notebooks/nb19_pure_shear.ipynb

{
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Notebook 19: Progressive strain\n",
    "\n",
    "So far, we have focused on the undeformed (initial) and deformed (final) states. However, finite strain is the cumulative result of a series of strain increments:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&{ }^1 x_i={ }^1 F_{i j}{ }^1 X_j \\\\\n",
    "&{ }^2 X_i={ }^1 x_i \\\\\n",
    "&{ }^2 x_i={ }^2 F_{i j}{ }^2 X_j \\\\\n",
    "&{ }^3 X_i={ }^2 x_i \\\\\n",
    "&{ }^3 x_i={ }^3 F_{i j}{ }^3 X_j \\\\\n",
    "& \\cdots \\\\\n",
    "&{ }^n x_i={ }^n F_{i j}{ }^n X_j\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "where $F_{ij}$ is the Green deformation gradient, and 1 to $n$ are the strain increments. This can also be written as:\n",
    "\n",
    "$$\n",
    "x_i={ }^n F_{i j} \\ldots{ }^3 F_{i j}{ }^2 F_{i j}{ }^1 F_{i j}{ }^1 X_j\n",
    "$$\n",
    "\n",
    "Notice that since ${ }^2 \\mathbf{F}^1 \\mathbf{F} \\neq{ }^1 \\mathbf{F}^2 \\mathbf{F}$, for finite strain we must know the order of the deformation. For example, if we want to determine the finite strain of a group of faults in a region, we must know the order in which these faults occurred. This is often difficult to determine.\n",
    "\n",
    "In this and the next two notebooks, we will look at some simple deformations, which are characterized by the same incremental deformation gradient through time. For simplicity, we will assume that there is no strain along the $\\mathbf{X}_2$ axis. Thus, we are dealing with plane strain.\n",
    "\n",
    "## Pure shear:\n",
    "\n",
    "The first type of deformation we will cover is pure shear. For this deformation, the principal stretches are along the coordinate axes. Let’s assume the maximum principal stretch, $S_1$, is along $\\mathbf{X}_1$, and the minimum principal strecth, $S_3$, is along $\\mathbf{X}_3$. $S_2 = 1$ and is parallel to $\\mathbf{X}_2$. The Green deformation gradient for this case is ([Allmendinger et al., 2012](https://www.cambridge.org/core/books/structural-geology-algorithms/C5AB97C135925A5D49726B741738DCA9)):\n",
    "\n",
    "$$\n",
    "{ }^{P S} F_{i j}=\\left[\\begin{array}{ccc}\n",
    "S_1 & 0 & 0 \\\\\n",
    "0 & 1 & 0 \\\\\n",
    "0 & 0 & S_3\n",
    "\\end{array}\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Python function\n",
    "\n",
    "The function [pure_shear](../functions/pure_shear.py) deforms a collection of points using pure shear and a maximum stretch, $S_1$. The function displays on the left the undeformed (blue) and deformed (red) geometries (and by default the displacement paths), and on the right the value of $S_1$ versus the angle, $\\Theta$, $S_1$ makes with the $\\mathbf{X}_1$ axis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Application:\n",
    "\n",
    "Let's use this function to deform a square using pure shear:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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EREREZCBMvhERERERERERERkIk29EREREREREREQGwuQbERERERERERGRgTD5RkREREREREREZCBMvhERERERERERERkIk29EREREREREREQGwuQbERERERERERGRgTD5RkREREREREREZCBMvhERERERERERERkIk29EREREREREREQGwuQbERERERERERGRgTD5RkREREREREREZCBMvhERERERERERERkIk29EREREREREREQGwuQbERERERERERGRgTD5RkREREREREREZCBMvhERERERERERERkIk29EREREREREREQGwuQbERERERERERGRgTD5RkREREREREREZCBMvhERERERERERERkIk29EREREREREREQGYpTJt0OHDmHevHkYPHgwBEHA119/fctl0tLSMG7cONjZ2WHo0KH48MMPDR8oEREREUnWrFmDCRMmwNnZGZ6enrj//vuRk5PT5TKpqakQBEHn7/z581rldu7cidDQUNja2iI0NBS7du0yZFWIiIiIus0ok291dXUIDw/H+vXru1U+Ly8Pc+fOxbRp03D69Gn86U9/wgsvvICdO3caOFIiIiIi0khLS8Py5ctx9OhRpKSkoLm5GdHR0airq7vlsjk5OSgsLJT+QkJCpOfS09OxaNEiLF68GFlZWVi8eDEefvhhHDt2zJDVISIiIuoWK7kD6I3Y2FjExsZ2u/yHH34If39/rF27FgAwcuRInDx5Ev/85z/x4IMPGihKov6lUqlQU1MDlUoFpVIpdzg9plKpUF5eDqVSCYVCIXc4PcbtLy9j3/5E5mLv3r1a05s2bYKnpydOnTqF6dOnd7msp6cnXF1d9T63du1azJkzB6tWrQIArFq1CmlpaVi7di0+//zzPomdiMxXfn4+srOzERYWhqCgILnDISIjZJTJt55KT09HdHS01ryYmBhs3LgRarUa1tbWMkVG1DdOnTqFhIREqNXWOH8+HrGxsYiIiJA7rG7LyMiQLsgEQTC6+DMzM5GcnAxRFI1y+2dmZiIpKQmA8W7/pKQkWFur8f777yMuLg6RkZFyh0VE3VBdXQ0AcHd3v2XZsWPHoqGhAaGhoXjllVcwa9Ys6bn09HT8/ve/1yofExMj/fBKRNRbH3/8MZ555hm0trbir3/9K+Lj47F06VK5wyIiI2MWybeioiJ4eXlpzfPy8kJzczPKysrg4+Ojs0xjYyMaGxulaZVKBQBQq9VQq9WGDdgIabYJt03/q6ioQEJCIj755Clcv+4PAHjjDZmD6rHIn//aGF/8ET//tWH8/S0CQAT8/K7h6ac3ITExEQEBAUbZgs9Y8RjQNW4X/URRxMqVK3HnnXdi9OjRnZbz8fFBfHw8xo0bh8bGRnz22We46667kJqaKrWW6+xcr6ioqNP1DoRzPXP67JhLXc2lnoB51DU/P19KvAFAa2srnnnmGcyePRu+vr4yR9f3zGGfarCupkmOunb3tcwi+Qa0teZoTxRFvfM11qxZg9WrV+vM379/PxwcHPo+QBORkpIidwhmpbm5Gbm5uVCrraXEG5G5un7dH2q1NWxs1EhOToazs7PcIZkdHgP0q6+vlzuEAen555/HmTNncOTIkS7LDR8+HMOHD5emo6KicP36dfzzn//UulVV37leZ+d5wMA61zOnz4651NVc6gmYdl2zs7OlxJtGS0sL/vOf/2DMmDEyRWV4prxPO2JdTVN/1rW753lmkXzz9vbW+eWzpKQEVlZWnfYNtGrVKqxcuVKaVqlU8PPzQ3R0NFtT6KFWq5GSkoI5c+bwNt5+Ultbiy+++AINDQ0AftnmL730Nmxtm7Fs2TKjeK/u27cPZ86c0ZonCILRxK9SqRAfHy8l9AHG359UKhXWr9+Et99+SWt+WFgYRo4cKVNU5ofHgK5pWlTRL1asWIHdu3fj0KFDvWo9MnnyZGzdulWa7uxcr2NruPYGwrmeOX12zKWu5lJPwDzqGhYWhr/+9a9aCThLS0s89thjJtvyzdT3qQbraprkqGt3z/PMIvkWFRWFhIQErXn79+/H+PHjO90htra2sLW11ZlvbW1t8m/Y28Ht0z8qKirw2WefoaqqCo6Ojpg4caL0nK1tMxYsiIG//8DvdL6yshIXLpyGjU0rBEGQWinExcUZRfwA4OqqxPz5d2v1mWZs8S9YEIPExEQpARcREWFU8c+ffzfeflt7fkJCAmxtbbVay5Dh8RigH7fJL0RRxIoVK7Br1y6kpqb2uuPy06dPa3UbEhUVhZSUFK1+3/bv348pU6Z0uo6BdK5nTp8dc6mrudQTMO26BgUF4b333sPy5csBtCXePvroI5MfdMGU92lHrKtp6s+6dvd1jDL5Vltbi9zcXGk6Ly8PmZmZcHd3h7+/P1atWoWCggJ8+umnAIBnn30W69evx8qVK/Gb3/wG6enp2LhxI0e/IqNUWFiI//znP6irq4ObmxsWL14MGxs36flly5YZTeLkwIEDaG1txdChQzF//nxUVFTA3d3dKFpctRceHi4l35YtWwZvb2+ZI+qZyMhIBAcHIy0tDRkZGbh8+bJRDUbTfnCIpUuX4tixA7hw4QK2b9+OefPmYezYsfIFR0Rali9fjm3btuGbb76Bs7Oz1FrNxcUF9vb2AKBzHrd27VoEBgZi1KhRaGpqwtatW7Fz507s3LlTWu/vfvc7TJ8+HW+99Rbmz5+Pb775Bt9+++0tb2klIrqVJUuWSMm3rKwsjBo1SuaIiMgYWcgdQG+cPHkSY8eOlS6oVq5cibFjx+Ivf/kLgLbkxLVr16TyQUFBSEpKQmpqKiIiIvD6669j3bp1ePDBB2WJn6i38vLysHnzZtTV1cHb2xtPP/003NzctMoYS+KqoKAAP/74IwBgzpw5UCgUCAwMNJr4O2Os/YwpFArcc889UCgUUKlUOH78uNwh9Yq7uzsWLVqEiIgIiKKI3bt348iRI1q31RKRfDZs2IDq6mrMnDkTPj4+0t/27dulMh3P45qamvDSSy8hLCwM06ZNw5EjR7Bnzx4sWLBAKjNlyhR88cUX2LRpE8LCwrB582Zs374dkyZN6tf6EZFpGzJkiNwhEJGRMsqWbzNnzuzyQmrz5s0682bMmIGMjAwDRkVkGCqVCuXl5SgvL8fevXvR0tKCwMBALFq0CHZ2dnKH1yvV1dXSreDh4eFG11KsKzU1NXB0dJQ7jF6xtrbGrFmz8M033+DQoUNQKpUYPHiw0SVELSwscN9998HBwQE//PADvvvuO9TV1WHy5MmoqKiAUqk0ujoRmYruJMI7nse9/PLLePnll2+53EMPPYSHHnqot6ERERERGYxRJt+IzEVGRoZWX1wAMHLkSCxYsABWVsb58c3IyNDqg3HQoEEyRtM3srKypMfx8fGIi4tDZGSkjBH1XlhYGA4ePAiVSoXt27dLfdgZW30EQcCcOXPg6OiIlJQUHD16FEePHpWeM8Y6ERERERGRcTLK206JzIFKpdJJvAFAdHS00SbeNHVq77vvvjPqkQBVKhWSk5OlaVEUkZiYaLR1qq2t1Yrd2OszZcoUxMTEaM0z9joREREREZFxYfKNaIDKz8/Xe3tOVVVV/wfTR8rLy3XqJIoiKioqZIro9plancrLy3XmGXN9AMDLy0tnnrHXiYiIiIiIjAeTb0QD0JUrV7Bnzx6d+YIgwN3dXYaI+oa+ZKKx10mpVEIQBK15xlwnU6sPoL9OQNvnjAMxEBERERGRoTH5RjSAiKKIw4cP49NPP0V9fT2cnZ2lpIGmnypj7Si+tbUV3333ndY8Y68T0DZKaGxsrDRt7HVSKBSIi4vTSlZZWFigtbVVxqhuj746AUBaWhp27NiBhoYGmSIjIiIiIiJzYJwdRxGZoPr6euzatQu5ubkA2kYBvffee3Hz5k1UVFTA3d3daBM6AJCeno4bN27Azs4OixcvRlNTk9HXSSM8PBxJSUkAgGXLlhn96K2RkZEIDg5GeXk5UlJSUFhYiMTERDz22GN6W5AZA02dKioq4ObmhpycHOzbtw/nzp1DcXExFi5caPT7jYiIiIiIBia2fCMaAPLz8/HRRx8hNzcXVlZWuO+++3D//ffD2toaCoUCgYGBRp2kKisrw8GDBwEAMTExGDx4sNHXqTPOzs5yh9AnFAoFgoKC8OCDD8LKygqXLl1CZmam3GHdFs1nycXFBRMnTsTTTz8NFxcXVFRU4OOPP8apU6d4GyoREREREfU5Jt+IZKJSqXD58mWkpqZi06ZNUKlUcHd3x69//WuMHTtW7vD6TFVVFf773/+ipaUFwcHBCA8Plzskg6qpqZE7hD6lVCoxc+ZMAMDevXvx008/mcwooUOGDMEzzzyDYcOGoaWlBYmJifj6669RVlaGvLw8k6knERERERHJi7edEskgIyMDiYmJWq1sQkNDcd9998HW1lbGyPpWRkYGEhISpOnAwECjvW2xK1lZWdLj+Ph4xMXFITIyUsaI+lZUVBROnjyJqqoqfPnll1K/dqZQR3t7ezzyyCP44Ycf8N133+HMmTM4c+YMAJhUPYmIiIiISD5s+UbUz1QqFRISEnRub4uOjjapxJtKpUJiYqLWvO+++87kWhOpVCokJydL06IoIjEx0aTqWVtbi+rqamna1OooCAKmTp2Khx56SGu+qdWTiIiIiIjkweQbUT+qqanBV199pfe5ysrKfo7GsG7cuKGTYBRFERUVFTJFZBjl5eUmX09zqCPQ1gquI1EUkZOTI0M0RERERERkKnjbKVE/EEURp06dwrfffovGxkad5wVBgLu7uwyRGYYoijh27JjOfFOrJ9DWJ5ogCFrJKVOrp746AjCplppA5/VMSkpCWVkZZs+ebXJ1JuqJpqYmlJSUoLW1VWu+v7+/TBERERERGQe2fCMysNLSUmzatAl79uxBY2MjhgwZghkzZkh9n2n6lTKlkT/T0tJw5coVWFhYmHQ9gbYRNGNjY6VpU6ynQqFAXFycTn99+/bt07kIN2Yd6ykIAnx9fQEAx48fxwcffMBWcGSWLl68iGnTpsHe3h4BAQEICgpCUFAQAgMDERQUJHd4RERERAMeW74RGUhzczMOHz6MI0eOoLW1FTY2Npg9ezYmTJgACwsLREZGoqKiAu7u7iaVqMnJyUFaWhoA4L777kNQUJBJ1rO98PBwJCUlAQCWLVsGb29vmSPqe5GRkQgODpZuNf38889x9epVpKSkICYmRubo+k77emres5cvX0ZiYiIqKyvxxRdfYOTIkYiNjYWzs7Pc4RL1iyeffBJWVlZITEyEj4+PSQ6cQ0RERGRITL4R9SGVSoXy8nLU19fj4MGDKC8vBwAMGzYMc+fOhYuLi1RWoVCYVDJKpVIhLy9PSkJNnDgR4eHhAGBS9TRn7d+z999/P/773//i6NGjcHV1haenJ5RKpUns646fzaFDh+K3v/0t0tLS8MMPP+DcuXO4fPky7r77boSEhKCiosJk6k6kT2ZmJk6dOoURI0bIHQoRERGRUWLyjaiPZGRkIDExUau/KCcnJ8TGxmLkyJEm3VKgY93d3d0RHR0tc1T9JysrS3ocHx+PuLg4REZGyhiR4Y0cORJ33nknjhw5gr179wL45ZZbU6y7tbU17r77bowZMwYJCQkoKCjAnj17pOdNue5EoaGhKCsrkzsMIiIiIqPFPt+I+kB5eTkSEhJ0OmpfvHgxQkNDTTrxplKpdJKOlZWVqKurkzGq/qNSqZCcnCxNi6KIxMREqFQqGaPqH+PGjdOaNoe6e3l54emnn8bMmTO15ptD3cm8qFQq6e+tt97Cyy+/jNTUVJSXl2s9x/c8ERER0a2x5RvRbWhpaUFGRgYOHDig9/n6+vp+jqj/lZWV6SQdRVFERUWFWdyGV15ebrb1r6ys1JlnDnW3sLDQO7qjKIrYu3cv7r33Xjg6OsoQGVHfcXV11frhSBRF3HXXXVplRFGEIAhoaWnp7/CIiIiIjAqTb0S90NraiuzsbKSmpqKqqkpvGUEQ4O7u3r+B9TNRFHHq1Cmd+eZQdw2lUglBELQScOZSf311BwAHBweZIuo/ndX93LlzuHTpEqKiohAVFQVbW1uZIiS6PQcPHpQ7BCIiIiKTweQbUQ+IooicnBwcPHgQJSUlANr6dZs+fToEQUBSUpLUEiAuLs6kW/9oWvmcPXsWAKREhDnUvT2FQoHY2FhpoAlzqr9CoUBcXJzObce7d+/G4sWLTTrx1LHugiBg4sSJuHr1KoqKipCWlobjx49j2rRpmDBhAqyseLgl4zJjxgy5QyAiIiIyGbwaIOqCZvRSpVKJ8vJyHDhwAPn5+QAAOzs7TJ06FRMnToSNjQ2AtlFNKyoq4O7ubrLJF802OXfuHE6cOAGgbeTLoKAgk697Z8LDw6Xk26OPPorg4GCZI+o/kZGRCA4ORkVFBVpbW/Hll1+ioKAAX3zxBeLi4qBSqUx2JND2dde870VRxNmzZ6XRjvfv34+jR49i+vTpGDt2LGpra6XvFFPcJmSaNm3aBCcnJyxcuFBr/o4dO1BfX48lS5bIFBkRERGRcWDyjagT+kYvBdpGPZw0aRKmTJkCe3t7recUCoVJX1Dr2yZz585FeHg4AJh03bvSfrTTbdu2md2ol+3f948//ji2bNmCK1euYP369QBMeyTQjp95QRAwatQojBw5EpmZmUhLS5MGJTl48KA0EIkpbxMyPX//+9/x4Ycf6sz39PTEsmXLmHwjIiIiugWOdkqkR3V1td7EW3h4OF544QXcddddOok3U6dvVFMAGD58uEwRDQzmPNqpPoMHD8b8+fO15pnjNrGwsEBkZCRWrFiBmJgY2NnZaY0AbI7bhIzX1atXERQUpDM/ICAA165dkyEiIiIiIuPC5BtRO83NzcjKysKWLVt0kkwAEBERAScnJxkik5++UU0BoKKiQoZoBo6uRjs1V/oS0+a6TaysrDB58mQ88MADOs+JooiDBw+axajIZNw8PT1x5swZnflZWVlQKpUyRERERERkXHjbKRGAuro6nDx5EidPnkRtba3eMuYygqU+arUa6enpOvPNeZtomPNop53pbCRQS0tLmSKSn7e3t95tkpmZiR9//BFhYWGYNGkSPD09ZYqQqHOPPPIIXnjhBTg7O2P69OkAgLS0NPzud7/DI488InN0RERERAMfW76RWSsuLsY333yDd955B6mpqaitrYWzszNmz56NmJgYCIIAwLxGsOyovr4en332GXJzcyEIArdJB5rRTjW4XX4ZCVTzXtHYvn07bty4IVNU8uq4TQRBwNixY+Hj44Pm5mZkZGRgw4YN+Oyzz3Dx4kW9rUyJ5PK3v/0NkyZNkrpcsLe3R3R0NGbPno033nhD7vCIiIiIBjy2fCOzoRml093dHcXFxTh69Cjy8vKk5wcPHozJkycjNDRUaqETGhpqtiN4qlQqXLlyBQcPHkRVVRXs7OywaNEiuLu7m+026Yw5j3bamfYjgVpbWyMhIQHFxcXYvHkzHnroIXh7e5vdqJ+djY56/fp1HD16FOfPn8fly5dx+fJlKJVKTJo0CeHh4bCxsdEaedlcthcNHDY2Nti+fTv+9re/ITMzE/b29hgzZgwCAgLkDo2IiIjIKDD5Rmahs5FLBUHAyJEjMXnyZPj6+uq01DH10Us703F72dvb46mnnsKgQYMAmO+opp0x99FOO9P+8/PUU0/hv//9Ly5fvozPP/9cKmNuo37qGx3V398f/v7+qKysxPHjx3H69GmUl5cjKSkJBw4cgK+vLy5dugRRFM1ue9HA8Nprr+Gll15CSEgIQkJCpPk3b97E22+/jb/85S8yRkdEREQ08PG2UzJpoiji7NmzSEhI0Em8jRs3Di+88AIWLlwIPz8/ncSbuaqurtbZXg0NDbC1tZUxqoGLo512j62tLR599FGEhoZqzef2+oWbmxtiYmLw+9//Hvfccw/c3NzQ0NCA3Nxc6fPI7UVyWL16td7+UOvr67F69WoZIiIiIiIyLmz5RiapvLwcWVlZyM7ORlVVld4yo0ePhqura7/GNdA1Njbim2++0ZmvGamSLd50dTXaKbeXNktLS4wbNw5nz57Vms/tpc3W1haTJk3ChAkTcOTIERw8eFDreVEUkZCQgDvvvBP+/v784YAMTtPqsqOsrCyzHlyGiIiIqLuYfCOTUV9fj59++glZWVkoKCiQ5ltbW0OtVmuVNffRKPUpKCjAzp07UVlZqfMct1fnONppz3h4eOgd9bOwsBABAQFMJLVjYWGBiIgIpKam6myv3Nxc5ObmwtXVFWPGjEF4eDiUSqVMkZKpcnNzkwbaGTZsmNbns6WlBbW1tXj22WdljJCIiIjIODD5RkalY6fjzc3NuHjxIs6cOYMLFy6gtbUVQFvy44477kB4eDiGDx+O7OxsqQ8zjkbZpv0AFD/99BO+++47tLa2wsXFBWPGjMH333/P7dUNmtFONQMuAOD26oJm1M+OfTDu378fhYWFuPfee9HY2MjBBX7WcXsJgoCoqCjU19fj7NmzqKqqwuHDh3H48GEMGTIEYWFhGD16NBwcHADofmcS9cTatWshiiKefvpprF69Gi4uLtJzNjY2CAwMRFRUlIwREhERERkHJt/IaLQfBEDTSXlxcTEaGhqkMt7e3ggLC8OYMWPg5OQkzdc3yqA562wAitDQUMybNw92dnaYMGECt1cvsOXWrbX/PLq6uiI7OxsHDx5EdnY2Ll26hJs3b3JwgXY6+/6aO3cucnJycObMGeTm5qKgoAAFBQXYt28fQkJC4OzsjFOnTnFbUq8tWbIEABAUFISpU6fCyoqnjURERES9wbMoMgrV1dVaySJRFHH16lUAgLOzs3TblaenZ6frMNeRSztSqVR6E2933XUXpk6dKiWPuL26p7MBF4KDg7n9utD+/TVt2jQEBgZix44dqKmpkcpwW/5C3+fR2toao0ePxujRo1FbW4sff/wRWVlZKCoqQk5OjlZZbku6HTNmzMClS5ewadMmXLp0Ce+++y48PT2xd+9e+Pn5YdSoUXKHSETULwoKCthnNBH1Ckc7pQFLrVYjJycHCQkJ+PDDD3WSRQAwZ84cvPjii5gzZ06XiTf6xdWrV/VuS19fX7ba6oWuBlyg7vPz88O9996rM5/bsnucnJwwefJkPPPMM/jtb3+rNxkiiiK+/PJLnD59GnV1dTJEScYqLS0NY8aMwbFjx/DVV19JI5+eOXMGf/3rX2WOjojIsLZs2SI9DgsLw8aNG2WMhoiMFVu+0YBSW1uLCxcu4MKFC7h06RKam5s7LSsIAkaPHg0LC+aQu6O5uRk//PADDh06pPMcBwjoPQ640Hd8fHz0DsZw7NgxeHh4aN1KTp3z9PREdHQ0zp49q7Mtr1+/juvXrwNoS3gOGzYMw4cPlwbCINLnj3/8I/72t79h5cqVcHZ2lubPmjUL7777royREREZVn5+PlasWCFNt7a24plnnkFMTAx8fX1ljIyIjA2Tb9SvOnb+LYoiSktLkZOTg5ycHK1RSgHAxcVFujisrKxEUlISBwHopvbbuqysDElJSSgvLwfQljCqqKjgtuwDHHCh73Q2GMP58+eRl5eH2bNnY/z48aitreUgAregb6CGadOmQRAEXLhwAYWFhVIi7rvvvoObmxuGDx+O4cOHw8/PD5aWlgA4YAO1yc7OxrZt23TmDxo0SDquEBGZoosXL0oDumm0tLQgNzeXyTci6hGjTb598MEHePvtt1FYWIhRo0Zh7dq1mDZtmt6yqampmDVrls78c+fOYcSIEYYOlX7WsZP/oKAgVFZWoqqqSqvc4MGDpYSbl5eXVmuMYcOGcRCAbuhsQAVHR0fExMRg9OjRqKmp4bY0ALYeuj0dBxeoqalBUlISbty4geTkZPzwww9QqVRaiePhwzmIgD6dDdQwc+ZMqFQqXLhwATk5OcjLy0NlZSWOHj2Ko0ePws7ODiEhIbC2tsbp06c5YAPB1dUVhYWFCAoK0pp/+vRpDBkypEfrWrNmDb766iucP38e9vb2mDJlCt566y0MHz6802W++uorbNiwAZmZmWhsbMSoUaPw6quvIiYmRiqzefNmPPXUUzrL3rx5E3Z2dj2KkYhIIyQkBBYWFloJOEtLSwQHB8sYFREZI6NMvm3fvh0vvvgiPvjgA0ydOhUfffQRYmNjcfbsWfj7+3e6XE5OjlaSYdCgQf0RrtkTRRF5eXlISEjQmp+Xlweg7QA2dOhQDB8+HMOGDdO6paUjDgJwa50NqBAREYGYmBjpIoTbsm9wwIW+1/69qVAosHTpUpw6dQrfffcdqqurpXKabe3jEwyA21qfzj7nCoUC48ePx/jx49HU1IRLly4hJycHFy9eRH19PbKzs7XKa7Z1UFAQ3Nzc+it8GiAeffRR/OEPf8COHTsgCAJaW1vx/fff46WXXsITTzzRo3WlpaVh+fLlmDBhApqbm/HnP/9Zuk3a0dFR7zKHDh3CnDlz8Oabb8LV1RWbNm3CvHnzcOzYMYwdO1Yqp1AodAYbYeKNiG6Hr68v3nvvPSxfvhxA23XLRx99xFZvRNRjRpl8+9e//oWlS5fi17/+NQBg7dq12LdvHzZs2IA1a9Z0upynpydHp+kHoiiivLwceXl5uHr1Kq5cudJp596zZs3C5MmTYWNj089Rmq60tDS9AyqEh4fzIsQAuhpwgcm3vmFhYYEJEybAyckJ//3vf7WeE0Xx5z7M2gYYUKlUcHVVyhCl8bKxscHIkSMxcuRItLa2Ij8/H8ePH8dPP/2kVU4URbz//vsICAhAYGAgAgMDMXjwYOkWVTJdb7zxBp588kkMGTIEoigiNDQULS0tePTRR/HKK6/0aF179+7Vmt60aRM8PT1x6tQpTJ8+Xe8ya9eu1Zp+88038c033yAhIUEr+SYIAry9vXsUDxHRrSxZskRKvmVlZXGEZyLqFaNLvjU1NeHUqVP44x//qDU/OjoaP/zwQ5fLjh07Fg0NDQgNDcUrr7yi91ZU6jlNoqGsrAxff/01rl27Jo2EpmFpaYmWlhateYIgICIigom3PnDixAkAEwC09Y/VcZNyAADD4YAL/WfIkCF6B2T45ptvoEm+xcfHY8GCGN4e2UsWFhbw9/eHq6ur3gEbWlpacPnyZVy+fBlAW+LO398ffn5+qKur0+kXh4yfKIq4ceMG/v3vf+P1119HRkYGWltbMXbsWISEhNz2+jWtWXvyndna2oqamhqdZWpraxEQEICWlhZERETg9ddf10rOERHdrp7eak9EpGF0ybeysjK0tLTAy8tLa76XlxeKior0LuPj44P4+HiMGzcOjY2N+Oyzz3DXXXchNTW1019ZGxsb0djYKE2rVCoAgFqthlqt7qPaGBeVSoWKigq4ubmhtbUVV69exbVr13D16lXU1NRolbW0tISvry/8/f0REBCAwYMH48cff0RycrLUf1BsbCzs7e3NdnveLpVKhRs3buDEiRO4dKkImuSbhiZJwW1tWPb29oiOjsa+ffukedzehmFvb4/Y2Fit7xEXFxeUlPzSslZze6RSqURTUxP7NOwlfds6NjYWgwcPlr77r127hps3byI3Nxe5ubkA2lqma773/f394eXlBQsLC+n4Ya77w5i/C0RRREhICH766SeEhIRg6NChfbrulStX4s4778To0aO7vdz//d//oa6uDg8//LA0b8SIEdi8eTPGjBkDlUqFd999F1OnTkVWVlanScKBcK6neR1jfo90l7nU1VzqCZhPXdvXz9SvBc1lnwKsq6mSo67dfS2jS75pdOzUXHNxoI9mBDeNqKgoXL9+Hf/85z87Tb6tWbMGq1ev1pm/f/9+ODg43EbkxkcURRQXF3ea3ATa9oeDgwOcnJzg5OQER0dHWFhYoKamBj/++CN+/PFHAMDIkSPR2NgIW1tb3LhxAzdu3OivapiUoqKiDvvDWqeMv78/rKysuK37QWlpqdZ0dnY2t7cBtf8eaWxs1Eq+AW3fWZs3b5am/fz8oFTyVtTe6Ow7297eHsOGDUNDQwNqampQW1uL2tpaNDU1aSXjLC0tYW1tjYaGBmmd5rg/6uvr5Q6h1ywsLBASEoLy8vI+aenW3vPPP48zZ87gyJEj3V7m888/x6uvvopvvvkGnp6e0vzJkydj8uTJ0vTUqVMRGRmJ9957D+vWrdO7roF0rpeSktKvrycnc6mrudQTMP26tj+GHThwwCy6cTH1fdoe62qa+rOu3T3PM7rkm4eHBywtLXUSQSUlJTqt4boyefJkbN26tdPnV61ahZUrV0rTKpUKfn5+iI6ONvlf7WtqaqSLrBs3bqCwsBBNTU065by9vTF06FAEBATAy8sLqampmDNnDqytdRNB1HvtW4yUlpZi//79qKys7HIZQRAwb948k3+vDgQqlQrvv/++1rz8/HzMnz+f278fqFQqnD8f32WZ69evY968ebCwsDDr1leGpFarsX//foSHh6OgoEBqHdfU1KTT5cD169fh4uIi9RmnuXXblGlaVBmrf/zjH/h//+//YcOGDT1qodaVFStWYPfu3Th06FC3Oy7fvn07li5dih07duDuu+/usqymr8iLFy92WmYgnOup1WqkpKSYxfmTudTVXOoJmE9d2/ddPXv2bJPuQ9xc9inAupoqOera3fM8o0u+2djYYNy4cUhJScEDDzwgzU9JScH8+fO7vZ7Tp0/Dx8en0+dtbW1ha2urM9/a2tqk3rANDQ24ceMGCgoKpP8dbyHtTExMDAIDAwH80tTS1LaP3DIyMnRGib0VQRAQFxdndi1L5KJSqfQOuFBTU8N90A+USiViY2Pxxhtt050lcTZs2CDtJ81nhP3C9S1BEODr64ugoCDceeedaG1txalTp5CUlKRTtn2LaFtbWwwePBiDBw/GkCFDMGTIEJNLjhr7cfHxxx9HfX09wsPDYWNjA3t7e63nKyoqur0uURSxYsUK7Nq1C6mpqQgKCurWcp9//jmefvppfP7557j33nu79TqZmZkYM2ZMp2UG0rmeOZ0/mUtdzaWegOnXtX3dTL2uGuZST4B1NVX9Wdfuvo7RJd8AYOXKlVi8eDHGjx+PqKgoxMfH49q1a3j22WcBtP2SWVBQgE8//RRA2yhZgYGBGDVqFJqamrB161bs3LkTO3fulLMaBqdSqVBeXg6lUgmFQoHm5mYUFxdrJdrKysp0lhMEAZ6entKFkIuLC7Zt28YO5fuJZr/dvHlTb+LNzs5Oq/k7oJ1wWLZsGfz9mfTpLxxwQX4RERHS48ceeww7dmzWmxBt/zgxMRFeXl5oamqSviOpb1lYWGD48OFSv3EamsF2ysvLUVhYiMbGRuTl5SEvL08q4+zsjCFDhkjHocGDB0u3+XQ8tpHhvfPOO33WOnH58uXYtm0bvvnmGzg7O0t3Mri4uEhJvY7ncZ9//jmeeOIJvPvuu5g8ebK0jL29PVxcXAAAq1evxuTJkxESEgKVSoV169YhMzNTp2UyERERkRyMMvm2aNEilJeX47XXXkNhYSFGjx6NpKQkBAQEAAAKCwtx7do1qXxTUxNeeuklFBQUwN7eHqNGjcKePXswd+5cuapgcCdPnkRSUpJ0wePq6oqamhqd2380z2laGwwZMgTe3t46I5DGxcUhMTFR6lsvLi6OFz0GcPLkSezZs6fLMosWLUJFRYXW/mjf8of7pX8pFAqMHj0a2dnZ0rywsDDuB5n4+PjofF9FRETg9OnTWuVEUcTHH38sTc+bN48t4QxAoVDoPX5otnVraytKS0tRUFAg/ZWUlKCmpgbnz5/H+fPnpXV5eHjAzs4O+fn5ANiCsT89+eSTfbauDRs2AABmzpypNX/Tpk3S63Q8j/voo4/Q3NyM5cuXY/ny5dL8JUuWSP07VlVVYdmyZSgqKoKLiwvGjh2LQ4cOYeLEiX0WOxEREVFvGWXyDQCee+45PPfcc3qfa9/RNgC8/PLLePnll/shqv4niiKqqqpQXFyMkpISlJSUoLCwUOcWkKqqKgCAg4ODTmsCR0fHW75OZGQkgoOD2V9SH2rfeqO4uBgHDx5EYWFhl8toWlQFBgZq7Q9LS+4PuahUKun2OY0zZ85g9uzZ/JzIpOP3FQBkZmbqtIZrLyEhAdXV1ZgxYwZqa2vZsqoPdXX8sLCwgJeXF7y8vKQkWlNTE4qKirRaaVdWVuq01BZFEQkJCcjOzsaQIUPg5eUFT09PqW9Y6juWlpYoLCzUGuAAAMrLy+Hp6an3h73OdPU51Oh4HpeamnrLZd555x2888473Y6DiIiIqD8ZbfLN1HTnNpq6ujopwaZJtpWWluodDEGfBQsWYPTo0b2+dUShUPBC9Da038e5ubm97stNsw/a74+6uq6WJEMqLy/Xe4tjRUUFPy8y6vh91bH1lb4EwKFDh3Do0CFpun3LKt7qeHt6cvywsbGBv78//P39pXn19fXIyMjAd999p1P+ypUruHLlijRtYWEBpVIpJeM8PT3h5eUFFxeXTo9/3L9d6yxh1tjYqNNSnoiIiIh0Mfk2AGRkZCAxIQFWTU0QBAHR0dEYPHiwlFwrLS1FSUmJ1kg77dlZWsLDwwODBg3CoEGD4OTkJF1kagiCgAAPDwjdHAa3x9RqWDY0tGWBzKQTx57IzMzU6feo41bqrC+3JUuWQK1Ww83Nre2iUN/7oA5wkB6ruQ/6kdLODtZ6EuDutrbMivaXbrz/I4cPR7CPDyorK2FtbY0tW7Z0qwXO3p07cePiRZw5cwYApNu82/czRzD4McABQNgdd+Dw3r06x7Zp06ahpqYGZWVlKCkpQWNDA6oKClBVUICcduuwsbGRjpODBg2Cp6cnBg0ahAsXLiA5ORlNVlYQLCx4K2s769atA9C2nT/++GM4OTlJz7W0tODQoUMYMWKEXOERERERGQ0m32SmUqmQmJCAJzduhP/1620zf+68q/OxWG9N79hemk7BDMAaQJzB1m78In7+65Vu7DdHAFKax7e3L0S9oQDwJ31PvPlmP0divrr7/lf8/AcAq3r4Glrfbwb8LjVW/XEMUKDn+607In7+u+bnh01PP43ExEQEBwezBRwg3cYpiiI+/PBDrdt5bWxsEBgYiA8//FCu8IiIiIiMBpNvMisvL4dVU9MviTciIiLqd/7Xr8NarYbaxoa3jf9MMwLtrFmz8NVXX8HNzU3miIiIiIiME5NvMlMqlVp90Lz90ktotrXF8uXLjerEX61WY9++fYiJiYG1Gd7yWFJSojVy4q2073OqL25jq6sDPL3aHhfkq+Hqan77QC4qlQrvv/++zq1wxvYZNmZ9+f5vf4u4IAiYNWsWDhw40K1lzXm/G+sxoLS0FFs++AAvvf22NE8zsA394uDBg1rTLS0tyM7ORkBAABNyRERERN3A5JvMFAoFYmNjpduYmm1tEbNgARQ+t3PTqQzUarTY2QGOjmbR31hzczOuXbuGvLw8XL58GTdu3AD0dDo9depUTJ06FefOndPq7D0uLq7PR4+VevNzVAOOpr8PBgqFoyNiFizQ2b9G9xk2cn31/o+YOhVDx4zR+mzauLlp9aM5ceJEVFZW4uLFizrLf/z55xg2bBiCgoIQFBQEBwcHnTImyUiPAYMcHXH3/PnAz8m3jgPbUJsXX3wRY8aMwdKlS9HS0oLp06cjPT0dDg4OSExMxMyZM+UOkYiIiGhAY/JtAGjf4mn58uW8aB9ANCPgubm5oa6uDpcvX0ZeXh6uX7+O5ubmLpcVBAETJ06Evb09IiMj9SbbeIFnGiIjIxEQEIDk5GTExsZCqVTKHRLdho4jc+r7/KpUKqxdu1Zn0IaamhqcOnUKp06dAgB4e3tj6NChCAoKQkBAAG7evMlRNQcYHoNvbceOHXj88ccBAAkJCbhy5QrOnz+PTz/9FH/+85/x/fffyxwhERER0cDG5NsAw4uxgaGlpQVpaWk4fPhwp2WcnJyki+qhQ4ciNzdXt/VTu/3Z8YKeTItCoYCzszP3sYnq+PlVKBSIi4vT+szHxMTA1dVVStKXlpaiqKgIRUVF+OGHH7RuNweAe+65B5MmTZKjOtQJfn71Ky8vh7e3NwAgKSkJCxcuxLBhw7B06VJpRFQiIiIi6hyTb2Q2NK3YOrY4EUURKpUK+fn50t+NGzfQ2tqqs46hQ4di2LBhGDp0KDw8PLT66+usdRsRmabOPvPDhw8H0NYKLi8vD3l5ecjNzUVtba3W8nv37sXx48cREBAAX19f+Pr6wsPDAxYWFjqv1dn3F1F/8PLywtmzZ+Hj44O9e/figw8+AADU19drjYBKRERERPox+UZmISMjQ6uFSlRUFBwcHFBQUID8/HzU1NR0az3Tpk1DYGBgp8+zdRuReenqM+/s7IywsDCEhYXh8uXL+Oyzz3TKVFRUoKKiAqdPnwYA2NjYYMiQIVIyztfXF+fPn9dpVRsZGWnQehG199RTT+Hhhx+Gj48PBEHAnDlzAADHjh3DiBEjZI6OiIiIaOBj8o1MWlNTE/Ly8pCQkCDNE0URP/zwg1Y5QRDg7e0tXfS6urpiy5YtOiNYcgQ8IuoNTUvZjt8p8+bNQ0VFBfLz81FQUCB9Z+Xl5eldjyiKSExMRHBwMBP91G9effVVjB49GtevX8fChQtha2sLALC0tMQf//hHmaMjIiIiGviYfCOj0tWto9XV1SguLpb+ioqKUFFR0em6/P39MWzYMPj6+mLw4MGw7jBCX8f+nDgCHhH1lr4+4uLi4jB27FipTGtrK0pLS7VugS8rK9NZlyiK2LBhA3x9feHp6Qlvb294eXnpvWWVt6tSX3nooYd05i1ZskSGSIiIiIiMD5NvZDQ63joaFhYGGxsblJSUoLi4GA0NDXqXc3BwQH19vdY8QRDw4IMPdnkxyj7ciKgv3eo7xcLCAl5eXvDy8sK4ceMAACUlJdiwYYPOuhoaGpCbm4vc3FxpnqWlJQYNGiQl41QqFY4ePcrbVYmIiIiIZMbkGw1IoiiitrYW5eXlKCsrw40bN6Q+kTTPZ2VlaS1jYWGBQYMGSRevXl5e8Pb2hqOjo07irrut2NiHGxH1pZ5+p3h6emLevHla31+xsbHw9vbWaulbXFyMpqYmaXTVjkRRREJCAqqrq+Hr6wulUglXV1e9gzsQEREREVHfYvKN+lXHW6DUarWUYCsvL5f+ysrK0NTUdMv1hYaGYtiwYfDy8sKgQYM6HXWNrdiIyFh19v3l5+cnlRFFEVVVVSgqKkJxcTEuX76M69ev66zr0KFD0mNLS0u4u7tDqVRKfx4eHlAqlXBwcADA21aJiIiIiPoCk29kcA0NDaiqqkJGRgZOnDghzbezs+v0VlGg7dZQV1dXeHh4wNHREZmZmTrPx8TEdPuCkK3YiMhY3er7SxAEuLm5wc3NDSNHjkRkZCTWrl2rNcADAISEhKC6uhoVFRVobm5GaWkpSktLddZnb28POzs7VFZWSvPuvPNOTJo0CY6OjhAEoe8qR0RERERk4ph8o27rrAVEY2MjysrKUF1djRMnTqCmpgZVVVXSX2cJNs18e3t7qbVF+9YXbm5usLL65S3q5+fHARCIiLqhswEeNH2+aQap0dfqWKVS4ebNm7h586bWOo8cOYIjR47AysoKrq6uWn9OTk6or69HXV0dXFxcdJJzbEFn/C5duoRNmzbh0qVLePfdd+Hp6Ym9e/fCz88Po0aNkjs8IiIiogGNyTfqkiiKqK+vx4kTJ5CWlibN9/HxAQBUVVVpXaDl5eXpXY+trS0aGxt15i9atAgjRozoViy8dZSIqPu6+s7UtCx2dXVFcHCw1nJNTU3Izs5GYmKi3vU2NzejrKxM70isFy5cgLW1tVZirq6uDmfPnpVe995775UGlCDjkJaWhtjYWEydOhWHDh3CG2+8AU9PT5w5cwYff/wxvvzyS7lDJCIiIhrQmHwzYbdqadDc3IyamhqoVCqt/x0ft7S06CxbWFioNW1vbw8A8Pf3h7u7u06riIaGBp1boARBwODBg3tUJ946SkTUfb35zrSxsUFISAgEQdD5zl6xYgUAoLKyUquFc2VlJYqLi6FWq6FWqzu9nVUURSQmJuLAgQNwdXWFs7MznJ2doVAodP7b2trqjY+t6PrfH//4R/ztb3/DypUr4ezsLM2fNWsW3n33XRkjIyIiIjIOTL6ZoObmZhw7dgzfffeddOE0bNgwODo6aiXXOt5S1FOzZs3C8OHDpRHzkpKSMHfuXFhbW+uUtbGx0XsLFC+ciIgGns5uW3VzcwMA6b+GWq1GUlISoqOjUV9fLyXl8vLy8NNPP+msv76+HvX19V3GYGNjo5WQc3Z2RnV1NX788UcAkEZ+HT9+PPugM7Ds7Gxs27ZNZ/6gQYNQXl4uQ0RERERExoXJtwFGpVJB4eioNU8URTQ2NqKurg51dXWora2VHnf8q62t1Xt754ULF/S+npWVlc7FTccWCK2trVi/fr1OC4iIiAgpeaZWq29ZN942SkRkPHrznW1lZSX13Qm0DfBw9uxZnePHI488AlEU9ba4VqlUaGxsRFNTk9QXnT6iKCIpKQn79u2Ds7MzHB0d9f45OTlJj+3t7WFhYdFp/PqOwQS4urqisLAQQUFBWvNPnz6NIUOGyBQVERERkfFg8m0AyMzMRMTPj9evXw/vO+6Ara2tVlJN362fPRUeHg5/f3+t5JqdnV23Wgz0Vas13jZKRGQ8bvc7u7MWdMOGDetyuaamJp2EXEFBAc6fP69TtqWlRWppdyuCIMDBwUErKddQXo5Hf37+/fffR8yCBdLAFNTm0UcfxR/+8Afs2LEDgiCgtbUV33//PV566SU88cQTcodHRERENOAx+SYzlUqF5ORkKfkGANevX9db1sbGRusX/M5+4W9tbcWHH36o09Jg9uzZvb6IYqs1IiLqjd4cP2xsbLRa0AFtx8ucnBydY9uTTz4JQRC6bBFeV1eHmzdvQhRFaX5JSQkAwLqpSVqfpk+64OBgHufaeeONN/Dkk09iyJAhEEURoaGhaGlpwaOPPopXXnlF7vCIiIiIBjwm32RWXl6udSGhMWXKFAQEBGgl1vT1pdYZQ/SvxlZrRETUG31x/OisFZ2/v3+3lm9paUF9fb1WYu7atWs4k56uVU4URVRUVPB41461tTX+85//4PXXX0dGRgZaW1sxduxYhISEyB0aEVG/KigogKurq9xhEJERYvJNZkqlUue2T0EQMGnSpNs68WdLNSIiMjW3c2yztLSU+jbVCAwMRPbRo1rlBEGAu7t7n8VsCl577TW89NJLGDp0KIYOHSrNv3nzJt5++2385S9/kTE6IiLD2rJli/Q4LCwM8fHxWLp0qYwREZEx6rzXYeoXCoUCsbGx0nRfjgKqUCgQGBjIxBsREZmMvjy2GfIYbEpWr16N2tpanfn19fVYvXq1DBEREfWP/Px8rFixQppubW3FM888g/z8fBmjIiJjxJZvA0BERIT0ePny5VD4+MgXDBERkRnhMfjWNLf5dpSVlcVWgkRk0i5evIjW1lateS0tLcjNzYWvr69MURGRMWLybYDhr+1ERETy4DFYm5ubGwRBgCAIGDZsmFYCrqWlBbW1tXj22WdljJCIyLBCQkJgYWGhlYCztLREcHCwjFERkTFi8o2IiIiIdKxduxaiKOLpp5/G6tWr4eLiIj1nY2ODwMBAREVFyRghEZFh+fr64r333sPy5csBtCXePvroI7Z6I6IeY/KNiIiIiHQsWbIEABAUFIQpU6b0aNR1IiJTsWTJEin5lpWVhVGjRskcEREZIybfiIiIiEiLSqWSbsMdO3Ysbt68iZs3b+oty9t1ichcDBkyRO4QiMhIMflGRERERFrc3NxQWFgIT09PuLq66h1wQTMQQ0tLiwwREhERERkPJt+IiIiISMuBAwekkUwPHjwoczRERERExo3JNyIiIiLSMmPGDL2PiYiIiKjnmHwjIiIioi5VVVXh+PHjKCkpQWtrq9ZzTzzxhExRERERERmHXiffLl26hD//+c8QBAFvvvkm/v73v+Pzzz9HaGgotm7diuDg4L6Mk4iIiIhkkJCQgMceewx1dXVwdnbW6v9NEAQm34iIiIhuodfJt2XLlkl9gKSnp+PGjRsIDQ3FiRMnsHLlSuzevbvPgiQiIiIiefzP//wPnn76abz55ptwcHCQOxwiIiIio2PR2wVPnDiBP/7xj0hKSsK1a9fw5ptvIjMzEy+//DLS09P7MkYiIiIikklBQQFeeOEFJt6IiIiIeqnXybfW1laMGDEC48ePBwBEREQAAIYNG4a6uro+Ca4rH3zwAYKCgmBnZ4dx48bh8OHDXZZPS0vDuHHjYGdnh6FDh+LDDz80eIxERERExi4mJgYnT57sk3WtWbMGEyZMgLOzMzw9PXH//fcjJyfnlst15zxu586dCA0Nha2tLUJDQ7Fr164+iZmIiIjodvU6+TZixAicPXsWSqUS586dw9SpUwG0tYgLDAzsq/j02r59O1588UX8+c9/xunTpzFt2jTExsbi2rVresvn5eVh7ty5mDZtGk6fPo0//elPeOGFF7Bz506DxtkbKpWqT9eVl5fXZ+vsi/Xd7jpuZ/neLNvTZXpSvrtlexMDkbnq6v1viM+cIb8j5Fyur5bv6/X09br0rZt03Xvvvfh//+//4dVXX8XOnTuxe/durb+eSEtLw/Lly3H06FGkpKSgubkZ0dHRXf5w253zuPT0dCxatAiLFy9GVlYWFi9ejIcffhjHjh3rdb2JiIiI+kq3+3xTqVRQKBTS9OHDhyGKIgRBwPDhwwG0nRzdddddWLRoUd9H2s6//vUvLF26FL/+9a8BAGvXrsW+ffuwYcMGrFmzRqf8hx9+CH9/f6xduxYAMHLkSJw8eRL//Oc/8eCDDxo01u7IzMxExM+P33//fdw9fz7Cw8Nva51ZWVlITk6W9lFsbOxtrfNW61Or1WhpaUFTUxNEUTRITLezfG+W7ekyPSnf3bLdLXfqVDaAcQCA+Ph4LFgQg8jIyC7rR2QqMjMzgZ+/RePj4zF//t06n5O+/sz1tGxvysu1XG+W7+oY0JfHo74+tgFA9qlTP397th2DYxYs4PdnB7/5zW8AAK+99prOc4IgoKWlpdvr2rt3r9b0pk2b4OnpiVOnTmH69Ol6l+nOedzatWsxZ84crFq1CgCwatUqpKWlYe3atfj888+7HR8RERGRIXQ7+TZmzBhs3rwZs2bNAgDY29trPR8fH4+XXnrJ4L8aNzU14dSpU/jjH/+oNT86Oho//PCD3mXS09MRHR2tNS8mJgYbN26EWq2GtbW1zjKNjY1obGyUpjX1UqvVUKvVt1sNrfUmJydLyTdRFJGUlISkpKQ+e42+XmdX68vOzu6XmG5n+d4s29NlelK+u2W7KtfUZA1N8k0URSQmJiIgIEArYU6Gpfle6MvvB7o1zXeoJvnWnc9TX3zmbqdsb8rLtVxPl7/VMaAvj0d9tS7rpiYp+Wao709j/15obW012Lqrq6sBAO7u7p2W6c55XHp6On7/+9/rlNEk7PTpr3O9rpjTscNc6mou9QTMp67t69ef3w9yMJd9CrCupkqOunb3tbqdfLt+/TrmzJmDFStW4O9//ztsbW0BAMXFxVi6dOnPFz+GV1ZWhpaWFnh5eWnN9/LyQlFRkd5lioqK9JZvbm5GWVkZfHx8dJZZs2YNVq9erTN///79fdrhcE1NTactxYh6SxRFJCcnw9nZWe5QzE5KSorcIZgVfodSXzPE92d9fX2frcuUiKKIlStX4s4778To0aM7Lded87jOynR2bgj037led5jTscNc6mou9QRMv64NDQ3S4wMHDsDOzk7GaPqHqe/T9lhX09Sfde3ueV63k29RUVFIT0/HunXrsH//fnz66afIy8vDb3/7W1RUVEAURSxZsqTXAfeUIAha05pbUHpSXt98jVWrVmHlypXStEqlgp+fH6Kjo/v013CVSoX48+d1Yl22bFmvT/xramoQHx+vdUF6O+vszvrUajUOHDiA2bNn621JeLsx3c7yvVm2p8v0pHx3y/ak3Pr1m7ReQ3M7Flu+9R+1Wo2UlBTMmTNH72eADEOlUuH8+XiteR0/J339metp2d6Ul2u53i7f2TGgL49HfX1s06xz0/r1WvMM8f1pjH3JrVu3DsuWLYOdnR3WrVvXZdkXXnihV6/x/PPP48yZMzhy5Mgty3bnPK6n54b9da7XFXM6dphLXc2lnoD51LV9n5SzZ8+Gq6urfMEYmLnsU4B1NVVy1LW753ndTr4dPnwYb731FlavXo1z585h8uTJaG1thSiKUCqViI+PxwMPPNDrgLvLw8MDlpaWOr9klpSU6PziqeHt7a23vJWVFZRKpd5lbG1tpdZ97VlbW/fpTlQqlYiNjQXeeANA24ljXFwcvL29e71OR0dHxMXFITExUTrxvJ11dmd9arUalpaWcHR01Lt9bjem21m+N8v2dJmelO9u2Z6Ui42N1byFpHKdvbfJsPr6O4K6pvkO7fj+b/856evPXE/L9qa8XMv1dvnOjgF9eTzq62ObZp36jsF9/f1pjN8J77zzDh577DHY2dnhnXfe6bScIAi9Sr6tWLECu3fvxqFDh+Dr69tl2e6cx3VWprNzQ6D/zvW6w5yOHeZSV3OpJ2D6dW1fN1Ovq4a51BNgXU1Vf9a1u6/T7eSbhYUFVq1ahbvvvhszZsxAY2MjRFFEYGAg0tPTuzy56Us2NjYYN24cUlJStJJ9KSkpmD9/vt5loqKikJCQoDVv//79GD9+/IB480VEREiPly9fDoWe22B7KjIyEsHBwaioqIC7u/tt/4LbF+u73XXczvK9Wbany/SkfHfLdrdc+/fQsmXL4O/PxBuZj+68//v6M9fTsr0pL9dyfbV8X6+nr9elYYhjsCnIzMyEi4sLgLYBtfqKKIpYsWIFdu3ahdTUVAQFBd1yme6cx0VFRSElJUWr37f9+/djypQpfRY7ERERUW91O/kGAD/++COWLVsmJd4A4OrVq/jNb36Df//73/2WgFu5ciUWL16M8ePHIyoqCvHx8bh27RqeffZZAG23ERQUFODTTz8FADz77LNYv349Vq5cid/85jdIT0/Hxo0bB+ToV315m4NCoRhw67vdddzO8r1ZtqfL9KR8d8v2JgYic9XV+98QnzlDfkfIuVxfLd/X6+nrdelbN7Vxd3dHYWEhPD09MXv2bHz11Vd9cqvV8uXLsW3bNnzzzTdwdnaWWqu5uLhIg3n15jzud7/7HaZPn4633noL8+fPxzfffINvv/22W7e0EhERERmaRXcLvv3225gwYQKysrJgZWWFV199FY899hhEUcSePXswevRofPnll4aMVbJo0SKsXbsWr732GiIiInDo0CEkJSUhICAAAFBYWIhr165J5YOCgpCUlITU1FRERETg9ddfx7p166Th6YmIiIjoF05OTigvLwcApKam9tmoYRs2bEB1dTVmzpwJHx8f6W/79u1Smd6cx02ZMgVffPEFNm3ahLCwMGzevBnbt2/HpEmT+iRuIiIiotvR7ZZvf/jDHwAAI0eOxGeffYbIyEgAwP3334/f/va3KCsrwyOPPILm5mbDRNrBc889h+eee07vc5s3b9aZN2PGDGRkZBg4KiIiIiLjd/fdd2PWrFkYOXIkAOCBBx6AjY2N3rIHDhzo9nq7Mzpxb8/jHnroITz00EPdjoWIiIiov3Q7+SYIAl588UW8+eabWp3TPvjgg5g2bRqWLl2KpKQkgwRJRERERP1n69at2LJlCy5duoS0tDSMGjUKDg4OcodFREREZJS6nXz79ttvMWvWLL3PeXp6IiEhARs3buyzwIiIiIhIHvb29lJfuidPnsRbb73VJ32+EREREZmjbiffOku8tbd06dLbCoaIiIiIBpaDBw/KHQIRERGRUev2gAtERERERERERETUM0y+ERERERERERERGQiTb0RERERERERERAbC5BsREREREREREZGBdHvABSIiIiIyTw0NDThz5gxKSkrQ2tqq9dx9990nU1RERERExoHJNyIiIiLq1N69e/HEE0+grKxM5zlBENDS0iJDVERERETGg7edDjAqlUruEIiIiMwSj8H6Pf/881i4cCEKCwvR2tqq9cfEGxGZk4KCArlDICIjxeTbAJCZmSk9fv/995GRkSFfMERERGaEx+BbKykpwcqVK+Hl5SV3KERE/W7Lli3S47CwMGzcuFHGaIjIWPG2U5mpVCokJycj4udpURSRkJCA06dPw8XFBY6OjnB0dISTk5P0WPNnY2Nzy3WXl5dDqVRCoVAYvC5ERESG1t1jW0tLC+rq6rT+amtrtaZVKhWqCgq0jsGJiYkIDg7mcbOdhx56CKmpqbjjjjvkDoWIqF/l5+djxYoV0nRrayueeeYZxMTEwNfXV8bIiMjYMPkms/LycoiiqDM/Pz8f+fn5XS5rbW2tlZhzcHCQHpeUlOD06dMQRRGCICAuLg6RkZGGqgYREZHBnThxAsnJydJxc8yYMVAqlaitrUV9fb1Wgq2hoaFb67TuMC2KIioqKph8a2f9+vVYuHAhDh8+jDFjxsDaWnurvfDCCzJFRkRkWBcvXtQZZKalpQW5ublMvhFRjzD5JjOlUglBELTmCYKAmJgYiKIoXUTU19dr/WLf3NwMtVqNqqoqVFVVdfkamtZ0hw8fhqurK5ydneHs7AyFQqH138nJCZaWlp2uhy3piIioN251/BBFEfX19VCpVKipqdH5X1NTg+rqajQ2Nmotl52d3eXrCoLQZQtyQRCQtGOHzjLu7u63X2kTsm3bNuzbtw/29vZITU3VOm8RBIHJNyIyWSEhIbCwsNBKwFlaWiI4OFjGqIjIGDH5JjOFQoHY2FjgjTcAoFut1ERRRFNTU6e30pSUlODq1as6y3UnUefk5CQl5JycnKTEXElJCY4dO8aWdERE1CMnT55EUlKS1FotNDQUzs7OUlJNk2Dr2LKgu0JCQuDt7a03wWZvb6/zA1dHYm2tzjGYPzBpe+WVV/Daa6/hj3/8Iyws2F0wEZkPX19fvPfee1i+fDmAtsTbRx99xFZvRNRjTL4NABEREdLj5cuXQ+Hj02V5QRBga2sLW1tbvb/Oq1QqrF27Vut2VkEQ8OCDD6K1tVWrJUH7x62traitrUVtbS0KCws7fX1NS7rz589j0KBBUmu6hoYGqNVqndtROsbG1nNERMahO9/Zra2tqKqqQk1NDbKyslBTUyP92FNRUYHa2lqt8mfPnu309RwdHaUffTq20BYEAVu3btU5tt1usqynx2Bz1NTUhEWLFjHxRkRmacmSJVLyLSsrC6NGjZI5IiIyRky+DTB9kZBSKBSIi4tDYmKiVku1rg4Uoiiirq5O7+0+JSUluHHjhs4yFy9exMWLF7XmnT9/Ho6OjnBzc4OrqytcXFykxzdu3MDBgwfZeo6IyAhkZGRoHUeioqLg6ekpJdY0f9XV1VJC7NKlS91a96hRo+Dr66uVXLtV1wcA9B7b+vKHHP4opN+SJUuwfft2/OlPf5I7FCIiWQ0ZMkTuEIjISDH5ZqIiIyMRHByMiooKuLu73/KCQhAEODk5wcnJCT4dfvXvrCXd9OnT0dDQgKqqKlRWVqKsrAytra3S7a9dDRihaT2nUqng6+sLpVIJFxcX/qpORCQDzQ8w5eXlKCsrw40bN5CRkaH1/A8//NDp8paWlrCyssLgwYPh5uYm/ehibW2N7du36xw/oqOje5Xo6umxjfpGS0sL/vGPf2Dfvn0ICwvTaeH+r3/9S6bIiIiIiIwDk28mTKFQGLQlXftWa2q1Gnv27MHs2bNRV1cnJeQ0rSKKi4tRXV2ts+60tDTpsaWlJdzd3eHh4QGlUgmlUik9tre3B8DbVomIeqLjd6ZarUZFRQXKyspQXl4uJdvKy8t1BjPQx9vbGz4+PnB1dYWrq6uUZLO1tUVycjLmzp2rk5jp69ZqfXVso+7Lzs7G2LFjAQA//vij1nO36lOPiIiIiJh8o27qTmsDQRBgb28PhULRrdZzABAcHIzq6mpUVFSgpaUFpaWlKC0t1Vm3g4MDbG1tUVlZKc2Ljo5GVFRUH9WQiMh0NDY24siRIzhy5Ig0z97eHjdv3uxyOVdXV3h4eMDJyQmZmZlazwmCgF/96ld6v//VanWn62RrNeN38OBBuUMgIiIiMmpMvlG33U5rg1u1nmttbUV1dbVWKwzN45qaGtTX16O+vl5rnfv378fhw4cxePBgeHp6wtvbG15eXvDw8NDbbxBbzRGRsers+0sURVRVVaG4uFj6Kyoq0vqhQkOTeLOzs9NqYaxpZezu7g4rq19OC/z8/PqsxRpbqxERERGROWPyjfpNV60fLCwspH6CgoODtZZrampCdnY2EhMTddZ58+ZNXLp0SauTbwsLCwwaNEhKxnl5eaGkpAT79+/nYA9EZHQ6DnwwZswY2NjYoKSkBMXFxd26XVTj4YcfxogRI7p1qyBbrJHGrFmzunzPHDhwoB+jISIiIjI+TL5Rv+pN6wcbGxuEhIRAEASdTrsXLVqE2tparVYfjY2N0mN9RFFEYmIi/Pz8MGjQoNuqDxGRIbS0tKC4uBgXL15EamqqNF8URZw5c0arrKWlJQYNGiT92ODl5QUHBwfEx8frfGcOGTKkR310scUaAUBERITWtFqtRmZmJn788UcsWbJEnqCIiIiIjAiTb2QUOrttdfjw4Vrl9N2Cdf36ddTW1uqU++CDD+Dl5YUhQ4bA19cXvr6+8PDw0Low5a2qRNSXOvtOqampQX5+vvR348YNNDc3d7qeUaNGYdiwYV3eat/XAx2Q+XrnnXf0zn/11Vd1jq9EREREpIvJNzIa3R30QXP76ogRIwB0PtgDAClBl5GRAQCwtbWFr68vhgwZgsbGRhw/fpy3qhJRn+h4++jIkSMBAPn5+VCpVDrl7ezs4O3tjStXrmjNFwQB0dHRt0yk8bZRMrTHH38cEydOxD//+U+5QyEiIiIa0Jh8I6PSm1ugOms1FxISIrUyKSgoQEFBARobG3X6kAN+uVXV19cXnp6efVklIjJxLS0tyMnJQUJCgjRPFEWcPXtWmhYEAZ6enlIrXF9fXyiVSgiCoJO060kLNt42SoaUnp4OOzs7ucMgIiIiGvCYfCOz0FkLkJEjR0qtT1paWlBSUoL8/HycP38ely9f1lqHKIrYsGEDhgwZgqCgIAwdOhR+fn5aowPyNlUi86LvMy+KIoqLi3H58mXk5eXh6tWrUKvVepePjIzEmDFjMHjwYNjY2HRahi3YSE4LFizQmhZFEYWFhTh58iT+93//V6aoiIiIiIwHk29kNm7VAsTS0hI+Pj7w8fHB8OHDO71VVdNK7siRI7CysoK/vz+CgoLQ1NSEI0eO8DZVIjOhbxTSlpYW5OXlob6+XqusnZ0dGhoatOYJgoAZM2Z0K5nGFmwkJxcXF61pCwsLDB8+HK+99hqio6NlioqIiIjIeDD5NsCoVCooHB3lDsPsdXar6h133IG8vDzk5eXh8uXLqK2txeXLl/W2kktMTERwcLB0wcxWcaZNpVKhpqYGKpUKSqVS7nCoj3X8/FZWVurcRtp+FFJra2sEBgZKrWQ9PT1x+vRpDoAwwPEYrN+mTZvkDoGIiIjIqDH5NgBknj6NiJ8fx7/zDu6ePx8RERFdLDEAqdWwbGgA6uoAa2u5o+kTkcOHI9jHB5WVlXBzc5MukiNCQhAREgJRFFFWVoYrV67g3LlzyM/P11nHl1u2IDw8HGq1GgcPHpQuumNjY/t2H9cBDtJjtcnsA2ORmZmJ5ORkiKKI+PPn+37/UtcM/P5vv38BYPDgwSgtLYW1nltJx4wZg4iICAwePFh7BNL6ev3fKXV1fRqrbIz4GHAmPR1hPz9+//33EbNgAVstd6G2thatra1a85hEJiIiIuoak28yU6lU+Hb3bin59tLbbwNvvy1nSL1iDSBO7iAMQPHznz4CgEE//03oxromt594443bC6wDRwDSJbxvn66auiHi5z9JH+9f6pqh3/8R6LB/b0NX3ynGzJiPAWHtHutrtUxAXl4enn/+eaSmpmrdPq35QamlpUXG6IiIiIgGPibfZFZeXq63XzEiIiLqP9f8/KC2tgZEERUVFUy+tfPYY48BAD755BN4eXlBEASZIyIiIiIyLky+yUypVOKmkxPefuklAGg78RcEuLi4QKVSdZqYc3FxwaBBgzBo0CB4enpi0KBBUCqVWrc5qVSqfhsdT61WY9++fYiJiYG1kd1y1JdUKpXObaoqlQrvv//+LZOsjz76KAIDA3u13+rqAE+vtscF+Wq4uprvPuhv+vavIAhYvnw5L977SW/f/+0/azY2Nvjuu++QlZV1y+Xa7199n3lz1J/HAH3fkaIoorq6GqWlpSgpKUFpaSlKS0tRXl6uc4ukhpOTE5RKJa5evdpWh5+Pv4IgwN3d3aB1MDZnzpzBqVOnMHz4cLlDISIiIjJKTL7JTKFQIG7ePJ1OuCMjI6FWq1FWVobi4mKUlJRIfzU1NSi7eRNl167h3LVr0rosLS3h4eEBT09PNDc349y5cwDQPyNvqtVosbMDHB2Nrr+fvqRwdITCx0dnXsyCBVr7WF8ibsuXX8LGxgZNTU0Aer7fpLEVHdWAo/nug/6mcHTE8MhIZGdnS/PCw8N13gdkWD19/7cfqVSLjY1O2SlTpiA9PV17oISf96++z7xZ6qdjQMf95u/vD1EUUVJSgsbGRt0FrKxga2sLT09PeHp6wsvLS3psb2+vtU5wIIxOTZgwAdevX2fyjYiIiKiXmHwbACIjIxEcHKzzS761tTV8fHzg0+HCrr6+XkrEtU/MNTU1obi4GMXFxVrlRVFEQkICSktLcccdd2DIkCHSRQf1j/b72NraGhs3btSbgNMk3oBf+h7y8vJCU1MTR0kdoFQqFX788UeteWfOnMHs2bO5vwYYzYildXV1WiOVdkUQBEyaNAmTJk3qt5bE9Au1Wo2ioiIUFBTg6tWrOH/+vNbz19r9AGVhYSG1Bm+fbFMoFF3eJtnZMZh+8fHHH+PZZ59FQUEBRo8erdO6MSwsrJMliYiIiAhg8m3AUCgU3T7hd3BwQGBgIAIDA6V5mltuSkpKcP78eZw+fVpnuaNHj+Lo0aMAAHd3dwwePBhDhgzBkCFD4O3tbda3i/aH9vs4Li5Op7VjXV0dDhw4oLWMKIr4+OOPpel58+ZxFL4BRl+/jSL7jBpwMjIybplwe/zxx1FdXa3z2dTsR+5Pw2ptbUVZWRkKCgqkv5KSkk5vG9WYPn06Ro0apdP1Qk/05BhsjkpLS3Hp0iU89dRT0jxNK24OuEBERER0a0y+mQhBEODq6gpXV1d4e3sjMzNTJyEwYsQIqQ+ciooKVFRUSC12LCws4OnpKSXjhgwZAg8PD1hYWEjLa1qNsAXW7dPX0kKlUuHgwYNd9g2XkJAANzc3BAUFae0PS0vuD7kolUqdW4nZZ5T8NJ8PR0dHpKWl4ezZs12WFwQBgwYNwh133MFWUAbQ8fghiiJUKpVWou3GjRtQq9U6yzo6OsLX1xfu7u5IT0/Xek4QBIwbN477ycCefvppjB07Fp9//jkHXCAiIiLqBaNLvlVWVuKFF17A7t27AQD33Xcf3nvvPbi6una6zJNPPoktW7ZozZs0aZLUCszUKBQKvS2rNC2mbt68iRs3bkgXO/n5+airq0NRURGKiopw6tQpAG23vQ4ePBiDBw9GU1MTMjIy9K6PeqdjSwt9+01fIu7TTz+Fo6Mj6urqALRdfN51130AIvopcmpPoVBg9OjRWn2+hYWFMRkgo077c+ugfcudji3cuP/6Tsf94eXlhdraWuk7rD0bGxvpuKP5Iaj9baMeHh6dtkwkw7l69Sp2796N4ODg217XoUOH8Pbbb+PUqVMoLCzErl27cP/993daXt85HACEhobip59+AgBs3rxZq1Wexs2bN2FnZ3fbMRMRERHdLqNLvj366KPIz8/H3r17AQDLli3D4sWLb3k70T333INNmzZJ0zZ6OtU2JV31YWNvb4877rgDd9xxBwDotEC4ceMGbty4gaamJly9elUaCU5D0xfZoEGD4Ofn16/1MnXd7Ruu/UWrKIpITk6GJvmmUqng6qrsp4iJfb4NLJmZmUhLS7plOUEQsHTpUqjVarZwM4CbN2/iypUruHDhAjIzM7We0/RLamFhAS8vL61EW8cW1x2xfzZ5zJ49G1lZWX2SfKurq0N4eDieeuopPPjgg7cs/+677+Lvf/+7NN3c3Izw8HAsXLhQq5xCoUBOTo7WPCbeiIiIaKAwquTbuXPnsHfvXhw9ehSTJk0CAPz73/9GVFQUcnJyuhyFy9bWFt7e3v0V6oDQ3dYbgiDAxcUFLi4uCA0NBaDd98758+dx4cIFrWVEUcQnn3wCFxcXBAUFwc/PT2uwAOq9W/UNV1paqtNqs32CLj4+HgsWxLBlYj9hn2/ya0vuRAAAUlJS9A1YiqioKBw9elTrszRkyJD+DNOkNTQ0oLq6Gt9++y2uXbuGoqKiLsvHxsZi7NixveprlC0T+9+8efPw+9//HtnZ2RgzZozOfrvvvvu6va7Y2FjExsZ2u7zm/ETj66+/RmVlpU5LN0EQzO48j4iIiIyHUSXf0tPT4eLiIiXeAGDy5MlwcXHBDz/80GXyLTU1FZ6ennB1dcWMGTPwxhtvwNPTs9PyjY2NaGxslKZVKhWAtpHX9PVJY4rc3Nzg5uYGf39/XLx4USfBIAgCqqurkZmZKbVsKCgoQGBgIAICAhAQEABnZ2etZVQqFVss9MCYMWMQEBCAyspKuLm5SX3DHTt2rNNb6jQtE5VKJZqamritDUxzS1zHPt+cnZ3N5ruiv7X/HlGpVEhKSkJXt11r+gUbN26c1meJ++fWOvvObmxsxPXr16XW0cXFxRBFEXl5eVIZpVIJHx8fnZahgiBILa/NZR8Yez2fffZZAMBrr72m81x/D7iwceNG3H333QgICNCaX1tbi4CAALS0tCAiIgKvv/46xo4d2+W6BsK5nuZ1jP090h3mUldzqSdgPnVtXz9TvxY0l30KsK6mSo66dve1jCr5VlRUpDdh5unp2eWv7LGxsVi4cCECAgKQl5eH//3f/8Xs2bNx6tQp2Nra6l1mzZo1WL16tc78/fv3w8HBofeVMFK+vr64fv26NO3n5wdXV1fU1dWhtrYWtbW1qK+vR3V1NbKyspCVlQWgrcWhk5MTnJycoFarcePGDa11KJW8PbI3Ou6PjkRRxObNm6VpbmvDcnFxQVVVlTTt6uqKI0eOyBeQCSsvL9fz3u+69ZSvry/3Ry903NaaW0I13/cdtf++d3JyklpH+fn5aa3HHPeHvu1lTG414mx/KSwsRHJyMrZt26Y1f8SIEdi8eTPGjBkDlUqFd999F1OnTkVWVhZCQkI6Xd9AOtdLSUnp19eTk7nU1VzqCZh+XRsaGqTHO3bsMIuW86a+T9tjXU1Tf9a1u+d5AyL59uqrr+o9+WnvxIkTAKB3hC3NbUSdWbRokfR49OjRGD9+PAICArBnzx4sWLBA7zKrVq3CypUrpWmVSgU/Pz9ER0ebbSsilUql1WqkPbVajb179yIkJAQFBQVSSwjNr8rl5eU668vPz8f8+fPNdnveLs3+sLa2xr//va3LstzWhqNSqaRks0ZVVRUee+wxbu8+plKp8P7779+ynCAIWLJkCdRqtd7vK7q16upqfPDBB1rzysrKtKZdXV2lVs6DBw/G0aNHMWfOHL23knZ1/DAHmhZVdHs2b94MV1dXnQEaJk+ejMmTJ0vTU6dORWRkJN577z2sW7eu0/UNhHM9tVqNlJSUTj87psRc6mou9QTMp64ffvih9HjFihXYsGGD3kFeTIG57FOAdTVVctS1u+d5AyL59vzzz+ORRx7pskxgYCDOnDkjddTcXmlpKby8vLr9ej4+PggICMDFixc7LWNra6u3VZy1tbXJv2E7o1Qqu2w9ZWlpiREjRmDMmDEA2n4lunr1Kq5cuYKcnBxUVlZqlRdFEQkJCRg7dixCQkLMskXh7Wi/P2JjY/HGG52X1fRBxtZvfU+lUunt862mpobbuw+JoiiNuNxR+64INP25dbwljW6tubkZeXl5yMnJwdmzZ/Vu6zvuuANjxoxBYGCgVj9cmub2nR0jb3X8MHXGeN6wbt06LFu2DHZ2dl0msADghRdeMHg8mr5mFy9efMtBsywsLDBhwoQuz/OAgXWuZ07nl+ZSV3OpJ2Dadc3Pz8eLL74oTbe2tuK5557D3Llz4evrK19gBmbK+7Qj1tU09Wddu/s6AyL55uHhAQ8Pj1uWi4qKQnV1NY4fP46JEycCAI4dO4bq6mpMmTKl26+nuZXGx8en1zHTrdnZ2WH48OEYPnw4oqKisHbtWp2LOU1/QYIgwM/PTypvzhdpvRERESE9fvzxx7Fjx2adbb17927MnTsXI0aM6LKlKPWMUqnU2+ebu7u7jFGZluLiYiQlJeHatWs6zwmCgAkTJkjTy5Ytg78/vz+6q66uDhcvXkROTg4uXbrUZZ8VgiDgvvvuM8uWa+bonXfewWOPPQY7Ozu88847nZYTBKFfkm9paWnIzc3F0qVLb1lWFEVkZmZKPwYSEfXWxYsXdW69b2lpQW5urkkn34io7w2I5Ft3jRw5Evfccw9+85vf4KOPPgLQdqEVFxenNdjCiBEjsGbNGjzwwAOora3Fq6++igcffBA+Pj64cuUK/vSnP8HDwwMPPPCAXFUxOwqFQmfkzjvvvBOCICAnJwfFxcW4du0arl27hpSUFCiVSgwbNgzDhw+Hn58fLCwsALS1MiovL4dSqeQFYCd8fHx0trWdnR1qa2vx3//+F8HBwYiNjYWVlRW3ZR9QKBSIjY39udP/X1pecZv2nuZz7uTkhIyMDGmAEWtra4SEhODcuXNao5a239bc7to6fmeKooiysjJcuHABOTk5Ov3nOTs7S9+91dXVSEpK6nRbk2lrP3hG+8e3q7a2Frm5uVrrzszMhLu7O/z9/bFq1SoUFBTg008/1Vpu48aNmDRpEkaPHq2zztWrV2Py5MkICQmBSqXCunXrkJmZ2a3b1ImIuhISEgILCwutBJylpSWCg4NljIqIjJFRJd8A4D//+Q9eeOEFREdHA2gb3n79+vVaZXJyclBdXQ2g7csxOzsbn376KaqqquDj44NZs2Zh+/btOiNxkmFFRkYiODhYZ+S8WbNmoaqqChcuXMCFCxeQl5eH8vJypKenIz09Hfb29hg2bBisra1x6tQprQvByMhImWs1MHXc1vb29jh8+DB++OEH5ObmYv369VJLLW7LvtXZKLTUPRkZGVLiuL3Q0FDExMRII/62/x6pq5Mp2AGu/bYUBAFBQUGoqqpCRUWFVjlvb2+p1bG3t7dWy9hhw4ZxhGrCzZs3YW9vr/e5wsLCHt1JcPLkScyaNUua1vS5tmTJEmzevBmFhYU6rVyrq6uxc+dOvPvuu3rXWVVVhWXLlqGoqAguLi4YO3YsDh06JN0lQUTUW76+vnjvvfewfPlyAG3Xlh999BFbvRFRjxld8s3d3R1bt27tskz7izZ7e3vs27fP0GFRNykUCr0XcK6urpg4cSImTpyIxsZG5ObmSsm4mzdv6nRoL4oiEhMTERwczAvCTnTc1rNnz0Z4eDh2796tdWHDbXl7VCoVkpOTteZxe/aOSqXSm3h74IEHEBYWJk139j1Cv6iurtbalqIo4vLlywDaLhyCgoIwbNgwDBs2TKvvto64rQkAxo4di23btun8SPPll1/it7/9LUpLS7u9rpkzZ3b5I0X7kbo1XFxcuhxJ7J133uny1lgiotuxZMkSKfmWlZWFUaNGyRwRERkjo0u+kemztbXFqFGjMGrUKLS2tuL69es4fvw4zp49q1VOFEXs3r0bU6dORWBgIPsx6walUokZM2bgs88+05qvuRWNF9k9V15ernfAhYqKCm7PHsrKytJ7Uc7t2H2lpaXIysrC6dOn9W7LGTNmICoqSm8n80SdmTNnDqZMmYJXX30Vf/jDH1BXV4fnn38eO3bswN///ne5wyMi6jdDhgyROwQiMlJMvtGAZmFhgYCAALi5uUn9PLV36dIlXLp0CQqFAmPGjEF4eDgGDRokU7TGwcPDQ2eAAAA4ePAgPDw8mOjoIQ64cPuam5uRkpKC48eP6zzHbXlrdXV1yM7OxpkzZ1BYWNhpOUEQEBkZycQb9dh7772He++9F0899RT27NmDGzduQKFQ4MSJEwgNDZU7PCIiIqIBj8k3Mgr6BmyYMmUKbt68ibNnz0KlUuH777/H999/Dx8fH4SFhWHMmDFwdHSUO/QBR9+2tLCwQH5+Pj788EPMnz9fawAT6hoHXLg9ZWVl2LlzJ4qKigAAQUFBuHLlCjv5vwW1Wo2cnBycOXMGubm5UvLXwsICISEhCAsLQ319PQdMoD4THR2NBQsWYMOGDbCyskJCQgITb0RERETdxOQbGY3OBmyIjY3FhQsXcObMGVy8eBGFhYUoLCzE/v37ERwcjLCwMAwfPhw3b97k6J4/67gt1Wo1vvzySxQVFeGLL77AxIkTMWnSJFRXV3N7dUN4eLiUfHv00Uc5AlY3VFdX4/jx4zh+/Diam5vh4OCA+fPnY9iwYToDKlBbf3hlZWVoaGhAbm4uzp49i8bGRun5IUOGICwsDKNGjdL60YEDJlBfuHTpEh599FEUFRVh3759SEtLw/z58/HCCy/gjTfegLW1tdwhEhEREQ1oTL6RUdHX+beVlRVCQ0MRGhqKuro6/PTTTzhz5gwKCgpw8eJFXLx4EVZWVmhubgbA0T01Om7LpUuX4rvvvsPRo0elpAjA7dUd7QcE2bZtG7fXLRw/flxrkAoPDw888cQT0gjU7ORf2/fff49vv/1WZ76LiwvCwsIQFhYGDw8PvctyW1JfiIiIwL333ot9+/bB1dUVc+bMwdy5c/HEE08gJSUFp0+fljtEIiIiogGNyTcyKY6OjtKoqWVlZThz5gwyMzNRU1MjldGM7jl06FC4urrKF+wAY2VlhZiYGHh7e+Prr7+W5nM01K51HO2U26trN27c0BkdVt+gFeZOFEXk5+fjyJEjuHDhgs7zDz30EEJDQznQDPWLDz74AIsXL9aaN2XKFJw+fRovvviiPEERERERGREm38hkeXh4YPbs2QgMDNQ7uue///1vTJkyBZGRkbC3t5cpyoFHX8KIo3d2jqOddl9paSm2bdumM5/b6xctLS04e/Ysjh07hoKCgk7LOTo6MvFG/aZj4k3D2dkZGzdu7OdoiIiIiIwPk29k8job3bO+vh7ffvst0tLSEB4ejkmTJnV665Y50Td6JwBcvnwZAQEBvODvgKOdds+VK1fwxRdfaPVTpsHt1fZ9lJGRgePHj0stdS0tLTF8+HCdkZ65vUguZ8+exbVr19DU1CTNEwQB8+bNkzEqIiIiooGPyTcyefpG95w7dy6srKxw9OhRFBcX4+TJkzh58iRCQkIwadIkDB06FIIgQKVSmd0gDR23l8bhw4fR0NCAKVOmoLKy0qy2SVc42mnnNJ+fkpISpKSkoKWlBX5+fggNDcX+/fvNchTOjt8ppaWlOHbsGLKysqR+KR0dHTFhwgSMHz8ejo6OyMjI0Pr+MqftRQPD5cuX8cADDyA7O1vrxwbNjzEtLS1yhkdEREQ04DH5Rmahs5FSw8PDceXKFRw7dgw5OTnSAA2DBg3C4MGDcebMGa0LXnPpRL/99nJzc8PZs2exf/9+nDhxAidOnADAgRg6w77L2rRPGGmEhobi/vvvh7W1NUJDQ81uFM6O28TT0xMlJSXS897e3pg8eTJGjRoFK6tfDs+dfX8R9Zff/e53CAoKwrfffouhQ4fi+PHjKC8vx//8z//gn//8p9zhEREREQ14TL6R2dA36p8gCAgKCkJQUBAqKipw7NgxnD59GqWlpSgtLZXKmWMn+u23V1RUFKysrKTWXYB5bhN9Og64AMDst4tKpdJJvAFAdHQ0rK2tAZjfKJz6tokm8TZixAhMnjwZ/v7+nd7WbW7biwaW9PR0HDhwAIMGDYKFhQUsLCxw5513Ys2aNXjhhRc42ikRERHRLVjIHQDRQOHu7o7Y2FisXLkS48eP13leFEWtVirmRl9/eJqO8s1ZVwMumKuysjK9LQArKytliEZ+oigiIyND7zZZsGABFi1axP4UaUBraWmBk5MTgLZjwY0bNwAAAQEByMnJkTM0IiIiIqPA5BtRB3Z2dpg2bZreC+Fdu3bh5MmTZtm/jWZggY6cnZ1liGbg0LddzLlDfFEUcfbsWZ355rhNRFHEpUuX8PHHHyMtLU3neUEQEBAQIENkRD0zevRonDlzBgAwadIk/OMf/8D333+P1157DUOHDpU5OiIiIqKBj8k3Ij00gw5okiqCIMDe3h719fXYs2cP3n//fak/OHPRcZtoJCcnSx3FmyPNgAsa5t4h/uHDh3Hq1CkA0Pr8mNs2yc/Px6effoqtW7fixo0bsLa2RkhIiFlvEzJer7zyClpbWwEAf/vb33D16lVMmzYNSUlJWLdunczREREREQ187PONqBMdOzl3cHBARkYGDh06hMrKSuzatQvff/89Zs+ejWHDhpnFLWPtt0lDQwO++uorXLp0CTt37sTChQthYWGe+fzw8HCpP7xly5bB29tb5ojkcfToURw8eBBAW/9uo0aNMrtBAoqLi3Hw4EHpVjxLS0uMHz8e06ZNg6OjI1QqldltEzJ+MTEx0uOhQ4fi7Nmz0oA85nDsIyIiIrpdTL4RdaFjJ+cTJ05EREQEjh07hu+//x4lJSX44osv4Ovri7vuugvu7u4oLy+HUqk02Qvr9tvkkUcewbZt23D+/Hns2LEDEyZMgIeHh8nWnfRTqVQ4evQo0tPTAQAzZ85EVFQUAJj8e0GlUqG8vByWlpY4efIksrOzAbS1bAsPD8fMmTPh4uIilefACWQqzO02ciIiIqLbweQbUQ/Z2Nhg2rRpGD9+PL7//nscO3YM+fn52LJli1RGc0tZZGSkjJEa3tChQ7Fw4UJs374d58+fx/nz582m7u1lZWVJj+Pj482q/hkZGUhISJCmhw4diunTp8sYUf/JyMjQO6praGgoZs2apXeQEiJj8vTTT3er3CeffGLgSIiIiIiMG5NvRL1kb2+Pu+++G5MmTcK3334rdUYNtHW0npiYiODgYJNv5eLj46OVfDCnugNtLZ+Sk5OlaXOqv0qlQmJiota8vLw81NTUmHzdq6qqtJKOGr/61a8wbNgwGSIi6nubN29GQEAAxo4da1Z9nBIRERH1NSbfiG6Ts7MzIiIitJJvQFsS5vTp05gxY4ZMkfWP8vJynXmiKKKiosLkEzBAW/07XpSaS/2vX79ulnUvLi7Gl19+qfc5Gxubfo6GyHCeffZZfPHFF7h8+TKefvppPP7447zdlIiIiKgXzLN3dKI+plQq9XY6nZqaiu3bt0OlUskQVf/orO7mMviCvvoLgmDyF6jNzc04cuSIznxTrrtarcZ3332H+Ph4lJWV6TxvynUn8/TBBx+gsLAQf/jDH5CQkAA/Pz88/PDD2LdvH1vCEREREfWAeVwdExmYQqFAXFyclIQRBAEhISGwsLDA+fPn8f777+P48eNobW2VOdK+17HuGklJSVCr1TJF1X8UCgViY2OlaU2fd6bc8gsA9u7di6KiIlhZWWm970217nl5efjwww9x5MgRtLa2YsSIEZgzZ45Z1J3Mm62tLX71q18hJSUFZ8+exahRo/Dcc88hICAAtbW1codHREREZBR42ylRH4mMjERwcDAqKirg7u4OhUKBkpISJCQkID8/H8nJycjOzkZcXBy8vLzkDrdPta+7tbU1Pv/8cxQXFyMhIQEPPPCA3pZxpiQ8PBxJSUkAgGXLlsHb21vmiAwrIyMDp06dAgA8/PDD8PLy0nrfm5L6+nqkpKQgMzMTQNtt5rGxsRg5ciQAYPTo0SZbd6KOBEGAIAgQRdEkf0wiIiIiMhQm34j6kEKh0LoA9/T0xNNPP42TJ0/i22+/RX5+PuLj4zFlyhRERERApVJBqVSaxEV7+7ovXLgQn376KbKzs+Hu7o6AgACTqac5U6lUyMnJwd69ewEAs2bNQkhICACY1L5VqVQoKytDaWkpDh06hPr6egDAhAkTMHv2bNjZ2UllO37miUxNY2MjvvrqK3zyySc4cuQI4uLisH79etxzzz1m070AEZFGQUEBXF1d5Q6DiIwQk29EBiYIAiZMmIDhw4dj7969OHfuHI4cOSL1l6W5XS0yMlLmSPtOQEAAoqOjsXfvXqSlpQEwzXpqZGVlSY/j4+NNsp4ZGRlITEyU+nny8vLCtGnTZI6q73WsJ9CWRI+Li4Ofn5+MkRH1v+eeew5ffPEF/P398dRTT+GLL76AUqmUOywion61ZcsW6XFYWBji4+OxdOlSGSMiImPE5BtRP1EoFHj44YeRkZGBhIQEab4oikhMTERwcLBJtaAZMWKE1EIKMN16qlQqJCcnS9OmWE+VSqWTkCopKUFNTY3J1BFoq2f7z6bGI488Ajc3NxkiIpLXhx9+CH9/fwQFBSEtLU36MaWjr776qp8jIyLqH/n5+VixYoU03draimeeeQYxMTHw9fWVMTIiMjZMvhH1M30X8aIo4vr16xg1apQMERlGRUWFzjxRFFFRUWFSCZvy8nKdUf9MrZ7mUMfm5mbs2bNH73PV1dVMvpFZeuKJJ0y+z04ioq5cvHhRp4/LlpYW5ObmMvlGRD3C5BtRP1MqlVKH1e0lJibCzs4Od9xxh0yR9S199RQEAe7u7jJG1ffMoZ62trY680ypjpWVldixYwcKCwt1njOlehL11ObNm+UOgYhIViEhIbCwsNBKwFlaWiI4OFjGqIjIGLGnXKJ+plAoEBcXJ7UmEAQBCoUCDQ0N2Lp1K1JTU01iFLmO9QQAGxsb2NjYyBhV31MoFIiNjZWmNX3bmUqLMFEUcejQIa15plTHnJwcxMfHo7CwEPb29pg0aZLWZ9NU6klEREQ95+vri/fee0+atrS0xEcffcRWb0TUY2z5RiSDyMhIBAcHo6KiAu7u7nBwcMDevXtx6tQppKWl4fr161iwYAEcHR3lDvW2aOpZUlKCPXv2oKqqCvv378d9990nd2h9Kjw8HElJSQCAZcuWwdvbW+aI+s6PP/6InJwcWFhY4LHHHoOFhQXc3d2NPiHV0tKC7777Dunp6QDaTq4feughuLi4YMqUKdJn09jrSURERLdnyZIlWL58OYC2QbZMqZsYIuo/TL4RyUShUGhd2MfFxcHf3x+JiYm4fPkyPvroIzz44INwc3NDeXk5lEqlUSYCNPV84IEHsGnTJpw+fRqBgYFwdnY22jqZA5VKhfz8fCmpOH36dAwdOlTmqG6PSqVCeXk5bGxssG/fPly/fh0AMHnyZNx9992wtLQEoPvZJCIiIgKAIUOGyB0CERkpJt+IBpCwsDD4+Pjgv//9L8rKyrT629HcAhcZGSlfgLfB398fEydOxPHjx7Fr1y4Axl8njaysLOlxfHy80dcpIyNDa3RThUKBO++8U+aobk/HOgFtfdnNnz8fI0eOlDEyIiIiIiIydezzjWiAGTRoEH7zm99gxIgRWvNFUURiYiJUKpVMkd2+CRMmaE2bQp1UKhWSk5OlaWOvk0ql0klS1dTUoK6uTsaobo++OgHAo48+ysQbEREREREZHJNvRAOQjY2NTqIKaEvsVFRUyBBR36ipqdGZZ+x1Ki8v10nqGHOdTK0+AFBaWqpTJwAmMbAJERERERENfEy+EQ1QHh4eWiOFalhYGO/HVqlU6tRJEAS4u7vLFNHtM7U6KZVKnXnGXB+1Wo0jR47ozDfmOhERERERkXEx3qt4IhOnUCgQFxenk9j573//i8LCQpmiuj366jRx4kSj7txeoVAgNjZWmtb0Y2esdbKysoKV1S/dgRpzfW7evInPPvsMV65cgYWFhfS+M+Y6ERERERGR8eGAC0QDWGRkJIKDg1FRUQFbW1t88803KC4uxpYtW/DII48gMDBQ7hB7TFOnvXv34ty5c7hy5QpaW1uNukVfeHi4NCrosmXL4O3tLXNEvZeWlobm5mYMGjQIsbGxRjsirUqlwtatW1FaWgo7Ozv86le/gqurKyoqKuDu7m6UdSIiIiIiIuNkvFe7RGZCoVAgMDAQPj4+ePLJJxEQEIDGxkZs3boV586dkzu8XlEoFJg3bx7s7OxQXFyMM2fOyB1Sn3F2dpY7hF6rqKjAyZMnAQD33HMPgoKCjDJJVVZWhk8++QSlpaVwdnbGk08+CX9/f+mzZIx1IiIiIiIi42V0ybc33ngDU6ZMgYODA1xdXbu1jCiKePXVVzF48GDY29tj5syZ+OmnnwwbKJEB2NnZ4fHHH8eIESPQ0tKCHTt24NSpU3KH1Sv29va48847AQAHDx6EWq2WOSI6cOAAWltbcccdd2Do0KFyh9MrhYWF2LRpE6qrq+Hu7o6nn34aXl5ecodFRD87dOgQ5s2bh8GDB0MQBHz99dddlk9NTYUgCDp/58+f1yq3c+dOhIaGwtbWFqGhodi1a5cBa0FERETUM0aXfGtqasLChQvx29/+ttvL/OMf/8C//vUvrF+/HidOnIC3tzfmzJmjd+RFooHOysoKCxcuxNixYyGKIhITE7U6lFepVDJG1zOTJk2Ci4sLVCoV0tLSkJeXZ1Tx62Os3ys5OTnSjxJz5syROZre++KLL1BfXw8fHx88/fTT3f6Rhoj6R11dHcLDw7F+/foeLZeTk4PCwkLpLyQkRHouPT0dixYtwuLFi5GVlYXFixfj4YcfxrFjx/o6fCIiIqJeMbo+31avXg0A2Lx5c7fKi6KItWvX4s9//jMWLFgAANiyZQu8vLywbds2PPPMM4YKlchgLCwsMG/ePDg5OeHw4cNISzsEoK0V2fr1mzB//t2IiIiQNcbuscLkyXchISEBBw8ex8GDxyEIAmJjY40k/janTmWjqckaQNv2N7b4MzMzf+6zrq0OubmFcHIyntZi6elnAIQBAJqbmzF4sAeWLFkCW1tbeQMjIh2xsbFag9R0l6enZ6fJ9LVr12LOnDlYtWoVAGDVqlVIS0vD2rVr8fnnn99OuERERER9wuiSbz2Vl5eHoqIiREdHS/NsbW0xY8YM/PDDD50m3xobG9HY2ChNa1rjqNVq3h6nh2abcNv0r2nTpgEAkpN/ufX07bdfwttvyxVRb4z5+e8Xb7whTyS9N+7nvzbGF3/Ez39t3nxTrjh6K0xrqry8HLW1tUY9iIex4TGga9wut2/s2LFoaGhAaGgoXnnlFcyaNUt6Lj09Hb///e+1ysfExGDt2rVdrnMgnOuZ02fHXOpqLvUEzKeu7etn6teC5rJPAdbVVMlR1+6+lskn34qKigBAp88fLy8vXL16tdPl1qxZI7Wya2///v1wcHDo2yBNSEpKitwhmB1jvc2RqK/5+V2DtbUaoggkJycb9eAXxorHAP3q6+vlDsFo+fj4ID4+HuPGjUNjYyM+++wz3HXXXUhNTcX06dMBtJ3r6TvP05wDdmYgneuZ02fHXOpqLvUETL+uDQ0N0uMDBw7Azs5Oxmj6h6nv0/ZYV9PUn3Xt7nnegEi+vfrqq3pPfto7ceIExo8f3+vXEARBa1oURZ157a1atQorV66UplUqFfz8/BAdHc2R8vRQq9VISUnBnDlzYG1tLXc4ZkWlUuHSpffx0kttzd2srdWwsBCwbNkyo3ivqlQqxMfHQxRFaZ4gMP7+YkrxW1urIQiQbl02hvhNBY8BXTP2vizlNHz4cAwfPlyajoqKwvXr1/HPf/5TSr4BPT/PAwbGuZ45fXbMpa7mUk/AfOpaV1cnPZ49e7ZJ9ydrLvsUYF1NlRx17e553oBIvj3//PN45JFHuiwTGBjYq3V7e3sDaPtV1MfHR5pfUlLS5Qh4tra2evsLsra2Nvk37O3g9ul/SqUS8+bFITExUbrYiIuLg7+/Uu7QusXVVYkFC2IYv0xMK35I8SuVxhG/qeExQD9uk741efJkbN26VZr29vbWaeV2q/M8YGCd65nTZ8dc6mou9QRMv67t62bqddUwl3oCrKup6s+6dvd1BkTyzcPDAx4eHgZZd1BQELy9vZGSkoKxY8cCaBsxNS0tDW+99ZZBXpOov0VGRiIgIADJycmIjY01usRDZGQkgoODUVFRAXd3d6NrscTtLy9j3/5E1DOnT5/W+kE1KioKKSkpWv2+7d+/H1OmTJEjPCIiIiIdAyL51hPXrl1DRUUFrl27hpaWFmRmZgIAgoOD4eTkBAAYMWIE1qxZgwceeACCIODFF1/Em2++iZCQEISEhODNN9+Eg4MDHn30URlrQtS3FAoFnJ2djS5xoqFQKIw2doDbX27Gvv2JzEVtbS1yc3Ol6by8PGRmZsLd3R3+/v5YtWoVCgoK8OmnnwJoG8k0MDAQo0aNQlNTE7Zu3YqdO3di586d0jp+97vfYfr06Xjrrbcwf/58fPPNN/j2229x5MiRfq8fERERkT5Gl3z7y1/+gi1btkjTmtZsBw8exMyZMwEAOTk5qK6ulsq8/PLLuHnzJp577jlUVlZi0qRJ2L9/PzvjJiIiIupHJ0+e1BqpVNPn2pIlS7B582YUFhbi2rVr0vNNTU146aWXUFBQAHt7e4waNQp79uzB3LlzpTJTpkzBF198gVdeeQX/+7//izvuuAPbt2/HpEmT+q9iRERERF0wuuTb5s2bsXnz5i7LtO84HGjrA+jVV1/Fq6++arjAiIiIiKhLM2fO1DlPa6/jOd7LL7+Ml19++Zbrfeihh/DQQw/dbnhEREREBmEhdwBERERERERERESmisk3Ivr/7d17VFTl/sfxz4A4anmFlJsppittlYlYil2UStPMMsvTXSwsNTWt7GJ2Es/JTCv1hJVYHKWbslpmt0NH6KRSv7S8AKmlQaEGQl5T8wLIPL8/XM5yuDmaw2Zm3q+1WGv23s+e+X73wOyHz9wAAAAAnEZRUZHVJQDwUoRvAAAAAABU49TPG+/atatSUlIsrAaAtyJ8AwAAAACgksLCQo0fP9657HA4NGrUKBUWFlpYFQBvRPgGAAAAAEAleXl5cjgcLusqKiqUn59vUUUAvBXhGwAAAAAAlXTq1EkBAa7/MgcGBqpjx44WVQTAWxG+AQAAAABQSWRkpJKSkpzLgYGBSk5OVmRkpIVVAfBGhG8AAAAAAFQjPj7eeTk3N1cJCQkWVgPAWxG+AQAAAABwGhEREVaXAMBLEb4BAAAAAAAAHkL4BgAAAAAAAHgI4RsAAAAAAADgIYRvAAAAAAAAgIcQvgEAAAAAAAAeQvgGAAAAAAAAeAjhGwAAAAAAAOAhhG8AAAAAAACAhxC+AQAAAAAAAB5C+AYAAAAAAAB4COEbAAAAAAAA4CGEbwAAAAAAAICHEL4BAAAAAAAAHkL4BgAAAAAAAHgI4RsAAAAAAADgIYRvAAAAAAAAgIcQvgEAAAAAcBpFRUVWlwDASxG+AQAAAABQjdTUVOflrl27KiUlxcJqAHgrwjcAAAAAACopLCzU+PHjncsOh0OjRo1SYWGhhVUB8EaEbwAAAAAAVJKXlyeHw+GyrqKiQvn5+RZVBMBbEb4BAAAAAFBJp06dFBDg+i9zYGCgOnbsaFFFALwV4RsAAAAAAJVERkYqKSnJuRwYGKjk5GRFRkZaWBUAb0T4BgAAAABANeLj452Xc3NzlZCQYGE1ALwV4RsAAAAAAKcRERFhdQkAvBThGwAAAAAAAOAhhG8AAAAAAACAhxC+AQAAAAAAAB5C+AYAAAAAAAB4iNeFb9OnT1fv3r3VpEkTtWjRwq19RowYIZvN5vLTq1cvzxYKAAAAF1lZWRo8eLDCw8Nls9n08ccf1zr+o48+Ur9+/XTBBReoWbNmio2N1fLly13GLFq0qMo8z2az6dixYx7sBAAAwH1eF76VlZVp2LBhGjNmzBntN2DAABUXFzt/0tPTPVQhAAAAqnP48GFdfvnlmjdvnlvjs7Ky1K9fP6Wnp2v9+vWKi4vT4MGDlZ2d7TKuWbNmLvO84uJiNWrUyBMtAAAAnLEGVhdwpqZNmybpxLOcZ8Jutys0NNQDFQEAAMAdAwcO1MCBA90eP3fuXJflF198UZ988ok+++wzRUdHO9fbbDbmeQAAoN7yuvDtbK1cuVKtW7dWixYt1KdPH02fPl2tW7eucXxpaalKS0udywcPHpQklZeXq7y83OP1epuTx4RjYx3uA2tx/K3F8bcWx792HJdzx+Fw6NChQ2rVqpXL+j///FPt2rVTRUWFunXrpn/+858u4Vx16sNcz5/+dvylV3/pU/KfXk/tz9f/F/SX+1SiV19lRa/u3pbNGGM8XItHLFq0SBMnTtQff/xx2rFpaWk6//zz1a5dOxUUFOjvf/+7jh8/rvXr18tut1e7T2JiovNVdqf64IMP1KRJk79aPgAA8BNHjhzRPffcowMHDqhZs2ZWl1Nv2Gw2LVu2TEOGDHF7n5dfflkvvfSSfvrpJ+eTqGvWrFF+fr4uu+wyHTx4UP/617+Unp6u3NxcderUqcbrYq4HwB3Hjh3TXXfdJUlasmQJb2kH4MLdeV69CN9qmvycau3aterRo4dz+UzCt8qKi4vVrl07LVmyREOHDq12THXPhrZt21Z79uxh4lyN8vJyZWZmql+/fgoKCrK6HL/EfWAtjr+1OP7W4vjX7uDBgwoJCSF8q+RMw7fFixdr5MiR+uSTT3TDDTfUOM7hcKh79+669tpr9dprr9U4rj7M9fzpb8dfevWXPiX/6fXw4cNq2bKlJGnXrl1uf+mfN/KX+1SiV19lRa/uzvPqxdtOx40b53w2oSbt27c/Z7cXFhamdu3aKS8vr8Yxdru92lfFBQUF+fwv7F/B8bEe94G1OP7W4vhbi+NfPY7JX5eWlqaEhAR9+OG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      "text/plain": [
       "<Figure size 1500x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import sys, os\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# this makes visible our functions folder\n",
    "sys.path.append(os.path.abspath(os.path.join(\"..\", \"functions\")))\n",
    "\n",
    "# import pure_shear function\n",
    "from pure_shear import pure_shear\n",
    "\n",
    "# initial points coordinates\n",
    "pts = np.zeros((16,2)) \n",
    "pts[:,0]=[-1,-1,-1,-1,-1,-0.5,0,0.5,1,1,1,1,1,0.5,0,-0.5] \n",
    "pts[:,1]=[-1,-0.5,0,0.5,1,1,1,1,1,0.5,0,-0.5,-1,-1,-1,-1]\n",
    "\n",
    "# maximum stretch\n",
    "S1 = 2.5\n",
    "\n",
    "# number of increments\n",
    "ninc = 10\n",
    "\n",
    "# deform and plot\n",
    "fig,ax = plt.subplots(1,2,figsize=(15,5)) \n",
    "paths, psf = pure_shear(pts,S1,ninc,ax) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$S_1$ and $S_3$ do not rotate throughout the deformation ($\\Theta$ is 0 throughout the deformation). Pure shear is a *non-rotational* deformation."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}