{ "cells": [ { "cell_type": "markdown", "id": "a9f0d445", "metadata": {}, "source": [ "## gwModelRemS : remnant properties of non-precessing quasi-circular BBH mergers\n", "\n", "`gwModelRemS` predicts five remnant quantities from the mass ratio and the two\n", "aligned spins $(q, \\chi_{1z}, \\chi_{2z})$:\n", "\n", "| Quantity | Function | Units |\n", "|---|---|---|\n", "| Final mass $M_f/M$ | `gwModelRemS_mf` | dimensionless |\n", "| Final spin $\\chi_{f,z}$ | `gwModelRemS_chif` | dimensionless, signed |\n", "| Peak luminosity $L_{\\rm peak}$ | `gwModelRemS_Lpeak` | geometric, $c^5/G$ |\n", "| Peak GW frequency $M\\omega_{\\rm peak}$ | `gwModelRemS_omega_peak` | dimensionless |\n", "| Recoil $v_{\\rm kick}$ | `gwModelRemS_kick` | km/s |\n", "\n", "`gwModelRemS(q, chi1z, chi2z)` returns all five at once. The model is calibrated\n", "to NR (SXS, RIT, Maya) and BHPT simulations over $1 \\le q \\lesssim 1000$ and\n", "$|\\chi_{iz}| \\le 1$.\n", "\n", "---\n", "\n", "**Reference:** Islam, Wadekar & Khanna (2026), [arXiv:2608.00934](https://arxiv.org/abs/2608.00934)" ] }, { "cell_type": "code", "execution_count": 1, "id": "1616423b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lal.MSUN_SI != Msun\n" ] } ], "source": [ "import sys\n", "!{sys.executable} -m pip install -e ../ --no-deps --quiet\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import time\n", "import warnings\n", "warnings.filterwarnings(\"ignore\", \"Wswiglal-redir-stdio\")\n", "\n", "import gwModels\n", "gwModels.utils.set_rcparams()" ] }, { "cell_type": "markdown", "id": "ce9447ee", "metadata": {}, "source": [ "### 1. Basic evaluation" ] }, { "cell_type": "code", "execution_count": 2, "id": "ca0b04fd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "q = 3.0, chi1z = 0.5, chi2z = -0.2\n", " Mf/M = 0.961276\n", " chi_f,z = 0.749482\n", " L_peak [c^5/G] = 6.988052e-04\n", " M omega_peak = 0.373187\n", " v_kick [km/s] = 73.039\n" ] } ], "source": [ "q, chi1z, chi2z = 3.0, 0.5, -0.2\n", "\n", "Mf, chif, Lpeak, wpeak, vkick = gwModels.remnants.gwModelRemS(q, chi1z, chi2z)\n", "\n", "print(f'q = {q}, chi1z = {chi1z}, chi2z = {chi2z}')\n", "print(f' Mf/M = {Mf:.6f}')\n", "print(f' chi_f,z = {chif:.6f}')\n", "print(f' L_peak [c^5/G] = {Lpeak:.6e}')\n", "print(f' M omega_peak = {wpeak:.6f}')\n", "print(f' v_kick [km/s] = {vkick:.3f}')" ] }, { "cell_type": "code", "execution_count": 3, "id": "358d39f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " q = 1.0 : Mf/M = 0.943877 chi_f = 0.760850\n", " q = 2.0 : Mf/M = 0.949876 chi_f = 0.778639\n", " q = 4.0 : Mf/M = 0.968283 chi_f = 0.729315\n", " q = 10.0 : Mf/M = 0.987226 chi_f = 0.636518\n", " q = 100.0 : Mf/M = 0.999090 chi_f = 0.518992\n", " q = 1000.0 : Mf/M = 0.999917 chi_f = 0.501976\n" ] } ], "source": [ "# Individual quantities, and full vectorization over any input\n", "q_arr = np.array([1.0, 2.0, 4.0, 10.0, 100.0, 1000.0])\n", "\n", "Mf = gwModels.remnants.gwModelRemS_mf(q_arr, 0.5, 0.0)\n", "chif = gwModels.remnants.gwModelRemS_chif(q_arr, 0.5, 0.0)\n", "\n", "for qi, mi, ci in zip(q_arr, Mf, chif):\n", " print(f' q = {qi:7.1f} : Mf/M = {mi:.6f} chi_f = {ci:.6f}')" ] }, { "cell_type": "markdown", "id": "06b0ecf8", "metadata": {}, "source": [ "### 2. Behaviour across the mass-ratio range\n", "\n", "The model interpolates smoothly between the equal-mass and point-particle regimes. As $q \\to \\infty$ the remnant retains essentially all the mass and the spin approaches the primary's." ] }, { "cell_type": "code", "execution_count": 4, "id": "d90a65bc", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "q_plot = np.logspace(0, 3, 600)\n", "\n", "plt.figure(figsize=(8, 5))\n", "for chi1z, chi2z, label in [\n", " (0.0, 0.0, r'$[\\chi_1,\\chi_2]=[0,0]$'),\n", " (0.5, 0.0, r'$[\\chi_1,\\chi_2]=[0.5,0]$'),\n", " (-0.5, 0.5, r'$[\\chi_1,\\chi_2]=[-0.5,0.5]$'),\n", " (0.8, 0.8, r'$[\\chi_1,\\chi_2]=[0.8,0.8]$'),\n", "]:\n", " Mf = gwModels.remnants.gwModelRemS_mf(q_plot, chi1z, chi2z)\n", " plt.semilogx(q_plot, Mf, lw=2, label=label)\n", "\n", "plt.xlabel('$q$')\n", "plt.ylabel('$M_f/M$')\n", "plt.legend(frameon=False)\n", "plt.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "id": "800e6b36", "metadata": {}, "outputs": [ { "data": { "image/png": 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/x6SAoPpfovIwUFUM1JYDNaVAjWzLtFIn82dLf8w6bWuVbUOzqZqxQEq4QzEDEbFAZDwQGadtoxoeRycBselAVII2YIaIiIiIOpVhg38xbdq0Ft109IHArmb6kSDf1WBhSSbk7n/IkOC9eDdQtEvbSik/BFTkAeX52rZSkisf97UzR2pJQFxaw1ZKJpCUBST1aCg9ted4F4qIiIgoNIJ/6acvd/gd5/qXufsd5++XLkCycq+8Rp/NR7r4NF8FWF63dOnS4FvhV+7AF+0E8n4F8n8D8rcCh7dpgX5VgK5rYKkFyvZrpa0kIbEhIUjtC6T1bywpfYDwKF9dMREREZEhGDr4l7v4EqxLEjBmzBh1Rz8tLa1Jn33pFrRu3bom3YMkEZC+/TKvvz42QN5n+MC/thI4+DOw/0etHNoMHP4dsNR4fq7waO1ue3yGto1J0brj2It010nUuvCYIxq79ajHUkwNsxPUNy3SPUi6CtVWaN2I9K10Jaoq0roYVRRo28oC7T2tJQlFuVrZuarpczJvcHIvLRFIPwLIHAJ0GQJkDAYiYz3/PoiIiIiCQJjN2QSg5HS0dFJSkpruzF+z/chMQ5mZmdrgDfnPJnfwd60G9q0H9m/U7u7bLG2fTAJjuWMuwXFyb22b0rBN6AbEZQRGv3v5GauLtWRAuiOV7gNK9gAlex3KPqBGm4LOPWFaK4FKBoZqpfsIrRuRv39e8l39ISK3sf4QGbcOOYtfDX3nP6RYLQg//CuQ+x6wezWw6zvt7nhrwsxAWjaQMaihDAQyB2t3w43QJUaCcWlxkJLe3/XrZDBy4Q6gIAco2O5QcoDasmYvtmmvlfLbx42HZfyAJAGOJbGb1340IiIiIn9g8B/o5O73gssQlrsS6TLTTmuBvgT23YcD3Udqwavc1TZCkN9RMclA1kitNP/upMVAWkTyfgEO/QLkbQHyfgPqm82FK4nU9qVa0UkriHyPPUYDvY7XHkf4f3EOIiIiovZi8G+Eu99lBxHWPPCPSgJ6Hw/0PgHoeSzQ9Uj2ZXf23SV01Ur2yS0HQcuYCH2MxL4NLQdAlx0Atkr5VNuXsQySXMn33es4oOdx2pgIIiIiIoNg8G8EvcfCVrQTNV1HIXLAyTD1Haf1WZc588lzpobuUFKGnNfYSiAzIOmDpVXZ2HQ8gaxhsHetVr57QTuWmq0lAtIy0PdEbZYhIiIiogDFAb9GGPBbWwmrOQp5+fkccOVLMltRYQ6w+3tgz/fA7jVAwe+tv0cGTfc5Cegr5UQgsbuvrpZawQGLRO3H+kPUMRzwS56T7jwSiJJvSQVNH6CVkZdrxyoOA3vWNCQEa7QWAplyVCetBxv/qxUhg6slEehzolbYTYiIiIj8iME/kSdkteFBZ2lF1FVrCcDOb4Dcr4E9PzRdV0GfeWjdv7X9zKHa+IPsU1R3Lg4gJiIiIl9i8E/UERHRDQOvjwfG36klA3t/AHJXAbkrgX3rmi5UpmYb2qKNGZCF1GTAdv+JQPZEbSpWrjVAREREXsTgn6izkwHV3/8kAPdoKxfLeAE9GTiwEbA1dOGqrwZyvtSKkIXXpEVAkoF+E7T1DYiIiIg6EYN/Im+Kigf6T9KKqCzUugdtl6B/ubZqsU4e//iGVmQV5qxR2vuOOA3oerQ2BoGIiIioAxj8E/lSbCow9A9akYm28rdqd/4lGdi1WmsNENI6oE8ruuJxIL4LMGAycMTpWqtAVIK/fxIiIiIyIAb/RP4i/fszB2nl+OuBuipg17dai4AkA/m/Nr5WVir+8b9akcXG+pygJQIDTtXWKyAiIiJyA4N/okAhM/9If38ppz0KlOwDfv9CKztWAHWVjYuNyb6Uz+7WphPVEwFZbCw80t8/CREREQUoBv9EgSopCxh9lVZkFiGZTnTbZ8Dvn2vrCehkKlGZPUhKZII2laieDHBdASIiInLA4J/IKLMIDZikFds/gPzfgG2fa60CsuCYzaK9rrYM+PVDrSAM6HkMMPAMYOBZ2mJlnEqUiIgopDH4JzLkWIHBWhl3C1BVpI0R0LsIyb5i01YhlrLsASA1uyEROBPoeSxgZvUnIiIKNfzXn8joZD2AI6doxWoB9q4Dti0Bti7RWgh0hTmN3YPkPQNOAwadqa0twNmDiIiIQgKDf6JgYjIDvY7VyqQHgIIcbZyAJAIyk5DePUhaBza9rRVzpLYombQKHHGGNtaAiIiIghKDf6JgJtOAyjSiUmSBsd+XAls/1boJyfgAYakFti/Tyie3A92Ga12DJBnoeiTHCRAREQURBv9EobTA2NEXaaW+Rps9SFoEpJTubXzdgY1aWfEYkNijYZzAGUCfEzmNKBERkcEx+DeA7Xkl2HJ4C7qgO6rDKxEVYUaE2aRKXKQZ4WaTvy+RjCY8qnFNgTP/ARzc1JAIfAoc+KnxdZIUrJ2vFZlGVGYbklaB/pO0ZIKIiIgMhcG/AVz/0UvYH/4W6kqORk3eGbDVJzd5PiEqHIkxEUiO1UpqXBS6J0eje1IMuifHoFtSNHqkxCA5lndtyQnp1tPtaK1MuBso2dvYIpC7UltUTEg3oS3vaSXMDPQe29g9KLWvv38KIiIickOYzWazufPCUFdaWoqkpCSUlJQgMTHRZ59bUlOC8f87DZawCrVvs4ajtuAk1BaMB2xRHp0rLS4S2ZnxGJAZj/5qm4Ch3ROREsekgFyoLgVylmuJgCwuZp9GtJmMwcDA07UBwz1GawOPA4jVakVeXh4yMzNhMrGljMgTrD9Exq1DzuJXBv8BHvzXW+tx26dzsbrgTdSirHHNJySjm/VCRFWPRkllPUqq6lBcWYd6q+f/OXumxuCorGQc1SMJR/VIxtE9kxAbyUYhasZSD+z5XksEfvsEKMp1/rrYNG11YVllWKYRjfZdfXGFwQtR+7H+EHUMg3+D8lfwryuuLsaza57F+7vfVwmBbljaMNx7/L0YkjYE8p+yotaC/LIa7C+uaijVaru7sBLb88vVc20JN4WpROC4fmmqjO6TwmSAmpI/G4e3aUmAJAN712qLijVnigD6jNMSAWkZSOnjj6tl8ELUAaw/RB3D4N+g/B386784VdFVeHrD01ixZ4X9OVOYCZcMugTXD78e8ZHxrZ6npLIO2/PLsD2vHFsPlmPT3mJs3l+C6jprq8nAiF7JmDAwExMHZ2JglwSEcfpHclSep60uLGsKbF8O1Gnd1Fx3Dzod6DHGZ92DGLwQtR/rD1HHMPg3qEAJ/vVfnO/2f4fZP8xGTkmO/TWZMZm4+9i7ManXJI+C83qLVbUKbNpTgh/3FGNNbgF25LsI3gB0T4rGyYO0ROCE/umICg+s/t3kZ2oa0VXAts+BrZ8BJbv93j2IwQtR+7H+EHUMg3+DCrTgX9RZ6vB/v/wf5v40F9WWavtrT+pxEu497l50jeva7s/LK63G97mFWLOjAN/lFGDHYefJQEJ0OCYP6YKzj+qGcf0zEBnOfxjIgfx5yftF6xokyUCr3YNO0AYMe6F7EIMXovZj/SHqGAb/BhWIwb9ub9lePLrmUXyz7xv7sfiIeNw55k78of8fOqWLzq6CCiz/LU+VNTsKUWtp2U0oMTocpw7tij+MyMLx/dJgMrFrEDVTnt/QPWgJkPMVUFvu/HUZgxrGCZzRKd2DGLwQtR/rD1HHMPg3qEAO/oX8Z1y2exmeWPME8qry7MdP6H4CHhj7QIdaAZqrqKnHN9sP4/PNB7H0l0Moq2kcgKzLSo7BhSOzcOGoHuidFtdpn01BRF9lWMYJtNY9KCZF6xbUf7K2KFl8pscfxeCFqP1Yf4g6hsG/QQV68K8rrS3FnB/m4IOcD+zH4iLicOfoO3HBgAs6faBudZ0Fq34/jE9/PqASgXInicAxfVNx8ZieOPPIboiO4PgActU96FetRUC6B+35wXn3INFtODBAEoHJbq8pwOCFqP1Yf4g6hsG/QRkl+Net3LsSD377YJNWgPE9xuPBsQ8iLSbNK9coicCXv+Zh8fo9+HpbPpovOZAaF4lpo3vi0mN7oWdqrFeugYJExeHG2YNyVgA1Jc5fF52stQqoZGCSy1YBBi9E7cf6Q9QxDP4NymjBv6tWgLToNDw67lGckHWCF68WOFRajfd+3IfF6/eqaUUdSePDyQMzccXxvTH+iAxOG0ptLy629wfg96XA9qXAwZ9dv7bb0VqLgCQDWaMBs7Y+BYMXovZj/SHqGAb/BmXE4F/39Z6vcd+396GwutB+7LLBl+GWUbcgyhwFb5Jfr/W7ivDG97tU16A6S9NfN1kzYPpJ/XDu0d05UxC5p+wgsH2ZlgzIoGGXrQJJWqtAv5Nh7TseebXRDF6I2oHBP1HHMPg3KCMH/+Jw1WHcu/reJjMCHZFyBOacNAfZydmdfLUurqG8BgvW7sFba3ZjX3FVk+e6JEbhqhP64pJjeyExOsIn10PB0iqwVmsRkGTg4CaXL61P6gPzgIkIk0HDsuqwJAdE1CYG/0Qdw+DfoIwe/Av5T/3Wb2/h6XVPo9Zaq47FhMeoNQHOyT4HvmKx2tTg4PmrdqhWAUfxUeH44zE9VWtAZkK0z66JgqlV4EstGchZDlS7aBUIM2uDhfudDGSfDGSNAsxMOomcYfBP1DEM/g0qGIJ/3baibZi5cia2F2+3H7twwIW4+5i7ER3u24B7/a5CzP16B5b+ekhN+KKLCjfh0mN749rx/ZCZyCSA2tkqsH+D6hpkk0Rg3zqEWVvORqVEJgB9T2xMBtL6a4NTiIjBP1EHMfg3qGAK/kV1fTWe+OEJvPP7O/Zjg1IH4anxT6FXYi/4Wk5+OV5ZlYt3NuxFbb21SRLwx2N64a8TstGFSQB1oP7k792BjIqtMOV+Dez4Cji8zfUbEnsA/cYDfU7UkoKkHr68XKKAwuCfqGMY/BtUsAX/ug+2f4BHvn8E1ZZq+8rAD5/wMCb1ngR/yCurxryvd+C/a3ahuq4xCZDBwJcc0wvXTchmSwB1Tv0p2QvsWKENGpZt5WHXJ0jpq40T6HuSlhAkdvPZtRP5G4N/oo5h8N/JduzYgdmzZyM7Wxu0mpycjBkzZrj93rlz5yItLQ0FBQUYM2YMpkyZElLBv94N6PYVt2Nn6U77selHTscNI26AKcw/f+jzy2owb2WOmiXIMQmIiTDj6nF9MWN8Pw4Mps6rP1YrcGiz1iIgycDu74B6LSF2KjVbaxHo01ASunj1+on8icE/Uccw+O9EEryPGjUKubm5KugXM2fOVMH8XXfd1ep7ly1bpgL/RYsWqf3i4mJMnDgR69evD7ngX1TUVahFwZbsXGI/dlKPk/DEiU8gQfpD+4kkATIw+I3vdqGqzmI/nhIbgetP7o/Lj++NqHCuGkydXH/qqrVZhHZ+A+xcpT22aIPknUo/oiERGAf0HgskdO3U6yfyJwb/RB3D4L8TXXPNNSrolzv/OgniU1JS1Mw2rshr+vbt2yRpkGRg6tSpKCpqOvtMqAT/Qr6zN355A0+tfwpWm3a3vU9iHzx7yrPol9QP/iTThL6wfDveXLOryVoBWckxuG3yETh/RBbMJg7QJC/Vn7oqYM8PWiKQuwrYtx6w1rXeTajX8UCv47Rt+gAOICbDYvBP1DEM/juRBPkS+Dfv5iMrxi5duhSTJjnvty6tAxs2bFCvcVcoBP+67/Z/hztX3omShsWT4iLiVAvAhJ4T4G+7Cyrx9NKt+OCn/U1mBxrcLRH3nT0Ex2en+fPyKEB1ev2prQD2rNESAWkdkFmFXM0kJGLTgJ7HAb0lITge6HoUEB7Z8esg8gEG/0TBFfwbthbL3Xsp/fq1vCMtd/MluHdl8eLFmDx5sv2Of2uvDUXHdz8e/zvrfxiQMsDeJeim5Tfhtc2vtdqi4gu90mLxzMUj8PGN4zD+iAz78V8PlOKP87/HtW+sVwkCkVdFxmmrB0+6H/jLUmDmLuDSd4BxtwK9xgLNV86uLAC2fgJ88XfglYnAE72A184Glj+irVbsaj0CIiKiThYOA/f3dyU1NVUN4G3rvfPmzcO0adPUviQD0oowcuTIVj83PT1dtSw4qqpqulqtt7JGCbxl6wtZcVl4/bTXcf939+OLXV/ABpvqDrSrdJdaDyDC5N/BtoO7JuA/fxqN73IK8PiS37B5f6k6/tmWg1j+2yE1KFimB5VFw4i8Xn8iYrVkQIqQwcL7NwJ7vkfY7u9VK0FYdXHj6+urtC5EUqTLHcKAjIFA1mjYZPExWXQsYzBg4ngW8j9f//tDFGysPqpDMTExLY45u2kbtJGRtAq0FvhLlx+9248E/NIVSAb8uurz3xppyvE2+YWRJhv5j+jLJqM7Bt6BLuFd8EbOG2p/8e+LkVuYi3uPvld1B/K37ARg7pT++PTXAry0eh+KKutRa7Hh5a93YOHa3fjrCVk4c0gaTOxvHdL8Un+i+wEDpFwC2KwIL8pBxMH1iDygFXP5PvtLw2AD8n9TJWzjf7VrjohFXcaRqOtyNOoyj1Zba2xjaxeRr/jr3x+iYGENsDpk2OBfH6jrTGFhYZvvb36HX8YHSMIgrQGtTRUqgb6/+vxLi0NGRobPf3Hu6HIHBnUdhAe+ewB11jqsL1iP29ffjhdOeQHd47sjEFzdtQumHT8AL67IwWurd6oEoKCyHo8s3YUPfy3GQ+cOxVE9kvx9meQn/qw/dl26AoNOaLwmWWdAWgT2fA/sXaemGnVcgdhUV4mo/WtU0dmSegI9RsOWNRroPgLoeiQQGe/zH4VCS0DUHyIDs/qoDjnriSJ9/mWMbFAE/9K1x9UdfjnmKjnQ36evC9Ccq6k+dfIfzV9//OQXx1+ff27/c5GVkIWbv7pZDQTOKcnBZUsuw/OnPI8jM45EIEiKjcLfzhyCS4/tjUc/+RVf/HJIHd+0twR/ePlbXHZsb9xx2kAkxXB9gFDkz/rjVEovrRw1VduvrQQO/ATsW6dNLSoJQWlj64AIK9kDlOxB2Jb39CPaNKOSCHQfDnSTcpQ2JoEomOsPkcGE+akOOfs8wwb/EtxLcXWXXx/Q6+p9rroFuUoKCBjVZRTePPNNXP/l9arvf0F1Af78+Z8x+6TZOKVXQ1/nANA7LQ7zrhiNb7cfxgMfbcG2Q+VqZiBZMGzJ5gO456zBOH94VouxG0R+FRmrzQYkRVe6X0sCVEIg2w3aeAE7G3B4q1Y2va0dkoX5JCGQREBPClQLARMCIiIKwnn+pU+/BPCt/VjyPkka9AW+HNcHkDv/zgb9htJUn20pri7GLStuwfpDWiuJrAJ833H34cIjLkSgqbNY8Z/VuXhm2e+orG1cJOy4fql45Pxh6J/pvwXMKDTrT4dY6oG8X7RkQAYUH9gIHPql9TUHHBOCLkOBLsO0ZEC2shgZk2AKlfpD5CfWAJvq09DBvz5LT05Ojv2YDNyV4F/vty9BvSze5TiTjxyTlYFlwK8+VaizhMARg/+mai21uHf1vfg091P7sRtH3IjpR04PyDvq+4ur8NBHv6jZgHQR5jD85cR+uOmUAYiJ5KwqwSzQ6k+nqq8BDm3REgFJCPb/COT92nZCoK8/oBKCI4Guw7THGYOA8GZTlVJIC+r6Q+QDDP47mczRv2DBAowZM8Y+k89dd91lf16OSaAvQb3jol+SAEiioI8NSEtLa/K+5hj8tySrAD+57km1KrDuj4P+qKYCldaAQPTVb3m478PN2FPY2HWid1osHr/gSIzNTvfrtVFo1R/fJQQ/akmBzCZkqW37vabwpq0EmUO0aUhlsHEofHfUQsjVH6JOxuDfoBj8Oye/Pq9teQ1Pr3/afuy0PqfhsXGPIdIcmCuYVtVa8NKK7fjX1zmoszT++l88pidmnTmYA4KDUKDWH5+y1AGHtwEHN6uZhVSRxxVuTlUsU/tmHKG1DNjLQCC5N5OCIMf6Q9QxDP4NisF/6z7Y/gHu//Z+WGxav/pjux2LZyY8g/gAnoZwe145Zr27CWt3Nq7tkJEQhYfPG4rTh3Xz67VRaNUfvyrPAw7+rLUU6AmBDCB2mHa0VeExrpMCs2HnlCAHrD9EHcPg36AY/Ldt5d6VuH3F7ai2VKv9oWlD8a9J/0JytOs1GfzNarXhzTW78MSS31DhMCD4jGFd8eB5Q5GZEO3X66PQqT8B121IWgkkIZDxA/lbtW5DRTu1GYbcId2HUvoCaf2BtOyGbUPhQGNDYf0h6hgG/wbF4N89G/M24oblN6i1AMSAlAGYN3ke0mMCuz+9DAj++/ubsfy3xi4QidHh+PtZQzB1dI+AHMRMwVd/Ap6sRVDwu5YMNEkKctUqxm6TLkTNEwIpqX2BmBQmBgGG9YeoYxj8GxSDf/dtL9qO6Uun43DVYbXfJ7EP5p86H13juiKQSVX48Kf9ePCjX1BY0Tgwclz/dMyechSykmP8en0UGvXHkOqqmyYF8rggRytN1iVwQ1QSkNIbSOnTUPTHfbVBx+GBOZYomLH+EHUMg3+DYvDvGVkE7C9f/AUHK7SpNbPis1QC0DOhJwKdBP4Pf/wL3vuxcXXVhKhw3Hs2WwGMymj1J2hYrUDZfqBge0PJaXxctAtoGCPkNplFLDGraVKQLKUnkNQDiO/KcQZewPpD1DEM/g2Kwb/n9pfvVwnAnrI9aj8zJhPzT5uPfkna2gqB7quteZj1zs84WKqNYRCnDMpU04J2SeRYACMxYv0JevW1QPEuh8RAEoKdWine43liIMLMQGJ3LRFQpWezbQ8g2vd/v42O9YeoYxj8GxSD//bJr8zH9C+mI6dEW4gtNTpVjQEYmDoQRlBSVacWB3tnw177MZkK9MFzh+K84d3ZCmAQRq0/IUtWMi7d25gMNC9VjTN0eUy6FemJgCQKUmQAckK3xhKbynEHDlh/iDqGwb9BMfhvv8LqQlyz9Br8Vvib2k+MTFRdgIakDYFRLP3lEGa9+zMOl9fYj502tAse/cORSI/naqiBzsj1h5yoKtZaDVQysAso3QeU7AWKd2vbqsKOnV/WKJEuRIndWiYG+r48J1MZh0CSwPpD1DEM/g2KwX/HlNaW4q/L/opN+ZvsCcArp76CwWmDYRRFFbW478Mt+Oin/fZjqXGRePT8YTjjSK4LEMiMXn/IQ7UVQIkkBHu0ZMBeGvYlWXBntWN31jiIywDiM4C4TCAuHYiXbUbDcf1xpjaLkUF/91h/iDqGwb9BMfjvuIq6CpUA/Jj3o2ETAPHpzwfUtKCOMwKde3R3PHzeMCTFcnXgQBQM9Yc6eSCyrGxcuh8oOwiUHXDYOjyuLOi8z5TxCJIcNE8SJCmQbkYxqUBsmsPjVCA8MFoVWX+IOobBv0Ex+O+8BODapddiY/5GtZ8UlYT5k+cbLgGQ7j/3vPczPt9yyH6sW1I0npp6NMb2D+w1DUJRsNQf8sNiZyoRcJYgHAAqDmsrJKskwQv/lMp6CCohSGlMCPStHFeP5bkUQBZTjE7Sirlzb0Kw/hB1DIN/g2Lw790EQFoABqUOgpHo6wLc+/5mlFbX24//ZVxf3HHaQERHmP16fRSc9YcCdICyjDOQRKAiXyuuHkvpjC5HrYmIbUgEHBICt0oyEJXQYi0F1h+ijmHwb1AM/jtXsCQA4kBJFe5Y9BNWb2/sIjCoawKeuXg4BnXltIKBINjqDxmY/JNbXdKQCBzWkoZKKQWNj2U2o+bH2jP1aUcGPMtg5qh4IDIBtsg41IZFIjIhHWENx7TnGl+jkgb7sYTG56T1gnWOQpyVwb8xMfj3TQLw6qmvGmYaUEdWqw3/Xp2LOZ9vRW29VR2LNJtw1+kD8ecT+sJkCv4ZQQJZMNYfCiHyz3RNaUNCIMmB47ZASyakyCxI+mO91FX4+eLDtJaIiBggUrYORe3HaAmC42P12oZtk9c6eRwezYXdKOBZGfwbE4N/3yQAsg7Aa6e/hr5JfWFEvx0sxS1vb8RvB8vsx8Zmp+GpaUejW1KMX68tlAVr/SFqk6UOqC4Fqp0kBi1KMVBTBtSUA7X6thyob1zoMCCZwrUkQAZI27cxzfYbthHOjke3/jppCWlSIhofhzdsTRFs4SCXGPwbFIN/7yYAM5bOsE8Dmhmbif87/f/QI6EHjKi6zoKnvtiK+aty7ccSo8PVmgDnHN3dr9cWqoK5/hB5m7WuBvn7cpGRGA1TXaWWEEiSoG+bJws1+vMNx+qqtBYI2dZWAnIObwyQDoQkxJ4cRLVMFOSxJBTNj6mt43HZSjIR3pBUmB32HYr9mLnhdfoxs8N75Zjj+9w4X5gpJNav8CUG/wbF4N/76wBc/fnV9oXAsuKzVAtA17iuMKpvtx/G7Yt+woGSxrtmfxiRhQfPG4rEaE4J6kvBXn+IDFV/JOyQ1gSVDFQ4Tw70ovYdn9dfL89VaIOnZV9mZpJzqm3DvhwPxiTDF/TEQRIFmaZW/rurbcO+JAjNj7l6rUl/vdnN4x6eVxIVtXVSpNtZq68Ja2Pf8RwevMfxGMIgnYELi4qR2n8MTJG+7QXA4L8DGPz7ZiXgqz67CjtKdqj9Pol98J/T/4P0GONOnVlSWYe/f7C5ycJgWckxeHra0Ti2X5pfry2UhEL9IfIWw9YfCW+s9Q2JRrVDcqA/bnbM1Wuk65QkGVLqG7aq1Dlsa5odc3hsf0/jCvEUmqw3bIApPdunn8ngvwMY/PtGXmUe/vTZn7CnbI/aPyLlCPz7tH+rwcBG9sHGffj7e5tRVqNNCSrjf68/uT9unjgA4ebg/e8ZKEKl/hB5A+tPZyYjFofkwFki0ZAsWOu0xEW9Xn8sW4v22H7MoVj05x2ek2lo7e9tfj433iuzTMlx+9babF8/Zm35Wra6tGC98UeY0vrB3/Erh8hTQJH+/jLl55WfXYmDFQexrWibGhA8/9T5iJep4wzqvOFZGNU7Bbcv/AlrcgthtQHPL9+O1dsP49mLR6Bnaqy/L5GIiLxJuoJI/3s1O1Fs6CQ77iQQ7T2uis3hcfPS8Bzaeo2tlef197vxOS5eY7NZUVVZiWiZBjcA8M6/m3jn37d2le7ClUuuREG1Nnf+yMyReHnSy4iVqd0MzGK14V9f5+DppdvUY5EQFY5H/jBMJQjkHaFWf4g6E+sPUXAN+GUtpoDUO7G3utufHJWs9jfkbcBtX9+GOmmaNDCzKUx191l07fHomaoN+pGuQDe/vVG1CpQ3dAsiIiIi8gYG/xSwBqQMwNzJcxEfoXX3Wb1vNe5ZfQ+sqgnO2Eb2SsEnN52I84Y3Tv35zoa9OPu5VfhpT7Ffr42IiIiCF4N/CmhD0obghYkvIErmQAawJHcJZv8wG8HQW02m+5T+/jLzT1ykWR3bWVCJC1/+VnUNklWDiYiIiDoTg38KeKO6jMKT45+EWeb1BfDWb29h7qa5CBYXjOyBT28+EUf31Lo41VtteGLJb7j832twqDTAV9YkIiIiQ2HwT4YwoecEPDj2Qfv+ixtfxILfFiBY9E6Lw+Jrj8dfJ2TbF1Zcvb0AZzy7Cst+OeTvyyMiIqIgweCfDOO8/ufhjtF32PcfXfMoPtv5GYJFhNmEmacPwptXH4suiVo3p8KKWvzl9XW4/4PNqK6TeZOJiIiI2o/BPxnKlUOvxJ+H/Vk9tsGGWatm4dv93yKYjO2fjiU3n4RJg7vYj/3fd7tw3gurse1QmV+vjYiIiIyNwT8Zzi0jb8EFAy5Qj+ut9bjlq1vwc/7PCCapcZGYf8UoPHz+MESFa9V066EynPP8N3jj+11BMeCZiIiIfI/BPxlOWFgY7j3uXpzS8xS1X1Vfheu+vE4tDBZsP+flx/XGhzeMw8Au2qqANfVW3Pv+Zsx4Y73qEkRERETkCQb/ZEjhpnDMGT8HY7qOUfvFNcW4dum1OFx1GMFmYNcEfHDDCbjy+N72Y0t/OYQznl2Jb7cH389LRERE3sPgnwxL5v5/9uRn1WJgYm/5Xtzw5Q2orKtEsImOMOPB84bh1StHqy5B4lBpDS59dY2aFrTOYvyFz4iIiMj7GPyToSVEJuCliS+hS6w2OHZLwRbc8fUdaixAMJo4uAuW3HwixvVPV/vS9V8WBJvy8rfYebjC35dHREREAY7BPxle17iueHnSy0iI0PrFr9q3Co98/0jQDortkhiN1/98DGadMQjhJm1RgJ/2luCs51bhnfV7g/bnJiIioo5j8E9BQbr+PHvKs4gwRaj9d35/B//a9C8EK5MpDNeMz8a7141F3/Q4dayi1oLbF/2EWxZsRGl1nb8vkYiIiAIQg38KGjL499Fxj9r3X9r4Et77/T0Es6N6JOPjG8dh6qge9mMfbNyvWgE27C7y67URERFR4GHwT0HljL5nNFkF+MHvHsSqvasQzOKiwvGPqUfjuT+OQEJUuDq2p7AKU//1HZ7/8ndYrOwGRERERBoG/xR0rhhyBS4bfJl6bLFZcPvXt2PL4S0Iduce3R2f3nwiRvVOUfsS9D+1dBv+OP977C+u8vflERERUQBg8E9BRxbHkrv/k3tPbrII2N6yvQh2PVNjsWDGcbh54gA0jAXGD7mFOOPZVfhs8wF/Xx4RERH5meGD/x07duCaa67BnDlzVJk3b167zjN5shYoUnAwm8x4/MTHMTJzpNovrC7E9V9ej9LaUgS7cLMJt04+Am/POB7dk6LVsZKqOlz73w2Y9e4mVNYG5zSoREREFOTBvwT+o0aNwuzZs3HXXXepkpOTo5IAT8jrly1b5rXrJP8tAvbcKc+hT2Iftb+jZAduW3Eb6qyhMRPOMX1TseTmk3DWkd3sx/73wx6c8/w32LK/xK/XRkRERP5h6OBfgv4ZM2YgOTnZfmzWrFmYOXOmRwnE2rVrvXSF5G9JUUlqEbCUKK0f/JoDa4J6DYDmkmIj8MIlIzDnwqMQE2FWx3LyK/CHF7/Fq9/kwsrBwERERCHF0MH/woULkZ2d3eSYngi4eyd/8eLFuOiii7xyfRQYeib2VGsARJoi1f67v7+LVze/ilAaAzFtTE98fNM4DMtKVMdqLVY8/PEvuOq1tcgvq/H3JRIREZGPGDb4Ly4uVqVfv34tnpMEYMOGDW4F/lOmTPHSFVIgGZE5Ao+Me8S+/+yGZ/H5zs8RSrIz4vHOX8di+ol97ce+3paPM55diRVb8/x6bUREROQb2qTgBiTddVxJTU1FQUFBq++XxKGwsFAlD+4kCrr09HR1J9VRVZX3p1G0Wq2qq4psqX1O630a9gzfg+c3Pq/2/7bqb8iMycTRGUcjVESYwjDrjEEY1z8Nty/ahMPltar86T9r8ecT+uDO045AVLjWPSiYsP4QtR/rD5Ex6lBMTEyLY866ORs2+G+LBPetkVmBZIBwZ8jL8/5dU/mFKSkpUf8RTSbDNtj43TmZ52Br9634Yv8XqLXW4qblN+G5Y59Dt9jGQbGhYGAS8Polg/Do0l1YnasN/v336p34ZtshPHRGP/RJ1WYJChasP0Ttx/pDFFx1yLDBv+Mg3+bkjn5rZDzApEmT2h3oJyZq/aZ9/YsjLQ4ZGRkB8YtjZI+lP4aiL4uw9tBaFNcW4/6f7sfrp7+OxCjf/3f1p0wAr/+lO17/bhce/2wrauut2JZfhT/971fcc+ZgXHJMzxatXEbF+kPUfqw/RMaoQ856opSWliIlRZv0xPDBv3TtcXWHX461lhxIN5/23vWX/2j++uMnvzj+/PxgEWWKwj9P/icuX3I5cktykVuaiztW3oGXJ72MCHMEQs1V4/rhuOx03Pi/H7E9rxzVdVbc+8EWfLU1H09ceCQyE4KjFYD1h6j9WH+IjFmHnH2eYWuxBPdSXN3ld7Vol3T3kbUAZDpQvcydO1c9J489XSOAjDsF6IsTX0RqtJZErjm4Bg99/1DITAHa3OBuifjohnG47Lhe9mPLf8vD6c+swhdbDvr12oiIiKjzhNkMHO3Iyr6SAMh8/44DgWX6T09+LEkI5FytvUeaTZKSklSfLX91+5EuR5mZmbzz0ok25m3E1Z9frfr/i5tH3oy/HPkXhLKvfsvDnYtlMHDjFKAXje6Je88ZgvgoYzYWsv4QtR/rD5Fx65Cz+NXQtVju1Mt0nY7kLr5+J1/vAiStAK3N6NPW4GAKXsMzh+PREx9tMgXosl2hvdrzyYMy8fktJ+LUIV3sxxas24Mzn12F9buK/HptRERE1DGGDv5lms5FixbZkwDpspOWlqZW/dVJt6B169Y57R4krQSO3X6mTp2qWgEotJze53TcNOIm+/7fvvkbfi34FaEsLT4Kcy8fpVYGjovUpv7cXViJqf/6Fk99sRV1Fk75R0REZESG7vbjS+z2E9ykGkjQ//GOj9V+Zmwm3j7rbWTEZiDU7S6oxK0LNza5639kVhL+edFw9M+MhxGw/hC1H+sPUcew2w9RgI7Cf2DsA/YFv/Iq89QaANX11Qh1vdJisWDGcbjj1CMQbtKm/vx5XwnOfn4VXv9uZ8gOkiYiIjIiBv9EDaLMUXjm5GfQLU5b8GtzwWbcu/peBrcyJ7DZhBtOGYB3rxuLfhlx6phMCXrfB1vU6sB5pUySiIiIjIDBP5GD9Jh0PH/K84gNj1X7n+38DP/66V/+vqyAcVSPZHxy44m44vje9mNfb8vHqc+sxIc/7WeiREREFOAY/BM1MzB1IGafNBth0Lq4vPTTS/gs9zN/X1bAiIk046HzhuG1q8YgIyFKHSuurMNN//sR1725AQUOU4QSERFRYGHwT+TEhJ4TcNuo2+z7f1/9d2w+vNmv1xRoJgyUKUFPwllHad2kxJLNB3HqP1fis80H/HptRERE5ByDfyIXrhx6Jc7vf756XGOpUQOAD1ZwtVtHqXGRePGSkXjhkhFIiY1QxwoqanHtfzeoloDiSm3xNCIiIgoMDP6JWpkB6L7j7sPIzJFqP78qXyUAlXWV/r60gHP2Ud3xxa3jMdlhYTAZAzD5nyvx5a+H/HptRERE1IjBP1ErIswRagagrPgstf9r4a+455t7YLVxkavmpP//vMtH4Z8XHY3E6HB1LL+sBlf/3zrcvvAnlFTV+fsSiYiIQh6Df6I2pESn4MWJLyI+QlvQatnuZXjhxxf8fVkB21ryhxE9VCvAhIGNC6S9s2EvTn9mpZoZiIiIiPyHwT+RG7KTs/GP8f+AKUyrMvN/nm9fDZha6poUjf/8aQxmX3gk4qO0VoADJdW48t8/YNa7m1BWzVYAIiIif2DwT+SmcVnjcNeYu+z7962+DxvzNvr1mgK9FeCiMb3w+a0nYVz/dPvx//2wR80ItPw3jgUgIiLyNQb/RB64ZNAlmHrEVPW4zlqHW766BQfKOa1la7KSY/DG1cfgkfOHITbSbG8F+PNr63Dz2z9yXQAiIiIfYvBP5OHd7FnHzsIxXY9R+wXVBbjpK84A5M73dtlxvdW6ACcOaGwF+GCjNiPQBxv3cXVgIiIiH2DwT+ShCFMEnhr/FHom9FT7vxX+xhmA3NQzNRav//kYPDn1aCTFaOsCFFbU4ua3N+Iv/7cOB0qq/H2JREREQY3BP1E7JEcn44VTXmgyA9CLG1/092UZphVgyqgeWHrbSTjzyK7241/+lofJT6/Ef7/fBauVrQBERETewOCfqJ36JfdrMgPQvE3z8OmOT/19WYaRmRCNly4dhX9dNkqtESDKa+rx9/c34+L53yP3cIW/L5GIiCjoMPgn6uAMQHeMvsO+f+/qe/Fz/s9+vSajOX1YVyy7dTwuGq11oxI/5BaqdQFeWrEddRZ2pyIiIuosDP6JOuiywZfhwgEXqse11lo1APhgxUF/X5ahJMVGYPaUo/DmX45Fr9RYdaym3oo5n23FWc+twtqdhf6+RCIioqDA4J+oE/qw33PsPRjVZZTaP1x1GDd/dTOq6jl41VMn9E/HZ7eciL+M6wtTmHZs26FyTP3Xd5i5eBOKKmr9fYlERESGxuCfqBNEmCPwzwn/RFZ8ltr/peAX/P2bv3MGoHaIjQzH388egg9vGIejeiTZjy9YtwcTn/4ai9fv5bSgRERE7cTgn6iTpESnqBmAYsO1bitf7PoCc3+a6+/LMqxhWUl477oT8NB5QxEfFW6fFvSORT/h4nnfY3teub8vkYiIyHAY/BN1ov4p/THnpDkIg9Zn5aWfXsLnOz/392UZltkUhiuO74Mvbx+Ps47qZj++JrcQZzy7Ek99sRXVdRa/XiMREZGRMPgn6mTje47HbaNus+9L958tBVv8ek1G1yUxGi9eMhKvXTUGPVNj1LE6iw3PL9+OU/+5El/+esjfl0hERGQIDP6JvODKoVfi/P7nq8fVlmrc9OVNyKvM8/dlGd6EgZn44pbxuP7kbESYtdaV3YWVuPr/1uGq//zAtQGIiIjawOCfyEszAN173L0YkTlC7edV5eHm5Tejur7a35dmeDGRZtx52iB8etOJOLZvqv34V1vzcdo/V+Ifn/+Gytp6v14jERFRUAb/y5cv77wrIQoykeZINQNQ97juan9zwWbct/o+zlTTSQZ0ScDbM47Dc38cga6J0epYrcWKF7/KwcSnvsZHP+3nd01ERNSZwf+oUaPw5JNP2vfnz5+PWbNmdeSUREElLSYNz53yHGLCtX7qS3YuwbxN8/x9WUHVwnLu0d3VgOC/TmjsCnSgpBo3/u9H/HH+99h6sMzfl0lERBQcwX9SUhJ++OEHvPvuu2p/+vTpSE1NxXXXXddZ10dkeANTB2L2ibPtMwC9sPEFLNu1zN+XFVTiosIx8/RB+PyWkzBhYIb9+Pc7CnHmc6vw0Me/oKyaXYGIiIg6FPyPGTMG2dnZuOCCC+xdgCZNmoQFCxZ01vURBYWTe52Mm0beZN//2zd/w68Fv/r1moJRv4x4/OdPY/DKFaPRK1Vbb8FiteG1b3dhymub8fp3u1Bn4cJrREQUujoU/BcVFeGiiy5Sj1NSUpCbm4u7774bTzzxRGddH1HQuHrY1Tin3znqcVV9FW5cfiMOVx3292UFZVegSUO64ItbT8Ltk49AdIT2Z66k2oIHPvoFpz2jTQ3K8QBERBSKOhT8r1+/Hm+//TZKS0sxYsQIbNiwQd35l+4/RNQyKL1/7P04KuMotX+o8pCaAajGUuPvSwtK0RFm3DhxAL68fQLOG64NuhY78ivU1KCXvboGv+wv9es1EhERGa7Pv9zlT0xMVPsXXnghkpOT7WMAiKipKHMUnj35WXSN66r2Nx3ehAe+fYB3ob0oKzkG/5x2NF69eBBG9U6xH1+9vQBnPb8KMxdvQl4pp2AlIqLQ0Onz/Mtdf2kFICLn0mPS8fwpz9tnAPp4x8d4dfOr/r6soDe0axwWzjgWL1860j4eQHKuBev2YMKTK/Dcl7+jqtbi78skIiIy3iJfffv29cZpiYLGoNRBeGzcY/b95zY8h+W7uW6GL7penXFkNyy97STcc+ZgJESHq+OVtRY8vXQbJjz5Fd5asxv1HBRMRERByivB/86dO7Fx40Y1FoCInJvUexJuHHGjemyDDXevuhtbC7f6+7JCQlS4GdNP6oev7zwZVx7fG2aTNg3rodIa/O29n3HqP1fi058PsDsWEREFnU4P/mW2H1n8S/r+L126FK+88opKBIiopelHTscZfc9oMgNQQVWBvy8rZKTGReLB84ap9QEmD+liP77jcAWue3MDzntxNVZv54xMREQUPLQ2704kU3/K3P99+vRRRcgUoETkvBvKQ2Mfwp7SPdhcsBkHKg7g1hW34pVTX0GkOdLflxcy+mfGY/4Vo7F+VxFmf/YbfsgtVMc37S3Bpa+swbj+6WoRsSN7JPn7UomIiDokzMZ2bbdIFyaZ3aikpMQ+u5EvWa1W5OXlITMzEyaTV3prkR/lV+bj4k8uRl5lnto/N/tcPHLCIyo5IN/WH/mTuGJbPuZ8thW/HmjadfGsI7vh1skD0D8zwctXTBQ4+O8PkXHrkLP41aMr+Mc//mFf1IuIOk9GbAaeO+U5RJuj1f6HOR/i/7b8n78vKyRJwnXywEx8cuM4PHvxcPvMQOKTnw9g8j9X4ua3f0ROfrlfr5OIiMgn3X7GjBljfyzz+V9wwQXwpx07dmD27Nmqq5GQsQYzZsxo833Lli1TYxKKi4vVOaZOnerW+4i8ZWjaUDwy7hHc8fUdav/p9U+jb1JfjO853t+XFpJMpjCcNzwLZwzrhrfX7lZTgR4ur1XTg36wcT8++mk/zh+epRYS65se5+/LJSIi6vzgv6CgQDUbSNA/cuRIrF271q/BvwTtMrhYxhRI0C9mzpyJOXPm4K677mo18JfViCVpEJIAyHlkxeK5c+f67PqJmjutz2nYUbwDL/30kpoB6K6Vd+G/Z/4XA1IG+PvSQlZkuAlXHN8HU0b1wBvf7cLclTtQWFELqw1498d9+OCn/fjDiCzcdMoA9EprbCUgIiIKij7/8+fPx6JFi1QALc3jkyZNUomA3HkfPXo0hg8fDl+55pprVNCvB/F6IJ+SktLqFH1yl19+Bkfz5s1T58vJyUG/fv1avId9/slX5Hf3zpV34vOdn6v9rPgsvHXWW0iNTvX3pRlWZ9afipp6/N93OzFv5Q4UV9bZj8t0oReOzMINJzMJoODCf3+IQrjPv76C7xdffKF+EHksXWUkWFm4cCFOOeUUmM1mDBgwAH/961+9PsWnfKbe3UentwBIcuLK4sWLVQuBI0lc2nofkS9IUv3wCQ9jSNoQtb+vfB9uW3Eb6iyNgSb5T1xUOK6b0B+r7joZd5x6BJJiItRxi9WGhev24uSnVuDWBRux7VCZvy+ViIiohQ6lH3IH/cILL8QTTzyhEoLCwkJVJCiXu+ePPfaYGiDsjSRA7vBLcXaXXhIA6dbjypQpU1okDUSBJCY8Bs+d/BwyYjLU/vpD6/HImke46FQASYiOwA2nDMCqmSfj1klH2FcLliTgvR/3qYXCrnljHX7eW+LvSyUiIuqcef4nTpzY4pg0LYwYMUIVaWKQfvlyN72zuwPJeV1JTU1V4xNcad7lR6xbt05tpRtTa9LT01tMv1hVVQVvk5YWCfxkS6FBAv9nJjyDP3/xZ9RYavDu7++iX2I/XD7kcn9fmuF4s/7ER5px4ynZuPL4Xnj9u134z7c7UdTQHejzLYdUOWlAOq6bkI1j+rLrFhkP//0hMkYdiomJaXHM2U3DTl/kq3lAPXnyZDUA19ekVcATMm5AirOWhLZIPy5vk18YSabkPyL7XIaOTGTi9qG347FNj9lnAEqxpeCYjGP8fWmG4qv6M21YIs4+Yig+2HwYb60/hPwKLQlY+fthVY7uHo8rx3TF8X0SuYYDGQb//SEKrjrk1eBfWga8leXoffudka5HnnZfkjv+rc0Q5Bjo+2vArwQLGRkZAfGLQ75zUeZFyLflY/7P82GFFY///DjeOOMN9EvyPFENVb6uPzf36IZrJw3BO+v3qdmB9hRprYM/7S/HbR9sx4DMeFw9rg/OG94dUeFmr18PUUfw3x8iY9QhZz1RZMCvTITjUfC/fPlyNZA30EjXHld3+OVYa8lB81l+5FzuTvEp/9H89cdPfnH8+fnkPzeMuAE7S3di6a6lKK8rx01f3YS3znwLydHu/Z6T7+tPTKQJlx3fBxcf0wsfbdqPl77Kwe952sJgsr373c148ovf8aexvXHpsb2REhfpk+siag/++0NkzDrk7PPavAJponjyySc9+qB33nnH6zP9SHAvxdVdfulu1BaZ9UcSBcfA39PuQkS+YAoz4ZETHsGg1EFqf0/ZHtz2NWcAMoJwswl/GNEDn99yEuZdPgrH9Gns93+4vAZPfrENY59Yjvs+2IxdBRV+vVYiIgp+Jne67siMPrNmzXL7pPL6BQsWwNumTZum5uV3NhC4rYG7MhuQJA6OXX0k8OdUnxSoYiNi8fwpzyMtOk3trz24Fo/98BhnADLQisGnDu2Khdcej/euG4uzjuwGU0O3/6o6ixosPOHJFbj2jfX4fkcB/7sSEZFXuNX20LdvX9x9992qBUD6DrVFXtPaVJudRebql7v3juQufvM7+dIK4Hg9kiA8/vjjqruPvF8vcr72DPgl8pWucV3x7CnPItKkdRFZvG0x3vrtLX9fFnloRK8UvHjpSHx958n409g+iI3U+v1LvP/ZloO4eN73OOPZVfjfD7tRVWvx9+USEVGor/ArwXSfPn1aPCddfSTwln70Mpe+L+7+S1AvnzNmzBj7XX/Hu/lybNSoUWp6T701QAY+uOre4+rr4Aq/FEg+3vExZq2aZe8S9PLElzE2a6y/LytgBXr9Ka6sxZtrduP/vt2JvLKaJs/JImIXjemJy4/rjZ6pXDmYfC/Q6w9RoLMG2Aq/Hgf/ep9+WSRL5u6XgF+Cb7lzLoG2nE4Cf0kS5MOCBYN/CjTPbngWr/z8inqcEJGAN896E32T+vr7sgKSUepPbb0VSzYfwGvf7sSPu5veoJCZQScO6oIrx/bGuP4t1xshCvX6QxSorAEW/Ldrqk8ZaDt9+nR7VxoJ+KW7jKz0K4G/dBMiIu+6ccSNyCnOwVd7vkJZXRluXH4j3jzzTSRFBU/SHWoiw004b3iWKpv2Fqsk4OOfDqDWIgvEAMt+PaRK3/Q4XDymJ6aM6oG0+Ch/XzYRERmI23f+3333XdWlRx8QK2+TbjQyaPaVV17p9BV8Aw3v/FMgqqyrxOVLLse2om1q/9hux+LlSS8jwhTh70sLKEauPzIj0Ns/7MZ/v9+Ng6XVTZ6LMIfhtKFdcckxvXB8dhpbA8grjFx/iAKBNcDu/Ld5BT/++CPS0tLUQlhLly5VM/ksXLhQ/SBffPEFvvzyS5UUlJWV+eJnICInMwClRmvTR645sAazf5jt78uiTpQeH4UbThmAVTNPxouXjMTYbG22J1FnseHjTQdwyStrcPKTKzD36xyVLBAREbX7zv/o0aPV4FiZCUe6+rhy7bXXqhmBnA0EDga880+B7Me8H3H151ejzqrN+3/Psffg4kEX+/uyAkaw1Z/cwxWqNWDR+r0orKht0RoweUgX1SXopAEZap0Boo4ItvpDFOp3/tsM/mUufbnT7w4J/k899dSAXBG4oxj8U6D7YPsH+Pvqv6vH5jAz/jX5Xziu23H+vqyAEKz1p6begqW/HFJTgq7eXuC01eAPI7rjwlE9MKir7/9uUXAI1vpDFKrBf5tXIAN53ZnbX8iAX1l0S8YAEJFvndf/PFw19Cr12GKz4PYVt2NX6S5/XxZ5UVS4GWcf1R1v/uU4rLhjAq4dn430eG0NCCFdgOavysXpz6zC2c+vwn9W57ZoKSAiotDS5p1/yRTWrVunVvp1l4wDkLECd9xxB4IF7/yTEVisFtz81c34eu/Xar9PYh81BWhiZGjf9Q2l+lNnseLrrfl4Z8NeNTOQjAto3i3o5IGZqjVgwsAMlUAQtSaU6g9RKNz5b9c8/+6QD+E8/52Hf3zJXeW15WoGoO3F29X+2O5j8eLEFxFuatfMvkEhVOtPUUUtPtq0H4vX78WmvSUtnk+IDsfpQ7vi3OHdcXy/NI4PIKdCtf4QdZaQCf6DDYN/MpK9ZXtxySeXoKimSO1fOvhS3H3M3QhVrD/A74fKsHjDXry3YV+LVYRFWlwkzjyym0oERvVKgcnEaUNJw/pD1DEM/g2KwT8ZzbqD6zB96XTUW+vV/n3H34epR0xFKGL9aVRvseKb7Yfx4cb9+HzLQVTUWlq8pltSNM4+qhvOPToLw7ISuX5AiGP9IeoYBv8GxeCfjOjd39/F/d/erx6Hh4Vj3qnzMKbrGIQa1h/nquss+Oq3PNU16Mtf81BTb23xmp6pMapr0OnDumJET7YIhCLWH6KOYfBvUAz+yajmrJ2DN355Qz1OikrCG2e8gb5JfRFKWH/aVlZdpwYIf/TTAazclo96a8t/GjISonDqkC4qETiuXxoiOEYgJLD+EHUMg3+DYvBPRp4B6IblN+Cbfd+o/R7xPdQMQPqqwKGA9cfzgcKfbTmIjzftx/c7CmFxkggkRodj0pAuOG1oV7WYWEwkZw0KVqw/RB3D4N+gGPyT0WcAuvKzK7GtaJvaPyrjKLx66quIDo9GKGD9ab/iylrVJUiSAWkRcNY1KDrChBOy03HyoEycMigT3ZNj/HKt5B2sP0Qdw+DfoBj8k9EdrDiISz+9FHmVeWp/Uq9JeHL8kzCbgv+OLetP56ioqcfX2/LVQOHlv+ahrEYbTN7coK4JKgmYODgTw3umwMxxAobG+kPUMQz+DYrBPwWDrYVbVQtARV2F2r98yOW4a8xdCHasP52vpt6Cb3MK8MWWg6plwNn0oSIlNgITBmaqVoFx/dORGte4AjEZA+sPUXAF/6G76g9RCBqYOhBPjX8K1395PSw2ixoInBWfpdYBIPKErAwsKwVLkXtIW/aXYvlvefjytzxs2lsM/bZSUWUd3vtxnyoyY+iw7kk4cUA6xg1Ix6jeKVxhmIjIx3jn302880/B5J1t7+CB7x5Qj01hJjwz4Rmc3OtkBCvWH9/KL6vBiq15+GprHlZuO4xyF92DYiLMOLZfqmoROOmIDAzIjOeaAgGI9YcouO78M/h3E4N/CjbPbXgO83+erx5Hm6Pxn9P/g2HpwxCMWH/8p7beinU7C9VYgZW/H8avB0pdvrZLYhTGZqfjuH6pairRXqmxTAYCAOsPUccw+DcoBv8UbKTq373qbnya+6nal6k/3zzzTfRI6IFgw/oTWK0Cq7cfxqrfD+Ob7fk4VOp8rIDomhitEoFj+6WpZKBPGpMBf2D9IeoYBv8GxeCfglGtpRbXLL0G6w6tU/uy+JcsAiaLgQUT1p/AJP/8/J5XrhKBVb/nY82OQlTVWVy+PjMhSiUB0lXo2L5pyM6IYzLgA6w/RB3D4N+gGPxTsCqpKcHlSy5Hbkmu2h/dZTTmTp6LSHPwzMrC+mOcLkI/7ytWC4t9v6MA63YWtZoMJMdGYGSvFDVweESvZAzvmYzYSM5j0dlYf4g6hsG/QTH4p2C2t2yvWgOgsLpQ7Z/V7yw8Pu7xoLmryvpjTHUWSQZKVCIgrQIydqCi1nUyIOsJDO6WYE8IZNsjJSZofo/9hfWHqGMY/BsUg38KdpsPb8ZVn12Faku12r962NW4ZdQtCAasP8GTDGzeV4I1uVoisH5XkZpKtDUZCVGqReCorCQc2SMJR/VI5loDHmL9IQqu4J/to0SkyEw/s0+ajVu+ugU22PDq5leREZvBNQAoYESYTRjRS7r4pADjs9WYgZ0FlSoJkLJhVxG25ZXZ1xjQBxgv/eWQKjppDTi6R7KWDGQlYViPJCRGR/jnhyIi8jEG/0Rkd0qvU3DPsffgkTWPqP3ZP8xGWkwaTu9zur8vjagF6c7TNz1OlSmjtFmqSqvrsHF3sZYM7C5Sj8uarTOwt6hKlU9+PmA/1i89DsOykjC4W6LqOjSkW6JqNWCXISIKNgz+iaiJiwZdhLyqPMzbNE+1APxt1d+QGpWKY7od4+9LI2qT3MGXBcOkCKvVhtyCCvy8twSb9paoAcWb95W2GEi843CFKh/+tN9+LC0uUiUDQ7prCYE8zs6IVy0QRERGxeCfiFq4YfgNyK/Mx3vb30OdtQ43f3UzXjv9NQxMHejvSyPyiMkUpgJ2KeePyFLH6i1W5ORXYNPeYjWg+Ke9Jfh1fylqLdYm7y2oqMU322U9gsP2Y5FmE/pnxqtEYGDXeAzITFD7Wckx6rOIiAIdg38iakG6Otx3/H1q9p+v936N8rpy/HXZX/HGmW8gK14LoIiMKtxswsCuCapMHd3TPs1oTn65WoFYK2VqKwmAI0kQfjlQqoqjmAizSgIGdNESggENj3ukxKpZiIiIAgWDfyJyKtwUjn+M/wf+8sVfsCl/E/Kr8nHt0mvx+hmvIyU6xd+XR9SpIsNNDf39G2dzkwHFeWU1KtB3TAh25JfD2myePOlGJK0IUhxFhZtUq4MkBn3S49TYgj4N4xSSYjjImIh8j8E/EbkUEx6DF095US0CtrN0pyo3fHkD5p86H7ERsf6+PCKvt4B1SYxW5eSBmfbj1XUW/H6oHL/nlakVivXHuwsrm8w0JGrqnbcUCJlyVJKAPmlx6JehbdV+eiwXKyMir+FfFyJqVXJ0slrx97JPL1N3/zcd3oQ7vr4Dz57yLCJMvHNJoSc6wqymCZXiSJIC6Tq03SEhkO3OgooWLQWisKJWFZmZqLkuiVHolRqLnimx6KG2Megp29RYdE2MZlciImo3Bv9E1Kbu8d3x8qSX8afP/qT6/6/atwoPffcQHhr7EKdCJHJICoZ2T1LFUU29BbsLKpF7uEIlArLVy6HSGqfnkuNS1u5smRiEm8LQPVmSgRiVHEhCIGsXqG1yDNLjozj4mIhcYvBPRG6RmX6eO+U5XLP0GjUD0Pvb30d6TDpuHnmzvy+NKKBFhZsxoEuCKs1V1tZj5+GWicHOwxUtBhvr6q021cVIClDQ4vkIs9ZdqVuSlBh0S45GN9lPjrEfk2lMmSAQhSYG/0TktjFdx+DxEx/HnV/fqdYAeOXnV5AclYwrh17p70sjMiTp2y/rCEhxlhjIYmR7Ciu1oj+WRcoKK1ssXqars9jsC5kBLVsO9ClLuyRFoVuilhxIspCZEKUWNpOSmRCNzMQoJEQxTCAKNqzVROSR0/qcpqYAfWzNY2r/yXVPIiEyARcMuMDfl0YUdInBEV0SVGlOZiIqqarDnkIJ8iUhkAShCvuKq3CgpBoHSqpQXFnn8twyZam8XkproiNMKilIijIhK3WvliQkRjskCVFIi4tSg5dlxiQiCnwM/onIY38c9EeU1JTgxY0vqv0Hv3tQJQCTe0/296URhQQZa5McG6lK84HHji0HB1Ui0FCKq7C/pBoHS7QEYX9xFUqrnbce6KrrrNjdkCD8fKCi1ddKK0FqfKRKBCQhkK5Fsq+2DUUlCg3HZIwEEfkeg38iapdrjrpGJQD//fW/sNqsmLlyJuImxmFs97H+vjQiamg56JcRr4orFTX1KhHIK6tGflmNKrK2QV5pNfLLZavtSytDW6QbkpRdBZVuXp8ZKSqBidBKTCQSY/TH2jYpJlKth+D4GmmN4EQDRO3H4J+I2kX+8b1zzJ0oqy3DBzkfqEHAt3x1C+ZNnofhmcP9fXlE5Ia4qHC1AJkUV6xWK/bsPwhTTBLyK2pVQpCvJwvlNSgo16YslQHKBeU1bbYm6CprLais1boqeULGKyQ1SRAikBgdgfjocCSoEoH4KO2xs+NSOFUqhTLDB/87duzA7NmzkZ2drfaTk5MxY8YMr72PiBqZwkx4YOwDKgFYvmc5quqrcP2X1+M/p/8HR6Qc4e/LI6JOIisVZ8p0omlxbb62zmJFUUMyIEnB4fIa+5oG6li5bGvU45LKOhRX1cHibCGEVsYr6K0U7aUnAVpSEI746AjtcVS4SojiIs2IbdjGRDbdlxaVuKjGbXS4mTMnkaGE2WTUkEFJAD9q1Cjk5uaq4F3MnDkTaWlpuOuuuzr1faWlpUhKSkJJSQkSE1vOyuBtcuclLy8PmZmZMJk4qIoCS42lBtcvux5rDq5R+zIF6Ounv46eiT0RCFh/iAK3/kgYUl5TrwYoS/ciKfK4uKpW269suu/4Omk98DfpgRQT0SwpaJI8mNXzMsZBuizpj6Mi9OMmlUDI69Rj+2ubPs8Ew7isfvw3yFn8aujg/5prrlHBu9zB1xUXFyMlJUX9MenM9zH4J2pdRV0Fpn8xHT8f/lntZ8Vn4fUzXkdmbKa/L431hyhI648soCZJQFl1vSrlaqvtl1bXqaRCe67xsXRLKm94jZSqOv8nEO6Q2ZSiw00NSYLW4iCJgRyXtSRkK12i1FYdc3hsNqlkw/F5eRwV0fI9rs4VYTapBeakyxTHXBg7+Dd0t5+FCxc2CeCFfid/2bJlmDRpUqe+j4hci4uIw0sTX1KrAOeU5GBf+T61INi/T/s3UqJT/H15RBSEJFDNTJDS/nPUW6wOSUK9miVJG49Qj4qahq3s12jHK5w8V9Vsv7beis4m55Ti7pgKb5LEINwcppIBSQ7CTdq+JAiyyJzsy1YlDPrWpD/f8rWy33hOLeGQ14c7JByyldaPxn0TzCbALO9v9pxewls8NsEcFgZzw7WbwhqON98P8gTHsMG/3KmX0q9fvxbPSSC/YcMGp0F8e99HRG1Ljk7G3MlzceVnV6rgf3vxdpUAvHLaK0iM9H2LGRFRWyTA1KdN7Swy7kEShSqVLNSjus7SUKxqW9XwWLY1Dc85HpP9GofH+nON52k85g8y7iIAelx5lSkMDQlG0wRCkgxJIOR59bhhX3IFc0MCoW+118q5wmCpr8MLlyUgK6XtcTPeZtjgX/rtu5KamoqCgoJOfR8RuadLXBfMnzxfJQD5Vfn4tfBX/HXZX9UsQNI6QEQU7OSudlKMlAivfo50VZYVnVUw3tAyIF2htK21yfHGY9rzjq+RRKP5a9Vxh3PVW2yot8pxm2otkX1Jcuqs+mNtX56rs2qPjduxHJAx6PIdoBOTHPmOAoFhg/+2yN19b7wvPT29RVNQVZVn05S1t7+YVHLZEgU66e8vwf6fP/8zimqKsCl/kxoQ/OLEFxETHuPz62H9IWo/1p/AJgsryx3q2IjAGo8hZBYnSQYkiK5Xj7VERU8eGo9bG5OHhsRB9uW4OofVBovNBotKQGyw2hqOOZSW+1bIr6xsLfr7G67B6vB+dT6n73d4XcN16fvyekkOLA3HGreSNDgea/p9hHm5HsXEtPz31dlYVsMG/3offWcKCws7/X2tkUEc3ia/LDJYQ/4jBtqAKyJn4hGPJ0Y9gTvW3oGyujKsz1uP6764Dg+PeBiR5s5rXncH6w9R+7H+UGeSthB7e4i5obRoIAlrKMb+fbOpRAAqeSgqKYa5thR5ea2vlO0Lhg3+pYuOqzv1csxVkN/e9zkG+v6a7UdaHDIyMvjHlwxDZjaYlzwP05dOR3ldOTYUbMATvz6Bf47/JyLM3m0Od8T6Q9R+rD9EHa9DEeEmr9chZz1RZLYfmc0yKIJ/CdKluLpbP3ny5E59n07+o/nrj5/88fXn5xO1x7CMYXh50suYsXSGWgRs1b5VmLV6FuacNAfhJt/9CWL9IWo/1h8iY9YhZ59n6Fo8bdo05OTkOB3Q29qMPe19HxG1z/DM4aq/f5Q5Su0v3bUU93xzDyzWIJ8ugoiIKMAYOviXVXkXL17c5NjcuXNVcezKI3fzZQpPT95HRJ1rTNcxeO7k5xBh0rr7fJr7KR787kFYbRxESERE5CuG7fYjZK7+RYsWqWB+zJgx6u59WloaZsyYYX+NdO9Zt25dk24+7ryPiDrf2KyxeHrC07j1q1tRb6vHe9vfg9lkxr3H3QtTmKHvRRARERlCmM3ZHEDk1vLIvhTIy6sTeeqLnV/gzpV32u/6XzjgQtx3/H1eSwBYf4jaj/WHyLh1yFn8ylpMRD53ap9T8cSJT9iD/Xd+fwcPffcQuwARERF5GYN/IvKLM/qegdknzoY5zGxPAB749gEmAERERF7E4J+I/Ob0vqfjiZOesCcAMgbg/m/vZwJARETkJQz+icivTu9zOmaf1NgC8P7293Hf6vs4DSgREZEXMPgnIr87rc9p+Mf4fyA8TJuA7IOcD3Dft0wAiIiIOhuDfyIKCJN7T26SAHyY8yHuXX0vEwAiIqJOxOCfiALGpN6T8OT4J+0JwEc7PsLfvvkb6q31/r40IiKioMDgn4gCysTeE/HkhMYEQFYCvuPrO1BrqfX3pRERERkeg38iCjgTe01UKwFHmCLU/pe7v8RNX92Eqvoqf18aERGRoTH4J6KAdHKvk/HCxBcQbY5W+6v3rcZ1y65DRV2Fvy+NiIjIsBj8E1HAGtt9LP41+V+Ii4hT++sOrcOML2agpKbE35dGRERkSAz+iSigjeoyCq+c+gqSopLU/qbDm3D151ejoKrA35dGRERkOAz+iSjgDUsfhn+f9m+kRaep/a1FW3HV51fhUMUhf18aERGRoTD4JyJDOCLlCLx2+mvoEttF7eeW5OLKz67EntI9/r40IiIiw2DwT0SG0SepD/7vjP9Dz4Sean9f+T5cvuRy/Fb4m78vjYiIyBAY/BORoWTFZ6kWgP7J/dV+QXUBrvrsKqw9uNbfl0ZERBTwGPwTkeFkxmaqBGB4xnC1X15XjmuXXqvWAyAiIiLXGPwTkSHJ7D/zTp2Hk3qcpPZrrbW4bcVtePf3d/19aURERAGLwT8RGVZMeAyeOfkZnNPvHLVvtVlx/7f345WfX4HNZvP35REREQUcBv9EZGgRpgg8Mu4RXDHkCvuxZzc8i3+s+4dKBoiIiKgRg38iMjxTmAl3jL4Dt4y8xX7sjV/ewN0r70atpdav10ZERBRIGPwTUVAICwvD1UdejQfHPqiSAbFk5xLMWDoDJTUl/r48IiKigMDgn4iCygUDLsCzJz+rxgOI9YfWq8XADlYd9PelERER+R2DfyIKOhN6TsC/T/s3UqNT1X5uaS5u+v4mbCnY4u9LIyIi8isG/0QUlIalD8ObZ76JPol91H5RbRH+/Pmf8fWer/19aURERH7D4J+IglaPhB7475n/xYjMEWq/2lKNm766CQu3LvT3pREREfkFg38iCvrFwOZOmovxXcerfZn+8+HvH8bT656GxWrx9+URERH5FIN/Igp6UeYo/O2ov+FPQ/5kP/afLf/BLStuQWVdpV+vjYiIyJcY/BNRSJDpP28ddSv+fuzfYQ4zq2Mr9qzA5Usux/7y/f6+PCIiIp9g8E9EIeWiQRfhpUkvISEiQe1vK9qGP37yR2zM2+jvSyMiIvI6Bv9EFHLGdh+L/571X/RK6KX2C6sL1UxAH+V85O9LIyIi8ioG/0QUkvol9cNbZ72FY7oeo/brrHX42zd/w3MbnlODgomIiIIRg38iCumZgP41+V+YcsQU+7H5P8/HrV/dioq6Cr9eGxERkTcw+CeikBZhisB9x92Hu4+5Ww0KFsv3LMeln1yKnSU7/X15REREnYrBPxGFvLCwMFw6+FK8OPFF+0DgnJIcNRCYKwITEVEwYfBPRNRgXNY4/O/s/6F/cn+1X15XjhuW34CXN77McQBERBQUGPwTETnondgbb575Jib3nmw/9tJPL+Hm5TejrLbMr9dGRETUUQz+iYiaiY2IxVPjn8ItI2+xjwNYsXcFLvnkEuwo3uHvyyMiImo3Bv9ERC7GAVx95NV4eeLLSIxMVMd2lu5U4wA+2/mZvy+PiIioXcJhYDt27MDs2bORnZ2t9pOTkzFjxow237ds2TIsXboUxcXF6hxTp051631EFHrGZo3F22e/jVu+ukWtBlxZX4k7v74T6w+ux51j7kSkOdLfl0hERBT8wb8E7aNGjUJubq4K+sXMmTMxZ84c3HXXXa0G/hs2bFBJg5AEQM6zfv16zJ0712fXT0TG0TOhJ9444w089P1D+GTHJ+rY21vfxqbDm1T3oB4JPfx9iURERMHd7UeCd7lbrwf+YtasWSoBaI0E+I7Jgbxf3jNv3jyVUBARuRoH8Pi4x3H/8fcj0qTd7f+l4BdM+2gavtz9pb8vj4iIKLiD/4ULF9q7++j0REDu7ruyePHiFgnC6NGj23wfEZGMA5DVgN886030SuiljpXVlakuQf9Y+w/UWev8fYlERETBF/xLVx0p/fr1a/GcJADSrceVKVOmtEgaiIg8MSh1EBacvQCn9j7Vfuz1X17Hnz77Ew6UH/DrtREREQVd8N9a95zU1FQUFBS4fH7RokUtBveuW7dObSdNmtSJV0lEwSw+Mh5Pjn8Ss46ZhXCTNnxqU/4mXPjRhZwNiIiIApZhB/y2RloFPB0/IMVZS0Jz6enpqunfUVVVFbzNarXCZrOpLREFTv25eODFGJY2DHeuvBP7K/arhcBkNqDVe1dj5piZaqwAkZHx3x8iY9ShmJiYFsfkc4Mi+Hcc5NtcYWGhR+eSaT7ljn9rMwS1JS8vD94mvzAlJSXqP6LJZMgGGyK/8Xb9yUQmXjz2RTz7y7NYcXCFOvZ+zvtYe2AtZh01CwOTBnb6ZxL5Cv/9IQquOuTX4F/65k+fPt3t18+fPx8jR45UXXtc3eGXY60lB45khh85lydTfEqgn5ioLfjj618caXHIyMgIiF8cIiPxRf2RBOCZ7s/gox0f4bEfHkNVfRX2Ve7DLWtuwQ0jbsCVQ660rxZMZCT894fIGHXIWU+U0tJSpKSkBE7wL4G8zK/vKQnupbi6yz958uQ2zyGz/kii4Bj4u5M4yH80f/3xk18cf34+kZH5qv6cP+B8jOwyEnetvAtbCrag3laPZzY8g+8OfIdHT3gUXeK6ePXzibyB//4QGbMOOfs8w9biadOmIScnx+lA4LYG7kqLgyQOjl19JPDnVJ9E1Bl6JfZSi4JdPexqhEEbI7TmwBpc8OEFWJK7xGkfTCIiIl8wbPAvc/XL3XtHche/+Z18aQVwnPpTEoTHH39cdfeR9+tFzufOgF8iIndEmCNwy6hb8MqpryAzNlMdK60tVS0Cd3x9B4qqi/x9iUREFILCbAa+BSVB/YIFCzBmzBj7XX/Hu/lybNSoUWp6T701QPo9uZoNqLWvQvpMJSUlqQEb/urzL+MNMjMz2exKZLD6U1xdjMfWPIYlO5fYj6VGp6rVgk/pdYrPr4fISPWHyOisfqxDzuJXQwf/vsTgn8i4AqX+yPz/j37/KIprGm9AnJt9LmYeMxOJkb7/u0JkpPpDZFTWAAv+WYuJiHzk9D6n473z3sOEnhPsxz7M+RB/+OAPWL1vtV+vjYiIQgODf1KuueYaVTxdIM0fZIpWudbmYz6M/t34+uci/0iPScdzJz+HR054BPER8epYXmUerl12Le5dfS9Kakr8fYlERBTEGPyTfYpTGSzt7hoJ/jRjxgx1rWvXrg2q78aXPxf5f8q38/qfp1oBju92vP34+9vfx7nvn6u6B7FHJhEReYMhV/gl8rc5c+bYkwFJEDxZIboj76Xg0jWuK+ZOnovFvy/G0+ueRnldOQqrC3Hn13fik56f4J5j71GvISIi6iy880/kIQne9Tv1UmSxOumu4+33UvC2Akw9Yio+OP8DnNKzceafFXtW4PwPzsfCrQthtVn9eo1ERBQ8GPwTeUjWiZDAXSfTyEp/fW+/l4KbrAXwzMnP4OkJT6txAaKirgIPf/8wrvrsKuQUN13UkIiIqD0Y/JNTEpDKwmdTp05t8VxHV0P25rm9TdaO0McBNNfWdXfkvRQ6rQCTe0/G++e9jwsGXGA/viFvA6Z8OAVPr38alXWVfr1GIiIyNvb595Jznv8G+WU1nXhGGyxWK8xqftgwj96ZkRCFj24c59F7pk2bpoJUWRRNZp+ZMmWK/bmFCxc2uXvtKW+e29v0xeSak5+nrdmAOvJeCi1JUUl4cOyDOLPvmXjwuwexp2wP6m31+M/m/2BJ7hLcNeYuTOo1SSULREREnmDw7yUS+B8srYZR6Xen9Rlo9ABdgvWOBufePLcjd/vSyyrQHf3c1NRUFBYW+vy9FNyO7XYs3j33Xfx787/x6s+votZai4MVB3HbittwQvcTMOvYWeid2Nvfl0lERAbC4N9L5G575+rYnf/2uuiii+yDVDds2KAGqDqSO9Z6n3VPZ61p69ySDEhQvH79etVFSPrHe0ISC1/pSPDOwJ9aEx0ejeuGX4ez+52Nx354zL4Y2Or9q9XiYH8e9mf85ci/qNcRERG1hcG/l3jazSZQl4aWgFzu1EsgLtvmAbr0VS8oKEBaWlqnnluSASF35CXB6Nu3L4qKiuBv/fr1c3pcrtHVc53xXqJeib3w8sSX8eXuLzF77WzVAlBnrcPcTXPxUc5HuG30bTi196nsCkRERK1i8E9tkjvuCxYswKJFi1o8J1125M51e/usuzq3nHPp0qXq/JIYSNcYZ60Dvu72I0G6XI/0328esLfVMtGR9xIJCewn9Z6Esd3HqqD/9S2vq7EA+yv2446v78DIzJFqPMDQ9KH+vlQiIgpQDP6pTRKoyt15T0iAK60CbQXVrs4twbBjQCzJgCeBvze7/cyaNavJz9Z8rEJrP3tb7yVyR2xELG4ddSvOzT4Xs3+Yje8OfGefFejiTy5Wx28eebOaPpSIiMgRp/qkVsnd9uzsbPs0le6SAFem82ztPe6eW+7gz58/H4FCxjbI9UrgLmXt2rVNEo3Wfva23kvkiezkbLVC8IsTX0SfxD724x/mfIiz3zsbc3+ai+p64048QEREnY/BP7kkQaoE5nJnWu7QyzSc7pL3yEBdV4NZ3T23BMiTJ09uMh1oIJAgXq5JyuzZsz362Vt7L1F7ugKd1OMkNSvQzDEzkRCZoI5X1VfhhY0v4Jz3z8H729+HxWrx96USEVEAYPBPLsksPnrQLVvpg+8JZ33bPTm33EGXPvLyvLQSuJonPxC19rMTeUOEOQKXDbkMn/7hU1w88GKYw8zquAwMvnf1vZjy0RSs2LMCNpvN35dKRER+xD7/5DI4d+yLLtNyysBYvSuLPle/BOgSuOsz1jjeoXfVlcedc0vw7LgCsDxnpKCFi3aRvyRHJ+Oe4+7BRQMvwlPrn8I3+75Rx7cXb8eNy2/EiMwRaryAbImIKPTwzj/Zu9dI33oJWuUu++jRo+0BvpDBttJdRfqyS8Cvk0G5MlOPPjNPW9NXuntuea9M7akXx8BfkgfHxMCX34072jt1p69/Lgpu/VP64+VJL+Pfp/0bR6YfaT/+Y96PuGLJFSoRyCnO8es1EhGR74XZjHQ71Y9KS0uRlJSEkpISJCYm+vzz/TXPP1EwCPX6I3/mZX2AZzc8i52lO+3HTWEmnNn3TFx79LVcKZhcCvX6Q2TkOuQsfmUtJiIKkfUB3jvvPdx//P3IjNGmALXarPh4x8c49/1zcc8392B36W5/XyoREXkZg38iohARbgrHlCOm4OMLPsYtI29BUlSSPQmQ6UElCfj7N3/HnrI9/r5UIiLyEgb/pEifdk/6tfuT9I2Xa/V04bFg/G58/V1QcIgJj8HVR16Nzy74DDeOuBGJkVpTsMVmwQc5H+Cc987BfavvYxJARBSEGPyTCmplAK4sNuU4EDdQyUxBcq2yQFaofze+/C4o+MRHxmPGUTPw2YWf4frh19vXCJAk4L3t76mFwmaunIltRdv8falERNRJONUnUTvMmTPHngxIgiCzFbVGZjGSIF0WLJOZgGR2pDFjxri9eJmnn0fkCQn6ZdDvJYMvwZu/vIk3fnkDZXVlqjvQp7mfqjKhxwTVWjA8c7i/L5eIiDqAd/6JPCSBuH7XXYpMVSpdb1ojAbskAHoXouzsbI8Cf08/j6g9pPvPX4f/FUsuXKJaApKjGlu7VuxdgcuXXI6rPrsKq/etNtS6G0RE1Ih3/ok89PjjjyM3N7fJWgdyR1/u7LdG3tOerkPt/Tyi9pKBwNIScMWQK/Du7+/itS2v4VDlIfXcukPrVBmUOkg9f3qf09XqwkREZAy8808uB5LKolvOFp3S72IH4rm9TVYe1scBNOeN6/b15xE5io2IxWVDLsOSC5bgobEPoU9iH/tzvxX+hr998zec9s5pmLdpHoqqi/x6rURE5B7e+feWueOB8rxOO10YgAyrBWEms+dvjs8Ervnao7dMmzZNBZwpKSlqJhnHLioLFy5U3U/ay5vn9jYJxp2Rn6et2YDkZ0tNTUVhYSFycnIwe/Zsr34eUWeRO/t/GPAHnJt9LpbvWY5Xf34VWwq2qOfyq/Lx/I/PqwTgnOxzcPngy9Ev2fMVromIyDcY/HuLBP5l+zs1+G9H2N9u+p1mfTYZPUCXYL2jwbk3z+3I3X7xo0aN6vDn6kG9K9JPX8hgX731Q1o+Fi1a5JXPI/IGs8mMyb0nY1KvSfgx70c1MFiSARkYXGOpweJti1U5IesEXDH4ChzX/Ti1ijAREQUOBv/eInfbO5EMrbNaLTCZzCoR8NW1XHTRRfYBpxs2bLAHsTq5+yyBrPB0Bpq2zi3JgAS469evV4Gy9HX3hC/7xLcViOtBv2Prh752QHvGATDwJ3+vGDyyy0hV9pbtxZu/vqmmBq2oq1DPy4BgKb0Te2PqEVNxXvZ5SI4OvKlyiYhCEYN/b/Gwm01bbFYr8vPykJmZiTCT7+6kSUAuwakE4rJtHqBLv/OCggKkpaV16rklGRByR14C5L59+6KoyP99ipsH8Tq5RlfPiebdm/SAX7r1NP9OO+PziHylR0IPzDxmppodSAYHv/XbW9hXvk89t6t0F55c9ySe2/AcTu97OqYNnIaj0o9SyQMREfkHg39qk9xxX7BggdMuKhLQyl3o9vY/d3VuOafMhS/nl0BZurk4ax3wdbcfCbjleiRobx58u2qZkO9GWi6kn7/+Hv37aiuAb8/nEflrwbArhl6BSwdfiq/2fIW3t76NNQfWqOdqrbX4MOdDVWSWIGkNOLvf2WpAMRER+RaDf2qTBJ1y59oTEqxKq0BbQbWrc0tg6xjcSjLgSeDvzW4/s2bNavKzNR+rID+7HNO7QUnwLo8dg3fpKqUnNm19X219HlGgjQuY1HuSKrkluVi0bRE+2P4BSmtL7bMEPfz9w3h6/dM4o+8ZOL//+WwNICLyIY7EolbJ3XZZkEqfctJdEqzKdJ6tvcfdc8sd/Pnz5yNQSCAv1ytBuJS1a9c2STT01XybB/AyvkEv0lXKsbWjte+rrc8jClR9k/rirjF34cupX+LhEx7GkelH2p+T8QEyOPiyTy/D+R+cj39v/jfyK/P9er1ERKGAd/7JJQk4JTCXu8wyLaUn03DK6+TOvdyxdzag1d1zS7ArC1q5uxqurzgObm5+bfpKvI70u//t/b5a+zyiQBcdHq3u8Ev5peAXLNy6EJ/mfoqq+ir1/I6SHfjn+n+qsQEyU5C8bnyP8Yg0R/r70omIgg7v/JNLetcUIVvpg+8JZ/3UPTm33A2XQFiel1YCV3PeB4vWvi+iYDEkbQgeGPsAVkxboRYOG9VllP05i82ClXtX4rYVt2Hiool4bM1j+Cn/J9hsMt8ZERF1Bt75J5fBuePda5mWUwbG6t1S9LvTEqBL4K7PPuN4V9pVVx53zi2BsOMKwPJcsAcAXLSLQokM9pWFw6TsLt2N97e/rwYEH6o8pJ4vrinG/377nypZ8Vk4s++ZqvRP6e/vSyciMrQwW7BHVJ2ktLQUSUlJKCkpQWJios8/32q1Iq9hqk9TJ0/1KUGnBN/S7US64Oh32JsPsNX7pLvTDUfv1tP8HPoUnh05tyQPknBIsuHOKrmd+d20Z05+dz+nrWk//f1dGJk36w91HovVomYIej/nfXy560s1S1BzA1IGqCRABgtLUkDex/pD1DH+rEPO4lcG/24K5uCfKNix/hhPWW0Zvtz9JT7d8SnWHFyjVhFubnjGcG3F4d6T0D2+u1+uMxSw/hB1DIN/g2LwT2RcrD/GdrjqMD7f+bkaJLwpf5PT1wxNG6qSAEkGZGVh6jysP0Qdw+C/E0k3CenqINNFCumS0Z75z6WrSVuDWRn8ExkX60/w2FO2B5/lfqYSge3F252+pn9yf3uLwIDkAVxDoINYf4g6hsF/Jwb+0hc7NzfX3g9b+o2npaW1OqViczLnuryvra8h2IN/fTVcb/Zr7yzSz339+vU+mwLUSN9NsHznnY3BS3DaUbwDS3ctxbLdy9TiYc70iO+B8T3H46QeJ2F0l9GcPrQdWH+IOobBfycGZBKIOQ5ylEGTKSkpbs8KIwmEBP4yl3woB//yvT3++OOGGzAq/+18MeDXiN+Nkb9zb2DwEhotAst2LVNl02HnXYNiw2MxtvtYlQic2ONEpMek+/w6jYj1hyi4gn/DTvUpi0I1D0Icp5+U2VnaIkG/TDMpWyJvk1Ym/XdUkoq2Wqj0lYLlbrvM5iNd08aMGeP2nXdffx6RP/VM6Imrhl2lysGKg2qw8PLdy7Hh0AbU2+rVayrrK1UrgRQhKw5LIiBlUOogmMIY2BJR8DNk8C+BjD6vfHMS7Mh0km0F/xLw64tHEXmbBOJCH5Migba0Xkmw7Yr8jsvr5HdVftflrrsngb8vP48okHSN64pLB1+qSmltKb7d/y1W7V2lSlFNkf11Px/+WZUXN76IlKgUHNftOBzf/XhV5BxERMHIkMF/ayu9pqamoqCgoNX3S5BTWFioAhxPg//09PQWg8eqqrQl6r3dZCRdk2RrpHN7ky+uubO+G+k6lJOTYz/PKaecou6wv/zyy61+trzHcZyBu9fhrc8z4u+JkX/HqePiw+Nxaq9TVZF1BDYXbFarCK/ctxLbirbZXydJwZKdS1QR/ZL6qWRAypguY9SiZKGK9YfIGHUoJiamxTFn3doNGfx3dKVUGbzoyaDgtkg/Lm+TXxjpryX/ETu7v5ict7KyssnP8cYbb2DXrl2qzJ8/v8Xrf/rpJ5x00knt+rzOOnfza/YGZ9+Np+TnlN/J2traFueRu+yuflbpp5efn6/eFyif54vv3Gj1h4ylG7rhoqyLVMmrysOa/DVYX7AePxb+qLoF6XaU7FDlrd/eQnhYOAYnD8bw1OE4KuUo9TjKHIVQwfpDFFx1yJDBf2szrsgd/da4Ox7AFQl83Bnw+8dP/ojD1YfRaWzaL4/6pfFw1rr06HT876z/uXw+MjISsbGxaiCK7uqrr1bfs8yetHLlyibdP95///12Tana2edufs3e4Oy78dSmTdrgw+bn0H+PXZ1bfs+++uor1Zolv9fS4vXEE0/49fN88Z17g9QdabHLyMgIiD+8FBgykYlhvYfhalyNems9Nh/ejO8OfIfvD3yvugNZbBb1Ohkz8HPRz6qICFMEhqUPU7MHSTkq/aigbhlg/SEyRh1y1hNFbuzJZDgBE/xLl5vp06e7/Xq5Szxy5EgVnLi6wy/HWksO5DM7ctdf/qO58x9OAv+8ysC5Q9raNctz8kvp+Br9O5ZAXL73adOm2e8cX3vttR26ls46d/NrdjVFZ1tkylhXCYez78ZT+nubn0O+B/l9dXXu0aNHq60+tkVarGSA+qJFi/z2eR39LvxJv3ajXj95V6QpEiO7jlTl+hHXqxWGfzj4A77b/50qu8t2219bZ63Dj3k/qjL/5/mqZWBo+lCVCIzsMhJHZxyNpKgkBBPWHyJj1iFnn+fX4F8CeZk73FMS3EtxdZdf+jY7I8GM9GmWgYw6vc9/e9YIaI03ppCzWqwwmU0+vRYJ/vTBo/JdyX8zRxJMyvcqPP3u2jq3JAPy31h+R6ZOnepxi01rg1s7Qq5rwYIFbb5u1qxZLX4mT1qpmg9olyRJEpq2EtxA+TwiI0uITMDEXhNVETKD0NqDa7Hu0DqsO7iuSTIgLQM/5f+kyqubX1XH+ib1VUmAlOEZw9EvuR9nEyKigGDIbj96YCKBvLOBwK6CRGd3dyVwla5AnT13+YKz2w4OjTBHrASvEvhJwCvb5sGsfHcywFoSp848t56UyX8zCT779u2LoqLGWTr8SbopeTILjrNZqYSrGauaz0il0wNw+T1vLanw9ecRhQKZ/eec7HNUEYcqDmH9ofVYe2itSgZ2lu5s8vrcklxV3t/+vtpPiEjAkRlH2pMBeSwJBhGRrxk2+Jc79XKH3zFolzu9jnd7JdiRO8byGlfBS1uDg0lLpuROt7PuJhIsyh3l9n6Prs4t55R55uX8EoRKlxVnrQOt6YxuP51BAm75GSSIbh58u0pU9d9dSXD19+jfcWsBvD8+jygUdYnrgjP7namKOFx1WLUK/JSntQD8WvirGkegK6srU1OOStH1SeyDwWmDMTRtKIakDcHg1MGIj4z3y89DRKHDsMG/BCQSMEoSIAsRSaAjd58dgzgJINetW+e0u4O8XhIFfYEvCXwkmfBmEGjk79rThdDk+5VWgba+T1fnliDVMVCV/4ae3n32Vref9pAuQI7fh/zMjt+NfF9yTO86JcG7PHYMvKWVSk+G2vqOvfF5RNR698rT+5yuiqiur1YJwMa8jSoZkG1BddNpqKW1QMqSXG160TCEoXdibzV+YEjqELWVhCCYBxMTke8ZNvgXEgy21f3BVVcReU5aBDq7u0+wkbvt2dnZKlj0pO+3BJ6SmEn3LFfvcffccge/+ZSgRiOBtYxv0BOdtWvXNklO9NV1HcdNSACvj4kQ0r3KsYWkte/YG59HRO6LDo/GiMwRqgiZ4m9f+T57IrClYAu2Fm5FrbVxal0bbPaE4JMdn9gTgl6JvXBEyhFNSvf47hxDQETtEmZzNvs/OZ0qKSkpSc3T6s5Un53Nm33+JfCWRaGaJ0L6iq9y91eCdAk0XY2bkNc2H/Crj8Fw1m3E3XPrwauzPvbyHm8nb66+m0DR2nfsDb74zr3BX2NmiFojswblFOdgy+Et+KXgF5UQyMJjcrwtcRFxGJA8oDEhSD1C7Xuj2xDrD5Fx65Cz+NXQd/7JuxwXQ5PgW/rge9ItSgJTV33M3Tm3JAdyR1vOIa0E8pj9z93/jokosMl6AYNSB6lyIS5Ux+osdfi9+Hd7MvBrwa/YXrwdNZaaJu+tqKvAxvyNqjjqHtcdfZP7qhWKHUtyNLvvEZGGwT+5DM4dg3GZllMGxuqDQPVuJhKgS+CuzyTjeIfe1SBgd84tQa2Mw3A8FxupWuKAdaLgEmGOUIN/pUyB9vfUYrVgV9ku1SqwrXAbfi/6XT3eX7G/xfvlmJTV+1Y3OZ4anaqmH22SFCT3Q2ZsJrsPEYUYBv9k714jgaR06ZDAWxZ8cuxHLmMr5E69PsuSHuQ3H5jb1rSScgffnXO3Nl5DkgdJOHzVCuD43QTS4Ne2pu7sTL7+zomokdlktgfs+oBiUVpbiu1F27WkoGgbthZtxY7iHSivK29xjsLqQlVkelJH0eZo9EjogV4JvdTYgp4JPdWgY9mXGY2YGBAFH/b5d1Mw9/knCnasPxQq5J/0/Kp87CjZoRIB2cp6A7KV6Ug9XfVYEgNJCNLN6RjUZZBKELrFd1MDjqPMUV77OYiCiZV9/omIiMgbwsLCVFceKcd1O67JcyU1JfbFx/SkQFYq3lu21+kgY5mJSCURJdrEAtjVcnpTSQJknIFss+Kz0C2um7aN74aY8Biv/qxE1D4M/omIiEJAUlQShmcOV8WRjCk4VHlIJQK7SxtK2W7sKdujSvPBxjppSZCyKX+T0+dlnIEkBrI6snQhkoSkS2wXe8mMy2TrAZEfMPinJqvhBlq/dlf9z9evX99k7IE3Gem7CcTvj4gCf0yBuoMf371Fa4HVZsXB8oPYtHsTSs2l9gHF+8u1Il2MXNHHGWwu2OzyNSlRKVpSENeQEDgkCGkxaap1ITkqWV0jEXUOBv9kX2DLKPO36zMFyQBhbwevRvtuAu37IyJjkwG/cufelGZy2l9ZWgUOVhxUC5jpCYGeHMix/Mp8tXiZK0U1RarIYGVXzGFmpESnqERAJQTRDduYdHuR/bToNCRGJqquT0TkGoN/onaQlXD1VgBnC5w5oy+GJu/LyclRK+q625Lg688jInKHdNuR2YGkOCPrFkjrQF5lHg5WHsShikPqsXQzUtuG/XpbvcvPsNgs9i5G7gxSlkRBirQYSMuCehytPZZtalRq435UsppelSiUMPgn8pAE4o530GWtA+kaNHfu3FbfI693DOCnT5+ORYsWBdznERF1Fgms9S5FrkjXIukepBKCisbEoKC6AAVVBfbAXx63liTog5Tl/VLcFR8RryUMDcmBtB6oEtWwjUxEQmRCi2MyoJmtDGREDP6JPPT4448jNzfXvi/rHEj/+daCcZkj3/FuvQTl7i7Q5evPIyLyddcivfvO0LShrSYJpTWlKinQEwI9KdCPSStDcXWx6kpUb209UdDJughSZHCzJ8JN4U4TBT1ZiI+MV4lFXERc4zay6X6kOdKjzyTqDAz+yWWXEekqIgt+Nb9bLEHkunXrnC7u5e9ze5tcs96Vpjm5I+/quuX1ErDLz6uvYOzOglm+/jwiokBOEuTOvJTs5Ow21zuQgF5PBIprilXrgr5fVK2NNXDcl0XTPCHJhT6oub0iTBEuEwO1jYxDbHisamWQEhvh8LjhuNpGaMekcGE2aguDfy/JvXAK6g97tqBKWywWC8rMns94EJ6ejr7vLPboPdOmTVNBY0pKilrh1nFg6MKFC+1dUNrDm+f2NgminWnrzvr8+fMxatQo9TPLHfns7OxW79z76/OIiIKBdMeRu+9SeqKn28G8rIUgSYAqNaVNHpfVljXuN3u+oq6iXdcp6yvog547i6zarCcCzRMGvUSHR6vXRYVHqXEbepHjamuOVq0SjvuOr5V9aflgtydjYvDvJRL41x861PnnhW/od5olEJegUQ/QJVjvaHDuzXM7m6KzLRIkd/RzU1NTUVhY2OrPLLPrSHcc6Y8vd+z1JMgIn0dEFOwkmFWzBsWkefxeSRwkObAnCDWlqKivQHltuUoMpBWisq7S3sVIHXN4Tt9va0yDO6ot1ap0ZkLhjLQwOEscpEjiIIOvZcyHvpVWDvvxhsf25/Xn5JgpwvVx/X0O55L/bnqRmaGYkLSNwb+XyN32ziZ3/s3tvPPfXhdddJF9wOmGDRswcuTIJs/L3WfpxiPcmYHGk3NLMiABrsxJP3XqVI+7AvnyTndrgbiQQFzvhiN38+XnkaRDuj8Z4fOIiMg1CTz1WYbaS7oqyYDl5kmBJA2V9ZWoqq+yFzlmf+z4XF2z/YbiDTIGw5vnby+VCIQ1JgT2EuZ632wyq21EWETTYw6vkYRDTzAczyPH5ZgkQ/rz8l79dXJc/ldeWo7JKZMRHxXv76+Iwb+3eNrNpi1WqxV5eXlO51n2JgnI5W6xBOKybR6gS7/zgoICpKWldeq5JRkQckdeEoy+ffuiqMi7dzHc4arfvFyjq+f0fvt68iKvk4RGgvHm3Z78/XlEROQfcsda3TmPiWpX60NrQXp1fXWTZKGmvka1Dsg6DarUa1s5VmupVa/X9/XnnO2rYw2vdSz+JK0w8j9YEHBG9BrB4J+MQYLIBQsWOJ0mUgJJuQvd3plkXJ1bzildVuT8khhINxdnrQO+7vYjgbSrAbSuWibktc6627hzfb7+PCIiCi5y51n6/UvxBUk2JACXJEJaMmStB30rYxzsxxse249ba7V9/bi1zv7e1o6rYN9Wr20birxG1odwPGYvtsbHrS1A5w2BslI1g39qkwSdcsfYExKASqtAW0G1q3NLYOsY3Eoy4Eng781uP7JYluPP1nysgvzsckzvBiU/h6wQ3HzWHrkbr19ja9+XNz6PiIjIW8mG3k8/0FmsFpUMyFYShuYJgv24Q8Kg3tPwGv09esIjCYfjY3mtnoSUlJWoaWADAYN/apXcbZeZYlqbctIZCVal33lrg0zdPbfcsZbZawKFBNkyVkFPWtauXdskqJafXfYdx0BIy4bM1y/do/SZeiRAd+f78sbnERERhTqz9M2HGfJ/b9K7bsvsU4GAwT+5JAGjBOZyl1kCR0+m4ZTXyR1ouWPvLKh399wS8MrA1UDrp+4YaDe/Nvk5mv8s8h20Fny39X119ucRERFRaOJKEOSSzOKjB5qylT74nmhtYSl3zi13tCWIleellcDVnPfBggtxERERkbfxzj+5DM4d7ybLtJwyMFYf2KvfnZYAXQJ3ffYZx7vSrgYBu3NufXpKx3PJNGjBrL2DpomIiIjcxTv/ZO9eI33rJQCVu+yjR49u0v1EBttK1xPply4Bv066qkj/cn1mnramonT33PJemdpTL46BvyQPjomBL78bb2lt6s7O5uvvj4iIiAJHmC3Yb6d2ktLSUiQlJaGkpASJib4fre2vef6JggHrD1H7sf4QGbcOOYtfWYuJiIiIiEIEg38iIiIiohDB4J+IiIiIKEQw+CciIiIiChEM/omIiIiIQgTn+TeImJgYta2qqvL3pRAZDusPUfux/hAFVx3inX8iIiIiohDB4J+IiIiIKEQw+PeSF1980SuvDUWB+P346po6+3M643ztPYen73P39YH4+xFoAu07Mmr96YxzBlr9ac+5Q00gfj9GrUP++jfIm+95MQB/P9okK/xS20pKSmQlZLV1x+DBg90+tzuvjYyMVMVisdhCjSffZbBdU2d/Tmecr73n8PR97r6e9cd4dcio9aczzhlo9ced17L+BFb9MXId8te/Qd58z+AA/zfIWfzKAb9ustls9mWS3WGxWDr1tY6fH2rLq3vyXQbbNXX253TG+dp7Dk/f5+7rWX+MV4eMWn8645yBVn/ceS3rT2DVHyPXIX/9G+TN91gC/N8g/dr0axBhkgH49CoMau/evejZs6e/L4OIiIiIyCN79uxBjx491GMG/26yWq3Yv38/EhISEBYW5u/LISIiIiJqlYT5ZWVl6N69u73VgcG/we3YsQOLFy9Gv379sHbtWlxzzTXqMRG5X4dmzpyJ+fPnIzk52d+XQ2QYGzZswLJly9Rj+fdn9uzZ/PeHyAN6/SkuLlZ1aPLkyZg0aRK8jcG/wY0aNQrr16+3//JMnDjRvk9Ebf/hTU1NVfWoqKiIwT+RB+bMmYO77rpLPZ43b54K/nNycvx9WUSGkZKSgi+//BIjR45UN3KnT5+u/i3yttAbuRNkd10cSeAiCYDcySSitskdFvmjy6CfyPN/fx5//HH7/rRp09S/Pfz3h8h9euAvCgsLMXr0aPgCZ/sJAHLHRO6WyF2T5uQPqRzPzs5W+xKkzJgxQz1et26dyz/KbHqlUNHe+kNE7a8/ErAsWrTI/loJXIS0pBGFknkd+DdID/zldUuXLsXcuXN9cs0M/v1E/4UQCxcudBqQyGukO0Jubq79zqT0TdabWuUuf/M/tPI6/Y8wUbDqjPpDFKo6q/449k2WoEXOw1Y0CgU7OvHfILlhKzdzfXnTln3+A4D8csgf0eZZowzelV8Yx+MS8EsfMfnPJtmm/MF17OMv2aW8fsqUKT79GYiMVn8cyTHHP9BEoaIz6o/0VfblXUuiYKtD+hg0GfArrQjeTgTY5z+ASTapNxXp9OBEfkmc9Q2Tu/56MxJRKGur/hBRx+uPPJZ/d/TAX4IbIkKbdUiK4/N6TOeLcTMM/gOU/AGV4iz7k18eaSaSIN/xD63+evb3p1DnTv1p/noi8qz+yFYCFRnsK6+X1mgiglt1SLptO/bSkK4/8pwvBv2yz3+Aai3zk1+YgoIC9VgGXEkfsjFjxqg5Yh0HYBGFKnfrj9x50QMZmblE6hG7zFGoc6f+6P2Z9e4NOg6oJ4JbdUhu4Mrr9KRZunDL7D++6H7K4N+g9DuV8sujd/Nh0ELkWf2RfppSOACYyH36HU0OGSTq2L9B/orb2O0nQLWW+XE2H6LWsf4QtR/rD1Fw1yEG/wFKn8LTWV9kOcZZSYhcY/0haj/WH6LgrkMM/gOU/GK0Nme/TAdFRM6x/hC1H+sPUXDXIQb/AUxmUJD5Xp0NInFcXIWIWmL9IWo/1h+i4K1DDP4DaEqo5mQWH1k8xZHMpcyFVIgasf4QtR/rD1Ho1SGu8Osn8osiUwvqcyNL85BkibLgQ/NlnxcsWKCmINQzRs5MQqGO9Yeo/Vh/iEK7DjH4JyIiIiIKEez2Q0REREQUIhj8ExERERGFCAb/REREREQhgsE/EREREVGIYPBPRERERBQiGPwTEREREYUIBv9ERERERCGCwT8RERERUYhg8E9EREREFCIY/BMRERERhQgG/0REREREIYLBPxERERFRiGDwT0REREQUIhj8ExERERGFiHB/XwAREYW2OXPmICcnB9nZ2UhOTsaMGTMwc+ZMXHPNNejXr5+/L4+IKKiE2Ww2m78vgoiIQtPUqVNVgD979my1v2PHDhX0r1u3DkVFRf6+PCKioMPgn4iI/Bb4S7C/fv36JselBUASgqVLl/rt2oiIghW7/RARkc9t2LABixcvbhHgFxcX2+/+ExFR5+OAXyIi8jnp0y8mTZrU5PiyZcucHicios7B4J+IiHxO+vQ7C/D1loCRI0f64aqIiIIfg38iIvI56d7jLMCXO/+8609E5D0M/omIyOdkSs+0tLQW4wCkv//kyZP9dl1ERMGOwT8REfmczOW/du1a+74E/dOnT1ePeeefiMh7ONUnERH5hczoo7cAyFam/Jw3bx74zxIRkfcw+CciooDA+f2JiLyP3X6IiMjv9Pn92d+fiMi7GPwTEVFATP0p2N+fiMi7GPwTEZHfcX5/IiLfYPBPRER+s3jxYtXVZ86cOWpfHssxIiLyDg74JSIiIiIKEbzzT0REREQUIhj8ExERERGFCAb/REREREQhgsE/ERERERFCw/8DXLZSPtLjBSIAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8, 5))\n", "for chi1z, chi2z, label in [\n", " (0.0, 0.0, r'$[\\chi_1,\\chi_2]=[0,0]$'),\n", " (0.5, 0.0, r'$[\\chi_1,\\chi_2]=[0.5,0]$'),\n", " (-0.5, 0.5, r'$[\\chi_1,\\chi_2]=[-0.5,0.5]$'),\n", " (0.8, 0.8, r'$[\\chi_1,\\chi_2]=[0.8,0.8]$'),\n", "]:\n", " chif = gwModels.remnants.gwModelRemS_chif(q_plot, chi1z, chi2z)\n", " plt.semilogx(q_plot, chif, lw=2, label=label)\n", "\n", "plt.xlabel('$q$')\n", "plt.ylabel(r'$\\chi_{f,z}$')\n", "plt.legend(frameon=False)\n", "plt.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "id": "e27de23f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Recoil velocity: peaks at intermediate mass ratio, vanishes at both ends\n", "plt.figure(figsize=(8, 5))\n", "for chi1z, chi2z, label in [\n", " (0.0, 0.0, r'$[\\chi_1,\\chi_2]=[0,0]$'),\n", " (0.9, -0.9, r'$[\\chi_1,\\chi_2]=[0.9,-0.9]$'),\n", " (0.5, 0.0, r'$[\\chi_1,\\chi_2]=[0.5,0]$'),\n", " (-0.9, 0.5, r'$[\\chi_1,\\chi_2]=[-0.9,0.5]$'),\n", "]:\n", " vk = gwModels.remnants.gwModelRemS_kick(q_plot, chi1z, chi2z)\n", " plt.semilogx(q_plot, vk, lw=2, label=label)\n", "\n", "plt.xlabel('$q$')\n", "plt.ylabel(r'$v_{\\rm kick}$ [km/s]')\n", "plt.legend(frameon=False)\n", "plt.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "id": "74237c71", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Peak luminosity and peak frequency\n", "fig, axes = plt.subplots(1, 2, figsize=(13, 4.5))\n", "\n", "for chi1z, chi2z, label in [\n", " (0.0, 0.0, r'$[0,0]$'),\n", " (0.5, 0.0, r'$[0.5,0]$'),\n", " (0.8, 0.8, r'$[0.8,0.8]$'),\n", "]:\n", " axes[0].loglog(q_plot, gwModels.remnants.gwModelRemS_Lpeak(q_plot, chi1z, chi2z),\n", " lw=2, label=label)\n", " axes[1].semilogx(q_plot, gwModels.remnants.gwModelRemS_omega_peak(q_plot, chi1z, chi2z),\n", " lw=2, label=label)\n", "\n", "axes[0].set_xlabel('$q$')\n", "axes[0].set_ylabel(r'$L_{\\rm peak}$ [$c^5/G$]')\n", "axes[0].legend(frameon=False)\n", "axes[0].grid(alpha=0.3)\n", "\n", "axes[1].set_xlabel('$q$')\n", "axes[1].set_ylabel(r'$M\\omega_{\\rm peak}$')\n", "axes[1].legend(frameon=False)\n", "axes[1].grid(alpha=0.3)\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "3fc01ce4", "metadata": {}, "source": [ "### 3. Physical limits, exact by construction\n", "\n", "The ansatz is built so that the equal-mass and point-particle limits hold identically rather than approximately.\n", "\n", "- At $q=1$ the weights $(1-4\\eta)$ vanish and only the equal-mass polynomial survives, giving $M_f/M = 1 - \\hat E_{\\rm EM}/4$.\n", "- Equal-mass equal-spin binaries are symmetric, so $v_{\\rm kick} = 0$.\n", "- As $\\eta \\to 0$ the Kerr ISCO anchors take over: $M_f/M \\to 1$ and $\\chi_f \\to \\chi_{1z}$." ] }, { "cell_type": "code", "execution_count": 8, "id": "3d876ab1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " q=1, chi1=chi2=+0.00 : v_kick = 0.000e+00 km/s\n", " q=1, chi1=chi2=+0.50 : v_kick = 0.000e+00 km/s\n", " q=1, chi1=chi2=-0.80 : v_kick = 0.000e+00 km/s\n", " q=1, chi1=chi2=+0.99 : v_kick = 0.000e+00 km/s\n" ] } ], "source": [ "# Equal-mass equal-spin binaries have zero recoil, to machine precision\n", "for chi in [0.0, 0.5, -0.8, 0.99]:\n", " vk = gwModels.remnants.gwModelRemS_kick(1.0, chi, chi)\n", " print(f' q=1, chi1=chi2={chi:+.2f} : v_kick = {vk:.3e} km/s')" ] }, { "cell_type": "code", "execution_count": 9, "id": "e63ba62c", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Point-particle limit: compare against gwModelEMRI, which evaluates the\n", "# exact Kerr test-particle result with no fitted terms\n", "q_pp = np.logspace(2, 5, 40)\n", "chi_pp = 0.7\n", "\n", "Mf_S = gwModels.remnants.gwModelRemS_mf(np.minimum(q_pp, 10000.0), chi_pp, 0.0)\n", "chif_S = gwModels.remnants.gwModelRemS_chif(np.minimum(q_pp, 10000.0), chi_pp, 0.0)\n", "Mf_E, chif_E = gwModels.remnants.gwModelEMRI(q_pp, chi_pp, 0.0, 0.0)\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(13, 4.5))\n", "axes[0].semilogx(q_pp, Mf_S, lw=2, label=r'\\texttt{gwModelRemS}')\n", "axes[0].semilogx(q_pp, Mf_E, '--', lw=2, label=r'\\texttt{gwModelEMRI}')\n", "axes[0].set_xlabel('$q$')\n", "axes[0].set_ylabel('$M_f/M$')\n", "axes[0].legend(frameon=False)\n", "axes[0].grid(alpha=0.3)\n", "\n", "axes[1].semilogx(q_pp, chif_S, lw=2, label=r'\\texttt{gwModelRemS}')\n", "axes[1].semilogx(q_pp, chif_E, '--', lw=2, label=r'\\texttt{gwModelEMRI}')\n", "axes[1].axhline(chi_pp, color='grey', ls=':', lw=1.5, label=r'$\\chi_{1z}$')\n", "axes[1].set_xlabel('$q$')\n", "axes[1].set_ylabel(r'$\\chi_{f,z}$')\n", "axes[1].legend(frameon=False)\n", "axes[1].grid(alpha=0.3)\n", "\n", "plt.suptitle('Approach to the point-particle limit')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "f04399b5", "metadata": {}, "source": [ "### 4. Comparison with other remnant models in gwModels" ] }, { "cell_type": "code", "execution_count": 10, "id": "8f83494a", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Single-spin slice: chi2z = 0, sweep chi1z\n", "chi1_arr = np.linspace(-0.99, 0.99, 400)\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(13, 4.5))\n", "for q_fix, ls in [(1.0, '-'), (4.0, '--')]:\n", " mf_s = gwModels.remnants.gwModelRemS_mf(q_fix, chi1_arr, 0.0)\n", " mf_u = gwModels.remnants.bbh_final_mass_non_precessing_UIB2016(q_fix, chi1_arr, 0.0)\n", " cf_s = gwModels.remnants.gwModelRemS_chif(q_fix, chi1_arr, 0.0)\n", " cf_u = gwModels.remnants.bbh_final_spin_non_precessing_UIB2016(q_fix, chi1_arr, 0.0)\n", "\n", " axes[0].plot(chi1_arr, mf_s, ls, lw=2, color='C0', label=rf'\\texttt{{gwModelRemS}}, $q={q_fix:.0f}$')\n", " axes[0].plot(chi1_arr, mf_u, ls, lw=1.5, color='C1', alpha=0.8, label=rf'UIB2016, $q={q_fix:.0f}$')\n", " axes[1].plot(chi1_arr, cf_s, ls, lw=2, color='C0', label=rf'\\texttt{{gwModelRemS}}, $q={q_fix:.0f}$')\n", " axes[1].plot(chi1_arr, cf_u, ls, lw=1.5, color='C1', alpha=0.8, label=rf'UIB2016, $q={q_fix:.0f}$')\n", "\n", "axes[0].set_xlabel(r'$\\chi_{1z}$')\n", "axes[0].set_ylabel('$M_f/M$')\n", "axes[0].legend(frameon=False, fontsize=9)\n", "axes[0].grid(alpha=0.3)\n", "\n", "axes[1].set_xlabel(r'$\\chi_{1z}$')\n", "axes[1].set_ylabel(r'$\\chi_{f,z}$')\n", "axes[1].legend(frameon=False, fontsize=9)\n", "axes[1].grid(alpha=0.3)\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "id": "a1012785", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Recoil: gwModelRemS vs HLZ2014 and the earlier gwModel_kick_q200\n", "q_k = np.logspace(0, 2, 400)\n", "\n", "plt.figure(figsize=(8, 5))\n", "plt.semilogx(q_k, gwModels.remnants.gwModelRemS_kick(q_k, 0.9, -0.9),\n", " lw=2, label=r'\\texttt{gwModelRemS}')\n", "plt.semilogx(q_k, gwModels.remnants.gwModel_kick_q200(q_k, 0.9, -0.9),\n", " '--', lw=2, label=r'\\texttt{gwModel\\_kick\\_q200} (IW2025)')\n", "plt.semilogx(q_k, gwModels.remnants.bbh_final_kick_nonprecessing_HLZ2014(q_k, 0.9, -0.9),\n", " ':', lw=2, label='HLZ2014')\n", "\n", "plt.xlabel('$q$')\n", "plt.ylabel(r'$v_{\\rm kick}$ [km/s]')\n", "plt.title(r'$[\\chi_1,\\chi_2]=[0.9,-0.9]$')\n", "plt.legend(frameon=False)\n", "plt.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "907de8a7", "metadata": {}, "source": [ "### 5. Timing\n", "\n", "The model is a closed-form polynomial evaluation, so cost is dominated by numpy array overhead and it vectorizes essentially for free." ] }, { "cell_type": "code", "execution_count": 12, "id": "c7129067", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " N time per binary\n", " 1 0.565 ms 564.7209 us\n", " 10 0.489 ms 48.8583 us\n", " 100 0.533 ms 5.3251 us\n", " 1000 0.846 ms 0.8458 us\n", " 10000 3.342 ms 0.3342 us\n", " 100000 32.217 ms 0.3222 us\n" ] } ], "source": [ "sizes = [1, 10, 100, 1000, 10000, 100000]\n", "means = []\n", "\n", "for n in sizes:\n", " q_t = np.random.uniform(1, 10, n)\n", " c1_t = np.random.uniform(-0.9, 0.9, n)\n", " c2_t = np.random.uniform(-0.9, 0.9, n)\n", " reps = 20 if n <= 10000 else 5\n", " t = []\n", " for _ in range(reps):\n", " t0 = time.perf_counter()\n", " gwModels.remnants.gwModelRemS(q_t, c1_t, c2_t)\n", " t.append(time.perf_counter() - t0)\n", " means.append(np.mean(t))\n", "\n", "means = np.array(means)\n", "print(f'{'N':>8s} {'time':>10s} {'per binary':>13s}')\n", "for n, m in zip(sizes, means):\n", " print(f'{n:>8d} {m*1e3:8.3f} ms {m/n*1e6:10.4f} us')" ] }, { "cell_type": "code", "execution_count": 13, "id": "937e84ff", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8, 5))\n", "plt.loglog(sizes, means * 1e3, 'o-', lw=2, ms=8, label='all five quantities')\n", "plt.xlabel('number of binaries')\n", "plt.ylabel('evaluation time [ms]')\n", "plt.legend(frameon=False)\n", "plt.grid(alpha=0.3, which='both')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 14, "id": "e81df320", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " mf : 2.136 ms for 10000 binaries\n", " chif : 2.344 ms for 10000 binaries\n", " Lpeak : 0.412 ms for 10000 binaries\n", " omega_peak : 0.363 ms for 10000 binaries\n", " kick : 0.621 ms for 10000 binaries\n" ] } ], "source": [ "# Cost of each quantity separately, for 10000 binaries\n", "n = 10000\n", "q_t = np.random.uniform(1, 10, n)\n", "c1_t = np.random.uniform(-0.9, 0.9, n)\n", "c2_t = np.random.uniform(-0.9, 0.9, n)\n", "\n", "for name, fn in [\n", " ('mf', gwModels.remnants.gwModelRemS_mf),\n", " ('chif', gwModels.remnants.gwModelRemS_chif),\n", " ('Lpeak', gwModels.remnants.gwModelRemS_Lpeak),\n", " ('omega_peak', gwModels.remnants.gwModelRemS_omega_peak),\n", " ('kick', gwModels.remnants.gwModelRemS_kick),\n", "]:\n", " t = []\n", " for _ in range(20):\n", " t0 = time.perf_counter()\n", " fn(q_t, c1_t, c2_t)\n", " t.append(time.perf_counter() - t0)\n", " print(f' {name:>11s} : {np.mean(t)*1e3:7.3f} ms for {n} binaries')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.9" } }, "nbformat": 4, "nbformat_minor": 5 }