{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The HFM library - A fast marching solver with adaptive stencils\n", "\n", "## Part : Seismology and crystallography\n", "## Chapter : Tilted transversally isotropic metrics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook, we demonstrate anisotropic fast marching with a class of metrics arising in seismic traveltime tomography. \n", "The intended use cases are fairly similar to [metrics defined by a Hooke tensor](Seismic.ipynb), which illustrates a closely related model. Under the hood, however, we use a completely different implementation.\n", "\n", "**Tilted transversally isotropic models.**\n", "We consider eikonal equations of the following form \n", "$$\n", " l(X^2+Y^2,Z^2) + q(X^2+Y^2,Z^2) = 1\n", "$$\n", "where $l$ is a linear form, and $q$ a quadratic form, and where \n", "$$\n", " (X,Y,Z) = A \\nabla u\n", "$$\n", "for some linear transformation $A$. In dimension two, simply ignore the $Y$ coordinate.\n", "\n", "Some algebraic conditions are required on $l$ and $q$ for this equation to make sense. On the other hand, the linear map $A$ is arbitrary.\n", "In the special case where $q=0$, one recovers a Riemannian eikonal equation.\n", "\n", "The numerical scheme is based on rewriting this equation as an extremum of a family of Riemannian eikonal equations, in the form\n", "$$\n", " \\max_{t \\in [0,1]} \\|\\nabla u\\|_{D(t)} = 1, \n", "$$\n", "where $D(t)$ depends on the parameters $l$,$q$ and $A$, in addition to $t$. From this point, one can rely on the Eulerian discretization of [Riemannian eikonal equations](Riemannian.ipynb)." ] }, { "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. Two dimensions](#1.-Two-dimensions)\n", " * [1.1 Induced norm](#1.1-Induced-norm)\n", " * [1.2 Fast marching method](#1.2-Fast-marching-method)\n", " * [1.3 Construction from Thomsen parameters, and comparison with a Hooke tensor norm](#1.3-Construction-from-Thomsen-parameters,-and-comparison-with-a-Hooke-tensor-norm)\n", " * [1.4 Taking into account the topography](#1.4-Taking-into-account-the-topography)\n", " * [2 Three dimensions](#2-Three-dimensions)\n", " * [2.1 Constant metric](#2.1-Constant-metric)\n", " * [2.2 Varying metric](#2.2-Varying-metric)\n", " * [3 Building a model from an array of Thomsen parameters](#3-Building-a-model-from-an-array-of-Thomsen-parameters)\n", " * [3.1 Hexagonal materials and Thomsen's parameter $\\delta$](#3.1-Hexagonal-materials-and-Thomsen's-parameter-$\\delta$)\n", " * [3.2 A numerical example, with the TTI eikonal solver](#3.2-A-numerical-example,-with-the-TTI-eikonal-solver)\n", " * [3.3 Using the Hooke eikonal solver](#3.3-Using-the-Hooke-eikonal-solver)\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": "2024-04-30T08:54:58.292781Z", "iopub.status.busy": "2024-04-30T08:54:58.291991Z", "iopub.status.idle": "2024-04-30T08:54:58.308744Z", "shell.execute_reply": "2024-04-30T08:54:58.308123Z" } }, "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('TTI','FMM'))" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:54:58.312107Z", "iopub.status.busy": "2024-04-30T08:54:58.311834Z", "iopub.status.idle": "2024-04-30T08:54:58.573513Z", "shell.execute_reply": "2024-04-30T08:54:58.573177Z" } }, "outputs": [], "source": [ "from agd import Eikonal\n", "from agd import LinearParallel as lp\n", "from agd.Metrics import Seismic \n", "from agd import AutomaticDifferentiation as ad\n", "from agd.Plotting import savefig; #savefig.dirName = 'Images/TTI'\n", "norm_infinity = ad.Optimization.norm_infinity\n", "mica = Seismic.TTI.mica[0]" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:54:58.575265Z", "iopub.status.busy": "2024-04-30T08:54:58.575151Z", "iopub.status.idle": "2024-04-30T08:54:58.580512Z", "shell.execute_reply": "2024-04-30T08:54:58.580244Z" } }, "outputs": [], "source": [ "import numpy as np; xp=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": "2024-04-30T08:54:58.581880Z", "iopub.status.busy": "2024-04-30T08:54:58.581799Z", "iopub.status.idle": "2024-04-30T08:54:58.583667Z", "shell.execute_reply": "2024-04-30T08:54:58.583443Z" } }, "outputs": [], "source": [ "def ReloadPackages():\n", " from Miscellaneous.rreload import rreload\n", " global Eikonal,ad,lp,Seismic\n", " Eikonal,ad,lp,Seismic = rreload([Eikonal,ad,lp,Seismic],rootdir=\"../..\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 0.1 Optional configuration" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:54:58.585028Z", "iopub.status.busy": "2024-04-30T08:54:58.584946Z", "iopub.status.idle": "2024-04-30T08:54:58.586415Z", "shell.execute_reply": "2024-04-30T08:54:58.586186Z" }, "tags": [ "EikonalGPU_config" ] }, "outputs": [], "source": [ "#xp,plt,Eikonal,mica = map(ad.cupy_friendly,(xp,plt,Eikonal,mica))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Two dimensions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1 Induced norm" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:54:58.587802Z", "iopub.status.busy": "2024-04-30T08:54:58.587710Z", "iopub.status.idle": "2024-04-30T08:54:58.590148Z", "shell.execute_reply": "2024-04-30T08:54:58.589900Z" } }, "outputs": [], "source": [ "n=50\n", "hfmIn = Eikonal.dictIn({\n", " 'model':'TTI2',\n", " 'exportValues':1,\n", " 'seed':[0.,0.],\n", " 'factoringRadius':-1, # Source factorization over the whole domain\n", " 'order':2\n", "})\n", "w=1\n", "hfmIn.SetRect(sides=[[-w,w],[-w,w]],dimx=2*n+1,sampleBoundary=True) # Define the domain\n", "X = hfmIn.Grid() # Horizontal and vertical axis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The metric constructor takes as input the linear form $l$, and the quadratic form $q$, presented as a symmetric matrix (not necessarily positive definite)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:54:58.591489Z", "iopub.status.busy": "2024-04-30T08:54:58.591411Z", "iopub.status.idle": "2024-04-30T08:54:58.593326Z", "shell.execute_reply": "2024-04-30T08:54:58.593070Z" } }, "outputs": [], "source": [ "metric = Seismic.TTI([1.,2.],[[0.,0.2],[0.2,0.]],vdim=2).rotate_by(0.5)\n", "hfmIn['metric'] = metric" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:54:58.594619Z", "iopub.status.busy": "2024-04-30T08:54:58.594540Z", "iopub.status.idle": "2024-04-30T08:54:59.885589Z", "shell.execute_reply": "2024-04-30T08:54:59.885209Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title(\"Level sets of a non-elliptical norm\"); plt.axis('equal')\n", "plt.contour(*X,metric.norm(X));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As described in the introduction, the dual unit ball of a TTI norm is defined by a quartic equation.\n", "We rely on a sequential quadratic programming approach to solve this equation, and check below that it is satisfied in the end." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:54:59.887208Z", "iopub.status.busy": "2024-04-30T08:54:59.887094Z", "iopub.status.idle": "2024-04-30T08:54:59.891746Z", "shell.execute_reply": "2024-04-30T08:54:59.891497Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "v=[0. 1.], grad=[0.25418816 0.77540509], lvl=0.0\n" ] } ], "source": [ "v=xp.array((0.,1.))\n", "grad = metric.gradient(v)\n", "a=lp.transpose(lp.inverse(metric.inverse_transformation))\n", "lvl = metric._dual_level(lp.dot_AV(a,grad))\n", "print(f\"v={v}, grad={grad}, lvl={lvl}\")\n", "assert np.abs(lvl)<1e-6" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.2 Fast marching method" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:54:59.893172Z", "iopub.status.busy": "2024-04-30T08:54:59.893077Z", "iopub.status.idle": "2024-04-30T08:54:59.924998Z", "shell.execute_reply": "2024-04-30T08:54:59.924685Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity 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 0.014501 s.\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:54:59.926718Z", "iopub.status.busy": "2024-04-30T08:54:59.926603Z", "iopub.status.idle": "2024-04-30T08:54:59.985385Z", "shell.execute_reply": "2024-04-30T08:54:59.985094Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.axis('equal')\n", "plt.contourf(*X,hfmOut['values']);" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:54:59.987133Z", "iopub.status.busy": "2024-04-30T08:54:59.987001Z", "iopub.status.idle": "2024-04-30T08:55:01.230971Z", "shell.execute_reply": "2024-04-30T08:55:01.230646Z" } }, "outputs": [], "source": [ "assert norm_infinity(hfmOut['values']-metric.norm(X)) < 0.01" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:01.232710Z", "iopub.status.busy": "2024-04-30T08:55:01.232618Z", "iopub.status.idle": "2024-04-30T08:55:01.234248Z", "shell.execute_reply": "2024-04-30T08:55:01.234022Z" } }, "outputs": [], "source": [ "#plt.axis('equal')\n", "#plt.scatter(*hfmOut['spreadedSeeds'].T)\n", "#plt.scatter(0,0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.3 Construction from Thomsen parameters, and comparison with a Hooke tensor norm\n", "\n", "Some examples of elastic materials, transversally isotropic, are reproduced from (Thomsen, 1986). \n", "The can be handled by TTI norms, as well as by the more general norms defined by a full Hooke tensor." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:01.235612Z", "iopub.status.busy": "2024-04-30T08:55:01.235534Z", "iopub.status.idle": "2024-04-30T08:55:01.237677Z", "shell.execute_reply": "2024-04-30T08:55:01.237450Z" } }, "outputs": [ { "data": { "text/plain": [ "odict_keys(['Taylor sandstone', 'Mesaverde (4903) mudshale', 'Mesaverde (4912) immature sandstone', 'Mesaverde (4946) immature sandstone', 'Mesaverde (5469.5) silty sandstone', 'Mesaverde (5481.3) immature sandstone', 'Mesaverde (5501) clayshale', 'Mesaverde (5555.5) immature sandstone', 'Mesaverde (5566.3) laminated siltstone', 'Mesaverde (5837.5) immature sandstone', 'Mesaverde (5858.6) clayshale', 'Mesaverde (6423.6) calcareous sandstone', 'Mesaverde (6455.1) immature sandstone', 'Mesaverde (6542.6) immature sandstone', 'Mesaverde (6563.7) mudshale', 'Mesaverde (7888.4) sandstone', 'Mesaverde (7939.5) mudshale', 'Mesaverde shale (350)', 'Mesaverde sandstone (1582)', 'Mesaverde shale (1599)', 'Mesaverde sandstone (1958)', 'Mesaverde shale (1968)', 'Mesaverde sandstone (3512)', 'Mesaverde shale (3511)', 'Mesaverde sandstone (3805)', 'Mesaverde shale (3883)', 'Dog Creek shale', 'Wills Point shale - 1', 'Wills Point shale - 2', 'Cotton Valley shale', 'Pierre shale - 1', 'Pierre shale - 2', 'Pierre shale - 3', 'shale (5000) - 1', 'shale (5000) - 2', 'Oil Shale', 'Green River shale - 1', 'Green River shale - 2', 'Berea sandstone - 1', 'Berea sandstone - 2', 'Green River shale - 3', 'Lance sandstone', 'Ft. Union siltstone', 'Timber Mtn tuff', 'Muscovite crystal', 'Quartz crystal (hexag. approx.)', 'Calcite crystal (hexag. approx.)', 'Biotite crystal', 'Apatite crystal', 'Ice I crystal', 'Aluminium-lucite composite', 'Sandstone-shale', 'SS-anisotropic shale', 'Limestone-shale', 'LS-anisotropic shale', 'Anisotropic shale', 'Gas sand-water sand', 'Gypsum-weathered material'])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "th = Seismic.Thomsen\n", "th.ThomsenData.keys()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:01.238997Z", "iopub.status.busy": "2024-04-30T08:55:01.238915Z", "iopub.status.idle": "2024-04-30T08:55:01.240741Z", "shell.execute_reply": "2024-04-30T08:55:01.240501Z" } }, "outputs": [], "source": [ "# Set the center point to exactly (0,0), otherwise hooke norm yields NaN with float32\n", "if Eikonal.dictIn.default_mode=='gpu': X[:,n,n]=0" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:01.242030Z", "iopub.status.busy": "2024-04-30T08:55:01.241947Z", "iopub.status.idle": "2024-04-30T08:55:05.170632Z", "shell.execute_reply": "2024-04-30T08:55:05.170333Z" } }, "outputs": [ { "data": { "image/png": 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JZHJ6q6Ure/fuRWxsLPz9/dGmTRuX31uTnZ2Njh07wmw2o2PHjti8ebMMoyciIiK9kjVwfvrpJ3Tp0gXLli1za/1Tp05h6NCh6NWrF/Ly8vDSSy9h2rRpyM7Otq+Tm5uLlJQUpKam4osvvkBqairGjBmDw4cPy7UbREREpDOKvYvKZDJh8+bNGDFiRJXrvPDCC9i6davDd85MmTIFX3zxhf2DvlJSUmCz2fDRRx/Z1xk8eDCaNGmCDRs2yDZ+IiIi0g9NfQ5Obm4ukpKSHJYNGjQIq1evRnl5OXx9fZGbm4vnnnvOaZ2lS5dWud3S0lKUlpbar9+6dQs//vgjmjVrxg+iIiIi0glJklBSUoKIiAiHL/t1RVOBU1xc7PTdQKGhoaioqMDly5cRHh5e5TquvrunUnp6usMnwBIREZF+nTlzpsZPbddU4ADOX8ZW+QzanctdrVPdTMysWbOQlpZmv261WtGyZUucOXMGQUFB3hi2rpw8K9b3w3xQ0kXtIahu9wWx/k2JvKFf6LdqD0FW/0+H99UeguJsNhsiIyPRqFGjGtfVVOCEhYU5zcRcvHgR9evXt3+DcVXr3D2rcyez2ezym3aDgoIMGTgNG4nz6QD/tnWDf0O1R6GenOL2AID6DVQeCJEG7b9e9ReQDgz7r4IjkYcRz1+V3Hl5iaYCJyEhAdu2bXNYtmvXLsTFxcHX19e+Tk5OjsPrcHbt2lWn778h/fm3rZvaQ1BVZdgQUe1U9TskQvjQbbIGzvXr1/Hdd9/Zr586dQr5+flo2rQpWrZsiVmzZuHcuXNYu3YtgNvvmFq2bBnS0tIwefJk5ObmYvXq1Q7vjnr22WfRu3dvLF68GA899BC2bNmCjz/+GAcOHJBzV0hDjBo3jBoi+TF8xCFr4Bw9ehT9+vWzX698HcyECROQmZmJoqIiFBYW2n/eunVr7NixA8899xyWL1+OiIgIvP322xg1apR9ncTERGzcuBEvv/wy5syZg7Zt2yIrKws9evSQc1dIAxg2RKQWho/+GPLbxG02GywWC6xWqyGfwyw4E6H2EDxmxLhh2BDpk1LRM7vTh4rcj5Z4cv7W1GtwiFwxWtwwbIj0jbM92sDAIc1i2BCRSFz9jjN65MPAIU0yUtwwbIiMi9EjHwYOaYqRwgZg3BCRM0aPdzBwSDOMFDcMGyLyhKu/GbM7qTAQHWHgkCYYJW4YNkREymDgkKoYNkREJAdxvpSIdIdxQ0REcuEMDqnCCHHDsCEiUg8DhxTFsCEiIiXwKSpSDOOGiIiUwhkcUoToccOwISLSFgYOyUr0sAEYN0REWsTAIdmIHjcMGyIi7WLgkCxEjhuGDRGR9jFwyKtEDhuAcUNEpBcMHPIakeOGYaOs02ebqz0Et7VqcUntIRCRCwwc8grGDblDT+HirrruEwOJSB4MHKoThg3dTcSIkZOnx4tBROQeBg7VGuOGGDPKc/eYM4TI6Bg4VCuixg3DpnoMGv1w59+KEUQiY+CQxxg3xsGgERsjiETGwCG3iRo2AOPmTowaulN1jwfGD2kZA4fcImrcMGxuY9RQbdT0uGEAkZoYOFQjxo2YGDUkN87+kJoYOFQtEeOGYcOwIfVV9Thk+JC3MHDIJRHDBjBu3DBqSC8YPuQtDBxywrgRB8OGRMHwIU8xcMiBiHHDsCESF8OHqsLAITvGjf4xbIhuY/gQA4cYNgJg2BC5x9XvCqNHTAwcg2Pc6BvDhqjuGD1iYuAYGONGvxg2RPLiU1z6x8AxIIaNvjFuiNRz9+8fg0e7GDike0aJG4YNkfbw6S3tqqfEnWRkZKB169bw9/dHbGws9u/fX+W6EydOhMlkcrp06tTJvk5mZqbLdW7cuKHE7pCGGCFuTp9tzrgh0pHK39k7L6Q82WdwsrKyMH36dGRkZKBnz55YuXIlhgwZghMnTqBly5ZO67/11ltYtGiR/XpFRQW6dOmCRx55xGG9oKAgFBQUOCzz9/eXZydIc4wSNkQkBj61pTzZA+eNN97ApEmT8Ic//AEAsHTpUvznP//BO++8g/T0dKf1LRYLLBaL/foHH3yAq1ev4vHHH3dYz2QyISwsTN7BkyYxbohI7/jUlvxkfYqqrKwMx44dQ1JSksPypKQkHDx40K1trF69GgMGDEBUVJTD8uvXryMqKgotWrRAcnIy8vLyqtxGaWkpbDabw4X0SfS44XQ2kXHxaS3vkjVwLl++jJs3byI0NNRheWhoKIqLi2u8fVFRET766CP77E+l9u3bIzMzE1u3bsWGDRvg7++Pnj174uTJky63k56ebp8ZslgsiIyMrP1OkWqMEDdERJUYPHWjyLuoTCaTw3VJkpyWuZKZmYnGjRtjxIgRDsvj4+MRHx9vv96zZ09069YNf/3rX/H22287bWfWrFlIS0uzX7fZbIwcHWHYEBHxb4WnZA2c4OBg+Pj4OM3WXLx40WlW526SJOEf//gHUlNT4efnV+269erVw29/+9sqZ3DMZjPMZrNngydNEDlu+MeKiEg+sj5F5efnh9jYWOTk5Dgsz8nJQWJiYrW33bt3L7777jtMmjSpxvuRJAn5+fkIDw+v03hJWxg3RERUW7I/RZWWlobU1FTExcUhISEBq1atQmFhIaZMmQLg9tNH586dw9q1ax1ut3r1avTo0QMxMTFO25w/fz7i4+PRrl072Gw2vP3228jPz8fy5cvl3h1SAMOGiIjqSvbASUlJwZUrV7BgwQIUFRUhJiYGO3bssL8rqqioCIWFhQ63sVqtyM7OxltvveVym9euXcOTTz6J4uJiWCwWdO3aFfv27UP37t3l3h2SGeOGiIi8wSRJkqT2IJRms9lgsVhgtVoRFBSk9nAU98rXyWoPwSVR44ZhQ0RyOD3hBbWHoDhPzt+KfFUDUU0YN0RE5E38sk1SFcOGiIjkwMAh1TBuqC7MhdV/fERtlbYsk2W7RKQsBg6pgnFDd5IrVmrDW2NhKBGpi4FDihMxbhg2NdNSxCjB0/1lEBF5FwOHFCNi2ACMG1eMFjPe4O4xYwgRuYeBQ4oQMW4YNr9i0CjHnWPNCCJi4JACGDdiYtRoV03/NgwgMgIGDsmKcSMWRo0Yqvt3ZPyQKBg4JAuGjVgYNsbB+CFRMHDI6xg3YmDU0N2qekwwfEiLGDjkVYwb/WPYkKcYPqRFDBzyGtHihmFDVDcMH1ITA4e8gnGjXwwbUhrDh5TAwKE6ES1sAOPEDcOGtMbVY5LRQ7XFwKFaEy1uGDZE2sPoodpi4FCtMG70h2FDomD0kDsYOOQxxo2+MGzICBg9dDcGDnlEpLgRPWwAxg0Z292PfwaPsTBwyC0ihQ0gftwwbIiccZbHWBg4VCPGjX4wbIg8w1kecTFwqFqMG/1g3BDVHYNHHAwcqpJIccOwIaLaYPDoFwOHXGLc6APjhkhZDB79YOCQE8aN9jFsiLThzt9Fxo62MHDITqSwARg3RKQszu5oCwOHAIgVNwwbItICzu6oi4FDjBsdYNwQ6Rtnd5THwDE4xo22MWyIxMTZHfkxcAyMcaNtjBsiY2DsyIOBY0AMG+1j3BAZE2PHexg4pFsixg3DhogqMXbqhoFDusS4ISIjYex4joFDuiNa3DBsiMgT/JvhnnpqD4DIE4wbIiJyhyIzOBkZGXj11VdRVFSETp06YenSpejVq5fLdffs2YN+/fo5Lf/mm2/Qvv2vL47Nzs7GnDlz8P3336Nt27Z45ZVXMHLkSNn2gdQlWtgAjBt3NPpBUnsITkqiTGoPgYjcIHvgZGVlYfr06cjIyEDPnj2xcuVKDBkyBCdOnEDLli2rvF1BQQGCgoLs15s3//UEl5ubi5SUFPzlL3/ByJEjsXnzZowZMwYHDhxAjx49ZN0fUp5occOwcaTFiKmOp+NlEBGpwyRJkqx/XXr06IFu3brhnXfesS/r0KEDRowYgfT0dKf1K2dwrl69isaNG7vcZkpKCmw2Gz766CP7ssGDB6NJkybYsGFDjWOy2WywWCywWq0OEWUUfT+ZqfYQ3Ma4EY/egkYpDCHyVMGc59QeguI8OX/L+hqcsrIyHDt2DElJSQ7Lk5KScPDgwWpv27VrV4SHh6N///7YvXu3w89yc3Odtjlo0KAqt1laWgqbzeZwIe1j3Iih0Q+Sw4Vcu/s48bgR1Y2sT1FdvnwZN2/eRGhoqMPy0NBQFBcXu7xNeHg4Vq1ahdjYWJSWluK9995D//79sWfPHvTu3RsAUFxc7NE209PTMX/+fC/sESlFpLgxctiQ91R3PDn7Q+RMkRcZm0yOv3ySJDktqxQdHY3o6Gj79YSEBJw5cwavvfaaPXA83easWbOQlpZmv26z2RAZGenxfpAyGDf6xahRB+OHyJmsgRMcHAwfHx+nmZWLFy86zcBUJz4+HuvWrbNfDwsL82ibZrMZZrPZg5GTGkQKG8BYccOw0a6q/m0YPiQ6WV+D4+fnh9jYWOTk5Dgsz8nJQWJiotvbycvLQ3h4uP16QkKC0zZ37drl0TZJWxg3+sTXh+gXX+tDopP9Kaq0tDSkpqYiLi4OCQkJWLVqFQoLCzFlyhQAt58+OnfuHNauXQsAWLp0KVq1aoVOnTqhrKwM69atQ3Z2NrKzs+3bfPbZZ9G7d28sXrwYDz30ELZs2YKPP/4YBw4ckHt3SAYixY2RwobE5OrflrM9pEeyB05KSgquXLmCBQsWoKioCDExMdixYweioqIAAEVFRSgsLLSvX1ZWhpkzZ+LcuXMICAhAp06dsH37dgwdOtS+TmJiIjZu3IiXX34Zc+bMQdu2bZGVlcXPwNEhxo2+MGyMidFDeiT75+BoET8HRxufg8O40Q+GDbmD0aMsfg5O9edvftkmqYJxow8MG/IEZ3pISxg4pCiGjX4wbsgb7n4cMXhIKQwcUgzjRh8YNiQnzvKQUhg4pAjGjfYxbEgtnOUhOTBwSHaMG+1j3JCWMHjIGxg4JCtR4oZhQ6SeOx+njB1yFwOHZMO40TbGDekRZ3fIXQwckgXjRrsYNiQSzu5QVRg45HWMG+1i3JDIGDt0JwYOeRXjRpsYNmQ0jB1i4JBXiBI2AOOGSDSMHWNi4FCdiRI3ooUNwLghuhtjxzgYOFQnjBttYtgQ1YyxI7Z6ag+A9Itxo02MGyLPNfpB4u+OYDiDQ7XCuNEm/oEmqhvO6oiDgUMeY9xoD8OGyPsqf68YOvrEp6jII4wb7WHcEMmLT1/pE2dwyG0ixI1IYQMwboiUxBkdfWHgkFsYN9rCsCFSD0NHH/gUFdWIcaMtjBsibeDvorYxcKhajBtt4R9UIm3h63O0i09RkUsihA3AuBGZ5ftSr27P2tbs1e2RsTT6QeJTVhrDwCEnjBttMXLYeDtivHlfDCK6G1+boy0MHHLAuNEWo8WNkkFTV+6MlRFkTJzN0QYGDtkxbrTFKHGjp6jxVHX7xvgRGyNHfQwcAiBG3IgSNoD4cSNy1LiL8SM+Ro66GDjEuNEYkeOGYeMeV8eJ0aNPjBz1MHAMjnGjHQwbqk5Vx5Dho32MHHUwcAyMcaMdjBuqLc726AMjR3kMHAMSIWwAxo3WMWzUc/exZ/CQETFwSJcYN9rFsNEeBo82cBZHWQwc0h3GjXYxbvSBwUNGwMAhXREhbhg2pDUMHuVwFkc5DBzSDcaNNjFuxHPnvyljh/SKgUO6wLjRHoaNMXB2x/s4i6OMekrcSUZGBlq3bg1/f3/ExsZi//79Va67adMmDBw4EM2bN0dQUBASEhLwn//8x2GdzMxMmEwmp8uNGzfk3hVSAeNGexg3xmX5vtR+IdIy2QMnKysL06dPx+zZs5GXl4devXphyJAhKCwsdLn+vn37MHDgQOzYsQPHjh1Dv379MGzYMOTl5TmsFxQUhKKiIoeLv7+/3LtDCjIX+jFuNIgnNqrE0CEtk/0pqjfeeAOTJk3CH/7wBwDA0qVL8Z///AfvvPMO0tPTndZfunSpw/WFCxdiy5Yt2LZtG7p27WpfbjKZEBYWJuvYST0ihA0gVtzwREZV4Wt2SItkncEpKyvDsWPHkJSU5LA8KSkJBw8edGsbt27dQklJCZo2beqw/Pr164iKikKLFi2QnJzsNMNzp9LSUthsNocLaRfjRnsYN+QuzuqQVsgaOJcvX8bNmzcRGhrqsDw0NBTFxcVubeP111/HTz/9hDFjxtiXtW/fHpmZmdi6dSs2bNgAf39/9OzZEydPnnS5jfT0dFgsFvslMjKy9jtFsmLcaAtPVlRbfK0OqU2RFxmbTI6vFpckyWmZKxs2bMC8efOQlZWFkJAQ+/L4+Hg8+uij6NKlC3r16oV//etfuPfee/HXv/7V5XZmzZoFq9Vqv5w5c6ZuO0SyECFuGv0gCRU3RN7AxxKpQdbX4AQHB8PHx8dptubixYtOszp3y8rKwqRJk/D+++9jwIAB1a5br149/Pa3v61yBsdsNsNs5vPCWiZK3IiCJyTytsrHFF+jQ0qRdQbHz88PsbGxyMnJcViek5ODxMTEKm+3YcMGTJw4Ef/85z/x4IMP1ng/kiQhPz8f4eHhdR4zKY9xoy2MG5ITn7Yipcj+Lqq0tDSkpqYiLi4OCQkJWLVqFQoLCzFlyhQAt58+OnfuHNauXQvgdtw89thjeOuttxAfH2+f/QkICIDFYgEAzJ8/H/Hx8WjXrh1sNhvefvtt5OfnY/ny5XLvDnkZ40Y7eNIhJVm+L+VsDslK9sBJSUnBlStXsGDBAhQVFSEmJgY7duxAVFQUAKCoqMjhM3FWrlyJiooKPPPMM3jmmWfsyydMmIDMzEwAwLVr1/Dkk0+iuLgYFosFXbt2xb59+9C9e3e5d4e8iHGjHYwbUoNRI4efYqwMkyRJYvyF9oDNZoPFYoHVakVQUJDaw1Fcq3cXqz0Exo2GMG5IC4wUOt4KnII5z3llO3riyflbkXdREd2JcaMdjBsiEhUDhxTFuNEOxg1pCR+P5G0MHFIM40Yb+C4W0iojPC75+hvlMHBIEYwbbTDCCYSICGDgkAIYN9rAuCE9EPlxytkbZTFwSFaMG20Q+aRBROQKA4dkw7jRBsYNERkRA4dkofe4EeVLMxk3pEciPm759JTyZP8kYzIeEeJGBCKeJCr5/fesbNsua99Ctm0TkXIYOORVjBv1iRo2ckaNu/fD+KHa4OyNOhg45DWMG/WJGDdKhY07qhoLw8e7jPS1DSQfBg55BeNGfaLFjZbCpiauxsroIYCzN2pi4FCdMW7Ux7jRnrv3gcFjPIwbdTFwqE4YN+oTKW5ECJuqMHiIlMXAoVpj3KiPcaNfd+4vY+dXorz+hrM36mPgUK0wbtQnStwYLWxcYewQeR8/6I88xrhRH+NGXH7/PcvjonOcvdEGBg55hHGjPsaNMRgxdER4eopxox0MHHIb40Z9IsSNEU/cdcFjRVQ7DBxyC+NGfaLEDXnOCFHI2RvyNgYO1Yhxoz7GDQE8hlrGuNEeBg6RxjFu6E4iHksRZm9Iexg4VC3O3qiLcUOkfZy90SYGDlWJcaMuxg0Zgd5nbxg32sUP+iOXGDfq0nvcMGzIHXqPG9I2zuCQE8aNuhg3RPrA2RttY+CQA8aNuhg3ZBR6n71h3GgfA4fsGDfqYtyQO0T4rirGDSmBgUMAGDdqY9wQ6QPjRj8YOMS4URnjhtzF2Rsi9zFwDI5xoy7GDRmJ3uOGszf6wsAxMMaNuhg35Am9z94wbkhpDBzSJcaNuhg3ZCSMG33iB/0ZEGdu1MW4IU9x9obIc5zBIV1h3KiLcaM8xo26OHujXwwcIoUwbshTjBt1MW70TZHAycjIQOvWreHv74/Y2Fjs37+/2vX37t2L2NhY+Pv7o02bNlixYoXTOtnZ2ejYsSPMZjM6duyIzZs3yzV80gg9z94wbshoGDekNtkDJysrC9OnT8fs2bORl5eHXr16YciQISgsLHS5/qlTpzB06FD06tULeXl5eOmllzBt2jRkZ2fb18nNzUVKSgpSU1PxxRdfIDU1FWPGjMHhw4fl3h1SiZ7jRu8YN+rQ8+wN44a0wCRJkqxnjh49eqBbt25455137Ms6dOiAESNGID093Wn9F154AVu3bsU333xjXzZlyhR88cUXyM3NBQCkpKTAZrPho48+sq8zePBgNGnSBBs2bHDaZmlpKUpLf/0/aJvNhsjISFitVgQFBXllP/Uk+i9vqj0Ej+g9bvQ8e8O4UYee4wbQd+DoKW4K5jyn9hAUZ7PZYLFY3Dp/yzqDU1ZWhmPHjiEpKclheVJSEg4ePOjyNrm5uU7rDxo0CEePHkV5eXm161S1zfT0dFgsFvslMjKytrtECmPckNEwboi8Q9bAuXz5Mm7evInQ0FCH5aGhoSguLnZ5m+LiYpfrV1RU4PLly9WuU9U2Z82aBavVar+cOXOmtrtECmLcqIuzN8pj3KhLT7M3VDNFPgfHZHJ80EiS5LSspvXvXu7JNs1mM8xmff/iGQ3jRl2MG+UxbtTFuBGPrDM4wcHB8PHxcZpZuXjxotMMTKWwsDCX69evXx/NmjWrdp2qtkmkJMYNeYpxoy7GjZhkDRw/Pz/ExsYiJyfHYXlOTg4SExNd3iYhIcFp/V27diEuLg6+vr7VrlPVNklf9Dx7w7ghTzFu1MW4EZfsT1GlpaUhNTUVcXFxSEhIwKpVq1BYWIgpU6YAuP36mHPnzmHt2rUAbr9jatmyZUhLS8PkyZORm5uL1atXO7w76tlnn0Xv3r2xePFiPPTQQ9iyZQs+/vhjHDhwQO7dIZnpOW6IjIZxQ1ome+CkpKTgypUrWLBgAYqKihATE4MdO3YgKioKAFBUVOTwmTitW7fGjh078Nxzz2H58uWIiIjA22+/jVGjRtnXSUxMxMaNG/Hyyy9jzpw5aNu2LbKystCjRw+5d4dkpPe44ewNeUrPszeMG9I62T8HR4s8eR+9iLT4OTiMG3UxbpSn57gB9B04eo+b0pZlAIDTE15QeSTK08zn4BAZAeOGPMW4UY8ocUM1Y+CQ6vQ+e0PkCcYN1RbjxjMMHFKV3uOGszfkCcaNuvQ8e8O48RwDh1TDuCEjYdyoS89xQ7WjyCcZE92NcaM+zt4oQ+9hAzBu1MbZm9rhDA4RkUwYN+pj3BgXA4cUx9kbMgLGjfoYN8bGwCFFMW7ICBg36mPcEAOHFKP3uCFyB+NGfYwbAhg4RG7j7A3VhHGjPsYNVWLgkCI4e0OiY9yoj3FDd2LgkOxEiBsRZ29EOCFrhQjHknGjLsaN9zFwiGogYtxUEuHErKay9i2EOIaMG3UxbuTBwCFZiTB7IzoRTtBqEOW4MW7UxbiRDwOHZCNC3Ig8e3MnUWYilCLKsWLcqItxIy8GDhHZMXRqJsrxYdyoi3EjP34XFclChNkbI6s8ifP7qn4lStgAjBu1MW6UwcAhrxMlbozy9FR17jypGzl2GDfawbghdzFwiMgtRowdkcIGYNyojXGjLAYOeZUoszdUvbtP/CIGD+NGW/QeN6Q8Bg6RC3x6yjMiBQ/DRntEiBvO3iiPgUNew9kbquQqErQePaKFDcC40QrGjToYOESkiKoCQu3wETFsAMaNVjBu1MPAIa/g7A3VVnWBIVf8iBo1lRg32sC4URcDh4g0S/QQkQPjRhsYN+rjJxlTnXH2hkgbGDfawLjRBgYOkQsinCjIWER4zDJuyJsYOFQnnL0hUh/jRhsYN9rC1+AQEemUCGEDMG5IHpzBoVoTffZGlJMHiUmUxyfjhuTCwCGqhignERKLKI9Lxg3JiYFDRKQjjBvtYNxoGwOHqAainFBI/0R5LDJuSAl8kTHViuivv7mbta2ZX8BJqhElbAD9xw3DRj84g0PkJmtbs1AnGtIHkR5zjBtSkqyBc/XqVaSmpsJiscBisSA1NRXXrl2rcv3y8nK88MIL6Ny5Mxo0aICIiAg89thjOH/+vMN6ffv2hclkcriMHTtWzl0hshPphEPaJspjrSTKxLghxckaOOPGjUN+fj527tyJnTt3Ij8/H6mpqVWu//PPP+Pzzz/HnDlz8Pnnn2PTpk349ttvMXz4cKd1J0+ejKKiIvtl5cqVcu4KkQNRTjykXaI8xvQeNgDjRq9kew3ON998g507d+LQoUPo0aMHAOBvf/sbEhISUFBQgOjoaKfbWCwW5OTkOCz761//iu7du6OwsBAtW7a0Lw8MDERYWJhcwyeqUeUJiK/NIW8SJWwAxg2pS7YZnNzcXFgsFnvcAEB8fDwsFgsOHjzo9nasVitMJhMaN27ssHz9+vUIDg5Gp06dMHPmTJSUlFS5jdLSUthsNocLkbfwtTnkLSI9jhg3pDbZZnCKi4sREhLitDwkJATFxcVubePGjRt48cUXMW7cOAQFBdmXjx8/Hq1bt0ZYWBi++uorzJo1C1988YXT7E+l9PR0zJ8/v3Y7QuQmzuhQXTButIVxo38eB868efNqjIUjR44AAEwm5we5JEkul9+tvLwcY8eOxa1bt5CRkeHws8mTJ9v/OyYmBu3atUNcXBw+//xzdOvWzWlbs2bNQlpamv26zWZDZGRkjWMgqo07T1SMHaqJSGEDMG5IOzwOnKlTp9b4jqVWrVrh+PHjuHDhgtPPLl26hNDQ0GpvX15ejjFjxuDUqVP49NNPHWZvXOnWrRt8fX1x8uRJl4FjNpthNov1R4T0gbM6VB3GjfYwbsThceAEBwcjODi4xvUSEhJgtVrx2WefoXv37gCAw4cPw2q1IjExscrbVcbNyZMnsXv3bjRr1qzG+/r6669RXl6O8PBw93eESEGc1aG7MW60h3EjFtleZNyhQwcMHjwYkydPxqFDh3Do0CFMnjwZycnJDu+gat++PTZv3gwAqKiowOjRo3H06FGsX78eN2/eRHFxMYqLi1FWdvuB9/3332PBggU4evQoTp8+jR07duCRRx5B165d0bNnT7l2h8hrKl+ULNoJjtwj2r+9CJ9xAzBuRCTrVzWsX78e06ZNQ1JSEgBg+PDhWLZsmcM6BQUFsFqtAICzZ89i69atAID777/fYb3du3ejb9++8PPzwyeffIK33noL169fR2RkJB588EHMnTsXPj4+cu4OkddxZsdYRAobQIxZG4BxIypZA6dp06ZYt25dtetI0q/fadSqVSuH665ERkZi7969Xhkf1V5JlMlw30clt7tPfgwecYgWNgDjhrSPX7ZJpFEMHjEwbrSLcSM2Bg7VGmdxlMXg0RcRwwZg3JB+MHCIdIrBo12MG20TIW5atbik9hA0j4FDdcJZHO1g8KhP1LABGDdawrhxDwOH6oyRo02uTraMHnkwbLRPhLABGDeeYOCQVzBy9KGqEzHDp3ZEDhuAcaMlDBvPMXDIaxg5+sXZHs+IHjYA40ZLGDe1w8Ahr2LkiKO6k7hR48cIYQMwbrSEcVN7DBzyOkaO+IwUP0aJGkCcsAEYN8TAIZkwcozLnSDQcgQZKWjuxLjRFsZN3TFwSDaMHKpKbSLCW1Fk1ICpDuNGWxg33sHAIVlV/uFk6FBdMUzkwbjRFsaN99RTewBkDCL9ESUSQUmUSajfS8YN3Y0zOKQYzuYQaQPDRnsYN97HGRxSnGj/50ikJyL97jFuqDoMHFINQ4dIWSL9vjFuqCZ8iopUx6euiOQlUtgAjBtyD2dwSDM4o0PkfaL9TjFuyF2cwSHNufMPMmd1iGqPcaNNjBtlMHBI0/j0FZHnGDbaxLBRFgOHdIGzOkTuYdxoE+NGeXwNDukOX6tD5JpovxeMG6oLzuCQbnFWh+g20cIGYNxQ3TFwSAiMHTIqxo12MW7UxcAh4dz9B5/BQyISMWwAxg15DwOHhMfZHRKNiHEjStgAjButYOCQoXB2h/RMxLABGDckDwYOGRpnd0gvGDfax7jRFgYO0f+PszukRaKGDSBO3DBstImBQ1QFBg+pTdS4ESVsAMaNljFwiNzk6mTD6CE5iBo2AOOGlMPAIaoDzvKQN4kcNgDjhpTFwCHyIs7yUG0xbvSDcaMPDBwimTF6qDqihw3AuCF1MHCIVMDoIYaN/jBu9EXWbxO/evUqUlNTYbFYYLFYkJqaimvXrlV7m4kTJ8JkMjlc4uPjHdYpLS3Fn/70JwQHB6NBgwYYPnw4zp49K+OeEMmv8lvS77yQeIzybytS3LRqcYlxo0OyBs64ceOQn5+PnTt3YufOncjPz0dqamqNtxs8eDCKiorslx07djj8fPr06di8eTM2btyIAwcO4Pr160hOTsbNmzfl2hUiVbiKHiOcHEVkpH870eKG9Em2p6i++eYb7Ny5E4cOHUKPHj0AAH/729+QkJCAgoICREdHV3lbs9mMsLAwlz+zWq1YvXo13nvvPQwYMAAAsG7dOkRGRuLjjz/GoEGDvL8zRBpT1YmST3Npj1GiBhArbADGjd7JNoOTm5sLi8VijxsAiI+Ph8ViwcGDB6u97Z49exASEoJ7770XkydPxsWLF+0/O3bsGMrLy5GUlGRfFhERgZiYmCq3W1paCpvN5nAhElFVMz5GOslqgRGPO+OGtEa2GZzi4mKEhIQ4LQ8JCUFxcXGVtxsyZAgeeeQRREVF4dSpU5gzZw4eeOABHDt2DGazGcXFxfDz80OTJk0cbhcaGlrldtPT0zF//vy67RCRzlV3suXMT90ZKWbuxrghLfI4cObNm1djLBw5cgQAYDI5/8JLkuRyeaWUlBT7f8fExCAuLg5RUVHYvn07Hn744SpvV912Z82ahbS0NPt1m82GyMjIaveByEhqOjkzgFwzctRUYtyQVnkcOFOnTsXYsWOrXadVq1Y4fvw4Lly44PSzS5cuITQ01O37Cw8PR1RUFE6ePAkACAsLQ1lZGa5eveowi3Px4kUkJia63IbZbIbZbHb7PonIkbsncpFDiDHjiGFDWudx4AQHByM4OLjG9RISEmC1WvHZZ5+he/fuAIDDhw/DarVWGSKuXLlyBWfOnEF4eDgAIDY2Fr6+vsjJycGYMWMAAEVFRfjqq6+wZMkST3eHiLzI0wjQWhAxYtzDuCE9kO01OB06dMDgwYMxefJkrFy5EgDw5JNPIjk52eEdVO3bt0d6ejpGjhyJ69evY968eRg1ahTCw8Nx+vRpvPTSSwgODsbIkSMBABaLBZMmTcKMGTPQrFkzNG3aFDNnzkTnzp3t76oiIn1gUOgP44b0QtZPMl6/fj2mTZtmf8fT8OHDsWzZMod1CgoKYLVaAQA+Pj748ssvsXbtWly7dg3h4eHo168fsrKy0KhRI/tt3nzzTdSvXx9jxozBL7/8gv79+yMzMxM+Pj5y7g4RkWGJFjYA40Z0JkmStDVHrACbzQaLxQKr1YqgoCC1h6O4Vu8uBgCYC/1UHgkR6QHjRpv29H9N7SEozpPzN7+LysDu/KPF2CGiuzFsSM8YOASAsUNEjhg3pHcMHHLC2CEyNsaNtg0M+6/aQ9AFBg5Vi7FDZBwihg3AuDEqBg65jbFDJC7GjbYxbDzHwKFaYewQiYFho32Mm9ph4FCd3f0HksFDpA+MG+1j3NQeA4e8jrM7RNomatgAjBv6FQOHZMXZHSJtYdzoA+Om7hg4pCgGD5E6GDb6wbjxDgYOqYrBQyQ/xo1+MG68h4FDmsLgIfIekcMGECtuGDbex8AhTWPwEHmOYaMvjBt5MHBIV1z94Wb0EP2KcaMvjBv5MHBI9zjLQyR+2ACMG/IMA4eEw1keMhIjhA3AuCHPMXDIEBg9JCIjxA3DhmqLgUOGxeghvTJC2ACMG6obBg7RHRg9pGVGCRuAcUN1x8AhqkFVJxWGDymFYaNvjBt1MHCIaonhQ3IzUtgAjBvyLgYOkZcxfKgujBY1lUSLG4aN+hg4RAph+FB1GDbiYNxoAwOHSGXVndgYP2IzatRUYtyQnBg4RBrG+BGP0aOmEuOG5MbAIdKpmk6UDCDtYNT8SsSwARg3WsTAIRKUOydVRpA8GDSuiRg3DBvtYuAQGZi7J2KGUNUYMzUTMWwAxo3WMXCIqEaensRFCyJGTO0xbkgtDBwi8jpvBoG3Y4mxohzGDamJgUNEmsYg0R+GDWlBPbUHQERE4mDckFZwBoeIiOpM1LABGDd6xRkcIiKqE8YNaRFncIiIqFYYNqRlss7gXL16FampqbBYLLBYLEhNTcW1a9eqvY3JZHJ5efXVV+3r9O3b1+nnY8eOlXNXiIjoDowb0jpZZ3DGjRuHs2fPYufOnQCAJ598Eqmpqdi2bVuVtykqKnK4/tFHH2HSpEkYNWqUw/LJkydjwYIF9usBAQFeHDkREbkictgAjBuRyBY433zzDXbu3IlDhw6hR48eAIC//e1vSEhIQEFBAaKjo13eLiwszOH6li1b0K9fP7Rp08ZheWBgoNO6REQkH5HjhmEjHtmeosrNzYXFYrHHDQDEx8fDYrHg4MGDbm3jwoUL2L59OyZNmuT0s/Xr1yM4OBidOnXCzJkzUVJSUuV2SktLYbPZHC5G1qrFJYcLEVF1RP9bwbgRk2wzOMXFxQgJCXFaHhISguLiYre28e6776JRo0Z4+OGHHZaPHz8erVu3RlhYGL766ivMmjULX3zxBXJyclxuJz09HfPnz/d8Jwzi7j9cp882V2kkRKQlIkdNJcaNuDwOnHnz5tUYC0eOHAFw+wXDd5MkyeVyV/7xj39g/Pjx8Pf3d1g+efJk+3/HxMSgXbt2iIuLw+eff45u3bo5bWfWrFlIS0uzX7fZbIiMjHRrDEbE4CEixg3pnceBM3Xq1BrfsdSqVSscP34cFy5ccPrZpUuXEBoaWuP97N+/HwUFBcjKyqpx3W7dusHX1xcnT550GThmsxlms7nG7ZBrrv7QMXqIxMSwIVF4HDjBwcEIDg6ucb2EhARYrVZ89tln6N69OwDg8OHDsFqtSExMrPH2q1evRmxsLLp06VLjul9//TXKy8sRHh5e8w6QV3CWh0g8jBsSiWyvwenQoQMGDx6MyZMnY+XKlQBuv008OTnZ4R1U7du3R3p6OkaOHGlfZrPZ8P777+P111932u7333+P9evXY+jQoQgODsaJEycwY8YMdO3aFT179pRrd6gGnOUh0i8jhA3AuDEaWT8HZ/369Zg2bRqSkpIAAMOHD8eyZcsc1ikoKIDVanVYtnHjRkiShN///vdO2/Tz88Mnn3yCt956C9evX0dkZCQefPBBzJ07Fz4+PvLtDHmMszxE2sawIZGZJEmS1B6E0mw2GywWC6xWK4KCgtQejuL6fjJT7SHYMXqIlGeUsAHEjJvRQZ8DAKIjz6s8EuV5cv7md1GRqvjUFpFyjBQ2gNhxQzVj4JDmVPVHmOFDVHtGihuGDQEMHNIRzvYQec5IYQMwbuhXDBzSNc72ELnGsBED46b2GDgkJM72kBEZLWoqMW7IFQYOGQZne0hURg0bQMy4Ydh4BwOHDK+6kwPjh7SMYSMexo33MHCIqsFZH9IaI0dNJcYNuYOBQ1QLnPUhpTFsxA0bgHEjBwYOkZfVdCJiAJG7GDW/EjVuGDbyYeAQKYyzP1QdRo0zxg3VBgOHSEPcObkxgsTCoKmaqGEDMG6UwMAh0hlGkL4xaNwjatwwbJTDwCESkLsnUYaQfBgytSNq2ACMG6UxcIgMzNOTMIPIGUPGexg35E0MHCJyW11P5noJJEaLskQOG4BxoxYGDhEphuFAdxM5bhg26mLgEBGR4kQOG4BxowX11B4AEREZC+OGlMAZHCIiUgTDhpTEwCEiIlmJHjYA40aL+BQVERHJhnFDauEMDhEReR3DhtTGGRwiIvIqxg1pAWdwiIjIK4wQNgDjRi8YOEREVCcMG9IiBg4REdWKUcIGYNzoEV+DQ0REHmPckNZxBseAXP1hyilur8JIiEhvGDakFwwcAsDoIaLqGSlsAMaNCBg4VCVGDxEZLWwAxo0oGDjkEUYPkTEwbEjvGDhUZ1X9IWT4EOmPEcMGYNyIiIFDsuFsD5F+MGxINAwcUhRne4i0xahhAzBuRCfr5+C88sorSExMRGBgIBo3buzWbSRJwrx58xAREYGAgAD07dsXX3/9tcM6paWl+NOf/oTg4GA0aNAAw4cPx9mzZ2XYA1LKwLD/urwQkTyM/Ds2Ouhzxo0ByBo4ZWVleOSRR/D000+7fZslS5bgjTfewLJly3DkyBGEhYVh4MCBKCkpsa8zffp0bN68GRs3bsSBAwdw/fp1JCcn4+bNm3LsBqmI4UPkXUb/HWLYGIdJkiRJ7jvJzMzE9OnTce3atWrXkyQJERERmD59Ol544QUAt2drQkNDsXjxYjz11FOwWq1o3rw53nvvPaSkpAAAzp8/j8jISOzYsQODBg2qcTw2mw0WiwVWqxVBQUF13j+9eeXrZLWHICs+3UXkyMhBcyfR4iY68rzaQ1CcJ+dvTb0G59SpUyguLkZSUpJ9mdlsRp8+fXDw4EE89dRTOHbsGMrLyx3WiYiIQExMDA4ePOgycEpLS1FaWmq/brVaAdw+UEZ043q52kOQVa+GX7pcvvvCvQqPhEhd/UK/BQDcuK7yQFQ2otEXAIDrJTWsqDNGPIdV7rM7czOaCpzi4mIAQGhoqMPy0NBQ/PDDD/Z1/Pz80KRJE6d1Km9/t/T0dMyfP99peWRkpDeGTbqxS+0BECnq/9QegEb8v2oPQDYWtQegmpKSElgs1e+/x4Ezb948l7FwpyNHjiAuLs7TTduZTCaH65IkOS27W3XrzJo1C2lpafbrt27dwo8//ohmzZrVuF0R2Ww2REZG4syZM4Z8ik5pPN7K4vFWHo+5sox8vCVJQklJCSIiImpc1+PAmTp1KsaOHVvtOq1atfJ0swCAsLAwALdnacLDw+3LL168aJ/VCQsLQ1lZGa5eveowi3Px4kUkJia63K7ZbIbZbHZY5u67ukQWFBRkuF8ONfF4K4vHW3k85soy6vGuaeamkseBExwcjODgYI8H5I7WrVsjLCwMOTk56Nq1K4Db78Tau3cvFi9eDACIjY2Fr68vcnJyMGbMGABAUVERvvrqKyxZskSWcREREZG+yPoanMLCQvz4448oLCzEzZs3kZ+fDwD4zW9+g4YNGwIA2rdvj/T0dIwcORImkwnTp0/HwoUL0a5dO7Rr1w4LFy5EYGAgxo0bB+B2uU2aNAkzZsxAs2bN0LRpU8ycOROdO3fGgAED5NwdIiIi0glZA+fPf/4z3n33Xfv1ylmZ3bt3o2/fvgCAgoIC+7uaAOD555/HL7/8gj/+8Y+4evUqevTogV27dqFRo0b2dd58803Ur18fY8aMwS+//IL+/fsjMzMTPj4+cu6OMMxmM+bOnev0tB3Jg8dbWTzeyuMxVxaPt3sU+RwcIiIiIiXJ+knGRERERGpg4BAREZFwGDhEREQkHAYOERERCYeBQ0RERMJh4BjAK6+8gsTERAQGBrr9Cc6SJGHevHmIiIhAQEAA+vbti6+//lregQrk6tWrSE1NhcVigcViQWpqKq5du1btbSZOnAiTyeRwiY+PV2bAOpORkYHWrVvD398fsbGx2L9/f7Xr7927F7GxsfD390ebNm2wYsUKhUYqDk+O+Z49e5weyyaTCf/9L7/V3B379u3DsGHDEBERAZPJhA8++KDG2/Ax7oyBYwBlZWV45JFH8PTTT7t9myVLluCNN97AsmXLcOTIEYSFhWHgwIEoKRHs63hlMm7cOOTn52Pnzp3YuXMn8vPzkZqaWuPtBg8ejKKiIvtlx44dCoxWX7KysjB9+nTMnj0beXl56NWrF4YMGYLCwkKX6586dQpDhw5Fr169kJeXh5deegnTpk1Ddna2wiPXL0+PeaWCggKHx3O7du0UGrG+/fTTT+jSpQuWLVvm1vp8jFdBIsNYs2aNZLFYalzv1q1bUlhYmLRo0SL7shs3bkgWi0VasWKFjCMUw4kTJyQA0qFDh+zLcnNzJQDSf//73ypvN2HCBOmhhx5SYIT61r17d2nKlCkOy9q3by+9+OKLLtd//vnnpfbt2zsse+qpp6T4+HjZxigaT4/57t27JQDS1atXFRid2ABImzdvrnYdPsZd4wwOOTl16hSKi4uRlJRkX2Y2m9GnTx8cPHhQxZHpQ25uLiwWC3r06GFfFh8fD4vFUuPx27NnD0JCQnDvvfdi8uTJuHjxotzD1ZWysjIcO3bM4bEJAElJSVUe29zcXKf1Bw0ahKNHj6K8vFy2sYqiNse8UteuXREeHo7+/ftj9+7dcg7T0PgYd42BQ06Ki4sBwP4N7pVCQ0PtP6OqFRcXIyQkxGl5SEhItcdvyJAhWL9+PT799FO8/vrrOHLkCB544AGUlpbKOVxduXz5Mm7evOnRY7O4uNjl+hUVFbh8+bJsYxVFbY55eHg4Vq1ahezsbGzatAnR0dHo378/9u3bp8SQDYePcddk/S4qks+8efMwf/78atc5cuQI4uLian0fJpPJ4bokSU7LjMTdYw44Hzug5uOXkpJi/++YmBjExcUhKioK27dvx8MPP1zLUYvJ08emq/VdLaeqeXLMo6OjER0dbb+ekJCAM2fO4LXXXkPv3r1lHadR8THujIGjU1OnTsXYsWOrXadVq1a12nZYWBiA2/9XEB4ebl9+8eJFp/9LMBJ3j/nx48dx4cIFp59dunTJo+MXHh6OqKgonDx50uOxiio4OBg+Pj5OMwfVPTbDwsJcrl+/fn00a9ZMtrGKojbH3JX4+HisW7fO28Mj8DFeFQaOTgUHByM4OFiWbbdu3RphYWHIycmxfwN8WVkZ9u7di8WLF8tyn3rg7jFPSEiA1WrFZ599hu7duwMADh8+DKvVisTERLfv78qVKzhz5oxDZBqdn58fYmNjkZOTg5EjR9qX5+Tk4KGHHnJ5m4SEBGzbts1h2a5duxAXFwdfX19ZxyuC2hxzV/Ly8vhYlgkf41VQ8xXOpIwffvhBysvLk+bPny81bNhQysvLk/Ly8qSSkhL7OtHR0dKmTZvs1xctWiRZLBZp06ZN0pdffin9/ve/l8LDwyWbzabGLujO4MGDpfvuu0/Kzc2VcnNzpc6dO0vJyckO69x5zEtKSqQZM2ZIBw8elE6dOiXt3r1bSkhIkO655x4e87ts3LhR8vX1lVavXi2dOHFCmj59utSgQQPp9OnTkiRJ0osvviilpqba1//f//4nBQYGSs8995x04sQJafXq1ZKvr6/073//W61d0B1Pj/mbb74pbd68Wfr222+lr776SnrxxRclAFJ2drZau6ArJSUl9r/TAKQ33nhDysvLk3744QdJkvgYdxcDxwAmTJggAXC67N69274OAGnNmjX267du3ZLmzp0rhYWFSWazWerdu7f05ZdfKj94nbpy5Yo0fvx4qVGjRlKjRo2k8ePHO71l9s5j/vPPP0tJSUlS8+bNJV9fX6lly5bShAkTpMLCQuUHrwPLly+XoqKiJD8/P6lbt27S3r177T+bMGGC1KdPH4f19+zZI3Xt2lXy8/OTWrVqJb3zzjsKj1j/PDnmixcvltq2bSv5+/tLTZo0kX73u99J27dvV2HU+lT5Nvu7LxMmTJAkiY9xd5kk6f9/JRIRERGRIPg2cSIiIhIOA4eIiIiEw8AhIiIi4TBwiIiISDgMHCIiIhIOA4eIiIiEw8AhIiIi4TBwiIiISDgMHCIiIhIOA4eIiIiEw8AhIiIi4fx/VV7bYKW4LzgAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "value = th.ThomsenData['Muscovite crystal']\n", "tti = Seismic.TTI.from_ThomsenElastic(value)[0].extract_xz().rotate_by(0.3)\n", "hooke = Seismic.Hooke.from_ThomsenElastic(value)[0].extract_xz().rotate_by(0.3)\n", "\n", "assert np.allclose(tti.norm(X),hooke.norm(X))\n", "plt.title(\"Unit ball for a Thomsen norm\"); plt.axis('equal')\n", "plt.contourf(*X,hooke.norm(X));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The TTI norm and Hooke tensor norm defined from these models coincide up to machine precision." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:05.172414Z", "iopub.status.busy": "2024-04-30T08:55:05.172307Z", "iopub.status.idle": "2024-04-30T08:55:12.735040Z", "shell.execute_reply": "2024-04-30T08:55:12.734750Z" } }, "outputs": [], "source": [ "tested = list(th.ThomsenData.items())[:3]\n", "for key,value in tested:\n", " value = xp.asarray(value)\n", " tti = Seismic.TTI.from_ThomsenElastic(value)[0].extract_xz()\n", " hooke = Seismic.Hooke.from_ThomsenElastic(value)[0].extract_xz()\n", " \n", " assert np.allclose(tti.norm(X),hooke.norm(X),atol=1e-5) # atol for float32" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.4 Taking into account the topography\n", "\n", "We reproduce a numerical experiment presented in the notebook [Seismic.ipynb], where the metric is constant, but the domain is a diffeomorphically mapped rectangle." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:12.736705Z", "iopub.status.busy": "2024-04-30T08:55:12.736611Z", "iopub.status.idle": "2024-04-30T08:55:12.738521Z", "shell.execute_reply": "2024-04-30T08:55:12.738303Z" } }, "outputs": [], "source": [ "def h(x,z,alpha=0.5): return ad.array([x, z + alpha*z*np.sin(np.pi*x)])" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:12.739955Z", "iopub.status.busy": "2024-04-30T08:55:12.739872Z", "iopub.status.idle": "2024-04-30T08:55:12.803484Z", "shell.execute_reply": "2024-04-30T08:55:12.803185Z" } }, "outputs": [ { "data": { "image/png": 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oc02adA1SO5KwYY6uBnqNaYRGA1G/p3Byd4rakWyeFCNCCPEvSgpLWTv7KKZiM4F1PegypL50WBX/qWY9L9rcWQuArUtOcj6tUN1ANk6KESGE+AcWi3Ld/3xqIa5eDtzxcFN0ennZFFenzZ21CKzrQWmJmfVfHsdcZlE7ks2SvyohhPgHf6w6Q9zxLPQGLXc+0gxnd6PakYQd0eq09BrTGAdnPWnn8vjjQp8j8XdSjAghxBWc3J3Cwd/iAOjxQAR+oW4qJxL2yM3bkR6jlAX1Dm2I59yxTJUT2SYpRoQQ4i/SzuWyeVEUAK3uCKNemwCVEwl7VruFH027BQOw8esTFOSUqJzI9kgxIoQQlyjIKWHt7KOYSy3UaupDu/61//skIf5Dh0F18Al2pSivlA1fncBqkeniLyXFiBBCoMyuWlpQym+fH6HgfAleNZy5bUxjNFoZOSOun96g4/ZxjdEbtSREZXPgt3NqR7IpUowIIQRgLbWQ+sYf3JJdjLOznjsfaYaDk17tWKIK8arhQuch9QHY/WMMKWdzVE5kO6QYEUIIIPFkdvnt7iMb4hngrGIaUVVFdAikXht/rBYrv807TklhqdqRbIIUI0KIaq+kqIwtS6LK74c29lExjajKNBoNXUc0xN3XkbysYjYvOonVKv1HpBgRQlR7O787TUG2Se0YoppwcNLTe2wTtFoNZw6kcWJHktqRVCfFiBCiWos9kkHkrmSQfqriJgoId6ft3cpIrR3fniYrqUDlROqqcDGybds2+vXrR82aNdFoNKxatepfj//+++/p1asXfn5+uLu70759e9atW3eteYUQotIU55eWzyfSrJssfidurpa3hRLayJuyUgvr5h2jzGRWO5JqKlyMFBQU0Lx5cz799NOrOn7btm306tWLtWvXsn//frp3706/fv04ePBghcMKIURl2rbsJIW5JrxqONPmrnC144hqRqPV0HN0I5zcjWQlFbBzRbTakVRT4XFrffr0oU+fPld9/IwZMy67//bbb7N69Wp++uknWrZsWdGnF0KISnF6Xyqn96WVvyHoDTq1I4lqyNndyG2jI/jpk8Mc25ZIcIQXdVr6qx3rprvpfUYsFgt5eXl4e3v/4zElJSXk5uZetgkhRGUpyClh29JTALS+I4yAWu4qJxLVWWgjH1r2DgVg8zdR5GYWqZzo5rvpxciHH35IQUEBgwcP/sdjpk2bhoeHR/kWEhJyExMKIaoyq9XKlsUnKS4oxTfElTZ31lI7khC0HVAb/1rulBSWsWH+CSxmi9qRbqqbWowsXbqUqVOnsnz5cvz9/7kZasqUKeTk5JRv8fHxNzGlEKIqO/lHCrFHMtDqNNw2uhE6vQwqFOrT6bT0HtsYo6OO5DM57F0Tq3akm+qm/RUuX76csWPH8u2333Lbbbf967EODg64u7tftgkhxPXKyypm+3Ll8syt/cLxCXJVOZEQF3n4OdHt/oYA7PslloRLZgWu6m5KMbJ06VJGjx7NkiVL6Nu37814SiGEuIzVamXTwkhMxWYCwt1p2StU7UhC/E29NgFEdAwEK2yYf5yi/OoxGV+Fi5H8/HwOHTrEoUOHAIiJieHQoUPExcUByiWWUaNGlR+/dOlSRo0axYcffki7du1ISUkhJSWFnBxZIEgIcfMc35ZIQlQ2eoOW20Y3QquTyzPCNnUeXB+vGs4U5JjY9HVktZguvsJ/jfv27aNly5blw3InT55My5YteeWVVwBITk4uL0wA5syZQ1lZGZMmTSIwMLB8e+KJJyrpRxBCiH+Xk17IzpXKHA7tBtaRRfCETTM46Og9rgk6vZbYo5kc2ZSgdqQbrsLzjHTr1u1fq7QFCxZcdn/Lli0VfQohhKg0FouVjV9HUmayENTAk2bdgtWOJMR/8g12peO9ddm27BS7vo+mZj1P/ELd1I51w0g7pRCiSju8MZ7k6BwMjjp6jIxAo5VFaIR9aNI1iPDmvljKLKz/fD/F2blV9pKNFCNCiCorK6mA3avPAtDpvnq4+zqpnEiIq6fRaOgxKgJ3dw0tv3+EmPZtsRZVzQnRpBgRQlRJZrOFDQtOYC6zENbEh4gOgWpHEqLCHF0MdB/ZsPx+wqmqOdxXihEhRJV04NdzpMfl4eCsp/v9DdFo5PKMsE8163qW396+7BSlJVVvdV8pRoQQVU56XB77Lsxg2WVYfVw8HdQNJEQlyc0s5o/VZ9SOUemkGBFCVCnmUuXyjMVipU4rP+q1CVA7khCV6sjmBJLPVK25uqQYEUJUKXt+PktWUgFObga6Dmsgl2dEldLglgCwwuZvIikrrTqXa6QYEUJUGclncjj4mzLpYrcRDXFyM6qcSIjK1e6eOji5G8lOKWTf2li141QaKUaEEFVCaYmZjQtOYLVCg3Y1qN3CT+1IQlQ6R2cDXYfVB+DAujjS4/NUTlQ5pBgRQlQJv686Q056ES6eDnQeXE/tOFWKpbiYgp27yu+f//4H8jZvpujYcUpTU7GWlamYrvqp09KfOq38sFqUxR/NZovaka5bhaeDF0IIW5MQlcXRzcr6HT1GNcTB2aByIvtniosjf9t28rdtpXDPXgotVvh4AQCpb7xJrqnk4sEaDTpvb/S+vuj9/JTtz9v+fpft1zrLukCVocvQBiREZZMRn8+h9XG0vqOW2pGuixQjQgi7ZioqY+PCSAAadwkitJGPyonsk6WkhMI9e8nfvo2CrdswnTt32eP64JDy266dOmFISaYsPZ2yzEywWDBnZmLOzKTk5Ml/fR6ts3N5YaLzU4qUUh9/QJmUzmo2I29N/83Z3UinwfXYuCCSvT/HUruFH141XNSOdc3kf1wIYdd2rDhNflYJ7r6OdLinjtpx7IopPp78bdso2Ladgt27sRYXX3xQr8e5VStcu3TGpXMXzHVqw/ZjAATN/BgXnQ5QigdzdrZSmGRkUJaWfvF2+uW3rUVFWAoLMZ07d1mxU6wzQr+3AYi5ZxBBYx7AY8AAtEbpgPxvGrStwem9qcQdz2LTwigGPtMKrZ2uvSTFiBDCbsUezSByZzJooOcDERgd5SXt31hKSijcu4+C7dvI37YdU0zMZY/r/f1x7doFl86dcenQAZ2ra/ljBeYrDyPV6HTKZRhf3399bqvViqWg4GKBkp6O+UKRkpeeWX5caVw8KS+/QsYnM/EePRrPIYMvyyEu0mg0dBvRkKWv7SblbA5HtyTQvEfIf59og+QvVwhhl4rzS9n8TRQAzXuGULOel8qJbJMpIeHy1o9LF1rT6XBu2RKXrl1w7dIFh/r1b9i8LBqNBp2rKzpXVxzCwy97zNVUBq+sA8Dv6aco+noBZamppL3/Phlz5uA1fBjeI0ei95FLcH/l5q20CG5deoo/Vp0hvJmvXS4IKcWIEMIubVt+isJcE141nGnXv7bacWxK/u9/ULx9D/nbt2M6e/ayx/R+fkrx0bkLLh3ao3NzUynllXnffz9O9w8n56efyZw3D1NMDJmfzyHrqwV4DhqE95gHMQYHqx3TpjTuHMTpfWkknT7P5kVR9H+ihd1N9ifFiBDC7kTvT+P03lQ0Wg09H2iE3qhTO5LqSpOTy28nTJyI1nThzUinw6llC1y7dMW1S2ccGtj+rLQaoxHPQffgMfBu8jZuJHPuFxQfPUr2kiVkL1+Oe58++Dw0DscGDdSOahM0Wg3d72/Isjf3kBCVTeSuZBp1rKl2rAqRYkQIYVcKc01sXaKM2Gh9RxgB4e4qJ1KX1Wwme/FiUmbNAKUPKHpfX9zadcW1y4XWD3f7/DfSaLW49+qF2223Ubh7D5lffEHBzp3k/vwzuT//jEvXLvg+9BDObdqoHVV1ngHOtO1Xm13fR7NzRTRhjX3saoFIKUaEEHbDYrGw8esjFOUX4hPsSZs7a6kdSVXFJ0+R/PLLFB85gtVoLd9f57d16PX2O8zzrzQaDS7t2uLSri1Fx4+TOW8eeet+o2CrMgzZqVUrfB4ah2vXrmi01Xcuz+Y9g4nen0rauTy2Lj1JnwlNbb4V7E/V939NCGF3InfFc2rHVErOz6Tb8Dro9NXzJcxSUkLajBnEDBpE8ZEjaF1cCHjhhfLH7eUN6Fo4NW5M8EcfUWftGjwHD0ZjMFB04AAJj0wkZsAAclavxlpaqnZMVWh1WnqMikCr0xBzOIPo/WlqR7pq1fMvWQhhd4ryTPy+Mrr8vm9Q9RzuWbBnDzED7ibz8zlQVoZrz57UXrsGr/vuVTvaTWWsVYvA11+jzsYN+Iwbi9bFhZLT0ST973mib7+drG8WYbl05FA14RPkSus7wgDYvvwURfkmlRNdHSlGhBB2Yfu3pykurL5roJhzc0l++RXiRj2AKTYWnZ8vQR9/TPCnMzEEBKgdTzUGf3/8n3mGups34Td5MjofH8qSkkl96y2ie/QkfdYszDk5ase8qVr3qYV3TReK8krZvvy02nGuihQjQgibF3s0Qxk9U3WvPvwjq9VK7q/rONO3L+e/+w4Az8GDqbNmDe63967Sl2QqQufuju/DD1F34wZqvPoKhuBgzNnZZHwyk+g7+6od76bS6ZXLNRoNnN6bSuyRDLUj/ScpRoQQNs1UXFY+eqZJtyCV09xcpampJDz6GIlPPok5PQNjrVqEfbOQwNdfs9sRMjea1tERr2HDqPPrL9T84AMcGjbEWlhY/njOr7+qmO7mCajlTvPbQgHYsuQkJUW23aooxYgQwqb9seos+dnK2jO33Bn+3ydUAVaLheylSzl7Z1/yN24EvR6fRyYQvnoVzrfconY8u6DR6/G4qy/hP3xP8Geflu9PnvICqe+8i7XMtt+cK8Ot/cLx8HOi4HwJu76P/u8TVCTFiBDCZiWfyeHo1gQAuo1oiKEaTG5WEh3NuftHkvLa61gKCnBs3ozwlSvxf+IJtA72M2+ErdBoNLh26HDZvqwFC4gbM1ZZcbgKMxh1dB/ZEIAT25NIOJmtcqJ/JsWIEMImmUstbP4mEqzQsH0NQiK81Y50Q1lMJtJnfsrZgfdQdOAAWmdnAl58kVpLluDYoL7a8aqMmh+8j9bZmcI9e4gZdC9FR46oHemGCqrvReMuyuXNzd9EUlpy5QUP1SbFiBDCJu3/NZbslEKc3Ax0vLee2nFuqMIDB4gZeA8Zn30GpaW4du1K7Z9/wnvk/Wh0Vb816GZy79mTWt99izE8nLKUFM6NuJ/sCx2Dq6oOA+vg6uVAbkYxu388+98nqECKESGEzclMymf/r+cA6DykPo4uBpUT3Rjm/HySX3uNc8NHYDpzBp2PD0HTPyT489kYatrX2iL2xKFOHWp99y2ut/XEWlpKysuvkPzyK1hM9jEnR0UZnfR0G6Fcrjm8KZ6Us7Y31FmKESGETbFYrGz+JgqL2UqtZr7Ube2vdqQbIm/jRs72vYvzS5cB4DHoHuqs+Rn3O++U4bo3gc7VleBPPsHvqadAo+H8d99x7v6RlKakqB3thghr4kODtjXACpsWRmIutagd6TJSjAghbMrRLQmkxuRicNTRdVj9KvnGnPjMsyRMepSy1FQMoaGELviKmm+9hc7TU+1o1YpGq8V3/MOEzJ2L1sOD4iNHiLlnEAW796gd7YbodF89nNwMZKcUsu+XWLXjXEaKESGEzcjNLOKP1co17Q731MXVy1HlRDdG/saNoNPh89BD1P5xNS7t2qkdqVpz7dyJ8JUrcIiIwJyVRdyYMWQuWIDVav3vk+2Io6uBLkMbAHDg13NkJOSpnOgiKUaEEDbBarWydfFJykrMBNb1oHGnqtVnImvBgvLbDo0aEb7iO/yfnozWsWoWXPbGGBxMrSWLce/fD8xm0t55l6Snn8FyyYRpVUHd1v7UbumHxWJl08IoLGbbuFwjxYgQwiac2pNK3IksdHot3e9viEZbNS7PWK1WUt9/n/SPPynfF/b1AhwjIlRMJa5E6+REzXffJeDFF0GvJ3ftWmKHDMV07pza0SpVl6H1cXDWkx6Xx6EN8WrHAa6hGNm2bRv9+vWjZs2aaDQaVq1a9Z/nbN26ldatW+Po6Ejt2rX5/PPPryWrEKKKKsozseNbZUGvNn1r4VXDReVElcNaVkbyiy+R9eX8y/Zr9HqVEon/otFo8B55P2ELvkLn60vJ6dPE3HsfeVu2qB2t0rh4OJQPl9/zUwzZKQUqJ7qGYqSgoIDmzZvz6aef/vfBQExMDHfeeSedO3fm4MGDvPDCCzz++OOsXLmywmGFEFXT9m9PU1xQik+QKy17h6odp1JYSkpIeOJJcr7/HrRaakydqnYkUQHObdoQvnIlTi1aYMnLI+GRiaR/9hlWi21c1rheDdvXILSRN+YyC5sXRWG1qNs/psLFSJ8+fXjzzTe55557rur4zz//nNDQUGbMmEFERATjxo1jzJgxfPDBBxUOW5msViulxcUUnM+vcp2UhLAnl67I231kQ3Q6+796bM7LI37cQ+Rv3IjGaCR45id4DOivdixRQYYAf8IWfo3nsKFgtZIx81MSJk7CnJurdrTrptFo6DqiAXqjluToHA5tjFf1vfCG/9X//vvv9O7d+7J9t99+O/v27aO0tPSK55SUlJCbm3vZVtlKi4v55IF7+Xz8UFLO2v7yykJURZeuyNusZwgBtex/JdqyzEzOPfAAhXv3onVxIWTeF7j17Kl2LHGNNEYjga++SuBbb6ExGsnfsoXY+wZTfOqU2tGum7uPE2371wZg18pospLVu1xzw4uRlJQUAgICLtsXEBBAWVkZGRlXLgKmTZuGh4dH+RYSElLpuS6du2DrklM206NYiOrk0hV52/arrXac62ZKSOTc8BGUnIhE5+ND2DcLcbn1VrVjiUrgOegewpYsQV8zENO5c8QOHUbuL7+oHeu6Nep4cdRa9L401XLclPbQv05a9GdT0D9NZjRlyhRycnLKt/j4G9vbNyMhn4Pr427ocwghLve3FXkd7HsNlpLTpzk3fDimc+cw1KxJrcWLcGzUSO1YohI5NWlM+IoVOLdvh7WwkMSnJpP63vtYzba5+NzVuHTUmpr9tW54MVKjRg1S/jK9blpaGnq9Hh8fnyue4+DggLu7+2Xbjbb351ib6FEsRHVQ1VbkLTx4kNj7R1KWloZDvbqELV2CsVYttWOJG0Dv7U3oF1/gM24sAFnz55MwcZLKqSqHmrMd3/BipH379qxfv/6yfb/99htt2rTBYLCNxa9CIrxspkexENXBviq0Im/+9h3EjRmLJScHp+bNCfvmGwx/uTQtqhaNXo//M88QNOMjNM7OFO7dq3Yku1fhYiQ/P59Dhw5x6NAhQBm6e+jQIeLilMscU6ZMYdSoUeXHT5gwgXPnzjF58mQiIyOZP38+X375Jc8880zl/ASVoPOQ+hgcdCRH53B0a6LacYSo0jIT8zlQRVbkzVmzhviJE7EWFeHSuTOhX82X9WWqEfc77iD82+UYQy9e3ig+elTFRParwsXIvn37aNmyJS1btgRg8uTJtGzZkldeeQWA5OTk8sIEIDw8nLVr17JlyxZatGjBG2+8wSeffMKgQYMq6Ue4fm5ejrQfWAeA31edITejSOVEQlRNFouVzYuqxoq8WUuWkPTMs1BaivuddxLy2adonZ3VjiVuMoe6dQlb9E35/fhJj1J07LiKiexThacB7Nat27+ORV5wyfoLf+ratSsHDhyo6FPdVE26BBG9P42k0+fZsjiKfo+3qJKrhQqhpqqwIq/VaiXjs1lkXJj40Wv4cAJeehGN1v7nRxHXRuvqWn7bkp9P3NixypT/DRuqmMq+yF/PBRqthu73N0Rn0BIfmU3U78lqRxKiSqkKK/JaLRZS33yrvBDxffRRAl5+SQoRUc6pWTMsOTnEPTimSsxFcrPIX9AlPAOcubVfOAA7V0RTkFOiciIhqoaqsCKv1WQi6dnnyF68GDQaAl5+Cb9HJ9ll6464cYI/nYljkyaYs7OJGzOWkrNn1Y5kF6QY+YsWPUPwD3OjpFCZGVKmihfi+tn7iryWwkLiJz1K7po1oNdT8/338R4xQu1YwgZpXV0JnfcFDhERmDMyiHtgdJVb9fdGkGLkL7Q6LT1GRaDVaog5nMGZA+lqRxLCrtn7irzm8+eJGzOWgu3b0Tg6EjJ7Fh539VU7lrBhOk9PQud/iUO9epSlp3Nu9IOYEhLUjmXTpBi5Ap8gV1r1CQNg27KTFOdfeQ0dIcR/s+cVeUtT0zg3chRFhw6h9fAg9Kv5uHburHYsYQf0Xl6EfjUfY+3alCUnE/fAaEqTktSOZbOkGPkHbfrUwrumC0V5pWz/TjohCXEt7HlFXtO5c5wbPpyS06fR+/kR9s1CnC9MaSDE1dD7+hL61VcYwkIpTUzk3OgHKU1NVTuWTbKfV4abTKfX0mNkBBoNnNqdSuxRWdlXiIqw5xV5SyKjiB0+gtLERAxhoYQtXYJj/fpqxxJ2yBDgT9iCBRiCgymNiyNu9IOUpcvl/7+SYuRfBIS707ynsmLw1iUnMRWVqZxICPthzyvyxj30MObMTBwiIqi1eDHG4GC1Iwk7ZggMJHTBAmXF35gY4saMoSwrS+1YNkWKkf9wa//aePg5kZ9dwq7vo9WOI4RdsPcVeS0F+Ti3aUPYwq/R+/qqHUdUAcbgIMIWLEDv70/J6WjiHhxDWXa22rFshhQj/8Fg1NF9pDKL3vHtSSSelF8eIf6Nva7IW3T4cPlt165dCZn3BTo3NxUTiarGGBpK6IIF6Px8KTl5kvix4zDn5qodyyZIMXIVgup70bhLEACbFkVRajKrnEgI22S1Wtn981myUwpxdNXbzYq8JdHRJDz+RPn9mu+/h9bR/maIFbbPoXY4YV99hc7bm+ITJ4h76CHM+flqx1KdFCNXqcPAOrh6OZCbXsSeH2VGPSGuJDUmh4PrlIUyOwyqZxcr8pYmJxM37iEsl3xC1RhsP7ewXw516yorPHt4UHz4CPEPj8dSUKB2LFVJMXKVjE56ug5vAMDhjfGkxkjTmhCXUi7PnCy/X6eln4ppro75/HniHnqIspQUjLXC1Y4jqhHHBg0Imf8lWnd3ig4cIP6RiViKqu+K8VKMVECtpr7UbxuA1QqbvonEXGpRO5IQNmPvmhiyki9+urP1NVssRUXEPzIRU/QZ9AEBhMz6VO1IoppxatyY0HlfoHVxoXDPHhImPYqlpHquiSbFSAV1vq8+Tm4GspIK2PdrrNpxhLAJKTE5HFhnP+tvWMvKSHxqMkUHD6J1dyfki7noAwPVjiWqIadmzQj54gs0zs4U7NpFwuOPYzGZ1I5100kxUkGOrga6DFUu1xz45RwZCdLxSFRvpSYzGxdEYrVCnVb+asf5T1arleRXXiV/yxY0Dg6EzJ4lE5oJVTm3aknI57PRODpSsHUbiU9NxlpavZYhkWLkGtRp5UftFn5YLFY2LYzEYpbLNaL62r3qLOdTC3H2MNLx3rpqx/lP6R/NIOf770GrJeij6Ti3bq12JCFwufVWQmZ9hsZoJH/jRhKfeRZrWfWZaFOKkWug0WjoMqw+Ds560uPyOLQxXu1IQqgi8WQ2hzcpv/89RkbY/OiZrIULyZw7F4DA11/DrUcPlRMJcZFLhw4Ef/YpGoOBvHXrSPrf81jN1WMqCSlGrpGLh0P5p8A9P8VwPrVQ5URC3Fym4jI2LowEoFGnmoQ18VE50b/LWbOG1LenAeD35JN43nuvyomE+DvXzp0J+vhj0OvJXbOG5Bdfwmqp+q3vUoxch4btAwlp5I251MKmbyKxWqxqRxLiptm5Mpq8zGLcfBxt/vJM/s6dJD0/BQCvkSPxGf+wyomE+GduPboT9OGHoNORs2oVqW+9pXakG06Kkeug0WjoNrwBegcdydE5HNuWqHYkIW6Kc8czObE9CYCeoyIwOupVTvTPio4eI/Gxx6G0FPc7+xAw5XmbH3YshPvtvan53rug1ZLzwyq149xwUoxcJ3dfJ9rfXQeA3384Q25m9Z20RlQPxQWlbL5weaZZj2CCGnipnOifmWJjiR8/HkthIS4d2hP4zjtotPKyJ+yDR9++BL5d9VtFQIqRStG0axCBdTwoLTGzdfFJrFa5XCOqru3fnqIgx4RngDPtLhTitqg0LY24cQ9hzsrCsXFjgj6ZidZoVDuWEBXieffd+L/8Uvn97BUrVUxz40gxUgk0Wg3dRzZEp9cSdyKLk3+kqB1JiBvizME0Tu1ORaOBng9EYDDq1I50Rea8POIfHk9pQgKGsFBC5s5B5+qidiwhronXwIHlt9OmTSN/61YV09wYUoxUEq8aLtxyVy0Adnx3moKc6jmlr6i6CnNNbF2irD3T8vYwatT2UDnRlVlKSkiY9CglUVHofH0JnTcPvY9tj/QR4qpZrSQ8NZniEyfUTlKppBipRC17heIX6kZJYRnbl51SO44QlcZqtbJ16UmK8krxCXLh1r62uaic1Wwm6dnnKNyzB62LC6FfzMUYEqJ2LCEqjdOtt2AtLCR+/ARKk5PVjlNppBipRFqdlh6jGqLVajhzMJ0zB9LUjiREpTi1J5WzB9PRajX0HN0IncH2XjqsVispb7xB3m+/oTEYCP7sMxwjItSOJUSlCvrgAxzq1aUsPZ34h8djzstTO1KlsL1XFDvnG+xGqzvCANi67BTFBdVrfQFR9eRnl7B9udLSd8tdtfALcVM50ZVlzJrF+WXLQaOh5vvv49KurdqRhKh0OldXQubMQe/nR8np0yQ+8WSVWMdGipEboE2fWnjVcMaUa2Ln8lMyukbYLavVyuZFkZQUluEf5kar28PUjnRF2cuWkzHzUwBqvPIy7nfcrnIiIW4cQ82aBH8+u3yl3+SpU+3+fUaKkRtAZ9DSfVgD7vI00OBUFmf3paodSYhrcmJHEnHHs9DptfQc3QitzvZeMnJ/+42U118HwHfiRLyGDVM5kRA3nlPjxgR/NF2ZFG3l92R+/rnaka6L7b2yVBEB4e7lt7ctPSWToQm7k5tRxM4V0QC0u7s23oG2NzS2YM8ekp55FiwWPAcPxvexR9WOJMRN49q1KzVeeRmA9I8/IefHH1VOdO2kGLkJSgrL2DD/BBZz1V/sSFQNVouVjV9HUlpiJrCuB8162N6IlOJTJ0mYOAmryYRbr9uo8eorMs27qHa8hg7Fe+wYAJJefImC3XtUTnRtpBi5CYyOOpLP5LB3TazaUYS4Kkc2J5B0+jx6Bx09H4hAq7W9N/n4Rx/Fkp+Pc5s21PzgAzQ625yATYgbzf/pp3G74w4oLSXhsccoOXNG7UgVJsXITdB5SH0A9v0SS8LJbJXTCPHvslMK+H2V8mLWcVBdPPycVU50ZeaMTBzq1yd41mdoHRzUjiOEajRaLTXffQenli2x5OYS//B4yjIy1I5VIddUjMyaNYvw8HAcHR1p3bo127dv/9fjFy9eTPPmzXF2diYwMJAHH3yQzMzMawpsj+q09ieiYyBYYcP84xTlm9SOJMQVWcwWNn4dibnUQkiEF40711Q70mUshQXltw01Agn54gt07u7/coYQ1YPWwYHgWZ9hCAulNDGR+AmPYCksVDvWVatwMbJ8+XKefPJJXnzxRQ4ePEjnzp3p06cPcXFxVzx+x44djBo1irFjx3L8+HG+++479u7dy7hx4647vD3pPLg+XjWcKcgxsenrSLsfhiWqpoPr40iNycXopKf7yAib6oNhNZtJmvJC+f3g2Z9hCPBXMZEQtkXv5UXo3LnoPD0pPnaMxGeexWo2qx3rqlS4GJk+fTpjx45l3LhxREREMGPGDEJCQpg9e/YVj//jjz+oVasWjz/+OOHh4XTq1Inx48ezb9++6w5vTwwOOnqPa4JOryX2aCZHNiWoHUmIy2Qk5LPnpxgAOg+ph5u3o8qJLpf6zrvkX9IK6xBWS70wQtgoY1gYwbNmoTEayd+0idR33lU70lWpUDFiMpnYv38/vXv3vmx/79692bVr1xXP6dChAwkJCaxduxar1UpqaiorVqygb9++//g8JSUl5ObmXrZVBb7BrnS8ty4Au76PJj2uakzjK+yfuczChgUnsJithDf3pUHbGmpHukzWN4vI/uYbtWMIYRecW7Wk5ntKEZL9zTdkff21yon+W4WKkYyMDMxmMwEBAZftDwgIICUl5YrndOjQgcWLFzNkyBCMRiM1atTA09OTmTNn/uPzTJs2DQ8Pj/ItpAotdNWkaxDhzX2xmK2sm3cMU3GZ2pGEYN/aWDIT8nF0MdBtREObujyTt2ULqdOmAeD7+GMqpxHCPrjfcQf+zz4LKK2KuevXq5zo311TB9a/vlBZrdZ/fPE6ceIEjz/+OK+88gr79+/n119/JSYmhgkTJvzj958yZQo5OTnlW3x8/LXEtEkajYYeoyJw9XIgJ62IbbK6r1BZakwu+389B0DX4Q1wdjeqnOii4shIEic/DRYLHvcOwueB0WpHEsJueI95EM9hQ8FqJenZ5yg6fFjtSP+oQsWIr68vOp3ub60gaWlpf2st+dO0adPo2LEjzz77LM2aNeP2229n1qxZzJ8/n+R/WP7YwcEBd3f3y7aqxNHFQK8xjdFo4OQfKZzcfeVWJSFutDKTmY1fn8BqsVLvlgDqtradDqGlqanEj5+AtbAQ5/btCHz1VZtqsRHC1mk0Gmq8+CKuXbtiLS4m/pGJmGz0w32FihGj0Ujr1q1Z/5fmnvXr19OhQ4crnlNYWIhWe/nT6C5MTlSdR5TUrOfJLXeFA7B1yUnOp9rPECxRdfyx+izZKYU4exjpMrS+2nHKWQoKiJ/wCGVpaRjr1iH444/RGAxqxxLC7mj0eoKmf4hjo0aYs7KIf3g85vPn1Y71NxW+TDN58mTmzZvH/PnziYyM5KmnniIuLq78ssuUKVMYNWpU+fH9+vXj+++/Z/bs2Zw9e5adO3fy+OOPc+utt1Kzpm3NYXCzte5Ti5r1PCktMfPbl8cxl8p08eLmSTyVzeFNyqek7vc3xNHFNt7srWYziU8/Q0lkJDofH0I+/1zmEhHiOmhdXAj+fDb6wEBMMTEkPPoYFpNtzXdV4WJkyJAhzJgxg9dff50WLVqwbds21q5dS1iYsrR4cnLyZXOOjB49munTp/Ppp5/SpEkT7rvvPho0aMD3339feT+FndJqNfQa0wgHFz3pcXnls14KcaOZisvYtDASrNCoYyC1mvqqHalc6jvvkr9lCxoHB0JmfYYxOFjtSELYPYO/PyFzPkfr6krhvn0kT3kBq8V2PgDrr+WkiRMnMnHixCs+tmDBgr/te+yxx3jsMekFfyWuXo70HBXB2tlHObwxnuCGXjb1xiCqpl0ro8nNKMbN25GO99ZTO065S4fw1nz3XZyaN1c5kRBVh2P9+gTP/IS4hx4md80aDMHBeE20jfdmWZvGBoQ396Npd+XT38avIyk4X6JyIlFVWa1Wzu1PIHJLDFit9HggAqPTNX0mqXR5mzeXD+H1e3oy7nfcrnIiIaoel/btCXzjDQAy58zh/A+2cZVCihEb0eGeOviGuFKcX8r6r05gsVTfzr3ixslNOk/hiF502z6ZZp38CG7gpXYkAIpPnCDx6WfAYsHzvnvxqWbLRQhxM3kOvBvfSZMASH1rmsppFFKM2Ai9QUfvsY3RO+hIPJnNgXXn1I4kqphSk5l1Xxwrv39rv3AV01xUmpJC/IRHsBYW4tKhPTVeeUWG8Apxg/k+OgmPAQPARtausY32WZWVxJzFENFI7Rh41XChy5D6bFoYyZ6fYgiq70VgHQ+1Y4kqwGq1smlhJJmJ+eX7DEadiokUloIC4h+ZWD6EN2jGDBnCa2NKLaWcPX+WwxkngVAAlkQuwcfBBXejO25GN9yMbpfd1mrkc66t02g0BL7xOkUpGeX7SlNTMYSqM8q12hYjl/YiTnj0ceouX4beV/2Oow3b1yA+MovTe1P57ctjDHnxVpsZcins14F154jel4ZeazstDlazmcTJT18yhHeODOFVWWFpIaeyTxGVFUVUVhSRWZFEZ0djspiwahwgZB4AHx/4GI31yn3bNGhwNbji7uD+tyLlz9t/fvVw8MDN6Ibe6nIzf0xxgcZoJOjD9+GlgwDkrF6F82NXHpxyo1XbYkRzyURspclJxD8ykbCvF6B1dlYxlVKtdhvegNTYXHLTi9iyKIrbH24izdbimsUeyeCP1WcBlIUat6oc6ILUae+Qv3XrJUN4g9SOVK1kF2cTmRWpFB6ZSuFxLvccVv7eX83F4EIdr8ZsvHD/9lq3U2TKJs+UR64plzxTHnmmPIrNxVixkleaR17p1S8EarUYAKVT5aQNk7gtvAs9QnoQ6BpYCT+p+Dc6t4sfAHweeli1HNW2GLmUzsOD4qNHSXz2OYI/+RiNTt3ma6OTnt5jG/P9e/s5czCd49uTaNJFXqhFxWUlF/Db/ONghcZdgmjUsSYn1Q4FZC38huxFiwAZwnujWa1WkgqSyguOk1knicyKJLUw9YrH+zr50tC7IRHeETTwbkCEdwTBbsEUWazU2XYUgNc7vo7LFV4nS8wllxUouSW5fytYck255dufx+QUF/PnBcS9qXvZl76Ld/a8Q4R3BD1Ce9AjtAf1POvJh7IbTM1/XylGgKCPPiL54fHkb9xI6jvvUuPFF9SOREAtd9oNrMOuldHs+O40gXU88AlyVTuWsCPFBaWsnX2E0mIzgXU96Dy4HpiK1Y6lDOF95x0A/J95Wobw3gBrz64l6nxM+eWWXFPuFY8LdQuloXfD8i3CJwJfp3+6XP3fHR0ddA44ODn8y/e4skJTGY2OrgPgiZZPsCN5EwfTDhKZFUlkViSfHfqMYNfg8sKkhV8LdFr1+zyJyiPFCODcogU1332HxKcmk/3NNxhDgvG+ZEp7tbToGUJCVBZxx7P47cvj3Pt8G5vodChsn8ViZf2Xx8lJK8LV24E7Hm6KTq/FovIM0H8dwus9dqy6gaqI5Pxkvo1aRJML96f+PhWT9eKnXL1GTx3POuUFR0PvhjTwaoCr0fY+4IxoNIKHWjxAZlEm2xK2sSluE7uSdpGQn8DCEwtZeGIhXg5edAvpRo/QHrQLbIej3lHt2OI6STFygXufPpQmJpL2wYekTnsHfWAg7r16qZpJo9XQ84FGLH9zD1lJBez47jTdRzRUNZOwD7//cIa4E1noDVrufKQZzu5GtSPJEN5KZrVa2ZuylyVRS9gcvxk9Zt67MHN+c7/m1PVuTIS3UnjU8ayDUaf+70BF+Dj5MLDeQAbWG0hhaSG7knaxKW4TWxO2kl2SzQ/RP/BD9A846Z3oWLMj3UO70zW4Kx4OMgLRHkkxcgnvsWMxJSRwftlykp59DsPXC1S/lu3sbuS2Bxvx4yeHOLE9iZCG3ja1zLuwPSf/SObQemV9qB4PROAX4qZyIjDnyxDeylJYWsjPZ39madRSos9Hl+9vXaMNsB2AL3p/gU6nbmf8yuRscOa2sNu4Lew2Si2lHEg9wKa4TWyK30RKQQob4jawIW4DOo2O1gGt6RHag+4h3anpWr0XY7UnUoxcQqPRUOOllyhNTqZg6zbiH5lIreXLMIaEqJorJMKbVr3DOLDuHJsXReEf5oa7r5OqmYRtSo3NZfMipYtq6z5h1GsToHIisJaVkfS0DOG9XvF58SyLWsYP0T+QZ1JGqjjpnehXux/DGg4j3L0mW7Y2VTnljWfQGmgb2Ja2gW15/tbnicyKLC9MTmefZk/KHvak7CnvANs9tDs9a7SnvtrBxb+SYuQvNHo9wdOnEztyJCUnIol/eDy1li5B5+mpaq5b+4eTeCqb1Jhc1s8/zt1Pt0Knk4mFxEUFOSX8MvsI5jILtZr50rZfbbUjARdW4ZUhvNfEYrXwR9IfLIlawraEbeXDbkPcQhjaYCh317sbd6NS2JnNhWpGVYVGo6GRTyMa+TTi0ZaPEp8bz6b4TWyK28Sh9EPlHWC/snzKngvnZBVn422UeU1sjRQjV6B1cSFk9ufEDh2KKSaGhEcfI2T+l2iN6l1z1em09B7bmOVv7SXlbC57f4qh3d11VMsjbIu51MIvnx+lIMeEVw1nej3YCI0NTHAmQ3ivTb4pn9VnVrMsahmxubHl+zvW7MjwiOF0Cuoks5xeQYh7CA80foAHGl/SATZ+EwcTdpYfM3D1QAY3Hc0DjR6wyQ681ZUUI//AEOBPyOefc27ECAr37SN5ygvUfP+9yyZLu9ncfZ3ofn9D1n1xjP3rzhHU0IuQht6q5RG2wWq1smXpSVJjcnFw1nPnI81sYiXevK1bZQhvBcXkxLA0aik/nvmRgtICQJlw7O66dzOkwRDCPWxjPSF7cFkH2IIMeF/58FZUVsjnhz9nWdQyxjUdx5AGQ2Q0jg2Q0vpfODaoT/AnH4NeT+6aNaR//Inakajb2p9GnWpitVr5bf5RzmfmY7XKCr/V2ZFNCUTtSkajgd7jGuMZYBsdF5NfeEGG8F4Fs8XM1vitjF8/nv6r+rM0aikFpQWEe4TzQtsX2HjfRp6/9XkpRK6Ds+FiH7tpnaZRy70W50vO88G+D+j7Q1++O/UdpZZSFRMKKUb+g0uHDgS+/joAmXPmkP3ddyongk6D6+FZw5F4583MmPkBxUVXXiNCVH3xkVnsXKmMqOgwqC6hjXxUTnSRtbBIhvD+i5ySHL4+/jV3/XAXj256lF1Ju9CgoVtwN+b0msPqAasZ1nAYLgbp31CZeob15IcBP/B6h9ep4VKDtMI0Xv/9de5edTe/xPyCxWr5728iKp0UI1fB856B+E5UFg9Kmfoa+dt3qJrHYNRx2+iI8vubFkZiMcsfUHWTk17Iui+OYbVYadCuBs17qjvqC8Ccf8mqwHXCCfr4YxnCewVv736bXit68cG+D0jIT8DN6MboxqNZc88aZvacSYeaHaSAu4H0Wj0D6w3k54E/89wtz+Hl4EVcXhzPbXuOwT8NVjoLS4vzTSXFyFXyfexRPAb0B7OZxCefpDgqStU83jUvdryKOZzB5m+isFrkj6e6MBWXsXb2UUoKy/Cv5U63EQ1Uf/OymEwkTn66/H7wxzPRuak/x4mtSMhPKL+9KnoVRWVF1POqx6vtX2XjfRt5us3ThLipX1BWJw46B0Y2Gskvg35hUotJuBpcOZl9kkkbJzH619HsT92vdsRqQ4qRq6TRaAh84w2c27bFUlBA/PgJlKZeeaGpm02j0RD1Rwrbl5+Sar4asFqsbPjqBFlJBTh7GLlzQlP0BnWXCbCazSQ9+xxFe/eW7zMGyYRTACaziblH5jLs52Hl+3qE9mD+7fNZ2W8l99a/Fye9zBukJheDCxOaT+CXe35hdOPROOgcOJB2gNG/juaRDY8QmRmpdsQqT4qRCtAYjQR/8jHGOnUoS00lfvyEy5ql1dJtRAPQwNGtifyx6qzaccQNtufnGGIOZ6DVa+gzoSkung6q5rFaraS+9TZ569aBXJK5zJ7kPQz6cRAzD86kxHyxb9c7nd/hlhq3qN6aJS7n6ejJ022eZs3ANdxX/z50Gh07Encw+OfBPLv1WWJzYtWOWGVJMVJBOg8PQubMQefrS0lUFIlPPoW1VN1e2PVuCaDb8AYAHFh3jn2/xKqaR9w40fvT2Lc2FoDuIxpSI1z9dTgyP/+c7CVLQKMh8M031I5jEzKKMnh++/OM/W0ssbmx+Dj68HqH19WOJa5SgEsAr7R/hR/v/pE+4X0A+DX2V+5efTdTd00lpSBF5YRVjxQj18AYHETI7NlonJwo2LGDlNffUP3ySOPOQXQYVBeA3avPcnhTvKp5ROXLSMhj49cnAGjeM4SG7QNVTgTZ335bPuQ94IUXcO/dW+VE6jJbzCyLWkb/H/qz5uwaNGgY2mAoPw78kTvC71A7nqigUPdQ3uvyHiv6raBLcBfMVjMrT6+k7/d9eX/v+2QXZ6sdscqQYuQaOTVtQtCHH4JWy/nvviPzi3lqR6Jlr1Bu6VsLgB3fnubEziR1A4lKU5RvYu2so5SZLIREeNHhHvVn383bsIGUqa8B4DNhPN4j71c5kbqOZx7n/rX389but8grzaORTyOW9F3Ci+1eLJ+yXdinBt4N+KznZyzss5DWAa0xWUwsPLGQPt/3Yfah2RSWVb+p+CubFCPXwa1HdwJeeAGA9OnTyfl5jcqJ4Ja7wml+m9Ijf8uiKE7vs41OtuLamc0W1s09Rl5WMe5+TvQe1wStyusSFe7dq4ycsVjwuHcQfk88oWoeNeWZ8pi2exrD1wznWOYxXA2uTLl1CkvuXEIT3yZqxxOVqKV/S766/Stm3zabCO8ICkoLmHV4FgNXDVQ7mt2TYuQ6ed8/Au/RowFInjKFwn37VM2j0WjoOKgujTrXxGqFDfNPEHskQ9VM4vrs/PY0iafOY3DQ0feRZji6qNtJtPjkKeInTsJqMuHaoweBU6dWy46YVquVX2J+of+q/iyJWoLFaqFPeB9+vPtHhkcMR6dVd4STuDE0Gg2dgjqx7K5lvN/1fWU2V9P58sePpB9RL5wdk2KkEvg/9yxuvXphLS0lftKjlJyNUTWPRqOh67AG1LslAIvFyq9zj5EQlaVqJnFtjm9P5OjWRNBArzGN8K6p7mycpoRE4seNw5KXh1Pr1gRN/xCNXv11cG622JxYHl7/MM9te46Mogxquddibq+5vNflPfyc/dSOJ24CrUbLHbXu4IcBP/Bi2xfL9z+8/mFm7J+ByWxSMZ39kWKkEmi0Wmq+/x5OzZtjyckhfvx4yjLVffPXajX0HB1BeHNfzGUW1sw+SsrZHFUziYpJij7PtmWnAGjbrzbhzdV9kyvLziZ+3DjK0tNxqFeXkFmfoXWsXguMlZhL+OzQZ9zz4z38kfwHRq2RSS0msbL/StrXbK92PKECvVZP/zr9y+9bsfLlsS8ZumYoJ7NOqpjMvkgxUkm0jo4Ez/oMQ0gIpfHxJD71pNqR0Om03D6uCSERXpSVmPlp5mHS4/LUjiWuQl5WMb/OOYrFbKVOK39a9wlTNc+fE/2ZYmPR1wwkZN48dB7qDyu+mXYm7mTg6oF8fvhzSi2ldAzqyKoBq5jQfAJGnVHteMJGvNv5XbwdvTmdfZqha4byxZEvKLOUqR3L5kkxUon0Pj6EzJ2DzsOD4qPH1I4DgM6gpc+EZgTW9cBUVMaPnxwiK7lA7VjiX5hKylg9Zx+5Bfn4hLjQ84EIVftkWEtLSXjiSYqPHEHn4UHovHkYAgJUy3OzpRak8vSWp5mwYQLxefH4O/nzQdcPmN1zNiHuMn27uFy3kG583/97eob2pMxSxicHP+GBXx+QCdP+gxQjlcwhPJzgzz61qcXBDA46+k5qjl+oG8X5pfw44yA56UVqxxJXUJRv4vuZe3i35iN82fY5uo+rh8FBvY6QVouFpBdfpGDHDjROToTMnYND7dqq5bmZyixlLDqxiAGrB/Dbud/QarTcH3E/q+9eze21bq+WnXbF1fFx8uGjbh/xVqe3cDW4ciT9CPf9dB+LIxfLqsD/QIqRG8C5TRtqvP5a+f2MuXNVTKNwcNLT7/HmeAW6UJBj4sePD5KfXfLfJ4qbJjulgBXv7Lusb4+bt7p9MtLe/4DcH38CnY7gj2fg1Ly5qnlulmMZxxi2Zhjv7n2XgtICmvk1Y/ldy/nfrf/D1ej6399AVHsajYb+dfrzw4AfaBfYjmJzMe/seYeHf3uY5PxktePZHClGbhD3Oy7Otpg5+3MyvvhCxTQKJ1cjA55sgbufE7kZxfz48UEKc6XHty2Ij8pi5Xv7yc0oxs3HNjqFZn45n6yvvgIg8K03ce3SReVEN8/YdWOJyorC3ejOK+1f4Zs+39DQu6HasYQdquFSgzm95vBC2xdw1DmyO2U39/x4D6ujV6s+c7ctkWLkJkn/cDqZCxaoHQMXDwcGPNkCVy8HslMK+WnmIUoK1V1bp7o7sSOJnz85TElhGTVqu3P3U63UjsT5VatIe/99APyffRbPu+9WN9BNcDTjaPltK1b61+nPj3f/yH3170OrkZdKce20Gi3DGg5jRf8VNPdrTn5pPi/tfIknNj9BRpHMAwXXWIzMmjWL8PBwHB0dad26Ndu3b//X40tKSnjxxRcJCwvDwcGBOnXqMH/+/GsKbI98xo8HIO2dd8lavFjlNODu48SAJ1vi5GYgIz6fn2YexlQsvb1vNqvFyq6V0WxeFIXFYqXeLQEMeEr5f1FT/tatJL/4EgDeDz6Iz9gxqua50SxWC18e/ZKHf3u4fN/nt83mrU5v4ePko2IyUdWEuYfx9R1f80SrJ9Br9WyO38w9q+9h/bn1akdTXYWLkeXLl/Pkk0/y4osvcvDgQTp37kyfPn2Ii4v7x3MGDx7Mxo0b+fLLLzl58iRLly6lYcPq0+TpM/5hfB5WXuhS33iT7G+/VTkReAY40/+Jljg460mNyWXt7KOUlZrVjlVtlJaY+XXuMQ6uV/5ubulbi15jGqE3qDtrZ9GhQyQ8+RSYzXgM6I//s8+omudGyyjK4JENjzDjwAzM1ou//60CWquYSlRlOq2OcU3HsazvMup71Se7JJvJWyYzZfsUck25asdTTYWLkenTpzN27FjGjRtHREQEM2bMICQkhNmzZ1/x+F9//ZWtW7eydu1abrvtNmrVqsWtt95Khw4drju8vdBoNPg99STeDz4IQMqrUzn/wyp1QwG+wa70e6wFBgcdiSezWTf3GGaz9PS+0QrOl/DDhwc4eygdrV7DbQ824tZ+tVUfnVFy5gzx4ydgLSrCpUtnAt98E4226l6e+D3pd+798V52Je3CUefIS5fMoinEjdbAuwHL+i7joaYPodVo+fnszwxcPZBdibvUjqaKCr3SmEwm9u/fT++/LBPeu3dvdu268j/gjz/+SJs2bXjvvfcICgqifv36PPPMMxQV/fPQ0pKSEnJzcy/b7J1Go8H/uWfxuv9+sFpJfvFFm1hYLyDcnb6TmqEzaIk9msmGr05gsUinqhslIyGPFe/uIz0uD0dXAwOebEmDtjXUjkVpSgpx4x7CnJODY7NmBM+YYVPD0ytTqaWUjw98zPj148kszqSuZ12W3bWM/nUHqB1NVDMGnYHHWz3O13d8TZh7GGmFaYzfMJ43/3iTwtLqtRJwhYqRjIwMzGYzAX+Z8CggIICUlJQrnnP27Fl27NjBsWPH+OGHH5gxYwYrVqxg0qRJ//g806ZNw8PDo3wLCakaEwtpNBoCXnwBzyFDwGIh6X//I/fXdWrHIqi+F33GN0Wr0xC9L40ti6KwSkFS6WKPZLDy/QPkZ5fgVcOZe//Xmpp1PdWOhTknh/iHHqIsORljeDghcz5H6+ysdqwbIik/iTG/jmHe0XlYsXJf/ftY2ncpdTzrqB1NVGMt/Fvw7V3fMqzhMACWn1zOvT/dy8G0gyonu3muqQ32r83JVqv1H5uYLRYLGo2GxYsXc+utt3LnnXcyffp0FixY8I+tI1OmTCEnJ6d8i4+Pv5aYNkmj0VDj1VfwuOceMJtJfOYZ8jZuVDsWYU186D22MRoNRO5KZsd3p2XYWSWxWq0c3hjP2tlHKCsxE9TAi3uebY2Hn/pv+JbiYuIfmUjJ6Wj0/v6EzvsCvZeX2rFuiA3nNnDvT/dyKP0QrgZXPuj6Aa+0fwVHvW0MpRbVm7PBmRfavsAXvb+ghksN4vPiGf3raKbvn14tFt2rUDHi6+uLTqf7WytIWlra31pL/hQYGEhQUBAel6xjERERgdVqJSEh4YrnODg44O7uftlWlWi0WgLfeB33fv2grIyEJ58if+tWtWNRp5U/PUZFAHBkczx//Hgcs7lQipLrYDFb2Lbs1IXiDhp1DKTf481xdFH/Eoi1rIzEyU9TdOAAWnd3QuZ9gSEoSO1Yla7EXMKbf7zJU1ueIs+UR1PfpnzX7ztur3W72tGE+Jt2ge34vv/39K/TH4vVwlfHvmLUrw+oHeuGq1AxYjQaad26NevXXz4Maf369f/YIbVjx44kJSWRn59fvu/UqVNotVqCg4OvIXLVoNHpqDntbdzuuANKS0l47HHyd+5UOxYN2wfSZWh9NDoThW4D2LK1KcUFsrjetTAVlbFm1hGObU0EDXS4py7d7m+ITmcbnUJT3n6b/E2b0Dg4EDLrMxzr11c7UqU7m3OW4WuGs/zkcgAebPIgX/f5mmC36vvaI2yfm9GNtzq9xYzuM/B29Obs+TPlj1XVD4cVflWcPHky8+bNY/78+URGRvLUU08RFxfHhAkTAOUSy6hRo8qPHz58OD4+Pjz44IOcOHGCbdu28eyzzzJmzBicnJwq7yexQxq9nqD338P1tp5YTSYSJk6iYPcetWPRtFswbfuHl9//9u29nDmYVmX/CG6E3MwiVr6/n7jjWegNWvo83JSWvUNVHzFzqdxVq0GrJWj6hzi3aaN2nEpltVpZFb2KoT8P5VT2KbwdvZl922wmt56MQat+q5QQV6NnaE9+GPAD3UO6l+97bttzVXIIcIWLkSFDhjBjxgxef/11WrRowbZt21i7di1hYcoS58nJyZfNOeLq6sr69es5f/48bdq0YcSIEfTr149PPvmk8n4KO6YxGAiePh3Xrl2xlpQQ/8gjFO7fr3YsWtwWWn67IMfEr3OOsXb2UfKyilVMZR9SYnJY8c4+spIKcPYwMvCZVtRu6ad2rCuq8dpU3Hr2VDtGpSooLeCFHS/w8s6XKSorom2Ntqzot4JOQZ3UjiZEhXk7evNO53fK729N2MrQn4cSlRWlYqrKp7+WkyZOnMjEiROv+NiCK0x53rBhw79d2hEXaYxGgj75WGkZ2bmT+IfHEzr/S5tZlKxl7xAO/ZZO7JEMEk5m07ZfOM26B6O1kcsNtuT0vlQ2fh2JudSCT7Ard01qhquXbXSQtFqtZHw+p/y+76SJeN13n4qJKt+JzBM8u/VZ4vLi0Gl0TGwxkbFNxqLTqjuZnBDX49IW1UCXQGLz4hmxZgQvtnuRe+rdo2KyyiPvJjZC6+BA8Gef4ty2LZaCAuLGPUTRseNqxwLg1rtqM/jFWwis60FZiZmdK6L57p19pMZWvabCa2W1Wtn3Syy/zTuOudRCraY+3PNMK9spRCwWUt94k8xLVpD2HlN1pnm3Wq0sjlzM/WvvJy4vjhouNZh/+3webvawFCKiSlnY5xu6BHfBZDHx6q5Xy1sA7Z0UIzZE6+hIyOxZOLVpjSUvj7ixYymOso2mOJ+argyc3IruIxvi4KwnIz6fFe/uY9vyU5iKqve6NuZSC5u+jmT36rMANO8RQp9HmmF0vKaGx0pnNZlIevY5spcsuWy/LfVfuR7ni8/z+KbHeWfPO5RaSukR0oMV/VbQKkD9BQeFqGweDu7M7DGTJ1o9gVajZVX0Ku5fez/ncs+pHe26SDFiY7TOzoR8Pgen5s2x5OQQ9+AYSk6fVjsWABqthkYdazJ8ajvq3xoAVji6OYElU/+oth1ci/NL+fGTQ0T9kYJGq6HL0Pp0GlwPrdY23ugthYXET3qU3DVrQK+nxttvqR2pUu1P3c+9P93LloQtGLQGXmj7AjO6z8DDweO/TxbCTmk1WsY1HcfcXnPxdvTmVPYphvw8hA3nNqgd7ZpJMWKDdK4uhHwxF8cmTTBnZ3PuwTGUnI1RO1Y5Z3cjvcY0pv/jLXD3c7rYwXXWEXIz7b+58GqdTy1kxbv7SDp9HoOjjr6TmtG0m+0MGTWfP0/cmLEUbN+OxsmJkNmz8LjjDrVjVZp5R+cxZt0YUgtTqeVeiyV9lzCs4bAq0+IjxH9pG9iW7/p9Ryv/VhSUFvDUlqd4f+/7lFpK1Y5WYVKM2Ciduzuh877AISICc0YGcaNHYzpnW81wIY28GfbyrbS5sxZanYbYo5ksfW03B9fHYanKC+5ZrSSdSGTVuzvISS/EzduRQc+2Jqyx7Sw3X5qayrmRIyk6dAithweh87/EtXNntWNVqrlH5mKxWuhfpz/L71pOQ+/qsxK4EH/yd/Zn3u3zGN14NAALTyxk7LqxpBakqhusgqQYsWE6T09C53+JQ726lKWlcW70g5gSEtWOdRm9UUfb/rUZ8uKtSgdXk4VdK6tmB9eyUjOn96Wy5pM/qPltI0a730fNWkbufb4NPkGuascrZ4qN5dyw4eVTvNda9A3OLVuqHatS7E7eXX7bUe/I253e5q1Ob+FsUH9qfSHUYtAaeLrN08zoNgNXgysH0w4y+OfB/JH8h9rRrpoUIzZO7+VF6FdfYaxdm7LkZOIeeIDS5GS1Y/2Nd02XK3dwXWbfHVytVivpcXlsW3qSBf/byW/zjpMQlV3+eL9Hm+PsblQx4eWKT5wgdvgISpOSMISFErZkCQ716qkd67pZrBbmHpnL45seL9/3TZ9v6Fenn4qphLAtPcN6svyu5TTwakBWcRYP//Ywcw7PwWK1/ZZqKUbsgN7Xl9CvvsIQFkppYiLnHhhNaVq62rH+5rIOrm0vdHDdcqGD6wH76uBanF/K4U3xLH9rL9++vZejWxMpKSzD1cuBVr3Dyo/TG21n2GjB7j2cGzkKc1YWDo0iqLV4McZg+19rJteUyxObnmDmwZlYufg7FOYe9i9nCVE9hbqHsujORdxT7x6sWPn00KdM2jiJ88Xn1Y72r2xj7KH4T4YAf8IWLODcyFGUxsURP3483GKbU3g7uxvp9WBjGrYLZOuSk+SkF/Hr3GPUaupD56H1cfexzWUALBYr8SeyiNyVRMyRDCxlyhufVq+hdgs/IjoEEtzQG21ZIRxWOexf5G3cSOJTk7GaTDjfcgvBsz5D5+amdqzrdjLrJE9ufpKE/ASMWiMvtPsfsb8tVDuWEDbNUe/Iax1eo4VfC97a/RY7Encw+OfBfNj1Q5r6NVU73hVJMWJHDIGBhC5YwLmRIymOjbXZYuRPIRHeDH3lVvb/co4D684RezSThJO7ubVfbZr3sJ0ZXM+nFhL1ezJRf6RQcL6kfL9fqBsRHQKpd0uATayy+0/Or/ye5JdfBosF1549CZr+IVoHB7VjXbcfz/zI67+/Tom5hCDXIKZ3m049l9p8ghQjQlyNgfUG0sinEZO3TCYuL45Rv47if7f8jyENhtjcqDMpRuyMMTiIsAVfceaB0eX7SmJjMdroiqt6g9LBtd4tAWxZHEVydA47V0ZzdF8Kne6tR1htD1VWsTUVl3HmQDqRu5JIjs4p3+/oYqB+2wAiOgTiG2z7LQuZX84n7f33AfAYOJDAN15Ho7fvP2uT2cS7e97l21PfAtApqBPvdH4HDwcPSotlbSQhKqKBdwOW3bWMV3a+woa4Dby1+y0OpB1gavupNtXx275ftaopY1gYwXPmwFJlRs24kaMInfY2bj16qJzsn3kHKh1cI39PZsuqaJ5rZ4SEc0yZmY2PhyPuvo64+Trh7uOIu68T7j5OuPk44uRmqLQK3mq1knImh8jfk4nel0ZpiRkAjQZCGvkQ0SGQ8Ga+6Ay20WLzb6xWK+nTp5P5xTxAmdrd/9lnbO7TTkUl5yczectkjmUeQ4OGR1o8wvhm49FqbP//RAhb5WZ0Y3q36Sw8sZCP9n/ELzG/cDLrJB91+4gQJ9voeyXFiJ1yCK9VftuSn0/CxEn4TnwE30mT0Ohsp1Plpf7s4OrfyJvXDynT3FvMVnLSi8hJLwKy/3aO3kGnFCg+fylWfB1x93HC6PTfv8IF50s4uTuFyF3JnE8tLN/v4edERMdAGrQNxNXLfi5rWMvKSJ46lZwVKwHwf+ZpfMaNUznV9duVtIv/bfsf50vO4+HgwTud35GVdoWoJBqNhgcaP0BT36Y8s/UZzuacZeiaobzSeiqg/hpaUoxUAZ7DhpG/aBEZs2ZTdOwYQe+9h87TU+1Y/8jJ/WL/i2FT22LOMpGbWURuRjG5mUXkZRaTm1FMQU4JZSVmspIKyEoquOL3cnDR4+7jdFmx4ubjiNHTSFZKATG7U4k/nsWfA3n0DjrqtvIjokNNAut62F1LgqWkhKRnniFv/QbQagl8/TU8771X7VjXxWK1MO/oPD49+ClWrDTyacT0btMJcrX/kUBC2JpWAa34tt+3PL/teXan7OblXS8zjvfVjiXFCEBMTgz1HSPUjnHNAp57FvdmTUl+5VUKtm0n5r7BBM/8BMeGtj8jpZu3Iy5+LgTh9bfHzKUW8rKKyc0oIjfzwteMYvIylfvF+aWUFJSRXpBHelxe+XkmrHzsqfQteOK8I0Y0BNbxoGGHQOq29reZBewqypyfT8KkRyncvRuNwUDN6R/i3quX2rGuS05JDi/teIktCVsAGFRvEFPaTsFBZz8tVULYG18nX+b0msOsw7OYf3BB+f7k/GRCHdRZ0sI+X5UrwaWTwDzw6wO83Hkqd9a+U8VE18ejf38c6tUj4dHHKI2PJ3boMALfeAOPfnepHe2a6QxaPAOc8Qy4cicrU3HZhVaUy1tVMtKLoFApRlrcFkKLTkF41XC5mdErXVlmJvEPPUzxiRNoXVwI/uwzXNq1VTvWdYnKiuKpzU+VD9t9qd1LDKw3UO1YQlQLOq2Ox1o+RlOPZhzfo/SfW3duHQ/5jFUlT7UtRi7tEFdcVsz/tv+Pg2kHefaWZzHqbGdGzYpwjIggfOUKEp95loIdO0h69lmKjh4h4Nln0Rhsd2jqtTI66vEJcv3bVOyFpjJeeWUdAG3718bZaN+/5qWJicSNHYcpNhadlxchX3yBU5PGase6LqujV/PGH29cNmy3kU8jtWMJUe10DOrEcbYCMDJipGo5pIs68GCTBwFYdnIZo38dTVJ+ksqJrp3O05OQOZ/jM2E8ANkLvyHuwTGUZWSonExcC9PZs8QOH4EpNhZ9zUDCFi+260LEZDbx+u+v89LOlygxl9ApqBPL71ouhYgQNkCnVW/wgxQjwCPNH+Gznp/hbnTnaMZRBv88mO0J29WOdc00Oh3+Tz5J0MxP0Lq4ULhvHzH3DKLo0CG1o4kKihszlrLUVIx16lBryRIcaoerHemaJecn88AvD/Ddqe/QoGFii4l81vMzPBw81I4mhFCZFCMXdAnuwnf9vqOJTxNySnKYuHEiMw/OxGwxqx3tmrn36kWt775VFtlLSyN25Ciyly23qzViqjtzbi6OzZsRtugbDDVqqB3nmu1K3MXgnwdzLPMYHg4ezLptFo80f0TmDxFCAFKMXKama02+7vM1QxoMAWDukbmM3zCezKJMlZNdO4fatan17be49e4NpaWkTJ1K8ssvYykp+e+TxU1nNZvJXrKk/L5L27aEzZ+P3uvvo43sgcVqYc7hOUzYMIHzJedp5NOI5Xctl/lDhBCXkWLkL4w6pVf/O53fwUnvxO7k3Qz+eTAH0w6qHe2a6VxdCPp4Bn5PTwatlpwVKzk34n5Kk+y3b0xVVHzyJLHDhpP2wYfl+2p+8jFaF/scCZRbksPjmx7n00PK/CGD6g1iYZ+FMn+IEOJvpBj5B31r92Vp36WEe4STVpjGmF/HsPD4Qru9xKHRaPB96CFCvpiLzsOD4mPHiBl0LwV/7FY7WrVnKSkh7aMZxAy6l+IjRy4rPrR2PArqgV9HszVhK0atkdc7vM7UDlNl/hAhxBVJMfIv6njWYVnfZfSp1Ycyaxnv73ufp7c+Tb4pX+1o18y1Y0dqrVyJQ6MIzNnZxI0ZQ+b8r+y2yLJ3Bbv3ENN/AJlz5kBZGW69ehG+cqXasSpFYn4iQa5BfHPnNzJ/iBDiX0kx8h+cDc682+VdXmj7AnqtnvXn1jN0zVBOZp1UO9o1MwYHUWvJEjwGDACLhbT33iNx8mQsBVeecl1UPnNODskvv0zcAw9gOncOvZ8fQTM/IXjmJ+j9/dSOd00KSwuZuuvV8vvta7aXYbtCiKsixchV0Gg0DGs4jIV3LCTQJZBzuecYsXYEq6JXqR3tmmkdHQl8ZxoBr7wMej15v/xK7NBhmGJj1Y5WpVmtVnJ/XceZvndx/rsVAHgOGULtNT/b9dTukZmRDP55MGtjfinf91G3j2TYrhDiqkgxUgFN/Zry7V3f0imoEyXmEl7e+TJTd02luKxY7WjXRKPR4D18OGELv0bn50vJ6dPE3DeYvM2b1Y5WJZWmpJAw6VESn3wSc0YGxtq1CVv0DYGvTUXn7q52vGtitVpZHLmYEWtHcC73HP7O/uWPybBdIcTVkleLCvJ09OSznp/xaItH0aBh5emVjPxlJPG58WpHu2bOrVoRvnIlTq1aYcnLI+GRiWTMnqN2rCrDarGQtXgxZ/veRf6mTWAw4DtxIuGrfsC5TRu1412znJIcntj8BO/seYdSSyndQrqxuM8itWMJIeyQFCPXQKvRMr75eOb0moOXgxdRWVEM+XkIm+I2qR3tmhn8/Qlb8BVeI0YAkDFXipHKUBIdzbkR95P6xptYCgpwatGC2t+vxO/xx9Aa7XMNJIADqQe496d72Ry/GYPWwPO3Ps8n3T/Bw9FT7WhCCDskxch1aF+zPd/2+5YWfi3IK83jic1PMH3fdMosZWpHuyYao5EaL79E4LRpaBwuDsFMfe99ShMTVUxmfywmE+kzP+XswHsoOngQrbMzAS+/RNiSxTjUq6d2vGtmtpiZc3gOD657kJSCFELdQll05yJGRIxAo9GoHU8IYaekGLlONVxqMP+O+YxspKx2+NXxrxi7biwZhfa7MJ3nwLsJ/Wp++f3spUuJvv0Okv73PCWnT6uYzD4UHjhAzMB7yPjsMygtxbV7d2qv+RnvESPQaO33Ty69MJ3x68fz6aFPsVgt9K3dl2/7fSujZYQQ181+XxltiEFr4LlbnmN6t+m4GFw4kHaAkWvvVzvWdXGKiCi/7dz2VigrI2f1as7260/8IxMpPGC/M9LeKOa8PJJfe41zw0dgOnMGna8vQTM+InjWZxgCA9WOd112JO7g3p/uZXfKbpz0TrzZ8U2mdZqGi8E+Z4cVQtgWvdoBqpJeYb2o51mPyVsnE5d5rny/2WJGi3pLM1+v0M8/x3TiDJlfzCNv/XryN28mf/NmnNq0xvehh3Dp0qXaN9HnbdhAyutvUJaWBoDHvYMIePZZdB72PbS11FzKzIMz+er4VwDU96rP+13fp7ZHbZWTCSGqEmkZqWS1PGqx+M7F9A3vW77vkQ2PEJ9nv6NtAJyaNiX4k4+pvWYNHvcOAoOBon37iR8/gZi7B5Lz089Yy+yzr8z1KE1LJ+Gxx0l49DHK0tIwhoUR+vXX1HzzTbsvROLz4nng1wfKC5GhDYaypO8SKUSEEJXumoqRWbNmER4ejqOjI61bt2b79u1Xdd7OnTvR6/W0aNHiWp7WbjjpnXil/Svl9w+lH2LQj4P47tR3dj/tukPtcGq++SZ1N6zH+8EH0To7U3LyJEnPPsuZO/qQtWQJlmL7nHflWsTcey9569eDXo/Pww8TvnoVLm1vVTvWdVsXu47BPw3maMZR3IxufNTtI15s96KsLSOEuCEqXIwsX76cJ598khdffJGDBw/SuXNn+vTpQ1xc3L+el5OTw6hRo+jZs+c1h7Unl162aOnfkqKyIl7//XUmbpxIWmGaiskqhyEggID/PUfdTRvxe+JxdF5elCYkkPr6G0T36EnG53Mw5+aqHbPSmeLjyVq2vPy+JS8Px6ZNCV+5Av/JT6F1dFQx3fUrKivitd9f45mtz5Bfmk9zv+as6LeC28JuUzuaEKIKq3AxMn36dMaOHcu4ceOIiIhgxowZhISEMHv27H89b/z48QwfPpz27dtfc1h7Nfu22TzT5hmMWiM7EncwcPVA1p5da/etJAA6T098H3mEups2EvDSSxhq1sSclUX6jBlEd+9B6vvvU5pqv8WXpaSE/B07SXn7bc7c0YczvXqT9u675Y/7P/M0tZYtxbFBAxVTVo7o7GiGrxnOilMr0KBhXNNxfHXHV9R0ral2NCFEFVehYsRkMrF//3569+592f7evXuza9eufzzvq6++4syZM7z66qv/eMylSkpKyM3NvWyzZ1qNlgcaP1A+DDLXlMv/tv+PZ7Y+Q3ZxttrxKoXWyQnv+0dQZ92v1Hz/PRzq1cNSUEDWl/M5c9ttJL/8it2se2NKSCBr8WLix0/gVLv2xI8bR/bCb5T8ej3OrVuXH+s9YgQanf12TgZlSveVp1YybM0wos9H4+Pow5xec3ii1RMYtAa14wkhqoEKjabJyMjAbDYTEBBw2f6AgABSUlKueM7p06d5/vnn2b59O3r91T3dtGnTeO211yoSzS7U8azDojsXMe/IPOYemctv535jf+p+XuvwGl1Duqodr1JoDAY8+vXD/a67yN+6lcy5X1B04ADnv/uO8ytW4Hb77TiNHat2zMtYTCYK9+6lYNs28rdtxxQTc9njen9/XLp0xrVzF1w6tEfnoIW3q0ZrQZ4pj9d/f51fY38FoEPNDrzV6S18nXxVTiaEqE6uaWjvX4dxWq3WKw7tNJvNDB8+nNdee4369etf9fefMmUKkydPLr+fm5tLSEjItUS1OQatgUdaPEKXkC68uP1FzuSc4dFNjzKw7kCeu+U5XI2uakesFBqNBrdu3XDr1o3C/fvJnPsF+Vu3kvfrr6Rt2gwfLwCgNDEJS4A/Woeb2zHSlJBIwfZt5G/dRsHu3ViLii4+qNPh3LIlLl264NqlMw4NGlz++20quKlZb5QTmSd4ds/LJOQnoNfoeazVY4xuPFoWuBNC3HQVKkZ8fX3R6XR/awVJS0v7W2sJQF5eHvv27ePgwYM8+uijAFgsFqxWK3q9nt9++40ePXr87TwHBwccbvKb083W2Kcxy/stZ+aBmSw8sZAfon9gd/Ju3uj4BrcG2v9ojEs5t26N85zWFJ88ReaX8yhav7H8sbN39cPJVILW3R29ry96Pz9l+/O2v99l+7Xu7tc0p4nFZKJo3z7yt20nf9s2TGfPXva43s/v8tYPO11FtyLGrRtHgcFMkGsQ73Z5l+Z+zdWOJISopipUjBiNRlq3bs369esZOHBg+f7169czYMCAvx3v7u7O0aNHL9s3a9YsNm3axIoVKwgPD7/G2FWDg86BZ255hm4h3Xhp50sk5icy9rex3B9xP0+0egJHvX2PzPgrxwb1CXrvPVziEuCMMl2+xmgAUwmW3FxMubl/KxL+SmM0lhcnOr8rFC9+/pR6epUff/67FWTuuND6UVh48RvpdDi1bIFr5wutHw0bVouJ287lXhz1VmYto1dYb6Z2mIq7seoXX0II21XhyzSTJ09m5MiRtGnThvbt2zN37lzi4uKYMGECoFxiSUxMZOHChWi1Wpo0aXLZ+f7+/jg6Ov5tf3XWpkYbVvZfyQf7PmDFqRUsilzEjsQdvN3pbZr6NVU7XqUzBAWWFyP1//gdx8JCytLTL2wZF29nXH7bkpOD1WSiNCmJ0qSkf/z+xToj9HsbgNS3p+FoNgGg8/MtLz5cOnSoFq0ffyouK2be0XksPvAlf6469L9bn+feZrLAnbgCiwWKsiA/VdnyUiEvHeiiPL71fTAYQO8IeocLXy/dLuwz/OW+3gH0TqAzgPzeiUtUuBgZMmQImZmZvP766yQnJ9OkSRPWrl1LWFgYAMnJyf8554j4OxeDC6+2f5UeIT14dderxObGMvKXkYxtOpYJzSZg0FXRUQ0aDTp3d3Tu7jjUqfOvh1pKSihLz8CckU5pefGSjjkjg7K0i0UL5y+OvnJs0Ry/zh0vtn7Y8UJ112pH4g7e3v028XnxOFguDicfVO8eKUSqm9LiiwXGpYXGX+8XpMFfVx/XOkLnC8XIjo/Acj2TG2ouFicGJ9C6AhcGLax6FALqgG898K0P3rWVokZUadfUgXXixIlMnDjxio8tWLDgX8+dOnUqU6dOvZanrRY6B3fmhwE/8Nbut/gl5hfmHpnL9oTtvNXpLep52e/S85VB6+CAMTgIgoNw+pfjCopK4LUNAIR9NR9nY/Vcgim1IJX39r7Hb+d+A8DfyZ/n2z4JHz6nbjBxY1zasfr3WVCQDXkplxcaxTkV+57OPuBaA1z9wS344v7Wo6GsAMpKoKz4wteiy++XFv398XLWC8cXQfF5sF7SR/D493Ci5OJ9jRY8w5TC5M8C5c/NxadiP4+wWdXzVdrGeTh48F6X9+gZ2pM3/3iTyKxIhvw8hMdaPsaoRqPQae17Xosbzd7n/bheZZYylkYt5dODn1JYVohWo2VExAgmtZiEU6mGk2oHFNfPYob0KEjYB4n7IfEAZJyAjhf6S216Ayz/cK7OAdwCwPWSze1CwfFn4eEaoHy9tEXWbIZtF/oA3vE2VPTvzGoFs+mS4qRYaakpK4aiYpibrhzX/QU4fwrST0LGaSjJgewYZTu97vLv6eR9hSKlnlK86OTtzZ7I/5YNu73W7bQOaM3UXVPZmrCV6funsyV+C292fJMAx7+PXhLicPph3vzjTaKyogBo5teMl9u9TEPvhgBYSgv/7XRhi6xWyE1Uio6EfUrhkXQQSv8yxPzSK5BN7gXXmlcuNBw91OmvodFc6DNyhZGSpjLgQqHR4VH4szXTaoX8NMg4dWE7ffFrTpzSryX+D2W7lM4I3pdc6vEMu6E/mrh+UozYOF8nX2b2mMmq6FW8s+cdDqQdYNBPg5jcYvJ/nyyqjZySHGYcmMHKUyuxYsXd6M5TrZ/innr3yLwh9qY4F5IOXCg+9itf868wqaTRFWq2hKDWENwGajSCgxdmxx4wE3TONzf3jaDRKK04bgEQ3vnyx0yFkBn99yIl87TS2pIeqWx/9fUAqNsDwrtC8C2gN96cn0X8KylG7IBGo2FgvYHcGngrL+98mb0pe3lnzzvczd1qRxMqs1qt/HjmR6bvn05WcRYA/ev05+k2T+Pt6K1yOvGfzKWQeuzipZaEfcqbKn9Zt0qjg4BGENTmYvHhWx8uvWRrrmatXkZnCGymbJeyWCAn/pIC5RSkRUH878rjiXuVbeu7YHCGsA5Qu5tSnAQ0gWrYyd0WSDFiR4Jcg5jXex5LIpcwc9/M8v2fHvyUsS3G4uHgoWI6cbOdOX+GN/54g/2p+wGo41GHl9q9RJsabVROJv7T+lcheR+kHFE+xf+VZ+jFwiOoNQQ2V958xX/TasErTNnqXVht2lRwcQmHPu9D3O8Qsw0KMyB6g7KB0mE3vItSmNTuBt7Vey6sm0mKETuj1Wi5v9H93OJ/C0s/XQrAwhMLWXFmBQ82eZARESNwNsiLVlVWVFbEnMNz+Pr415RZy3DUOTKh+QRGNRpVdYeA2yurFdJOwMm1cOJX4MKlhr1zgQtDZx09LhQdlxQfrn5qJa76Wo6Atg8rLShpx+HsVji7Bc7tgsJMOP6DsoFSFP7ZahLeVf5fbiApRuxUuPvFir2OZx1O5Z7ik4OfsDhyMQ83e5j76t8nb0xV0Jb4LUzbPY2kAmXSt24h3Zhy6xRqulaNhfuqBHMZxO2CqLVKEXL+3IUH9JQXI63HQOiF4sOnjkwApgatFmo0VbYOj0KZSblcdnYLxGyFhL1wPg4OLFQ2UC7j/FmchHUAh6qxlpgtkGKkCljUZxEbkzby2cHPSMhPYNqeaSw8sZCJLSbSN7yvDAWuApLzk5m2Zxqb4zcDEOgSyJRbp9A9tLvKyQSgdDo9s1EpQE7/psyd8SedA9TpDnVuh18uTAh5+1tglI6TNkVvhLD2ytZ9CpTkwbnflcLk7Balb8+f2++fglavdIAN76qcI66LFCNVgE6r467ad3F72O18f/p75hyZQ2J+Ii/ueJGvjn3Foy0fpUdID5lt0w6VWcqYf2w+nx/+nKKyIvQaPaMaj2J8s/FyOU5tOYlw6helAIndrsyh8SdnH6h/BzS4UylEjC5gMsEvb6uXV1SMgxvU761sAPnpSmHyZ3FyPk7pexL3u9KyVevCyvInVkNEf+X/XFw1KUaqEIPOwJCGQ+hftz9Lo5by5dEviT4fzZObn6Spb1Meb/U47QLbqR1TVMDIX0ZyNkdZPLCVfytebvcydb3qqpyqmrJalU/Ff15+ST50+ePedaDhndCgL4TcevlIF2H/XP2g6b3KBpAVc7Ewidl28bhVj8DPk5VitMkgqHubTGd/FaQYqYKc9E6MaTKGe+vfy4JjC1gUuYijGUd56LeHaBvYlidaPlElF+CrKlIKLs4pcTbnLF4OXkxuM5kBdQZI69bNZi6F2B1w8hdly7l03S2NUnQ0uFPZ/OqrFlOowDtc2VqPhpJ8WHbhUo1HiNJqcvx7ZXNwh4Z9lcKkdrfLZ7UV5aQYqcLcje483upxhkcM54sjX/DtqW/Znbyb4cnD6Rnak8daPkYdz39fnE7cHFarlT0pe1gatZRNcZvK9w+oM4Bn2jyDp6OneuGqo+M/wJm1cHqDMh35n/ROUKcHNOijfPKV0RUCLp+bZOIfylT9x75Xfo9yE+HwUmVz8lIu4TS5B2p1ltazS0gxUg34Ovkype0URjUexaxDs/j57M9sjNvI5vjN3FX7Lia2mEiQa5DaMaulwtJCfj77M0ujlhJ9Pvpvj7/Q9gXpG3IzlJVA5K/AhYniVk0EzYXF2lz8lMKjYV+ls6LM9yH+jUZzcYh2rzcgfjccWwknVkFBOhz4Wtlc/KHRAKXFJKRttZ9sTYqRaiTINYi3Or3FmCZj+PTgp2yI28CPZ35kbcxa7qt/Hw83exhfJ1+1Y1YL8bnxLD25lFWnV5FXmgcol9f61+nPwLoDGbpmqMoJqwGrVZnx9PAS5VNsURGwUnnMpz40uk25/BLUptq/UYhrpNVeHKFzxztwbofyuxb5IxSkwd4vlM09CBoPhMb3QFCrajnUW4qRaqiOZx0+6v4RxzKO8fGBj/kj+Q+WRi1lVfQq7o+4n9FNRuMiK15WOovVwu9Jv7MkagnbE7ZjvTDld6hbKEMbDmVA3QG4G90plMXsbqzsc3DkW6XZPOvMxf3u4XBh4VgmbAWjNKGLSqTTK31GaneDvh8qHV+PrYTIn5VLOb9/qmyeYcplnCaDlHlNqklhIu841VgT3yZ80fsLdifv5uMDH3M04yhfHP2C5SeXM7bx/cg6l5Uj35TP6jOrWRa1jNjc2PL9nYI6MazhMDoFdZLF7G604lxlyOXhZcqn0z8ZXKBRf2g+FGp2gKm71csoqg+dAer1Ura7ipXp6I+thFO/KpPk7fhI2XzrK60lde5UO/ENJ8WIoG1gWxbfuZjN8ZuZeXAm0eej+ezQZ7wXrDx+POM4TfxbyxtmBZ3NOcvSyKX8eOZHCsuU1g5Xgyt3172boQ2HEuYu5d4NZS5TPn0eXgpRP1+yBoxGWX+kxXBoeNfFWTRNZrWSiurM4AgRdymbqUApSI59D6fXK4v8bX0HNr4LBCrHF2SAc6iqkW8EKUYEoKwM3CO0B12Du7I2Zi1zD80ElCbsB9c9iKdjAN1Du9MjpAe31LhFppr/B2aLme2J21katZRdSbvK99f2qM2whsPoV6cfLgaZDOmGSj2uFCBHvoP8i8Ok8a0PzYdBs8HgEaxePiH+idFFuTzTZJDSmndyrdJicvLiCDtmtoRGd0DLkcocJlXkknrV+ClEpdFpdfSr049eIV3YuaMVAM4GF9KK0lh+cjnLTy7H1eBK5+DO9AjtQaeanXA1yvoMOSU5rIpexbKoZSTkJwCgQUPXkK4MbzicdoHtZI6QGyk/DY5+pxQhKUcv7nfyhqb3XbgM07LaXH8XVYCju/J723woZCbCtxdWILaYlZa+qJ/BNUApsFveD7711M17naQYEVd0acvHb4PWsT/9GJviNrE5fjMZRRn8EvMLv8T8gkFroG1gW3qE9qB7SPdqNxon+vwZFp/5gTVn11BUVgQo87vcU+8ehjQYQrCbfAK/YUqLIHqN0g8keiNYL1xm0RqgwR3Ki3TdXsqaI0LYMyevi7fHbYKTK5XCOz8Vds5QtpB2SlHSeKBdLuAnxYj4T0adkU5BnegU1ImX2r3E0YyjbIrbxKa4TcTmxrIjcQc7Enfwxu9v0MyvGT1Ce9AjpAe1PGqpHb3SWa1WkvOT+HON3OFrhlF0YdhnPa96DG84nL61++Kkd1IvZFVmtV68/XELKDt/8X7wLcqnyMb3gLP3zU4mxM3h3xBqvQU9X1X6lxxcBNHrIf4PZfvlf9BkoHIZJ6St3bQGSjEiKkSr0dLcrznN/ZrzVOunOJtzVmkxidvMkYwjHE4/zOH0w3y0/yNqe9QuL0wa+za2uw6wZZYyYnJiiMqKumwrLT7PngvHaDU6eoXdxvCGw2kd0FouxdwoeanKJ8F9i4Aayj5TLniFQLMhSiuIr6zZI6oRvVEZCdaoP+QmK38fBxcpw9UPLlI2n7pKa0nzYeBWQ+3E/0qKEXFdanvUpnbT2oxrOo60wjS2xG9hU9wmdqfs5mzOWc4ePcu8o/Pwd/Iv7wDb2K+12rH/pqisiNPZp4nKiiIyK5KozChOnz9Nibnkb8e6ai/+2awesIoAr9o3M2r1YS6DMxvhwEJlXRirGSxayouRESugXneZkEwI90DoPBk6PQVxfyiFyPEfIDMaNkyFjW9Avd5KYVL/dptcH0eKEVFp/J39GdxgMIMbDCbPlMeOxB1sitvE9sTtl3WAdTZ6Q42PAdidvBt/R3fcjG64G91xNbpi0N7YP5SckpzygiMyK5KorChic2OxWC1/O9ZZ70xD74blW4RPBHWcasC7yrDcAJeAG5q1WsqKUV5MDy2GvOSL+4NvgSbD4eT3yv2wjlKICHEpjebijK993lEKkoOLlCnpT/2ibC5+Smtiy5HKJR8bIcWIuCHcjG70Ce9Dn/A+mMwm9qTsKe8Am16cV37c45seR2O9vPXBWe+sFCcO7rgZlK/uxosFy5W+ejh44GZ0w1l/+bohKfkpxOafKm/xOJl1kuSCZK7Ex9GHhj4NifCOKC8+QtxC/n55yVRQOf9I4qLSYoj8CQ4uvHw5didvpYm51Ujwj4DiYuB71WIKYTcc3KDVKGVLPwWHFsGhpco09H/O9hrUBpqMBNSft0SKEYAzmyGit6ygeIP8tQPs3rQjDDihPFbXsy4FpkzyTHkUlCpv8oVlhRSWFZJamFrh59JpdLjovIGnAei/uj8abenfjgtxC7m8xcM7Aj9nWYH1pks5qlyGOfItFJ+/sFMDdborL6IN7gS9g5oJhbB/fvWh1+vQ42VltteDi5TOr4n7IP4osEw5Lvkw1GqlSkQpRgCWDwfPwAvjtUeAt/QBuFG0Gi1NfJsCylwQi/suxkWnFIFlljLyTfnkmfLINeWWb3/ezzPlKbdLcsktzSWv5PLjyixlmK1mckzny59Pr9FTxyu8vOBo6N2QBt4NcDO6qfDTCwCKc+DoCjj4DSQdvLjfIwRajFD+Bj3V/6QmRJWjM0CDPsqWn6YMi9+/DNIuPJ56QooRVTl6KgsVbf9A2Wp1Vjr6RPSX5cJvIr1Wj6ejJ56OnhU+12q1UmIuIdeUS1p+DnedPAXAliFb8XSSYbaqs1oh7nelFeT4KrgwJwtaAzTsq1yGqd1dWieFuFlc/aHj49B6Ijx54dJoxF2qxZFiBOCxg3Buk9J0dWYTxG5XtrXPKqsnthxVbZd1thcajQZHvSOOekdc9d6AUowYbbDXeLWSnwaHliitIJnRF/f7NVQ60DUfCi7Va6I8IWzKpe9rDuq1GEsxAspCRU3uUbbz8UrT1cFvlNUT9y9QNr8IpbWk2RBwlb4FQvynFWPgzM9gKVPuG1yUv7FWo5SRMVLcCyEukGLkrzxDoOuz0PlpZanxg4uUpcfTI+G3F2HDq8r1tpYjoU7PKrNIkRDXLfUE7F8OdFXun/wFtGVK4dFq1IVpqqWvjhDi7+Sd9J9otcoy4+FdoM97ysqJBxdB0gFlCGLkT+BaA1oMgxb3y+yPonrKT4djK5TZH5MPg8WB8mLk1ofh1hHKkFwhhPgXUoxcDSdPuGWssqUeh4OL4cgyZXnyHR8pW2gH5TJOowF2uUiREFettFiZPOnwMji9/vIF6ur1udgzv9dr4CAdUoUQ/+2api+cNWsW4eHhODo60rp1a7Zv3/6Px37//ff06tULPz8/3N3dad++PevWrbvmwKoLaAx3vA2To2DwQmWKXY0W4nbB6onwYQNY/SjE71U7qRCVx2pVppn+6Qn4oD58N1qZp8BqhqDWcOcH8PRJuHe+2kmFEHaowi0jy5cv58knn2TWrFl07NiROXPm0KdPH06cOEFo6N/nBti2bRu9evXi7bffxtPTk6+++op+/fqxe/duWrZsWSk/hCr0RqUVpNEAyE26ZJGis0rn1wPfAiuVY8/Hg38tNdMKcW2yYpQJyQ4vheyYi/vdg6H5EGg2VJlQ6U8l5pufUQhh9ypcjEyfPp2xY8cybtw4AGbMmMG6deuYPXs206ZN+9vxM2bMuOz+22+/zerVq/npp5/suxi5lHtNpcNrp8lwbteFRYp+gT9nOf/sVghpBk0GQaO7lUWNhLBVxTnKXCCHlyktfn8yuCjFd4thENZJ1oURQlSaChUjJpOJ/fv38/zzz1+2v3fv3uzatesfzrqcxWIhLy8Pb2/vijy1fdBooFZHZeuZDW8f+/MBSNirbL9OURb4ajJQKUxkjgVhC8xlcHazMifIybVQVnzhAQ3U7qbMThxxFxhd1EwphKiiKlSMZGRkYDabCQi4fKXSgIAAUlJSrup7fPjhhxQUFDB48OB/PKakpISSkouLp+Xm5lYkpm1wdL94+7EDEP2TMiInYY8yZPjcDlj7nDJap8kg5YXeyUu9vKJ6SjmqtIAc+VZZQOtPfg2VAqTZYKXlTwghbqBrGk2j+ctkRVar9W/7rmTp0qVMnTqV1atX4+/v/4/HTZs2jddee+1aotkm9xrQboKynY9TlnU+9j0kH1I+jZ7dDD8/BXV7KoVJgz4yH4O48ebdBlnHL9539oGm9ylFSGBzmZRMCHHTVKgY8fX1RafT/a0VJC0t7W+tJX+1fPlyxo4dy3fffcdtt932r8dOmTKFyZMnl9/Pzc0lJCSkIlFtl2codHxC2TLPwPHvlcIk7YQyOuHUr6B3VEbpNLkH6t0u6+OI62O1Ki0gJ3+BYz9f3J92AhyMSvHbfBjUvU1ZSEsIIW6yChUjRqOR1q1bs379egYOHFi+f/369QwYMOAfz1u6dCljxoxh6dKl9O3b9z+fx8HBAQeHarBsuE8d6PKssqVFKkXJ8e+VNTwif1Q2g4vyZtFkkNJyIsupi6thLoXYHUr/j5O/QE68sr9MA1zoQH3HO9B6iFweFEKorsKXaSZPnszIkSNp06YN7du3Z+7cucTFxTFhwgRAadVITExk4cKFgFKIjBo1io8//ph27dqVt6o4OTnh4eFRiT+KnfOPgB4vQvcXIOWIUpgc+x5y4pQZLo+tAAcPpW9J43sguL3aiYWtKToP0RuUAuT0BijJufiY3gnq9IBat8GK95V9rUaBk7S6CSHUV+FiZMiQIWRmZvL666+TnJxMkyZNWLt2LWFhYQAkJycTFxdXfvycOXMoKytj0qRJTJo0qXz/Aw88wIIFC67/J6hqNBrlen1gc7htKiTuVzq+Hv8B8pLh0GJlc/QHRijnmArAaFQztVDL+Til5ePkWqUl5M9F6QBc/KHBHdDgTmVEjMEJCguB99VKK4QQV3RNHVgnTpzIxIkTr/jYXwuMLVu2XMtTCFAKk+A2ytb7LYj7XbmMc3wVFGZdPO7DCAhtpbzhhHeFoFZy7b+qslqVjs8nf4GotZB69PLHfRtAwzuVAiSojcwFIoSwC7I2jb3Qai/OYXLHu3B6CyzboTxmLYVzO5Vt81tgdFOOC++qFCj+ETIywp6VlUDsdqX4OPkL5CVdfEyjhdD2Sr+iBncq/ZCEEMLOSDFij3R6qN0FuFCMTNgJCbvg7BaI2QZF2RdH5oDSXF+764XipKsyokfYh+8fhjNbwJR3cZ/BBer2gAZ9lVFXLj6qxRNCiMogxUhV4F0bajSENmPAYlE6wMZshbNblenpC9Lg6HfK9ufxf7aahHcB5yo4G649sZghPQoS9il9hBL3wZ/9SqN+Vi7NuNa40P+jr/J/ZnBUNbIQQlQmKUaqGq0WarZQto5PKE38CXuVVpOzW5U3u6yzyrb/K0ADgc0utpqEdpB5TW4kqxVyEy8pPA5A0kEoLbh4jEYDtS7Mq9PhCYjoDzVbSv8PIUSVJcVIVad3gFqdlK3HS1Ccq/QtObtVKVDSIyH5sLLt+gR0Rgi+FcI7qp28aijOUYqNhH1K4ZG4D/JT/36c0VUpOIJaK8Xh/qnK/m7/A4MUh0KIqk2KkerG0f1CZ8c+yv28VKWfydktypaboKybE78D/t/e3QdFdd57AP8u+4oIq4iyoIjoVVExvQpVMEaMGtRem2TqRE2MUsc6JTNpfGmmxWRatTcvOEltml5fEguaSWvlpmjyhzZWGzVOwCYqTTX4FkPURJDgFcHIyy77u38cWDnsArvrLmch38/Mzp599jnPPr99zsP+OHvO2aktP+L3P5OA6FFAzCggZmTL/Sig7yAeGNtWsx24fkbZ4/HVSeW++gIAUdfT6YHYcUriMThVOVsqZhQQpleet9+5m4wQEX0HMBn5rouMBe57TLmJKF/ffHEEKP8AwHGlzq2rwM2rwKV/qNc1W9skJ22SlOik786pxZ+9qyQgX51QjtVx/dptG/2GKqfZtiYetvv4VRgRURtMRugunU45NXTACGDi48DR8Ur50veA/7ui/JdffVG5v/mlcoXPr08ot7bCDED/JPckJeY/Qv/S4yLKNVxuXwduVwK3q5TluustZdeVi8+1eq/d9XYs1pY9Hml393z0Hdi9MRAR9TBMRqhrCZOAYdPVZY5GZS9K9QV1klJ9EWi6Ddy4qNzOt2srYhAwcByQuF55fGInYDQpPw5oMN+9N4arHxssbW5m378esjcoZxW5koqWRKOuTcJx+7qy7LR7327cfwIJk+8mHgNG8KsrIiIfMRkh/xjMysXUBo1Rl4soew5UCUrLcu3XSkJQXwskttQ/8Bzg9PDVRlf0ZuX01vZJjCEcCIsAsEKpty0TuPMV0FDjW/vh0UCkTTkupm/LfaQN6BsLmKOAXY8p9ZbtB0wRvvefiIhcmIxQYOl0QFS8chs+Xf1cY53yi8TffA60Xs0++b8Ax7fKsRaORuXe3qB+7GgA7PVQHQja3KjccAtuxAxXMnLjIqBrVJb1ZiWZiIxV7t0SjZbHEQMBQye/9dP0bcfPERGRz5iMUPcxRyqnr8beB3zY8psq87cDen3X64ooPwLXmqTY69skK633LWUNDcDulvWe+F8gOk5JNCz9+BUKEVEIYjJCPYNOp5yhozcqSU1nmhwADijLSVMBEzdzIqJQxks6EhERkaaYjBAREZGmmIwQERGRppiMEBERkaaYjBAREZGmmIwQERGRppiMEBERkaaYjBAREZGmmIwQERGRppiMEBERkaaYjBAREZGmmIwQERGRppiMEBERkaaYjBAREZGmmIwQERGRppiMEBERkaaYjBAREZGmmIwQERGRppiMEBERkaaYjBAREZGmmIwQERGRpvxKRrZs2YKkpCRYLBakpqbi2LFjndY/evQoUlNTYbFYMHz4cGzbts2vzhIREVHv43MyUlhYiFWrVuH5559HaWkpHnjgAcydOxdXrlzxWL+8vBw/+MEP8MADD6C0tBTPPfccnnnmGRQVFd1z54mIiKjnM/i6wqZNm7B8+XL85Cc/AQC89tprOHDgALZu3YqXX37Zrf62bdswdOhQvPbaawCAMWPG4MSJE3j11Vcxf/78e+v9PRAR1/KdJgeMYY7Att/U7Fqub3JAB+mktu+amu72906TA44Af+PW3KxuX68P3PtT3+y8u9zUDJ0+sO/NnXbvTcA1OdBH1X5gX6Pe0WbbsTcDErj2ne3emzBDYPtub7Pd32lywKgL7Nja2/U/kPOWc7ZzwZy3nLOdC+a8bTtn234udjefkpGmpiacPHkSubm5qvKsrCwUFxd7XKekpARZWVmqstmzZyM/Px92ux1Go9FtncbGRjQ2Nroe19bW+tJNr9Tb7w5A6guH4Ahz78e9sAA4hChX+w0BbR0woBlPWpTltBcOwQF9QNs36RuxdaaynPrCITQ1mwPWtuh1wKx4V9u65uBNgLQX/hHwNsPRgLMt733qC4dQD0tgX0DXhMjklvb/+xAgpoA1bXY04t2W5dQXDqHRELhxBQCjAKsQDkDZLu26gDYPg9OOp1qWAz1vOWc7113zlnPWXTDnbds5W29vhsni8z6KgPApNa+urkZzczNiY2NV5bGxsaisrPS4TmVlpcf6DocD1dXVHtd5+eWXYbVaXbeEhARfuklEREQ9iE582C9z7do1DB48GMXFxcjIyHCVv/jii3j77bdx7tw5t3VGjRqFZcuWYe3ata6yjz76CFOnTkVFRQVsNpvbOp72jCQkJODWrVuIioryOrjOOJ1O1N2+AwAwmM3Q6QL7L5yIAPaW3ZrGsKC0b7fbleaNxqC073TWAwDCwsID2r6IoN6pbHbhYbqg9L11z1e4UR/w9iEC2JVtB8Y+QBD639Cs/F9u0VsC/t5LvTKuuvDAjmtr+44mZbs3mIKz3Tta/jYEet5yznbdfrDmLeds1+0Ha962nbOREUaEhQX268Pa2lpYrdYuP7992h8TExMDvV7vthekqqrKbe9HK5vN5rG+wWDAgAEDPK5jNpthNgd2F2N7YWFhsEb1DeprILghAObAfrXkLnjtRwSt5Zb2g/3emK1BbT4iiO990Lebnrzd9+S+AwjmnAWCO285Z7vQk7d7L/iUAplMJqSmpuLgwYOq8oMHD2LKlCke18nIyHCr//e//x1paWkejxchIiKi7xaf98esWbMGf/zjH1FQUICzZ89i9erVuHLlCnJycgAAa9euxdKlS131c3JycPnyZaxZswZnz55FQUEB8vPz8eyzzwYuCiIiIuqxfD5sduHChbhx4wZ+85vfoKKiAikpKdi/fz8SExMBABUVFaprjiQlJWH//v1YvXo1Nm/ejPj4eLz++uuantZLREREocOnA1i14u0BMERERBQ6vP385m/TEBERkaaYjBAREZGmmIwQERGRppiMEBERkaaYjBAREZGmmIwQERGRppiMEBERkaaYjBAREZGmmIwQERGRpny+HLwWWi8SW1tbq3FPiIiIyFutn9tdXey9RyQjdXV1AICEhASNe0JERES+qqurg9Vq7fD5HvHbNE6nE9euXUNkZCR0Ol3A2q2trUVCQgKuXr3aa3/zprfHyPh6vt4eY2+PD+j9MTI+/4kI6urqEB8fj7Cwjo8M6RF7RsLCwjBkyJCgtR8VFdUrN7C2enuMjK/n6+0x9vb4gN4fI+PzT2d7RFrxAFYiIiLSFJMRIiIi0tR3Ohkxm81Yt24dzGaz1l0Jmt4eI+Pr+Xp7jL09PqD3x8j4gq9HHMBKREREvdd3es8IERERaY/JCBEREWmKyQgRERFpiskIERERaarXJyMvvvgipkyZgj59+qBfv35erSMiWL9+PeLj4xEeHo7p06fjs88+U9VpbGzEz372M8TExCAiIgIPP/wwvvrqqyBE0LmbN29iyZIlsFqtsFqtWLJkCWpqajpdR6fTeby98sorrjrTp093e37RokVBjsadP/H9+Mc/dut7enq6qk6ojB/ge4x2ux2//OUvMX78eERERCA+Ph5Lly7FtWvXVPW0GsMtW7YgKSkJFosFqampOHbsWKf1jx49itTUVFgsFgwfPhzbtm1zq1NUVISxY8fCbDZj7Nix2Lt3b7C67xVfYtyzZw8eeughDBw4EFFRUcjIyMCBAwdUdXbu3OlxTjY0NAQ7FI98ie/IkSMe+37u3DlVvVAaQ1/i8/T3RKfTYdy4ca46oTR+H374IX74wx8iPj4eOp0O7777bpfrhMQclF7u17/+tWzatEnWrFkjVqvVq3Xy8vIkMjJSioqK5PTp07Jw4UKJi4uT2tpaV52cnBwZPHiwHDx4UE6dOiUPPvigfO973xOHwxGkSDybM2eOpKSkSHFxsRQXF0tKSorMmzev03UqKipUt4KCAtHpdHLp0iVXnczMTFmxYoWqXk1NTbDDceNPfNnZ2TJnzhxV32/cuKGqEyrjJ+J7jDU1NTJr1iwpLCyUc+fOSUlJiUyePFlSU1NV9bQYw927d4vRaJTt27dLWVmZrFy5UiIiIuTy5cse63/xxRfSp08fWblypZSVlcn27dvFaDTKX//6V1ed4uJi0ev18tJLL8nZs2flpZdeEoPBIMePHw9qLB3xNcaVK1fKxo0b5eOPP5YLFy7I2rVrxWg0yqlTp1x1duzYIVFRUW5zUwu+xnf48GEBIOfPn1f1ve1cCqUx9DW+mpoaVVxXr16V6OhoWbdunatOKI3f/v375fnnn5eioiIBIHv37u20fqjMwV6fjLTasWOHV8mI0+kUm80meXl5rrKGhgaxWq2ybds2EVE2TqPRKLt373bV+frrryUsLEzef//9gPe9I2VlZQJAtUGUlJQIADl37pzX7TzyyCMyY8YMVVlmZqasXLkyUF31i7/xZWdnyyOPPNLh86EyfiKBG8OPP/5YAKj+oGoxhpMmTZKcnBxVWXJysuTm5nqs/4tf/EKSk5NVZT/96U8lPT3d9XjBggUyZ84cVZ3Zs2fLokWLAtRr3/gaoydjx46VDRs2uB57+/epO/gaX2sycvPmzQ7bDKUxvNfx27t3r+h0Ovnyyy9dZaE0fm15k4yEyhzs9V/T+Kq8vByVlZXIyspylZnNZmRmZqK4uBgAcPLkSdjtdlWd+Ph4pKSkuOp0h5KSElitVkyePNlVlp6eDqvV6nU/rl+/jn379mH58uVuz/35z39GTEwMxo0bh2effdb168nd5V7iO3LkCAYNGoRRo0ZhxYoVqKqqcj0XKuMHBGYMAeDWrVvQ6XRuX0V25xg2NTXh5MmTqvcVALKysjqMpaSkxK3+7NmzceLECdjt9k7rdPdYAf7F2J7T6URdXR2io6NV5bdv30ZiYiKGDBmCefPmobS0NGD99ta9xDdhwgTExcVh5syZOHz4sOq5UBnDQIxffn4+Zs2ahcTERFV5KIyfP0JlDvaIH8rrTpWVlQCA2NhYVXlsbCwuX77sqmMymdC/f3+3Oq3rd4fKykoMGjTIrXzQoEFe9+Ott95CZGQkfvSjH6nKFy9ejKSkJNhsNpw5cwZr167Fp59+ioMHDwak797wN765c+fiscceQ2JiIsrLy/GrX/0KM2bMwMmTJ2E2m0Nm/IDAjGFDQwNyc3PxxBNPqH7kqrvHsLq6Gs3NzR7nTkexVFZWeqzvcDhQXV2NuLi4Dut091gB/sXY3m9/+1t8++23WLBggassOTkZO3fuxPjx41FbW4vf//73uP/++/Hpp59i5MiRAY2hM/7EFxcXhzfffBOpqalobGzE22+/jZkzZ+LIkSOYNm0agI7HubvH8F7Hr6KiAn/729+wa9cuVXmojJ8/QmUO9shkZP369diwYUOndT755BOkpaX5/Ro6nU71WETcytrzpo43vI0PcO+nr/0oKCjA4sWLYbFYVOUrVqxwLaekpGDkyJFIS0vDqVOnMHHiRK/a7kiw41u4cKFrOSUlBWlpaUhMTMS+ffvcki5f2vVFd42h3W7HokWL4HQ6sWXLFtVzwRzDzvg6dzzVb1/uz3wMJn/785e//AXr16/He++9p0pC09PTVQdZ33///Zg4cSL+8Ic/4PXXXw9cx73kS3yjR4/G6NGjXY8zMjJw9epVvPrqq65kxNc2g83fvuzcuRP9+vXDo48+qioPtfHzVSjMwR6ZjDz99NNdnhUwbNgwv9q22WwAlGwxLi7OVV5VVeXKDG02G5qamnDz5k3Vf9dVVVWYMmWKX6/blrfx/fvf/8b169fdnvvmm2/cslhPjh07hvPnz6OwsLDLuhMnToTRaMTFixfv+YOsu+JrFRcXh8TERFy8eBFA8McP6J4Y7XY7FixYgPLycnzwwQdd/vR3IMfQk5iYGOj1erf/ltrOnfZsNpvH+gaDAQMGDOi0ji/bQKD4E2OrwsJCLF++HO+88w5mzZrVad2wsDB8//vfd22z3eVe4msrPT0df/rTn1yPQ2UM7yU+EUFBQQGWLFkCk8nUaV2txs8fITMHA3b0SYjz9QDWjRs3usoaGxs9HsBaWFjoqnPt2jXNDmD95z//6So7fvy41wc/Zmdnu52B0ZHTp08LADl69Kjf/fXVvcbXqrq6Wsxms7z11lsiEjrjJ+J/jE1NTfLoo4/KuHHjpKqqyqvX6o4xnDRpkjz11FOqsjFjxnR6AOuYMWNUZTk5OW4Hz82dO1dVZ86cOZoewOpLjCIiu3btEovF0uXBhK2cTqekpaXJsmXL7qWrfvEnvvbmz58vDz74oOtxKI2hv/G1Hqh7+vTpLl9Dy/FrC14ewBoKc7DXJyOXL1+W0tJS2bBhg/Tt21dKS0ultLRU6urqXHVGjx4te/bscT3Oy8sTq9Uqe/bskdOnT8vjjz/u8dTeIUOGyKFDh+TUqVMyY8YMzU7tve+++6SkpERKSkpk/PjxbqeFto9PROTWrVvSp08f2bp1q1ubn3/+uWzYsEE++eQTKS8vl3379klycrJMmDAh5OOrq6uTn//851JcXCzl5eVy+PBhycjIkMGDB4fk+In4HqPdbpeHH35YhgwZIv/6179UpxI2NjaKiHZj2HraZH5+vpSVlcmqVaskIiLCdeZBbm6uLFmyxFW/9bTC1atXS1lZmeTn57udVvjRRx+JXq+XvLw8OXv2rOTl5YXEqb3exrhr1y4xGAyyefPmDk+zXr9+vbz//vty6dIlKS0tlWXLlonBYFAlqaEa3+9+9zvZu3evXLhwQc6cOSO5ubkCQIqKilx1QmkMfY2v1ZNPPimTJ0/22GYojV9dXZ3rcw6AbNq0SUpLS11n2oXqHOz1yUh2drYAcLsdPnzYVQeA7Nixw/XY6XTKunXrxGazidlslmnTprllw/X19fL0009LdHS0hIeHy7x58+TKlSvdFNVdN27ckMWLF0tkZKRERkbK4sWL3U6xax+fiMgbb7wh4eHhHq87ceXKFZk2bZpER0eLyWSSESNGyDPPPON2rY7u4Gt8d+7ckaysLBk4cKAYjUYZOnSoZGdnu41NqIyfiO8xlpeXe9ym227XWo7h5s2bJTExUUwmk0ycOFG1JyY7O1syMzNV9Y8cOSITJkwQk8kkw4YN85ggv/POOzJ69GgxGo2SnJys+qDTgi8xZmZmehyr7OxsV51Vq1bJ0KFDxWQyycCBAyUrK0uKi4u7MSI1X+LbuHGjjBgxQiwWi/Tv31+mTp0q+/btc2szlMbQ1220pqZGwsPD5c033/TYXiiNX+senI62t1CdgzqRliNViIiIiDTA64wQERGRppiMEBERkaaYjBAREZGmmIwQERGRppiMEBERkaaYjBAREZGmmIwQERGRppiMEBERkaaYjBAREZGmmIwQERGRppiMEBERkaaYjBAREZGm/h+LkwvLg1IVswAAAABJRU5ErkJggg==\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": 20, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:12.805000Z", "iopub.status.busy": "2024-04-30T08:55:12.804888Z", "iopub.status.idle": "2024-04-30T08:55:12.807530Z", "shell.execute_reply": "2024-04-30T08:55:12.807285Z" } }, "outputs": [], "source": [ "hfmIn = Eikonal.dictIn({\n", " 'model':'TTI2',\n", " 'exportValues':1,\n", " 'seed':[0.,0.5],\n", "})\n", "\n", "# Define the domain\n", "hfmIn.SetRect(sides=[[-1,1],[0,1]],dimx=101)\n", "hfmIn.SetUniformTips((6,6))\n", "\n", "X0 = hfmIn.Grid() # Grid coordinates (horizontal and vertical)\n", "X = h(*X0) # Physical coordinates" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By default, for the GPU eikonal solver, the TTI norm is obtained as the envelope of $7$ Riemannian norms. This turns out to be insufficient for the strongly anisotropic crystal chosen here. We change below this value to $15$, in order to have better behaved geodesics. (The CPU eikonal solver uses a different formulation, and has no such restriction.)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:12.808893Z", "iopub.status.busy": "2024-04-30T08:55:12.808797Z", "iopub.status.idle": "2024-04-30T08:55:12.810406Z", "shell.execute_reply": "2024-04-30T08:55:12.810194Z" } }, "outputs": [], "source": [ "if hfmIn.mode=='gpu':hfmIn['traits']={'nmix_macro':15}" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:12.811774Z", "iopub.status.busy": "2024-04-30T08:55:12.811690Z", "iopub.status.idle": "2024-04-30T08:55:12.814080Z", "shell.execute_reply": "2024-04-30T08:55:12.813847Z" } }, "outputs": [], "source": [ "X0_ad = ad.Dense.identity(constant=X0,shape_free=(2,))\n", "Jac = h(*X0_ad).gradient().swapaxes(0,1)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:12.815466Z", "iopub.status.busy": "2024-04-30T08:55:12.815385Z", "iopub.status.idle": "2024-04-30T08:55:12.817376Z", "shell.execute_reply": "2024-04-30T08:55:12.817135Z" } }, "outputs": [], "source": [ "hfmIn['metric'] = mica.extract_xz().rotate_by(-np.pi/6).inv_transform(Jac) " ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:12.818733Z", "iopub.status.busy": "2024-04-30T08:55:12.818652Z", "iopub.status.idle": "2024-04-30T08:55:12.859728Z", "shell.execute_reply": "2024-04-30T08:55:12.859415Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.023079 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.Run()" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:12.861294Z", "iopub.status.busy": "2024-04-30T08:55:12.861188Z", "iopub.status.idle": "2024-04-30T08:55:12.929073Z", "shell.execute_reply": "2024-04-30T08:55:12.928823Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[6,4]); plt.axis('equal');\n", "plt.title('Minimal distance, Seismic metric (constant) with topography'); \n", "plt.contourf(*X,hfmOut['values']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The geodesics are expected to be straight lines, except for the ones tangent to the topography." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:12.930628Z", "iopub.status.busy": "2024-04-30T08:55:12.930540Z", "iopub.status.idle": "2024-04-30T08:55:13.006190Z", "shell.execute_reply": "2024-04-30T08:55:13.005904Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[5,4]); plt.axis('equal'); \n", "plt.title('Minimal geodesics, Seismic metric (constant) with topography');\n", "for geo in hfmOut['geodesics']: plt.plot(*h(*geo)) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the computation involved a rather strongly anisotropic and non-constant metric, on a rectangle." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:13.007792Z", "iopub.status.busy": "2024-04-30T08:55:13.007686Z", "iopub.status.idle": "2024-04-30T08:55:13.075489Z", "shell.execute_reply": "2024-04-30T08:55:13.075232Z" } }, "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": "markdown", "metadata": {}, "source": [ "## 2 Three dimensions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1 Constant metric" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:13.077084Z", "iopub.status.busy": "2024-04-30T08:55:13.076978Z", "iopub.status.idle": "2024-04-30T08:55:13.080182Z", "shell.execute_reply": "2024-04-30T08:55:13.079879Z" } }, "outputs": [], "source": [ "hfmIn_Constant = Eikonal.dictIn({\n", " 'model':'TTI3',\n", " 'arrayOrdering':'RowMajor',\n", " 'exportValues':1,\n", " 'seeds':[[0.,0.,0.]],\n", " 'factoringRadius':20,\n", " 'seedRadius':2,\n", "# 'order':2\n", "# 'exportGeodesicFlow':1,\n", "})\n", "\n", "hfmIn_Constant.SetRect(sides=[[-1,1],[-1,1],[-1,1] ],dimx=31,sampleBoundary=True) # Define the domain\n", "X = hfmIn_Constant.Grid() \n", "\n", "metric = Seismic.TTI([1.,1],[[0.5,0.1],[0.1,-0.2]],vdim=3).rotate_by(0.5,axis=(1,2,3))\n", "hfmIn_Constant['metric'] = metric" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:13.081587Z", "iopub.status.busy": "2024-04-30T08:55:13.081501Z", "iopub.status.idle": "2024-04-30T08:55:13.335155Z", "shell.execute_reply": "2024-04-30T08:55:13.334821Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field order defaults to 1\n", "Field factoringPointChoice defaults to Seed\n", "Field exportFactoring defaults to 0\n", "Fast marching solver completed in 0.209421 s.\n" ] } ], "source": [ "hfmOut = hfmIn_Constant.Run()" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:13.336775Z", "iopub.status.busy": "2024-04-30T08:55:13.336680Z", "iopub.status.idle": "2024-04-30T08:55:13.392001Z", "shell.execute_reply": "2024-04-30T08:55:13.391721Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.axis('equal')\n", "plt.contourf(hfmOut['values'][:,5,:]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The largest difference between the exact value and the fast marching result is in the corners, because several of the stencil points may be outside the domain." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:13.393509Z", "iopub.status.busy": "2024-04-30T08:55:13.393423Z", "iopub.status.idle": "2024-04-30T08:55:17.166998Z", "shell.execute_reply": "2024-04-30T08:55:17.166728Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.axis('equal')\n", "plt.contourf(hfmOut['values'][:,5,:]-metric.norm(X)[:,5,:]);" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:17.168665Z", "iopub.status.busy": "2024-04-30T08:55:17.168546Z", "iopub.status.idle": "2024-04-30T08:55:20.918869Z", "shell.execute_reply": "2024-04-30T08:55:20.918438Z" } }, "outputs": [], "source": [ "assert norm_infinity(hfmOut['values'] - metric.norm(X)) < 2e-2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2 Varying metric" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:20.920590Z", "iopub.status.busy": "2024-04-30T08:55:20.920489Z", "iopub.status.idle": "2024-04-30T08:55:20.922678Z", "shell.execute_reply": "2024-04-30T08:55:20.922439Z" } }, "outputs": [], "source": [ "hfmIn = Eikonal.dictIn({\n", " 'model':'TTI3', \n", " 'exportValues':1,\n", " 'seed':[0.,0.,0.5],\n", " 'factoringRadius':7,\n", " 'order':2\n", "})\n", "\n", "# Define the domain\n", "n=30; \n", "hfmIn.SetRect(sides=[[-1,1],[-1,1],[0,1]],dimx=n)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:20.924103Z", "iopub.status.busy": "2024-04-30T08:55:20.924006Z", "iopub.status.idle": "2024-04-30T08:55:20.925935Z", "shell.execute_reply": "2024-04-30T08:55:20.925693Z" } }, "outputs": [], "source": [ "X,Y,Z = hfmIn.Grid()" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:20.927278Z", "iopub.status.busy": "2024-04-30T08:55:20.927171Z", "iopub.status.idle": "2024-04-30T08:55:20.931311Z", "shell.execute_reply": "2024-04-30T08:55:20.931041Z" } }, "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)\n", "\n", "hfmIn['metric'] = mica.rotate(rotation)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:20.932732Z", "iopub.status.busy": "2024-04-30T08:55:20.932648Z", "iopub.status.idle": "2024-04-30T08:55:20.934372Z", "shell.execute_reply": "2024-04-30T08:55:20.934127Z" } }, "outputs": [], "source": [ "if hfmIn.mode=='gpu':hfmIn['traits']={'nmix_macro':10}" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:20.935728Z", "iopub.status.busy": "2024-04-30T08:55:20.935649Z", "iopub.status.idle": "2024-04-30T08:55:21.399394Z", "shell.execute_reply": "2024-04-30T08:55:21.399028Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity 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 0.402343 s.\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.401092Z", "iopub.status.busy": "2024-04-30T08:55:21.400976Z", "iopub.status.idle": "2024-04-30T08:55:21.469482Z", "shell.execute_reply": "2024-04-30T08:55:21.469220Z" } }, "outputs": [ { "data": { "image/png": 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A5rZiS+XrcxISEhAZGYlt27YBsH87DwwMRKtWrTB//ny89NJLOHDggHl7chZH9zmdTodBgwZZTOvYsaPFdmGLadkrfzfDhg2zOq29YcMG9O7dG2FhYRbblWl73LFjh0X7+++/H76+vubn/v7+GDRoEL788ktcv34dV69exRdffIGhQ4eifv36FvMcMGAArl69il27dlnM87777rNaRgDm5czJycHVq1erXNeVl8eRMbF3794WNx+EhIQgODi4xu+4JjqdDgMGDDA/N+3ToaGh6Ny5s3l6YGBgjZ/3yy+/4NixY5gwYYLFd1+Zo2OvLb1790aDBg3Mz03Hn6SkJOh0OqvpN68je7btn3/+GWfOnMHIkSMt5hcZGYmEhASL927YsAGNGjXCoEGDLNbl7bffjqZNm7rsbizNhReTuLg4/Otf/8KaNWtw5swZTJs2DSdOnLDrot2b/fbbbzXefXT27Fl899138PHxsXj4+/tDCFFtYCoqKgIAm3dChIWFmV93VEpKCp5++mkMGTIEn3zyCXbv3o09e/agU6dOuHLlilX7qu7EqF+/PgICAuz6zPHjx+P06dPIysoCAKxevRqlpaUWO9I333yDxMREAMD//vc/fP3119izZw9mzpwJADb75gqV7+DR6/WoX7++1aCk1+tx9epV83N71/Wdd96JDz/8EOXl5RgzZgyaNWuG9u3bY/Xq1bXqb1FREZo2bWox0ABAcHAwvL29rbYTe++suXTpEnr27Indu3fjueeew/bt27Fnzx6sW7cOgP3ro2nTpjanmfpl73au0+nwxRdfoH///pg3bx66dOmCJk2aYMqUKbh48aJdfamJo/ucre3CYDBYbBfVfU7l78bb2xuNGze2mHb27Fl88sknVttVu3btAMBqDKnq+7527RouXbqEoqIilJeX47XXXrOap+lgXnmelftkMBgA/LkNVLU8tqY5OiZW/mzT59d1PKhqn7Z1B1/lfb0y0/UdNR0PHB17bbE1PlU33dRve7dtR9flhQsXoNfrrdZnQUGBwwUBe2nubiNbfHx8MGvWLLz88sv44YcfHHpvkyZNcOrUqWrbBAUFwc/PDxkZGVW+XhXTTpufn2/12pkzZ6p9b3XeeecdjBkzBs8//7zF9MLCQpu3GVY+KNY03Zb+/fsjLCwMK1asQP/+/bFixQp069bN4s6Q9957Dz4+PtiwYYPFoPLhhx/a/Tme5Mi6Hjx4MAYPHozS0lLs2rUL6enpGDlyJFq0aIH4+HiHPrdx48bYvXs3hBAW6+TcuXMoLy+32k7sXW9bt27FmTNnsH37dnO1BYDDv6VRUFBgc9qtt95q7j9g33YeGRmJ5cuXA7jxv933338fs2fPxrVr17B06VKH+mWLq/a5qj6noKAA4eHh5unl5eVWASkoKAgdO3bEf/7zH5vzCgsLs3he1fet1+vRsGFD+Pj4wMvLC6NHj8ajjz5qc55RUVG1Xh5bn33zBfx1GROVynRReE3HA0fHXmeyd9uuaV3eLCgoCI0bN8bmzZttfqarfq5Dc5UXWysN+LP8XXkQqElSUhK2bdtmddX9zQYOHIhjx46hcePGiIuLs3pU94M/8fHx8PPzwzvvvGMx/dSpU9i6dav57h5H6XQ68/+cTDZu3Fjn0xfVMQ2WH374IXbu3Im9e/da3V1jugXby8vLPO3KlSt4++23a/25zvgfmr1qs64NBgN69eqFuXPnAgAOHDjg8Of27dsXly5dsgp5prsD6rKdmPp4s2XLljk0n1WrVlk8z87OxsmTJ813BNV2O2/Tpg3+/e9/o0OHDti/f3+Vn1+5SlAdV+1zlZmWvfJ38/7771vcQQTc2K5Mt8jb2q4qj1vr1q2zqBJcvHgRn3zyCXr27AkvLy/Ur18fvXv3xoEDB9CxY0eb87RV7ahO9+7d4evrW+W6rrw8tR0Tq+LIOnaFNm3aoFWrVsjIyKj2TjNPjL0m9m7b0dHRCA0NxerVqy3u8jx58iSys7Mt3jtw4EAUFRXh+vXrNtdldHS0S5ZFc5WX/v37o1mzZhg0aBDatm2LiooKHDx4EC+++CIaNmzo8A+rzZkzB59++inuvPNOPPXUU+jQoQMuXLiAzZs3IyUlBW3btsXUqVOxdu1a3HnnnZg2bRo6duyIiooK5ObmYsuWLZg+fTq6detmc/6NGjXC008/jaeeegpjxozBX//6VxQVFSEtLQ2+vr6YNWtWrb6HgQMHYuXKlWjbti06duyIffv2Yf78+S7/Ab7x48dj7ty5GDlyJPz8/DB8+HCL1++991689NJLGDlyJP7+97+jqKgICxYssNrZHdGhQwe89957yMzMRMuWLeHr64sOHTrUdVFssnddP/PMMzh16hT69u2LZs2a4cKFC1i4cKHF9SSOGDNmDBYtWoTk5GScOHECHTp0wFdffYXnn38eAwYMQL9+/Wq1PAkJCbjlllswadIkzJo1Cz4+Pli1ahW+/fZbh+azd+9eTJw4EQ899BDy8vIwc+ZMhIeH4x//+AcA+7fz7777DpMnT8ZDDz2E1q1bQ6/XY+vWrfjuu+8wY8aMKj/f398fkZGR+Oijj9C3b18EBgYiKCjI5kHSVftcZTExMfjb3/6GV155BT4+PujXrx9++OEHLFiwwOpU7Jw5c5CVlYWEhARMmTIF0dHRuHr1Kk6cOIFNmzZh6dKlFvuul5cX7r77bqSkpKCiogJz585FSUmJ+Yf6AGDhwoXo0aMHevbsif/7v/9DixYtcPHiRRw9ehSffPIJtm7d6tDy3HLLLXjiiSfw3HPPWazr2bNnW51qqMuYWBXTPr1w4UIkJyfDx8cH0dHRbv2hzkWLFmHQoEHo3r07pk2bhubNmyM3NxefffaZOdR5auwF7N+269Wrh2effRYTJ07E0KFD8fDDD+PChQs21+WIESOwatUqDBgwAI8//ji6du0KHx8fnDp1Ctu2bcPgwYMxdOhQ5y+MUy77lUhmZqYYOXKkaN26tWjYsKHw8fERzZs3F6NHj7a6Y8ieu42EuHGb3vjx40XTpk2Fj4+PCAsLE8OGDRNnz541t7l06ZL497//LaKjo4Verzffojht2jRRUFBQY7/feOMN0bFjR/N7Bw8ebL7DwMSRu43Onz8vJkyYIIKDg0X9+vVFjx49xM6dO62W2XRF/Zo1a6zmkZycLBo0aGBz/pXvNrpZQkKCACBGjRpl8/WMjAwRHR0tDAaDaNmypUhPTxfLly+3upPA3ivXT5w4IRITE4W/v7/5NkMhqr/b6LfffrNrWW3d+WPPut6wYYNISkoS4eHhQq/Xi+DgYDFgwACxc+fOGpfH1mcKceOOiEmTJonQ0FDh7e0tIiMjRWpqqrh69apFOwDi0UcfrfFzTLKzs0V8fLyoX7++aNKkiZg4caLYv3+/1Xdni2mb3LJlixg9erRo1KiR+W6HI0eOWLWvaTs/e/asGDt2rGjbtq1o0KCBaNiwoejYsaN4+eWXLW7ZtbVtfP7556Jz587CYDBY3M1j61Zpe/oiRNXbhWk7qklpaamYPn26CA4OFr6+vqJ79+4iJydHREZGWtxtJMSNO6amTJkioqKihI+PjwgMDBSxsbFi5syZ5jtPTNv03LlzRVpammjWrJnQ6/Wic+fO5p8xuNnx48fF+PHjRXh4uPDx8RFNmjQRCQkJ5rvAhKh6DLC1/1RUVIj09HQREREh9Hq96Nixo/jkk09srg97x8Sqtldb31FqaqoICwsT9erVs7oTqDJH9mnT5917771W30vlz8jJyRFJSUnCaDQKg8EgWrVqZXEXkb1jb1VsfR+mdTF//nyL6VWtO3u2bVO71q1bC71eL9q0aSMyMjJsju1lZWViwYIFolOnTsLX11c0bNhQtG3bVjzyyCMW+7kz7zbSCVGLX/4iIrLDypUrMW7cOOzZswdxcXGe7o7qnThxAlFRUZg/fz6eeOIJT3eHyGU0d80LERERyY3hhYiIiKTC00ZEREQkFVZeiIiISCoML0RERCQVhhciIiKSiup+pK6iogJnzpyBv7+/Qz9dT0RERJ4jhMDFixcRFhaGevWqr62oLrycOXMGERERnu4GERER1UJeXl6Nvzjs0vDy5ZdfYv78+di3bx/y8/Oxfv16DBkypMr269atw5IlS3Dw4EGUlpaiXbt2mD17Nvr372/3Z5p+CjovL8/uv3ZMREREnlVSUoKIiAi7/qSDS8PLH3/8gU6dOmHcuHF44IEHamz/5Zdf4u6778bzzz+PRo0aYcWKFRg0aBB2796Nzp072/WZplNFAQEBDC9ERESSseeSD7f9zotOp6ux8mJLu3btMHz4cDzzzDN2tS8pKYHRaERxcTHDCxERkSQcOX4r+pqXiooKXLx4EYGBgVW2KS0ttfjz4yUlJe7oGhEREXmIom+VfvHFF/HHH39g2LBhVbZJT0+H0Wg0P3ixLhERkbopNrysXr0as2fPRmZmJoKDg6tsl5qaiuLiYvMjLy/Pjb0kIiIid1PkaaPMzExMmDABa9asQb9+/aptazAYYDAY3NQzIiIi8jTFVV5Wr16NsWPH4t1338W9997r6e4QERGRwri08nLp0iUcPXrU/Pz48eM4ePAgAgMD0bx5c6SmpuL06dN46623ANwILmPGjMHChQvRvXt3FBQUAAD8/PxgNBpd2VUiIiKShEsrL3v37kXnzp3Nv9GSkpKCzp07m297zs/PR25urrn9smXLUF5ejkcffRShoaHmx+OPP+7KbhIREZFE3PY7L+7C33khIiKSjyPHb8Vd80JERERUHYYXIiIikgrDCxEREUmF4YWIiIikwvBCREREUmF4ISIiIqkwvBAREZFUGF6IiIhIKgwvREREJBWGFyIiIpIKwwsRERFJheGFiIiIpMLwQkRERFJheCEiIiKpMLwQERGRVBheiIiISCoML0RERCQVhhciIiKSCsMLERERSYXhhYiIiKTC8EJERERSYXghIiIiqTC8EBERkVQYXoiIiEgqDC9EREQkFYYXIiIikgrDCxEREUmF4YWIiIikwvBCREREUmF4ISIiIqkwvBAREZFUGF6IiIhIKgwvREREJBWGFyIiIpIKwwsRERFJheGFiIiIpMLwQkRERFJheCEiIiKpMLwQERGRVBheiIiISCouDS9ffvklBg0ahLCwMOh0Onz44Yc1vmfHjh2IjY2Fr68vWrZsiaVLl7qyi0RERCQZl4aXP/74A506dcJ///tfu9ofP34cAwYMQM+ePXHgwAE89dRTmDJlCtauXevKbhIREZFEvF0586SkJCQlJdndfunSpWjevDleeeUVAEBMTAz27t2LBQsW4IEHHnBRL4mIiEgmirrmJScnB4mJiRbT+vfvj71796KsrMzme0pLS1FSUmLxICIiIvVSVHgpKChASEiIxbSQkBCUl5ejsLDQ5nvS09NhNBrNj4iICHd0lYiIiDxEUeEFAHQ6ncVzIYTN6SapqakoLi42P/Ly8lzeRyIiIvIcl17z4qimTZuioKDAYtq5c+fg7e2Nxo0b23yPwWCAwWBwR/eIiIhIARRVeYmPj0dWVpbFtC1btiAuLg4+Pj4e6hUREREpiUvDy6VLl3Dw4EEcPHgQwI1boQ8ePIjc3FwAN075jBkzxtx+0qRJOHnyJFJSUnD48GFkZGRg+fLleOKJJ1zZTSIiIpKIS08b7d27F7179zY/T0lJAQAkJydj5cqVyM/PNwcZAIiKisKmTZswbdo0LFq0CGFhYXj11Vd5mzQRERGZ6YTpiliVKCkpgdFoRHFxMQICAjzdHSIiIrKDI8dvRV3zQkRERFQTRd1t5Ezf58WgoT+zmVq8fT7B011wuS250Z7uAmnApeNGT3fBYxpGFXu6C9JLbP6zy+Zdesn2j9HawqM7EZEGXDpu1HRwAbQd3NRGtZUXUgdWXIhqhwdq227+XliJcdyW3GiXVl/sxfBCiqX24MLQQs7EsOI403fGEOMYJQQYhhdSHLWHFoDBheqGQcW5GGIc5+kAw/BCiqL24MLQQrXBsOIeDDGO8WSAYXghRWBoIa1jQFEOhhj7eSrAMLyQR6k9tAAMLq7myYO+Iwc3hhP5MMTYxxMBhuGFPEbtwYWhxXGyHeBl6y/VDkNMzdwdYBheyO0YWgjggZ/kw9usq+fOAMPwQm7F4KI9DCmkRpeOGxlgbHBXgGF4IbdgaNEGBhXSEp5Oss0dAYZ/HoBcjsFF3Uw/O8/gQlrFbd+aq8dFVl7IZRha1IuDNZElVmGsubICw8oLuQSDi/qwwkJUM+4jllw1VrLyQk7F0KIuHISJaocX9P7JFRUYhhdyCoYW9WBgIXIOnkpyHZ42ojpjcJEfTwkRuQ73K+ePo6y8UK0xtMiPgyqRe7AK49zTR6y8UK0wuMiNVRYiz9D6fuessZWVF3IIQ4vctD5wEikBL+atO1ZeyG4MLvJipYVIWbS8TzpjrGXlhWqk9tACqDe4aHVwJJIFqzC1w8oLVUvtwWVLbrQqg4uW/1dHJBst7qt1HXdZeSGb1B5aAHVWW7Q4CBKR9jC8kAWGFjkxtBDJTYunj+py6zRPG5EZg4t8eHqISD24L9uPlRdiaJEQBzkiddJaBaa21RdWXjSOwUU+DC5E6sZ9vGasvGgUQ4t8OKARaYeWKjC1qb4wvGiMFkILwOBCRPLTUoBxFE8baQiDi3x4QS6Rtmll/3d03GblReW0ElgA9YUWIiKAFRhbGF5USEuBxYTBhYjUTAsBZuup1na3ZXhRCS0GFoChhcjV/I/9eXXBxVYVHuwJaSHA2IvhRWJaDSwmDC5EVbs5dLhrngw3rscAcwPDi4QYWhha6Ia6HKBlPtC6Ipg4Q3X9kvn7VhoGGIYXaWg9sJgwuKibOw/KzvgsZx2QlRpGnKnyMjLMUF0wvCgEw0nN1BJcGFpuUMMBWw3L4Cm8lobqguHFDRhM6kYtoQXQdnDhgZ6qwqqM47R+6sgto8nixYsRFRUFX19fxMbGYufOndW2X7VqFTp16oT69esjNDQU48aNQ1FRkTu66hRvn0+weFDtMbjIyf9YPasHkb243VBNXF55yczMxNSpU7F48WLccccdWLZsGZKSknDo0CE0b97cqv1XX32FMWPG4OWXX8agQYNw+vRpTJo0CRMnTsT69etd3d1aYUBxPoYW+fBAQ67A00tV03L1RSeEEK78gG7duqFLly5YsmSJeVpMTAyGDBmC9PR0q/YLFizAkiVLcOzYMfO01157DfPmzUNeXl6Nn1dSUgKj0YivfghDQ3/XDaYMLK7D4CIXhhZyN4aYP6kpvFy/XIpDI+ahuLgYAQEB1bZ1aeXl2rVr2LdvH2bMmGExPTExEdnZ2Tbfk5CQgJkzZ2LTpk1ISkrCuXPn8MEHH+Dee++12b60tBSlpaXm5yUlJc5bgJswrLiHWoKL2kMLAwt5kmn7Y4jRbvXFpeGlsLAQ169fR0hIiMX0kJAQFBQU2HxPQkICVq1aheHDh+Pq1asoLy/Hfffdh9dee81m+/T0dKSlpTm97wADizupJbQA6g4uDC2kJP7H6jHAaJRbRiKdTmfxXAhhNc3k0KFDmDJlCp555hns27cPmzdvxvHjxzFp0iSb7VNTU1FcXGx+2HNqqSa80Na9GFyUjxdPklJxu1TvuFMdl1ZegoKC4OXlZVVlOXfunFU1xiQ9PR133HEHnnzySQBAx44d0aBBA/Ts2RPPPfccQkNDLdobDAYYDAan9JeBxf3UElzUOHjwoECy4Gkk7XFpeNHr9YiNjUVWVhaGDh1qnp6VlYXBgwfbfM/ly5fh7W3ZLS8vLwA3KjbOxsDiGWoJLYD6ggtDC8mKp5G0w+W3SqekpGD06NGIi4tDfHw8Xn/9deTm5ppPA6WmpuL06dN46623AACDBg3Cww8/jCVLlqB///7Iz8/H1KlT0bVrV4SFhTmtXwwtnsPgokwMLaQGWg0wWrtw1+XhZfjw4SgqKsKcOXOQn5+P9u3bY9OmTYiMjAQA5OfnIzc319x+7NixuHjxIv773/9i+vTpaNSoEfr06YO5c+c6pT8MLZ7D0KJMDC2kNjyNpH4u/50Xd6vqd14YWjyLwUV5GFpIC7QWYGSuvijmd16UgKHF8xhclIWhhbSEVRh1Um14ee9CNxjKfTzdDU1jaFEeBhfSKq1cC6OVa184kpFLMLgoC3+nhYjhXU24JsnpGFyUhQM2EamNak8bkfsxtCgLQwuRNS2cPtLCqSOObuQUDC7KwuBCVDXuH/Jj5YXqjMFFOTgoE5EWMLxQrakptAAMLkRaovbTR2o/dcTwQrWipuDC0EJEJBeOeuQwBhflYHAhqj3uP/Ji5YXspqbQAsgdXDjoElFN1HzqiCMg2YXBRTkYXIich/uTnFh5oWoxtCgLB1oiIlZeqBoMLsrBn/cnch0171syj3vVYeWFrKgttABy78BqHlid4Zafr1X52vlovRt7QkTuwvBCFhhclEVrwaW6IOLK+THkkNp/90VtGF7ITG3BhaFFDs4OLK7qAwMOyUqNdx0xvJDqQgvA4KJ0Sggsjqqpzww38mP1RR4MLxrH4KIsag0uMoYVR9VmGRl4iGqH4UWj1BhaAAYXJdFCYKkrR78jhh2iGxheNEiNwYWhRRkYWFyL1+a4Hk8dyYHhRWMYXJSFwYWcrar1wFBDasLwoiEMLsqiluDC0CIH03piiCE1YHjRADWGFoDBRQkYXOTDEENqwPCiYmoNLQCDi6cxtMjv5nXIIGOJ170oH8OLSqk1uMgcWgD5gwtDizqxGkOyYXhRGbWGFkDu4CJ7aAEYXLSAIYZkwfCiEmoOLQCDiycxtGgPTymR0sk9qhIABhclY3Ah2d3y8zVNbgey77tqx8qLxNQeWgAGF0/R4sGKqnfLz9dYhSHFYHiREEOL8skaXBhaqDoMMHJS21+UBnjaSDoMLsrH4EJqxu2ElICVF0loIbQAcgcXWUMLwAMSOUYrFRj+3otyMbwonFZCC8Dg4gkMLVRbWgkwpEwMLwrF0CIPBhfSKgYY8hQ5R12VY3CRB4MLaR23JfIEVl4UREuhBWBw8RQebMjZWIEhd2N4UQgGF7nIGFwYWoi0R423SQM8baQIDC5yYXAh0gbeaaRcrLx4kNZCC8Dg4gkMLkSkNm4ZiRcvXoyoqCj4+voiNjYWO3furLZ9aWkpZs6cicjISBgMBrRq1QoZGRnu6KrbMLjIh8GFiEgZXF55yczMxNSpU7F48WLccccdWLZsGZKSknDo0CE0b97c5nuGDRuGs2fPYvny5bj11ltx7tw5lJeXu7qrbqO14MLQ4hkMLkS1p4ZTRmq93gVwQ3h56aWXMGHCBEycOBEA8Morr+Czzz7DkiVLkJ6ebtV+8+bN2LFjB3799VcEBgYCAFq0aOHqbrqF1kILwODiKQwuRKRmLh2Zr127hn379iExMdFiemJiIrKzs22+5+OPP0ZcXBzmzZuH8PBwtGnTBk888QSuXLlis31paSlKSkosHkrE4CIfBhciImVyaeWlsLAQ169fR0hIiMX0kJAQFBQU2HzPr7/+iq+++gq+vr5Yv349CgsL8Y9//AO///67zete0tPTkZaW5pL+OwuDi3xkDC5aCS1+P5y2q92V9uEu7gmRcqn5lBHgpruNdDqdxXMhhNU0k4qKCuh0OqxatQpG440D4EsvvYQHH3wQixYtgp+fn0X71NRUpKSkmJ+XlJQgIiLCyUtQO1oMLQCDiyeoJbjYG0xqOy8GGrKHGq53UTuXhpegoCB4eXlZVVnOnTtnVY0xCQ0NRXh4uDm4AEBMTAyEEDh16hRat25t0d5gMMBgMDi/83XE4CInBhfPcWZwceQzGGiI5OPSkVqv1yM2NhZZWVkW07OyspCQkGDzPXfccQfOnDmDS5cumaf98ssvqFevHpo1a+bK7joNg4ucGFw8w++H024JLjV9vqf7QUT2c/lonZKSgjfeeAMZGRk4fPgwpk2bhtzcXEyaNAnAjdM+Y8aMMbcfOXIkGjdujHHjxuHQoUP48ssv8eSTT2L8+PFWp4yUiMFFTgwu7qfUsMAwQ7JT+/UugBuueRk+fDiKioowZ84c5Ofno3379ti0aRMiIyMBAPn5+cjNzTW3b9iwIbKysvDYY48hLi4OjRs3xrBhw/Dcc8+5uqt1xuAiJwYX95MpFFTuK08zqRuvd5GDTgghPN0JZyopKYHRaMTkr4bC0NDHbZ+rxeAie2gBGFzcTabQYg8GmT+p5a9KqyG8yFp5uX65FIdGzENxcTECAgKqbcu/beQEDC5yYnBxL7UFF8BymRhkSAlkDS6OYnipIwYXOTG4uI8aQ4stPL0kPzVUXbRCvhGcPIrBxTMYXOSj5WUncjVWXupAa1UXBhfPkDG48MCtLWq53kV2WjllBLDyUmsMLvJhcHEPBheSEU8ZeV6fZkfsbivfaK4ADC7yYXBxDwYXS1r4Plh1IU+Qb0T3MAYX+TC4uIcWDtREpAzyjeoexOAiHwYX92BwIZmp4ZSRlq53AXjBrt0YXOQiY2gBGFxILjxlRM6S2PxnlF6quZ2JnCO8mzG4yIXBxX0YXIjIE+Qc5d2IwUUuDC7uw+CibWqpuvCUkZzkHOndhMFFLgwu7sPgYj9+V0TVS2z+s8PvkXO0J6djcPEMBhciIsfJOeK7gZaqLgwunsHgQrLiKSPyNDlHfRdjcJEHg4v7MLgQKY8Wr3cBGF6sMLjIg8HFfRhcyEQtVRdShtpc7wIwvGgWg4tnMLhoE79D5eEpI7nJeQRwEa1UXRhcPIPBhYicSaunjACGFzMGFznIGlxkxODiPFfah3u6C07BU0bkTLU9ZQQwvABgcJGFzMFFtqoLg4vzMLgoD08ZyU/eowE5hMHFc2QLLuQ8DC7kKlo+ZQQwvGim6kKeweCiXWoJLmrDqos6aDq8aCW4sOpCjuApo7pTU3Bh1YVcoS7XuwAaDi8MLnKQObiw6qJNDC7KpZaqi9ZPGQEaDi9awODiOQwu2sTgQuQe8h4d6kArVRciR/GUUe0xuBDZp66njAANhhetBBdWXTyHVRftUVNwUSueMlIXeY8QVCUGF8+RObiw6lI7agsurLqQDOQ9StSCVqouMpM5uJD2MLjIQS1VF/qTZo4UWgkuslddZCZz1YUcx+BC7qaGU0bOuN4F0Eh4YXCRg8xVF9mDC08ZOYbBRR6suqiTvEcLssDgQuQeagsuRDLy9nQHXE0rVReZyR5cWHXRBrWGFlZd5MBTRpbkPmrUQCvBRfaqi8xkDy5kHwYXImVRbXjZeqq1p7vgFrIHF5mrLmoILqy61IzBRU5qqrqQNXmPHMTgQuRiDC6kBDxlZI1HD/II2YOLGqougHoPzs6g1u9GC8GFVRf1U/0Fu2ole9WFlMN0kOYppBvUGloAbQQXtVFD1cUVGF7I7WSvuqjVlfbhmg4wDC3qwKqL8jj7lBHA8CIlVl3IVbRYhVFzaAEYXGTGqkvV3PJf4MWLFyMqKgq+vr6IjY3Fzp077Xrf119/DW9vb9x+++2u7SC5DasucrjSPtz8UCu1L9/5aL2mggtpi8uPJJmZmZg6dSpmzpyJAwcOoGfPnkhKSkJubm617ysuLsaYMWPQt29fV3dRKqy6kLup7SCvtuWxRYuhRW1VF7VwxSkjwA3h5aWXXsKECRMwceJExMTE4JVXXkFERASWLFlS7fseeeQRjBw5EvHx8a7uIrkJqy5yk/2gL3v/7aHVaosagwtPGVXPpUeTa9euYd++fUhMTLSYnpiYiOzs7Crft2LFChw7dgyzZs2q8TNKS0tRUlJi8VArVl2UQS23SdeWbCFAtv7WlhZDC2mXS8NLYWEhrl+/jpCQEIvpISEhKCgosPmeI0eOYMaMGVi1ahW8vWu+njg9PR1Go9H8iIiIcErfyblYdVEfGUKB0vvnDFqttpiw6qJcrjplBLjpgl2dTmfxXAhhNQ0Arl+/jpEjRyItLQ1t2rSxa96pqakoLi42P/Ly8pzSZ6Vh1YWUSokhRol9cgUthxZAncGF7OPSW6WDgoLg5eVlVWU5d+6cVTUGAC5evIi9e/fiwIEDmDx5MgCgoqICQgh4e3tjy5Yt6NOnj8V7DAYDDAaD6xaC6oxVF22oKiy46rZrLYSTqmg9tKgZqy72cWl40ev1iI2NRVZWFoYOHWqenpWVhcGDB1u1DwgIwPfff28xbfHixdi6dSs++OADREVFubK7isWqC8msppBRXbjRckCpCoPLDay6aJvLf6QuJSUFo0ePRlxcHOLj4/H6668jNzcXkyZNAnDjtM/p06fx1ltvoV69emjfvr3F+4ODg+Hr62s1neTAqgvVhAHFPgwtf1JrcFFL1cUdXB5ehg8fjqKiIsyZMwf5+flo3749Nm3ahMjISABAfn5+jb/5omWsuhARgwvJxNWnjABAJ4QQLv8UNyopKYHRaMRt7/0TXvXlvxZG5vCi1qqL1m+VJvdhaLHGqovy1Ta8lF4qw397rEdxcTECAgKqbavOowsRkeQYXKypNbiQ4/iHGRWMVRci7WFosU3NwYVVF8fxCEMuoeaBhgcXcgWt/9hcddQ8nlDtsPJCVAumgwyvf6G6YmCpntqDC6sutcPKC7mM2gcdgP9bprrhtlM9LYwhVDusvBA5wc0HIVZjqCYMLTXTQnBh1aX2GF6InIynlKgqDC0100JoURt3BxeA4YVc7GKrCs3eecQQQyYMLfbRUnBRU9XFE7R5VCFyI14Xo21c9/bRUnBRE09UXQBWXhRL5t94qUzL1Zeb8boYbWFosZ/WggurLnXH8ELkATylpF4MLY5hcJGXp6ouAMMLuQmrL7YxxKgHQ4vjtBZcyHkYXogUgKeU5MXQ4jithhZWXZyH4YXchtUX+7AaIweGltrRanAh5+KRhEiheJeScnG91I6WgwurLs7Fygu5FasvjuMpJeVgaKk9LQcXcj6GF3I7Bpja4yklz2BoqT2GFlZdXIHhhUhCrMa4B0NL3TC4qCu4KAnDC3kEqy/Ow2qM8zG01A1DizoppeoCMLwoVsOoYlX9yq4tpgGOIcY5Kh9wGWYcw8BSdwwtltRUdVFScAEYXkgBWIVxDYaZmjGwOAdDizU1BRclYnhRMC1UX0xYhXE9hpkbGFici8HFmtqCi9KqLgDDCykMQ4z7aOmiXwYW52No0QYlBheA4UXxtFR9uRlPJblXVQd3mUMNA4trMLRUT21VF6VieCHFYhXG82QINQwp7sHQUjO1BRelVl0AFYeXPs2OYMfv7T3dDXICVmGUx52hhuHEcxhY7Mfg4l6qDS9qotVTRzdjFUYODBrqwNDiGLUFFxkwvEiCAeYGhhgi12BgqR01BhelV10AhheS1M0DLYMMUe0wsFBlMgQXgOFFKqy+2MYgQ2Q/BhbnUWPVRRYML5JhgKkeTysRWWNgcT41BhdZqi4AwwupFKsxpHUMLK7D4OJ5DC8SYvXFMQwypAUMK+6hxuAiI4YX0hQGGVILhhX3U2twka3qAjC8SIvVl7pjkCGZMKx4FoOLsjC8SIwBxnkYZEiJGFiUQa3BRWYML5JjgHE+BhnyJAYWZVFzcJG16gKoPLwkNv8ZW3KjPd0Nl2OAcZ3KBxKGGXIFBhZlYnBRLlWHFy0x7WQMMa7Fqgw5E0OLcjG4KBvDi8qwCuM+DDJUGwwsysfgonyqH3HVsqIc0TCqWNU7nxJdbFVhfhDZwu1DDhw75eCW8LJ48WJERUXB19cXsbGx2LlzZ5Vt161bh7vvvhtNmjRBQEAA4uPj8dlnn7mjm6rDndAzeJAiE4Zauah9zFTTf+ZdHl4yMzMxdepUzJw5EwcOHEDPnj2RlJSE3Nxcm+2//PJL3H333di0aRP27duH3r17Y9CgQThw4ECt+6CmFeYote+MSsYDl3ZxvctH7WOl2o6DOiGEcOUHdOvWDV26dMGSJUvM02JiYjBkyBCkp6fbNY927dph+PDheOaZZ6xeKy0tRWlpqfl5SUkJIiIiMPmroTA09DFP18JdRzXhtTDKwOtj1IlhRV4MLspQeqkM/+2xHsXFxQgICKi2rUtH0WvXrmHfvn1ITEy0mJ6YmIjs7Gy75lFRUYGLFy8iMDDQ5uvp6ekwGo3mR0RERJ37rVa8FkYZWJFRF65LuXFMlJNLw0thYSGuX7+OkJAQi+khISEoKCiwax4vvvgi/vjjDwwbNszm66mpqSguLjY/8vLybLaTJXm6A0OMcjDIyInrTR20MA6q9djnlluldTqdxXMhhNU0W1avXo3Zs2fjo48+QnBwsM02BoMBBoPBKf3UGv42jLLwB/GUj2FFPRhc5ObS8BIUFAQvLy+rKsu5c+esqjGVZWZmYsKECVizZg369evnym5qHkOMMvF3ZJSBgUV9GFzk59IRUa/XIzY2FllZWRbTs7KykJCQUOX7Vq9ejbFjx+Ldd9/Fvffe67T+qH1l1hVPJynXzacpeDB1PX7X6sUxTh1cftooJSUFo0ePRlxcHOLj4/H6668jNzcXkyZNAnDjmpXTp0/jrbfeAnAjuIwZMwYLFy5E9+7dzVUbPz8/GI2sDLgDKzHKx6qMczGkqJ+WQosW/qPu8vAyfPhwFBUVYc6cOcjPz0f79u2xadMmREZGAgDy8/MtfvNl2bJlKC8vx6OPPopHH33UPD05ORkrV66sc3+08scanYEhRg62DrwMNDVjYNEOBhf1cfnvvLhbSUkJjEaj1e+83IzhpXYYYuSm9UDDsKJNDC7ycOR3XviHGcluNw8CDDLy0drdTAwr2qal0KJFmgwvPHVUdwwy8qvq4C5TqGFAIVu0GFxkr7o4SpPhBWCAcSYGGXWpKRC4O9wwoJC9tBhaAO0FF0DD4YVcg0FG/RgmSIkYXOQ3otFu/NfOtvLUh11ATStdiUy/G6PVQYWIXE/LY4yajmGjb7Hv7x2aaDq8AOpa+Up2c5DR6kBDRM6l5bFETccuR4MLwNNGAHj9iydUHnR4iomI7KXl0AIwuAAML6QQDDNEVBOthxZAXcGlLhhe/j9WX5SFYYaITBhablBbcKlt1QVgeLHAAKNcDDNE2sLAYonBxRLDC0mJYYZInRharDG4WGN4qYTVFzkxzBDJjaHFNgYX2xhebGCAkR/DDJHyMbBUj8GlagwvpAm2BkkGGiLPYGipGYNL9RheqsDqi/rxTxkQuQ8Di3Y5O7gADC/VYoDRDgYZIudiWKk9tVVdXIHhpQamjYghRjsYZEhJGkYVK347ZFBxHrUFF1dUXQCGF7uxCqNNDDLkbraCgCPhwNXbKYOK6zC42I/hxQGswmgbgwy5grPDAMOFnBhcHMPwUgsMMcQgQ7XBYEG2MLg4juGlDhhiCOBvylDVGFaoJgwutcPw4gQMMXQzVmW0jYGF7KG20AK4L7gADC9OxRBDlTHIaAMDCzmCwaXuGF5cgCGGbOHpJfVgWKHaYnBxDoYXF7K1kTLQkAmrMnJhYKG6YnBxHoYXN2OgIVtYlVEmBhZyFgYX52J4UQAGGqqMYcYzGFbI2dQYWgDPBheA4UWxqtrgGWq0iWHG+RhUyNUYXFyH4UUyrNIQwDBTGwwr5E4MLq7F8KICDDRU1YFZq6GGQYU8icHF9RheVIqBhgDbB3G1BBoGFFIiBhf3YHjREAYaAuSq0jCgkCzUGloA5QUXgOFF8xhoyMTRoOBo2GEQIbVicHE/hheyUnlHZJghWxhGiBhcPIXhhWrE6gwRkTUGF8+p5+kOkJzUvNMSEZGy6YQQwtOdcKaSkhIYjUYUFxcjICDA090hIiIiOzhy/GblhYiIiKTC8EJERERSYXghIiIiqbglvCxevBhRUVHw9fVFbGwsdu7cWW37HTt2IDY2Fr6+vmjZsiWWLl3qjm4SERGRBFweXjIzMzF16lTMnDkTBw4cQM+ePZGUlITc3Fyb7Y8fP44BAwagZ8+eOHDgAJ566ilMmTIFa9eudXVXiYiISAIuv9uoW7du6NKlC5YsWWKeFhMTgyFDhiA9Pd2q/b/+9S98/PHHOHz4sHnapEmT8O233yInJ6fGz+PdRkRERPJRzN1G165dw759+5CYmGgxPTExEdnZtn8AJycnx6p9//79sXfvXpSVlVm1Ly0tRUlJicWDiIiI1Mul4aWwsBDXr19HSEiIxfSQkBAUFBTYfE9BQYHN9uXl5SgsLLRqn56eDqPRaH5EREQ4bwGIiIhIcdxywa5Op7N4LoSwmlZTe1vTASA1NRXFxcXmR15enhN6TERERErl0r9tFBQUBC8vL6sqy7lz56yqKyZNmza12d7b2xuNGze2am8wGGAwGJzXaSIiIlI0l1Ze9Ho9YmNjkZWVZTE9KysLCQkJNt8THx9v1X7Lli2Ii4uDj4+Py/pKREREcnD5aaOUlBS88cYbyMjIwOHDhzFt2jTk5uZi0qRJAG6c9hkzZoy5/aRJk3Dy5EmkpKTg8OHDyMjIwPLly/HEE0+4uqtEREQkAZeeNgKA4cOHo6ioCHPmzEF+fj7at2+PTZs2ITIyEgCQn59v8ZsvUVFR2LRpE6ZNm4ZFixYhLCwMr776Kh544AFXd5WIiIgkwL8qTURERB6nmN95ISIiInI2hhciIiKSCsMLERERSYXhhYiIiKTC8EJERERSYXghIiIiqTC8EBERkVQYXoiIiEgqDC9EREQkFYYXIiIikgrDCxEREUmF4YWIiIikwvBCREREUmF4ISIiIqkwvBAREZFUGF6IiIhIKgwvREREJBWGFyIiIpIKwwsRERFJheGFiIiIpMLwQkRERFJheCEiIiKpMLwQERGRVBheiIiISCoML0RERCQVhhciIiKSCsMLERERSYXhhYiIiKTC8EJERERSYXghIiIiqTC8EBERkVQYXoiIiEgqDC9EREQkFYYXIiIikgrDCxEREUmF4YWIiIikwvBCREREUmF4ISIiIqkwvBAREZFUGF6IiIhIKi4NL+fPn8fo0aNhNBphNBoxevRoXLhwocr2ZWVl+Ne//oUOHTqgQYMGCAsLw5gxY3DmzBlXdpOIiIgk4tLwMnLkSBw8eBCbN2/G5s2bcfDgQYwePbrK9pcvX8b+/fvx9NNPY//+/Vi3bh1++eUX3Hfffa7sJhEREUlEJ4QQrpjx4cOHcdttt2HXrl3o1q0bAGDXrl2Ij4/HTz/9hOjoaLvms2fPHnTt2hUnT55E8+bNa2xfUlICo9GI4uJiBAQE1GkZiIiIyD0cOX67rPKSk5MDo9FoDi4A0L17dxiNRmRnZ9s9n+LiYuh0OjRq1Mjm66WlpSgpKbF4EBERkXq5LLwUFBQgODjYanpwcDAKCgrsmsfVq1cxY8YMjBw5ssoUlp6ebr6mxmg0IiIiok79JiIiImVzOLzMnj0bOp2u2sfevXsBADqdzur9Qgib0ysrKyvDiBEjUFFRgcWLF1fZLjU1FcXFxeZHXl6eo4tEREREEvF29A2TJ0/GiBEjqm3TokULfPfddzh79qzVa7/99htCQkKqfX9ZWRmGDRuG48ePY+vWrdWe+zIYDDAYDPZ1noiIiKTncHgJCgpCUFBQje3i4+NRXFyMb775Bl27dgUA7N69G8XFxUhISKjyfabgcuTIEWzbtg2NGzd2tItERESkYi672wgAkpKScObMGSxbtgwA8Pe//x2RkZH45JNPzG3atm2L9PR0DB06FOXl5XjggQewf/9+bNiwwaJCExgYCL1eX+NnFhcXo1GjRsjLy+PdRkRERJIoKSlBREQELly4AKPRWH1j4UJFRUVi1KhRwt/fX/j7+4tRo0aJ8+fPW7QBIFasWCGEEOL48eMCgM3Htm3b7PrMvLy8KufBBx988MEHH3wo+5GXl1fjsd6llRdPqKiowJkzZ+Dv72/XhcGyMSVTrVaWuPxcfi0vP8DvgMuv3uUXQuDixYsICwtDvXrV30/k8DUvSlevXj00a9bM091wuYCAANVtuI7g8nP5tbz8AL8DLr86l7/G00X/H/8wIxEREUmF4YWIiIikwvAiGYPBgFmzZmn2t224/Fx+LS8/wO+Ay6/t5TdR3QW7REREpG6svBAREZFUGF6IiIhIKgwvREREJBWGFyIiIpIKwwsRERFJheFFYc6fP4/Ro0fDaDTCaDRi9OjRuHDhQrXv0el0Nh/z5883t7nrrrusXh8xYoSLl8ZxtVn+sWPHWi1b9+7dLdqUlpbiscceQ1BQEBo0aID77rsPp06dcuGS1J6j30FZWRn+9a9/oUOHDmjQoAHCwsIwZswYnDlzxqKdUreBxYsXIyoqCr6+voiNjcXOnTurbb9jxw7ExsbC19cXLVu2xNKlS63arF27FrfddhsMBgNuu+02rF+/3lXdrzNHln/dunW4++670aRJEwQEBCA+Ph6fffaZRZuVK1faHA+uXr3q6kWpFUeWf/v27TaX7aeffrJop9b1b2us0+l0aNeunbmNbOu/1uz/M4vkDvfcc49o3769yM7OFtnZ2aJ9+/Zi4MCB1b4nPz/f4pGRkSF0Op04duyYuU2vXr3Eww8/bNHuwoULrl4ch9Vm+ZOTk8U999xjsWxFRUUWbSZNmiTCw8NFVlaW2L9/v+jdu7fo1KmTKC8vd+Xi1Iqj38GFCxdEv379RGZmpvjpp59ETk6O6Natm4iNjbVop8Rt4L333hM+Pj7if//7nzh06JB4/PHHRYMGDcTJkydttv/1119F/fr1xeOPPy4OHTok/ve//wkfHx/xwQcfmNtkZ2cLLy8v8fzzz4vDhw+L559/Xnh7e4tdu3a5a7Hs5ujyP/7442Lu3Lnim2++Eb/88otITU0VPj4+Yv/+/eY2K1asEAEBAVbjghI5uvzbtm0TAMTPP/9ssWw378dqXv8XLlywWO68vDwRGBgoZs2aZW4j0/qvC4YXBTl06JAAYLGT5eTkCADip59+sns+gwcPFn369LGY1qtXL/H44487q6suUdvlT05OFoMHD67y9QsXLggfHx/x3nvvmaedPn1a1KtXT2zevNkpfXcWZ20D33zzjQBgMQgqcRvo2rWrmDRpksW0tm3bihkzZths/89//lO0bdvWYtojjzwiunfvbn4+bNgwcc8991i06d+/vxgxYoSTeu08ji6/LbfddptIS0szP1+xYoUwGo3O6qJLObr8pvBy/vz5KueppfW/fv16odPpxIkTJ8zTZFr/dcHTRgqSk5MDo9GIbt26mad1794dRqMR2dnZds3j7Nmz2LhxIyZMmGD12qpVqxAUFIR27drhiSeewMWLF53Wd2eoy/Jv374dwcHBaNOmDR5++GGcO3fO/Nq+fftQVlaGxMRE87SwsDC0b9/e7u/VXZyxDQBAcXExdDodGjVqZDFdSdvAtWvXsG/fPov1AgCJiYlVLmtOTo5V+/79+2Pv3r0oKyurto3S1nVtlr+yiooKXLx4EYGBgRbTL126hMjISDRr1gwDBw7EgQMHnNZvZ6nL8nfu3BmhoaHo27cvtm3bZvGaltb/8uXL0a9fP0RGRlpMl2H915Xq/qq0zAoKChAcHGw1PTg4GAUFBXbN480334S/vz/uv/9+i+mjRo1CVFQUmjZtih9++AGpqan49ttvkZWV5ZS+O0Ntlz8pKQkPPfQQIiMjcfz4cTz99NPo06cP9u3bB4PBgIKCAuj1etxyyy0W7wsJCbH7e3UXZ2wDV69exYwZMzBy5EiLvzqrtG2gsLAQ169fR0hIiMX06tZLQUGBzfbl5eUoLCxEaGholW2Utq5rs/yVvfjii/jjjz8wbNgw87S2bdti5cqV6NChA0pKSrBw4ULccccd+Pbbb9G6dWunLkNd1Gb5Q0ND8frrryM2NhalpaV4++230bdvX2zfvh133nkngKq3EbWt//z8fHz66ad49913LabLsv7riuHFDWbPno20tLRq2+zZswfAjYtvKxNC2JxuS0ZGBkaNGgVfX1+L6Q8//LD53+3bt0fr1q0RFxeH/fv3o0uXLnbNu7ZcvfzDhw83/7t9+/aIi4tDZGQkNm7caBXiHJmvM7lrGygrK8OIESNQUVGBxYsXW7zmyW2gOpWXq6ZltdW+8nRH5+lJte3r6tWrMXv2bHz00UcWgbd79+4WF6zfcccd6NKlC1577TW8+uqrzuu4kziy/NHR0YiOjjY/j4+PR15eHhYsWGAOL47O09Nq29eVK1eiUaNGGDJkiMV02dZ/bTG8uMHkyZNrvKujRYsW+O6773D27Fmr13777TerdG7Lzp078fPPPyMzM7PGtl26dIGPjw+OHDni8gOXu5bfJDQ0FJGRkThy5AgAoGnTprh27RrOnz9vUX05d+4cEhIS7J5vXbjjOygrK8OwYcNw/PhxbN261aLqYos7twFbgoKC4OXlZfW/zHPnzlW5rE2bNrXZ3tvbG40bN662jSPbkDvUZvlNMjMzMWHCBKxZswb9+vWrtm29evXwl7/8xbw/KEVdlv9m3bt3xzvvvGN+roX1L4RARkYGRo8eDb1eX21bpa7/OvPMpTZki+lizd27d5un7dq1y+6LNZOTk63uMKnK999/LwCIHTt21Lq/zlbX5TcpLCwUBoNBvPnmm0KIPy/YzczMNLc5c+aMoi/YdfQ7uHbtmhgyZIho166dOHfunF2fpYRtoGvXruL//u//LKbFxMRUe8FuTEyMxbRJkyZZXbCblJRk0eaee+5R7AWbjiy/EEK8++67wtfXV6xfv96uz6ioqBBxcXFi3LhxdemqS9Rm+St74IEHRO/evc3P1b7+hfjzwuXvv/++xs9Q8vqvC4YXhbnnnntEx44dRU5OjsjJyREdOnSwuk02OjparFu3zmJacXGxqF+/vliyZInVPI8ePSrS0tLEnj17xPHjx8XGjRtF27ZtRefOnRV3q7Cjy3/x4kUxffp0kZ2dLY4fPy62bdsm4uPjRXh4uCgpKTG/Z9KkSaJZs2bi888/F/v37xd9+vRR9K3SjnwHZWVl4r777hPNmjUTBw8etLg9srS0VAih3G3AdKvo8uXLxaFDh8TUqVNFgwYNzHdPzJgxQ4wePdrc3nSr9LRp08ShQ4fE8uXLrW6V/vrrr4WXl5d44YUXxOHDh8ULL7yg+Ftl7V3+d999V3h7e4tFixZVecv77NmzxebNm8WxY8fEgQMHxLhx44S3t7dFIFYKR5f/5ZdfFuvXrxe//PKL+OGHH8SMGTMEALF27VpzGzWvf5O//e1volu3bjbnKdP6rwuGF4UpKioSo0aNEv7+/sLf31+MGjXK6rZAAGLFihUW05YtWyb8/Pxs/m5Hbm6uuPPOO0VgYKDQ6/WiVatWYsqUKVa/haIEji7/5cuXRWJiomjSpInw8fERzZs3F8nJySI3N9fiPVeuXBGTJ08WgYGBws/PTwwcONCqjVI4+h0cP35cALD52LZtmxBC2dvAokWLRGRkpNDr9aJLly4WlaDk5GTRq1cvi/bbt28XnTt3Fnq9XrRo0cJmYF+zZo2Ijo4WPj4+om3bthYHN6VxZPl79eplcz0nJyeb20ydOlU0b95c6PV60aRJE5GYmCiys7PduESOcWT5586dK1q1aiV8fX3FLbfcInr06CE2btxoNU+1rn8hblSS/fz8xOuvv25zfrKt/9rSCfH/r3YjIiIikgB/54WIiIikwvBCREREUmF4ISIiIqkwvBAREZFUGF6IiIhIKgwvREREJBWGFyIiIpIKwwsRERFJheGFiIiIpMLwQkRERFJheCEiIiKp/D/xR6zPhXR5MwAAAABJRU5ErkJggg==\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": [ "## 3 Building a model from an array of Thomsen parameters\n", "\n", "We discuss in slightly more detail the manipulation of Thomsen parameters, see \"Weak elastic anisotropy\" (Thomsen, 1986).\n", "\n", "In Thomsen's notation, an elastic material is specified via six parameters: \n", "$$\n", " (V_p,V_s,\\epsilon,\\eta,\\delta,\\gamma,\\rho).\n", "$$\n", "- $V_p$ and $V_s$ are measured in m/s, and related to the velocity of pressure and shear waves.\n", "- $\\epsilon,\\eta,\\delta,\\gamma$ are dimensionless parameters, specifiying the shape of the anisotropy.\n", "- $\\rho$ measured in g/cm^3, is the material density." ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.471019Z", "iopub.status.busy": "2024-04-30T08:55:21.470910Z", "iopub.status.idle": "2024-04-30T08:55:21.473057Z", "shell.execute_reply": "2024-04-30T08:55:21.472799Z" } }, "outputs": [ { "data": { "text/plain": [ "ThomsenElasticMaterial(Vp=4420, Vs=2091, ε=1.12, η=-1.23, δ=-0.235, γ=2.28, ρ=2.79)" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tem = th.ThomsenData['Muscovite crystal']\n", "tem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note on the fieldname $\\epsilon$.**\n", "At the time of writing, the `namedtuple` fields must be normalized unicode characters.\n", "This is why the 'ε' is used instead of 'ϵ' as a fieldname in `ThomsenElasticMaterial`.\n", "See https://stackoverflow.com/a/30505623/12508258 for more discussion." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.474543Z", "iopub.status.busy": "2024-04-30T08:55:21.474439Z", "iopub.status.idle": "2024-04-30T08:55:21.476188Z", "shell.execute_reply": "2024-04-30T08:55:21.475947Z" } }, "outputs": [], "source": [ "import unicodedata; assert 'ε' == unicodedata.normalize('NFKC','ϵ')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.1 Hexagonal materials and Thomsen's parameter $\\delta$ \n", "\n", "Thomsen parameters can be converted into the (reduced) Hooke tensor coefficients of a material with hexagonal symmetry.\n", "This step is done implicitly when producing `Seismic.TTI` or `Seismic.Hooke` objects which can be handled by the eikonal solvers." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.477575Z", "iopub.status.busy": "2024-04-30T08:55:21.477479Z", "iopub.status.idle": "2024-04-30T08:55:21.479249Z", "shell.execute_reply": "2024-04-30T08:55:21.479017Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Hooke tensor coefficients : HexagonalMaterial(c11=63297936.00000001, c12=14678171.280000009, c13=6828108.80578232, c33=19536400, c44=4372281)\n", "Density : 2.79\n" ] } ], "source": [ "hexa,ρ = tem.to_hexagonal()\n", "print(\"Hooke tensor coefficients :\", hexa)\n", "print(\"Density :\",ρ)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recall that the *reduced* Hooke tensor is measured in $m^2/s^2$, and already incorporates the speed modulation due to density. Some coefficients have particularly simple expressions." ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.480618Z", "iopub.status.busy": "2024-04-30T08:55:21.480523Z", "iopub.status.idle": "2024-04-30T08:55:21.482241Z", "shell.execute_reply": "2024-04-30T08:55:21.482008Z" } }, "outputs": [], "source": [ "assert np.allclose(hexa.c33,tem.Vp**2)\n", "assert np.allclose(hexa.c44,tem.Vs**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The parameter $\\delta$ is ignored in this conversion." ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.483651Z", "iopub.status.busy": "2024-04-30T08:55:21.483553Z", "iopub.status.idle": "2024-04-30T08:55:21.485302Z", "shell.execute_reply": "2024-04-30T08:55:21.485052Z" } }, "outputs": [], "source": [ "tem_δnan = th.ThomsenElasticMaterial(tem.Vp, tem.Vs, tem.ε, tem.η, np.nan, tem.γ, tem.ρ)\n", "assert tem_δnan.to_hexagonal() == tem.to_hexagonal()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Indeed, Thomsen parameters are *not* independent, and the parameter $\\delta$ is defined as \n", "$$\n", " 2 \\delta = \\epsilon + \\frac \\eta {1-V_s^2/V_p^2}.\n", "$$\n", "The `get_δ` function implements this formula." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.486701Z", "iopub.status.busy": "2024-04-30T08:55:21.486610Z", "iopub.status.idle": "2024-04-30T08:55:21.488350Z", "shell.execute_reply": "2024-04-30T08:55:21.488121Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Thomsen original data : δ = -0.235\n", "Reconstructed : δ = -0.23232337862819452\n" ] } ], "source": [ "print(\"Thomsen original data : δ =\",tem[4])\n", "print(\"Reconstructed : δ =\", th.get_δ(*tem[:4]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Unfortunately Thomsen's own published data seems inconsistent in this regard. *Or maybe I missed something ?*" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.489679Z", "iopub.status.busy": "2024-04-30T08:55:21.489599Z", "iopub.status.idle": "2024-04-30T08:55:21.492027Z", "shell.execute_reply": "2024-04-30T08:55:21.491773Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Consistent published and reconstructed δ : 34 cases\n", "Factor two omitted : 11 cases\n", "Unexplained : {'Mesaverde (5837.5) immature sandstone': 1.6391370492618653, 'Mesaverde shale (1599)': 2.198347682314651, 'Mesaverde shale (1968)': 1.8155430928298144, 'Mesaverde shale (3511)': -0.0, 'Lance sandstone': 0.5510408013430982, 'Ft. Union siltstone': 1.3518799584691759, 'Timber Mtn tuff': -3.639828155038852, 'Sandstone-shale': 1.5040028850050553, 'SS-anisotropic shale': 1.6876274645369542, 'Limestone-shale': -0.0, 'LS-anisotropic shale': -0.0, 'Anisotropic shale': 1.2866379663485796, 'Gas sand-water sand': 1.8832132129622101}\n" ] } ], "source": [ "consistent,factor_two,weird = {},{},{}\n", "for name,tem in th.ThomsenData.items():\n", " δ_ratio = tem.δ/ th.get_δ(*tem[:4]) # Published data / Reconstructed data\n", " if abs(δ_ratio-1)<0.1: consistent[name] = δ_ratio\n", " elif abs(δ_ratio-2)<0.1: factor_two[name] = δ_ratio\n", " else: weird[name] = δ_ratio\n", " \n", "print(\"Consistent published and reconstructed δ :\",len(consistent),\"cases\")\n", "print(\"Factor two omitted :\",len(factor_two),\"cases\")\n", "print(\"Unexplained :\",weird)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2 A numerical example, with the TTI eikonal solver\n", "\n", "We compute traveltimes in a two dimensional test case, that is made of two different materials." ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.493599Z", "iopub.status.busy": "2024-04-30T08:55:21.493503Z", "iopub.status.idle": "2024-04-30T08:55:21.495930Z", "shell.execute_reply": "2024-04-30T08:55:21.495676Z" } }, "outputs": [], "source": [ "n=50\n", "hfmIn = Eikonal.dictIn({\n", " 'model':'TTI2',\n", " 'exportValues':1,\n", " 'seed':[0.2,0.2],\n", " 'factoringRadius':-1, \n", " 'order':1\n", "})\n", "hfmIn.SetRect(sides=[[0,2],[0,1]],dimx=2*n,sampleBoundary=True) # Define the domain\n", "hfmIn.SetUniformTips([4,2])\n", "X,Z = hfmIn.Grid() # Horizontal and vertical axis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In some use cases, the material may be specified as \n", "- an array of thomsen parameters\n", "- an array of angles specifying the tilt. (In three dimensions, an additional axis must be specified, or alternatively the full rotation matrix.)\n", "\n", "For illustration, we consider a piecewise constant material.\n", "\n", "**Note on the scheme order.**\n", "High order accuracy can only be achieved with smooth data. In the case of a piecewise constant material, using the second order scheme may do more harm than good, depending on the case." ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.497325Z", "iopub.status.busy": "2024-04-30T08:55:21.497231Z", "iopub.status.idle": "2024-04-30T08:55:21.498816Z", "shell.execute_reply": "2024-04-30T08:55:21.498563Z" } }, "outputs": [], "source": [ "top = Z >= 1.2-X/2" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.500288Z", "iopub.status.busy": "2024-04-30T08:55:21.500195Z", "iopub.status.idle": "2024-04-30T08:55:21.552084Z", "shell.execute_reply": "2024-04-30T08:55:21.551840Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.contourf(X,Z,top);" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.553570Z", "iopub.status.busy": "2024-04-30T08:55:21.553489Z", "iopub.status.idle": "2024-04-30T08:55:21.555723Z", "shell.execute_reply": "2024-04-30T08:55:21.555511Z" } }, "outputs": [], "source": [ "θ = xp.where(top,np.pi/6,-np.pi/4)\n", "def broadcast(tem): return xp.array(tem)[:,None,None]\n", "tem = np.where(top, broadcast(th.ThomsenData['Ice I crystal']), broadcast(th.ThomsenData['Muscovite crystal']) )" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.557049Z", "iopub.status.busy": "2024-04-30T08:55:21.556962Z", "iopub.status.idle": "2024-04-30T08:55:21.559291Z", "shell.execute_reply": "2024-04-30T08:55:21.559029Z" } }, "outputs": [], "source": [ "# Produce the TTI geometry and density from the material data.\n", "vti,ρ = Seismic.TTI.from_ThomsenElastic(tem) \n", "# Slice in two dimensions, and rotate by chosen tilt.\n", "hfmIn['metric'] = vti.extract_xz().rotate_by(θ)" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.560653Z", "iopub.status.busy": "2024-04-30T08:55:21.560572Z", "iopub.status.idle": "2024-04-30T08:55:21.562150Z", "shell.execute_reply": "2024-04-30T08:55:21.561888Z" } }, "outputs": [], "source": [ "if hfmIn.mode=='gpu':hfmIn['traits']={'nmix_macro':15}" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.563458Z", "iopub.status.busy": "2024-04-30T08:55:21.563377Z", "iopub.status.idle": "2024-04-30T08:55:21.596708Z", "shell.execute_reply": "2024-04-30T08:55:21.596345Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity 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 0.012146 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.Run()" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.598349Z", "iopub.status.busy": "2024-04-30T08:55:21.598135Z", "iopub.status.idle": "2024-04-30T08:55:21.654295Z", "shell.execute_reply": "2024-04-30T08:55:21.654056Z" } }, "outputs": [ { "data": { "image/png": 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wsGHfLswciMBQVPxq+SoMBkNuN4vy5KyupSUCFvcJ9QxWZjyG68z4W6Y6c+2xXVjW14GEouLx5Veye8llOa/OCIGrDu7Hgt5uWJKMl5auQE8ZK2/Fqioza8mW0FvGIONFDDMewxWA/W/Rjh7ctu9dAMDTiy/B6XClyy2iXLvk2BEs7zwJB8DG1mU4WVXjdpMKrlS6mqrTQUazJfSUpQb75jrIsKtp+hhmPESVbGiyDYBhxreEwJ/3bEHQtrCrphmvzF3udosoLVfVmRUdJ3DxsSMAgE0Ll+BQXUNOHpe8pzrdtZQJMpvzEGQoNxhmPCQz+BfgAGC/unzoAJYmOmBKCh5f/ikIdi8VlYXdXfjUoX0AgPfmzMPOGbNcbpG7irk6Ux0tbJBhdWZ6GGY8JDNexnBU2ILx32+qrCj+tDc1e+nX1athHOdgUK+ZTnVmZqQP1+7bBQnAjhkz8f6ceTlrF3lLdRS4Yj8rMn7CMOMhI1sZcME83xECt/W8jbBI4ohWjz9ULnO7RZRD9UOD+NzuT6AIgYN1Ddi0YAkHdacVW3XGzSDD6szUMcx4SFBOLZiXYBeT71wSPYSV8eOwIOPH9evhSKlTayq7a1N+ZVudqUjEceOuj6HbNk5UVmPjkqXsPixSrMj4F8OMh2iyBQAwHZ49flJpxXBrb2r20m+qV6FDGzuzhYHGv0KmiT/e+RHKkia6w2V4aekK2DLPzzMVQ3WmZlSQ6WaQ8R2GGQ/JVGYM7svkH0LgSz1vI+yYOKrV4ZWqC9xuEU3CZKozAcvCDbs/RnUijgE9iF8tWwVT5blZjGqiwPpRQWaLi0GGXU1TwzDjIWWqAQCI2rrLLaHJWhM7ggvjx9LdS1cMdy+didUZf5EdB5/duwNNQ4OIqwH8cvkqxHSel8VoTJApdzfI0NQxzHhIWEmFGa4x4w9ldgK39rwDAHi5eiVOaqW3cJqfTVidEQLX7N+Duf19SMoKfr1sJSKhcGEb50N+7GqqGTX9urtcYMsibwQZVmeyxzDjIWXp2UyszPjDrb3vosIxcCJQjZcn0b3E6owPCIH1hw9gSXcnbEnCb9uWo6uCKzgXo0yQCTipILPZI0GGpoZhxkNYmfGPlbF2XBw9DAcS/qP+CtjS5K6CDDTecmZ1ZvWJdlzYcRwA8OqiNhyrqXOjWb7ll+pMzdBIkDmdDjK2x4IMqzPZYZjxkMwKwDFWZjwtbBu4redtAMDGyuU4qte73CLKhdauDqw7eggA8Na8hdjXOMPlFlE+1AylZi1lgswWDwYZyh7DjIfo6anZhqO63BI6lz/tfQ9Vdhyn1Er8uvrCrO/P6oy3VByU0dLbjav37wUAbJs1Bx/Nmutyq/zLy9WZWgaZosUw4yFBhVOzvW5F7Bgujx6EA+A/6q+AJTN4+l2T0Yfr9u6EDIE9DTPwdstCt5tEeVA7lJq15Kcgw66myWOY8ZBMN1OUY2Y8KWQb+PN099IfKpfjULBxyo/F6ow3NJp9uLr/QwQcB0dqavHaolZuU5ADXqvO+DHIUHYYZjykLD0AOM4xM570hb4PUG3H0KlW4lfVq91uDk1To9mHa/o+QkA4OKHV4eW2FXBkXhKLzegg01XhvyDD6szk8Mz1kMyu2ZzN5D1t8ZNYP7QfDoAf169HMgfdS6zOuKfB7E8HGRsntVq8VnMBtykoQmcGmbd9FmRo8hhmPCTEMONJupPEl7s3AwDeqFiKQ8Eml1tE09Fg9uMzfR+OCjIr4UhK1htQ0rm53dVUNzgy2Hc4yPj0R8zqzPn59EdbnFiZ8abP921DnR1Fj1KGX9RclNPHZnWmsOYkunBt73YEhI0OrQav1ayc9BpB5B91g8D6AxLUIggyNDn88XpIpjITZ5jxjEWJTnx6cDcA4Kn6dTDk3M80Y6ApjLboMfxR/ydQ4eCYXo9Xa1adFWRYncktN6oz9aOCTGdmjAx/rEWPP2IPyeyaneDUbE8IOBZu734LALC5fDF2h2a53CKaEiFw0eB+XDK4DxKAvaFZeL36AlZkilDDALBufzrIVKYqMk6RvMuxq+nciuTH7H+KZEOTbQCszHjFzX1b0WgNolcJ47nai/P6XKzO5IcsHFwZ2YkV0XYAwLbyhXi3shVigt3NAVZncq1Q1ZnGAWDdAQmqkHCqUuDthcUTZOj8fPWjDu3qQGjHCbebkReZNWYAIO4wzLhtYaITf5TuXvpJ/XokZP5M/KbMTmBD7zbMT3TCgYS3qpZhR/k8riNThBoHgMsPSFCEhI4qgXeKNMiwOjMxX/64QztOFF2oCaVX/006MizB8rebVMfC7d2bIYPdS341K9GNG7vfRWMyAlNS8YeaVTgUap70/Vmdya18VmeaImODzLsLijPI0Ln5+keeCTXFEGy4yaR3XB/5GE3WAPqVEJ6vWVuw52VX0/RJwsGagf24pv8j6MJCt1qBX9ddgg6du18Xo6YIcNnBVJA5WSXwTgkEGVZnxlc0G8tkAk18hT//is5My45z8K+rZpp9uC7yCQDgmdrLEFcYLv1Cd5K4qv9jzDD7AQC7w7OxtWIxnHOMjzmXioMyBhc6OWwh5dKMCHBpOsicqBZ4b76AKPIgQxMruh+9Xys1nJbtPkXY+Er3m1Ag8GFoDj4MF37nZFZnpqbB7McN3e9hhtmPpKTg9eoL8H5l65SDDOVeLruaZvSPVGROVAu8t4BBptQVTWXmTKMDjR+qNZyW7b7P9n+MuWYvhmQdT9ddzoGiPiAJgeXRo7hw6BBkCAwoIbxevRL9gfKcPD6rM97T3A9cekiCLCQcrxZ4f4GAKLFT9ZX2VmyYu9ftZnhK0YaZ0fzQBZWpzCRshhk3zDZ6cH3kYwDAz+ouw4Aadq0tNXtN9LWyQnc+IdvAFZGdaDb7AACHgjPwTmUrrBzsm0X5MXS4CuXzI1O+/5ggUyPw/vzSCzI0vpIqzHm5C2qkMsM3sUJLdS+9BQUCW8Mt2Fo23+0m0XnMNHpwY8+7aDb7kJRkbK5cireqluUlyHBmkzfM7EuNkZGFhGMMMhwIfIaS/BPGi5WakTEzrMwU2mcjn2B2sg+Dso5n6i5zuzkAWJ2ZiCwcXDh0cHgRvF61HJuqV2BALXO5ZTRZU6nOzOwDLjkkQUYqyHxQ4kGGzlbSf3J4qVITSldmuGBeYc00+/DZ/lT30jN1l2FQCbncIppIuRXHdb1bh4PMnvBsvFS3tiBBhtUZ94wOMu21DDKjsTozoiQrM2fyQqWGs5kKTxIO/rxnC1Q4+Cg0B1vD89xu0hiszoxoiXfi8oHd0IQNQ1KxpWopjgUb3W4WTdFkqzOz+oCL00HmaK3A1nkCYJChcTDMjOJmqAmzm6ngPj2wGwuM04hLATxddxlnL3mQImxcPLAPS+InAQBdgSq8Wb0cURcqaJzZVFizeoGLDzPI0ORMqXb66KOPYv78+QgGg1izZg3efPPNcx5vGAa+853voKWlBbquY+HChXjiiSem1OBCcKP7KchupoJqTEbw+f5tAIAXatci4tExF6W87kx1cgg39LyPJfGTEAA+LpuH39Ve5EqQocKa3QtckgkydQwy58KuppSsKzPPPPMM7r33Xjz66KNYv349fvCDH+D666/Hrl27MHfu+IuM3XLLLejs7MQPf/hDLFq0CF1dXbAsa9qNz7dCVmqCrMwUjCQc3NG9GZqwsTvYjLfKl7jdJBpNCCyOn8TFA/ugwkFM1vBW1XKc0mvdbhnl0ERdTbPTFRkJEo7UCWxrYZCh88s6zDzyyCO48847cddddwEAvv/97+N3v/sdHnvsMTz88MNnHf/yyy/jjTfewKFDh1Bbm7oYzZs3b3qtLrBChBpOzS6cqwd2Y6HRhbgUwE/q17N7yUMCThKXD+zBvEQXAOCEVovNVcuRULxxXrCrKb/m9gBrjqSCzOF6ge1zGWQmg4voZdnNZJomtm7dig0bNoy5fcOGDdiyZcu49/nlL3+JtWvX4h/+4R8wa9YsLFmyBP/1v/5XxOPxCZ/HMAwMDAyM+fCCfHY/lSkGACDGAcB51ZiM4I/T3UvP116MXjU3K8XmU6l0NdWbEdzY8x7mJbrgQMIHFYvwh5oLPRNkKPdGb3Ew/zSw9ojMIENTklVlpru7G7Zto6mpacztTU1NOHXq1Lj3OXToEN566y0Eg0G8+OKL6O7uxj333IPe3t4Jx808/PDDeOihh7JpWkHlo1KTGQAc5a7ZeSMJgdvT3Uu7gjOxuXyx200iABACy2PtWD14EDIEBpUgNlWtQI+Wu718yNsWdgKrjqf+tj7QKPDxbAYZys6UBgBLZ5TlhRBn3ZbhOA4kScJTTz2FSy65BJ/73OfwyCOP4Mknn5ywOvPAAw8gEokMfxw7dmwqzcy7XFZqMmGGlZn8uWJwLxYZXUhIKp7y2d5LxVqdCdomrun7EGsGD0CGwJFgI35dd6mngwzXnMmtObtCw0FmbxODzFSV+kDgrCoz9fX1UBTlrCpMV1fXWdWajObmZsyaNQtVVSMXp6VLl0IIgePHj2Px4rP/OtZ1HbrunwpFLio14XQ3E9eZyY8qK4Y/6dsKAPhlzUXoDVS43CJqNnqxPrITYceEBRnvVS7BgdBMX4VMmp7lcRNr4qlr354ZArtmMsjQ1GT1J4amaVizZg02btw45vaNGzdi3bp1495n/fr1OHnyJIaGhoZv27dvH2RZxuzZs6fQZO+aTqUmpHBqdt4IgT/v2YKQSOKwVo/XK9rcbtGUFEt1RhIOLhw8iM/0bUfYMdGnluE3dRfjQHgWg0wJWR43hoPM7mYGmVwo5epM1vXS++67D//2b/+GJ554Art378a3v/1ttLe34+677waQ6iK64447ho+/7bbbUFdXh6997WvYtWsXNm3ahL/+67/GX/zFXyAUKs71IrINNRIEdDk1VZ1Ts3Pv0uhBXBA/jiRk/Lj+CgiJ3QRuKbPjuK53G1ZGj0ACsDc0Cy/VXYxIwPsDsUdjV9P0rIgbWBNPhfMPQxreNyoZZGhasp6afeutt6Knpwff/e530dHRgRUrVuCll15CS0sLAKCjowPt7e3Dx5eXl2Pjxo34y7/8S6xduxZ1dXW45ZZb8L3vfS93r8KjQjtOTKrrKTMtGwAMh2Eml6qtKG7peRcA8JvqC3FKq3a3QSVsbqILl0d2QxcWTEnB21VLcTQ4fvc0Fa8L4gZWp4PM9pCGT0L+GVLgB6U6TXtK2xncc889uOeee8b93pNPPnnWbW1tbWd1TZWKyYynyezL5AggwTCTO0Lgy92bEU53L22sWuF2i6bNj/s1ycLG2sH9aIulzoXTgUq8WbUCQ2pxVmZpYivjBi5MB5ltIQ07RgWZqeymTZTBvZkK5FyhZmSNGR2stebOZdGDWJ44CVNS8O/1V8Bh91LBVVpRfKp/B2qt1Ji5HWUt2F6+oCi6+riAXnZWxQysSowfZIimy/9XFJ8ZbzxNiNOyc67CjuMLve8DAH5TtQqdRdS95IuBwEJgYewkbuh5D7XWEOJyAL+vuRDbKhYVRZChLAgxJshsPUeQGb2IHk1dKQ4EZmXGJaPH03CNmdy7tecdlDsGjgdq8Psi6F7yE9WxcNnAHixIdAIATmq1eKtqGRIK/xIvOULgwriJlekg80FIx64Qr3OUe/wTyUWZKk1ITm8yyWnZObE6egRrYkdhQ2L3UoHVJgdwY897WJDohAMJ28oX4vc1FxZtkOGspnMQAqtHBZn3wwwyhVRq1RmeiR5Q05FahDBqFecFv5DCtoFbe94BALxSdQGO63Uutyg/PNfVJASWRttxfc8HqLTjGJKD+F3tRdhRPo9rx5QiIXBR3MQF6SDzXljH7uDkggy7mmgqGGY8IKylTnijn4MJp+sLfe+jykmgI1CFl6pXud2ckqA7Jj7d/zEuHtwPBQJH9Qb8uv4SnC6icUqUBSFwUdzAilFBZs8kgwzlVilVZxhmPEBXbQBAPKnmdWfuYrcidgzrhg7AAfCTunWwJMXtJuWVF6ozTWYfbup+D3OMbtiQ8U5lK96ovgCmXDpLDLCraRQhsDZmYEUitXbWu1MMMqzOULY4ANgDNCUVZpL2yJtvPnbmLmZh28CXe7YAAP5QuRyHuBhbXklC4ILoYawcOgwZQL8SxqbqFejnnlelSwhcGjPQaqSCzDthHftYkaEC4Z8UHqCrqa0MDOvsbMkqzeTc3LcVVXYcp9RK/Kp6tdvNKWohO4Fre7fhwnSQORBqxkt1lzDIlDBJCKyLJtBqJCEAbCkLTjvIsDqTG6XS1cTKjAeEA+lNJpPj/zhYpTm3JfEOXDm0DwDwVP16JOXS+bUu9IrAsxLdWB/ZhaBIIikpeKeyFYdDzQV7fq8q5QX0JCGwPprAAtOCA2BzWRCH9dLpZiRvYGXGA0LDYebcFwBWac6mO0nc3rMZALCpohUH2L2UF7JwsHZgH67p/whBkUSPWoFf113CIFPiJCFw5dBIkNlUziDjRaVQnSmdP2E9LKylwkzsPGEGYJXmTH/ctw311hB6lDK8ULPW7eYUpQorhk/170CdNQgA2BWeg20Vi7h+T4mThcBVQwnMSVqwAbxRHsJxLbdvKdyviSaLVyMPyHQzxczJdxewSgPMT3ThjwZ3AwCeql8Ho4Rm0IyWz1lNC+IduLHnPdRZg0hIAbxavRIfVC5hkBlHKc1qUoTAp4fimJO0YAF4LQ9BhigbpXP2eVimmyk2wZiZCe9XwtO4VcfC7T2bIQN4u2whdodYqcol1bGwvn8nrojsQkDYOBWoxq/qL8HxYIPbTSOXqULgmsE4ZiVtWABerQjhZB6DDAcC50axdzUxSntAMD2bKTGJbqbxjN7nqVTc2P8hmpMRRJQQnqu9xO3muC6XA4Frk4P4VP8nqLTjcAB8XD4fn5TNh+BKviVPdwSuGYyh3nZgIhVkugJ8GyH3sTLjAZnKTGKcqdmTfowSqtK0GKdx7cBOAMBTdesQK9J9fwpOCLRGj+H6nvdRaccRlXW8UnsRPi5fwCBDCDkONqSDTEKS8EpluGBBhtWZ3Cjm6gwjtQcMV2amEWYyir1Kowgbt3dvhgyBd8sW4JPwHLebVBQCThLrIrvRYpwGABzT67GlalnJjkOaqmKdol1pO7hmMIYKRyAmSdhYGUJEKe4VtslfWJnxAD2Q6WbKTbYs5irN9f0fY1ayH4OyjmfZvTTGVAcC15kR3NjzHlqM07Ah4b2KxXiteiWDDAEAGpI2rh+IosIRGJAlvFwZdiXIsDqTG8VanWFlxmWy5CCY3pspF5WZ0YqtSjPL7MVnIx8DAH5WdzmiStDlFvmcEFgaO4aLBg9AgcCgEsSm6gvQE6h0u2XkEXPMJK4cSkAFcFqR8VpFCAmZfwOT9zDMuCzTxQRkNzV7soplXRpJOPhy92YoENgWbsG2snluN8nXNCeJ9ZFdmGN0AwCO6I14u2ppSa2enC9F0dUkBJYaSayNGZAAHAsoeLM8BItjp8ijGLFdllkwL2nLSDr5K936vdvp0wO7Mc/sQUwK4JnaS91ujmdNpqup0ezDTd3vpne6lvBuZSs2Va9gkCEAqVV9L40ZuDgdZPbpAbzukSDDrqbcKMauJl69XDbZrQxy8lw+7XaqTw7ij/u3AwBerF2LATXscov8SRICK6JHsGroEGQAA0oIm6ovQC83iKS0oOPgyqEEmi0bAsDWkI5dwQDggSBDdC6szLgslzOZJsN3g4OFwJ/3bIEuLOwNzsDm8iVut8iXQraBa/u2YXU6yBwMzsCv6y5hkMkTP64G3JS0cGMkhmbLRhKpVX13hTTPBRlWZ3Kj2KozrMy4rNBhJsMvVZorhvahLdEBU1Lwk7p1XO9kEs5cQG+W0Y31/SM7Xb9b2YpD3CCS0iQhsDJu4oKECRlAvyLjjbIgIiqnXpN/+O/PhyKjp8OMYRX+wuH1Ck2NNYQv9L4PAPh5zRp0c5ZNVmThYM3AflzTl9rpulctx6/rLmGQoWFVto3rB2JYlQ4yBzQVL1WGPR9kWJ3JjWKqzrAy47KRrQzc+VF4tkIjBP68520EhYUDeiNer1jqdot8Zdb+CFbV7EV9eqfr3eHZ2FqxmBtEFpCXZzXJQmB5wsTKuAkFgCEB74aDOKJzbSHyJ4YZl2VmM8WSuZ+WPVlenL59SfQQlsdPIAkZP6lfz+6lLMwMdGFl6AAClg1DUrGlahmOcYNISmtMWrg0ZqDGTgWt4wEFb5cFEef6MeRjDDMuCw/PZnL/R+GVKk2FHcef9b4HAPhN9YXoDLCkPBkKbKwIHcRcrRMA0BmoxpvVyxHj4oIEoNaysSZmoNlKLdIZlyR8ENZxWFM9N8h3MoYOV6F8fsTtZvjeK+2t2DB3r9vNmDb330FLXLCAU7MnwwuB5s9630O5Y+BYoAYbq1a42ha/qJCjWBPejQolDiGAfcZc7I/MRayOm3CWupDjYHXMwELTggTABnBAD+DDkA5D9l+IIRoP64ouC+V4X6ZccHNg8MpYOy6OHoYDCT+pX88xHucl0KKdxJXl21GhxBF3NLwdvQD7jBYI8I3KbW5O0Q4IgZVxAzf3R7EoHWQOaSp+XlWGd8uCRRFkOBA4N4phILB33kFL1PBsJttbPwo3xtGEbQNf6nkbALCxcjna9fqCPbcfBZDEqvB+NAd6AACdyRp8GF8CU7g3/orcF3QcLE0k0WqY0ETqti5VxgfhILo9PkuJaKq89Q5agtyezXQ+hex2+lLP26i24zilVuI31RcW5Dn9qkYZwEXhPQjLBhwhYXdiPg6ZM4EzqjFnrjlDxavcdrA8YWKRkUQmsvTLMj4OaTji03Exk8GxMwQwzLhuZJ0Z7/4oChFoVkePYG3sCGxIeLLhU9wnaEICi/TjaNWPQJaAqB3E1ngbIjZX8vWqvE7RFgL1loOlhokW0xoeN3BakbEjpOFYoHhDDOWW3wcC8x3DZZkxMzGPDACeSD4DTdg2cGvPOwCAV6ouwFF2L41Ll0ysDu1FQ6AfAHDcbMAn8UWweBqXHEUIzDMttCVM1NkjQel4QMGOoIYuVWGIoZLCq6DLwoHULscx09thBshfoPnT3vdQ5STQEajCS9Wrcv74xaBB7cPq0F7ochKWkLEjvhDHkk04s1tpPOxqKh5ltoNWI4nFhgk9PR7GBnBYU7E7qKGvRMfEsKspN/xcnWGYcVk4XZmJW94PM0DuA83y2HFcHj0IB8B/1K2HJZXmxXgiEhy0BY9ikX4cABCxy7At1oYhhzuH+8l0upokITA7aWGRkcTspD0cX4dkCXv1AA7oWlHMTCKaDoYZl+kenJp9PrkKNGHbwJd7tgAAXq1chsPBxmk/ZjEJSQmsCe9BjZrakuCw0YxdiflwwMBXCipsB4uNJBYaSYSEGL79pKpgT1DDiYDClbFHYXUmN/xanfHPO2iRCqqpRfMKvWv2dOUi0NzS+y6q7Rg61Ur8svqiHLWsODSrp7EqvB8ByYYpVHwUW4xT1tTHErGryR8UIdBiWlhsJNGUXqkXSK3We0hXsV/XMKBw7SWiM/nrHbQI6WrqguW3MANML9CsjLXj0ughOJDw7/VXcPZSmgwHy4OHME/vAAD0WpXYFmtFXHBLgqIlBOpsB4uMJOabyeG1YRwAJwMK9usBHA+orMIQnQPfQVyWWWfG8FE302hTCTRh28BtoxbHY/dSSpkcx5rwblQpUQDA/sQc7DXmQnCh7qJw5riZoONgnpkaC1M7akbSoCzhgB7AQT2AGDd/zAq7mnLDj11N/nwHLRKK5CCgpC5iCY+tAJyNbAPNF/reRxUXxxtjZqALq0IHoEo2DCeA7fFWnLZqcvoc7GpynyQEZiZtLDaSmJ0cWRfGBnBUU3FAD+AUp1UTZc2/76BFIKyZw1/7YWr2uUw20LTFT2Ld0IHU7KX69SXfvaTAxvLQIbRopwAA3VYVtsVaYQhuEFlMymQbc7Uk5kRMlDkjg3m7FRkH9QAOawGYnJGUE6zO5IbfqjOl/U7isnAgM/hXgSP8X04+X6DRnSS+3L0ZAPBGRRsOBZsK1TRPOnOn6/3GHG4QWURUCMzUkmjRTNQH0oN5HcCQgINaAPuDAUQUzkwjygWGGRfpPh8vk60/6duKOjuKHqUMv6hZ43ZzXCTQonVgefAQFEkg4WjYHluCbju33UrjYVdTvgnUqzbmaiZmaUmo6VwqBNBlqThqBLBvjgKH3Uh5xepM6SmNd1GPCqZnMnltx+zpmKg6szR+AlcN7gEA/KR+PQzZ391qUxWQklgVGr3TdS0+jC/mTtc+F5YdzNFMtGgmypSRbqQhW8ZRM4B2Q0MiXX11pDzt00SUY37qaiqed1Ef8uOCeZNxZqAJ2QZuT3cvvVaxFHtCM91qmqtqlAguCu8d3ul6V2I+Do+z0zX5g5LuRpqrmWgMjKwJkxTACTOAo4aGXlsBf75E+Vdc76I+k5mW7cc1Zs5ndKD5f/o+QE16cbwXS7J7SWCRfgyt+lHIEjBkB7Et1oaI485O1+xqmg6BWsVGi57qRgqMyildSQXtpoaTZgD2OQJMXnfRpmHsasoNv1Rniu9d1EeKOcxktMY7cMXQfgCp7qVSm72kSyZWh/eiQe0HkNrp+uP4Itg89XwlKDmYq5uYqyVRoYwEkagt4aipod3UEHf8P4ifyK94RXVRZmq236dlT6RqRzv+vPp9AMAbFa04UGKzlxrUXqwO7Rve6fqT+CIcTzaC3Q7+IEOgOZBEi55Eo2oNL/1iZbqRTA09FruRvIzVmdzwQ3WGYcZFZVpqanY8WZxh5jrtIBqsQfQqZfh5CXUv+WGna3Y1TUSgRkmtCTNbM6GNKrZ0JxUcTXcjWdMMMOxqIsothhkXZbqZYkUYZmbLEVwVOAoA+Gnd5UjIpfHGOf5O1wvgcEsCT9MlB3O0JFp0E5WjupFijoR2Q0O7GUDU4ZowfsTqTGlgmHHR8DozRTZmRoGDL+k7IUvAtuQMHDokASvcblX+5Xqna8ovGQIzAhZadBONqoXMArx2uhup3dRwmt1IRAC839VUXO+iPjO8yaRVXH/xXacdRLMSxaATwItGK4Dp7bDtdQpsLA8eQoue2pLALztdl2ZXk0C14mCuZmKOloQmj6wJ02MpaDc0HM9BN9JksKuJKHcYZlw0MpupeLqZ5sgRXB04AgB4zliGKIr7zbJcjmJNeA8qlRiEAA4Yc7CXWxJ4jpbpRtJMVKlju5GOpbuRhtiNVLTY1ZQbXq7OMMy4aHjRvCLpZlLg4Iv6ruHupU/sxjHfL67qjMDcwCmsCB2CIjlIOAFsj7UWZEsCmhwp3Y00VzMxIzC2G+lkMoB2I4AuSwW7kYj8rzjeRX0qs9FksUzN/nTgCJqVoTHdS8VIhYWVof2YpXUDALqSNdgeX8ItCTyiUrGHu5GCo7qRei0F7UYAx5MakoIBptSwOlPcGGZcNBxmimA2U4MUxQbtEADgRbNtwu4lv1dnqpVBXBTegzI5AUdI2JOYh4PmLPj1r/tiGTeT6Uaaq5moHtWNlHAkHEtvLTDowW4kjpshv/FqVxPDjItC6TDj972ZJAh8MbgTqiSw26rDh9a5F8fzZ6ARWKCdwNLgEciSQMzRsTXWhn670u2GlTCBJtXCPH1sN5IjgI6kinZTQ2dS5fglGsbqTPHy97uoz+lFMgD4jwJHMV+JIC5UPGsshV+rFBPRJBOrQ/vQGOgDAJw06/FRfDEsnj6uCKarMPN1Y8wO1b2WgnYzgBNmAKbguj5E+eLF6gyvxi4qhqnZM+QhXK8dAAD8wliCfhGa1P38Up2pU/pxUXgvgrIJW8jYEV+A9uQMFFNg80NXkwqB2elF7WrVkR2qTQdoNzUc8Wg30mSwq4lo+hhmXBQM+HsFYBkOvqTvgCoJ7LTq8Z410+0m5YwEgSX6USzWj0GSgEE7jK2xNgw6ZW43rYQI1Kk2WrTUDtVqOj8KAfTZCo6k14Q51w7VRGdiV1NxYphxjRhZZ8anYeaPAkcxRxlETKj4T2MZsq1WeLU6E5ISuCi8F7XqAADgqDkDO+MLYMOff/n7zUQ7VA/aMo6m14Qx2I1E5CqvdTUxzLhEVy0o6WmjcR8OAK6XorguPXvp50YrBoXucotyY4bajVWh/dBkC0mh4OP4IpxMNp7/jj7ndlfT6K0Fms7Yofp4ejZSr82tBSg3WJ0pPv57Fy0SmR2zbUfy4aJ5An+q70FAcrDXqsUHVrPbDZo2GQ6WBQ9hvt4BAOizyrEt1obYJMcA0dRUKalupDO3FsjlDtV+wHEz5Edeqs5MqVb76KOPYv78+QgGg1izZg3efPPNSd1v8+bNUFUVF1544VSetqiMXTDPXxfri9WTWKL2IilkPDfN2UuhHSdy17ApKpNjuKL8w+Egc8CYhc3RVQwyeaJJDhboBj5dMYirK4ewMGhCkwXijoS9cR2vRMrx5lA52k2tJIIMEU1f1mHmmWeewb333ovvfOc72L59O6688kpcf/31aG9vP+f9IpEI7rjjDlxzzTVTbmwxyawxE/fZtOwaKY4/0VNJ/GVzIXpE2OUWTc/sQCc+Vb4dVUoUhqPi3ehy7E4sgJhazve1mr1m3h5bgkCTmsQlZVFcXzWIVeEEqlUHdrobafNgGC9HKrArEUTUp7OSyF+GDle53YSi8Eq7N1Z7z/qK/cgjj+DOO+/EXXfdhaVLl+L73/8+5syZg8cee+yc9/v617+O2267DZdffvmUG1tMgj7cl0mCwJeCOxGUbByyq/F6siUnj+tGdUaBhQtDe7E6vA+q5KDbqsIbQxehy6oteFuKWblsY3kogeuqBrGuIoZZWmpxuz5LxkexIH4bqcD70TC6LP9VKHOt4mDpBWiiXMnqndQ0TWzduhX333//mNs3bNiALVu2THi/H/3oRzh48CB+8pOf4Hvf+955n8cwDBiGMfzvgYGBbJrpC2Efrv57ReAYFil9MISCpxPLfbuyaqU8hDXhPShX4hAC2Gu0YL8xB6X+ZporKgRmpdeEqRu1JoyR2VrA1DBgs/pC7uNA4OKR1Ttpd3c3bNtGU9PY5eqbmppw6tSpce+zf/9+3H///XjzzTehqpN7uocffhgPPfRQNk3znZDPNpmsk2K4QdsPAPilsTjn3UuFmaYtMF87iaXBw1AkgbijYVusDb02y83TJ1CfXhNm5hlrwnQmVRw1NXRwawGiouSFgcBTKgtI0tgLkhDirNsAwLZt3HbbbXjooYewZMmSST/+Aw88gPvuu2/43wMDA5gzZ85UmupZ/tpkUuBP9d3QJAf7rFq8bc12u0FZC0hJXBjahxmBXgDAqWQdPowvRlL44f+/cLKdoh1KrwnTopljthbgmjDkF6zOFIeswkx9fT0URTmrCtPV1XVWtQYABgcH8cEHH2D79u345je/CQBwHAdCCKiqildeeQVXX331WffTdR26XhzrlkykTEsNtoyZ3l5GHgDWqh1ozdHspXPJV3WmVongovAehGQTtpCwKzEfR8yZYLfS1MgQmBlIokVPomHUmjDJ9GDedq4JM2Wcok1+5XZ1Jqswo2ka1qxZg40bN+JP/uRPhm/fuHEjPv/5z591fGVlJT755JMxtz366KN49dVX8dxzz2H+/PlTbLb/hdPrzEQ9XpkplwzcnJ699DtzAbp9NXtJYLF+DK36UUgSMGSHsDXWhgGn3O2G+ZBAjWJjrp7E7IAJbVSx5fSoNWG4tQARuSHrbqb77rsPt99+O9auXYvLL78cjz/+ONrb23H33XcDSHURnThxAj/+8Y8hyzJWrFgx5v6NjY0IBoNn3V5qMlsZxD0eZr6g70FYsnDcrsjZ7KVC0CUDF4X3ol5NlY+PmY34JL4QNteJPK/RXU16eofqFt1E5aitBWK2hKOmhnZTQ8xhNxL5G7ua/C/rK/utt96Knp4efPe730VHRwdWrFiBl156CS0tqTe6jo6O8645Q0BASc3ySNrefSNYpXRildoFW0j4mbEcTgHWXslFV1Oj2osLQ3uhyxYsIeOT+CIcT57dDUrjkySB5kASczUTMwKpqdQAYAvgZHo20mmL3Uj5wq4m8is3u5qm9GfqPffcg3vuuWfc7z355JPnvO+DDz6IBx98cCpPW1T0dGXG8Og6MxWSgS8EdwMA/pCch5NOhcstOj8JDpYGj2Chnlq3JmKXYWusDVHHT11j7gmHHDQ32Giqt6CNGsrVayk4agRwIqkhKRhgqDixOuNv3nwnLQGZvZm8OQBY4BZ9F8qlJE7Y5dhoLijos0+lOhOW41gT2oNqdQgAcMiYid2J+QWpJvmZqgg01tuY0WChsnxkNpJpAkcdDUcNDYNckZeIJsmt6gzDjEsys5m8OAB4tXoKy9VuWELCT40VsD0eCGYGurAydAAByYbpqPgwvgSdVp3bzfIwgZoqBzMabNTX2lDSP17HAXr6ZZw6raK3X0bvkuKeUUh0JlZn/IthxiWZAcBeWzSvDObw3ksbzQXo8HD3kgoLF4QOYrbWBQDosSqxLdaGhOCb8HiCeirAzGiwEdRHqjBDMQmnuhR0dqtIWuxG8gKOmyHKDsOMS4Y3mvRYZeZmfS/KpSQ67HK8mpznWjvO19VUKQ9hbXg3ypQEhAD2G3Owz2jhCrNnkCSBhlobzY02aqpG3hyTFtDVreDUaRWDUQkczEtEueJGVxPDjEsyYcZLG00uVU5jTeAUHAE8YyzzaPeSwNxAJ1aEDkCRBGKOjm2xNvTZlW43zFMqyhzMaLRQX2NDTw/LEgLoi8g4dVpBd68C5zyDebNdDZioGLCryZ+8805aYsr11JiZIcMbbxY6LPypvgcAsCk5F+2O9/YrUmBh5ahupc5kLbbHl3BLgjRFEWistdHcdPZg3pNdKjq6FBimFwMqERWbQldnGGZcoCkWgundhAcNb4zvuEnfhxo5gW4nhN+ai9xuDoCxXU2jd7p2BLDXmIcDxmywe0SgpnLUYN70xCPHAbp6FHR1K+gbkCE4pdp3OG7GPazO+A/DjAsy07Id4Y2NJtuUbqwLpNZm+U9jGZLw0lRcgRatA8uDh7jT9SihYCrANNWPHcwbjUk4dTo1FiYXg3nZ1UREU/VKeyuuqt1RkOdimHFBZvVf01LhdmUhiCRu1XcBADaZc3HArnW1PaOpio014d2YGegBAJxK1uLDEu5WUhWBhrrUbKSqCg7mJSLKYJhxQWb1X9N2vwJyvXYQVbKB004Iv/FI9xIAVJYncEFrF0IBC46QsDsxH4dKcqdrgepKB82NY9eEEQLoTa8J093HbqRixa4m97CrKTdePb64IM/DMOOCzBozbs9kWiD3YX3gGADgOWOpR7qXBObOjGBRSy9kGYglVHxgrUDE9u56N/mgBQRmNFhobrQRCp7djdTZrcJMMsAQEQEMM64IBtJhJunef78GG18K7oQsAe8kZ2K/7f6KuQHVxrLFp9FQGwMAdHaXYdeBBtj2ALCi+MOMBIHaGgfNDRbqahxI6axiWUCni91IHDdDRF7HMOOCCs0A4O7g389qB1Anx9HnBPELo9W1dmRUV8axYkkXgroN25Gw73AdTpyqQCl0K4WDDmY0pjZ41Edlhv4BGR1dCk73KnCc4v9/IPIadjX5B8OMCyqDqTATSQRdef7Z8gA+FWgHADxntMFw9ddAYP7sfiyY2wdJAqLxAD7Z04ihmDemrOeLIqcG8zY3jh3MayaBU6dTa8LEE1wThjhuhmgyGGZckNlkctCFBfNkOLhVT3UvbUs2YbfdUPA2ZGgBC8uXnEZddRwA0NFVjj0H62E7Z7+JT2Unbe9Jb/BYP3ZNGCGAnr7UYN6efm8O5mVXExF5GcOMCzKzmQwXBgB/OnAUs5QhREUAPzfbCv78GbVVMSxfchq6ZsO2Jew5WI+O08U5LkZRBJrqbcyeYSEcGhnMG4tL6OjiYF4ioulimHHB8ADgAoeZZnkQ12kHAQC/MJZgSBT+L21JElg4txfzZqf6oYeiAXy8twmxeLH91Z+eUt1go75uZEp1ZjBvZ7eKgSGuCUPkdRw34w8MMy4YnppdwAHAChzcpu+AKgnssOrxgdVcsOfOCAWTWLGkC1UVqTFDxzsqsO9IHZxxupXGvb8Pupp0LbUy74yGs6dUn+xUceq0ApuDeSlLHDdDdG4MMy4IubDOzPXaQcxShjAkAnjWWIZCVwSaGwbRurAbqiJgJmXsPtCA071lBW1DvsiSQH1tKsDUVJ0xpbpHwamu4liZl+NmiMirGGZcEErvzRQv0Dozc+UI/ihwBADwTGIZBkXhZgrJsoO2Bd2Y2TQEAOiLBLFjXyMM0/+/euVhBzMaLTTV2wiMejl9kdSU6u4+TqkmIioE/7+j+FBmNtNQAWYzyXDwp/puyBLwQbIZO+3GvD9nRlnYxMrWTpSFkxACONReg8PHqzGdCoXbXU2qItDUYKO5wUJ52Ug3UsLIbPCoIGFwSjXlHrua3MNxM97HMOOCTJiJmfkPM1cF2jFbGURUBPALY0neny9FYGbTIFrn90BRBBKGgh37GtE/ECrQ8+deedjBrBkWGutGplQ7DnC6NxVg+iIy/N6NNBnsaiIiL2KYcYGupnbNTtj5/e9vlKL4bHr20i+NxYgi/29CiuKgbWE3mhtS3UrdfSHs3NeIpOWFfZ+yoygC9TU2ZjVZqKwYqcIMRSV0dKno7FZg2cUfYIiIvI5hxgW6kt41O49v8DIcfCm4EwHJwW6rDu9bM/P2XBk1VXEsW3QaoaAFRwAHj9bi6Ikq+KtiIVBV4WBm49gp1ZkqzMlOBZHB0qjCEBH5BcOMC0LpdWbyOQD4msARtCgRxIVagNlLArNnDKB1QQ8kCYgnVOzY14jIYH62a8jHuBk1vbDdzCYLZeGxC9udOq2g47SKJBe2I5dx3Ix7OG7G2xhmCk6MDAA28zOrqEkewgbtEADgeaMN/SJ/e0AFVBttC7vRVB8FAJzsLMfew/WwbT8Mgk0vbNeY3l4g3WTbTi1s11EkU6pzjeNmiMhrGGYKLBxIQpFTf/nnYzaTBIFb9F1QJIEdVgO2WTNy/hwZdTUxLFuU2pLAcYCD7f7oVtICAs2N1lkL2w1FJZxMj4WxORaGiMg3GGYKLLNjdsJSYNq5HzNzuXoc85UIEkLBC0Yb8hMsBObOjGDxvF5IUmpLgp37GzEYLdz6Ndl3NaU2eZzZZKG+pngXtiOi/GFXk3cxzBRYVTABAIjEg8j1G2e1lMCN+n4AwG/NRXnpXgqoNpYtPo2G2hgA4PipCuw9VO/JnZ4BIKAKzGi0MLNxbBWmfyC1sN3pXi5sNxXsanIPx80QnY1hpsA0JTUt28j5tOxU91JQsnHErsJbyTk5fnygujKOFUu6ENRT3Ur7Dtfh+KlKeK+aIVBT6aC5yUZ9jQ151CaPp04rONmlIhb3w5geIiKaDIaZApOlVHVAiPMcmKVL1ZNoU3uQFDJ+llgOkdOAIbBgTh/mz+mHJAHRWACf7GvEUAG7lcZzZleTFhCY0WCh+YwqzMBgaixMVw+rMERExYhhpsAC6cqMlcPxMpVSAn+s7wMAvGwuRJfI3QaOumZhxZIu1FSlusdOdpZj76F62JPc6Tr/0mNhGi3U1ThjqjCd3akqTDTmlbYSkd9x3Iw3McwUWIWempY9mLOZTAJf0PcgJFlotyvxRnJujh4XqK+JYtni09ACDixbwp6D9Th1uiJnjz8dgZCEhiU66i8wxlRhIoOp1XlZhck/jptxD8fNEI3FMFNgFXpqNtOAkZsumgvVTlygnoYtJDxjLIOD6VchJElg8bwezJ05AAAYGNLwyd4mxBOBaT/29BoGVM8OoKFVR83cACRZAiBSY2HS68KwCkNEVHoYZgqsIj01ezAHYaZCMvAFfQ8A4PfJ+ehwpl81CQdNrGjtQmV5qoJ09EQVDhytdXW2kl4uo36JjsZWHVrZSFgZ7Eyia4+BE6F6VmGIiEoYw0yBVeq5CzNf0PegTEriuF2B35vzp/14MxoG0bawG6oiYCZl7NzfiJ6+8LQfdyokBahp0dDYqqNq1khFKJlw0L3fxOm9BuL9qfFHzgoGGSo97GpyD8fNeA/DTIFlBgAb1vT+65crXVipdsEWEp42lsOeRveSLDtoXdCDWU2DAIDeSBA79zXCMAv/6xGqUdDQqqN+kYZAcOQ1RU4k0bXXQN8RE4LXb8/guBki8gKGGR+qkeL4UnAnAGBTcu60upfCIRMrWztRXpaEEMChYzU4fKwahVw7RgkAtQtS3UjljSO/ksaQjdP7THTvM2AMTZxg8rHxJBER+QfDTIFNf50ZgduCOxCWLBy1q/CSuWjKbZnRMIilC7uhKAKGqWDHvkb0RUJTfrxslTepaFiio26BBiWQCk+OI9B/NFWFiZxIAjlej4eIiIoPw0yBVYfS2xkkprbVwFq1AwuVfhhCxn8kLphS99KZ3Uo9/SHs3NcAM5n/Xwc1KKF+caoKE6oeWWsn3m+ja6+B7v0GrAQTjJ+wq8k9HDfjHo6b8RaGmQKrD6f2NOqJZj+wNogkbtJSey9tNBegV2RfRXGlW0kCqmYF0Niqo3puALKSei47KdB72ETXXgNDnda0noJdTUREpYthpsBqMmEmln2YuVo7ggrZRJcTxhvJlqzvP3q2UiG6lbRyGQ1LdDQs0aCXj1RhhrosdO010HvIgJ3M29MTEVGJYJgpKDG8AvBAIrup2TPlQVwVaAcA/MpYnFX3UiG7lSR5ZEp15SwVkpSqwiQTDnoOmOjaZyDea+f8eYmIqHQxzBRQULUQUFL924Pm5McYlEsm/iL4IQKSg91WHXbaDZO+b6G6lUI1Smp7gcUTTKk+akIwwxQtjptxD8fNuIfjZryDYaaAyrVUVcZypCzWmRG4Rd+FWjmBLieMnyQuwGSDSL67leQAUDfOlGoz6uD0PgOn9xkwBgt3keW4GSKi0sQw44LU1gCTCyQXqp1YoZ6GJST8e2Il4jj//kiy7KB1fg9mzUgvgtcfxI59jTnrVipvVNHQqqFugT52SnV7ansBTqkmIqJCYpgpIEVOVSnsSe5zpMPC57W9AIDfm5PbeykcMnFBaxcqysycdiupQQn1i3Q0tGoI14z82sT7bZzea+D0AQNWnAmGiIgKj2GmgMrTg3+HJrkv02e0w6iSTXQ7IbyanHfe43PerSQBVTMDaGjVUNOijUyptgR6D+VmSnWusavJPRw34x6Om3EPx814A8NMAVVMcpPJyLxmLOppx1XOUQDAz41WWFAmPF6WHSyZ34PZOepWGp5SvViDXjFqSvVpC6f3Gug5aMJOsgqTCwICQjPhlA3BLosi0DkDcpKBoFjJQoIOBZpQoEOBLhQMSCYisuF20yjHFEdC0FEQtBXojoKgLSPoKNBtBQnFxu5KBqBcYpgpoIrhyszEb1bJcBDdFy/B//fW76AOCnxsNWKXXT/h8Wd2Kx0+Vo1Dx2qQbbeSJAM1cwNoaNVRNTswPKXaSjjoPpjapTrGKdVZGwkrUTjhKOzyoXRwGYJTHoVTFoUIjCy2U/n7DZBPN7rYYjonAWiQoUMdDiRnftaFAg3jf08dZ0mFD5RT2CZ3uvBiSpssAF3ICAkFQSGP+lAQEjKCzsi/g0JO3XbGsSGhQBcyyiJiVGhJfQ6IiZfP2FHZh/92wQcFfLXFj2GmgMqHKzMTh5mu1Yvxtb0vY95gJwYdDc8mlmKiYNJUP4Sli05Pq1spVC2nd6nWEQiNnVJ9eq+BXk6pPicBAaEbqZASisEJx+CUD8Iui8IpT4UWBM7fFSfFg1Ci5eDI6fxThJQKG2eGkPTX431v+DMUSNMcfyYgYMCGCRumZCMheaur1iukdNjQRwWJUPrfwVEhJCRk6M6oEHJG6DgrhDipr/UpbAUzIXPib9lwkFBsGHLqc0K20RGM5e65CQDDTEFlpmYPTbDGTLyuCq2hftz80VsAgKeN5Yji7GOn260kq0DdAg0NrToqmkZmR7k1pTrXcjluZnRlxS4fTAWVisFUaAnFYJdFJxdWEjrkaDmUaFnq81A55GhZ6nOsDJJdHKdi3sfNCECBhAAUaJDHhI9xQ8gZ39MmqI5ky4IDAzYMKRVKhj+nA4oBC6bkwIA15hgDNpJw8rJ7SKHHzUgC0NKhYKSKcY5Kxxlh4uyqx5khZOKu9VxyIJCQnPSHPeprB3HJhiE5iEsOEnLq+3HJSd829lhp5sBwWEmFl9RnSxJ53S2GUorjCuoTmQHA0XEqMwKAecFM/NW2HwIANplzsGec7qXpdCuVNShobNVTU6q11PHCEehrT1Vh+o+X3pRqIdsjFZVgYria4pRFh8exQD1PaUoAciwMOR5OfR4OK+VQhlLhRXIKc2H2CzldHUm9GaZCRlCow900qc+j/60imMMw4kCkKiOjQoY50edxjnEkH5woAtAgpQKCkwoMo4NGOPO1MxI2Rlc7QsP3G6mIZD60XFc2zsOAg7hsnxUyEpmgcWYIke2zAsp4ISQu2zCRm7BRXsUxMG5imCmgUHpsRDx59loxg3Ob8KXOzagyozgmKvErc8kZRwjMbBzEkgU9w91KO/c1oDdy7j2eVF1C/aJUFSZcO2pKdSQ1pbp7v4FkEU+pFoqVCillQ6muoExYCcXhlA3BCcdSnefnISV0KEMVkIfKoQxWQo6WQY6HoERTFZZSDCuqJCMgqwjICjRZQUBWEJBVzLS1dGVEHRVMxgaUXAQSM13lMCQL5vDnUcFjvMpJnqsjU6FCQhAygpKMEJRUpUOSEYSS/pz+kJTh44IY+3XmPlrn2AqJUqAXacIZGx7kkZAxXNk4I3Skqh1jQ0dccs4KIQnJwSRXs6ASxjDjAnHGBcaRZVQsLMdn3t8KAHg23jZm7yVds7CyrRNVFakxN72RIHbsPXe3UuUsFY2t+rhTqk/vMzB4qjj66Z2ADbsmDqvagF2VgF1twKqJIznrE9jlgxDBScwSsWXIsTLIma6gTFUl3SUkx8JFGVZUSYGmKNDSgSQVSka+DsgKAtLZt2X+nRkkfpYsfrUy1ZHEcNiwkBgOHdZw+Mj8O3NcIcOIBAwHCj0dKEJSqqKUui39vfTX+qivR4cQfXRgSX8vBAXKRP+PUzFBEdHIhI10eIhJY6scoysV8VG3ZQJJXE5VNQzJgYFRX0sOTMmBzbBBLmOYcYF0Rl9O94r5+H8PvQIA+MBuxnGnavh75WEDFy47haBuw7IkHD5eg6MnqjDelVwrk9GwREPDEr0oplQLScApN2FXGrCrDFjViVRwqTFgVyZgVxlwyiex7balQI6HUyFlqCIVUmLh9JiVCkiJ4LQHdbolEy60dFVEGxU2NEU95/cnDCNZcIQD07GRdGwkHWv466EKMUEgGRlTkkRu/+LWhysYmWrGqMqGlKpehEZ9Pf5xY6seevr4QkgKBwk4iAs7FT7gIC5SY3MS6e8lRn8tUv82hr9OffTNthAfU+WwGTYKgOvNuIthpoDqwqkR7H3xkRlHiepyXFAdwQWHDsGAgpcSC9PfEZjTPIBFLb1QFIFoLIDtu2YgYZzRRSUB4drUJo+NbfpwFcYyHHQf8PaUaqHasCtNWNUJWLVx2NWJVHCpNIYrLFAn0QUUV6H2BaFEdCiRINR+HUpvCHZtC+ShMkhJzbNhRYI03E2jySoCoyolkwkp02U7DkzHQtKxhz+nvh4JKMP/FiPfzxzviPF/Pn214w8CDkBCCAqqJHWC7pOzQ0imqhHKdKmMqmqMrorIuaxwjMMRYjhkJIQ9HB4M4aQDRSpYGOnbEmd8PTak2MP3zTyOnaMBa4MB/w7eJ5oqhpkCml01AAA4OZDalkAAUC5owjc+fhIA8AdjHvpFCKpiY9ni02isS4Wf7t4QduxrhGWP/QuxdoGGuReHxlRhBjpS+yP1HnF/SrWjWalQUhtPhZWaeCq81MZhVScgwpPoj3AAZUBPfUR0KH2hscElokOOj79fVXxFbY5f0fjG66I539eZkBKQp/9Xv5UOG6kwMlIdMe3M19ao74/9PF4YUSQJuiwjKCvQZQW6LKNMVqArMoJyALoiD98++pjUh4KgrEDR1OHKRmjUuI6cdqlMYDhoDAcKO13hGBtCMpWN8aoeRvp78fRxmZBCRN7EMFNAH3XMQCQRxLH+VDdSfHY9/mbfsyi3EjgoavBach7KywysautEKGjBcYB9h+tw/FQlACm1sN08DdWzA6iaFYBWlhpXY5kOBjssnNqZwMDJwo2FEbIDqz4Oqy4GuzyZ6gKqS3/UxCGC509TkimnQklvEEp/cCS0RHSofSEoER2Sk99ZE+ONBxkbPEbfNhJCMl/nwvlDiAXLsQEIQDiQhICE1Icmy2M/JBnlsgw9kG6zFBj+ni7LCKRDhy5lbkuHESX1WZXyP0slExZGVybODCEThYvM1+MFEgNOqU3IOwu3NnAPu5rcwzBTQI9uuWz4ayFJWN0Qwcz9PehVwngyshIVlQYuXHoKqioQS6j4ZE8TBqM6ZCUVYmavCSFYOfKXvG0KnPw4jlOfJODkoQojkBqzYtWlKil2lQG7OgGrPgarJvVvKOd+65DiKtTeINSecKqiMqBD6U+HlwEdUkKddheQqqoIBAJQ1QA0TYOqBhAIBBCIBoBZteeslASk3IwdsRwbjmPDEQ6EsAE4EMKBhFTwAARkCMgSoABQRn0OSFIqVKgKgoqCkKxBl2Vo6ZARkFODSVW5cFNhASDpODAcG0b6c+KMfxuOg4Q99t+pz6mvu2fK44SUVFcL32qJKJcYZlxiV4XwhWOvAQB+n2hB05whzJvTD1kC+iJBfLS7CUJWMXttEDNWBKGoqTdcM+qg+6CByPEkBk9ZENN8V3BCyVRQqTRSIaU+FVycCgN2pQmn7NwDbCVDgXo6DGVIS4WU7hDU3tSHEtEhm+f/FRsdRgKBsR9n3jb635mvsw0jEgBVSn8AUCUJUiZ4pKsdCpxRYSMTPKT0/SQEZBla+rOenqKc7zEbGY4QMB0HpnBSnx0bpuPASN+WTH+dCSMjx43cxxh9n/GCij39MRx9M7jHFBEVBsOMS+YOdEILJdArh9DbHMSCWf0AgFOny3AiMRMtnwqitkWDnA4xxpCNrj0GTu1IwMmiJ8kJJmHVJoZnBNmVCdgVJqz6GJKNMYjQeR7MQSqk9AWhRFJjVdSedFjpC0IZ1BFQxgkdWgCBmZMLJROFERmpwJEJFaokjfo6871UwJCFgCQcyCIdQiBSnwMK1HT1Y3QAySdzVJAwRgeHCYKEMSZU2IjbY+83EkDSM4cmGHRLRFSqGGZcctKpwN9Gr8Dsigjmz+yHkCQcS85HeHUVlowa0BvrtXB8axx9R8evkAgI2LUJmM2DcMqSsMtNJGcOwa6Ow6oyJjXIVh7UoAxq0LrLEe6pRdlgNYKxcujJMoTi5QjIOjRNS3/o0IIatHkatCWp26V0yFCldNBAOnicUf1QpLHdKwpGjlEABCBGBQ8p75UO07ERtx0k0iEiYY98jo8KFsNdKSJVsTDFSFAxndFfp8IHu1BS8r61AU2I42bcw3Ez7phSmHn00UfxP//n/0RHRweWL1+O73//+7jyyivHPfaFF17AY489hg8//BCGYWD58uV48MEHcd11102r4cXAhIy6+XFAlhBpXoqaqtRqvsm4g56DJroPGIh22xCKA6shDrvKgDk3AqMlAimpwAkmkWyKQoQtKI4KAQeO7EASEnQrjLBVi+BgGKGBKoSGqhCKVSCUKEcwWY6yZDnK7DJoCCKkaQhrGnRVhVoOqBWprhVNkqBJGB7noUoSAunwERj1tQrkZNzJRJK2DdOyYVgWDMuCadlIDH9tIZG0hr9nWBaMpAXDtlOfLQsDc6phpENLJnjEbTtnU2GJiMhdWYeZZ555Bvfeey8effRRrF+/Hj/4wQ9w/fXXY9euXZg7d+5Zx2/atAnXXnst/vZv/xbV1dX40Y9+hJtuugnvvvsuVq9enZMX4WcnTlVAXlwNpSoMy3RwZFc/DtcfhHapBHutjbgVg1MfRwjlCJuVmB2fi+WDbRABB8eUDjSdaMK8xBy0WHWQJAlRx0JQUqFLEnQ5NT5EAqDLEtQAIGsjYSQfEslkKmgkreHPo4OGadkwbRvm6K9tGwkziXgy9RFLf505fqK1TCYrXlPYgbNERFRYkhDZvVNceumluOiii/DYY48N37Z06VLcfPPNePjhhyf1GMuXL8ett96Kv/mbv5nU8QMDA6iqqsJnmr8OVS6usnXlTBVLP1cJx3GgSSEsMVsQtEO4QKqDI4C4IyCQnvEiAZqc+xBi2Q7i6RCSSCZhJC1ETRNRw0TUNGFaNizHRnxU4Eh9bQ3/20haSNrerHXkagdtyh67mdzDbib3sJtphB0zsOuL/4BIJILKysq8PU9WlRnTNLF161bcf//9Y27fsGEDtmzZMqnHcBwHg4ODqK2deEEzwzBgGCN76gwMDGTTTF8ZOGnhSF8Xrg9fhvVifurGTCFBSlVUzrqPYUKRZZQFVMSSFnpjcRw83Q3TslAdDmMokUAkFsdAIgHLSV3QBuIJxJNJWI4D07IRicdhWDYkCbAdL0aQ3AntOMFA4xKOm3EPx824h+NmCi+rMNPd3Q3bttHU1DTm9qamJpw6dWpSj/GP//iPiEajuOWWWyY85uGHH8ZDDz2UTdN87WbnaqwVTXCEwLGhKDRZwcade3C46zQaKishQWAgHseQYWIgkUDMTA0GVmRp+kGkuHMMERGVgCkNAD5zsKcQYlIDQJ9++mk8+OCD+MUvfoHGxsYJj3vggQdw3333Df97YGAAc+bMmUpTfeEnv30XTTdcg2ff+RC7T5wc873j/ROn+2KvqBAREU1GVmGmvr4eiqKcVYXp6uo6q1pzpmeeeQZ33nknnn32WXzmM58557G6rkPX9Wya5mvRhIHvPv+S280gIiLypaymeWiahjVr1mDjxo1jbt+4cSPWrVs34f2efvppfPWrX8VPf/pT3HDDDVNrKdE0hHaccLsJJatmr+l2E0pWxUHO5HPL0OEqt5tQUrLuZrrvvvtw++23Y+3atbj88svx+OOPo729HXfffTeAVBfRiRMn8OMf/xhAKsjccccd+Kd/+idcdtllw1WdUCiEqir+sImIiGh6sg4zt956K3p6evDd734XHR0dWLFiBV566SW0tLQAADo6OtDe3j58/A9+8ANYloVvfOMb+MY3vjF8+1e+8hU8+eST038FREREVNKyXmfGDcW8zgwVDqdnu4fTs93D6dnu4fTswq0zww5VKhkcN+MejptxD8fNuIfjZgqHv+VERETkawwzRERE5GsMM0RERORrDDNUUjhuxj0cN+MejptxD8fNFAZ/w4mIiMjXGGaIiIjI1xhmiIiIyNcYZoioYDhuxj0cN+MejpvJP/52U8nhIGAiouLCMENERES+xjBDREREvsYwQ0RUIjhuhooVf7OpJHHcjHs4CJhKEQcB5xfDDBEREfkawwwRERH5GsMMERER+RrDDJUsjptxD8fNuIeDgN3DcTP5w99qIiIi8jWGGSIiIvI1hhkiIiLyNYYZInIFx824h+Nm3MNxM/nB32gqaRwETETkfwwzRERE5GsMM0RERORrDDNE5BqOm3EPx824h+Nmco+/zVTyOG6GiMjfGGaIiIjI1xhmiIiIyNcYZojIVRw34x6Om3EPx83kFn+TiYiIyNcYZojAQcBERH7GMENERES+xjBDRFTCOG7GPRw3kzv8LSYi13EQMBFNB8MMERER+RrDDFEaBwETEfkTwwwRERH5GsMMEXkCx824h4OA3cNBwLnB32AiIiLyNYYZIiIi8jWGGaJROAiYiMh/GGaIiIjjZlzEcTPTx99eIvIMDgImoqlgmCEiIiJfY5ghIiIiX2OYIToDBwFTqeK4Gfdw3Mz08DeXiDyF42aIKFsMM0RERORrDDNERETkawwzRERE5GsMM0Tj4CBgKlUcBOweDgKeOv7WEpHncBAwEWWDYYaIiIh8jWGGiIiIfI1hhoiIyCM4bmZqGGaIJsBBwFSqOAiY/Ia/sUTkSRwETESTxTBDREREvsYwQ0RERL7GMENERGfhuBn3cBBw9vjbSkRERL7GMEN0DpzR5C4OAiaiyWCYISIiIl9jmCEiIiJfU91uwGQIIQAAlsOSMxWeZSXcbkJJsw3H7SaULCfB/3u3DOzWUdYy4HYzps2OGQBG3sfzRRL5foYcOHToEBYuXOh2M4iIiGgKDh48iAULFuTt8X1RmamtrQUAtLe3o6qqdKasDQwMYM6cOTh27BgqKyvdbk7B8HXzdZcCvm6+7lIQiUQwd+7c4ffxfPFFmJHl1NCeqqqqkvolyKisrOTrLiF83aWFr7u0lOrrzryP5+3x8/roRERERHnGMENERES+5oswo+s6/sf/+B/Qdd3tphQUXzdfdyng6+brLgV83fl93b6YzUREREQ0EV9UZoiIiIgmwjBDREREvsYwQ0RERL7GMENERES+5kqYefTRRzF//nwEg0GsWbMGb7755jmPf+ONN7BmzRoEg0EsWLAA//f//t+zjnn++eexbNky6LqOZcuW4cUXX8xX86csm9f9wgsv4Nprr0VDQwMqKytx+eWX43e/+92YY5588klIknTWRyLhrb2Esnndr7/++rivac+ePWOOK7af91e/+tVxX/fy5cuHj/HDz3vTpk246aabMHPmTEiShJ///OfnvU8xnN/Zvu5iOb+zfd3Fcn5n+7qL4fx++OGHcfHFF6OiogKNjY24+eabsXfv3vPer1Dnd8HDzDPPPIN7770X3/nOd7B9+3ZceeWVuP7669He3j7u8YcPH8bnPvc5XHnlldi+fTv++3//7/jWt76F559/fviYt99+G7feeituv/12fPTRR7j99ttxyy234N133y3UyzqvbF/3pk2bcO211+Kll17C1q1b8elPfxo33XQTtm/fPua4yspKdHR0jPkIBoOFeEmTku3rzti7d++Y17R48eLh7xXjz/uf/umfxrzeY8eOoba2Fn/2Z3825jiv/7yj0ShWrVqFf/mXf5nU8cVyfmf7uovl/M72dWf4/fzO9nUXw/n9xhtv4Bvf+AbeeecdbNy4EZZlYcOGDYhGoxPep6DntyiwSy65RNx9991jbmtraxP333//uMf/t//230RbW9uY277+9a+Lyy67bPjft9xyi/jsZz875pjrrrtOfPGLX8xRq6cv29c9nmXLlomHHnpo+N8/+tGPRFVVVa6amBfZvu7XXntNABB9fX0TPmYp/LxffPFFIUmSOHLkyPBtfvh5jwZAvPjii+c8pljO79Em87rH48fze7TJvO5iOb9Hm8rPuxjO766uLgFAvPHGGxMeU8jzu6CVGdM0sXXrVmzYsGHM7Rs2bMCWLVvGvc/bb7991vHXXXcdPvjgAySTyXMeM9FjFtpUXveZHMfB4ODgWZt1DQ0NoaWlBbNnz8aNN9541l92bprO6169ejWam5txzTXX4LXXXhvzvVL4ef/whz/EZz7zGbS0tIy53cs/76kohvM7F/x4fk+Hn8/vXCiG8zsSiQDAOTeQLOT5XdAw093dDdu20dTUNOb2pqYmnDp1atz7nDp1atzjLctCd3f3OY+Z6DELbSqv+0z/+I//iGg0iltuuWX4tra2Njz55JP45S9/iaeffhrBYBDr16/H/v37c9r+qZrK625ubsbjjz+O559/Hi+88AJaW1txzTXXYNOmTcPHFPvPu6OjA7/97W9x1113jbnd6z/vqSiG8zsX/Hh+T0UxnN/TVQzntxAC9913H6644gqsWLFiwuMKeX67smu2JElj/i2EOOu28x1/5u3ZPqYbptrGp59+Gg8++CB+8YtfoLGxcfj2yy67DJdddtnwv9evX4+LLroI//zP/4z/83/+T+4aPk3ZvO7W1la0trYO//vyyy/HsWPH8L/+1//Cpz71qSk9plum2sYnn3wS1dXVuPnmm8fc7pefd7aK5fyeKr+f39kopvN7qorh/P7mN7+Jjz/+GG+99dZ5jy3U+V3Qykx9fT0URTkrcXV1dZ2VzDJmzJgx7vGqqqKuru6cx0z0mIU2lded8cwzz+DOO+/Ef/7nf+Izn/nMOY+VZRkXX3yxZ5L8dF73aJdddtmY11TMP28hBJ544gncfvvt0DTtnMd67ec9FcVwfk+Hn8/vXPHb+T0dxXB+/+Vf/iV++ctf4rXXXsPs2bPPeWwhz++ChhlN07BmzRps3LhxzO0bN27EunXrxr3P5Zdfftbxr7zyCtauXYtAIHDOYyZ6zEKbyusGUn+xffWrX8VPf/pT3HDDDed9HiEEPvzwQzQ3N0+7zbkw1dd9pu3bt495TcX68wZSMwYOHDiAO++887zP47Wf91QUw/k9VX4/v3PFb+f3dPj5/BZC4Jvf/CZeeOEFvPrqq5g/f/5571PQ8zur4cI58LOf/UwEAgHxwx/+UOzatUvce++9oqysbHhU9/333y9uv/324eMPHTokwuGw+Pa3vy127dolfvjDH4pAICCee+654WM2b94sFEURf/d3fyd2794t/u7v/k6oqireeeedQr+8CWX7un/6058KVVXFv/7rv4qOjo7hj/7+/uFjHnzwQfHyyy+LgwcPiu3bt4uvfe1rQlVV8e677xb89U0k29f9v//3/xYvvvii2Ldvn9ixY4e4//77BQDx/PPPDx9TjD/vjC9/+cvi0ksvHfcx/fDzHhwcFNu3bxfbt28XAMQjjzwitm/fLo4ePSqEKN7zO9vXXSznd7avu1jO72xfd4afz+//8l/+i6iqqhKvv/76mN/ZWCw2fIyb53fBw4wQQvzrv/6raGlpEZqmiYsuumjM1K6vfOUr4qqrrhpz/Ouvvy5Wr14tNE0T8+bNE4899thZj/nss8+K1tZWEQgERFtb25iTwyuyed1XXXWVAHDWx1e+8pXhY+69914xd+5coWmaaGhoEBs2bBBbtmwp4CuanGxe99///d+LhQsXimAwKGpqasQVV1whfvOb35z1mMX28xZCiP7+fhEKhcTjjz8+7uP54eedmXo70e9tsZ7f2b7uYjm/s33dxXJ+T+X33O/n93ivF4D40Y9+NHyMm+e3lG4kERERkS9xbyYiIiLyNYYZIiIi8jWGGSIiIvI1hhkiIiLyNYYZIiIi8jWGGSIiIvI1hhkiIiLyNYYZIiIi8jWGGSIiIvI1hhkiIiLyNYYZIiIi8jWGGSIiIvK1/x/3gd3IG80agQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.contourf(X,Z,hfmOut['values']);\n", "for geo in hfmOut['geodesics']: plt.plot(*geo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.3 Using the Hooke eikonal solver\n", "\n", "Similar results can be obtained using the eikonal solver based on Hooke tensors." ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.655851Z", "iopub.status.busy": "2024-04-30T08:55:21.655747Z", "iopub.status.idle": "2024-04-30T08:55:21.657547Z", "shell.execute_reply": "2024-04-30T08:55:21.657300Z" } }, "outputs": [], "source": [ "if xp is not np: raise ad.DeliberateNotebookError(\"Hooke eikonal solver is not implemented on the gpu\")" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.659013Z", "iopub.status.busy": "2024-04-30T08:55:21.658914Z", "iopub.status.idle": "2024-04-30T08:55:21.662272Z", "shell.execute_reply": "2024-04-30T08:55:21.661988Z" } }, "outputs": [], "source": [ "hfmIn['model']='Seismic2'\n", "# Produce the TTI geometry and density from the material data.\n", "vti,ρ = Seismic.Hooke.from_ThomsenElastic(tem) \n", "# Slice in two dimensions, and rotate by chosen tilt.\n", "hfmIn['metric'] = vti.extract_xz().rotate_by(θ)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.663897Z", "iopub.status.busy": "2024-04-30T08:55:21.663783Z", "iopub.status.idle": "2024-04-30T08:55:21.713843Z", "shell.execute_reply": "2024-04-30T08:55:21.713475Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field cosAngleMin defaults to 0.5\n", "Field seedRadius defaults to 2\n", "Field factoringPointChoice defaults to Seed\n", "Field exportFactoring defaults to 0\n", "Fast marching solver completed in 0.015097 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.Run()" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:55:21.715489Z", "iopub.status.busy": "2024-04-30T08:55:21.715376Z", "iopub.status.idle": "2024-04-30T08:55:21.772748Z", "shell.execute_reply": "2024-04-30T08:55:21.772482Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.contourf(X,Z,hfmOut['values']);\n", "for geo in hfmOut['geodesics']: plt.plot(*geo)" ] } ], "metadata": { "celltoolbar": "Format de la Cellule Texte Brut", "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.8" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }