsdv0dtbS333HMPvr6+BAQE8MADD7Bw4UJmz57tOF7Pnj1ZuXKl0zni4uJYsWKF475Go+HFF19k5syZeHh48Pjjj0tXVCuTdWxaSFYeFqJrsdoUVn2dctoWddVYvV4PtO036iUTYjDqm3eO8vJy3n77bWJiYggICGhwv6NHj/LVV1+xaNGiZkZZ3zvvvMMtt9zCr7/+SkJCArfffjtRUVEsXrwYULvNkpOT+eSTT/D29uaBBx7gyiuv5ODBgxgMBgAqKyt5/PHHefPNNzEajdx5551cd911/Pjjjw2ed/v27YSHhzNgwIBmxf3uu+9yxRVXEBsb67Rdq9Xyhz/8geuvv549e/YQFxfHP/7xD9555x1Wr17NwIEDee6559i4caNTKZ/GWrFiBf/3f//HypUr0ev1HD9+vFnxi7OTxKaFZOVhIYSrbNq0CU9PTwAqKioIDQ1l06ZN9dYLmT9/PjqdjtraWqqrq5k+fTrLly932qekpMRxrKaKiIjgX//6F1qtlv79+7Nv3z7+9a9/sXjxYkdC8+OPP3LhhRcCaiIUGRnJxo0bmTt3LqB2ybzwwguMGTMGUMfODBw4kF9//ZXRo0ef9bwt6YYCNclrKDEZOHCgY5+4uDief/55li9fzpw5cwB44YUX2Lx5c7POu2DBAqcCzJLYtC5JbIQQ4jQGnYYlE2Ic9xVFwVJtwWxq+1VjDbqmHX/ChAm8+OKLgNrd85///IepU6fy66+/Eh0d7djvX//6FxMnTsRms5GSksKyZcu48cYbef/99x37eHl5nbV7qm/fvueNY9SoUU7XZuzYsTzzzDPYbDYOHTqEXq93JCwAAQEB9O/fn0OHDjm26fV6p2UzBgwYgK+vL4cOHTprYqMoCp9++inr1q07b3zn0pjuv5KSEnJycpzi0Ol0xMfHY7fbm3zOkSNHNvk5ovEksRFCiNNoNBqn7iBFUbDXajHqtR1ucKeHhwcxMf9Lwl599VV8fHx45ZVXnAYHh4SEOPbr378/ZWVlzJ8/n7///e+O7Vqt1ulYHd2vv/5KbW2toxWoOfr16+eUXJ2ubnu/fv0afTytVlsvUbJarfX28/DwaEKUoqlk8LAQQnQRGo0GrVZLVVXVOffT6XQA592vsRISEpzu//LLL/Tt2xedTsfAgQOpra1lx44djscLCgo4cuQIgwYNcmyrra11Os6RI0coLi52dAmd6eOPP2batGmO36U5rrvuOrZt28aePXucttvtdv71r38xaNAgYmNj8fHxITg42Gm9MpvNVq+Fq0ePHmRlZTnul5aWkpqa2uz4RPNIYiOEEJ1UdXU12dnZZGdnc+jQIe6++27Ky8uZMWOG037FxcVkZ2eTmZnJt99+y9/+9jf69evXYNLQVGlpaSxbtowjR47w3nvv8fzzz7N06VJA7cqaNWsWixcv5ocffmDPnj3ccMMNhIeHM2vWLMcxDAYDd999Nzt27CAxMZFFixZxwQUXNDi+5pNPPmnR+BqAP/zhD4wePZoZM2awfv16Tp06xc6dO7n66qs5dOgQr732mqOV7u677+bJJ5/k448/5siRIyxdupSioiKnVrzLLruMt956i++//559+/axcOHCFiVeonmkK6qFZFaUEMJVtmzZQmhoKKCOkRkwYADr169n/PjxTvvVDVTVaDSEhIRw6aWX8sQTT/w206vlFixYQFVVFaNHj0an07F06VJuv/12x+OrV69m6dKlTJ8+nZqaGi699FI2b97smBEF4O7uzgMPPMCCBQvIyMjgkksu4bXXXjvr+Y4dO0ZKSgqTJ09uUdxms5mvvvqKJ554gj//+c+cPHkSLy8vJkyYwC+//MKQIUMc+z7wwANkZ2dz0003odPpuP3225k8ebJT4rJ8+XJSU1OZPn06Pj4+PPbYY9Ji4wIapakLJ4izqpsVVVJSgre3d7uc02azkZyc7GjyFfXJNTq37n59LBYLqamp9OrVC7PZfNZ9FEXBYrFgNrf94OHOaPz48QwZMoTnn3++2ddnzZo13HvvvY1ex+XZZ59l27ZtzZ6V1BrsdjsDBw5k3rx5PPbYY+fcV15DqnP9vRUVFeHv798qn6HSYiOEEKJTiYiIqDddva2dPHmSL7/8knHjxlFdXc0LL7xAamoqCxYsaNc4xPlJYiOEEKJTmTdvXrufU6vVsmbNGv74xz+iKApDhgxh27ZtrTZOSbQeSWyEEEI029dff43FYmnRMRYtWtSqKyG3hcjIyHOugiw6DpkVJYQQQoguQxIbIYQQQnQZkti00KpVqxg0aJDTUuBCCCGEcA1JbFpoyZIlHDx40GlFSiGEEEK4hiQ2QgghhOgyJLERQgghRJchiY0QQgghugxJbIQQohNatGgRGo0GjUaD0WgkJiaGv/3tb9TW1rbpeTUaDRs3bnTc12q1fPLJJw0+fqZFixYxe/Zsp20ffPABZrOZZ555plVi3LNnD/PnzycyMhI3NzcGDhzIc889V2+/b775hhEjRmAymYiJiWHNmjVOjz/55JOMGjUKLy8vgoKCmD17NkeOHHE8XlhYyN13303//v1xc3MjKiqKe+65h5KSklb5PUTzSGIjhBCd1JQpU8jKyiI5OZn77ruPFStW8NRTT7k6rCZ59dVXuf7663nxxRe57777WuWYiYmJBAUF8fbbb3PgwAEeeughli9fzgsvvODYJzU1lWnTpjFhwgSSkpK49957ue222/jiiy8c+3z77bcsWbKEX375ha1bt2K1Wpk0aRIVFRUAZGZmkpmZydNPP83+/ftZs2YNW7Zs4dZbb22V30M0kyJaRUlJiQIoJSUl7XbO2tpa5dChQ0ptbW27nbOzkWt0bt39+lRVVSkHDx5Uqqqq/rfRblcUa7XjZrdalMqyYsVutThtb5Ob3d7o2BcuXKjMmjXLadsVV1yhXHDBBYqiKEphYaFy4403Kr6+voqbm5syZcoU5ejRo459V69erfj4+CgbNmxQYmJiFJPJpEyaNEk5derUOc8LKBs2bHC6//777yv232I/8/Fzxf2Pf/xDMZvNykcffeS0z8aNG5Xhw4crJpNJ6dWrl7JixQrFarU6nfOVV15RZs+erbi5uSkxMTHKxx9/fM6477zzTmXChAmO+/fff78yePBgp32uvfZaZfLkyQ0eIzc3VwGUb7/9tsF91q1bpxiNRqd47Xa7UllZ6bhG3dVZ/95+U1hY2GqfoVJSQQghTmezwvend4ko6GtrQa8H2rgy8yX3gd7Y7Ke7ublRUFAAqF0+ycnJfPLJJ3h7e/PAAw9w5ZVXcvDgQQwGAwCVlZU8/vjjvPnmmxiNRu68806uu+66dikd8MADD/Cf//yHTZs2cfnllzu2f//999x00038+9//5pJLLuHYsWPcfvvtADzyyCOO/R599FH++c9/8tRTT/H8889z/fXXc/LkSfz9/c96vpKSEqfHfv75ZyZOnOi0z+TJk7n33nsbjLmui6mhc9Tt4+3tjV4vH6+uIl1RraywvNrVIQghuhlFUdi2bRtffPEFl112mSOhefXVV7nkkkuIjY3lnXfeISMjw2n8i9Vq5YUXXmDs2LHEx8fzxhtv8NNPP/Hrr7+2abyff/45//znP/n444+dkhpQE5YHH3yQhQsX0rt3b6644goee+wx/vvf/zrtt2jRIubPn09MTAxPPPEE5eXlDcb9008/sXbtWkeCBJCdnU1wcLDTfsHBwZSWllJVVVXvGHa7nXvvvZeLLrqIIUOGnPU8+fn5PPbYY07nEe1PUsoWWrVqFatWrcJmswHw0e4M5nt4Eurj5uLIhBDNojOoLScOCrUWC3qzmTZvsdEZmrT7pk2b8PT0xGq1YrfbWbBgAStWrGD79u3o9XrGjBnj2DcgIID+/ftz6NAhxza9Xu+0avqAAQPw9fXl0KFDjB49uuW/TwOGDRtGfn4+jzzyCKNHj8bT09Px2J49e/jxxx95/PHHHdtsNhsWi4XKykrc3d0dx6jj4eGBt7c3ubm59c61f/9+Zs2axSOPPMKkSZOaHfOSJUvYv38/P/zww1kfLy0tZdq0aQwaNIgVK1Y0+zyi5SSxaaElS5awZMkSSktL8fHxodpq56NdGUwfFkp0gIerwxNCNJVG49wdpCigs4POqD7WgUyYMIEXX3wRo9FIWFhYp+n+CA8P54MPPmDChAlMmTKFzz//HC8vLwDKy8t59NFHueqqq+o9z2w2O36u606ro9FosNvtTtsOHjzI5Zdfzu23385f/vIXp8dCQkLIyclx2paTk4O3tzdubs5fTO+66y42bdrEd999R0RERL24ysrKmDJlCl5eXmzYsKFebKJ9SVdUK4v0d6Om1s7HSZkczSlzdThCiC7Mw8ODmJgYoqKinJKagQMHUltby44dOxzbCgoKOHLkCIMGDXJsq62tJSEhwXH/yJEjFBcXM3DgwDaPPTo6mm+//Zbs7GymTJlCWZn6fjlixAiOHDlCTExMvZtW2/iPrAMHDjBhwgQWLlzo1PpTZ+zYsWzfvt1p29atWxk7dqzjvqIo3HXXXWzYsIGvvvqKXr161TtOaWkpkyZNwmg08sknnzglX8I1JLFpZdOGhdE/xAubXWHzviz2pBW7OiQhRDfTt29fZs2axeLFi/nhhx/Ys2cPN9xwA+Hh4cyaNcuxn8Fg4O6772bHjh0kJiayaNEiLrjggjbthjpdZGQk33zzDbm5uUyePJnS0lIefvhh3nzzTR599FEOHDjAoUOHeP/99+u1uJzL/v37mTBhApMmTWLZsmVkZ2eTnZ1NXl6eY5/f/e53HD9+nPvvv5/Dhw/zn//8h3Xr1vGHP/zBsc+SJUt4++23effdd/Hy8nIcp24MTl1SU1FRwWuvvUZpaaljn7rhCaL9SWLTynRaDVMGhxAb6YOiwFeHc/nleAGKorg6NCFEN7J69Wri4+OZPn06Y8eORVEUNm/e7NRN4u7uzgMPPMCCBQu46KKL8PT0ZO3ate0aZ0REBN988w35+flMnjyZsWPHsmnTJr788ktGjRrFBRdcwL/+9S+io6MbfcwPPviAvLw83n77bUJDQx2308cT9erVi88++4ytW7cSGxvLM888w6uvvsrkyZMd+7z44ouUlJQwfvx4p+PUXaNdu3axY8cO9u3bR0xMjNM+aWlprXeRRJNoFPnEbRV1Y2zqpvopisLPxwvYcbwQgLgoX8b364GmFfvobTYbycnJ9O3bF51O12rH7UrkGp1bd78+FouF1NRUevXq1WAXgqIoWCwWzGZzq/79utqaNWu49957KS4ubtFxuur1aU1yjVTn+nsrKirC39/f8RnaEtJi00Y0Gg0X9glkfP8eACSdKuaLA9nY7JJHCiGEEG1FEps2NjzKjylDQtBqNBzKKuPTPZlYbfbzP1EIIYQQTSaJTTsYGOrNzLgwDDoNqfkVbNiVgcUqA8uEEK6zaNGiFndDCdERSWLTTnoFejBnRAQmg5aM4irWJ6ZTXt22VXiFEEKI7kYSm3YU7uvG3PhIPE168suqWbczjeLKGleHJYQQQnQZkti0sx5eJuaNjMTX3UBJlZV1CWnklllcHZYQQgjRJXSO9be7GB93A/NGRrJhdwZ5ZdV8kJjOzNgwIvzcXROQ3Q5VRVBdAjUVUFMJih1QAA0Y3MDgDiZPcA8Avck1cQohhBDnIYmNi3iY9FwTH8EnezLJKKpiw64Mpg0LpXcPz/M/uaVsVig+BYWpUJoOFXlga8J4H5MXePQAnwj15h3W5OJ9QgghRFuQxKaFzqzu3RRmg445w8PZvC+L43kVfLoniysGBTMorGWLE52V3Q7FJyBrL+Qng/2MREanBzc/MHqqrTPa3xZrU+xgtYC1AqrLoLr8t3/LoPC4uo9WD349ITAGAmLUxEcIIYRwAUlsWujM6t5NZdBpmT4sjK0HcziUVcoXB7KpstqIj/ZrnQBtVsjaA2m/gqXkf9tNXuDfW01IvELA7AuNKTBntUBlPpTlQEmaeqsuh4IU9abRgG80hAyBwP7OVZKFEC7Xs2dP7r33Xu69915XhwLAihUr2LhxI0lJScD/pqFv3LixUc8/ceIEvXr1Yvfu3cTFxbVZnKLzkMHDHYBOq2Hy4GBG/JbMfHc0jx9T8ltWX8pWC6d2wC//geStalKjN0H4CIhfCGOXwIArIXgQuPs3LqkBMJjV7qeIeBg8G8beBaNug97j1C4pRYGiE3BoE/z0bziyBcpzm/97CCHOatGiRWg0GjQaDUajkZiYGP72t79RW3vubuWdO3dy++23t1OUTffcc8+xZs2aVj3m+PHjHddKo9EQHBzM3LlzOXnypGOfEydOOO1Td03//ve/O70Xr1ix4qwJVN3z6xK0s5kwYUK9hPK5557DZDLx/vvvt/TXBOCbb75h1qxZhIaG4uHhQVxcHO+88069/davX8+AAQMwm80MHTqUzZs3Ox6zWq088MADDB06FA8PD8LCwrjpppvIzMx07HPixAluvfVWevXqhZubG3369OGRRx6hpsb1M32lxaaD0Gg0XNo3EDeDjh9T8vk1tZCqGhuXDQhCq21CbRFFgfyjcOwrqCpWt7n5QuRoCBnW+mNhNBrw7KHeoi9UByHnHFBvlYWQuVu9+URA5BgI7Ks+RwjRYlOmTGH16tVUV1ezefNmlixZgsFgYPny5fX2rampwWg00qNHDxdEqn5Ynl6AsyHNaflujMWLF/O3v/0NRVE4efIk9957LzfccAPff/+9037btm1j8ODBVFdX88MPP3DbbbcRGhrKrbfe2uoxPfLIIzz99NN8/PHHTJkypVWO+dNPPzFs2DAeeOABgoOD2bRpEzfddBM+Pj5Mnz7dsc/8+fN58sknmT59Ou+++y6zZ89m165dDBkyhMrKSnbt2sVf//pXYmNjKSoqYunSpcycOZOEhAQADh8+jN1u57///S8xMTHs37+fxYsXU1FRwdNPP90qv0tzSYtNB6LRaBjdy5+JA4PRaGBfRgmb92dR29gSDJZS2P8h7P9ITWpMnmqrzOg7IDy+fQb4uvlBz4th9O0QtwCCBoBGCyXpamy/vgKZSWCXlZdFx6QoClab1SW3prbSmkwmQkJCiI6O5ve//z0TJ07kk08+AdQWndmzZ/P4448TFhZG//79AbUrauXKlY5jaDQa/vvf/zJ9+nTc3d0ZOHAgP//8MykpKYwfPx4PDw8uvPBCjh075nTuF198kT59+mAymYiNjeWtt95yelyj0fDiiy8yc+ZMPDw8ePzxxwH4v//7P4KDg/Hy8uLWW2/FYnFe7qIu7jpbtmzh4osvxtfXl4CAAKZPn14vlsZwd3cnJCSE0NBQLrjgAu666y527dpVb7+AgADHNb3++uu56KKLzrpfSyiKwt13382///1vtm7d6pTUvPrqqwwcOBCz2cyAAQP4z3/+43isrlXoo48+YsKECbi7uxMbG8vPP//s2OfPf/4zjz32GBdeeCF9+vRh6dKlTJkyhY8++sixz3PPPceUKVP405/+xMCBA3nssccYMWIEL7zwAqAml1u3bmXevHn079+fCy64gBdeeIHExEROnToF/C+pnjRpEr1792bmzJn88Y9/dDqPq0iLTQc0NMIHs0HL5/uzSc4pp9qayfTYUEz6c1Rfzt6ndjnVVqsDfyPHQNRY141x0WjAL1q9VZdBRiJk7ILKAjjyOZz8SU2Agoc0vhtMiHZQa6/llX2vOO4rikJtbS16vb7NKzMvHroYQwu+gLi5uVFQUOC4v337dry9vdm6des5n/fYY4/x7LPP8uyzz/LAAw+wYMECevfuzfLly4mKiuKWW27hrrvu4vPPPwdgw4YNLF26lJUrV3L55ZezceNGbrnlFiIjI5kwYYLjuCtWrOD//u//WLlyJXq9nnXr1rFixQpWrVrFxRdfzFtvvcW///1vevfu3WBsFRUVLFu2jGHDhlFeXs7DDz/MnDlzSEpKQtvM947CwkLWrVvHmDFjzrlfQkICiYmJ3HTTTc06z9nU1tZyww038NVXX/Htt98ybNgwx2PvvPMODz/8MC+88ALDhw9n9+7dLF68GA8PDxYuXOjY76GHHuLpp5+mb9++PPTQQ8yfP5+UlBT0+rN/pJeUlDBw4EDH/Z9//plly5Y57TN58uRzjmsqKSlBo9Hg6+t7zn38/f3PcwXaniQ2HVTfYC9Meh2f7s3kVGElH+3KYHZcOG5G5+RGY6uBw5sg96C6wTsU+k9Tu4Y6CpMX9B6vJlqZSZC2Qx3zc/gzOPUL9LoEegyQLiohmklRFLZv384XX3zB3Xff7dju4eHBq6++itF47i84N998M/PmzQPggQceYOzYsfz1r39l8uTJACxdupSbb77Zsf/TTz/NokWLuPPOO1EUhXvuuYfExESefvppp8RmwYIFTs+77rrruPXWWx3dOn//+9/Ztm1bvVab01199dVO919//XV69OjBwYMHGTJkyPkujcN//vMfXn31VRRFobKykn79+vHFF1/U2+/CCy9Eq9VSU1OD1Wrl9ttvr5fY7Nu3D09P56U5Gtva9soratK8Z88eBgwY4PTYI488wjPPPMNVV10FQK9evTh48CD//e9/nRKbP/7xj0ybNg2ARx99lMGDB5OSklLveADr1q1j586d/Pe//3Vsy87OJjg42Gm/4OBgsrOzzxqzxWLhgQceYP78+Xh7n33WbkpKCs8//7zLu6FAEpsOLSrAnatHRLAxKYPsEgvrEtKYMyIcb/Nv3+gq8vE9thGNp05tpel5iZo8dNQWEL0JosaoA5gzEtWkprIADmwEzyDodak6XVwSHOFCeq2exUMXO+4rioLFYsFsNrd5i41e27S35E2bNuHp6YnVasVut7NgwQJWrFjheHzo0KHnTWoAp1aDug+8oUOHOm2zWCyUlpbi7e3NoUOH6g1AvvDCC/n3v//ttG3kyJFO9w8dOsTvfvc7p21jx47l66+/bjC25ORkHn74YXbs2EF+fj52u9o1f+rUqSYlNtdffz0PPfQQADk5OTzxxBNMmjSJxMREvLz+t0TF2rVrGThwIFarlf3793P33Xfj5+fH//3f/zn26d+/v6PLr05GRgbjx48/bxwXX3wxSUlJ/PWvf+W9995ztLJUVFRw7Ngxbr31VhYv/t/rr7a2tt64o9P/v0JDQwHIzc2tl9h8/fXX3HzzzbzyyisMHjz4vLGdjdVqZd68eSiKwosvvnjWfTIyMpgyZQpz5851it1VJLHp4EJ8zMwbGclHu9IprKhh3c40rhoRgX/VKTQHNqKrLoGAaBg8B3wjXR1u4+gMEHUBhA2H9J1qC055Luz7AHzCIWaiOsNKCBfQaDRO3UGKomDT2TDoDG2e2DTVhAkTePHFFzEajYSFhdXrivDw8GjUcU4f1Fv3O55tW11S0ViNPf+5zJgxg+joaF555RXCwsKw2+0MGTKkybNvfHx8iImJASAmJobXXnuN0NBQ1q5dy2233ebYLzIy0rHfwIEDOXbsGH/9619ZsWIFZrMZwDFj6nQNdQOdaejQoTzzzDNMnDiRa6+9lrVr16LX6ykvLwfUFp0zu8h0OueW+sb833z77bfMmDGDf/3rX/VanEJCQsjJyXHalpOTQ0hIiNO2uqTm5MmTfPXVV2dtrcnMzGTChAlceOGFvPzyy425BG2ug361F6fz9zAyb1Qk/h5GyqqsfLt9E2UJ74OtGqtHKMqIRZ0nqTmd3qSOs7ngTjXR0emhJAMS31Cni1eXuTpCITo0Dw8PYmJiiIqKavQHa2sYOHAgP/74o9O2n376iUGDBp33eTt27HDa9ssvvzS4f0FBAUeOHOEvf/kLl19+OQMHDqSoqKj5gZ+mLlmoqqo67361tbWtOo05Li6O7du389133zFv3jysVivBwcGEhYVx/PhxYmJinG69evVq0vG/+eYbpk2bxj/+8Y+zTu0fO3Ys27dvd9q2detWxo4d67hfl9QkJyezbds2AgIC6h2nrpUqPj6e1atXN3vMU2uTFptOwttsYF58ODu2rsOUt5tDWg1RQy6kJKQfQcaWfytyKYMb9JkAESPh+DeQvV8dDJ13WJ1CHjFaTXqEEB3Cn/70J+bNm8fw4cO5/PLL2bBhAx999BHbtm075/OWLl3KokWLGDlyJBdddBHvvPMOBw4caHDwsJ+fHwEBAbz88suEhoZy6tQpHnzwwWbFXFlZ6RhDkpOTw2OPPYbZbGbSpElO+xUUFJCdnU1tbS379u3jueeeY8KECQ2OLWmu2NhYvvrqKy6//HLmzZvHunXrePTRR7nnnnvw8fFhypQpVFdXk5CQQFFRUb3Bvg35+uuvmT59OkuXLuXqq692/M5Go9ExsHfp0qWMGzeOZ555hmnTpvH++++TkJDgaHGxWq1cc8017Nq1i02bNmGz2RzH8ff3x2g0OpKa6Ohonn76afLy8hwxnNny097k06KzsNtwS9nExW4nOOpmYK8pnp+KBzHQVk1fV8fWWkxeMHAGhI2AlG1QmgnHv1UHHPe5DHr0l/E3QnQAs2fP5rnnnuPpp59m6dKl9OzZk9dff/28Y0yuvfZajh07xv3334/FYuHqq6/m97///VkH8QJotVref/997rnnHoYMGUL//v3597//3aixLGd65ZVXHAN3/fz8GDZsGJs3b3ZMg68zceJEQG2pCQ0N5corr3RMVW9tQ4cOdSQ3c+fOZd26dbi7u/PUU0/xpz/9CQ8PD4YOHdqkVaLfeOMNKisrefLJJ3nyyScd28eNG8c333wDqOOh3n33Xf7yl7/w5z//mb59+7Jx40bHmKWMjAzHGKIzFyP8+uuvGT9+PFu3biUlJYWUlBQiIiKc9mnR4rKtQKO4OoIuoq6kQklJSatn9tiscGADFBwDrY7afleyJc+fo9mlFBYWcs2FA4iLcv0Uu1alKOoif8e/Vks2gFr+od9kdaXkRrLZbCQnJ9O3b996/dRCro/FYiE1NZVevXo5xk+cqT0HD3dGcn3OT66R6lx/b0VFRfj7+7fKZ2jH6BATDautgX3r1aRGp4eh16APHcKVQ0IZEuaDosBXh3P5NbXQ5Vlyq9Jo1HpTo++AnhephTaLTsDOVyH1+6ZVIxdCCNFtSGLTkdlq1dV6i06qM4mGXasWrgS0Wg2XDejBkGA16/0xJZ/vkltYX6oj0hvVaeCjbgX/XuqKxSd+UBOcuuriQgghxG8ksemo7DY4uFFtpdAZIPY68I1y2kWj0TA8zJ1L+gYCsOtkEV8cyMFm72LJDajdT8OuVQtvmjzVmlR71qpr4MjsKSGEEL+RxKYjstvh0CeQn6x2wQydqxaRbMCIKD8mDw5Bq9FwKKuUTXszsTa2vlRnotFA0EC1DlXEKPV+7iH49WW1XENXa60SQgjRZJLYnGbOnDn4+flxzTXXuC4IRYEjmyH3sLqa8JCr1HpL5zEozJvpsaHotRqO51WwYXcGFmsXLTSpN0HfiRC/SC0hUVsDR7+ApHfUiuJCNFGX68IVogNqr78zSWxOs3TpUt58803XBaAo6jTn7H1qRexBsyCgT6Of3qeHJ3NGhGPUa8koquKDxHQqqrvwIFuvEBh+E/S9Qu2uK06Dna+ppRqauEKq6J7qVnCtrKx0cSRCdH11f2enr5zcFmQdm9OMHz/eMc/fJdJ2QHqC2sUyYJq6bksTRfi5M3dkBBt3Z5BXVs26hDSuGh6Bj3vbvpBcRqtVF/YLiIGjW6AwFY59rRYF7T8N3ANdHaHowHQ6Hb6+vuTm5gLg7u5ebzquoihUV1cDdOupug2R63N+3f0a1RUezc3NxdfXt82Xlugyic13333HU089RWJiIllZWWzYsIHZs2c77bNq1SqeeuopsrOziY2N5fnnn2f06NGuCfhMuYfUD2SAPperU52bKcirrr5UBsWVVtYmnGLO8Ah6eJlaKdgOyM1XHVycvQ+ObYeyHEhco47FsQe5OjrRgdWtklqX3JxJURRqa2vR6/Xd8kPpfOT6nJ9cI5Wvr2+7rErcZRKbiooKYmNjueWWWxwl30+3du1ali1bxksvvcSYMWNYuXIlkydP5siRIwQFufiDrzhNrY0EautD5KgWH9LXXa0vtWF3Bvll1axPTGNWXDjhvm4tPnaHpdFA6DB1SnzKVsg9jObUz/iW2yHEC/zPP1ZJdD8ajYbQ0FCCgoKwWq31HrfZbJw8eZLo6OhuuYjh+cj1OT+5Rmr3U3v97l0msZk6dSpTp05t8PFnn32WxYsXc/PNNwPw0ksv8dlnn/H66683q/ZIdXW1o2kR1JWHQX0B22xNGLRbWYhm73qw1UBAX5Re46GRz7fZbNjt9gbP56bXcFVcKJ/sySKrpIoPE9K4cmgIvQI7eW2p89G7wYCZENAf5egX6CxpsOstbBEj1TVx9F245aqJzvca6m7O1vdfV9ivPd+YOxO5Pucn10h1rveZ1nwP6jKJzbnU1NSQmJjI8uXLHdu0Wi0TJ07k559/btYxn3zySR599NF6248dO4anp2ejjqGpteB7bCO6mjKs7j0oMQyClGONjsFut1NYWEhKSso5q6oO9VIoyi8no9TKG1/nMzbKg97+3eHDXYviOw6l4CsozERTtBXbkZ8pD7sEq1fD0+e7k8a+hrozuUbnJtfn/OQanV9d40Br6BaJTX5+PjabjeDgYKftwcHBHD582HF/4sSJ7Nmzh4qKCiIiIli/fr1TGffTLV++3KnaamlpKZGRkfTp06dxdS7sNjT71oKXAcy9UYbf2OQq3TabjZSUFGJiYs77LaBfX4Vth3I4nF3G4XIIDutBXKRvk87XGdlsNlL0ZnwC9OiPbQVLMT3KdqB41kDv8d2+9aYpr6HuSq7Rucn1OT+5RudXVFTUasfqFolNY23btq3R+5pMJkym+h+KOp2ucS/cY9uhJF39YB02D9yaV/RLq9U26pw6HUwdGoabKY+kU8V8l1xAtU1hbO+ALj+YTavVogvsgzagJ6R+q848y94DxSdgwJVqcc1urLGvoe5MrtG5yfU5P7lG59aa16VbtIkFBgai0+nIyclx2p6Tk9PiEdqrVq1i0KBBjBrVhAG/mbshI1Ed7DpoFnj2aFEMjaXRaBjfrwcX9gkAYMfxQr4+kou9K5ZgOBu9UV3zJm4BmH3AUgJJ78HRL9VF/oQQQnR63SKxMRqNxMfHs337dsc2u93O9u3bG+xqaqwlS5Zw8OBBdu7c2bgnFKdB8lb1556XQGDfFp2/qTQaDWN6B3DZgCA0GtiTVsKWA9lds75UQ/yiYdRtED5CvZ+RCAmvqcVGhRBCdGpdpiuqvLyclJQUx/3U1FSSkpLw9/cnKiqKZcuWsXDhQkaOHMno0aNZuXIlFRUVjllS7cJSAgc+UgtcBg2A6Avb79xniI30xc2oY8v+bI5kl2Gx2pg+LAyjvlvkumrrTb/JENhPLWFRVQxJ76rT7XuNUx8XQgjR6XSZxCYhIYEJEyY47tcN7F24cCFr1qzh2muvJS8vj4cffpjs7Gzi4uLYsmVLvQHFbcZWCwc2QE0leAapq+K6eGxLv2AvTHotn+7J5GRBJR/tSmdWXDhuxm7UB+zfS229OfYVZCap428KjqkrP/tGujo6IYQQTdRlvp6PHz8eRVHq3dasWePY56677uLkyZNUV1ezY8cOxowZ0+LzNnqMzbHtUJoFBjMMubrDtAhEB3hwdXwEZoOOrBIL6xPTKLPUX6SsS9OboP9UdRC3yQuqitSCminbwNbNroUQQnRyXSaxcZVGjbHJ3gcZu9QWmoEz1eX/O5BQHzfmjYzAy6ynoLyGtTvTKKrohoNpA/qorTehw9SCpGk7IeF1KMlwdWRCCCEaSRKbtlaeqxZnBIi+qEnVuttTgKeJuSMj8XM3UGapZV1CGjmlFleH1f4MZrUbatg8MHlCZSHsfkvtqrJ14UrpQgjRRUhi05asFtj/kfqB6N8bel7s6ojOycfNwLxRkQR5m6issfFBYjpphZWuDss16lpvQoaorTendkDiaijNdHVkQgghzkESm7aiKHDkM3W8htkbBs5w+WDhxnA36rkmPoJIf3dqau1s2J1BSm6Zq8NyDYOb+v829BowekBFPux6C1K/U2e2CSGE6HAksWmhBgcPZ+yCvKOg1cHgOWB0d02AzWDS65gdF0ZMkCc2u8KmvVnszyhxdViuE9hXbb0JGgiKHU78CLveUBMdIYQQHYokNi101sHDZTnqLCiA3hPAO8w1wbWAXqdl2tBQhoT7oCiw9WAOCScKXR2W6xjdYfBsdaVog1n9P05YrXZR2e2ujk4IIcRvJLFpbbXVcHCj2lUR2Fdd8K2T0mo1TBwYxKie/gB8n5zPd0fzUJRutErxmYIHqa03AX3AXqsOKt7zrtrlKIQQwuW6zAJ9HUbKNnUmjdlbnV3TCcbVnItGo+HivoG4GbV8dzSfxJNFWKw2Jg4MRqvt3L9bs5m8YOhcyEqClO1qmYydr0HM5RAa1+n/z4UQoi1Y7VYstRbHrcpW5fg5tyC31c4jiU1ryz0Mnu7qejUGN1dH02rio/0x6XVsO5TDgcxSLLV2rhwSgl7XTRv9NBoIG65WBj/8mZrcHNkC+cnqYn8mL1dHKIQQbUZRFKpt1WqCUltFla2Kqtr/JSpVtVWOm6XWgsVmodbe8JIZFaUVrRabJDYttGrVKlatWoXNdtosmV6XdMnl+IeE+2A26Ph8XxbHcsvZsDuDGbFhmA3dqATDmdz8IHYBpO+E1G/Vcgw7X4V+U9TBxkII0QnYFTuWWguVtZVOyYnFZnFKUBz/2qqaNSxBo9HgpnPDrDc7bm46N6zm1lvlXRKbFlqyZAlLliyhtLQUHx8ftXJ0VMsqhndkMUGezB4ezid7MkkvquLDXenMGR6Ou7Ebv5S0Wogao65VdPhTdWDxgY2Qd0QttNmFWu6EEJ1DXbfP6QmJI1Gx1k9Yqm3VzTqPUWfErDPjpv9fsuKmd3PczLr/bTPrzRi1RjRn6a4vKmq9cYrd+NOojfSb0uXHWET6uzM3PoINuzPILa1m3c405oyIwMfN4OrQXMuzB4xYCCd/hJM/Q+4hKEmD/ld22BWnhRCdw+ktKlW1VVRaK526e868navbpyEaNJj0JkdC4khOTktM3HRuuBn+l7DotR0vjeh4EXV2Jk9XR9AugrzNzBsZyUe7MyiqtP6W3IQT6GlydWiupdVBr0shIAYObYLKAti7DsLioM/lHab4qRDCtRRFwWq3OhKRukSlLnE582apbXqJG61GWz85+S0hcde7OyUsddu1ms4/blISG9Fsfh5G5o2MYOPuDPLLa1ifkM6suDDCfKXrBe8wGHkzHP9WHX+TmQRFJ9SZcr5Rro5OCNEGbHabo4vn9BaV8ppyjhce52jqUart1VRZ1e02pWkrmGvQOJIRd4O7U5fP2W4GreGs3T5dnSQ2okW8zAbmjoxk4+4MskosfLQrnenDwugZ6OHq0FxPZ4C+EyEwRp05VVUMSe9CxCjoNQ508ucnREdnV+yORKWyttKpZeXMbQ2NU7Hb7RRWFuJf6o9W69wiYtAaHInI+ZKVrtKi0tbknbWFzjorqpsxG3RcNSKCz/ZlciK/kk/2ZDJ5cAj9Q2TKM6BOCR91m7rGUdZeSPsVCo+rdai8QlwdnRDdjqIo/+v2sVY5jVuprHVOViy1FhQaP/unbtaPm14di+Kud8ekNZFvy6dfZD88jB6Ox+paVUTrksSmherNiuqmjHotM2PD+eJANkeyy/h8fxYWq43YSF9Xh9Yx6E1qN1RgPziyWa0zlfgG9LwIoi5UZ1YJIZqtbl2VeknKGa0qdQlNU6Yqa9A4taa4G9xx17s7/j29tcWsM9fr/rHZbCRXJNPXvy86XTdeHqOdSGIjWo1Oq2HqkBDcDDqS0or56nAulTU2Lujt3y37ec8qsC943wZHv1Cng6d+DwUpMGAGeAS4OjohOpy62UAV1goqayupsFZQYa2gqrZK3WatdDxmV5pWt61uEK0jUfntZze92tJS1+IiXUCdiyQ2olVpNBrG9++B2aDjl+MF/HK8AIvVxvj+PSS5qWP0UCu+5xyA5C+hNAsSXofe49XaYnKdRDdgs9v+l5yc1rJSl7icvq0prStGnfGsrSlOCYzBHbPOjE4rrSddkSQ2otVpNBrG9gnAzajj68O5JKUVY7HamDQ4BF13rS91Jo0GQoaoM6SObIbCVHUMTkGyuu6Nm6+rIxSiWWrttf9LSk5rTTmzpaUpY1c0aP6XoBjc8dB7qP8aPOolLR1xXRXRvuQVINpMXKQvZoOWL/bncDi7DEutjWlDwzDqpUnXwewNw66FzF1qpfCik5DwGsRcASFDpfVGdBinD7gtrymnoraCipoKyqrLOJZ/jN3KbkdRw8bSaDSOpMRD7/G/ROW3JMXDoG5z07tJV5BotFZJbKxWK9nZ2VRWVtKjRw/8/f1b47CiCxgQ4o1Zr2PTXnXG1Ibd6cyKC+/e9aXOpNFAeDz49YLDm6AkQ50eXpCsrmRtlKnzom1Z7VZH60q5tZxKayXl1nJHK0vd7WxjWOx2O4WWQmqqahxTmbUarVNicnqi4mhpkbEroo00O7EpKyvj7bff5v333+fXX3+lpqYGRVHQaDREREQwadIkbr/9dkaNGtWa8XY4Mt37/HoGenDViAg+Tsoks9jC+gS1BIOnSRoMnbj7Q9wNkPYLnPgB8o5CSbraNRXY19XRiU6orpXlzATlzASmKXWC3PRujoTF0+CJWWemQClgYO+BeJm88DB4nHVmkBDtpVmfLM8++yyPP/44ffr0YcaMGfz5z38mLCwMNzc3CgsL2b9/P99//z2TJk1izJgxPP/88/Tt2zXfmGW6d+OE+boxd2QEG3apqxSv3ZnG1SPC8XWXEgNOtFqIvhD8+8ChT9Rp4fs+gNBYiLlcnTYuBM5JS5m1jIoaNVkpt5arXUW/JS+NnSmk1+odCYuHwUPtGjKq/3oaPR3dRWcOuLXZbCSXJhPlFSVTmUWH0KzEZufOnXz33XcMHjz4rI+PHj2aW265hZdeeonVq1fz/fffd9nERjReoKfpt/pS6RRXWlm7M405w8MJ8ja7OrSOxysY4m+G1N9KMmTtUUsyDJwuJRm6AUVRsNjUKc5lNWWOJKW8ptzRRVReU96oJflPH3jrafB0dAfV/Vx3M+lM0soiuoRmJTbvvfdeo/YzmUz87ne/a84pRBfl425g3shINuzOIK+smvWJ6cyMDSPS393VoXU8Or3aShPwW0kGS4lakiFyNPS8VEoydFJ1C8mdnqCc3tJSt70x1ZnrkhZPo6cjUfEyejm6iepaXGRas+hO5J1RtDsPk55r4iP4ZE8mGUVVbNydwZXDQunTo3tURm8yv2gYdev/SjKc2gEFx2DgTLVlR3QodsXuSFjKrGWU1ZQ5fi6vKaespgyr3dqoY50rafE0ekrSIsRZtFpis2PHDsaMGdNahxNdnNmgY87wcDbvy+J4XgWb9mQxcVAQg8NknNJZ1ZVkCOgLRz9Xx97segN6XgKRY6QkQzuy2q2OBOX0ZKWspszR8tKYBeXMerOaoPyWpNQlL6f/LGuyCNF0rfZXM3fuXE6dOtVahxPdgEGnZcawMLYeyuFgZilfHsjBYrURHy3LBTSoRz/wCYcjn0N+Mhz/Rp0WPmC6OqtKtEjdgNy6bqHSmlJKq0tJLkhmD3uoqK1o1DotWo3WkbB4Gb3wMnipPxu81FYXo4cUPxSijTQpsZk3b95ZtyuKQmFhYasEJLoXrVbDpEHBuBl0JJ4s4ruj+VTV2LkoJkAGMjbE6AFDrobsfZCyVV33JuF1dTxOaJws6nce1bZqSqtLKaspUxOXmlJHi8vZuonsdjuFVYX4V/o71mkx6oz/S1aMXngafktgfvvZ3eAu67MI4SJNSmy2bdvGW2+9haen81gIRVH47rvvWjUw0X1oNBou7dcDd6OO75Pz2XmikCqrjcsHBKGVEgxnp9FA6DB1htThz6D4FBzZorbi9J8KJi9XR+gyVpu1XsJS93NpTSk1tprzHuPMcSxF9iIG9RyEj5sPXkYvTDqZdi9ER9WkxGb8+PF4eXlx6aWX1nts2LBhrRaU6J5G9vTHbNCx7VAO+zNKsFhtTB0Sgl4n33wb5OYLcQvUKeHHv1UHFe98TV2xOGiAq6NrE7X2WqeE5cwEpjFdRW56N7yMXngbvR3/1v3safR0Gttis9lILk+mp09PWadFiE6gSYnNRx991OBjW7dubXEwnZGsPNy6hoT7YDZo2bwvm5TccjYmZTIjNhSTXj5QGqTRqFPA/XrB4U+hLAcObID8wdB3Ehg63zpBlloLJdUljsTF8XN1KRXWivMWTzTpTPUSFi+jF94mb7wMXhh0Mr5FiK6qRYOHs7OzCQkJaa1YOiVZebj1xQR5MWe4jk/2ZJJWWMmHiRnMHh6Gu1FmiJyTZw8YsVAtx3DqZ8g5oHZRDZgG/r1cHZ0Tu2Kn3FpOafUZictvP5+vu8igNTi1uNQlLXX3patIiO6rRZ8UkyZNYu/eva0VixAOkf7uXBMfwYbdGeSUWlifkM6cEeF4m+Wb9jlpddB7nLqo36FPoaoI9rwPESOh93hox5aKWnutI2E5M3Epqyk771L/HgYPR4tLXdLiY/LB2+iNm95NBpcLIc6qRYlNY9ZqEKK5gr3NagmGXekUVtSw7rcSDAGe8m38vHzCYeQtcPxryNgF6QlQmKqWZPAOa7XT2Ow2SmtKKa4upqS6RL3VlFBsKT5vl5FWo3W0utQlLN4mb3yMPnibvGU6tBCiWVqU2Mg3JtHW/D2MzBsVycbdGRSU17AuIZ3Zw8MI9XFzdWgdn94I/SarrTdHNkNlAex6Sy2yGX2h2rrTCDa7jbKaMjVhOT2B+a3l5VzJi1FndEpcTk9gPA2eMiVaCNHqZNCC6PC8zQbmxkeyMSmD7BILH+3KYPqwUKIDPFwdWucQ0AdG3QZHv4DcQ+oYnIIUtSSD2RdQW19La0opsajJS3F1MSU1JY4upHO1zhq0BnxMPo6br8kXH6P6s3QZCSHamyQ2olNwM+q4ekQEm/ZmcrKgko+TMpkyJIR+wd13vZYmMbjB4NlY/XtTfPgTigoOU/z9fgoCe5NcUcs3lm+w0/CYF71W70hWnBIYkw/uendJXoQQHUaLEhtZ00G0J6Ney8zYML44kMPRnDI278vCYrUxLMLX1aF1KIqiUG4tp9hSTFF1kaMFpshSRIW1Arw8ID8TqopQ0jKoqjWgdYtDb1IH6/qafB1JS10C42HwkORFCNEptCix2b17d2vFIUSj6HVapg4JwWzQsje9hO2HcqmqsTG6l3+3++Cttdc6EpbT/y2uLqbWXtvg88xmH/x6T8S3shCf7MNQUk7PCgu+kVegDRkqJRmEEJ1aixIbm83Gp59+yuWXX46Xl3QJiPah1Wq4bEAQbkYdO44X8tOxAqqsNsb169Elkxur3UqxpZhCSyFF1UUUWYootBRSWl3a4MBdjUaDj9EHP7OfowWm7mez/n8L9tnK8sj97nV8lVq0hz9Tx970mwJG9/b69YQQolW1uCtq/vz5HDhwQBIb0a40Gg0X9gnEbNDx7ZE8dp8qxmK1ccWgEHSdtL5Uja2GIksRRdVq4lJkUZOYc808MuqM+Jv9nRIXP5MfXkYvdI2Z9eTuT0nvGQSZCuDUT5B3BErSof+VEBjTyr+hEEK0vRYPHh41ahSpqan07t27NeIRoklGRPnhZtDx5YEcDmWVUV1r58qhoRg6cH0pq81KgaXAkbzU/VtuLW/wOWa9GT+TH/5mf/zMfviZ1Z9bZeCuRqtO/w6MgcOboCIf9q2HsDjoc7k6bVwIITqJFic2d999N3/+85/54IMPiIyMbI2YhGiSgaHemPRaPtubxfG8CjbsymBmXBhmg2sHt9sVO8XVxRRUqUlMoaWQgqoCSmtKG3yOu97dKXHxM/vhZ/LD3dAOXUPeoRC/CFK/hbSdkJkERSdgwHTwlb9tIUTn0OLE5tprrwVg8ODBzJw5k/HjxzN8+HCGDh2K0Sjf9ET76N3Dk6viI/g4KYOM4irWJ6YzZ3g4bvq275aqm4VUl7jUJTGFlsIGywa4693xd/N3JC/+JvXf08e/uITOADET1UX9Dn8GVcWQ9A5EjoGel4BOVogQQnRsLX6XSk1NZc+ePSQlJbFnzx6efPJJTpw4gV6vp3///l2+lpRU9+44wn3dmBsfyYbd6eSXVbNuZxqzYlu3SGtdN1JBVQH5VflqMmMpaLBoo0FrwN+sJjABbgGOn9ulBaYl/HrCyFshZRtk74NTv0DhMXVRP88gV0cnhBANanFio9VqmTlzJjNnznRsKysrIykpqcsnNSDVvTuaHl6m3+pLZVBSZWV9YgbDvBue+twQRVGorK0kvyrf6dbQTCSNRuMYA3N6EuNt9O68M7UMZrW2VGBfOPI5lOdB4hrodSlEjAZtxx3HJITovlqc2AwYMID77ruPBx98EHd39Vuol5cXl1xyCZdcckmLAxSiqXzd1fpSG3ZnkFdaxdaUMiKjq4gM8Dzr/ja7jeLqYvKr8tWWGIuaxFhqLWfd313vToBbAIFugY4kxtfki17bRbtpevQH73A4ugXyk+HY1+q08AHTwM3P1dEJIYSTFr8Tb926lT/84Q+89tprPP744yxatKgVwhKiZTxNeubGR7BxVzr7Cgr5aHcmM2LDiAwwObqR8irzyLfkU1hViE2p35WoQYOv2ZdAt0D1Zg4kwC2g43cjtQWTJwy5GrL3QvJWKE6Dna+p43FCY2VRPyFEh9HixObCCy9kx44dvPnmmzz00EM8//zzrFy5UlprhMvpdHYu6KflcHYaxytT+MePJYQH2Aj0qj+o3agzEmAOcLTEBJgD8Hfzx6A1uCDyDkqjUZMY3yh1YHFxmtpFVbeon+nsLWJCCNGeWq3t/KabbuKaa67h//7v/5g6dSpTpkzhqaeeolevXq11CiEaZLVZ1VaYqjzyKvPIq8qjyFKEzW4D9wK0djOV5TUk54JWE0BsaCRB7kGO1phOPRamvbn5QewCSN+pTg3PT/5tUb+pareVEEK4UKsPCpg0aRKlpaU8//zzfPbZZ9x99908/PDDeHrKtznROmrttRRUFZBbmaveqnIpthSfdVCvu8GdcDcTk3sO4WS+gZM5egyVbgQoAYwOCZBkprm0WogaA/694NCnUJ4L+z+CkCEQc4U68FgIIVygxYnNSy+9xM6dO9m5cyeHDh1Cq9UyZMgQfve73xEbG8v777/PoEGD+Oijjxg5cmRrxCy6EUVRKK4uJrcyl5zKHHIrc8mvyj/r+jAeBg96uPWgh3sPx79mrZnk5GT6hvblgnAtO08U8WNKPjtSC6my2pjQPwhtJy3B0CF4BsGIhXDyB3VKePZ+KD6lDiz26+nq6IQQ3VCLE5vHH3+cMWPGcNNNN3HBBRcQHx+Pm5ub4/Hbb7+dJ554gkWLFrF///6Wnk50cRXWCkcCU3c72xoxZr2ZIPcggt2D6eHWgyD3oLMO6j19fSGNRsPoXv6YDVq+OpzL3vQSqqw2pgwOQd+BSzB0eDo99B4P/n3UkgxVxZD0HkSMgt7j1EX/hBCinbQ4sUlLSzvvPrfeeit//etfW3oq0cXY7Dbyq/LJrswmpyKH7Irss9ZL0ml0BLkHOd1aMiZmWIQvZoOOLfuzSc4pp9qqzpgy6iW5aRHfSHVRv2NfQeZudQxOUapaksE71NXRCSG6iSYnNkVFRSiKgr+/P3l5eXz//ff079+fwYMHN/icoKAgvvrqqxYFKjq/SmslOZVqApNdkU1eVR61dufF8zRo8Df7qwmMh9oi42fya1yl6iboF+yFSa9l094sThVW8uGudGbHheNmdG19qU5Pb4T+U9RF/Q5/phbU3PUm9LwIoi6URf2EEG2uSYnNq6++yhNPPAHAn/70J9555x1iY2N55JFHWLp0KbfddttZn6fRaBg3blzLoxWdhqIoFFoKya7MdiQyJdUl9fYz6UyEeIQ4bkFuQRjaqesiOsCDq0dEsDEpg+wSC+sS0pgzIhxvs3SdtFhAHxh1GyR/AbmHIfV7dVr4wJng7u/q6IQQXViTEpt///vfHDhwgKqqKqKiokhNTaVHjx6UlJQwbty4BhMb0fVZbVanJCanMuesY2P8zH6EuP8vkfE1+bp0ZlKIj5m58RFs2J1BYUUN63amcdWICPw9pIBrixndYdBsCDwIR7+A0ixIeA16XwbhI2RRPyFEm2hSYqPX63Fzc8PNzY2YmBh69OgBgI+Pj0yb7WZqbDVkVWSRWZ5JVkUWOZU5KIrzdGuD1kCwRzDB7sGEeIQQ7B7s+urVZxHgaVJLMOz6LblJSGPO8HCCvTterJ2ORgPBg8EnUu2aKjoByV9CQTL0vxLM3q6OUAjRxTQpsdHpdFgsFsxmM99++61je3l5/QGfomupqq0iqyKLrPIsMisyya/Mr7dujKfBk1DPUEI9QgnxCMHf7I9W0znGVHibDcwdGcHG3ZnklFr4IDGdmbFhRPp3w/IJbcHsDbHXQcYuOP4VFKbCzleh32Q18RFCiFbSpMRm27ZtmEwmAKdK1pWVlbz88sutG5lwqUprJZnlmWRWZJJVnkWBpaDePj4mH0I9QgnzDCPMMwwvg1enbrlzN+q5Oj6cT/dkkVZYyYbdGVw5NISYIC9Xh9Y1aDQQEa+ub3P4U7Vr6uAn6srF/SaDwe28hxBCiPNpUmJzejJzuqCgIIKCglolIOEalloLmeWZpJenk16WTnF1cb19/Mx+hHmEEeoZSphHGJ7GrreatEmvY3ZcGJ/vzyYlt5xNe7OYONDOkPCzv/ZFM3gEwPCb4NRPcOJHyD0EJWlq11RAH1dHJ4To5Fq0jk12djYhISGtFYvLbdq0ifvuuw+73c4DDzzQpQdDW+1WsiuySS9LJ708vV7XkgYNAW4BjhaZUI/QblPVWq/TMm1oKF8dzmVfRglbD+ZQZbUxMtqvU7dIdShaLfS8WF3U79CnUFkAe9dB2HDoc5k6bVwIIZqhRYnNpEmT2Lt3b2vF4lK1tbUsW7aMr7/+Gh8fH+Lj45kzZw4BAQGuDq1V2BU7uZW5ZJRnkF6WTnZFNjbF5rSPn9mPcM9wIrwiCPMI65ADfduLVqvh8oFBuBl1/JpayA/J+VTW2Li0b6AkN63JOxRG3gzHv1UX9MvcrQ4wHjgdfCJcHZ0QohNqUWJz5iyYzuzXX39l8ODBhIeHAzB16lS+/PJL5s+f7+LImkdRFEqqS0grSyO9PJ2M8ox60689DB5EeEUQ4RlBhFcEHgYPF0XbMWk0Gi6KCcRs0PLd0Xx2nSzCYrVxxcBgqS/VmnQG6DtR7YY6/BlUFcHutyHqAuh5CbTy4oxCiK6tRYlNR/rm+t133/HUU0+RmJhIVlYWGzZsYPbs2U77rFq1iqeeeors7GxiY2N5/vnnGT16NACZmZmOpAYgPDycjIyM9vwVWsxqs5JRnsGpslOcKj1FaU2p0+NGndGRxIR7hrt8DZnOIj7aH7NBx7aDuRzMLMVitXHl0FAMUl+qdfn3Uhf1S9mqFtM8+TMUHocBM8Czh6ujE0J0Ei2uFdVRVFRUEBsbyy233MJVV11V7/G1a9eybNkyXnrpJcaMGcPKlSuZPHkyR44c6bQDnxVFocRawp68PWRUZJBRnuFU9Vqr0RLqEUqkVyQRXhEEugV2munXHc3gMB/MBh2b92ZxPK+CDbszmBkbhtkgrQmtymCGgTMgoC8c3QJlOZC4BnpdCpGjZVE/IcR5dZnEZurUqUydOrXBx5999lkWL17MzTffDMBLL73EZ599xuuvv86DDz5IWFiYUwtNRkaGozXnbKqrq6murnbcLy1VW0dsNptTRenWdnqrzMmSk5zMOYl/jb+j5cXL6EWUVxRRXlGEe4Y7lSdQ7Ao22i62jshms2G321vl/6SnvxuzYkP5ZG8m6YUVrN95illxYXiYOu+fUWten1YV0BfiQ9Ec2QKFKZCyDfKPovSfBub2naHWYa9RByHX5/zkGp1fa16bFr0j63Sd49tqTU0NiYmJLF++3LFNq9UyceJEfv75ZwBGjx7N/v37ycjIwMfHh88///ycFcmffPJJHn300Xrbjx07hqdn606DrqitINOSSWZVJnk1eY5WGUVRqLZUY6gwEOoWSqg5FC+dF5oqDdYqKydyT7RqHJ2R3W6nsLCQlJQUtK1UgHGEby3bj5dRUKCQkZ3D5X288DJ1jr+FM7XF9WlVpmGYzEY8s3agKUjCfuIAFaFjqfbt126tNx3+GrmYXJ/zk2t0fnWNA62hRYnN7t27WyuONpWfn4/NZiM4ONhpe3BwMIcPHwbUchHPPPMMEyZMwG63c//9959zRtTy5ctZtmyZ435paSmRkZH06dMHb++WLROvKAp5VXmcLD3JidIT5NfkgxbwAF8PX7xN3mqLjHs4VdlVDOg3oNMkme3NZrORkpJCTExMq16j/n1r2LA7k1KLlV3FembHhRHoaWq147eXtro+rasfVF2K5sgmKEknsGo/uFej9JsCxrYf8N45rpHryPU5P7lG51dUVNRqx2pxG/pPP/2Et7c3Q4YMaY14XGrmzJnMnDmzUfuaTCbHKsyn0+l0zXrh1tprySzP5ETpCVJLUqmwVvzvmFodIR4h9PLpRU/vnviafQH1jyU5P7nZ5+wutFptq1+jAC83rhsTzYZd6eSX1/Dh7kxmx4UT5tv5Vs9ti+vT6jwDYPiNkLYDTnwPhcdg12roNxV69Gvz03eKa+RCcn3OT67RubXmdWlxYrNkyRLuuuuueonNsWPHCAoKwsvL9cvRBwYGotPpyMnJcdqek5PT4gUGV61axapVq5rVP1htq+ZEyQlOlJ4grSzNaTq2QWsg0iuSXj69iPKOwk3f+T4wuzpPk565IyP5OCmDzGILH+1KZ9qwMHoFyrT5NqHVQvRYdVr4oU+gPA/2fwihwyBmIug7X4uZEKL1tTixOXLkCOPHj6+3fdu2bXz66ads2rSppadoMaPRSHx8PNu3b3dMAbfb7Wzfvp277rqrRcdesmQJS5YsobS0tMGSE6ertlWTWpLKseJjpJWlOc1i8jB40NO7Jz19ehLuGY5e23kHpXYXZoOOOcMj2Lwvi9T8Cj5JymTykGAGhEjV6jbjGQQjFqktN2k7IGsvFJ2EAdPAL9rV0QkhXKzFn5ze3t5n7Ru75JJLeOihh1p6+EYrLy8nJSXFcT81NZWkpCT8/f2Jiopi2bJlLFy4kJEjRzJ69GhWrlxJRUWFY5ZUW7LUWtRkpuQY6WXpTsmMn9mP3j696endkyD3IFlXphMy6rXMiA3jywPZHM4u4/N92VTV2Bge5efq0LounR76TICAGDi8CaqKYc97EDEKeo1THxdCdEst/uufMmUKTz/9NO+//77Tdq1WS01NTQPPan0JCQlMmDDBcb9uYO/ChQtZs2YN1157LXl5eTz88MNkZ2cTFxfHli1b6g0obi1VtVWOlpn08nSnVZr9zf708e1DH98++Jv92+T8on3ptBqmDAnBbNSRdKqYb47kUWW1MbZ3gCSrbck3EkbeAse+gswkSPtVXdRv4Azw6jp17IQQjdfixOaxxx5j9OjRXH311axYsYKhQ4disVj4xz/+wbBhw1ojxkYZP378eUs83HXXXS3uejrTmWNskguTyczLrJfMBJgD6OPbh96+vSWZ6aI0Gg3j+/XAzaDj52MF7DheiMVqY0J/aYlrU3oT9J+qrn1zZDNU5MOuN9Uim5EXqGNzhBDdRosTm8jISH755Rd+//vfExsbi8lkora2Fh8fHz799NPWiLFDO3OMzTfp3+DmqQ70DXQLVFtmfPo4ZjKJrk2j0XBB7wDcDDq+PpLLnrQSLFY7kweHoJP6Um0rMAa8b1VXLM47qhbWLEiBAdPBXb5MCNFdtEpHdHR0NJs3b+bUqVPs3r0bo9HImDFj8Pfvfm8m3iZv4kLi6OvbV5KZbiw20hezQccXB7I5kl1Gda2NaUPDMOql9aBNGT1g8FWQsx+Sv4SSDEh4DfpcBmEjpCSDEN1Aq42wy8jIQKfTMWvWrNY6ZKc0r9+8Rs2OEl1f/xAvTHotm/ZmciK/ko92pTN7eLjUl2prGg2EDAXfKLVaeNFJOPol5KfAgCvB5PolKIQQbafFXx9//PFHevXqRVRUFFFRUQQHB/PAAw+06vLInYmMpRCn6xnowdXxEZgNOrJKLKxPSKPMYnV1WN2D2Qdi56tr3Gj16qDina9C7iFXRyaEaEMtTmzuuOMOBg4cyM6dOzly5AhPPfUU27ZtY8SIEU5FJbuqVatWMWjQIEaNGuXqUEQHFerjxtyREXia9OSX17AuIZ2iivabMditaTQQOQpG3qzOkrJa4MBGOPgxWKtcHZ0Qog20OLE5duwYK1euZMSIEcTExHDTTTeRkJDA8OHDuffee1shxI5tyZIlHDx4kJ07d7o6FNGBBXqamDcqEj93A6VVVtYlpJFbanF1WN2HRyCMuAl6XgQaLeQchJ2vqa04QogupcWJzcCBA8nNzXXaptFo+Nvf/saWLVtaenghugwfNwPzRkUS5G2issbG+sR00gorXR1W96HVQa9LYcSN6iyp6jLYs1Ydf2OT7kEhuooWJzaLFi3i7rvvJi0tzWl7SUlJi6tcC9HVuBv1XBMfQYSfGzW1djbuziAlt9zVYXUv3mHqon7h8er9jERIeB1KM10blxCiVbR4VlRdd1Pfvn256qqriIuLw2az8fbbb/PPf/6zpYcXossx6XXMGR7O5v3ZHMstZ9PeTCYODGZIuMymazc6A/SbpK59c3gzVBbCrrfUIpvRF6mtO0KITqnFiU1WVhZJSUkkJSWxZ88e1qxZQ3JyMhqNhn/+8598/vnnDBs2jGHDhjFlypTWiLlDaUl1b9F96XVapg8NZduhHA5klrL1YA4Wq42RPbvf2k8u5d8bRt2qrnmTcxBO/AgFx9SSDB6Bro5OCNEMGuV8dQiawWKxsG/fPkeyk5SUxP79+ykuLm7tU3UYdSsPt2cXnM1mIzk5mb59+6LTyTfMs+no10hRFH5IySfhhFpIdmRPPy6OCWy3ZQM6+vVpV7mH1FWLrRZ1enjv8RAxEpvdLtfoHOQ1dH5yjc6vqKgIf3//VvkMbXaLzYcffshjjz1GUlISAA8++CD9+/cnNjaWwYMHM2rUKJkCLcR5aDQaLumr1pf6PllNcCxWO5cPCEIrJRjaV9BA8IlQu6YKj0PKNihIhr5TXR2ZEKIJmp3YrF69mkWLFjnu13XHWCwWdDodAwcO5LvvvsPX17cVwhSiaxvZ0x+zQce2QznszyjBYrUxdUgIep2UYGhXJi8YNg8yd6kVw4tOokl8HZOhLygxro5OCNEIzX7XPHDgAJMmTXLatm/fPo4fP85HH32EwWDgpZdeanGAQnQXQ8J9mD4sDL1WQ0puORuTMqmulbFb7U6jUWdMjbxVnUFVa8Er/Vs0BzdCjUzPF6Kja3Zik5WV5VQTSafTodFo6NmzJzNmzOBPf/pTt6juLURrignyZPbwcIx6LWmFlXyQmE5lTa2rw+qe3P1h+I0oPS9F0Wgg/4hakiE/xdWRCSHOodmJTWBgICdOnHDcz87OJjo62nE/Li6OgwcPtii4zkBKKojWFunvztz4CNyNOnJLq1m3M42SKllAziW0Woi+kOI+s8E9EGoqYN96OPI51EpZDCE6omYnNpdddhmvvfaa477ZbHYa7a3VarFau/6bsZRUEG0hyNvMvJGReJn1FFVaWZ+QRn55tavD6rZsboEo8YvUulMaDWQmQcJrUJx2vqcKIdpZsxObP/3pT7z77rs899xzZ338xx9/pHfv3s0OTIjuzs/DyLWjIgnwNFJmqWV9QjpZJVK40WW0erVSeOx8MHtDVTEkvQPHvgabdBcK0VE0O7EZOnQob7/9Nn/605+YOHEiH374IadOnSIzM5N169axfPlyrr/++taMVYhux8tsYN7ISEJ9zFisNj5MTOdEfoWrw+re/KLVgcUhQ0FR4NQvsGsNlOee96lCiLbXormk11xzDTt27KC2tpa5c+fSq1cvIiMjue666xgzZgzLli1rrTiF6LbMBh1XjYigZ6A7VpvCJ3syOZJd5uqwujeDGQZOhyFXgcENyvMgcY2a5Njtro5OiG6txSUVhg8fzjfffMOpU6fYt28fZWVlDB48mKFDh7ZGfEIIwKjXMjM2nC8OZHMku4zP92dhsdqIjfR1dWjdW4/+4B2urlicn6x2SxWkwIBp4Obn6uiE6JZanNjUiYqKIioqqrUOJ4Q4g06rYcrgEMwGLXvSSvjqcC5VVhtjevm3WwkGcRYmTxhyNWTvheSt6oDina+p43FCY9XBxkKIdtOsrqhTp041af+MjIzmnKZTkOneoj1ptRom9A9iTG+1WObPxwr45mgebVDyTTSFRqMmMaNuBd9IsFnVKeH7P4TqcldHJ0S30qzEZtSoUdxxxx3nnOJcUlLCK6+8wpAhQ/jwww+bHWBHJ9O9RXvTaDRc2CeQ8f17AJB0qpgvDmRjs0ty43JufhC7APpcBlqd2j2181XIO+LqyIToNprVFXXw4EEef/xxrrjiCsxmM/Hx8YSFhWE2mykqKuLgwYMcOHCAESNG8M9//pMrr7yyteMWotsbHuWH2aDjywM5HMoqw2K1M21YKAapL+VaWi1EjQH/XnDoU3W21P6P1FlUMRPVgcdCiDbTrHfAgIAAnn32WbKysnjhhRfo27cv+fn5JCcnA3D99deTmJjIzz//LEmNEG1oYKg3M+PCMOg0pOZX8NGudCxWqS/VIXgGwYiFED1W7arK3qcu6ld0wtWRCdGltWjwsJubG9dccw3XXHNNa8UjhGiiXoEezBkRwcdJGWQWW1ifkMacERF4mlptboBoLp0eeo8H/z5weNNvi/q9p65g3Gu8+rgQolW1epv16WUVhBDtI9zXjbnxkXia9OSX17BuZxrFlVLLqMPwjVQX9QuLU++n7YTE1VCW7dKwhOiKWj2xOXN2xq5du1r7FEKIs+jhZWLeyEh83Q2UVFlZl5BGbpnF1WGJOnoj9J8KQ+eC0QMq8iHxDTjxoyzqJ0QranRis23bNi644ALGjRvHtm3bAMjKymL16tXMnz/fsd+Z62mMHj263grEmzdvbknMQogG+LirJRh6eJmoqLaxPiGd9KJKV4clThcYA6NuUxf3U+yQ+h3sfgsqC10dmRBdQqMTm7vuuov77ruPZ599lg0bNnDzzTfTv39/tm3bxsyZMxt83tChQ/H29ubmm292bPvLX/7SsqiFEA3yMOm5Jj6CcD83amrtbNiVwbE8WUulQzG6w+A5MHAG6E1QmqkOLM5IVOtPCSGardEj19zc3Jg7dy4AcXFx9OjRg4MHDxIREXHO52k0GlasWMHKlSu55ppreO+992QxMSHamNmgY87wcDbvy+J4XgWb9mRxxaBgBoV5uzo0UUejgZAh6vibw59B0Uk4+iXkp8CAK8Hk5eoIheiUGt1ik5eXx9q1a9m1axdVVVX07NnzvEkNgLe3+kZ67733MmPGDGbOnElVVVXzI+5gZOVh0VEZdFpmDAtjUJg3dkXhiwPZJJ4scnVY4kxmH4idD32vAK0eCo+ri/rlHHR1ZEJ0So1ObO677z6+/PJLfv/73xMWFsaBAweYNWsWjzzyCBs2bKi3/7FjxwD45ptvHNsWLlzI7bffTm5ubssj7yBk5WHRkWm1GiYNCmZEtFqQ8bujefyYki+tph2NRgMRI2HkzeAVAlYLHPxYvVm7zhdBIdpDo7uiZs6cyR/+8AfH/dTUVPbv38/+/fv54IMPmDNnjtP+v/vd70hJSSEkJIRhw4Y5bpdddhmFhTJIToj2otFouLRvIO5GHT8k5/NraiFVNTYuGxDk6tDEmTwCYcRNcPIn9ZZzEIpPqdXC/Xu7OjohOoVGJzYNJSp33nknPj4+9fbfunUrAE888QQ7d+4kIyODTz75hO3bt9OzZ09SUlJa77cQQpyTRqNhVE9/zHod2w/nsC+jBEutjSsG9HB1aOJMWh30ugQC+qglGSoLYc9aCI9XF/vTG10doRAdWqMTm+YmKuvWrSMpKclx/8svv+Ttt99uWdRCiGYZGuGD2aDl8/3ZJOeUU1VTS3836ZbqkLzDYOQtcOxrdbZURiIUpcKA6eAT7urohOiwmryed1MTFbPZzMGDBxk0aBAAkyZNYvny5U2PVAjRKvoGe2E26PhkTyZphZWkVZXRu7cNTzdZNbzD0Rmg3yR17ZvDm9XWm91vq/Wnoi9SW3eEEE6avPJwXaJSZ9KkSRw4cKDB/V977TWuvfZa7r77bl577TXuvffeeov4CSHaV6S/O9fER2A26CiorGV9YjqlFqurwxIN8e8No26F4EHqon4nfoRdb6irFwshnDQ5sWlqojJ48GASExO55JJLOHHiBNHR0Xz++ectCloI0XLB3mbmxkfgYdRSVKnWlyoor3Z1WKIhBjcYNAsGzwaDGcpyIGG1WndKZrkJ4dDkrqi6RGXjxo3s27eP6OhoHnroIcfjZ5tGajQamTdvHvPmzWtZtEKIVuXvYWRyXy/2lhoprlJbbmbHhRPiY3Z1aKIhQQPBJwKOfA4FxyBlGxQkqzOnzPUncgjR3TQ5sYFzJyp2KeYmRKfiYdQxNz6CT/dlk11i4cNd6cwYFkZUgLurQxMNMXmpxTQzd8Ox7eqqxTtfhb6TIHiIui6OEN1Uq1f3FkJ0Pm5GHVeNCCfK352aWjsbkzJIzilzdVjiXDQaCB8BI29VZ1DV1sChTXDgI6iRwqei+5LERggBgEmvY1ZcGH2DPbHZFT7bl8Xe9GJXhyXOx90fht8IvceBRgt5R9XWm3xZK0x0T5LYCCEc9DotVw4JZViED4oC2w/l8mtqoZRg6Oi0Woi+EOIXqqsX11TAvvXqFPFaGRAuuhdJbIQQTrRaDZcNCGJML38AfkzJ57tkqS/VKXiFQPzNEDla7arK2gMJr0NxmqsjE6LdSGLTQlLdW3RFGo2GC2MCGddfLbmw62QRXxzIwWaX5KbD0+kh5nK1YrjZB6qKIekdOPYV2GpdHZ0QbU4SmxaS6t6iKxsR5cfkwSFoNRoOZZWyaW8mVpvMfOwU/KLVRf1Chqrr3JzaAbvWQHmuqyMTok1JYiOEOKdBYd7MiA1Fr9VwPK+CDbszsFhtrg5LNIbeBAOnw5CrwegO5XmQuAZO/QKyNIfooiSxEUKcV+8enswZEY7JoCWjqIoPEtOpqJZujU6jRz8YdRsE9gW7TS2smfQOVBW5OjIhWp0kNkKIRonwU+tLeZh05JVVsy4hjZJKqS/VaRg91JabAVeC3ggl6bDzNchMkpIMokuRxEYI0WhBXmbmjYzEx81AcaWVtQmnyCuT6cSdhkYDobHqon6+kWCzqqUZ9n0A1eWujk6IViGJjRCiSXzdjcwbFUmgl4mKahvrE9PIKK5ydViiKdx8IXYB9LkMtDooSFEX9cs74urIhGgxSWyEEE3madIzNz6CcF83qq12NuxK53iefOPvVLRaiBqjrnvjGQTWKtj/ERz6FKwWV0cnRLNJYiOEaBazQcecEeH07uGB1abw6Z4sDmWVujos0VSePSB+EUSPVbuqsvdDwmtQdMLVkQnRLJLYCCGazaDTMn1YGANDvbArClv2Z7P7lMy06XS0Oug9HobfAG5+YCmFpPcgeZs6DkeITkQSGyFEi+i0GiYPDmF4lC8A3xzJ46djUoKhU/KJgJG3QNhw9X76TnXdm9Isl4YlRFNIYiOEaDGNRsO4fj24sE8AADuOF/LV4VzsUoKh89Ebof8UGDZPnSJekQ+73oQTP8iifqJTkMRGCNEqNBoNY3oHcPnAIDQa2Jtewuf7s6W+VGcV0Edd1K9Hf1DskPo97H4LKgtdHZkQ5ySJjRCiVQ2L8OXKoaHotBqO5pTxcVIGNbXyTb9TMrrD4DkwcIZanqE0Ux1YnJEoi/qJDksSGyFEq+sX7MWsuDCMei0nCyr5aFc6VTVSX6pT0mggZIhaUNOvp1oh/OiXsHetOshYiA5GEhshRJuIDvDgqhHhmA06skosrE9Mo8wiM2w6LbMPxF4Hfa8ArR4KU9XWm9yDro5MCCeS2Agh2kyojxvzRkbgZdZTUF7D2p1pFFbUuDos0VwaDUSMVGdOeYWA1YLm0Cd4pW1XF/gTogOQxOY0c+bMwc/Pj2uuucbVoQjRZQR4mpg7MhI/dwNlllrWJaSRUyor23ZqHgEw4iboeTFotJiKj6NJeA0Kjrk6MiEksTnd0qVLefPNN10dhhBdjo+bgXmjIgn2NlNVY+ODxHTSCitdHZZoCa0Oel2CEncDtSZfqCmHvevg6BdQK61ywnUksTnN+PHj8fLycnUYQnRJ7kY9V8eHE+nvTk2tnQ27M0jJLXN1WKKlvMMojpmDEh6v3s/YBYmroSTDtXGJbqvTJDbfffcdM2bMICwsDI1Gw8aNG+vts2rVKnr27InZbGbMmDH8+uuv7R+oEKJBJr2O2XFhxAR5YrMrbNqbxf6MEleHJVpKq4eYK9TBxSYvda2b3W/B8W/BLrPhRPvqNIlNRUUFsbGxrFq16qyPr127lmXLlvHII4+wa9cuYmNjmTx5Mrm5uY594uLiGDJkSL1bZmZme/0aQnR7ep2WaUNDGRLug6LA1oM5JJyQRd+6BP9e6rTw4MHqOjcnf4Jdb6irFwvRTvSuDqCxpk6dytSpUxt8/Nlnn2Xx4sXcfPPNALz00kt89tlnvP766zz44IMAJCUltVo81dXVVFdXO+6XlqrrOdhsNmy29vmGYrPZsNvt7Xa+zkiu0bm58vpM6BeASQcJJ4v47mgu5RYrF8cEoNFo2j2Wc5HX0LnVuz5aI/SfBn690SR/qdaZ2vkaSq9LIXyUOrOqm5HX0Pm15rXpNInNudTU1JCYmMjy5csd27RaLRMnTuTnn39uk3M++eSTPProo/W2Hzt2DE9PzzY555nsdjuFhYWkpKSg1Xaaxrd2Jdfo3Fx9fYKAnmYLiRmVbC0oJPVUOmMi3dF2oA8/V1+jjq7h66NH6zcOz4zvMZalQd4H1Hj+RHn4OOzG9nmP7CjkNXR+dY0DraFLJDb5+fnYbDaCg4OdtgcHB3P48OFGH2fixIns2bOHiooKIiIiWL9+PWPHjj3rvsuXL2fZsmWO+6WlpURGRtKnTx+8vb2b94s0kc1mIyUlhZiYGHQ6Xbucs7ORa3RuHeH69O0LfTNL2X44lyJF4ajFkymDgzHoOsYHQEe4Rh3Zea/PwFjISkJz7CuwW6DoG5SYiRA8pNu03shr6PyKiopa7VhdIrFpLdu2bWv0viaTCZPJVG+7Tqdr1xeuVqtt93N2NnKNzq0jXJ+hkX64mQx8vi+L1PxKPt2bzYzYMMyGjvF/1hGuUUd23usTORICesPhTepsqaOfQ9Ex6DdFrSDeDchr6Nxa87p0jK9ELRQYGIhOpyMnJ8dpe05ODiEhIW167lWrVjFo0CBGjRrVpucRoquLCfJk9vBwjHot6UVVfJCYTkV1ravDEq3F3R/iboDe49Q1cPKOws5XIT/Z1ZGJLqZLJDZGo5H4+Hi2b9/u2Ga329m+fXuDXUmtZcmSJRw8eJCdO3e26XmE6A4i/d2ZGx+Bu1FHXlk16xLSKKmS+lJdhlYL0RfCiIXgEQg1lbDvAzi8GWqrz/98IRqh0yQ25eXlJCUlOWY2paamkpSUxKlTpwBYtmwZr7zyCm+88QaHDh3i97//PRUVFY5ZUkKIziHI28y8kZF4uxkorrSybmca+eXyodeleAVD/M0QOVodZ5O1BxJeh+JTro5MdAGdZoxNQkICEyZMcNyvG7i7cOFC1qxZw7XXXkteXh4PP/ww2dnZxMXFsWXLlnoDioUQHZ+fh5FrR0WyYVc6+eU1rE9IZ1ZcGGG+bq4OTbQWnR5iLoeAGDj8GVQVQ9K7arLT81L1cSGaodO02IwfPx5FUerd1qxZ49jnrrvu4uTJk1RXV7Njxw7GjBnT5nHJGBsh2oanSc/ckZGE+ZqxWG18tCudE/kVrg5LtDa/aHVRv9Bh6qJ+p3bArjVQlnPepwpxNp0msemoZIyNEG3HbNAxZ3gEPQPdsdoUPk7K5HB26613IToIvQkGTIMhV4PRHcrz1BWLT/4MdruroxOdjCQ2QogOzajXMjM2nAEhXtgVhS37s0lKK3Z1WKIt9OgHo26DwL5qjanj30DSO1DVemuciK5PEhshRIen02qYMiSEuEhfFAW+PpzLz8cKUBTF1aGJ1mb0UFtuBkwDvRFK0mHna5C5W+2qEuI8JLERQnQKGo2G8f17cEHvAAB+OV7AN0fyJLnpijQadczNyFvBNwpsVjiyRZ0aXl3u6uhEByeJTQvJ4GEh2o9Go2FsnwAmDAhCo4GktGK27M/GZpfkpkty84W4BdDnMnVRv4IUdVG/3MaXyhHdjyQ2LSSDh4Vof3GRvkwdEopWo+Fwdhmf7MmgplYGmXZJGg1EjVHXvfEMAmsVHNgAhz4Fq8XV0YkOSBIbIUSn1D/Ei1lxYRh0Gk7kV7JhdzoWq83VYYm24tkD4hdB9Fg12cneDwmvQdEJV0cmOhhJbIQQnVbPQA+uGhGB2aAjs9jC+oQ0yixSgqHL0uqg93gYfgO4+YGlFJLeg+Rt6jgcIZDERgjRyYX5ujF3ZASeJj355TWsS0inqKLG1WGJtuQTASNvgbDh6v30nZC4BkqzXBqW6BgksWkhGTwshOsFepqYNyoSX3cDpVVW1iWkkVsq4y+6NL0R+k+BYfPUKeIV+bDrTTjxgyzq181JYtNCMnhYiI7Bx83AvJGRBHmbqKyxsT4xnbTCSleHJdpaQB91Ub+gAaDYIfV72P0mVBS4OjLhIpLYCCG6DA+TnqtHRBDh50ZNrZ2NuzM4lifrnnR5RncYNBsGzVTLM5RmQeLrkJ4oi/p1Q5LYCCG6FLW+VDh9gjyptSts2pPFgcwSV4cl2ppGA8GD1dYbv55gq4XkL2HvWnWQseg2JLERQnQ5ep2W6UNDGRzmjV1R+PJADoknC10dlmgPZm+IvQ76TgKdHgpT1UX9cg64OjLRTiSxEUJ0SVqthisGBTOypx8A3x3N54fkfCnB0B1oNBARD/G3gHco1FbDwU/gwEZ1gT/RpUli00IyK0qIjkuj0XBJ3x5c0jcQgJ0nCtl2KBe7lGDoHjwCYPiN0PNi0Ggh95DaelNwzNWRiTYkiU0LyawoITq+kT39uWJQMBoN7M8o4bN9WdTaZEpwt6DVQa9LYMRN4B6gFtHcu04tqlkr6x11RZLYCCG6hSHhPkwfFopOqyElt5yNSZlU10oJhm7DOxRG3gwRI9X7mbsh4XUoyXBtXKLVSWIjhOg2YoK8mDM8HKNeS1phJR8mZlBZU+vqsER70Rmg7xXq4GKTF1QVwe634Pi3YJckt6uQxEYI0a1E+rtzTXwEbkYdOaUW1u1Mo1TqS3Uv/r3UaeHBg9V1bk7+BLvegPI8V0cmWoEkNkKIbifY28y8kZF4mfUUVVpZtzONgvJqV4cl2pPBrC7oN3iO+nNZjlpvKu1XWdSvk5PERgjRLfl7GLl2VCQBnkbKLLWsS0gnq0SmAnc7QQPU1puAPmCvhZTtkPQuVBW7OjLRTJLYtJBM9xai8/IyG5gbH0mojxmL1cZHuzI4WVDh6rBEezN5wdC5alFNnQGKT0HCa5C1V1pvOiFJbFpIpnsL0bm5GXVcNSKC6AB3amrtfJyUydGcMleHJdqbRgNhw2HkLeATrk4FP/wZHPgIaiTZ7UwksRFCdHtGvZZZceH0D/HCZlfYvC+LPWnFrg5LuIK7P8TdAL3Hq2vg5B1VF/XLT3Z1ZKKRJLERQghAp9UwZXAIsZE+KAp8dTiXHccLpARDd6TVQvRYGLEQPAKhphL2faC24NTKIPOOThIbIYT4jVarYUL/IMb09gfgp2MFfCf1pbovr2CIvxkiR6tdVVl7Yedr6hgc0WFJYiOEEKfRaDRc2CeQ8f17AJCUVsyPpyqwSX2p7kmnh5jLIW4BmH3AUqLOmkrZDjZZ3LEjksRGCCHOYniUH1OGhKDVaEgtrOGzfVlYpb5U9+UbBaNuhdBYdaZU2q+QuFpd/0Z0KJLYCCFEAwaGejN9WCh6rYbU/Ao27MrAYpWl97stvQkGXAlDrwGjO1TkqysWn/wZ7JL0dhSS2AghxDn0CvTg8j6emPQ6MoqrWJ+YTnm1dEF0a4F91UX9AvuqNaaOfwNJb0NloasjE0hiI4QQ5xXkaeCa+HA8TDryy6pZtzON4soaV4clXMnoAUOuhgHTQG9Uq4QnvK5WDZfB5i4liU0LycrDQnQPgZ4mrh0Zha+7gZIqK+sS0sgts7g6LOFKGg2EDoORt6pjcGxWOLIF9q2Halnk0VUksWkhWXlYiO7Dx93AvJGR9PAyUVFt44PEdNKLKl0dlnA1N1911lTM5aDVQ8ExdVp47mFXR9YtSWIjhBBN4GHSc018BOF+blRb7WzYlcHxvHJXhyVcTaNR17uJXwSeQWCtggMb4OAnUCste+1JEhshhGgis0HHnOHh9O7hQa1d4dM9WRzMLHV1WKIj8OyhJjfRF6rJTs4BNAmvYSjPcHVk3YYkNkII0QwGnZbpw8IYGOqNXVH44kA2u04VuTos0RFoddB7HAy/Adz8oLoMn9TNkLJVHYcj2pQkNkII0Uw6rYbJg4MZEe0HwLdH8vgpRUowiN/4RMDIW1DCRgCgyUiEhNVQmuXiwLo2SWyEEKIFNBoNl/YN5KKYQAB2pBby1eFc7FKCQYA6FbzvJEp6TgGjJ1QWwK434cQP6ho4otVJYiOEEC2k0WgY3cufiQOD0Whgb3oJm/dnUSslGMRvrF6RKCNvgaABoNgh9XvY/RZUFLg6tC5HEhshhGglQyN8mDY0FJ1WQ3JOOR8nZVJdK9/KxW8M7jBoNgyaqZZnKM2CxNchPVEW9WtFktgIIUQr6hvsxey4cIx6LacKK/loVwZVNZLciN9oNBA8WC3J4N9LrRCe/CXseR8sMrOuNUhiI4QQrSwqwJ2rR0TgZtSRXWJhXUIapRaZDSNOY/aGYddC30mg00PRCdj5KmTvl9abFpLERggh2kCIj5l5IyPxMusprKhh3c40CiukvpQ4jUYDEfEQfwt4h0JtNRz6FA5uhBpZ0bq5JLERQog24u9hZN6oSPw9jJRZalmXkEZ2iaxCK87gEQDDb4Jel4BGq5ZiSHhNLc0gmkwSGyGEaEPeZrW+VIiPmaoaGx/uSudUgXwbF2fQaqHnxTDiJnAPgOpy2LtOLapZKy19TSGJTQtJdW8hxPm4GXVcNSKcKH93amrtbEzKIDlHqj+Ls/AOhZE3Q8RvnymZuyHhdShJd21cnYgkNi0k1b2FEI1h0uuYFRdG32BPbHaFz/ZlsS+9xNVhiY5IZ4C+EyH2OjB5QVUR7H4bjn8ji/o1giQ2QgjRTvQ6LVcOCWVouA+KAtsO/X97dx4T1b32Afx7ZoYZdmTYBi6LLC5Ftiso5bZB6lBB+xq325suaXGJTVs0IkkXmlhjYqLRf6zRdElv9E3fopYq9bb39SpRoW97qctwp26Va1ErCiMKZXGQRea8f5w6vcgyqDCHOfP9JJMwZ05mHh4f9cmc3+88N3HqagtHMNDg9LHStnBDkrRT6pdqwLQbuHNL7sjGNTY2REROpFIJMD4RipmxegDAd5du49tLnC9FQ/DwBJ6YD0xbBHh4AXeapObm2gluCx8CGxsiIicTBAFPJQQje3IIAKDml19x5MJN9HG+FA0ldCowYwUQFA/Y7gF1xwBzKXC3Ve7Ixh02NkREMkmPCUTeNANUgoALDe345kwDejlfioai8wOSnwem5EvrcFqvSdvCG3/ktzf/gY0NEZGMEiP88V+p4dCoBFy+ZUX5v26gq5cLRGkIggBE/BHIWA4EREpbwS/+L3BuP9BjlTu6cYGNDRGRzOJDfLFoujRf6savd/Gl6Tqs3ffkDovGM289kPYyEJcDqNTA7UvSSIZb/5Y7MtmxsSEiGgciA73xfEYkfHRq3Oroxhen69HWyflSNAyVCojJAqYXAL4h0hiGc/uBi3+XxjO4KTY2RETjRKifNF8qwMsDrZ29+OJ0PW51uO9/UDRCfmHA9KVAdKZ0qarxDHDqr9IaHDfExoaIaByZ4C3Nlwr20+FO9z2UmerR0HpX7rBovFNrgPjZQNpLgGcA0NUm7Zr6+SjQ516XNdnYEBGNM746DZ5Pj0TEBE9099pwoOY6rtzmwlAagQnR0rbw8FRpp1T9ScC0C+i4KXdkTsPGhohoHPL0UGPx9EjEBvugt0/E38wNuGhplzsscgUaHTB1HpD8Z0DrDVhvAzX/DfzyT8Cm/NsJsLEhIhqnPNQqzE+NwBPhfrCJIg6dteBf136VOyxyFcGTpJEMIZOlGVOXqwDz/wCdLXJHNqbY2BARjWNqlYC8aQakRU8AAFTW3sI/6ziCgUZI6wNMWwxMfQ7QaIG2G9K08Bs1ir2pHxsbIqJxThAE5EwOwZ/igwAAJy634HhtE2wcwUAjIQhAeAqQsUJag9PXC/z7MHC2DOjukDu6UcfGhojIBQiCgMy4IMyeGgpBAH6sb8M/zls4X4pGzmuCtGsqwQioNEBznXRTv6af5I5sVLGx+U19fT1ycnKQmJiIlJQUlJWVyR0SEdEAqVETMC85HGqVgFpLBw6ab6DnnvIXhNIoEQQgaiaQvlS6/01vF3D+K+DC36SfFYCNzW80Gg22bduGCxcu4MiRIygqKoLVyu2VRDT+TA7zw4K0CHioBfzS3IkDNddxt4fzpegh+IZIdyyO+ZPU7Nw8L31703JF7sgeGxub34SHhyMtLQ0AYDAYEBwcjJYWZa8cJyLXFRPkgyXpkfD0UKOxrQtlpnp0dHEEAz0ElRqImwX88RXAK1Bab/PjXuBShbQOx0W5TGPz7bffYv78+YiIiIAgCPjqq68GnLNz505MnDgRnp6eyMzMxMmTJx/ps0wmE/r6+hAVFfWYURMRjZ3wAC/8JSMSfp4aNN/pwRenr+NXa4/cYZGrCfiDNC38D9Ol59dPA6d3Ae0N8sb1iFymsbFarUhNTcXOnTsHfX3fvn0oLi7G+vXrUVNTg9TUVOTl5aGpqcl+TlpaGpKSkgY8Ghp+/8NraWnBq6++ik8++WTMfycioscV5KvD8xlRCPT2QPtdab5UU7sy1kqQE2m0wOQ8IOUvgM4X6GwGaj4DrvyfdA8cFyKILngzBEEQUF5ejoULF9qPZWZmYsaMGdixYwcAwGazISoqCqtXr8a77747ovft7u7Gs88+i5UrV+KVV15xeG539+/D6dra2hAdHY2rV6/C39//4X+pR9DX14fLly8jLi4OarXaKZ/papij4TE/jrlKjjp77uHvZxtxu6MHHhoV8qeFITLQe8w/11XyIyeXy1HvXaDuGITbtdJz3zCIk+cC3vox+8jW1lbExcWhtbUVAQEBj/VemlGKSVY9PT0wmUwoKSmxH1OpVMjNzUV1dfWI3kMURSxduhSzZ8922NQAwKZNm7Bhw4YBxydOnDjiuImIxsrbcgdA9Aiam5vZ2ADA7du30dfXh7CwsH7Hw8LCcPHixRG9x/fff499+/YhJSXFvn7ns88+Q3Jy8qDnl5SUoLi42P7cZrOhpaUFQUFBEATh0X6Rh9Te3o6oqCjU19c77VsiV8McDY/5cYw5Gh7z4xhz5Nj9qx56/eN/K6SIxmY0PP3007A9xHAwnU4HnU7X79iECRNGOaqR8ff3518WB5ij4TE/jjFHw2N+HGOOHFOpHn/pr8ssHh5OcHAw1Go1bt7sP5b95s2bMBgMMkVFREREzqaIxkar1SI9PR1Hjx61H7PZbDh69CiysrJkjIyIiIicyWUuRd25cwc///yz/fmVK1dgNpuh1+sRHR2N4uJiFBQUICMjAzNnzsS2bdtgtVqxbNkyGaMeWzqdDuvXrx9wSYx+xxwNj/lxjDkaHvPjGHPk2GjmyGW2e1dWVuKZZ54ZcLygoAC7d+8GAOzYsQNbt26FxWJBWloatm/fjszMTCdHSkRERHJxmcaGiIiIyBFFrLEhIiIiAtjYEBERkYKwsSEiIiLFYGPjAhxNNhdFEe+//z7Cw8Ph5eWF3NxcXLp0SZ5gZeAoP0uXLoUgCP0e+fn58gQrg02bNmHGjBnw8/NDaGgoFi5ciNra2n7ndHV1obCwEEFBQfD19cWSJUsG3BdKyUaSo5ycnAF19Prrr8sUsfN9+OGHSElJsd9kLisrC4cOHbK/7u415Cg/7l4/g9m8eTMEQUBRUZH92GjUERsbF+BosvmWLVuwfft2fPTRRzhx4gR8fHyQl5eHri73mPDrKD8AkJ+fj8bGRvtjz549ToxQXlVVVSgsLMQPP/yAiooK9Pb2Ys6cObBarfZz1q5di6+//hplZWWoqqpCQ0MDFi9eLGPUzjWSHAHAypUr+9XRli1bZIrY+SIjI7F582aYTCacPn0as2fPxoIFC3D+/HkArCFH+QHcu34edOrUKXz88cdISUnpd3xU6kgklwJALC8vtz+32WyiwWAQt27daj/W2toq6nQ6cc+ePTJEKK8H8yOKolhQUCAuWLBAlnjGo6amJhGAWFVVJYqiVC8eHh5iWVmZ/ZyffvpJBCBWV1fLFaasHsyRKIrirFmzxDVr1sgX1DgUGBgofvrpp6yhIdzPjyiyfv5TR0eHOGnSJLGioqJfXkarjviNjYu7cuUKLBYLcnNz7ccCAgKQmZk54snm7qCyshKhoaGYMmUK3njjDTQ3N8sdkmza2toAwD5szmQyobe3t18NTZ06FdHR0W5bQw/m6L7PP/8cwcHBSEpKQklJCTo7O+UIT3Z9fX3Yu3cvrFYrsrKyWEMPeDA/97F+JIWFhXjuuef61Qswev8Wucydh2lwFosFAAadbH7/NXeXn5+PxYsXIzY2FnV1dXjvvfcwd+5cVFdXQ61Wyx2eU9lsNhQVFeGpp55CUlISAKmGtFrtgCGu7lpDg+UIAF566SXExMQgIiICZ86cwTvvvIPa2locOHBAxmid6+zZs8jKykJXVxd8fX1RXl6OxMREmM1m1hCGzg/A+rlv7969qKmpwalTpwa8Nlr/FrGxIcV74YUX7D8nJycjJSUF8fHxqKyshNFolDEy5yssLMS5c+fw3XffyR3KuDVUjl577TX7z8nJyQgPD4fRaERdXR3i4+OdHaYspkyZArPZjLa2Nnz55ZcoKChAVVWV3GGNG0PlJzExkfUDoL6+HmvWrEFFRQU8PT3H7HN4KcrF3Z9ezsnmIxcXF4fg4OB+s8fcwapVq/DNN9/g+PHjiIyMtB83GAzo6elBa2trv/PdsYaGytFg7o9rcac60mq1SEhIQHp6OjZt2oTU1FR88MEHrKHfDJWfwbhj/ZhMJjQ1NWH69OnQaDTQaDSoqqrC9u3bodFoEBYWNip1xMbGxcXGxsJgMPSbbN7e3o4TJ05wsvkQrl+/jubmZoSHh8sdilOIoohVq1ahvLwcx44dQ2xsbL/X09PT4eHh0a+Gamtrce3aNbepIUc5GozZbAYAt6mjwdhsNnR3d7OGhnA/P4Nxx/oxGo04e/YszGaz/ZGRkYGXX37Z/vNo1BEvRbkAR5PNi4qKsHHjRkyaNAmxsbFYt24dIiIisHDhQvmCdqLh8qPX67FhwwYsWbIEBoMBdXV1ePvtt5GQkIC8vDwZo3aewsJClJaW4uDBg/Dz87Nfqw4ICICXlxcCAgKwYsUKFBcXQ6/Xw9/fH6tXr0ZWVhaefPJJmaN3Dkc5qqurQ2lpKebNm4egoCCcOXMGa9euRXZ29oDtqkpVUlKCuXPnIjo6Gh0dHSgtLUVlZSUOHz7MGsLw+WH9SPz8/PqtWwMAHx8fBAUF2Y+PSh2N7iYuGgvHjx8XAQx4FBQUiKIobflet26dGBYWJup0OtFoNIq1tbXyBu1Ew+Wns7NTnDNnjhgSEiJ6eHiIMTEx4sqVK0WLxSJ32E4zWG4AiLt27bKfc/fuXfHNN98UAwMDRW9vb3HRokViY2OjfEE7maMcXbt2TczOzhb1er2o0+nEhIQE8a233hLb2trkDdyJli9fLsbExIharVYMCQkRjUajeOTIEfvr7l5Dw+WH9TO0B7fBj0Ydcbo3ERERKQbX2BAREZFisLEhIiIixWBjQ0RERIrBxoaIiIgUg40NERERKQYbGyIiIlIMNjZERESkGGxsiIiISDHY2BAREZFisLEhIiIixWBjQ0RERIrBxoaIFOvq1asQBGHAIycnR+7QiGiMaOQOgIhorERFRaGxsdH+3GKxIDc3F9nZ2TJGRURjidO9icgtdHV1IScnByEhITh48CBUKn5hTaRE/MaGiNzC8uXL0dHRgYqKCjY1RArGxoaIFG/jxo04fPgwTp48CT8/P7nDIaIxxEtRRKRo+/fvx4svvohDhw7BaDTKHQ4RjTE2NkSkWOfOnUNmZiaKi4tRWFhoP67VaqHX62WMjIjGChsbIlKs3bt3Y9myZQOOz5o1C5WVlc4PiIjGHBsbIiIiUgxuDSAiIiLFYGNDREREisHGhoiIiBSDjQ0REREpBhsbIiIiUgw2NkRERKQYbGyIiIhIMdjYEBERkWKwsSEiIiLFYGNDREREisHGhoiIiBTj/wEcW6pMwb4lpQAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# normalization factor is different\n", "# plot the merger rate density (source frame)\n", "# factor 1e9 is to convert to Gpc^-3 yr^-1 from Mpc^-3 yr^-1\n", "plt.figure(figsize=(6,4))\n", "plt.plot(z, rate1_src*1e9, color='C0', linestyle='-', alpha=0.5, label=\"BBH popI/II Oguri\")\n", "plt.plot(z, rate3_src*1e9, color='C1', linestyle='-', alpha=0.5, label=\"Pop III Ken2022\")\n", "plt.plot(z, rate4_src*1e9, color='C2', linestyle='-', alpha=0.5, label=\"Primordial BBH Ken2022\")\n", "# labels\n", "plt.xlabel(\"z\")\n", "plt.ylabel(r\"$\\frac{dR}{dz} (Gpc^{-3} yr^{-1})$\")\n", "plt.yscale(\"log\")\n", "plt.xlim(8, 40)\n", "plt.ylim(1e-2, 1e2)\n", "plt.legend()\n", "plt.grid(alpha=0.5)\n", "plt.title(\"Merger rate density (source frame)\")\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Merger rate density (detector frame)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the pdf of zs (detector frame)\n", "plt.figure(figsize=(6,4))\n", "plt.plot(z, rate2_det, color='C0', linestyle='-', alpha=0.5, label=\"SFR Madau & Dickinson\")\n", "plt.plot(z, rate1_det, color='C1', linestyle='-', alpha=0.5, label=\"BBH popI/II Oguri2018\")\n", "plt.plot(z, rate3_det, color='C2', linestyle='-', alpha=0.5, label=\"Pop III Ken2022\")\n", "plt.plot(z, rate4_det, color='C3', linestyle='-', alpha=0.5, label=\"Primordial BH Ken2022\")\n", "# labels\n", "plt.xlabel(\"z\")\n", "plt.ylabel(r\"pdf\")\n", "#plt.yscale(\"log\")\n", "plt.xlim(0, 15)\n", "plt.legend()\n", "plt.grid(alpha=0.5)\n", "plt.title(\"Merger rate density (detector frame)\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* You can see there is a delay in the BBH pop I/II merger peak compared to the SFR peak. This is due to the delay in the formation of BBHs compared to the formation of stars. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion\n", "\n", "* The merger rate density of binary black hole (BBH) mergers from Population III (Pop. III) stars, primordial black holes (PBHs), and Population I/II (Pop. I/II) stars is a topic of active research. All three models suggest that BBH mergers are a common occurrence in the universe, but there is still a significant range of uncertainty in the merger rate density and mass spectrum of BBH mergers from each channel. Future observations of gravitational waves from merging BBHs will help to constrain these uncertainties and provide valuable insights into the formation and evolution of black holes and binary star systems.\n", "\n", "* In particular, Einstein Telescope and Cosmic explorer, next-generation gravitational wave detectors (3G), are expected to detect a significant number of BBH mergers from all three channels. This will provide a wealth of new information about the formation and evolution of black holes and binary star systems." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bonus plot\n", "\n", "* Star formation rate source frame (SFR) vs redshift" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(4,4))\n", "plt.plot(z, rate2_src, color='C0', linestyle='-', alpha=0.5, label=\"SFR Madau & Dickinson\")\n", "# labels\n", "plt.xlabel(\"z\")\n", "plt.ylabel(r\"P(z)\")\n", "plt.xlim(0, 5)\n", "plt.legend()\n", "plt.grid(alpha=0.5)\n", "plt.title(\"Star formation rate (source frame)\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "ler", "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": "3.10.14" } }, "nbformat": 4, "nbformat_minor": 2 }