{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The HFM library - A fast marching solver with adaptive stencils\n", "\n", "## Part : Seismology and crystallography\n", "## Chapter : Metrics defined by a Hooke tensor" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook, we demonstrate anisotropic fast marching with a class of metrics arising in seismic travel time tomography. They characterize the first arrival time of seismic P-waves (compressive waves), in the high frequency asymptotic. The seismic models are implemented in dimension $d \\in \\{2,3\\}$. \n", "\n", "The eikonal equation arising from the high-frequency asymptotic of seismic waves reads\n", "$$\n", " \\det(m_x(\\nabla u) - \\rho(x)\\mathrm{Id}) = 0,\n", "$$\n", "where for each co-vector $p$ one defines\n", "$$\n", " m_x(p)_{ij} = \\sum_{k,l} c_{ijkl}(x) p_k p_l.\n", "$$\n", "We denoted by $c(x) = (c_{ijkl}(x))$, where $i,j,k,l \\in \\{1,\\cdots,d\\}$ the Hooke tensor, which describes the elastic properties of the geological medium. The user must take care to only provide elliptic (or positive) Hooke tensors. This assumption, satisfied in physical contexts, ensures that $m=m_x(p)$ is positive definite as soon as $p\\neq 0$. \n", "\n", "The `Seismic.Hooke` class is constructed from the ratio $c/\\rho$ of the hooke tensor, given in Voigt notation, divided by the medium density $\\rho$.\n", " \n", "\n", " \n", "\n", "\n", "**Accuracy.**\n", "Our implementation of the fast marching method for seismic metrics is designed to achieve high accuracy, up to third order, in smooth test cases. However this capability is not demonstrated in the present notebook, but in [C1 Achieving high accuracy](http://nbviewer.jupyter.org/urls/rawgithub.com/Mirebeau/HFM_Python_Notebooks/master/Aa_HighAccuracy.ipynb)\n", "\n", "**Work in progress.**\n", "The experiments presented in this notebook are part of the internship of François Desquilbet [link](https://www.see.asso.fr/en/distinction/24512_prix-jeunes-national-andre-blanc-lapierre-2018-trophee-ile-france).\n", "Tutors : J.-M. Mirebeau (CNRS, U. PSud, U. PSaclay), L. Métivier (CNRS, LJK, ISTerre, Univ Grenoble, France) [link](https://www-ljk.imag.fr/membres/Ludovic.Metivier/)\n", "\n", "**References** \n", "The main techniques used are presented in the following publication.\n", "\n", "Mirebeau, J.-M. (2014). Efficient fast marching with Finsler metrics. Numerische Mathematik, 126(3), 515–557. [link](https://hal.archives-ouvertes.fr/hal-00736431)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[**Summary**](Summary.ipynb) of volume Fast Marching Methods, this series of notebooks.\n", "\n", "[**Main summary**](../Summary.ipynb) of the Adaptive Grid Discretizations \n", "\tbook of notebooks, including the other volumes.\n", "\n", "# Table of contents\n", " * [1. A constant medium, with tilted and anelliptic anisotropy](#1.-A-constant-medium,-with-tilted-and-anelliptic-anisotropy)\n", " * [1.1 Mandel notation](#1.1-Mandel-notation)\n", " * [2. Varying medium](#2.-Varying-medium)\n", " * [2.1 Position dependent tilt orientation.](#2.1-Position-dependent-tilt-orientation.)\n", " * [3. Taking into account the topography](#3.-Taking-into-account-the-topography)\n", " * [4. Testing reproduction](#4.-Testing-reproduction)\n", " * [4.1 Case of a constant metric](#4.1-Case-of-a-constant-metric)\n", " * [4.2 Case with topography](#4.2-Case-with-topography)\n", " * [5. Three dimensional example](#5.-Three-dimensional-example)\n", " * [5.1 Case of a constant metric](#5.1-Case-of-a-constant-metric)\n", " * [5.2 Position dependent metric](#5.2-Position-dependent-metric)\n", " * [5.3 Topography](#5.3-Topography)\n", "\n", "\n", "\n", "This Python® notebook is intended as documentation and testing for the [HamiltonFastMarching (HFM) library](https://github.com/mirebeau/HamiltonFastMarching), which also has interfaces to the Matlab® and Mathematica® languages. \n", "More information on the HFM library in the manuscript:\n", "* Jean-Marie Mirebeau, Jorg Portegies, \"Hamiltonian Fast Marching: A numerical solver for anisotropic and non-holonomic eikonal PDEs\", 2019 [(link)](https://hal.archives-ouvertes.fr/hal-01778322)\n", "\n", "Copyright Jean-Marie Mirebeau, University Paris-Sud, CNRS, University Paris-Saclay" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 0. Importing the required libraries" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:29.230288Z", "iopub.status.busy": "2024-04-30T08:52:29.229593Z", "iopub.status.idle": "2024-04-30T08:52:29.238473Z", "shell.execute_reply": "2024-04-30T08:52:29.238018Z" } }, "outputs": [], "source": [ "import sys; sys.path.insert(0,\"..\") # Allow import of agd from parent directory (useless if conda package installed)\n", "#from Miscellaneous import TocTools; print(TocTools.displayTOC('Seismic','FMM'))" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:29.241050Z", "iopub.status.busy": "2024-04-30T08:52:29.240849Z", "iopub.status.idle": "2024-04-30T08:52:29.492822Z", "shell.execute_reply": "2024-04-30T08:52:29.492474Z" } }, "outputs": [], "source": [ "from agd import Eikonal\n", "from agd import LinearParallel as lp\n", "from agd import FiniteDifferences as fd\n", "from agd.Metrics.Seismic import Hooke\n", "from agd import AutomaticDifferentiation as ad\n", "from agd.Plotting import savefig, quiver; #savefig.dirName = 'Images/Seismic'\n", "norm_infinity = ad.Optimization.norm_infinity\n", "reduced_models=False" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:29.494532Z", "iopub.status.busy": "2024-04-30T08:52:29.494412Z", "iopub.status.idle": "2024-04-30T08:52:29.499784Z", "shell.execute_reply": "2024-04-30T08:52:29.499517Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import scipy.linalg\n", "from copy import copy\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:29.501181Z", "iopub.status.busy": "2024-04-30T08:52:29.501103Z", "iopub.status.idle": "2024-04-30T08:52:29.503035Z", "shell.execute_reply": "2024-04-30T08:52:29.502785Z" } }, "outputs": [], "source": [ "def reload_packages():\n", " from Miscellaneous.rreload import rreload\n", " global HFMUtils,lp,Hooke,ad\n", " HFMUtils,lp,Hooke,ad = rreload([HFMUtils,lp,Hooke,ad],rootdir='..')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 0.1 Additional configuration\n", "\n", "**Requires the HFM library**\n", "This notebook is CPU only, requires the HFM library, and in particular it *cannot be run on Google Colab*. Indeed, the generalized fast marching method based on a Hooke tensor is not implemented on the GPU. See this [closely related notebook](TTI.ipynb) for GPU compatible experiments, involving the simpler *Tilted Transversally Isotropic* (TTI) models.\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:29.504362Z", "iopub.status.busy": "2024-04-30T08:52:29.504279Z", "iopub.status.idle": "2024-04-30T08:52:29.505903Z", "shell.execute_reply": "2024-04-30T08:52:29.505671Z" } }, "outputs": [], "source": [ "#raise ad.DeliberateNotebookError(\"Hooke tensor based eikonal equations not implemented on the CPU\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. A constant medium, with tilted and anelliptic anisotropy\n", "\n", "The Hooke tensors and densities of a a small number of geophysical media are provided. \n", "Here we construct three tensors corresponding to the slice, tilted, of uniform media.\n", "\n", "We will use the hooke tensors for the following materials." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:29.507239Z", "iopub.status.busy": "2024-04-30T08:52:29.507159Z", "iopub.status.idle": "2024-04-30T08:52:29.508805Z", "shell.execute_reply": "2024-04-30T08:52:29.508569Z" } }, "outputs": [], "source": [ "mica,stishovite,olivine = Hooke.mica[0],Hooke.olivine[0],Hooke.stishovite[0]" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:29.510182Z", "iopub.status.busy": "2024-04-30T08:52:29.510104Z", "iopub.status.idle": "2024-04-30T08:52:29.512470Z", "shell.execute_reply": "2024-04-30T08:52:29.512221Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[178. 14.5 0. ]\n", " [ 14.5 54.9 0. ]\n", " [ 0. 0. 12.2]]\n", "[[323.7 71.6 0. ]\n", " [ 71.6 235.1 0. ]\n", " [ 0. 0. 78.7]]\n", "[[453. 203. 0.]\n", " [203. 776. 0.]\n", " [ 0. 0. 252.]]\n" ] } ], "source": [ "print(mica.extract_xz().hooke) \n", "print(stishovite.extract_xz().hooke)\n", "print(olivine.extract_xz().hooke)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:29.513777Z", "iopub.status.busy": "2024-04-30T08:52:29.513698Z", "iopub.status.idle": "2024-04-30T08:52:29.516033Z", "shell.execute_reply": "2024-04-30T08:52:29.515801Z" } }, "outputs": [], "source": [ "metric_mica = mica.extract_xz().rotate_by(np.pi/6)\n", "metric_stishovite = stishovite.extract_xz().rotate_by(-np.pi/8)\n", "metric_olivine = olivine.extract_xz().rotate_by(np.pi/12)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:29.517365Z", "iopub.status.busy": "2024-04-30T08:52:29.517290Z", "iopub.status.idle": "2024-04-30T08:52:29.519797Z", "shell.execute_reply": "2024-04-30T08:52:29.519557Z" } }, "outputs": [], "source": [ "hfmIn_Constant = Eikonal.dictIn({\n", " 'model': 'Seismic2',\n", " 'exportValues':1,\n", " 'seed':[0.,0.],\n", " 'metric':metric_mica,\n", " 'stencilGeometry':'Square', # Non-adaptive 8-point square stencil\n", " 'exportGeodesicFlow':1,\n", "})\n", "hfmIn_Constant.SetRect(sides=[[-1,1],[-1,1]],dimx=201) # Define the domain\n", "X = hfmIn_Constant.Grid() # Horizontal and vertical axis\n", "hfmIn_Constant.SetUniformTips((6,6))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:29.521135Z", "iopub.status.busy": "2024-04-30T08:52:29.521055Z", "iopub.status.idle": "2024-04-30T08:52:29.687590Z", "shell.execute_reply": "2024-04-30T08:52:29.687225Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field cosAngleMin defaults to 0.5\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.098914 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn_Constant.Run()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:29.689210Z", "iopub.status.busy": "2024-04-30T08:52:29.689123Z", "iopub.status.idle": "2024-04-30T08:52:29.691948Z", "shell.execute_reply": "2024-04-30T08:52:29.691668Z" } }, "outputs": [ { "data": { "text/plain": [ "(0.098914, 4.5e-05)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hfmOut['FMCPUTime'], hfmOut['StencilCPUTime']" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:29.693319Z", "iopub.status.busy": "2024-04-30T08:52:29.693235Z", "iopub.status.idle": "2024-04-30T08:52:29.765021Z", "shell.execute_reply": "2024-04-30T08:52:29.764759Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[4,4]); plt.title('Minimal distance, Seismic metric (constant)'); plt.axis('equal')\n", "plt.contourf(*X,hfmOut['values']);" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:29.766663Z", "iopub.status.busy": "2024-04-30T08:52:29.766543Z", "iopub.status.idle": "2024-04-30T08:52:29.832581Z", "shell.execute_reply": "2024-04-30T08:52:29.832313Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The geodesics are straight lines, since the metric is constant\n", "fig = plt.figure(figsize=[4,4]); plt.title('Minimal geodesics, Seismic metric (constant)'); plt.axis('equal'); \n", "for geo in hfmOut['geodesics']: plt.plot(*geo) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The geodesic flow is normalized w.r.t the metric." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:29.834195Z", "iopub.status.busy": "2024-04-30T08:52:29.834085Z", "iopub.status.idle": "2024-04-30T08:52:29.926832Z", "shell.execute_reply": "2024-04-30T08:52:29.926555Z" } }, "outputs": [ { "data": { "image/png": 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r1o1iYmJkdSEiio6O1lr36NEjWr16tewuRES+vr5a65RKJZ04cUJ2l5MnT9KpU6d0PhcVFSWry7Nnzyg1NZVmzpypsx+Zk5OTrD6ZGBkZ0fz586XHmX2lWrduLcTn8OHDNGPGDCIiMjc3Jz8/P2rQoAFVrFhRdie1Wk2jR4+mVatWST6HDh2inj17UseOHennn3+mIkWKyOr0WaL/vGV4cAVHE7VajUaNGmldSRUrVgzLly9HamqqrD47d+7UeaVpZ2eHXbt2yery77//ZnvlO2TIENkrS46OjjpdOnToILvL/Pnzdbo4ODggJiZGVpf09HQUKVJEp4/cfUxUKhVq164Ne3t7VK1aVcvnzz//lNUnE6VSCWdnZ6n/Ro0aNUBE8PPzE+KzYMEC6T3p1q0bHj16BHNzc/j6+sru8ujRI9ja2ko+69evBwDs2bMHCxYskNVFV+XmxIkT0vNnzpzB+/fvZXUyJLiJKhc44Gijqz9F5lKhQgVs374dKpVKFpeUlBQ4ODhk6zNo0CDEx8fL4qJWq1GyZMlsXb766iskJyfL4gIAderU0dkMQ0T48ccfZfMAdDd7ZLpMnDhRVpfM72/RokUlF1tbWxgbG8Pe3h7p6emyuURHR+PGjRtQqVTw9vaWfMaPHw9zc3P4+PjI5pKVw4cPSy6enp4ICwtDmTJlcPv2bdldQkNDUahQISlsPXv2DACwcOFC2ZsUExIS4OrqKr03I0eOlJ5TKpWyNgXlFm4YbqJi/gMtW7akzp0763zu6dOn1LdvXxo/fjypVCq9u5ibm1P//v211ltbW1O/fv2oZs2aFB4erncPIiKFQkGtWrXSWj9u3Dh6/vw5bdiwgczNzWVxISIqVaqU1roDBw5QYmIieXt7y9psltlEVadOHWnd6tWrKTAwkEqVKkVpaWmyuQQGBtKiRYvo2bNn0rrmzZvTo0ePqEePHnT9+nXZXOzt7alu3bpkZGRE165dIyIiMzMzmj9/Pl2+fJksLS1lc8nKmjVrpP9///33VKpUKTp27Fiuc4nogx9//JGSkpKIiGjKlClUrlw5Ispo/rW1tZXNAwB5eXnR3bt3iYioadOmtHTpUul5Y2Nj2ZqCsmuWat++vSy/P1+i97hlgHAFRze3b9/W6OCbuXTv3h1hYWGyu3zoYWRkhDNnzsjqAQBr1qyRmuwyR+k4ODggOjpadpdhw4bB2tpaGv1GRPjyyy9l9wCAXr16YePGjQgODpZchg8fLsQlc3i6Wq2WXDw8PLSel5O0tDRYWFiAiNCwYUOhLi9fvoSRkRGICDVr1hQ6nN/Pz0+jOixnBfRDFi1aJLk4OTnh1atXQjy4cvPxcBNVLnDAyR5PT0+dzQ4ihv82aNBAOiBnuhQvXlz2sPXw4UMQEfbv348ffvhBchk1apSsHgAwd+5cnDx5Emq1WmquUigUePLkiewumaPtlEolChcuDCKCm5ub7B5ZyS7giCAoKEhyGT16tFAXHx8f4X2AACA1NVWjX5KI/jaZnDp1Sgp9JiYmuHTpkhAPDjd5gwNOLnDAyZ7nz5/DzMwMRIQmTZoIDTmrV6+Gubk5wsPDMWDAAMmlSZMmsnZ8VqvV+OGHHwAAMTExKFasmFRRunXrlmweQMbkjJn8/fff0nsid5+XD2nTpo30noicoNGQAk5m5Y+IsHHjRmEe6enpUj8yKysrYcPmAc2KicjP5/nz5xr9/FasWCHEg8NN3jGYgHP+/Hl4eHigRIkS0hVwbpw7dw5169aFubk5ypcvj1WrVmlts2fPHlSrVg1mZmaoVq0a9u3blycvDjg5M378eFhYWCAhIUGjI6ncISc2NlaahCwpKUmjkjNmzBjZPABodLBeu3at5PHFF18IK/cnJSVJIz/s7e2Fjqz4+eefpfdERDNiJoYUcIYMGSK5iJqrCAAOHDggeXh5eQnzCAsLkzoWm5ubC6k6AsD79+9Rt25djQ7XIvZhDjf/DYMJOEePHsXUqVOlCcFyCzhPnz6FlZUVvL29ce/ePfz9998wNTXFnj17pG38/f1hbGyMefPm4f79+5g3bx5MTExw5cqVj/bigJMzb9++xeDBgwFknDBEhpysk8Y9evQINjY2ksu2bdtk88iKSqVCw4YNJY8tW7YI8QCgMSPshg0bhHn4+vpKHvPmzRPmYUgBx83NDUQZkzHKNQJRF506dZLek6tXrwrz6NOnj+QhaiSZWq3WaIavW7eukAsDDjf/HYMJOBq/6CMCzqRJk1C1alWNdd9//z0aN24sPe7Vqxc6duyosU2HDh3Qp0+fj3bhgJM7WZtCRIecrGS9GrWyssKdO3eEeFy9elXqkF2iRAnZhq1/SGb/ICJCgwYNhDgAQFRUlOTRtWtXYR6GEnCSkpKkDukibxfx7Nkz6Xtat25dYdXGM2fOSJ9LuXLlhFUbV6xYIXkULVoUz58/l92Bw83/j892mHhAQIDWkLgOHTrQ9evXKT09Pcdt/P39s33d1NRUio+P11iYnLGyspL+r1AoaNGiRTRhwgQiypgdtk+fPjrvbqtvunXrRpMnTyYiovfv39OwYcNkn1GYiKhBgwbk5eVFREQRERG0bNky2R2IiKpUqSLN/Hzt2jVZh0NnpVixYlSpUiUiythHRXwmhkRQUJA0pUKDBg2Eefz999/SZ/H9998Lufs8AJo0aZL0eNmyZUKGyoeHh9P48eOJKGMW5Z07d1LZsmVl99i2bRsPBZcJE9ECWYmMjCRHR0eNdY6OjqRUKunt27dUokSJbLfJ6WQ7f/58mjlzpl6cCwqZIYeIaMmSJbRhwwZhU7zPnj2bAgMDKT4+nrZt2ybkoE1ENG/ePDp8+DANGzaMfvzxRyEORESjRo2i9PR0GjVqFLm5uQnzGDx4MMXFxVHjxo1JrVaTsbGxEI+5c+cSEUmBSwSVKlWitWvX0tWrV4WevLy9vcnW1pa2b99Offv2FeKgUCho165dNHbsWEpPT6euXbsK8ShZsiTt27ePvv32W5o2bRq1adNGiEffvn3p9OnTtH37dg43ekYBmS61FAoF7d+/n7p3757tNlWqVKFBgwbRlClTpHWXL1+mL774giIiIsjJyYnMzMxo48aNGjvr1q1bycvLi1JSUnS+bmpqKqWmpkqP4+PjqUyZMhQXF0c2Njb//z+uAAGAgoODqXbt2kI93r17R1ZWVmRhYSHUIzk5WdjEbQzzuWEI+0t4eDiVKFFC2IUREZFKpaKQkBChFySfK/Hx8WRra/tR52+DquA4OTlpVWKioqLIxMSEHBwcctzmw6pOVszNzWWdbTY/o1AohIcboozZYg0B0QdrhvmcMIT9pWTJkqIVyNjYmMONDBhUH5wmTZqQn5+fxrqTJ09S/fr1ydTUNMdtmjZtKpsnwzAMwzCGjV4rOImJifT48WPp8bNnz+jWrVtkb29Pzs7ONGXKFHr16hVt2rSJiIiGDx9Of/75J40fP56GDh1KAQEBtHbtWtq+fbv0Gt7e3tSiRQtauHAhdevWjQ4ePEinTp2iS5cu6fNPYRiGYRjmM0KvFZzr169TnTp1pJvxjR8/nurUqUM+Pj5ElDH65OXLl9L25cuXp6NHj9K5c+eodu3aNHv2bPrjjz+oZ8+e0jZNmzalHTt20Pr166lWrVq0YcMG2rlzJzVq1EiffwrDMAzDMJ8RsnUyNiTy0kmJYRiGYRjDIC/nb4Pqg8MwDMMwDPMp4IDDMAzDMEy+gwMOwzAMwzD5Dg44DMMwDMPkOzjgMAzDMAaPWq0WrZAtBXCszmcBBxyGYRgZiYqKEq2gk4SEBDpx4oRoDZ0cP36cDh06JFpDCwDk6+tL//zzj2iVbPn3338pLS1NtIYQOOAwDJPv8Pf3F62gk+fPn9Nvv/0mWkOLlJQU6tatG71//160igbp6ek0efJk6tGjB7Vq1Uq0jgb+/v7UokUL6tevX473WBRBYmIirV+/npo3b06rV68mMzMz0UpC4IDDMMx/4ty5c6IVdPL27VuaOnWqaA2djB07lqKjo0VraJCenk69evWis2fPUs2aNUXrSISGhlKrVq1o4cKF1LlzZ7KzsxOtRERE9+/fpx49elCzZs3o0qVLNHHiRCpWrJhoLQJAly9fJi8vL3JycqLBgwdTQkICzZs3T7SaMDjgMIyBExYWZnBX1kREs2fPpvv374vW0OLYsWN04cIFevfunWgVDY4cOUIHDx40qM9SpVKRp6cn+fr6kqWlJVWoUEG0EhERHT58mGrXri1V4gYMGCDYKGM/HDJkCNWoUYMOHDhARESOjo40btw4oV4RERG0cOFCqlq1Kn3xxRe0bt06SkpKIktLS9q+fXuBvtE0BxyGMXDUajX16NGDUlNTRatokJiYSN9//73Bdf709fUltVpNx44dE60ikZycTGPGjCEiMpiAA4BGjBgh3evP1dWVjIzEnhLS0tLoxx9/pC5dukgB1d7enjp16iTMKSYmhiZPnkyVK1emtWvXanzffXx8qHDhwrI7paWl0f79+6lLly5UpkwZmjx5Mj169Ehjm6VLl1K1atVkdzMoUACJi4sDESEuLk60CmOAHD16FLGxsaI1JNRqNWxtbdGjRw+kp6eL1pGoXbs2iAhr164VrSKRmpoKa2trEBF69+4tWkfCx8cHRAQiQrt27UTrQK1WY8KECZITEWHQoEFCnZ49e4ZGjRppOBERRowYIcQnOTkZv/76K4oUKaLlRESoVKkS0tLSZPdatWoVihUrptMpc+nevTvUarXsbnKQl/M3BxyG+YCzZ8+iUqVKCAoKEq0i8cUXX4CI0K9fP6hUKtE6AIDq1auDiFCkSBG8fv1atA4AwM/PTzrI29raCjkBfci///4Lc3NzyeuLL74QrYTZs2drnRSXLFkizGf//v2ws7PTebL29/eX3efBgweoWLFijiFi586dsnsBQHp6OrZu3Srtfx8uJUuWxNu3b4W4yUFezt/cRMUIJyQkhFJSUkRrSDRv3pzev39PTZo0obVr1xrEHBe1atUiIqKtW7fSyJEjDcIpc+hpTEwM/fjjj4JtMvD19ZX+HxcXRxcvXhRok9EMNGbMGI3mRdFNVH/88QdNnz5da72IDsapqank7e1NPXr0oNjYWK3nK1asSI0bN5bdy8XFha5fv04bNmzQ2QRVv359+vrrr2X3IiIyMTGhevXqkUKh0HpOoVDQ5s2bycHBQYCZ4cEBhxGOhYUFubq60vr160mlUonWIWNjY+rduzelpKTQkCFDaNCgQcJPSpkBh4hozZo1NHHiROEhJ+vcGlu2bKFTp04JtPnfnCRZOXz4sCCbDPbv30/Hjx/XWCfyu7Rhwwby9vbW+VyNGjVktiEKDg4mY2Njatu2LVlYWGg9379/f50ncjmwsbGhwMBASkxM1Hpu4cKFwvor7dmzhxo0aEB3797Vem7SpEnUpk0bAVYGin6LSYYJN1FllISvX78uWkNi1KhRICK4urri0KFDwtuPr127plH2rVmzJh48eCDMx9/fX6sUPWPGDGE+AODk5KTVJ+H9+/fCfO7evauzn4So71JCQgLKlCmj5eTs7CzEZ/fu3TAyMtLZrFG0aFGh+9zly5dhbGys5fXo0SMhPiqVCiNGjJA8zM3NUbJkSRAROnToIMQpLS0N48aN03h/mjVrBk9PTxAR6tevj9TUVCFucsJ9cHKBAw4QERGBokWLok6dOli5cqXwTrWRkZEoVKiQRj+Fy5cvC/NRq9WoVKmSxsGkcOHCwtrd4+PjdZ6YFi9eLMQHgM7Ol1OnThXms2DBAp3v0f3794X4TJo0KdswITdKpRLbt2/Hxo0bdXq1bt1adqdMoqOj4ezsLLlk9i1p3LixEB9d4ebEiRNSvyURffPCwsLQrFkzjc9s3LhxSEtLw65du1CoUCFhYVBuOODkAgecDPbv3y/tLFZWVhg0aBACAgKEXcn98ssvWgfebt264e7du0J8pk+frvMENWbMGCFXSuXLl9fps3r1atldAGgE0szF1NQUISEhQnw+PAFkLosWLZLd5e7duzAxMQERQaFQaPgUKlRIdp+s9OzZU3IpVaqU9J0WgVqtRrdu3SSf7t27IzIyElZWVlixYoXsPtmFGyCj43G/fv1kdzpz5gyKFy8uOVlbW2P37t3S848fP8a6detk9xIFB5xc4IDzPwYPHqx1QqhRowb++OMPvHv3TlaX+Ph4ncMfjYyM4OXlhdDQUFl97t27p/OESURo2LAhnj9/LqtP1hNB1kWhUGDz5s2yugCAqampTp8vvvhC9pFeb968ybb5pXnz5rK6AMCxY8dw+PBhvHr1SgqCDg4OMDU1hUKhEHYRERwcLL0vVapUwatXr+Dk5IS//vpLiM/vv/8u+ZQtW1Y65kydOhVv3ryR1SWncJOJnKOTVCoV5s+fr/G9dnV11WoqV6vVwpv05YQDTi5wwPkf8fHxqFChgs4Tg4WFBQYMGIALFy7ItgMtX74821BhYWGBn376SdbglTnXi66lZs2asoYcXRUlNzc3fPfdd/Dy8kJkZKRsLmq1WsvF1tYW3377LVxcXGSfG2fTpk2wsLCAt7e35FOrVi106tQJxsbGiI6OltUnk0uXLkk+3t7eOH36NGxtbZGcnCzEJ2v1ZsuWLQAyKgRXr16V3eXatWtSSDYxMUFAQID0nNzzPX1MuJGTmJgYdO3aVWP/6t+/PxITE4U5GQoccHKBA44m/v7+2V79Zi59+/aV5aCcmpqabeAqVaoUvL29ZW0DX7hwoZaHq6urkBPm7t27tZo8atSoIWRenNTUVBBldGxs0KCB5JV51S33/DPHjh1DeHi4RvDy8PAAAFy5ckVYM+fMmTMln4MHDwIAQkJChHTGvnXrlkb1RqlUyu6QSWxsrMZ+LqIZMRNDCzdBQUEa742ZmRlWrlxZoKo0OcEBJxc44Ggzbdo0naGiQoUKOH78uKw717Zt23Q2w+zfv182h0xevHghOWT2qSAi/Prrr7K7PHz4EEQZo6c8PDwkl127dsnukpCQgA4dOiAhIUGjc+/27dtld8mKroAjkpYtW0rNrDExMUJdvvrqK63qjQjUajV69eoluXTq1EnY5JWGFm7Wrl0LCwsLycfZ2VlIdc2Q4YCTCxxwtElLS0P9+vV1Bou5c+fKegBSqVSoU6eOloupqSkOHDggm0cmX3zxBRwcHHD27FmppG5qair7MHulUokvv/wSSqUS169fl96X6tWry341np6eLlVpbt68KbmInu7fkAJOUlISzMzMQJTRZ0skWas3Li4uQqs3a9askVxKliyJqKgoIR6GFG7ev3+v1R+yY8eO+XpG4v8KB5xc4ICjmwcPHsDS0lK64sy6s3Xv3l3W9+vkyZNSH5Os98wREXJWrFghldB/++03yaVSpUqIj4+X1SUpKUn6f9ZOxyIrJyqVShrlUapUKaGldEMKOJnfYSLC5MmThbpkrd5s3bpVmEdwcLBUoTAyMsL58+eFeBhSuHny5IlGXz+FQoGZM2cazC1ZDA0OOLnAASd7VqxYASJC586d8ddff0lXoJlXfvfu3ZPNpW3btpg7d67WjQHlDjlv376VgoVKpULHjh0lF09PT9k8PiQoKMhgrsr79esnuYjq7wIYVsCZPHmy5HLy5ElhHoZSvUlISEDVqlUll9mzZwvxMKRwc+jQIY17cDk4OOD48eNCXD4XOODkAgec7FGr1ejUqZM0S+6VK1ekuTKIMia727t3rywu169flyavEh1yshIZGQlHR0fJZdu2bUI8AM0rcxFDxTPZuHGj5CHypo2GFHAaNmwofVezVt7kpkePHgZRvcmccZeI4O7uLiRoGUq4SU9Px5QpUzSq5A0bNsSLFy9kd/nc4ICTCxxwciYiIkJjyGZkZKTUWTJryV3uA5QhhZwTJ05IHjY2Nnjy5IkQj9u3b0selStXln14bSbh4eEafQdEYSgBJyYmRmrmbdGihTCPrFW+qlWrCqvebNiwQfIoXrw4IiIiZHcwlHATGRmJ1q1baxxPR44ciZSUFNldPkf4buLM/wsnJyeNO/g6OjqSn58fjRs3Tlp37tw5UiqVsnopFApatGgRTZgwgYiI0tPT6fr167I6ZNK+fXvJQ6lUUkhIiBCPmjVr0jfffENEGXdmfvbsmRCPEiVKSDcEffnyJanVaiEehsKDBw/IysqKiIjc3d2FeQQHB0s3sfTx8SFjY2NhHkQZ+/DWrVvJyclJdofk5GQKCgoiIiJzc3M6dOgQtW/fXnaPmJgYunbtGhERWVlZ0datW2nFihVkbm4uu0u+R4bAZXBwBee/s23bNpQvXx5hYWHCHDIrOVOmTBHaoTU1NRUDBw4Udq+jTO7evYvVq1cLv9HepUuX8OjRI+GdjN+8eYM3b94I37/T0tIQEBAg+4zXHxIREYHZs2cL7aMFADt27MDcuXOFOsTGxqJVq1ZCh4IDwK5du+Di4iLstiafM3k5fysAQHTIkpv4+HiytbWluLg4srGxEa3z2ZGWlkZmZmZCHTK/tgqFQqgHwzCfFwAM4rhhCMfRz5G8nL9NZHJi8hGGsFMawgGKYZjPD0M5dhjCcTS/w31wGIZhGIbJd8gScFauXEnly5cnCwsLqlevHl28eDHbbQcOHEgKhUJrcXV1lbbZsGGDzm1SUlLk+HMYhmEYhjFw9B5wdu7cSWPHjqWpU6dSUFAQNW/enDp16kQvX77Uuf3vv/9OERER0hIaGkr29vbSSJFMbGxsNLaLiIiQRgswDMMwDFOw0XvAWbJkCXl5edGQIUOoWrVqtGzZMipTpgytWrVK5/a2trbk5OQkLdevX6eYmBgaNGiQxnYKhUJjOxHDDhmGYRiGMUz0GnDS0tLoxo0bWnMNtG/fnvz9/T/qNdauXUtt27alsmXLaqxPTEyksmXLUunSpcnDw0Oa30AXqampFB8fr7EwDMMwDJN/0WvAefv2LalUKnJ0dNRY7+joSJGRkbn+fEREBB07doyGDBmisb5q1aq0YcMGOnToEG3fvp0sLCyoWbNm9O+//+p8nfnz55Otra20lClT5r//UQzDMAzDGDyydDL+cFjex85DsGHDBrKzs6Pu3btrrG/cuDH179+f3NzcqHnz5rRr1y6qUqUKLV++XOfrTJkyheLi4qQlNDT0P/8tDMMwDMMYPnqdB6do0aJkbGysVa2JiorSqup8CABat24dDRgwINf5AoyMjKhBgwbZVnDMzc15GmyGYRiGKUDotYJjZmZG9erVIz8/P431fn5+1LRp0xx/9vz58/T48WPy8vLK9fcAoFu3blGJEiX+X74MwzByYeiTyMfGxtL79+9Fa+TImzdvKCkpSbQGY6DovYlq/Pjx9M8//9C6devo/v37NG7cOHr58iUNHz6ciDKaj7777jutn1u7di01atSIatSoofXczJkz6cSJE/T06VO6desWeXl50a1bt6TXZBimYJOWliZaIUdevnypdeFnSDx+/Jh69epFlpaWolV0kpSURHPmzCEvLy/ppqaGiFqtpuvXrxf4m8+KQu8Bp3fv3rRs2TKaNWsW1a5dmy5cuEBHjx6VRkVFRERozYkTFxdHe/fuzbZ6ExsbS8OGDaNq1apR+/bt6dWrV3ThwgVq2LChvv8chmEMHAD0+++/i9bIFpVKRQMGDDDYiUnPnj1LDRs2pIoVKxrMbQ0ySU9Pp1WrVlHFihVp+vTpNHXqVINzBEDXr1+nCRMmUNmyZSk4OJiMjPimAULQ2y0/DRi+mzjD/HeCg4Px+vVr0RrZcuvWLZQtW1boXc1zYu7cuSAi+Pn5iVbRYs2aNTAxMQER4ciRI6J1JNRqNXbt2oVKlSqBiEBE6Nmzp2gtDUJCQjBt2jQNx0GDBonW0iAlJQUXLlzAhQsXRKv8Z/Jy/uabbTIMkyeSkpLI09OTjhw5YpBXpr6+vvTixQsKCQmhmjVritbR4OrVq/TLL78QERlU849SqaQJEyZIlS8rKytq06aNYKsMzpw5Q5MnT6Zr165J64yNjWnu3LkCrTJ48uQJ7dy5k3bs2EF37tzReM7NzY1WrFghyCyDlJQUunr1Kp07d47Onz9P/v7+5OrqSmfOnBHqJRcccBjGQImNjaXTp09Tz549RatoYG1tTcePH6fFixfTpEmTROto4evrK/1rSAEnMTGRvv32W1IqlUREBtN3JC4ujnr37k0nTpyQ1rVv3174rW9u3bpFkydP1vDKxMvLi1xcXARYEb169Yp27dpFO3bsoKtXr+rcxsbGhvbs2SN7iE1JSaErV65IgSYgIIBSU1Ol56tUqULHjh0jGxsbWb2EIUNFyeDgJirmc6Fu3bqYP3++QTW3vHjxAkQEExMT+Pv7i9bRICIiQmoeaNy4sWgdDQYNGiS5ERHu378vWgmPHz9GtWrVNLyICGvXrhXm9PTpU/Tr10/LKXOxtLTEq1evhLilpKRg4sSJMDc3z9aPiLB//37ZnAICAuDj44MWLVrk6FW6dGm8ePFCNi99kZfzt+HVlxmGkejUqRNNmTKFhgwZYjAjgzKv/pRKJfXp04diYmIEG/2Po0ePSv8PDAykqKgogTb/Y/fu3bR+/XqNdaIrOOfPn6eGDRvS/fv3NdYrFArq3LmzECelUkk7duzI8dY748aNo5IlS8po9T/Mzc1p0aJF9OjRo2xnxJ84caLW5LT6xNHRkQICAujChQsa1ZqsODg40MmTJ8nZ2Vk2L4NAhsBlcHAFh/kQlUqF+fPn49mzZ6JVNLh8+bJ0Bda6dWu8e/dOtBKUSqXGlWGPHj0MpsLUvXt3Dbf169eLVsKLFy9gZ2endUUdFRUlzOnvv/+WOhN/uDRq1EiYVyYqlQpdu3bVcrO3t0dsbKxQt5cvX6JFixY637sWLVogPT1ddqe0tDS0bdtWp1OhQoUQGBgou5O+4AoOw+QRIyMjql69Orm4uNC4cePo7du3opWIiKhRo0Zkb29PRBnDd5s0aUJPnjwR6mRsbEyFChWSHu/fv194Z0qijP4HJ0+e1FiX2R9HFJlDwmNjY7WeE1XBCQwMpF27dlGFChXI1NRU6/kuXboIsPofarWaRo8eTYcOHdJ6burUqWRrayvAKoO9e/eSm5sbXbhwgYiILCwspGHqjo6OtGPHDjIxkbdr67lz56hu3bp06tQpredMTU3pwIEDBXcKFRkCl8HBFRzDIDAwEIGBgQZz9a9Wq9GsWTMQEaytrTF79mwkJiaK1kLfvn01rsgcHBxw8eJFoU4lSpTQcDIzM8PNmzeFOh09elTr6rVw4cJISUkR5pQ5JFzXolKphHkBQHh4uM7KUnBwsDAnlUqFESNGSC7m5uaYMGECiAjOzs5ITk4W4pWYmIihQ4dqvE81atTAnTt3UKFCBRgbG+PcuXOyOoWGhqJPnz4aTqamplAoFCAiKBQK7Nq1S1YnOcjL+ZsDTgHDUMIEALx//x61atVC5cqVMXPmTDx58kS0Ei5duqRxwHBycsKqVauQlpYmzGnz5s1aJyEzMzNs3bpVmJOLi4uWU6VKlRAfHy/MKeuJMety/PhxIT6BgYHZNgOZm5sLccpErVZrNAHVqVNHChGijhG6ws2JEyeQmpoKOzs7bNy4UYjXzZs3tb7vY8aMwfv37wEAHh4eWLhwoWw+KSkpmD9/PgoVKqTh1KFDBzx48ADFixcHEWH16tWyOckJB5xcKMgB5/79++jWrRtmzJiBc+fOCb26BYAHDx5o7KhNmzbFypUr8fbtW2FO3bp10zohVa5cGbt27RJy8I+KipKuyj5cZsyYIcSpQYMGOn2+/fZbIT5qtRplypTR6TR69GjZfQDg3LlzuHDhAu7fvy+Nbsn8HO3s7IQ4ZbJ161aNYJqYmIiGDRti1KhRQnyyCzeZLF26FEqlUnan3377DaamppJX0aJF4evrq7HdmTNnZPvOHzt2DJUrV9b4fpcrVw4HDhyQHKpWrYq5c+fK4iMCDji5UJADDpBx4M084FpYWKB169aYOXMmLly4ICTwbNmyReukZGpqiq5du2L37t2yl6Xv3r0LIyMjnSfLBg0a4MyZM7L6AECjRo2ybero16+f7J+bu7t7tj4ihhjfunVLI0Bk/b/oWY2zfr+nTJmCnj17omTJksJ8IiMjYW9vLzmdP38eAODv768RKuQit3ADyF95joiIQPv27TW+1+3atUN4eLisHpk8efJEq9O1hYUFZs6cKVWSMtmxY4dBVeo/NRxwcqGgBxwA2L9/v86TuIWFBdq0aYNZs2bh4sWLSE1NlcVnyJAh2Z4wbWxs4OXlhbNnz8rWb2Hw4MHZ+hARunXrJutojpkzZ2o5uLi4YNGiRdi2bRtCQ0NlcwGAHj16aPmsWbMGR48exaZNm2TvXzJ37lz07t0bd+7ckXw6d+6M/fv3o3bt2rh9+7asPlnx8PCQnO7evYu0tDRMnDhRmE/Pnj2zrW7JfWL8mHAjN4cPH0axYsU0LrYWL14spM9UUlISfHx8tOa3+eqrrwxuxKdccMDJBQ44Gfzzzz85nsSJMibV+vnnn/V+4Hv//j1q1qyZo0uXLl3w6NEjvXpk8vLlS1hYWGg5VKlSBZs2bZJ9qOq1a9e0XMzMzIRNFvfdd9/Bzs4OCxculHyGDRsmxAUAYmJiAGScoDN9PDw8pHWihha/e/dOauKoUaOGtF7UFfauXbuk96d8+fJISEgQ4gEYXrhJTk7GmDFjtPb3GzduyO6iVquxd+9eODs7a13UiA6AouGAkwsccP7HggULsg0UhQoVwrJly2Rr+75//75Wx7nMZe/evbI4ZGXSpElaHqampjhw4IDsLiqVCsWLF0exYsUwffp0yadZs2ZCriynTJmCK1euID09HY6OjiDK6Fciuk+XroAjknXr1kk+s2fPFuoSFRWlUZkQ0dSaiaGFm5CQEK0LLC8vLyEB8P79+2jXrp2GS+HChfHrr7/KVlE3ZDjg5AIHnP+hVqsxfvx4naHCwcEB//zzj6wnUF0jhogyJvg6ePCgbB5AxtV35jBaJycn4SHH09MT69atQ3p6OurXry/5/Pnnn7K7ZA0yY8eOlVz27dsnu0tWDC3gdOjQQfKRq/qYHb1795Zchg8fLszDkMKNWq3GihUrNKq1dnZ2QoZXx8fHY8KECVoj7/r16yfs1hSGCAecXOCAo4lKpcJ3332XbSWnUaNGuHbtmmw+Wfu/ZO0MSUTw9vaWtUqwaNEiEGUMNc6cj0NUyLl9+7YUNoODg6UDYeHChYXeY+b69evS+9KjRw9hHoBhBZw3b97A2NgYRIS6desKddm3b5/0vjg7Owsbzm9I4ebNmzdaHXebN28u+76kVquxefNmrbml3NzccOHCBVldPgc44OQCBxxt0tLS0LlzZ2nn+vrrrzU6ISsUCgwbNkyW4dtJSUlwdXUFEeHOnTsYPny4xo5fr149PH78WO8eQEbfoNq1ayMtLQ1qtVp4yMnK1KlTJZcvv/xSWL8OtVqNqlWrSv2CoqOjhXhkuhhKwFm9erXksmjRImEeb9++lZoRiUhYoDCkcHPq1CmNQGFsbIxZs2bJPhQ9KCgIX3zxhcbxzc7ODitWrBByy4fPAQ44ucABRzdJSUnSTL5v377FrVu3tHY+e3t7rFq1Su8Hgnv37qF48eJSxWLXrl2wsbGRPKytrbF9+3a9OmQSFhYm/d+QQk5ycrLGBGQiJ/7LOmPvmjVrhHkYUsBp3bq15PL8+XNhHv3795c8hgwZIsTBUMJNamoqJk2apDGdQLly5XD58mVZPaKjozFy5Eiti8ihQ4cKvUfZ5wAHnFzggJM97969g5ubmxRg1Go1Nm3apHEFSERo1aqV3isGV69e1Xj85MkTjb4nRCTrDKKZ6Ao5ly5dkt0DyJh5OfNgXbRoUbx580aIx7NnzzTK/KIwlIATEREhnbwaN24szMPX11d6P0qXLi1sNNm0adOEhxu1Wo1WrVppHD/69u0r+3vy+PFjODg4CO0G8DnDAScXOODkjK6TZGxsLMaNGyf1Kfj1118FmGVcgWV2ira2tpatqepDsoYcDw8PoaOHRo0aBUtLSyxevFhoWbtFixZo1qwZVq9eLbS5rEePHujRo4fQ2VwjIyMxZcoUlC9fHsuWLRPm8ebNG+leZkePHhXm8ejRI5QqVUr4aKm1a9dK/dY2bdokbNbtzMp48eLFsW7dOuH3JfucyMv5WwEAVMCIj48nW1tbiouLIxsbG9E6nxV3796lJUuW0KpVq8jMzEyYx+HDhyktLY2++uorYQ4AaOPGjdS3b18yNzcX5pGQkEBRUVFUsWJFYQ5EGXfztrCwEOpgaAAgpVKp867dcnLz5k2qW7euUIfHjx/TixcvyN3dXZgDAJo5cyYNGDBA6P4SHBxM69evpxkzZpCdnZ0wj8+RvJy/OeBwwGEYhmGYz4K8nL+NZHJiGIZhGIaRDQ44DMMwDMPkOzjgMAzDMAyT7+CAwzAMwzBMvoMDDsMwDMMw+Q4OOAzDMAzD5Ds44DAMwzAMk+/ggMMwDMMwTL6DAw7DMAzDMPkODjgMwzCCuXnzpmiFPHH16lW6ePGiaA2GyRFZAs7KlSupfPnyZGFhQfXq1ctxxzh37hwpFAqt5cGDBxrb7d27l6pXr07m5uZUvXp12r9/v77/DIZhPhOePHkiWuGjCQgIoKlTp4rW+CgePnxIX3/9NfXo0YPq1asnWodhckTvAWfnzp00duxYmjp1KgUFBVHz5s2pU6dO9PLlyxx/7uHDhxQRESEtlStXlp4LCAig3r1704ABAyg4OJgGDBhAvXr1osDAQH3/OQzDGDhJSUk0ZcoU0RofRXBwMH355ZdUvnx50So5EhERQcOHDydXV1fau3cvzZgxg6ysrERr5UhMTAzt3LmTvv/+e3r06JFoHUYE+rytOQA0bNgQw4cP11hXtWpVTJ48Wef2Z8+eBREhJiYm29fs1asXOnbsqLGuQ4cO6NOnz0c55eV26wzDZJDTPmlIHDx4EJaWlnj//r1olRx58OABihcvDiLCypUrRevoJDY2FlOnToWVlRWICEQEFxcXpKeni1bTQq1WIygoCHPnzkWzZs1gZGQEIsKWLVtEqzGfkLycv/VawUlLS6MbN25Q+/btNda3b9+e/P39c/zZOnXqUIkSJcjd3Z3Onj2r8VxAQIDWa3bo0CHb10xNTaX4+HiNhWGYvLFo0SK6ffu2aI1c8fX1peTkZDp9+rRolWx58eIFtW3blqKiooiIqGbNmoKNNElNTaWlS5dSxYoVae7cufT+/Xvpufnz55OJiYlAu/8RFxdHe/bsIS8vLypVqhTVqVOHpk6dSpcvXya1Wk0zZsygfv36idZkBKHXb+nbt29JpVKRo6OjxnpHR0eKjIzU+TMlSpSgv/76i+rVq0epqam0efNmcnd3p3PnzlGLFi2IiCgyMjJPrzl//nyaOXPmJ/iLGKbgUrp0aWrXrh1dvHiRqlSpIlpHJ2q1mg4fPkxEGUHHw8NDsJE2kZGR1LZtWwoLC5PWubq6CjT6HyqVirZt20bTp0+nFy9eaD3fuHFj6t69u/xiWbhz5w4dPXqUjh49Sv7+/qRUKnVu179/f/Lx8ZHZTjfR0dEUHBxMwcHBVKJECerTp49opQKBLDFcoVBoPAagtS4TFxcXcnFxkR43adKEQkNDafHixVLAyetrTpkyhcaPHy89jo+PpzJlyuT572CYgoybmxtFRUWRu7s7Xbx4kcqVKydaSYsbN25IFzqHDx/O8bgggnfv3lG7du3o8ePH0rrSpUtTkSJFBFplcP78efrhhx9yrNItWLBA+Pv5+vVr2rBhg9bAk6w0b96c/vnnH9ldlUol/fvvv1KYCQ4Optu3b9OrV6+IiKhbt260c+dOWZ0KMnoNOEWLFiVjY2OtykpUVJRWBSYnGjduTFu2bJEeOzk55ek1zc3NydzcPA/mDCOG6OhosrOzI2NjY9EqWtSoUYOIiMLCwsjd3Z0uXLhApUqVEmylSWb1hogoPDycgoKCqG7dugKN/kdCQgJ16tSJQkJCNNYbSvNU48aNac6cObRr1y6N420mnTt3ppYtWwow06Rt27Z069Ytat26NQUEBGg9X7lyZdq/f78sx/zAwEAKDAyk27dvU3BwMIWEhFBKSorObfv06UObNm0iU1NTvXsxGei1D46ZmRnVq1eP/Pz8NNb7+flR06ZNP/p1goKCqESJEtLjJk2aaL3myZMn8/SaDGOIqNVqatWqFR07dowAiNbRwNbWVqraPH36lNq2bUtv3rwRK/UBvr6+OT4WRXJyMnXt2pWuXr2q9ZyhBBxzc3Pq3LkzWVtbaz2nUCho/vz5Aqy0uXfvHrVp00ZnuLG3t6cjR46Qg4ODLC6Wlpa0atUqWrt2LV2/fj3bcDN48GDasmWLkHCjVCopNDSU/P39adeuXbRkyRLavHmzwR1f9IJ++zsDO3bsgKmpKdauXYt79+5h7NixKFSoEJ4/fw4AmDx5MgYMGCBtv3TpUuzfvx+PHj1CSEgIJk+eDCLC3r17pW0uX74MY2NjLFiwAPfv38eCBQtgYmKCK1eufJQTj6JiDJnZs2eDiNCqVSsEBgaK1tGgW7du0mgaIkLt2rXx7t070VoAgNDQUA03IkK9evVEayE1NRWdO3fWcstcNm/eLFoRAKBSqTBixAjJy9zcHAqFAkQET09P0XpITU3FzJkzYWZmJjmamJhIo6VMTU1x/vx52b3i4uJQrVq1bD/f0aNHQ6VS6e33v3z5EpcuXcKOHTuwePFieHt7o2fPnmjUqBFKliwpvT+ZS8+ePZGYmKg3H32Tl/O33gMOAKxYsQJly5aFmZkZ6tatq/El9PT0RMuWLaXHCxcuRMWKFWFhYYEiRYrgiy++wJEjR7Rec/fu3XBxcYGpqSmqVq2qEYBygwMOk0lycrJoBS0SExPh6OiocUB68OCBaC0AwPTp07UO4I0aNUJ8fLxoNaxatUrnCebVq1dCvU6fPo2xY8di7NixKFasmJZfUFCQUD9Ad7g5ceIEWrRoAXNzc7x48UKoX0BAAFxdXTXet4YNG+L27duoVKmSkKCoUqmwfft2uLi4ZBtuJk2aBLVarVePLVu2aIS+nJbp06frNWzJgcEFHEODAw6TyfHjx9GqVSssXLgQ9+7d0/vB6GNZuXKlxoHJ2NgY33//PcLDw4V67d69W+eBs2XLlkhKShLq9uWXX+p0W7NmjVCvTO7cuSM5ZZ6QjI2NkZKSItQru3ADAMuXL8f48eOFuSUkJMDb21uqJBERrKyssHTpUiiVSgBAq1at4OPjI5uTSqXCnj17tALXh8usWbNkO55cunQJtra22bpYWFhgx44dsrjoGw44ucABRyyG0qSRyZIlS6QDQYUKFeDt7Q0/Pz+kpqYKc0pLS5OuTLMuVlZWmDp1KmJjY4V4PXr0KNuDaMeOHYWdrBMTE2Fubq7Tq0uXLkKcPuSbb76RnNavX4927dqhWrVqQp1yCjcAEBkZibdv3wpxO378OMqWLavxWbZr1w5Pnz7V2O7gwYOyBAm1Wo1Dhw6hdu3aWt+xr776CsuXL5ceL168WO8+QMZxYteuXWjevHm2+2XJkiVx7do1WXzkgANOLnDAEcv+/ftRpkwZtGnTBt7e3vj7778REBAgrJlDrVZjyJAhWgcGa2trfP3119i4cSOioqJk99q1a1e2By0HBwcsWbJE9kChVCo1ZrXNXKpWrQpXV1f88ssvsvpkcvDgQRARvvjiC8nJ2dkZpUuXNohZjW/fvi15Va5cGenp6YiMjMTYsWOFOeUWbkTx5s0bDBgwQOP7ZW9vj40bNwqpsKrVahw/fhwNGzbUGZ5v3rwJADh//jyI5JmV+vXr15gzZw5KlSqVYxWpfv36CAsL07uPnHDAyYWCGHAePnyIQYMGwdvbG/PmzcPatWtx5MgRXL9+HaGhobJXK06dOoVChQpp7ZDlypWDh4cHJk+ejC1btiA4OFiWk3hqaipatWqV7YFCoVCgadOmmDdvHh49eqR3HyDjwNqgQYNsnVxdXbFhwwZZXLKi60B/4MAB2T2ysm7dOpw+fRoqlUpy8vDwQEpKClauXInr168L9fv6668lr6x9RdLS0oT4GGK4UavV2LZtm1Y/pd69eyMyMlKI05kzZ9CsWTOt73uHDh20BgD4+/vrfX+8evUqBgwYoLPPzRdffAE3NzeN9010s7E+4ICTCwUx4ADAjRs34OzsnO0J097eHtWqVUOrVq3Qu3dvjB07Vq8HFn9/f9jZ2eV4BUKUMVJi1apVevPI5O3btzqbhTIXIyMjDB8+HG/evNG7SyanT5/W6TJ//nzZHD5k6NChUCgUmD9/vuTj5uZmEJ0X1Wq1RsAxBLJWb6pUqSL8Pk6GGG5evHih1YeqVKlSOHTokBCfS5cuoXXr1lr7XevWrXHx4kWdP6Ov6lJKSgo2b96MRo0aaflYWFjAy8tLqiJ17doVRPL2/5EbDji5UFADDgBERUWhTZs2uYYKU1NTbNu2Te8+wcHBGiOGPlxsbW3zNELu/8v9+/ez7awnqvmlQ4cOOkOfqKrJ8uXLpfeiU6dOktOePXuE+GTFEANOz549JSfRN340tHCjUqmwfPlyFC5cWOP7PXLkSCHH58DAQJ37W7NmzXDmzBlZXcLCwjB9+nTphqxZl7Jly2LhwoVa/aM6depkEPuhPuGAkwsFOeAAQHp6OsaPH59jwBk9erRszVaPHj3KtrJUtGhR/Prrr7LO23Dy5EkYGxvr9Pnmm2/w+vVr2VwAICgoSKogDR06VHjICQsLk0awXL16VfJxdXUVXsUxtIATHBws+bi4uEjvmwgMLdzcu3cPTZs21di/XFxcsq2Q6JObN2/Cw8NDa39v2LAhTpw4IVs1RK1W4+LFi+jVqxdMTEy0fNzd3bF///5sv0eiR1nKAQecXCjoASeTrVu3wtLSMtuQU7x4cfz00094/Pix3l1evnyZ43wSxYoVkzXorFixQuN3Z3VxcHDAtm3bZC0B9+vXD61bt4ZarcaECROEh5ysZJbFiQjbt28X6mJoAeerr76SfLZu3SrMw5DCTXYT9k2bNk32eanu3Lmj8RllLnXq1IGvr69s+/j79++xdu1anSO0ChUqhBEjRuDu3buyuBg6HHBygQPO/wgKCtIaiqlradeuHfbs2aPXTpGvX7/W2MG/+OILrc50xYoVw6JFi2QJOqNGjZKapvz8/FCuXDkNl27dusl2xfT06VOsXbsWAAwu5Ny8edNgqhSGFHBu3bplEO+LIYWbK1euoEaNGhr7UYMGDRAcHCyrx4MHD9CnTx+N+XWICDVq1MDevXtlCzbPnz/HpEmTYG9vr3XMrVSpEpYtWyZsSghDhQNOLnDA0eTNmzdwd3eXdqyNGzdi5MiRsLGx0drpHB0dMWXKFK25KD4VMTEx0qiFAwcOIDQ0FKNHjxYSdNLT09G+fXspWCQkJGD06NEaHnZ2dli/fr1s83Bk/b8hhZysV8Eibz1gSAHHEKo3hhJuspuwb8mSJbIGv8ePH+O7777Tun2Bi4sLtm/fLksTq1qtxqlTp9CtWzctDyJCp06dcPToUeHNvYYKB5xc4ICjTXp6OiZOnAgiwsmTJwFkTJ72zz//6Byq3KtXL725JCYmon379hon7LCwMIwZM0ZrMrfdu3frzQPICFz379/XWHf+/HmN0VbW1tZChrF+GHLc3NyEVQlu374tnbzatm0rxAEwnIDz+vVrab6gqlWrCvtcQkJCYGFhIbxys3PnTq2KsL4uknLi22+/1fCoWLEiNm3aJOvItsTERK2LRxsbG4wdOxb//vuvbB6fKxxwcoEDTvZs375dZyXg5s2bGD58OKytrUFEOH36tF49UlJS8PLlS631r169wg8//ABzc3OhnVqTkpIwfvx4KBQKobcCyAw51apVQ0REhDAPABg7dixWr14tdAbozEnZjh8/jhs3bgjzAICIiAiMGzdO7yE8N06ePIkiRYoI7VCsVqvRqVMnFClSBBs2bBA2hPnBgwcwMjJC2bJl8c8//wibh8jb2xtEhOrVq2PVqlVISEgQ4vE5kpfztwIoCPdM1yQ+Pp5sbW0pLi6ObGxsROsYHABIoVDofC4xMZEOHDhA/fr1y3YbOQgPD6eIiAiqV6+eMAciotu3b1PNmjWFvhcAKCEhgb/LTLbExcWRra2tUIfw8HAyNjYmR0dHoR6nT5+m5s2bk5mZmTCHFy9e0JMnT6h169ZCjx2fI3k5f3PA4ZMCwzAMw3wW5OX8bSSTE8MwDMMwjGxwwGEYhmEYJt/BAYdhGIZhmHwHBxyGYRiGYfIdHHAYhmEYhsl3cMBhGIZhGCbfwQGHYRiGYZh8BwcchmEYhmHyHRxwGIZhPiOSk5OpAM7PyjB5hgMOwzD5jvwYAJRKJf399980bdo0nt6fYT4CDjgMw+Q7du/eLVrhkwGA9u/fTzVq1KCRI0fSiBEjRCsxzGcBBxyGYfIVz58/p7lz54rW+CRcuHCBmjZtSl999RU9fPiQhg0bRpUqVRKtxTCfBRxwGIbJV/j6+tLt27fpxYsXolX+MyEhIdSlSxdq2bIlXblyhYiIChUqRNOnTxdsxjCfDxxwGIbJV/j6+hIR0eHDhwWb5J2XL1/SwIEDqVatWlr+P/74Izk5OQky++8kJydTWFiYaA2mAGIiWoBhGOZTkZCQQOfOnSOijIAzatQosUIfSXR0NM2fP5/+/PNPSk1N1Xq+WLFi9OOPPwowyxtRUVF069YtaQkODialUkknT54UrcYUQDjgMAyTbzh58iSlp6cTEdGZM2coMTGRChcuLNgqZ2JiYsjT05OOHDmS7TbTpk0jGxsbGa1yRqVS0ePHjzWCzK1btygiIkJju6pVq9KZM2eoVKlSgkyZggwHHIZhtDh06BA1a9aMHBwcRKvkiczmKSKitLQ08vPzox49egg0yp0iRYrQ4cOHKSwsjNq2bUsPHz7UeL58+fL0/fffC7LTRK1W08SJE2n16tX0/v37HLetWbMm+fn5kaOjo0x2DKMJ98FhGEYLR0dHqlSpEi1YsCDXE5mhoFKptKogWQOPIaNWq2nevHla4YaIaM6cOWRubi7AShsjIyNasGABeXt75zgXT926dens2bMcbhihyBJwVq5cSeXLlycLCwuqV68eXbx4Mdtt9+3bR+3ataNixYqRjY0NNWnShE6cOKGxzYYNG0ihUGgtKSkp+v5TGKZA0KhRI3J3d6cpU6ZQ5cqV6Z9//iGlUilaK0cCAwPp7du3GuuOHDlCarVakNHHoVarafTo0bRq1SoiIjI3N6dWrVoREVHt2rWpT58+Au20SU9PJ3t7+2yb/po0aUKnT582mOofAEpKSjL47wHz6dF7E9XOnTtp7NixtHLlSmrWrBmtWbOGOnXqRPfu3SNnZ2et7S9cuEDt2rWjefPmkZ2dHa1fv566dOlCgYGBVKdOHWk7GxsbrasdCwsLff85DFNgmDt3Lh04cIDCw8Np6NCh9Ntvv9G8efOoe/fuBjmTrq5RU1FRUXTt2jVq1KiRAKPc0RVuDh06JF3cLVy4kIyMDKPQnpqaSn///TfNnTuXIiMjdW7TokULOnz4MFlbW+vN4/79+xQVFUUxMTEftSQnJ9OCBQt4gsSCCPRMw4YNMXz4cI11VatWxeTJkz/6NapXr46ZM2dKj9evXw9bW9v/7BQXFwciQlxc3H9+DYYpCHz//fcgIo2lcePGuHDhgmg1LWrUqKHlSkSYOnWqaDWdqFQqjBgxQvI0NzfHiRMnAABqtRqDBg2CWq0WbAmkpaXh77//RpkyZTTeV3Nzc9SqVUt63K5dOyQlJend5+jRo7C0tNT5WX+4lCtXDteuXdO7EyMfeTl/6/XSIC0tjW7cuEHt27fXWN++fXvy9/f/qNdQq9WUkJBA9vb2GusTExOpbNmyVLp0afLw8KCgoKBsXyM1NZXi4+M1FoYxBPz9/Wn37t304MEDg2wC+uWXX8jKykpj3ZUrV6hFixbUpUsXCgkJEWSmyfPnz7N1McR+ONlVbjKPlQqFgtasWSO0UqZSqWjLli1UrVo1Gjp0KIWGhhIRkYmJCQ0fPpweP35MXl5eRETk4eFBhw4d0vqu6INOnTqRn58fFSpUKMftunXrRjdv3qT69evr3YkxUPSZtF69egUiwuXLlzXWz507F1WqVPmo11i0aBHs7e3x+vVraV1AQAA2b96MW7du4cKFC+jZsycsLS3x6NEjna/xyy+/6Ez3XMFhRJOamorevXuDiGBmZgY3Nzf069cP8+fPh6+vL549ewaVSiXUcerUqdleISsUCnh6eiI0NFSo4x9//IEqVapg48aNklvz5s0xbdo0WFtb4/nz50L9spJT5cYQUKlU2L17N6pVq6bxWRsZGWHgwIF4+vSptO2KFSvQs2dPpKamyuL25s0b/P7776hbt26230kTExP89ttveqt+LV26FBYWFihcuDBsbW3h4OAAR0dHlCpVCmXLlkXFihVRpUoVVK9eHbVq1ULdunUxb948pKWl6cWnoJGXCo4sAcff319j/Zw5c+Di4pLrz2/btg1WVlbw8/PLcTuVSgU3NzeMGTNG5/MpKSmIi4uTltDQUA44BRSlUolnz54hMjIScXFxBnHQUSqVGDZsWLYH7MKFC6NRo0bw8vLC0qVL4efnJ2voiY2NhYODg5aXpaUlvvvuO/j6+iIlJUU2H13cvn0b6enpUKvVkp+HhwcAIDo6Gi9evBDql4khhxu1Wg1fX1/Url1b67Pu06cPHjx4oPUzDx8+RHp6ul690tLScODAAfTo0QOmpqY5NkmVLl1a64JaH0yYMOGjmsicnJywZ8+eTxq24uLi0LdvX3z77bcYNWoUpk+fjiVLlmDDhg04ePAgLl68iJCQEISHhyM5OfmT/V5DwWACTmpqKoyNjbFv3z6N9T/88ANatGiR48/u2LEDlpaWOHz48Ef9riFDhqBjx44ftS33wTEslEol4uPjERkZiadPnyIkJARXr17FuXPn9PIZ7dixA7a2ttJByNjYGIULF0axYsXg7OwMFxcX1K5dG02aNEGbNm3QuXNnrFy58pN7ZEWtVmPixIm5HjBtbW219ic5WLJkiZaLqakpDhw4ILtLTugKOIaCoYYbtVoNPz8/NGrUSOsz7t69O4KDg4V4BQUFYezYsShWrJiWl5GRETp27AhHR0dpXYcOHfDmzRu9OiUlJeHo0aMYPXo0jIyMctxXhw4dinfv3unF4/jx47n+/qwXIo0aNcL169f14iI3BhNwgIxOxiNGjNBYV61atRw7GW/btg0WFhbYv3//R/0OtVqN+vXrY9CgQR+1fUEMOEqlEq9fv8bt27dx6tQpbNu2DcuWLcPPP/+MIUOGoEuXLmjUqBHKly+PUaNGffLy7tWrV9G2bVu4ubmhcuXKKFWqFIoUKQJzc/Nsd8wBAwborcz84sULtGjR4qMOEG3atJGl86Rarca8efNyrOSEhITo3UMXKSkpKFu2rNQEYKghx1ADjqGGm4sXL6Jly5Za37WOHTvi6tWrsvu8fv0aS5YsgZubm859oFq1ali4cCFevXoFAChZsiSMjIwwZ84cvVQ11Wo1Hjx4gGXLlqFDhw6wsLDI9XhRuXJlnDt37pO7ZKJSqXDnzh20adMmVxcrKyvMnDkTiYmJevORG4MKODt27ICpqSnWrl2Le/fuYezYsShUqJDUJj558mQMGDBA2n7btm0wMTHBihUrEBERIS2xsbHSNjNmzMDx48fx5MkTBAUFYdCgQTAxMUFgYOBHORWUgKNWq7F161aULVsWCoXio07mdevWxfv37/Xi8/LlS3z99dcf5dGqVSu9t+srlUrMmzdP44T94WJmZoZ9+/bJ2pS1YsWKbH0cHR3x22+/yRK4PmTTpk0gIkyYMAE//vijQYYcQww4hhhurl69ig4dOmh9v1q2bImLFy/K6pKamoq9e/eia9euOvfFIkWKYOTIkbh69arGBU96ejpKlSqFM2fOfFKfxMREHDp0CCNHjkT58uWz3Rc/DDsmJib4+eefP3mzUFxcHPz8/DBz5kx06NABNjY2H3UM9fT0RFhY2Cd1MQQMKuAAGQfssmXLwszMDHXr1sX58+el5zw9PdGyZUvpsa6ricwPK5OxY8fC2dkZZmZmKFasGNq3b6/VzycnCkrAySQsLAxeXl4fVdLs1asXtm/fjsePH+utenL8+HFUrlw5Rw9bW1t07doVS5cuRXBwsF77nFy9ejVXHwcHBwwdOhSnTp3Se58DANi8eTOMjY2z9SlevDgWL14s65WZUqlErVq1EBgYCLVabZAhx9ACjqGFm+DgYHTr1k3r+9SoUSOcOnVKtmHparUa169fx5gxY3T27zI2Nkbnzp2xe/fubPt3JScnIyIi4pO43L17F4sXL0bbtm1hZmaW7X7n5uaGyZMn4/z58zh16pS0vmHDhp+kKU+tVuPJkyfYvHkzRowYATc3t49uispcWrRokW+ao3RhcAHH0ChoASeTu3fvomvXrh+9o9jb26N9+/aYNm0aDh48iPDw8E/mkpKSgjlz5nxUyZeIULRoUXzzzTdYtWoVHjx48MkPxAkJCRgyZMhHuRQvXhwjRozAuXPnoFQqP6lHVg4cOCAdbL28vDBy5Eitg2+xYsXw66+/yhZ0rl27Jr33hhhyDCngGFK4uX//vjRaL+tSu3ZtHD58WLZgExERgcWLF2c7Z5Grqyt+/fXXT3qs0UV8fDz279+PYcOGwdnZOdt93c7ODt988w3WrVsnNYtlsmzZMhQqVAi///77fz4OJCcn4/Lly/j111/Ro0cPjT5FuhaFQoEaNWpg2LBh2LBhA4oXLy49V6FCBezdu9cg5k7SJxxwcqGgBpxMLl68iCZNmuTpqiBzKVWqFLp3745Dhw59Epdnz55phS4nJydUrVo1R4+SJUuif//+ePny5SfxyGTv3r2wt7eXTthnz57FqFGjNA4kWZcSJUrgp59++qQOWTl16hQKFSoEHx8fAEBoaChGjRqlM+hs2rRJbx7ZoSvkfKrvxn/1MYSAo1arDSLcqFQqDBo0SKsKUL16dezZs0e20XjPnz9H586ddVYl7e3tMXr0aFy/fl3vJ2dfX1+0bt06x9FY9erVw9SpU3Hp0qUcq7Vbt279z9MP+Pj4oEmTJjlWi4gy+t21bdsWPj4+OH78OGJiYqTXyBylbGtri8WLFwsfySgXHHByoaAHHCDjALxv3z64uLhIO1Pr1q0RGBiI5cuX47vvvkO1atWy7bvzxx9/fFIfX19fqb07cwqBV69eYcuWLRg8eLDUwTXrYmRkpNE361MRFhYGd3d3EJE0vFipVOL06dMYNmyYVkn9q6+++uQOWbly5QqWLVumsS40NBSjR4/WOEDu3LlTrx7ZkTXkFClSBDdu3BDikeni7OwMZ2fnjx50oC+WLl0qvHIDAH369JG+IxUrVsSWLVv0WnnURUJCAgoVKiR5GBsbo0uXLti7d6+sJ+bMfmQfBqy+ffti48aNiIyMlMWjdevWOo+r5cuXR79+/bBixQoEBQXlGLB27dqFUaNGISoqShZnQ4EDTi5wwPkf6enpWLNmDZycnGBlZaXVsTcuLg5nzpzBwoUL8fXXX0tB48qVK5/c5f379/jll19gYWGhc3jl06dP8c8//+Dbb7+Fk5MTGjZs+MkdMlGpVFi8eLHOOTXS0tJw4sQJDB48GHZ2drIEi+yutMPCwjBmzBjUq1dP6ISAarUaPj4+QsONIfL7778L71D88OFDVKhQAf/884/QeZ8GDhyIWrVqYcmSJbIFiQ95/fo1jI2N0bBhQ/j4+CAgIED2sAcA06ZNg5mZGZo0aYIff/wRe/fuzXOznCHM4SWCvJy/FQBABYz4+HiytbWluLg4srGxEa1jECQlJdGyZcvoyy+/1LipqS6ioqKoSJEiZGpqqheXx48fk4WFBZUuXTrbbQBQTEyM1i08PjUAcpwuPy0tjYiIzMzM9OqRGyqVioyNjYU6MIaLWq0WftPO5ORksrS0FOpARBQbG0t2dnbCHSwsLPgG0f+BvJy/OeBwwGEYhmGYz4K8nL/FRnqGYRiGYRg9wAGHYRiGYZh8BwcchmEYhmHyHRxwGIZhGIbJd3DAYRiGYRgm38EBh2EYhmGYfAcHHIZhGIZh8h0ccBiGYRiGyXdwwGEYhmEYJt/BAYdhGIZhmHwHBxyGYRiGYfIdHHAYhmEYhsl3cMBhGIZhGCbfwQGHYRiGYZh8BwcchmEYhmHyHRxwGIZhGIbJd3DAYRiGYRgm38EBh2EYhmGYfAcHHIZhGIZh8h0ccBiGYRiGyXdwwGEYhmEYJt/BAYdhGIZhmHwHBxyGYRiGYfIdHHAYhmEYhsl3cMBhGIZhGCbfwQGHYRiGYZh8BwecAk5iYiLt27ePXrx4IdTj8ePHtGPHDqEO6enpdPr0abp27ZpQj6ioKNq0aROlpKQIcwBAN27coOPHjwtzKGio1WrauHEjhYWFCfW4e/cuHT16VOj3j4ho//79dPfuXQIgzCE6Opq2b99OMTExwhyIiM6dO0f+/v6kUqmEenxuyBJwVq5cSeXLlycLCwuqV68eXbx4Mcftz58/T/Xq1SMLCwuqUKECrV69WmubvXv3UvXq1cnc3JyqV69O+/fv15d+vuPFixe0YsUK6tixIzk4ONC0adOodOnSsjoolUq6cOECTZo0iapVq0aVK1emiIgIWR2IMg5gW7Zsod69e1PRokWpS5cuVLZsWVkdANDt27dp7ty51LhxY3JycqITJ06QhYWFrB7v378nX19fGjZsGJUuXZrq169PlpaWsjoUZIyMjOj27dtUpkwZqlOnDvn4+NC1a9dIrVbL6lGuXDkaOHAgOTg4UPfu3Wnt2rUUGRkpqwMRUXJyMtWoUYMqVqxI3t7edOrUKUpLS5PVwd7enlavXk3FihWj1q1b05IlS+jRo0eyOhARFS9enL744gtycnIiT09P2rNnD8XHx8vu8dkBPbNjxw6Ympri77//xr179+Dt7Y1ChQrhxYsXOrd/+vQprKys4O3tjXv37uHvv/+Gqakp9uzZI23j7+8PY2NjzJs3D/fv38e8efNgYmKCK1eufJRTXFwciAhxcXGf5G80dJRKJQICAvDzzz+jZs2aICKNZfv27bJ4xMbGYseOHejXrx/s7e01HBwdHZGUlKR3B7VajXv37mHhwoX44osvYGRkpOExYcIEvTsAQEpKCo4dO4ZRo0bB2dlZw0GhUOD+/fuyeISFhWHNmjXw8PCAhYWFhkfr1q1lcWD+R0REBCwtLTU+BycnJ3h5eeHAgQNITEyUxePXX3/VOk40bNgQs2bNQlBQENRqtd4dlEolXFxcNBysra3x9ddfY+PGjXjz5o3eHQDgzJkzWu9FlSpV8OOPP+LcuXNIT0+XxaNPnz4aDqampmjXrh3++OMPPH36VBYHQyAv528FoN/6X6NGjahu3bq0atUqaV21atWoe/fuNH/+fK3tf/rpJzp06BDdv39fWjd8+HAKDg6mgIAAIiLq3bs3xcfH07Fjx6RtOnbsSEWKFKHt27drvWZqaiqlpqZKj+Pj46lMmTIUFxdHNjY2n+TvNDQSExPp5MmT5OvrS0eOHKE3b95ku22ZMmXIyChvxbw//viDunbtmut2jx8/Jl9fX/L19aWLFy+SUqnUuZ2lpSUVL148Tw6FCxemkJCQXLdLT0+nCxcu0OHDh8nX15eePHmS7bbFixfPc9Vi6NChNHXq1Fy3i4qKoiNHjpCvry+dPHmSkpKSdG5nbGz8nypqZ86coQoVKuS4jVqtpqCgIOkzuXnzZrbb2tnZka2tbZ4cGjduLLypcdOmTbRnzx769ddfycXFRZhHQkIC1axZM88/FxERkW2lwtzcnNzd3alLly7k4eHxUd+Tv/76i+bNm5cnh7S0tBwrqmXKlCEPDw/y8PCgNm3afFS1sXXr1vTs2bM8eURHR1NiYqLO5xQKBTVp0oS6dOlCXbp0oerVq5NCocjx9QICAqhv3755cgBAL1++zPZ5Ozs76tSpE3Xp0kU6D+XGmDFjyNfXN08eiYmJFB0dne3zrq6u0nvRqFEjMjY2ztPrfy7Ex8eTra3tx52/9Zm0UlNTYWxsjH379mms/+GHH9CiRQudP9O8eXP88MMPGuv27dsHExMTpKWlAQDKlCmDJUuWaGyzZMkSODs763zNX375RSuBUz6t4KhUKqxduxZFixbV+Td/qmXbtm05ekRGRsLT01OvDtbW1rm+HydPntS6CvzUy48//pijQ1JSEqZPnw5zc3O9ejx8+DBHj5CQELRq1UqvDq1atcr1M9E3FStWBBFh/PjxQj0yrzT1tRgbG8Pb2xuxsbE5euiqxnzKxdnZGXv37s21qlO5cmW9evTo0QPPnz/P0UFXNeZTLjY2Nli6dKl0rsqOD6sxn3qpX78+AgMDc3T4XMlLBceE9Mjbt29JpVKRo6OjxnpHR8ds23QjIyN1bq9UKunt27dUokSJbLfJ7jWnTJlC48ePlx5nVnDyI0ZGRjR48GDq378/nT9/XrpSf/78ebY/U6VKFTIxydtXIbfk7OjoSBs2bKD58+dLVQs/Pz9KTk7Wub21tXWeP5NChQrluk27du3o3r17dP36damCc+vWrWy3d3Z2psKFC+fJ48Pv4odYWVnRrFmzaMKECRpVteyuxkxMTKhKlSp5ciAiMjMzy/F5V1dXOnv2LD169Ej6Xly6dCnbjovFihWjYsWK5cmhXLlyedpeH8yfP5/2799Po0aNEuphZGRE1atXz/PPPX36NNsOvra2ttSxY0epWuDg4JDr6zk4OOTZIyUlhZ4+fZrt89WqVZOqSE2aNPmo40elSpXI1NQ0Tx7h4eEUGxur8zkzMzNq3bq15PExfeesrKzy/F4A0GhR+JCSJUuSh4cHdenShdq0aUNWVla5vmbp0qXz7BETE5NtVU2hUFCjRo2kCk6NGjVyrWYVCPSZtF69egUigr+/v8b6OXPmwMXFRefPVK5cGfPmzdNYd+nSJRARIiIiAACmpqZaFYQtW7bA3Nz8o7wKWh8ctVqNkJAQzJ8/H02bNoVCodBI+5s2bZLF4/379zhy5AiGDx+O0qVLazg4ODggISFBFo+XL19i5cqV6NSpk1ZV5cPqob5QKpW4dOkSJk+eDFdXV60rsDt37sjiER0dja1bt6Jv376ws7PTcGjWrJksfS2Y/xEWFgYzMzONz6FixYoYO3YsTp8+nWtl4FMxb948DQcTExO4u7tj6dKlePz4sSwO6enpUjUucylevDgGDRqEffv2yXa8OHHihNb+Wa9ePcyYMQM3btyQbR/56quvNBwKFy6Mr776CuvXr8fr169lcTAE8nL+LhBNVB9S0ALOh0RFRWHjxo34+uuvYW1tjUqVKsnWUS4TtVqNmzdvYtasWWjQoAGICAsWLJDVAQASExNx4MABeHl5wdHREebm5nj16pXsHk+ePMHvv/+Otm3bwtTUFF9//bXsDmlpaTh79izGjx8vNSf4+fnJ7lGQGT16NIyMjNC8eXMsWrQI9+/flz1kxsXFwd7eHvb29ujfvz927tyZazOYPli/fj2ICLVq1cLUqVNx5coVqFQqWR3UajUaN24MS0tLdOnSBX/99ZeQ48OtW7ek5sBRo0bh+PHjSElJkd3DEDC4Tsb16tWjlStXSuuqV69O3bp1y7aTsa+vL927d09aN2LECLp165ZGJ+OEhAQ6evSotE2nTp3Izs5OZyfjD8lTJ6V8TlpaGp0/f56qVq0qtNkuIiKCrl69St26dRPmoFar6fr162Rqakp16tQR5hEfH0+nTp2iL7/8Uvah4ll59OgRhYWFUZs2bYQ5FCTUajXt27ePWrdu/VFNT/riwYMH9ObNm49uetIXR48eJVdXV9mnbchKdHQ0BQQEfHTTk77w9/cna2trbnoiA+pkDPxvmPjatWtx7949jB07FoUKFZI6g02ePBkDBgyQts8cJj5u3Djcu3cPa9eu1RomfvnyZRgbG2PBggW4f/8+FixYwMPEGYZhGCafYzCdjIkyqi3R0dE0a9YsioiIoBo1atDRo0elVB4REaExBK98+fJ09OhRGjduHK1YsYJKlixJf/zxB/Xs2VPapmnTprRjxw6aNm0aTZ8+nSpWrEg7d+6kRo0a6fvPYRiGYRjmM0DvTVSGCDdRMQzDMMznR17O33wvKoZhGIZh8h0ccBiGYRiGyXdwwGEYhmEYJt/BAYdhGIZhmHwHBxyGYRiGYfIdHHAYhmEYhsl3cMBhGIZhGCbfwQGHYRiGYZh8BwcchmEYhmHyHRxwGIZhGIbJd3DAYRiGYRgm38EBh2EYhmGYfAcHHIZhGIZh8h0ccBiGYRiGyXdwwGEYhmEYJt/BAYdhGIZhmHwHBxyGYRiGYfIdHHAYhmEYhsl3cMBhGIZhGCbfwQGHYRiGYZh8BwcchmEYhmHyHRxwGIZhGIbJd3DAYRiGYRgm38EBh2EYhmGYfAcHHCZPAKAXL15Qenq6UA+1Wk2vX78W6kBElJycLPy9ICKDcGAMl7S0NNEKFBMTQ2q1Osdtcnv+UxAaGprrNpcvX6bY2Fi9OURFRdG7d+9y3W7lypW0efNmWd6X/AgHnAKGWq3O08EuLS2Nrl69SkuXLqVvvvmGSpcuTeXKlaObN2/q0VI3b9++pW3bttGAAQPIycmJunXrJrsDUUbIu3z5Mg0bNoycnJzo4MGDQjyIMg7W33//PdWrV49UKpUwD7VaTRMmTCB/f39hDobIggULhH4/iIju3LlDZcqUoUWLFlFiYqLObZRKpd49hg8fTmXLlqXx48fTlStXCIDWNr/++isdO3ZMbw5hYWHk7OxMFSpUIC8vL9q6dSuFh4drbffs2TOqWrUqbd68Wafn/5fFixeTg4MDVapUifr27UtLliyhixcvUlJSksZ2lSpVou+++47q1q1Lx48f14tLvgYFkLi4OBAR4uLiRKvIyoULF9CkSRMkJCRku01UVBQOHjyIn376Cc2bN4eFhQWISGtZsmSJ3n2VSiUCAgLg4+ODhg0bQqFQaDgoFAq8efNG7x6ZvHjxAnPmzEHlypU1PDp37iybQyYRERH44YcfYGZmJnls2rRJdg8AUKlUGDFiBIgI1tbWuHz5shAPAFCr1XBwcICDgwP69u0rzAMA5syZAyKCqakpDhw4IMzj66+/lr4jRYsWxYIFC7SOAYMGDcLr16/15pCYmAgrKyuN/aZs2bKYOHEirl27BrVaDQBYvnw5iAhjxozB+/fvP7nHpk2bdB7PqlatipEjR2L37t148+YNHj16JD3XvHlz3L59+5N6tGrVSqeHkZERatasicGDB2PVqlW4cOECTExMpOfbtGmD69evf1KXz428nL854BQAnjx5gp49e4KI0KhRI2m9SqVCSEgI1qxZA09PT60Tt66lTJky6N27N44cOfKfXPbt24erV69m+3xkZCQ2btyIPn36wN7ePluPkiVLwsvLCy9fvvxPHh9LYmIiNm/eDHd3d62ARUQoUaIEfv75Z+kArW/evn2LSZMmwdLSUstj27ZtsjhkJWu4ISKYm5vjxIkTsntkolarJRcPDw+hHhMmTJBcRIUctVqNsWPHwtzcXOP74uDggHnz5iE+Ph4A4ObmBhcXF73tT+Hh4fD09IStra3O/blixYqYMmUKFi1aJK2rUaPGJw8WZ86cwTfffAMHB4ccj3O1atXSeGxsbIzx48d/snPG4sWL4eHhAUdHx1yPubqWPn364PHjx5/E5XODA04uFJSAExsbi4kTJ2pc5Xfq1AmzZs1Cx44dsz3YZC4mJiZo0KABvL29sXPnzv/Xwe/Vq1f46quvQEQIDQ2V1qenp+PixYuYOnUq6tatm6NLq1atsHDhQgQHB+s1UKjVapw/fx6DBw9G4cKFtVzMzc3Ru3dvHD16FOnp6XrzyEpsbCx8fHxgbW2t4VK0aFH89ttvernazQ1DCzeA4QScTJecQk5ISAiio6NlcXn16hW8vb21KrL29vaYO3cuqlSpAiKCs7MzHj16pDePlJQUHDp0CP369dO5b+na15YtWwaVSvVJPVQqFYKDg7F06VJ06dIFNjY2HxUsSpQoge3bt3+y449arcbLly+xd+9e/PTTT2jTps1Hu5iammLMmDF6rbwZIhxwciG/B5z09HSsXLkSRYsWzdNVgYODA7p06YL58+fj/PnzSEpK+n+7qFQqrFmzRgpTDg4OePXqFdauXYtvvvkGdnZ22fqUKVMGw4YNw/79+z/ZZ/XgwYNsn3v27BlmzpyJChUq6PRp3LgxVq1ahXfv3n0Sl48hISEB8+bNQ5EiRTRc7OzsMHfuXOkKXG4MMdwAhhVwMn2yCzmTJk3CxIkTZfUJDw/H2LFjs216JiI4OjoiODhY7y7v37/Hvn370Lt3b63mqw+XDh06IDw8XG8u6enpCAwMxPz589GuXTutiteHS5s2bXDv3j29uKhUKjx48ACbN29GnTp1cj1uFy5cGLNmzcqx60F+ggNOLuTngHP8+HG4urp+VKCpXr06hgwZgnXr1uHBgwefvCry4MEDNG/eXON3GhkZZetjZmYGd3d3LF68GHfv3v2kPunp6ZgyZQq++uorjfUJCQnYsGFDtm3ipUqVwuTJk3H//v1P5vIxvH//HkuWLEGxYsW0DmbTpk1DTEyMrD5ZMdRwAxhewAGyDznly5eHubm53ptZdREREYHx48drNXVmDdABAQGy+SQmJmLKlCk5Hq+KFi2KgwcP6t3l9u3bWpVSXYuJiQkmTZqkt2ARGBioUX3PabG3t0fr1q0/eZOeIWIwAefdu3fo378/bGxsYGNjg/79++d4YE5LS8OkSZNQo0YNWFlZoUSJEhgwYABevXqlsV3Lli21PuDevXt/tFd+DDh3795Fx44dP2pnmDVrll6rEKmpqZg9e/ZH7ZzlypXDiBEjcOjQIb0dKMLDw6XvzOjRo6FSqXD27Fl4enqiUKFCWk4WFhbo27cvTpw4AaVSqRen7EhNTcXKlStRsmRJLacJEyYgKipKVp8PMeRwAxhmwAG0Q07WoD9o0CBhXsuWLct23yxUqBD8/Pxk8bh+/XqO1dysy/Dhwz9JdVkXr169QunSpbV+p0KhQOHChVG8eHGUK1cOrq6uaNCgAVq2bIlhw4Z98v0yJiYGzZo1Q/369fHll19i4MCB+Omnn/Dbb79h8+bNOHHiBG7duoXw8HCkpaV90t9t6BhMwOnYsSNq1KgBf39/+Pv7o0aNGjkedGJjY9G2bVvs3LkTDx48QEBAABo1aoR69eppbNeyZUsMHToUERER0hIbG/vRXvkp4KjVaqxbtw6VK1f+6ANEyZIl9VbuDQgIQI0aNXL8/c7Ozli6dKleqkYfcvr0aRQvXlz63fXq1UO5cuV0ejVt2hR//fVXnr5Ln4r09HSsW7dOy83U1BSjR4/Wa3n+YzH0cAMYbsABtENO1rATEhIiq0tycjKGDx+e67HCzMwM+/fv17uLt7c3vvnmG3h4eMDd3R1NmzZFnTp1ULVqVZQtWxbFixeHtbW1NKLIxcUFN27c+OQuL1++RFBQEB4+fIjQ0FBER0cjJSVFtkEETO4YRMC5d+8eiAhXrlyR1gUEBICIcuwH8SFXr14FEeHFixfSupYtW8Lb2/s/u+WngPMhSqUS0dHR+Pfff3H16lUcP34c27dvx4oVKzB79myMHz8eAwcOxPz58z/p742Pj8eYMWN0jjT6cDE2Nsbhw4c/6e//EJVKhVmzZuXYJEaU0c9n6tSpePjwoV59AODx48da3zmVSoVt27ZJnTyzvkdDhgzB8+fP9e71MRh6uLl+/TpSU1N1Bpzw8HA8ffpUqN+LFy/w22+/oXHjxjq/h127dpXVJy4uDidPnsSSJUswePBgNGzYUGc1M/O7KGoKAl2kp6cjPj5e1r5wjOFgEAFn7dq1sLW11Vpva2uLdevWffTr+Pn5QaFQaPwxLVu2RNGiReHg4IDq1avjxx9/zLGzZUpKCuLi4qQlNDQ03wYcEURERMDT0xPNmzdHkyZN0KBBA9SpUwe1atVC9erVUaVKFVSoUAFly5ZFqVKl4OjoiDJlyiAoKEgvPlFRUWjfvn22ocbS0hL9+/fHqVOnPvnojOy4f/8+SpYsibCwMAAZV/P79u3TqnYpFAr0798f//77ryxeH4OhhxsAWLlyJcqUKYOVK1dqVOTGjh0LS0tL6X0XRWBgYLb9vDKXixcvCnVUqVR4+vQpDh06hHnz5qFv376oWbMmTE1NQURYvny5UD+GAQwk4MydOxeVK1fWWl+5cmXMmzfvo14jOTkZ9erVQ79+/TTW//XXX/Dz88OdO3ewfft2lCtXDm3bts32dX755RedBxQOOPmPS5cuoVSpUjmeSGrUqIGIiAjZnG7fvi01kz1//hzHjh1DvXr1tLy+/vpr3L17Vzav7EhOTpb+/zmEGyCjQpLd512nTh3RegAyQu2xY8e05ljJGsgMsSkkLS0Nd+/exc6dO2XdbxhGF3oNONmFhazLtWvXpLkVPqRSpUof1TySlpaGbt26oU6dOrn+IdevXwcRZdsmyxWc/I9arcavv/4KY2PjXL+fRBkTi8nRbHH9+nWNCQt19U/y8PDAzZs39e7yMYSGhmLcuHEAPp9wk4mbm5vOz9rHx0e0mgYqlQqbN29G2bJltVxFznjMMJ8DeQk4JpRHRo8eTX369Mlxm3LlytHt27d13gzxzZs35OjomOPPp6enU69evejZs2d05swZsrGxyXH7unXrkqmpKf37779Ut25drefNzc3J3Nw8x9dgPl9iYmLo+++/p/Pnz1OlSpWoSJEiH7Xk9r36/xIQEECdOnWiuLg4aV1ISIj0/7Zt29Ls2bOpcePGevXICzNnzqSDBw/SwoULydvbm1atWkVEGfvQoUOHqH379oINs6dLly4UHBysc70hYWRkRP3796dvvvmGVq1aRXPmzKHo6GgiIpoyZQp17tyZTEzyfGhmGOZD9JWyMjsZBwYGSuuuXLmSayfjtLQ0dO/eHa6urh899O7OnTsgIpw/f/6jts/PnYwLIkql0uBK++fPn892plY3NzecPXtWtKIW9+7dkzplZ52KwdArN5kEBgZqvdclSpSQrZ/VfyU2NhbTpk2TJrtbu3ataCWGMVgMog8OkDFMvFatWggICEBAQABq1qypNXTTxcUF+/btA5DRO75r164oXbo0bt26pTEMPDU1FUDGSJSZM2fi2rVrePbsGY4cOYKqVauiTp06Hz1nCQccRp+cPHky2wnUiAg2NjbYvn27aE0tunfvruX6uYQbIKPp58N7+wwdOlS01kcTHh6O4cOHo1y5ckJuvcEwnwMGE3Cio6PRr18/WFtbw9raGv369dOa6I+IsH79egAZU+Vnd1LIvOJ9+fIlWrRoAXt7e5iZmaFixYr44Ycf8nRPFw44jL7w9fX9qAkOK1asKMusrB/L5cuXdXoOHDjwsxqOO3jwYA1/Q3qPP5aHDx/i1q1bojUYxiDJy/lbAQCfqrnrcyE+Pp5sbW0pLi5O7/0wmILD3r17qU+fPqRUKqV15ubmVLNmTXJzc6PatWtT7dq1qVatWgb1vQNALVq0oEuXLul83tTUlH7++Wf65ZdfSKFQyGyXNw4cOEA9evQgIiILCwuKjo4mKysrwVYMw3wq8nL+5p5sDPMJ2Lp1K02YMIFatWolBZnatWuTi4uLwXcYPXz4cLbhplKlSjRv3jz6+uuvDT7cEBG1a9eOzM3NKTU1ldzd3TncMEwBxrCPvAzzGQCA3N3dKTw8/LMIAVlRqVQ0ZcoUrfWOjo70yy+/0JAhQ8jU1FSA2X+jUKFC1KZNGzp27JjBjZ5iGEZejEQLMMznjkKhICcnp88u3BARbd68me7evSs9tra2ptmzZ9Pjx49pxIgRn1W4ySQz2Hh4eAg2YRhGJFzBYZgCSnJyMk2fPp2IMvrZjBw5kqZOnUrFihUTbPb/o3PnzlS3bl0qVaqUaBWGYQTCAYdhCigrVqygV69eUb9+/Wj27NlUvnx50UqfBGdnZym4MQxTcOGAwzAFkJiYGAoKCqKbN29S7dq1Ret8crp16yZagWEYwXDAYZgCSKFChWjr1q2iNfTG59gfimGYTwt3MmaYAoiZmZloBYZhGL3CAYdhGIZhmHwHBxyGYRiGYfIdHHAYhmEYhsl3cMBhGIZhGCbfwQGHYRiGYZh8BwcchmEYhmHyHRxwGIZhGIbJd3DAYRiGYRgm38EBh8kTcXFxtHbtWlKr1UI9nj17RleuXBHqQETk7+9PKpVKqINarabo6GihDoxh8/btW9EK9PLlSwoNDRWtQQcOHKCkpCShDg8fPqR9+/ZRenp6ttuIPsbmBzjgMB/FvXv3aOTIkVSqVCkaMmQInT59WohHaGgoff/991SlShUaOHAgKZVKIR7v3r2jwYMHU7NmzWjFihVCHIgyDoKjR4+mRo0aCT95DB8+nH777Td6//69MAcAtG/fPtq3bx/5+/sL8yAievHiBQ0ZMoQ2b94s1OPQoUNUrlw5OnjwoDAHADRo0CBydXWlv//+mwAI8QgJCaEePXpQuXLlaNGiRZSYmKi1zb179/Tu8fvvv1PPnj3J2dmZpk2bRs+fP9faZtq0aRQcHKx3l3wNCiBxcXEgIsTFxYlWMWiUSiX2798Pd3d3EJHG0q1bN1ldwsPDMXr0aJiZmWl4bN26VVYPtVqNXbt2wdHRUXIoVKgQXr9+LasHAKhUKowYMULycHV1hVKplN0DAIKCgiSPli1bCnEAMj6fTA8PDw9hHq9fv4aFhQWICOXLl0daWpoQj5CQEJiamoKIYGpqigMHDgjx2LJli8Z+6+7ujqdPn2psc+7cOajVar169O3bV8OjaNGiWLBgARISEqRtBg0aBB8fH725JCUlwdraWsNDoVCgY8eO2L9/P9LT0wEAo0ePhqWlJbZt26YXj8+VvJy/OeAwWrx9+xYLFy5E2bJltYKNo6MjfHx88OrVK1lcXr9+jfHjx0sni8zFyckJf/zxB5KTk2XxAICwsDB069ZNw6NEiRLYt2+fbA6ZfBhuzM3NceLECdk9MunevbvkIvKAbCgBBwC+/fZbyeXvv/8W4qBWqzFhwgTJQ1fIUalUevdITk7GTz/9BCMjI40Lg+XLl0u/38PDA/Pnz9erx6tXr+Dt7a11PHFwcJCCzqBBg0BE8Pb21tt7c/36dQwbNgyFChXSOsaWLFkS06dPx9ChQ6V1P/74oxR8CjoccHKBA45ugoKCMHjwYK2dn4jQuHFjbNmyBSkpKbK4vH37FpMnT9Y6ABQrVgy//fYbkpKSZPEAMk4Aq1atgo2NjYbL0KFDERMTI5tHVh9DCjc3b96UXKpVqyasigQYVsB58OCBdEJ3dnZGamqqEI/cQs6ECRNkCTkAcPXqVdSoUUNjP2revDkePXqEWrVqgYhkuWAIDw/H2LFjdQadSpUqSY8HDhyo12ARHx+P1atXo06dOlrH3A8Xd3d3vHnzRm8unwsccHKBA87/SEtLw44dO/DFF19o7VBmZmb47rvvcO3aNdl8YmJi4OPjo1XCtbe3x/z58zVKyXLw4MEDtGjRQsOlUqVKOHv2rKwemRhauAE0qzfbt28X6mJIAQcAvvvuO8ln1apVwjyyCzlRUVEwMjLCli1bZHNJSUmBj48PTExMJB8LCwup+dnKygo3b96UxSW7oJN16dmzp94v7NRqNa5evQovLy9YWVll61K2bFnZ3htDhQNOLhSUgKNWq/HixQudz0VGRmLWrFkoWbKk1k5UqlQpzJkzR9Z+JfHx8ZgzZw7s7Ow0XGxsbDBz5kzZP6u0tDTMnTsX5ubmkouxsTF++uknvH//XlaXTAwx3GSt3lSvXl1o9QYwvIDz77//wtjYGESE0qVLS02qjx8/1nt/kw/RFXJ69eoFIkK5cuVkq85mcuvWrWwrF6VLl0Z4eLhsLuHh4Rg3bpxG6Mq6tG/fHomJibK4xMTESNUsXYuFhYWsgdTQ4ICTCwUh4KSkpMDT0xNLly7VWH/lyhX069dP6niYdWnRogV2794ta1tvYmIiFi1aBAcHBw2XwoULY+rUqXj37p1sLplcu3YNbm5uGj5169YVeuVkiOEGgEafpB07dojWMbiAAwBeXl6SU2a/MTc3Nzx//lx2lw9DTtZl2bJlsvukpKSgcePGOn0aNmwo28XE+/fvMWzYsBybiJo2bar3JumUlBT06dMn1+YqIsLYsWMLZL8cDji5kN8DTmRkJJo2bQoiwrp165CSkoKNGzeiQYMGWjuJpaUlhg4dilu3bunFJbu2/eTkZCxdulRjNFKmz6RJk4S0NSclJeHHH3/U6AhpYWGBhQsXCj2QGGq4MbTqDWCYAefZs2dSZcDJyUkKPIcOHRLi8/79e61mV6KM/iexsbGyeZw/fx61a9fO8STeu3dvvVe6MkNF1v0+u6V27dp6rWxfvHgREydOxIABA9C+fXu4ubnByckpW7dWrVohKipKbz6GCAecXMjPAefWrVtwdnbWKK0WK1ZMa8coV64cfv31V0RHR+vNJTk5GYMGDdJYl5KSghUrVmg1jZmbm2Ps2LGIjIzUm09O+Pn5oUKFChpOrVu3xr///ivEJxNDCzdZmzG6du0qee3cuVOYEwCsWbMGBw8ehEql0gg4mRXCq1evCvX7/vvvtfbB2bNny+qQnJyM4cOHo3DhwtmewKdNmyaLi1qtRmBgIKZOnapVLf1wmTFjhixOycnJCAoKwubNm/HTTz+hc+fOOkeSVqlSBS9fvpTFKROlUonXr1/j9u3b8PPzw+bNm7F48WJMnDgR06ZNk635zBDggJML+TXg7N+/X+eww6xLu3btcPDgQb1fbSclJaFdu3aws7MDkNGn5e+//9YIX0QZ/QBGjhyJsLAwvfpkR3R0tDQsNHOxtbXF33//LXsfiQ8xtHCjVCrRs2dPqFQq3LhxQ/JydXWVbRROdhw+fBhEpNGno1SpUihatCgKFSok63QCmcTHx6Nt27ZwdnZG0aJFtfbFb775RnanN2/eYNy4cVrzSWUuVlZWiIiIkN3rxYsXWLlyJTp16qTR7y1zEdn8GRcXB39/f/z111/44Ycf0KZNG9SvXx8PHz4U5lSQ4YCTC/kt4KjVasybNy/bUFO4cGGMGjUK9+/fl8UnPj5eKoEXLlwYGzdu1KqOmJiYYOjQodl2gv7UhIWF4cKFC9JjXRP2ERG++uorWTs3ZiUoKEj6v6GFGyBjRBkRYdGiRRrVm127dgn1AjKaXSwtLXV+/7t37y7M6/nz5yhTpoxOLxcXF2Fez549w4ABA6BQKLS8RowYIcwLyOiXd+DAAXh5ecHJyQlEGU3FgYGBQr0+RNRgg4IOB5xcyE8BJzk5Gf369cuxalO3bl3ZTtrv3r1Dw4YNs3UxMjKCp6cnnjx5IosPACQkJKBOnTr47bffAGQ/Yd/evXtlc/qQ1NRUVKxYEU+fPjXIcAMAu3fvBhFJo4IMpXqTSdbQlXVZu3atUK9Hjx5pBenMfUHO+Zx0cevWLXTq1EnDy9jY2GCqEyqVClevXoWPjw86d+4srNLLGA4ccHIhvwSc8PBwNGrUKMdwk7mULl1abx2JM4mKisq206BCoUDfvn3x4MEDvTp8iFKpRJcuXUCUMepg9erVBjNhX1aWL18OIsLChQsNMtwAgI+Pj87w7OXlhWHDhgnrP5XJ33//rfN7J9oLAO7cuQN7e3stP9F9gzI5e/asxoWJiOazj6EgjhpiNOGAkwv5IeDcuHEDpUuX1jhYOjg4oHbt2vDw8MDw4cMxZ84cbNy4EadPn8bDhw/1erX46tUrVKtWLduA9f333wvp0+Lt7a3RLJbVqVKlSjhz5ozsTh8SHx8vdQTP2jfCkMINAPTo0SPbz3fDhg2i9RAeHq7l1ahRI9FaEtevX9cK1//8849oLQm1Wo09e/agSpUqICKDaxJiGMCAAs67d+/Qv39/2NjYwMbGBv3798/1StnT0zPXg1RKSgpGjx4NBwcHWFlZoUuXLggNDf1or8894MTHx2PZsmXYtGkTzpw5g3///Vdoe/Dz589RsWLFXKtInTt3lnX4959//qnTQ/SEfR/yyy+/aDkaWrgBoDGFfdbljz/+EK0mUb9+fQ03uUcq5calS5c0ZqodM2aMaCUt0tLSsHr1avTr1094R3uG+RCDCTgdO3ZEjRo14O/vD39/f9SoUSPXuSk8PT3RsWNHRERESMuHQ5mHDx+OUqVKwc/PDzdv3kTr1q3h5ub20SODPveAY0g8evQo206URBnD0bt16wYfHx/s3btXtr5AR44cyXbuCH3eKTivREZG6hz5Zmdnh1GjRuH8+fMGMb9MUlKSzg6pc+bMEa2mwcyZMzX89N0s+184deqUNFJI5J3XcyMxMVHYXdAZJjsMIuDcu3cPRIQrV65I6wICAkBEOfbD8PT0RLdu3bJ9PjY2FqamphrDBl+9egUjIyMcP378o9w44HwaQkJCpFEOlpaWaNCgAYYMGYLly5fjwoULsk4alpVbt27lONcHUcb8QHL3B9LF6NGjs3U0MjLC4MGDhQzb/ZBr165p+U2aNMlggmImWScfLFOmjMH5ZXLo0CGYmJigSJEiBuvIMIZIXs7fJqQnAgICyNbWlho1aiSta9y4Mdna2pK/vz+5uLhk+7Pnzp2j4sWLk52dHbVs2ZLmzp1LxYsXJyKiGzduUHp6OrVv317avmTJklSjRg3y9/enDh06aL1eamoqpaamSo/j4+M/xZ9YoElJSaGTJ0/SsmXLyM3NjSpXrkzGxsaitSg8PJw8PDwoMTFR5/MlSpSgTp060ZdffklOTk4y22ny5MkTWr16tc7nunXrRvPmzaPq1avLbKWbO3fuaDwePnw4LViwgBQKhSAj3dSuXZtKly5NYWFh1KVLF4Pzy6RLly60ZcsW+vbbbyksLIzKlCkjWolh8h16CziRkZFSKMlK8eLFKTIyMtuf69SpE33zzTdUtmxZevbsGU2fPp3atGlDN27cIHNzc4qMjCQzMzMqUqSIxs85Ojpm+7rz58+nmTNn/v/+IEYDCwsLGjdunGgNDZKSkqhLly4UFhYmrTMyMqKmTZtKocbNzc1gTnrTpk0jpVKpsa5Zs2a0cOFCatasmSAr3WQNOP369aMVK1YYzPuYFYVCQR4eHrR69Wrq0qWLaJ0c6d27NyUnJ9OdO3c44DCMHshzwJkxY0auYeHatWtERDoPgAByPDD27t1b+n+NGjWofv36VLZsWTpy5Ah99dVX2f5cTq87ZcoUGj9+vPQ4Pj6eDyj5DJVKRd9++y3dvHmTihcvLgWadu3aaYVhQ+DGjRu0Y8cO6XH16tVp/vz5Blt1yAw43bp1o/Xr15ORkZFgo+zx8PCgzZs3U6tWrUSr5MrAgQMpISFBtAbD5EvyHHBGjx5Nffr0yXGbcuXK0e3bt+n169daz71584YcHR0/+veVKFGCypYtS//++y8RETk5OVFaWhrFxMRonLiioqKoadOmOl/D3NyczM3NP/p3Mp8fe/fupfr165OPjw/VqVPHoE/ARESTJ08mIqLSpUvTrFmz6LvvvjOIJr7suHPnDrm7u9OOHTvI1NRUtE6OtGnThrp3704WFhaiVT4Ka2tr0QoMky/Jc8ApWrQoFS1aNNftmjRpQnFxcXT16lVq2LAhEREFBgZSXFxctkFEF9HR0RQaGkolSpQgIqJ69eqRqakp+fn5Ua9evYiIKCIigkJCQmjRokV5/XOYfELmd+FzwM/Pj65fv06LFi2i0aNHk6WlpWilHHnz5g1VqFCBDhw48FmEBktLS5o3b55oDYZhBKO3PjjVqlWjjh070tChQ2nNmjVERDRs2DDy8PDQ6GBctWpVmj9/PvXo0YMSExNpxowZ1LNnTypRogQ9f/6cfv75ZypatCj16NGDiIhsbW3Jy8uLfvzxR3JwcCB7e3uaMGEC1axZk9q2bauvP4dhPhkxMTH09OlTg2w600VqaiodOXKEChcuLFrlo3F2dhatwDCMYPQWcIiItm7dSj/88IM04qlr1670559/amzz8OFDiouLIyIiY2NjunPnDm3atIliY2OpRIkS1Lp1a9q5c6dGGXfp0qVkYmJCvXr1ouTkZHJ3d6cNGzYYdImfYTL5nKpNRBnNaAzDMJ8bCgAQLSE38fHxZGtrS3FxcWRjYyNah2EYhmGYjyAv52/D7onJMAzDMAzzH+CAwzAMwzBMvoMDDsMwDMMw+Q4OOAzDMAzD5Ds44DAMwzAMk+/ggMMwDMMwTL6DAw7DMAzDMPkODjgMwzAMw+Q7OOAweeLq1avUu3dvSklJEeqxbds22rx5s1AHtVpNf/75J71//16oR0xMjHS3b5EkJSWJVjA4lEql8O8HALp8+bJQByKiu3fvkq+vr1AHADR58mR68OCBUI/r16/TkCFD6M2bN0I98j0ogMTFxYGIEBcXJ1rls+H169cYPHgwiAhEhLlz5wrxiIuLw4ABA0BEsLKywoMHD4R4qFQqjBgxAkQEd3d3JCUlCfEAAE9PT5iammLmzJlIS0sT5tG8eXPUrl0bCxcuhFqtFuKgVqvRvn17tG/fHtOnTxfiAAARERHw9vZG8eLFsXDhQmEeoaGh8PDwABHh0KFDwjxCQkJQvHhxmJiY4MCBA8I8li9fDiJCoUKFsHHjRiEOKpUKjRo1AhHBzs4Of/75J9LT0zW2iYqK0lrHZJCX8zcHHCZH0tPT8fvvv8PW1lYKN0SEjh07yn4SCwwMRIUKFTQ8li9fLqsDoBluiAjm5uYICAiQ3QMAjh49KnmUKFEC7969E+IRGhoqeTRv3lyIA5ARcDI9PDw8hHm8ffsWJiYmICLUqFFDWOA7fvy49H6UKlUKsbGxQjxmzZoleYgKOWq1Gu7u7hrHj++++w4JCQnSNpGRkXj48KFePZ4+fYqSJUtqeLi5ueHSpUvSNvv27YOXl5ew740hwwEnFzjgfBznzp1DzZo1NXbEkiVLYtu2bbLueEqlEvPmzZNOGEQEJycnnDx5UjaHTHSFmxMnTsjuAQCxsbEoVaqU5CLyCn3JkiWSx59//inMw1ACDgB07dpVcrl165Ywj8yKJxFh+PDhQhzUajUmTJiQbchJT09HaGio3j3S09MxdepUKBQKycXFxQXBwcEAgGPHjsHNzQ3Jycl69YiPj8fEiRM1jmlEhAEDBiAiIgL//PMPiAg//fSTXj0+Rzjg5AIHnJwJDQ1Fnz59NHY8U1NTTJo0CfHx8bK7tGrVSsPFw8MDUVFRsnoAhhVuAGDIkCGSS79+/YR5AJBK7kZGRoiMjBTmYUgBZ9euXZLLhAkThHm8ffsWxYoVk1zOnTsnxCOnkOPn54fvvvtONpeTJ0+iePHiGvvyqlWrsGjRIhARRowYIYvHvXv3tKpK1tbWaNasmfR48eLFsrh8LnDAyQUOOLpJSUnBggULUKhQIY0drn379kL6uuzduxdFihTROAj9+eefQsq2hhZuTpw4Ibk4Ojri7du3wlyePn0qubi7uwvzAAwr4CQnJ8PGxkaqfCqVSmEu27dvl96XypUr4/379wCAhw8fytpslV3IGTZsGBQKhVRJkYOIiAid4SLz/zt37pTFQ61WY/fu3ShTpoyGS9ZFVH8hQ4QDTi5wwNHm2LFjqFKlisZOVa5cOezfv1/2QJGYmIhhw4ZpuLi6uuL27duyemRiaOEmPj4ezs7Oks++ffuEuQDAggULJJe//vpLqIshBRwA8PLyknz8/PwAZDjK3SldrVajS5cuksvkyZOhVqvRoUMH7NmzR3aXD0NO4cKFQUT48ssvZXVRKpWYM2cOjIyMtEKFtbU1/v33X9lcEhMTMXXqVJ0uxsbGQpugDQkOOLnAAed/PH36FN26ddPYmSwsLDBjxgzpKk9OgoKCULVqVQ2fUaNGCXEBDC/cAMDw4cMln969ewt1AYA6depIJyqRlSTA8ALO2bNnJR9PT08AwNSpU3Hq1CnZXUJDQ6UKhbGxMWbMmAEiwuDBg2V3+TDkZF3Onj0rq0tKSgoGDhyo06VOnTp674+TyatXr9CjR49sqzgWFha4ePGiLC6GDAecXOCAAyQlJcHHxwfm5uYaO1GPHj3w7Nkz2X1UKhWWLFkCMzMzycXBwQEHDx6U3SWrk6GFm9OnT0s+xYoVE9IXKWtF7+HDh5JPp06dZHfJJPN90BVw0tPThQUvlUqF0qVLg4hQuHBh+Pj4CK26rVq1SuvE6eTkJGuVVq1WIzg4GNOmTdPY3zOXhg0byuazZ88ejWqormXUqFF694iOjoaHhwdMTU1zdLG1tZW1Gc8Q4YCTCwU54KjVauzbtw9ly5bV2HFcXFyEnbwjIyPRsWNHDR93d3e8evVKiA9gOOFGpVJJ/09ISEC5cuVk7yPwISEhIVi6dCkAzeG/GzZsEOIDAPPnz0fnzp0RGBgo+XTs2BGbN29GlSpVcPfuXVl9wsLCsGLFCvj6+mp12BfxXl2+fBl//PEHJkyYoPMkevPmTdlcbt68CVdX1xxP5Hv37pXFJSUlBfv370fPnj11hq3MZffu3bL4JCUlwc/PD1OnTkWzZs20RlllBtInT57I4mOIcMDJhYIQcN6+fatV/bh//z7atWunsbMULlwYixYtQmpqqhDPo0ePaoxmMDExwaJFizRO7HKQ9YrRUMINAMycOVOap2P06NGSU8+ePYXNkXH16lUQEf744w/pRGVmZiZsjhUAuHPnTrYnpwoVKsj+XqnVavTq1Stbpz/++ENWn9DQULi5uWXrM2fOHFl9lEolNmzYkG3H2ipVqsg+0d27d+/w119/oUWLFlo+NjY2ePz4saw+QEa/nJMnT+Lnn39G06ZNpcBTsWJFoaMVRcIBJxfye8BJSEhAo0aNMGnSJADZz7nQr18/2aokL1680CitJicnw9vbW8OncuXKuHbtmiw+Wbl9+7bUZGBI4UalUqFEiRKYNm0azp8/r9F0J/LgltUla8Xtxo0b2LVrF+7fvy+7k1qt1qhuZV28vb1l9wEy5in6cGJKUYECyDgOdO7cWadP06ZNZfcBMo4Dixcv1hgtmbmsWbNGiBMAPH/+HHPnztXoD1ivXj2kpKQIcwIyju0nTpzAlClTMHLkSKEzqIuCA04u5OeAk5KSIlVpvLy8sGXLFpQoUULjwFGrVi2cP39eVqeGDRtKB6y7d+9qXU0OHjxYY0ZROfHw8ECvXr0MKtwAwLVr10CU0bkw68l769atwpyAjBF32VUCatWqJVunzA8ZM2aMTicRHXozuXbtms4mocyLD7lRKpX44YcftHyMjIyEdhCPiYnB5MmTYWFhITmVKFECiYmJwpyAjOB848YNjBs3Do6OjhgzZoxQH4YDTq7k14CjVCo1yuIfVmzs7OywfPly2Uu/o0aNAhFh7NixWL16NSwtLSWn/2vvzOOiKvc//hlkVxgVRCAVEhX3jVTADTURDfdMRQnTuOhV09Rbmf4ELW9kuZRe9eZ1yZTQVLS0C7miJpQLuCtqCCLiQsgiyjLn+/uD35wYZxDxJ+cZ4Pt+vZ7Xi3PmzPDm4cyczzzbUavVwsaSEP3VGmFtba2zcJ7ocENE8oDU0mXIkCHCl2/ftWuXwSBhaWlJFy5cEOZVem2g0l0LorpftSxfvlzPS9SKwlpWrlypNx05IiJCqBNRydild999V3YTdc87QxQVFVFMTAzdv39ftEqNhgNOOVTHgCNJEoWEhBi88KhUKnr33XeFzLjZunWr7PH0IL4ePXrQzZs3FXfSIkkSeXp66tWXMYQbor+mX5cu5ubm5ObmRiNHjqSsrCwhXlu2bDF4nom8RQNRSUuhdj0VbRk1apRQJyL9NWgAUEBAgGgt2rdvn059iV4NuzSXLl2i4cOHk62tLQcKRgcOOOVQHQPO/Pnzy+w20M54UZqLFy+StbW1webwhQsXCr9bblRUlMH6WrdunVAvIt2bVz5dmjVrJmSci5Z169bpOb3xxhvCW5aIiEaOHKnjtXnzZtFKRFQy6F87XRwwjjV6iIjOnj0rD/S1s7MTutqyIU6cOKHYjCqmasABpxyqW8BZsWJFmRdDbQvO1KlTFb2PVG5urt6CfdoycuRIYeNttBQVFZXpB4A8PT2FrhBsaL0SANS3b1/KzMwU5kVE9NVXX+k4NWzYkO7evSvUScumTZt0grTohQdLc+zYMapVqxYBoF69eonWkUlPTycPDw8CQHFxcaJ1GOaZVOT6bQKmSrNlyxbMnDmzzMebNGmCwMBAdO7cGXl5eYo4ERGCg4Nx5coVg4/v3LkTbm5u2LJliyI+hti0aVOZfg0aNMC4cePwxhtvKGz1Fz/99JPevsmTJyM6Ohr169cXYPQXjx8/1tnetGkTHBwcBNnoMmjQIKhUKgCAt7c37OzsBBv9RY8ePbBo0SIAQE5OjmCbv3ByckJsbCyGDx+On3/+WbQOw7w8Kj9vGR/VpQVn79698jdCbXF1daWgoCDauHGjkBWJiUoGMKKMlpE6depQYGAg7du3T9jgz0ePHpGzs7OeW+3atSk0NFTxO6Y/TV5ens4K0yYmJrRy5Uqj6AIi0h38LGoK9rPw8vIiABQeHi5aRQ+NRkOvv/46NW3aVLSKHhqNhiIjI0VrMMwzqcj121TZOMW8LI4dO4Y333wTLi4u6N27N3x8fNC7d2+4uLgI9YqPj8esWbN09llaWsLf3x9jxozBoEGDYGVlJciuhK+//hrp6enytqmpKUJCQvA///M/aNiwoUCzEg4cOICCggIAgFqtxvbt2+Hr6yvY6i+0LTjt2rVDeHi4YBt9Bg8ejLi4OAwePFi0ih4mJib47rvv0L9/f9EqepiYmGD06NGiNRjmpcEBpwoiSRKys7ORlJSExo0bi9aRefDgAd566y0UFRXB1NQUAwYMwNixYzFkyBDY2NiI1gMAZGZm6lyUx4wZg08++QTNmjUTaKWLtnuqWbNm+Omnn9CyZUvBRrrk5+fDwsICERERsLS0FK2jx+DBg/Gf//wHrVq1Eq1iEEdHR6xevVq0BsNUezjgVEFMTEzg7+8vWkMHjUaDt99+G82bN8eCBQswYsQI4WNFDPHZZ58hOzsb/fr1w+effw4PDw/RSjpIkoS9e/eiT58+2LFjh1HW4ePHj/Hll1+ibdu2olUM0qZNG8yYMUMei2OM9OzZU7QCw1R7OOAwL4WsrCysX78eTk5OolXKJDU1FSdOnMAvv/xilF0EAHDq1CkMHToUq1atgpmZmWgdg/Tt2xcBAQGiNcpEpVLh73//u2gNhmEEU6mzqLKyshAYGAi1Wg21Wo3AwEA8fPjwmc9RqVQGyxdffCEf4+Pjo/f4mDFjKvNPYcrB3t7eqMMNAFhYWOD48eNGG24AoGnTpli7dq3RhhsACAgIMOrWEaBkXBXDMDWbSv0UCAgIQFpaGqKjowEAf/vb3xAYGGhwCqyWO3fu6Gz/97//xaRJkzBy5Eid/cHBwfKUSwDCB64yxo8xDCAuD3t7e9EK5WLs4YZhGAaoxIBz+fJlREdHIz4+Ht26dQMArFu3Dl5eXrh69Src3d0NPs/R0VFne8+ePejTpw+aNm2qs9/a2lrvWIZhGIZhGKASu6ji4uKgVqvlcAMAnp6eUKvVOHHixHO9xt27d7Fv3z5MmjRJ77GtW7fC3t4ebdq0wZw5c5Cbm1vm6xQUFCAnJ0enMAzDMAxTfam0FpyMjAyDq5s6ODggIyPjuV7j22+/hY2NDUaMGKGzf9y4cXj11Vfh6OiICxcuYO7cuTh79iz2799v8HU+++wzLFy4sOJ/BMMwDMMwVZIKt+CEhYWVORBYW06dOgXAcF89ET13H/6GDRswbtw4vbU2goOD8frrr6Nt27YYM2YMduzYgQMHDuDMmTMGX2fu3LnIzs6Wy61btyr4VzMMwzAMU5WocAvOtGnTyp2x5OrqinPnzuHu3bt6j92/f/+5BnseO3YMV69exbZt28o9tnPnzjAzM8O1a9fQuXNnvcctLCxgYWFR7uswDMMwDFM9qHDAsbe3f66ZHl5eXsjOzsbvv/+Orl27AgB+++03ZGdnw9vbu9znr1+/Hh4eHujQoUO5x168eBFFRUVGP02ZYRiGYRhlqLRBxq1atYKfnx+Cg4MRHx+P+Ph4BAcHw9/fX2cGVcuWLREVFaXz3JycHPzwww9499139V73xo0bWLRoEU6dOoWbN2/i559/xqhRo9CpUyd07969sv4chmEYhmGqEJW60N/WrVvRrl07+Pr6wtfXF+3bt8d3332nc8zVq1eRnZ2tsy8yMhJEhLFjx+q9prm5OQ4ePIgBAwbA3d0d7733Hnx9fXHgwAHUqlWrMv8chmEYhmGqCCoiItESSpOTkwO1Wo3s7GzY2tqK1qly5Ofnw9raWqiD9rTlRecYhqkIkiTBxKRSv9s/F48fP+YFal+Aily/xf+XmSoDEWHNmjVwc3PDzZs3hXlIkoSpU6di5syZEJnP8/PzMXz4cCQkJAhzAIBz585h2bJlyM/PF+px5MgRJCYmQpIkYQ5EhJSUFKSkpODevXvCPICS8yMmJgbXrl0T6nHz5k18+OGHKC4uFuZARNiwYQMWLFggzAEA/vzzT3h7e2PPnj1CPbZs2YI2bdogMTFRqEe1h2og2dnZBICys7NFq1QZ8vLyaPz48QSAAJCHhwc9efJEcQ+NRkNTpkyRPebMmaO4g5bg4GACQObm5hQVFSXMY/jw4QSAHBwc6OrVq8I8OnToQACocePGpNFohDhIkiSfG/7+/kIciIji4+PJwsKCANC8efOEeaxfv55MTU0JAG3YsEGYh/a9AoCio6OFOOTm5lKnTp0IAJmZmdHu3buFeCQmJpKVlRUBICsrK/ruu++EeFRVKnL95hYcplyuXr2Kbt26YcuWLQAAExMTjBo1SvEbQkqShGnTpmHNmjUASqb/i7px5vfff49169YBAGxsbNClSxchHomJifIgfTs7O7i5uQnxuH//Ps6ePQugZOKAMXQBiKRt27Zy62JMTIwwD09PT2g0GgDAJ598gqKiIiEePj4+8s9BQUEGlxCpbGrXro2+ffsCAIqKijBq1CghLTmNGzdG7969AZR0UwUGBmLGjBk6/5vIyEihLaHVhsrPW8YHt+A8Pz/88APZ2NjI374cHBzo0KFDins83XJjYWFBMTExinsQESUlJVGdOnVkl3379gnxICIaNmyY7PH9998L89i+fbvsER4eLszDWFpwiIj69u1LAEilUtH9+/eFeQQEBMh1sm7dOmEeQUFBsoefn5+QVj5Jkmj27Nmyx9MtOVu3bqXHjx9XukdxcTHNnz9f9gBAPXv2pDt37hARUfv27WnFihWV7lEVqcj1mwMOY5DCwkJ6//33dd6A3bt3p9u3byvuYkzh5smTJ3IzNwD6xz/+IcSDiOjMmTOyR6tWrai4uFiYy+TJk2WX33//XZiHMQWc8PBw2SUyMlKYx5UrV8jExIQAkIuLCxUUFAjxyMnJoWbNmsl1smzZMvmxP/74QzGPZ4Wczp0705dffqmYS1RUlM4XSGdnZzp48CDVqlWLLCws6MKFC4q5VBU44JQDB5xnk5aWRt27d9cJN7NmzaLCwkLFXYwp3BARTZs2TXbx9PQUUidajKX1hoioefPmBIDUarXQoGVMASchIUF2mThxolCXwMBA2WXt2rXy/pycHEU9Tp06RWZmZnKwOH36NEmSRN26daObN28q5mEo5CxfvpwAUP369SkrK0sxlytXrlCrVq10Pm+1pWPHjsICqbHCAaccOOCUzaFDh8jBwUF+g9nY2NAPP/wgxMXYws3OnTtll7p161JycrIwl9KtN61btxYaKlJTU2WXoUOHCvMgMq6Ao9Fo5PfSK6+8QpIkEVHJYFelSUpKolq1ahEAatSoET158oSuXr1KEyZMUNzliy++kP9HLVq0oK1btwrp2nw65JQuc+fOVdQlJyeHRo4cadDlww8/VNTF2OGAUw4ccPTRaDT02WefyU3ZAKht27bCZuUYW7j5448/SK1Wyz67du0S5kJENHToUKPo/iAi+vbbb2WXr776SqiLMQUcIqJx48bJPhcvXqTffvuNRo8eLcRlwoQJssvSpUupQ4cO1KJFC8U9NBoN+fr6yi7az5wOHToo7iJJkk73qrZYWVlRWlqaYh5ZWVm0ePFiecZb6aJSqSg2NlYxF2OHA045cMDRJSsri4YMGaLzpho/fjzl5eUJ8TG2cFNQUEBdu3aVfaZPn664g/bbP5FxtN6cO3eOHj58SES6g0fPnz+vuAsR0Z49eyg5OVkv4EiSRAcPHlTUS5Ik+b1TOvyNGDGCrK2tyc/PTzGX0ty4cUNuxSkdLh49eqSoR2FhIR06dMjgxfzixYuKOEiSRFu2bCE/Pz+DHgAoODhYEZfr16+Tu7u7QQdtcXFxkd9vNR0OOOXAAecvEhISqGnTpvIbydzcnNasWaNzQVUSYwg3T/d5z5kzR/bp3LmzkPV/vv76a7p37x4RGUfrTWRkJLVr145SU1OpUaNGBJTMsBN13mzdupVMTU1p0qRJOuGvZ8+eZGpqquiYCiKit956i1q3bk2DBg3Su1gNGTJEUZeYmBgaOXIkDR8+nOrVq6fnc/LkScVcoqKiyNLSsswL+fz58xVzuX79Oo0dO7ZMFxMTE7p8+bIiLoWFhRQVFUWDBg0ilUpl0CcwMFARF2OHA0451MSAY2hK5vr163U+bJo0aaL4DJiMjAz5Z2MIN0REGzZskKfC7927V/axsbGha9euKe5DRDRw4EDy8/OjU6dOCW+9ISL68ccfCQDZ29vLPiNHjqQzZ87QmjVrFLswaMnMzNRrndCWPn36KOpCVDJQv/TsmNJl1KhRirpoNBqaOHFimRfy9evXK+pz5MgRcnR0NOji5uameEg+ffq0TpdZ6TJixAhFXYiIUlJSKDQ0VP7iULps375dcR9jgwNOOdS0gKPRaGjWrFnydn5+vt4Hnp+fHz148EBRr4cPH5KnpydJkmQ04YaIqE+fPtSzZ0+6desW2dnZyU4iZyppP+waNGgg+2zbtk2Yz4EDB8q8YL722mtCglevXr0M+ixdulRxFyKilStXGvQZN26c4i7FxcU0evRogz4zZsxQ3OfOnTvk4+Nj0EfUMgP79++nzp076/nExcUJ8SkuLqa9e/fSkCFD5PBer149RccGGSMccMqhpgWc5cuXk0qlory8PLpx4wZ17NhRfvOqVCpauHChkEW35s2bRwDo9OnTRhNuUlNT5SZiNzc32Ump/nhDZGVl6X3oWltb06pVq2j16tV08OBBxZ1OnDhh8OKkUqmEXaBKz84pXZKSkoT4FBcX64zd0pZ33nlHiE9hYSENHjzYKFq4iIiKioro448/1vOZOXOmEB+iki+DkZGROt32PXv2FNb1quX27dv06aefkouLC/Xv31/YrVCMAQ445VCTAk5iYiKZm5sTUNK/XXomkJ2dnbD7wqSnp8v3YyndFCt6QHHpxdm0pW3btooPxCzNsWPHymwtadq0qZDFF0uv8VK6TJ48WXEXLVeuXNHzcXd3F+ZDVFJPT3edhYSECPN5/Pgx9evXT8fHzs5O6AV87969OmODnJychC57QFQyDm/VqlVyi+nevXuF+mjRaDQUExOj2GBsY4QDTjnUlIDz6NGjMheQ6tq1K6WkpAhzCwkJ0XMSHW4kSaI2bdroednZ2ZGvry/NmTNHyJL7q1evNvg/fOWVVxRdAbY0V69e1fOxt7enzMxMIT5atAsOaovIm7FqKT1IHRAzC680ubm55O3treOUnp4u1Ck5OZm6dOki+4i4HYwhcnJyKCwsjLy8vISHLqYEvtkmAwCYPXs2Ll++rLd/6tSpOHr0KJo0aSLACkhKSsJ//vMfvf2tW7dGfn4+njx5IsAKOHv2LC5evKi3PzMzE6dOnYKPjw/s7e0V97pw4YLePnt7e+zfvx+vvvqq4j4AYG1trbdvyZIlqF+/vgCbvxg8ePAzt0UQFham814zNzcXaAPUqVMH+/btQ6dOneR9586dE2gEuLq64tixY5g6dSoAICIiQqiPFhsbG4SGhiIqKgqZmZmidZgKwgGnmrJnzx6sXbvW4GNXrlxBXFycfLdjpZk3b558h+PSJCQkYPjw4Zg4cSIeP36suNd3331ncH/37t2RmJiIN954Q2GjEs6fP6+zbWtri5iYGLRq1UqIDwBYWVnpbHt7eyMoKEiQzV/4+/vLP9erVw/e3t4CbUqoXbs2Vq9eLW+LDjgAULduXZ1zSHTAAQALCwusWrUK33//PWJiYlBYWChaSaZhw4ZwcHAQrcFUlMpvUDI+qnsXVVpaGtWvX7/McRsAyNvbm06dOqW4W3x8fJlO3bp1oyNHjijuRFQy4NHQ1NW5c+dSUVGRECeikm6zunXryj5WVlZ07NgxYT5a8vPzZScTExNKTEwUrUREJQNptePMAgICROvoMGrUKAJAoaGholVkbt++TU2bNqXx48eLVtHh8uXLwlZRZ4wb7qKqwUiShKCgIPz55596jzk6OuKDDz7A5cuX8euvv8LDw0NRNyLChx9+qLff3d0du3btQlxcHHr37q2ok5ZDhw4hIyND3m7QoAGio6Pxz3/+E6ampkKcAOD27dt4+PAhAMDMzAxRUVHo0aOHMB8tlpaW8s/Tp09Hhw4dBNr8hZmZGQYOHAjAOLqnSrNixQrY2toaRQuOFmdnZxw8eBBZWVmiVXRo2bIlWrRoIVqDqeKI++RmKoWlS5fi4MGD8rapqSn8/f0xceJEDBw4UOjFOjo6GrGxsfK2k5MTFi5ciHfeeUeoF6DbPdW7d29ERETA2dlZoFEJ2vE3JiYmiIyMxIABAwQblaBSqWBtbQ1bW1ssXLhQtI4OgwcPxo4dO+Dn5ydaRQdnZ2d89tlnyM/PF62ig6urK1atWgUigkqlEq3DMC+PSm9PMkKqaxfVyZMn5fuqtG7dmr788kudlYJFotFoqH379gSA1Go1/fOf/xQ69bo0ubm5ZG1tTSqVihYsWCC0S+pplixZQgBo06ZNolX0sLOzo4iICNEaemRmZlL//v1FaxikuLhY2MJxDFMdqMj1m1twqgl5eXmYMmUKJk6ciIkTJ6Jr165G9W0sIiICV65cwezZszF37lzY2dmJVpLZvXs3bGxs8OOPP6Jfv36idXQ4f/48Vq5caRQDeJ/G398fY8aMEa2hR/369bF48WLRGgapVasWPD09RWswTI2AA041IS8vD7GxsQan74qmqKgI169fR1JSElxcXETr6HHnzh0kJibC0dFRtIoeo0ePFjZ7qzyWLl1qVCG6NF26dBGtwDCMYFREguYKCyQnJwdqtRrZ2dmwtbUVrcMIhnjsAcMwTJWgItdvnkXF1Hg43DAMw1Q/OOAwDMMwDFPt4IDDMAzDMEy1gwMOwzAMwzDVDg44DMMwDMNUOzjgMAzDMAxT7eCAwzAMwzBMtaNSA87ixYvh7e0Na2tr1K1b97meQ0QICwuDs7MzrKys4OPjg4sXL+ocU1BQgOnTp8Pe3h61a9fGkCFDkJaWVgl/AcMwDMMwVZFKDTiFhYUYNWoUpkyZ8tzPWbJkCZYtW4ZVq1bh5MmTcHR0RP/+/ZGbmysfM3PmTERFRSEyMhLHjx9HXl4e/P39odFoKuPPYBiGYRimqlHJ98UiIqKNGzeSWq0u9zhJksjR0ZHCw8PlfU+ePCG1Wk1r164lIqKHDx+SmZkZRUZGysfcvn2bTExMKDo6+rl8quvNNpVAo9HQ8ePHRWtQRkYG5eTkiNYwinNIkiTRCoyRYwzniCRJRvGeTU5OJo1GI9ShqKiIb7r6glTk+m1UY3CSk5ORkZEBX19feZ+FhQV69+6NEydOAABOnz6NoqIinWOcnZ3Rtm1b+ZinKSgoQE5Ojk5hKo4kSZg2bRp69uyJDRs2CPMoKCjAsGHD4OnpiaSkJGEe6enpcHV1xezZs4WeU1FRUejWrRs2bNiAR48eCfNYuHAhpk+fjs2bNwtrTSUifPzxx/j444+xefNmIQ5Ayf3NVq5ciXHjxuG///2vMI+0tDQsWLAAzZs3x8OHD4V5XLp0Cf3798eIESNAAu8OtH37drRr1w7h4eHCHIqLixEQEICePXtiz549wjxqBJUet+j5W3B+/fVXAkC3b9/W2R8cHEy+vr5ERLR161YyNzfXe27//v3pb3/7m8HXDQ0NJQB6xRi+fVcVNBoNTZkyRa47KysrunPnjhCXkJAQ2aNHjx7Cvp0GBATIHp9++qkQB6KSc1/rcfr0aWEezZs3JwDUoEEDYf8TSZLkuvD39xfiQEQUHx8ve8ycOVOYR1hYmOyxfPlyIQ6SJFGXLl1kjx07dgjxuHXrFllYWBAAMjExof379wvx2LJli1wXpqamtHv3biEeVZVKbcEJCwuDSqV6Zjl16tQLBy5A/95A9Bw3Q3zWMXPnzkV2drZcbt269f/yq2loW27WrFkDoKRVbffu3ULuvr1+/Xr8+9//BgDUrVsXmzZtEnIvqdjYWERERAAAXFxc8P777yvuAAA3btzA/v37AZTcQbtz585CPLKysnDt2jXZo6bf36tjx44wNzcHAMTHxwvzCA4OhqmpKQBg9erVkCRJcQeVSoVly5bJ27NmzUJ+fr7iHo0aNcLXX38NoOQzbezYsUKuBQEBAZgzZw6AktacN998U68lp/SYU+bFqXDAmTZtGi5fvvzM0rZt2xeS0V4wMzIydPbfu3cPDRs2lI8pLCxEVlZWmcc8jYWFBWxtbXUK83wYCjc//vijThehUpw8eRJ///vfAZR8aEZERMDNzU1xj6KiIkybNk3eXr58OaytrRX3AIB169bJP4eEhAhxAKDzpaZr167CPIwFCwsLOWyeOXMGBQUFQjycnZ0xfPhwAMC1a9dw8OBBIR49evTA+PHjAQCpqanCuoiCg4MxYcIEAMCDBw/w5ptv6vxvlPg/qVQqLFmypMyQ8+jRIwQGBla6R42g0tuTqOKDjD///HN5X0FBgcFBxtu2bZOPSU9P50HGlcDT3VIWFhYUExMjxOXu3bvUqFEj2WXRokVCPIiIli9fLnsMGDBAWHdMQUEBNWjQgACQra0t5eXlCfEgIlq8eLFcJ/v27RPmYSxdVERE77//vuwickDp4cOHZY9hw4YJ80hPT6c6derInyU3btyQHysqKlLMIz8/nzp27CjXyZQpU4ioZELLxIkTFfOQJInmzJmj1121fft2AiCsC83Yqcj1u1IDTkpKCiUkJNDChQupTp06lJCQQAkJCZSbmysf4+7uTrt27ZK3w8PDSa1W065du+j8+fM0duxYcnJy0hl9P3nyZGrUqBEdOHCAzpw5Q3379qUOHTpQcXHxc3lxwCkfYwo3RUVF5OPjI7sMGTJE2CyIO3fukK2tLQEgMzMzunr1qhAPIqLIyEi5TqZOnSrMg4ho6NChssu9e/eEeRhTwNm2bZvssmzZMmEekiRR69at5bEnKSkpRERUWFhI+fn5irp88cUXOu9jopIvL3PnzlXU48aNG1S3bl3ZZfPmzfTNN9+QSqWimzdvKuZhKORo/1ceHh7CZ3sZI0YTcIKCggwO7j18+PBfAgBt3LhR3pYkiUJDQ8nR0ZEsLCyoV69edP78eZ3Xffz4MU2bNo3q169PVlZW5O/vT6mpqc/txQHn2RhTuCEimjVrluzSokULevjwoTCXwMBA2UXpD+Wn6dOnj+xy7tw5oS7Ozs4EgFxdXYV6GFPASU1NlV3eeust2S8tLU1xl1WrVsku8+bNI0mSKDg4mBISEhT1KCgoIHd3d9nl559/pjFjxlCLFi0U9SAi+umnn3QmTbzyyisEgEJDQxX1eDrklC6ll0NhSjCagGOscMApG2MLNxEREbJLnTp16OLFi8Jcjh49Krs0btxYaJfQlStXZBcvLy8hDtpvl2lpaXoXcqXRtt6WFXCet3X3ZSJJkhz8tOfLW2+9RRs2bFDcJTs7W+4ecnBwoEWLFgnrToyJiZH/R3Z2dvLP6enpirvMmzdPL1Q0adJE0fOluLiYjhw5Iges0sXNzY0KCgoUc6kKVNl1cBixGNOAYgA4d+4cJk2aJG9v2rQJrVu3Vuz3l55xUlxcjKlTp8rby5YtQ+3atRVzAYC4uDh5nZtvvvlG3i9qcPHbb7+Ne/fu4eTJk/K+Ll26CHH54osvEBoaqjf54OLFixg9evT/e2ZnRbhw4QJWrFiBc+fOoVu3bgCAW7duoUuXLti+fTvs7OwUc8nOzsb169fltVeAkgkZCxYsAADcvn1bMZfHjx8jJSUFDRo0QMeOHQEAmZmZ8uOxsbGKuezduxezZ882+DtTU1MVG4ydkZGBbt26wcfHx+D/4saNGzoTCZgKokDgMjq4BUcfY2i5Kb2uzp9//klNmzaVfT766CNFXYhK1lz6/fffiYjoq6++kl1ef/11IQOLFy1aRIMGDaLc3FyqX78+AaC6desqPo5CS8eOHalRo0Y642+OHDlCmZmZ9Msvvyjqcvz4cXmwtdaldu3apFKpqEGDBop/I2/fvr3BLgcAiq4Enp+fr7MGzdMlLCxMMZebN29SixYtynQJCQlRzOX69evk6elZpouSLZGPHj2Sx54acnFwcDCKFaCNBe6iKgcOOESxsbF0//59IjKOcENE1KtXL7p//z4VFxfTwIEDZZ/+/fsL6WJ45513qH379pSWlqYzsPjy5cuKuxARTZ06lQDoXDxnzJghxIWIyNfXV+/DuE2bNqRSqeiTTz5R1KW4uFinu6N0mTBhgqIuRES//PJLmRdPpc+ftLQ0cnJyMuhS1uKolcW9e/fIw8PDoEvLli0VdSksLKQFCxaQiYmJnou5uTk9ePBAUZ/MzEyaM2eOvBihqCBq7HDAKYeaHnC0K4t+8803RhNuTp8+TQBowYIFNH/+fNnH1dVV8Q8aLa6urgRAp2/8ww8/FOJCRDRy5EiDF+/33nuPZs+erehUWyKi8ePHG7xQOTk5CRmfVHoAeOkiauXc0iG9dBExyyw+Pt7ghfONN95Q3CU7O1tngHzpImJ19OPHj5OLi4uey4oVKxR3ISqZffzOO+/oBK86derQ3bt3hfgYGxxwyqGmB5wffvhB7moxhnBDVDL1HwBZW1vLPpaWlnTmzBkhPsnJyXofeDY2NnTu3DnKzs4W0kXVvXt3gxcFMzMz+vXXXxX3KT27rXT597//rbgLEcnrhzz9TVxU8/6FCxcMtg4oHUS1fPvtt3ounTp1EuLy+PFjGjZsmJ5P6fXNlOThw4c0btw4HZd27doJvUnp+fPnafDgwbLP9OnThbkYExxwyqEmB5zCwkL5nkGli8hwk5eXRzY2NnpOmzdvFuJDVLI4ZVldDJaWlkJmnzRr1syoAkV4eLjBbgZRF/Ds7GwyMzPT8dHew04Upe+bBpSMmRLJ7NmzdXwaNmwozKWoqIgmTpyo46NddE8UW7Zs0RnHpR2DJ5KjR4+Sl5cXmZmZ0fXr10XrCIcDTjnU5ICzZs0agy0AIqeCr1+/3uCFu169euTr60ubNm1S3Ontt9826KRWq+nYsWOK+xCRPM23dFF6DEVpNmzYoOcTFRUlzIeI6PXXX9fxWblypVCfjIwMnf+bm5ubUJ/i4mIaMGCA7KNSqaiwsFCYjyRJ9MEHH8g+rVu3Fuai5Y8//pBbS5Uc+PwsJEmi3bt3C13B3VjggFMONTXg5ObmUsOGDQ1euN3d3Wn+/PmUlJSkuFe3bt3KbC0JCQlRfDyHJEnUuHFjPRcnJyc6e/asoi5a8vLy9Hy8vLzoyZMnQnyIiPbu3avj4+3tLbRJn0h3thsARVelLYtPP/1U9unatatoHfrzzz91WnErskhqZbFkyRLZxxjGmhQVFdGiRYuofv369OjRI9E6MryyccWu3yW3ma1hEBEAICcnR7CJsixZsgR37941+FhKSgqePHkCS0tLRevlwoUL+O233/T229vb41//+hf8/Pyg0WgUdUpOTta7y3DTpk0RFRUFV1dXIedNcnKyznbDhg2xadMmFBQUCLuR49M3GA0LCxN+F2QfHx/559atW6NevXrC3+eTJk3C6tWrkZ6eDltbW+E+tWrVQkREBPr27Yvc3FwkJSVBrVYLdQoJCYG1tTWmT5+O6OhoDBs2TKgPAMyYMQPe3t44fvw4PD09Resw/4f2/aO9jj8LFT3PUdWMtLQ0NG7cWLQGwzAMwzAvwK1bt9CoUaNnHlMjA44kSUhPT4eNjQ1UKpVonSpHTk4OGjdujFu3bsHW1la0TpWH6/PlwvX58uE6fblwfb44RITc3Fw4OzvDxOTZN2OokV1UJiYm5SY/pnxsbW35zfkS4fp8uXB9vny4Tl8uXJ8vxvN2qfK9qBiGYRiGqXZwwGEYhmEYptrBAYepMBYWFggNDYWFhYVolWoB1+fLhevz5cN1+nLh+lSGGjnImGEYhmGY6g234DAMwzAMU+3ggMMwDMMwTLWDAw7DMAzDMNUODjgMwzAMw1Q7OOAwDMMwDFPt4IDDlMvixYvh7e0Na2tr1K1b97meQ0QICwuDs7MzrKys4OPjg4sXL1auaBUiKysLgYGBUKvVUKvVCAwMxMOHD5/5nAkTJkClUumUmnoTwNWrV+PVV1+FpaUlPDw8cOzYsWceHxsbCw8PD1haWqJp06ZYu3atQqZVh4rU6ZEjR/TORZVKhStXrihobLwcPXoUgwcPhrOzM1QqFXbv3l3uc/gcfflwwGHKpbCwEKNGjcKUKVOe+zlLlizBsmXLsGrVKpw8eRKOjo7o37+/8LtNGwsBAQFITExEdHQ0oqOjkZiYiMDAwHKf5+fnhzt37sjl559/VsDWuNi2bRtmzpyJefPmISEhAT179sTAgQORmppq8Pjk5GQMGjQIPXv2REJCAj7++GO899572Llzp8LmxktF61TL1atXdc7H5s2bK2Rs3Dx69AgdOnTAqlWrnut4PkcrCWKY52Tjxo2kVqvLPU6SJHJ0dKTw8HB535MnT0itVtPatWsr0bBqcOnSJQJA8fHx8r64uDgCQFeuXCnzeUFBQTR06FAFDI2brl270uTJk3X2tWzZkj766CODx3/wwQfUsmVLnX0hISHk6elZaY5VjYrW6eHDhwkAZWVlKWBXtQFAUVFRzzyGz9HKgVtwmJdOcnIyMjIy4OvrK++zsLBA7969ceLECYFmxkFcXBzUajW6desm7/P09IRarS63fo4cOQIHBwe0aNECwcHBuHfvXmXrGhWFhYU4ffq0zrkFAL6+vmXWXVxcnN7xAwYMwKlTp1BUVFRprlWFF6lTLZ06dYKTkxP69euHw4cPV6ZmtYbP0cqBAw7z0snIyAAANGzYUGd/w4YN5cdqMhkZGXBwcNDb7+Dg8Mz6GThwILZu3YpDhw5h6dKlOHnyJPr27YuCgoLK1DUqHjx4AI1GU6FzKyMjw+DxxcXFePDgQaW5VhVepE6dnJzwzTffYOfOndi1axfc3d3Rr18/HD16VAnlagefo5WDqWgBRgxhYWFYuHDhM485efIkXnvttRf+HSqVSmebiPT2VSeet04B/boByq+f0aNHyz+3bdsWr732GlxcXLBv3z6MGDHiBa2rJhU9twwdb2h/TaYideru7g53d3d528vLC7du3cKXX36JXr16VapndYXP0ZcPB5wayrRp0zBmzJhnHuPq6vpCr+3o6Aig5FuJk5OTvP/evXt631KqE89bp+fOncPdu3f1Hrt//36F6sfJyQkuLi64du1ahV2rKvb29qhVq5Zey8Kzzi1HR0eDx5uamsLOzq7SXKsKL1KnhvD09MSWLVtetl6NgM/RyoEDTg3F3t4e9vb2lfLar776KhwdHbF//3506tQJQEk/f2xsLD7//PNK+Z3GwPPWqZeXF7Kzs/H777+ja9euAIDffvsN2dnZ8Pb2fu7fl5mZiVu3bumEyOqOubk5PDw8sH//fgwfPlzev3//fgwdOtTgc7y8vPDTTz/p7Pvll1/w2muvwczMrFJ9qwIvUqeGSEhIqFHn4suEz9FKQuQIZ6ZqkJKSQgkJCbRw4UKqU6cOJSQkUEJCAuXm5srHuLu7065du+Tt8PBwUqvVtGvXLjp//jyNHTuWnJycKCcnR8SfYHT4+flR+/btKS4ujuLi4qhdu3bk7++vc0zpOs3NzaXZs2fTiRMnKDk5mQ4fPkxeXl70yiuv1Lg6jYyMJDMzM1q/fj1dunSJZs6cSbVr16abN28SEdFHH31EgYGB8vF//PEHWVtb0/vvv0+XLl2i9evXk5mZGe3YsUPUn2B0VLROly9fTlFRUZSUlEQXLlygjz76iADQzp07Rf0JRkVubq78OQmAli1bRgkJCZSSkkJEfI4qBQccplyCgoIIgF45fPiwfAwA2rhxo7wtSRKFhoaSo6MjWVhYUK9evej8+fPKyxspmZmZNG7cOLKxsSEbGxsaN26c3pTb0nWan59Pvr6+1KBBAzIzM6MmTZpQUFAQpaamKi9vBPzrX/8iFxcXMjc3p86dO1NsbKz8WFBQEPXu3Vvn+CNHjlCnTp3I3NycXF1dac2aNQobGz8VqdPPP/+c3NzcyNLSkurVq0c9evSgffv2CbA2TrTT6J8uQUFBRMTnqFKoiP5vJBPDMAzDMEw1gaeJMwzDMAxT7eCAwzAMwzBMtYMDDsMwDMMw1Q4OOAzDMAzDVDs44DAMwzAMU+3ggMMwDMMwTLWDAw7DMAzDMNUODjgMwzAMw1Q7OOAwDMMwDFPt4IDDMAzDMEy1gwMOwzAMwzDVjv8FFOzkcFDJ2NUAAAAASUVORK5CYII=\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title(\"Geodesic flow\"); plt.axis('equal')\n", "quiver(*X,*hfmOut['flow'],subsampling=(20,20));" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:29.928417Z", "iopub.status.busy": "2024-04-30T08:52:29.928292Z", "iopub.status.idle": "2024-04-30T08:52:35.091711Z", "shell.execute_reply": "2024-04-30T08:52:35.091379Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "flow at the seed point : [-0. -0.].\n" ] } ], "source": [ "flowNorms = hfmIn_Constant['metric'].norm(hfmOut['flow'])\n", "print(f\"flow at the seed point : {hfmOut['flow'][:,100,100]}.\")\n", "assert (np.abs(flowNorms - 1.)>1e-12).sum() == 1" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:35.093638Z", "iopub.status.busy": "2024-04-30T08:52:35.093510Z", "iopub.status.idle": "2024-04-30T08:52:35.679357Z", "shell.execute_reply": "2024-04-30T08:52:35.679040Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hfmIn_Constant['verbosity']=0\n", "hfmIn_Constant.pop('exportGeodesicFlow',None)\n", "for name,metric in zip(['Mica','Stishovite','Olivine'],[metric_mica,metric_stishovite,metric_olivine]):\n", " hfmIn_Constant['metric'] = metric\n", " hfmOut = hfmIn_Constant.Run()\n", " \n", " fig = plt.figure(figsize=[4,4]); plt.title(\"Constant tilted \" + name + \" medium\"); plt.axis('equal')\n", " plt.contourf(*X,hfmOut['values']);\n", " \n", " savefig(fig,\"Distance_Constant\"+name+\".png\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1 Mandel notation\n", "\n", "Mandel notation is a variant of the Voigt notation, introducing normalizing factors of magnitude $\\sqrt 2$ and $2$." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:35.681098Z", "iopub.status.busy": "2024-04-30T08:52:35.680976Z", "iopub.status.idle": "2024-04-30T08:52:35.683560Z", "shell.execute_reply": "2024-04-30T08:52:35.683314Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[1. , 1. , 1.41421356],\n", " [1. , 1. , 1.41421356],\n", " [1.41421356, 1.41421356, 2. ]])" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "metric_mica._Mandel_factors(2) # In dimension two" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:35.684934Z", "iopub.status.busy": "2024-04-30T08:52:35.684823Z", "iopub.status.idle": "2024-04-30T08:52:35.687154Z", "shell.execute_reply": "2024-04-30T08:52:35.686925Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[1. , 1. , 1. , 1.41421356, 1.41421356,\n", " 1.41421356],\n", " [1. , 1. , 1. , 1.41421356, 1.41421356,\n", " 1.41421356],\n", " [1. , 1. , 1. , 1.41421356, 1.41421356,\n", " 1.41421356],\n", " [1.41421356, 1.41421356, 1.41421356, 2. , 2. ,\n", " 2. ],\n", " [1.41421356, 1.41421356, 1.41421356, 2. , 2. ,\n", " 2. ],\n", " [1.41421356, 1.41421356, 1.41421356, 2. , 2. ,\n", " 2. ]])" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "metric_mica._Mandel_factors(3) # In dimension three" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The eigenvalues of the hooke tensor given in Mandel notation make physical sense, and are invariant upon rotations." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:35.688505Z", "iopub.status.busy": "2024-04-30T08:52:35.688411Z", "iopub.status.idle": "2024-04-30T08:52:35.690665Z", "shell.execute_reply": "2024-04-30T08:52:35.690432Z" } }, "outputs": [], "source": [ "metric = metric_mica.rotate_by(0.5)\n", "eigvals0 = np.linalg.eigvals(metric.to_Mandel())\n", "eigvals1 = np.linalg.eigvals(metric_mica.to_Mandel())\n", "assert norm_infinity(np.sort(eigvals0) - np.sort(eigvals1)) < 1e-12" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define a hooke tensor can be defined from the Mandel notation." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:35.692035Z", "iopub.status.busy": "2024-04-30T08:52:35.691929Z", "iopub.status.idle": "2024-04-30T08:52:35.693725Z", "shell.execute_reply": "2024-04-30T08:52:35.693501Z" } }, "outputs": [], "source": [ "metric2 = Hooke.from_Mandel(metric.to_Mandel())\n", "assert norm_infinity(metric2.hooke - metric.hooke) < 1e-14" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Varying medium" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1 Position dependent tilt orientation." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:35.695179Z", "iopub.status.busy": "2024-04-30T08:52:35.695075Z", "iopub.status.idle": "2024-04-30T08:52:35.697382Z", "shell.execute_reply": "2024-04-30T08:52:35.697145Z" } }, "outputs": [], "source": [ "hfmIn_Varying = Eikonal.dictIn({\n", " 'model':'Seismic2',\n", " 'exportValues':1,\n", " 'seed':[0.,0.],\n", "})\n", "\n", "# Define the domain, get the coordinate grid\n", "hfmIn_Varying.SetRect(sides=[[-2,2],[-1,1]],dimx=201)\n", "hfmIn_Varying.SetUniformTips((6,6))\n", "X = hfmIn_Varying.Grid()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:35.698795Z", "iopub.status.busy": "2024-04-30T08:52:35.698666Z", "iopub.status.idle": "2024-04-30T08:52:35.703123Z", "shell.execute_reply": "2024-04-30T08:52:35.702870Z" } }, "outputs": [], "source": [ "# Make small oscillations in the tilting angle\n", "tiltAngle = (np.pi/6.)*np.sin(np.pi*X[0]+1)\n", "metric_var = mica.extract_xz().rotate_by(tiltAngle)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:35.704546Z", "iopub.status.busy": "2024-04-30T08:52:35.704454Z", "iopub.status.idle": "2024-04-30T08:52:35.706066Z", "shell.execute_reply": "2024-04-30T08:52:35.705835Z" } }, "outputs": [], "source": [ "#fig = plt.figure(figsize=[6,3]); plt.title(\"Varying medium orientation\"); plt.axis('equal')\n", "#plt.streamplot(*X,np.cos(tiltAngle),np.sin(tiltAngle))\n", "#savefig(fig,\"Medium_MicaVaryingTilt.png\")" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:35.707428Z", "iopub.status.busy": "2024-04-30T08:52:35.707346Z", "iopub.status.idle": "2024-04-30T08:52:35.708865Z", "shell.execute_reply": "2024-04-30T08:52:35.708620Z" } }, "outputs": [], "source": [ "hfmIn_Varying['metric']=metric_var" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:35.710152Z", "iopub.status.busy": "2024-04-30T08:52:35.710073Z", "iopub.status.idle": "2024-04-30T08:52:35.887066Z", "shell.execute_reply": "2024-04-30T08:52:35.886651Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field cosAngleMin defaults to 0.5\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.073756 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn_Varying.Run()" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:35.888953Z", "iopub.status.busy": "2024-04-30T08:52:35.888805Z", "iopub.status.idle": "2024-04-30T08:52:35.958399Z", "shell.execute_reply": "2024-04-30T08:52:35.958060Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[6,3]); plt.title('Minimal distance, Mica medium with varying tilt'); plt.axis('equal')\n", "plt.contourf(*X,hfmOut['values']);\n", "savefig(fig,\"Distance_MicaVaryingTilt.png\")" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:35.960037Z", "iopub.status.busy": "2024-04-30T08:52:35.959923Z", "iopub.status.idle": "2024-04-30T08:52:36.036825Z", "shell.execute_reply": "2024-04-30T08:52:36.036509Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[6,3]); plt.title('Minimal geodesics, Mica medium with varying tilt'); plt.axis('equal'); \n", "for geo in hfmOut['geodesics']: plt.plot(*geo) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "TODO : a piecewise constant medium.\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Taking into account the topography\n", "\n", "The arrival time of seismic waves is, usually, measured at ground level. In order to compute this quantity accurately, a good discretization of the surface topography may be required. \n", "\n", "However, the HFM software can only use rectangular domains (possibly with periodic boundary conditions). A change of variables toward the actual domain is this required, which jacobian matrix locally distorts the metric. Note that Hooke tensors do not define an class of metrics invariant under linear tranformations, as opposed to e.g. Riemannian, Rander, or asymmetric quadratic metrics, hence the jacobian matrix must be specified separately.\n", "\n", "\n", "\n", "Chosen physical domain is the image of the rectangle $[-1,1]\\times [0,1]$ by the smooth mapping $(x,z) \\mapsto h(x,z)$ defined below." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:36.038736Z", "iopub.status.busy": "2024-04-30T08:52:36.038559Z", "iopub.status.idle": "2024-04-30T08:52:36.040726Z", "shell.execute_reply": "2024-04-30T08:52:36.040446Z" } }, "outputs": [], "source": [ "def h(x,z,alpha=0.5): return ad.array([x, z + alpha*z*np.sin(np.pi*x)])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We take into account the surface topography, while leaving invariant the other axes." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:36.042151Z", "iopub.status.busy": "2024-04-30T08:52:36.042045Z", "iopub.status.idle": "2024-04-30T08:52:36.118418Z", "shell.execute_reply": "2024-04-30T08:52:36.118110Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.linspace(-1,1,20)\n", "Z = np.linspace(0,1,5)\n", "for z in Z: plt.plot(*h(X,z)) \n", "for x in X: plt.plot(*h(x+0.*Z,Z))" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:36.120929Z", "iopub.status.busy": "2024-04-30T08:52:36.120775Z", "iopub.status.idle": "2024-04-30T08:52:36.124374Z", "shell.execute_reply": "2024-04-30T08:52:36.123987Z" } }, "outputs": [], "source": [ "hfmIn_Topo = Eikonal.dictIn({\n", " 'model':'SeismicTopographic2',\n", " 'exportValues':1,\n", " 'seed':[0.,0.5],\n", "})\n", "\n", "# Define the domain\n", "hfmIn_Topo.SetRect(sides=[[-1,1],[0,1]],dimx=101)\n", "hfmIn_Topo.SetUniformTips((6,6))\n", "\n", "X0 = hfmIn_Topo.Grid() # Grid coordinates (horizontal and vertical)\n", "X = h(*X0) # Physical coordinates" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use automatic differentiation to compute the jacobian matrix of the change of variables." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:36.126046Z", "iopub.status.busy": "2024-04-30T08:52:36.125956Z", "iopub.status.idle": "2024-04-30T08:52:36.128699Z", "shell.execute_reply": "2024-04-30T08:52:36.128254Z" } }, "outputs": [], "source": [ "X0_ad = ad.Dense.identity(constant=X0,shape_free=(2,))\n", "Jac = np.moveaxis(h(*X0_ad).gradient(),0,1)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:36.130884Z", "iopub.status.busy": "2024-04-30T08:52:36.130354Z", "iopub.status.idle": "2024-04-30T08:52:36.133288Z", "shell.execute_reply": "2024-04-30T08:52:36.132904Z" } }, "outputs": [], "source": [ "metric_topo = mica.extract_xz().rotate_by(-np.pi/6)\n", "metric_topo = metric_topo.inv_transform(Jac) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Rotations are handled by modifying the hooke tensor, but general linear transformations are stored separately." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:36.135142Z", "iopub.status.busy": "2024-04-30T08:52:36.134977Z", "iopub.status.idle": "2024-04-30T08:52:36.137287Z", "shell.execute_reply": "2024-04-30T08:52:36.136942Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Required model : SeismicTopographic2. Stored Jacobian shape : (2, 2, 101, 50).\n" ] } ], "source": [ "print(f\"Required model : {metric_topo.model_HFM()}.\",\n", " f\"Stored Jacobian shape : {metric_topo.inverse_transformation.shape}.\")" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:36.139142Z", "iopub.status.busy": "2024-04-30T08:52:36.138950Z", "iopub.status.idle": "2024-04-30T08:52:36.141119Z", "shell.execute_reply": "2024-04-30T08:52:36.140771Z" } }, "outputs": [], "source": [ "hfmIn_Topo['metric'] = metric_topo #.to_HFM() #HookeTopo_to_HFM(hooke,h_grad(X0,Z0))" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:36.142676Z", "iopub.status.busy": "2024-04-30T08:52:36.142555Z", "iopub.status.idle": "2024-04-30T08:52:36.200716Z", "shell.execute_reply": "2024-04-30T08:52:36.200332Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field cosAngleMin defaults to 0.5\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.017735 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn_Topo.Run()" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:36.202510Z", "iopub.status.busy": "2024-04-30T08:52:36.202372Z", "iopub.status.idle": "2024-04-30T08:52:36.267015Z", "shell.execute_reply": "2024-04-30T08:52:36.266709Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[4,4]); plt.title('Minimal distance, Seismic metric (constant) with topography'); plt.axis('equal')\n", "plt.contourf(*X,hfmOut['values']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The geodesics are straight lines, except for those which would cross the surface." ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:36.268703Z", "iopub.status.busy": "2024-04-30T08:52:36.268596Z", "iopub.status.idle": "2024-04-30T08:52:36.337906Z", "shell.execute_reply": "2024-04-30T08:52:36.337636Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[4,4]); plt.axis('equal'); \n", "plt.title('Minimal geodesics, Seismic metric (constant) with topography');\n", "for geo in hfmOut['geodesics']: \n", " plt.plot(*h(*geo)) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the computation involved a distorted metric, on a distorted domain." ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:36.339869Z", "iopub.status.busy": "2024-04-30T08:52:36.339719Z", "iopub.status.idle": "2024-04-30T08:52:36.419746Z", "shell.execute_reply": "2024-04-30T08:52:36.419427Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title('Minimal distance, Seismic metric (constant) with topography, deformed grid'); plt.axis('equal')\n", "plt.contourf(*X0,hfmOut['values']);" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:36.421503Z", "iopub.status.busy": "2024-04-30T08:52:36.421376Z", "iopub.status.idle": "2024-04-30T08:52:36.505312Z", "shell.execute_reply": "2024-04-30T08:52:36.504897Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title('Minimal geodesics, Seismic metric (constant) with topography'); plt.axis('equal'); \n", "for geo in hfmOut['geodesics']: plt.plot(*geo) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Testing reproduction\n", "\n", "In this section, we check the soundness of the proposed discretization by comparing the numerical solution with the exact solution, when it is known." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.1 Case of a constant metric\n", "\n", "If the metric is constant and if source factorization is used over all the domain, then the exact solution is recovered, up to floating point accuracy." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:36.507321Z", "iopub.status.busy": "2024-04-30T08:52:36.507174Z", "iopub.status.idle": "2024-04-30T08:52:36.509675Z", "shell.execute_reply": "2024-04-30T08:52:36.509427Z" } }, "outputs": [], "source": [ "n=101\n", "hfmIn_Constant.SetRect(sides=[[-1,1],[-1,1]],dimx=n)\n", "hfmIn_Constant.update({\n", " 'factoringRadius':-1, # factorization is used over all the domain \n", " 'verbosity':1,\n", "})\n", "X = hfmIn_Constant.Grid()" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:36.511148Z", "iopub.status.busy": "2024-04-30T08:52:36.511041Z", "iopub.status.idle": "2024-04-30T08:52:37.923472Z", "shell.execute_reply": "2024-04-30T08:52:37.923092Z" } }, "outputs": [], "source": [ "exactSolution = hfmIn_Constant['metric'].norm(X)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:37.925524Z", "iopub.status.busy": "2024-04-30T08:52:37.925402Z", "iopub.status.idle": "2024-04-30T08:52:37.973603Z", "shell.execute_reply": "2024-04-30T08:52:37.973114Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field cosAngleMin defaults to 0.5\n", "Field order defaults to 1\n", "Field seedRadius defaults to 2\n", "Field factoringPointChoice defaults to Seed\n", "Field exportFactoring defaults to 0\n", "Fast marching solver completed in 0.025819 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn_Constant.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Exact and numerical solution match up to machine arithmetic precision." ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:37.975393Z", "iopub.status.busy": "2024-04-30T08:52:37.975257Z", "iopub.status.idle": "2024-04-30T08:52:37.977693Z", "shell.execute_reply": "2024-04-30T08:52:37.977444Z" } }, "outputs": [], "source": [ "assert np.allclose(exactSolution,hfmOut['values'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The fast marching algorithm, used under the hood, requires the numerical scheme to be causal, and therefore the stencils to be sufficiently refined. If this condition is not met, then a systematic error will occur.\n", "For that purpose, the field *stencilGeometry* should be set to:\n", "* 'None' (default), to produce adaptive stencils automatically obeying the causality property. (With some computational overhead.)\n", "* 'Square', or 'SpikySquare', which are fine enough for the anisotropies encountered in seismology.\n", "\n", "In the following example, we purposedly use an under-refined stencil, to illustrate inconsistencies in the lack of causality." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:37.979369Z", "iopub.status.busy": "2024-04-30T08:52:37.979257Z", "iopub.status.idle": "2024-04-30T08:52:37.981095Z", "shell.execute_reply": "2024-04-30T08:52:37.980851Z" } }, "outputs": [], "source": [ "hfmIn_Constant['stencilGeometry']='Diamond' # This stencil is causal only for isotropic metrics" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:37.982547Z", "iopub.status.busy": "2024-04-30T08:52:37.982470Z", "iopub.status.idle": "2024-04-30T08:52:38.024053Z", "shell.execute_reply": "2024-04-30T08:52:38.023649Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field cosAngleMin defaults to 0.5\n", "Field order defaults to 1\n", "Field seedRadius defaults to 2\n", "Field factoringPointChoice defaults to Seed\n", "Field exportFactoring defaults to 0\n", "Fast marching solver completed in 0.012434 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn_Constant.Run()" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:38.025765Z", "iopub.status.busy": "2024-04-30T08:52:38.025630Z", "iopub.status.idle": "2024-04-30T08:52:38.099484Z", "shell.execute_reply": "2024-04-30T08:52:38.099165Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title(\"Seismic traveltimes. Under-refined stencil causes systematic error\"); plt.axis('equal')\n", "plt.contourf(*X,hfmOut['values']);" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:38.101390Z", "iopub.status.busy": "2024-04-30T08:52:38.101261Z", "iopub.status.idle": "2024-04-30T08:52:38.104076Z", "shell.execute_reply": "2024-04-30T08:52:38.103754Z" } }, "outputs": [ { "data": { "text/plain": [ "0.0009596592201516277" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.max(np.abs(exactSolution-hfmOut['values']))" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:38.105870Z", "iopub.status.busy": "2024-04-30T08:52:38.105743Z", "iopub.status.idle": "2024-04-30T08:52:38.107463Z", "shell.execute_reply": "2024-04-30T08:52:38.107152Z" } }, "outputs": [], "source": [ "hfmIn_Constant['stencilGeometry']='None' # Use automatically generated adaptive stencils (default)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.2 Case with topography\n", "\n", "In the instance involving ground topography, the discretization grid is distorted. Therefore the numerical metric is non-constant, and we cannot expect the numerical method to exactly reproduce the arrival times. \n", "We compute the exact arrival times as above, by requiring the factor used in the constant case." ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:38.108983Z", "iopub.status.busy": "2024-04-30T08:52:38.108880Z", "iopub.status.idle": "2024-04-30T08:52:38.831233Z", "shell.execute_reply": "2024-04-30T08:52:38.830815Z" } }, "outputs": [], "source": [ "X0 = hfmIn_Topo.Grid() # Rectangular coordinates\n", "X = h(*X0) # Physical coordinates\n", "hooke = Hooke(hfmIn_Topo['metric'].hooke[:,:,0,0]) # Hooke tensor only, omits the change of vars\n", "seed = hfmIn_Topo['seed']\n", "exact = hooke.norm(X - fd.as_field(seed,X.shape[1:]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We introduce source factorization so as to reduce the numerical error of the numerical method. " ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:38.833031Z", "iopub.status.busy": "2024-04-30T08:52:38.832917Z", "iopub.status.idle": "2024-04-30T08:52:38.834720Z", "shell.execute_reply": "2024-04-30T08:52:38.834455Z" } }, "outputs": [], "source": [ "hfmIn_Topo['factoringRadius']=-1 # factorization is used over all the domain " ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:38.836234Z", "iopub.status.busy": "2024-04-30T08:52:38.836112Z", "iopub.status.idle": "2024-04-30T08:52:38.892145Z", "shell.execute_reply": "2024-04-30T08:52:38.891835Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field cosAngleMin defaults to 0.5\n", "Field order defaults to 1\n", "Field seedRadius defaults to 2\n", "Field factoringPointChoice defaults to Seed\n", "Field exportFactoring defaults to 0\n", "Fast marching solver completed in 0.0172 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn_Topo.Run()" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:38.893677Z", "iopub.status.busy": "2024-04-30T08:52:38.893565Z", "iopub.status.idle": "2024-04-30T08:52:38.895460Z", "shell.execute_reply": "2024-04-30T08:52:38.895198Z" } }, "outputs": [], "source": [ "error = exact-hfmOut['values']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Actually, our 'exact' solution is only exact outside the shadow zone, in the upper left part of the domain, which is not connected to the seed by a straight line in the domain." ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:38.896892Z", "iopub.status.busy": "2024-04-30T08:52:38.896792Z", "iopub.status.idle": "2024-04-30T08:52:38.987859Z", "shell.execute_reply": "2024-04-30T08:52:38.987583Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.contourf(*X,error)\n", "plt.colorbar()\n", "plt.scatter(*hfmIn_Topo['seed']);" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:38.989519Z", "iopub.status.busy": "2024-04-30T08:52:38.989400Z", "iopub.status.idle": "2024-04-30T08:52:38.991830Z", "shell.execute_reply": "2024-04-30T08:52:38.991588Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Numerical error outside shadow region : 0.010099956307889076\n", "Time difference inside shadow region : 0.034512658642058686\n" ] } ], "source": [ "shadowRegion = np.logical_and(X[0]<=-0.4, X[1]>=0.4)\n", "print(\"Numerical error outside shadow region : \", np.max(np.abs(error * (1-shadowRegion))))\n", "print(\"Time difference inside shadow region : \", np.max(np.abs(error*shadowRegion)))" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:38.993214Z", "iopub.status.busy": "2024-04-30T08:52:38.993107Z", "iopub.status.idle": "2024-04-30T08:52:39.050534Z", "shell.execute_reply": "2024-04-30T08:52:39.050232Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.contourf(*X,shadowRegion);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5. Three dimensional example\n", "\n", "We illustrate the computation of three dimensional seismic wave traveltimes." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.1 Case of a constant metric\n", "\n", "The geological medium is defined as tilted mica." ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:39.052603Z", "iopub.status.busy": "2024-04-30T08:52:39.052437Z", "iopub.status.idle": "2024-04-30T08:52:39.055434Z", "shell.execute_reply": "2024-04-30T08:52:39.055123Z" } }, "outputs": [], "source": [ "# Define a rotation matrix by its angle and axis\n", "rotation_params = np.pi/3.,(2.,1.,3.)\n", "hooke3D_1 = mica.rotate_by(*rotation_params)\n", "hooke3D_2 = olivine.rotate_by(*rotation_params)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:39.057265Z", "iopub.status.busy": "2024-04-30T08:52:39.057138Z", "iopub.status.idle": "2024-04-30T08:52:39.060191Z", "shell.execute_reply": "2024-04-30T08:52:39.059774Z" } }, "outputs": [], "source": [ "hfmIn3D_Constant = Eikonal.dictIn({\n", " 'model':'Seismic3', \n", " 'metric':hooke3D_1,\n", " 'seeds':[[0.,0.,0.]],\n", " 'factoringRadius':8,\n", "\n", " 'exportValues':1,\n", " 'exportGeodesicFlow':1\n", "})\n", "\n", "# Define the domain\n", "n=21; nHalf = n//2\n", "hfmIn3D_Constant.SetRect(sides=[[-1,1],[-1,1],[-1,1]],dimx=n)\n", "X,Y,Z = hfmIn3D_Constant.Grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At the time of writing, the *Seismic3* model does not support an adaptive stencil construction, automatically enforcing the causality property. The *stencil geometry* must therefore be explicitly defined, chosen among the following possibilities:\n", "* **CutCube** uses $18$ neighbors. Causal for moderately anisotropic models, such as olivine or stishovite.\n", "* **Cube** uses $26$ neighbors. Intermediate refinement.\n", "* **SpikyCube** uses $50$ neighbors. Causal for the mica medium, which is one of the most strongly anisotropic encountered in seismology.\n", "\n", "The numerical cost of the fast marching method is directly impacted by the numeber of neighbors used." ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:39.062105Z", "iopub.status.busy": "2024-04-30T08:52:39.061987Z", "iopub.status.idle": "2024-04-30T08:52:39.064180Z", "shell.execute_reply": "2024-04-30T08:52:39.063825Z" } }, "outputs": [], "source": [ "hfmIn3D_Constant['stencilGeometry']='SpikyCube' # Largest stencil, suitable for mica (strong anisotropy)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:39.065976Z", "iopub.status.busy": "2024-04-30T08:52:39.065854Z", "iopub.status.idle": "2024-04-30T08:52:39.817999Z", "shell.execute_reply": "2024-04-30T08:52:39.817523Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field checkAcuteness defaults to 0\n", "Field order defaults to 1\n", "Field seedRadius defaults to 2\n", "Field factoringPointChoice defaults to Seed\n", "Field exportFactoring defaults to 0\n", "Fast marching solver completed in 0.682113 s.\n" ] } ], "source": [ "hfmOut = hfmIn3D_Constant.Run()" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:39.819966Z", "iopub.status.busy": "2024-04-30T08:52:39.819831Z", "iopub.status.idle": "2024-04-30T08:52:39.892238Z", "shell.execute_reply": "2024-04-30T08:52:39.891890Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.axis('equal'); plt.title('Slice of arrival times for the mica model')\n", "plt.contourf(Y[nHalf],Z[nHalf],hfmOut['values'][nHalf]);" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:39.893957Z", "iopub.status.busy": "2024-04-30T08:52:39.893844Z", "iopub.status.idle": "2024-04-30T08:52:41.647892Z", "shell.execute_reply": "2024-04-30T08:52:41.647520Z" } }, "outputs": [], "source": [ "sx,sy,sz = hfmIn3D_Constant['seed']\n", "exact = hfmIn3D_Constant['metric'].norm((X-sx,Y-sy,Z-sz))" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:41.649696Z", "iopub.status.busy": "2024-04-30T08:52:41.649574Z", "iopub.status.idle": "2024-04-30T08:52:41.651641Z", "shell.execute_reply": "2024-04-30T08:52:41.651411Z" } }, "outputs": [], "source": [ "error = hfmOut['values']-exact\n", "factoringRegion = np.sqrt(X**2+Y**2+Z**2) < hfmIn3D_Constant['factoringRadius']*hfmIn3D_Constant['gridScale']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because the metric is constant, the arrival times are exact in the factoring region." ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:41.653163Z", "iopub.status.busy": "2024-04-30T08:52:41.653013Z", "iopub.status.idle": "2024-04-30T08:52:41.655148Z", "shell.execute_reply": "2024-04-30T08:52:41.654875Z" } }, "outputs": [], "source": [ "assert norm_infinity(error * factoringRegion) < 1e-16" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A small error is omitted elsewhere, which may be improved using a higher order scheme." ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:41.656645Z", "iopub.status.busy": "2024-04-30T08:52:41.656537Z", "iopub.status.idle": "2024-04-30T08:52:41.658366Z", "shell.execute_reply": "2024-04-30T08:52:41.658076Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Global error : 0.0013982669216928145\n" ] } ], "source": [ "print(\"Global error : \", norm_infinity(error))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again the geodesic flow is normalized w.r.t. the metric, except at the center point and its immediate neighbors, which are used as seed points." ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:41.659801Z", "iopub.status.busy": "2024-04-30T08:52:41.659695Z", "iopub.status.idle": "2024-04-30T08:52:43.391173Z", "shell.execute_reply": "2024-04-30T08:52:43.390808Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Flow norm at a seed point : 0.0\n" ] } ], "source": [ "flowNorms = hfmIn3D_Constant['metric'].norm(hfmOut['flow'])\n", "print(f\"Flow norm at a seed point : {flowNorms[nHalf,nHalf,nHalf]}\")\n", "assert np.sum(np.abs(flowNorms-1.)>1e-8) <= 3**3" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:43.392840Z", "iopub.status.busy": "2024-04-30T08:52:43.392723Z", "iopub.status.idle": "2024-04-30T08:52:43.394698Z", "shell.execute_reply": "2024-04-30T08:52:43.394320Z" } }, "outputs": [], "source": [ "assert (np.abs(flowNorms-1.)>=1e-12 ).sum() <= 27 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The less anisotropic olivine model can accomodate less refined stencils, and enjoy faster computation times." ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:43.396405Z", "iopub.status.busy": "2024-04-30T08:52:43.396280Z", "iopub.status.idle": "2024-04-30T08:52:43.398071Z", "shell.execute_reply": "2024-04-30T08:52:43.397804Z" } }, "outputs": [], "source": [ "hfmIn3D_Constant.update({\n", " 'metric':hooke3D_2,\n", " 'stencilGeometry':'CutCube',\n", "})" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:43.399745Z", "iopub.status.busy": "2024-04-30T08:52:43.399633Z", "iopub.status.idle": "2024-04-30T08:52:43.739945Z", "shell.execute_reply": "2024-04-30T08:52:43.739586Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field checkAcuteness defaults to 0\n", "Field order defaults to 1\n", "Field seedRadius defaults to 2\n", "Field factoringPointChoice defaults to Seed\n", "Field exportFactoring defaults to 0\n", "Fast marching solver completed in 0.272964 s.\n" ] } ], "source": [ "hfmOut = hfmIn3D_Constant.Run()" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:43.741632Z", "iopub.status.busy": "2024-04-30T08:52:43.741539Z", "iopub.status.idle": "2024-04-30T08:52:43.743466Z", "shell.execute_reply": "2024-04-30T08:52:43.743178Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.272964\n" ] } ], "source": [ "print(hfmOut['FMCPUTime'])" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:43.744909Z", "iopub.status.busy": "2024-04-30T08:52:43.744819Z", "iopub.status.idle": "2024-04-30T08:52:43.844439Z", "shell.execute_reply": "2024-04-30T08:52:43.844155Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.axis('equal'); plt.title('Slice of arrival times for the olivine model')\n", "plt.contourf(Y[nHalf,:,:],Z[nHalf,:,:],hfmOut['values'][nHalf,:,:]);" ] }, { "cell_type": "code", "execution_count": 71, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:43.846080Z", "iopub.status.busy": "2024-04-30T08:52:43.845961Z", "iopub.status.idle": "2024-04-30T08:52:45.634143Z", "shell.execute_reply": "2024-04-30T08:52:45.633739Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Global error : 0.0004408255515693446\n" ] } ], "source": [ "exact = hfmIn3D_Constant['metric'].norm((X-sx,Y-sy,Z-sz))\n", "error = hfmOut['values']-exact\n", "\n", "assert norm_infinity(error * factoringRegion) < 1e-14\n", "print(\"Global error : \", norm_infinity(error))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly to the two dimensional case, using insufficiently refined stencils breaks the numerical method consistency, and yields inconsistent results." ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:45.635941Z", "iopub.status.busy": "2024-04-30T08:52:45.635813Z", "iopub.status.idle": "2024-04-30T08:52:45.637838Z", "shell.execute_reply": "2024-04-30T08:52:45.637440Z" } }, "outputs": [], "source": [ "hfmIn3D_Constant.update({\n", " 'metric':hooke3D_1,\n", " 'stencilGeometry':'CutCube', # Also fails with 'Cube'\n", "})" ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:45.639436Z", "iopub.status.busy": "2024-04-30T08:52:45.639312Z", "iopub.status.idle": "2024-04-30T08:52:45.968963Z", "shell.execute_reply": "2024-04-30T08:52:45.968612Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field checkAcuteness defaults to 0\n", "Field order defaults to 1\n", "Field seedRadius defaults to 2\n", "Field factoringPointChoice defaults to Seed\n", "Field exportFactoring defaults to 0\n", "Fast marching solver completed in 0.263265 s.\n" ] } ], "source": [ "hfmOut = hfmIn3D_Constant.Run()" ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:45.970686Z", "iopub.status.busy": "2024-04-30T08:52:45.970575Z", "iopub.status.idle": "2024-04-30T08:52:47.810428Z", "shell.execute_reply": "2024-04-30T08:52:47.810088Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Error in factoring region (non-zero due to insufficient refinement): 0.0005878288075511287\n", "Global error : 0.0033546075602274295\n" ] } ], "source": [ "exact = hfmIn3D_Constant['metric'].norm((X-sx,Y-sy,Z-sz))\n", "error = hfmOut['values']-exact\n", "print(\"Error in factoring region (non-zero due to insufficient refinement): \",norm_infinity(error * factoringRegion))\n", "print(\"Global error : \", norm_infinity(error))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.2 Position dependent metric" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:47.812290Z", "iopub.status.busy": "2024-04-30T08:52:47.812152Z", "iopub.status.idle": "2024-04-30T08:52:47.814826Z", "shell.execute_reply": "2024-04-30T08:52:47.814518Z" } }, "outputs": [], "source": [ "hfmIn3D_Varying = Eikonal.dictIn({\n", " 'model':'Seismic3', \n", " 'exportValues':1,\n", " 'seed':[0.,0.,0.5],\n", " 'factoringRadius':7,\n", " 'stencilGeometry':'SpikyCube',\n", " 'order':2\n", "})\n", "\n", "# Define the domain\n", "n=30; \n", "hfmIn3D_Varying.SetRect(sides=[[-1,1],[-1,1],[0,1]],dimx=n)" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:47.816468Z", "iopub.status.busy": "2024-04-30T08:52:47.816346Z", "iopub.status.idle": "2024-04-30T08:52:47.818488Z", "shell.execute_reply": "2024-04-30T08:52:47.818185Z" } }, "outputs": [], "source": [ "X,Y,Z = hfmIn3D_Varying.Grid()" ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:47.820177Z", "iopub.status.busy": "2024-04-30T08:52:47.820043Z", "iopub.status.idle": "2024-04-30T08:52:47.824861Z", "shell.execute_reply": "2024-04-30T08:52:47.824539Z" } }, "outputs": [], "source": [ "rotation1 = lp.rotation( (np.pi/6)*np.sin(2*np.pi*(X+0.4)), (1,0,0))\n", "rotation2 = lp.rotation( (np.pi/6)*np.sin(2*np.pi*(Y-0.7)), (0,1,0))\n", "rotation = lp.dot_AA(rotation1,rotation2)" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:47.826552Z", "iopub.status.busy": "2024-04-30T08:52:47.826449Z", "iopub.status.idle": "2024-04-30T08:52:47.834308Z", "shell.execute_reply": "2024-04-30T08:52:47.834005Z" } }, "outputs": [], "source": [ "hooke3D_3 = mica.rotate(rotation)" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:47.836070Z", "iopub.status.busy": "2024-04-30T08:52:47.835974Z", "iopub.status.idle": "2024-04-30T08:52:47.838012Z", "shell.execute_reply": "2024-04-30T08:52:47.837672Z" } }, "outputs": [], "source": [ "hfmIn3D_Varying['metric'] = hooke3D_3" ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:47.839560Z", "iopub.status.busy": "2024-04-30T08:52:47.839460Z", "iopub.status.idle": "2024-04-30T08:52:48.957497Z", "shell.execute_reply": "2024-04-30T08:52:48.957120Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field checkAcuteness defaults to 0\n", "Field seedRadius defaults to 2\n", "Field factoringPointChoice defaults to Seed\n", "Field exportFactoring defaults to 0\n", "Fast marching solver completed in 1.07488 s.\n" ] } ], "source": [ "hfmOut = hfmIn3D_Varying.Run()" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:48.959400Z", "iopub.status.busy": "2024-04-30T08:52:48.959254Z", "iopub.status.idle": "2024-04-30T08:52:49.034663Z", "shell.execute_reply": "2024-04-30T08:52:49.034365Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nHalf=n//2\n", "plt.axis('equal'); plt.title('Slice of arrival times for a position dependent mica model')\n", "plt.contourf(Y[nHalf,:,:],Z[nHalf,:,:],hfmOut['values'][nHalf,:,:]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.3 Topography\n", "\n", "$$\n", " (x,y,z) \\mapsto (x,y,z+h(x,y,z))\n", "$$" ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:49.036465Z", "iopub.status.busy": "2024-04-30T08:52:49.036324Z", "iopub.status.idle": "2024-04-30T08:52:49.038678Z", "shell.execute_reply": "2024-04-30T08:52:49.038382Z" } }, "outputs": [], "source": [ "def h(x,y,z,alpha=0.3):\n", " return ad.array([x,y,z + alpha*z*np.sin(np.pi*x)*np.cos(np.pi*y)])" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:49.040301Z", "iopub.status.busy": "2024-04-30T08:52:49.040167Z", "iopub.status.idle": "2024-04-30T08:52:49.043778Z", "shell.execute_reply": "2024-04-30T08:52:49.043514Z" } }, "outputs": [], "source": [ "hfmIn3D_Topo = Eikonal.dictIn({\n", " 'order':2,\n", " 'model':'SeismicTopographic3',\n", " 'exportValues':1,\n", " 'seed':[0.,0.,0.5],\n", " 'stencilGeometry':'Cube'\n", "})\n", "\n", "# Define the domain\n", "n=40\n", "hfmIn3D_Topo.SetRect(sides=[[-1,1],[-1,1],[0,1]],dimx=n)\n", "\n", "X0,Y0,Z0 = hfmIn3D_Topo.Grid() # Rectangular coordinates\n", "X,Y,Z = h(X0,Y0,Z0) # Physical coordinates" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:49.045504Z", "iopub.status.busy": "2024-04-30T08:52:49.045399Z", "iopub.status.idle": "2024-04-30T08:52:49.052667Z", "shell.execute_reply": "2024-04-30T08:52:49.052291Z" } }, "outputs": [], "source": [ "X_ad,Y_ad,Z_ad = ad.Dense.register(inputs=(X,Y,Z), shape_bound=X.shape)\n", "Jac = np.moveaxis(h(X_ad,Y_ad,Z_ad).gradient(),0,1)" ] }, { "cell_type": "code", "execution_count": 85, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:49.054462Z", "iopub.status.busy": "2024-04-30T08:52:49.054328Z", "iopub.status.idle": "2024-04-30T08:52:49.057117Z", "shell.execute_reply": "2024-04-30T08:52:49.056767Z" } }, "outputs": [], "source": [ "metric = stishovite.rotate_by(np.pi/6,(1,2,3))\n", "metric = metric.inv_transform(Jac)\n", "hfmIn3D_Topo['metric'] = metric" ] }, { "cell_type": "code", "execution_count": 86, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:49.058902Z", "iopub.status.busy": "2024-04-30T08:52:49.058765Z", "iopub.status.idle": "2024-04-30T08:52:49.061203Z", "shell.execute_reply": "2024-04-30T08:52:49.060874Z" } }, "outputs": [ { "data": { "text/plain": [ "(6, 6, 40, 40, 20)" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "metric.hooke.shape" ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:49.062768Z", "iopub.status.busy": "2024-04-30T08:52:49.062645Z", "iopub.status.idle": "2024-04-30T08:52:50.602661Z", "shell.execute_reply": "2024-04-30T08:52:50.602302Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field checkAcuteness defaults to 0\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 1.40534 s.\n" ] } ], "source": [ "hfmOut = hfmIn3D_Topo.Run()" ] }, { "cell_type": "code", "execution_count": 88, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:50.604671Z", "iopub.status.busy": "2024-04-30T08:52:50.604538Z", "iopub.status.idle": "2024-04-30T08:52:50.677858Z", "shell.execute_reply": "2024-04-30T08:52:50.677485Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nHalf=n//2\n", "plt.axis('equal'); plt.title('Slice of arrival times for a 3D model with topography')\n", "plt.contourf(X[:,nHalf,:],Z[:,nHalf,:],hfmOut['values'][:,nHalf,:]);" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Format de la Cellule Texte Brut", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.8" } }, "nbformat": 4, "nbformat_minor": 2 }