{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "# Lee's Frame (Continuum Elements)\n", "\n", "The problem provided in this example is a L frame with pinned-pinned boundary conditions subjected to a point load at the center on top of the frame. The frame is modeled using continuum elements with a compressible neo-Hookean material constitutive law. \n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from dolfin import *\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import os\n", "from arc_length.force_control_solver import force_control # import force control formulation of arc-length solver\n", "\n", "\n", "parameters[\"form_compiler\"][\"cpp_optimize\"] = True\n", "ffc_options = {\"optimize\": True, \\\n", " \"eliminate_zeros\": True, \\\n", " \"precompute_basis_const\": True, \\\n", " \"precompute_ip_const\": True}" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Import Mesh and define function space" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[,\n", " ]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Create mesh and define function space\n", "h = 10\n", "L = 1200\n", "l1 = L / 5\n", "E = 7200\n", "nu = 0\n", "\n", "mesh = Mesh('mesh/lees-frame-2d.xml')\n", "V = VectorFunctionSpace(mesh, \"Lagrange\", 1)\n", "\n", "# Define functions for the arc length method\n", "du = TrialFunction(V) # Incremental displacement\n", "v = TestFunction(V) # Test function\n", "u = Function(V) # Solution\n", "\n", "plot(mesh)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Define Dirichlet Boundary Conditions" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def Hinge1(x, on_boundary):\n", " return near(x[0], 2*h, 1e-6) and near(x[1], 0.0, 1e-6)\n", " \n", "def Hinge2(x, on_boundary):\n", " return near(x[0], L+h, 1e-6) and near(x[1], L-h, 1e-6)\n", "\n", "def force(x,on_boundary):\n", " return between(x[0],[l1-l1/25,l1+l1/25]) #and near(x[1],L-h,1e-6)\n", "\n", "facets = MeshFunction(\"size_t\", mesh, mesh.topology().dim()-1)\n", "facets.set_all(0)\n", "AutoSubDomain(force).mark(facets,1)\n", "\n", "bc1 = DirichletBC(V, Constant((0.0, 0.0)), Hinge1, method='pointwise')\n", "bc2 = DirichletBC(V, Constant((0.0, 0.0)), Hinge2, method='pointwise')\n", "bcs = [bc1, bc2]" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Define Function for Point Load\n", "Note that this is an approximation of a point load since the FEniCS UserExpression will be projected into a discontinuous space. To approach a point load the area near the point load will need to have fine mesh. In our case it is not neccessary since the point load is just a perturbation." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Function for Point Load\n", "class PointLoad(UserExpression):\n", " def __init__(self, x0, f, tol,**kwargs):\n", " super().__init__(**kwargs)\n", " self.x0 = x0\n", " self.f = f\n", " self.tol = tol\n", " def eval(self, values, x):\n", " if near (x[0], self.x0[0],self.tol) and near(x[1], self.x0[1],self.tol):\n", " values[0] = self.f[0]\n", " values[1] = self.f[1]\n", " else:\n", " values[0] = 0\n", " values[1] = 0\n", " def value_shape(self):\n", " return (2,)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Kinematics and Weak Form" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Kinematics\n", "I = Identity(mesh.topology().dim()) # Identity tensor\n", "F = I + grad(u) # Deformation gradient\n", "C = F.T*F # Right Cauchy-Green tensor\n", "\n", "# Invariants of deformation tensors\n", "Ic = tr(C)\n", "J = det(F)\n", "\n", "# Elasticity parameters\n", "mu, lmbda = Constant(E/(2*(1 + nu))), Constant(E*nu/((1 + nu)*(1 - 2*nu)))\n", "\n", "# Stored strain energy density (compressible neo-Hookean model)\n", "psi = (mu/2)*(Ic - 3) - mu*ln(J) + (lmbda/2)*(ln(J))**2" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Applied Traction and Body Force\n", "load = Expression(\"-t\", t=0, degree = 0)\n", "T = Constant((0,1)) # Traction\n", "B = Constant((0,0)) # Body Force\n", "P = PointLoad(x0 = [l1,L+h], f = [0,1], tol = 1e-4, degree = 5, element=V.ufl_element()) # Point load\n", "\n", "# define sub domains\n", "ds = Measure('ds', domain=mesh, subdomain_data=facets)\n", "\n", "# Solve Variational Problem - Arc Length Method\n", "F_int = derivative(psi*dx, u, v)\n", "F_ext = derivative(dot(B, u)*dx + load*dot(P,u)*ds , u, v)\n", "residual = F_int-F_ext\n", "J = derivative(residual, u, du)\n", "\n", "# Plot the point load function\n", "plt.figure(figsize = (7,7))\n", "plot(project(P,V), mode = 'displacement', edgecolor = 'k', cmap = 'Reds', linewidth = 0.1)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Solver\n", "To use our solver we first have to define the type of solver (i.e. displacement control or force control) and solver parameters before using the solver. Note that the correct type of solver has to first be imported (see first cell).\n", "### Solver parameters\n", "Here the parameters for both types of solvers:\n", "\n", ">* `psi` : the scalar arc-length parameter. When psi = 1, the method becomes the spherical arc-length method and when psi = 0 the method becomes the cylindrical arc-length method\n", ">* `abs_tol` *(optional)* : absolute residual tolerance for the linear solver (default value: 1e-10)\n", ">* `rel_tol` *(optional)* : relative residual tolerance for solver; the relative residual is defined as the ration between the current residual and initial residual (default value: DOLFIN_EPS)\n", ">* `lmbda0` : the initial load parameter\n", ">* `max_iter` : maximum number of iterations for the linear solver\n", ">* `solver` *(optional)*: type of linear solver for the FEniCS linear solve function -- default FEniCS linear solver is used if no argument is used.\n", "\n", "Aside from these solver parameters, the arguments need to solve the FEA problem must also be passed into the solver:\n", ">* `u` : the solution function\n", ">* `F_int` : First variation of strain energy (internal nodal forces)\n", ">* `F_ext` : Externally applied load (external applied force)\n", ">* `J` : The Jacobian of the residual with respect to the deformation (tangential stiffness matrix)\n", ">* `displacement_factor` : The incremental displacement factor \n", "\n", "The solver can be called by:\n", "\n", "`solver = force_control(psi,abs_tol,rel_tol,lmbda0,max_iter,u,F_int,F_ext,bcs,J,displacement_factor,solver)`\n", "\n", "### Using the solver\n", "1. Initialize the solver by calling solver.initialize()\n", "2. Iteratively call solver.solve() until desired stopping condition" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# Solver Parameters\n", "psi = 1.0\n", "abs_tol = 1.0e-6\n", "lmbda0 = 4.0\n", "max_iter = 30\n", "\n", "# Set up arc-length solver\n", "solver = force_control(psi=psi, abs_tol=abs_tol, lmbda0=lmbda0, max_iter=max_iter, u=u,\n", " F_int=F_int, F_ext=F_ext, bcs=bcs, J=J, load_factor=load)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Initializing solver parameters...\n", "Starting initial Force Control with Newton Method:\n", "Iteration 0: | \n", "Absolute Residual: 2.8284e+01| Relative Residual: 1.0000e+00\n", "Iteration 1: | \n", "Absolute Residual: 1.2595e+04| Relative Residual: 4.4530e+02\n", "Iteration 2: | \n", "Absolute Residual: 1.3625e+02| Relative Residual: 4.8172e+00\n", "Iteration 3: | \n", "Absolute Residual: 4.5732e+03| Relative Residual: 1.6169e+02\n", "Iteration 4: | \n", "Absolute Residual: 1.5026e+01| Relative Residual: 5.3124e-01\n", "Iteration 5: | \n", "Absolute Residual: 3.6557e+02| Relative Residual: 1.2925e+01\n", "Iteration 6: | \n", "Absolute Residual: 1.0960e-01| Relative Residual: 3.8749e-03\n", "Iteration 7: | \n", "Absolute Residual: 1.1267e-01| Relative Residual: 3.9836e-03\n", "Iteration 8: | \n", "Absolute Residual: 8.9173e-09| Relative Residual: 3.1528e-10\n", "\n", "Arc-Length Step 1 :\n", "Iteration: 0 \n", "|Total Norm: 8.9295e-09 |Residual: 8.9173e-09 |A: 4.6566e-10| Relative Norm : 1.0000e+00\n", "\n", "Arc-Length Step 2 :\n", "Iteration: 0 \n", "|Total Norm: 4.6279e+04 |Residual: 4.6279e+04 |A: 4.6566e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 3.8857e+05 |Residual: 2.5306e+03 |A: 3.8856e+05| Relative Norm : 8.3962e+00\n", "Iteration: 2 \n", "|Total Norm: 3.3018e+05 |Residual: 4.5160e+03 |A: 3.3015e+05| Relative Norm : 7.1344e+00\n", "Iteration: 3 \n", "|Total Norm: 1.6699e+04 |Residual: 6.2596e+02 |A: 1.6688e+04| Relative Norm : 3.6084e-01\n", "Iteration: 4 \n", "|Total Norm: 1.9658e+05 |Residual: 2.8620e+03 |A: 1.9656e+05| Relative Norm : 4.2478e+00\n", "Iteration: 5 \n", "|Total Norm: 6.9296e+03 |Residual: 1.1737e+02 |A: 6.9286e+03| Relative Norm : 1.4973e-01\n", "Iteration: 6 \n", "|Total Norm: 2.7110e+04 |Residual: 3.0103e+02 |A: 2.7108e+04| Relative Norm : 5.8579e-01\n", "Iteration: 7 \n", "|Total Norm: 2.3607e+02 |Residual: 2.9648e+00 |A: 2.3606e+02| Relative Norm : 5.1011e-03\n", "Iteration: 8 \n", "|Total Norm: 9.1752e+01 |Residual: 9.5373e-01 |A: 9.1747e+01| Relative Norm : 1.9826e-03\n", "Iteration: 9 \n", "|Total Norm: 3.6673e-03 |Residual: 4.8428e-05 |A: 3.6669e-03| Relative Norm : 7.9242e-08\n", "Iteration: 10 \n", "|Total Norm: 2.7570e-08 |Residual: 2.2956e-09 |A: 2.7474e-08| Relative Norm : 5.9572e-13\n", "\n", "Arc-Length Step 3 :\n", "Iteration: 0 \n", "|Total Norm: 3.8695e+04 |Residual: 3.8695e+04 |A: 2.7474e-08| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 2.1289e+05 |Residual: 1.2919e+03 |A: 2.1288e+05| Relative Norm : 5.5018e+00\n", "Iteration: 2 \n", "|Total Norm: 4.4531e+04 |Residual: 6.9012e+02 |A: 4.4526e+04| Relative Norm : 1.1508e+00\n", "Iteration: 3 \n", "|Total Norm: 4.6822e+03 |Residual: 1.2545e+02 |A: 4.6805e+03| Relative Norm : 1.2100e-01\n", "Iteration: 4 \n", "|Total Norm: 7.2786e+03 |Residual: 8.4133e+01 |A: 7.2782e+03| Relative Norm : 1.8810e-01\n", "Iteration: 5 \n", "|Total Norm: 4.6482e+02 |Residual: 6.5173e+00 |A: 4.6477e+02| Relative Norm : 1.2012e-02\n", "Iteration: 6 \n", "|Total Norm: 4.5428e+01 |Residual: 5.2681e-01 |A: 4.5425e+01| Relative Norm : 1.1740e-03\n", "Iteration: 7 \n", "|Total Norm: 2.3996e-02 |Residual: 2.9607e-04 |A: 2.3994e-02| Relative Norm : 6.2013e-07\n", "Iteration: 8 \n", "|Total Norm: 8.9482e-08 |Residual: 3.6537e-09 |A: 8.9407e-08| Relative Norm : 2.3125e-12\n", "\n", "Arc-Length Step 4 :\n", "Iteration: 0 \n", "|Total Norm: 3.1291e+04 |Residual: 3.1291e+04 |A: 8.9407e-08| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 1.2123e+05 |Residual: 8.8470e+02 |A: 1.2123e+05| Relative Norm : 3.8743e+00\n", "Iteration: 2 \n", "|Total Norm: 6.4124e+03 |Residual: 1.0960e+02 |A: 6.4115e+03| Relative Norm : 2.0493e-01\n", "Iteration: 3 \n", "|Total Norm: 3.0028e+03 |Residual: 5.5386e+01 |A: 3.0023e+03| Relative Norm : 9.5961e-02\n", "Iteration: 4 \n", "|Total Norm: 1.2052e+02 |Residual: 1.5574e+00 |A: 1.2051e+02| Relative Norm : 3.8516e-03\n", "Iteration: 5 \n", "|Total Norm: 5.2743e+00 |Residual: 6.1432e-02 |A: 5.2740e+00| Relative Norm : 1.6855e-04\n", "Iteration: 6 \n", "|Total Norm: 2.1733e-04 |Residual: 2.4746e-06 |A: 2.1731e-04| Relative Norm : 6.9453e-09\n", "Iteration: 7 \n", "|Total Norm: 4.2888e-09 |Residual: 4.2888e-09 |A: 0.0000e+00| Relative Norm : 1.3706e-13\n", "\n", "Arc-Length Step 5 :\n", "Iteration: 0 \n", "|Total Norm: 2.6358e+04 |Residual: 2.6358e+04 |A: 4.6566e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 8.8896e+04 |Residual: 7.2061e+02 |A: 8.8893e+04| Relative Norm : 3.3726e+00\n", "Iteration: 2 \n", "|Total Norm: 6.0449e+03 |Residual: 1.2585e+02 |A: 6.0435e+03| Relative Norm : 2.2934e-01\n", "Iteration: 3 \n", "|Total Norm: 1.8833e+03 |Residual: 3.2735e+01 |A: 1.8830e+03| Relative Norm : 7.1450e-02\n", "Iteration: 4 \n", "|Total Norm: 4.3943e+02 |Residual: 4.7284e+00 |A: 4.3941e+02| Relative Norm : 1.6672e-02\n", "Iteration: 5 \n", "|Total Norm: 8.0747e+00 |Residual: 8.6750e-02 |A: 8.0743e+00| Relative Norm : 3.0635e-04\n", "Iteration: 6 \n", "|Total Norm: 3.6395e-03 |Residual: 3.7576e-05 |A: 3.6393e-03| Relative Norm : 1.3808e-07\n", "Iteration: 7 \n", "|Total Norm: 4.8955e-09 |Residual: 4.8733e-09 |A: -4.6566e-10| Relative Norm : 1.8573e-13\n", "\n", "Arc-Length Step 6 :\n", "Iteration: 0 \n", "|Total Norm: 2.3328e+04 |Residual: 2.3328e+04 |A: -9.3132e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 9.3070e+04 |Residual: 6.6958e+02 |A: 9.3068e+04| Relative Norm : 3.9897e+00\n", "Iteration: 2 \n", "|Total Norm: 4.0511e+03 |Residual: 9.3121e+01 |A: 4.0501e+03| Relative Norm : 1.7366e-01\n", "Iteration: 3 \n", "|Total Norm: 1.0910e+03 |Residual: 2.0626e+01 |A: 1.0908e+03| Relative Norm : 4.6769e-02\n", "Iteration: 4 \n", "|Total Norm: 6.3259e+01 |Residual: 6.3480e-01 |A: 6.3256e+01| Relative Norm : 2.7118e-03\n", "Iteration: 5 \n", "|Total Norm: 4.8411e-01 |Residual: 5.0766e-03 |A: 4.8408e-01| Relative Norm : 2.0753e-05\n", "Iteration: 6 \n", "|Total Norm: 4.4585e-06 |Residual: 4.4010e-08 |A: 4.4582e-06| Relative Norm : 1.9112e-10\n", "Iteration: 7 \n", "|Total Norm: 5.5275e-09 |Residual: 5.4485e-09 |A: -9.3132e-10| Relative Norm : 2.3695e-13\n", "\n", "Arc-Length Step 7 :\n", "Iteration: 0 \n", "|Total Norm: 2.0633e+04 |Residual: 2.0633e+04 |A: -9.3132e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 1.7032e+05 |Residual: 2.0131e+03 |A: 1.7031e+05| Relative Norm : 8.2547e+00\n", "Iteration: 2 \n", "|Total Norm: 1.5018e+04 |Residual: 2.1754e+02 |A: 1.5016e+04| Relative Norm : 7.2785e-01\n", "Iteration: 3 \n", "|Total Norm: 2.7075e+04 |Residual: 3.2949e+02 |A: 2.7073e+04| Relative Norm : 1.3122e+00\n", "Iteration: 4 \n", "|Total Norm: 1.3125e+02 |Residual: 9.0033e-01 |A: 1.3125e+02| Relative Norm : 6.3614e-03\n", "Iteration: 5 \n", "|Total Norm: 5.3725e+01 |Residual: 4.7797e-01 |A: 5.3723e+01| Relative Norm : 2.6039e-03\n", "Iteration: 6 \n", "|Total Norm: 3.9028e-04 |Residual: 1.9599e-06 |A: 3.9027e-04| Relative Norm : 1.8915e-08\n", "Iteration: 7 \n", "|Total Norm: 7.8770e-09 |Residual: 7.8633e-09 |A: -4.6566e-10| Relative Norm : 3.8177e-13\n", "\n", "Arc-Length Step 8 :\n", "Iteration: 0 \n", "|Total Norm: 1.7928e+04 |Residual: 1.7928e+04 |A: -4.6566e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 3.5112e+04 |Residual: 3.3668e+02 |A: 3.5111e+04| Relative Norm : 1.9586e+00\n", "Iteration: 2 \n", "|Total Norm: 4.7559e+03 |Residual: 7.6024e+01 |A: 4.7553e+03| Relative Norm : 2.6528e-01\n", "Iteration: 3 \n", "|Total Norm: 1.4531e+03 |Residual: 1.1969e+01 |A: 1.4530e+03| Relative Norm : 8.1052e-02\n", "Iteration: 4 \n", "|Total Norm: 2.0507e+01 |Residual: 1.8418e-01 |A: 2.0506e+01| Relative Norm : 1.1439e-03\n", "Iteration: 5 \n", "|Total Norm: 2.5959e-02 |Residual: 2.1549e-04 |A: 2.5958e-02| Relative Norm : 1.4480e-06\n", "Iteration: 6 \n", "|Total Norm: 1.1075e-08 |Residual: 8.5946e-09 |A: 6.9849e-09| Relative Norm : 6.1777e-13\n", "\n", "Arc-Length Step 9 :\n", "Iteration: 0 \n", "|Total Norm: 1.6219e+04 |Residual: 1.6219e+04 |A: 6.5193e-09| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 1.9509e+04 |Residual: 3.6790e+02 |A: 1.9505e+04| Relative Norm : 1.2028e+00\n", "Iteration: 2 \n", "|Total Norm: 9.8209e+03 |Residual: 1.3267e+02 |A: 9.8200e+03| Relative Norm : 6.0551e-01\n", "Iteration: 3 \n", "|Total Norm: 3.3106e+03 |Residual: 3.3224e+01 |A: 3.3104e+03| Relative Norm : 2.0412e-01\n", "Iteration: 4 \n", "|Total Norm: 2.2870e+02 |Residual: 2.1682e+00 |A: 2.2869e+02| Relative Norm : 1.4100e-02\n", "Iteration: 5 \n", "|Total Norm: 1.7736e+00 |Residual: 1.5767e-02 |A: 1.7735e+00| Relative Norm : 1.0935e-04\n", "Iteration: 6 \n", "|Total Norm: 5.5722e-05 |Residual: 4.8990e-07 |A: 5.5720e-05| Relative Norm : 3.4356e-09\n", "Iteration: 7 \n", "|Total Norm: 8.5548e-09 |Residual: 8.5421e-09 |A: 4.6566e-10| Relative Norm : 5.2745e-13\n", "\n", "Arc-Length Step 10 :\n", "Iteration: 0 \n", "|Total Norm: 1.5839e+04 |Residual: 1.5839e+04 |A: 4.6566e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 2.2634e+04 |Residual: 4.1333e+02 |A: 2.2630e+04| Relative Norm : 1.4290e+00\n", "Iteration: 2 \n", "|Total Norm: 1.6271e+04 |Residual: 1.9949e+02 |A: 1.6270e+04| Relative Norm : 1.0272e+00\n", "Iteration: 3 \n", "|Total Norm: 1.1131e+03 |Residual: 1.6208e+01 |A: 1.1130e+03| Relative Norm : 7.0273e-02\n", "Iteration: 4 \n", "|Total Norm: 1.3356e+02 |Residual: 1.4270e+00 |A: 1.3355e+02| Relative Norm : 8.4320e-03\n", "Iteration: 5 \n", "|Total Norm: 1.2732e-01 |Residual: 1.2897e-03 |A: 1.2731e-01| Relative Norm : 8.0382e-06\n", "Iteration: 6 \n", "|Total Norm: 1.2150e-06 |Residual: 1.5430e-08 |A: 1.2149e-06| Relative Norm : 7.6708e-11\n", "Iteration: 7 \n", "|Total Norm: 1.0172e-08 |Residual: 1.0162e-08 |A: -4.6566e-10| Relative Norm : 6.4223e-13\n", "\n", "Arc-Length Step 11 :\n", "Iteration: 0 \n", "|Total Norm: 1.6273e+04 |Residual: 1.6273e+04 |A: -4.6566e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 2.7116e+04 |Residual: 4.7038e+02 |A: 2.7112e+04| Relative Norm : 1.6663e+00\n", "Iteration: 2 \n", "|Total Norm: 4.3349e+04 |Residual: 4.6506e+02 |A: 4.3346e+04| Relative Norm : 2.6639e+00\n", "Iteration: 3 \n", "|Total Norm: 1.1793e+03 |Residual: 2.8243e+01 |A: 1.1789e+03| Relative Norm : 7.2469e-02\n", "Iteration: 4 \n", "|Total Norm: 5.9373e+01 |Residual: 9.7497e-01 |A: 5.9365e+01| Relative Norm : 3.6486e-03\n", "Iteration: 5 \n", "|Total Norm: 4.2291e-01 |Residual: 4.6703e-03 |A: 4.2288e-01| Relative Norm : 2.5989e-05\n", "Iteration: 6 \n", "|Total Norm: 5.5849e-07 |Residual: 1.3396e-08 |A: 5.5833e-07| Relative Norm : 3.4320e-11\n", "\n", "Arc-Length Step 12 :\n", "Iteration: 0 \n", "|Total Norm: 1.7185e+04 |Residual: 1.7185e+04 |A: 5.5879e-07| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 3.5182e+04 |Residual: 6.2641e+02 |A: 3.5177e+04| Relative Norm : 2.0472e+00\n", "Iteration: 2 \n", "|Total Norm: 9.5370e+05 |Residual: 8.9702e+03 |A: 9.5366e+05| Relative Norm : 5.5495e+01\n", "Iteration: 3 \n", "|Total Norm: nan |Residual: nan |A: 2.9767e+09| Relative Norm : nan\n", "\n", "Arc-Length Step 12 :\n", "Iteration: 0 \n", "|Total Norm: 6.5161e+03 |Residual: 6.5161e+03 |A: 1.3970e-07| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 3.7284e+03 |Residual: 4.5992e+01 |A: 3.7281e+03| Relative Norm : 5.7218e-01\n", "Iteration: 2 \n", "|Total Norm: 4.3400e+03 |Residual: 4.6610e+01 |A: 4.3398e+03| Relative Norm : 6.6605e-01\n", "Iteration: 3 \n", "|Total Norm: 1.8961e+01 |Residual: 1.5799e-01 |A: 1.8961e+01| Relative Norm : 2.9100e-03\n", "Iteration: 4 \n", "|Total Norm: 3.6750e-02 |Residual: 3.8852e-04 |A: 3.6748e-02| Relative Norm : 5.6399e-06\n", "Iteration: 5 \n", "|Total Norm: 1.2820e-08 |Residual: 1.2074e-08 |A: 4.3074e-09| Relative Norm : 1.9674e-12\n", "\n", "Arc-Length Step 13 :\n", "Iteration: 0 \n", "|Total Norm: 4.6268e+03 |Residual: 4.6268e+03 |A: 4.3074e-09| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 1.8116e+03 |Residual: 2.0941e+01 |A: 1.8115e+03| Relative Norm : 3.9155e-01\n", "Iteration: 2 \n", "|Total Norm: 2.4525e+03 |Residual: 2.5966e+01 |A: 2.4524e+03| Relative Norm : 5.3006e-01\n", "Iteration: 3 \n", "|Total Norm: 5.7014e+00 |Residual: 4.4027e-02 |A: 5.7013e+00| Relative Norm : 1.2323e-03\n", "Iteration: 4 \n", "|Total Norm: 3.1425e-03 |Residual: 3.5973e-05 |A: 3.1422e-03| Relative Norm : 6.7918e-07\n", "Iteration: 5 \n", "|Total Norm: 1.1578e-08 |Residual: 1.1576e-08 |A: 2.3283e-10| Relative Norm : 2.5024e-12\n", "\n", "Arc-Length Step 14 :\n", "Iteration: 0 \n", "|Total Norm: 1.4510e+04 |Residual: 1.4510e+04 |A: 9.3132e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 2.9439e+04 |Residual: 4.7535e+02 |A: 2.9435e+04| Relative Norm : 2.0289e+00\n", "Iteration: 2 \n", "|Total Norm: 5.0892e+07 |Residual: 3.5587e+05 |A: 5.0891e+07| Relative Norm : 3.5075e+03\n", "Iteration: 3 \n", "|Total Norm: 4.5917e+07 |Residual: 1.9459e+05 |A: 4.5917e+07| Relative Norm : 3.1646e+03\n", "Iteration: 4 \n", "|Total Norm: 1.9823e+07 |Residual: 2.8255e+05 |A: 1.9821e+07| Relative Norm : 1.3662e+03\n", "Iteration: 5 \n", "|Total Norm: 1.2212e+08 |Residual: 3.3796e+05 |A: 1.2212e+08| Relative Norm : 8.4164e+03\n", "Iteration: 6 \n", "|Total Norm: nan |Residual: nan |A: 1.7034e+08| Relative Norm : nan\n", "\n", "Arc-Length Step 14 :\n", "Iteration: 0 \n", "|Total Norm: 4.8884e+03 |Residual: 4.8884e+03 |A: 4.6566e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 2.1889e+03 |Residual: 2.6376e+01 |A: 2.1888e+03| Relative Norm : 4.4778e-01\n", "Iteration: 2 \n", "|Total Norm: 4.3286e+03 |Residual: 4.6887e+01 |A: 4.3284e+03| Relative Norm : 8.8550e-01\n", "Iteration: 3 \n", "|Total Norm: 2.1227e+01 |Residual: 1.7320e-01 |A: 2.1227e+01| Relative Norm : 4.3424e-03\n", "Iteration: 4 \n", "|Total Norm: 2.0632e-02 |Residual: 2.7602e-04 |A: 2.0631e-02| Relative Norm : 4.2207e-06\n", "Iteration: 5 \n", "|Total Norm: 1.3508e-08 |Residual: 1.3394e-08 |A: 1.7462e-09| Relative Norm : 2.7632e-12\n", "\n", "Arc-Length Step 15 :\n", "Iteration: 0 \n", "|Total Norm: 5.2545e+03 |Residual: 5.2545e+03 |A: 1.5134e-09| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 2.9512e+03 |Residual: 3.6518e+01 |A: 2.9510e+03| Relative Norm : 5.6166e-01\n", "Iteration: 2 \n", "|Total Norm: 8.3161e+03 |Residual: 9.1486e+01 |A: 8.3156e+03| Relative Norm : 1.5827e+00\n", "Iteration: 3 \n", "|Total Norm: 1.0052e+02 |Residual: 8.8760e-01 |A: 1.0052e+02| Relative Norm : 1.9130e-02\n", "Iteration: 4 \n", "|Total Norm: 1.7992e-01 |Residual: 3.1852e-03 |A: 1.7989e-01| Relative Norm : 3.4241e-05\n", "Iteration: 5 \n", "|Total Norm: 1.3123e-07 |Residual: 1.2657e-08 |A: 1.3062e-07| Relative Norm : 2.4975e-11\n", "\n", "Arc-Length Step 16 :\n", "Iteration: 0 \n", "|Total Norm: 1.7133e+04 |Residual: 1.7133e+04 |A: 5.2201e-07| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 6.2450e+04 |Residual: 8.8482e+02 |A: 6.2444e+04| Relative Norm : 3.6450e+00\n", "Iteration: 2 \n", "|Total Norm: 8.1605e+04 |Residual: 8.8383e+02 |A: 8.1601e+04| Relative Norm : 4.7631e+00\n", "Iteration: 3 \n", "|Total Norm: 9.3255e+04 |Residual: 1.0126e+03 |A: 9.3250e+04| Relative Norm : 5.4430e+00\n", "Iteration: 4 \n", "|Total Norm: 1.3381e+05 |Residual: 1.3315e+03 |A: 1.3380e+05| Relative Norm : 7.8098e+00\n", "Iteration: 5 \n", "|Total Norm: 1.7512e+07 |Residual: 1.6210e+05 |A: 1.7511e+07| Relative Norm : 1.0221e+03\n", "Iteration: 6 \n", "|Total Norm: 4.8909e+07 |Residual: 5.4697e+04 |A: 4.8909e+07| Relative Norm : 2.8547e+03\n", "Iteration: 7 \n", "|Total Norm: 1.9413e+07 |Residual: 2.0253e+05 |A: 1.9412e+07| Relative Norm : 1.1331e+03\n", "Iteration: 8 \n", "|Total Norm: 1.3814e+09 |Residual: 3.7140e+06 |A: 1.3814e+09| Relative Norm : 8.0629e+04\n", "Iteration: 9 \n", "|Total Norm: 8.1738e+08 |Residual: 2.2081e+06 |A: 8.1738e+08| Relative Norm : 4.7708e+04\n", "Iteration: 10 \n", "|Total Norm: nan |Residual: nan |A: 2.3962e+08| Relative Norm : nan\n", "\n", "Arc-Length Step 16 :\n", "Iteration: 0 \n", "|Total Norm: 5.7875e+03 |Residual: 5.7875e+03 |A: 1.3073e-07| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 4.5741e+03 |Residual: 5.5447e+01 |A: 4.5737e+03| Relative Norm : 7.9034e-01\n", "Iteration: 2 \n", "|Total Norm: 1.7537e+04 |Residual: 1.9386e+02 |A: 1.7536e+04| Relative Norm : 3.0301e+00\n", "Iteration: 3 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1.4769e+03| Relative Norm : 2.2401e-01\n", "Iteration: 5 \n", "|Total Norm: 8.9655e+00 |Residual: 1.3307e-01 |A: 8.9645e+00| Relative Norm : 1.3598e-03\n", "Iteration: 6 \n", "|Total Norm: 3.1738e-03 |Residual: 2.9769e-05 |A: 3.1737e-03| Relative Norm : 4.8137e-07\n", "Iteration: 7 \n", "|Total Norm: 1.2942e-08 |Residual: 1.2941e-08 |A: 1.1642e-10| Relative Norm : 1.9629e-12\n", "\n", "Arc-Length Step 18 :\n", "Iteration: 0 \n", "|Total Norm: 2.3105e+04 |Residual: 2.3105e+04 |A: 4.6566e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 2.2265e+05 |Residual: 2.4105e+03 |A: 2.2264e+05| Relative Norm : 9.6364e+00\n", "Iteration: 2 \n", "|Total Norm: 2.3044e+04 |Residual: 5.9228e+02 |A: 2.3036e+04| Relative Norm : 9.9735e-01\n", "Iteration: 3 \n", "|Total Norm: 3.4929e+04 |Residual: 4.0310e+02 |A: 3.4926e+04| Relative Norm : 1.5117e+00\n", "Iteration: 4 \n", "|Total Norm: 1.4648e+05 |Residual: 1.6359e+03 |A: 1.4647e+05| Relative Norm : 6.3396e+00\n", "Iteration: 5 \n", "|Total Norm: 1.4033e+07 |Residual: 1.2209e+05 |A: 1.4032e+07| Relative Norm : 6.0733e+02\n", "Iteration: 6 \n", "|Total Norm: 3.4112e+07 |Residual: 1.2620e+05 |A: 3.4112e+07| Relative Norm : 1.4764e+03\n", "Iteration: 7 \n", "|Total Norm: 1.7729e+07 |Residual: 3.2642e+05 |A: 1.7726e+07| Relative Norm : 7.6734e+02\n", "Iteration: 8 \n", "|Total Norm: nan |Residual: nan |A: 1.3379e+10| Relative Norm : nan\n", "\n", "Arc-Length Step 18 :\n", "Iteration: 0 \n", "|Total Norm: 7.8406e+03 |Residual: 7.8406e+03 |A: 1.1642e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 1.7713e+04 |Residual: 1.7786e+02 |A: 1.7712e+04| Relative Norm : 2.2592e+00\n", "Iteration: 2 \n", "|Total Norm: 2.7663e+05 |Residual: 3.0211e+03 |A: 2.7661e+05| Relative Norm : 3.5281e+01\n", "Iteration: 3 \n", "|Total Norm: 3.3224e+04 |Residual: 4.3476e+02 |A: 3.3221e+04| Relative Norm : 4.2375e+00\n", "Iteration: 4 \n", "|Total Norm: 3.4438e+05 |Residual: 2.7505e+03 |A: 3.4437e+05| Relative Norm : 4.3923e+01\n", "Iteration: 5 \n", "|Total Norm: 8.2087e+04 |Residual: 1.0439e+03 |A: 8.2080e+04| Relative Norm : 1.0469e+01\n", "Iteration: 6 \n", "|Total Norm: 8.5872e+03 |Residual: 1.2083e+02 |A: 8.5864e+03| Relative Norm : 1.0952e+00\n", "Iteration: 7 \n", "|Total Norm: 1.1322e+05 |Residual: 1.3013e+03 |A: 1.1321e+05| Relative Norm : 1.4440e+01\n", "Iteration: 8 \n", "|Total Norm: 4.7764e+04 |Residual: 3.7823e+02 |A: 4.7763e+04| Relative Norm : 6.0919e+00\n", "Iteration: 9 \n", "|Total Norm: 9.3625e+05 |Residual: 8.2386e+03 |A: 9.3621e+05| Relative Norm : 1.1941e+02\n", "Iteration: 10 \n", "|Total Norm: 7.0541e+05 |Residual: 7.5036e+03 |A: 7.0537e+05| Relative Norm : 8.9969e+01\n", "Iteration: 11 \n", "|Total Norm: 1.2695e+05 |Residual: 8.2069e+02 |A: 1.2695e+05| Relative Norm : 1.6192e+01\n", "Iteration: 12 \n", "|Total Norm: 1.0583e+06 |Residual: 9.9214e+03 |A: 1.0583e+06| Relative Norm : 1.3498e+02\n", "Iteration: 13 \n", "|Total Norm: 2.5486e+05 |Residual: 1.7170e+03 |A: 2.5486e+05| Relative Norm : 3.2506e+01\n", "Iteration: 14 \n", "|Total Norm: 3.7569e+04 |Residual: 4.5904e+02 |A: 3.7566e+04| Relative Norm : 4.7916e+00\n", "Iteration: 15 \n", "|Total Norm: 3.0911e+04 |Residual: 4.5085e+02 |A: 3.0907e+04| Relative Norm : 3.9424e+00\n", "Iteration: 16 \n", "|Total Norm: 3.3119e+04 |Residual: 3.2167e+02 |A: 3.3118e+04| Relative Norm : 4.2241e+00\n", "Iteration: 17 \n", "|Total Norm: 2.7000e+03 |Residual: 2.5507e+01 |A: 2.6998e+03| Relative Norm : 3.4436e-01\n", "Iteration: 18 \n", "|Total Norm: 8.3665e+02 |Residual: 7.8830e+00 |A: 8.3661e+02| Relative Norm : 1.0671e-01\n", "Iteration: 19 \n", "|Total Norm: 4.9741e-01 |Residual: 2.9090e-03 |A: 4.9740e-01| Relative Norm : 6.3440e-05\n", "Iteration: 20 \n", "|Total Norm: 1.2324e-04 |Residual: 1.3652e-06 |A: 1.2323e-04| Relative Norm : 1.5718e-08\n", "Iteration: 21 \n", "|Total Norm: 1.2550e-08 |Residual: 1.2545e-08 |A: -3.4925e-10| Relative Norm : 1.6006e-12\n", "\n", "Arc-Length Step 19 :\n", "Iteration: 0 \n", "|Total Norm: 9.7302e+03 |Residual: 9.7302e+03 |A: -1.1642e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 4.1256e+04 |Residual: 3.6961e+02 |A: 4.1254e+04| Relative Norm : 4.2399e+00\n", "Iteration: 2 \n", "|Total Norm: 9.1756e+05 |Residual: 1.0655e+04 |A: 9.1749e+05| Relative Norm : 9.4299e+01\n", "Iteration: 3 \n", "|Total Norm: 1.8798e+06 |Residual: 2.8710e+04 |A: 1.8796e+06| Relative Norm : 1.9319e+02\n", "Iteration: 4 \n", "|Total Norm: 9.0113e+06 |Residual: 7.8267e+04 |A: 9.0109e+06| Relative Norm : 9.2611e+02\n", "Iteration: 5 \n", "|Total Norm: 4.7525e+06 |Residual: 6.9160e+04 |A: 4.7520e+06| Relative Norm : 4.8842e+02\n", "Iteration: 6 \n", "|Total Norm: 4.2332e+06 |Residual: 1.5435e+05 |A: 4.2304e+06| Relative Norm : 4.3506e+02\n", "Iteration: 7 \n", "|Total Norm: 8.0982e+06 |Residual: 2.0830e+05 |A: 8.0955e+06| Relative Norm : 8.3227e+02\n", "Iteration: 8 \n", "|Total Norm: 7.8557e+06 |Residual: 2.3198e+05 |A: 7.8523e+06| Relative Norm : 8.0735e+02\n", "Iteration: 9 \n", "|Total Norm: 7.7839e+06 |Residual: 1.6025e+05 |A: 7.7822e+06| Relative Norm : 7.9997e+02\n", "Iteration: 10 \n", "|Total Norm: 1.0799e+07 |Residual: 8.1717e+04 |A: 1.0799e+07| Relative Norm : 1.1099e+03\n", "Iteration: 11 \n", "|Total Norm: 1.0266e+07 |Residual: 1.8161e+05 |A: 1.0265e+07| Relative Norm : 1.0551e+03\n", "Iteration: 12 \n", "|Total Norm: nan |Residual: nan |A: 1.2119e+11| Relative Norm : nan\n", "\n", "Arc-Length Step 19 :\n", "Iteration: 0 \n", "|Total Norm: 3.6745e+03 |Residual: 3.6745e+03 |A: -8.7311e-11| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 4.3968e+03 |Residual: 3.6821e+01 |A: 4.3967e+03| Relative Norm : 1.1966e+00\n", "Iteration: 2 \n", "|Total Norm: 7.5690e+03 |Residual: 8.3220e+01 |A: 7.5685e+03| Relative Norm : 2.0599e+00\n", "Iteration: 3 \n", "|Total Norm: 2.0725e+02 |Residual: 2.4798e+00 |A: 2.0723e+02| Relative Norm : 5.6401e-02\n", "Iteration: 4 \n", "|Total Norm: 1.1846e+00 |Residual: 2.0617e-02 |A: 1.1844e+00| Relative Norm : 3.2238e-04\n", "Iteration: 5 \n", "|Total Norm: 4.8261e-05 |Residual: 7.2364e-07 |A: 4.8255e-05| Relative Norm : 1.3134e-08\n", "Iteration: 6 \n", "|Total Norm: 1.1992e-08 |Residual: 1.1991e-08 |A: 1.1642e-10| Relative Norm : 3.2636e-12\n", "\n", "Arc-Length Step 20 :\n", "Iteration: 0 \n", "|Total Norm: 2.9231e+03 |Residual: 2.9231e+03 |A: 1.4552e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 3.0452e+03 |Residual: 2.2992e+01 |A: 3.0451e+03| Relative Norm : 1.0418e+00\n", "Iteration: 2 \n", "|Total Norm: 2.8823e+03 |Residual: 3.0791e+01 |A: 2.8822e+03| Relative Norm : 9.8604e-01\n", "Iteration: 3 \n", "|Total Norm: 3.0354e+01 |Residual: 3.9760e-01 |A: 3.0351e+01| Relative Norm : 1.0384e-02\n", "Iteration: 4 \n", "|Total Norm: 3.3009e-02 |Residual: 5.3524e-04 |A: 3.3005e-02| Relative Norm : 1.1292e-05\n", "Iteration: 5 \n", "|Total Norm: 6.3794e-08 |Residual: 1.2421e-08 |A: 6.2573e-08| Relative Norm : 2.1824e-11\n", "\n", "Arc-Length Step 21 :\n", "Iteration: 0 \n", "|Total Norm: 9.6917e+03 |Residual: 9.6917e+03 |A: 2.5029e-07| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 4.4145e+04 |Residual: 3.4715e+02 |A: 4.4144e+04| Relative Norm : 4.5549e+00\n", "Iteration: 2 \n", "|Total Norm: 1.8273e+06 |Residual: 2.0695e+04 |A: 1.8272e+06| Relative Norm : 1.8854e+02\n", "Iteration: 3 \n", "|Total Norm: 1.9482e+06 |Residual: 2.1617e+04 |A: 1.9481e+06| Relative Norm : 2.0102e+02\n", "Iteration: 4 \n", "|Total Norm: 6.5545e+06 |Residual: 5.7443e+04 |A: 6.5543e+06| Relative Norm : 6.7630e+02\n", "Iteration: 5 \n", "|Total Norm: 1.5769e+07 |Residual: 2.2359e+05 |A: 1.5767e+07| Relative Norm : 1.6270e+03\n", "Iteration: 6 \n", "|Total Norm: 1.1710e+07 |Residual: 2.2068e+05 |A: 1.1708e+07| Relative Norm : 1.2083e+03\n", "Iteration: 7 \n", "|Total Norm: 6.0905e+06 |Residual: 1.7860e+05 |A: 6.0879e+06| Relative Norm : 6.2843e+02\n", "Iteration: 8 \n", "|Total Norm: nan |Residual: nan |A: 1.0641e+09| Relative Norm : nan\n", "\n", "Arc-Length Step 21 :\n", "Iteration: 0 \n", "|Total Norm: 3.2546e+03 |Residual: 3.2546e+03 |A: 6.2573e-08| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 3.8821e+03 |Residual: 2.7695e+01 |A: 3.8820e+03| Relative Norm : 1.1928e+00\n", "Iteration: 2 \n", "|Total Norm: 2.1860e+03 |Residual: 2.3637e+01 |A: 2.1859e+03| Relative Norm : 6.7167e-01\n", "Iteration: 3 \n", "|Total Norm: 2.3875e+01 |Residual: 3.2589e-01 |A: 2.3873e+01| Relative Norm : 7.3358e-03\n", "Iteration: 4 \n", "|Total Norm: 1.7689e-02 |Residual: 2.7091e-04 |A: 1.7687e-02| Relative Norm : 5.4353e-06\n", "Iteration: 5 \n", "|Total Norm: 2.9300e-08 |Residual: 1.2837e-08 |A: 2.6339e-08| Relative Norm : 9.0029e-12\n", "\n", "Arc-Length Step 22 :\n", "Iteration: 0 \n", "|Total Norm: 3.5279e+03 |Residual: 3.5279e+03 |A: 2.6281e-08| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 4.1142e+03 |Residual: 2.7079e+01 |A: 4.1141e+03| Relative Norm : 1.1662e+00\n", "Iteration: 2 \n", "|Total Norm: 7.7908e+02 |Residual: 9.2653e+00 |A: 7.7903e+02| Relative Norm : 2.2084e-01\n", "Iteration: 3 \n", "|Total Norm: 4.9716e+00 |Residual: 6.8680e-02 |A: 4.9711e+00| Relative Norm : 1.4092e-03\n", "Iteration: 4 \n", "|Total Norm: 3.7196e-04 |Residual: 5.5751e-06 |A: 3.7192e-04| Relative Norm : 1.0543e-07\n", "Iteration: 5 \n", "|Total Norm: 1.3147e-08 |Residual: 1.3147e-08 |A: 2.9104e-11| Relative Norm : 3.7267e-12\n", "\n", "Arc-Length Step 23 :\n", "Iteration: 0 \n", "|Total Norm: 1.0831e+04 |Residual: 1.0831e+04 |A: -2.3283e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 3.5994e+04 |Residual: 2.4203e+02 |A: 3.5994e+04| Relative Norm : 3.3232e+00\n", "Iteration: 2 \n", "|Total Norm: 6.4908e+03 |Residual: 1.1371e+02 |A: 6.4898e+03| Relative Norm : 5.9926e-01\n", "Iteration: 3 \n", "|Total Norm: 9.2306e+02 |Residual: 1.0378e+01 |A: 9.2300e+02| Relative Norm : 8.5221e-02\n", "Iteration: 4 \n", "|Total Norm: 2.8341e+02 |Residual: 3.3541e+00 |A: 2.8339e+02| Relative Norm : 2.6166e-02\n", "Iteration: 5 \n", "|Total Norm: 8.1679e-01 |Residual: 7.6468e-03 |A: 8.1675e-01| Relative Norm : 7.5409e-05\n", "Iteration: 6 \n", "|Total Norm: 2.2184e-04 |Residual: 2.5540e-06 |A: 2.2183e-04| Relative Norm : 2.0481e-08\n", "Iteration: 7 \n", "|Total Norm: 1.2876e-08 |Residual: 1.2876e-08 |A: -1.1642e-10| Relative Norm : 1.1888e-12\n", "\n", "Arc-Length Step 24 :\n", "Iteration: 0 \n", "|Total Norm: 3.8080e+04 |Residual: 3.8080e+04 |A: -9.3132e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 3.8182e+05 |Residual: 2.7098e+03 |A: 3.8181e+05| Relative Norm : 1.0027e+01\n", "Iteration: 2 \n", "|Total Norm: 4.4581e+06 |Residual: 8.1859e+04 |A: 4.4573e+06| Relative Norm : 1.1707e+02\n", "Iteration: 3 \n", "|Total Norm: 1.1244e+06 |Residual: 1.4979e+04 |A: 1.1243e+06| Relative Norm : 2.9528e+01\n", "Iteration: 4 \n", "|Total Norm: 5.6965e+05 |Residual: 2.2196e+04 |A: 5.6922e+05| Relative Norm : 1.4959e+01\n", "Iteration: 5 \n", "|Total Norm: 1.4352e+05 |Residual: 2.5714e+03 |A: 1.4350e+05| Relative Norm : 3.7689e+00\n", "Iteration: 6 \n", "|Total Norm: 6.5277e+06 |Residual: 6.6777e+04 |A: 6.5274e+06| Relative Norm : 1.7142e+02\n", "Iteration: 7 \n", "|Total Norm: 1.4348e+06 |Residual: 9.0614e+03 |A: 1.4348e+06| Relative Norm : 3.7678e+01\n", "Iteration: 8 \n", "|Total Norm: 2.2885e+05 |Residual: 1.6219e+03 |A: 2.2884e+05| Relative Norm : 6.0097e+00\n", "Iteration: 9 \n", "|Total Norm: 1.0099e+05 |Residual: 3.0348e+03 |A: 1.0094e+05| Relative Norm : 2.6521e+00\n", "Iteration: 10 \n", "|Total Norm: 3.6759e+03 |Residual: 9.6082e+01 |A: 3.6747e+03| Relative Norm : 9.6533e-02\n", "Iteration: 11 \n", "|Total Norm: 3.6155e+05 |Residual: 6.0626e+03 |A: 3.6150e+05| Relative Norm : 9.4946e+00\n", "Iteration: 12 \n", "|Total Norm: 1.6533e+04 |Residual: 9.8012e+01 |A: 1.6533e+04| Relative Norm : 4.3417e-01\n", "Iteration: 13 \n", "|Total Norm: 3.0244e+03 |Residual: 5.3247e+01 |A: 3.0240e+03| Relative Norm : 7.9424e-02\n", "Iteration: 14 \n", "|Total Norm: 3.2828e+00 |Residual: 4.3550e-02 |A: 3.2825e+00| Relative Norm : 8.6209e-05\n", "Iteration: 15 \n", "|Total Norm: 4.1418e-03 |Residual: 9.7772e-05 |A: 4.1406e-03| Relative Norm : 1.0877e-07\n", "Iteration: 16 \n", "|Total Norm: 1.3319e-08 |Residual: 1.3286e-08 |A: 9.3132e-10| Relative Norm : 3.4977e-13\n", "\n", "Arc-Length Step 25 :\n", "Iteration: 0 \n", "|Total Norm: 3.1426e+04 |Residual: 3.1426e+04 |A: 9.3132e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 2.2799e+05 |Residual: 1.2024e+03 |A: 2.2798e+05| Relative Norm : 7.2547e+00\n", "Iteration: 2 \n", "|Total Norm: 3.4383e+05 |Residual: 6.7427e+03 |A: 3.4377e+05| Relative Norm : 1.0941e+01\n", "Iteration: 3 \n", "|Total Norm: 1.3346e+04 |Residual: 2.2112e+02 |A: 1.3344e+04| Relative Norm : 4.2468e-01\n", "Iteration: 4 \n", "|Total Norm: 6.8367e+04 |Residual: 1.7128e+03 |A: 6.8346e+04| Relative Norm : 2.1755e+00\n", "Iteration: 5 \n", "|Total Norm: 1.1967e+03 |Residual: 9.6134e+00 |A: 1.1967e+03| Relative Norm : 3.8079e-02\n", "Iteration: 6 \n", "|Total Norm: 4.0802e+03 |Residual: 4.7701e+01 |A: 4.0799e+03| Relative Norm : 1.2983e-01\n", "Iteration: 7 \n", "|Total Norm: 1.0422e+01 |Residual: 7.8938e-02 |A: 1.0422e+01| Relative Norm : 3.3164e-04\n", "Iteration: 8 \n", "|Total Norm: 4.3546e-01 |Residual: 4.8218e-03 |A: 4.3544e-01| Relative Norm : 1.3857e-05\n", "Iteration: 9 \n", "|Total Norm: 1.6305e-07 |Residual: 1.3197e-08 |A: 1.6252e-07| Relative Norm : 5.1884e-12\n", "\n", "Arc-Length Step 26 :\n", "Iteration: 0 \n", "|Total Norm: 2.3965e+04 |Residual: 2.3965e+04 |A: 1.6252e-07| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 1.1688e+05 |Residual: 1.1421e+03 |A: 1.1687e+05| Relative Norm : 4.8771e+00\n", "Iteration: 2 \n", "|Total Norm: 4.4668e+03 |Residual: 1.9675e+02 |A: 4.4625e+03| Relative Norm : 1.8639e-01\n", "Iteration: 3 \n", "|Total Norm: 3.4277e+03 |Residual: 3.6778e+01 |A: 3.4275e+03| Relative Norm : 1.4303e-01\n", "Iteration: 4 \n", "|Total Norm: 3.7230e+02 |Residual: 4.2702e+00 |A: 3.7228e+02| Relative Norm : 1.5535e-02\n", "Iteration: 5 \n", "|Total Norm: 1.4047e+01 |Residual: 1.4129e-01 |A: 1.4046e+01| Relative Norm : 5.8614e-04\n", "Iteration: 6 \n", "|Total Norm: 6.6511e-03 |Residual: 6.6720e-05 |A: 6.6508e-03| Relative Norm : 2.7753e-07\n", "Iteration: 7 \n", "|Total Norm: 1.5214e-08 |Residual: 1.4484e-08 |A: 4.6566e-09| Relative Norm : 6.3484e-13\n", "\n", "Arc-Length Step 27 :\n", "Iteration: 0 \n", "|Total Norm: 2.1730e+04 |Residual: 2.1730e+04 |A: 5.5879e-09| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 8.6210e+04 |Residual: 6.4378e+02 |A: 8.6208e+04| Relative Norm : 3.9673e+00\n", "Iteration: 2 \n", "|Total Norm: 5.7578e+03 |Residual: 9.2190e+01 |A: 5.7571e+03| Relative Norm : 2.6497e-01\n", "Iteration: 3 \n", "|Total Norm: 1.2540e+03 |Residual: 1.3372e+01 |A: 1.2539e+03| Relative Norm : 5.7705e-02\n", "Iteration: 4 \n", "|Total Norm: 1.4192e+02 |Residual: 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"Iteration: 5 \n", "|Total Norm: 4.0643e-04 |Residual: 4.1460e-06 |A: 4.0641e-04| Relative Norm : 2.0355e-08\n", "Iteration: 6 \n", "|Total Norm: 1.5499e-08 |Residual: 1.5499e-08 |A: 0.0000e+00| Relative Norm : 7.7622e-13\n", "\n", "Arc-Length Step 29 :\n", "Iteration: 0 \n", "|Total Norm: 1.9503e+04 |Residual: 1.9503e+04 |A: 0.0000e+00| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 6.7342e+04 |Residual: 4.0182e+02 |A: 6.7341e+04| Relative Norm : 3.4528e+00\n", "Iteration: 2 \n", "|Total Norm: 8.8934e+03 |Residual: 1.0985e+02 |A: 8.8927e+03| Relative Norm : 4.5599e-01\n", "Iteration: 3 \n", "|Total Norm: 8.6688e+01 |Residual: 5.4285e+00 |A: 8.6518e+01| Relative Norm : 4.4447e-03\n", "Iteration: 4 \n", "|Total Norm: 3.5514e-01 |Residual: 1.6536e-02 |A: 3.5476e-01| Relative Norm : 1.8209e-05\n", "Iteration: 5 \n", "|Total Norm: 1.3422e-05 |Residual: 7.7838e-07 |A: 1.3399e-05| Relative Norm : 6.8816e-10\n", "Iteration: 6 \n", "|Total Norm: 1.5585e-08 |Residual: 1.5585e-08 |A: 0.0000e+00| Relative Norm : 7.9908e-13\n", "\n", "Arc-Length Step 30 :\n", "Iteration: 0 \n", "|Total Norm: 2.0136e+04 |Residual: 2.0136e+04 |A: 4.6566e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 6.3741e+04 |Residual: 3.7528e+02 |A: 6.3740e+04| Relative Norm : 3.1656e+00\n", "Iteration: 2 \n", "|Total Norm: 1.1461e+04 |Residual: 7.1536e+01 |A: 1.1461e+04| Relative Norm : 5.6920e-01\n", "Iteration: 3 \n", "|Total Norm: 4.5811e+02 |Residual: 9.3043e+00 |A: 4.5802e+02| Relative Norm : 2.2751e-02\n", "Iteration: 4 \n", "|Total Norm: 1.0607e+01 |Residual: 1.2099e-01 |A: 1.0606e+01| Relative Norm : 5.2677e-04\n", "Iteration: 5 \n", "|Total Norm: 4.9916e-03 |Residual: 5.2681e-05 |A: 4.9913e-03| Relative Norm : 2.4790e-07\n", "Iteration: 6 \n", "|Total Norm: 1.5827e-08 |Residual: 1.5820e-08 |A: 4.6566e-10| Relative Norm : 7.8599e-13\n", "\n", "Arc-Length Step 31 :\n", "Iteration: 0 \n", "|Total Norm: 2.1848e+04 |Residual: 2.1848e+04 |A: 4.6566e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 1.0711e+05 |Residual: 7.4886e+02 |A: 1.0711e+05| Relative Norm : 4.9028e+00\n", "Iteration: 2 \n", "|Total Norm: 6.0557e+04 |Residual: 1.2371e+02 |A: 6.0557e+04| Relative Norm : 2.7718e+00\n", "Iteration: 3 \n", "|Total Norm: 5.3200e+03 |Residual: 9.0501e+01 |A: 5.3192e+03| Relative Norm : 2.4350e-01\n", "Iteration: 4 \n", "|Total Norm: 1.1583e+02 |Residual: 1.2889e+00 |A: 1.1583e+02| Relative Norm : 5.3019e-03\n", "Iteration: 5 \n", "|Total Norm: 4.6912e+00 |Residual: 5.4836e-02 |A: 4.6909e+00| Relative Norm : 2.1472e-04\n", "Iteration: 6 \n", "|Total Norm: 7.1440e-05 |Residual: 8.2681e-07 |A: 7.1436e-05| Relative Norm : 3.2699e-09\n", "Iteration: 7 \n", "|Total Norm: 1.6554e-08 |Residual: 1.6547e-08 |A: 4.6566e-10| Relative Norm : 7.5770e-13\n", "\n", "Arc-Length Step 32 :\n", "Iteration: 0 \n", "|Total Norm: 2.6281e+04 |Residual: 2.6281e+04 |A: 4.6566e-10| Relative Norm : 1.0000e+00\n", "Iteration: 1 \n", "|Total Norm: 3.7475e+06 |Residual: 1.2820e+04 |A: 3.7475e+06| Relative Norm : 1.4259e+02\n", "Iteration: 2 \n", "|Total Norm: 1.0457e+06 |Residual: 2.4465e+03 |A: 1.0457e+06| Relative Norm : 3.9788e+01\n", "Iteration: 3 \n", "|Total Norm: 3.3021e+05 |Residual: 3.2819e+02 |A: 3.3021e+05| Relative Norm : 1.2564e+01\n", "Iteration: 4 \n", "|Total Norm: 4.1320e+04 |Residual: 6.1620e+02 |A: 4.1315e+04| Relative Norm : 1.5722e+00\n", "Iteration: 5 \n", "|Total Norm: 4.4405e+03 |Residual: 5.9815e+01 |A: 4.4401e+03| Relative Norm : 1.6896e-01\n", "Iteration: 6 \n", "|Total Norm: 2.2128e+03 |Residual: 2.5250e+01 |A: 2.2126e+03| Relative Norm : 8.4196e-02\n", "Iteration: 7 \n", "|Total Norm: 3.2994e+01 |Residual: 3.9106e-01 |A: 3.2991e+01| Relative Norm : 1.2554e-03\n", "Iteration: 8 \n", "|Total Norm: 9.5014e-02 |Residual: 1.0361e-03 |A: 9.5008e-02| Relative Norm : 3.6153e-06\n", "Iteration: 9 \n", "|Total Norm: 7.7840e-08 |Residual: 1.9191e-08 |A: 7.5437e-08| Relative Norm : 2.9618e-12\n" ] } ], "source": [ "disp = [u.vector()[:]]\n", "lmbda = [0]\n", "\n", "for ii in range(0,38):\n", " solver.solve()\n", " if solver.converged: \n", " disp.append(u.vector()[:])\n", " lmbda.append(load.t)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Post Processing\n", "Here we plot the final deformed shape and the equilibrium path." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot final deformation\n", "plt.figure(figsize=(7,7))\n", "plot(u, mode = 'displacement', cmap = 'Reds', edgecolor= 'k', linewidth = 0.1)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Load Factor')" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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FqlWr2Lx5MwA7d+4knU6fMKayspJ58+ZNjNmyZQuBQGCihAFccMEFBAKBiTFvJJlMEg6HT3iIiIicjl45cITWwVGuuWAhC2dMpzzfw6+27qGnp9vsaDIFJqWI9fX1AVBWVnbC8bKysonn+vr6cDqdFBYW/sExpaWlr/v6paWlE2PeyP333z9xTVkgEKCmpuZPOh8REZHJ0lRXSzydYcvB48SSKQ73jdBQWkhFaYnZ0WQKTOpdkxaL5YSPDcN43bHXeu2YNxr/x77OPffcQygUmnh0dnaeYnIREZGpEQj4mV9dQsaAA83HiUVjzKwuhz/9yiE5A0zKPmLl5eXAb2e0KioqJo4PDAxMzJKVl5eTSqUYHR09YVZsYGCAlStXTozp7+9/3dcfHBx83Wzb/+VyuXC5XG/JuYiIiEymfUeP0+eAi2bV43I5WdZQwbO7D2MUV9B03vI//gXkjDYpM2INDQ2Ul5ezYcOGiWOpVIqNGzdOlKwlS5bgcDhOGNPb28v+/fsnxqxYsYJQKMT27dsnxmzbto1QKDQxRkRE5Ew2o6GOdDbL3o5+ItEoGw+0MLOmjKa6WrOjyRR40zNikUiEY8eOTXzc2trKnj17KCoqora2lnXr1nHffffR1NREU1MT9913H16vl7Vr1wIQCAS4+eabufPOOykuLqaoqIi77rqL+fPnc/nllwMwe/Zs3v72t/ORj3yE73znOwB89KMf5eqrrz7pOyZFREROZy6niwtn1PDykQ4OHW/n/PmzKfZ56NfO+ueEN13EXnnlFS699NKJj++44w4AbrzxRh555BHuvvtu4vE4t956K6Ojoyxfvpz169eTn58/8Tlf//rXsdvtXH/99cTjcS677DIeeeQRbDbbxJgf/ehHfOITn5i4u/Laa6/9vXuXiYiInGl2HzzMSJ6d1XOmkZeXx7K6Mn6z9zAxzwhNyy8xO55MsrdkH7HTnfYRExGR09WRlzaQ7mtnKBJlPJYgWBDAY8nhq5tJ04WXmR1P3gTT9xETERGRk2O125heVoDH7aK9u5d0JkOhzw1amjwnTMpdkyIiInJymls7ODbWx5qFM8CApXWlbD3cSnfPOE0XX2F2PJlkKmIiIiImaprWQOjwGNta++jqGyQWT9AQLCLo14au5wItTYqIiJjJYmVWdZB4LM7w2CgOhx27zaKlyXOEipiIiIiJ2rq7eX5fC6tm1bCgaTorGsroGxphx74DZkeTKaClSRERERM11NTgs0fZ1trH0fZubFYLLouF82fPMDuaTAHNiImIiJjJaqXA48JmsZBOpzFyORLpLIaWJs8JKmIiIiIm6hsc4te7D7OspphZdVWcXxskz2Fhy6tamjwXaGlSRETEROVlZdQ2lPPy8V6a2zvJGgYNxfmsKC43O5pMAc2IiYiImMlixe9ykc1msORyWAyD8UQaI6ulyXOBipiIiIiJRsdC/GpPMxc1lDGtspSLppcTcFp5Ydc+s6PJFNDSpIiIiIkKi4r48yUz2dszyt7jHbjcXtxkuHThTLOjyRTQjJiIiIiZrFaSqRTj8QQVhQES8Rg5q410KmV2MpkCKmIiIiImisUSPLnnGBfVlzKnrpJVTVVU+Fy8sPeQ2dFkCmhpUkRExETevDzef/5s9vaOsq+1k7FEFUW2HFcsmmV2NJkCKmIiIiImstntRJIpUtkcfpeLPJuFgUSGPKJmR5MpoKVJERERE1ltVn6xq5kFQR+zK4tZUB6gymvnQHuv2dFkCmhGTERExEQeXx7XLWhgT9cQx/qG2dc1yIWNVaxsqjY7mkwBzYiJiIiYyOly0zs6TsZiY2ZZIT5rls5IitGwlibPBSpiIiIiJrJarezoHGS630FNoZfzasuoy3eyS0uT5wQtTYqIiJjI5XKxenoFGcPCxsPt5Ht9zAnmcVlTFblcDqtVcyZnMxUxEREREzkcDoajCeJWJ9V5bgrz3YzkbCRCIeozGZxOp9kRZRKpZouIiJjIarWyta2PRr+ThdUl5NsgYKQZSWZJJBJmx5NJphkxERERE1ksFi6bWctQOMLhoQhD4XGuW9hI0OvAMAyz48kk04yYiIiIyXrGxhnO2FhQ6ifosHJkLEF/NEVK7zd51lMRExERMVl3OE6+kaLK76E84KUhz8GhwTHi0YjZ0WSSqYiJiIiYbFldGTUFPn51pJtNbX0kEwmuaarAYnYwmXS6RkxERMRkw9EEQxYb84vzcGWSDGVs9HSPUJPW0uTZTjNiIiIiJjvSN0LQaWVGaSF5LheudAIcTqJR7a5/tlMRExERMdnKxhqK7Dn+e387e7oHqSnwcmGFH5fDYXY0mWRamhQRETFZ+1CIQaeN1XVBdlqy7BuOUORx4cllzY4mk0wzYiIiIiYbT2VIJ2IUue24nQ5q8930hePEIrpr8mynGTERERGTzasqoc6S4BeHezjY3cv0gJfLawpo9fnMjiaTTEVMRETEZN0jYfrJcV5JHoXOaoZzVo51jlAxK2l2NJlkWpoUERExWd94FJ8dqgt82Ox20okEPpeLpN5r8qynIiYiImKyJXUVLMi3859729l2rINpfhfLipzk53nNjiaTTEuTIiIiJmvuHWbIaeGaGeXsGfBycDiKxwuuaMzsaDLJNCMmIiJiNquFZDqFJZvFarVSnu8lkkyS1Zt+n/VUxEREREw2ozzIqjIfL/aMselIO5ZElFVlPvLz8syOJpNMS5MiIiImaxsapS+T5PwSHwWeegyXi419UbzVwzSZHU4mlWbERERETJZIZ3DZrbidDrDAwHiMfIcNj9NpdjSZZCpiIiIiJptdWcoyv42njvay7WgHjXlOzgvY8bo9ZkeTSaalSREREZMd6B5g2Jbh2ukl7B4N0D0epzVthaEhLU2e5TQjJiIiYrJ8p4N0zqA/ksQAHG4PsVgcv97i6KynIiYiImKy2mAhKwM2joaSvHS4FUssyqVlPtwuXSN2ttPSpIiIiMmO9g/TlYhxUakbn7ueYp+Nl4aSGL29NJodTiaVZsRERERM5rRacDochLO//bV8OJzAb7dQURI0OZlMNhUxERERk9WVFLE8D17qHGbH8U4a85wszLdit+rX9NluUn/CmUyGf/iHf6ChoQGPx8O0adP4whe+QC6XmxhjGAb33nsvlZWVeDweVq9ezYEDB074Oslkkttvv51gMIjP5+Paa6+lq6trMqOLiIhMmd0d3bwayfFn9UWcP72adCLJS6Npunt7zY4mk2xSi9iXv/xl/vVf/5UHH3yQQ4cO8ZWvfIWvfvWrfOtb35oY85WvfIUHHniABx98kB07dlBeXs4VV1zB+Pj4xJh169bxxBNP8Pjjj7Np0yYikQhXX3012Wx2MuOLiIhMidrCAlKGhf2jcTLZHGM2N0YiTkVpidnRZJJNahHbsmUL73rXu7jqqquor6/nPe95D2vWrOGVV14Bfjsb9o1vfINPf/rTvPvd72bevHn84Ac/IBaL8dhjjwEQCoX43ve+x9e+9jUuv/xyFi9ezKOPPsq+fft49tln3/D7JpNJwuHwCQ8REZHTVXG+jyXeHCMZg63HOsjFIlxS6sOqpcmz3qT+hC+66CJ+85vf0NzcDMDevXvZtGkT73znOwFobW2lr6+PNWvWTHyOy+Vi1apVbN68GYCdO3eSTqdPGFNZWcm8efMmxrzW/fffTyAQmHjU1NRM1imKiIj8yQ509fPSYJzVxS4ubKqj0e/i+eEkLR26DOdsN6nbV3zyk58kFAoxa9YsbDYb2WyWL33pS7z//e8HoK+vD4CysrITPq+srIz29vaJMU6nk8LCwteN+d3nv9Y999zDHXfcMfFxOBxWGRMRkdNWud9HKjVOSwJSmQy7w1DutuOsrDA7mkyySS1iP/7xj3n00Ud57LHHmDt3Lnv27GHdunVUVlZy4403ToyzWCwnfJ5hGK879lp/aIzL5cLlcv3pJyAiIjIFivN9VEQz/GYwScvgGFfNrKbRY6HlD/8qlLPApBaxv/u7v+Pv//7ved/73gfA/PnzaW9v5/777+fGG2+kvLwc+O2sV0XF/2v9AwMDE7Nk5eXlpFIpRkdHT5gVGxgYYOXKlZMZX0REZEpsPdbOIqeNqyt8bMnzUmQkeXbQgr27W+81eZab1GvEYrHY6y40tNlsE9tXNDQ0UF5ezoYNGyaeT6VSbNy4caJkLVmyBIfDccKY3t5e9u/fryImIiJnhUU1FSQMC1uGEiTTGY7l3PhyaWortDR5tpvUGbFrrrmGL33pS9TW1jJ37lx2797NAw88wIc//GHgt0uS69at47777qOpqYmmpibuu+8+vF4va9euBSAQCHDzzTdz5513UlxcTFFREXfddRfz58/n8ssvn8z4IiIiU8LjdNDgyLArZWdnSxcX1JSwsshFm9nBZNJNahH71re+xWc+8xluvfVWBgYGqKys5GMf+xif/exnJ8bcfffdxONxbr31VkZHR1m+fDnr168nPz9/YszXv/517HY7119/PfF4nMsuu4xHHnkEm802mfFFRESmxK62bqriCS4q9mCdXsMST44NQykc3T1amjzLWQzDMMwOMdnC4TCBQIBQKITf7zc7joiIyAkO/Ov99B1vptDtpCeSwO/1UmXPkrvkXTRddpXZ8eQUnUrv0E5xIiIiJnPa7cxwZAmlc7QNjpJvzVHnPOvnSQQVMREREdNtam5j3GLnknxYWFPGLHuKX/dG6eh54/0y5eyhIiYiImKyldOrSWPjhZE0w5EYu9Nuap0WaivLzY4mk0xFTERExGQWoMKSxul00jY0QiwaYXa+HYt+TZ/1JvWuSREREfnjtrd0MjMeZ2WxBUttJcvdWZ4aSJDf10uj2eFkUqlqi4iImOz8uioSFjuvJGx0jobZlnKyrMilDV3PASpiIiIiZjMMCm1Z0gaEYwmc5Ciy6q7Jc4GKmIiIiMlePt6BJZfjAkeSOeVFLLLG+VV/jK7+AbOjySTTNWIiIiImW1lfidGdYGPUQvdoCKOkmEXeNEZ5mdnRZJJpRkxERMRshoETA5vVSiyZIZ1OU+SwmJ1KpoCKmIiIiMk2t3QRjUS5yJViblkhq7xZnh1J0zM4bHY0mWQqYiIiIiZbWVtG3GJje9rFkcEQr6TdXF7kpLKs1OxoMslUxERERE4DqZyBNWdgMXJg5LBhgEXLk2c7FTERERGTbW7posBIsdQWo7Eon6XWGE8PJOgfHjI7mkwy3TUpIiJispU1pbgGUryUdHBkcIhMSRGXBSyMBbU0ebbTjJiIiIjJjJxBCDtGJoPHasFqtZI2AKt+TZ/t9BMWEREx2QutPRSmI1ziTlOT7+JCW5TnxzKMjIXMjiaTTEVMRETEZJdWBxlJ59iS8bBnMMS+rJv3FDsoKi4yO5pMMl0jJiIiYrJ0Ok3anUcqHmVavpdxw8JgKgMWzZec7fQTFhERMdmL3UOUZhKs8hpML8znAkuEFyMG4WjM7GgyyVTERERETHZZRSHJZJJNGS/bekc4kPPwnkIr/oDf7GgyybQ0KSIiYrJQLE7U4aPQSFPqcRGz2AjlLGC1mR1NJplmxEREREx2JJygJBllnjVBg9fOwlyY9aEc8VTa7GgyyTQjJiIiYrLzC5wEEkl+PW6jPxJmPN/Ne/INuvLzzY4mk0xFTERExGTDsSTDjnxKMsMEXFYy3jxaoyN4XS6zo8kk09KkiIiIyQ6EU1RkYiz1WSl1WKmNDrM34wSr5kvOdipiIiIiJrso30Y2HuPXCRdbwhmyTg+XOpLkBQJmR5NJpiImIiJisuPjcfq8xSywJqm0Zui2eenPWnA6nWZHk0mmIiYiImKibDZLBDuuyAjebIrZXgfT0+NsjlpwOBxmx5NJpsVnERERE6VSKZbbkvhsNn4VtmC3Wjgvm+QSn00zYucAzYiJiIiYKJlM0mPYOeT0U5aKstyZY9hXRHcqh8ViMTueTDIVMRERERNFI+P05KxUZhIUOWxU2A2842P0WrR1xblAS5MiIiImysTjvN2eZDhusD6UpdPl4lJnGp9by5LnAhUxERERE8XHw2zNOvF7vSz2JJiei3HIGcSazZkdTaaAliZFRERMlE4k8LjdGNEQbqeT6U4rhekEh+IqYucCFTERERETuWwWlqZC1Ftz7ImkeCLhoCwxzoVBvc/kuUBLkyIiIiaKjY+zx1nAeCzOwoCVOc4s+91BsskMc8wOJ5NOM2IiIiImyiUTRDI56pzgcNgpNNKkYzFCOf2KPhdoRkxERMREeU4nc9JjHImm2BTOEAkWcLk9RlvJdLOjyRRQERMRETFRf38f3c5CSohycb6Dktg4O/KCWFMZs6PJFNC8p4iIiIl8FgtOw2A8kcZisVFuM3AYObriWbOjyRRQERMRETGR12HnvPgwhZYc23oHeS4Oi2PDLKwpNzuaTAEtTYqIiJios7OTPm8Q38ggK6vLqYmOsdntx55Imh1NpoBmxERERExU4HKRSqbJ97oBC9FEAgsQyxpmR5MpoCImIiJiony7lYtSo7SEorzU3k3E4eKC6BANVdVmR5MpoKVJERERE+1rbWfYU8yi9BD+0ipsw/3sKAzizuiuyXOBZsRERERMVOd1kc0ZdBg2bBjku5zkDBhLpMyOJlNARUxERMREeRYL540PErHZea6tm97xcc4PD1BXW2t2NJkCk17Euru7+eAHP0hxcTFer5dFixaxc+fOiecNw+Dee++lsrISj8fD6tWrOXDgwAlfI5lMcvvttxMMBvH5fFx77bV0dXVNdnQREZFJt7+nl012H4uSUS6vKafKl8cmTyHjqbTZ0WQKTGoRGx0d5cILL8ThcPD0009z8OBBvva1r1FQUDAx5itf+QoPPPAADz74IDt27KC8vJwrrriC8fHxiTHr1q3jiSee4PHHH2fTpk1EIhGuvvpqslltdiciIme2KqsFq9PNiNuLkc3Rms7htVrJ2BxmR5MpMKkX63/5y1+mpqaG73//+xPH6uvrJ/5sGAbf+MY3+PSnP8273/1uAH7wgx9QVlbGY489xsc+9jFCoRDf+973+OEPf8jll18OwKOPPkpNTQ3PPvssV1555eu+bzKZJJn8f/uvhMPhSTpDERGRP02ALA2jfWx0+Gkd7mdtnp1geJDucm3oei6Y1BmxJ598kqVLl/IXf/EXlJaWsnjxYr773e9OPN/a2kpfXx9r1qyZOOZyuVi1ahWbN28GYOfOnaTT6RPGVFZWMm/evIkxr3X//fcTCAQmHjU1NZN0hiIiIn+aTX3DDLjzuDob4YpiP12GlZ15xaStuoz7XDCpP+WWlhYeeughmpqa+J//+R9uueUWPvGJT/Af//EfAPT19QFQVlZ2wueVlZVNPNfX14fT6aSwsPD3jnmte+65h1AoNPHo7Ox8q09NRETkLbHQkmXE7eNw1ko6lcSa5ycWS2BxecyOJlNgUpcmc7kcS5cu5b777gNg8eLFHDhwgIceeogPfehDE+MsFssJn2cYxuuOvdYfGuNyuXC5XH9iehERkcnnzSSpiMbZ5srj8MgwH4hHabAAlVVmR5MpMKkzYhUVFcyZM+eEY7Nnz6ajowOA8v9d/37tzNbAwMDELFl5eTmpVIrR0dHfO0ZERORMlM1m2ZY0GE5lWRkZ4i9cVuI+P88788l/zUqQnJ0mtYhdeOGFHDly5IRjzc3N1NXVAdDQ0EB5eTkbNmyYeD6VSrFx40ZWrlwJwJIlS3A4HCeM6e3tZf/+/RNjREREzkThcJiF0VFGiko5krMwks7Q5/LiMsDn85kdT6bApC5N/u3f/i0rV67kvvvu4/rrr2f79u08/PDDPPzww8BvlyTXrVvHfffdR1NTE01NTdx33314vV7Wrl0LQCAQ4Oabb+bOO++kuLiYoqIi7rrrLubPnz9xF6WIiMiZKNTfR6PDxqtjw2zP2ijP8/P20X76A0V/9BIdOTtMahFbtmwZTzzxBPfccw9f+MIXaGho4Bvf+AYf+MAHJsbcfffdxONxbr31VkZHR1m+fDnr168nPz9/YszXv/517HY7119/PfF4nMsuu4xHHnkEm802mfFFREQm1WhvL8/ZfLwjNU7M7uCiVJgd7nxGbB4WmB1OpoTFMAzD7BCTLRwOEwgECIVC+P1+s+OIiIgAcOT53+D+wt9xtLCU/pExFrisDOYHGLM5ePePnzQ7nrxJp9I7tEmJiIiISYxYBF82gyeTYiCT5TB25vZ30VgSNDuaTBEVMREREZN0tLTxrN3HnJEBFhQFuCI2SmtBkAPxjNnRZIpM6jViIiIi8vvV+DyUpGLsKqkikkqz2e0nz2anqqjA7GgyRTQjJiIiYhIjFoFcjkw2x+GREF6nk/lDvRSXap/Mc4VmxEREREzyavMxCi12lg314iqvYXZvO5sKS7FEosw1O5xMCRUxERERk8zJ82C329iSX0QsGsVSWo0lEqGmrt7saDJFtDQpIiJikmw4TNRmx2m10xNNEItGWBEP4wjo7Y3OFSpiIiIiJnmpswtHNMLigS6WBnwsiIzxbF4Ro1ndNXmu0NKkiIiISS60Whh1uBjyB2gPjxMtq2FGaARvbZ3Z0WSKqIiJiIiYZHR4mLjHh8+ARCZHMBqmOBbBEiw1O5pMERUxERERE8TjcY5g4dLhAbLZHMUOO7lQjPX5RXygqsrseDJFVMRERERMMNDVyTsjo/QVFLMjGmdOno+400nJ+Dgej8fseDJFdLG+iIiICeL9/Yy6vYx780hnc6TsDgIjw1QES8yOJlNIRUxERMQEfS0t7Hd6mdnTQWO+j0VDfeRbLGzOmZ1MppKWJkVEREwQtFmZPjrIzoIgx+MJ7KWV+BJxVtTVmB1NppCKmIiIiAmi/f0cKyjG5/Xiz2TJGlA+HiJeVGx2NJlCWpoUERExQWdrK1mszOzuoK6ggPP6ujlgd3E8njQ7mkwhzYiJiIiYoN5mpWhkkH1llRweHiJVXkV+Xx8Vs+eYHU2mkIqYiIiICTp7uhmsqiUeDlHhcJFIZ2jMpMgWFZkdTaaQliZFRERMMDwexReNsmw8TIXFYGl/L8/mFxBzOMyOJlNIM2IiIiJTzDAMZowO4RsP85uiUiKJBOnSclb29VIyS0uT5xLNiImIiEyx3p4ejhtWBqpqyR8aJJhOY+RyxNweKmprzY4nU0hFTEREZIqNtbUR9LqxDA6SczlZnoxTPNDPFn8BdrsWq84l+mmLiIhMMWNkiDn9fQw73byMBVtFFdahYVaWlZsdTaaYipiIiMgU6zh4iFx1HZHQGPPdXnypNFm7HXtp0OxoMsW0NCkiIjLFXOMRopksMyLjeF1OGgf7CaVSHMpkzY4mU0wzYiIiIlPMFxmnuquTFz0+ugaHsJVVMKevDxYsNDuaTDHNiImIiEyxV1pbOVpVzbxUgvleLyGLlZzNhr201OxoMsVUxERERKZY2egYoWwWVypFfjbL3K4uNuflE/f6zI4mU0xLkyIiIlMokUhQMjhIYTLBrwsKsadShL1elgyPMH3pUrPjyRRTERMREZlCh155hcOFhdQmkyxKJMikUqQqKxh3eygK6q7Jc42WJkVERKaQbXiY6akUESBXVERDJoN3ZJQ9gQAWi8XseDLFVMRERESmUKa3l7KhIWzpNC+NjrLV76c4HObC6dPNjiYmUBETERGZQnt27mJXcZCqsRArSkqpcLtpLyjAUVlpdjQxgYqYiIjIFJqWTGK32YgUFmI1DHw9vYQcTnpsNrOjiQlUxERERKZQpruLsr4+DtisvDw4SCovj/MHB2nSHZPnJBUxERGRKZJKpdgaDmNxubhgYIiLcjn6Cwvpd7konDHD7HhiAhUxERGRKdK6dy+XDgzTW1bOLreL0kiUQDzBK8XFVNbXmx1PTKAiJiIiMkUSbW3Ycjnykwk63W5e8vup6htgWbBUW1eco1TEREREpsir27azO89HdXc/iwqLWZxI8WpNNc6aGrOjiUlUxERERKZIXTROSSpLa3UlVmAgl8Vps9HucpodTUyiIiYiIjJFxo8dJ+ywkbTZ2DI0QFEmy8y2DuZfdKHZ0cQkeq9JERGRKZBOp9kzNMgFo2O4R0P4/Hn0FxWRSqWYPaPJ7HhiEs2IiYiITIHju3dzaW8/ozW1bMr34k4k8bhdHPTnUzd7ttnxxCQqYiIiIlNg/NBhBgoCGC4nUaeLgwUBaju6WFRait2uBapzlYqYiIjIFHh161aSbhe1x1uYU1TEkqFhDtTXkqmpNjuamEgVXEREZArUjoXI9PZzsL6OZDxOrKwUj81GtLjI7GhiIs2IiYiITLJcLsfeI80MT2/AA3REI1SFxqk9epxZl1xidjwx0ZQVsfvvvx+LxcK6desmjhmGwb333ktlZSUej4fVq1dz4MCBEz4vmUxy++23EwwG8fl8XHvttXR1dU1VbBERkT9Z1/HjFFgsuNs7MdrauTgUYcDt4khZCfXLzzc7nphoSorYjh07ePjhh1mwYMEJx7/yla/wwAMP8OCDD7Jjxw7Ky8u54oorGB8fnxizbt06nnjiCR5//HE2bdpEJBLh6quvJpvNTkV0ERGRP9nQrt3M6urBXhCgOVhEuKQEW1Exo0WF5Pv9ZscTE016EYtEInzgAx/gu9/9LoWFhRPHDcPgG9/4Bp/+9Kd597vfzbx58/jBD35ALBbjscceAyAUCvG9732Pr33ta1x++eUsXryYRx99lH379vHss8/+3u+ZTCYJh8MnPERERMxy6OWX6WycxpjPCxYLYw471c3NLNK2Fee8SS9it912G1dddRWXX375CcdbW1vp6+tjzZo1E8dcLherVq1i8+bNAOzcuZN0On3CmMrKSubNmzcx5o3cf//9BAKBiUeN3sNLRERMlGnvIJNOM62tgxn5+czo7OLItHqMhnqzo4nJJvWuyccff5xdu3axY8eO1z3X19cHQFlZ2QnHy8rKaG9vnxjjdDpPmEn73Zjfff4bueeee7jjjjsmPg6HwypjIiJiimw2i+/oMQKDw+ysrmA8NEamaTq+ZBJ7Q4PZ8cRkk1bEOjs7+Zu/+RvWr1+P2+3+veMsFssJHxuG8bpjr/XHxrhcLlwu16kFFhERmQQ7nv0NPXk+Ur48sgP9FAYCFPX0kbTC8quvMjuemGzSliZ37tzJwMAAS5YswW63Y7fb2bhxI9/85jex2+0TM2GvndkaGBiYeK68vJxUKsXo6OjvHSMiInJaa20lmM5iDA7iLw4yv2+QQZeTwRlNeDwes9OJySatiF122WXs27ePPXv2TDyWLl3KBz7wAfbs2cO0adMoLy9nw4YNE5+TSqXYuHEjK1euBGDJkiU4HI4TxvT29rJ///6JMSIiIqez8b2vUtHdQ8rp5FAsQmfTdFJuD576OrOjyWlg0pYm8/PzmTdv3gnHfD4fxcXFE8fXrVvHfffdR1NTE01NTdx33314vV7Wrl0LQCAQ4Oabb+bOO++kuLiYoqIi7rrrLubPn/+6i/9FREROR6/sP0BReSm+/gGaysqIxOPM6ukhXxu5Cia/xdHdd99NPB7n1ltvZXR0lOXLl7N+/Xry8/Mnxnz961/Hbrdz/fXXE4/Hueyyy3jkkUew2WwmJhcREfnjOo4coeboMeI1NdgMKB8cwpPJ8nJVGTevWGF2PDkNWAzDMMwOMdnC4TCBQIBQKIRfG+eJiMgU2fb9RwjfdQ+H3A72eVwsD5bhSSaJul18dMsms+PJJDmV3qH3mhQREZkk29Zv4HChn2nJNBeWlpNMp/H3DTBt+XKzo8lpQkVMRERkEhiGQVlLG4F8PyNuN9Z4gqaOTg4XBUg16EJ9+S1TrxETERE5Wx1/9VWMtnYIFtFc4MeSThIqKaJweISF11xjdjw5TWhGTEREZBLs/Pkv6CgqpLR/iAq7gwXxFE6LlYLZs6maph315bdUxERERCaBp/kYlaEQPbXVeL0ePKNjjESj9E3TsqT8PypiIiIib7Hx8XF27dpFtKKChM3K7qFBhgr8zBuPseLqq82OJ6cRFTEREZG32KENz1Ls81HS2kZ6YJALh8eIFBcR8ecz6wptSC7/jy7WFxEReYuNbt5CfUs7ndMaAAPicVzjEVpmNeHLyzM7npxGNCMmIiLyFjIMg73btzMwqwmrxcLRcIgeI0fF4DCXvPMdZseT04xmxERERN5Ch17ejKd/CG8qTTgW4UIsjNfU0t/Tw3wtS8praEZMRETkLdSz4VnqhoYZddjoCBbT7fWQAvpmz6Ju1iyz48lpRkVMRETkLWIYBhtfeJ7BhlqcVivpXJYKu53a9k4ueNulZseT05CKmIiIyFukefsOZh45zng6A0PDLAhHCRsGI4UBqrQsKW9ARUxEROQt0v7rp/AkUzgGh9hZ6CdZUYa9pIS2qgpmLj/f7HhyGlIRExEReQvkcjk2PLOeI24XebE40335jKdSFB85yoWXvg2LxWJ2RDkNqYiJiIi8BfZueJalzcdwVlUQcTko6esnODhMS0UZdVdp2wp5Y9q+QkRE5C2w6T8eJVFSjC2VYleej6UlJVgNg6zXy4xlS82OJ6cpzYiJiIj8iSLhMNFDhwmMhant7GGhN49kJkNx83GWXfVOs+PJaUwzYiIiIn+i3T/+CdNb2xmqq+HgyCjTu7rJGAbHp9Wx8s//zOx4chpTERMREfkTvfzTn1IwswnDgG63A3egEiMRJ1daSmVDg9nx5DSmpUkREZE/weGt23AcasY5NITrSDPnpXJYnA7qBoZZfeMNZseT05yKmIiIyJ+g+bH/pDo8TshqpbumEvvoKMn2drZMq2XJn7/b7HhymlMRExEReZNG+vvZuullhirLcRjQEYsRdruoTed4+9VX43Q6zY4opzkVMRERkTfple//gKbuXuLZDJFshouHx0hWVZB2u5j/oQ+aHU/OALpYX0RE5E2IRqNs/dF/UuB2EzUM+h028muq8OWg6/wlVDc1mR1RzgAqYiIiIm/C1h/+CLfDQVEoTDrlwVHgx9LTQ34mx0X/+EWz48kZQkVMRETkFGWzWVr+41F8Le2M1FRh8XioPnKM/un1OAsLWHTlGrMjyhlCRUxEROQUPf5PX2MkmcQ9q5Hu8Qi5aATb7CacOQPHpav0Bt9y0nSxvoiIyCnIZrNEf/kUWcMgcKiZoNdDkWHgaT6OG/jA33/S7IhyBtGMmIiIyCl4+YePYtu7n2KbjebKUir7BskLh+ltbOD8m27AbtevVjl5+tsiIiJykpLJJP/9rW/jy/Nht9sYymRJOG3kFxQQzWY5/wZtWSGnRkuTIiIiJ+mFh77DvCPH8VeU4U8kmB9NUJHvp3J4hCv/6mby8/PNjihnGM2IiYiInISRgQGe/dFjFDbWE4sn6C/Ip9pig0iE7tkzuOkjN5sdUc5AKmIiIiIn4Tdf+RqFqQyFx1owigopdbsIDo1gT2VY9el7cLlcZkeUM5CKmIiIyB/RvHMX3T94jEAsRl9DLV6bjdqWdoZnTCdYUMglN95gdkQ5Q6mIiYiI/AGGYfBvd91NxuXAV1BGdzJJmcuFZWYT8Uyamhvej9WqS67lzdHfHBERkT/gue9+j5rtuyksLaGou48ZFit5Dif5h4/SNHcu77jpRrMjyhlMM2IiIiK/R39HB089/G8UNk1jPBTiUFkxjV09+LHQ1VjPR//hHrMjyhlOM2IiIiJvwDAMfvnJT1OQSpN/5Dh5kSglThceq42E10P5xRdSN3uW2THlDKcZMRERkTfw71/8Es2/fpqydJae6gr8Thf1LW3EmqYT8Pn4yNe+anZEOQtoRkxEROQ1Wvbtp/XHP8WTMRgvLKA7kyZttxOfO4v+XJoLPvsp3G632THlLKAiJiIi8n8k4nF+efvfUtjSQW7GNJweDzMGRrAZBp6DzaxccyXL3nGl2THlLKEiJiIi8n9882Mfp62nh9jsJkaTSVpyWXA4iI2OEp89g2s+/xmzI8pZREVMRETkf/3Pv36X7E9+ToEvD9eBZvxOF5UFBRjJFFGrhYV3fAKf3k9S3kIqYiIiIsCuZ5/jyW//K7HGejoHB+irr8J3+BiOoRGwWnjbX3+Mqz7wfrNjyllGRUxERM55rfsP8MwttxO0O8g71kqV000okyU7czpGaZDYJSu49u47zY4pZyEVMREROacNdHfz7VtuI5ZOk+voYrA4QDIeozCZxHq0BW/O4O5Hvqe3MZJJob9VIiJyzgqNjPDo2ptwRuO4egcYctjpdDrxlpfhsVgZa6rn6u98i+KyMrOjyllqUovY/fffz7Jly8jPz6e0tJTrrruOI0eOnDDGMAzuvfdeKisr8Xg8rF69mgMHDpwwJplMcvvttxMMBvH5fFx77bV0dXVNZnQRETnLRcJh/r/3foDufftJtneS8LjxFxbQZLFhOdiMY3SMxTfdyKzzl5kdVc5ik1rENm7cyG233cbWrVvZsGEDmUyGNWvWEI1GJ8Z85Stf4YEHHuDBBx9kx44dlJeXc8UVVzA+Pj4xZt26dTzxxBM8/vjjbNq0iUgkwtVXX002m53M+CIicpaKhMP829ob8Q6P4k1lsJcGOVKUR2I8grWzh5GqcuZ9+m4+cMffmB1VznIWwzCMqfpmg4ODlJaWsnHjRi655BIMw6CyspJ169bxyU9+Evjt7FdZWRlf/vKX+djHPkYoFKKkpIQf/vCHvPe97wWgp6eHmpoannrqKa688vWb6iWTSZLJ5MTH4XCYmpoaQqEQfr9/ak5WREROS+GxMb74F+/HuW03htdNdixEumkalkya/JZOEsFC3Ksv4rOP/gCLxWJ2XDkDhcNhAoHASfWOKb1GLBQKAVBUVARAa2srfX19rFmzZmKMy+Vi1apVbN68GYCdO3eSTqdPGFNZWcm8efMmxrzW/fffTyAQmHjU1NRM1imJiMgZZLCnh3+97r04h0aIGjnSwSKOlBbibm3H3tJJKuCn9rLV/MN/fF8lTKbElBUxwzC44447uOiii5g3bx4AfX19AJS95iLIsrKyief6+vpwOp0UFhb+3jGvdc899xAKhSYenZ2db/XpiIjIGab9SDP3vud99O3cxdjwMHnJFBmLhdmFxURtNowZ08guXciHv/sQNpvN7LhyjrBP1Tf6+Mc/zquvvsqmTZte99xr/9dhGMYf/Z/IHxrjcrlwuVxvPqyIiJxV9m58iZ/d/Nf4833gcILfz6vkmHvoKNniQtzxJJWN0/nIjx7R7w+ZUlMyI3b77bfz5JNP8vzzz1NdXT1xvLy8HOB1M1sDAwMTs2Tl5eWkUilGR0d/7xgREZHf59f/9u88dOsnSAwOY0lnsGYyGLkcc4uCZKvKsVaWk7j4Aj7yo0fweL1mx5VzzKQWMcMw+PjHP87PfvYznnvuORoaGk54vqGhgfLycjZs2DBxLJVKsXHjRlauXAnAkiVLcDgcJ4zp7e1l//79E2NEREReK5PJ8P07PslLH/87Apkc0VyOrniM7qIAvqNtpNJpXL0DVM6ayf2/ekIlTEwxqUuTt912G4899hi/+MUvyM/Pn5j5CgQCeDweLBYL69at47777qOpqYmmpibuu+8+vF4va9eunRh78803c+edd1JcXExRURF33XUX8+fP5/LLL5/M+CIicobqamnhazd9BNtYiESeB7/XQ15RAdZ4krjVQrihhlgmTeX7/5xb//1hXRMmppnUIvbQQw8BsHr16hOOf//73+emm24C4O677yYej3PrrbcyOjrK8uXLWb9+Pfn/593tv/71r2O327n++uuJx+NcdtllPPLII/qHIyIir/Of33yQAw88iL2nn7DDRsBi5fDoMAWZLBVDo7jnzMB65Dgr77mD937mHt0dKaaa0n3EzHIq+3mIiMiZaWxkhB/f81kOvLwZq2HgDEUYd9jw5OUx0tlFcTyJrbGBUauF6+9axxU33mB2ZDlLnUrvmLK7JkVERCbLSz9/kke/eB/+V49gaajB3dJBpKiAXrtB09AIpeMx0kUF+LI5bn/oWyy45GKzI4sAetNvERE5gzUfPMiDN/4Vv7j+JgLRJLGKUgbTKVIzp2OJJ5hZUExqeJT07EasC2Zz6/onVcLktKIZMREROeMkk0l+8fVv8vwPH8NlsZJ2Och3OrF09+ILFjIWjeIJ5GMkkrgcduZfezXv/8Jnsdv1a09OL/obKSIiZwzDMPjNY4/zk299G+/ewzgKA9gHhrAGizg4Nkyjz4envYeRYAGu0XHG5hTy4f/6ARdc9U6zo4u8IRUxERE57RmGwU8e/jd2P/pj4i9vJ392I9GSQqIWA3dpEb7CAmqNHIbLIGKz4vG6qb/yctZ+5UsE/3fzcJHTkYqYiIictgzDYMPj/8W27z7CQFsHdgskggXkWe0YY2FyxQWkvU6M1g6sddXYWtrx1tcw58M3cPPf3212fJE/SkVMREROO/F4nGe//0O2/eBR2oaGKI4lsbpdWNq7Mfw+DoWGmW6zUdTew5jTRjJYTCSX46KP3sj1X/gMhcGg2acgclJUxERE5LRxdP9+Xv7BY2z+zXNYR8Zwd/ZSUFlKIhYj7HUSnN2Ic2SMmQVF5PKyJDNZcg4LlY2NvOOzf8/St602+xRETomKmIiImGpsZISX/uunPPOj/yQ9OILrSAt5C2aTHBghMb2OZCRCXk0l1nAYw2vBOjiCtTQIR5pxzp3BRX/+Lj76mU9htWpHJjnzqIiJiMiUGx4cZPuTv+bg/zzLK/v3k3ekjWRJAb7+EbJzGrEZBnG3A6/TQb/diudAM8HpdVgOHiXRUE3CApd/6TNc/Ylb8erNuuUMpiImIiKTLpfL8fwzz9C761XaNm2lubODQChCrrsPa2EerqZ60skkBpBKJGjLJKmNJcgcaCbo9WCf2Ugkk6KgppJVN36Qd9z2MQqKisw+LZE/mYqYiIi85ZLJJLtffInj23exe8sWUgeaydhtZBx27IeOUTR3JpFEgkxFEFvvAONeL6N2K0VlxfhauqifOY1cXR7jXT3kxRK4bTZmvOtdfOhTn8QfCJh9eiJvGRUxERF50+LxOM2v7mOotY1d27bhGh2n93Azx0aGKD7aTq4sSBpwxxI4G2rJvnqQ9IxpEI2QdtgZc9opqKkir7OXwgWzydqjxCIxLPE4rp5BvBcs5LoP/yVX3LBWu+LLWUl/q0VE5JRsfOppnvz6gxg9/Qxl01j6h3GNjZGqrsRqGCTD4/jHY1hmN+Gx2rAfOEJ6ei0j4THyG2rJGjn6Mykq+gapm91EbGgYa0UJ1pxB+ngH9rlNlC9awHvXfZw5S5eYfboik0pFTERETkme309k16ukA/n48/LIFgYYdlgJdPXiqKqA8jKy4y2MjI6SdDmonjuT+OgoSZtBYWcPybJiKsJRsvU1WB0O3ENjRGrKKWuo5h333MElf/5nuFwus09TZEqoiImIyCmZs+Q8krEEht/HYDxKmc9LJJugfN5syGXpHw9R6nHj7xtitCxILjoAFoPynhFys5vwW6zk+ofJZTPY6qq48m9vY+V11xIoKDD71ESmnIqYiIicEo/HQ3pGPd7mNvKm15MeC1PYO0za4iTd0UMg34u9rgrGxinq6ydZU43H5yYXSRAsLMTZ2MBl//gFLnj7GhwOh9mnI2IqFTERETllsyuraO7qZSgagkyakmyGVDYDtRX423vIJDuJNtYyZ+F8qhfNx1FZxjve/16KS0rMji5yWlERExGRU+avqcbX1gYDw+Dzki0qxHC5SBb6ec/n7qFmwXxmL1qIzWYzO6rIaU1FTERETlnC48Rmd+DJyyNrt5EGfJkc82bO4h1/eaPZ8UTOGHpjLhEROWXzFy0ks/8IyY4uRnJpovleMqEwkcEhs6OJnFE0IyYiIqfMEywm3ViLJ5Yg3taNDwtJm42jQ4NmRxM5o6iIiYjIKcsLBnFiJe3zkPLnUZSXT8rjwjMaNjuayBlFRUxERE7ZtJkzSLa0Y3e7yBTnk/Llkertx2KzYRgGFovF7IgiZwRdIyYiIqesoKCA7IwGkm4neb3DGIeP4Y4mGCvMZ2xszOx4ImcMFTERETllVquVXCpFXmUlef58xksKcMxowN/aTVhFTOSkqYiJiMibUmRzEmk+RrakmJzXQzY0jiOXIzwyYnY0kTOGipiIiLwpI34v7jwfziMtBDOQ6e4lMr2W0SFtYSFysnSxvoiIvCnBjEGyJEjU4yZng/y5M8k1t+D1eM2OJnLG0IyYiIi8KS67nWxvP54CP+MWg2g4jCOdIpfNmh1N5IyhIiYiIm9Kn80glk7BgaOUG3acnb2MT68lFNJeYiInS0VMRETelJJkFntJEKbXMkYO57xZ5HUPUlhUaHY0kTOGipiIiLwp2XSGXDKF1eUkg0EuPI4tkcRm1+XHIidL/1pERORN6bHlcPUPkesforC0mNTAEMnGOnJW7aovcrJUxERE5E0pGAxhqS4n4bQTicUpntNEvLmFiupqs6OJnDG0NCkiIqcsk8kQi0Wx5flIZbJYHTYSwyO47HaKgkGz44mcMTQjJiIip2xocJBoSSGu5lYyVoO8TA6rw8FIQxUul8vseCJnDBUxERE5Zb1t7QSPd5KqKiNm5PB6vLhsNsoBi0XXiImcLC1NiojIKQv3DxAvKyavqBCnxYLd7iDbO0CBliVFTomKmIiInLL2I804CgqI7jtE0JeH7chx4nYbYY/T7GgiZxQVMREROWW2RAr7keO4p9UxkEpinzcTw+VixrTpZkcTOaOoiImIyCk7duQIzrmzSGLgdzhJ57I4+wYorqkyO5rIGUVFTERETtlofz+ZZBJ7Syd+mw3LwWOk6qtJubQ0KXIqVMREROSU5dp7SB9rIdZYR3c8imNOE+7BEWYvPc/saCJnFBUxERE5Jb29vYxYc7hnNpLp6sWdTJMZj5LNZpm1REVM5FRoHzERETklx3fvwZ/MEE1FsQXy8fUNEbfbycxpJBAImB1P5IyiGTH5o3K5HHt37zY7hoicJnoPHibX0YMlGmfIacUxbxbZkkJm1NaaHU3kjKMiJn/UgT27GBvo4cCe3RiGYXYcETHZ9pc3k22sJ5nO0BgoJp3NYusbpnb+XLOjiZxxzpgi9u1vf5uGhgbcbjdLlizhpZdeMjvSOeHo4UPUV5Tg9/sp8Xv40Q++TzQSMTuWiJjIaO0Ehw1f1sCIJ7AcOkaiphx7WYnZ0UTOOGdEEfvxj3/MunXr+PSnP83u3bu5+OKLecc73kFHR4fZ0c5qQ4MD7Ni2lWPtnby0eTMDQ8PU11TS33aMvp5us+OJiAn6enoIH2wm1tLOcFUx/dkMlvpqPH2DXPjOt5sdT+SMc0YUsQceeICbb76Zv/qrv2L27Nl84xvfoKamhoceeugNxyeTScLh8AkPOTXJRILh3m6qKsoYHBrmHVdcgcvpxGW3Y2QzPPWLn9N8cL/ZMUVkir34i18SqSrFl87hS2bxj0exZLMUTKunoanJ7HgiZ5zTvoilUil27tzJmjVrTji+Zs0aNm/e/Iafc//99xMIBCYeNTU1UxH1rLJ/3z46u7pwu9z09fYSCo/z86eeIZZI4Ha7mTVjOrXF+ex7ZRupZNLsuCIyRUKHjxIYHSdXW0mguAj38BjjoRCW6XVmRxM5I532RWxoaIhsNktZWdkJx8vKyujr63vDz7nnnnsIhUITj87OzqmIelZZsmwZ8xYtIZFKMXtWE9lclmBRMU6Hk1A4hMPhoKd/gLGRYX70ve8yNDBgdmQRmQIHX9pM1uPG7nLSEholUVuBNRLn4isuMzuayBnptC9iv2OxWE742DCM1x37HZfLhd/vP+Ehp668spJ5i5YQGo+zZME85s2dzYpl5zE8Osazz72A1+WmrrKcd115GamRPrZs0g0UImezjtZWOsOjWPr6SR5poXwkjM3rxZnLMfOSi8yOJ3JGOu03dA0Gg9hsttfNfg0MDLxulkzeesUlJVz2jqs4tO9Vjre0EovGmN3YQGlxEUda27BYLHicTgwgPDrKqzu2Mve8ZdhsNrOji8hbbPev/4fg8U6ysxrJxeK4OroJtXXCghnMXrTQ7HgiZ6TTfkbM6XSyZMkSNmzYcMLxDRs2sHLlSpNSnVssFgtzFixk5SWraairobmllen1tTgddvbsO4DVYuH8hfOoLC9nfkM1P33sPxgdHTE7toi8xTY+/TTW2U14nE6GjSzJshL8iRQXXbDy965QiMgfdtrPiAHccccd3HDDDSxdupQVK1bw8MMP09HRwS233GJ2tHNKbcM0xkZHad28DZfTxcI5szEMKCsJ8vRzG7FaLAyPjFJWXEi48zjh0VHqpk03O7aIvAVCY2NEj7SQGRkjNzpKdVUF2XwfltA4M1ZpWVLkzTrtZ8QA3vve9/KNb3yDL3zhCyxatIgXX3yRp556iro63aUz1QoKC1l704dx5/vJZXMkEgnCkQhtHZ2k02kuWDQXr8dDdVmQQzu38fOf/Fi78YucBTb//EkcLR143S5GqytI9w1ijcQJN1Sz/CrtHybyZp0RM2IAt956K7feeqvZMQSw2WzMX3I++3fvpq29kwsWzmN07hxWLlnItj372Ln3VSxGjrkzppHLZtm/7SXq5izSTRMiZ7DnfvpzrPNmkkomSSUTRAvyKOobZPFFK/Drjb5F3rQzYkZMTk/zFi/m2r94Hx39Q9jtdjZu2Y7Tbiff6yWbyXK8rZPqijKyyTi//K8f0dnWYnZkEXkTBvv7GXl5G7lkCppbKEtlCdqdJIsLmPv2y82OJ3JGUxGTP0mwtJRp88+jtauXJfPnUhYs4rKLLqBpWi3bdu/lha2vMGdaHfVVFXjjo+zdvkVLlSJnmE2P/zeesQjh4220V5WQsEK2IEC2PMgF77ra7HgiZ7QzZmlSTl9Ol4v33fiXNB/YT/vRFooKA4yHx1m98gIy2Qx9g8PEIxH2Hj5KW0cn1kyS+vlLyM/PNzu6iJyEp//rJ2SKAjijUcrz8slLZTGaW1j0/j+nKBg0O57IGU0zYvKWmTF3HsG6aeR5faxavgS328V5s5t44pln6ekfYPX5i5nROI15dRW0797K5pe0AazI6W7vy5txbN2Dq7QYI5HCPTxGfGgYS1U5C6/TbJjIn0ozYvKWWnzeUmKxGLt3befI4SPYLPC2i1dQFSzihe27sVqt7DzYTDKRYGhklP0eJ3OXnK89iEROUz/55kPEK4LYE0m6qkqYUxjEZbUwZrdw8Z9da3Y8kTOeZsTkLef1ejnvotUsWr6SsuJC0pksbpcLr8fD1ld2UVbgp7aijJWL5hLIRXn04W8TDofMji0irzHY18fwq/uxD47gau2i0uEknU6R2XeYt7397djt+r+8yJ9K/4pk0sxeeB7dne0c2fIK8UiUpfNmUpjnJZ7OsGPvPmoqyqkpL2F2fTVDh3YyVlJL7bRGs2OLyP969rvfx3GkBdvMaWSTKXytHaScDiwN1Vxy0wfMjidyVtCMmEyqqpo6rnnvB8krKmbrnv14XU76BofI5QxS6TS15SU47DYCHhfbfvM0r7z4nO6qFDkNJBIJnn/yl1jnzcRitXI8FSPT1ABVFXhnTKe+qcnsiCJnBRUxmXR5eXksWLmasayN7oEhLj5vPjOm1XPpskX8auNWduzdR2/fADMballcns+BFzcwMjxsdmyRc9ozD38Pa3s3ue5ejKER6npGMLDgaO3k+r/5uNnxRM4aKmIyJSwWC+96z/XULljG8Z4BhkdG2L6/meh4mJWL5hNPpUlnchxu7SA8NszGJx6j9chBs2OLnJNSqRSbv/PvOAdHSBX4SRcVgJEj1t1NevkiLrjyCrMjipw1VMRkSlXW1FI+dymRVI7zZjZQU1XJ7IZqDMNg/cZNFPrzWDajntl1lRRH+/jlf/4HmUzG7Ngi55Qn/+U7dEXCJPJ9JEIheqNhDJcTdzzFVR++UXc5i7yFLMY5cEFOOBwmEAgQCoX0foenkcN7d/HKpo00VJczvaKMo+2dOFwuuru7mdc0jd7hMVKpNDXVlRTPOo/SikqzI4uc9WKxGF9YchGJoWHi2Qyu6kqy+w5jnTGdvDwfX9z+IjabzeyYIqe1U+kdmhET08xaeB6XvPNdlBQVUxzIg1yWquJCegdHONTSySULZ5Gf56MpmM+mXzzO+l/81OzIIme9hz79GbIOO/byEkKFfsZjMVyzGonmssz6i+tUwkTeYtq+QkxV2zCNeHkFzzzxX9izGbLpFEsWzmVebQXP7T5Ie0cndotBSb6XeSUuXn3uKRqWXkS+ZjZF3nKDfX20/+QX2NwuLK1dlM5uJAvkDh2jYvE8PnDX35odUeSsoxkxMZ3H4+GatTfSuOh8nG43DruDg60deJ0OUuk0LgvksJLncZMaG+IX3/s27c2HzY4tctb5xX1fxd47SDwSJVZRQubwcewt7cQqS1n1N7dpA1eRSaAiJqeNpvmLcDTM52BLO7NqKqgI+HjfZSspLS7glf2HeenVIyyqK6eurJBA/xGe+/mPdSG/yFvk0I5X2LR+PZmyIG6Ply6rgWdGA45p9bin1XP5B95ndkSRs5KKmJxWSsrKWfvX6+hIOegeHqNnLMKB1i6WLZiNy+Wia2CYsZFRdrd2M9TSTPOGn9LX2W52bJEzmmEYPPHpz1PY2UcasDjt1HT2k0lnSB85zg2f/iRWq35diEwG/cuS047dbmf+hZeSLaokm8lx6cKZ+L1ezquv5OebdjAUHmfVnAaqK0qZVeyjb+t6fvHoI9qRX+RN+pfPfp6Rvn7sDbWEvS76YjGMgJ+xsTGKr7mCZWsuNzuiyFlLC/5y2lp1xTsIh0Ls37mJfc3HIFfPZcsWUlcc4KVDrYyGxtmczVHqcZAXHWD/0z+hcukqikvLzI4ucsboaWuj499/RDbfh+1YGyVzGsm43Di7B8gG8rnm7jvMjihyVtOMmJzW/IEA8y99J0tWXUFpQT4ZLFgt4HQ46R8cwm2Fwjwv1YV5xIf7eOYHD3HklS1mxxY5IxiGwQMf+zip3n6SoRCx8iCpo604+4aI+/N429/exuILLjA7pshZTTNictqzWCzMOX8lA73dNP/scaLhcVbObiDPYaXC7+M/n9/C3MZ6FteUYlgd1Ibb2P7zFkrmL6dheqPZ8UVOW8/827+T6u7FyPdidzjotBo0zWgEqxWLx8mfaTZMZNJpZ305o2SzWQ6+/Dz+8X7ae/vA6SISiRIM5OOxGiQtdhwY9A+NEEskmfu2d9J03nKzY4ucdtoOH+E7b3sn6UiMuMOGq7Kc5PE2nHl5EImy9snHWXb5ZWbHFDkjaWd9OWvZbDbmX3I5Q0XTiBtWLmqsojRYyJL6csKJNM9s2k5dvpPqYj/vWDgdjmzjR/98P2Mjw2ZHFzltpNNpvvqx20gHi7BPr2U44CM8MorNMMgGi5j7kRtVwkSmiJYm5Yy0ZMUK4osWcXDzc3T1DxKLJqgLeLhu5WIODkUYHB6ldyxCfTDAjKI8xjY+wUDtPGYs0fUuIv/56c/hfnkHRkUZmaERCsuKsRiQTmVIWA2u/dTfmR1R5JyhGTE5Y3k8HuZddhXTz19NVUkB47E4FQU+0skEQ2MhcrkctQVe7FZwGBn2rH+Srf/5XUaHBs2OLmKax775IK/8+mkipcVEPC4yjfUEuvvxFBbg9Xr4xIP/TGmZ7jwWmSoqYnLGm7/8QkovuY49w0n2dA6xtK6MBTOmsaqpiheau9i6r5lwOMKcyiDLCiwMb/hPfvHo97TvmJxzjr26j/1f+Wdy6TRFA8NkMmnG4lGYMwOLzUrx2vewePUlZscUOafoYn05qxzfuxNL66v0jo7htEAkEsVm5EhjpTDfRyoew+Fwks5l8RWXUnbBGkqrqs2OLTLpRoaG+Oyaq/HtO0xuWi2W8SjJWAxLVTnu5laKLl/Fnb/6GTabzeyoImc8Xawv56zpC5cQvPTPODYcZUaxDydZltaXU53v5vnd+zEyaRZVBPA4bNTkxln/b19n/3NPkc1mzY4uMmkymQyP/NWteJMpRn0eIkaO4y4r7vIykt29xGZO44MP/bNKmIgJdLG+nHX8gQJuvOsfOLZnB8d2HyNlG2Z6UR4XLZpDjcfOc0d76RseJlpayIKqUmaNHePwf7USq5rHsktWmR1f5C1lGAZf/+hfE/r1euK1FRRF48TtDhqdLmxHjuNyOrj4b26jsr7e7Kgi5yQVMTlrNS5aRkFlLb07XqAgM0J3OEEqZ5BIJvE6HDhtVnJWK0cHxhjLWIj3bGB/uJf6Ve8kL19L2HJ2+O/7v0Lblm3kT6/D53ZzsCJB3fFWDIuNseICLrvzE/z5R242O6bIOUtLk3JWC5aWMf+q9zLUsJzm3iFyyTh+W4ar59VT5vPw1NbdpLJZLqj0U5rnoXG8k59++R84smWjLuaXM97T//pd9nzxq+SnM9iOtZHLpJmeX4DL4YLaKgovWs677/pbs2OKnNN0sb6cM2KxKMc3Pk37nh0EPG7yvW4SOQjYoT8cZTQcIeD1UOR1Myvg5JitAMe8FcxcsMjs6CKn7IUfPc4Pv3Q/QacLaybN8WiUmp4hclaw+3wEFy/kE0/+BI/HY3ZUkbPOqfQOLU3KOcPr9TH/He8h7MjH2b6feYUOtveFKfW4aO5PEorGmFWUR8Jmo288xkgyRqTlUTIdzdSvfie+vDyzT0HkpLz0k5/ym9vuIK84gOtYO5naKvIcDrI1FXjz8wm7HHz4Bw+rhImcBrQ0KeecCy+/ksU3/g1HAtM51jdIy9AY5Y4cfzG/AZ/HzVPbXyWSgQtLvVQFfDQNN/PTL36Swy/9RsuVctrb9JOf8uMv3g/T6sik0/RXl5MaG6N0JIS1uxdHeJw7/u0hSiorzY4qImhpUs5xA90dDLz8P/Q0H6Q8z0sEO4bFgteaIxpPEIolcDudBD0OZuU5OGorID1rKYtXatNLOf1s/NHjbLz9LjLlJTha2kmVldDmsFCXX0A0GiHidPI33/kX5l24wuyoImc17SMmcpJKq2qZd/1HMGYsY9xiZ3mZD5sVZuY7iKRztPUNUe2yYNjsDETiDPX3MrDhZxz4r+8xMtBvdnyRCc985994/P5/JFNfTWx0jN7yIPFEgoJkBsuBw+SFxnn/vf+gEiZymlEREwGuvH4ti27+Ow776zneN8T2vnEWFbi4Zk4NPq+HZ3YfZiCd5eJSD6X5XhqHj/HrL3+K/b/8MfF4zOz4co77yZf+kR133kOxzYHrYDNWp50RuwVPRRm+WJxofRXv/O6/8Lb3vNvsqCLyGlqaFHmN7mPNjG1Zz1jLIQo8LoZxQM6gyGWlPxwjlkzjcTkod1qYHXDTknFw2F/DVR/6CFar/m8jUyeTyfCjOz/J5meeocyXR3dPP6VeD9nwOO7KChzNxxnP97HgU3/HB//2E2bHFTlnaGlS5E9Q1TiDOR+8jfEZy+nO2Lkw6MHjdjEjz47N7qBzeJSAJQc2B13jcXpDEYq6j3D4X/8/ju/YbHZ8OUf09fTwzfe8j97v/DuVeX48h45SGMij32bBKCkm2tHJaEE+7/7eQyphIqcxzYiJ/AGxaJSW537Fwa0vUuxycEmphyOhJBVuO/+++xiLKop5W3UBu6Mwy5HmpaEkY4adC9f+FbXzFpodX85SbQcP8dhNH6Wrt4fSkhJCkQhelwtLSzv2WY04DjQzXlPB0rv/lvd85K/MjityzjmV3qEiJnIS+jvbGXrpaWpG29jVM4LFm4cjl6XWa+V4zKBraJSagJf5PgtdIxHKAz6eirq4/KZbqGqaZXZ8OYv85F//lT1f+SYFvf3Ep9fjPNbKsepS3HYHhekscZuFwpyFdz3yMPMuWml2XJFzkpYmRd5iZTV1zF17CyMXX08vLlYEbHjcTkqdVuwWiKdSpA0LQ7EUw8kMx5NWGh053D/5Z/b9+9fZs+Vls09BznDZbJb//uzn2Xv/A7ijEWKzmxjMphlrqmd6Zx++nIGzq4dIno8/+89HVMJEzhDaWV/kFNQvOI+6+Ytp3vQbjj/zC0ZsOS4pduKtrWS+O8ODu7opzvNwvcdgZxIMoL/5ILFXd+E8spPCS95JxbRGs09DzjA9rW38y20fx7fnAP7REP1eF8HBYaIuG0GPl+GSYvL9+fhXXcjHvv8wpVVVZkcWkZOkpUmRNymRSNDy/K/xHd5G8+AYTqeLgnSUmfkuDiVtvHS8i/MrCllW6GLTcJJ6Z45n+mJcfOFKCi55J5WNM80+BTkDvPyT/2bbpz5HNC+PzPFWrNPraQ2HqQpFSKZSFGRzWA2IrVnFpx/7IR6v1+zIIuc8vdekyBRwu93MecefE17xNmKPPMTcVD9jURtYIJTJ0VQWxOF28NJQnM5QhLLKIDP9aWZ276fj3/fyKAVcsvbD1M5bYPapyGlobGiIX/3D59j8wosUZrMYkQgF2RzjhkGBy4m9pgrXwBAxt4vzP/qXvOvuu7BYLGbHFpFTpBkxkbfIcF8PL//wYSwDXbw96GBn3MESZ4Jnh9N0DI3SFPRDJk19II/eaAKHN4+ZuSjb3WV4F1/IyqvepV+kAsBP/uVfaPnOv5PX0s5QQy3+1k5eLSvCYbEyu2eA+MxGXEeOEaooZc6623nf7beaHVlE/g/dNfkaKmIylfrbWxne+Gv27dxBRZ6HC7xZXh5JsjLg4Jv7u6kO5PHuCh978WKJhPG7nMRjcVxVdYzPOI8l17wHm81m9mmICQY6O/mfz36BQy+9hCOdxRXwk7HZsORyZLq7STldeMtKGRwfp6lhGtd9+5+padI1hyKnGxWx11AREzMce3UPqVeep6zrINuHYzhcHtKhMS4vz2Nfys7Th9tZ21RCjcvG4biBw2Fnz8A4CyqDcN4lVK5+B4HCIrNPQ6ZAJpPhN99+iN/88DHye/uJJpNUxhIkAvnsdjuYa7GT3zdApLYGZ08v/g9ez00P/BMul8vs6CLyBk6L7Sva2tq4+eabaWhowOPxMH36dD73uc+RSqVOGNfR0cE111yDz+cjGAzyiU984nVj9u3bx6pVq/B4PFRVVfGFL3yBc6A/yhmuccEi5nz4b0muvYtBXymLPDmcdguRdJrRdI6LZtQyjpNNcRvb+kPYYhFmF3ppSocYeP6XrL/nrzn0vX+mu/mQ2acik+jJRx7hny+9gvZPfZ6gYRBIprCWlXC0ooRkNst5/gKcvQOMNE0j7Pdx6X8+wsf+5VsqYSJniUm7WP/w4cPkcjm+853v0NjYyP79+/nIRz5CNBrln/7pn4Df7otz1VVXUVJSwqZNmxgeHubGG2/EMAy+9a1vAb9tlVdccQWXXnopO3bsoLm5mZtuugmfz8edd945WfFF3jKVjTP50H1fp7flGIM/+A7bw/1clp9hd87L9Gyc/oyDPLuNXoef0NgIvW4vy5xpjrrzaTr0Es/v2sJGm4vzrrmexkuvxG7XPTZng6O7drP1qw9w6OWXybdaCdfXYLXayATyceZyOLCSLirEHonitlqZvuQ8rvrS5ykuLzc7uoi8haZ0afKrX/0qDz30EC0tLQA8/fTTXH311XR2dlJZWQnA448/zk033cTAwAB+v5+HHnqIe+65h/7+/on/Af7jP/4j3/rWt+jq6nrDi5uTySTJZHLi43A4TE1NjZYm5bQw2NXB0Au/5sDWTRTaLKzKM9ifdlCbifCjzjCLayuwRELkfAESqRTLiLIzZrDCZ+X7owZvW/N2Ci9+O+UN08w+FXkT2g8fZvs/P8grW7YQiMaJjYWoSySJut3s9HuZFYkRjCUIVVXg7eyhZcY03v33f8dF773e7OgicpJOi6XJNxIKhSgq+n/XvGzZsoV58+ZNlDCAK6+8kmQyyc6dOyfGrFq16oRp+CuvvJKenh7a2tre8Pvcf//9BAKBiUdNTc3knJDIm1BSXcvsD/41q//hn6i88DLaLR46wjGOW32sKfOx2Igw3WPlxeY2LOk0ViCJla05NzMtaZp2PE38y3/Df3z8Lzn09M+Jx+Nmn5KchPZDh/jaB2/gv/78vUQf+zElNgeFI2PEiwtor6kg5nSwuLAI7HZGp9WTdrkIfvgGPrP+KZUwkbPYlBWx48eP861vfYtbbrll4lhfXx9lZWUnjCssLMTpdNLX1/d7x/zu49+Nea177rmHUCg08ejs7HwrT0XkLREsr2D29X9J5ae+iW/ZKnz5+eRbDfaGkhxOO1jVWMMqb5btcQv7B8coiYdxZpL0ZaA952C2LU3jkw/zwq3v45efvZNjW1/StZOnoSPbd/CP17+P9ZeuIbVrD86+QQan1ZPJZYlWlWNPpDAyWXDYIZujODSOv7CAhXf+De/71jcoLCkx+xREZBKd8sUm9957L5///Of/4JgdO3awdOnSiY97enp4+9vfzl/8xV/wV3/1VyeMfaOlRcMwTjj+2jG/+2Xz+/ZccrlcupBVzhger5fLbr4NwzA4tHEDx3/+X1xljLAvbeFw1qAiz8OFvjzKMmFeTVnZ1RXmw+Vujhlu9iasNDlhfKiLyoe/wI8eymPm8pWUXnwFdfMXmX1q56xcLsfPv/Mdkr95geTzG4kXBBiqKMeSTBBIpxlKpTmYjLI8HKc+FifqceOxWGkvsXLFl7/I2275qLYwETlHnHIR+/jHP8773ve+Pzimvr5+4s89PT1ceumlrFixgocffviEceXl5Wzbtu2EY6Ojo6TT6YlZr/Ly8tfNfA0MDAC8bqZM5ExmsViYs3oNc1avobv5EP2PfR9LfxsrifOK3U8YNzM8CRZ6/HTa7Wxs66XR62Chw8oeq4/9jgDnR4fo2/Akvpef5jv4ufiyK8hbdjG187V7/1RobW7m0M+eYOAXv2QolSZnGFRmstgzGapa2tgYLCRcWUpjRxeLZjcRyQ3jLCokkojT+P73svaOdZoBEznHnHIRCwaDBIPBkxrb3d3NpZdeypIlS/j+97+P1XriSuiKFSv40pe+RG9vLxUVFQCsX78el8vFkiVLJsZ86lOfIpVK4XQ6J8ZUVlaeUPhEziZVM2Zz/b1fITIe5tjzz9C+/te4ohEW+2wcyLkJpzIs8Ls5z5nhVWs+G1s7Od8F9QE37VYnO+wepsXGmfbcf9O94Wd81xrgwksuwrloOdOWrXjdv0V58zKZDC//108Y2fAbjm3ejCsvH29bG96mJgoPHeF4XQ2DsRi2slJmuBz4MgZDwUIcQCASw3HVxaz+yF+xeOUKs09FREwwaXdN9vT0sGrVKmpra/mP//iPE6bZy//39utsNsuiRYsoKyvjq1/9KiMjI9x0001cd911E9tXhEIhZs6cydve9jY+9alPcfToUW666SY++9nPnvT2FdrQVc4GbXteIb7tOba+tIlrvBmSqTTJdJruvCDRZIb5Rox2l5/1xzr4ULGL4VSWAo+Lbpsbj8fHgvEBNuNlxOZgzsLFpBpnU71yNSX/+58gOXm5XI6NP/8FiS3b6F+/gaOZNDMicRJ5Pop6ehmqraE7k6IsL49oby9DThdNmSzhgJ+ytk7GAn6iy5dy/Wc+xfQFmq0UOducFjvrP/LII/zlX/7lGz73f79lR0cHt956K8899xwej4e1a9fyT/904o7R+/bt47bbbmP79u0UFhZyyy238NnPfvak35dPRUzOJtHIOJ0vrCe7axMbdu7lQwELe3Cz1Iix1RbA43BQGRvliMXNvt4h3pVvJR4oYjyRosFI05VXxLyxXp63+UmMhZgzby5HC8qYe+nl1F9w4cTMs5wonU7zPz96jNyr+wi9tIlBw8CWSlPW0UXI6yHp8TDi81BqQMrlojceoyIaxzc6RsTIYQn46SkqYvnKFSz+648yTQVM5Kx1WhSx04mKmJyt+ttaGXn5WV555leUWGF1bpy9vhJqx4c5hBO/00FxPMwvxlKUejw0pmPECoPE0lkujg2z3VVAQTxCWzLHhdYUI548Xs4vZeXFl2CbMZva81fg9XrNPk3TdBw9SvP/rGff8y9QcvAwo243aauF+tZ2uuvrCPb0sSuQx7R4CqOyjIMjI8y32ijsH2SkrhrXWJhjDhtVOah775+z6MMfpqpxutmnJSKTTEXsNVTE5GxnGAbte3cR37GJg1teoiAR5ULi7PEFMcIhSi0GLeEY81zwvZE0K6rLyYRDJF1eam0wLTJCs93HuNODIxphXnKco1YnB50+zqupIlffSKcnn7mXXUHdnLln5TVmhmFwdN8+RnftZmzPXjbv2MGC5uOEAn4cVhuJRByqqig53EzL9HqGRkepD5ZwODRK0OFkRlcvQ7NmYLS1Q0mQXDJFXlkpeWsu54rb/hp/YaHZpygiU0RF7DVUxORcYhgGx3dsI7VrC1s2vcjK9Dj1RpLN9nzsFiuWoV6mu5ykMll+mbSxrKKURCbL7v5hrrEm8VthWzxLWUkpY5kMK6JjbPWXYrdamDfQxfP+UhxFQWbMmcOQv4CSufOpOW8p/kDA7FM/aYZh0N3SwsCevex84UVKR4aJHzpCCzkqh0axxOJgs5CoqcZptVJyvI3hijKac1nqAwEGRscIGzmWDQzTU19HsLub3uoK3HYHvr5BjFUXUn7F5bz9hg+e9CUUInL2UBF7DRUxOVcZhkH7q3uI7dzMKy++wOLhLqY7rbySdWB4fPjjERqSMbp8BRxMZmkgS9SXzwvt3Sx3WSnMpBnxBZgRG2MoWI53sB/DF2DM62NeXycvBUqwj4/TkE3xdF4xFzfU4a6qpt1iY/r8+VhLyylubKKkrMyUQhIKhWjZswcGBmjfd4BYTy+BoSGO9vfjDIWZOThMZ2MDqWyOqpZWWnxe/EVF9MXjLBgaocNp53Agn9mBQiLDw4w47TQOjZLy+wkODtEyvR6v3YG/pY3s0sVklyzmuk/cTlFp6ZSfq4icPlTEXkNFTOS3Bru7GNr6Etv+5xmWhvqoiIzxbNJCrdPBOBZWZGNs9BWT73CwYKibTVYPrcks80uL6BgcZjSZ4QZLkh0FpdhtVuYP9vJqWQ2W0Bg1yRiD3jyCiQS7c1bmxCLYLAbP5hWy1MiSKyxij8PFBbU15PL9tMeTzJg+Dbw++mNxqmtqSFktZK028gJ+Etksbpcbq9VKNJHAY7djpDOMjAwTcLrIxeN0dLRT7vaSGx9n39GjNNodJIaG2NPfz8zRENFIhP7CAOd393K0poqUYdDU0U1n4zTyxkLExsaw5ufjHh3lYFkJDaEwRlkpO8LjTHc6KOwboKu8jJpcjvGBQYqwEKmtJpzLUtXVS3bhAsJzZ/COW26hfs4cs3+8InKaUBF7DRUxkdfLZrO0bNvMvvVP0xQaYuTgq/RYnFyejdLiK6QiGuKo3Y09z8+iwS425gVJRaPUWC3sTOVw2q1Uu90cGQ0xy+VgcXycvWXVRJJplg/3scNfhOFwUdnbhcXlYbCwCG90nLKxMfaXlmOx2FjU18ORsnKSVhtzOzvZVVqG12ajqbubg9XVpMYjzB8ZZXN5OdOiMUpDIbaVl1E8PEZ1NMb20mJmxZLYkknaXE7ycjkibheBsRCOQAHRwgJKW1tpLQni9fmoPNbCkfpaskPDFGWzbHO7mFtYBIbBgdAYC1JpKsaj9NbXEbbkqGnroMtmx+320Ovz0BgK4z5/KeON01l904dUvkTkDamIvYaKmMgfF4vFOPz8s7g6WxnYvZMjbR38RWKU7Z4AFouVBZERjpZWUT/Qx1GnG5fbw+zhfp7xFeIcHaGqsIAXwjEWlQSxArsGhqnKZalJxGgvLac+HGJaKslvfH5mWoHRURIeL2GrnaDFIDoyhrMoyGAuS1UsxpDFiqW4GFdPLx6Xk57iYkrGwljGQozU1xENR5g7MMjhhjrclt/eyXisrgbDaqGhpZ1Xy0oYSSZptNk4Aljtdqp9Pg6NjOA1cpw3PMZA03TimSwz2zpoqa8hE49TMDhM1u0hEIvxSlkJM/PzKV6+jOT0aVzy/vdReJIbWovIuUtF7DVUxEROXTabpXXXTjq3bSFxvJnKkUGO93Rjszu5ODTIzmAl8USCJWND7C+ppCo8ynAqjdXtpTg0wt68IupCIwQMgx9gY01BAFweXhwdZUVpCQZWXu7rY1lhIZl0mm2jId4W8GNYLLwcHmeFx0MyHmdLJsNqq5Ww1cphA5a6vUQNg/2JOMsKihjNpDk6HmJBcZChWIzueJxpwEAiScCfz8LeAY7UVGG126g/1kbnjEYyoTHKR0OMVpRT2N3L8eICnKEwRYbBnrpaLl6ylMIliyhdtpRpc+ea/aMQkTOMithrqIiJvDVCoRA9r+4h19HG4R078IwOUzrYT1c6g9UwWDY2xN7yapLpLEv6e9hVUo47m6Oyr5uBwiCxTJaCZIJ4NoPf6WJv1uD8eJwRq5XWPD/LhoeIen1st9tZPTZGv9XKkeJiVg0MMuz1csDrY2VvP835eSTz8pjd1UNnZTljuRyz+gY4Vl9LQTSGZWSU8Wn1ODs6cbtdjBcVUt7aQXNVOblonFkjo7xYVU6dN4/KuXMYKQgw65KLqV+5gsLiYrNfZhE5w6mIvYaKmMjk6uzoINJyjFxfLwf37KY4GiNvPMThgUEsIyOcHwnxankV/nSGpqEB9lVWk8xkWdzbzeGKKtIWK3M62tkdLMHp8dLY2kpHeTkJt5tpbe0cKQhgDxRQc7SFgbJSkj4f9cdbOVhRhtXpZEZrOy11NdgzWWp7ejlYX0tmaISSVJLmqkoq/PlUTZvOgNtF3YIFFMxopOG88/B4PGa/dCJyFlIRew0VMRHzZDIZ+js7adu3j4CRIxcao+XwEQptNryZNK92dlFuGAQwOBIO40mmKLdY2ZdOU5rNUoKF43Y7jlSaWrebgxiU2Z2UBAK05zLk5+VRUVZOWzxKTW09/qpKYg4HJdOnUTtr1glvlyYiMhVUxF5DRUxERESmyqn0jrPvfUpEREREzhAqYiIiIiImURETERERMYmKmIiIiIhJVMRERERETKIiJiIiImISFTERERERk6iIiYiIiJhERUxERETEJCpiIiIiIiZRERMRERExiYqYiIiIiElUxERERERMoiImIiIiYhIVMRERERGTqIiJiIiImERFTERERMQkKmIiIiIiJlERExERETGJipiIiIiISVTEREREREyiIiYiIiJiEhUxEREREZOoiImIiIiYREVMRERExCQqYiIiIiImURETERERMYmKmIiIiIhJVMRERERETKIiJiIiImISFTERERERk6iIiYiIiJhERUxERETEJCpiIiIiIiZRERMRERExiYqYiIiIiElUxERERERMMiVFLJlMsmjRIiwWC3v27DnhuY6ODq655hp8Ph/BYJBPfOITpFKpE8bs27ePVatW4fF4qKqq4gtf+AKGYUxFdBEREZFJY5+Kb3L33XdTWVnJ3r17TziezWa56qqrKCkpYdOmTQwPD3PjjTdiGAbf+ta3AAiHw1xxxRVceuml7Nixg+bmZm666SZ8Ph933nnnVMQXERERmRSTXsSefvpp1q9fz09/+lOefvrpE55bv349Bw8epLOzk8rKSgC+9rWvcdNNN/GlL30Jv9/Pj370IxKJBI888ggul4t58+bR3NzMAw88wB133IHFYnnd90wmkySTyYmPQ6EQ8NtSJyIiIjKZftc3Tmr1zphEfX19RlVVlbFjxw6jtbXVAIzdu3dPPP+Zz3zGWLBgwQmfMzIyYgDGc889ZxiGYdxwww3Gtddee8KYXbt2GYDR0tLyht/3c5/7nAHooYceeuihhx56mPbo7Oz8o11p0mbEDMPgpptu4pZbbmHp0qW0tbW9bkxfXx9lZWUnHCssLMTpdNLX1zcxpr6+/oQxv/ucvr4+GhoaXvd177nnHu64446Jj3O5HCMjIxQXF7/hDNq5LBwOU1NTQ2dnJ36/3+w4pyW9RidHr9PJ0et0cvQ6/XF6jU6OGa+TYRiMj49PrPb9IadcxO69914+//nP/8ExO3bsYPPmzYTDYe65554/OPaNipFhGCccf+0Y43+n+n5fqXK5XLhcrhOOFRQU/MEc5zq/369/yH+EXqOTo9fp5Oh1Ojl6nf44vUYnZ6pfp0AgcFLjTrmIffzjH+d973vfHxxTX1/PF7/4RbZu3fq6QrR06VI+8IEP8IMf/IDy8nK2bdt2wvOjo6Ok0+mJWa/y8vKJ2bHfGRgYAHjdbJqIiIjImeSUi1gwGCQYDP7Rcd/85jf54he/OPFxT08PV155JT/+8Y9Zvnw5ACtWrOBLX/oSvb29VFRUAL+9gN/lcrFkyZKJMZ/61KdIpVI4nc6JMZWVla9bshQRERE5k0zaPmK1tbXMmzdv4jFjxgwApk+fTnV1NQBr1qxhzpw53HDDDezevZvf/OY33HXXXXzkIx+ZmD5cu3YtLpeLm266if379/PEE09w3333/d47JuXUuFwuPve5z71u5lL+H71GJ0ev08nR63Ry9Dr9cXqNTs7p/jpZDGNqdkZta2ujoaGB3bt3s2jRoonjHR0d3HrrrTz33HN4PB7Wrl3LP/3TP53wgu3bt4/bbruN7du3U1hYyC233MJnP/tZFTERERE5o01ZERMRERGRE+m9JkVERERMoiImIiIiYhIVMRERERGTqIiJiIiImERF7Bz27W9/m4aGBtxuN0uWLOGll14yO9KUuf/++1m2bBn5+fmUlpZy3XXXceTIkRPG3HTTTVgslhMeF1xwwQljkskkt99+O8FgEJ/Px7XXXktXV9dUnsqkuvfee1/3GpSXl088bxgG9957L5WVlXg8HlavXs2BA/9/e/cb0lTbxwH8azElRFZma1vSEEkEtySVSikNoeFoGQimKWZEgqGlZKARIkEvpBe+spt6IVIU2BuVwDCUpiFqipvln/4sXBrlnxI103RTf8+Lm87T8V883dPz3Du/Dwzmda4dz/Xld43Lze3qE53D0zMC/v4S6+U5eXl5IScnB4A8a+n58+c4efIktFotvLy8UFtbKzrurtqZmJhARkYGlEollEolMjIyMDk5ucGjc5/1cnK5XCgsLITBYICvry+0Wi3Onj2Lz58/i85x7NixFfW1/IvXPTknwH1zTIqceCEmU48ePUJ+fj6uX78Om82Go0ePwmQyYWhoSOpL2xTNzc3IyclBe3s7GhoasLCwAKPRiJmZGVG/hIQEDA8PC7cnT56Ijufn56OmpgZVVVVoaWnB9+/fYTabsbi4uJnD2VBhYWGiDHp6eoRjt27dQllZGcrLy9HZ2Qm1Wo3jx49jenpa6COHjDo7O0UZNTQ0AACSk5OFPnKrpZmZGYSHh6O8vHzV4+6qnbS0NHR3d6O+vh719fXo7u5GRkbGho/PXdbLaXZ2FlarFcXFxbBaraiursa7d++QmJi4om9WVpaovu7evSs67sk5/eSOOSZJTr/dFpx5pIMHD1J2draoLTQ0lIqKiiS6ImmNjY0RAGpubhbaMjMz6dSpU2s+ZnJykhQKBVVVVQltnz59oi1btlB9ff1GXu6mKSkpofDw8FWPLS0tkVqtptLSUqFtbm6OlEol3blzh4jkkdFq8vLyKDg4mJaWloiIawkA1dTUCD+7q3b6+/sJALW3twt92traCAC9efNmg0flfstzWk1HRwcBoMHBQaEtLi6O8vLy1nyMHHJyxxyTKid+RUyGnE4nurq6YDQaRe1GoxGtra0SXZW0pqamAAD+/v6i9qamJqhUKoSEhCArK0vY5xQAurq64HK5RDlqtVro9XqPytFut0Or1SIoKAipqakYGBgAADgcDoyMjIjG7+Pjg7i4OGH8csnoV06nEw8ePMD58+dFXzrNtfRf7qqdtrY2KJVKYds8ADh8+DCUSqVH5gb8/Vzl5eWF7du3i9ofPnyIgIAAhIWF4erVq6JXFuWS0z+dY1Ll9D/vNcn+/b5+/YrFxcUVm6bv3r17xQbrckBEuHLlCo4cOQK9Xi+0m0wmJCcnQ6fTweFwoLi4GPHx8ejq6oKPjw9GRkbg7e2NHTt2iM7nSTkeOnQI9+/fR0hICEZHR3Hz5k3ExMSgr69PGONqdTQ4OAgAsshoudraWkxOTuLcuXNCG9eSmLtqZ2RkBCqVasX5VSqVR+Y2NzeHoqIipKWlCdsAAkB6ejqCgoKgVqvR29uLa9eu4eXLl8Jb5HLIyR1zTKqceCEmY8u3iCIiWW4blZubi1evXqGlpUXUnpKSItzX6/WIioqCTqdDXV0dkpKS1jyfJ+VoMpmE+waDAdHR0QgODsa9e/eEf4T9kzrypIyWq6iogMlkglarFdq4llbnjtpZrb8n5uZyuZCamoqlpSX89ddfomNZWVnCfb1ej3379iEqKgpWqxUREREAPD8nd80xKXLityZlKCAgAFu3bl2xwh8bG1vxF6qnu3TpEh4/fgyLxSJsRr8WjUYDnU4Hu90OAFCr1XA6nZiYmBD18+QcfX19YTAYYLfbhU9PrldHcstocHAQjY2NuHDhwrr95F5L7qodtVqN0dHRFef/8uWLR+Xmcrlw+vRpOBwONDQ0iF4NW01ERAQUCoWovuSQ06/+ZI5JlRMvxGTI29sbkZGRwsvWPzU0NCAmJkaiq9pcRITc3FxUV1fj2bNnCAoK+u1jxsfH8fHjR2g0GgBAZGQkFAqFKMfh4WH09vZ6bI7z8/N4/fo1NBqN8FbIr+N3Op1obm4Wxi+3jCorK6FSqXDixIl1+8m9ltxVO9HR0ZiamkJHR4fQ58WLF5iamvKY3H4uwux2OxobG7Fz587fPqavrw8ul0uoLznktNyfzDHJctqwjwGw/2tVVVWkUCiooqKC+vv7KT8/n3x9fenDhw9SX9qmuHjxIimVSmpqaqLh4WHhNjs7S0RE09PTVFBQQK2treRwOMhisVB0dDTt2bOHvn37JpwnOzubAgMDqbGxkaxWK8XHx1N4eDgtLCxINTS3KigooKamJhoYGKD29nYym83k5+cn1ElpaSkplUqqrq6mnp4eOnPmDGk0Glll9NPi4iLt3buXCgsLRe1yraXp6Wmy2Wxks9kIAJWVlZHNZhM+7eeu2klISKD9+/dTW1sbtbW1kcFgILPZvOnj/VPr5eRyuSgxMZECAwOpu7tb9Fw1Pz9PRETv37+nGzduUGdnJzkcDqqrq6PQ0FA6cOCAbHJy5xyTIideiMnY7du3SafTkbe3N0VERIi+usHTAVj1VllZSUREs7OzZDQaadeuXaRQKGjv3r2UmZlJQ0NDovP8+PGDcnNzyd/fn7Zt20Zms3lFn3+zlJQU0mg0pFAoSKvVUlJSEvX19QnHl5aWqKSkhNRqNfn4+FBsbCz19PSIzuHpGf309OlTAkBv374Vtcu1liwWy6pzLDMzk4jcVzvj4+OUnp5Ofn5+5OfnR+np6TQxMbFJo/zn1svJ4XCs+VxlsViIiGhoaIhiY2PJ39+fvL29KTg4mC5fvkzj4+Oi3+PJOblzjkmRkxcR0ca93sYYY4wxxtbC/yPGGGOMMSYRXogxxhhjjEmEF2KMMcYYYxLhhRhjjDHGmER4IcYYY4wxJhFeiDHGGGOMSYQXYowxxhhjEuGFGGOMMcaYRHghxhhjjDEmEV6IMcYYY4xJhBdijDHGGGMS+Q+7CrQhY9Wv2wAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from matplotlib import animation, rc\n", "\n", "plt.rcParams[\"animation.html\"] = \"jshtml\"\n", "\n", "u_plot = Function(V)\n", "\n", "fig = plt.figure(figsize=(7,7))\n", "ax = fig.gca()\n", "\n", "ax.set_xlim([-L/5,L+L/5])\n", "ax.set_ylim([-L/5,L+L/5])\n", "\n", "def drawframe(n):\n", " fig.clf()\n", " ax = fig.gca()\n", " ax.set_xlim([0,L])\n", " ax.set_xlim([-L/5,L+L/3])\n", " ax.set_ylim([-L/3,L+L/10])\n", " u_plot = Function(V)\n", " u_plot.vector()[:] = disp[n][:]\n", " p = plot(u_plot, mode = 'displacement', cmap = 'Reds', edgecolor= 'k', linewidth = 0.1)\n", " return p,\n", "# blit=True re-draws only the parts that have changed.\n", "anim = animation.FuncAnimation(fig, drawframe, frames=len(lmbda), interval=40, blit=True)\n", "anim" ] } ], "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": "3.10.11" }, "orig_nbformat": 4, "vscode": { "interpreter": { "hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1" } } }, "nbformat": 4, "nbformat_minor": 2 }