{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "from myst_nb import glue\n",
    "%config InlineBackend.rc = {'figure.dpi': 300}\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "mpl.rcParams['contour.negative_linestyle'] = 'solid'\n",
    "import sys\n",
    "sys.path.append(\"../py_figures\")\n",
    "import diagrams_2d_chap6 as diagrams_2d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": true
   },
   "source": [
    "(content:chap6.4:well_sem_con_aqu)=\n",
    "# Wells in a semi-confined aquifer\n",
    "Steady flow to a well in the bottom aquifer of a two-aquifer system is considered in the next two sections. The two aquifers are separated by a leaky layer. In this section, the head in the top aquifer is fixed, for example by a system of ditches and drains, so that the bottom aquifer is a semi-confined aquifer ({numref}`Figure %s <fig_well_pumping6.4>`). The case for a two-aquifer system, where water is flowing through both aquifers, is presented in the next section. Recall that solutions for semi-confined flow and two-aquifer flow were written in terms of heads in {numref}`Chapter %s <content:chap2:steady_semi_flow>` as the discharge potentials defined in Table ({numref}`%s <tab_def_dis_pot6.0>`) cannot be used."
   ]
  },
  {
   "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_bessel"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_bessel = diagrams_2d.solution_bessel_well()\n",
    "glue('fig_bessel', fig_bessel, display=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{glue:figure} fig_bessel\n",
    "---\n",
    "name: fig_well_pumping6.4\n",
    "---\n",
    "A well pumping in a semi-confined aquifer.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The differential equation for steady radially symmetric semi-confined flow is\n",
    "\n",
    "$$\n",
    "\\nabla^2 h = \\frac{\\text{d}^2 h}{\\text{d} r^2}+\\frac{1}{r}\\frac{\\text{d} h}{\\text{d}r} = \\frac{h-h^*}{cT}\n",
    "$$(eq_DE_radial_sym_flow6.4)\n",
    "\n",
    "where $T$ is the transmissivity of the aquifer, $h^*$ is the constant head above the semi-confining layer, and $c$ is the resistance to vertical flow of the semi-confining layer (see {numref}`Chapter %s <content:chap2:steady_semi_flow>`). A solution is sought for radial flow to a fully penetrating well with discharge $Q$. The boundary condition at the well is the same as that for a well in confined flow\n",
    "\n",
    "$$\n",
    "\\lim_{r \\to 0} -2\\pi r Q_r = Q\n",
    "$$(eq_bc2semiwell6.4)\n",
    "\n",
    "The boundary condition at infinity is that the head is equal to the fixed head $h^*$ in the top aquifer\n",
    "\n",
    "$$\n",
    "h|_{r=\\infty} = h^*\n",
    "$$(eq_bc_inf6.4)\n",
    "\n",
    "The solution is ({cite:alp}`deglee1930grondwaterstroomingen`)\n",
    "\n",
    "$$\n",
    "h = h^* -\\frac{Q}{2\\pi T} \\text{K}_0(r/\\lambda)\n",
    "$$(eq_besselwell6.4)\n",
    "\n",
    "where the leakage factor is $\\lambda=\\sqrt{cT}$ (see {numref}`Chapter %s <content:chap2:steady_semi_flow>`) and $\\text{K}_0$ is the modified Bessel function of the second kind and order 0. The Bessel function $\\text{K}_0(r/\\lambda)$ approaches zero for $r$ approaching infinity. In practice, $\\text{K}_0$ can be approximated as zero for $r>4\\lambda$, as will be shown later.\n",
    "<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The main difference between the solutions for pumping in a confined aquifer and pumping in a semi-confined aquifer is that in a confined aquifer, all water pumped by the well comes from infinity (and hence the head keeps increasing toward infinity), while in a semi-confined aquifer, all water pumped by the well comes from the overlying aquifer by leakage through the semi-confining layer.\n",
    "<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The radial component of the discharge vector is obtained from differentiation\n",
    "\n",
    "$$\n",
    "Q_r = -T\\frac{\\text{d}h}{\\text{d}r} = \\frac{-Q}{2\\pi\\lambda}\\text{K}_1(r/\\lambda)\n",
    "$$(eq_Qrsemiwell6.4)\n",
    "\n",
    "where it is used that $\\text{dK}_0/\\text{d}r = -\\text{K}_1$, where $\\text{K}_1$ is the modified Bessel function of the second kind and order 1. It can be shown that $Q_r$ fulfills boundary condition ({eq}`eq_bc2semiwell6.4`) by using that $\\text{K}_1$ may be approximated near $r = 0$ as (e.g., {cite:alps}`abramowitz1965handbook`)\n",
    "\n",
    "$$\n",
    "\\text{K}_1 \\approx \\lambda / r {\\hskip 2em} r/\\lambda \\ll 0\n",
    "$$(eq_k1approx6.4)\n",
    "\n",
    "The total flow $Q_\\text{tot}$ in the aquifer toward the well as a function of the radial distance $r$ may be computed as $-Q_r$ multiplied by the circumference of a circle with radius $r$\n",
    "\n",
    "$$\n",
    "Q_\\text{tot} = -2\\pi r Q_r\n",
    "$$(eq_Q_tot6.4)\n",
    "\n",
    "Substitution of Eq. ({eq}`eq_Qrsemiwell6.4`) for $Q_r$ using Eq. ({eq}`eq_k1approx6.4`) shows that boundary condition (Eq. {eq}`eq_bc2semiwell6.4`)  is indeed fulfilled\n",
    "\n",
    "$$\n",
    "Q_\\text{tot} = -2\\pi r \\frac{-Q}{2\\pi\\lambda} \\frac{\\lambda}{r} = Q {\\hskip 2em} r/\\lambda \\ll 0\n",
    "$$(eq_Q_tot26.4)\n",
    "\n",
    "The head near the well may be approximated as\n",
    "\n",
    "$$\n",
    "h = h^* + \\frac{Q}{2\\pi T} \\ln\\left(\\frac{r}{1.123\\lambda}\\right) {\\hskip 2em} (r/\\lambda \\ll 1)\n",
    "$$(eq_besselwellapprox6.4)\n",
    "\n",
    "where it is used that ({cite:alps}`abramowitz1965handbook`)\n",
    "\n",
    "$$\n",
    "\\text{K}_0(r/\\lambda) \\approx -\\ln\\left(\\frac{r\\text{e}^\\gamma}{2\\lambda}\\right) \\approx -\\ln\\left(\\frac{r}{1.123\\lambda}\\right) {\\hskip 2em} (r/\\lambda \\ll 1)\n",
    "$$(eq_K_0_approx6.4)\n",
    "\n",
    "where $\\gamma=0.5772...$ is Euler’s constant. Note that Eq. ({eq}`eq_besselwellapprox6.4`) is the Thiem solution ({eq}`eq_thiem6.1`) where the head is equal to $h^*$ at a distance of $R=1.123\\lambda$; the approximate formula gives accurate results near the well. The Bessel functions $\\text{K}_0$ and $\\text{K}_1$ are available as `k0` and `k1` in the `scipy.special` package.\n",
    "<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The solution for a well (Eq. {eq}`eq_besselwell6.4`) and the approximate formula ({eq}`eq_besselwellapprox6.4`) near the well are plotted in the left graph of {numref}`Figure %s <fig_well_semi_con_aquifer6.4>`. In the right graph, $Q_\\text{tot}$ is plotted as a function of $r/\\lambda$. Note that $Q_\\text{tot}/Q$ is indeed equal to 1 at the well and reduces to $Q_\\text{tot}/Q=0.05$ at $r=4\\lambda$. For practical purposes, the effect of the well may be neglected beyond a distance of $4\\lambda$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# parameters\n",
    "T = 200 # transmissivity of bottom aquifer, m^2/d\n",
    "c = 1000 # resistance of leaky layer, d\n",
    "hstar = 0 # fixed head in top aquifer, m\n",
    "rw = 0.3 # radius of the well, m\n",
    "lab = np.sqrt(T * c) # leakage factor, m\n",
    "Q = 500 # discharge of well, m^3/d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# solution\n",
    "from scipy.special import k0, k1\n",
    "r = np.linspace(rw, 4 * lab, 200)\n",
    "h = -Q / (2 * np.pi * T) * k0(r / lab) + hstar\n",
    "happrox = Q / (2 * np.pi * T) * np.log(r / (1.123 * lab)) + hstar\n",
    "Qtot = 2 * np.pi * r * Q / (2 * np.pi * lab) * k1(r / lab)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAi8AAAGdCAYAAADaPpOnAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjAsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvlHJYcgAAAAlwSFlzAAAPYQAAD2EBqD+naQAAYqRJREFUeJzt3Xl8VNX9//HXzCSZJJCFJGQBQojsEDbDYqLIooZFUdEq1lZFwRYVFalakX6V+rNS+0XL1yqoVcEFlbrgCkKqsiiggIR93xJIQiBAFiDbzP39MSQSCZhAJncm834+HvMIc+fezGeiufedc849x2IYhoGIiIiIl7CaXYCIiIhIXSi8iIiIiFdReBERERGvovAiIiIiXkXhRURERLyKwouIiIh4FYUXERER8SoKLyIiIuJV/MwuoL45nU6ys7MJCQnBYrGYXY6ITzIMg6KiIlq0aIHV6h1/I+ncIWKuupw3Gl14yc7OJj4+3uwyRATIysqiVatWZpdRKzp3iHiG2pw3Gl14CQkJAVwfPjQ01ORqRHxTYWEh8fHxVb+P3kDnDhFz1eW80ejCS2Vzb2hoqE5AIibzpu4XnTtEPENtzhve0RktIiIicorCi4iIiHgVhRcRERHxKgovIiIi4lUUXkRERMSrKLyIiIiIV1F4EREREa+i8CIiIiJeReFFREREvIrCi4h4nKVLlzJixAhatGiBxWLhk08++dVjlixZQnJyMoGBgVx00UW8/PLL7i9UREzRIOFlxowZJCYmEhgYSHJyMsuWLTvrvosXL8ZisZzx2Lp1a0OUKiIe4Pjx4/To0YMXX3yxVvvv2bOH4cOH079/f9auXcvjjz/OAw88wEcffeTmSkXEDG5f22ju3LlMmDCBGTNmcOmll/LKK68wbNgwNm/eTOvWrc963LZt26qtL9K8eXN3lyoiHmLYsGEMGzas1vu//PLLtG7dmunTpwPQuXNnVq9ezbRp07jxxhvdVKWImMXtLS/PP/88Y8aMYezYsXTu3Jnp06cTHx/PzJkzz3lcdHQ0sbGxVQ+bzebuUkWkJk4H5G2FdXNh4WRY9brZFZ1hxYoVpKWlVds2ZMgQVq9eTXl5eY3HlJaWUlhYWO1RG7O/38PfvtzMhv0FF1y3iJwft7a8lJWVsWbNGh577LFq29PS0li+fPk5j+3VqxclJSV06dKFv/zlLwwaNKjG/UpLSyktLa16XtsTkIjUoKIU8rZAzjrXI3c95G6EipM/79OmP/QZY16NNcjNzSUmJqbatpiYGCoqKjh8+DBxcXFnHDN16lT++te/1ul9DMPgrZX72H3oOP9etoc7UhL4yzVd8Ldp+KBIQ3JreDl8+DAOh6PGk0pubm6Nx8TFxfHqq6+SnJxMaWkpb7/9NldccQWLFy/m8ssvP2P/8zkBiQiuoHJwIxz4CbIzIHedK7g4K87c178JxHaDuB7Qul+Dl1obFoul2nPDMGrcXmnSpElMnDix6nlhYSHx8fHnfA/DgEeHdOTz9Tl8uT6HN1fso+BkOc/f3BOrteb3EZH65/YxL1DzSeVsJ5SOHTvSsWPHqucpKSlkZWUxbdq0GsPL+ZyARHyOowIObYXstZD9kyuwHNwEzhq6VIKauUJKbHfX17geENEWrJ7buhAbG3vGH0R5eXn4+fkRGRlZ4zF2ux273V6n97FaLQxNimNoUhwjuucy/t2f+CQjm4uaN+WBK9qfd/0iUjduDS9RUVHYbLYaTyq/bI05l0suuYR33nmnxtfO5wQk0qg5nXBkd/Wgkrseyk+cuW9QBLS8GFr0grieENcdwuLhLH9ceKqUlBQ+//zzatsWLVpE79698ff3d8t7Dk2K5ZkbuvHoh+uZ/t/tXNoukuSECLe8l4hU59bwEhAQQHJyMunp6YwcObJqe3p6Otddd12tv8/atWtr7LMWEeD4Ydi/CrJ+hANrXF1ApTUMJg0IgRY9XUGl5cXQ4mIIb+2RQaW4uJidO3dWPd+zZw8ZGRlERETQunVrJk2axIEDB3jrrbcAGDduHC+++CITJ07k7rvvZsWKFbz++uu89957bq3z5t7xrNiVz7y1B5g8byNf3H8Zfhr/IuJ2bu82mjhxIrfddhu9e/cmJSWFV199lczMTMaNGwdwxklo+vTptGnThq5du1JWVsY777zDRx99pPkaRMDV/ZO3Gfb/CFmrXF+P7D5zP79A1xiVFhf/HFQi23l018/pVq9eXW2QfmXX8B133MHs2bPJyckhMzOz6vXExETmz5/PQw89xEsvvUSLFi144YUXGuQ26f+5pgvfbM1ja24Rc37I5I7UNm5/TxFf5/bwMmrUKPLz83nqqafIyckhKSmJ+fPnk5CQAHDGSaisrIyHH36YAwcOEBQURNeuXfnyyy8ZPny4u0sV8TzH812tKvt/PNWy8hOUHz9zv6iOEN8HWvVxBZXozmBzT3dJQxg4cGDVgNuazJ49+4xtAwYM4KeffnJjVTWLaBLAw2kd+J9PN/Hcom1c3T2OqKbqyhZxJ4txrjOEFyosLCQsLIyCgoJqk9yJeDzDgPxdkLkc9q1wBZb8nWfuZw+FlskQ3xda9YVWya5Bth7EG38PL6Rmh9NgxL++Y3NOIaNT2zDl2q5uqlKk8arL72CD3G0kIjVwOlx3/GSugH3fuwLL8bwz94vq4Aop8X1cX5t3BKsmbfQkNquFx4d35vev/8B7P2Zy76C2RIcEml2WSKOl8CLSUCrKICfjVFBZDpk/nDmw1maHVr2hdQq0vsTVwhKsO1i8waXtIrm4dTg/ZR7j30t3M/nqLmaXJNJoKbyIuEtFmevunz1LYe8y2L+6+ky14LoDqHU/V1hJuNQ1uNZP4yW8kcVi4f4r2nPnrFW8szKTPw5oq7EvIm6i8CJSX5xO13wqe5bCniWubqBfDq4Njvw5qCSkQkwS2PRr2FgM7NCc7q3CWL+/gFnf7+GRIZ3MLkmkUdJZU+R8GQYc3uEKKnuWwN7v4OTR6vsER0Li5a71gNpc5hq/4oHzqkj9sFgs3DuwLePe+Yl3f8jk/sHtCfTX+CSR+qbwIlIXxw/Drm9h539dgaUop/rrASHQ5lJXYEkcANFdvGZuFakfV3WJpWV4EAeOneTTjAOM6tPa7JJEGh2FF5FzcVTAgdWusLLzv67ZazltdgGb3TVmJfFySBzomr1W3UA+zWa1cEdqAs/M38qs7/dyc+/4s67lJiLnR2dZkV8q2A87v3aFld1LzrwjKKYbtLsC2g6C+H7gH2ROneKxRvVuzT/Td7A1t4gVu/NJbRtldkkijYrCi4jT4ZrFdtsC2L4QDm2p/npQM2g7GNpd6foaEmtOneI1woL9uTG5Je+szOTtFfsUXkTqmcKL+KbSItj1DWz7CnYshBP5P79msULL3q6w0u4KV1eQJoWTOvpdvwTeWZnJf7ccJL+4lEjdNi1SbxRexHccy4LtX7laWPYuA0fZz68FhkH7NOgw1NW6oonh5AJ1jgulR6sw1u0vYN7aA4ztf5HZJYk0Ggov0ngZBhzaCps/hS1fwMEN1V+PuAg6DncFltaXePVChuKZRvVpzbr9G3h/VRZjLkvUwF2ReqLwIo2LYcDBja7AsvlTOLz959csVtcA2w5DXaElqr3mXBG3GtEjjv/3xWZ25hXzU+YxkhM8awFNEW+l8CLezzAge+3PgeXonp9fswW4uoE6X+sKLU0izatTfE5IoD/Du8Xx0U/7mbsqU+FFpJ4ovIh3MgzI3QAbPoDNn8CxzJ9f8wt0Dbbtcj10GAKB515aXcSdbukbz0c/7eeL9Tk8MaIrTe067YpcKP0WiXc5utcVWNZ/AIe3/bzdP9g14LbLda6v9qamlShyut4JzbioeRN2HzrOF+uyuaWvZtwVuVAKL+L5jh+GTfNg/X9g/48/b7fZXS0r3X4D7a6CgGDzahQ5C4vFws294/n7gq18uGa/wotIPVB4Ec9UUeq6pTljjmu2W8Nx6gWLayr+7jdD5xGuW5xFPNz1PVvy7FdbWb3vKFlHThAfoaAtciEUXsSz5G6Ete/A+rlw8sjP2+N6ugJL1xsgNM608kTOR2xYICkXRbJ8Vz6frcvmvkHtzC5JxKspvIj5Th5zjWNZ+w7kZPy8PSQOevwWet7quq1ZxItd37Mly3fl88naA9w7sK3mfBG5AAovYg7DgH3LYc0s2PI5VJS4tlv9oeMw6HWb6xZnrdAsjcTQbrH85dON7MgrZnNOIV1bqMtT5HzpyiANq6TQ1SW06vXqCyBGd4Vev3d1DTXRInbS+IQG+nNFp2gWbMzl04xshReRC6DwIg3j4GZY9ZoruJQVu7b5B0O3myB5tGvxQzWjSyN3Xc+WLNiYy2cZ2fx5aCdsVv0/L3I+FF7EfZwOV5fQj6/Cvu9/3h7ZHvqMhZ6/1d1C4lMGdWpOaKAfuYUl/LAnn9S2amUUOR8KL1L/Sotdg29XzoBj+1zbLDbodLUrtCRerlYW8Ul2PxvDu8Xx/qosPl2brfAicp4UXqT+FGbDD6+4BuGWFLi2BTWD3mOg910Q1tLc+kQ8wLU9W/D+qiy+2pTL/7s+iQA/q9kliXgdhRe5cAc3wfJ/wYYPwVnu2hbRFlLuhR63auZbkdP0S4wkqqmdw8WlfL/rMIM6RptdkojXUXiR85e9Fpb8L2z78udtrVMhdbxrBWerzbzaRDyUzWphWFIsb6/cx/z1OQovIudB4UXqLutHWPIP2Jl+aoMFulwLqQ9Cq2RTSxPxBsO7xfH2yn0s2nyQv1U41XUkUkcKL1J7e7+HJc/CniWu5xab61bn/n+C5h3MrU3Ei/RNjFDXkcgFUHiRX5e9Fr5+CnZ943pu9XNN299/IkRcZG5tIl5IXUciF0bhRc7u8A745mnY/InrudUfLr4dLnsIwuNNLU3E253edfSMw4m/TV1HIrWl8CJnKtgPi/8OGe+C4QAsrmn7B06CiESzqxNpFKp1He08zEC1vojUmqK+/Ky0GL7+f/DCxbD2bVdw6Tgc7vkebnhVwUWkHlV2HQF8uT7H5GpEvIvCi4DT6Wpl+VcyLJsGjlJIuBTGpMNv34OYrmZXKNIoDe8WB8CizQcpdzhNrkbEe6jbyNdlroSvHnMNygVolghpT7um8tcU/iJupa4jkfOjlhdfdfwwzLsH3hjiCi4BIXDVU3DfD9D5GgUXkQagriOR89Mg4WXGjBkkJiYSGBhIcnIyy5YtO+f+S5YsITk5mcDAQC666CJefvnlhijTNzid8NNb8GJvWPcuYHHdQfTAT3Dpg+BnN7tCEZ+iriORunN7eJk7dy4TJkxg8uTJrF27lv79+zNs2DAyMzNr3H/Pnj0MHz6c/v37s3btWh5//HEeeOABPvroI3eX2vjlbYHZV8Nn98PJoxCT5BrXcu2/oKmaq0XM0DcxgsgmARScLOfHPUfMLkfEK7g9vDz//POMGTOGsWPH0rlzZ6ZPn058fDwzZ86scf+XX36Z1q1bM336dDp37szYsWO56667mDZtmrtLbbwqyuDbqfDyZZC5HPyDXeNa/rAE4vuYXZ2IT7NZLVzZOQaAhZtyTa5GxDu4NbyUlZWxZs0a0tLSqm1PS0tj+fLlNR6zYsWKM/YfMmQIq1evpry83G21NloHN8Frg2HJ38FZ4br1+b4fIfV+sGm8ttSO02lQVuGkpNxBSbnD7HIanSFJrvCyaNNBnE7D5GpEPJ9br16HDx/G4XAQExNTbXtMTAy5uTX/hZGbm1vj/hUVFRw+fJi4uLhqr5WWllJaWlr1vLCwsJ6q93KOClj+f64WF2c5BDWDq5+DpBvNrswnOJwGpRUOSsudlPzya7mD0gonFU4nZRUGFU4n5Q4n5Q6DcoeTilNff37upMxhUOE4tZ/ToLzCSYXToOzU6xUOg3KngdNp4Kh8GK6vTsOgwuH6evp2R+X+hoHDCQ6n89T+nPE9TjegQ3PevKuvST/Zxim1bRRNAmzkFpawbv8xerVuZnZJIh6tQf70tvzizhXDMM7Y9mv717QdYOrUqfz1r3+thyobkcM7YN4f4cAa1/OOw+Ga6RASc87DfIlhGJRWOCk8Wc7xMgfHSys4UebgeFkFJ0orv1ZwvMzBibIKjpee+lrm4ERpBSdPBZCScmdVSCmtcFQ9L3c03r+enUbj/WxmCfS3MbBTNF+uz2HhpoMKLyK/wq3hJSoqCpvNdkYrS15e3hmtK5ViY2Nr3N/Pz4/IyMgz9p80aRITJ06sel5YWEh8vI+uu2MYrsnm5j8M5SfAHgbDnoUetzTaW58dToOjJ8o4cryM/GLX16MnyigsKafwZMWpr+UUllS4vp4sr3qtrIHu7PCzWgj0t2H3s1Z9DTj18LNa8LdZTz0s+NmsBNis+NksVdv8bVb8rFb8/Syu107929/68zH+Ngt+Vis2qwWr1YKf1YLVYsFmtWCzgs1qxWaxYLWCzWLBz/bz69ZTz12vu766jjvt9VPf13bqe0v9G9o1li/X57BoUy5/HtrxnH/gifg6t4aXgIAAkpOTSU9PZ+TIkVXb09PTue6662o8JiUlhc8//7zatkWLFtG7d2/8/f3P2N9ut2O36/ZeSovgyz/B+rmu54mXw/UvQ1hLc+s6D4ZhcPREObkFJRwsLCG3sITcghIOF5e6QsrxyrBSyrGT5VxIQ4DVAk0C/Ai226q+Bgf40STARrD91NcAP5qcvj3Aj8AAG4F+Vuz+p331t2L3qx5S7H5W/LTgntTCwI7NCbBZ2X34ODvzimkfE2J2SSIey+3dRhMnTuS2226jd+/epKSk8Oqrr5KZmcm4ceMAV8vJgQMHeOuttwAYN24cL774IhMnTuTuu+9mxYoVvP7667z33nvuLtV75ayDD+6EI7vAYoNBk+CyiWC1mV1ZjUrKHRw4dpLMIyfIOvXIOS2oHCwspayibq0i4cH+RDQJILJJAOHBAYQF+RMa6O/6GuRHaKA/oUH+hAb6ERbsX/W8SYBNf+GKRwgJ9OfSdpF8u+0QCzflKryInIPbw8uoUaPIz8/nqaeeIicnh6SkJObPn09CQgIAOTk51eZ8SUxMZP78+Tz00EO89NJLtGjRghdeeIEbb9RA0xqtex8+fxAqSiC0Fdz4GiSkmF0VpRUO9hw+zo6Dxew+dNwVVI66gkpuYUmtWksimwQQExpIbFggMaGBNA+xE9kkoCqkRDa1E9EkgGbB/mrdkEZhSNdYvt12iK825TJ+cHuzyxHxWBbDaFyj7woLCwkLC6OgoIDQ0FCzy3EfRzks+gv8cGr24fZDYOTLEBzRoGWUO5zsOFjMtoOF7DhYzI68YnblFbM3/zjnuuOzSYCN+IhgWkcEEx8RTFyYK6TEhrqCSnSoHbufZ7Ycya/zxt9DT6j5cHEpff/2X5wGfPfnQbRqFmxKHSJmqMvvoCb68EbFh+CDO2Df967nA/4MAx4Dq3tbH0orHGzLLWLjgUI2Zhew6UABW3KLztrFExLoR/voprRt3pSEyOCqsNI6IpiIJgHqrhH5haimdnonRPDj3iMs2nSQuy5LNLskEY+k8OJt8rbAnJugIMu1mOLIl10LKbrB0eNlrNl3lFX7jrBm71HW7y+o8Q6dkEA/OseF0j66qesRE0K76KZEh9gVUETqKK1rDD/uPcLCTbkKLyJnofDiTXYvgbm3QWkBRLSF374HzTvW27c/dqKM5bvyWbbjMKv2HmFnXvEZ+zQL9iepZZjr0SKMpJahtI4IVkgRqSdDusby9JdbWLX3CPnFpUQ21d2UIr+k8OIt1r0Pn453zZbbOgVuefeCx7c4nAY/ZR5l2fZDLN1xmPX7j50xTqVddFN6JzSjd5sIeic0IyFSQUXEneIjgunaIpRN2YV8vSWPm/v46LxVIueg8OLpDAOWToNvn3Y97zrSNX+Lf+B5fbvSCgfLd+WzcGMu6ZsPkn+8rNrr7aOb0r99c1LaRpKc0IyIJgEX+glEpI6GdI1lU3YhX23KVXgRqYHCiyczDNcdRStedD2/9EG4YkqdB+aWO5ws23GITzOy+WZLHkWlFVWvhQb6cXmH5lzeoTn920cRFxZUjx9ARM7HkK6xPJ++ne92HKa4tIKmdp2qRU6n3whP5XTCgkdg1Wuu50OfhUvG1fpwwzDYlF3Ixz8d4LN1Bzhc/HMLS/MQO0O6xjC0axz9LorAX3OkiHiUDjFNaRMZzN78Eyzelsc13VuYXZKIR1F48UROB3z2AGS8A1hgxP9B8h21OrSk3MHn67J5a8U+NhwoqNoe2SSAET1aMKJHHL3im2HV+jQiHstisTCkayyvLN3Nwk0HFV5EfkHhxdM4KuCTcbDhA9dU/yNfhu43/+phB46d5O0V+5i7KpOjJ8oBCLBZubJLNDde3IrLOzRXC4uIFxmS5Aov327No7TCoUkbRU6j8OJJnE74bLwruFj94DdvQJeaF7CstOfwcWYu3snHPx2g4tStQi3Dg/j9JQmM6hOvAbciXqpnq3CiQ+zkFZWyfFc+gzpGm12SiMdQePEUhgELHoV177laXG5685yTz+04WMS/vtnJF+uzq25vTrkokjsvbcMVnWOwqVtIxKtZrRau6hLDnB8yWbTpoMKLyGnUj+Apvv4rrPo3YIGRr5w1uOQVlTDp4/UMmb6Uz9a5gsvgTtF8dE8q7/3hEtK6xiq4SKMwY8YMEhMTCQwMJDk5mWXLlp1z/zlz5tCjRw+Cg4OJi4vjzjvvJD8/v4GqdY8hXWMBSN98EOe5FgsT8TEKL55gxQz47p+uf1/zT+h+0xm7nCir4IWvdzDwfxfz3o9ZOA1I6xLDF/dfxhuj+5Cc0KyBixZxn7lz5zJhwgQmT57M2rVr6d+/P8OGDau2Av3pvvvuO26//XbGjBnDpk2b+OCDD1i1ahVjx45t4Mrr1yUXRRJi9+NwcSlrs46aXY6Ix1B4MduWL2Dh465/XzkFet95xi7pmw9yxXNLeD59OyfKHPSID+eDcSm8entvklqGNWy9Ig3g+eefZ8yYMYwdO5bOnTszffp04uPjmTlzZo37r1y5kjZt2vDAAw+QmJjIZZddxh//+EdWr17dwJXXrwA/K4M6ubqLFm06aHI1Ip5D4cVM+9fAR2MBA3rfBZdOqPbywcIS7nlnDXe/tZqcghJaNQviX7/txSf3ptKnzYUtDSDiqcrKylizZg1paWnVtqelpbF8+fIaj0lNTWX//v3Mnz8fwzA4ePAgH374IVdfffVZ36e0tJTCwsJqD09U2XW0cFMuhqGuIxFQeDHPsUx4bxRUnIR2V8Gw/4XT1gz6bF02Vz6/hAUbc7FZLdwzsC3pDw1gRI8WWltIGrXDhw/jcDiIiYmptj0mJobc3Nwaj0lNTWXOnDmMGjWKgIAAYmNjCQ8P51//+tdZ32fq1KmEhYVVPeLjPXMa/gEdmxNgs7I3/wQ7algsVcQXKbyYofwkzP09HD8Esd3gpllgc934VVRSzsS5GTzw3lqKSiro0SqMz8dfxp+HdiIoQPM8iO/4ZUg3DOOswX3z5s088MADPPHEE6xZs4avvvqKPXv2MG7c2WelnjRpEgUFBVWPrKyseq2/vjS1+3Fpu0gAFm2qObyJ+BrdKt3QDAO+/BPkrIPgSLjlPbCHALDxQAH3zFlD1pGTWC1w/+D23D+4HX6aXE58SFRUFDab7YxWlry8vDNaYypNnTqVSy+9lEceeQSA7t2706RJE/r378/TTz9NXFzcGcfY7Xbsdnv9fwA3GNI1lm+3HWLhpoOMH9ze7HJETKerYkNb/QZkzAGL1TUJXbirqfrTjAP85uXlZB05SatmQfznjyk8dFUHBRfxOQEBASQnJ5Oenl5te3p6OqmpqTUec+LECay/WLDUZnO1VDaGcSJXdI7BYoENBwrIPnbS7HJETKcrY0PavwYW/Nn17yuehIsG4nAaPDN/Cw++n0FJuZOBHZvz5f396a0BueLDJk6cyGuvvcYbb7zBli1beOihh8jMzKzqBpo0aRK333571f4jRozg448/ZubMmezevZvvv/+eBx54gL59+9KihfevC9Q8xE5ya9d0COmbddeRiLqNGkppEXw0Bpzl0HkEXPogJeUOJryfwVen+rHvHdiWP6V11CRz4vNGjRpFfn4+Tz31FDk5OSQlJTF//nwSEhIAyMnJqTbny+jRoykqKuLFF1/kT3/6E+Hh4QwePJhnn33WrI9Q74Z0jWX1vqMs3JTLHaltzC5HxFQWozG0qZ6msLCQsLAwCgoKCA0NNbucn316H6x9B8LiYdx3FFma8Ie31rBidz4BNivP3dyDET28/y9EEfDg38Nz8PSa9+UfZ8D/LsZmtbDmL1cSHqx1y6RxqcvvoLqNGsLmz1zBBQuMfJl8RxC3vLqSFbvzaWr3Y/ZdfRRcROScEiKb0Ck2BIfT4JuteWaXI2IqhRd3K8yGzx9w/fuyCRRE9+P3r//IpuxCopoG8P4fLiG1bZS5NYqIV0jr4rrbaqFumRYfp/DiToYBX0yEk0chrgfFqY9yx6wf2ZJTSFRTO3P/mKLp/UWk1tJOzba7ZPshTpY5TK5GxDwKL+605XPYvgCs/pRcM4O73l5HRtYxwoP9mTO2H22bNzW7QhHxIl1bhNIyPIiSciff7TxsdjkiplF4cZeSQljwKADGpQ/ywNcl/LjnCCF2P96+qx8dY0NMLlBEvI3FYuEqdR2JKLy4zTdPQ1EORFzEtJPXsGjzQQJsVl4f3YdurdRVJCLnJ62rK7x8veUgFQ6nydWImEPhxR32r4EfXwVgSYfHeem7bAD+8Zvu9E3U5HMicv76tokgPNifoyfKWb3vqNnliJhC4aW+OZ0w/2HA4Fj7G/nDd65xLQ8Mbsf1vVqaW5uIeD0/m5UrOqnrSHybwkt92/gRZP+EEdCEOw+MoLTCNeX/hCs7mF2ZiDQSlV1HizYdbBRrN4nUlcJLfSo/Cf+dAsAXob9l7ZEAWoYH8c+be2LVlP8iUk8ub9+cQH8rB46dZHNOodnliDQ4hZf6tHIGFO7nRFAcD++/DJvVwou39qJZE03jLSL1JyjAxuXtmwOwcJMWahTfo/BSX04eg+//D4CnT/6GUgK4b1A7ep1aCVZEpD5VTli3SONexAcpvNSXlTOhpIAD/m14v6Qf3VqGcf/gdmZXJSKN1BWdorFZLWzNLSIz/4TZ5Yg0KIWX+nDyqKvLCPjb8WuxWm08d3MP/G368YqIezRrEkDfNq6pFxZtVuuL+BZdXevDipegtJCdlgQWOPty9+UX0SFGM+iKiHudfteRiC9ReLlQpUXwg2tCummlI2kR3oQHBrc3uSgR8QWV415W7TvC4eJSk6sRaThuDS9Hjx7ltttuIywsjLCwMG677TaOHTt2zmNGjx6NxWKp9rjkkkvcWeaF+eltKC1gtxHHQmdvnhzRhaAAm9lViYgPaBkeRFLLUAzDtVyAiK9wa3i59dZbycjI4KuvvuKrr74iIyOD22677VePGzp0KDk5OVWP+fPnu7PM8+eoqBrr8u+K4fRNjKpaNE1EpCEM6VJ515HCi/gOP3d94y1btvDVV1+xcuVK+vXrB8C///1vUlJS2LZtGx07djzrsXa7ndjYWHeVVn82fwIFWRw2QvnY0Z/3h3XCYtFkdCLScNK6xvJc+naW7TxMcWkFTe1uO62LeAy3tbysWLGCsLCwquACcMkllxAWFsby5cvPeezixYuJjo6mQ4cO3H333eTl5Z1139LSUgoLC6s9GsyKlwB4syKNQV1ba04XEWlwHWKakhAZTFmFk6XbD5ldjkiDcFt4yc3NJTo6+ozt0dHR5Oae/ba+YcOGMWfOHL755huee+45Vq1axeDBgyktrXkw2tSpU6vG1ISFhREfH19vn+GcsjMg+ydKDT/edV7Jw0O0dpGINDyLxcIQTVgnPqbO4WXKlClnDKj95WP16tUANXahGIZxzq6VUaNGcfXVV5OUlMSIESNYsGAB27dv58svv6xx/0mTJlFQUFD1yMrKqutHOj8/vQnAQmcf+iV1oF20bo0WEXOknRpr9/XWPMoqnCZXI+J+de4cHT9+PLfccss592nTpg3r16/n4MEzB5AdOnSImJjaD2qNi4sjISGBHTt21Pi63W7HbrfX+vvVi9JinOv+gxV413EFjw9o27DvLyJyml6tmxHVNIDDxWX8sCef/qfWPRJprOocXqKiooiKivrV/VJSUigoKODHH3+kb9++APzwww8UFBSQmppa6/fLz88nKyuLuLi4upbqPhs/wlpezG5nLH6J/eneKtzsikTEh9msFq7qEsN7P2axaNNBhRdp9Nw25qVz584MHTqUu+++m5UrV7Jy5Uruvvturrnmmmp3GnXq1Il58+YBUFxczMMPP8yKFSvYu3cvixcvZsSIEURFRTFy5Eh3lVpnjtWzAHjPMZh7Bmn9IhExX1rlLdObc3E6DZOrEXEvt87zMmfOHLp160ZaWhppaWl0796dt99+u9o+27Zto6CgAACbzcaGDRu47rrr6NChA3fccQcdOnRgxYoVhIR4yJiSwzux5aylwrCyttlQUttGml2RiAgpbSNpEmDjYGEp6w8UmF2OiFu5dUKAiIgI3nnnnXPuYxg//4UQFBTEwoUL3VnSBTM2fogF+M7ZjeGXdNe8LiLiEQL9bQzsFM2X63NYtCmXnvHhZpck4jZa26guDIPStf8BYD6XcuPFrUwuSETkZ5V3HS3ULdPSyCm81EXuBgILdlFi+OPXZQRhwf5mVyQiUmVQp2j8bRZ2HTrOzrxis8sRcRuFlzooW+dqdfnG2YsbUzubXI2ISHWhgf6ktHXdDZq+WWsdSeOl8FJbhkHF+o8AWBk8kItbh5tbj4hIDdR1JL5A4aW2Dm4i+EQ2J40AmvW4WgN1RcQjVYaXjKxjHCwsMbkaEfdQeKmlki0LAPje2ZWhvS4yuRoRkZpFhwbS61TLsLqOpLFSeKml4vWutZU2BPejU6yHzDkjIlKDygnr1HUkjZXCS22cOELE0XUAhHRTl5GIeLYhXV1dRyt25VNwstzkakTqn8JLLZRsXYQVJ1ud8Qzs28vsckREzumi5k1pF92UCqfB4m15ZpcjUu8UXmrhaMbnAKyx96FdtLqMRMTzVQ7c/Wqjuo6k8VF4+TVOB2EHlgJwMuEKk4sREamd4d3iAPh2Wx4nyipMrkakfim8/Arj4EaCHYUUGUEk9hxkdjkiIrXStUUorSOCKSl38u3WQ2aXI1KvFF5+xZHNiwFYa7TnkvYx5hYjIlJLFouFYd1cdx3N35hjcjUi9Uvh5VcUbV8GQHbYxTSxu3URbhGRejU86VTX0dY8TpY5TK5GpP4ovJyLYdDs0GoAAtteZnIxIiJ1071VGC3DgzhR5mDJdnUdSeOh8HIOZXk7CHMepdTwo+PFA8wuR0SkTiwWC8Mru442qOtIGg+Fl3PIXv8NAJss7ekU39zkakRE6m7YqbuOvt5ykJJydR1J46Dwcg6lu74DIDe8l2bVFRGv1Cs+nBZhgRwvc7Bsx2GzyxGpFwov5xBxeBUAloRUkysRETk/FouFoacG7i5Q15E0EgovZ+EsyKF5RS4Ow0LL7gPNLkdE5LxVjntJ33yQ0gp1HYn3U3g5i4PbVgCwi5Z0btPS5GpERM7fxa2bERNqp6i0gu93qutIvJ/Cy1kc2+XqMjoQ1BF/m35MIuK9rFYLw051Hc3foLWOxPvpqnwW1px1AJQ072ZyJSIiF25YkqvraNGmXMoqnCZXI3JhFF7OonnxFgCC2/Q2uRIRkQvXu00EUU3tFJZUsHyXuo7Euym81KC8IIcI5xEchoX4zv3MLkdE5ILZrJaq1pcF6joSL6fwUoPc7WsA2EccbWI1OZ2INA6VCzUu3JxLuUNdR+K9FF5qULDPNd4lN/AirFZNTicijUPfNhFENgng2IlyVu7ON7sckfOm8FID4+AmAE6GdzC5EhGR+uNnszIkSWsdifdTeKlB04IdAPjFdjW5EhGR+nX1qbWOvtqoriPxXgovv+R0EFe2F4BmF/U0tRQRkfrWLzGCqKYBHD1RrgnrxGspvPxCUe4uAimj1PAnoV2S2eWIiNQrP5uV4adaXz5fp64j8U4KL7+Qu3sjAFnWFoQ1CTS5GhGR+jeiRwvANWFdSbnWOhLvo/DyC8dztgGQb483uRIREfdIbt2MuLBAikorWLL9kNnliNSZwssvOA+7BuuWhLYxtxARHzdjxgwSExMJDAwkOTmZZcuWnXP/0tJSJk+eTEJCAna7nbZt2/LGG280ULXexWq1cE33yq6jbJOrEak7P7ML8DRBhXsBsES1M7cQER82d+5cJkyYwIwZM7j00kt55ZVXGDZsGJs3b6Z169Y1HnPzzTdz8OBBXn/9ddq1a0deXh4VFRUNXLn3GNGjBf9etoevt+RxoqyC4ABdDsR76P/WX4goyQKgaVwnkysR8V3PP/88Y8aMYezYsQBMnz6dhQsXMnPmTKZOnXrG/l999RVLlixh9+7dREREANCmTZuGLNnrdGsZRkJkMPvyT/DfLXlce2ocjIg3ULfRaZylJ2judPX/RiV0MbkaEd9UVlbGmjVrSEtLq7Y9LS2N5cuX13jMZ599Ru/evfnHP/5By5Yt6dChAw8//DAnT5486/uUlpZSWFhY7eFLLBYLI7q7Aou6jsTbKLycJi9rG1aLQZERRIsWrcwuR8QnHT58GIfDQUxMTLXtMTEx5ObWvKDg7t27+e6779i4cSPz5s1j+vTpfPjhh9x3331nfZ+pU6cSFhZW9YiP971B+pV3HS3ZdoiCk+UmVyNSe24NL3/7299ITU0lODiY8PDwWh1jGAZTpkyhRYsWBAUFMXDgQDZt2uTOMqscyd4JwEFbLH5+tgZ5TxGpmcVSfV0xwzDO2FbJ6XRisViYM2cOffv2Zfjw4Tz//PPMnj37rK0vkyZNoqCgoOqRlZVV75/B03WMDaFDTFPKHE4WbdJK0+I93BpeysrKuOmmm7jnnntqfcw//vEPnn/+eV588UVWrVpFbGwsV111FUVFRW6s1OVk3l4ACgJi3f5eIlKzqKgobDbbGa0seXl5Z7TGVIqLi6Nly5aEhYVVbevcuTOGYbB///4aj7Hb7YSGhlZ7+KKqrqP1mrBOvIdbw8tf//pXHnroIbp161ar/Q3DYPr06UyePJkbbriBpKQk3nzzTU6cOMG7777rzlIBcB7LBKAkWAPXRMwSEBBAcnIy6enp1banp6eTmppa4zGXXnop2dnZFBcXV23bvn07VquVVq3UBXwu15zqOvp+52Hyi0tNrkakdjxqzMuePXvIzc2tNlDPbrczYMCAsw7Uq89Bd36FBwAwwnyv71vEk0ycOJHXXnuNN954gy1btvDQQw+RmZnJuHHjAFeXz+233161/6233kpkZCR33nknmzdvZunSpTzyyCPcddddBAUFmfUxvEJiVBO6tQzD4TT4Sl1H4iU8KrxUNhPXZaBefQ66Cy5xNZv6RdY8j4SINIxRo0Yxffp0nnrqKXr27MnSpUuZP38+CQkJAOTk5JCZmVm1f9OmTUlPT+fYsWP07t2b3/3ud4wYMYIXXnjBrI/gVUb0cE1Y91mG7joS71Dn8DJlyhQsFss5H6tXr76gouoyUK8+B901Kz8IQNPoxPP+HiJSP+6991727t1LaWkpa9as4fLLL696bfbs2SxevLja/p06dSI9PZ0TJ06QlZXFc889p1aXWrr61LiXH/Yc4cCxs99eLuIp6jxJ3fjx47nlllvOuc/5Tg4VG+saKJubm0tcXFzV9nMN1LPb7djt9vN6v9M5y0uJch4BC0S0aHvB309ExFu0DA+iX2IEP+w5wmcZ2dwzUOdA8Wx1Di9RUVFERUW5oxYSExOJjY0lPT2dXr16Aa47lpYsWcKzzz7rlvesdCRnD1EWgxLDn+hYDfATEd8ysldLfthzhHlr9zNuwEVnbe0W8QRuHfOSmZlJRkYGmZmZOBwOMjIyyMjIqHZHQKdOnZg3bx7g6i6aMGECzzzzDPPmzWPjxo2MHj2a4OBgbr31VneWSn7uPgAOWaM0x4uI+Jxh3eIIsFnZfrCYLTnun5pC5EK4dW2jJ554gjfffLPqeWVryrfffsvAgQMB2LZtGwUFBVX7PProo5w8eZJ7772Xo0eP0q9fPxYtWkRISIg7S+XkEddAtUK/CLe+j4iIJwoL8ueKztEs2JjLJxkH6NLCN+e9Ee/g1paX2bNnYxjGGY/K4AKuwbijR4+uem6xWJgyZQo5OTmUlJSwZMkSkpKS3FkmAOUFrruZTga4p0tMRMTTjezVEoBPMw7gcBomVyNydh51q7SZnEWuO43KgpqbXImIiDkGdowmPNifg4WlrNydb3Y5Imel8HKK7UQeAEYThRcR8U0Bflau7ua603Pe2gMmVyNydgovpwScPAyALaTmW7JFRHxBZdfRVxtzOVnmMLkakZopvJzSpNzVRBoQHvcre4qINF7JCc1o1SyI4tIK/rvloNnliNRI4eWUkIqjAARHaFFGEfFdFoulqvVFXUfiqRReAMPpoJlxDIDQ5i3NLUZExGTX9XSdB5dsP6SVpsUjKbwARUcO4W9x9e1GKLyIiI9rF92U7q1cK01/sT7H7HJEzqDwAhw75FrM8QghBAYGmlyNiIj5rj/V+vKxuo7EAym8AMVHXBPUFVrDTK5ERMQzjOjRApvVwrqsY+zMK/71A0QakMILUFp0BICTNk2HLSIC0DzEzsAOrnmvPlyz3+RqRKpTeAEqjrvCS6mfwouISKWbercC4OOf9lPhcJpcjcjPFF4A54ljAJT7K7yIiFQa3CmGZsH+5BWVsmzHYbPLEami8AIYJccAcNg15kVEpFKAn7Xqtml1HYknUXgBrKfCi6HwIiJSTWXXUfrmgxw7UWZyNSIuCi+ArazA9Y+gZuYWIiLiYbq2CKNLXChlDiefZmSbXY4IoPACQEC5K7zYmii8iIj8UmXrywdrskyuRMRF4QUIrCgCwL9phMmViIh4nut6tsTfZmHjgUK25BSaXY6IwgtAsMMVXuwKLyIiZ4hoEsCVnWMA+GC1Bu6K+RRegCaGa/bIoNBIkysREfFMlV1Hn2QcoKxCc76IuXw+vBhOByHGcQCahEWZXI2IiGe6vH1zmofYOXK8jG+25pldjvg4nw8vxYXHsFkMAELCFV5ERGriZ7NyQ6/KOV80cFfMpfBS4Jo1ssTwJzC4icnViIh4rsquo2+3HSKvqMTkasSX+Xx4OXEqvBRZmmKxWEyuRkTEc7WLDuHi1uE4nIZm3BVT+Xx4OVmYD8AJq1pdRER+zW/7tgbg/R+zcDoNk6sRX+Xz4cVR4hqsW2oNNrkSERHPd033FoQE+pF55ATf79JijWIOnw8vFWWu8FJuDTS5EhERzxcUYKsauPvej5kmVyO+yufDi7P0BAAVNoUXEZHa+G0/V9fRok0HNXBXTKHwUnYqvKjlRUSkVjrFhtKrdTgVGrgrJvH58GKcCi9OvyCTKxER8R63auCumEjhpfwkoPAiIlIXGrgrZvL58EK5Wl5EROoqKMDGSA3cFZP4fHixnmp5QeFFRKRObj1t4O6holKTqxFf4vPhxVJxKrwEKLyIiNTF6QN3P9B6R9KAfD682Byu2/ws/pqkTkSkrjRwV8yg8OJwtbxYAxReRETq6vSBu9/t1MBdaRg+H178TrW8KLyIiNRdUICNGy92rTb91op9JlcjvkLhxXkqvNi1MKOIyPn4/SUJAHy99SBZR06YXI34AreGl7/97W+kpqYSHBxMeHh4rY4ZPXo0Foul2uOSSy5xW43+p8KLn10tLyIi56NddFP6t4/CMOCdH9T6Iu7n1vBSVlbGTTfdxD333FOn44YOHUpOTk7VY/78+W6qEAKcrtv7/ALV8iIicr5uT2kDwNxVWZSUO8wtRho9P3d+87/+9a8AzJ49u07H2e12YmNj3VBRDe9luFpe/AObNsj7iYg0RoM7RdMyPIgDx07y2bpsbu4db3ZJ0oh55JiXxYsXEx0dTYcOHbj77rvJy8s7676lpaUUFhZWe9SFHVfLS0CQWl5ERM6XzWqpGvvy1oq9GIZumxb38bjwMmzYMObMmcM333zDc889x6pVqxg8eDClpTXP3jh16lTCwsKqHvHxdUv7gUYZAAHqNhIRuSCj+sQT4Gdl44FC1mYdM7scacTqHF6mTJlyxoDaXz5Wr1593gWNGjWKq6++mqSkJEaMGMGCBQvYvn07X375ZY37T5o0iYKCgqpHVlbtZ3l0VFRgt5QDYA9St5GIyIWIaBLAtT1aAPDW8r3mFiONWp3HvIwfP55bbrnlnPu0adPmfOs5Q1xcHAkJCezYsaPG1+12O3a7/by+d8nJYirbWwKbKLyIiFyoO1La8OGa/Xy5IYfJV3ehecj5nZ9FzqXO4SUqKoqoqCh31FKj/Px8srKyiIuLq/fvXXLitPCibiMRkQvWrVUYvVqHszbzGHN+2MeEKzuYXZI0Qm4d85KZmUlGRgaZmZk4HA4yMjLIyMiguLi4ap9OnToxb948AIqLi3n44YdZsWIFe/fuZfHixYwYMYKoqChGjhxZ7/WVnjwOwEkjAKvNVu/fX0TEF41ObQPAOyv36bZpcQu3hpcnnniCXr168eSTT1JcXEyvXr3o1atXtTEx27Zto6CgAACbzcaGDRu47rrr6NChA3fccQcdOnRgxYoVhISE1Ht95SeLACixqFlTRKS+DO8WR1xYIIeLy/hsXbbZ5Ugj5NZ5XmbPnv2rc7ycfjtdUFAQCxcudGdJ1ZSVuFpeSlF4ERGpL/42K3ektuHvC7byxnd7uCm5FRaLxeyypBHxuFulG1L5qW6jMqvCi4hIffptn9YEB9jYmlvE9zvzzS5HGhmfDi8Vpa7wUq5uIxGRehUW7M9Nya7Vpl//brfJ1Uhj49PhxemoAMBhcWvvmYiIT7rz0kQsFvh22yF25hWZXY40Ij4dXgynaxS84ds/BhERt2gT1YQrO8cA8Mb3e80tRhoVn75qVw4WNiw+/WMQEXGbMZclAvDxT/s5crzM5GqksfDtq7ZR2fKiUfAiIu7QLzGCpJahlJQ7mbNyn9nlSCPh0+HFcKrlRcRTzZgxg8TERAIDA0lOTmbZsmW1Ou7777/Hz8+Pnj17urdAqRWLxcLYyy4CYPbyvZq0TuqFb1+11fIi4pHmzp3LhAkTmDx5MmvXrqV///4MGzaMzMzMcx5XUFDA7bffzhVXXNFAlUptXNM9jpbhQeQfL+OD1bVfPFfkbHw6vBiG0/VVLS8iHuX5559nzJgxjB07ls6dOzN9+nTi4+OZOXPmOY/74x//yK233kpKSkoDVSq14Wez8ofLXa0vry7bTYXDaXJF4u18+6rtPBVe1PIi4jHKyspYs2YNaWlp1banpaWxfPnysx43a9Ysdu3axZNPPunuEuU83Nw7nogmAWQdOcn8jblmlyNezqfDi1peRDzP4cOHcTgcxMTEVNseExNDbm7NF70dO3bw2GOPMWfOHPz8ajdvU2lpKYWFhdUe4j5BATbuSGkDwMuLd1VbGkakrnz7qm1UNl369o9BxBP9ci0cwzBqXB/H4XBw66238te//pUOHTrU+vtPnTqVsLCwqkd8fPwF1yzndntKAkH+NjbnFLJ0x2GzyxEv5tNX7Z9bXtRtJOIpoqKisNlsZ7Sy5OXlndEaA1BUVMTq1asZP348fn5++Pn58dRTT7Fu3Tr8/Pz45ptvanyfSZMmUVBQUPXIytJAUndr1iSA3/ZtDbhaX0TOl0+Hl5/HvPj2j0HEkwQEBJCcnEx6enq17enp6aSmpp6xf2hoKBs2bCAjI6PqMW7cODp27EhGRgb9+vWr8X3sdjuhoaHVHuJ+Y/sn4me1sGJ3Puuyjpldjngp317UR2NeRDzSxIkTue222+jduzcpKSm8+uqrZGZmMm7cOMDVanLgwAHeeustrFYrSUlJ1Y6Pjo4mMDDwjO1ivhbhQVzbswUf/3SAGYt38sptvc0uSbyQT4cXo2rMi7qNRDzJqFGjyM/P56mnniInJ4ekpCTmz59PQkICADk5Ob8654t4rnsGtGXe2gMs3HSQrbmFdIpVq5fUjW83OajlRcRj3Xvvvezdu5fS0lLWrFnD5ZdfXvXa7NmzWbx48VmPnTJlChkZGe4vUs5L+5gQhifFAfCvb3aaXI14I9++ale2vGjArohIgxo/uB0A8zfksDOvyORqxNv4dHgxNGBXRMQUneNCGdI1BsOAF9X6InXk21ftqpYX3/4xiIiY4f7B7QH4bF02ew4fN7ka8Sa+fdXWmBcREdMktQzjik7ROA146Vu1vkjt+fZVW3cbiYiY6v4rXK0v89YeIDP/hMnViLdQeEEtLyIiZukZH87lHZrjcBpqfZFa8+mrdtXCYAovIiKmefAK151HH/60n70a+yK14NtXbcPh+qJuIxER0yQnRDCwo6v15f++3mF2OeIFfDq8WNTyIiLiEf50VUcAPsk4wPaDmvdFzs2nr9qGxryIiHiEbq3CGNo1FsOAf6ZvN7sc8XC+fdVWy4uIiMeYmNYBiwUWbMxl44ECs8sRD+bbV21NUici4jE6xIRwfc+WAExbtM3kasST+fRV26J5XkREPMqDV7THZrWweNshVu89YnY54qF8OrxozIuIiGdpE9WEm3u3AuB/F277eUoLkdP49lVb3UYiIh7n/sHtCfCz8sOeIyzedsjscsQD+fZV+1SiV8uLiIjnaBEexJ2XtgFg6oItVDic5z5AfI5PX7Utpyapw6IxLyIinuTege0ID/Zn+8FiPvppv9nliIfx6fBS2W1k0YBdERGPEhbkz/hBrmUDnk/fzomyCpMrEk/i2+GFym4jm8l1iIjIL92WkkCrZkEcLCzlje/2mF2OeBDfDi9VA3bV8iIi4mnsfjYeGeJaNuDlJbs5XFxqckXiKXw6vFh0t5GIiEcb0b0F3VqGUVxawQtatFFOcdtVe+/evYwZM4bExESCgoJo27YtTz75JGVlZec8zjAMpkyZQosWLQgKCmLgwIFs2rTJPUVWjnlReBER8UhWq4VJwzsBMOeHTHZo0UbBjeFl69atOJ1OXnnlFTZt2sQ///lPXn75ZR5//PFzHvePf/yD559/nhdffJFVq1YRGxvLVVddRVGRG/6H1SR1IiIeL7VtFFd2jsHhNHjqi82auE7cF16GDh3KrFmzSEtL46KLLuLaa6/l4Ycf5uOPPz7rMYZhMH36dCZPnswNN9xAUlISb775JidOnODdd991Q5VamFFExBv85erO+NssLNtxmG+25pldjpisQa/aBQUFREREnPX1PXv2kJubS1paWtU2u93OgAEDWL58eY3HlJaWUlhYWO1RWxYN2BUR8Qptoppw12WJAPy/LzZTVqGJ63xZg4WXXbt28a9//Ytx48addZ/c3FwAYmJiqm2PiYmpeu2Xpk6dSlhYWNUjPj6+9kVVjXnRrdIiIp7u/sHtaR5iZ2/+CWZ9r1unfVmdw8uUKVOwWCznfKxevbraMdnZ2QwdOpSbbrqJsWPH/up7WH7REmIYxhnbKk2aNImCgoKqR1ZWVu0/TNXyAGp5ERHxdE3tfjx66tbpf32zk7yiEpMrErP41fWA8ePHc8stt5xznzZt2lT9Ozs7m0GDBpGSksKrr756zuNiY2MBVwtMXFxc1fa8vLwzWmMq2e127HZ7LauvzqK7jUREvMqNF7fi7ZX7WL+/gGkLt/GP3/QwuyQxQZ3DS1RUFFFRUbXa98CBAwwaNIjk5GRmzZqF1XrukJCYmEhsbCzp6en06tULgLKyMpYsWcKzzz5b11Jr4VSf6a/UJSIinsFqtfDkiK7cOHM5H6zZz2/7tqZX62ZmlyUNzG1X7ezsbAYOHEh8fDzTpk3j0KFD5ObmnjF2pVOnTsybNw9wdRdNmDCBZ555hnnz5rFx40ZGjx5NcHAwt956a73XqEnqRES8T3JCM264uCWGAX/5ZKNWnfZBdW55qa1Fixaxc+dOdu7cSatWraq9dvo9+tu2baOgoKDq+aOPPsrJkye59957OXr0KP369WPRokWEhITUf5GGbpUWEfFGjw/vzH83H2RTdiFvr9zHnZcmml2SNCC3XbVHjx6NYRg1Pk5nGAajR4+uem6xWJgyZQo5OTmUlJSwZMkSkpKS3FKjBbW8iIh4o6imdv48zDXz7nOLtnOwUIN3fYlPX7U1YFdExHv9tk9resaHU1xawf/7YrPZ5UgD8u2rtrqNRES8ltVq4enrk7Ba4Iv1OSzbccjskqSB+PRVW91GIiLeLallGHektgHgfz7ZSEm5w9yCpEH49lVbdxuJiHi9iVd1ICbUNfPuv77ZYXY50gB8+qptObUwo0XzvIiIeK2QQH/+eq3rxo6Xl+xm44GCXzlCvJ1PX7U1YFdEpHEYmhTL8G6xOJwGj364nnLN/dKo+fZV+1R4MRReRES83l+vTSI82J/NOYW8unS32eWIG/n0Vbuq20jhRUTE6zUPsfPENV0A+L+vd7Azr9jkisRdfPqqXdVtpDEvIiKNwsheLRnQoTllFU7+/NF6nE7j1w8Sr+PTV23dKi0i0rhYLBaeuaEbTQJsrNl3lDe+32N2SeIGPn3VtlROUqeWFxGRRqNleBCPX90ZgH8s3MaOg0UmVyT1zcev2rrbSESkMbq1b2sGdnR1Hz30nwzKKnT3UWPi01ftypYXhRcRkcbFYrHwjxu7Ex7sz8YDhZq8rpHx6at25ZgXDdgVEWl8okMDefp61+R1L327k58yj5pckdQXn75qV415sdjMLURERNzimu4tuK5nC5wG/Ok/6zhRVmF2SVIPfDu8aMyLiEij99S1ScSGBrLn8HH+3xdbzC5H6oFPX7UrJ6nT3UYiIo1XWLA/z93cA4sF3vsxky/X55hdklwgn75qa20jERHfcGm7KO4Z0BaAxz5eT9aREyZXJBfCp6/aWh5ARMR3PHRVB3q1DqeopIL731urxRu9mE9ftXW3kYiI7/C3WXnhll6EBPqRkXWM59O3m12SnCefvmpbdbeRiIhPiY8I5tkbuwMwc/Eulm4/ZHJFcj58Orz83PJiMbkSERFpKMO7xXFrv9YATJibQfaxkyZXJHXl4+GlcsyLWl5ERHzJE9d0oWuLUI4cL+OeOT9RWuEwuySpAx8PLxrzIiLiiwL9bbz8+2TCgvxZl3WM//fFZrNLkjrw6at21dpGCi8iIj4nPiKY6bf0xGKBd1Zm8vFP+80uSWrJp6/ammFXRMS3DeoYzQOD2wPw+LwNbM4uNLkiqQ2fvmpbNcOuiIjPe/CK9gzs2JyScid/eHs1+cWlZpckv8Knr9qVM+xarRqwKyLiq6xWC9NH9SQhMpj9R09yz5yfKKvQBHaezLfDi2bYFfFYM2bMIDExkcDAQJKTk1m2bNlZ9/3444+56qqraN68OaGhoaSkpLBw4cIGrFa8XXhwAK/f0ZsQux8/7jnCE59uxKicC0w8jk9fta2620jEI82dO5cJEyYwefJk1q5dS//+/Rk2bBiZmZk17r906VKuuuoq5s+fz5o1axg0aBAjRoxg7dq1DVy5eLN20SG8cGsvrBZ4f1UWs5fvNbskOQuL0ciiZWFhIWFhYRQUFBAaGnrOfQ9NaUNzjrLrhgW07Z7aQBWKNH51+T2sSb9+/bj44ouZOXNm1bbOnTtz/fXXM3Xq1Fp9j65duzJq1CieeOKJBqlZGo/Xlu3m6S+3YLXArDv7MqBDc7NL8gl1+R306SaHygG7Fo15EfEYZWVlrFmzhrS0tGrb09LSWL58ea2+h9PppKioiIiIiLPuU1paSmFhYbWHCMCYyxK5KbkVTgPGz/mJLTn6f8PT+HR4Ac3zIuJpDh8+jMPhICYmptr2mJgYcnNza/U9nnvuOY4fP87NN9981n2mTp1KWFhY1SM+Pv6C6pbGw2Kx8PTIJPolRlBUWsGds1ZpCQEP49NX7cqWF6sG7Ip4HIul+ppjhmGcsa0m7733HlOmTGHu3LlER0efdb9JkyZRUFBQ9cjKyrrgmqXxsPvZePW23rSPbkpuYQmjZ/1Iwclys8uSU3z6ql05SR3qNhLxGFFRUdhstjNaWfLy8s5ojfmluXPnMmbMGP7zn/9w5ZVXnnNfu91OaGhotYfI6cKC/Zl9V1+iQ+xsP1jMH99erTWQPIRPh5eqlhetKi3iMQICAkhOTiY9Pb3a9vT0dFJTzz6w/r333mP06NG8++67XH311e4uU3xEy/AgZt3Zh6Z2P1buPsIjH6zH6WxU97l4JZ8OL5WT1GlVaRHPMnHiRF577TXeeOMNtmzZwkMPPURmZibjxo0DXF0+t99+e9X+7733HrfffjvPPfccl1xyCbm5ueTm5lJQUGDWR5BGpGuLMGb+/mL8rBY+W5fNk59t0hwwJnNbeNm7dy9jxowhMTGRoKAg2rZty5NPPklZWdk5jxs9ejQWi6Xa45JLLnFLjbrbSMQzjRo1iunTp/PUU0/Rs2dPli5dyvz580lISAAgJyen2pwvr7zyChUVFdx3333ExcVVPR588EGzPoI0Mv3bN+e5m3tgscDbK/cxbdE2s0vyaX7u+sZbt27F6XTyyiuv0K5dOzZu3Mjdd9/N8ePHmTZt2jmPHTp0KLNmzap6HhAQ4JYaLbrbSMRj3Xvvvdx77701vjZ79uxqzxcvXuz+gsTnXdezJcWlFUyet5GXvt1FSKA/4wa0Nbssn+S28DJ06FCGDh1a9fyiiy5i27ZtzJw581fDi91uJzY21l2lVamcYdeq8CIiIrXwu34JFJVU8PcFW/n7gq2EBPrxu34JZpflcxr0ql1QUHDOSaMqLV68mOjoaDp06MDdd99NXl7eWfe9kImmrGp5ERGROho3oC33DXK1uPzlk438Z5Vus29oDXbV3rVrF//617+qBtydzbBhw5gzZw7ffPMNzz33HKtWrWLw4MGUlta8RPmFTDRlqbrbSGNeRESk9h5O68jo1DYYBvz54/UKMA2szuFlypQpZwyo/eVj9erV1Y7Jzs5m6NCh3HTTTYwdO/ac33/UqFFcffXVJCUlMWLECBYsWMD27dv58ssva9z/Qiaa0sKMIiJyPiwWC0+O6MIdKQkKMCao85iX8ePHc8stt5xznzZt2lT9Ozs7m0GDBpGSksKrr75a5wLj4uJISEhgx44dNb5ut9ux2+11/r4ANsupbiPNsCsiInVksViYcm1XAN5csY8/f7wegJv7aKkJd6tzeImKiiIqKqpW+x44cIBBgwaRnJzMrFmzzmtgbH5+PllZWcTFxdX52HMxnE4qp6ZTt5GIiJyPXwaYRz9aT2mFg9tS2phbWCPntiaH7OxsBg4cSHx8PNOmTePQoUNVE0edrlOnTsybNw+A4uJiHn74YVasWMHevXtZvHgxI0aMICoqipEjR9ZrfU6ns+rfuttIRETOV2WAufPSNgD8z6ebeOnbnZrIzo3cdqv0okWL2LlzJzt37qRVq1bVXjv9P+i2bduqZsG02Wxs2LCBt956i2PHjhEXF8egQYOYO3cuISEh9Vqf0+mgqr1FLS8iInIBLBYLT1zThRC7Hy98s5P/XbiNwpJyHhvaqVYLikrduC28jB49mtGjR//qfqcHmaCgIBYuXOiukqpxOn9eXEstLyIicqEsFgsT0zoSEujP3+Zv4ZUluyk8WcHT1ydh0xp69cpt4cXTGeo2ahQcDgfl5VqmvqH5+/tjs6nFUqQmd19+ESGBfkyat4H3fszkcHEpL9zSi6AA/c7UF58NL9VbXvQ/lLcxDIPc3FyOHTtmdik+Kzw8nNjYWDWJi9Tglr6tCQ3yZ8LcDNI3H+SWf6/k9Tt6E9X0/O6Olep8OLz83PKieV68T2VwiY6OJjg4WBfQBmQYBidOnKia+bq+7wQUaSyGd4ujeYidu99azbqsY4yc8T2z7+xL2+ZNzS7N6ym8oJYXb+NwOKqCS2RkpNnl+KSgoCAA8vLyiI6OVheSyFn0aRPBx/ekMnrWKjKPnODGmct59bbe9E389aVy5Ox8tslBY168V+UYl+DgYJMr8W2VP3+NORI5t4uaN2Xevan0jA/n2Ilyfv/aD3z8036zy/JqPnvVNjTmxeupq8hc+vmL1F5kUzvv3X0JQ7rGUOZwMvE/6/h/X2ymwuH89YPlDD4bXk4fsKuTsIiIuFtQgI2Zv0vm/sHtAHj9uz3c/saPHDleZnJl3seHw4sr7ToNiwbsSoMYOHAgEyZMaPD3bdOmDdOnT2/w9xWRM1mtFv6U1pGXf38xTQJsLN+Vz4h/fcem7AKzS/MqvnvVrgwvqNVFREQa1tCkOObddyltIoM5cOwkN85czry1GgdTWz4bXpyGwouIiJinQ0wIn953GQM6NKek3MlDc9fxyAfrOFFWYXZpHs93w8upMS+G7/4IxAROp5NHH32UiIgIYmNjmTJlStVrBQUF/OEPfyA6OprQ0FAGDx7MunXrql7ftWsX1113HTExMTRt2pQ+ffrw3//+t9r3z8vLY8SIEQQFBZGYmMicOXMa6qOJyHkIC/bnjdF9eOjKDlgt8MGa/Vz74vdsyy0yuzSP5rNX7sq7jdTy4v0Mw+BEWYUpj7quGvvmm2/SpEkTfvjhB/7xj3/w1FNPkZ6ejmEYXH311eTm5jJ//nzWrFnDxRdfzBVXXMGRI0cA16rrw4cP57///S9r165lyJAhjBgxgszMzKrvP3r0aPbu3cs333zDhx9+yIwZM6omkxMRz2SzWnjwyvbMGXsJ0SF2duYVc+2L3/Hej5lamfosfHaSOsPp+h/CUHjxeifLHXR5omEW9PylzU8NITig9r9G3bt358knnwSgffv2vPjii3z99ddVK6rn5eVht7umD582bRqffPIJH374IX/4wx/o0aMHPXr0qPpeTz/9NPPmzeOzzz5j/PjxbN++nQULFrBy5Ur69esHwOuvv07nzp3r8ROLiLuktI1kwYP9mfifdSzZfohJH29g2Y5DPH19NyKaBJhdnkfx3ZYXo7LlxWd/BGKC7t27V3seFxdHXl4ea9asobi4mMjISJo2bVr12LNnD7t27QLg+PHjPProo3Tp0oXw8HCaNm3K1q1bq1petmzZgp+fH7179676/p06dSI8PLzBPp+IXJjIpnZmje7DpGGd8LNamL8hl7R/LuW/mw+aXZpH8dmWl6pbpTXHi9cL8rex+akhpr13Xfj7+1d7brFYcDqdOJ1O4uLiWLx48RnHVIaPRx55hIULFzJt2jTatWtHUFAQv/nNbygrc80RUdm8rHmLRLyb1WrhjwPakto2ion/yWBHXjFj31rNb5Jb8cSILoQG+v/6N2nkfDa8GFUDdnWi93YWi6VOXTee6OKLLyY3Nxc/Pz/atGlT4z7Lli1j9OjRjBw5EnCNgdm7d2/V6507d6aiooLVq1fTt29fALZt26aVt0W8VLdWYXx+/2U8n76dfy/bzYdr9rN852Ge/U13+rdvbnZ5pvLZPhOjap4Xn/0RiAe58sorSUlJ4frrr2fhwoXs3buX5cuX85e//IXVq1cD0K5dOz7++GMyMjJYt24dt956a7UFRjt27MjQoUO5++67+eGHH1izZg1jx46tWkRRRLxPoL+Nx4d35j9/TKF1RDDZBSXc9vqPTJybQX5xqdnlmcZnr9zGqXle1PIinsBisTB//nwuv/xy7rrrLjp06MAtt9zC3r17iYmJAeCf//wnzZo1IzU1lREjRjBkyBAuvvjiat9n1qxZxMfHM2DAAG644YaqW69FxLv1aRPBggf7c0dKAhYLfLz2AFc8v4T/rM7yyTuSLEYj+9SFhYWEhYVRUFBAaGjoWffbs+kHEj9I4zDhRE3Z14AVyoUqKSlhz549JCYmEhgYaHY5Putc/x1q+3voSbyxZvFNazOPMunjDWw9NRdMv8QInrmhG22bNzW5sgtTl99Bn215cepWaRER8UK9Wjfj8/svY9KwTgT6W/lhzxGGTl/K1PlbKCopN7u8BuGz4UUDdkVExFv526z8cUBb0h8awKCOzSl3GLyydDeDpi3m/R8zcTgbVafKGXw3vBgasCsiIt4tPiKYWXf2ZdboPlzUvAmHi8t47OMNXPvid/y454jZ5bmNz165K+82UsuLiIh4u0Gdovnqwcv5y9WdCQn0Y1N2ITe/soKxb65ia26h2eXVOx8OL6e6jSw++yMQEZFGJMDPytj+F7H44YHc2q81NquF/27JY9j/LeOhuRlk5p8wu8R647NX7p+7jdTyIiIijUdkUzvPjOzGoocu5+pucRgGzFt7gCueX8wTn24kt6DE7BIvmM+GF6q6jXz3RyAiIo1X2+ZNeel3F/P5+Mvo3z6KcofBWyv2cfk/vmXyvA1kHfHelhifvXI7Kyep0zowIiLSiHVrFcbbY/rx7th+9G0TQZnDyZwfMhk0bTGPfLCOvYePm11inXn3gjAXwFDLi4iI+JDUdlGktoti5e58XvxmJ9/tPMwHa/bz0U/7GZoUy5jLLiI5oZnZZdaK74YXQ/O8iIiI77nkokguuSiSNfuO8tK3O/lmax7zN+Qyf0MuPePDGds/kaFdY/Gzee4f9z4bXjTmRUREfFlyQjPeGN2HrbmFvPHdHj5Zm01G1jHGv7uWluFB3JGawKjerQkL9je71DP47JW76m4jjXmRRs7hcFRbfVpE5HSdYkP5x2968P1jg3nwivZENgngwLGTPDN/K32f+S9/+s861uw74lELQPpueFHLi5jgq6++4rLLLiM8PJzIyEiuueYadu3aBcDevXuxWCy8//77pKamEhgYSNeuXVm8eHHV8YsXL8ZisfDll1/So0cPAgMD6devHxs2bKjaZ/bs2YSHh/PFF1/QpUsX7HY7+/bt4+jRo9x+++00a9aM4OBghg0bxo4dOwA4dOgQsbGxPPPMM1Xf54cffiAgIIBFixY1zA9HREzVPMTOQ1d14PvHBvPsjd3oFBtCaYWTj37az40zVzB0+jJmf7+HghPmr5/ks1fuypYXjXlpBAwDyo6b86jjXyLHjx9n4sSJrFq1iq+//hqr1crIkSOrtYw88sgj/OlPf2Lt2rWkpqZy7bXXkp+fX+37PPLII0ybNo1Vq1YRHR3NtddeS3n5zyeUEydOMHXqVF577TU2bdpEdHQ0o0ePZvXq1Xz22WesWLECwzAYPnw45eXlNG/enDfeeIMpU6awevVqiouL+f3vf8+9995LWlrahf33ERGvEuhvY1Sf1ix4sD8f3ZPKb5JbEehvZdvBIqZ8vpm+z/yXCe+vZcn2Q1Q4zGnV9d0xL6cG7KJuI+9XfgKeaWHOez+eDQFNar37jTfeWO3566+/TnR0NJs3b6ZpU9dy9uPHj6/ab+bMmXz11Ve8/vrrPProo1XHPfnkk1x11VUAvPnmm7Rq1Yp58+Zx8803A1BeXs6MGTPo0aMHADt27OCzzz7j+++/JzU1FYA5c+YQHx/PJ598wk033cTw4cO5++67+d3vfkefPn0IDAzk73//+3n+YETE21ksFpITmpGc0Iz/uaYLn6w9wLs/ZLLtYBGfZGTzSUY2zUPsXNujBSN7taRri1AsDXRN9dnwYpxacVMtL9KQdu3axf/8z/+wcuVKDh8+XNXikpmZSZcuXQBISUmp2t/Pz4/evXuzZcuWat/n9H0iIiLo2LFjtX0CAgLo3r171fMtW7bg5+dHv379qrZFRkaecdy0adNISkriP//5D6tXryYwMLCePrmIeLOwIH/uSG3D7SkJZGQdY97aA3y+LptDRaW8/t0eXv9uD+2im3JdjxYM6xZHu+imbq3Hh8NL5a3SPttz1nj4B7taQMx67zoYMWIE8fHx/Pvf/6ZFixY4nU6SkpIoKys753G1+Wvm9H2CgoKqPT/bQDvDMKrtt3v3brKzs3E6nezbt69aABIRsVgs9GrdjF6tm/GXq7uwdPsh5mUcIH3zQXbmFfNc+naeS99O++imDOsWx7CkWDrFhtR7i4zvhpdTJ3MtzNgIWCx16roxS35+Plu2bOGVV16hf//+AHz33Xdn7Ldy5Uouv/xyACoqKlizZg3jx48/Y5/WrVsDcPToUbZv306nTp3O+t5dunShoqKCH374oarbKD8/n+3bt9O5c2cAysrK+N3vfseoUaPo1KkTY8aMYcOGDcTExFz4hxeRRifAz8qVXWK4sksMhSXlfLUhly835LB812F25BWz4+sdvPD1DtpEBjM0KY5RfeJJjKqfc7XPhhc0SZ00sGbNmhEZGcmrr75KXFwcmZmZPPbYY2fs99JLL9G+fXs6d+7MP//5T44ePcpdd91VbZ+nnnqKyMhIYmJimDx5MlFRUVx//fVnfe/27dtz3XXXcffdd/PKK68QEhLCY489RsuWLbnuuusAmDx5MgUFBbzwwgs0bdqUBQsWMGbMGL744ot6/TmISOMTGujPzX3iublPPAUny/l6y0EWbMxlyfZD7M0/wctLdtGrdXi9hRe3Njtce+21tG7dmsDAQOLi4rjtttvIzj53875hGEyZMoUWLVoQFBTEwIED2bRpU73XFpGQxMpWd1LU8cZf31mkHlitVt5//33WrFlDUlISDz30EP/7v/97xn5///vfefbZZ+nRowfLli3j008/JSoq6ox9HnzwQZKTk8nJyeGzzz4jICDgnO8/a9YskpOTueaaa0hJScEwDObPn4+/vz+LFy9m+vTpvP3224SGhmK1Wnn77bf57rvvmDlzZr3+HESkcQsL8ueGi1vx79t7s/Z/ruLFW3txXc8WDOjQvN7ew2K4cdaZf/7zn6SkpBAXF8eBAwd4+OGHAVi+fPlZj3n22Wf529/+xuzZs+nQoQNPP/00S5cuZdu2bYSEhPzqexYWFhIWFkZBQQGhoaH19lnEc5SUlLBnzx4SExMb1YDSvXv3kpiYyNq1a+nZs2eN+yxevJhBgwZx9OhRwsPDG7S+XzrXfwdv/D30xppFGpO6/A66tdvooYceqvp3QkICjz32GNdffz3l5eX4+5853bBhGEyfPp3Jkydzww03AK7bQGNiYnj33Xf54x//6M5yRURExAs02GjVI0eOMGfOHFJTU2sMLgB79uwhNze32qRYdrudAQMGnLW1prS0lMLCwmoPERERabzcHl7+/Oc/06RJEyIjI8nMzOTTTz896765ubkAZ9zdEBMTU/XaL02dOpWwsLCqR3x8fP0VL9KA2rRpg2EYZ+0yAhg4cCCGYZjeZSQiYqY6h5cpU6ZgsVjO+Vi9enXV/o888ghr165l0aJF2Gw2br/99l9d3OmX94P/ci6K002aNImCgoKqR1ZWVl0/koiIiHiROo95GT9+PLfccss592nTpk3Vv6OiooiKiqJDhw507tyZ+Ph4Vq5cWW2G0EqxsbGAqwUmLi6uanteXt5Z55qw2+3Y7fa6fgwRERHxUnUOL5Vh5HxUtriUlpbW+HpiYiKxsbGkp6fTq1cvwDVx1pIlS3j22WfP6z2l8Tp9MUNpePr5i4hZ3Ha30Y8//siPP/7IZZddRrNmzdi9ezdPPPEEbdu2rdbq0qlTJ6ZOncrIkSOxWCxMmDCBZ555hvbt29O+fXueeeYZgoODufXWW91VqniZgIAArFYr2dnZNG/enICAgAZbDExcf4SUlZVx6NAhrFbrr84vIyJS39wWXoKCgvj444958sknOX78OHFxcQwdOpT333+/WjfPtm3bKCgoqHr+6KOPcvLkSe69916OHj1Kv379WLRoUa3meBHfYLVaSUxMJCcn51cnPRT3CQ4OpnXr1litWmJDRBqWWyepM4MmmvIdhmFQUVGBw+EwuxSfY7PZ8PPzO2uLlzf+HnpjzSKNicdMUifiThaLBX9//7POGyQiIo2T2ntFRETEqyi8iIiIiFdReBERERGv0ujGvFSOP9YaRyLmqfz986b7AXTuEDFXXc4bjS68FBUVAWiNIxEPUFRURFhYmNll1IrOHSKeoTbnjUZ3q7TT6SQ7O5uQkJBfnbissLCQ+Ph4srKyvP7WSH0Wz9SYPgvU/vMYhkFRUREtWrTwmnlganvuaEz/TRvTZ4HG9Xl88bPU5bzR6FperFYrrVq1qtMxoaGhXv8/RyV9Fs/UmD4L1O7zeEuLS6W6njsa03/TxvRZoHF9Hl/7LLU9b3jHn0QiIiIipyi8iIiIiFfx6fBit9t58sknq6215K30WTxTY/os0Pg+z/loTD+DxvRZoHF9Hn2Wc2t0A3ZFRESkcfPplhcRERHxPgovIiIi4lUUXkRERMSrKLyIiIiIV/HZ8DJjxgwSExMJDAwkOTmZZcuWmV3SeVm6dCkjRoygRYsWWCwWPvnkE7NLOm9Tp06lT58+hISEEB0dzfXXX8+2bdvMLuu8zJw5k+7du1dNypSSksKCBQvMLqteTJ06FYvFwoQJE8wuxRQ6d3iWxnTegMZ77qjv84ZPhpe5c+cyYcIEJk+ezNq1a+nfvz/Dhg0jMzPT7NLq7Pjx4/To0YMXX3zR7FIu2JIlS7jvvvtYuXIl6enpVFRUkJaWxvHjx80urc5atWrF3//+d1avXs3q1asZPHgw1113HZs2bTK7tAuyatUqXn31Vbp37252KabQucPzNKbzBjTOc4dbzhuGD+rbt68xbty4ats6depkPPbYYyZVVD8AY968eWaXUW/y8vIMwFiyZInZpdSLZs2aGa+99prZZZy3oqIio3379kZ6eroxYMAA48EHHzS7pAanc4fna2znDcPw7nOHu84bPtfyUlZWxpo1a0hLS6u2PS0tjeXLl5tUldSkoKAAgIiICJMruTAOh4P333+f48ePk5KSYnY55+2+++7j6quv5sorrzS7FFPo3OEdGst5AxrHucNd541GtzDjrzl8+DAOh4OYmJhq22NiYsjNzTWpKvklwzCYOHEil112GUlJSWaXc142bNhASkoKJSUlNG3alHnz5tGlSxezyzov77//Pj/99BOrVq0yuxTT6Nzh+RrDeQMaz7nDnecNnwsvlX655L1hGGdsE/OMHz+e9evX891335ldynnr2LEjGRkZHDt2jI8++og77riDJUuWeN1JKCsriwcffJBFixYRGBhodjmm07nDczWG8wY0jnOHu88bPhdeoqKisNlsZ/yllJeXd8ZfVGKO+++/n88++4ylS5fSqlUrs8s5bwEBAbRr1w6A3r17s2rVKv7v//6PV155xeTK6mbNmjXk5eWRnJxctc3hcLB06VJefPFFSktLsdlsJlbYMHTu8GyN5bwBjePc4e7zhs+NeQkICCA5OZn09PRq29PT00lNTTWpKgHXX7Djx4/n448/5ptvviExMdHskuqVYRiUlpaaXUadXXHFFWzYsIGMjIyqR+/evfnd735HRkaGTwQX0LnDUzX28wZ457nD3ecNn2t5AZg4cSK33XYbvXv3JiUlhVdffZXMzEzGjRtndml1VlxczM6dO6ue79mzh4yMDCIiImjdurWJldXdfffdx7vvvsunn35KSEhI1V+4YWFhBAUFmVxd3Tz++OMMGzaM+Ph4ioqKeP/991m8eDFfffWV2aXVWUhIyBnjB5o0aUJkZKRXjys4Hzp3eJ7GdN6AxnPucPt5o17uWfJCL730kpGQkGAEBAQYF198sdfeVvftt98awBmPO+64w+zS6qymzwEYs2bNMru0Orvrrruq/v9q3ry5ccUVVxiLFi0yu6x646u3ShuGzh2epjGdNwyjcZ876vO8YTEMw7jwCCQiIiLSMHxuzIuIiIh4N4UXERER8SoKLyIiIuJVFF5ERETEqyi8iIiIiFdReBERERGvovAiIiIiXkXhRURERLyKwouIiIh4FYUXERER8SoKLyIiIuJVFF5ERETEq/x/fm7ETeTVGTIAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# basic plot\n",
    "plt.subplot(121)\n",
    "plt.plot(r / lab, h, label='head')\n",
    "plt.plot(r / lab, happrox, label='approx')\n",
    "plt.legend()\n",
    "plt.subplot(122)\n",
    "plt.plot(r / lab, Qtot / Q);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true,
    "tags": [
     "remove-input",
     "remove-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/papermill.record/image/png": "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",
      "application/papermill.record/text/plain": "<Figure size 800x320 with 2 Axes>"
     },
     "metadata": {
      "scrapbook": {
       "mime_prefix": "application/papermill.record/",
       "name": "fig_semi_con"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x320 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "fig = plt.figure(figsize=diagrams_2d.figdef2)\n",
    "plt.subplot(121)\n",
    "plt.plot(r / lab, h, label='head')\n",
    "plt.plot(r / lab, happrox, '--', label='approx')\n",
    "plt.text(1.2, -2, 'r=1.123$\\\\lambda$', rotation=90)\n",
    "plt.legend(loc='best')\n",
    "plt.axvline(1.123, ls='-.', color='k')\n",
    "plt.xlabel('$r/\\\\lambda$')\n",
    "plt.ylabel('head (m)')\n",
    "plt.title('(a)', loc='left')\n",
    "plt.grid()\n",
    "plt.subplot(122)\n",
    "plt.plot(r / lab, Qtot / Q)\n",
    "plt.xlabel('$r/\\\\lambda$')\n",
    "plt.ylabel('$Q_{tot}/Q$')\n",
    "plt.title('(b)', loc='left')\n",
    "plt.ylim(0, 1.03)\n",
    "plt.grid()\n",
    "plt.tight_layout()\n",
    "glue('fig_semi_con', fig, display=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{glue:figure} fig_semi_con\n",
    "---\n",
    "name: fig_well_semi_con_aquifer6.4\n",
    "---\n",
    "A well in a semi-confined aquifer; head (left) and total flow in the aquifer (right).\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{exercise}\n",
    ":label: ex_610_compute_head_example\n",
    "\n",
    "For the values of the example, compute the head at the well as a function of $c$ for $c$ varying from 100 d to 5000 d. Plot the head at the well vs. $c$.\n",
    "\n",
    "<details>\n",
    "<summary><strong> Solution </strong></summary>\n",
    "\n",
    "<img src=\"figures_chap6/sol_ex_6_10.png\" width=300px align=center>\n",
    "\n",
    "</details>\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{exercise}\n",
    ":label: ex_611_compute_head_well_0_1\n",
    "\n",
    "Consider two pumping wells in a semi-confined aquifer. Aquifer properties are $T=200$ m$^2$/d, $c=200$ d, $h^*=-2$ m. Well 0 is located at $(x_0, y_0) = (0, 0)$ and has a discharge $Q_0=500$ m$^3$/d, and well 1 is located at $(x_1, y_1)=(400, 200)$ and has a discharge $Q_1=200$ m$^3$/d; the radius of the wells is 0.2 m. Make a contour plot of the heads in the aquifer. Compute the head at wells 0 and 1 for the case that $c = 200$ d. Next, compute the head at wells 0 and 1 for the case that $c = 1000$ d.\n",
    "\n",
    "<details>\n",
    "<summary><strong> Solution </strong></summary>\n",
    "\n",
    "$h_0 = -4.81$ m, $h_1 = -3.15$ m for $c = 200$ d\\\n",
    "$h_0 = -5.18$ m, $h_1 = -3.41$ m for $c = 1000$ d\n",
    "\n",
    "<img src=\"figures_chap6/sol_ex_6_11.png\" width=300px align=center>\n",
    "\n",
    "</details>\n",
    "\n",
    "```"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Tags",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.5"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}