projekt_cfd_roe+ausm.ipynb

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    "# Projekt CFD WS 2016 / 2017\n",
    "\n",
    "## Advanced Upstream Splitting Method:\n",
    "\n",
    "$\n",
    "\\frac{\\partial}{\\partial t}\\left(\\begin{array}{c}\n",
    "\\rho\\\\\n",
    "\\rho u\\\\\n",
    "e\n",
    "\\end{array}\\right)+\\frac{\\partial}{\\partial x}\\left(\\begin{array}{c}\n",
    "\\rho u\\\\\n",
    "\\rho u^{2}+p\\\\\n",
    "\\left(e+p\\right)u\n",
    "\\end{array}\\right)=-\\frac{S_{x}}{S}\\left(\\begin{array}{c}\n",
    "\\rho u\\\\\n",
    "\\rho u^{2}\\\\\n",
    "\\left(e+p\\right)u\n",
    "\\end{array}\\right)\n",
    "$\n",
    "\n",
    "For the AUSM approach the second term is splitted into a convection-term and a term containing the information of acustic wave transport. So these terms can be treated in different way.\n",
    "\n",
    "$\n",
    "\\mathbf{F}=M\\cdot c\\left(\\begin{array}{c}\n",
    "\\rho\\\\\n",
    "\\rho u\\\\\n",
    "e+p\n",
    "\\end{array}\\right)+\\left(\\begin{array}{c}\n",
    "0\\\\\n",
    "p\\\\\n",
    "0\n",
    "\\end{array}\\right)=\\mathbf{f}^{(c)}+\\mathbf{P}\n",
    "$\n",
    "\n",
    "\n",
    "The speed of the convection-transport is the local velocity of the fluid $u$. For the 1D-case the direction is given by the sign of $u$. No convection-information can \"flow\" upstram. This term can be numerical represented by splitting the flux with regard to the local velocity.\n",
    "The pressure information is send up and down the stream if the velocity is smaller then the local speed of sound c. Thus a central discretization scheme is used to represent the information transport if M < 1. Else the discretization is choosen according to the local velocity.\n",
    "With AUSM a central differenziation is weighted by the local velocity. According to the weight of upstream and downstream  information is choosen by some polynomials.\n",
    "These polynomials are functions of the local Mach-number M and a shape-function \n",
    "$\\alpha$ and $\\beta$. The functions are implemented in *AUSM_1D.M_split* and *AUSM_1D.P_split*."
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    "import numpy as np\n",
    "import scipy.optimize\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = 11, 8"
   ]
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    "class AUSM_1D(object):\n",
    "    \"\"\"This class provides methods to solve a 1D nozzle flow problem\n",
    "       described with the euler-flow-equations.\n",
    "       AUSM: Advection Upstream Splitting Method\"\"\"\n",
    "    \n",
    "    # default values for the splitting polynoms\n",
    "    beta = 1 / 8\n",
    "    alpha = 3 / 16 * 0.5\n",
    "    \n",
    "    @staticmethod\n",
    "    def M_split(M, sign, beta):\n",
    "        \"\"\"13-99\"\"\" # splitting polynom for the Mach number\n",
    "        if abs(M) >= 1:\n",
    "            return 0.5 * (M + abs(M) * sign)\n",
    "        else:\n",
    "            par = sign * beta * (M**2 - 1)**2\n",
    "            return sign * 0.25 * (M + sign) ** 2 + par\n",
    "\n",
    "    @staticmethod\n",
    "    def P_split(M, sign, alpha):\n",
    "        \"\"\"13.101\"\"\" # splitting polynom for the pressure\n",
    "        if abs(M) >= 1:\n",
    "            return 0.5 * (1 + sign * (np.sign(M)))\n",
    "        else:\n",
    "            par = sign * alpha * M * (M**2 - 1)**2\n",
    "            return 0.25 * (M + sign)**2 * (2 - sign * M) + par\n",
    "        \n",
    "    @staticmethod\n",
    "    def lr_split(value):\n",
    "        \"\"\"if value >= 0 -> left, else right\"\"\"\n",
    "        return ((value >= 0) * value, (value < 0) * value)\n",
    "\n",
    "    @staticmethod\n",
    "    def cellFunc(foo, *args):\n",
    "        \"\"\"map foo @ args, args are array of equal lengths\"\"\"\n",
    "        # is needed to map a function at a matrix/ array\n",
    "        return np.array([foo(*[val[i] for val in args]) \n",
    "                                for i in range(len(args[0]))])\n",
    "        \n",
    "    def __init__(self, parameter):  # 1\n",
    "        # entry point for object creation\n",
    "        self.parameter = parameter\n",
    "        self.time = 0.\n",
    "        self._computeGeometry()  # 1.1\n",
    "        self._initUVector()      # 1.2\n",
    "    \n",
    "    def _computeGeometry(self):  # 1.1\n",
    "        \"\"\"compute the geometry and derivatives\"\"\"\n",
    "        par = self.parameter\n",
    "        self.x = np.linspace(par[\"xmin\"], par[\"xmax\"], par[\"numx\"])\n",
    "        self.S = par[\"ymin\"] + (par[\"ymax\"]-par[\"ymin\"])*(self.x/par[\"xmax\"])**2\n",
    "        self.dS = 2 * (par[\"ymax\"] - par[\"ymin\"]) * self.x / par[\"xmax\"] ** 2\n",
    "        self.dx = self.x[1] - self.x[0]\n",
    "        \n",
    "    def _initUVector(self):     # 1.2\n",
    "        \"\"\"initialize the U-Vector\"\"\"\n",
    "        par = self.parameter\n",
    "        rho_tot = par[\"p_tot\"] / par[\"R\"] / par[\"T_tot\"]\n",
    "        p_start = (par[\"p_tot\"] + par[\"p_exit\"]) / 2\n",
    "        self.u = np.array([\n",
    "            self.vec_1 * rho_tot,                        # u[0]\n",
    "            self.vec_0,                                  # u[1]\n",
    "            self.vec_1 * p_start / (self.gamma -1)  # u[2]\n",
    "        ])\n",
    "    \n",
    "    def timeStep(self):   # 2.1\n",
    "        \"\"\"compute one time-step\"\"\"\n",
    "        max_eigen = max(list(abs(self.u_vel + self.c_wave)) + \n",
    "                        list(abs(self.u_vel - self.c_wave)))\n",
    "        dt = self.parameter[\"cfl\"] * self.dx / max_eigen\n",
    "        self.time += dt\n",
    "        self.dt = dt\n",
    "        return dt\n",
    "\n",
    "    def compute_c_star(self): # 2.2\n",
    "        \"\"\"return an array with len(u - 1)\"\"\"\n",
    "        u_l, u_r = self.lr_split(self.u_vel)\n",
    "        c_l = self.c_wave**2 / self.cellFunc(max, self.c_wave, abs(u_l))\n",
    "        c_r = self.c_wave**2 / self.cellFunc(max, self.c_wave, abs(u_r))\n",
    "        return np.array([min(c_lr) for c_lr in zip(c_l[:-1], c_r[1:])])\n",
    "    \n",
    "    def compute_m_star(self, c_star): # 2.3\n",
    "        M_split_n = np.vectorize(lambda M: AUSM_1D.M_split(M, -1, self.beta))\n",
    "        M_split_p = np.vectorize(lambda M: AUSM_1D.M_split(M, +1, self.beta))\n",
    "        M_l = self.u_vel[:-1] / c_star\n",
    "        M_r = self.u_vel[1:] / c_star\n",
    "        return M_split_p(M_l) + M_split_n(M_r)\n",
    "    \n",
    "    def compute_p_star(self, c_star): # 2.4\n",
    "        P_split_n = np.vectorize(lambda M: AUSM_1D.P_split(M, -1, self.alpha))\n",
    "        P_split_p = np.vectorize(lambda M: AUSM_1D.P_split(M, +1, self.alpha))\n",
    "        M_l = self.u_vel[:-1] / c_star\n",
    "        M_r = self.u_vel[1:] / c_star\n",
    "        return P_split_p(M_l) * self.p[:-1] + P_split_n(M_r) * self.p[1:]\n",
    "    \n",
    "    def compute_f_star(self, c_star, m_star, p_star): # 2.5\n",
    "        m_star_p = 0.5 * (m_star + abs(m_star))  # 13.106\n",
    "        m_star_n = 0.5 * (m_star - abs(m_star))\n",
    "        f_star = c_star * (m_star_p * self.phi[:,:-1] + m_star_n * self.phi[:,1:])\n",
    "        return f_star + np.array([self.vec_0[:-1], p_star, self.vec_0[:-1]])\n",
    "    \n",
    "    def compute_source(self):   # 2.6\n",
    "        return self.dS / self.S * (self.u_vel * self.phi)\n",
    "\n",
    "    def applyBoundaries(self):  # 2.7\n",
    "        par = self.parameter\n",
    "        cp = self.gamma / (self.gamma - 1) * par[\"R\"]\n",
    "        rho_tot = par[\"p_tot\"] / par[\"R\"] / par[\"T_tot\"]\n",
    "        p_tot = par[\"p_tot\"]\n",
    "\n",
    "        # in->|.|.|...\n",
    "        rho = 2 * self.u[0][1] - self.u[0][2]\n",
    "        if rho > rho_tot:\n",
    "            rho = rho_tot\n",
    "        p = p_tot * (par[\"R\"] * par[\"T_tot\"] * rho / p_tot) ** self.gamma\n",
    "        \n",
    "        temp = 1 - (p / p_tot) ** ((self.gamma - 1) / self.gamma)\n",
    "        vel = (2 * cp * par[\"T_tot\"] * temp) ** 0.5\n",
    "        e = p / (self.gamma - 1) + rho * vel ** 2 / 2\n",
    "        self.u[0, 0] = rho\n",
    "        self.u[1, 0] = rho * vel\n",
    "        self.u[2, 0] = e\n",
    "    \n",
    "        # ...|.|.|->out\n",
    "        p = par[\"p_exit\"]\n",
    "        rho = 2 * self.u[0][-2] - self.u[0][-3]\n",
    "        if rho > rho_tot:\n",
    "            rho = rho_tot\n",
    "        self.u[0, -1] = rho\n",
    "        self.u[1, -1] = 2 * self.u[1][-2] - self.u[1][-3]\n",
    "        self.u[2, -1] = 2 * self.u[2][-2] - self.u[2][-3]\n",
    "        \n",
    "        if (par[\"subsonic_exit\"]):\n",
    "            p = par[\"p_exit\"]\n",
    "            e = p / (self.gamma - 1) + self.u[1][-1] ** 2 / 2. / rho\n",
    "            self.u[2][-1] = e\n",
    "\n",
    "    def makeStep(self):  # 2\n",
    "        \"\"\"compute one time step\"\"\"\n",
    "        dt = self.timeStep() # 2.1\n",
    "        c_star = self.compute_c_star() # 2.2\n",
    "        m_star = self.compute_m_star(c_star) # 2.3\n",
    "        p_star = self.compute_p_star(c_star) # 2.4\n",
    "        f_star = self.compute_f_star(c_star, m_star, p_star) # 2.5\n",
    "        source = self.compute_source() # 2.6\n",
    "    \n",
    "        # Integration of u\n",
    "        du = -dt / self.dx * (f_star[:,1:] - f_star[:,:-1]) - source[:,1:-1] * dt\n",
    "        self.u[:,1:-1] += du\n",
    "        \n",
    "        self.applyBoundaries() # 2.7\n",
    "    \n",
    "    @property\n",
    "    def gamma(self):\n",
    "        return self.parameter[\"kappa\"]\n",
    "    \n",
    "    @property\n",
    "    def phi(self):\n",
    "        \"\"\"Eq.13.96\"\"\"\n",
    "        return np.array([self.u[0], self.u[1], self.u[0] * self.H])\n",
    "    \n",
    "    @property\n",
    "    def rho(self):\n",
    "        return self.u[0]\n",
    "    \n",
    "    @property\n",
    "    def p(self):\n",
    "        return (self.u[2] - self.rho * self.u_vel ** 2 / 2)*(self.gamma - 1)\n",
    "    \n",
    "    @property\n",
    "    def H(self):\n",
    "        \"\"\"13.89\"\"\"\n",
    "        return self.u_vel ** 2 / 2 + self.c_wave ** 2/(self.gamma - 1)\n",
    "    \n",
    "    @property\n",
    "    def u_vel(self):\n",
    "        return self.u[1] / self.rho;\n",
    "    \n",
    "    @property\n",
    "    def c_wave(self):\n",
    "        return (self.gamma * self.p / self.rho) ** 0.5\n",
    "    \n",
    "    @property\n",
    "    def Mach(self):\n",
    "        return self.u_vel / self.c_wave\n",
    "    \n",
    "    @property\n",
    "    def vec_1(self):\n",
    "        \"\"\"[1, 1, ..., 1, 1]\"\"\"\n",
    "        return np.ones(self.parameter[\"numx\"])\n",
    "    \n",
    "    @property\n",
    "    def vec_0(self):\n",
    "        \"\"\"[0, 0, ..., 0, 0]\"\"\"\n",
    "        return np.zeros(self.parameter[\"numx\"])"
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G5AJ5jY87rLWnv1ClDSOkA5utxwIHL9Cm1BgTAPQGKhAREZEOU1tby8GDB53l\n008/pa6ujsceewyAe++9l4KCAidoLliwgFWrVjmfDw4OJjo6mqioKPr378/IkSMZOnSo8/6zzz7b\nIkB+8MEH+Pv7t7q+sWNbHnANCwv7XPsp7mlNMH0Y+BrwBvAJkEzD7Ph7gRQg5gvWsB5INMbEAweA\n24HPnvSwFLgHWA3cDKzylvNLRUREfMXevXspKSlhwoQJADz33HOsWLHCueHI+S67FxUV5QTTjIwM\nIiIinPd+/vOfc/bsWSeMNp0LeiGfDZaXE0rFN1wymFprXzDG/I6GgPossBD4VlsFw8ZzRucDK2i4\nXNRL1trtxpgngQ3W2qXA74D/NcYU0TBSentbfG0REZGuwOPxcPDgQfbt2+fcOrnpVspHjhxh9erV\nGGP4/ve/z1/+8hdqamowxrB//37Ky8sZPHgwV111lXN95/79+ztLeHi483WaAmqT0aNHd/SuSifX\n2uuY1gBPG2MWAf8KrDPGzLfWrm2LIqy1bwFvfea1HzR7Xgvc0hZfS0RExFdt376ddevWcc899+Dn\n58d//ud/8qtf/YrS0tJzbqMcHh7u3L3uzJkzBAUF8S//8i888MADWGsxxvBf//VfLu2JdFWXDKbG\nmAk0HLIf1vgYBZykYVa8iIiItDNrLeXl5ezZs4fi4mKKi4tbPN+8eTNhYWG8+uqr/OQnP2H69On0\n69eP6Ohoxo8fz+DBg52l6XbK5zusPnLkSBf2TuSfWjNi+gGwFXgVWKg7LomIiLSP8vJyNm7cyIQJ\nEwgJCeH111/nxz/+McXFxVRXV7do269fP+Lj47n66qupra0F4KGHHuKrX/0qUVFRAHzlK1/hK1/5\nSofvh8jn1Zpg+g0gA/gS8Jgx5igNs/LzgG3W2v9rx/pERER8RlVVFUVFRRw9epSioiJ2795NUVER\nzz//PGlpafztb3/j61//Oh9//DFXXXUVoaGhDB06lKlTpzJkyBDi4+NJSEhg8ODBBAcHn7P9fv36\nubBXIm2nNZOfftN83RgTCwynIazOBRRMRUREGlVVVeHn50ePHj3Iy8vjmWeeYdeuXRQVFVFWVtai\nbVRUFEOGDHFGQ2fNmsXHH3/MiBEjAJgxYwYzZszo8H0Qcctl3/mp8SL3pXxmspKIiEhXUVNTw+7d\nuyksLGTXrl1MnTqVUaNGkZOTwzXXXMMrr7zCnXfeSVVVFcuXLycxMZGZM2cydOhQTp8+zezZsxky\nZAihoaFg6eYuAAAgAElEQVQtthsTE0NMzBe9CqNI5+UNtyQVERHxStXV1XzwwQcUFha2WEpKSmh+\n1cQePXowatQoUlNT+elPf+qMeF555ZUcPNjynjE5OTmMGjWqQ/dDpLNQMBURkS7LWsvRo0epq6sj\nJiaGo0ePct999zFr1izmzZvHsWPHmDlzJgC9e/cmKSmJCRMmkJSURFJSEomJiSQmJjojn1FRUXzv\ne99zc5dEOjUFUxER8Xlnzpxh9+7dFBQUsHPnTnbu3Ok8P3bsGPPnz+f5558nNDSU3bt3c+rUKQD6\n9+/Phx9+SHJyMpGRkRhjXN4TEd+mYCoiIj7l448/BmD8+PFYaxk+fDj5+fl4PB6nTb9+/UhOTubW\nW28lOTmZ8ePHAxAYGEhubq7Tzhjj3J5TRNqfgqmIiHQqdXV1FBcXU1BQ4CyRkZE89dRTANx1110k\nJCSwatUqjDFMmTKFG2+8keTkZIYNG0ZSUtI5k45ExDsomIqIiFdbunQp69atIz8/n4KCAnbt2sXZ\ns2ed96Ojo5kyZYqz/uc//9m5wDzAf//3f3dovSLy+SmYioiIa5putbl//37GjBkDwGOPPcb69ev5\n8MMPAfj1r3/NO++8w9ChQxk2bBjXX389w4YNIyUlheTkZPr06dNim1dccUWH74eItA0FUxERaXce\nj4fi4mLy8/Odkc+mx+PHj9O9e3dOnTqFn58fkZGRDBkyBGstxhh+//vf07t3b7p16+b2bohIO1Mw\nFRGRNrV3717WrFnDLbfcgr+/P08++SQ//elPOX36tNMmJiaGlJQU7rjjDlJSUkhJSXGuC/r444+3\n2F5kZGSH1i8i7lEwFRGRy3bs2DFn9LNpefnll4mMjOSPf/wj/+///T+uuOIKhgwZwqhRo3j44Yed\nADps2LBzDr+LiICCqYiIXEJxcTHLli1rEULLy8ud94OCgkhOTubIkSNERkZy7733Mnv2bAYNGgTA\n9ddfz/XXX+9W+SLSiSiYioh0cR6Ph7179xIREUGfPn345JNPeOyxx/jFL37B+PHj2bJlCw8//DCh\noaGkpKQwY8YMUlNTnRHQuLg4/P39ne3FxsYSGxvr4h6JSGelYCoi0kWcPn2aXbt2kZ+fz44dO5zR\nz8LCQmpra/nDH/7Al7/8ZXr27ElwcLBzQfqpU6dy8OBBYmJidOcjEWlXCqYiIj7m7NmzbNmyhfDw\ncIYMGcLu3buZMWMGe/bsccKmMYa4uDhSUlKYMmUKqampzh2ORowYwapVq5zt9ezZk549e7qyLyLS\ntSiYioh0UkeOHGkx+jlu3Dhuv/12KioqGDNmDN/97nd56qmniImJISMjg9tuu42UlBRSU1NJSkqi\nR48ebu+CiEgLCqYiIl7OWsvKlSvPOQR/5MgRp02PHj3o1asXAFFRUbz55puMHDkSaBjxXLx4sSu1\ni4hcDgVTEREvUFdXx/Hjx+nbty8ADzzwANHR0UyePBmAO+64g4qKCsLDw0lJSeHGG29sMQFp4MCB\n+Pn5AQ2H6W+44QbX9kVE5PNSMBUR6UC1tbUUFhY6o55NI6CFhYWMGzeODz74AIB9+/Y5M92NMaxc\nuZIBAwYQFRWlCUgi4rMUTEVE2kFlZSWlpaWkpqYC8Oijj7J06VKKi4upr68HwM/Pj/j4eFJTU5k5\ncyZZWVnO55cvXw5ATk4OAJmZmR27AyIiLlAwFRH5nKy1HD582Bn1/PTTT3nyyScBuOuuu1i9erVz\nHmhQUBCZmZncddddziH4pKQkunfv7uYuiIh4FQVTEZFWKC8vZ8uWLU4IbXqsqKhw2oSGhvLv//7v\nBAUF8eijj1JZWUl9fT1+fn787Gc/c7F6EZHOQcFURKRRXV0dfn5++Pn5sWLFCv74xz+yaNEievXq\nxTPPPMPTTz8NQEREBKmpqdx8883O6GdqaioDBgxwzv+85ppr3NwVEZFOScFURLqcpglIzS+9tGPH\nDnbt2kVubi7Jycns2rWL999/n4MHD5KUlMRXv/pVZs6cSUpKCpGRkW7vgoiIT3I1mBpjwoHXgThg\nL3CrtfbYedp5gLzG1f3WWl0HRUQuqaqqCn9/f4KDg1m9ejVPPfUUO3bsYM+ePS0mICUkJJCSksKX\nvvQlgoODAXjooYeYP3++s63k5GSSk5Nd2Q8Rka7C7RHTx4H3rLVPGWMeb1z/7nna1VhrR3ZsaSLS\nWRw7dowdO3awY8cOJk6cSHJyMitWrGD69OksWbKEm266ibNnz7J7925GjRrFnXfe2eIOSOebgKRL\nMomIdDy3g+lsILvx+e+BHM4fTEWki2s+A775BKQdO3ZQVlbmtFu4cCHJyclkZGTwk5/8hJSUFAAm\nTpzItm3b3CpfRERawVhr3fvixhy31vZptn7MWht2nnZ1wBagDnjKWvt/F9je/cD9ANHR0aNfe+21\n9incx1RVVTm3MpTOz1f6s6amhrfeeov4+HgyMzM5cOAAd999t/N+jx49GDx4MIMHDyYuLo5BgwYR\nHx9PVFSUcwckX+Ar/Sn/pD71LerP1rnmmms2WmuzLtWu3UdMjTHvAjHneevfL2Mzg6y1B40xCcAq\nY0yetXb3ZxtZa18EXgTIysqy2dnZn6fkLicnJwf9W/mOztKf1loOHjzI9u3bnZHP7du3M23aNH7w\ngx9QXV3Nl770JRYsWMCjjz6Kx+Ph8OHDziz42NjYLnG4vbP0p7Se+tS3qD/bVrsHU2vtdRd6zxhT\nbozpZ6391BjTDzh0gW0cbHzcY4zJAUYB5wRTEfFuzz33HHl5eU4YraysdN6LiIggLS3NuVd8jx49\nKCsrc2bA+/v788gjj7hSt4iIdAy3zzFdCtwDPNX4+OZnGxhjwoBqa+1pY0xfYDzw8w6tUkQuyVpL\nWVkZR44cISMjA4AbbriBXr168ac//QmA559/nsrKStLS0rj77rtJTU0lLS2N1NRUoqKiztnm+V4T\nERHf5XYwfQp4wxgzD9gP3AJgjMkCHrTW3gekAL8xxtQDfjScY7rDrYJFBA4fPsz27dvZtm1bi8dj\nx46RkZFBbm4uAAkJCfTp45xGzubNmwkJCXGrbBER8XKuBlNr7VHg2vO8vgG4r/H5J0BGB5cmIkBl\nZSV79uxh5MiGq7U9+uijvPLKKxw69M+zbvr06UN6ejq33noraWlpDB8+3Hnv2WefbbE9hVIREbkY\nt0dMRcQLnD59moKCAvLy8igsLOSJJ57AGMNDDz3EG2+8QVVVFYGBgQwYMIBZs2aRnp5OWloa6enp\n9OvXr0tMQhIRkfanYCrShdTX17Nv3z7y8vLIy8sjNzfXCaMejweAwMBAFixYQGRkJN/85je59dZb\nnc8/9thjbpUuIiJdgIKpiA/bs2cPb7/9NnfccQfh4eH84he/4Lvf/ec9LOLj48nIyGDOnDmkp6eT\nkZFBUlISgYGBAFx55ZVulS4iIl2QgqlIJ+fxeCgqKmLr1q3k5uayatUqFi1axIgRI1i9ejXz588n\nKSmJKVOmMHPmTMLCwsjIyCAtLU3nfIqIiFdRMBXpRGpqati4cSNbt25ly5YtbN26lW3btlFTUwM0\nXOszNjaWiooKAK6//npKSkoYMGAAAOnp6aSnp7tWv4iIyMUomIp4sSNHjrBo0SImTJhAdnY2BQUF\nTJgwAYDw8HBGjBjBAw88wIgRIxg+fDipqamsWbPGuQtJaGgooaGhLu6BiIhI6ymYirjM4/Gwa9cu\nNm/e7CyzZs3iW9/6FgA//OEPeeKJJ8jOziY1NZW//e1vjBw5kgEDBmg2vIiI+BQFU5EOZK1l69at\nbNq0iU2bNrF582a2bt3KqVOnAOjWrRvp6enO5KO+fftSWVlJr169AAgKCmLWrFmu1S8iItKeFExF\n2tnvf/976urqmDdvHgDTp0+nvLycXr16MXLkSObNm8eoUaPIzMwkJSXFCaVNmkKpiIiIr1MwFWkD\nZ8+eZfv27WzYsIENGzZQX1/Piy++CMAvf/lLrLXMmzcPYwyvvfYa/fv3Z+jQofj5+blcuYiIiPdQ\nMBW5TPX19ezcuZP169ezYcMG1q9fz5YtW6itrQWgd+/eTJw40Wm/fPlywsLCnPWmiUkiIiLSkoKp\nyCWUl5ezdu1arr/+eowxPPDAA/z2t78FoGfPnmRmZvLNb36TK664gtGjRzNkyJAWI6Hh4eFulS4i\nItKpKJiKNFNdXc3GjRtZs2YNDz74ICEhIfzqV7/iySefZM+ePcTHx3P33Xdz1VVXMWbMGIYNG4a/\nv7/bZYuIiPgEBVPpsqy17N69m9WrV7N69WrWrFlDbm6uc8/4K6+8kquvvpp77rmH6dOnOxepnzRp\nEpMmTXKzdBEREZ+kYCpdzvbt2/ne977HmjVrOHz4MAAhISGMGTOGxx9/nHHjxjF27FgiIyMBSEhI\nICEhwc2SRUREugQFU/FZHo8Hf39/9u7dy2233cb999/PvHnzCA4OZufOncycOZOrrrqKK6+8ktTU\nVB2SFxERcZmCqfgEay2FhYX84x//4B//+AcfffQRN998M0899RTR0dH06NGDkJAQoGEEdOfOnS5X\nLCIiIp+lYCqdksfjIS8vjw8//JAPPviAjz76yDks37dvX66++moyMzMBCA4O5v3333ezXBEREWkF\nBVPpFOrq6ti/f79zrucVV1zB5s2bAYiLi2P69OlMmDCBCRMmkJycrHvIi4iIdEIKpuKVPB4PO3fu\nJDU1FYDZs2ezYcMGysrKMMbw8MMPExAQwMSJExk0aJDL1YqIiEhbUDAVr2CtZceOHbz33nusWrWK\nnJwcTp48ybFjxwgNDeWhhx6isrISj8dDQEAA9957r9sli4iISBtTMBXX7N+/n5UrV/Luu++yatUq\nDh06BDRMTrr11lvJzs4mIKDhv+jMmTPdLFVEREQ6gIKpdJjjx4/j5+dHaGgoixcv5uabbwYgJiaG\nKVOmMHnyZCZPnkxcXJy7hYqIiIgrFEyl3Xg8HqqrqwkJCWHz5s1kZWXx3HPPMX/+fK6++mqeeeYZ\npkyZQmpqqiYriYiICH5uFyC+5eDBg7z00kvceuutREZG8sQTTwCQnp7O97//fedWntHR0TzyyCOk\npaUplIqIiAigEVP5gurq6lizZg1vv/02b731Flu2bAGgX79+zJ49mylTpgAQGBjohFQRERGR81Ew\nlc/tscce46WXXuL48eP4+/szfvx4fvaznzFjxgyGDx+ukVARERG5LAqm0mqvvfYar7zyCm+++SZ+\nfn706tWLm266iZkzZ3LdddfRp08ft0sUERGRTszVc0yNMbcYY7YbY+qNMVkXaTfdGLPTGFNkjHm8\nI2vsqurq6vjggw947LHHOHHiBAAHDhzgwIEDlJWVAfDEE0/w0ksvcfPNNyuUioiIyBfm9uSnbcAc\n4MMLNTDG+AO/BGYAqcAdxpjUjimva6muruavf/0r99xzDzExMWRnZ/PCCy84t/589NFH2bRpE/37\n93e5UhEREfFFrh7Kt9bmA5c6F3EMUGSt3dPY9jVgNrCj3QvsAo4dO8Y777zDwoULWb58OTU1NYSF\nhTFr1ixuuOEGpk2bRkhICHDJfhIRERH5QjrDOaYDgJJm66XAWJdq8Ql1dXUEBARw/PhxYmJiOHPm\nDAMGDOBrX/sac+bMYeLEic4dl0REREQ6SrunD2PMu0DMed76d2vtm63ZxHlesxf4WvcD90PDdTJz\ncnJaW2aX8W//9m9Ya/nZz34GwIMPPsigQYMYNWoUfn4NZ3b84x//cLNE+YKqqqr0f9+HqD99j/rU\nt6g/21a7B1Nr7XVfcBOlwMBm67HAwQt8rReBFwGysrJsdnb2F/zSnVthYSFLlixh69atvPrqqwBM\nnjyZHj160PRvk52dTU5ODl3938qXqD99i/rT96hPfYv6s211huO164FEY0w8cAC4HbjT3ZK8k7WW\nvLw8Fi9ezJIlS9i2bRsAV1xxBZWVlYSGhvIf//EfLlcpIiIicn6uBlNjzE3A80Ak8HdjzBZr7TRj\nTH/gt9bamdbaOmPMfGAF4A+8ZK3d7mLZXqW+vp7169ezZMkSlixZQlFREX5+fkyYMIHnnnuOm266\niYEDB156QyIiIiIuc3tW/l+Bv57n9YPAzGbrbwFvdWBpXs3j8VBTU0OvXr1YuXIl06dPJyAggGuv\nvZbvfOc73HjjjURFRbldpoiIiMhlcfs6pnKZysvL6devH08//TTQcI7o//7v/3L48GGWL1/O/fff\nr1AqIiIinVJnOMe0y6qurmbFihUsWbKEPn368PzzzxMVFcWdd97JxIkTAQgKCuLuu+92uVIRERGR\nL07B1MtUVlaybNkylixZwttvv011dTXh4eF85StfARoucv/ss8+6XKWIiIhI21Mw9QJHjhxh6dKl\nLF68mHfffZczZ87Qr18/7r33XueC94GBgW6XKSIiItKuFExdcvDgQcLDw+nevTuLFi3iBz/4AXFx\ncSxYsIA5c+Ywbtw454L3IiIiIl2Bkk8Hqq+vB2DZsmUMGDCA5cuXA/C1r32NjRs3smfPHn7xi19w\n1VVXKZSKiIhIl6P008527NjBj3/8Y0aNGsXzzz8PwPjx453XAAYMGEBmZibGnO/uqyIiIiJdgw7l\ntzFrLZs2bXIueF9QUADAVVddRf/+/QEICwvj+9//vptlioiIiHgdBdM2smbNGt544w2WLFnCvn37\n8Pf3Jzs7m/nz53PTTTc5oVREREREzk/BtI089dRTvP3220ydOpUf/vCHXH/99fTt29ftskREREQ6\nDQXTNvLss8/yhz/8gdDQULdLEREREemUFEzbSFxcnNsliIiIiHRqmpUvIiIiIl5BwVREREREvIKC\nqYiIiIh4BQVTEREREfEKCqYiIiIi4hUUTEVERETEKyiYioiIiIhXMNZat2toF8aYw8A+t+voJPoC\nR9wuQtqM+tO3qD99j/rUt6g/W2ewtTbyUo18NphK6xljNlhrs9yuQ9qG+tO3qD99j/rUt6g/25YO\n5YuIiIiIV1AwFRERERGvoGAqAC+6XYC0KfWnb1F/+h71qW9Rf7YhnWMqIiIiIl5BI6YiIiIi4hUU\nTLsgY8wtxpjtxph6Y8wFZxIaY6YbY3YaY4qMMY93ZI3SesaYcGPMSmPMrsbHsAu08xhjtjQuSzu6\nTrm4S32/GWOCjDGvN76/1hgT1/FVSmu1oj/vNcYcbvY9eZ8bdUrrGGNeMsYcMsZsu8D7xhizsLG/\nc40xmR1do69QMO2atgFzgA8v1MAY4w/8EpgBpAJ3GGNSO6Y8uUyPA+9ZaxOB9xrXz6fGWjuycbmh\n48qTS2nl99s84Ji1dijwDPB0x1YprXUZPz9fb/Y9+dsOLVIu18vA9Iu8PwNIbFzuBxZ1QE0+ScG0\nC7LW5ltrd16i2RigyFq7x1p7BngNmN3+1cnnMBv4fePz3wM3uliLfD6t+X5r3s9/Aa41xpgOrFFa\nTz8/fYy19kOg4iJNZgN/sA3WAH2MMf06pjrfomAqFzIAKGm2Xtr4mnifaGvtpwCNj1EXaNfdGLPB\nGLPGGKPw6l1a8/3mtLHW1gEngIgOqU4uV2t/fs5tPOz7F2PMwI4pTdqJfme2kQC3C5D2YYx5F4g5\nz1v/bq19szWbOM9ruoSDSy7Wn5exmUHW2oPGmARglTEmz1q7u20qlC+oNd9v+p7sPFrTV38DXrXW\nnjbGPEjDaPjkdq9M2ou+P9uIgqmPstZe9wU3UQo0/ws+Fjj4Bbcpn9PF+tMYU26M6Wet/bTx0NGh\nC2zjYOPjHmNMDjAKUDD1Dq35fmtqU2qMCQB6c/FDi+KeS/antfZos9X/QecMd3b6ndlGdChfLmQ9\nkGiMiTfGdANuBzST2zstBe5pfH4PcM6IuDEmzBgT1Pi8LzAe2NFhFcqltOb7rXk/3wyssroQtbe6\nZH9+5vzDG4D8DqxP2t5S4CuNs/PHASeaTrGSy6MR0y7IGHMT8DwQCfzdGLPFWjvNGNMf+K21dqa1\nts4YMx9YAfgDL1lrt7tYtlzYU8Abxph5wH7gFoDGS4E9aK29D0gBfmOMqafhD9KnrLUKpl7iQt9v\nxpgngQ3W2qXA74D/NcYU0TBSert7FcvFtLI/HzbG3ADU0dCf97pWsFySMeZVIBvoa4wpBX4IBAJY\na38NvAXMBIqAauCr7lTa+enOTyIiIiLiFXQoX0RERES8goKpiIiIiHgFBVMRERER8QoKpiIiIiLi\nFRRMRURERMQrKJiKiIiIiFdQMBURERERr6BgKiLiZYwxDxhjrDFmUrPX5je+9kVvNywi4rUUTEVE\nvM9wIJeGO3ZhjOkBzAMOA3ku1iUi0q4UTEVEvE8G8CowrHH9YeDPQL21tty1qkRE2pmCqYiI90kB\n3gCGGWN6A7cBnwDbXK1KRKSdKZiKiHgRY8xA4Ki1dg8QBfwr8DyQRMPhfRERn6VgKiLiXYbzz/NI\nTwLTgd/TcHhf55eKiE8LcLsAERFpoXkA/U8aRk89xpgM4GXXqhIR6QAKpiIi3iUDWAxgrV3W7PVU\nYIcrFYmIdBBjrXW7BhERERERnWMqIiIiIt5BwVREREREvIKCqYiIiIh4BQVTEREREfEKCqYiIiIi\n4hUUTEVERETEKyiYioiIiIhX8NkL7Pft29fGxcW5XUancOrUKXr27Ol2GdJG1J++Rf3pe9SnvkX9\n2TobN248Yq2NvFQ7nw2mcXFxbNiwwe0yOoWcnByys7PdLkPaiPrTt6g/fY/61LeoP1vHGLOvNe10\nKF9EREREvIKCqYiIiIh4BQVTEREREfEKCqYiIiIi4hW8IpgaY14yxhwyxmy7wPvGGLPQGFNkjMk1\nxmR2dI0iIiIi0r68IpgCLwPTL/L+DCCxcbkfWNQBNYmIiIhIB/KKy0VZaz80xsRdpMls4A/WWgus\nMcb0Mcb0s9Z+2iEFtsKvfvUrVq9efdE23bt353/+53+c9ps3b26x3tGf37RpE7/97W8BWLRoEWvX\nrsUYg7+/P4GBgQQGBhIQEOA8DwkJ4bvf/S4AH330EZ9++im33norAPv27aO2tpbQ0FBCQkLo2bMn\nxpiL1iMiItJRPB4PJ0+e5OTJk1RWVjqPVVVV1NTUnLOcOXOGs2fPtljq6uqor6/HWussZWVl/O53\nv3N79z6XhQsXEhYW5nYZLXhFMG2FAUBJs/XSxtdaBFNjzP00jKgSHR1NTk5OR9XHqlWrWhUMm2pa\ntWoVmzdvbrHu1uerqqpYuXIln3zyCdZa6uvr8Xg81NXVUVdX5zwPDg5m7NixADzxxBOsX7+eqKgo\nAJ588knef/9952v5+fk5IbXpMTw8nO985zsAbNu2jdraWrKysi5as1y+qqqqDv2/L+1L/el71Kdt\n48yZM1RUVDjL8ePHOXbsGMeOHePEiRNO+GweQC+Hv78/AQEBBAQE4O/v7yx+fn7OwIsxBmst/v7+\n7bGL7e79998nPDzc7TJaMA2DkO5rHDFdZq1NP897fwd+Zq39R+P6e8C/Wms3Xmh7WVlZVhfYb53W\nXhy4rq6OgICGv2XKy8uprKwkMTERgLVr17J7927nB8Dx48epqKjg2LFjzg+NwMBAJzzPmjWLDRs2\nUFZWBsBtt93G2rVriY2NdZZBgwYRHx9PQkICcXFxurNGK+liz75F/el71KeXZq3l6NGjFBcXU1xc\nzJ49eygpKaG0tNRZDh06dN7P9unTh8jISCIiIggPD3eWsLAwevfu3WLAJCQkhF69etGjRw+Cg4Od\npXv37q0Om+rP1jHGbLTWXnI0qrOMmJYCA5utxwIHXaqly2oKpdAwIh0dHe2sjx071hlNbY1FixZx\n5MgRZz07O5ugoCBKS0vZtGkTS5cupaampsVnsrKyWL9+PQB//vOf6dGjB1/60pc+7+6IiIjLKioq\n2LlzJzt37qSwsJCdO3dSVFTEnj17zhnhDAsLY+DAgcTGxpKVlUVsbCwDBgwgJibG+Z0UGRlJUFCQ\nS3sjbaGzBNOlwHxjzGvAWOCEN51fKpdv4MCBDBz4z781vvGNb/CNb3zDWbfWcvjwYecv5eLiYgID\nA533f/CDH9CnTx8nmN500014PB7S09NJT08nIyOD5ORkunXr1nE7JSIi53XixAm2bdt2ztJ8gCIg\nIICEhAQSExOZNGkSCQkJLY6ahYSEuLgH0lG8IpgaY14FsoG+xphS4IdAIIC19tfAW8BMoAioBr7q\nTqXSUYwxREVFERUVdd6R2PXr11NRUeGsR0REsGbNGt5++23q6uqAhh9yKSkpZGZmkpmZyYQJ/z97\ndx4XVfX/cfx1ENwVswIXUnEBRMBd3FAITdx3c01LpFzLpdxyyRLRrLSvWoqaS5q5JpZLpaK4iysI\noqgp7iluKCrI+f2hzU9LUxPmDsPn+XjMw7nM4d43Hu7wmXvvOdeHihUrmu1nEEKIrOjcuXPs3bv3\nkcepU6dMr+fNmxcPDw9atGiBm5sbrq6uuLi44Ozs/MgBCJE1WURhqrXu8JTXNdDbTHFEJpA3b17y\n5s1rWv5rdoG7d+8SFxdHdHQ0UVFR7N+/nzVr1jB37ly6d+/OzJkzSUtLo2fPnjRv3pxGjRoZ9SMI\nIUSmd/36dXbv3s3OnTvZsWMHu3fvNo0dAHBxcaFmzZq89957eHp64unpSbFixWTWFvFEFlGYCpFe\nsmfPbnrz69Dh/ucdrTXnzp0jJSUFuD9wa+XKlTg5OdGoUSOuXLlCs2bNqFGjBj4+PtSuXdvips8Q\nQgijaa05ceIEERERREREsGPHDmJiYvhrELWbmxtvvPEGlStXplKlSpQvX15Ov4vnJoWpsHpKKYoU\nKWJaLly48COF6sWLF0lNTWXy5Ml8/vnnKKXw8PDAx8cHHx8ffH19KVSokFHxhRDCEFprYmJi2LRp\nE5s3byYiIoKzZ++PO37ppZeoUaMG7dq1o3r16lStWlU+0It0IYWpyJKUUqaBUa6urmzfvp3k5GR2\n7WHl9mYAACAASURBVNplOhowd+5cpk2bBkC5cuWYM2eOzLsqhLBqJ0+eZP369fz+++9s2LCBCxcu\nAFC0aFHq1KlDnTp18PHxwd3dHRsbS7l5pLAmUpgK8UCuXLmoW7cudevWBe7P27pv3z42bNjAhg0b\nTEddv/nmG+bNm8fixYsfmVlACCEym5s3b7JhwwbWrl3LunXrOHbsGHB/SkB/f39ef/11/Pz8cHZ2\nlutChVlIYSrEE9ja2lK1alWqVq1quhUr3J+8OXfu3KbT+5999hmxsbEEBAQQEBDAq6++alRkIYT4\nV1prDh8+zOrVq1mzZg0RERHcvXuXPHny8Prrr9OvXz/8/f1xd3eXQlQYQgpTIZ5Thw4dTAOrAO7c\nucPvv//OwoULsbGxoWbNmjRr1oxmzZrh6upqYFIhhLh/9mfr1q2EhYURFhZGfHw8cP8SpX79+hEQ\nEEDt2rVlYnphEeQCESFe0Keffsq5c+eIjIxkxIgR3Lx5k48++gg3Nzfc3Nz46KOP2LPniXfPFUKI\ndJecnMyKFSt46623cHR0xNfXlylTplC6dGmmTZvGyZMniY6O5vPPP8ff31+KUmEx5IipEOnAxsaG\nypUrU7lyZUaPHs2pU6dYtWoVK1euZNKkSdy8eZPKlSuTlpbGjh07qF69ugwcEEKkq5s3b7J69WqW\nLl3KL7/8ws2bNylYsCCNGzemefPmvPHGGzJ9k7B4UpgKkQGKFStG79696d27N1evXiU5ORmAXbt2\nUatWLb788kv69+/PvXv3sLGxkWu5hBD/SXJyMj///DOLFi1izZo1JCcn4+DgQJcuXWjTpg1169bF\n1lb+1IvMQ35bhchgBQoUoECBAgB4eHjwww8/ULNmTQCWLVvG4MGDad++PR07dsTT09PIqEKITCAl\nJYX169ezcOFCVqxYQVJSEoUKFeKdd96hTZs2+Pj4kC1bNqNjCvGfSGEqhBnlzZuX9u3bm5YdHBxw\nc3Pj888/JyQkhHLlytG5c2c6d+6Mk5OTgUmFEJZEa83u3buZN28eP/74I5cuXcLe3p4333yTDh06\n4OvrK8WosApykZsQBvL19WXNmjWcPXuWqVOnYm9vz9ChQylWrBhvvPEGCxYs4NatW0bHFEIY5MyZ\nM4SEhODu7o63tzezZs3Cz8+PFStWcOHCBWbOnIm/v78UpcJqSGEqhAVwcHCgV69ebN26laNHj/Lx\nxx9z5MgROnfuTKNGjYyOJ4Qwozt37rBo0SIaNGjAa6+9xtChQ3n55ZeZMWMG58+fZ/HixbRo0UJG\n0gurJIWpEBamdOnSjBkzhuPHj7Nx40Y+/vhjAK5du0a1atUICwszOKEQIiMcOnSI/v37U6RIETp0\n6MDhw4cZPnw4R44cYcuWLfTo0QN7e3ujYwqRoeQaUyEslI2NDb6+vqbls2fPopQiLS3NtHz48GH8\n/PxkVL8QmdStW7f48ccfCQ0NZfv27djZ2dGiRQsCAwOpV6+eTCsnshwpTIXIJMqWLcvOnTvRWgMw\na9YsRo4ciZubGz179uStt94yjf4XQli2I0eO8O233/Ldd99x9epV3NzcmDhxIl26dMHBwcHoeEIY\nRj6KCZHJ/HV0dNCgQcydOxd7e3vef/99ihYtSlBQEEePHjU4oRDicVJTU1mxYgWDBg3C1dWV//3v\nfzRo0IDw8HBiYmIYOHCgFKUiy5PCVIhMKleuXLz11lvs2LGDyMhIOnTowPfff09QUBC1atVi8eLF\npKamGh1TiCzv8uXLhISE4OzsTKtWrTh16hSfffYZCQkJLFq0iLp168rlOEI8IIWpEFagcuXKzJw5\nkzNnztCrVy/Onz/Pm2++Sb9+/YyOJkSWFR0dTVBQkGlkvYuLCytWrOCHH35g+PDhFCpUyOiIQlgc\nKUyFsCIvvfQSbdu25ciRI6xcuZKePXsC9/9Avvvuu5w6dcrghEJYt7S0NFavXk29evXw9PRk/vz5\ndOrUiYMHD7J+/XpatGghc44K8S+kMBXCCmXLlo1mzZqZbnG6b98+vv/+e5KTkwFISkoyDaISQry4\nO3fuMHv2bDw9PWncuDGHDx8mODiYhIQEQkND5XbDQjwjKUyFyAK6dOnC+fPncXV1BeCtt96iWrVq\n/Pjjj3IdqhAvIDExkeDgYEqUKEH37t2xs7Nj/vz5nDhxgqFDh/LKK68YHVGITEUKUyGyiHz58pme\nN2zYkGvXrtG+fXvKlCnDtGnTTEdThRBPd/r0aQYMGECxYsUYPnw45cuX57fffmPfvn107twZOzs7\noyMKkSlJYSpEFtSjRw8OHz7MihUrKFSoEL1798bZ2ZmQkBCuXbtmdDwhLNaRI0cIDAykZMmSfP31\n17Rs2ZIDBw6wdu1a6tWrJ6PrhXhBUpgKkUXZ2NjQokULtm3bxsaNGylfvjxDhw6lePHiDBs2jMTE\nRKMjCmEx9u3bR9u2bXFzc2PBggUEBQURHx/P/Pnz8fLyMjqeEFZDClMhsjilFL6+vqxbt47IyEjq\n16/P119/TUpKCoAMkhJZ2q5du2jatCmVKlXi119/ZciQIfzxxx9MmTKFEiVKGB1PCKsjhakQwqRy\n5cosWbKEU6dO4ejoiNaa+vXrM2zYMKOjCWFWW7duJSAgAG9vb7Zt28ann37KqVOnCA4OxtHR0eh4\nQlgtiyhMlVIBSqk4pVS8UmrIY14vppTaqJTap5Q6qJRqZEROIbKKggULAvenwClevDi2trbA/aOn\nZ8+eNTKaEBkqIiICf39/ateuzd69exk/fjx//PEHH3/8Mfb29kbHE8LqGV6YKqWyAVOBhoA70EEp\n5f63Zh8Di7XWFYH2wDTzphQia8qZMyezZs1izJgxAPzyyy84OzvTp08fzpw5Y3A6IdLPtm3bqF+/\nPnXq1CEmJoYvv/ySEydO8NFHHz0yo4UQImMZXpgC1YB4rfVxrfVdYBHQ/G9tNJD/wXN7QA7ZCGEA\nLy8vunXrxvTp0ylVqhQffPAB58+fNzqWEP/Zrl27aNiwIbVq1eLgwYN8+eWXHD9+nP79+5MnTx6j\n4wmR5SijBzYopdoAAVrrwAfLXQBvrXWfh9oUBn4FXgLyAPW01nses64gIAjA0dGx8qJFi8zwE2R+\nSUlJ5M2b1+gYIp2Yoz/PnTvH/PnzWbduHXZ2djRv3pyOHTvKqc4MIPtnxoiPj2f27Nls376d/Pnz\n0759e1q0aEGuXLkyfNvSp9ZF+vPZ+Pn57dFaV3lqQ621oQ+gLTDzoeUuwP/+1mYAMPDB8xpADGDz\nb+utXLmyFs9m48aNRkcQ6cic/Xn06FHdpUsXrZTS+fLl06NHj9bXrl0z2/azAtk/01dcXJxu3769\nBnSBAgX0Z599pq9fv27WDNKn1kX689kAkfoZ6kJLOJV/GnjtoWUn/nmqvjuwGEBrvR3ICch93oQw\nWOnSpZk3bx5RUVHUr1+f0aNH89133xkdS4h/SEhIoEePHri7uxMWFsbw4cM5ceIEw4cPl2tIhbAg\ntkYHAHYDZZRSzsAZ7g9u6vi3NqcAf2COUqos9wvTP82aUgjxROXKlWPZsmVERkZSrlw5AJYvX05i\nYiLdunUzjeoXwtwuX75McHAwU6dORWtN7969GTZsmEz5JISFMvyvhdY6VSnVB1gHZANma60PKaXG\ncP+wbxgwEAhVSvXn/kCobg8OCwshLEiVKv9/+dCSJUvYsmULnTp1ksJUmN2tW7eYPHkyISEhJCUl\n0bVrV0aNGkXx4sWNjiaE+BcW8ddCa70aWP23r4186HkMUMvcuYQQ/93ChQs5c+YMuXLl4s6dO3Tt\n2pW+fftSq5bsyiLjpKam8t133zF69GjOnj1Ls2bNCA4ONh3JF0JYNku4xlQIYYWUUjg5OQFw5MgR\nNm/eTO3atWnevDmHDx82OJ2wNlprwsLC8PT0JCgoiBIlShAREcHKlSulKBUiE5HCVAiR4Tw9PYmP\nj2fs2LFs3LgRDw8PevfuzcWLF42OJqxAZGQkfn5+NG/eHK01K1asYMuWLdSuXdvoaEKI5ySFqRDC\nLHLnzs2wYcOIj4/nvffeY/r06ZQuXZpx48aRnJxsdDyRCZ08eZLOnTtTtWpVYmJimDZtGlFRUbRo\n0QKllNHxhBD/gRSmQgizcnBwYMqUKURHR+Pn58ewYcNwdXVl1apVRkcTmcT169cZOnQorq6uLFu2\nzPSBp2fPntjZ2RkdTwjxAqQwFUIYws3NjZUrV7Jx40YcHBxIS0sDQCbcEE9y7949QkNDKVOmDCEh\nIbRt25a4uDjGjh1L/vz5n74CIYTFs4hR+UKIrMvX15ddu3aZTr2OGTOGw4cPExoaKrf5EyYbNmyg\nf//+HDx4kFq1avHzzz9TtWpVo2MJIdKZHDEVQhjOxsbGVJhmz56dP//8kzx58gByBDWri4+Pp0WL\nFvj7+3Pt2jV+/PFHIiIipCgVwkpJYSqEsChDhw7lt99+QynFhQsXKFeuHAsWLJACNYu5ceMGgwcP\nxt3dnfXr1xMcHMzhw4dp166dDGwSwopJYSqEsDh/FR5Xrlwhd+7cdO7cmdq1a7Nnzx6Dk4mMlpaW\nxty5c3FxcWHChAl07NiRI0eOMHToUHLmzGl0PCFEBpPCVAhhsdzc3Ni1axezZs0iPj6eqlWrEhgY\nyIULF4yOJjLArl27qFmzJt26daNYsWLs2LGDOXPmULhwYaOjCSHMRApTIYRFs7Gx4Z133uHIkSMM\nGDDAdDRt0qRJpKSkGB1PpIOLFy/SvXt3vL29OXnyJHPnzmX79u14e3sbHU0IYWZSmAohMgV7e3sm\nTpxIdHQ0NWrUoH///lSsWJHdu3cbHU38R6mpqfzvf//DxcWF+fPn8+GHH3LkyBHeeustbGzkz5MQ\nWZHs+UKITMXV1ZU1a9bw008/cefOHXLkyGF0JPEfbN68mUqVKtGvXz+qVavGwYMHmTBhAvny5TM6\nmhDCQFKYCiEyHaUUzZs35/Dhw3h5eQHw3nvvMWHCBBm9b+HOnTtHp06dqFu3LtevX2f58uWsW7cO\nNzc3o6MJISyATLAvhMi0smXLBkBKSgoXLlzg1q1bMpWQhUpNTWXKlCmMHDmSu3fvMmLECIYMGULu\n3LmNjiaEsCByxFQIkenZ2dmxYsUKZs6cCcD+/fvp2LEjZ8+eNTiZANiyZQuVKlWif//+1KpVi+jo\naMaMGSNFqRDiH6QwFUJYjezZswNw4MABli9fjpubG1999RWpqakGJ8uaLl68SLdu3fDx8eHq1ass\nX76c1atXU7p0aaOjCSEslBSmQgir07VrV6Kjo6lduzYDBgygSpUqbN++3ehYWUZaWhrTp0/H1dWV\nhQsXMmTIEGJjY2nZsqVcaiGE+FdSmAohrFLp0qX55ZdfWLZsGZcvX6ZmzZoEBQWRmJhodDSrtn//\nfmrWrMl7771HhQoVOHDgAOPGjSNPnjxGRxNCZAJSmAohrJZSilatWhETE8OAAQOYPXs2rq6uzJ07\nV0bvp7MbN27Qv39/KleuzPHjx5k3bx4bNmygbNmyRkcTQmQiUpgKIaxevnz5+OKLL9i7dy9lypTh\n/fff59KlS0bHsgpaa5YtW4abmxuTJ08mKCiIuLg4unTpIqfthRDPTQpTIUSW4eXlxZYtW9i+fTuv\nvvqq6VrI27dvGx0tUzp58iTNmjWjTZs2vPrqq2zfvp1vvvmGl156yehoQohMSgpTIUSWYmNjYzq9\nvGnTJt577z2mTZtmcKrMJSUlhYkTJ+Lu7s6GDRv44osviIyMlHvbCyFemEywL4TIsvz8/AgPDzcV\nVLt376Z48eI4ODgYnMxy7dy5k3fffZcDBw7QtGlTpkyZQrFixYyOJYSwEnLEVAiRpdWtW5ecOXNy\n7949OnbsiJubG7NmzZLBUX9z/fp1+vbtS40aNbh06RLLly9n5cqVUpQKIdKVFKZCCMH925uuWrUK\nDw8PAgMD8fPzIy4uzuhYFuGnn37C3d2dqVOn0qdPH2JiYmROUiFEhpDCVAghHnBzcyM8PJzQ0FAO\nHDiAl5cXY8aM4c6dO0ZHM8SZM2do1aoVLVu25JVXXmHHjh18/fXX5M+f3+hoQggrZRGFqVIqQCkV\np5SKV0oNeUKbdkqpGKXUIaXUQnNnFEJkDTY2NgQGBhIbG0urVq0YNWoUFStWZOvWrUZHM5u0tDSm\nTp1K2bJlWbt2LePHj2f37t1Uq1bN6GhCCCtneGGqlMoGTAUaAu5AB6WU+9/alAGGArW01uWAD8we\nVAiRpRQqVIgffviB1atXc+vWLWrXrs1nn31mdKwMd+jQIWrXrk2fPn2oXr060dHRfPTRR9jZ2Rkd\nTQiRBVjCqPxqQLzW+jiAUmoR0ByIeahND2Cq1voKgNb6otlTCiGypIYNGxIdHc2IESNMRwzv3btH\ntmzZDE6Wvu7cucPYsWMJCQkhf/78zJ8/n06dOsl1pEJksJSUFE6fPm018ynnzJkTJyen//xhVhk9\n8lQp1QYI0FoHPljuAnhrrfs81OYn4AhQC8gGjNZar33MuoKAIABHR8fKixYtMsNPkPklJSWRN29e\no2OIdCL9mfFCQ0NJSEhg6NCh5MqVK0O3ZY7+jIqKYuLEiZw6dYr69evTq1cvChQokKHbzMpkH7Uu\nL9qfefPmxdHREXt7+0z/QVBrzbVr17hw4QJJSUmPvObn57dHa13laeuwhCOmj+uFv1fLtkAZwBdw\nAiKUUh5a66uPfJPWM4AZAFWqVNG+vr7pHtYahYeHI/9X1kP6M+NFRkZy7do1AgICMvwPSUb257Vr\n1xgyZAjffvstJUqUYO3atTRo0CBDtiX+n+yj1uVF+zM2NhYnJ6dMX5T+JV++fCQlJVGlylNr0Mcy\n/BpT4DTw2kPLTsDZx7RZqbVO0VqfAOK4X6gKIYTZDRo0iFWrVqGU4vTp0zRt2pQjR44YHeu5hIWF\nUa5cOWbMmMGAAQOIjo6WolQIg1hLUQov/rNYQmG6GyijlHJWSmUH2gNhf2vzE+AHoJR6BXABjps1\npRBCPOSvN9/Y2FgiIiLw8vIiJCSElJQUg5P9uwsXLtCuXTuaN29OwYIF2b59O1988QV58uQxOpoQ\nQhhfmGqtU4E+wDogFlistT6klBqjlGr2oNk64LJSKgbYCHyotb5sTGIhhPh/9evXJzY2lsaNGzN0\n6FCqVavG3r17jY71D1pr5syZQ9myZVm5ciWfffYZe/bskSmghBAWxfDCFEBrvVpr7aK1LqW1Hvvg\nayO11mEPnmut9QCttbvW2lNrLaOahBAWo3Dhwixbtoxly5Zx/vx5qlWrxuDBg0lOTjY6GgAnTpyg\nQYMGvP3225QrV44DBw4wfPhwmQJKCGFxLKIwFUIIa9CqVStiYmLo1q0bEyZMwMvLi/DwcMPy3Lt3\nj0mTJuHh4cH27duZNm0amzZtws3NzbBMQgjLNH36dAoVKkSFChUoWbIkc+bMMSSHFKZCCJGOXnrp\nJWbOnMnvv/9OWloaDRo04Ny5c2bPcejQIWrVqkX//v3x8/MjJiaGnj17YmMjb/tCiH86ePAgo0eP\nZv/+/SxdupSBAwf+o014eDjdunXL0BzyDiWEEBnA39+fqKgowsLCKFy4MAD79u3L8O3evXuXMWPG\nULFiReLj41mwYAGrVq3itddee/o3CyGyrKioKMqWLQuAk5MT9+7dMySHJcxjKoQQVil37tymKZjW\nr19PvXr1mD59OkFBQRmyvd27d/POO+8QHR1Nhw4dmDx5Mq+++mqGbEsIkf4++OAD9u/fn67rrFCh\nApMmTXpqu6ioKNzc3NBa8/XXX9OkSZN0zfGspDAVQggz8PHxISQkhDZt2gBw5coVChQokC7zF966\ndYuRI0fy1VdfUbhwYcLCwmjatOkLr1cIkTUkJCSQlJREgwYNsLOzo1q1akydOtX0ure3N3fu3CEp\nKYnExEQqVKgAwPjx49N9/mMpTIUQwgyyZ8/O4MGDAUhNTcXf35+iRYvyzTff4OTk9J/XGx4eTmBg\nIMeOHePdd99l/Pjx2Nvbp1dsIYQZPcuRzYxw8OBB/P39Wbv2H3d7B2Dnzp3A/febOXPmZOjAqHS/\nxlQpVf/floUQIqtTStGlSxfWr19vuvtSWlrac63j2rVrvPvuu/j5+QGwYcMGvv32WylKhRDPLSoq\nivLlyxsdA8iYwU/jn7IshBBZWrZs2ejfvz/R0dFUqVKFd999F39/f44dO/ZM3//zzz9Trlw5Zs6c\nycCBAzl48KCpQBVCiOcVFRWFl5eX0TEA84zKt54bwAohRDoqWbIkv//+OzNmzGDv3r14enry5Zdf\nPnE07KVLl+jUqRNNmzalQIECbN++nYkTJ5I7d24zJxdCWJMFCxbQqVOnp7bz9fXN8PlN060wVUp9\np5SaDRRTSs1+8FwIIcS/UErRo0cPDh06hL+/PwMHDqRWrVocOnTI1EZrzY8//oi7uzuLFy9m1KhR\n7N27V24nKoSwOul5xHQOMBe48uDfuem4biGEsGpOTk6EhYWxcOFC4uPjTYMNLl26RMuWLWnfvj3F\nixdn7969jB49muzZsxucWAgh0l+6jcrXWm8CUErd+Ov5Xy+l1zaEEMKaKaXo0KEDDRo0oECBAsye\nPZtevXqhtebzzz/ngw8+wNZWJlMRQlivjHiHu/uUZSGEEP/i+vXrtG/fnt9++40cOXLg7OzMgAED\n5HaiQgirl+6Fqda6+r8tCyGEeLy0tDSmTp3K0KFDUUoxbdo0ihYtiqurKzY2Nly/fp2oqChq1apl\ndFQhhMgQ8vFbCCEswOHDh/Hx8aFfv374+Phw6NAhevbsSf78+XF1dQVgwoQJ+Pj40LdvX27cuGFw\nYiGESH/pUpgqpboqpS4ppRKVUvOUUvnSY71CCGHtUlJSGDduHBUqVCA2Npa5c+eyevVqihUr9o+2\nQ4cOpV+/fkydOhUPDw/WrVtnQGIhhMg46XXEdARQH3ADTgLB6bReIYSwWvv378fb25thw4bRtGlT\nYmNjeeutt1Dq8dM/58mTh0mTJrFlyxZy585NQEAA3bp1IzEx0czJhRAiY6RXYXpda71Pa31Raz0C\nkMn1hBDiCW7fvs3w4cOpUqUKZ8+eZdmyZSxZsgRHR8dn+v6aNWuyb98+hg0bxvfff4+7uzvLli3L\n4NRCCGs2ffp0ChUqRIUKFShZsmSGT6T/JOlVmBZWSgUppXyUUq8Cdum0XiGEsCrbtm2jYsWKBAcH\n07lzZ2JiYmjVqtVzrydnzpyMHTuW3bt3U6RIEdq0aUObNm1ITU3NgNRCCGt38OBBRo8ezf79+1m6\ndCkDBw40JEd6FaajAC/gMyAO8FBKrVZKjVNKdUinbQghRKaVlJREv379qF27Nrdu3WLt2rXMmTOH\nggULvtB6K1asyM6dOxk3bhwODg4yz6kQ4j+JioqibNmywP0bfjzp1sgZLV3ewbTWMx5eVko5cb9Q\n9QQaAT+kx3aEECIz+u233wgKCuLkyZP07t2b4OBg8uVLvzGidnZ2DBkyxLS8b98+RowYwTfffMNr\nr72WbtsRQmQ8X1/fp7Zp0qQJgwYNMrX/+/LDwsPDn2m7UVFRuLm5obXm66+/pkmTJs8TO91kyEdr\nrfVp4DSwOiPWL4QQmUFiYiIDBgxg7ty5uLq6snnzZmrXrp3h242PjycyMlJO6wshnklCQgJJSUk0\naNAAOzs7qlWrxtSpU02v16tXj/Pnz//j+8aOHUvz5s3TNYuc8xFCiHSmtWbp0qX06dOHxMREhg0b\nxogRI8iZM6dZtt+2bVuaNm1Kzpw50VozfPhwOnfujLu7u1m2L4T47571COeT2j/v98P960v9/f1Z\nu3btY1///fffn3ud/5VMsC+EEOno7NmztGzZknbt2vHaa68RGRnJ2LFjzVaU/uWv7Z06dYrp06dT\nsWJFPv30U+7elbtECyEeFRUVRfny5Y2OAUhhKoQQ6SItLY3Q0FDc3d1Zt24dEyZMYMeOHYa/2Rcv\nXpzY2FhatWrFyJEjqVy5Mrt27TI0kxDCskRFReHl5WV0DEAKUyGEeGFHjx7l9ddfJygoiIoVK3Lw\n4EE+/PBDixkh7+DgwA8//EBYWBhXrlyhRo0aDBgwgJs3bxodTQhhARYsWECnTp2MjgFIYSqEEP9Z\nSkoKISEheHp6sn//fkJDQ9mwYQNlypQxOtpjNW3alEOHDvHuu+/y1Vdf4eHhwa+//mp0LCGEMLGI\nwlQpFaCUilNKxSulhvxLuzZKKa2UqmLOfEII8Xd79+6lWrVqDB06lEaNGhETE0NgYOATbydqKezt\n7Zk2bRqbN28me/bsNGjQgBUrVhgdSwghAAsoTJVS2YCpQEPAHeiglPrH0FGlVD6gH7DTvAmFEOL/\n3bx5k0GDBlG1alXOnz/PsmXLWL58OUWKFDE62nPx8fHhwIEDfPHFFzRu3Bi4P3BLa21wMiGyHmva\n7170ZzG8MAWqAfFa6+Na67vAIuBxk2J9CkwAbpsznBBC/OXXX3/F09OTL774gu7du//n24laipw5\nczJgwACyZ8/OjRs38Pb25p133jE6lhBZSs6cObl8+bJVFKdaay5fvvxCs5Aoo/8jlFJtgACtdeCD\n5S6At9a6z0NtKgIfa61bK6XCgUFa68jHrCsICAJwdHSsvGjRInP8CJleUlISefPmNTqGSCfSn+nv\n2rVrTJ06ld9++43XXnuNAQMGUKFCBbNs21z9ee/ePX766SccHR2pXbu26XaE2bJly/BtZzWyj1qX\nF+1PpRR58uSxmn3t3r173Lx58x+Ftp+f3x6t9VMvxbSEIaOPuyDL9NMopWyAr4BuT1vRg1ujzgCo\nUqWKfpbbeon7k/HK/5X1kP5MP1prFixYQP/+/bl69Soff/wxw4cPN+ucpObsT39/f9PzkJAQli1b\nRmhoqNmK8KxC9lHrIv2ZvizhVP5p4OGbOTsBZx9azgd4AOFKqT+A6kCYDIASQmSkY8eO0aBB+Uu8\n9gAAHa1JREFUA7p06UKpUqXYu3cvn376qdknyjdKqVKlOHXqFFWqVOGjjz6SqaWEEGZhCYXpbqCM\nUspZKZUdaA+E/fWi1vqa1voVrXUJrXUJYAfQ7HGn8oUQ4kX9NQWUh4cHO3bsYOrUqWzduhVPT0+j\no5lV27ZtiY2NpVu3bnz++ed4eHiwbt06o2MJIayc4YWp1joV6AOsA2KBxVrrQ0qpMUqpZsamE0Jk\nJTt37qRy5cqmKaBiY2Pp1auX1Vz79bwKFizIzJkz2bRpEzly5CAgIICOHTty4cIFo6MJIayU4YUp\ngNZ6tdbaRWtdSms99sHXRmqtwx7T1leOlgoh0tO1a9fo3bs3NWrUIDExkZ9++olly5ZRtGhRo6NZ\nhDp16nDgwAFGjx7NsmXLKFu2LDNnzrSKUcRCCMtiEYWpEEIYQWvNkiVLKFu2LN9++y19+/YlJiaG\n5s0fN2Nd1pYjRw5GjRrFgQMH8PLyYvHixUZHEkJYISlMhRBZ0okTJ2jcuDHt2rWjcOHC7Nq1i8mT\nJ5M/f36jo1k0Nzc3Nm7cyJIlS1BKcerUKUaMGEFycrLR0YQQVkAKUyFElnL37l3Gjx9PuXLliIiI\nYNKkSaZrS8WzUUphb28PQFhYGMHBwRw6dMjgVEIIayCFqRAiy9i8eTMVK1ZkyJAhBAQEEBsby/vv\nv4+trSVM6Zw59enTh7i4OKpUuT+DX2hoKGfOnDE4lRAis5LCVAhh9f7880/efvtt6taty82bN1m1\nahXLly/HycnJ6GhWoXTp0gCcO3eO999/n7JlyzJ58mRSU1MNTiaEyGykMBVCWK20tDRCQ0NxdXXl\n+++/Z8iQIcTExNCkSROjo1mlwoULExUVRa1atfjggw+oWrUqO3fuNDqWECITkcJUCGGV9u3bR61a\ntQgKCsLT05MDBw4wbtw4cufObXQ0q1aqVClWr17NkiVLuHjxIjVq1CAoKIjLly8bHU0IkQlIYSqE\nsCpXr16lb9++VKlShePHjzN37lzCw8Nxd3c3OlqWoZSiTZs2HD58mP79+zN79mxcXV2ZOXMmaWlp\nRscTQlgwKUyFEFZBa828efNwdXVl2rRp9OzZk7i4ON566y2UUkbHy5Ly5cvHF198wb59+3B3d6dH\njx58/vnnRscSQlgwGYoqhMj0Dhw4QJ8+fdiyZQve3t6sWbOGSpUqGR1LPODp6cmmTZtYuHAhjRo1\nAiAuLo5XX32VggULGpxOCGFJ5IipECLTunLlCn379qVSpUrExsYSGhrKtm3bpCi1QEopOnXqxEsv\nvYTWms6dO1OlShUZuS+EeIQcMRVCZDppaWl89913DBkyhMTERHr27MmYMWPk6FsmoZRi1qxZxMXF\nYWtri9aa6OhoPD09jY4mhDCYHDEVQmQqu3btonr16gQGBuLq6sqePXuYMmWKFKWZjJeXF23btgVg\n8eLFeHl50b17dy5evGhwMiGEkaQwFUJkCufPn+ftt9/G29ubhIQE5s+fT0REBBUqVDA6mnhBjRo1\n4sMPP2TevHmUKVOGL7/8krt37xodSwhhAClMhRAW7e7du3z++ee4uLiwYMECPvroI44cOULnzp1l\ntL2VyJcvHxMmTCA6OppatWoxcOBAvLy8WLt2rdHRhBBmJoWpEMIiaa355Zdf8PDw4KOPPqJu3boc\nOnSI8ePHky9fPqPjiQzg6urK6tWr+fnnn0lLS6Nhw4Y0bdqUo0ePGh1NCGEmUpgKISzOoUOHaNiw\nIU2aNMHGxoY1a9awatUqypQpY3Q0YQaNGzcmKiqK8ePHEx4eTrly5diyZYvRsYQQZiCFqRDCYly6\ndInevXtTvnx5du7cyZdffsnBgwcJCAgwOpowsxw5cpgu2xg0aBDe3t4AHD58WKaYEsKKSWEqhDDc\n3bt3+fLLLyldujTTp0+nZ8+eHD16lP79+5M9e3aj4wkDFS5cmODgYOzs7EhKSsLX15fWrVsbHUsI\nkUFkHlMhhGG01qxYsYLBgwcTHx9Pw4YNmThxotzXXjxWnjx5+Oabb8idOzcAt27d4o8//pDfFyGs\niBwxFUIYYufOnfj4+NC6dWty5MjB6tWrWb16tRQZ4omUUrRs2ZIGDRoAMHnyZDw9PXn33Xc5f/68\nwemEEOlBClMhhFmdOHGC9u3bU716deLj45kxYwb79++nYcOGRkcTmUxQUBB9+/Zl9uzZlC5dmk8/\n/ZSbN28aHUsI8QKkMBVCmMWlS5cYMGAAbm5uhIWFMXLkSOLj4+nRowe2tnJVkXh+L7/8MpMmTSIm\nJoaAgABGjhyJi4sLM2fOlAFSQmRSUpgKITLUrVu3CA4OplSpUkyePJnOnTtz9OhRPvnkE/LmzWt0\nPGEFypQpw9KlS9myZQvFihWjR48eeHl5sXLlSrTWRscTQjwHKUyFEBkiNTWV0NBQSpcuzfDhw/H1\n9eXgwYPMmjWLokWLGh1PWKFatWqxbds2li9fTlpaGi1atGDHjh1GxxJCPAcpTIUQ6UprzbJly/D0\n9CQoKIgSJUqwefNmVq5cSbly5YyOJ6zcXwOkoqOjWblyJTVq1ABgzpw5REVFGZxOCPE0UpgKIdKF\n1pp169ZRtWpV2rRpg1KKFStWsHXrVnx8fIyOJ7IYW1tbmjVrBkBycjJDhgxh0KBBBqcSQjyNRRSm\nSqkApVScUipeKTXkMa8PUErFKKUOKqXWK6WKG5FTCPF4W7duxdfXl4CAAC5dumQ6OtWiRQuUUkbH\nE1lcrly5iImJ4dtvvwXg1KlT9OrVizNnzhicTAjxd4YXpkqpbMBUoCHgDnRQSv19IsN9QBWttRew\nFJhg3pRCiMfZs2cPjRs3pnbt2sTFxTFlyhTi4uLo2rUr2bJlMzqeECYFCxbE2dkZgC1btjBz5kxK\nly7NwIEDuXDhgsHphBB/MbwwBaoB8Vrr41rru8AioPnDDbTWG7XWtx4s7gCczJxRCPGQ/fv307x5\nc6pUqcL27dsJDg7m2LFj9O7dmxw5chgdT4h/1bFjR+Li4njzzTeZNGkSJUuWZPDgwVy6dMnoaEJk\necroqTSUUm2AAK114IPlLoC31rrPE9pPAc5rrT97zGtBQBCAo6Nj5UWLFmVccCuSlJQk0/ZYkYzs\nz+PHjzNnzhwiIiLImzcv7dq1o1WrVuTJkydDtidk/8xoCQkJzJs3j/Xr15MzZ05atWpFu3btyJ8/\nf4ZtU/rUukh/Phs/P789WusqT22otTb0AbQFZj603AX43xPadub+EdMcT1tv5cqVtXg2GzduNDqC\nSEcZ0Z/79+/Xbdq00UopnT9/fj1q1Ch95cqVdN+O+CfZP80jJiZGv/nmm1oppfPly6eXLl2aYduS\nPrUu0p/PBojUz1AXWsKp/NPAaw8tOwFn/95IKVUPGA4001rfMVM2IbK0yMhImjdvToUKFfj1118Z\nNmwYJ06cYPTo0RQoUMDoeEKkm7Jly7Jo0SIOHjxIQECAaWqzkydPyjWoQpiRJRSmu4EySilnpVR2\noD0Q9nADpVRFYDr3i9KLBmQUIkvZvn07jRo1omrVqmzevJlPPvmEkydP8tlnn1GwYEGj4wmRYTw8\nPFi8eDFubm4ADBw4EBcXF65fv25wMiGyBsMLU611KtAHWAfEAou11oeUUmOUUs0eNPscyAssUUrt\nV0qFPWF1Qoj/SGvNr7/+ip+fHzVr1mTXrl0EBwdz8uRJRo4cKUdIRZYUHBzMV199ZbrmdNKkScTH\nxxucSgjrZWt0AACt9Wpg9d++NvKh5/XMHkqILOLevXusWLGCkJAQ9uzZQ5EiRfjiiy8ICgqSC/pF\nlufi4oKLiwsAZ86cYciQIQwcOJC2bdsyZMgQKlSoYHBCIayL4UdMhRDGuH37NrNmzcLd3Z22bdty\n/fp1QkNDOX78OAMGDJCiVIi/KVq0KH/88Qcffvghq1evpmLFijRq1Ijw8PC/BugKIV6QFKZCZDGX\nL19m7NixlChRgsDAQPLkycOPP/5IbGwsgYGBMg+pEP+iUKFChISEcOrUKcaOHUtkZCR+fn5UrVqV\nRYsWkZqaanREITI1KUyFyCKOHz9O3759KVasGB9//DEVK1bk999/Z8+ePbRr107u1CTEcyhQoADD\nhg3j5MmTTJ8+nRs3btChQwcqV65MWlqa0fGEyLSkMBXCimmt2bRpE61ataJMmTJMnz6ddu3aERUV\nxZo1a/D395d72QvxAnLlykVQUBCxsbGsXLmS3r17Y2Njg9aacePGceLECaMjCpGpWMTgJyFE+rp9\n+zY//PADkydP5sCBA7z88ssMHjyYPn36UKRIEaPjCWF1bGxsaNasmWk5OjqakSNHkpaWxvDhw0lL\nS0MpJR8EhXgKKUyFsCIJCQnMnj2bdu3a8eeff+Lh4UFoaCidOnUiV65cRscTIsvw9PTkxIkTpkGE\nS5YsYdy4cfTt25eiRYsanE4IyyWFqRCZXFpaGuvXr2fatGmEhYWhtaZp06a8//77+Pn5yREaIQzi\n5ORkep4nTx7S0tIIDAwkb968BAYG0rNnT9NUVEKI++QaUyEyqcTERL766ivc3Nx444032Lp1K4MH\nD2bhwoWsXLmS119/XYpSISxEkyZNOHDgAJs3b6ZatWpMnToVV1dX6tevz/Lly0lJSTE6ohAWQQpT\nITIRrTUbN26kY8eOFClShAEDBuDg4MCCBQtISEggODiYQoUKGR1TCPEYSil8fHwYMWIECQkJjB07\nlri4OFq3bk2xYsWYPn260RGFMJwUpkJkAufPn2f8+PG4uLjw+uuvs2bNGnr06MH+/fvZsmULHTt2\nlPlHhchEHB0dGTZsGMePHycsLIxq1aphZ2cHwJUrV/jhhx+4ffu2wSmFMD+5xlQIC3Xnzh1+/vln\n5s6dy5o1a0hNTaVOnTqMGjWK1q1by2AmIayAra0tTZs2pWnTpqavLV++nMDAQFatWkWTJk24c+cO\n2bNnl0tzRJYghakQFkRrze7du5k7dy6LFi0iMTHRdMq+e/fuMlBCiCzg7bffpnjx4tStWxeAMWPG\nsHz5crp27Urnzp0fGVQlhLWRU/lCWICjR48yZswY3N3d8fb2Zvbs2TRo0IC1a9dy6tQp02l8IYT1\ns7GxoV69eqZT+xUqVOCVV15h6NChFCtWjHr16jF79myuXr1qcFIh0p8UpkIY5OzZs3z11VdUq1YN\nFxcXRo8ejaOjIzNmzOD8+fMsXLiQBg0ayK1Chcji2rZtS0REBPHx8YwYMYKTJ0/SvXt3HB0dadmy\nJYsXL+bWrVtGxxQiXUhhKoQZnT17lilTpuDr64uTkxMDBgzg3r17TJw4kVOnThEeHk6PHj2wt7c3\nOqoQwsKUKlWKTz75hCNHjrBr1y569erFzp07efPNNxk0aBBw/3IgKVJFZibXmAqRwRISEli2bBlL\nly5l27ZtaK1xd3dnxIgRdOjQATc3N6MjCiEyEaUUVatWpWrVqkycOJFNmzbh4OAAQGRkJL6+vsyb\nN4/WrVsbnFSI5yeFqRDpTGvNgQMHCAsLY+XKlezduxcALy8vPvnkE1q3bo27u7vBKYUQ1iBbtmy8\n/vrrpmV7e3u6deuGl5cXAD/99BMzZsygefPmNG3alCJFihgVVYhnIoWpEOng9u3bbNq0iVWrVhEW\nFkZCQgJKKWrUqEFISAgtW7aUwUtCiAzn4uLC1KlTTcs3b97k8OHDrFmzhvfee4+qVavSrFkzGjdu\nTIUKFWQKKmFxpDAV4j+Kj49nzZo1rFmzhvDwcJKTk8mVKxf169dn9OjRNG7cGEdHR6NjCiGysE6d\nOtGxY0cOHTpkOoszYsQIRowYQaFChQgICKBx48a0adPG6KhCAFKYCvHMEhMT2bhxI+vXr+e3334j\nPj4egNKlSxMYGEhAQAC+vr7kzp3b4KRCCPH/lFJ4eHjg4eHBsGHDOH/+POvWrWPNmjWsXLmSQ4cO\nmQrT7777jrJly1K9enWDU4usSgpTIZ7gxo0bbNu2jfXr17N+/Xr27duH1pq8efNSp04d+vXrR8OG\nDSldurTRUYUQ4pkVKlSIrl270rVrV1JTU7lw4QIAKSkp9O3bl0aNGrF48WIAvvnmG6pUqULFihWx\ntZWSQWQ8+S0T4oGLFy+yZcsWNm/eTEREBPv37yctLQ07Oztq1qzJ6NGj8ff3f+Se1kIIkZnZ2tpS\ntGhRAOzs7Dh9+jTXrl0D4MyZM/Tq1QuAvHnzUqNGDXx8fPDx8cHb21tuiywyhBSmIktKSUnh4MGD\n7Nixg507d7Jjxw6OHj0KQM6cOalRowYff/wxPj4+1KxZU07PCyGyhAIFClCgQAEAihYtytmzZ4mI\niDB9YB81ahRaa+zs7KhYsSLe3t4EBgaaZgEQ4kVJYSqsXkpKCrGxsezdu5d9+/YRGRnJ3r17uX37\nNnD/tFb16tUJDAzEx8eHypUrkz17doNTCyGE8QoXLky7du1o164dAFeuXGHbtm1ERESwY8cOZs2a\nRcOGDfHy8mLLli2MGzeO4OBgypcvT2pqKtmyZZOR/+K5SGEqrMqlS5eIiooiOjqaqKgo9u/fz8GD\nB7lz5w4AefLkoUKFCvTq1Qtvb2+qV6/Oa6+9Jm+cQgjxDF566SUaN25M48aNAUhNTTW9dvXqVU6e\nPGn6YD9nzhwGDx5MpUqVKF++PB4eHnh6elK2bFk5CyWeSApTkemkpaVx+vRp4uLiTI/Y2Fiio6NN\nF/HD/TfQChUq0KdPHypVqkSlSpUoU6aM3HteCCHSycMDopo0aUKTJk1Myy4uLrRq1Yq9e/cyZcoU\n0wECpRSlSpXCw8MDNzc3hg4dSv78+UlNTZUBVkIKU2GZbt26xR9//MGJEyc4fvw4J06cMD0/evQo\nycnJprZ58+bFzc2NRo0amaZE8fT0pFChQnIkVAghDFKnTh3q1KkD3D+yeuzYMaKjox95rF27lk8+\n+QSAgQMHsmDBAhISEsiVKxfr1q3jzJkzODs74+zsTNGiRWXgaRZgEYWpUioAmAxkA2ZqrUP+9noO\nYB5QGbgMvKm1/sPcOcWLS05O5sKFC488zp07x+nTpx95XLly5ZHvy5UrF87OzpQsWZJ69erh4uKC\nq6srrq6uUoAKIYSFs7W1Nb1nt27d2vT1e/fumc5i1a1bF1tbW9No/1mzZrFkyRJTWxsbGwoVKoST\nk5PpUaJECfr37w9AQkICtra2FC5c2Iw/mUhvhhemSqlswFSgPnAa2K2UCtNaxzzUrDtwRWtdWinV\nHhgPvGn+tFlLWloaqamppKSkkJKSwu3bt0lOTn7kcevWLW7cuGF6XL9+nRs3bnD16lUSExMfeVy+\nfJmkpKTHbsvBwQEnJydKlixJnTp1KFq0KMWLF6dkyZI4Ozvj4OAgxacQQliZhy+tatWqFa1atTIt\nL1iwgJCQENMZs4SEBNPBi8OHD/P777+TP39+U2Has2dPIiMjOX/+vGl53759FCxY0PTInz8/+fLl\nI1++fOTPn59XX32VBg0aAHDixAnS0tIoVaoUcP/MHdyfRsvW1lb+BpmJ4YUpUA2I11ofB1BKLQKa\nAw8Xps2B0Q+eLwWmKKWU1lqbM+iTzJkzx7RjZCZaa7TWpKamYmNjY1q+d+8eKSkppKWl/af1Zs+e\nHXt7e15++WUKFixI0aJF8fT0pGDBgjg4OODo6PjIw8HBgRw5cqTzTyeEECIzs7Ozo2TJkpQsWfKJ\nbf4qHuH+pQAXL140LRcqVIgCBQpw6dIljhw5wuXLl7l+/fojf9tKlSpluotfYGAgf/zxB8eOHQOg\nadOmbNiwwdTW1tYWW1tbbGxsUEqZrpWdNGkSAM2aNeP06dPs3bvXtBwREfGvP6Ozs/Mj7c35/TNm\nzKBt27b/un4jWEJhWhRIeGj5NOD9pDZa61Sl1DXgZeDSw42UUkFAEICjoyPh4eEZFPlRSUlJvP76\n62bZVnpTSpGSkkL27NlNO5qNjY1pB8yWLRvZsmXD1taW7NmzkyNHDtO/fz1y5879yONZrwFKSkoi\nKSnJ9CYg0kdSUpLZfvdFxpP+tD7SpxlDKfXI3/66detSt27dR9porblz5w63bt3i1q1b3Lt3z9S+\nadOmJCcnm5Zr165N6dKlSU1NNT3u3btnOoijtcbe3t7Un87Ozrzyyium73d2dn7q30N7e/tH2pvz\n+xMTEy3y91AZfdBRKdUWaKC1Dnyw3AWoprXu+1CbQw/anH6wfOxBm8tPWm+VKlV0ZGRkxoa3EuHh\n4fj6+hodQ6QT6U/rIv1pfaRPrYv057NRSu3RWld5Wjsbc4R5itPAaw8tOwFnn9RGKWUL2AOJZkkn\nhBBCCCHMwhIK091AGaWUs1IqO9AeCPtbmzCg64PnbYANlnJ9qRBCCCGESB+GX2P64JrRPsA67k8X\nNVtrfUgpNQaI1FqHAbOA+UqpeO4fKW1vXGIhhBBCCJERDC9MAbTWq4HVf/vayIee3wYsb+iYEEII\nIYRIN5ZwKl8IIYQQQggpTIUQQgghhGWQwlQIIYQQQlgEw+cxzShKqT+Bk0bnyCRe4W83KxCZmvSn\ndZH+tD7Sp9ZF+vPZFNdav/q0RlZbmIpnp5SKfJZJb0XmIP1pXaQ/rY/0qXWR/kxfcipfCCGEEEJY\nBClMhRBCCCGERZDCVADMMDqASFfSn9ZF+tP6SJ9aF+nPdCTXmAohhBBCCIsgR0yFEEIIIYRFkMJU\nCCGEEEJYBClMsyClVFul1CGlVJpS6olTXCilApRScUqpeKXUEHNmFM9OKVVQKfWbUurog39fekK7\ne0qp/Q8eYebOKf7d0/Y3pVQOpdSPD17fqZQqYf6U4lk9Q392U0r9+dA+GWhETvFslFKzlVIXlVLR\nT3hdKaW+ftDfB5VSlcyd0VpIYZo1RQOtgM1PaqCUygZMBRoC7kAHpZS7eeKJ5zQEWK+1LgOsf7D8\nOMla6woPHs3MF088zTPub92BK1rr0sBXwHjzphTP6jneP398aJ+cadaQ4nnNAQL+5fWGQJkHjyDg\nGzNkskpSmGZBWutYrXXcU5pVA+K11se11neBRUDzjE8n/oPmwNwHz+cCLQzMIv6bZ9nfHu7npYC/\nUkqZMaN4dvL+aWW01puBxH9p0hyYp+/bARRQShU2TzrrIoWpeJKiQMJDy6cffE1YHket9TmAB/86\nPKFdTqVUpFJqh1JKilfL8iz7m6mN1joVuAa8bJZ04nk96/tn6wenfZcqpV4zTzSRQeRvZjqxNTqA\nyBhKqd+BQo95abjWeuWzrOIxX5O5xQzyb/35HKspprU+q5QqCWxQSkVprY+lT0Lxgp5lf5N9MvN4\nlr5aBfygtb6jlHqP+0fDX8/wZCKjyP6ZTqQwtVJa63ovuIrTwMOf4J2Asy+4TvEf/Vt/KqUuKKUK\na63PPTh1dPEJ6zj74N/jSqlwoCIghalleJb97a82p5VStoA9/35qURjnqf2ptb780GIocs1wZid/\nM9OJnMoXT7IbKKOUclZKZQfaAzKS2zKFAV0fPO8K/OOIuFLqJaVUjgfPXwFqATFmSyie5ln2t4f7\nuQ2wQcsdUizVU/vzb9cfNgNizZhPpL8w4K0Ho/OrA9f+usRKPB85YpoFKaVaAv8DXgV+UUrt11o3\nUEoVAWZqrRtprVOVUn2AdUA2YLbW+pCBscWThQCLlVLdgVNAW4AHU4G9p7UOBMoC05VSadz/QBqi\ntZbC1EI8aX9TSo0BIrXWYcAsYL5SKp77R0rbG5dY/Jtn7M9+SqlmQCr3+7ObYYHFUymlfgB8gVeU\nUqeBUYAdgNb6W2A10Aj+r727tQkgiKIwel+CxKEpYRFUQRmgECR0Q0IhGEJoAMWPQRAUggowiEEg\nCAXszoOcU8GVX2aSmbwk+UhyMmfp3+dLUgAAWnCVDwBAC8IUAIAWhCkAAC0IUwAAWhCmAAC0IEwB\nAGhBmAIA0IIwBWioqk6r6r2q7qvqtaqOZ28CWJsH9gEaqqqLJE9jjMuqOkxyM8bYm70LYE1OTAF6\nWvLzf/pbvr+2BPjXhClAT0uS56qqJOdJribvAVjdzuwBAPxWVftJdpNcJ/lMcpfkbOoogA0IU4B+\nDpLcjjGOZg8B2JKrfIB+liQPs0cAbE2YAvSzJHmcPQJga56LAgCgBSemAAC0IEwBAGhBmAIA0IIw\nBQCgBWEKAEALwhQAgBaEKQAALXwBy3VYl3DeXMsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd7d7c1d470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "M = np.linspace(-1.2, 1.2, 100)\n",
    "y1 = [AUSM_1D.M_split(Mi, 1, AUSM_1D.beta) for Mi in M]\n",
    "y2 = [AUSM_1D.M_split(Mi, -1, AUSM_1D.beta) for Mi in M]\n",
    "\n",
    "ax1 = plt.subplot(211)\n",
    "ax1.plot(M, y1, c=\"0\", linestyle=\"-\", label = \"$M+$\")\n",
    "ax1.plot(M, y2, c=\"0\", linestyle=\"-.\", label = \"$M-$\")\n",
    "ax1.set_ylabel(\"$M\\pm$\")\n",
    "ax1.set_xlabel(\"$M$\")\n",
    "ax1.grid()\n",
    "ax1.legend()\n",
    "\n",
    "ax2 = plt.subplot(212)\n",
    "y1 = [AUSM_1D.P_split(Mi, 1, AUSM_1D.alpha) for Mi in M]\n",
    "y2 = [AUSM_1D.P_split(Mi, -1, AUSM_1D.alpha) for Mi in M]\n",
    "ax2.plot(M, y1, c=\"0\", linestyle=\"-\", label = \"$P+$\")\n",
    "ax2.plot(M, y2, c=\"0\", linestyle=\"-.\", label = \"$P-$\")\n",
    "ax2.set_ylabel(\"$P\\pm$\")\n",
    "ax2.set_xlabel(\"$P$\")\n",
    "ax2.grid()\n",
    "ax2.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "par = {\"R\": 287.0,  \"kappa\": 1.4,    \"p_tot\": 1.0e5, \"T_tot\": 273.15,\n",
    "       \"cfl\": 0.9,  \"p_exit\": 0.8e5, \"xmin\": -1.,    \"xmax\": 1.,\n",
    "       \"numx\": 200, \"ymin\": 0.2,    \"ymax\": 0.3,    \"subsonic_exit\": True}\n",
    "\n",
    "\n",
    "nozzle = AUSM_1D(par)    # 1: create a AUSM_1D object + initialize\n",
    "for i in range(5000):\n",
    "    nozzle.makeStep()    # 2: make 10000 steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CAAAgUARSAAAABIpACgAAgEARSAEAABAoAikAAAACRSAFAABAoAikAAAACBSB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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd7a1252518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(11,11))\n",
    "ax1 = plt.subplot(211)\n",
    "ax1.set_title(\"nozzle geometry\")\n",
    "ax1.plot(nozzle.x, np.array([nozzle.S, -nozzle.S]).T, c=\"0\")\n",
    "ax1.grid()\n",
    "ax1.set_aspect(1)\n",
    "ax1.set_xlabel(\"x [m]\")\n",
    "ax1.set_ylabel(\"y [m]\")\n",
    "\n",
    "ax2 = plt.subplot(212, sharex=ax1)\n",
    "ax2.plot(nozzle.x, nozzle.p *1e-5, c=\"0\", linestyle=\"-\", label=\"p\")\n",
    "ax2.plot(nozzle.x, nozzle.rho, c=\"0\", linestyle=\"-.\", label=r\"$\\rho$\")\n",
    "ax2.plot(nozzle.x, nozzle.Mach, c=\"0\", linestyle=\"--\", label=\"MachNumber\")\n",
    "ax2.grid()\n",
    "ax2.legend()\n",
    "ax2.set_xlabel(\"x [m]\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "class ROE_1D(AUSM_1D):   \n",
    "\n",
    "    def makeStep(self):\n",
    "        dt = self.timeStep()\n",
    "        f_star = self.compute_f_star()\n",
    "        source = self.compute_source()\n",
    "        # Integration of u\n",
    "        du = -dt / self.dx * (f_star[:, 1:] - f_star[:, :-1]) - source[:, 1:-1] * dt\n",
    "        self.u[:, 1:-1] += du\n",
    "        self.applyBoundaries() # 2.7\n",
    "\n",
    "    def compute_f_star(self):\n",
    "        f_vector=np.array([self.rho * self.u_vel,\n",
    "                           self.rho * self.u_vel**2 + self.p,\n",
    "                          (self.u[2] + self.p) * self.u_vel])\n",
    "        R_m = (self.rho[1:] / self.rho[:-1])**0.5\n",
    "        rho_m = R_m * self.rho[:-1]\n",
    "        u_m = (R_m * self.u_vel[1:] + self.u_vel[:-1])/(R_m + 1)\n",
    "        H_m = (R_m * self.H[1:] + self.H[:-1]) / (R_m + 1)\n",
    "        c_m = np.sqrt((self.gamma - 1) * (H_m - u_m**2 / 2))\n",
    "        c_r = self.c_wave[1:]\n",
    "        c_l = self.c_wave[:-1]\n",
    "        u_r = self.u_vel[1:]\n",
    "        u_l = self.u_vel[:-1]\n",
    "        f_star = np.zeros([3, self.parameter[\"numx\"] - 1])\n",
    "        for i in range(len(c_m)):\n",
    "            R_eigen_i = self.R_eigen(rho_m[i], c_m[i], u_m[i])\n",
    "            L_eigen_i = self.L_eigen(rho_m[i], c_m[i], u_m[i])\n",
    "            eigenvalues_i = self.eigenvalues( c_l[i], u_l[i], c_m[i], u_m[i], c_r[i], u_r[i])#=Lambda_mod\n",
    "            A = R_eigen_i.dot(eigenvalues_i).dot(L_eigen_i)\n",
    "            f_star[:, i] =  0.5 * (f_vector[:, i + 1] + f_vector[:, i])\n",
    "            f_star[:, i] -=  0.5 * A.dot((self.u[:, i + 1] - self.u[:, i]))\n",
    "        return f_star\n",
    "        \n",
    "    def R_eigen(self, rho, c, u):\n",
    "        gamma = self.gamma\n",
    "        eig_R = np.zeros([3, 3])\n",
    "\n",
    "        eig_R[0, 0] = 1\n",
    "        eig_R[0, 1] = rho / (2 * c)\n",
    "        eig_R[0, 2] = rho / (2 * c)\n",
    "\n",
    "        eig_R[1, 0] = u\n",
    "        eig_R[1, 1] = rho / (2 * c) * (u + c)\n",
    "        eig_R[1, 2] = rho / (2 * c) * (u - c)\n",
    "\n",
    "        eig_R[2, 0] = u**2 / 2\n",
    "        eig_R[2, 1] = rho / (2 * c) * (c**2 / (gamma - 1) + u**2 / 2 + u * c)\n",
    "        eig_R[2, 2] = rho / (2 * c) * (c**2 / (gamma - 1) + u**2 / 2 - u * c)\n",
    "        return eig_R\n",
    "        \n",
    "    def L_eigen(self, rho, c, u):\n",
    "        gamma = self.gamma\n",
    "        eig_L = np.zeros([3, 3])\n",
    "        eig_L[0, 0] = 1 - (gamma - 1) / 2 * u**2 / c**2\n",
    "        eig_L[0, 1] = (gamma - 1) * u / c**2\n",
    "        eig_L[0, 2] = -(gamma - 1) / c**2\n",
    "\n",
    "        eig_L[1, 0] = ((gamma - 1) / 2 * u**2 - u * c) * 1 / (rho * c)\n",
    "        eig_L[1, 1] = 1 / (rho * c) * (c - (gamma - 1) * u)\n",
    "        eig_L[1, 2] = (gamma - 1) / (rho * c)\n",
    "\n",
    "        eig_L[2, 0] = ((gamma - 1) / 2 * u**2 + u * c) / (rho*c)\n",
    "        eig_L[2, 1] = -1 / (rho * c) * (c + (gamma - 1) * u)\n",
    "        eig_L[2, 2] = (gamma - 1) / (rho * c)\n",
    "        return eig_L\n",
    "\n",
    "    def eigenvalues(self, c_l, u_l, c_m, u_m, c_r, u_r):\n",
    "        lambda_l=np.array([u_l, u_l + c_l, u_l - c_l])\n",
    "        lambda_m=np.array([u_m, u_m + c_m, u_m - c_m])\n",
    "        lambda_r=np.array([u_r, u_r + c_r, u_r - c_r])\n",
    "        epsilon=self.cellFunc(max, np.zeros(3), lambda_m-lambda_l,lambda_r-lambda_m) #!\n",
    "        lambda_mod = np.zeros([3,3])\n",
    "        for i, l in enumerate(lambda_m):#Eq.13-91\n",
    "            if abs(l) >= epsilon[i]:\n",
    "                lambda_mod[i, i] = abs(l)\n",
    "            else:\n",
    "                lambda_mod[i, i] = epsilon[i]\n",
    "        return lambda_mod\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "par = {\"R\": 287.0,  \"kappa\": 1.4,    \"p_tot\": 1.0e5, \"T_tot\": 273.15,\n",
    "       \"cfl\": 0.9,  \"p_exit\": 0.8e5, \"xmin\": -1.,    \"xmax\": 1.,\n",
    "       \"numx\": 200, \"ymin\": 0.2,    \"ymax\": 0.3,    \"subsonic_exit\": True}\n",
    "\n",
    "\n",
    "nozzle = ROE_1D(par)    # 1: create a AUSM_1D object + initialize\n",
    "for _ in range (5000): #_ in = i in \n",
    "    nozzle.makeStep()        # 2: make 10000 steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PjxgxgpEjR1KrVq10751evXpRvnx5qlatiqenJ8uWLcv0sczMzBg0aBA3btzQHps0aRLN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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd7a0d67cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(11,11))\n",
    "ax2 = plt.subplot(212, sharex=ax1)\n",
    "ax2.plot(nozzle.x, nozzle.p *1e-5, c=\"0\", linestyle=\"-\", label=\"p\")\n",
    "ax2.plot(nozzle.x, nozzle.rho, c=\"0\", linestyle=\"-.\", label=r\"$\\rho$\")\n",
    "ax2.plot(nozzle.x, nozzle.Mach, c=\"0\", linestyle=\"--\", label=\"MachNumber\")\n",
    "ax2.grid()\n",
    "ax2.legend()\n",
    "ax2.set_xlabel(\"x [m]\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "class AUSM_ShockTube(AUSM_1D):\n",
    "    \"\"\"the same class as AUSM_1D but with special treatment of boundaries\n",
    "       and initialization\"\"\"\n",
    "    def _initUVector(self):\n",
    "        par = self.parameter\n",
    "        p_1 = par[\"p_1\"]\n",
    "        p_2 = par[\"p_2\"]\n",
    "        rho_1 = par[\"rho_1\"]\n",
    "        rho_2 = par[\"rho_2\"]\n",
    "        u_1 = np.array([\n",
    "            self.vec_1 * rho_1,                 # u[0]\n",
    "            self.vec_0,                         # u[1]\n",
    "            self.vec_1 * p_1 / (self.gamma -1)  # u[2]\n",
    "        ])\n",
    "        u_2 = np.array([\n",
    "            self.vec_1 * rho_2,                 # u[0]\n",
    "            self.vec_0,                         # u[1]\n",
    "            self.vec_1 * p_2 / (self.gamma -1)  # u[2]\n",
    "        ])\n",
    "        mult_vec = self.vec_0\n",
    "        for i in range(par[\"numx\"]//2):\n",
    "            mult_vec[i] += 1\n",
    "        self.u = u_1 * mult_vec - u_2 * (mult_vec - 1)\n",
    "        \n",
    "    def applyBoundaries(self):\n",
    "        \"\"\"overwrite, boundaries have no influence\"\"\"\n",
    "        pass\n",
    "\n",
    "class ROE_ShockTube(ROE_1D):\n",
    "    \"\"\"the same class as ROE_1D but with special treatment of boundaries\n",
    "       and initialization\"\"\"\n",
    "    def _initUVector(self):\n",
    "        par = self.parameter\n",
    "        p_1 = par[\"p_1\"]\n",
    "        p_2 = par[\"p_2\"]\n",
    "        rho_1 = par[\"rho_1\"]\n",
    "        rho_2 = par[\"rho_2\"]\n",
    "        u_1 = np.array([\n",
    "            self.vec_1 * rho_1,                 # u[0]\n",
    "            self.vec_0,                         # u[1]\n",
    "            self.vec_1 * p_1 / (self.gamma -1)  # u[2]\n",
    "        ])\n",
    "        u_2 = np.array([\n",
    "            self.vec_1 * rho_2,                 # u[0]\n",
    "            self.vec_0,                         # u[1]\n",
    "            self.vec_1 * p_2 / (self.gamma -1)  # u[2]\n",
    "        ])\n",
    "        mult_vec = self.vec_0\n",
    "        for i in range(par[\"numx\"]//2):\n",
    "            mult_vec[i] += 1\n",
    "        self.u = u_1 * mult_vec - u_2 * (mult_vec - 1)\n",
    "        \n",
    "    def applyBoundaries(self):\n",
    "        \"\"\"overwrite, boundaries have no influence\"\"\"\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "class ShockTube(object):\n",
    "    \"\"\"analytic solution to the shock-tube problem\"\"\"\n",
    "    @staticmethod\n",
    "    def shock_tube_function(p4, p1, p5, rho1, rho5, gamma):\n",
    "        z = (p4 / p5 - 1.)\n",
    "        c1 = np.sqrt(gamma * p1 / rho1)\n",
    "        c5 = np.sqrt(gamma * p5 / rho5)\n",
    "        gm1 = gamma - 1.\n",
    "        gp1 = gamma + 1.\n",
    "        g2 = 2. * gamma\n",
    "        fact = gm1 / g2 * (c5 / c1) * z / np.sqrt(1. + gp1 / g2 * z)\n",
    "        fact = (1. - fact) ** (g2 / gm1)\n",
    "        return p1 * fact - p4\n",
    "\n",
    "    def __init__(self, p_1, p_5, rho_1, rho_5, gamma=1.4):\n",
    "        self.gamma = gamma\n",
    "        self.p_1 = p_1\n",
    "        self.p_5 = p_5\n",
    "        self.rho_1 = rho_1\n",
    "        self.rho_5 = rho_5\n",
    "        self.u_1 = 0\n",
    "        self.u_5 = 0\n",
    "        self.p_4 = scipy.optimize.fsolve(self.shock_tube_function, self.p_1, \n",
    "                   (self.p_1, self.p_5, self.rho_1, self.rho_5, self.gamma))[0]\n",
    "        z = (self.p_4 / self.p_5 - 1.)\n",
    "        c5 = np.sqrt(gamma * self.p_5 / self.rho_5)\n",
    "\n",
    "        gm1 = self.gamma - 1.\n",
    "        gp1 = self.gamma + 1.\n",
    "        gmfac1 = 0.5 * gm1 / self.gamma\n",
    "        gmfac2 = 0.5 * gp1 / self.gamma\n",
    "        fact = np.sqrt(1. + gmfac2 * z)\n",
    "        self.u_4 = c5 * z / (self.gamma * fact)\n",
    "        self.rho_4 = self.rho_5 * (1. + gmfac2 * z) / (1. + gmfac1 * z)\n",
    "\n",
    "        # shock speed\n",
    "        self.w = c5 * fact\n",
    "        \n",
    "        self.p_3 = self.p_4\n",
    "        self.u_3 = self.u_4\n",
    "        self.rho_3 = self.rho_1 * (self.p_3 / self.p_1)**(1. / self.gamma)\n",
    "    \n",
    "    def get_positions(self, t):\n",
    "        c1 = np.sqrt(self.gamma * self.p_1 / self.rho_1)\n",
    "        c3 = np.sqrt(self.gamma * self.p_3 / self.rho_3)\n",
    "        return np.array([- c1 * t, (self.u_3 - c3) * t, self.u_3 * t, self.w * t ,])\n",
    "    \n",
    "    def get_points(self, t, num_points=10):\n",
    "        jump = 10e-10\n",
    "        c1 = np.sqrt(self.gamma * self.p_1 / self.rho_1)\n",
    "        c5 = np.sqrt(self.gamma * self.p_5 / self.rho_5)\n",
    "        gm1 = self.gamma - 1.\n",
    "        gp1 = self.gamma + 1.\n",
    "        pos = self.get_positions(t)\n",
    "        x_pos_1_2 = np.linspace(pos[0], pos[1], num_points)\n",
    "        x_min = pos[0] - (pos[-1] - pos[0]) * 0.4\n",
    "        x_max = pos[-1] + (pos[-1] - pos[0]) * 0.4\n",
    "\n",
    "        u_1_2 = 2. / gp1 * (c1 + x_pos_1_2 / t)\n",
    "        fact = 1. - 0.5 * gm1 * u_1_2 / c1\n",
    "        rho_1_2 = self.rho_1 * fact ** (2. / gm1)\n",
    "        p_1_2 = self.p_1 * fact ** (2. * self.gamma / gm1)\n",
    "\n",
    "        x_values = np.array([x_min] + list(x_pos_1_2) + \n",
    "                            [pos[2], pos[2] + jump, pos[3], pos[3] + jump, x_max])\n",
    "        p_values = np.array([self.p_1] + list(p_1_2) +\n",
    "                            [self.p_3, self.p_4, self.p_4, self.p_5, self.p_5])\n",
    "        u_values = np.array([self.u_1] + list(u_1_2) +\n",
    "                            [self.u_3, self.u_4, self.u_4, self.u_5, self.u_5])\n",
    "        rho_values = np.array([self.rho_1] + list(rho_1_2) +\n",
    "                            [self.rho_3, self.rho_4, self.rho_4, \n",
    "                             self.rho_5, self.rho_5])\n",
    "        return x_values, p_values, rho_values, u_values, x_min, x_max"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "par = {\"R\": 287.0,  \"kappa\": 1.4,   \"p_1\": 1.0,  \"p_2\": 0.1,\n",
    "       \"rho_1\": 1,  \"rho_2\": 0.125, \"cfl\": 0.1,  \"xmin\": -1.,\n",
    "       \"xmax\": 1.,  \"numx\": 70,     \"ymin\": 1,   \"ymax\": 1.}\n",
    "\n",
    "roe_tube = ROE_ShockTube(par)\n",
    "ausm_tube = ROE_ShockTube(par)\n",
    "for i in range(300):\n",
    "    roe_tube.makeStep()\n",
    "    ausm_tube.makeStep()\n",
    "\n",
    "analytic_tube = ShockTube(par[\"p_1\"], par[\"p_2\"], par[\"rho_1\"], par[\"rho_2\"])\n",
    "x, p, rho, u, x_min, x_max = analytic_tube.get_points(roe_tube.time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "plotting at time = 0.417574531256 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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FqojEZqkf/vCHXH311Tz22GNs2bKl3u2IiEjjEKmNt3l5eaSnpwOQnp5OXl4eZhawbsXx\nefPm8cYbb9C3b19mzpzJddddV61eeno6+fn5LF26lMsuu6xB/QsXBaciVURqs1RmZiZ79+5l5syZ\nDWpHRES8LxL/lmzfvp0VK1YwZswYUlJSmDFjBosWLaJdu3Z8/fXX1eru2LGDDh06VL4+5ZRTuPXW\nW/nzn//M888/X63uxRdfzNNPP01ycjJHHHFEvfsXTgpORaoItVkKCLhhat68ebVueDrxxBO56qqr\nmD17Nlu3bg17v0VExDuysrI4/PDDqx07/PDDycrKqnebS5YsYcSIERQWFrJx40Y+//xzunbtyo4d\nO9i8eTPr168HoLCwkHfffZdevXpRUlJCQUFBZRvr1q3D5/NVa7dVq1ZMnz69wbcchJOCU5EqQm2W\nAgJumMrNza3ThqnJkydTWlrK/fffH+m3ISIiMZSRkcHcuXOr/Vsyd+7coBMgdZGXl1dj2X3IkCHk\n5+fzzDPPMGrUKHr16sXQoUOZN28eSUlJOOfIycmhe/fu9OrVi6lTp7JgwYIabaenp9O7d+969y3c\nzDkX6z5ETGpqqotmrq6CgoJqKRqk6UlJSaGwsLDGcZ/Px8aNG2s9PyMjgz/84Q9s3Lix2pKLNC76\nrMcnjXv8qTrm69evp0ePHrHtUCMS6OdlZmudc6m1nauZU5FD0NCb3CdPnszu3bs1eyoiIhKEglOR\nQ9DQm9x79OjBsGHDeOSRR9i+fXs4uyYiItIkKDgVOQS1bZiqiylTprBr1y4eeOCBcHVLRESkyVBw\nKnIIAm2YysjIICkpqc6PPu3ZsyfDhg1j1qxZbN68OUbvRERExJsUnIocgkBPlxozZgwTJ048pEef\nZmVlUVZWxtSpU2PwLkRERLxLwalImBzKo09/8IMf8Mtf/pL58+fzwQcfRLprIiIijYaCU5EwOdSd\n/JMnT6Zt27ZMnDgxkt0SERGpZsGCBdx444211ql669mYMWP48MMPI901QMGpSNgc6k7+9u3bM3ny\nZF599VXeeOONSHZNRETkkBwcnM6bN4+ePXtG5doKTkXCpD47+W+88UZ8Ph+/+c1v2L9/f6S6JiIi\nTcSll15Knz59OOmkk5g7dy4Abdq0ITMzk1NPPZUzzzyTLVu2APDyyy9zxhlncNppp9G/f//K4xV2\n7txJ165dKSsrA+Dbb78lJSWF5557jjVr1pCRkUGvXr3Ys2cPaWlpVDzY6E9/+hO9e/fm1FNP5Wc/\n+1nY32PzsLcoEqcqdvLn5uZSVFREcnJytZ38xcXFAcuys7PJyMggNzeXa665JtZvQ0REanHLLbew\nbt26sLbZq1cvZs2aVWu9+fPn065dO/bs2cPpp5/OkCFD2LVrF2eeeSZZWVlMnDiRxx9/nMmTJ3PO\nOeewatUqzIx58+aRk5NT7SEwbdu2JS0tjVdeeYVLL72U/Px8hgwZwhVXXMGjjz7KzJkzSU2t/kCn\nbdu2MXbsWP7617/StWtXduzYEdafA2jmVCRsAu3kr/hFEWonf3p6On369CEzM5M9e/bE+m2IiIiH\n/e53v6ucIf3888/55JNPOOywwxg0aBAAffr0qXyc9qZNm7jgggs45ZRTmDFjRsANuGPGjOHJJ58E\n4Mknn2TUqFEhr79q1SrOO+88unbtCkC7du3C+O4O0MypSBSE2smflZXFzJkz6devH7/73e+YNGlS\nlHsnIiKHoi4znJFQUFDA8uXLeeuttzj88MNJS0ujtLSUFi1aYGYANGvWjH379gFw0003cdttt3HJ\nJZdQUFDAXXfdVaPNs88+m40bN/KXv/yF77//npNPPjlkH5xzldeKFM2cikRBbTv509LSGDRoENnZ\n2Xz11VfR7JqIiDQSxcXFHHXUURx++OF89NFHrFq1qtb6xx9/PAALFy4MWm/EiBEMHz682qxp27Zt\n2blzZ426Z511Fn/5y1/4z3/+A6BlfZHGqi47+adPn05JSQn33ntvtLolIiKNyIABA9i3bx8//vGP\nmTJlCmeeeWbI+nfddRdXXHEF5557Lh06dAhaLyMjg6+//prhw4dXHhs5ciQ33HBD5YaoCh07dmTu\n3LlcfvnlnHrqqQwbNqzhb+wgWtYXiYKMjAyys7MDHq/Qs2dPxowZw+zZs7nppps44YQTotlFERHx\nuJYtW/LHP/6xxvGSkpLK74cOHcrQoUMBGDx4MIMHD65Rf+TIkYwcObLy9d///neGDh3KkUceWXls\nyJAhDBkypPJ1QUFB5fcDBw5k4MCBDXkrIWnmVCQKKnby+3w+zAyfz4ff7ycpKalavbvvvpuWLVty\nxx13xKinIiIST2666SZuv/12pkyZEuuuVNLMqUgUVDwFKisrK2B51VRTu3btYsmSJVx77bWcdNJJ\neoKUiIhEzMMPPxzrLtSgmVMRD6iaaqrCU089xTfffBPDXomIiESfglMRDwiWamrevHlR7omIiATj\nnIt1FxqFhv6cPBOcmtkAM/vYzDaY2e0BypPNbKWZvWNm75nZhbHop0gkBEs1tW3btsrHyomISOwk\nJiayfft2Bai1cM6xfft2EhMT692GJ+45NbNmwKPAz4FNwGoze8k592GVapOBxc6535tZT+BVICXq\nnRWJgOTk5GpL+lXNmTOHG2+8Mco9EhGRqjp37symTZvYtm1brLvieYmJiXTu3Lne53siOAX6Ahuc\nc58BmFk+MBioGpw64Ijy75OAzVHtoUgEBUs15fP5uPvuu7nmmmtq7OwXEZHoadGiReUjOyWyzAvT\n02Y2FBjgnBtT/voa4Azn3I1V6hwLvA4cBbQG+jvn1gZoaxwwDqBTp0598vPzo/AODigpKaFNmzZR\nu554QzjGPS8vj127drF8+XK2bt3K0UcfTf/+/dmzZw8vvPACV111FWPHjg1Tj6Wh9FmPTxr3+KMx\nD69+/fqtdc6l1lbPK8HpFcAFBwWnfZ1zN1WpcxsH+nu/mZ0FPAGc7JzbH6zd1NRUt2bNmgj3/n8K\nCgpIS0uL2vXEGyI97r179+Zf//oXnTp1YvPmzSQnJ5ORkUFSUpLSTMWIPuvxSeMefzTm4WVmdQpO\nvbIhahPQpcrrztRcth8NLAZwzr0FJALBn8Ul0kT85Cc/Yd++fXzxxRc45ygsLCQ7O5vi4uJYd01E\nRCTsvBKcrgZONLOuZnYYkA68dFCdIuBnAGbWgwPBqe5KliZv2bJlAY8HSz8lIiLSmHkiOHXO7QNu\nBF4D1nNgV/4HZnaPmV1SXu3XwFgzexfIA0Y6L9yTIBJhwdJMBTsuIiLSmHlltz7OuVc5kB6q6rE7\nq3z/IXB2tPslEmvB0kwlJyfHoDciIiKR5YmZUxEJLiMj45COi4iINGYKTkU8LikpCb/fj8/nqzzW\nu3dv5T0VEZEmScGpiMdNnDiRrKwsNm7ciHOOW265hXfeeUfpTUREpEnyzD2nIlI399xzD4sXL+aG\nG27giiuuoKSkhNzcXIqKipQDVUREGj3NnIo0Mm3btmXWrFm88847rFy5kuzsbAoLC5UDVUREmgQF\npyKN0NChQxkwYADLly8PWK4cqCIi0lgpOBVphMyMRx55hGCpfpUDVUREGisFpyKN1A9/+MOgO/aV\nA1VERBorBacijdj1118f8LhyoIqISGOl4FSkEWvfvj3Dhw+vfO3z+fD7/cqBKiIijZZSSYk0YhXp\nosyMJUuW8Oc//5kTTzwxxr0SERGpP82cijQB999/P61atWLChAmVm6RycnLIzMwkJSWFhIQEUlJS\nyMzMJCcnJ8a9FRERCU7BqUgTcMwxx5CVlcXy5ctZtGgRAMXFxcqBKiIijY6CU5Em4oYbbiA1NZVb\nb72V4uLioLlOlQNVRES8TMGpSBPRrFkzHnvsMbZu3cqUKVOC5jpVDlQREfEyBaciTUifPn2YMGEC\njz76KJ06dQpYRzlQRUTEyxScijQxv/3tbzn66KMxs4DlyoEqIiJepuBUpIlJSkrigQce4Msvv+SC\nCy7A5/NhZsqBKiIijYLynIo0Qenp6TzxxBOsWrWKjz76iGOOOSbWXRIREakTzZyKNEFmxuzZs9mz\nZw8333xzrLsjIiJSZwpORZqobt26ceedd7J48WLy8/NrlCtJv4iIeJGCU5EmbNKkSZxxxhlMmDCB\nzZs3VytTkn4REfEiBaciTVjz5s156qmnKC0tZcyYMZWPNoXgyfiVpF9ERGJJwalIE9etWzdycnL4\n4x//yOOPP155XEn6RUTEixScisSBCRMm0L9/f2677TY+++wzIHgyfiXpFxGRWFJwKhIHEhISmD9/\nPs2bN+faa6/l+++/D5qMX0n6RUQklhScisSJLl268PDDD/P3v/+dBx98kKSkJPx+v5L0i4iIpygJ\nv0gcufrqq1m6dCmZmZmsXbuWk08+maysrFh3S0REpJJmTkXiiJnx2GOPceSRRzJixAi+++67gPWU\nA1VERGJFwalInOnYsSNz587lnXfe4d577w1YRzlQRUQkVhScisShwYMHM3LkSO677z7++c9/1ihX\nDlQREYkVBacicWrWrFkcf/zxjBgxgt27d1crUw5UERGJFQWnInEqKSmJBQsW8O9//5vbb7+9Wply\noIqISKwoOBWJY/369ePmm2/m4Ycf5o033qg8rhyoIiISKwpOReLcfffdx49+9CNGjRpVueFJOVBF\nRCRWlOdUJM61atWKp556irPOOoubb76ZBQsWMHHiRADlQBURkajzzMypmQ0ws4/NbIOZ3R6kzpVm\n9qGZfWBmz0a7jyJN1emnn05mZiYLFy5k6dKlIesqB6qIiESSJ4JTM2sGPAoMBHoCw82s50F1TgTu\nAM52zp0E3BL1joo0YZMnT6Z3796MGzeOrVu3Bq2nHKgiIhJJYVnWN7Pf1aHat865yUHK+gIbnHOf\nlbeXDwwGPqxSZyzwqHPuawDnXPB/PUXkkLVo0YKnnnqKPn36MGrUKF5++WUSEmr+/zVUDlTdBiAi\nIg1lzrmGN2JWCNxZS7XbnXM9gpw/FBjgnBtT/voa4Azn3I1V6iwF/g2cDTQD7nLO/SlAW+OAcQCd\nOnXqk5+fX493VD8lJSW0adMmatcTb2hq47506VIeeughxowZE3B3/k9/+lMC/d4wM1asWBGNLsZc\nUxtzqRuNe/zRmIdXv3791jrnUmurF64NUQ865xaGqmBmR4UqDnDs4H/9mgMnAmlAZ+BvZnayc+6b\naic5NxeYC5CamurS0tJC9zyMCgoKiOb1xBua2riff/75bNu2jfnz53PVVVfRr1+/auXJyckUFhbW\nOC85OblJ/RxCaWpjLnWjcY8/GvPYCMs9p865WQ2sswnoUuV1Z2BzgDp/cM6VOef+A3zMgWBVRMLI\nzJgzZw7du3cnPT2dzZurfxSVA1VERCIprBuizCzRzH5pZrPNbH7FVx1OXQ2caGZdzewwIB146aA6\nS4F+5dfpAHQDPgtn/0XkgDZt2vD888+za9cuhg0bRllZWWWZcqCKiEgkhTvP6dPAR8AFwD1ABrC+\ntpOcc/vM7EbgNQ7cTzrfOfeBmd0DrHHOvVRe9gsz+xD4HviNc257mPsvIuV69OjBvHnzGD58OH6/\nnxkzZgAoB6qIiERUuIPTE5xzV5jZYOfcwvJcpK/V5UTn3KvAqwcdu7PK9w64rfxLRKIgPT2dv//9\n78ycOZOf/OQnXHbZZSHr5+TkUFxcTG5uLkVFRSQnJ5ORkUFSUlJlUCsiIhJKuPOcVqz9fWNmJwNJ\nQEqYryEiUXT//ffTt29fRo4cyYYNG0LWVQ5UERFpqHAHp3PLd+VP4cA9ox8C08N8DRGJopYtW7J4\n8WKaN2/O0KFD2bNnT9C6oXKgioiI1EVYg1Pn3Dzn3NfOub84537gnDvaOTcnnNcQkejz+Xw888wz\nvPfee9x4441B6xUVFR3ScRERkYOFJTg1szPM7F0zKzGztw5+9KiINH4DBw5k8uTJzJ8/n/nzAyfh\nSE5OPqTjIiIiBwvXzOmjwP8B7YEHgAfD1K6IeMjUqVPp378/v/zlL1m3bl2NcuVAFRGRhgpXcJrg\nnPuzc26vc+45oGOY2hURD2nWrBnPPvss7du3Z+jQoTU2OikHqoiINFS4UkkdaWaXB3vtnHshTNcR\nkRjr2LGpDyGeAAAgAElEQVQjixYtIi0tjZEjR/LCCy9gduAJxMqBKiIiDRWumdO/ABdX+ar6elCY\nriEiHnH22WeTk5PD0qVLeeCBB2LdHRERaULCMnPqnBsVjnZEpPG45ZZbePPNN5k0aRJ9+/bl3HPP\nrfUcJekXEZHahGu3fq2zo3WpIyKNh5kxf/58fvCDHzBs2DC2bNlS6zlK0i8iIrUJ17L+DDM7zcx6\nB/sCssN0LRHxiCOOOILnn3+eb775hiFDhlBaWhqyvpL0i4hIbcK1IWoLB1JIhfJJmK4lIh5yyimn\nsHDhQq688kpGjRpFbm4uCQmB/9+rJP0iIlKbcN1zmhaOdkSkcbriiiuYNm0at99+OyeccAL33ntv\nwHrJyckUFhYGPC4iIgJhfnypiMSviRMnMmbMGH7729+yYMGCgHWUpF9ERGqj4FREwsLMmD17Nv37\n92fs2LGsWLGiRh0l6RcRkdqE655TERFatGjBkiVLOPvss7n88st566236NGjR2V5qCT9SjMlIiIQ\n5plTM0s0s9vM7AUze97MbjWzxHBeQ0S8LSkpiVdeeYXExEQuvPDCOqWYAqWZEhGRA8K9rP8UcBLw\nMPAI0AN4OszXEBGP8/l8vPzyy2zZsoXBgwezZ8+eWs9RmikREYHwB6fdnXOjnXMry7/GAd3CfA0R\naQROP/10cnNz+X//7/8xYsQI9u/fH7K+0kyJiAiEPzh9x8zOrHhhZmcAb4b5GiLSSFx22WXMnDmT\nJUuWcMcdd4SsGyydlNJMiYjEl3AHp2cA/zCzjWa2EXgLON/M/mVm74X5WiLSCNx6661MmDCBnJwc\n5s6dG7Se0kyJiAiEf7f+gDC3JyKNnJnx0EMP8Z///IcJEyaQkpLCL37xixr1KtJMBdqtLyIi8SOs\nwalzruajX0Qk7jVv3pxFixZxzjnnMHToUP7xj39w8sknV6sTKs2UiIjEDyXhF5GoaNu2La+88gpt\n27blwgsv5Msvv6zzuTk5OWRmZpKSkkJCQgIpKSlkZmaSk5MTwR6LiEgsKDgVkajp3Lkzy5YtY8eO\nHVx88cXs2rWrTucpB6qISPxQcCoiUXXaaaeRn5/PO++8w9ChQ9m7d2+t5ygHqohI/FBwKiJRN2jQ\nIObOncuf/vQnhg0bRllZWcj6yoEqIhI/FJyKSEyMHj2aRx55hD/84Q9cffXV7Nu3L2hd5UAVEYkf\nCk5FJGZ++ctfMnPmTBYvXsx1110X9ClSyoEqIhI/wp3nVETkkPz6179mz549TJkyhcTERObMmYOZ\nVaujHKgiIvFDwamIxNzkyZMpLS0lKyuLxMREHnrooWoBqnKgiojEDwWnIuIJ9957L3v27OGBBx4g\nMTGR6dOn15hBDSYnJ4fi4uKAM6sVga2IiDQOCk5FxBPMjJkzZ1JaWsqMGTNo1aoVd999d53OrciD\nWqEiD6rf749Ud0VEJEK0IUpEPMPMePjhhxk9ejT33HMP9913X53OUx5UEZGmQzOnIuIpCQkJzJkz\nh9LSUvx+P61ateKWW24JeY7yoIqINB0KTkXEc5o1a8aCBQvYu3cvt956Ky1btmT8+PFB6ycnJ1NY\nWBjwuIiINC6eWdY3swFm9rGZbTCz20PUG2pmzsxSo9k/EYmu5s2bk5uby8UXX8yECRN48skng9ZV\nHlQRkabDE8GpmTUDHgUGAj2B4WbWM0C9tsCvgH9Gt4ciEguHHXYYixcv5he/+AWjR4/m2WefDViv\nIg+qz+fDzPD5fPj9fuVBFRFphLyyrN8X2OCc+wzAzPKBwcCHB9W7F8gB/i+63RORWElMTOTFF1/k\noosuYsSIETRr1oxhw4ZVqxMqD6rSTImINC6emDkFjgc+r/J6U/mxSmZ2GtDFObcsmh0Tkdg7/PDD\nefnllznrrLMYPnw4jz32WJ3PrUgzVVhYiHOuMs1UcXFxBHssIiL1Zc65WPcBM7sCuMA5N6b89TVA\nX+fcTeWvE4AVwEjn3EYzKwD+zzm3JkBb44BxAJ06deqTn58fpXcBJSUltGnTJmrXE2/QuEdPaWkp\nd999N6tWrWLUqFFcc801tSbqT09PZ8uWLTWOd+rUifr+ftCYxyeNe/zRmIdXv3791jrnat0z5JXg\n9CzgLufcBeWv7wBwzt1X/joJ+BQoKT/lGGAHcEmgALVCamqqW7MmaHHYFRQUkJaWFrXriTdo3KOr\nrKyMMWPG8NRTT3HTTTcxa9YsEhKCLwIlJCQQ6PecmbF///569UFjHp807vFHYx5eZlan4NQr95yu\nBk40s67AF0A6cFVFoXOuGOhQ8TrUzKmING0tWrTgySefpH379jz44INs376dBQsW0KJFi4D1lWZK\nRKRx8cQ9p865fcCNwGvAemCxc+4DM7vHzC6Jbe9ExGsSEhK4//77yc7O5tlnn2Xw4MHs2rUrYF2l\nmRIRaVy8MnOKc+5V4NWDjt0ZpG5aNPokIt5lZtxxxx106NCBG264gZ///OcsW7aMdu3aVatXkWYq\n0G59ERHxHs8EpyIi9TF27Fjat2/P8OHDOe+883jttdc4/vj/JftQmikRkcbFE8v6IiINcfnll/PH\nP/6RwsJCzj77bP7973/X6TylmRIR8R4FpyLSJPz0pz+loKCAXbt2cc4557B27dpaz8nNzT2k4yIi\nEnkKTkWkyejTpw9vvvkmrVq1ol+/fqxcuTJk/aKiokM6LiIikafgVESalG7duvGPf/yDLl26MGDA\nAF544YWgdYOlk1KaKRGR2FFwKiJNzvHHH8/f/vY3evfuzRVXXMGjjz4aMBG/0kyJiHiPglMRaZLa\ntWvH8uXLufDCC7nxxhu5/vrr+e6776rVqUgz5fP5MDN8Ph9+v5+kpCRycnLIzMwkJSWFhIQEUlJS\nyMzMJCcnJ0bvSEQkPiiVlIg0Wa1bt2bp0qVMmTKF++67jw8//JDnn3+eTp06AaHTTGVmZpKdnV35\numInv9/vj07nRUTilGZORaRJa9asGdnZ2eTn5/P222+TmpqqnfwiIh6m4FRE4sKwYcN48803SUhI\n4JxzzuHZZ58NWV87+UVEYkPBqYjEjdNOO43Vq1dz+umnk5GRwaRJk/j+++8D1tVOfhGR2FBwKiJx\n5eijj2b58uWMHz+enJwcBg0axDfffFOjXm07+bVhSkQkMhScikjcOeyww5g9ezaPPfYYy5cv54wz\nzuCjjz6qVifUTn7Qo09FRCJFwamIxK3rr7+eFStW8PXXX3PGGWfwyiuvVJZNnDiRrKwsNm7cyP79\n+9m4cSNZWVmVO/y1YUpEJDKUSkpE4tq5557LmjVruPTSS7n44ovJzs5m0qRJmFnI80JtmMrJyaG4\nuJjc3FyKiopITk4mIyOj2qxroLKJEyfW+9z6lkXqmk3pvVSUPfHEE2zdujVs16z4j46IVGeBnprS\nVKSmpro1a9ZE7XoFBQWkpaVF7XriDRr3pmH37t2MHj2a/Px80tPTGTt2bNC669atY/r06WzdurVG\n2dFHH03//v0DZgO46qqrAIKWjR49mieeeKJe59a3LFLXbErvJVLXbN26Nbt27WL58uVs3bq18u9O\n69atSU9Pr3FONJgZffv2pXXr1jG5vtfo93t4mdla51xqrfUUnIaP/hLHJ4170+GcIycnhzvuuCPg\n405F4sGkSZOYNm1arLvhCfr9Hl51DU61rC8iUs7MmDRpEpdddhn//e9/g9Z75513WL9+Pbt27eLP\nf/4zW7ZsoVOnTvz85z+ndevWzJkzp17X/8tf/sL5559f3+576ppN6b1E6pqdOnViy5YtAY8vXryY\nxx9/nGeeeaZG+dVXXx1yZr8hLr74Ynbu3BmRtkXqSsGpiMhBunXrRrdu3YKW79+/n5tvvjlo+Z/+\n9CcKCwtrHPf5fABBy8477zx8Pl+9zq1vWaSu2ZTeS6SuGey+5a1bt3LeeecxYsSIgOV/+9vfePrp\npwOWNdRhhx0WkXZFDoV264uIhFmoHKm15U+t77leu2ak2m1K16ztQQ+1bbpTnl1pqhScioiEWagc\nqbXlT63vuV67ZlN6LxVlnTp1Cus1awt6QwWvyrMrTZk2RIWRbpyOTxr3+KMxj0/hHvdQKagmTpxI\nZmYm2dnZNc7z+/3k5uYGvV1g48aN9e5Tx44dufLKK3n00Ufr3UZTos96eGlDlIiIiIdV5DnNysoK\nWF4x6xooeK1vnl3lVpXGQMGpiIiIB4UKXmfPnh1w5rTqkn+FiiV/v98fuc6KhJHuORUREWlkQt2v\nqkfrSmOn4FRERKSRCbXRKtSSv0hjoGV9ERGRRqa+S/4ijYFmTkVERJqQUEv+yo8qjYGCUxERkSYk\n1JK/8qNKY6BlfRERkSYk1JJ/SkpKwHNyc3ODprQSiTbNnIqIiMQJbZaSxkDBqYiISJwI9UhUEa9Q\ncCoiIhInQm2WEvEKBaciIiJxItRmKRGv0IYoERGROBFqsxTAnj17WLVqFSkpKRQVFZGcnExGRgZJ\nSUmV54pEmmZORUREBID9+/fz9ttvK9WUxJRnglMzG2BmH5vZBjO7PUD5bWb2oZm9Z2ZvmJkvFv0U\nERFpqvbu3RvweG5ubpR7IvHME8GpmTUDHgUGAj2B4WbW86Bq7wCpzrkfA0sAPc5CREQkjPbv3x/w\nuFJNSTR5IjgF+gIbnHOfOee+A/KBwVUrOOdWOud2l79cBXSOch9FRESatISEwGGBUk1JNHklOD0e\n+LzK603lx4IZDfwxoj0SERGJMy1btgx4XKmmJJq8slvfAhxzASuaXQ2kAucHKR8HjAPo1KkTBQUF\nYepi7UpKSqJ6PfEGjXv80ZjHp3gYd+ccJ554It9++y1bt27l6KOPpn///nz11VdN/r0HEg9j7kVe\nCU43AV2qvO4MbD64kpn1BzKB851zAe/ads7NBeYCpKamurS0tLB3NpiCggKieT3xBo17/NGYx6d4\nGPc2bdrw85//nEcffTTWXfGEeBhzL/JKcLoaONHMugJfAOnAVVUrmNlpwBxggHNua/S7KCIiEr9y\ncnIoLi4mNzdXOVAlojxxz6lzbh9wI/AasB5Y7Jz7wMzuMbNLyqvNANoAz5nZOjN7KUbdFRERiTvF\nxcVkZ2crB6pEnFdmTnHOvQq8etCxO6t83z/qnRIREREgeK7T3NzcoE+cEqkPT8ycioiIiLcFy3Wq\nHKgSbgpORUREpFbBcp0qB6qEm4JTERERqVWwXKfKgSrhpuBUREREapWUlITf78fn82Fm+Hw+/H4/\nSUlJse6aNDGe2RAlIiIi3lWRLirQ5ielmZJw0sypiIiINIjSTEk4KTgVERGRBgmVZkrkUCk4FRER\nkQZRmikJJwWnIiIi0iBKMyXhpOBUREREGkRppiScFJyKiIhIg9SWZionJ4fMzExSUlJISEggJSWF\nzMxMcnJyYtxz8SKlkhIREZEGCZVmCv63m79CxW5+v98flf5J46LgVERERCIq1G7+pKQk5UiVarSs\nLyIiIhEVaje/cqTKwTRzKiIiIhGVnJxMYWFhwOP1nVUFQs64hnpqVahza2tXIk8zpyIiIhJRoXbz\n13dWtbYZ1/qeq5nc2NPMqYiIiFTasGEDS5YsCWubhYWFXHbZZfztb3/jq6++okOHDpx77rkUFhbS\nvn17vvrqqxrntG/fnrlz5wZsL9jxirLTTjut3ufW1m5Tcswxx3DOOefEuhs1KDgVERERANq1a8fr\nr7/O66+/HtHrfPXVV7z44ou11qlv2RVXXBH1dhujgQMH8uqrr8a6GzUoOBUREREAVq1axRdffBHV\na86fP5+dO3fyyiuv8OWXX3Lsscdy0UUX0bZtW/Lz8/nyyy9rnHPssccCBC17/fXX+cUvflGvc2tr\ntylp06ZNrLsQkIJTERERAeCoo47iqKOOiuo1H3jggaBlrVq1qpYftcKoUaMAgpadfPLJjBo1ql7n\n1tauRJ42RImIiIgnhXryVG1PparvubW1K5FnzrlY9yFiUlNT3Zo1a6J2vYKCAtLS0qJ2PfEGjXv8\n0ZjHJ417/NGYh5eZrXXOpdZWTzOnIiIiIuIZCk5FRERExDMUnIqIiIiIZyg4FRERERHPUHAqIiIi\nIp6h4FREREREPKNJp5Iys21AYRQv2QEI/uwzaao07vFHYx6fNO7xR2MeXj7nXMfaKjXp4DTazGxN\nXfJ3SdOicY8/GvP4pHGPPxrz2NCyvoiIiIh4hoJTEREREfEMBafhNTfWHZCY0LjHH415fNK4xx+N\neQzonlMRERER8QzNnIqIiIiIZyg4bQAzu8LMPjCz/WYWdDefmQ0ws4/NbIOZ3R7NPkr4mVk7M/uz\nmX1S/udRQep9b2bryr9einY/peFq++yaWUszW1Re/k8zS4l+LyWc6jDmI81sW5XP9phY9FPCx8zm\nm9lWM3s/SLmZ2e/K/068Z2a9o93HeKPgtGHeBy4H/hqsgpk1Ax4FBgI9geFm1jM63ZMIuR14wzl3\nIvBG+etA9jjnepV/XRK97kk41PGzOxr42jl3AvAgMD26vZRwOoTf14uqfLbnRbWTEgkLgAEhygcC\nJ5Z/jQN+H4U+xTUFpw3gnFvvnPu4lmp9gQ3Ouc+cc98B+cDgyPdOImgwsLD8+4XApTHsi0ROXT67\nVf8uLAF+ZmYWxT5KeOn3dRxyzv0V2BGiymDgKXfAKuBIMzs2Or2LTwpOI+944PMqrzeVH5PGq5Nz\n7kuA8j+PDlIv0czWmNkqM1MA2/jU5bNbWcc5tw8oBtpHpXcSCXX9fT2kfHl3iZl1iU7XJIb073iU\nNY91B7zOzJYDxwQoynTO/aEuTQQ4phQJHhdq3A+hmWTn3GYz+wGwwsz+5Zz7NDw9lCioy2dXn++m\npS7j+TKQ55zba2Y3cGDm/KcR75nEkj7nUabgtBbOuf4NbGITUPV/1p2BzQ1sUyIs1Lib2RYzO9Y5\n92X50s7WIG1sLv/zMzMrAE4DFJw2HnX57FbU2WRmzYEkQi8PirfVOubOue1VXj6O7jOOB/p3PMq0\nrB95q4ETzayrmR0GpAPaud24vQRcW/79tUCNGXQzO8rMWpZ/3wE4G/gwaj2UcKjLZ7fq34WhwAqn\n5NGNWa1jftC9hpcA66PYP4mNl4AR5bv2zwSKK27tksjQzGkDmNllwMNAR+AVM1vnnLvAzI4D5jnn\nLnTO7TOzG4HXgGbAfOfcBzHstjTcNGCxmY0GioArAMrTid3gnBsD9ADmmNl+DvwncJpzTsFpIxLs\ns2tm9wBrnHMvAU8AT5vZBg7MmKbHrsfSUHUc81+Z2SXAPg6M+ciYdVjCwszygDSgg5ltAqYCLQCc\nc48BrwIXAhuA3cCo2PQ0fugJUSIiIiLiGVrWFxERERHPUHAqIiIiIp6h4FREREREPEPBqYiIiIh4\nhoJTEREREfEMBaciIiIi4hkKTkVERETEMxScioiIiIhnKDgVEREREc9QcCoiIiIinqHgVEREREQ8\nQ8GpiIiIiHiGglMRERER8QwFpyIiEWRmC8zstxFs/wMzS4tU+yIi0dY81h0QEZH6c86dVPG9md0F\nnOCcuzp2PRIRaRjNnIqIiIiIZyg4FREJIzM7zczeNrOdZrYISKxSNsjM1pnZN2b2DzP7cZWyjWb2\nf2b2npkVm9kiM0ssL+tgZsvKz9thZn8zs4Qq5/U3swGAHxhmZiVm9q6ZXWFmaw/q36/NbGlUfhgi\nIvWg4FREJEzM7DBgKfA00A54DhhSXtYbmA9cD7QH5gAvmVnLKk1cCQwAugI/BkaWH/81sAnoCHTi\nQBDqql7bOfcnIBtY5Jxr45w7FXgJ6GpmPapUvbq8fyIinqTgVEQkfM4EWgCznHNlzrklwOrysrHA\nHOfcP51z3zvnFgJ7y8+p8Dvn3Gbn3A7gZaBX+fEy4FjAV97u35xz1YLTQJxze4FFHAhIMbOTgBRg\nWUPfqIhIpCg4FREJn+OALw4KHAvL//QBvy5fmv/GzL4BupSfU+G/Vb7fDbQp/34GsAF43cw+M7Pb\nD6FPC4GrzMyAa4DF5UGriIgnKTgVEQmfL4HjywPBCsnlf34OZDnnjqzydbhzLq+2Rp1zO51zv3bO\n/QC4GLjNzH4WqGqAc1cB3wHnAlehJX0R8TgFpyIi4fMWsA/4lZk1N7PLgb7lZY8DN5jZGXZAazO7\nyMza1tZo+UaqE8qD3m+B78u/DrYFSKnYLFXFU8AjwD7n3N/r+d5ERKJCwamISJg4574DLufARqav\ngWHAC+Vlazhw3+kj5WUb+N+Gp9qcCCwHSjgQAM92zhUEqPdc+Z/bzeztKsefBk5Gs6Yi0ghYHe6p\nFxGRRszMWgFbgd7OuU9i3R8RkVA0cyoi0vSNB1YrMBWRxkCPLxURacLMbCNgwKUx7oqISJ1oWV9E\nREREPEPL+iIiIiLiGU16Wb9Dhw4uJSUlatfbtWsXrVu3jtr1xBs07vFHYx6fNO7xR2MeXmvXrv3K\nOdextnpNOjhNSUlhzZo1UbteQUEBaWlpUbueeIPGPf5ozOOTxj3+aMzDy8wKa6+lZX0RERER8RAF\npyIiIiLiGQpORURERMQzmvQ9pyIiIiLhUFZWxqZNmygtLY11VzwvMTGRzp0706JFi3qdr+BURERE\npBabNm2ibdu2pKSkYGax7o5nOefYvn07mzZtomvXrvVqwxPL+mY238y2mtn7QcrNzH5nZhvM7D0z\n6x3tPoqIiEj8Ki0tpX379gpMa2FmtG/fvkEzzF6ZOV0APAI8FaR8IHBi+dcZwO/L/4y5nJwciouL\nyc3NpaioiOTkZDIyMkhKSgIIWjZx4sR6n1vfslhdU0REpClQYFo3Df05eebxpWaWAixzzp0coGwO\nUOCcyyt//TGQ5pz7MlSbqampLtJ5TjMzM8nOzq5xfPTo0ezbt4+FCxfWKLv22msZP348v//974OW\nA2Evi9U1n376aUpKSnjttdf473//yzHHHMMFF1xAmzZtuOaaa2qc19isXbuWESNG0KZNm1h3RaJE\nuQ/jk8Y9/lQd8/Xr19OjR4/YdqgRCfTzMrO1zrnUWk92znniC0gB3g9Stgw4p8rrN4DU2trs06eP\nizSfz+eAGl/NmzcPeFxfTfOre/fubteuXRH/+ybesHLlylh3QWJA4x5/qo75hx9+GLuOVPHCCy84\nwK1fv945d6CPF110UbU61157rXvuueecc869/PLLrlevXu7HP/6x69Gjh3vsscecc85NnTrVAe6T\nTz6pPO+BBx5wgFu9enWD+xno5wWscXWICb2yrF+bQPPDLmBFs3HAOIBOnTpRUFAQwW5BUVFRwOP7\n9u0Led60adO4/fbbI9Elz11z2rRpfPPNNzXKjjzySHr16hVwjNLS0khMTKS0tJR169bxzTffVNZP\nTEz01OxFUVERs2fPZuTIkUyYMCHW3ZEoKCkpifjvFvEejXv8qTrmSUlJ7Ny5s07nzZo1i969e3Pe\needVHvvrX//K22+/zS233NKgPj399NOcddZZLFy4EL/fz+7du9m3b1+1vpWVlbFnzx527NjB2LFj\nWblyJccffzx79+6lqKiInTt3snfvXk466SQWLlxYeQveokWL+NGPfsSuXbvq/F6DKS0trf/npS4R\nbDS+CD1zOgcYXuX1x8CxtbUZy5lTn88Xsqwh5za2a5pZwHIzC3mu3+8PWOb3+yM+rodi5cqVbvz4\n8c7M3Jtvvhnr7kgUaAYtPmnc4099Z05XrFjhOnTo4FasWBHwdX3t3LnTHXfcce7jjz923bt3r+xj\nsJnT7du3u44dO7rdu3fXaGvq1KluypQpLjU11Tnn3KeffuoGDhzozj///JjPnHpit34dvASMKN+1\nfyZQ7Gq53zRaMjIygh4PVdaQcxvbNZOTkwOWJycnB515LioqIjc3N2BZxfGcnBwyMzNJSUkhISGB\nlJQUMjMzycnJCXheJE2fPp3k5GSuu+469uzZE/Xri4iId/Tr14/Fixdz5ZVXcuedd3LllVeyePFi\n+vXr16B2ly5dyoABA+jWrRvt2rXj7bffDlm/Xbt2XHLJJfh8PoYPH05ubi779++vLD/iiCPo0qUL\n77//Pnl5eQwbNqxB/QsXTwSnZpYHvAV0N7NNZjbazG4wsxvKq7wKfAZsAB4HPLN2mpSUhN/vx+fz\nYWb4fD78fj9JSUkhyxpybmO7Zqjgtb6BKxzIEJCdnU1hYSHOOQoLC8nOzqa4uLhBY1ofbdu2Zd68\neXz88cdMnTo16tcXERFv6devH+PHj+fee+9l/PjxDQ5MAfLy8khPTwcgPT2dvLy8oDvjK47PmzeP\nN954g759+zJz5kyuu+66avXS09PJz89n6dKlXHbZZQ3uY1jUZXq1sX5FY1m/Ki35BDZ9+nTn9/ud\nz+erXMr3+/2VxwmydN+QWxRCXTPcqo77uHHjXEJCglu1alXYryPeoc96fNK4x5+GbIiqWMqfMmVK\nWJb0v/rqK5eYmOiSk5Odz+dznTt3dl26dHHvvfee+8lPflKt7sUXX+wKCgpqtLFt2zbXpk0b59yB\nZf0ZM2a43bt3u+TkZHf55Zc755yW9SU+TJw4kaysLDZu3Mj+/fvZuHEjWVlZTJw4MeSsa223C4Sa\nWY3VrOqMGTM4/vjjGTVqlB5xJyISp1auXFm5lH/PPfdULvGvXLmy3m0uWbKEESNGUFhYyMaNG/n8\n88/p2rUrO3bsYPPmzaxfvx6AwsJC3n33XXr16lVjE9+6devw+XzV2m3VqhXTp08nMzOz3n0LNwWn\nElP1DVwh9L2std2vGilHHHEEjz/+OOvXr+fuu++O6LVERMSbVq9eXe0e04p7UFevXl3vNvPy8mos\nuw8ZMoT8/HyeeeYZRo0aRa9evRg6dCjz5s0jKSkJ5xw5OTl0796dXr16MXXqVBYsWFCj7fT0dHr3\n9s7DNz2ThD8SopGEvyolaI6uYA9A8Pv93HfffQT6u21mTJs2LaxPtAo07mPGjOHJJ59k1apVnH76\n6VTJ1p8AACAASURBVIfcpnibPuvxSeMef5SEv/4akoRfM6fSaIWaWQ01qxqNJf/777+f4447jlGj\nRrF3796wtSsiItLUKTiVRivULQGh7leNxpJ/UlISc+fO5YMPPuDee+8NW7siIiJNnYJTaZJCzaqG\n2kgVztypAwcOZOTIkUybNo21a9c29C2JiIjEhcby+FKRQ1Jx72hWVlaNstmzZ1NYWFjjeNUl/woV\nS/5+v79e/XjggQd4/fXXGTVqFGvWrOGwww6rVzsiIiLxQjOnEneiueR/1FFHMWfOHP71r38FDJRF\nRESkOgWnEnfqu+RfX4MGDeKaa64hOzubd955p97tiIiIxAMFpxJ3Qm2kCrXLHwh4T+q8efNqvSd1\n1qxZdOjQgVGjRvHdd9+F/T2JiEh8ePHFFzEzPvroI+BAuqtBgwZVqzNy5EiWLFkCwLJlyzjttNM4\n9dRT6dmzJ3PmzAHgrrvuwszYsGFD5Xn/n717j6uqyv8//loYCpqSeMsbYDPZdLG8oNlkRWUzWuYl\nNDXK1JSab1ZqkxVomYUVajU2mhmVXQjG1PFSZllJjZWlU+Z0zylQtNTQIVFJlPX7Qzg/LufC5XDO\ngfN+Ph485Oy19t6fwwb8sPZan/34449jjMGXZTidUXIqUoanp1I5K0OVnp7usQxVZGQkTz/9NJ9/\n/jmPPPKI1+MWEZHAkp6eXm4gw1sVYTIyMujXrx+ZmZke+xYVFZGYmMiaNWv4/PPP+eyzz8rV6u3W\nrVu54yxbtoyzzjrLK3HWhpJTkTI8PZWqNnNSBw8ezHXXXceDDz7I559/7tW4RUQkcKSnp5OYmFhu\nICMxMbHWCWpBQQEffPABzz77bJWS04MHD3Ls2DFatWoFQJMmTTjjjDMc7UOHDmXVqlUA/PDDD0RE\nRNCmTZtaxegNSk5FynB3yx9czz2t6pzU+fPnExkZybhx4ygqKvJa3CIiEjiSk5M5fPhwuW2HDx+u\n9fPrV65cyYABA+jatSuRkZF8+umnbvtHRkYyePBgoqOjGT16NOnp6RQXFzvaW7RoQefOnfniiy/I\nyMhg5MiRtYrPW5ScilSDuzmpVamR2qpVKxYtWsRnn32m2/siIg1UXSyuhRO39EeNGgXAqFGjyMjI\nwBjjtG/p9rS0NN555x369OnD3LlzGT9+fLl+o0aNIjMzk5UrVzJs2LBaxectSk5FqsHdnNSqPhZ1\n2LBhjB49mlmzZrF582ZfhC0iIj7kaXFtTeTl5fHuu+8yYcIEYmJimDNnDv/4xz+IjIzkwIED5fru\n37+f1q1bO15369aNKVOmsH79epYvX16u79VXX81LL71EVFQULVq0qHF83qTkVKQanM1JTUhIICIi\nolrzURcsWED79u1JSEigoKCgrsMWEREfSklJoWnTpuW2NW3atFb1rpctW8aYMWPIyckhOzubnTt3\n0qVLF/bv38/u3bv5+uuvgRMPj/n888/p3r07BQUFZGVlOY6xdetWoqOjyx03PDycRx99tNZTDrxJ\nT4gSqQZnT57KysoiLi6Oe+65x+k+zm7jtGzZkpdeeolLL72UyZMnk5aWVjcBi4iIz5XeZUtOTmbH\njh1ERUWRkpLi8u5bVWRkZFT6fyY+Pp7MzExefvllxo0bR2FhIaGhoaSlpREREcHBgwdJTU3l5ptv\nJjw8nGbNmrFkyZJKxy6dKhAolJyKeElUVJTLx6I6c8kll3Dvvfcye/ZsBg4cSHx8fF2HKCIiPpKQ\nkFCrZLSisiOgpW6//XbH55s2barU3rx5c9auXev0eDNnzqzyeXxNt/VFvMTdfFRXi6VOPvlkYmNj\nmThxIrm5uT6OWEREJPAoORXxEnc1Ul0tliooKOCVV17ht99+48YbbyxX4kNERCQY6ba+iJc4m49a\nKiYmxuk+6enppKSkMH/+fCZMmMBjjz3GX//617oMU0REJKBp5FTEBzzVvBs/fjzXXHMNSUlJHosq\ni4iINGRKTkV8wFPNO2MMixcvpm3btlx33XWVniwiIiISLJSciviAu8VSpVq1asWLL77Id999x513\n3umr0ERERAKKklMRH3C3WApwrOYfP3481loWLVrEiBEjyj36VERExBuWLFnCpEmTPPbZvXu34/WE\nCRP46quv6jo0QAuiRHzC3WIpwLGav6xly5bRoUOHOo9NRESkoiVLlnDOOec4/h/y5cNiNHIqEgBc\nPfp08eLFKi8lIiIOQ4cOpVevXpx99tksXrwYgJNPPpnk5GTOO+88+vbty549ewBYs2YN559/Pj16\n9KB///6O7aUOHjxIly5dKCoqAuDXX38lJiaGV199lS1btpCQkED37t05cuQIcXFxbNmyBYB169bR\ns2dPzjvvPC6//HKvv0eNnIoEAFer+QsLC5k/fz6TJ0/2cUQiIuLK5MmT2bp1q1eP2b17d5544gmP\n/Z577jkiIyM5cuQIvXv3Jj4+nkOHDtG3b19SUlKYNm0azzzzDNOnT6dfv35s2rQJYwxpaWmkpqYy\nb948x7GaN29OXFwcr7/+OkOHDiUzM5P4+HhGjBjBggULmDt3LrGxseXOv2/fPiZOnMj7779Ply5d\n2L9/v1e/DqCRU5GA4Go1f3h4OHfffTfbtm3zcUQiIhKI5s+f7xgh3blzJ99//z2NGzdm0KBBAPTq\n1Yvs7GwAcnNz+fOf/0y3bt2YM2cOX375ZaXjTZgwgeeffx6A559/nnHjxrk9/6ZNm7j44ovp0qUL\nAJGRkV58dydo5FQkACQkJFSacwqQmJjIc889x+WXX054eDi5ublERUWRkJBARESEYy6riIj4TlVG\nOOtCVlYWb7/9Nh999BFNmzYlLi6OwsJCQkNDMcYA0KhRI44dOwbAbbfdxtSpUxk8eDBZWVnMnDmz\n0jEvvPBCsrOzee+99zh+/DjnnHOO2xistY5z1RWNnIoEAFer+Tt06MBVV13FL7/8ws6dO8s9+jQ/\nP9/fYYuIiA/l5+fTsmVLmjZtyjfffMOmTZs89u/YsSMAL7zwgst+Y8aMYfTo0eVGTZs3b87Bgwcr\n9b3gggt47733+PHHHwHq5La+Rk5FAkBtHn0qIiLBYcCAASxatIhzzz2XM844g759+7rtP3PmTEaM\nGEHHjh3p27evI6GsKCEhgenTpzN69GjHtrFjx3LLLbcQHh7ORx995Njepk0bFi9ezDXXXENxcTFt\n27Zl/fr13nmDJZScigQ4T48+FRGR4NCkSRPeeOONStsLCgocnw8fPpzhw4cDMGTIEIYMGVKp/9ix\nYxk7dqzj9caNGxk+fDinnHKKY1t8fDzx8fGO11lZWY7PBw4cyMCBA2vzVtxScioS4KKiosjJyXG6\nXUREpDZuu+023njjDdauXevvUBw051QkwFXl0aciIiI18eSTT7J9+3a6du3q71AclJyKBLiKi6Wa\nN28O4HQ0VURE6o611t8h1Au1/Trptr5IgKu4WOro0aNcfPHFrF69mmnTphEaGkp6ejo7duxQmSkR\nkToSFhZGXl4erVq1qvNSSvWZtZa8vDzCwsJqfIyASU6NMQOAvwGNgDRr7SMV2qOAF4BTSvrcY60N\nnAkSIj7SuHFjli5dSs+ePXnhhRfYu3evo620zFRSUpIfIxQRaXg6depEbm4u+/bt83coAS8sLIxO\nnTrVeP+ASE6NMY2ABcAVQC6w2Riz2lr7VZlu04Gl1tqnjDFnAWuBGJ8HKxIAoqKiePnll12ullSZ\nKRER7woNDXU8FUnqVqDMOe0DbLfW/mCtPQpkAhVrH1igRcnnEcBuH8YnEnAGDBjgsk1lpkREpL4K\nlOS0I7CzzOvckm1lzQSuN8bkcmLU9DbfhCYSuFyVk1KZKRERqa8C4rY+4GxmccWlXqOBJdbaecaY\nC4CXjDHnWGuLyx3ImEQgEaBdu3blisbWtYKCAp+eTwKDP6/7RRddRHp6eqXt/fr10/diHdLPenDS\ndQ8+uub+ESjJaS7QuczrTlS+bX8TMADAWvuRMSYMaA3sLdvJWrsYWAwQGxtr4+Li6ijkyrKysvDl\n+SQw+PO6f/LJJ0RHR/Pss8+yZ88ewsPDmTx5MqeccgqffPIJ+fn5WslfB/SzHpx03YOPrrl/BMpt\n/c3A6caYLsaYxsAoYHWFPjuAywGMMWcCYYCWzElQmzZtGikpKfz888/MmzePI0eO0Lp1a6ZNm0Z+\nfj6zZ88mJycHa61jJX9+fr6/wxYREXEpIJJTa+0xYBLwJvA1J1blf2mMmWWMGVzS7U5gojHmcyAD\nGGtVDVfEYcqUKQwbNoy7776bDz74wOntfsDldhERkUAQKLf1KalZurbCtvvKfP4VcKGv4xKpL4wx\nPP/88/Tq1YuRI0eya9cup/20kl9ERAJZQIycioh3REREsGzZMn755ReXT+fQSn4REQlkSk5FGpju\n3buzYMECCgsLnbYnJCT4OCIREZGqU3Iq0gCNHz+eXr16AdC2bVuMMURHR5OUlERERISfoxMREXEt\nYOacioj3GGN4//33ueCCC9ixYwfffvstp59+erk+qampKjUlIiIBRyOnIg1U06ZNWblyJY0aNWLw\n4MGVSkip1JSIiAQiJaciDViXLl1Yvnw527dvZ9SoURw/ftzRplJTIiISiJScijRwl1xyCX//+99Z\nt24dd999t2O7q5JSKjUlIiL+pORUJAjcfPPN3HrrrcybN48XXngBcF1SSqWmRETEn5ScigSJxx9/\nnMsuu4zExEQ++ugjlyWlVGpKRET8ScmpSJAIDQ1l6dKldO7cmWHDhmGtJSkpiejoaJWaEhGRgKFS\nUiJBpFWrVqxevZq+ffvy5ptv8q9//YuUlJRK/VRmSkRE/EUjpyJB5qyzziIjI4PPPvuMcePGYa2t\n1EdlpkRExF+UnIoEoauuuopHHnmEpUuXOh05VZkpERHxF93WFwlSd911F//5z3+YMWMGZ599NsOG\nDXO0qcyUiIj4i0ZORYKUMYZnnnmGPn36cMMNN7Bt2zZHm8pMiYiIvyg5FQliYWFh/POf/yQiIoLB\ngwezb98+wHU5KZWZEhGRuqbkVCTIdejQgZUrV7Jnzx7i4+M5evQoERERKjMlIiJ+oTmnIkLv3r15\n9tlnSUhIYNKkSTz99NMYY1RmSkREfE4jpyICwHXXXce9997LM888w/z58132U5kpERGpS0pORcTh\noYceYujQoUyZMoUVK1Y47aMyUyIiUpeUnIqIQ0hICOnp6Zx//vkkJCTwwQcfVOqjMlMiIlKXlJyK\nSDlNmzZlzZo1dO7cmauvvpqvv/66XLvKTImISF1ScioilbRu3Zp169YRGhrKwIED+emnnxxtKjMl\nIiJ1ScmpiDh12mmnsXbtWn755ReuvPJKfv31VwCVmRIRkTqlUlIi4lKvXr1YtmwZgwYNYvjw4bz2\n2muOclEqMyUiInVBI6ci4taAAQNIS0tj/fr1TJw4EWuty74qMyUiIrWl5FREPBo7diyzZs3ixRdf\nZPr06S77qcyUiIjUlm7ri0iVTJ8+nZ07dzJ79mw6d+7MLbfcUqmPykyJiEhtaeRURKrEGMPChQsZ\nNGgQt956K6tWrarUR2WmRESktpScikiVnXTSSWRmZhIbG8uoUaP46KOPyrWrzJSIiNSWklMRqZZm\nzZrx2muv0alTJ66++mq+++47R5vKTImISG1pzqmIVFubNm1Yt24dF1xwAQMGDODDDz/k1FNPdVtm\nClRqSkREPNPIqYjUyO9+9ztef/119uzZw6BBgygoKPC4j0pNiYiIJ0pORaTGevfuzdKlS9m6dSvD\nhg2jsLDQbX+VmhIREU+UnIpIrVx11VU899xzvP3221x77bUUFRW57KtSUyIi4omSUxGptTFjxrBw\n4ULWrFnD9ddfz/Hjx532U6kpERHxRMmpiHjFX/7yF+bOncvSpUu56aabKC4urtRHpaZERMSTaq3W\nN8ZEVqFbsbX2fzWMR0TqsTvvvJNDhw5x//33Ex4ezsKFCzHGONpLS005W60vIiIC1S8ltbvkw7jp\n0wio9j06Y8wA4G8l+6dZax9x0udaYCZggc+ttddV9zwiUrdmzJjB4cOHefTRR2nWrBlz5sxxJKie\nSk2JiIhUNzn92lrbw10HY8xn1Q3CGNMIWABcAeQCm40xq621X5XpczpwL3ChtfaAMaZtdc8jInXP\nGMPDDz/M4cOHmTdvHs2aNeOBBx7wuJ9qoIqICFR/zukFXupTUR9gu7X2B2vtUSATGFKhz0RggbX2\nAIC1dm8NziMiPmCM4YknnmD8+PHMmjWL1NRUj/uoBqqIiEA1k1NrbaUihsaY4576VEFHYGeZ17kl\n28rqCnQ1xnxgjNlUMg1ARAJUSEgIixcvZvTo0dx99938/e9/d9tfNVBFRAS88/hSd/NPa3MMW+H1\nScDpQBzQCfiXMeaciouvjDGJQCJAu3btyMrK8kJ4VVNQUODT80lg0HV3b/z48ezYsYPbbruNHTt2\ncOWVVzrt564GaqB9fXXNg5Oue/DRNfePKiWnxpgIa62re2u2pM+NJZ+3AH6z1j5TjThygc5lXnfi\nxMKrin02WWuLgB+NMd9yIlndXC4YaxcDiwFiY2NtXFxcNcKonaysLHx5PgkMuu6eXXTRRQwZMoS5\nc+fSo0cPRo8eXalPVFQUOTk5TrcH2tdX1zw46boHH11z/6jqbf1VxpjlxpgFxpgJxpjGTvq0Bf5g\nrf070KGacWwGTjfGdCk59ihgdYU+K4FLAYwxrTlxm/+Hap5HRPygSZMmrFixgosuuogbbriBlStX\nVuqjGqgiIgJVT04/sNbGA9OAnsBDTvpssNYmlXz+aXWCsNYeAyYBbwJfA0uttV8aY2YZYwaXdHsT\nyDPGfAVsAO6y1uZV5zwi4j9NmzbltddeIzY2lpEjR7Ju3bpy7aU1UKOjozHGEB0dTVJSkmqgiogE\nmarOOW1pjIkFtnHitv3Bih2stVsAjDFnAceMMZ2stblVDcRauxZYW2HbfWU+t8DUkg8RqYeaN2/O\nG2+8wWWXXcawYcNYu3Ytl156KeC+BqrKTImIBI+qjpzeA/QDFgGvAV+46fsA0BxINMa8ULvwRKSh\nadmyJW+99RannXYaV155JW+99ZbHfVRmSkQkeFQ1Ob3XWvuEtXY8sNNa+5KbvuuttUuttfdZa2/0\nQowi0sC0adOGDRs20LVrV66++mrWrFnjtr/KTImIBI+qJqdvGmMSjTEJgKf6on80xqwwxjxjjNEt\neBFxqm3btmzYsIFzzz2Xa665hmXLlrns667MlIiINCwek1NjzLPAYE6soD/bWjvDwy5fWGuvAf4C\nvFP7EEWkoYqMjOTtt9+mT58+jBw50uVIaFRUVLW2i4hI/eUxObXW3gQkAzOAvcaYpz3sMsgYcxtw\nmrX2cy/EKCINWEREBG+++SYXX3wxN9xwA88991ylPiozJSISPKp0W99ae8Ra+0HJvNObKzRXfLrT\nSOB74BpjTHUK8YtIkDr55JNZu3Ytf/rTn7jppptYuHBhuXaVmRIRCR61fnyptTakwus9wLqSDxGR\nKgkPD2fVqlVce+213HrrrRQWFjJ16olp6+7KTIFKTYmINCRVXRAFgDHGY3H9qvQREXGmSZMmLFu2\njBEjRnDnnXe6TEYrUqkpEZGGo7ojp2caY7a5aTeA7rOJSI2FhobyyiuvEBYWxvTp0yksLGTWrFkY\nU3EG0f/nrtRUVRNcEREJDNVNTv9QhT7HaxKIiEipk046iSVLltCkSRMeeughjhw5wpw5c1wmqCo1\nJSLScFQrObXW5tRVICIiZYWEhPD0008TFhbGvHnzKCwsZP78+YSEVJ6NFBUVRU5O5V9PKjUlIlL/\nVGvOqYiIL4WEhDB//nzuuusuFixYQGJiIsePV745o1JTIiINR41X6xtjQoAQa+0xL8YjIlKOMYZH\nH32U8PBwZs2axcGDB3nxxRdp0qSJo09pqSlnq/W1kl9EpH6pUXJqjJkE3A8cNcb8AjxprU3zamQi\nIiWMMTzwwAM0b96cu+66i71797Jy5UpHnVN3paaSk5OZPXu243XpSv6kpCTfBC8iItVS09v6dwLd\nrLUdgQHAhcaYmV6LSkTEib/+9a+8/PLLfPDBB1x00UXs2rXL4z7uVvKLiEjgqWlyWgDsBbDW/gTc\nBFzjraBERFxJSEhg7dq1ZGdnc8EFF/DVV1+57a+V/CIi9UtNk9OngFeNMb8veR0FHPZOSCIi7vXv\n35/333+foqIiLrzwQjZu3Oiyr6sV+1rJLyISmGqUnFprFwLpQJoxZj+wHfjWGDPCGHO6NwMUEXGm\ne/fufPTRR7Rr147+/fuzYsUKp/20kl9EpH6pcSkpa+0Ka20c0BboCbwL/BF42juhiYi4FxMTwwcf\nfECPHj0YPnw4CxYsqNSndCV/dHQ0xhiio6NJSkpyLKYSEZHAUuNSUqVKSkltK/l4odYRiYhUQ6tW\nrXjnnXcYPXo0kyZNYteuXaSkpDieJuVuJb/KTImIBB4V4ReReq9p06YsX76cxMREHn74YcaOHUtR\nUZHH/fLz85k9ezY5OTlYax1lpvLz830QtYiIOKPkVEQahJNOOolFixYxa9YsXnzxRQYNGsTBgwfd\n7qMyUyIigUfJqYg0GMYYZsyYwbPPPss777xDXFwcP//8s8v+KjMlIhJ4lJyKSIMzfvx4Vq1axTff\nfMMf//hHvv32W6f9VGZKRCTwKDkVkQbpqquuYsOGDRQUFHD++efz1ltvVeqjMlMiIoFHyamINFh9\n+vThk08+ISoqioEDB/LEE09grXW0uyszlZqaSnJyMjExMYSEhBATE0NycjKpqal+fEciIg1frUtJ\niYgEspiYGD788ENuuOEGpkyZwn/+8x8WLlxIkyZN3JaZSk5OZvbs2Y7XpSv5k5KSfBa7iEgw0sip\niDR4J598MsuXL2f69Ok899xzXH755ezZs8ftPlrJLyLiH0pORSQohISE8OCDD5KZmcmnn35K7969\n2bp1q8v+WskvIuIfSk5FJKiMHDmSjRs3Yq3lwgsvZPny5U77aSW/iIh/KDkVkaDTs2dPNm/ezHnn\nncfw4cOZOXMmxcXF5fpoJb+IiH8oORWRoHTqqaeyYcMGbrzxRh544AGuvfZaDh065Gh3t5If0Gp+\nEZE6otX6IhK0mjRpwvPPP8+5557LXXfdxX//+19WrVpFVFSU25X8WVlZ5OfnazW/iEgdUHIqIkHN\nGMPUqVM588wzGTVqFLGxsaxYsYJ+/fq53c/dav6IiAjy8/NJT09nx44dREVFkZCQQEREhCPpFRER\n55SciogAAwcO5OOPP2bw4MFcdtlldOvWzWXfgwcPkpOT47QtJyeHxx9/nJ9//rncttmzZ3Pqqacy\nf/58jh8/zv79+zl69CiNGzcmMjKSRo0a0a5dO/bs2eOyHahRW7t27bz4lQoMHTp0YMWKFYSGhvo7\nFBHxMiWnIiIl/vCHP/Dxxx9z7733smvXLpf98vLyyM3N5ciRI5XawsPDyc/Pd7pffn4+HTt2ZPv2\n7Y5tR48e5eeff+b3v/89HTp04Ndff3XZDtSo7ciRIxQVFbFr1y6OHDlCeHg4HTt2JDQ0lN/97ndV\n/OoEjpycHF577TV++eUX2rdv7+9wRMTLlJyKiJTRsmVLFi1a5LZPVlYW69evLzfntNSUKVN4+OGH\nne5XWFhIUVGR07aioiLWrFlDTEyMy3ZXPLVde+215WI9cuQI27dvJykpiZSUFFJTU+vVNISnn36a\nW265xd9hiEgd0Wp9EZEacLea312NVE/F/d2117TN09OuShd35eTkYK11TENwNQIsIlKXAmbk1Bgz\nAPgb0AhIs9Y+4qLfcOBVoLe1dosPQxQRcXC3mr/iSv5SCQkJpKenO52vWprQRkVFuW2vSZunhFiL\nu0QkkATEyKkxphGwABgInAWMNsac5aRfc+B24GPfRigiUnXuRlU9Ffd3117TNk9Pu3KXvGpUVUR8\nLSCSU6APsN1a+4O19iiQCQxx0u9BIBUo9GVwIiLVMW3aNFJSUsjOzqa4uJjs7GxSUlKYNm2ax+L+\n7tpr2uYpIXaXvLobVdWDCESkLhhrrb9jKL1VP8BaO6Hk9Q3A+dbaSWX69ACmW2vjjTFZwF+d3dY3\nxiQCiQDt2rXrlZmZ6Yu3AEBBQQEnn3yyz84ngUHXPfjUt2uekZHBoUOHePvtt9m7dy9t27alf//+\nNGvWjNGjR5OWluY0CU1ISOCVV17B2f8Txhiuu+46l/tNmDChTt4LwOrVq3n88cdZtmwZrVq1qrPz\nVFTfrrvUnq65d1166aX/ttbGeuoXKHNOjZNtjt+GxpgQ4HFgrKcDWWsXA4sBYmNjbVxcnHcirIKs\nrCx8eT4JDLruwae+XXNPsX7yySdER0c7nVe6ceNGl3NZN27c6PR4Gzdu5OWXX/ZG6E59++23APzx\nj3/0aSmp+nbdpfZ0zf0jUJLTXKBzmdedgN1lXjcHzgGyjDEApwKrjTGDtShKRKR2arq4y1XJrNI5\nrPWtRJWIBIZAmXO6GTjdGNPFGNMYGAWsLm201uZba1tba2OstTHAJkCJqYhIHatpySxQiSoRqZmA\nGDm11h4zxkwC3uREKannrLVfGmNmAVustavdH0FEROpCTUdVwX2JKmfHExGBAElOAay1a4G1Fbbd\n56JvnC9iEhER10pHVZ3dtgf3JapERFwJmORURETqF3ejquD+gQKajyoirgTKnFMREWlg3NVX1XxU\nEXFFyamIiNQJd4up3M1HFZHgptv6IiJSJ9zd9r/nnnuc7qP5qCKi5FRERHxO81FFxBXd1hcREZ/T\nfFQRcUXJqYiI+Jzmo4qIK7qtLyIiPqf5qCLiipJTEREJKJ7mo27YsAGADh06EB0drfmoIg2MbuuL\niEhA8TQfdd26dY5tmo8q0vAoORURkYCi+agiwU239UVEJKBoPqpIcFNyKiIi9Ya7+aiAaqSKJ5Dn\nbwAAIABJREFUNAC6rS8iIvWGu/mogGqkijQASk5FRKTeiIiIYMCAAY7XZeejguu5p5qTKlJ/6La+\niIjUG9OmTSMiIoJ169axe/du2rdvX67d1dzTHTt26Ja/SD2hkVMREWkwSueeOtuuW/4i9YOSUxER\naTDczUnVLX+R+kHJqYiINBjuaqR6uuWfnJxMTEwMISEhxMTEkJycTGpqqo/fgYhozqmIiDQY7mqk\nLly40GUZqtJb/qVKb/knJSXVXbAi4pSSUxERCQoJCQnlEtCy293d8o+IiCA/P59nn32WvXv3aiGV\nSB3TbX0REQkKNb3lXzqqumfPHqcLqTQlQMS7NHIqIiJBoaa3/N2NqqakpLidEqDyVSLVp5FTEREJ\neu5W+bsbVQX3hf/dla/SiKuIcxo5FRGReun55593PBmqtr788kv+9Kc/sWXLFvbv309kZCSxsbF8\n+eWXtGzZkv3791fap2XLlixYsMDpiCucGEFdtGiR07ZFixYRGxvLW2+9Va7/7Nmz+dOf/kSzZs1Y\nv349R44cqRRTeHg4V1xxhVfed0XGGAYPHkynTp3q5PgiVaHkVERE6pWOHTsCkJycXGfn2L9/f7nE\n0VWfSZMmeexT3eO/9dZbTtvK7rNq1Sq3562N7777jieeeKLOji/iiZJTERGpVwYNGsSBAwcoKiry\nyfmefPJJfv31V1555RX27dtHp06diI+Pp0WLFtx2222kpKTwt7/9rdJ+d9xxB8uXLyc3N7dSW6dO\nnZxuL7V371569uzpct9x48bx66+/Oo5fMaaa+sMf/uCzr6uIK0pORUSk3jnllFN8dq5Zs2YBMHTo\nUOLi4iq1d+jQgaSkJKeLnsaMGeO0fNWYMWNIT093OiUgOjqaNm3asGvXLqfx7Nq1i+PHj5dLiHNz\nc/nb3/5GUlISbdq0qeE7hZAQLUUR/1NyKiIiUgvuqgCkpqa6TFzd1V2FE5UCalJBoLQuqyoESH2l\nP5FERETqyLRp00hJSSE7O5vi4mKys7NJSUlh2rRpbuuuQs0rCLirECBSH2jkVERExA/cjbjC/39o\ngLMR0JqOqro6l0ggUXIqIiISgNwlrxUL/5dKSEjg4Ycfdnq8HTt26KEAUi/otr6IiEg9425KQFRU\nlNN9oqKidMtf6gWNnIqIiNQzNR1V1S1/qQ80cioiItKAuBtV9fQoVpFAoJFTERGRBsTdqOrChQtd\nLqQSCRQaORUREQkS7spTARw5coRNmzYRExNDSEgIMTExJCcnk5qa6sswJcgFTHJqjBlgjPnWGLPd\nGHOPk/apxpivjDHbjDHvGGOi/RGniIhIfeWptmpxcTGffvqpFkyJXwXEbX1jTCNgAXAFkAtsNsas\nttZ+VabbZ0CstfawMeYvQCow0vfRioiI1E+eaqv+9ttvTrdrwZT4UqCMnPYBtltrf7DWHgUygSFl\nO1hrN1hrD5e83AR08nGMIiIiDVpxcbHT7VowJb4UKMlpR2Bnmde5JdtcuQl4o04jEhERCTIhIc7T\nAi2YEl8KiNv6gHGyzTrtaMz1QCxwiYv2RCARoF27dmRlZXkpRM8KCgp8ej4JDLruwUfXPDgFw3UP\nDQ11emu/X79+3HzzzRw6dIi3336bvXv30rZtW/r370+zZs0YPXq0H6Kte8FwzQNRoCSnuUDnMq87\nAbsrdjLG9AeSgUustU4nxlhrFwOLAWJjY21cXJzXg3UlKysLX55PAoOue/DRNQ9OwXDdTzrpJM4+\n+2zy8vIqPd40Pz+fxYsXO/ru2bOH9PR0kpKSGuzXJRiueSAKlOR0M3C6MaYLsAsYBVxXtoMxpgfw\nNDDAWrvX9yGKiIg0bOHh4fTt25cFCxZUaouJiXG6jxZLibcFxJxTa+0xYBLwJvA1sNRa+6UxZpYx\nZnBJtznAycCrxpitxpjVfgpXREQk6OjpUuIrgTJyirV2LbC2wrb7ynze3+dBiYiICHBiUZSeLiW+\nEBAjpyIiIhLYPD1dSsRblJyKiIiIR+6eLpWamkpycrIeeypeETC39UVERCRwuXu6VHJyMrNnz3a8\nLn3saVJSks/ik4ZDI6ciIiJSK+np6dXaLuKOklMRERGpFa3kF2/SbX0RERGpFU8r+VNTU8nPzyc9\nPb1Scf/S6QIipTRyKiIiIrXiaSV/fn4+s2fPJicnB2utY05qfn6+L8OUekIjpyIiIlIrpSv5nY2M\ngvs5qaWPRtWoqpRScioiIiK14m4lP7ifk1o6qlqq7Ep/TQcITkpORUREpE65m5PqblQ1ISGhxomr\nu3agRm1KiH1Dc05FRESkTrmbk+puVNVd4uppHqu79pq2iW8Ya62/Y6gzsbGxdsuWLT47X1ZWFnFx\ncT47nwQGXffgo2senILhurdp04awsDDOPPNMrx43OzubY8eO8dNPP1FYWEhYWBjt27fnpJNOYufO\nnRQWFlbaJywszOl2T+1hYWFcdNFF/Otf/3LZDtSo7aKLLnL9Juuh3r17u5yKUReMMf+21sZ66qfb\n+iIiIgLAjTfeyIcffkhBQYFXj9u6dWsATj311Epthw8fZteuXZW2t2rVil9++YXffvutUluTJk1c\nJq6FhYUUFBS4bXfFU5u3vy7+5u79+pOSUxEREQFg7ty5Pj+nu7mhFRdLlbrzzjtJT093Oo81Ojqa\nDz/8kJiYGJftQI3aPvzww2q/P6k+zTkVERERv5k2bRopKSlkZ2dTXFxMdnY2KSkpTJs2zVGiKjo6\nGmMM0dHRJCUlERER4bG2qrv2mraJb2jkVERERAKSuxJVqampbmureqq9WtM2qXtaEOVFwTBZXirT\ndQ8+uubBSdc9+Oiae1dVF0Tptr6IiIiIBAwlpyIiIiISMJScioiIiEjAUHIqIiIiIgFDyamIiIiI\nBIwGvVrfGLMPqFxJt+60Bn7x4fkkMOi6Bx9d8+Ck6x58dM29K9pa28ZTpwadnPqaMWZLVUokSMOi\n6x58dM2Dk6578NE19w/d1hcRERGRgKHkVEREREQChpJT71rs7wDEL3Tdg4+ueXDSdQ8+uuZ+oDmn\nIiIiIhIwNHIqIiIiIgFDyamIiIiIBAwlp7VgjBlhjPnSGFNsjHFZasIYM8AY860xZrsx5h5fxije\nZ4yJNMasN8Z8X/JvSxf9jhtjtpZ8rPZ1nFJ7nn52jTFNjDH/KGn/2BgT4/soxZuqcM3HGmP2lfnZ\nnuCPOMV7jDHPGWP2GmO+cNFujDHzS74nthljevo6xmCj5LR2vgCuAd531cEY0whYAAwEzgJGG2PO\n8k14UkfuAd6x1p4OvFPy2pkj1truJR+DfReeeEMVf3ZvAg5Ya38PPA486tsoxZuq8fv6H2V+ttN8\nGqTUhSXAADftA4HTSz4Sgad8EFNQU3JaC9bar62133ro1gfYbq39wVp7FMgEhtR9dFKHhgAvlHz+\nAjDUj7FI3anKz27Z74VlwOXGGOPDGMW79Ps6CFlr3wf2u+kyBHjRnrAJOMUY09430QUnJad1ryOw\ns8zr3JJtUn+1s9b+BFDyb1sX/cKMMVuMMZuMMUpg65+q/Ow6+lhrjwH5QCufRCd1oaq/r+NLbu8u\nM8Z09k1o4kf6f9zHTvJ3AIHOGPM2cKqTpmRr7aqqHMLJNtXvCnDurns1DhNlrd1tjDkNeNcY8x9r\n7X+9E6H4QFV+dvXz3bBU5XquATKstb8ZY27hxMj5ZXUemfiTfs59TMmpB9ba/rU8RC5Q9i/rTsDu\nWh5T6pi7626M2WOMaW+t/ank1s5eF8fYXfLvD8aYLKAHoOS0/qjKz25pn1xjzElABO5vD0pg83jN\nrbV5ZV4+g+YZBwP9P+5juq1f9zYDpxtjuhhjGgOjAK3crt9WAzeWfH4jUGkE3RjT0hjTpOTz1sCF\nwFc+i1C8oSo/u2W/F4YD71o92aQ+83jNK8w1HAx87cP4xD9WA2NKVu33BfJLp3ZJ3dDIaS0YY4YB\nTwJtgNeNMVuttX82xnQA0qy1V1prjxljJgFvAo2A56y1X/oxbKm9R4ClxpibgB3ACICScmK3WGsn\nAGcCTxtjijnxR+Aj1lolp/WIq59dY8wsYIu1djXwLPCSMWY7J0ZMR/kvYqmtKl7z240xg4FjnLjm\nY/0WsHiFMSYDiANaG2NygfuBUABr7SJgLXAlsB04DIzzT6TBQ48vFREREZGAodv6IiIiIhIwlJyK\niIiISMBQcioiIiIiAUPJqYiIiIgEDCWnIiIiIhIwlJyKiIiISMBQcioiIiIiAUPJqYiIiIgEDCWn\nIiIiIhIwlJyKiIiISMBQcioiIiIiAUPJqYiIiIgEDCWnIiJ+ZIwZa4zZWMtjXGSM+dZbMYmI+JOS\nUxGRes5a+y9r7Rmlr40x2caY/v6MSUSkppScioiIiEjAUHIqIuIFxph7jDHLKmz7mzFmvjEmwhjz\nrDHmJ2PMLmPMQ8aYRi6O80djzGZjTH7Jv38s0xZpjHneGLPbGHPAGLOyZHucMSa35POXgChgjTGm\nwBgzzRjzujHmtgrn2WaMGertr4OISG0pORUR8Y4M4EpjTAuAkuTzWuAV4AXgGPB7oAfwJ2BCxQMY\nYyKB14H5QCvgMeB1Y0yrki4vAU2Bs4G2wOMVj2GtvQHYAVxtrT3ZWptacv7ry5znPKAjsLbW71pE\nxMuUnIqIeIG1Ngf4FCgdjbwMOAz8CAwEJltrD1lr93IiqRzl5DBXAd9ba1+y1h6z1mYA3wBXG2Pa\nlxznFmvtAWttkbX2vSqGtwo43RhzesnrG4B/WGuP1uCtiojUKSWnIiLe8wowuuTz60peRwOhwE/G\nmP8ZY/4HPM2Jkc+KOgA5FbblcGKUszOw31p7oLpBWWt/A5YC1xtjQkpifKm6xxER8YWT/B2AiEgD\n8iowzxjTCRgGXAD8D/gNaG2tPeZh/92cSGbLigLWATuBSGPMKdba/3k4jnWy7QVOJKQbgcPW2o88\nHENExC80cioi4iXW2n1AFvA88KO19mtr7U/AW5xIWlsYY0KMMb8zxlzi5BBrga7GmOuMMScZY0YC\nZwGvlRznDWChMaalMSbUGHOxi1D2AKdViO0joBiYh0ZNRSSAKTkVEfGuV4D+Jf+WGgM0Br4CDgDL\ngPYVd7TW5gGDgDuBPGAaMMha+0tJlxuAIk7MQ90LTHYRw8PA9JJpBH8ts/1FoBvwco3emYiIDxhr\nnd39ERGRhsYYMwZItNb283csIiKuaORURCQIGGOaAv8HLPZ3LCIi7ig5FRFp4Iwxfwb2cWIu6ise\nuouI+JVu64uIiIhIwNDIqYiIiIgEDCWnIiIiIhIwGnQR/tatW9uYmBifne/QoUM0a9bMZ+eTwKDr\nHnx0zYOTrnvw0TX3rn//+9+/WGvbeOrXoJPTmJgYtmzZ4rPzZWVlERcX57PzSWDQdQ8+uubBSdc9\n+Oiae5cxpuLjmZ3SbX0RERERCRhKTkVEREQkYCg5FREREZGA0aDnnIqIiIh4Q1FREbm5uRQWFvo7\nlIAXFhZGp06dCA0NrdH+Sk5FREREPMjNzaV58+bExMRgjPF3OAHLWkteXh65ubl06dKlRsdQcioi\n4kOpqank5+eTnp7Ojh07iIqKIiEhgYiICKZNm+axXUT8o7CwUIlpFRhjaNWqFfv27avxMZScioh4\nmbsEMz8/n9mzZzv65uTkMHv2bJKSkgDctrs7bum+1W3zlBAH2nH99V5EACWmVVTrr5O1tsF+9OrV\ny/rShg0bfHo+CQy67sHH0zVPSkqyQKWPpKQkGx0d7bQtOjraWmvdtrs7bk3bPMUbaMf1xzkfffRR\nm5SUZNu1a2eNMY5r8eijj1prraM9OjraabvUX2V/1r/66iv/BVLGihUrLGC//vpra+2JGK+66qpy\nfW688Ub76quvWmutXbNmje3evbs999xz7ZlnnmkXLVpkrbX2/vvvt4D9/vvvHfs99thjFrCbN2+u\ndZzOvl7AFluF/E0jpyIiFaxbt47vvvvOZfv333/Ptm3bXLY/9dRTLrcfOHDAaVtOTg7z588nJ8d5\njeqcnBy3x61uLKVt7dq1q1fH9cc5Y2NjWb9+vWNb6Wj2FVdcQVhYGG+//bbb9vrEGMOQIUOIiory\ndyj1WmpqKr179+bSSy91bNuwYQObN2+u9Uh8RkYG/fr1IzMzk5kzZ7rtW1RURGJiIp988gmdOnXi\nt99+Izs729HerVs3MjMzmT59OgDLli3jrLPOqlV8XlGVDLa+fmjkVHxB171heffdd52OoOlDH8Hy\ncccdd/j7xzBg1HTk9N1337WtW7e27777rtPXNXXw4EHboUMH++2339ozzjjDEaOrkdO8vDzbpk0b\ne/jw4UrHuv/+++2MGTNsbGystdba//73v3bgwIH2kksu8fvIqeqcioiUOHbsGJMnTyY6OpqffvqJ\nvLw8px+rVq1y2ZaXl0enTp2cHr9Tp05MmTLFaduUKVPIy8tz2+7uuDVt8xRvoB3XH+d0Jy8vz227\np+sdaB+RkZEUFRW5fU/i2aWXXsrSpUu59tprue+++7j22mtZunRpuZHUmli5ciUDBgyga9euREZG\n8umnn7rtHxkZyeDBg4mOjmb06NGkp6dTXFzsaG/RogWdO3fmiy++ICMjg5EjR9YqPm9RcioiUiIt\nLY1t27Yxd+5cTj31VCIjI51+tGjRgrS0NObNm0fPnj1p3bo1PXv2ZN68eaSlpTFmzBinxx8zZgyn\nnnoqSUlJREdHY4whOjqapKQkx/nctbs7bk3bIiMj69Vx/XHO6Ohop23R0dFERka6bV+xYoXTthUr\nVrj9HnL1vVfXHyEhSgu85dJLL+Uvf/kLDz74IH/5y19qnZjCiVv6o0aNAmDUqFFkZGS4XHxUuj0t\nLY133nmHPn36MHfuXMaPH1+u36hRo8jMzGTlypUMGzas1jF6g74LRUSAAwcOMH36dC6++GLi4+M9\n9i9dVZ+Tk4O11jHPMD8/n4iICKcJZunK75SUFLKzsykuLiY7O5uUlBTHPDR37e6OW9M2oF4d1x/n\nTEhIcPo9ULrdXfuOHTuctu3YscPt95DUfxs2bOCpp55ixowZPPXUU2zYsKFWx8vLy+Pdd99lwoQJ\nxMTEMGfOHP7xj38QGRlZaS77/v37ad26teN1t27dmDJlCuvXr2f58uXl+l599dW89NJLREVF0aJF\ni1rF6DVVufdfXz8051R8Qde9YZg8ebI1xtjPPvvMY98NGzZ4XHUvDUdtVuu7+z4JxO+h1q1b2//7\nv//z2/kDTSDNOV20aJFNTEwst+3iiy+2WVlZNiYmxhFfdna2jYqKsv/73//swYMHy72H9evX27PP\nPttae2LO6Zw5c6y11mZkZNh///vf1lobEHNOtVpfRILeN998w9///ncmTpxI9+7dq7SPuxExaVhK\nR7WvuOIK4uLiXLanpKRUaqtYt7ZUQkICDz/8sNPzlX4P6YEM9dfmzZvLzTEtnYO6efPmGt/ez8jI\n4J577im3LT4+nszMTF5++WXGjRtHYWEhoaGhpKWlERERwcGDB0lNTeXmm28mPDycZs2asWTJkkrH\nLp0qECiUnIpI0Js6dSpNmzblwQcfrPI+UVFRTss+qQSPlFU6XcBZgunpe8jTAxskcDn74+HSSy+t\n1bzTrKysSttuv/12x+ebNm2q1N68eXPWrl3r9HiuylA5O4+vKTkVkaC2du1a3njjDebNm0fbtm2r\nvF9CQoLLETGRUjUdVQVIT093esz09HSnxxNpKLQgSkSC1tGjR5kyZQpdu3Zl0qRJ1drX08IcEU88\nfQ9p6ogEK42cikjQWrBgAd999x2vv/46jRs3rta+7kbERKrC0/eQpo5IsNLIqYgEpb179/LAAw8w\nYMAArrzySn+HI1KJpxJWIg2VklMRCUozZszg0KFDPPbYY/4ORcQpTR2RYKXb+iISdLZu3cozzzzD\nHXfcwZlnnunvcESccnfbX2WmpCHTyKmIBBVrLZMnT6ZVq1bcd999/g5HpEb0dKng9c9//hNjDN98\n8w1wovTToEGDyvUZO3Ysy5YtA+C1116jR48enHfeeZx11lk8/fTTwIlSUsYYtm/f7tjv8ccfxxjD\nli1bfPRunFNyKiJBZfny5bz33ns8+OCDtGzZ0mW/1NRUkpOTiYmJISQkhJiYGJKTk0lNTfVhtCLO\nuSszJYEhPT293O8Pb12bjIwM+vXrR2Zmpse+RUVFJCYmsmbNGj7//HM+++yzcg+S6NatW7njLFu2\njLPOOssrcdaGklMRCRpHjhzhrrvu4txzz2XixIlu+2pkSgKZykwFtvT0dBITE8v9/khMTKx1glpQ\nUMAHH3zAs88+W6Xk9ODBgxw7doxWrVoB0KRJE8444wxH+9ChQ1m1ahUAP/zwAxEREbRp06ZWMXqD\nklMRCRqPPfYY2dnZPPHEEzRq1MhtX41MSSBzVU5KZaYCQ3JyMocPHy637fDhwyQnJ9fquCtXrmTA\ngAF07dqVyMhIPv30U7f9IyMjGTx4MNHR0YwePZr09HSKi4sd7S1atKBz58588cUXZGRkMHLkyFrF\n5y1KTkUkKOzatYuHH36Ya665pkqPENTIlAQylZkKbHX1+yMjI4NRo0YBMGrUKDIyMjDGOO1buj0t\nLY133nmHPn36MHfuXMaPH1+u36hRo8jMzGTlypUMGzasVvF5i1bri0hQuPfeezl27Bhz5sypUn8V\nQJdAVlpmytlqffG/uvj9kZeXx7vvvssXX3yBMYbjx49jjGHMmDEcOHCgXN/9+/fTunVrx+tu3brR\nrVs3brjhBrp06cKSJUscbVdffTV33XUXsbGxtGjRosbxeZOSUxFp8DZt2sRLL71EUlISp512WpX2\nSUhIcPvccxF/0hPKAltKSgqJiYnlbu03bdq0Vtdr2bJljBkzxrHaHuCSSy5h//797N69m6+//poz\nzzyTnJwcPv/8c7p3705BQQFbtmxxLILaunUr0dHR5Y4bHh7Oo48+SteuXWscm7cpORWRBq24uJjJ\nkyfTvn177r333irvp5EpEamp0j9ik5OTHb8/UlJSavXHbUZGBvfcc0+5bfHx8WRmZvLyyy8zbtw4\nCgsLCQ0NJS0tjYiICA4ePEhqaio333wz4eHhNGvWrNyoaanSqQKBQsmpiDRo6enpfPzxx7zwwguc\nfPLJVd7P3chUVlaWt8ITkQYqISHBq3danP3euf322x2fb9q0qVJ78+bNWbt2rdPjzZw5s8rn8TUt\niBKRBqugoIB77rmHPn36cP311/s7HBERqQKNnIpIg/XII4+we/duli9fTkiI/haX4KBHm0p9p9/W\nItIg/fjjj8ydO5frr7+evn37+jscEZ/RAySkvguY5NQYM8AY860xZrsx5h4n7VHGmA3GmM+MMduM\nMVf6I04RqR/uuusuGjVqxCOPPOLvUER8Sg+QkPouIJJTY0wjYAEwEDgLGG2Mqfhw1+nAUmttD2AU\nsNC3UYpIfZGVlcXy5ctJSkqiY8eO/g5HxKf0AAmp7wIiOQX6ANuttT9Ya48CmcCQCn0sUFodNgLY\n7cP4RKSeOH78OHfccQfR0dFMnTrVbd/U1FSSk5OJiYkhJCSEmJgYkpOTSU1N9VG0It6nR5tKfRco\nC6I6AjvLvM4Fzq/QZybwljHmNqAZ0N/ZgYwxiUAiQLt27XxaEqGgoCAgSjCIb+m6B5bVq1ezbds2\nZs6cyccff+y277Zt28rd6iydm5eQkOD2muqaB6f6ct379evn9OlE/fr18xh/UVERu3btqhfv0xfK\nXvPSuqENQXp6Op9++inz5s1z2+eyyy6jffv2AEyaNIlJkybxhz/8oUrnKCwsrPH3UaAkp84eDGsr\nvB4NLLHWzjPGXAC8ZIw5x1pbXG4naxcDiwFiY2Nt6VMRfCErKwtfnk8Cg6574Pjf//7HiBEjuOSS\nS7jvvvtcPnO61NixY51u37hxIy+//LLL/XTNg1N9ue6ffPIJ0dHRTlfre4o/NDSUjh071ov36Qtl\nr/nXX39N8+bN/RuQl4SFhdG4cWO37yczM5PY2FjHk6NeeOGFap+jR48eNYovUG7r5wKdy7zuROXb\n9jcBSwGstR8BYUBrRERKzJo1i7y8PJ544gmPiSlobp40TNOmTSMlJYXs7GyKi4vJzs4mJSVFZaQa\niKFDh9KrVy/OPvtsFi9eDMDJJ59McnIy5513Hn379mXPnj0ArFmzhvPPP58ePXrQv39/x/ZSBw8e\npEuXLhQVFQHw66+/EhMTw6uvvsqWLVtISEige/fuHDlyhLi4OLZs2QLAunXr6NmzJ+eddx6XX365\n199joIycbgZON8Z0AXZxYsHTdRX67AAuB5YYY87kRHK6z6dRikjA+uabb3jyySeZOHEi3bt3r9I+\nUVFRTm9/am6eiLgzefJktm7d6tVjdu/enSeeeMJjv+eee47IyEiOHDlC7969iY+P59ChQ/Tt29fx\nR8gzzzzD9OnT6devH5s2bcIYQ1paGqmpqeVu5Tdv3py4uDhef/11hg4dSmZmJvHx8YwYMYIFCxYw\nd+5cYmNjy51/3759TJw4kffff58uXbqwf/9+r34dIEBGTq21x4BJwJvA15xYlf+lMWaWMWZwSbc7\ngYnGmM+BDGCstbbirX8RCVJTp06lWbNmPPTQQ1Xex9WjBb35yEEREW+aP3++Y4R0586dfP/99zRu\n3JhBgwYB0KtXL7KzswHIzc3lz3/+M926dWPOnDl8+eWXlY43YcIEnn/+eQCef/55xo0b5/b8mzZt\n4uKLL6ZLly4AREZGevHdnRAoI6dYa9cCaytsu6/M518BF/o6LhEJfGvXruWNN95g3rx5tGnTpsr7\nRUREkJSU5HRunoiIK1UZ4awLWVlZvP3223z00Uc0bdqUuLg4CgsLCQ0NdUxlatSoEceOHQPgtttu\nY+rUqQwePJisrCxmzpxZ6ZgXXngh2dnZvPfeexw/fpxzzjnHbQzW2ipNm6qNgElORUQmKxVWAAAg\nAElEQVRq4ujRo0ydOpWuXbsyadKkau1bOgcvJSWlLkITEfGq/Px8WrZsSdOmTfnmm2/YtGmTx/6l\ntZ7dLWgaM2YMo0ePZsaMGY5tzZs3d1qd4IILLuDWW2/lxx9/dNzW9/boaUDc1hcRqakFCxbw7bff\n8thjj9G4cWN/hyMiUmcGDBjAsWPHOPfcc5kxY4bHRzPPnDmTESNGcNFFF9G6tes15AkJCRw4cIDR\no0c7to0dO5ZbbrnFsSCqVJs2bVi8eDHXXHMN5513HiNHjqz9G6tAI6ciUm/t27ePBx54gAEDBnDl\nlXqisYg0bE2aNOGNN96otL2goMDx+fDhwxk+fDgAQ4YMYciQis80OpF4li2lt3HjRoYPH84pp5zi\n2BYfH098fLzjddmapQMHDmTgwIG1eStuKTkVkXprxowZHDp0iMcee6zO50CJiDREt912G2+88QZr\n16713NlHlJyKSL20detWFi9ezO23386ZZ57p73BEROqlJ5980t8hVKLkVETqHWstkydPJjIykvvv\nv99t39TUVPLz852uyFdRchGRwKMFUSJS76xYsYL33nuPhx56iJYtW7rtm5+fz+zZs8nJycFaS05O\nDrNnzyY/P99H0YoEjtTUVJKTk4mJiSEkJISYmBiSk5NJTU31d2j1gsqrV01tv05KTkWkXjly5Ah/\n/etf6datGxMmTPDYPz09vVrbRRoy/bFWc2FhYeTl5SlB9cBaS15eHmFhYTU+hm7ri0i98thjj5Gd\nnc0777zDSSd5/hW2Y8eOam0Xacjc/bGmer/uderUidzcXPbt05PTPQkLC6NTp0413l/JqYjUG7t2\n7WL27Nlcc801XHbZZVXaJyoqipycHKfbRYKN/lirudDQUMcjO6Vu6ba+iNQb9957L8eOHWPOnDlV\n3ichIaFa20UaMld/lOmPNQkkSk5FpF7YtGkTL730ElOnTuW0006r8n4REREkJSURHR2NMYbo6GiS\nkpKIiIiow2hFApP+WJP6QLf1RSTgFRcXc8cdd9C+fXuSkpKqtW9puSjNpxP5/3+sOSutJhIolJyK\nSMBLT0/nk08+YcmSJTRv3tzf4YjUW/pjTeoD3dYXkYBWUFDA3XffTe/evbnhhhv8HY6IiNQxjZyK\nSEB7+OGH+emnn1i+fDkhIfp7WkSkodNvehEJWD/++CPz5s0jISGBCy64wN/hiIiIDyg5FZGA9f/a\nu/8oqco7z+OfL40YWEmnFRsdSFfLGTyDE+bgBo1kjCEMGZGTjaNhEpPGSfbYcPIDpQM00NUStKHb\npoFWVlt3hPWsMT2TmDRnlyXteCbEcjaThUiyStSAMdKNtOyAKO1pB+RHf/cPukkLVdW/qm7dqnq/\nzqlD33ufe+tbPFV1v/Xc+zxPZWWlCgoKVF9fn+lQAAAB4bI+gFB67rnn1NLSojVr1vQ700hDQ4M6\nOzvj9kDu7QACAMgOtJwCCJ0zZ86ooqJCkUhES5cu7bc884UDQO4gOQUQOlu2bNGePXu0fv16jR49\nut/yyeYLBwBkF5JTAKHy7rvvqrq6WjfddJPmzZs3oH2YLxwAcgfJKYBQqamp0TvvvKNNmzbJzAa0\nD/OFA0DuIDkFEBp79+7VI488ovLyck2bNm3A+zFfOADkDpJTAKGxZMkSjRkzRmvXrh3Ufr3zhUci\nEZmZIpGIotEo84UDQBZiKCkAodDa2qpnnnlGGzduVHFx8aD2Zb5wAMgdtJwCyLiTJ0/qu9/9rq6+\n+motWrQo0+EAADKIllMAGdfU1KTXXntN27dv16hRozIdDgAgg2g5BZBRhw8f1v333685c+Zo7ty5\nmQ4HAJBhJKcAMmrVqlV6//331djYOOChowAAuYvL+gAy5sUXX9TmzZt1zz33aMqUKQnLNTQ0qLOz\nU83NzTpw4IBKSkpUVlamwsLCc52hAAC5gZZTABnh7qqoqNCll16q1atXJy3b2dmpuro6tbe3y93V\n3t6uuro6dXZ2BhQtACAoJKcAMqKlpUXPP/+81q5dq6KioqRlm5ubB7UewNAcP35cO3fuVGlpqUaM\nGKHS0lJVV1eroaEh06Ehj5CcAgjc8ePHtWzZMk2dOlXl5eX9lj9w4MCg1gMYmu7ubv3mN7/hKgUy\nKjTJqZnNMbN9Zva6ma1MUObLZvaqmb1iZv8QdIwAUqOxsVHt7e166KGHNHJk/7e+l5SUDGo9gKH5\n4IMP4q7nKgWCFIrk1MwKJDVJukXSNZK+ambXnFdmsqQqSX/p7n8uqSLwQAEMW0dHh+rq6nT77bdr\n1qxZA9qnrKxsUOsBDE13d3fc9VylQJBCkZxKul7S6+7+hruflPRDSbeeV2aBpCZ3f1eS3P1wwDEC\nSIGVK1fqzJkzWr9+/YD3KSwsVDQaVSQSkZkpEokoGo2qsLAwjZEC+WfEiPhpAVcpEKSwDCU1QdKb\nfZYPSvrUeWWuliQz+1dJBZLuc/d/CiY8AKmwc+dO/eAHP1BVVZUmTZo04P16h4uqra1NV2gAJF18\n8cU6fvz4Beu5SoEghSU5jTfytp+3PFLSZEkzJU2U9L/N7BPufuxDBzJbKGmhJI0fP16xWCzlwSbS\n1dUV6PMhHKj3genu7tZ3vvMdXXbZZbrxxhuz+v+MOs9P+VDv7q7Jkyfrvffe0+HDh1VcXKzZs2fr\n7bffzvnXHk8+1HkYhSU5PSjp432WJ0p6K06Zne5+StJ+M9uns8nqC30Lufvjkh6XpOnTp/vMmTPT\nFfMFYrGYgnw+hAP1PjDf//73tXfvXj355JNZP00pdZ6f8qHeL7nkEn3+859XU1NTpkMJhXyo8zAK\nyz2nL0iabGZXmdkoSXdI2nZemf8h6XOSZGbjdPYy/xuBRglgSLq6urRy5Updf/31mj9/fqbDAQCE\nWChaTt39tJktkvSszt5P+oS7v2JmNZJ2u/u2nm1/bWavSjojqdLdj2YuagAD9cADD+jQoUNqaWlJ\n2OECAAApJMmpJLl7q6TW89Z9r8/fLmlJzwNAlti/f782btyo+fPna8aMGQnLNTQ0qLOzU83NzTpw\n4IBKSkpUVlamwsLCcx2iAAC5jyYMAGlVWVmpgoIC1dfXJy3X2dmpuro6ZqYBgDxHcgogbZ577jm1\ntLSoqqpKEyZMSFo20Qw0zEwDAPmF5BRAWpw5c0YVFRWKRCJaunRpv+UTzUDDzDQAkF9ITgGkxZYt\nW7Rnzx6tX79eo0eP7rd8ohlomJkGAPILySmAlHv33XdVXV2tm266SfPmzRvQPolmoGFmGgDILySn\nAFKupqZG77zzjjZt2iSzeBPAXaiwsFDRaFSRSERmpkgkomg0qsLCwjRHCwAIk9AMJQUgN+zdu1eP\nPPKIysvLNW3atAHv1ztcVG1tbbpCAwBkAVpOAaTUkiVLNGbMGK1duzbToQAAshAtpwBSprW1Vc88\n84w2btyo4uLiTIcDAMhCtJwCSImTJ0/qu9/9rq6++motWrQo0+EAALIULacAUqKpqUmvvfaatm/f\nrlGjRsUtwxSlAID+0HIKYNgOHz6s+++/X3PmzNHcuXMTlmOKUgBAf0hOAQzbqlWr9P7776uxsTHp\n0FFMUQoA6M+QLuub2aUDKNbt7seGcnwA2ePFF1/U5s2bdc8992jKlClJyzJFKQCgP0O95/Stnkey\n0bULJDHvIJDD3F0VFRW69NJLtXr16n7Ll5SUqL29Pe56AACkoV/W/527T3L3qxI9JB1NZaAAwqel\npUXPP/+81q5dq6Kion7LM0UpAKA/Q01OZ5y/wszO9FcGQO44fvy4KisrNXXqVJWXlw9oH6YoBQD0\nZ0iX9d39RJzVNoAyAHJEY2Oj2tratGPHDo0cObCvEqYoBQD0Z0gtp2Z2jZndYmYT+6z2FMUEIOQ6\nOjpUV1en22+/XbNmzcp0OACAHDLUy/r3SxoraaGZPdl3g5nN6vn3SjMrGGZ8AEKoqqpKp0+f1vr1\n6zMdCgAgxwy1t/4/u/vTkp6Os22Omb0mqUlSu6R7hhocgPDZuXOnnnrqKVVVVWnSpEmZDgcAkGOG\n2nL6aTPbamabzWzJeds+JmmFpOWSuO8UyCHd3d1avHixrrzySlVVVWU6HABADhpqy+nL7r7BzEZK\n+vPzttVI+jN332dm3cMLD0CYNDc361e/+pWefPJJjR079oLtDQ0N6uzsVHNzsw4cOKCSkhKVlZWp\nsLDwXGcoAACSGWpy+gUz+0DSs+7+Ut8N7n5Q0sGev1cOMz4AIdHV1aUVK1bo+uuv1/z58+OW6ezs\nVF1d3bnl9vZ21dXVKRqNBhUmgDThxyeCMtTL+l+R9HtJt5vZ5p51yWaLApDlHnjgAR06dEgPPfSQ\nRoyI/9XR3Nw8qPUAskfvj8/29na5+7kfn52dnZkODTlmSMmpu/+bu/+Tu9e7+4KedUNNdAGE3P79\n+7Vx40bNnz9fM2Yknl/jwIEDg1oPIHvw4xNBGeo4p79JRRkA2aGyslIFBQWqr69PWq6kpGRQ6wFk\nD358IihDbe2cYmZ7kjx+K2lcKgMFkBmxWEwtLS2qqqrShAkTkpYtKysb1HoA2YMfnwjKUDtE/dkA\nypwZ4rEBhMSZM2e0ePFiRSIRLV26tN/yhYWFikajcTtMAMhuZWVlH+rw2Hc9kEpDSk7dvT3VgQAI\nny1btmjPnj368Y9/rNGjR/dbvrfHbm1tbbpDAxAwfnwiKENtOQWQ444dO6Z7771XN910k770pS9l\nOhwAGcaPTwSFHvYA4qqpqdHRo0e1adMmmTFSHAAgGMNqOTWz78Vb7+41wzkugMzau3evHn74YS1Y\nsEDTpk370DYG4gYApNNwW07f7/M4I+kWSaXDPCaADFuyZInGjBmjNWvWXLCNgbgBAOk0rOTU3Tf2\nedRKmikp+VgzAEKttbVVzzzzjFavXq3i4uILtjMQNwAgnVJ9z+kYSZOGsqOZzTGzfWb2upmtTFJu\nnpm5mU0fcpQA4jp58qSWLFmiq6++WosWLYpbhoG4AQDpNNx7Tn8ryXsWCyRdLmnQ95uaWYGkJkmf\nl3RQ0gtmts3dXz2v3FhJ90jaNZy4AcTX1NSkffv2afv27Ro1alTcMiUlJWpvv3A0OQbiBgCkwnBb\nTr8g6T/1PP5a0p+4+yNDOM71kl539zfc/aSkH0q6NU65NZIaJJ0YYrwAEjhy5Ijuv/9+zZkzR3Pn\nzk1YjlmgAADpNKyW0xQOxj9B0pt9lg9K+lTfAmZ2raSPu/t2M1uW6EBmtlDSQkkaP368YrFYikLs\nX1dXV6DPh3DIlXpvbGxUV1eX7rjjDj3//PMJy7399tsqKyvTz372Mx0+fFjFxcWaPXu23n777Zz4\nfxiIXKlzDE4+1PupU6fU0dGR869zoPKhzsMoLIPwxxtE0c9tNBsh6UFJ3+jvQO7+uKTHJWn69Ok+\nc+bM1EQ4ALFYTEE+H8IhF+r9pZde0k9/+lPdfffd+vrXv560bLa/1lTIhTrH4OVDvV900UWaMGFC\nzr/OgcqHOg+jsAzCf1DSx/ssT5T0Vp/lsZI+ISlmZm2SbpC0jU5RwPC5uyoqKlRUVKTVq1dnOhwA\nQJ4LS8vpC5Imm9lVkjok3SHpa70b3b1T0rjeZTOLSVrm7rsDjhPIOVu3blUsFtNjjz2moqKiTIcD\nAMhzoUhO3f20mS2S9KzO9vp/wt1fMbMaSbvdfVtmIwRy04kTJ7Rs2TJNnTpV5eXl59YzCxQAIFNC\nkZxKkru3Smo9b12i6VFnBhETkOsaGxvV1tamHTt2aOTIP34d9M4C1at3FqhoNJqJMAEAeSQs95wC\nCFhHR4fq6up0++23a9asWR/axixQAIBMITkF8lRVVZVOnTql9evXX7CNWaAAAJlCcgrkoV27dump\np57S0qVLNWnShTMOJ5rtiVmgAADpRnIK5Jnu7m4tXrxYV1xxhaqqquKWYRYoAECmkJwCeaa5uVm7\ndu1SfX29xo4dG7dMYWGhotGoIpGIzEyRSETRaFSFhYUBRwsAyDeh6a0PIP26urq0cuVKXXfddbrz\nzjsTlusdLqq2tjao0AAAkERyCuSV+vp6vfXWW/rJT36iESO4cAIACB/OTkCe2L9/vzZs2KCysjLN\nmDEj0+EAABAXLadAnqisrFRBQYHq6+slMQsUACCcaDkF8kAsFlNLS4tWrlypiRMnSvrjLFDt7e1y\n93OzQHV2dmY4WgBAPiM5BXLcmTNntHjxYpWUlGjZsmXn1jMLFAAgjLisD+S4LVu2aM+ePXr66ac1\nevToc+uZBQoAEEa0nAI57NixY7r33nv1mc98RvPmzfvQNmaBAgCEEckpkMNqamp09OhRbdq0SWb2\noW3MAgUACCOSUyBH7d27Vw8//LDuuusuXXvttRdsZxYoAEAYcc8pkKOWLl2qMWPGJJzliVmgAABh\nRHIK5KDW1la1trZqw4YNKi4uznQ4AHIc4yYjlbisD+SYU6dOacmSJRo3bpyOHDmi0tJSjRgxQqWl\npaqurlZDQ0OmQwSQYxg3GalEcgrkmKamJu3bt0+f+9zntG7dOk4WANKOcZORSiSnQA45cuSI7rvv\nPt18883atWtX3DKcLACkGuMmI5VIToEcsmrVKnV1denBBx/Um2++GbcMJwsAqca4yUglklMgR7z0\n0kvavHmzFi1apClTpnCyABAYxk1GKpGcAjnA3VVRUaGioiKtXr1aEicLAMFh3GSkEkNJATlg69at\nisVievTRR1VUVCTpjyeLeEO7AEAqMW4yUonkFMhyJ06c0LJlyzR16lQtWLDg3HpOFgCAbERyCmS5\nxsZGtbW1aceOHRo5ko80ACC7cSYDslh1dbXWr1+v0aNHa/bs2czKAgDIenSIArLYtm3bdOrUKR0/\nfpyB9gEAOYHkFMhSO3fu1Msvvxx3GwPtAwCyFckpkIW6u7tVUVGRcDsD7QMAshXJKZCFmpubtWvX\nLl122WVxtzPQPgAgW5GcAlmmq6tLK1as0HXXXaeFCxfGLcNA+wCAbEVyCmSZ+vp6HTp0SJs2bdLH\nPvYxZmUBAOQUhpICssj+/fu1YcMGlZWVacaMGZoxY4YkBtoHAOSO0LScmtkcM9tnZq+b2co425eY\n2atmtsfMdphZJBNxAkFraGhQdXW1SktLNWnSJJ08eVJFRUVqaGjIdGgAAKRcKJJTMyuQ1CTpFknX\nSPqqmV1zXrH/K2m6u/+FpJ9I4syMvNDZ2am6ujq1t7dLktxdjzzyCGOZAgByUiiSU0nXS3rd3d9w\n95OSfijp1r4F3P05d//3nsWdkiYGHCOQEYnGLGUsUwBALgpLcjpB0pt9lg/2rEvkLknPpDUiICQS\njVnKWKYAgFwUlg5RFmedxy1oNl/SdEmfTbB9oaSFkjR+/HjFYrEUhdi/rq6uQJ8P4ZDueh83bpyO\nHDlywfri4mLebxnCZz0/5UO9nzp1Sh0dHTn/OgcqH+o8jMKSnB6U9PE+yxMlvXV+ITObLala0mfd\n/YN4B3L3xyU9LknTp0/3mTNnpjzYRGKxmIJ8PoRDuuv9qquuipuc3nXXXbzfMoTPen7Kh3q/6KKL\nNGHChJx/nQOVD3UeRmFJTl+QNNnMrpLUIekOSV/rW8DMrpX095LmuPvh4EMEgrd3717t3r1b06ZN\n07vvvqsDBw6opKREZWVljGUKAMhJoUhO3f20mS2S9KykAklPuPsrZlYjabe7b5O0XtIlkn5sZpJ0\nwN2/mLGggRRqaGhQZ2enmpubP5SAtrS06JJLLtGzzz6r4uLiTIcJAEDahSI5lSR3b5XUet667/X5\ne3bgQQEB6R0uqld7e/u55Q0bNpCYAgDyRlh66wN5LdGwUCNHjtTdd98dcDQAAGQOySkQAomGhTp9\n+rRGjRoVcDQAAGQOySkQAiUlJYNaDwBAriI5BUKgrKws7vr58+cHHAkApF5DQ4Oqq6tVWlqqESNG\nqLS0VNXV1WpoYCZyXIjkFAiBwsJCRaNRXXnllZKksWPHKhqNMlwUgJzQ2+mzvb1d7n6u02dnZ2em\nQ0MIhaa3PpDLEg0VVVhYqOXLl2v58uVyd/3yl7/UyZMn9fvf/15FRUWZDhsAUiJRp8/m5mbV1tYG\nHA3CjpZTIAADaTXYunWrYrGY1qxZQ2IKIKck6vSZaD3yG8kpEIBkrQaSdOLECS1btkxTp07VggUL\nggwNANKOTp8YDJJTIAD9tRo0Njaqra1NDz30kEaO5G4bALklUafPROuR30hOgQAkazXo6OhQXV2d\nbrvtNs2aNSvgyAAg/Xo7fUYiEZmZIpEInT6REE00QADKyso+ND1p3/VVVVU6deqUNmzYkIHIACD9\nli9fLkl0fsKAkJwCKZKsR35vq8H5244dO6annnpKK1eu1KRJkzL9EgAAyDiSUyBFenvk9+rtkR+N\nRs+1FvRtNeju7tanP/1pXXHFFYpGo4HHCwBAGHHPKZAi/fXIj7d+165dqq+v19ixY9MZGgAAWYPk\nFEiRwYzj19XVpRUrVui6667TnXfeme7QAADIGiSnQIoMZhy/+vp6HTp0SJs2bdKIEXwMAQDoxT2n\nwCDE6/R044036le/+lXSHvl97d+/Xxs2bNDXvvY1zZgxI6jQAQDICiSnwCDE6/TU3t6uSCSSsEf+\n+eP4VVZWqqCgQOvWrQs6fAAAQo/kFBiEZJ2b2traJCUfxy8Wi6mlpUU1NTWaOHFiOkIEACCrcbMb\nMAiD6fR0vjNnzmjx4sUqKSnRsmXLUh0aAAA5geQUGITBdHo635YtW7Rnzx5t2LBBo0ePTnVoAADk\nBJJToI+GhgZVV1ertLRUI0aMUGlpqaqrq9XQ0CDpws5NvRKt73Xs2DHde++9+sxnPqN58+alPG4A\nAHIFySnQR2+Hp/b2drn7uVmeOjs7Jelcp6dIJCIzUyQSidvp6Xw1NTU6evSoNm3aJDML4qUAQFbo\nr1EA+YfkFOijv1meli9frtraWrW1tam7u1ttbW0qLy/X8uXLEx5z7969evjhh1VeXq5rr702LXED\nQLbqr1EA+Yfe+sg78cYq7W39HE6Hp0SWLl2qMWPGaO3atUM+BgDkqmSNAslGP0HuouUUeSfZr/Th\ndHiKp7W1Va2trfre976n4uLi4YQNADkpHY0CyG4kp8g7yX6lD7XDUzynTp3SkiVLNHnyZN19992D\n3h8A8kGqGwWQ/bisj5w01Ev3A53laSCampq0b98+bd++XaNGjRruSwKAnDTQqZ+RP0hOkZPiTTNa\nV1enaDSqkpIStbe3X7BPSUnJuY5Nw73P6ciRI7rvvvt08803a+7cucM6FgDkslQ2CiA3kJwiJ/V3\n6T7dv9JXrVqlrq4uPfjggwwdBQBJpKpRALmD5BRZKwyX7uN56aWXtHnzZt19992aMmVKSo4JAPko\n2fd8siH8kN1ITpG1Mn3pPh53V0VFhYqKirR69eqUHx8A8kmy73nkLnrrI7T6mzUkqF73g7F161bF\nYjGtWbNGRUVFaX0uAMh1/U2MgtxEyykyKtklm/5+MWfy0n08J06c0LJlyzR16lQtWLAgbc8DAPmC\nMVDzE8kp0m6oCWh/s4Zk6tJ9Io2NjWpra9OOHTs0ciQfLQAYrmTf89yPmrtCcwY1szmSNkkqkLTF\n3evP236xpO9L+qSko5K+4u5tQceZ7ZJ9mCWlfNvy5cuHnID294s5TGPjdXR0qK6uTrfddptmzZoV\n+PMDQC5K9j3f39W1oZ7vSGwzz9w90zHIzAokvSbp85IOSnpB0lfd/dU+Zb4t6S/c/Ztmdoek29z9\nK8mOO336d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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd7a0d1eef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"plotting at time = \" + str(roe_tube.time) + \" s\")\n",
    "plt.figure(figsize=(11,14))\n",
    "ax1 = plt.subplot(311)\n",
    "ax1.set_title('pressure')\n",
    "ax1.plot(ausm_tube.x, ausm_tube.p, label='AUSM', c=\"0\", \n",
    "         linestyle=\"\", marker=\"x\")\n",
    "ax1.plot(roe_tube.x, roe_tube.p, label='AUSM', c=\"0\", \n",
    "         linestyle=\"\", marker=\"o\")\n",
    "ax1.plot(x, p, linewidth=1.5, color='0', label='analytic')\n",
    "ax1.legend()\n",
    "ax1.set_ylabel(\"p [Pa]\")\n",
    "ax1.grid()\n",
    "\n",
    "ax2 = plt.subplot(312)\n",
    "ax2.set_title('density')\n",
    "ax2.plot(ausm_tube.x, ausm_tube.rho, label='AUSM', c=\"0\", \n",
    "         linestyle=\"\", marker=\"x\")\n",
    "ax2.plot(roe_tube.x, roe_tube.rho, label='AUSM', c=\"0\", \n",
    "         linestyle=\"\", marker=\"o\")\n",
    "ax2.plot(x, rho, linewidth=1.5, color='0', label=r'analytic')\n",
    "ax2.legend()\n",
    "ax2.set_ylabel(r\"$\\rho$ $[\\frac{kg}{m^3}]$\")\n",
    "ax2.grid()\n",
    "\n",
    "ax3 = plt.subplot(313)\n",
    "ax3.set_title('velocity')\n",
    "ax3.plot(ausm_tube.x, ausm_tube.u_vel, label='AUSM', c=\"0\", \n",
    "         linestyle=\"\", marker=\"x\")\n",
    "ax3.plot(roe_tube.x, roe_tube.u_vel, label='AUSM', c=\"0\", \n",
    "         linestyle=\"\", marker=\"o\")\n",
    "ax3.plot(x, u, linewidth=1.5, color='0', label=r'analytic')\n",
    "ax3.set_ylabel(r\"u $[\\frac{m}{s}]$\")\n",
    "ax3.legend()\n",
    "\n",
    "ax3.set_xlabel(\"x [m]\")\n",
    "ax3.grid()\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "number",
   "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": 2
}