{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from myst_nb import glue\n",
    "%config InlineBackend.rc = {'figure.dpi': 300}\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "import sys\n",
    "sys.path.append(\"../py_figures\")\n",
    "import diagrams_2d_chap6 as diagrams_2d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(content:chap6.1:radially_sym_flow_island)=\n",
    "# Radially symmetric flow on a circular island\n",
    "\n",
    "Radial flow problems and solutions are important in groundwater engineering because they represent the local flow field around pumping wells. In this section, solutions are presented for radially symmetric two-dimensional flow on a circular island. The head is fixed along the perimeter of the island, the areal recharge on the island is uniform, and a pumping well is located at the center of the island. The head and flow are a function only of the radial coordinate $r$. The problem is depicted for unconfined flow in {numref}`Figure %s <fig_unc_well_isl6.1>`, but is equally valid for any of the flow types listed in {numref}`tab_def_dis_pot6.0`. The solution is derived as follows. First, the solution is derived for flow to a well at the center of a circular island without recharge ($N = 0$). Second, the solution is derived for flow on a circular island with uniform recharge, but no well ($Q = 0$). And third, the first two solutions are combined to solve the problem for flow to a well at the center of a circular island with uniform recharge. The purpose of this solution approach is to demonstrate the principle of superposition.\n",
    "<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The differential equation for the discharge potential in terms of r is given by Eq. ({eq}`eq_deq_rad_sym_potflow6.0`). The general solution to this differential equation is\n",
    "\n",
    "$$\n",
    "\\Phi=-\\frac{1}{4}Nr^2 +A\\ln r + B\n",
    "$$(eq_gensol_circisland6.1)\n",
    "\n",
    "where $A$ and $B$ are constants to be evaluated from boundary conditions. The corresponding radial component of the discharge vector is \n",
    "\n",
    "$$\n",
    "Q_r=-\\frac{\\text{d} \\Phi}{\\text{d}r} = \\frac{1}{2}Nr - \\frac{A}{r}\n",
    "$$(eq_gensol_Qr_island6.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "remove-input",
     "remove-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/papermill.record/image/png": 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",
      "application/papermill.record/text/plain": "<Figure size 500x200 with 1 Axes>"
     },
     "metadata": {
      "scrapbook": {
       "mime_prefix": "application/papermill.record/",
       "name": "fig_island"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 500x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_island = diagrams_2d.solution_well_island()\n",
    "glue(\"fig_island\", fig_island, display=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{glue:figure} fig_island\n",
    "---\n",
    "name: fig_unc_well_isl6.1\n",
    "---\n",
    "Unconfined flow to a well at the center of a circular island with radius $R$ and uniform recharge.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, consider flow to a pumping well at the center of a circular island of radius $R$; the radius of the well is $r_w$. The discharge potential that is the solution for this problem is referred to as $\\Phi_1$. The head is fixed to $h_R$ at the perimeter of the island ($r = R$). The corresponding discharge potential is computed with the appropriate equation from {numref}`tab_def_dis_pot6.0` and is referred to as $\\Phi_R$\n",
    "\n",
    "$$\n",
    "\\Phi_{1}|_{r=R}=\\Phi_R \n",
    "$$(eq_bc_phi_R6.1)\n",
    "\n",
    "The discharge of the well is $Q$ [L$^3$/T] and is positive for extracting water from the aquifer. The discharge is equal to the total flow into the well, which is the product of the discharge vector $Q_r$ (Eq. {eq}`eq_gensol_Qr_island6.1`) at the perimeter of the well and the circumference of the well, resulting in the boundary condition\n",
    "\n",
    "$$\n",
    "Q=-2\\pi r_w Q_{r_1}|_{r=r_w}\n",
    "$$(eq_Qrwellrw6.1)\n",
    "\n",
    "Note the minus sign, as $Q_r$ is defined as positive in the positive $r$ direction, and the discharge $Q$ of the well is positive for pumping water out of the aquifer. A slightly simpler boundary condition is\n",
    "\n",
    "$$\n",
    "Q=\\lim_{r_w \\to 0}-2\\pi r_w Q_{r_1}|_{r=r_w}\n",
    "$$(eq_bc_well_approx6.1)\n",
    "\n",
    "This condition often produces accurate results as the radius of the well is commonly much smaller than the horizontal scale of the groundwater problem being considered. Note that for this special case of a well at the center of a circular island without areal recharge, Eq. ({eq}`eq_Qrwellrw6.1`) is valid for any $r$, not just at $r_w$.\n",
    "<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Application of boundary conditions ({eq}`eq_bc_phi_R6.1`) and ({eq}`eq_bc_well_approx6.1`) to general solution ({eq}`eq_gensol_circisland6.1`), using $N = 0$, results in the solution for the discharge potential\n",
    "\n",
    "$$\n",
    "\\Phi_1=\\frac{Q}{2\\pi}\\ln{(r/R)} + \\Phi_R\n",
    "$$(eq_thiem6.1)\n",
    "\n",
    "This is the potential form of the well-known Thiem equation ({cite:alp}`thiem1906`). The corresponding radial component of the discharge vector is\n",
    "\n",
    "$$\n",
    "Q_{r_1} = -\\frac{\\text{d}\\Phi_1}{\\text{d}r} = -\\frac{Q}{2\\pi}\\frac{1}{r}\n",
    "$$(eq_Qrwell6.1) \n",
    "\n",
    "Note that $Q$ has the dimensions of a discharge (e.g., m$^3$/d), while $Q_r$ is the radial component of the discharge vector with dimensions of discharge per unit length (e.g., m$^2$/d).\n",
    "<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Neither the discharge potential (and thus the head), nor the discharge vector can be calculated at the well, where $r = 0$. In mathematical terms, such a point is called a singularity. The discharge potential (Eq. {eq}`eq_thiem6.1`), the corresponding head, and the discharge vector (Eq. {eq}`eq_Qrwell6.1`) have no physical meaning at the center of the well. These equations were derived for flow in the aquifer, but the aquifer stops at the well screen. Inside the well, the head is equal to the head in the aquifer just outside the well screen, provided the resistance to flow of the well screen is negligible. The head inside the well is computed by evaluating the head at the radius of the well ($r = r_w$).\n",
    "<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Next, consider uniform recharge on the island and no pumping well; this solution is referred to as $\\Phi_2$. As in the previous solution, the head (and thus the potential) is fixed at the perimeter of the island\n",
    "\n",
    "$$\n",
    "\\Phi_2|_{r=R}=\\Phi_R\n",
    "$$(eq_Phi_2_RBC6.1)\n",
    "\n",
    "The second boundary condition is obtained from symmetry: The gradient of the head is zero at the center of the island, and hence, the flow is zero\n",
    "\n",
    "$$\n",
    "Q_{r_2}|_{r=0}=0\n",
    "$$(eq_Q_rBC6.1)\n",
    "\n",
    "Application of these boundary conditions to the general solution ({eq}`eq_gensol_circisland6.1`) results in \n",
    "\n",
    "$$\n",
    "\\Phi_2 = -\\frac{1}{4}N (r^2-R^2) + \\Phi_R\n",
    "$$(eq_phi26.1)\n",
    "\n",
    "The total amount of groundwater flow in the aquifer at the perimeter of the island is equal to the total recharge on the island, as is to be expected from continuity of flow\n",
    "\n",
    "$$\n",
    "2 \\pi R Q_{r_2}|_{r=R}  = N \\pi R^2\n",
    "$$(eq_cont_flow6.1)\n",
    "\n",
    "The flow at the perimeter is outflow, which is opposite to the first solution, in which flow at the perimeter is inflow.\n",
    "<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Finally, consider both a pumping well with discharge $Q$ at the center of the island and uniform recharge $N$ on the island. This problem contains both features of the first two solutions: recharge and a pumping well. The solution is referred to as $\\Phi_3$. The boundary conditions are\n",
    "\n",
    "$$\n",
    "\\Phi_3|_{r=R}=\\Phi_R\n",
    "$$(eq_Phi_3BC16.1)\n",
    "\n",
    "and\n",
    "\n",
    "$$\n",
    "\\lim_{r_w \\to 0}-2\\pi r_w Q_{r_3}|_{r=r_w}=Q\n",
    "$$(eq_Phi_3BC26.1)\n",
    "\n",
    "Application of the boundary conditions to the general solution yields the following discharge potential\n",
    "\n",
    "$$\n",
    "\\Phi_3 = -\\frac{1}{4}N (r^2-R^2) + \\frac{Q}{2\\pi} \\ln{(r/R)} +\\Phi_R\n",
    "$$(eq_phi36.1)\n",
    "\n",
    "and the corresponding discharge vector\n",
    "\n",
    "$$\n",
    "Q_{r_3} = \\frac{Nr}{2} - \\frac{Q}{2\\pi}\\frac{1}{r}\n",
    "$$(eq_Dis_vec6.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparison of the three solutions $\\Phi_1$, $\\Phi_2$, and $\\Phi_3$ (Eqs. {eq}`eq_thiem6.1`, {eq}`eq_phi26.1`, and {eq}`eq_phi36.1`) reveals that the third solution is the sum of the first two solutions except for the additive constant. Addition of multiple solutions to obtain another solution is an example of the principle of superposition, which is applicable to all linear differential equations, including the equations of Laplace and Poisson. The sum of the potentials of the first two problems satisfies the differential equation of the third problem\n",
    "\n",
    "$$\n",
    "\\nabla^2\\Phi_3=\\nabla^2(\\Phi_1+\\Phi_2)=\\nabla^2\\Phi_1+\\nabla^2\\Phi_2= 0 - N=-N\n",
    "$$(eq_sum_two_pot6.1)\n",
    "\n",
    "Similarly, the boundary condition at the well is satisfied by the sum of the two potentials. Finally, the value of the sum of the two potentials at $r = R$ is a constant\n",
    "\n",
    "$$\n",
    "\\Phi_3|_{r=R}=\\Phi_1|_{r=R}+\\Phi_2|_{r=R}=2\\Phi_R\n",
    "$$(eq_bc_phi1236.1)\n",
    "\n",
    "This is not the value specified in the boundary condition ($\\Phi|_{r=R}=\\Phi_R$), but this is easily corrected by modification of the additive constant. In this example of superposition, two radially symmetric solutions were added such that the resulting solution is also two-dimensional radially symmetric flow, because the radial symmetry is about the same point (the center of the island).\n",
    "<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The flow rate and direction at the island’s perimeter depend on the relative magnitudes of the well discharge and the total recharge on the island. As an example, the head is computed for the case of unconfined flow in the code below. Two solutions are shown: the case for which the well pumps half the total areal recharge on the island and the case for which the well pumps exactly all the areal recharge on the island ({numref}`Figure %s <fig_hea_cen_isl6.1>`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# parameters\n",
    "k = 5 # hydraulic conductivity, m/d\n",
    "zb = 0 # bottom elevation of aquifer, m\n",
    "N = 0.001 # areal recharge, m/d\n",
    "R = 200 # radius of the island, m\n",
    "hR = 10  # head at edge of island, m\n",
    "rw = 0.3 # well radius, m\n",
    "Qhalf = 0.5 * N * np.pi * R ** 2  # discharge is half total recharge, m^3/d\n",
    "Qtotal = N * np.pi * R ** 2  # discharge equals total recharge, m^3/d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# solution\n",
    "r = np.linspace(rw, R, 400)\n",
    "PhiR = 0.5 * k * (hR - zb) ** 2\n",
    "Phi2 = -0.25 * N * (r ** 2 - R ** 2) + PhiR\n",
    "Phi3 = Phi2 + Qhalf / (2 * np.pi) * np.log(r / R)\n",
    "hhalf = zb + np.sqrt(2 * Phi3 / k)\n",
    "Phi3 = Phi2 + Qtotal / (2 * np.pi) * np.log(r / R)\n",
    "htotal = zb + np.sqrt(2 * Phi3 / k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# basic plot head for half total discharge\n",
    "plt.plot(-r, hhalf, 'C0', label='Q = half total recharge')\n",
    "plt.plot(r, hhalf, 'C0')\n",
    "plt.xticks(np.arange(-200, 201, 50), np.abs(np.arange(-200, 201, 50)))\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": [
     "remove-input",
     "remove-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/papermill.record/image/png": 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",
      "application/papermill.record/text/plain": "<Figure size 400x320 with 1 Axes>"
     },
     "metadata": {
      "scrapbook": {
       "mime_prefix": "application/papermill.record/",
       "name": "fig_head"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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L09GR9G8Ziu4m6ovYG3+ZLzYcZ+XB8+Rb1AM0P6PCo12ieKBDXSL8Hfd/s6NY1Oahv39Rk0HKMfv5PuEFNdeCGqxvuGPivIFIYhAV5+ar7vQbF1y1nnEB/ik4gju+Vj2Vdu8S9aF3h0Z90TS5B52lqob5qBwfNz2Db43ggXahfPHjb5xwieCXfYnsjb/MC0t2M2fNMUbf3pC7bvAEsSf+MnNWH+XPIxds0zrX92dIp3ByTuxgQK8Gjj9DymJBE7+VFme+x2XueMgodKah1gUiOkPDPmoNNaBRtZ1Fd7OSxCCunWcgtBmsPvLNapPT0T/g8M9wOQ4OrsDl4Aru1BrRmn+Fto9BVC/b6X2OEO4Jz/Zvwet3NeP7raf5OvYk/yRlMHrJbuauOcardzbhjqZBN9TwHMfOpzP9979Z+3cSoPYdDGwTxvCu9Wka6o3ZbOa34i+FqTmJB2DPYvU7k36OKOt0o/eVg5GoXmq/gag2khhE1dLp1Sp9ZFfo8zac2wUHf0I5+BMuqXFw6Cf14RUKrR+GNo+ppwc6SICnkTF3NOLJ6EgWbTrF/I0n+Ccpg+Hf7qBrwwAmDWhGo2DHnapbFS5nmZi9+hjfbT1NvkVBp9VwX9vajOrZgHoBHo4OTx0yYv9/YM/3anNkAcXoxRn3VoT2HolLo94lDv0iqp4kBlF9NBqo3R5qtyevxyQ2/+dTon3OoTvwH0hPgNhZ6iO8E3QcDk3vARfHdHJ6u+p54faGDL2tHvPWHeerjSfZeCyZfnM28uRt9Xi5T2Nc9U50WmY5KIrCit1nmfbLIdvAdH2aBTOhf1MiHZ0QFAXit8FfX8Lh/0F+wWliWr1aK2gzmLyIruxatYb+DfuCy41/7YAzkcQgaoZGw2WP+lj6jELX9221qWn3v9W+ifit6sMzBDo8Ae2fUDu8HcDbVc/4O5vw8C0RvPPbIVYePM/8jSdZcziJGf9qRYd6fg6Jq6LOp+Xw+vL9rCloNmoc7MXku5txW4MAxwZmzoYDy2DbF5C478r0kJZq7bHlA1dOJb3Jrh1wJpIYRM1zMUKzgeojLQF2LYIdX6sdjOumw4YPocX9cNsYCG7mkBAj/N354vEOrDl8ntdX7OdEciYPfLGFUT0bMOaORk7dOb3qYCKv/N9e0nLyMOi0vHhHQ57pVh/9tY46eC0yU2Db57B9AWRfVKe5uKqJ4JanIayN42ITRUhiEI7lHQo9XoPosWpn9V9fqk0M+35QH43vgm4vq01SDnB702BW1fVj2i+HWLbrDB+v/Ycdpy4x55E2BHk50YVeqENcz/jjb+ZvVHuQW9Xx4cMHWju2jyTtHGz+BHZ+A+aC0T19IuCWp6DdEHU4F+F0JDEI5+BigJb/Uh/ndqt9D4d+vjI0R/2eagKJ6FTjofm46/nowdZ0axTAhOX72XIihXs+3sTXw26hWZhzDLGRmm3mue93svm4enHak7dF8lq/JhjKOeJs1Qd0BjZ8oJ5hZO0/CG0NXV+GJgMcekaaKJskBuF8wtrCg9/ChSMQO1utOZz4U3006ge3T3ZIE9PANrVpHubDiO938k9SBg9+sYXPH2tnG9zPUc5dzmbYN39x9HwGHgYdHz7Qmn4tQ8tesDpkXYSNH8Ff869ckRzRRa31Rd0u1xtcJ+Q6ceG8AhvDfZ/D6N1qs4NGB0d/h8+7wE8j4XJ8jYfUIMiTZSO60Km+Hxm5eTzxzXZ+3ZdQ43FYnbiQwX2fbeLo+QyCvIz88GxnxyQFU5aaEOa0hi2fqEmhbjQM+w2e/B0a3CFJ4ToiiUE4v1p14Z6PYeRW9ZRWFNjzb/jkFlj/AZhLusd09fBx17PoyY4MbBNGnkVh9NLd/L6/5pPDqeRMHpm/lfNpuTQM8mTF87fRonYNX/ilKGqT36cdYc009eZSwS3h0f/AsF+g3m01G4+oEpIYxPUjsBE89B08vUZtnsjLhj/fhs86qcNx1CCji46ZD7bh/na1ybcovLBkN2v/Pl9jn3/ucrZdUljyTCdq+7rV2OcDkHwMvr8ffnwcUuPVMYvunw/PblDHypIawnVLEoO4/tTpAE/8BoMWqFdQXzoJix+EpY+qI8HWEJ1Wwwf/as29BTWHUYt3c+hc+W+fWFmZuXk8tWgHCak5RAV6sHh4JwI8a/Cq4DwT/DkdPuusjo2lM0C3cfD8X9DqQRnJ9AYg/0FxfdJo1DOYRm2HLqPVgdX+/gU+uxX2/QilDOdelXRaDR880JouUf5kmfJ5etF2ktKqr2kr36Lw4tLdHE5II8DTwKInOxLoVYNJIWEvzO8J698Di1kdyG7kVug10aGj6IqqJYlBXN+MXtDnLXhmPYS0Uu+BvXw4LB1cY7UHvU7L54+2p36gB+dScxi1ZLdtGOuq9umf/7D6cBIGFy1fDulAnVo1tDPOM8Had2B+L/Vuf+7+8K9vYPCP6p3PxA1FEoO4MYS0gOFroedEdbydI7+pZy/9s7pGPt7HXc+CobfgYdDx18mLfL6uhPsKX4Odpy8yZ416L4J372tZczcYunQKvrlTvdeGJU+9Yn3kNvXqdOlHuCFJYhA3Dp0euo+DZ9dDUHP1vhDfD4LVU9ThwKtZZIAH0wa2AGDW6mPsjb9cZevOzM3jxaV7yLco3NsmjH+1r1Nl6y7VwZ9gXjc4u1Md6vpf36jXmHg69toNUb0kMYgbT3BzGL4GOjylvo+dBQvvUsdlqmb3t6vN3a3DyLcovPHT/iprUpq75hhnLmVT29eNafe2qJJ1lirfDL+Ng/8bCrmp6i0yR8SqtQRxw5PEIG5MejcYMBMeWKTe5CV+m9ppenZntX6sRqNh8oBmeLm6cOBsGv/edvqa13n0fDoLYtXxj6YNbI63azUPQZ2VAt/eq45bBepghk/8Dr4R1fu5wmlIYhA3tub3qk1LgU3Ue0B83Q/Ngf+r1o8M9DIyrm9jAD5YeYSLmaZKr0tRFKb8fJA8i8IdTYO5vWn1DkfunR2Hy9e94XQsGLzgkaXQe6raTCduGpIYxI3Prz48FaOOs5Sfi8t/n6NxwopqPaX10Vvr0jTUm/ScPL7ccKLS69lyPIXNx1Mw6LS8eXf1jg+lObGOrkffRpMaB7Ui4enVV+7rLW4qkhjEzcHVGx5eDNEvAdAkcQXala+CJb9aPk6n1fBy70YAfLvlFCkZuRVeh6IozFp9FIBHOoYT7leNp6YeWIbuh0dwseRgqRutnuEV1KT6Pk84NUkM4uah1cIdU8jv8x4KGnQ7v4ZlT0FexXfa5XF70yBa1fEhy5Rv6yOoiK0nLrL91CUMLlpG9qzG+2Jv+xL+8xQai5mzvh3Jf/gHuU/CTU4Sg7jpWG55mh31nkPR6uHgCvjh8WpJDhqNhpE91B360u3x5JgrVjv5dsspAP7Vvg7B3tV0U6BNc+H3cYBCfvun2FFvpHqHPXFTk8QgbkrnanUi/6El4OIGx1bCj0PVq3ur2B1NgwjzceViponfKjACa0JqNqsOqVduD+1cr8rjAmDLpxAzSX3d/VUsfd8DjewShCQGcRNT6veAR5ao9x4++jv837AqvxDORadl8K3qaZ7fbin/qatL/oon36LQMdKPxiHVcGvOrfNg5evq6+6vQs/X5SpmYSOJQdzconqqndI6o3oL0Z9fqPKzlR66JQKdVsOe+MucuJBRZnlFUVi+6wwAj3WqW6WxALB3Kfzxqvq66yvQY0LVf4a4rkliEKLB7ep9HjQ62LsE1r5VpasP9DJyW4MAAH4px93e9sRf5sylbNwNOnpX9XULx9fCf59XX3cepY6KKjUFcRWnTwzp6emMGTOGunXr4ubmRpcuXdi+fXuJ5detW4dGoyny+Pvvv2swanHdadQX7p6jvt74EWxfUKWrH9BKvd3mL/vOlVnWmjxubxqMm0FXdUEk7IMfhqgD4bUYBL3fkqQgiuX0ieHpp58mJiaG7777jv3799OnTx/uuOMOzp49W+pyR44cISEhwfZo2LBhDUUsrlvtHr/SrPLbK+rRdRXp2zwEF62Go+czOJ2SWWrZ1YfVTue7qvLezennYfFDYEqHel3h3s/lhjqiRC6ODqA02dnZLFu2jP/+979069YNgClTpvDTTz/x+eef8/bbb5e4bFBQEL6+vuX6nNzcXHJzr5yumJam3oXLbDZjNpe/M9JatiLLVCdniue6iaXLWHQXT6HdtwTlP0+S9+Rq8L32dn53F2gb4cv2U5f48+/zPNoxvNhYTl/M4nRKFi5aDbfW86ma7ZVvRvfjELTp51D8G5I3aCEoWrhq3c70PwLniudGiKUi5TWKUkO3uqqE9PR0vL29Wb16NbfffrtteufOnTEajaxbt67IMuvWraNnz57Uq1ePnJwcmjVrxsSJE+nZs2eJnzNlyhSmTp1aZPrixYtxd5e7Ut1stBYT0cfepVbWCS67RRDbaBL52ms/t3/VGQ2/xutoWcvC000sxZaJTdTwfyd1RHkpjG5RNVdltzzzHfUvxGDWurGh8RQyXKuwJiKuG1lZWQwePJjU1FS8vb1LLevUiQGgS5cuGAwGFi9eTHBwMEuWLGHIkCE0bNiQI0eOFCl/5MgRNmzYQPv27cnNzeW7775j3rx5rFu3zlbruFpxNYbw8HCSk5PL3ICFmc1mYmJi6N27N3q94wcdc6Z4rrtY0s7isuB2NFnJWFoNJv/uudf8ufvPpnL/vG14GHVsn9ATvU5bJJaRi/cQcziJsXc04Lnu9a/5MzUHl+Py0zMA5D3wHUqjksc+cqb/kbPFcyPEkpaWRkBAQLkSg1M3JQF89913PPnkk9SuXRudTke7du0YPHgwu3btKrZ848aNady4se19586diY+P58MPPywxMRiNRozGokeEer2+Ul+Cyi5XXZwpnusmFv968MBC+PYetPsWo23cB5rfd02f1ybCH29XF9Jy8jiRkkOL2j52sbi4uLDj9CUAohsFXft2uhxXcFUz0G0cLs3vKddizvQ/AueK53qOpSJlnb73KSoqivXr15ORkUF8fDx//fUXZrOZyMjIcq+jU6dOHDt2rBqjFDekyK4QPVZ9/b8XIfXMNa1Oq9XQOtwXgL1nLheZf+ZSNpeyzOh1GpqHlb+mWixLPix/5spNdrq/dm3rEzcVp08MVh4eHoSGhnLp0iVWrlzJwIEDy73s7t27CQ2VdlVRCT1eg9rtIScVlj8LluL7BsqrdR1fgGJv+7mnYFrTUG+MLtd4mmrsTIjbot5T4f75oHP6xgHhRJz+27Jy5UoURaFx48b8888/jBs3jsaNG/PEE08AMGHCBM6ePcu3334LwOzZs6lXrx7NmzfHZDLx/fffs2zZMpYtW+bIP0Ncr3R6dcc6r6t685odC6Dj8Eqvzlpj2Hcmtci8fQW1CGvyqLSkv2Hd++rr/h+AX/lr10LAdVBjSE1N5fnnn6dJkyYMGTKE6OhoVq1aZWsvS0hIIC4uzlbeZDLxyiuv0KpVK7p27UpsbCy//vor998v96oVleQfBXe8qb5ePRXSyr5IrSSt66j9CkfPp5OZm2c3b2+8miysyaNSLBb432iwmKHRndD64cqvS9y0nL7G8OCDD/Lggw+WOH/hwoV278ePH8/48eOrOSpx07nladj3I5zdAb+Ng4f/XanVBHm7Euxt5HxaLkfPp9Mi1BNQx0c6nKBeP9Oi9jX0L+z8Rr2/tcET7vpIrmwWleL0NQYhnIJWB/fMBa0L/P0LHF1Z6VU1CFKTwfELV66AvpBhIj03D60GIgM8KrfizGS1RgNw+2TwqVPpGMXNTRKDEOUV3Bw6jVRfr3yj0kN0RwWqieGfpCsjrR4vGHU1ws+98h3P66arZyGFtFJrOEJUkiQGISqi2yvgHgApx2DH15VahTUxHC80BPeJgtqDdV6FJf0NO75RX985Xa3hCFFJkhiEqAhXH/WmNqAeoWdfqvAqik0MyVnqvKBKJoZVb4CSD00GQL3oyq1DiAKSGISoqHZDIbCpmhQ2f1LhxevUcgPg3OVsrCPSnLucDUB4wbwKORUL/6wGrR56T6v48kJcRRKDEBWlc4Feb6ivt30BWRcrtHiIjysAOWYLl7PVfoqEtBwAQn0qkRjWvac+t3tcPbVWiGskiUGIymh8FwS3VO9vsPWzCi3qqtcR4GkAICE1x+45zLeCieHUJji1Ua0tWIfvEOIaSWIQojK0WuhecL3M1nkVrjVYawYJl3Mw5cPFTLXmEObrWrE41hfUFto+Br7hFVtWiBJIYhCispoMgOAWaq3hr/kVWjS0oDkpIS2HyyZ1mpteh49bBUbujN8OJzeotYWuUlsQVUcSgxCVpdVC9Evq6+1fQV5u6eULsTYZJaTmkGpSr04O9XVFU5Erla1NWC0fAN+I8i8nRBkkMQhxLZoNBK9QyEyCgyvKvZi1j+FSlpkMs3VaBe4Sl3oWDv1Xfd3pufIvJ0Q5SGIQ4lro9FdGW93yKZTzhoi+7mpiuJxlJrNgLL1a7hVoRto+X71uoV5XCG1VkYiFKJMkBiGuVfsnwMUVEvdB/F/lWsS3IAlczjaTVZAYfN0M5fu8vFzYuVB9feuICgYrRNkkMQhxrdz9oMUg9fXu78q1iDUJpGaZycxT+xV8y1tj+PtX9eI6rzBoXPI9nIWoLEkMQlSFNo+qzwdXgCmz9LJcSQKphWsM7uWsMewpGPK7zWAZE0lUC0kMQlSFul3Arz6YMq50CpfCmhguZZspuIShfDWG1LPwzxr1dZvBlY1WiFJJYhCiKmg0V2oNu78vs3itgtqBKc9CRkFTUrk6n/cuARSoe5sMfyGqjSQGIapK60cADZzepB7Zl8LdoEOvUxOC9awkn/J0Pu//j/ostQVRjSQxCFFVfGpDRGf19eH/lVpUo9HYEkGmrY+hjBrDhSNw4bB6pXOTAdcarRAlksQgRFVqdo/6XIF+hpzyJoZDP6vPUT3BzbeSAQpRNkkMQlSlpnerz3FbIP18qUU9jC4AKGjs3pfImmya3nNNIQpRFkkMQlQlnzpQ5xZAgb9Lb05y02uvel/Kqacpx+H8ftDooMldVRCoECWTxCBEVbMe0ZfRz+BuuFJD0Os06HWl/Bz//kV9juymXlAnRDWSxCBEVbNejXx6c6kXu7kZrtQQSq0tgHrrzsLrFqIaSWIQoqr5N1CHwc43qfdjLkHhZFBqYsjNgNNb1NcN7qiqKIUokSQGIaqaRgNRt6uvrVcpF8O9cI3BUEpiOBULFjP41lWvrhaimkliEKI6NChIDMdLTgzlbkqyrqPB7WrSEaKaSWIQojpEdlPPIEr5By6dLraIXVNSaTWG42vVZ2stRIhqJolBiOrg6gNhbdXXcVuKL1IoMbi6lPBTTD+vJhc0UC+6ioMUonhOnxjS09MZM2YMdevWxc3NjS5durB9+/ZSl1m/fj3t27fH1dWV+vXrM2/evBqKVohC6hYMj1FCYnDRXmkWctGV0EQUv1V9Dm4uVzuLGuP0ieHpp58mJiaG7777jv3799OnTx/uuOMOzp4tfpCykydP0r9/f7p27cru3bt5/fXXGT16NMuWLavhyMVNzzpu0uniE0Ph6xZctCX8FK3LRnSqysiEKFUZ1+A7VnZ2NsuWLeO///0v3bp1A2DKlCn89NNPfP7557z99ttFlpk3bx4RERHMnj0bgKZNm7Jjxw4+/PBDBg0aVOzn5Obmkpuba3uflpYGgNlsxmw2lztea9mKLFOdnCmemzKW0PboAZKPYE5NBHd/u9kaLLbXOk3x8ehOb0YL5NXuiFLN8TrT/wicK54bIZaKlNcoSjnvXu4A6enpeHt7s3r1am6//UrHW+fOnTEajaxbt67IMt26daNt27bMmTPHNm3FihU8+OCDZGVlodcXHahsypQpTJ06tcj0xYsX4+7uXjV/jLgp9Tr8Gl4559gW+SKJvu3t5m1N0rDkuNrP0NbfwrBGFrv5LvnZ9N83Ag0KK5vPJscgVzyLysvKymLw4MGkpqbi7e1datlK1xji4+M5deoUWVlZBAYG0rx5c4xGY2VXVywvLy86d+7MW2+9RdOmTQkODmbJkiVs27aNhg0bFrtMYmIiwcHBdtOCg4PJy8sjOTmZ0NDQIstMmDCBsWPH2t6npaURHh5Onz59ytyAhZnNZmJiYujdu3exCaimOVM8N2ssWlbD7m/pEJyP5fb+9nHsOceS4wcACK8dSv/+re3ma06uR7NPQfGJoNe9j1VrnOBc/yNni+dGiMXaElIeFUoMp0+fZt68eSxZsoT4+HgKVzYMBgNdu3blmWeeYdCgQWhLajOtoO+++44nn3yS2rVro9PpaNeuHYMHD2bXrl0lLqO56lxva5xXT7cyGo3FJjW9Xl+pL0Fll6suzhTPTRdLeEfY/S268/vQXfVZRsOV9wYXl6KxJO0HQFOnfY1uM2f6H4FzxXM9x1KRsuXee7/44ou0bNmSY8eOMW3aNA4ePEhqaiomk4nExER+++03oqOjmTRpEq1atSrzzKHyioqKYv369WRkZBAfH89ff/2F2WwmMjKy2PIhISEkJibaTUtKSsLFxQV/f/9ilxGi2oS2Up8T9sFVrbZ6XRlnJSXsK1hH66LzhKhG5a4xGAwGjh8/TmBgYJF5QUFB9OrVi169evHmm2/y22+/cfr0aW655ZYqC9TDwwMPDw8uXbrEypUrmTFjRrHlOnfuzP/+Zz+q5apVq+jQoYPTZHpxEwlsqt5xLecyXI6DWnVtswqfiaTXFpcY9qrPIa2qOUgh7JU7MXzwwQflXmn//v3LLlROK1euRFEUGjduzD///MO4ceNo3LgxTzzxBKD2D5w9e5Zvv/0WgBEjRvDJJ58wduxYhg8fzpYtW1iwYAFLliypspiEKDcXAwQ3U3fyCXvtE4NdjeGqyntOGlw8rr6WGoOoYU5/HUNqairPP/88TZo0YciQIURHR7Nq1Srb0X9CQgJxcXG28pGRkfz222+sW7eONm3a8NZbbzF37twST1UVotpZj/gT99lNtr+O4aoaw3m1Uxrv2uARUJ3RCVFEpc5KSklJYfLkyfz5558kJSVhsdifZnfx4sUqCQ7gwQcf5MEHHyxx/sKFC4tM6969e6md00LUqNDWsPu7K01DBUq98tlaVmoLwgEqlRgee+wxjh8/zlNPPUVwcHCJZ/sIIbiyc786MegK9zFcVXmX/gXhQJVKDLGxscTGxtK6tRzNCFGmoGbqc8Z5yLpouzWnoXBiuLrGkHRYfQ5pURMRCmGnUn0MTZo0ITs7u6pjEeLGZPQE7zrq6+Rjtskldj4rypVyAY1rIkIh7FQqMXz22We88cYbrF+/npSUFNLS0uweQoirBDZSn5OP2CaVeB1D2lkwZ4LWBfyKv15HiOpUqaYkX19fUlNT6dWrl910RVHQaDTk5+dXSXBC3DACGqk33Ek+aptU4nUM1jK1IkEn196ImlepxPDoo49iMBhYvHixdD4LUR4BBWN7lacpyVomUJqRhGNUKjEcOHCA3bt307ixfHGFKBdrX8GFK01JXkY9LWt7k5iSSmRAoVF8rWUCih8oUojqVqk+hg4dOhAfH1/VsQhx4woo6GO4fBry1Ht/+LjrWT6iExPb5tOxXqEhta1NSdZlhKhhlaoxvPDCC7z44ouMGzeOli1bFhmDqFUrOfdaCDueQaB3B3MWpJ4B/6iSy14+rT771a+Z2IS4SqUSw0MPPQTAk08+aZum0Wik81mIkmg04BsBF/5Wd/wlJYb8PEgtuG2tb0TNxSdEIZVKDCdPnqzqOIS48fnWVRPDpdMll0k7C0o+6AzgGVJzsQlRSKUSQ926dcsuJISwZ60BXI4ruYx1nk84VNHNroSoqHJ/87Zs2VLulWZmZnLw4MFKBSTEDasiiUGakYQDlTsxDBkyhN69e/Pjjz+SkZFRbJlDhw7x+uuv06BBAxndVIirWe/FcLmUpiTrvFpSKxeOU+6mpEOHDvHFF18wefJkHn30URo1akRYWBiurq5cunSJv//+m8zMTO6//35iYmJo0UIG/xLCjtQYxHWi3IlBr9czatQoRo0axa5du9i4cSOnTp0iOzub1q1b89JLL9GzZ0/8/PzKXpkQNyPfglpAxnkwZ4PerWgZW2KQGoNwnEp1Prdr14527dpVdSxC3Njcal25liE9ofjrFNIKTlX1qVOzsQlRiJz2IERN0WjAM1h9nX6+6HxFuTLdWk4IB5DEIERNsu7wMxKLzstNg7xs+3JCOIAkBiFqkpc1MSQVnWedZvQGg3vR+ULUEEkMQtQkW1NSMTUG6zTPoJqLR4hiSGIQoibZmpKK6WOwTpOhMISDlfuspLlz55Z7paNHj65UMELc8LwKdvqlJQYv6V8QjlXuxDBr1iy79xcuXCArKwtfX18ALl++jLu7O0FBQZIYhChJaWcl2ZqSJDEIxyp3U9LJkydtj3feeYc2bdpw+PBhLl68yMWLFzl8+DDt2rXjrbfeqs54hbi+ldqUlGRfRggHqVQfw6RJk/j444/tbu3ZuHFjZs2axcSJE6ssOCFuONadfuYF9d4LhWVIjUE4h0olhoSEBMxmc5Hp+fn5nD9fzJGQEELlEQAaLaCoyaGwdOljEM6hUonh9ttvZ/jw4ezYsQNFUQDYsWMHzz77LHfccUeVBijEDUWrA3d/9XVWsv0863uPwJqNSYirVCoxfP3119SuXZuOHTvi6uqK0Wjk1ltvJTQ0lK+++qrKgsvLy2PixIlERkbi5uZG/fr1mTZtGhaLpcRl1q1bh0ajKfL4+++/qywuIa6JW8FAk9mXrkxTlCvv3WQgSuFYlRpELzAwkN9++42jR4/y999/oygKTZs2pVGjRlUa3Pvvv8+8efNYtGgRzZs3Z8eOHTzxxBP4+Pjw4osvlrrskSNH8Pb2totZCKfgVkt9LpwYTBlgybOfL4SDVCoxWDVq1KjKk0FhW7ZsYeDAgdx1110A1KtXjyVLlrBjx44ylw0KCrKdSiuEU7Hu+LMuXpmWc1l91hmLH45biBpU6cRw5swZfv75Z+Li4jCZTHbzZs6cec2BAURHRzNv3jyOHj1Ko0aN2Lt3L7GxscyePbvMZdu2bUtOTg7NmjVj4sSJ9OzZs8Syubm55Obm2t6npaUBYDabi+1kL4m1bEWWqU7OFI/EcoXO1QctkJ+ZYoshL/0CekBx8yUvL6/U5auLo7fL1ZwpnhshloqU1yjW3uMKWLNmDffccw+RkZEcOXKEFi1acOrUKRRFoV27dqxdu7aiqyyWoii8/vrrvP/+++h0OvLz83nnnXeYMGFCicscOXKEDRs20L59e3Jzc/nuu++YN28e69ato1u3bsUuM2XKFKZOnVpk+uLFi3F3l8HMRNVqfubfNLiwkmNB/TlU+2EAAtIPcts/75PmWps/m053cITiRpSVlcXgwYNJTU21a2YvTqUSQ8eOHbnzzjuZNm0aXl5e7N27l6CgIB599FHuvPNOnnvuuUoHX9jSpUsZN24cH3zwAc2bN2fPnj2MGTOGmTNnMnTo0HKv5+6770aj0fDzzz8XO7+4GkN4eDjJycllbsDCzGYzMTEx9O7dG71eX+7lqoszxSOxXKGNnYlu/btYWj9KTt8PiYmJ4c7wbIw/P4slojP5j/+vxmMCx28XZ47nRoglLS2NgICAciWGSjUlHT58mCVLlqgrcHEhOzsbT09Ppk2bxsCBA6ssMYwbN47XXnuNhx9Wj6patmzJ6dOnmT59eoUSQ6dOnfj+++9LnG80GjEajUWm6/X6Sn0JKrtcdXGmeCQWwFM9XVWbm2r7fBeT2nypdfdH6+Dt40z/I3CueK7nWCpStlKnq3p4eNiOsMPCwjh+/LhtXnJyckmLVVhWVhZarX2IOp2u1NNVi7N7925CQ0OrLC4hrklxZyVZO5/dfGs6GiGKqFSNoVOnTmzatIlmzZpx11138fLLL7N//36WL19Op06dqiy4u+++m3feeYeIiAiaN2/O7t27mTlzJk8++aStzIQJEzh79izffvstALNnz6ZevXo0b94ck8nE999/z7Jly1i2bFmVxSXENSnurCTbNQxyqqpwvEolhpkzZ5KRkQGoHbcZGRn88MMPNGjQoMgorNfi448/ZtKkSYwcOZKkpCTCwsJ49tlnmTx5sq1MQkICcXFxtvcmk4lXXnmFs2fP4ubmRvPmzfn111/p379/lcUlxDVx9VGfc9NskzQ5qfbzhHCgSiWG+vXr2167u7vz2WefVVlAhXl5eTF79uxST09duHCh3fvx48czfvz4aolHiCph8FKfczOuTDNl2M8TwoEqfQe3y5cv89VXXzFhwgQuXlSrxLt27eLs2bNVFpwQNySjp/psSleHwgAwZdrPE8KBKlVj2LdvH3fccQc+Pj6cOnWK4cOH4+fnx4oVKzh9+rStvV8IUQxDwc5fsUBetvraVmOQxCAcr1I1hrFjxzJs2DCOHTuGq6urbXq/fv3YsGFDlQUnxA2p8M6/oDlJY21WkhqDcAKVSgzbt2/n2WefLTK9du3aJCYmXnNQQtzQtFrQe6ivrTUF6WMQTqRSicHV1dU2nlBhR44ckVFMhSgPY0ECuDoxGCUxCMerVGIYOHAg06ZNsw3KpNFoiIuL47XXXmPQoEFVGqAQN6SCJiONNSHkpttNF8KRKpUYPvzwQy5cuEBQUBDZ2dl0796dBg0a4OXlxTvvvFPVMQpx47H2M+RmoFHy0OTn2k8XwoEqdVaSt7c3sbGxrF27ll27dmGxWGjXrp3c1lOI8irUlOSSn1d0uhAOdE036unVqxe9evWqqliEuHlYawamDFysQ3/pjKBzjgHaxM2t0olhzZo1rFmzhqSkpCKD2n399dfXHJgQN7RCfQwu+S5204RwtEolhqlTpzJt2jQ6dOhAaGgoGo2mquMS4sZWqI/BxWK0nyaEg1UqMcybN4+FCxfy+OOPV3U8QtwcjIWakvILhsWQ/gXhJCqVGEwmE126dKnqWIS4eegLbhmbl4POUtCvoHdzXDxCFFKp01WffvppFi9eXNWxCHHzcFGbjzR5uWiVgpu0u7iWsoAQNafcNYaxY8faXlssFr788ktWr15Nq1atitwybubMmVUXoRA3ImsSyMtBZymoPbgUvb2sEI5Q7sSwe/duu/dt2rQB4MCBA3bTpSNaiHKwJQapMQjnU+7E8Oeff1ZnHELcXOxqDJIYhHOp9I16hBDXwNpslJeDzmIqmCaJQTgHSQxCOEKxTUnSxyCcwzUNiSGEqKSCxKDJy0EnfQzCyUiNQQhHsNYO8qXGIJyPJAYhHKFwU5J0PgsnI4lBCEco3PksNQbhZCQxCOEIUmMQTkwSgxCOoL+SGKTGIJyNJAYhHKHQBW7afLmOQTgXSQxCOIJ1ED0UqTEIpyOJQQhHKFQ70MqVz8LJSGIQwhF0BttLF0tuwQupMQjn4NSJIS8vj4kTJxIZGYmbmxv169dn2rRpRe4xfbX169fTvn17XF1dqV+/PvPmzauhiIUoJ43GVkOQK5+Fs3HqITHef/995s2bx6JFi2jevDk7duzgiSeewMfHhxdffLHYZU6ePEn//v0ZPnw433//PZs2bWLkyJEEBgYyaNCgGv4LhCiFi1HtfJbTVYWTcerEsGXLFgYOHMhdd90FQL169ViyZAk7duwocZl58+YRERHB7NmzAWjatCk7duzgww8/lMQgnIuLK5AqQ2IIp+PUiSE6Opp58+Zx9OhRGjVqxN69e4mNjbXt9IuzZcsW+vTpYzetb9++LFiwALPZXORucwC5ubnk5uba3qelpQFgNpsxm83ljtdatiLLVCdnikdiKcpFZ0QD6Cx5ajwaF3BgTM6yXaycKZ4bIZaKlHfqxPDqq6+SmppKkyZN0Ol05Ofn88477/DII4+UuExiYiLBwcF204KDg8nLyyM5OZnQ0NAiy0yfPp2pU6cWmb5q1Src3d0rHHdMTEyFl6lOzhSPxHJFr9w8vACNoiaGtRs2k2M44tCYwPHb5WrOFM/1HEtWVla5yzp1Yvjhhx/4/vvvWbx4Mc2bN2fPnj2MGTOGsLAwhg4dWuJyV99eVFGUYqdbTZgwwe6e1mlpaYSHh9OnTx+8vb3LHa/ZbCYmJobevXsXWzOpac4Uj8RSlMvZGZBzDh35APS6oy94BjksHmfZLs4Yz40Qi7UlpDycOjGMGzeO1157jYcffhiAli1bcvr0aaZPn15iYggJCSExMdFuWlJSEi4uLvj7+xe7jNFoxGgs2r6r1+sr9SWo7HLVxZnikVgKcbH/bL3RDZxg2zh8u1zFmeK5nmOpSFmnPl01KysLrdY+RJ1OV+rpqp07dy5SxVq1ahUdOnRwmn+oEABoXUp/L4SDOHViuPvuu3nnnXf49ddfOXXqFCtWrGDmzJncd999tjITJkxgyJAhtvcjRozg9OnTjB07lsOHD/P111+zYMECXnnlFUf8CUKUTHvVgYpODlyEc3DqQ5SPP/6YSZMmMXLkSJKSkggLC+PZZ59l8uTJtjIJCQnExcXZ3kdGRvLbb7/x0ksv8emnnxIWFsbcuXPlVFXhfLS6q95LYhDOwakTg5eXF7Nnzy719NSFCxcWmda9e3d27dpVfYEJURWuriFcnSiEcBCnbkoS4oZWqIagaF3UYTKEcAKSGIRwlMKdzdLxLJyIJAYhHEUniUE4J0kMQjhK4WQgZyQJJyKJQQhHKXwWktQYhBORb+M1yM/PtxuYymw24+LiQk5ODvn5+Q6MzPnikViKYfAHz3AAFI9ANDk5jgnDYChyIam4uUliqARFUUhMTOTy5ctFpoeEhBAfH1/iuEw1yZnikViKEXoX+HdXX2td4ORJh4Sh1WqJjIx0+P9FOA9JDJVgTQpBQUG4u7vbflAWi4WMjAw8PT2d4gjMmeKRWIqR5go5lwBQtHo0AZE1HoLFYuHcuXMkJCQUO/KwuDlJYqig/Px8W1K4elA+i8WCyWTC1dXV4Ts/Z4tHYilGrh7y1IMKxUWHxtUxd3ALDAzk3LlzDm/iE87D8Xuv64y1T6Ey92kQwp6mhNc1y2AwAEhiEDaSGCpJ2mPFNdM4R2Kwfpet9y0RQhKDEA5TKBnIgYZwIpIYhHAUTYlvhHAoSQxCOIzUGIRzksQgasyAAQN46aWXrmkdPXr0YMyYMbb3iqLwzDPP4Ofnh0ajYc+ePdcW5DXEUnGSDIRzksRwk9qzZw8PP/wwISEhGAwGoqKimDJlit2V3NeDP/74g4ULF/LLL7+QkJBAixYtHB1S+UlTknBSkhhuQl9//TUdO3YkODiYX375hcOHDzNp0iTmzp3LsGHDHB1ehRw/fpzQ0FC6dOlCSEgILi5lX5pjMplqILLyKD4ZOE984mYliaEKKIpClimPLFMe2aZ82+uaeFT0FMP169czfPhw5s+fz5w5c+jQoQNRUVEMGzaMDz74gMWLF/P3339X05ZSLy4bP348fn5+hISEMGXKFLv5f/zxB9HR0fj6+uLv78+AAQM4fvx4sesaNmwYL7zwAnFxcWg0GurVq1dsuR49ejBq1CjGjh1LQEAAffv2BdT/24wZM6hfvz5ubm60bt2a//znP0Xiff/992nQoAFGo5GIiAjeeeedKv17evxrOKNem2qLr3fv3qSnp/Poo4/i4eFBaGgos2bNKrYZraz4hagMufK5CmSb82k2eaVDPvvQtL64G8r/b3zppZfo168fQ4cOLTKvZ8+eAOzdu5cmTZoUmf/uu+/y7rvvlrr+33//na5du5Y4/9tvv2Xs2LFs27aNLVu2MGzYMG677TZ69+4NQGZmJmPHjqVly5ZkZmYyefJk7rvvPvbs2VPkKuU5c+YQFRXFl19+yfbt29HpSr415qJFi3juuefYtGmT7UKuSZMmsWLFCj7//HMaNmzIhg0beOyxxwgMDKR7d3UMowkTJjB//nxmzZpFdHQ0CQkJdolz0aJFlf97CtUYvl26gudGjmTTpk0oisLYsWPZtGkTP//8M8HBwUyePJldu3bRpk0b2zITJ05k+fLlpcYvRGVIYriJ7N+/n927d9sd8RaWnZ0NUGJzzIgRI3jwwQdL/YzatWuXOr9Vq1a8+eabADRs2JBPPvmENWvW2HakgwYNsiu/YMECgoKCOHToUJH+Ax8fH7y8vNDpdISEhJT6uQ0aNGDGjBmAepSfkJDArFmzWLt2LZ07dwagfv36xMbG8sUXX9C9e3fS09OZM2cOn3zyiS2RRkVFER0dXTV/T2TwlfjqR9jiS09PZ9GiRSxevJjbb78dgG+++YawsDBb+czMTGbOnFlq/EJUliSGKuCm13FoWl8sFgvpael4eXvV2Bg8bvry30DeesZO4aPOwnbt2gVA69ati53v5+eHn59fheK7WsuWLe3eh4aGkpSUZHt//PhxJk2axNatW0lOTsZisQAQFxd3TR3LHTp0sHt/5MgRcnJybDtwK5PJRNu2bQE4fPgwubm5tp1zcVq1alX5v6dQYmjf+sp2OXHiBGazmY4dO9qm+fj40LhxY9v7Q4cOlRm/EJUliaEKaDQa3A0uWCwW8gw63A0uDh8orjjWTk3XEgZr+/TTT+nSpQsNGjQodn5VNCXp9fZ3KtNoNLadJcDdd99NeHg48+fPJywsDIvFQosWLa65Q9bDw8PuvfUzf/311yK1HKPRCICbm1uZ6722v+dKU5KHx5Wxt6z9RlcPu1K4P6k88QtRWZIYbiLWo9v169dz77332s376KOP2L9/Pxs2bChx+apoSipNSkoKhw8f5osvvrAll9jY2EqvrzSNGzfGaDQSFxdXYrNLw4YNcXNzY82aNTz99NMV/ozK/j1RUVHo9Xr++usvwsPVG/mkpaVx7NgxW6zNmjUrM34hKksSw03klltu4c477+T555/HbDbToUMHzp8/z1dffcWSJUtYvnw57du3L3H5qmhKKk2tWrXw9/fnyy+/JDQ0lLi4OF577bVq+SwvLy9efvllXnrpJSwWC9HR0aSlpbF582Y8PT0ZOnQorq6uvPrqq4wfPx6DwcBtt93GhQsXOHjwIE899VS1/T1eXl4MHTqUcePG4efnR1BQEG+++SZardZWi/Dy8uKVV14pNX4hKksSw01m2bJlTJ06lXHjxnHmzBny8/O58847OXr06DUd7VcFrVbL0qVLGT16NC1atKBx48bMnTuXHj16VMvnTZs2jeDgYKZPn86JEyfw9fWlXbt2vP7667YykyZNwsXFhcmTJ3Pu3DlCQ0MZMWJE1fw9pQyDMXPmTEaMGMGAAQPw9vZm/PjxxMfH2zUDvvXWWwQFBZUavxCVoogiUlNTFUBJTU0tMi87O1s5dOiQkp2dXWRefn6+cunSJSU/P78mwixTeeIZPny4EhkZqVy8eNHhsdQUp4klM1lRzu5SlLO7FEvKyVKLZmRkKD4+PspXX31V5WFYv9NpaWnKTz/9pJhMpir/jMowmUxOE8+NEEtp+7WrOV8PqahRH3/8MU899ZTtjCRRkzTFvgTYvXs3S5Ys4fjx4+zatYtHH30UgIEDB9ZgfOJmJU1JNzmj0cgbb7zh6DBEMcNjfPjhhxw5cgSDwUD79u3ZuHEjAQEBDohN3GwkMQjhhNq2bcvOnTsdHYa4STl9U1K9evXQaDRFHs8//3yx5detW1ds+eoc/0eISpF7MAgn5fQ1hu3bt9vdpPzAgQP07t2bBx54oNTljhw5gre3t+19YGBgtcUoxLWTJCGch9Mnhqt36O+99x5RUVFlXtQTFBSEr69vuT4jNzeX3Nxc2/u0tDQAzGZzkfsTmM1mFEXBYrHYXeEKV65Mtc53NGeKR2IpSqNcSQcKoDgoFovFgqIo5OXlATjNPTmscThDPDdCLBUp7/SJoTCTycT333/P2LFjiwwXcLW2bduSk5NDs2bNmDhxom3k0OJMnz6dqVOnFpm+atUq3N3d7aa5uLgQEhJCRkZGicM0pKenl+OvqTnOFI/EcoVLXhaeBa/NZhPZBQckNc1kMpGdnc3mzZsBiImJcUgcJXGmeK7nWLKysspdVqMoFRzQ34F+/PFHBg8eTFxcnN1Ik4UdOXKEDRs20L59e3Jzc/nuu++YN28e69ato1u3bsUuU1yNITw8nOTkZLvmKICcnBzi4+OpV69ekTGHFEUhPT0dLy+vMhNXTXCmeCSWojS5aWgunQTA4h4A3o65wDAnJ4dTp04RGhrKhg0b6N27d5ExoBzBbDYTExPjFPHcCLGkpaUREBBAampqkf3a1a6rGsOCBQvo169fiUkB1DFwCo9C2blzZ+Lj4/nwww9LTAxGo7HYgcf0en2RDZ+fn49Go0Gr1RYZKM/aLGGd72jOFI/EUoxCSUkDaBwUi3WoDetw68V97x3JmeK5nmOpSFnH773K6fTp06xevbpSg5l16tSJY8eOVUNUQlyLwhe4Ob6GKYTVdZMYvvnmG4KCgrjrrrsqvOzu3bsJDQ2thqiEEOLGc100JVksFr755huGDh1a5O5iEyZM4OzZs3z77bcAzJ49m3r16tG8eXNbZ/WyZctYtmyZI0IXQojrznWRGFavXk1cXBxPPvlkkXkJCQnExcXZ3ptMJl555RXOnj2Lm5sbzZs359dff6V///41GbIQZbNrPpKmJOE8rovE0KdPH0o6eWrhwoV278ePH8/48eNrICrh7Hr06EGbNm2YPXv2TfG5QlSV66aPQVStPXv28PDDDxMSEoLBYCAqKoopU6ZU6wU8AwYM4KWXXqrwcj169GDMmDFVH5DDSeezcE6SGG5CX3/9NR07diQ4OJhffvmFw4cPM2nSJObOncuwYcMcHZ7DXOt9pauTM8cmbjySGKqCooApU32Ys668rolHBa9PXL9+PcOHD2f+/PnMmTOHDh06EBUVxbBhw/jggw9YvHhxtQw4+MQTT7Bp0ybmzp1rG9jw1KlT5ObmMnr0aIKCgnB1dSU6Oprt27fblhs2bBjr169nzpw5dsv98ccfREdH4+vri7+/PwMGDOD48eMViqlXr16MGjWKsWPHEhAQQO/evQH1ArgZM2ZQv3593NzcaN26Nf/5z39sy1ksFt5//30aNGiA0WgkIiKCd955x27dFouF8ePH4+fnR0hICFOmTLGb/8cffxDdsze+Tbvh37wndz84xC7+Hj16FBtbeno6jz76KB4eHoSGhjJr1qwiNaqy4heiLNdFH4PTM2fBu2FoAd+a/uzXz4HBo9zFX3rpJfr161fsPYGtw4bs3buXJk2aFJn/7rvv8u6775a6/t9//9124/vCZs+ezeHDh2ndujVvvfUWoI6DNXbsWJYtW8aiRYuoW7cuM2bMoG/fvvzzzz/4+fkxZ84cjh49SosWLZg2bZptuZ07dzJ27FhatmxJZmYmkydP5r777mPPnj0Vumht0aJFPPfcc2zatMnWjzVx4kSWL1/O559/TsOGDdmwYQOPPfYYgYGBdO/enQkTJjB//nxmzZpFdHQ0CQkJRZLpokWLGDt2LNu2bWPLli0MGzaM2267zbaDz8zMZOyYF2gZ5kFmVjaTZ39dJP7iYhs7diybNm3i559/Jjg4mMmTJ7Nr1y7atGlj++yy4heiLJIYbiL79+9n9+7dRY5urbKzswGKnBJsNWLECB588MFSP6Ok+0b7+PhgMBhwd3cnJCQEUHeOn3/+OQsXLqRfv34AzJ8/n5iYGBYsWMC4ceOKXQ5g0KBBdutfsGABQUFBHDp0iBYtWpQaY2ENGjRgxowZtveZmZnMnDmTtWvX0rlzZwDq169PbGwsX3zxBe3atWPOnDl88skntuQaFRVFdHS03XpbtWrFm2++CUDDhg355JNPWLNmjS0xDBo0SK3xJR8F4KtPZhIc1dIu/qtjS09PZ9GiRSxevJjbb78dUK/vKTwSQFnxS2IQ5SGJoSro3eH1c1gsFtLS0/H28qq5oRb07mWXKbBnzx4Au6PLwqy392zdunWx8/38/PDz86tQeKU5fvw4ZrOZ2267zTZNr9fTsWNHDh8+XOaykyZNYuvWrSQnJ9uGuYiLi6tQYujQoYPd+0OHDpGTk2PbgVuZTCbatm3L4cOHyc3Nte2YS9KqVSu796GhoSQlJdnH/8YEtm7ZTPLFy1gKagSF4786thMnTmA2m+nYsaNtmo+Pj90QMGXFL0R5SGKoChqN2pxjsYA+X33tBGMlXc3agXn14H9Wn376KV26dKFBgwbFzr+WpqTiWJtHrh7ITlGUMge3u/vuuwkPD2f+/PmEhYVhsVho0aJFhTtpPTzsm+GsCebXX38tUvsxGo1cvny5XOu9elwajUZjN8T33XffTXjtMObPmEhYSCD5bgG0vLWHXfxXx1ba9ipv/EKUhySGm4j1KHb9+vXce++9dvM++ugj9u/fz4YNG0pc/lqakgAMBoPdTZcaNGiAwWAgNjaWwYMHA+rIkTt27LDrTL16uZSUFA4fPswXX3xhS0KxsbGlxlVezZo1w2g0EhcXV2yzS2BgIG5ubqxZs6ZS43ZBofg/nUPXxuo9nDceiCtjKbXJSq/X89dffxEeHg6oI2YeO3bMFmtZ8QtRHpIYbiK33HILd955J88//zxms5kOHTpw/vx5vvrqK5YsWcLy5ctp3759ictfa1NSREQEf/31F6dOncLT0xM/Pz+ee+45xo0bh5+fHxEREcyYMYOsrCyeeuop23L16tVj27Ztdsv5+/vz5ZdfEhoaSlxcHK+99lql4yrMy8uLV155hZdeegmLxUJ0dDRpaWls3rwZT09Phg4dyquvvsr48eMxGAzcdtttXLhwgYMHD9rFXJpatWqp8X/1DaEjHyLubCKvvT+vXLENHTrUtr2CgoJ48803baOjljd+IcoiieEms2zZMqZOncq4ceM4c+YM+fn53HnnnRw9erTUo/2qMGrUKF544QWaNWtGdnY2J0+e5L333sNisfD444+Tnp5Ohw4dWLlyJbVq1bIt98orrzB06FC75ZYuXcro0aNp0aIFjRs3Zu7cufTo0aNK4nzrrbcICgpi+vTpnDhxAl9fX9q1a8frr78OwKRJk3BxcWHy5MmcO3eO0NBQRowYUe71a7VaNf4XXqDF7ctoXL8ucz56n5797y9z2ZkzZzJixAgGDBiAt7c348ePJz4+3q55sKz4hSiTIopITU1VACU1NbXIvOzsbOXQoUNKdnZ2kXn5+fnKpUuXlPz8/JoIs0zliWf48OFKZGSkcvHiRYfHUlOcJhZTtqKc3aUoZ3cplvTzlVpFRkaG4uPjo3z11VeVDsP6nU5LS1N++uknxWQyVXpdVclkMjlNPDdCLKXt167mfD2kokZ9/PHHPPXUU7YzkoRz2717N0uWLOH48ePs2rWLRx99FICBAwc6ODJxI5GmpJuc0WjkjTfecHQYNydNiW9K9eGHH3LkyBEMBgPt27dn48aNBAQEVHl44uYliUEIh6n4wHlt27Zl586d1RCLEFdIU5IQQgg7khiEcBgZdls4J0kMQjiKVoti8CJPYwCX4q9GF8IRJDFUklLB4a6FKELrguJXnwy32igVGPOqqiklDLUhbl6SGCrIOgZOVlaWgyMRompYx2fS6XQOjkQ4CzkrqYJ0Oh2+vr62kTLd3d1tR1oWiwWTyUROTk7Nja5aCmeKR2JxzlgsFgsXLlzA3d1dEoOwkcRQCdb7AhQeRhnUKnl2djZubm5OUS13pngkFueNRavVEhER4fBtIZyHJIZK0Gg0hIaGEhQUhNlstk03m81s2LCBbt26FRl22RGcKR6JxXljMRgMaLVau++yuLlJYrgGOp3Orvqt0+nIy8vD1dXV4TscZ4tHYnH+WISwcnxDuBBCCKciiUEIIYQdSQxCCCHsSB9DMawX/KSlpVVoObPZTFZWFmlpaU7RXuxM8UgsEsv1HM+NEIt1f1aei3MlMRQjPT0dwHZfXSGEuFGkp6fj4+NTahmNImM7FGGxWDh37hxeXl4VOrc7LS2N8PBw4uPj8fb2rsYIr794JBaJ5XqO50aIRVEU0tPTCQsLK/NiSqkxFEOr1VKnTp1KL+/t7e3wL09hzhSPxFI8iaVkzhTP9R5LWTUFK+l8FkIIYUcSgxBCCDuSGKqQ0WjkzTffxGg0OjoUwLnikVgklopypnhutlik81kIIYQdqTEIIYSwI4lBCCGEHUkMQggh7EhiEEIIYUcSQxmmT5/OLbfcgpeXF0FBQdx7770cOXLEroyiKEyZMoWwsDDc3Nzo0aMHBw8etCuTm5vLCy+8QEBAAB4eHtxzzz2cOXOmwvFs2LCBu+++m7CwMDQaDT/99JPd/GHDhqHRaOwenTp1ckgsNbldrjZlypQi28F6573yxlYTPvvsMyIjI3F1daV9+/Zs3Lix2j/TkdvGmb4zzvRbcrb9jCSGMqxfv57nn3+erVu3EhMTQ15eHn369CEzM9NWZsaMGcycOZNPPvmE7du3ExISQu/evW1jLgGMGTOGFStWsHTpUmJjY8nIyGDAgAHk5+dXKJ7MzExat27NJ598UmKZO++8k4SEBNvjt99+s5tfU7HU5HYpTvPmze22w/79+ysUW3X74YcfGDNmDG+88Qa7d++ma9eu9OvXj7i4uGr/bEdtG2f6zjjTb8nZ9jMookKSkpIUQFm/fr2iKIpisViUkJAQ5b333rOVycnJUXx8fJR58+YpiqIoly9fVvR6vbJ06VJbmbNnzyparVb5448/Kh0LoKxYscJu2tChQ5WBAweWuExNxeLI7aIoivLmm28qrVu3LnZeeWKrCR07dlRGjBhhN61JkybKa6+9Vq2f6yzbxpm+M870W1IUx+9npMZQQampqQD4+fkBcPLkSRITE+nTp4+tjNFopHv37mzevBmAnTt3Yjab7cqEhYXRokULW5mqtG7dOoKCgmjUqBHDhw8nKSnJNq+mYnGG7XLs2DHCwsKIjIzk4Ycf5sSJE+WOrbqZTCZ27txpFwNAnz59aiQGZ9w2zvCduZqjfkuO3s9IYqgARVEYO3Ys0dHRtGjRAoDExEQAgoOD7coGBwfb5iUmJmIwGKhVq1aJZapKv379+Pe//83atWv56KOP2L59O7169SI3N7dGY3H0drn11lv59ttvWblyJfPnzycxMZEuXbqQkpJSrtiqW3JyMvn5+Q6JwVm3jaO/M1dz1G/JGfYzMrpqBYwaNYp9+/YRGxtbZN7Vw3MrilLmkN3lKVNRDz30kO11ixYt6NChA3Xr1uXXX3/l/vvvr9FYwHHbpV+/frbXLVu2pHPnzkRFRbFo0SJbB2JlYqtqjojB2bfNzf5bcob9jNQYyumFF17g559/5s8//7Qbktt6NsfVGTkpKcmW3UNCQjCZTFy6dKnEMtUlNDSUunXrcuzYsRqNxdm2i4eHBy1btuTYsWPliq26BQQEoNPpHBqDlbNsG2f7zlytJn5LzrKfkcRQBkVRGDVqFMuXL2ft2rVERkbazY+MjCQkJISYmBjbNJPJxPr16+nSpQsA7du3R6/X25VJSEjgwIEDtjLVJSUlhfj4eEJDQ2s0FmfbLrm5uRw+fJjQ0NByxVbdDAYD7du3t4sBICYmpsZisHKWbeNs35mrVedvyen2MxXvL7+5PPfcc4qPj4+ybt06JSEhwfbIysqylXnvvfcUHx8fZfny5cr+/fuVRx55RAkNDVXS0tJsZUaMGKHUqVNHWb16tbJr1y6lV69eSuvWrZW8vLwKxZOenq7s3r1b2b17twIoM2fOVHbv3q2cPn1aSU9PV15++WVl8+bNysmTJ5U///xT6dy5s1K7du0aj6Wmt8vVXn75ZWXdunXKiRMnlK1btyoDBgxQvLy8lFOnTpU7tuq2dOlSRa/XKwsWLFAOHTqkjBkzRvHw8LDFWF0cuW2c6TvjTL8lZ9vPSGIoA1Ds45tvvrGVsVgsyptvvqmEhIQoRqNR6datm7J//3679WRnZyujRo1S/Pz8FDc3N2XAgAFKXFxcheP5888/i41n6NChSlZWltKnTx8lMDBQ0ev1SkREhDJ06NAin1MTsdT0drnaQw89pISGhip6vV4JCwtT7r//fuXgwYO2+eWJrSZ8+umnSt26dRWDwaC0a9fOdnpidXLktnGm74wz/ZacbT8jw24LIYSwI30MQggh7EhiEEIIYUcSgxBCCDuSGIQQQtiRxCCEEMKOJAYhhBB2JDEIIYSwI4lBCCGEHUkM4oaxcOFCfH19be+nTJlCmzZtKrSO4m7xWJYePXowZswY2/t69eoxe/bsCq3jetKtWzcWL158Tev45JNPuOeee6ooIlHVJDGIG9Yrr7zCmjVravxzt2/fzjPPPFOustdbEvnll19ITEzk4Ycfvqb1DB8+nO3btxc7tLRwPEkMwqmYTKYqW5enpyf+/v5Vtr7yCgwMxN3dvcY/tybMnTuXJ554Aq322nYdRqORwYMH8/HHH1dRZKIqSWIQDtWjRw9GjRrF2LFjCQgIoHfv3gDMnDmTli1b4uHhQXh4OCNHjiQjI8Nu2YULFxIREYG7uzv33XcfKSkpdvOvbkravn07vXv3JiAgAB8fH7p3786uXbsqFG9mZiZDhgzB09OT0NBQPvrooyJlrq4FTJkyhYiICIxGI2FhYYwePdr2t58+fZqXXnoJjUZju5lKSkoKjzzyCHXq1MHd3Z2WLVuyZMmSIttt9OjRjB8/Hj8/P0JCQpgyZYpdmcuXL/PMM88QHByMq6srLVq04JdffrHN37x5M926dcPNzY3w8HBGjx5td/P5qyUnJ7N69eoiTUAajYYvvviCAQMG4O7uTtOmTdmyZQv//PMPPXr0wMPDg86dO3P8+HG75e655x5++uknsrOzS97gwiEkMQiHW7RoES4uLmzatIkvvvgCAK1Wy9y5czlw4ACLFi1i7dq1jB8/3rbMtm3bePLJJxk5ciR79uyhZ8+evP3226V+Tnp6OkOHDmXjxo1s3bqVhg0b0r9/f9LT08sd67hx4/jzzz9ZsWIFq1atYt26dezcubPE8v/5z3+YNWsWX3zxBceOHeOnn36iZcuWACxfvpw6deowbdo0EhISSEhIACAnJ4f27dvzyy+/cODAAZ555hkef/xxtm3bVmS7eXh4sG3bNmbMmMG0adNsY/FbLBb69evH5s2b+f777zl06BDvvfceOp0OgP3799O3b1/uv/9+9u3bxw8//EBsbCyjRo0q8W+JjY217fiv9tZbbzFkyBD27NlDkyZNGDx4MM8++ywTJkxgx44dAEXW3aFDB8xmM3/99VdZm13UtAqPxypEFerevbvSpk2bMsv9+OOPir+/v+39I488otx55512ZR566CHFx8fH9v7NN99UWrduXeI68/LyFC8vL+V///ufbRqgrFixotjy6enpisFgUJYuXWqblpKSori5uSkvvviibVrdunWVWbNmKYqiKB999JHSqFEjxWQyFbvOwmVL079/f+Xll1+2ve/evbsSHR1tV+aWW25RXn31VUVRFGXlypWKVqtVjhw5Uuz6Hn/8ceWZZ56xm7Zx40ZFq9Uq2dnZxS4za9YspX79+kWmA8rEiRNt77ds2aIAyoIFC2zTlixZori6uhZZtlatWsrChQuL/TzhOFJjEA7XoUOHItP+/PNPevfuTe3atfHy8mLIkCGkpKTYmjoOHz5M586d7Za5+v3VkpKSGDFiBI0aNcLHxwcfHx8yMjKIi4srV5zHjx/HZDLZfY6fnx+NGzcucZkHHniA7Oxs6tevz/Dhw1mxYgV5eXmlfk5+fj7vvPMOrVq1wt/fH09PT1atWlUkzlatWtm9Dw0NJSkpCYA9e/ZQp04dGjVqVOxn7Ny5k4ULF+Lp6Wl79O3bF4vFwsmTJ4tdJjs7G1dX12LnFY7FehtJa83IOi0nJ4e0tDS75dzc3MjKyip2ncJxJDEIh/Pw8LB7f/r0afr370+LFi1YtmwZO3fu5NNPPwXAbDYD6q0QK2rYsGHs3LmT2bNns3nzZvbs2YO/v3+5O7wr85nh4eEcOXKETz/9FDc3N0aOHEm3bt1sf0dxPvroI2bNmsX48eNZu3Yte/bsoW/fvkXi1Ov1du81Gg0WiwVQd7ilsVgsPPvss+zZs8f22Lt3L8eOHSMqKqrYZQICAorcT7i4WKx9JcVNs8ZndfHiRQIDA0uNVdQ8F0cHIMTVduzYQV5eHh999JHt7Jcff/zRrkyzZs3YunWr3bSr319t48aNfPbZZ/Tv3x+A+Ph4kpOTyx1XgwYN0Ov1bN26lYiICAAuXbrE0aNH6d69e4nLubm5cc8993DPPffw/PPP06RJE/bv30+7du0wGAzk5+cXiXPgwIE89thjgLozPXbsWLFt+yVp1aoVZ86c4ejRo8XWGtq1a8fBgwdp0KBBudfZtm1bEhMTuXTpErVq1Sr3ciU5fvw4OTk5tG3b9prXJaqW1BiE04mKiiIvL4+PP/6YEydO8N133zFv3jy7MqNHj+aPP/5gxowZHD16lE8++YQ//vij1PU2aNCA7777jsOHD7Nt2zYeffTRMo+sC/P09OSpp55i3LhxrFmzhgMHDjBs2LBST91cuHAhCxYs4MCBA7a/xc3Njbp16wLqGUwbNmzg7NmztiTVoEEDYmJi2Lx5M4cPH+bZZ58lMTGx3HECdO/enW7dujFo0CBiYmI4efIkv//+u20bvfrqq2zZsoXnn3+ePXv2cOzYMX7++WdeeOGFEtfZtm1bAgMD2bRpU4ViKcnGjRupX79+iTUU4TiSGITTadOmDTNnzuT999+nRYsW/Pvf/2b69Ol2ZTp16sRXX33Fxx9/TJs2bVi1ahUTJ04sdb1ff/01ly5dom3btjz++OOMHj2aoKCgCsX2wQcf0K1bN+655x7uuOMOoqOjad++fYnlfX19mT9/PrfddhutWrVizZo1/O9//7NdXzFt2jROnTpFVFSUrUll0qRJtGvXjr59+9KjRw9CQkK49957KxQnwLJly7jlllt45JFHaNasGePHj7fVTlq1asX69es5duwYXbt2pW3btkyaNInQ0NAS16fT6XjyySf597//XeFYirNkyRKGDx9eJesSVUvu+SyEKLfz58/TvHlzdu7caav1VMaBAwe4/fbbOXr0KD4+PlUYoagKUmMQQpRbcHAwCxYsKPeZXCU5d+4c3377rSQFJyU1BiGEEHakxiCEEMKOJAYhhBB2JDEIIYSwI4lBCCGEHUkMQggh7EhiEEIIYUcSgxBCCDuSGIQQQtiRxCCEEMLO/wMh/IlRCqWFiQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 400x320 with 1 Axes>"
      ]
     },
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    }
   ],
   "source": [
    "# plot\n",
    "fig = plt.figure(figsize=diagrams_2d.figdef1new)\n",
    "plt.plot(r, hhalf, 'C0', label='$Q$ = half recharge')\n",
    "plt.plot(-r, hhalf, 'C0')\n",
    "plt.plot(r, htotal, 'C1', label='$Q$ = total recharge')\n",
    "plt.plot(-r, htotal, 'C1')\n",
    "plt.xticks(np.arange(-200, 201, 50), np.abs(np.arange(-200, 201, 50)))\n",
    "plt.xlabel('radial distance (m)')\n",
    "plt.ylabel('head (m)')\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "glue(\"fig_head\", fig, display=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{glue:figure} fig_head\n",
    "---\n",
    "name: fig_hea_cen_isl6.1\n",
    "---\n",
    "Head along centerline of a circular island for unconfined flow with uniform recharge and pumping well at the center of the island.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; As expected, the drawdown is much larger for the latter case than for the former case. Note that for the latter case, the flow at the perimeter of the island is zero and thus the slope of the water table is zero there. In the former case, there is still outflow across the island perimeter. Inflow occurs along the perimeter once the well discharge exceeds the total recharge on the island. The maximum discharge of the well is reached when the water level in the well (at $r=r_w$) is at the bottom of the aquifer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{exercise}\n",
    ":label: ex_61_total_recharge\n",
    "\n",
    "Consider the case of a well at the center of a circular island with recharge where the discharge of the well is equal to half the total recharge on the island, using the example values above. Compute the distance $r_d$ from the center of the well to the water divide by setting $Q_r|_{r=r_d}=0$. Compare the total recharge on a circle with radius $r_d$ to the discharge of the well.\n",
    "\n",
    "<details>\n",
    "<summary><strong> Solution </strong></summary>\n",
    "\n",
    "$r_d = 141.4$ m\n",
    "\n",
    "</details>\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{exercise}\n",
    ":label: ex_62_total_flow_well\n",
    "\n",
    "Consider the case of a well at the center of a circular island with recharge where the discharge of the well is equal to half the total recharge on the island, using the example values above. Compute the total flow into the well at $r=r_w$ by integrating $Q_r$ around the well radius, and compare your answer to the discharge of the well. Is boundary condition ({eq}`eq_bc_well_approx6.1`) a good approximation?\n",
    "\n",
    "<details>\n",
    "<summary><strong> Solution </strong></summary>\n",
    "\n",
    "$Q = 62.83$ m$^3$/d\n",
    "\n",
    "</details>\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{exercise}\n",
    ":label: ex_63_redo_62_bottom\n",
    "\n",
    "For the example given above of a well at the center of a circular unconfined island with recharge, compute the maximum discharge of the well by setting the head at the well equal to the bottom of the aquifer.\n",
    "\n",
    "<details>\n",
    "<summary><strong> Solution </strong></summary>\n",
    "\n",
    "$Q = 251.2$ m$^3$/d\n",
    "\n",
    "</details>\n",
    "\n",
    "```"
   ]
  }
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