{ "cells": [ { "cell_type": "markdown", "id": "600b88c6-b549-4115-ac69-4b7e5c5be345", "metadata": {}, "source": [ "# MIMO TDM\n", "\n", "You can open this workbook in Google Colab to experiment with mmWrt \n", "[![](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/matt-chv/mmWrt/blob/main/docs/MIMO_TDM.ipynb)\n", "\n", "Below is an intro to mmWrt for simple targets position in (X,Y) plane based on 2D FFT (Range, Azimuth) FFTs with a TDM MIMO.\n", "\n", "## TDM MIMO ULA" ] }, { "cell_type": "markdown", "id": "1d695e52-2bbe-44c9-975b-fa6183e8e8a4", "metadata": {}, "source": [ "## Setup" ] }, { "cell_type": "code", "execution_count": 1, "id": "42af92ac-51a6-480b-9ba1-eee3386cf182", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "running from git folder, using local path (latest) mmWrt code c:\\git\\mmWrt\n", "version: 0.0.14.dev1+g243a05bf3.d20260717\n", "2026-07-17 18:56:19.971900\n" ] } ], "source": [ "# Install a pip package in the current Jupyter kernel\n", "import sys\n", "from os.path import abspath, basename, join, pardir\n", "import datetime\n", "\n", "# hack to handle if running from git cloned folder or stand alone (like Google Colab)\n", "cw = basename(abspath(join(\".\")))\n", "dp = abspath(join(\".\",pardir))\n", "if cw==\"docs\" and basename(dp) == \"mmWrt\":\n", " # running from cloned folder\n", " print(\"running from git folder, using local path (latest) mmWrt code\", dp)\n", " sys.path.insert(0, dp)\n", "else:\n", " print(\"running standalone, need to ensure mmWrt is installed\")\n", " !{sys.executable} -m pip install mmWrt\n", "\n", "from os.path import abspath, join, pardir\n", "import sys\n", "from numpy.fft import fft, fftshift\n", "from scipy.signal import find_peaks\n", "import matplotlib.pyplot as plt\n", "from numpy import arange, cos, sin, pi, zeros, abs as np_abs\n", "\n", "from mmWrt.Scene import Antenna, Medium, Radar, Receiver, Scatterer, Transmitter\n", "from mmWrt.Raytracing import rt_points\n", "from mmWrt import __version__\n", "print(\"version:\", __version__)\n", "\n", "print(datetime.datetime.now())" ] }, { "cell_type": "code", "execution_count": 2, "id": "e6bcf55c-e454-478a-a662-d2f2100e8059", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f0 = 62e9\n", "# Number of ADC samples\n", "NA = 64\n", "# Number of TX channels\n", "NT = 8\n", "# Number of RX channels\n", "NR = 8\n", "_fs = 4e3\n", "_k = 70e8\n", "chirp_bandwidth0 = 3.5e9\n", "\n", "chirp_slope0 = _k\n", "chirp_end_time0 = chirp_bandwidth0 / chirp_slope0\n", "chirp_count0 = NT\n", "chirp_period0 = chirp_end_time0*1.1\n", "\n", "adc_sample_rate0 = _fs\n", "adc_sample_count0 = NA\n", "\n", "void = Medium()\n", "c = void.v\n", "lambda0 = c/f0\n", "TXs = [Antenna(x=NR*lambda0/2*i) for i in range(NT)]\n", "RXs = [Antenna(x=lambda0/2*i) for i in range(NR)]\n", "\n", "radar = Radar(transmitter=Transmitter(chirp_end_time=chirp_end_time0,\n", " chirp_slope=chirp_slope0,\n", " chirp_count=chirp_count0,\n", " chirp_period=chirp_period0,\n", " frame_period=chirp_period0*64,\n", " antennas=TXs),\n", " receiver=Receiver(adc_sample_rate=adc_sample_rate0,\n", " adc_sample_count=adc_sample_count0,\n", " adc_sample_count_max=2048,\n", " antennas=RXs),\n", " debug=False)\n", "\n", "r1, theta1 = 10.1, 0\n", "x1, y1 = r1*cos(theta1), r1*sin(theta1)\n", "r2, theta2 = 20.1, pi/2\n", "x2, y2 = r2*cos(theta2), r2*sin(theta2)\n", "r3, theta3 = 30.1, pi\n", "x3, y3 = r3*cos(theta3), r3*sin(theta3)\n", "\n", "scatterer1 = Scatterer(x1, y1, 0) # 0 degrees on x-axis <=> -pi/2 vs bore sight\n", "scatterer2 = Scatterer(x2, y2, 0) # pi/2 degrees vs x-ax <=> 0 degree vs bore sight\n", "scatterer3 = Scatterer(x3, y3, 0) # 180 degrees on x-axis <=> pi/2 vs boresight\n", "scatterers = [scatterer1, scatterer2, scatterer3]\n", "\n", "bb = rt_points([radar],\n", " scatterers,\n", " radar,\n", " debug=False)\n", "cube = bb[\"adc_cube\"][0,:,:,:]\n", "\n", "virtual_cube = zeros((NR*NT, NA))\n", "# cube.reshape((NR*NT, NA)) is \n", "# equivalent to:\n", "# for chirp_idx in range(chirp_count0):\n", "# for rx_idx in range(NR):\n", "# virtual_cube[chirp_idx*NR+rx_idx,:] = cube[chirp_idx, rx_idx, :]\n", " \n", "virtual_cube = cube.reshape((NR*NT, NA))\n", "\n", "fast_time_axis = 1\n", "virtual_antennas_axis = 0\n", "# first compute the range FFT\n", "R_fft = fft(virtual_cube, axis=fast_time_axis)\n", "# then compute the AoA FFT\n", "A_FFT = fft(R_fft, axis=virtual_antennas_axis)\n", "\n", "# for Range vs AoA, display magnitude\n", "# and need to fftshift to have the negative frequencies moved around 0\n", "Z_fft = abs(fftshift(A_FFT[:,:], axes=0))\n", "plt.xlabel(\"Range (idx)\")\n", "plt.ylabel(\"AoA (idx)\")\n", "plt.title('AoA-Range 2D FFT')\n", "# plt.plot(np_abs(np.sum(R_fft, axis=0)))\n", "plt.imshow(Z_fft[:,:NA//2])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c6f8bebd-396b-4da7-bac1-b33d49646558", "metadata": {}, "source": [ "## ULA in elevation" ] }, { "cell_type": "code", "execution_count": 3, "id": "1b762f1d-14ec-4106-b605-ff433fe4fd1f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['x0:0.0, y0:0.0, z0:10.1', 'x0:1.2307700331430901e-15, y0:20.1, z0:1.2307700331430901e-15', 'x0:5.789296377354671e-17, y0:0.94546384825166, z0:-30.08514746700852']\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## ULA in elevation\n", "NT = 7\n", "# Number of RX channels\n", "NR = 7\n", "\n", "# Now define target1 with an elevation:\n", "r1, theta1, phi1 = 10.1, pi/2, pi*0.0\n", "x1 = r1 * cos(theta1)*sin(phi1)\n", "y1 = r1 * sin(theta1)*sin(phi1)\n", "z1 = r1 * cos(phi1)\n", "\n", "r2, theta2, phi2 = 20.1, pi/2, pi/2\n", "x2 = r2 * sin(phi2)*cos(theta2)\n", "y2 = r2 * sin(phi2)*sin(theta2)\n", "z2 = r2 * cos(phi2)\n", "\n", "r3, theta3, phi3 = 30.1, pi/2, pi*0.99\n", "x3 = r3 * sin(phi3)*cos(theta3)\n", "y3 = r3 * sin(phi3)*sin(theta3)\n", "z3 = r3 * cos(phi3)\n", "scatterer1 = Scatterer(x1, y1, z1) # 0 degrees on x-axis <=> -pi/2 vs bore sight\n", "scatterer2 = Scatterer(x2, y2, z2) # pi/2 degrees vs x-ax <=> 0 degree vs bore sight\n", "scatterer3 = Scatterer(x3, y3, z3) # 180 degrees on x-axis <=> pi/2 vs boresight\n", "\n", "# offset so that middle antenna is at 0,0,0\n", "TXs = [Antenna(y=NR*lambda0/2*i - (NR*lambda0/2)) for i in range(NT)]\n", "RXs = [Antenna(y=lambda0/2*i - ((NR-1)//2)*lambda0/2) for i in range(NR)]\n", "\n", "radar = Radar(transmitter=Transmitter(chirp_end_time=chirp_end_time0,\n", " chirp_slope=chirp_slope0,\n", " chirp_count=NT,\n", " chirp_period=chirp_period0,\n", " frame_period=chirp_period0*64,\n", " antennas=TXs),\n", " receiver=Receiver(adc_sample_rate=adc_sample_rate0,\n", " adc_sample_count=adc_sample_count0,\n", " adc_sample_count_max=2048,\n", " antennas=RXs),\n", " debug=False)\n", "\n", "scatterers = [scatterer1, scatterer2, scatterer3]\n", "print([f\"{s}\" for s in scatterers])\n", "bb = rt_points([radar], scatterers,\n", " radar,\n", " debug=False)\n", "cube = bb[\"adc_cube\"][0,:,:,:]\n", "\n", "# generate virtual antennas\n", "virtual_cube = cube.reshape(( NT * NR, NA))\n", "\n", "RX_antennas_axis = 0\n", "fast_time_axis = 1\n", "# first compute the range FFT\n", "R_fft = fft(virtual_cube, axis=fast_time_axis)\n", "# then compute the AoA FFT\n", "A_FFT = fft(R_fft, axis=RX_antennas_axis)\n", "\n", "# for Range vs AoA, display magnitude\n", "# and need to fftshift to have the negative frequencies moved around 0\n", "Z_fft = abs((A_FFT[:,:]))\n", "plt.xlabel(\"Range (idx)\")\n", "plt.ylabel(\"AoA (idx)\")\n", "plt.title('AoA-Range 2D FFT')\n", "plt.imshow(Z_fft[:,:NA//2])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "f95ff0b9-1a68-4f13-8aee-1c1956d5dc28", "metadata": {}, "source": [ "## URA\n", "\n", "We are now considering the case where the targets have an elevation (i.e. a `z` dimension not null).\n", "\n", "(r, $\\theta$, $\\phi$) are defined as per polar coordinates:\n", "\n", "![](https://cdn1.byjus.com/wp-content/uploads/2019/09/Spherical-coordinate-system.png)\n", "\n", "* $ x = r * \\sin(\\phi) \\cdot \\cos(\\theta) $\n", "* $ y = r * \\sin(\\phi) \\cdot \\sin(\\theta) $\n", "* $ z = r * \\cos(\\phi) $" ] }, { "cell_type": "code", "execution_count": 4, "id": "8f5f0d26-e085-441c-86c1-e2de26f3b911", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# first redefine the TX antennas: \n", "# instead of TX being NR*lambda0/2 apart on the x-axis to have a ULA,\n", "# we define them lambda0/2 on the y-axis to have a URA\n", "NT = 13\n", "NR = 13\n", "TXs = [Antenna(z=lambda0/2*i - ((NT-1)//2)*lambda0/2) for i in range(NT)]\n", "RXs = [Antenna(x=lambda0/2*i - ((NR-1)//2)*lambda0/2) for i in range(NR)]\n", "# then update the radar definition\n", "chirp_bandwidth0 = 3.5e9\n", "chirp_slope0 = _k\n", "chirp_end_time0 = chirp_bandwidth0/chirp_slope0\n", "adc_sample_rate0=_fs\n", "adc_sample_count0=NA\n", "chirp_period0 = NA*chirp_end_time0*1.1\n", "frame_period0 = NT*chirp_period0*1.1\n", "radar = Radar(transmitter=Transmitter(chirp_end_time=chirp_end_time0,\n", " chirp_slope=chirp_slope0,\n", " chirp_count=NT,\n", " chirp_period=chirp_period0,\n", " frame_period=frame_period0,\n", " antennas=TXs),\n", " receiver=Receiver(adc_sample_rate=adc_sample_rate0,\n", " adc_sample_count_max=2048,\n", " adc_sample_count=adc_sample_count0,\n", " antennas=RXs),\n", " debug=False)\n", "\n", "# Now define target1 with an elevation:\n", "theta, phi = pi*0.0, pi*1.0\n", "theta_steps = 3\n", "phi_steps = 3\n", "fig, axs = plt.subplots(ncols=4, nrows=theta_steps*phi_steps, figsize=(30,20))\n", "\n", "for phi_idx in range(phi_steps):\n", " for theta_idx in range(theta_steps):\n", " theta0, phi0 = theta_idx/theta_steps, phi_idx/phi_steps\n", " theta, phi = theta0*pi, phi0*pi\n", " r1, theta1, phi1 = 10.1, theta, phi\n", " x1 = r1 * cos(theta1)*sin(phi1)\n", " y1 = r1 * sin(theta1)*sin(phi1)\n", " z1 = r1 * cos(phi1)\n", " r2, theta2, phi2 = 20.1, theta, phi\n", " x2 = r2 * cos(theta2)*sin(phi2)\n", " y2 = r2 * sin(theta2)*sin(phi2)\n", " z2 = r2 * cos(phi2)\n", " r3, theta3, phi3 = 30.1, theta, phi\n", " x3 = r3 * sin(phi3)*cos(theta3)\n", " y3 = r3 * sin(phi3)*sin(theta3)\n", " z3 = r3 * cos(phi3)\n", " scatterer1 = Scatterer(x1, y1, z1)\n", " scatterer2 = Scatterer(x2, y2, z2)\n", " scatterer3 = Scatterer(x3, y3, z3)\n", " scatterers = [scatterer1, scatterer2, scatterer3]\n", " \n", " bb = rt_points([radar],\n", " scatterers,\n", " radar,\n", " debug=False)\n", " cube = bb[\"adc_cube\"][0,:,:,:]\n", " \n", " # define virtual cubes\n", " virtual_cube_azimuth = zeros(( NR, NA)).astype(complex)\n", " virtual_cube_elevation = zeros(( NT , NA)).astype(complex)\n", " for rx_idx in range(NR):\n", " virtual_cube_azimuth[rx_idx,:] = cube[(NT-1)//2, rx_idx, :]\n", " for tx_idx in range(NT):\n", " virtual_cube_elevation[tx_idx,:] = cube[tx_idx, (NR-1)//2, :]\n", " \n", " # compute (just to show this is the same\n", " # Range FFT from Azi and Ele cubes\n", " RF1 = fft(virtual_cube_azimuth, axis=-1)\n", " RF2 = fft(virtual_cube_elevation, axis=-1)\n", " \n", " # Range Azimuth cube\n", " RA = fftshift(fft(RF1, axis=0), axes=0)\n", " # Range Elevation cube\n", " RE = fftshift(fft(RF2, axis=0), axes=0)\n", " \n", " ax0, ax1, ax2, ax3 = axs[theta_idx+(theta_steps)*phi_idx, 0], axs[theta_idx+(theta_steps)*phi_idx, 1], \\\n", " axs[theta_idx+(theta_steps)*phi_idx,2],axs[theta_idx+(theta_steps)*phi_idx, 3]\n", " \n", " # show Range FFT from Azi FFT\n", " ax0.set_xlabel(\"Range (idx)\")\n", " ax0.set_ylabel(\"Amplitude\")\n", " ax0.set_title('Range A FFT')\n", " ax0.plot(abs(RF1[0,:NA//2]))\n", " \n", " # show Range FFT from Ele FFT\n", " ax1.set_xlabel(\"Range (idx)\")\n", " ax1.set_ylabel(\"Amplitude\")\n", " ax1.set_title('Range E FFT')\n", " ax1.plot(abs(RF2[0,:NA//2]))\n", " \n", " # Show Range Azi map\n", " ax2.set_xlabel(\"Range (idx)\")\n", " ax2.set_ylabel(\"Azimuth (idx)\")\n", " ax2.set_title(fr'Range/Azimuth FFT $\\theta = \\pi *{theta0}$')\n", " # use interpolation and aspect to have the map same size as Range FFT\n", " ax2.imshow(abs(RA), interpolation='nearest', aspect='auto')\n", " \n", " # Show Range Ele map\n", " ax3.set_title(f\"Range/Elevation FFT $\\phi= \\pi *{phi0}$\")\n", " # use interpolation and aspect to have the map same size as Range FFT\n", " ax3.imshow(abs(RE),interpolation='nearest', aspect='auto')\n", "plt.tight_layout()\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "f3cf4912-acf7-4c72-91e1-7a62264ad607", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "scatterers ['x0:10.1, y0:0.0, z0:6.184466335694133e-16', 'x0:1.2307700331430901e-15, y0:20.1, z0:1.2307700331430901e-15', 'x0:0.0, y0:0.0, z0:30.1']\n" ] }, { "data": { "image/png": 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J0hhjjCWb1k0sJyMNC1NqAitpMia0STMS1VJoJKqMuKnCbLxi9Y+flV7XPFAKq3shKLzqk1LrS82Un2dF8vKl8us65BA/Df3fIyo0IsXrR0cpPzmboOr6ujpbqB7OzqpxKk/Jy1g662rLdF94WCSMTVScTVgDTDL8nEU4XInAgzHGmPI4+GAqCwsNh3nGDDq3J80zZUDo9zBNF4MxxvQOBx9MZa+ef4CdY9wxXLSdnVMe+D59o+liMMaY3uHgg6nM69Eb5LfPCRNTrU0hipd96fzwvqt8zghjjDHlcPDBVOb96C0MjQxhVziXzuxNUzMT5CtsC687HHwwxpi6cfDBVObz7B0iwiPhWFx35kkpWCIvDA0NOPhgjDEN4OCDqSwiIgqP7/iieqMSOrM3a7Qqj4BP3/Dy8WtNF4UxxvQOBx8sVbjuuo6SFQoiv4P2j2Jram6C+h2r4tTW/xAZobmxNhhjTF9x8MFShdu5x/jyMQjNOlTS+j1au00l0c32+KZLmi4KY4zpJQ4+WKqgGoQTe2+ibsuyMLcw1eq92qxXLdw4/QDv/ZQf1ZUxxpjyOPhgqebEnhsiibPL0Hpau1frtq8C+1L5cXj1WU0XhTHG9BYHHyzVfHofhM2LT6NV1z9QrFwBrduzWW2sMMClA87tdsOdS080XRzGGNNbHHywVHVo61U8ufsKo/5uA9Nfc6doi+GLuiEiNAIrnXdpuiiMMabXOPhgqSo6WoqFk/Yju7UV+oxtrDV7t1HX6qjUsBSWjNqK4IDvmi4OY4zpNd0aD1vrp45WbbpvabTysaAEqnUZlYaHK72uQeA3hedv733D2un7MWRuB3x8+QF7l51JdH1JiPI1JNGhSU8MV6lxaQxd0AXHN1yA26EbCq9Jo5Q/ZtIoDXbT5anlldxvPLU8Y9og/QUfTCsc23IFWXJaotfEloiKiMKB1ec1Uo4KDUth0rahcDt2G0uHb9JIGRhjjCni4IOlmW3zj4s5X/pO+xOZMltg6z+uollGXWq3/wNj1vTFjZP3MLf7CkSrUMvBGGMs9XDwwdLU5rlH8T3oB3pPboXilQth4chtePfyU5ptr8uk1ug66U+c33UNdTr8gTPb/sPCges0HnjMPzcVltkyoV/psRotB2OMaQNOOFWCUxVHdJ3WDhZW5tAFTpUd0HVKm2SXN49DLgyY1xmLLkyF69cNOP1jG6zzZVd6+/tWnMW4Pxcjm7UVVpybiJa9a0EikcR5n/Py7jjhuwi9JjRTelt5HXPFNLfM670K8/utUVvgkS1XFnSd2haFSuWHOjXqVRvrHy7Ese/bsOnpv2g5uJFat88YYxoPPlxcXFChQgVkypQJOXPmRKtWrfDs2TOkJ05/FEa3aX8hY2YL6EywNKUtMmZOXvBRtJI9Wg5qCPOMZnj19G2qlOGBuzcG1nXBqR3XMGBWWyw+PhZ12lSAsenPyjfzjKaoVM8J/n6fUbNF2RR9NgUy5RuUxMwDo1GrXRW4n7iDfuXG49zOq1CnbLZZ0E0EH+ob46Rpv3oYvXagmCBv2fCNeOzuiSFLeqH92JZqKwNjjGm82eXSpUsYPHiwCEAiIyMxceJENGjQAI8fP4aFhW5crDXFJIMxwkMjNF0MuB+7jT9t+uFHcCjajmgC+9KpczEN+xGOVVP24b+jd9BxRCOMXdod/Wa0wend1xEc+AMGBgZYNHYX/rdrMEpUKoQH158n+nmZs2dEnc4V0bRPHdgWtIb3vZdw6b4cF/e6Q1/Ol56zOsD92C3M+muhWHZi3TlIDAzQeXIbHFt7lrsVM8b0I/g4efKkwvNNmzaJGpBbt26hRo0a0HXU3EK1HmSbz4qY5V3sBuH9q09o2KMW6naugQLF84pmjnfP3+PQ8hNwXaXY3XTr82V4+cgPh5edFBcQev+6iTtxcMkJ5MyXHUP+7YHSdYoj9HsYzu+8Co9Td+FyfCJG152J+5cex3xOkYr26DatLZwqO8LQ2BCeHi+wYcouPHbz/FneKW1ErYfYptfS39/DYSje+8afe/Hta9qOg/HoxnNM7rQcuQvmRJOu1dCoUxVksjJHRHgk2g2og8AvwegwtD4iIiIRERYpklRpwLJFh0Yk+Jkz2i/GtaO3RM7HqZCtaGjeNeY1en5k1Rnc/+8puk7+EzYFcuD5fV/8O2QDfO6/EsFL21FNkSN3Vjy57o35fVcr7Jstzxbj/uUnYnnsPA4ypu5MlKzphAW/no/dMFA8yD+9VuL0lt8T2OUrmhtDl/YSxy3463ccXHoCe+YfVfjcHHmzIYO5KfyeJV7rVLp2cVhlt8TRlacVlh9ZcRL1OldHpaZlcW77f4l+BmOMpcuE08DAQPEza9as8b4eFhYmHjJBQUHQZlcOXEceB1vU6VQNK0ZuRNCnn2NcBH78We5m/RvA97Ef3I56IDoyCpWbl8Pw5X1hIDHAkZWnFD4rr6MtnLcPx7E1Z3B8/Tn4efqLi84/Z6Yga67M4sL01T8QtTtWRemaTnHKUrp2MfztOgFet32wbfZ+cZFu0L0m5p2ejNG1Z+CZx3NcOXQTuR1yoU6Hqlg5eguCPsvKqzg2hya8efEBa2ccwNFt17D+0kTcOP8YRsaGMDYxQtnqhcUjttCQcLx//UU0z7z3+4LKdZ1gmS0jHl5LvGmv+B+FUblpGRz9NadL+zHNMXP/aOxZ4Irm/evBdfVZ0YzWbnQzjF7dD+MazUnRd3n15A02TduDHjP+guuas3h45alY/uhXEEgyZbGAyzFnXDl4A5f2uqNGm0roO7czfB764ebJuzHvG79pMErVdEJ9ow6JblNWI+XpoVhD5HXrBaKiosXrHHwwxvQu+IiOjsaIESNQtWpVFC9ePMEckRkzZkBX+Dx4Ba87L0Twce3QTbz3/fj7RYkEo2tPU2g6ObziFOYcn4g2I5vGCT4oKHBu/Dc8Tt/7tb4B2oxoAttC1pja+h+4Hb0lFtPFbJXH3DhlGb68D+5dfISJTedCYvAzgZOq2tfe/UdcBJ2buojyet/xEcHHtSNU3rTraaKsPxqWQHhYJBaM2oEf38NgWyA71l+ahBVTD+Dp7Zfiu9E+DQkOxce3AZD+GiiqTf/ayJk3m0gsDfocnOg28jjaoE/p8aJ2inwLCMGIZb3QaUJL9Co+RjQxEQNDA3Qc3xLW+bOnaF8FfAgUAQTt9yfuXji340qc92TPnRX/674cZ3/VRpzccB7bXixDo561FYKP5MqaKwuiIqMQ8CvwlZ9hmILMbLbxB/yMMZaue7tQ7sfDhw+xa1fCc2k4OzuL2hHZw8/PD7pMPvAwtzQT3SupmcS2kI14Lu/di/e/A49fKjQsjY+vP8cEHiQiLELUjMgrVLoA8jjmEk0ytA3ZI4NFBty58AglqheJt0eJNqrdqhxunn8sAg/y9uUneN73Q4lKBeH1wA+e917h5bN3+PDma0zgUbKKPXqOa4pDK04nK7H0zsXHMYEHeXbzZ20B1QzJAg/y9NfyXHY5U/17hnz7ERN4yIIEKkfsbVEzTlK1HsTEzEQ0VcWH5rCh1xljTK9qPoYMGQJXV1dcvnwZefLkSfB9pqam4pFeFBM9YdqhaBVHmFlkUHiNckBCgn7EPPf3+RBnfcr3oKAktrfeisty29vEVNEnhLan7nlMzDNlUJhQLiIiCsEBIQm+P6+9NeyL58G5/TeRK392hd4xzbpVFb1gQoIVh1DPbmMF52Xd8NjDB6vHb09WuT76fVZ4/j0wJNHladGT6dPrL3GWUd6HXYl8Sn1e+I9w0UQVH2NKXv6h/JD5jDGmU8EH3ZkOHToUBw8exMWLF2FnZwd9kaugNeadmQK/p2+xeswWcWGjO9OKjcug7chmojeHvLBQFeZT+dXMsnrcNjy/9zLeWg75O3p1GTCzLeq3rxzz/P41L4xv+2+C76/TpqL42X9aa/GIrWrjUjiz9/d8LJQTMmllD7Ff5wzenOwxPBJ6HzUNxkdxf8Y/Kis10aRkDBHKw0h6W8n35d1XMYJs5hyWCk0vtI+oFuzz27jBDmOMpcvgg5paduzYgcOHD4uxPvz9/cVyKysrmJkpNjukt8mpKjcrB5MMJpjS6n8Kd9SlaxVL9kd/ePVJ9IiIzdbeWuH521+1I1STcufcw5icjxQUN03QgGLnD9yMeZ5YrQep1boc7l7zwrGtcZtOOg6tL5pk5IOPAdP/REGn3Bj71zIEfEo8zyO1UO+f+MZIoYHX3snVXsmahNSFuhYTx/KFcOPEnZjl9NzQ0EAEpYwxphfBx8qVK8XPWrVqKSzfuHEjevTogfSAur/KqublE05ld8Hyd7KU50Hdb5OLckDK1S+JKs3LxeR9GJsao0nvugrv87rlgzfe/mg3qhnO77wixtCQZ5U9EwJ/9cSRldeCmhLSOOH0lZe/eCRHsYoFYZMvO7YuPIUrxxVzX0huuxzoOroxsua0xJcPQajfriKadvkDi8btEnkg6vLuxQcUr1pY1ChQngap1KTMzyYyueDj935WbeTb5Ha1vXv+oUgsbTaggULw0XxAA/z4Horrx26rVA7GGNOpZpf0zvPWC/Gz5+yOuLj7KiIjIuF+9BZunbmH8LAIzDo8HsfWnIVZxgxo3KcuAj4EJbvnAfVsaTGoISZuHya62n55FyB61oTLmmh+7V/azwv7r8Ec1wlYd3++GEvi05uvyJ47C0rVLIaQbyGY2nq+eK/X7V/lndEeF/deE7PMurveRmhI/NPRU8DUamAD8e9iVRzFzxYD6+N7QAiCA0PEmBmpoXbrCqK3BnWxjY/7mYfoMa4parYog3P7PTB4dhv4evqLJpfarcv93A9BPwOsq0duISyB76OqExsviG6xc46Ox6X912FbMCfqdKwqgj95b5+/x7evwWjWrx5+fAtF6PdQPL3hDf+Xcj2ikiG5XW0puXnT1N0YtrwPpuweKQLX4tWKol6XGtgwaWeaj9fCGGPK4onllEDjKmycslOM6VG+UWlRxU2DjL1+9haz2i1Aj1kd0O+frvjiHwDXVafEGCBjNgz+GTjIB2f0T4VgLRqhwT8wrt4MDF7SC62HNhZ5G2e3XsZjt2eYtm8Mwn+EAdKfNSz3Lz7E8KqT0HlyW7QY2EAEO1/8A8UFj7rcSn/NIEs9KjZO3S0uiuUblvpZ3kJDFXJCJJLf5aABv3pMb6fwnduNaCp+0oX0yArFQa2kYSnPXaFchWrNyuDxjef49v5rvO95ed8X73w/oU7Lsrh62AOmGUyQ39EG4xZ3ifPeroVH4P330Jj0jNhBsJT+k1sW829xTORyMWL+HR3z71un72H12K34c3gTDJzfRQSfU1v9g37zFMtBgdQ/PVei198dMHxFbxgZG4lBxvxf/h5kTLFQ0bKTIFYZZGVLOp/k6KrTiIyMEjlFlZuXF819K0ZuwsElx5Fm9OAGgzGWtiRSLauqoEHGKD+kFlrCSPK714ReSCTxsPWwJhi0qAc65O2Pz2/juVhLVOs1LTE0VHpdg4wq9gwxUj4GjlZ1ULqon80oypAFdyp8AHSSdv3JYIxpiUhpBC7isBg2w9LSMtH38qy2WjpnhzzK+aBai9eeb+MPPBhjjDEdws0uWmja/jGi1wv1VrCwNEfdztWRr2gezOmScJdVxhhjTFdw8KGFPE7dQ+PedVC3U3UxloTv49eY3XERLu1x03TRGGOMMZVx8KGFKFkwTRMGGWOMMQ3inA/GGGOMqRUHH4wxxhhTKw4+GGOMMaZWHHwwxhhjTK04+GCM6bQG3WvhTPReWOfPAW3SdVo7US6aYZgxpoh7uzCWDE6VHcSEfweWnMD3wMRn6tUGTlUcUa5+KRz491iyyksz4TboVhOlahWDdYEc+PY5GE+ue2HjlF144/UuzcrZfGADDFveV2xrWJWJ0DViPzcohQOLk7ef1Y0mudzjvw575x/G3QuPRKCmcIzdPdP8GDMWH675YCwZ6CLTdUpbZFRxxlp1capSGN2mtRMzLydH+3EtUe3PSrhz/iFWjtwk5gYqUb0oVnr8DwWK5U2zctJYNjQzcNFKDrAtZKPUZ9DcR03MOinMMK0uTn/Qfv4r2ftZ3YpUtEfmHJZihuP241r9OsYPsHLERhxbewYlajhh5a15aXqMGYsPBx+MaUgGc1Ot2ff7F7mKyRFXjNiIE+vPY8ecAxhVcyoMjQzQfnyrNNmmTYGcKFa1CFaP3oyvHwJRp3M1pT4nOjoaEWERqV6+9KBik7Lwf/lBDFS4f9FRdCkwCCuG/zrGfx/AqBpT0vQYM5YQbnZhLAldp7QRtR5kq9fSmOU0MzDNy9h+bAuUqVMcOfNlR1hImKjeXjN+u8KdeNepbdFtalv0LjEanSf+iQqNSuH9y48YWH68eL1kTSf0n9cVBYrnxac3X7Bn/hFktckiai/qG/6lUJ5stlnQY2YHVGpSBhaZLfDW2x/7Frni1MYLv7bVTqxHtr1Y/ru8BQcnWDvw2M0zzrI33v54+eg18hXJnSbnCAUbQV+CxV35f/vdRS3Itpn7Yl6nHI5tPisSXL++wc/vSE0JYzcOFsETfT/KtaDaiB6Fh6HLlLao0rw8IsIj4br6NDZP3Y0cebJhyNLeKFW7GMJCwkWTxL6FrgqfPXbDYJSs5YSuBQcrLJd9Nm1b9m8iX05ZOWSoVqT/P93wR6sKohnkyoHrWDpkHcJ+/J4NOm9hW4SGhOOj36dE99nQ5X3QYmDDRN8jv30KPm4cv530MS6aJ9HPZCy1cfCRXqg6Q6o04Rl103JmWJWpOLNscmam/e/ADeS2z4U6HatixajNCPr0TSwP/BCACo1Lo1gVR1zcfRUf33yBTf4caDagAeafm4I+xUf9vsD8mgl2yq4R4g/+hsk7IcHPfV6odAG4HJ+Iz+8CsGX6XjGkfpfJbRH4Me6MvZlzWmHJtb8BKXB4+SkEfgpChUalMWbdQJhnMhMj4145eB15HKm81bBi5CYEff5VXvnPS+bMtFmsreD7yC9NZrKlYOPqweuIjIjEhZ1XxEWVck88PZ7HlHdu1yUK6xgZG2LAwh4imEjK5F0j8erJG6xz3o5KTcqKffrtSzCa9quPuxceYt2E7aIM/ed3x7Obz/HgvycpKj8FEXkcbFGnE+3njb/Pi1jHbfLukfD3+YD1E3fAoawdmvSph4CPgWL7Mhue/It7Fx9hTJ3piW9zvzscyhYUge7acVtjlneb/hfCQyOw4+/9MYFHFuvMsC9TAJun7U7eMWZMjTj4YCwJPg9eweuOjwg+rh32+H1XK43+ddd+XeH97q63RIBQvU0lnN32n8JrL+77wqWL4gW1+/S/EBUVjZHVp+Dzu5+zFl/aew3rHy2KU5ZeszvA0NAAfUuNERdS4rr6DCZuHy5qO46tOfOzvLepvNVw7fBNpXMhaEJDqiVI6uKlDLqA0t32smEbxPOHV57ig98nsU1Z8BEaEoZz2xX339BlvWGWMQOmN5iV5Dae3vTGvwPWiH8fX3MWW32Wo//8btgwcQd2zzssllPQs+vNGjTqWSfFwcfP8+KFCD6uHUp4P3vffYmFfVbGPLfMmgmNetVRCD6Si3Jy+pkY4fkdH4V9M3hJL1za64YLu67GLKvYpIwISO6ef6iRY8xYYjjngzEV0B93GUMjQ2TKmlHUbHz7Ggz7MgXjvJ8CBYVfQAMJytQtIYIEWeBB3j5/j5sn78ZZnxIG3Vxviep76sIpe3icviuq9+minhqoGWDosj54dO0Zzmy+hNRWp3N1fPEPwL0Lj2KWXdpzDbXaV4WBQfx/lup1rYEWgxph7fhtopYgKSfWnVPIC/H0eCE+m/IdZKiHyutnb2FTMCfSiuuq0wrPH1x5AqvslqKmSoaacZKq9SBU/rxFcsNHrqaCgodMWTLi5cNXCu+t2Lis2L/hob+bd9R5jBlLDNd8MKYCkwzG6DihNRr0qIXsubMqXDgtrOL2jKHq99jNKJR4SnkbsVEQo/DeHJbiItOsX33xiE/mnJZQFVXXz3Z1FhfmWe0WiAt3QoyMjUTAJY+aHRJbh/ZR7fZ/4N6Fh7Cx+33Rf3rdC+1Gt0CZusVx68x9hXUKlSqA4Sv74fyOKyI5Njk+vFLMnwgJDBHNYLJmKBn6nmk5FkfscgR//S5+ZsxigZBvP1L0Wbb2NjA1M1FoJrErkU/8fPnQTyEQpq7h6yduV/kYM5YWOPhgTAVDlvRCgx61cfDfY3js7in+mFN6xKQdw0WtRmzySYYpJfn1eWe3XcbpLfHfqfrc94UqzC3NMef4RFGLMrLGVIXamPg4/eGIBRdmKCyLnXAZW+k6xZHNNitqd6wmHrHV6VRdIfigskzdNxpvPN9hYd/fzRdJiY6KTtYyIdahokTi+FA+TkoltE2qvUopSkiOHWjYlcwfZ1nxakVE8Hvj+B2VjzFjOhl8zJ07F87Ozhg+fDgWL16c1ptjLG0kcDGq3qYyzmy5hNVjfyf/GZsaJ3vch4APgSIgoTva2HLHWkY1Ct+DQsQF8M65B0qVNzFU7llHxiO3Yy6Mrz8Lr568TnKdF/d8Ma7+TIVl1JySGEry/Po+AEuHrI/zWrXWlVC1dUX8O3CtaC6gC7TztmFif1KZVAneUuJbwPd4j6F1vlijqKZBIm5SwQflB8kfG7vi+cT+pORjmUpNy+LlI784QaAyx5gxnQs+bt68idWrV6NkyZJpuRnG0lzo9zDxkwYZe++reFcb+wa21ZBGoto7OaKjpbh97gH+aFkB2XJlibkLtS1kLXqxxH4v9bCg2gIaFIouLvKssmdC4K8eF5SsGV95E2sKod4hNJjatFbzxMiXyREc8D3pQEiOSQYTVP2zIi7vcxfda2P7/PaLSOCs0qK8yAGh7qzlGpbGpCZ/i/Eq1OXdc38RfFCTBiWWkqw2mUVgFP95YaHSIGfJ7WprVyyfaLpT6KZbJLfoLhs738P92K1UOcaM6VTwERwcjM6dO2Pt2rWYPXt2Wm2GMbXwvP1C/Ow5qz0u7nYT3UPdj3rA/dht1OtSQzS3+D55DafKjiKBVP4uNClbZ+xBufqzsei/WSI5kWo2Wg5uJKrR7cvYKbx3nfMOMTz2Ere/RUIlbZPyQCjRlLbbJkevn+W99au8szuKbsCREVFwP3orJiiJrf+CbiIAcjviIXI4qBeEvNi9TpRFQYWFpTncjtyM9/Un7l5iwDGqHaGBsTpPboMHl5+I3Ji0KlN8qNdIn7ldMP3AWBxaegKm5iZoPqAhXnu+g2O530m9cfdzZKL7OSHJ7WpLNR+xu8VSUETjy1AzC52HNHhbfqc8WDJorUaOMWMaDT4GDx6Mpk2bol69eokGH2FhYeIhExSU/D/ajKkL9ZTYOHU3mvWrh/INS4vurjRoF40ISrUflKdAyafUc2B8g1lwOTEp2Z9N3WInNZ2DfvO6ovvM9vjo9xmbp+9GviJ5xF1t7GaaoZUnisGzqImi+cCGIoGSLkg0nsXv8j4Xc3Y0619fobyhCdydU0KnLDigR2ypdWGioILu2m/HSiiVz7W4cey26A1zestFcbdOwRY90qpM8aFuzNP//AcDFnRHn/91+TVOx3bkdsilGHyI/bwTzfo3QPlGv/az3aAE97MqKLmXmueuHLyhsPzmyTsikBi9biBmtlsguthSjdTDq081cowZSw6JNKHMKhXs2rULf//9t2h2yZAhA2rVqoXSpUvHm/Mxffp0zJihmLBGaqEljCTG0CtKJKCl2qYNk9dMEB8DcxXnO1Fh29HBP3sOKEuqygBpqg7slgS66y7glAc9igxP/Q9Xc64CU5+/XZ3xIzgUszvEHSeGsbQUKY3ARRxGYGAgLC0t1TvOh5+fn0gu3b59uwg8kkLJqFRQ2YPWZ0zfUK1J7GTTio3L4N6lxxorE9NN9y49wv7FxzRdDMbUW/Nx6NAhtG7dGoZyd7NRUVEia52qUKmJRf612KjZxcrKims+1IxrPjRb87Hr9Wqc3nxRzPBqnS87mg9oIHomDCw3Ls54H6mCaz4YYxqs+Uj1nI+6deviwQPF7PeePXuiSJEiGD9+fKKBB2P6yuPUXdTuUFUkD0aERYoxQzZM2pk2gQdjjGlYqgcfmTJlQvHixRWWWVhYIFu2bHGWM8Z+mt87+YNnMcaYruO5XRhjjDGW/oZXv3jxojo2wxjTAOoCSoNx5Xawgam5qchViYqIFF1qaV4T7zsvEfo9lI+NFqHmPRpDxjJ7JjFXDOXk0SSJNE4Izbz87sV7TReRpXM8twtTmao5yxJVEjfTuLsri3+U0uptKqFEDScxuBkFHsYmv/+UREVGKYzwSpOW0cyxNCAXTR53fucVMY4GUx8aEbd628rieNE4JTS3jvzxoV9hGqNEhmZl9r7tIwbXo3FX7l/mXldMB8b5UAX3dtG93i4SMzMVt22guXE+oqX6Gfgo8WtvW8gGzQbUR8OedWCZNaO4Q/a69QJet1+IwbZoRFIabpwuZnQnTd2HaVAuh3I/L3h04bMvWxDS6Ghc3HUNR1aewrOb3mny9djPGikaDr7FwIYoWdMJQV+C8eyGtzheXreei8HtPr/9KkZlJRQw0uy+hUoXiDlehSvaI0eebGIo/6MrT+Hs1sspnomX6Y/IFPR24eBDm+joIGMcfKTv4IOCjkGLe4rJymg01ZMbL+DY6jN4+zzlPXGssluiUa/aaNq/AXLZ5RRBy8pRm/DwiuJonEx5FPi1HNIIHSa0FvMF0bDtFOhdO3QzJtBIidK1i4uRdKu2qiCaZo6uOo0t03arbZI/pjs4+NBVHHykGNd8pF3wQRexVkMbo9ecTvjy7iu2zdqHS3vcxGyzqqIxf2g48k4T/0TRyg44uOQ4Nk7ayRc0FVGgOGbDIJSoXhQn1p/D/kWuokYqNVBTDdV8tRvdAp9ef8Y/vVbgUawh3Jl+i+SaDx3FwUeKcfCRNsGH/EXs4NLj2OC8I8WTpSU3CGk9vImYmI0vaMqLHSgu6L0yzfI0qClt7IZBKFrFUUy6t2HiDg4amcDBh67i4CPFOPhI/eCj2B+FMdvVWTSxpOVFTF4eR1uMWT8QRSo7YkHvFTiz5VKabzO9oFyNcZuGoE6naji07ATWT9ieJoFiQkEj5f5MajJHJKky/RapybldGGO6q0zdEph7egqe332JgWXHqa2Xw2vPtxhVc5poKqALaYtBDdWyXV1HvYym7R8jerLQjLbLh21I88CDUFIxNemMqDYZuQpaY8GlGcic0yrNt8vSDw4+GGOCUxVHzDg0DvcvPsLEJnPU3quBLmj/DliDfQuPYuiyPmjYoxYfmUQYGBpgwrbhKFe/JKa2mIv/9rurfX953/HBqBpTRO+nuScnw8JKxRmumd7g4IMxBuv8OURTi5fHC8xouyBVkkqVtXrMFriuPo2RaweKmhgWv37/dBU9UGa3XwSP0/c0tpv8nr3FhIazkSNvNkw/MFbknzCWFA4+GNNzdLEYvW4gQoJ+YErL/2k08JBZOng97l14iDHrB8E8k2rjyKRHNG5HmxHNsHrsFrgd9dB0ccQ4IDPazhfdcinxlbGkcPDBmJ5r2r++qGFY0GclQoJCoA2oCWZh31XImMUC/eZ303RxtEoGiwwiKKN8nENLTkBb3L/0WPSMoh43ue1tNF0cpuU4+GBMz5tb+s3rCtc1Z3Dn3ANNF0fBe9+PWDtuK5r2rSfyGthPvV06IYtNZtETScsGqBZdsqmr7+j1g7j5hSWKgw/G9BgFHtSldu3YrdBGrqvP4PbZ+yIBlXMJgALF86HVkMZibA1lRphNa9TTZn6vFWJ8mLqdq2u6OEyLcfDBmJ7KnjurmPtj97xDWj1fx6apu8XAVuUalIK+oy7In99+wZEVp6CtHvz3BB6n7nJ3aZYoDj4Y01NN+tYTI1Oe2/YftNkTd0/RpZMmSNNnlHhbr0sNHFt7VswcrM1oLpmilR3F5HSMxef3PNhaRmJqConEGLpEp6uFDZSPQyUmqh0naagKgyJJVIufJcrPpwcYGOnsuWZoYowm/erj3K5rCI2SwMA8+eMznPC+ptK2mxSpkeJ1XDdexrDFXWFb0h7v/T4rv3EVZlCmv0mqkFoo32snPLcV6rQsCxMzE7g+fo+o2mVTtP6XkcrP/hwRlfJfkkOSUAwMCUCd/X/h4ZBzSm87g79qCdAGwcr/bZGER6i0bagSIEpVzOVRZf1oFWbrjg4HktkayDUfjOmhio1KIZtNZriuOw9dcGGfO0K+haJ+pz+gr5o2KY2rVz3x6ZP2D2MeJY3GHt9baJq7BMwy6NZNJFMPDj4Y00PFKjvA3/cjXj5KnRlP01pYSDju/fcUxSrZQx+Zm5ugYMGccHP3hq645P8MZkYmsC+YU9NFYVqIgw/G9JBjWTt4330JXeJ91xf2JfNBH9nbW8PAQAJPT+3r4ZKQ598+IiwqAoUL8ZgfLC4OPhjTM5QvYl8qP7zu6Fbw4XX3JTJlsYBN/uzQN46ONggNjYCv7yfoikhpNJ4FvYejvbWmi8L0Jfh48+YNunTpgmzZssHMzAwlSpSAh4fmhwBmjAG5CuYUE4DpXvDhK346lMoPfePokAvPX3xAdLR2DSqWlMcBb1GYRztl8Uj1dP2vX7+iatWqqF27Nk6cOIEcOXLAy8sLWbJkSe1NMcaUYPurDd7P851O7b/AT98Q9CUYtgVzQN/Y2mbGq1cq9PLRkOffPuHPoinrmcP0Q6oHH//73/+QN29ebNy4MWaZnZ1dam+GMaYk6q4pG41S19C4JCYZfpZfn5iaGolmF10TGhUBE2Mjka+ia7U2TMeaXY4cOYLy5cujXbt2yJkzJ8qUKYO1a9cm+P6wsDAEBQUpPBhjacf417gsEWGROrebqczGplo7PFGaMTY2QniE7h2v8OifZTYyUmVAHZYepXrw8eLFC6xcuRIODg44deoUBg4ciGHDhmHz5s3xvt/FxQVWVlYxD6o1YYylnchfFzEjE927IBiZGOlk0KSqiMgoGOvgBdzY4GeZI7V8RFaWDoIPmgq7bNmymDNnjqj16NevH/r27YtVq1bF+35nZ2cEBgbGPPz8/FK7SIyxWE0XJIOZaiN2aoKpmQnCw3Sv+UFV4WGRMNXBwbrMDI0RERHFTS4s7YOPXLlywcnJSWFZ0aJF8erVq3jfb2pqCktLS4UHYyztvH/5UfzM46Bb4y9QN1urbBnh/1J3upumlnf+AcibJyt0TYGM2fH2fYCmi8H0Ifigni7Pnj1TWObp6Yn8+fWvexxj2ui1l7+YxdahTAHoEofSP8vrde9nl1t94uXpHzPQmC5xypwLnt7vNV0Mpg/Bx8iRI+Hu7i6aXby9vbFjxw6sWbMGgwcPTu1NMcaUIJVK4X3PFw5ldKsXmkPp/Pge9APvfH7W3OiTZ57vYGZmgrx5daf2w1BigCKWNnjmrTujsjIdDj4qVKiAgwcPYufOnShevDhmzZqFxYsXo3Pnzqm9KcaYkmiAMftfNQm6wr50fnjfeyWCJ33j5fU+ZrAxXWGXMbuY2+XZc675YGoa4bRZs2Z48OABQkND8eTJE5FwyhjTHo+ve4nBxvI66sbFzCSDMUpVL4InHs+hj75/D4OPz0dUqlQIuqKGtQPCoyLhxcEHi4fWdpiXhoVBKomGLlH5fkyiwfZcifJxqIGhal0AJcZGKp0nqpCqMvBRZLTOnmtu+64hYFF3NOleHStHbkrRug1tS6u49ZSP5VOtVU1YZs2IEytOIOrrV+gbQ0/g5NJj6DO3C7I9eo6AD4EpWj/HBah9/qBOXoNwaftVRO27ClMNnefcwVe9IqXJ74nGE8sxpociwiNxYv05NOheCxnMtb/LbfOBDXHz5F28fa6/+QOnN11EVGQUGveuA21XvmEp5CpojaMrT2m6KExLcfDBmJ46tvoMzC3NULtjVWgzx3IFUbSSg95fyIIDvuPCrqto1r8BDAwMtD5Y9Lr9Ak+ue2m6KExLafcZzBhLM+99P+K66220H99aDN6lrbpO+wv+Lz/g+rHb0HdHlp9EznzZ0bBXbWirIhXtUalpWRxZwbUeLGEcfDCmx1aP3YLsubOi598doY3qda2Bys3KYcXwjWL0ZH3nfccHJzacR//53ZAjb3ZoG2NTY4zdOBieHi9wevNFTReHaTEOPhjTY2+83mHj5J1oPawJilcrAm2SLVcWDFrcE2e3XobbUQ9NF0drrBq1Gd8DQzB67QBom+4z/oJNQWvM77Uc0VEcLLKEcfDBmJ47+O9xPHHzxJj1g7Qq+XTE6v4ID43AihEbNV0UrRISFILF/VejXINSaNK3HrQF5eW0Hd0CW2fsge/j15ouDtNyHHwwpueoOeOfXiuQNVcWTNk7GkYqdH1OLX3ndRXNLXSR/fY1WNPF0TrU8+fY2rMYvKQXytQtoeniwLaQDaYfHAfPm97Y888RTReH6QAOPhhjovllWut5KF2nOJy3DdNoANJlalv8NaYFlg/fAHfXW3x0ErBsyHrcPf8QMw6O02iTmXX+HJh7eorojTO15f+4uYUlCwcfjDHhzrkHmN1+Iaq0rIAZB8dqpAdMv3+6ovv09lg/cTsOLT3BRyYRkRGRmNl2Pp7d9IbLycmo0EjVwd9SLl+R3Fj03ywRcExoMAsBH1M+gBzTTxx8MMZiuB3xwJTmLihR0wlLr7uIMTbUgXpuuJyYhHajW2DZ0PXYNfcQH5VkCPsRjklNXXDn7APMOjIBPWd3hLGJemqtGvepiyXuc/DtSzBG1ZiCj68/q2W7LH3g4IMxpuDWmfsYVmUSIsMjscRtTppf0OgitvbBAuRzygPnxn/j8PKTfERSIDw0HDPazseWGXvQjpqrPP6XpkGjLFActWYALu9zx8gaU/HFP4CPGUsRiVTLpogMCgqClZUVaqEljCTG0Cu6OreLhblqmzZUftvRwd81N7eLVIe7Eibj197QyBAdJrRC58lt8drzLbZM241rRzxSrU2/RPWi6Dypjei1QWNXUBdS6snBlGdXIp8YZ6Ngyfw4uPQEDi05LgaTSw2ZsmREo9510HlyG9HVd1G/1fA4dZcPF1OY2+UiDiMwMBCWlpZIDAcf2oSDjxTj4ENJKbjnoAvakKW9UbKGk6haP772LE6sO4fP71I+wZt5JjPU7VJdDL9tVzwfXj19g1WjNoneGyx1UNDYflxLUQtCw+fTyLA0x4rHqXtQ5l7TsXwhtBjYELU6VIXEQCIGD1s7bhsHiiwODj50FQcfKcbBh5KUuAjR3XTzQQ1Rt3N10Qzz7IY3PG+/gKfHc3jdegG/p2/jjEJqY5dTNAE4lCsEh7IF4VTFESYZjHHt8E1xQbxz/qGy34AlgcZsoXl7WgxqBPsydiJwpPFc6JjR8aJH7G7MtE6h0gXgQMesbEExVHq+onnE8Pauq8/g1IbznFTKEsTBh67SYPAhMTRUfl0zM9W2bWSkueAjSoVJt9N5s0tCzC3NUbdzNZSoVlRcpPI42orlFHhQAmREWCSMjA1Fbxm6Cyd04aOL3ZPrnmLE0k9vvqTaV2HJGwCsRrsqcCxXCIXKFICF5c+m0vCwCESERohjR8fLJINJzPIX93zF5HA3jt/GjeN3eHh7liQOPnQVBx8pxsGHklIx1YuCEYeydsjjmEtcvKhmIyI8UoxO+sH3IzxvvUDAh8BU2x5TjUQiQW6HXOKYZcqaESZmJjAwkIjAMSToB17c94Xvo9eiKy9jaRV8aH4oQ8aYTqMk0XsXH4kH036U90EJxPRgTFO4qy1jjDHG1IqDD8YYY4zpdvARFRWFKVOmwM7ODmZmZihUqBBmzZqlVBcvxhhjjKU/qZ7z8b///Q8rV67E5s2bUaxYMXh4eKBnz55i4LBhw4al9uYYY4wxpu/Bx7Vr19CyZUs0bdpUPC9QoAB27tyJGzdupPamGGOMMaaDUr3Z5Y8//sC5c+fg6ekpnt+7dw9XrlxB48aN431/WFiYGFJd/sEYY4yx9CvVaz4mTJggAogiRYrA0NBQ5ID8/fff6Ny5c7zvd3FxwYwZM1K7GIwxxhjTl5qPPXv2YPv27dixYwdu374tcj/mz58vfsbH2dlZDEgie/j5+aV2kRhjjDGWnoOPsWPHitqPDh06oESJEujatStGjhwpajjiY2pqKkZCk38wxhhLvxp0r4Uz0XthnT8HtEnXae1EuSyzZdJ0UdK9VG92CQkJgYGBYkxDzS+xJ5xijLG0RJPYlWtQCgcWHxNTwKe38uZ3yoNu0/4S8+tkscmMsJAw+D5+jb3zj8Dd9VaalbP5wAYYtrwvnlz3wrAqE6FrtP28kEgk2OO/DnvnH8bdC49EoFaqVjFYF8iBb5+D8cTdExun7MIbr3fQZale89G8eXOR43Hs2DG8fPkSBw8exMKFC9G6devU3hRjjCXI6Y/C4uKcMbNFuiwv1RqYZTLD6S0XsWLERmyfvV8sn3VkApr0rZdm5azbqTre+XwQk9XZFrJR6jNocsEmZp3w3vcj1E3bz4siFe2ROYclrh+7jfbjWqHan5Vw5/wDrByxEcfWnkGJGk5YeWseChTLC12W6jUfS5cuFYOMDRo0CB8+fICtrS369++PqVOnpvamGGNMrWjK+dCQMK3Y6zdO3BEPeYeXncQKj/+hzchmOL72bKpv06ZAThSrWgTT//wHw1f1Q53O1bBt5r4Ufw7VhEeHcW14fCo2KQv/lx9ELdb+RUfh0vlfhUn+Lu2+hjX3F6D9+Fb4X7el0FWpHnxkypQJixcvFg/GGNNU2z3d3ZJtPitilnexGyRGW6Y/3GXqlEDOfNlFc8Xd8w+xZtxWhTtx2Wf0LjYSnSe1QYXGpfH+5UcMLDdOvF6yphP6/9MNBYrnxac3X7Dnn8PImiuLWKe+QTuF8mSzzYoes9qjUpOysMhsgbfe/ti38ChObbyQZHlTUjtAF/UPfp9QuII90gIFG0FfgsVd+X/73UUtiHzwQbUx8uWPTbZfqClh7MbBMd9P9v17FB6GLlPaokrz8mJmZNfVp7F56m7kyJMNQ5b2RqnaxRAWEi6aJPYtdFX47LEbBqNkLSd0LThYYbnss2nbyd3PVCtCx/aPVhVEM8iVA9exdMg6MfOvTN7CtggNCcdHv0+J7rOhy/ugxcCGib6ni9z2Kfi4cfy2+Pdjt59DVsh74+2Pl49eI1/RPNBlPKtteiHR3DQ9EkMVt63q+rq6z6UavPOTSJRfVwemSqCLRR4HW9TpVA0rRm5E0KdvYnngxyBUaFwGxaoUxsXdV/Hx9WdxN99sQAPMvzAdfYqNVLjAkCl7Ron29Q2TdsbstkKlC8DlxCR8fheALdP3wMDQAF2mtBOfH1vmnFZY4vY3IAUOLz/5swyNymDM+kEwtzTDwX+PJ1re5NTGmJiZwMLKHFValEfFxmVwcfc1pAUKNq4evC7uxC/svCIuqo7lC8HT43lMeed2XaKwjpGxIQYs7CGCiaRM3jUSr568wTrn7SJQ6zK5Lb59CUbTfvVx98JDrJuwXZSh//zueHbzOR789yRF5U/ufp68eyT8fT5g/cQdcChrhyZ96iHgY6DYvsyGJ/+KmZzH1Jme+Db3u8OhbEER6K4dtzVmebfpfyE8NAI7/t4fE3hksc4M+zIFsHna7kQ/M4u1FXwf6XbPUA4+GGPpjs+DV/C680JcZK4duqlwVyu7a5fnftQDS9zmoHqbyji77bLCay/u+cKly78Ky7pPb4+oqGiMrDYZn999Fcsu7XHD+seL4pSl198dYWhogL4lR4sLKXFdfQYTtw8Xd+HHVp9NtLxJ6b+gG5r1byD+TWW6euA6lg1dj9RGF1C62142bIN4/vDKU1HLUrdz9Zjgg5qkzm3/T2G9oct6wyxjBkxvMCvJbTy96Y1/B6wR/z6+5iy2+ixH//ndsGHiDuyed1gsp6Bn15s1aNSzToqDj+TuZ++7L7Gwz8qY55ZZM6FRrzoKwUdy3Tn/EP1MjPD8jo/Cvhm8pBcu7XXDhV1XY5ZVbFJGBCRUE5cQ2t9UE5RUgKLtdPSWkzHGlBMe+rtmw9DIEJmyZhRV2d++BsO+rF2c91PVvzzqzVemXglx8ZIFHuTtc3/cPHE3zvqUMOjmektU31MXTtnD4/Q9Ub1Pd9aqoF4b4+rPxP+6L8XNE3dELYyRSerfV9bpXB1f/ANw78KjmGWX9lxDrfZV4/RwlKnXtQZaDGqEteO3iVqCpJxYd06hCcnT44X47BPrz8cspx4qr5+9hU3BnEgrrqsUj/mDK09gld0S5pnMYpZRM05StR6Eyp+3SG74yNVU5MiTDZmyZMTLh68U3luxcVmxf+XPUXnU1DN0WR88uvYMZzZfgi7jmg/GmF4xyWCCjs6t0aBHLWTPnVXhwklNF7FR9bu8zDktRVMHBRuxvYm1jHot0EWmWb/64hEfapZRhd+zt+Ih60Uy9+Rk0eNlaGXneN9vZGwkAi551OyQ2HAItI9qt/8D9y48hI3d74v+0+teaDe6BcrULY5bZ+4rrFOoVAEMX9kP53dcwf5FivkZCfnwSjF/IiQwRDSDBX3+2TwiH4Ck5VgcscsR/PW7+JkxiwVCvv1I0WfZ2tvA1MxEoZnErkQ+8fPlQz+FQLhc/ZJYPzH+2hVqkpnt6iy++6x2C3R++AoOPhhjemXI0l5o0KM2Dv57TCT00R9zSkKdtHMEDOLJ44mdA5ISkl+BDQUF1CU2Pj73fZGaLu93x8jV/ZHH0RavPX8GJfKc/nDEgguKU1okldhauk5xkTRbu2M18YitTqfqCsEH1ehM3TcabzzfYWHf380XSYmOik7WMiFW2hIdw/hQTVBKJbRNqr1KKUpIjh1o2JXMH2dZ8WpFRPB747hiDyZibmmOOccniv06ssZUhRo3XcXBB2MsfUrgYkR5HWe2XMTqMVtilhmbGid73IeAD0EiIIlvjIvcsZZRjcL3oBBxAbxz7oFS5U0pustOqBZHlsNCzTTyqDklMZTk+fV9AJYOiZtLUq11JVRtXRH/DlwrmgvoAu28bZjYn+Prz1IpeEuJbwHf4z2G1vlyaDRhmoIPysV59eR1zDK74vnE/gz89DvRtVLTsnj5yC9OEEjn5qwj45HbMZfYn/Kfo8s4+GCMpUuh33+Ox0EXJPk/6HRXK4l129xqaGNR7Z0cVN19++x90Q0zW64sMXehFIxQd9zY772y/zpqd6qGAi55xcVFHuURyC5ACZU3IdSkExCrlwZ9h3pda4rETxonIj7BAd+TDoRiNVNV/bMiLu9zj5OoSz6//SISOKmnDeWAUHfWcg1LY1KTv8V4Fery7rm/2HfUpEGJpSSrTWYRGMlL6X5OSHK72toVyyea7hS66RbJLbrLxs73cD92K05zF/UAolFZp7WaJ0Y3TS84+GCMpUuet16Inz1ndxTdaql7qPvRW2LocUqEpBoJukA7VXYUCaTyd6FJ2Tpjrxiie9GV2XBddUrUbLQc3FhUo9uXUUwgpW6jND7FEvc5IqGStkk5Fw5l7FCmXkm0yd4z0fImNKjZ8FX9YWFphvv/PcbnN1/EEOtUQ0E9UlaN3ozQ76FIDRRUWFiaw+3IzXhff+Luha8fAsW26bt1ntwGDy4/Ebks1DNDXuyeMKmJeo30mdsF0w+MxaGlJ2BqboLmAxritec7OJYrGPO+lO7nhCS3qy3VfMTuFpv113D4VDtFzX7U3ZuGy18yaG2cnkx/tKwAtyMe4pxR5/5Maxx8MMbSJer+uXHKTtENtXyj0qK7K+U20FDkVCNBeQomGYzx6OozUZ3tcnJSsj/b6/YLTGoyB/3+6YruMzvgo99n0fUxX9Hc4q5WXsCHQAyt5IwuU9uJJormAxuKBEq6IK2bsC3J8oYmcHd+ac9VNOpVV1xgLbNlRMi3UHjdeiG6g7od9UBqoaCC7tpvx0oolc+1uHHstugNQ3ktdLdOc5HQI7a0vFhSN2YaeXXAgu7o878uv8bp2I7cDrkUg48U7mdVUHIvJZxeOXhDYfnNk3dEIDF63UDMbLdAdLGlGqmHV5/GSdqVBYD0iE2Xgw+JNKEsHQ0JCgqClZUVaqEljCTG0CuqDPyk4oBXEgPlt22QUcU5EoyUj4GjAxWz4FNKGhWl0vqqbVxHs9W160+GVqG7bppzg0bqZCy5/nZ1xo/gUMzuEHecGF0SKY3ARRxGYGBgkjPUc80HY4wpgXIh5MdjyG1vI4bGpmRWxlLi3qVHePCfYq1HesfBB2OMKWHL82U4vfki3r14L+Y0aT6gASLDI7Hn10icjCXXnn+O6N3O4uCDMcaU4HHyLmp3qCqSByPCIsWYIRsm7RCjpTLGEsfBB2OMKWF+74Rnb2WMJY7ndmGMMcaYWnHNB1O9t4wKvVXEpo2V79UkUWLo5NTqcSKNlmpun2uyp4wqvbJUxT1tGEsXuOaDMcYYY2rFwQdjjDHG1IqDD8YYY4ypFQcfjDHGGNPu4OPy5cto3rw5bG1txdTJhw4dUnidRmufOnUqcuXKBTMzM9SrVw9eXl6pWWbGGGOM6VPw8f37d5QqVQrLly+P9/V58+ZhyZIlWLVqFa5fvw4LCws0bNgQoaGpM8MiY4wxxnRbivtINm7cWDziQ7UeixcvxuTJk9GyZUuxbMuWLbC2thY1JB06dFC9xIwxxhjTaama8+Hj4wN/f3/R1CJDM9RWqlQJbm5u8a4TFhYmZrKVfzDGGGMs/UrV4IMCD0I1HfLouey12FxcXESAInvkzZs3NYvEGGOMMS2j8d4uzs7OCAwMjHn4+flpukiMMcYY05Xgw8bGRvx8//69wnJ6LnstNlNTU1haWio8GGOMMZZ+pWrwYWdnJ4KMc+fOxSyjHA7q9VKlSpXU3BRjjDHG9KW3S3BwMLy9vRWSTO/evYusWbMiX758GDFiBGbPng0HBwcRjEyZMkWMCdKqVavULjtjjDHG9CH48PDwQO3atWOejxo1Svzs3r07Nm3ahHHjxomxQPr164eAgABUq1YNJ0+eRIYMGVK35IwxxhjTSRIpDc6hRaiZhnq91EJLGEmUn2pdJ6kyVbkq07OLqekNlV7XwCqTats2Vv44R38NUGnb0shI5deN1uCvjjQaekm7/lwxxuRESiNwEYdF55Gk8jdTXPPB0ih4UDGAkBiotm2JsfKngsTCXKVtS01NlF85+LvGLmYSiVRjAYQ02kA/Ax9Vf8d0FQddLJ3ReFdbxhhjjOkXDj4YY4wxplYcfDDGGGNMrTj4YIwxxphacfDBGGOMMbXi4IMxxhhjasXBB2OMMcbUioMPxhhjjKkVBx+MMcYYUysOPhhjjDGmVhx8MMYYY0ytOPhgjDHGmFpx8MEYY4wxteLggzHGGGNqpfw86mlMYmoKicQ45StGRam0XWm0VGNTjUsMlJ8uXGKk2qGUmJspvW5YwRwqbftHdiWO8y+ZwyNU2rb0+w/lV44IV23bUcqfLxIVz3NEK79tqarTu6vyO6YqFX9HNUWlv0uqbxx6SdXznCWKaz4YY4wxplYcfDDGGGNMrTj4YIwxxphacfDBGGOMMe0OPi5fvozmzZvD1tYWEokEhw4dinktIiIC48ePR4kSJWBhYSHe061bN7x9+za1y80YY4wxfQk+vn//jlKlSmH58uVxXgsJCcHt27cxZcoU8fPAgQN49uwZWrRokVrlZYwxxpiOS3H/zMaNG4tHfKysrHDmzBmFZcuWLUPFihXx6tUr5MuXT/mSMsYYYyxdSPNxPgIDA0XzTObMmeN9PSwsTDxkgoKC0rpIjDHGGEuvCaehoaEiB6Rjx46wtLSM9z0uLi6ixkT2yJs3b1oWiTHGGGPpNfig5NO//vpLjIa4cuXKBN/n7OwsakdkDz8/v7QqEmOMMcbSa7OLLPDw9fXF+fPnE6z1IKampuLBGGOMMf1glFaBh5eXFy5cuIBs2bKl9iYYY4wxpk/BR3BwMLy9vWOe+/j44O7du8iaNSty5cqFtm3bim62rq6uiIqKgr+/v3gfvW5iYpK6pWeMMcZY+g8+PDw8ULt27Zjno0aNEj+7d++O6dOn48iRI+J56dKlFdajWpBatWqpXmLGGGOM6VfwQQFEYlNqqzrdtmz9SKmSU6VLVZtqXKXyqzj1tESF9VVZV6wfrfy09pGRoSptOzJC+WMWGf27m7YypNHhKqwcruK5psIxU/E8V+VcVXmmcU1OVa6j08Or+ndVH/eZyjS5z3VUJCKSfb5KpBo9q+N6/fo1d7dljDHGdBT1Ws2TJ49uBR/R0dFiLphMmTKJwclio0HIaCwQ+nKJ9aJhvN9Uxeca7zd14XON91t6ONconPj27ZuY183AwECzI5ymFBU4qYiJ0E7j4CPleL/xPlMXPtd4n/G5pn+/n1ZWVpof4ZQxxhhjLDYOPhhjjDGmVjoXfNBoqNOmTeNRUXm/8bmmpfh3lPcZn2vay1RLrqFal3DKGGOMsfRN52o+GGOMMabbOPhgjDHGmFpx8MEYY4wxteLggzHGGGNqxcEHY4wxxtRK54KP5cuXo0CBAsiQIQMqVaqEGzduaLpIWotmGaYh6uUfRYoU0XSxtM7ly5fRvHlzMSQw7aNDhw4pvE4dwqZOnYpcuXLBzMwM9erVg5eXF/RZUvusR48ecc69Ro0aQZ+5uLigQoUKYuqInDlzolWrVnj27JnCe0JDQzF48GBky5YNGTNmRJs2bfD+/Xvos+TsN5rwNPb5NmDAAOirlStXomTJkjGjmFapUgUnTpzQqvNMp4KP3bt3Y9SoUaKP8u3bt1GqVCk0bNgQHz580HTRtFaxYsXw7t27mMeVK1c0XSSt8/37d3EuUWAbn3nz5mHJkiVYtWoVrl+/DgsLC3He0S+wvkpqnxEKNuTPvZ07d0KfXbp0SfzBd3d3x5kzZxAREYEGDRqIfSkzcuRIHD16FHv37hXvp3mu/vzzT+iz5Ow30rdvX4XzjX5v9VWePHkwd+5c3Lp1Cx4eHqhTpw5atmyJR48eac95JtUhFStWlA4ePDjmeVRUlNTW1lbq4uKi0XJpq2nTpklLlSql6WLoFPqVOHjwYMzz6OhoqY2NjfSff/6JWRYQECA1NTWV7ty5U0Ol1O59Rrp37y5t2bKlxsqkCz58+CD23aVLl2LOK2NjY+nevXtj3vPkyRPxHjc3Nw2WVLv3G6lZs6Z0+PDhGi2XtsuSJYt03bp1WnOe6UzNR3h4uIjiqMpbfhI6eu7m5qbRsmkzah6gqvGCBQuic+fOePXqlaaLpFN8fHzg7++vcN7RxEnU5MfnXeIuXrwoqskLFy6MgQMH4vPnz2l+vHRJYGCg+Jk1a1bxk/6+0V29/LlGzaT58uXjcy2R/Sazfft2ZM+eHcWLF4ezszNCQkLUcRi1XlRUFHbt2iVqiqj5RVvOM62b1TYhnz59EjvR2tpaYTk9f/r0qcbKpc3oArlp0ybxx5+qIWfMmIHq1avj4cOHov2UJY0CDxLfeSd7jcXf5ELVuHZ2dnj+/DkmTpyIxo0biz9uhoaGer/LoqOjMWLECFStWlVcLGXnmomJCTJnzsznWgr2G+nUqRPy588vbrTu37+P8ePHi7yQAwcO6O259uDBAxFsUPMw5XUcPHgQTk5OuHv3rlacZzoTfLCUoz/2MpR8RMEI/YLu2bMHvXv35l3K0kyHDh1i/l2iRAlx/hUqVEjUhtStW1fv9zzlMNBNAOdgpc5+69evn8L5RsnhdJ5R4EvnnT4qXLiwCDSopmjfvn3o3r27yO/QFjrT7ELVaXTHFDsjl57b2NhorFy6hCJdR0dHeHt7a7ooOkN2bvF5pxpq9qPfYT73gCFDhsDV1RUXLlwQiYHy5xo1LwcEBCjsO/4bl/h+iw/daBF9Pt9MTExgb2+PcuXKiR5DlCD+77//as15ZqBLO5J24rlz5xSq4Og5VS2xpAUHB4s7AborYMlDzQb0Cyl/3gUFBYleL3zeJd/r169Fzoc+n3uUm0sXUKr+Pn/+vDi35NHfN2NjY4VzjZoOKE9Ln8+1pPZbfOiOn+jz+RYbXS/DwsK05zyT6pBdu3aJXgabNm2SPn78WNqvXz9p5syZpf7+/poumlYaPXq09OLFi1IfHx/p1atXpfXq1ZNmz55dZIuz3759+ya9c+eOeNCvxMKFC8W/fX19xetz584V59nhw4el9+/fF7047OzspD9+/NDb3ZjYPqPXxowZIzLn6dw7e/astGzZslIHBwdpaGioVF8NHDhQamVlJX4n3717F/MICQmJec+AAQOk+fLlk54/f17q4eEhrVKlinjos6T2m7e3t3TmzJlif9H5Rr+nBQsWlNaoUUOqryZMmCB6A9H+oL9Z9FwikUhPnz6tNeeZTgUfZOnSpWKnmZiYiK637u7umi6S1mrfvr00V65cYl/lzp1bPKdfVKbowoUL4gIa+0HdRWXdbadMmSK1trYWwW/dunWlz5490+vdmNg+o4tCgwYNpDly5BBd+vLnzy/t27ev3t8kxLe/6LFx48aY/UoB7aBBg0S3SHNzc2nr1q3FhVafJbXfXr16JQKNrFmzit9Pe3t76dixY6WBgYFSfdWrVy/xe0d/++n3kP5myQIPbTnPJPQ/9dWzMMYYY0zf6UzOB2OMMcbSBw4+GGOMMaZWHHwwxhhjTK04+GCMMcaYWnHwwRhjjDG14uCDMcYYY2rFwQdjjDHG1IqDD8YYY4ypFQcfjDHGGFMrDj4YY4wxplYcfDDGGGMM6vR/HJ0rIBH1gZoAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# first redefine the TX antennas: \n", "# instead of TX being NR*lambda0/2 apart on the x-axis to have a ULA,\n", "# we define them lambda0/2 on the y-axis to have a URA\n", "NT = 13\n", "NR = 13\n", "TXs = [Antenna(z=lambda0/2*i - ((NT-1)//2)*lambda0/2) for i in range(NT)]\n", "RXs = [Antenna(x=lambda0/2*i - ((NR-1)//2)*lambda0/2) for i in range(NR)]\n", "# then update the radar definition\n", "chirp_bandwidth0 = 3.5e9\n", "chirp_slope0 = _k\n", "chirp_end_time0 = chirp_bandwidth0/chirp_slope0\n", "adc_sample_rate0 = _fs\n", "adc_sample_count0 = NA\n", "chirp_period0 = chirp_end_time0*1.1\n", "frame_period0 = NT*chirp_period0*1.1\n", "radar = Radar(transmitter=Transmitter(chirp_end_time=chirp_end_time0,\n", " chirp_slope=chirp_slope0,\n", " chirp_count=NT,\n", " chirp_period=chirp_period0,\n", " frame_period=frame_period0,\n", " antennas=TXs),\n", " receiver=Receiver(adc_sample_rate=adc_sample_rate0,\n", " adc_sample_count_max=2048,\n", " adc_sample_count=adc_sample_count0,\n", " antennas=RXs),\n", " debug=False)\n", "\n", "# Now define target1 with an elevation:\n", "\n", "r1, theta1, phi1 = 10.1, 0, pi/2\n", "x1 = r1 * cos(theta1)*sin(phi1)\n", "y1 = r1 * sin(theta1)*sin(phi1)\n", "z1 = r1 * cos(phi1)\n", "r2, theta2, phi2 = 20.1, pi/2, pi/2\n", "x2 = r2 * cos(theta2)*sin(phi2)\n", "y2 = r2 * sin(theta2)*sin(phi2)\n", "z2 = r2 * cos(phi2)\n", "r3, theta3, phi3 = 30.1, pi/2, 0\n", "x3 = r3 * sin(phi3)*cos(theta3)\n", "y3 = r3 * sin(phi3)*sin(theta3)\n", "z3 = r3 * cos(phi3)\n", "scatterer1 = Scatterer(x1, y1, z1)\n", "scatterer2 = Scatterer(x2, y2, z2)\n", "scatterer3 = Scatterer(x3, y3, z3)\n", "scatterers = [scatterer1, scatterer2, scatterer3]\n", "print(\"scatterers\", [f\"{s}\" for s in scatterers])\n", "\n", "bb = rt_points([radar],\n", " scatterers,\n", " radar,\n", " debug=False)\n", "cube = bb[\"adc_cube\"]\n", "\n", "range_azimuth_fft = fftshift(fft(fft(cube[0,0,:NR,:], axis=-1), axis=-2), axes=-2)\n", "\n", "fig, (ax0) = plt.subplots(ncols=1)\n", "# ax0.imshow(abs(RA[(NT-1)//2,:,:NA//2]))\n", "ax0.imshow(np_abs(range_azimuth_fft[:,:NA//2]))\n", "ax0.set_title(\"Range Azimuth map\")\n", "azi_target1 = plt.Circle((8, 0.5), 1.5, fill=False, color=\"white\")\n", "azi_target2 = plt.Circle((15, 6), 1.5, fill=False, color=\"white\")\n", "azi_target3 = plt.Circle((22, 6), 1.5, fill=False, color=\"white\")\n", "ax0.text(2, 2.5, f\"target 1 - Azimuth: 0\", color=\"white\", fontsize=12)\n", "ax0.text(10, 4, f\"target 2 - Azimuth: $\\pi$/2\", color=\"white\", fontsize=12)\n", "ax0.text(17, 9, f\"target 3 - Azimuth: $\\pi$/2\", color=\"white\", fontsize=12)\n", "ax0.add_artist(azi_target1)\n", "ax0.add_artist(azi_target2)\n", "ax0.add_artist(azi_target3)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "id": "c91f4783-52a8-4e2f-8334-b838aa219ea9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "range_elevation_fft = fftshift(fft(fft(cube[0,:,0,:], axis=-1), axis=0), axes=0)\n", "\n", "fig, (ax0) = plt.subplots(ncols=1)\n", "ax0.imshow(abs(range_elevation_fft[:,:NA//2]))\n", "ax0.set_title(\"Range Elevation map\")\n", "ele_target1 = plt.Circle((8, 6), 1.5, fill=False, color=\"white\")\n", "ele_target2 = plt.Circle((15.5, 6), 1.5, fill=False, color=\"white\")\n", "ele_target3 = plt.Circle((22, 0.2), 1, fill=False, color=\"white\")\n", "ax0.text(2, 8.5, f\"target 1 - Elevation: $\\pi$/2\", color=\"white\", fontsize=12)\n", "ax0.text(10, 4, f\"target 2 - Elevation: $\\pi$/2\", color=\"white\", fontsize=12)\n", "ax0.text(17, 2, f\"target 3 - Elevation:0\", color=\"white\", fontsize=12)\n", "ax0.add_artist(ele_target1)\n", "ax0.add_artist(ele_target2)\n", "ax0.add_artist(ele_target3)" ] }, { "cell_type": "code", "execution_count": 18, "id": "b6325365-de2d-43ea-88d3-8b1d68278a71", "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "cube shape (1, 13, 13, 64)\n", "scatterer_detected [(np.int64(8), np.int64(7), np.int64(0)), (np.int64(15), np.int64(0), np.int64(0)), (np.int64(22), np.int64(0), np.int64(7)), (np.int64(23), np.int64(0), np.int64(7))]\n", "scatterer_range [(np.float64(10.714285714285714), np.int64(7), np.int64(0)), (np.float64(20.089285714285715), np.int64(0), np.int64(0)), (np.float64(29.464285714285715), np.int64(0), np.int64(7)), (np.float64(30.80357142857143), np.int64(0), np.int64(7))]\n" ] } ], "source": [ "from mmWrt.RadarSignalProcessing import cfar_ca, if2d\n", "from numpy import where, concatenate, abs\n", "def pcl(cube):\n", " Range_FFT = fft(cube, axis=-1)\n", " range0 = Range_FFT[0,0,0,:NA//2]\n", " \n", " # cfar_th = cfar_1d(range0, num_training_cells=8, mode=\"full\", cfar_type=\"CA\")\n", " cfar_th = cfar_ca(abs(range0), train_cell_count=8,\n", " guard_cell_count=1, pfa=1e-1)\n", " target_filter = ((abs(range0) > abs(cfar_th)) & (abs(range0) > 20))\n", " index_peaks = where(target_filter)\n", " # focus on range bins where some targets are detected\n", " # lowers memory constraints for follow-up FFTs\n", " # usually the highest return as the fast time dimension is usually the largest\n", " range_targets = Range_FFT[:,:,:,index_peaks[0]]\n", " azi_FFT = fft(range_targets, axis=-2)\n", " ele_FFT = fft(azi_FFT, axis=-3)\n", " scatterers = []\n", " for range_idx in range(len(index_peaks[0])):\n", " target0_azi = azi_FFT[0,0,:,range_idx]\n", " cfar_th_a = cfar_ca(abs(target0_azi),\n", " train_cell_count=4,\n", " guard_cell_count=1, pfa=1e-1) #, mode=\"full\", debug=False, cfar_type=\"CA\")\n", " target_filter = ((abs(target0_azi) > abs(cfar_th_a)))\n", " index_peaks_azi = where(target_filter)[0]\n", " mag_azis = abs(azi_FFT[0,0,index_peaks_azi,range_idx])\n", " # simplification: here we only look for one peak\n", " # FIXME: should do peak grouping here to retrieve all targets\n", " # the alternative to take all peaks from CFAR just yields too many targets\n", " azi_idxs = [[m for m in mag_azis].index(max(mag_azis))]\n", " for azi_idx in azi_idxs:\n", " target0_ele = ele_FFT[0,:,index_peaks_azi[azi_idx],range_idx]\n", " cfar_th_e = cfar_ca(abs(target0_ele), train_cell_count=4,guard_cell_count=1,\n", " pfa=1e-1)\n", " # mode=\"full\", debug=False, cfar_type=\"CA\")\n", " target_filter = ((abs(target0_ele) > abs(cfar_th_e)))\n", " index_peaks_ele = where(target_filter)[0]\n", " mag_eles = abs(ele_FFT[0,index_peaks_ele,azi_idx,range_idx])\n", " # same comment as for azimuth: here should do peak grouping\n", " # today only grabs the strongest echo in elevation\n", " e_idx = [m for m in mag_eles].index(max(mag_eles))\n", " scatterers.append((index_peaks[0][range_idx], index_peaks_azi[azi_idx], index_peaks_ele[e_idx]))\n", " return scatterers\n", "\n", "print(\"cube shape\",cube.shape)\n", "scatterer_detected = pcl(cube)\n", "print(\"scatterer_detected\", scatterer_detected)\n", "f2d = if2d(radar)\n", "scatterer_range = [(f_idx*_fs*f2d/NA, a, e) for f_idx, a, e in scatterer_detected]\n", "print(\"scatterer_range\", scatterer_range)" ] }, { "cell_type": "code", "execution_count": 20, "id": "52733d25-2b1d-40f0-807b-f47cc8264966", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "scatterer_detected idx [(np.int64(8), np.int64(7), np.int64(0)), (np.int64(15), np.int64(0), np.int64(0)), (np.int64(22), np.int64(0), np.int64(7)), (np.int64(23), np.int64(0), np.int64(7))]\n", "scatterer_polar [(np.float64(10.714285714285714), np.float64(0.39479111969976133), np.float64(1.5707963267948966)), (np.float64(20.089285714285715), np.float64(1.5707963267948966), np.float64(1.5707963267948966)), (np.float64(29.464285714285715), np.float64(1.5707963267948966), np.float64(0.39479111969976133)), (np.float64(30.80357142857143), np.float64(1.5707963267948966), np.float64(0.39479111969976133))]\n", "r, t, p 10.714285714285714 0.39479111969976133 1.5707963267948966\n", "y 4.120879120879119\n", "r, t, p 20.089285714285715 1.5707963267948966 1.5707963267948966\n", "y 20.089285714285715\n", "r, t, p 29.464285714285715 1.5707963267948966 0.39479111969976133\n", "y 11.332417582417577\n", "r, t, p 30.80357142857143 1.5707963267948966 0.39479111969976133\n", "y 11.847527472527467\n", "target cartesians [(np.float64(9.89010989010989), np.float64(4.120879120879119), np.float64(6.560607852575106e-16)), (np.float64(1.2301139723578325e-15), np.float64(20.089285714285715), np.float64(1.2301139723578325e-15)), (np.float64(6.939104459454436e-16), np.float64(11.332417582417577), np.float64(27.1978021978022)), (np.float64(7.254518298520547e-16), np.float64(11.847527472527467), np.float64(28.434065934065938))]\n" ] } ], "source": [ "def AoA_idx_to_rad(phi_idx, tot=13):\n", " from numpy import arcsin\n", " if phi_idx