Linstedt_Poincare.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [],
   "source": [
    "#%% Program 05d: The Lindstedt-Poincare Method\n",
    "# Deriving the order epsilon equations.\n",
    "# See Example 9.\n",
    "\n",
    "#from sympy import collect, expand, Function, Symbol\n",
    "import sympy as sp\n",
    "import scipy as sc\n",
    "from scipy.integrate import solve_ivp\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pprint\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - eps^{7} \\operatorname{x_{2}}^{3}{\\left(\\tau \\right)} + eps^{6} w_{2}^{2} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{2}}{\\left(\\tau \\right)} - 3 eps^{6} \\operatorname{x_{1}}{\\left(\\tau \\right)} \\operatorname{x_{2}}^{2}{\\left(\\tau \\right)} + 2 eps^{5} w_{1} w_{2} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{2}}{\\left(\\tau \\right)} + eps^{5} w_{2}^{2} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{1}}{\\left(\\tau \\right)} - 3 eps^{5} \\operatorname{x_{0}}{\\left(\\tau \\right)} \\operatorname{x_{2}}^{2}{\\left(\\tau \\right)} - 3 eps^{5} \\operatorname{x_{1}}^{2}{\\left(\\tau \\right)} \\operatorname{x_{2}}{\\left(\\tau \\right)} + eps^{4} w_{1}^{2} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{2}}{\\left(\\tau \\right)} + 2 eps^{4} w_{1} w_{2} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{1}}{\\left(\\tau \\right)} + eps^{4} w_{2}^{2} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{0}}{\\left(\\tau \\right)} + 2 eps^{4} w_{2} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{2}}{\\left(\\tau \\right)} - 6 eps^{4} \\operatorname{x_{0}}{\\left(\\tau \\right)} \\operatorname{x_{1}}{\\left(\\tau \\right)} \\operatorname{x_{2}}{\\left(\\tau \\right)} - eps^{4} \\operatorname{x_{1}}^{3}{\\left(\\tau \\right)} + eps^{3} w_{1}^{2} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{1}}{\\left(\\tau \\right)} + 2 eps^{3} w_{1} w_{2} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{0}}{\\left(\\tau \\right)} + 2 eps^{3} w_{1} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{2}}{\\left(\\tau \\right)} + 2 eps^{3} w_{2} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{1}}{\\left(\\tau \\right)} - 3 eps^{3} \\operatorname{x_{0}}^{2}{\\left(\\tau \\right)} \\operatorname{x_{2}}{\\left(\\tau \\right)} - 3 eps^{3} \\operatorname{x_{0}}{\\left(\\tau \\right)} \\operatorname{x_{1}}^{2}{\\left(\\tau \\right)} + eps^{2} w_{1}^{2} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{0}}{\\left(\\tau \\right)} + 2 eps^{2} w_{1} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{1}}{\\left(\\tau \\right)} + 2 eps^{2} w_{2} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{0}}{\\left(\\tau \\right)} - 3 eps^{2} \\operatorname{x_{0}}^{2}{\\left(\\tau \\right)} \\operatorname{x_{1}}{\\left(\\tau \\right)} + eps^{2} \\operatorname{x_{2}}{\\left(\\tau \\right)} + eps^{2} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{2}}{\\left(\\tau \\right)} + 2 eps w_{1} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{0}}{\\left(\\tau \\right)} - eps \\operatorname{x_{0}}^{3}{\\left(\\tau \\right)} + eps \\operatorname{x_{1}}{\\left(\\tau \\right)} + eps \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{1}}{\\left(\\tau \\right)} + \\operatorname{x_{0}}{\\left(\\tau \\right)} + \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{0}}{\\left(\\tau \\right)}$"
      ],
      "text/plain": [
       "-eps**7*x2(tau)**3 + eps**6*w2**2*Derivative(x2(tau), (tau, 2)) - 3*eps**6*x1(tau)*x2(tau)**2 + 2*eps**5*w1*w2*Derivative(x2(tau), (tau, 2)) + eps**5*w2**2*Derivative(x1(tau), (tau, 2)) - 3*eps**5*x0(tau)*x2(tau)**2 - 3*eps**5*x1(tau)**2*x2(tau) + eps**4*w1**2*Derivative(x2(tau), (tau, 2)) + 2*eps**4*w1*w2*Derivative(x1(tau), (tau, 2)) + eps**4*w2**2*Derivative(x0(tau), (tau, 2)) + 2*eps**4*w2*Derivative(x2(tau), (tau, 2)) - 6*eps**4*x0(tau)*x1(tau)*x2(tau) - eps**4*x1(tau)**3 + eps**3*w1**2*Derivative(x1(tau), (tau, 2)) + 2*eps**3*w1*w2*Derivative(x0(tau), (tau, 2)) + 2*eps**3*w1*Derivative(x2(tau), (tau, 2)) + 2*eps**3*w2*Derivative(x1(tau), (tau, 2)) - 3*eps**3*x0(tau)**2*x2(tau) - 3*eps**3*x0(tau)*x1(tau)**2 + eps**2*w1**2*Derivative(x0(tau), (tau, 2)) + 2*eps**2*w1*Derivative(x1(tau), (tau, 2)) + 2*eps**2*w2*Derivative(x0(tau), (tau, 2)) - 3*eps**2*x0(tau)**2*x1(tau) + eps**2*x2(tau) + eps**2*Derivative(x2(tau), (tau, 2)) + 2*eps*w1*Derivative(x0(tau), (tau, 2)) - eps*x0(tau)**3 + eps*x1(tau) + eps*Derivative(x1(tau), (tau, 2)) + x0(tau) + Derivative(x0(tau), (tau, 2))"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "x0 = sp.Function('x0')\n",
    "x1 = sp.Function('x1')\n",
    "x2 = sp.Function('x2')\n",
    "x = sp.Function('x')\n",
    "tau = sp.Symbol('tau')\n",
    "eps = sp.Symbol('eps')\n",
    "w1 = sp.Symbol('w1')\n",
    "w2 = sp.Symbol('w2')\n",
    "\n",
    "x = x0(tau) + eps * x1(tau) + eps ** 2 * x2(tau)\n",
    "exp1 = (1 + eps * w1 + eps ** 2 * w2) ** 2 * x.diff(tau, tau) + x - eps * x **3\n",
    "exp1= sp.expand(exp1)\n",
    "exp1\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to be careful with this expansion, we only used to second order in $\\epsilon$ for the expansion in $x$ and $\\tau$. "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Zeroth order LIndstedt Poincare."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Collect the coefficients for $\\epsilon^0=O(1)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          2       \n",
      "         d        \n",
      "x₀(τ) + ───(x₀(τ))\n",
      "          2       \n",
      "        dτ        \n"
     ]
    }
   ],
   "source": [
    "\n",
    "#%% Zeroth order\n",
    "eq0 = exp1.coeff(eps,0)\n",
    "sp.pprint(eq0)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and solve the equation with the initial conditions, "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x₀(τ) = cos(τ)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "sol0=sp.solvers.ode.dsolve(eq0,ics={x0(0): 1, x0(tau).diff(tau).subs(tau, 0): 0})\n",
    "sp.pprint(sol0)\n",
    "\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to assure that the $O(\\epsilon)$ is not secular, so we need to look at the $O(\\epsilon)$ problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 w_{1} \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{0}}{\\left(\\tau \\right)} - \\operatorname{x_{0}}^{3}{\\left(\\tau \\right)} + \\operatorname{x_{1}}{\\left(\\tau \\right)} + \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{1}}{\\left(\\tau \\right)}$"
      ],
      "text/plain": [
       "2*w1*Derivative(x0(tau), (tau, 2)) - x0(tau)**3 + x1(tau) + Derivative(x1(tau), (tau, 2))"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "# %% First order\n",
    "eq1 = exp1.coeff(eps,1)\n",
    "eq1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - w_{1} e^{i \\tau} - w_{1} e^{- i \\tau} + \\operatorname{x_{1}}{\\left(\\tau \\right)} - \\frac{e^{3 i \\tau}}{8} - \\frac{3 e^{i \\tau}}{8} + \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{1}}{\\left(\\tau \\right)} - \\frac{3 e^{- i \\tau}}{8} - \\frac{e^{- 3 i \\tau}}{8}$"
      ],
      "text/plain": [
       "-w1*exp(I*tau) - w1*exp(-I*tau) + x1(tau) - exp(3*I*tau)/8 - 3*exp(I*tau)/8 + Derivative(x1(tau), (tau, 2)) - 3*exp(-I*tau)/8 - exp(-3*I*tau)/8"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "prob1=eq1.subs(x0(tau),sol0.rhs)\n",
    "prob1=prob1.simplify().rewrite(sp.exp).expand()\n",
    "prob1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - w_{1} - \\frac{3}{8}$"
      ],
      "text/plain": [
       "-w1 - 3/8"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "#%%\n",
    "secular= prob1.simplify().rewrite(sp.exp).expand().coeff(sp.exp(sp.I*tau))\n",
    "secular"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-3/8]"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "#sp.pprint(secular)\n",
    "sw1=sp.solve(secular,w1)\n",
    "\n",
    "sw1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle t \\left(1 - \\frac{3 eps}{8}\\right)$"
      ],
      "text/plain": [
       "t*(1 - 3*eps/8)"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tau_exp=t*(1+eps*sw1[0])\n",
    "tau_exp"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The zeroth order expansion assuring that the next term is not secular:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\cos{\\left(t \\left(- \\frac{21 eps^{2}}{256} - \\frac{3 eps}{8} + 1\\right) \\right)}$"
      ],
      "text/plain": [
       "cos(t*(-21*eps**2/256 - 3*eps/8 + 1))"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "asymp_exp_0=sol0.subs('tau',tau_exp).rhs \n",
    "asymp_exp_0"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the $O(1)$ expansion, we are sure that the first neglected term is not secular. "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## First order\n",
    "Solving for the $O(\\epsilon)$ problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{x_{1}}{\\left(\\tau \\right)} - \\frac{e^{3 i \\tau}}{8} + \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{1}}{\\left(\\tau \\right)} - \\frac{e^{- 3 i \\tau}}{8}$"
      ],
      "text/plain": [
       "x1(tau) - exp(3*I*tau)/8 + Derivative(x1(tau), (tau, 2)) - exp(-3*I*tau)/8"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob1=prob1.subs('w1',sw1[0])\n",
    "prob1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{x_{1}}{\\left(\\tau \\right)} = - \\frac{e^{3 i \\tau}}{64} + \\frac{\\cos{\\left(\\tau \\right)}}{32} - \\frac{e^{- 3 i \\tau}}{64}$"
      ],
      "text/plain": [
       "Eq(x1(tau), -exp(3*I*tau)/64 + cos(tau)/32 - exp(-3*I*tau)/64)"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "#%%\n",
    "sol1=sp.solvers.ode.dsolve(prob1,ics={x1(0):0,x1(tau).diff(tau).subs(tau, 0): 0})\n",
    "sol1\n",
    "# %%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{x_{1}}{\\left(\\tau \\right)} = \\frac{\\cos{\\left(\\tau \\right)}}{32} - \\frac{\\cos{\\left(3 \\tau \\right)}}{32}$"
      ],
      "text/plain": [
       "Eq(x1(tau), cos(tau)/32 - cos(3*tau)/32)"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol1=sol1.rewrite(sp.cos)\n",
    "sol1"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to assure that the $O(\\epsilon^2)$ is not secular. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - w_{2} e^{i \\tau} - w_{2} e^{- i \\tau} + \\operatorname{x_{2}}{\\left(\\tau \\right)} + \\frac{3 e^{5 i \\tau}}{256} - \\frac{3 e^{3 i \\tau}}{32} - \\frac{21 e^{i \\tau}}{256} + \\frac{d^{2}}{d \\tau^{2}} \\operatorname{x_{2}}{\\left(\\tau \\right)} - \\frac{21 e^{- i \\tau}}{256} - \\frac{3 e^{- 3 i \\tau}}{32} + \\frac{3 e^{- 5 i \\tau}}{256}$"
      ],
      "text/plain": [
       "-w2*exp(I*tau) - w2*exp(-I*tau) + x2(tau) + 3*exp(5*I*tau)/256 - 3*exp(3*I*tau)/32 - 21*exp(I*tau)/256 + Derivative(x2(tau), (tau, 2)) - 21*exp(-I*tau)/256 - 3*exp(-3*I*tau)/32 + 3*exp(-5*I*tau)/256"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq2 = exp1.coeff(eps,2)\n",
    "prob2=eq2.subs(x0(tau),sol0.rhs).subs(x1(tau),sol1.rhs).subs('w1',sw1[0])\n",
    "prob2=prob2.simplify().rewrite(sp.exp).expand()\n",
    "prob2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - w_{2} - \\frac{21}{256}$"
      ],
      "text/plain": [
       "-w2 - 21/256"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "secular2= prob2.simplify().rewrite(sp.exp).expand().coeff(sp.exp(sp.I*tau))\n",
    "secular2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-21/256]"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sw2=sp.solve(secular2,w2)\n",
    "\n",
    "sw2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle eps \\left(\\frac{\\cos{\\left(\\tau \\right)}}{32} - \\frac{\\cos{\\left(3 \\tau \\right)}}{32}\\right) + \\cos{\\left(\\tau \\right)}$"
      ],
      "text/plain": [
       "eps*(cos(tau)/32 - cos(3*tau)/32) + cos(tau)"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "soltot1=sol0.rhs+eps*sol1.rhs\n",
    "soltot1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle t \\left(- \\frac{21 eps^{2}}{256} - \\frac{3 eps}{8} + 1\\right)$"
      ],
      "text/plain": [
       "t*(-21*eps**2/256 - 3*eps/8 + 1)"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tau_exp=t*(1+eps*sw1[0]+eps**2*sw2[0])\n",
    "tau_exp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle eps \\left(\\frac{\\cos{\\left(t \\left(- \\frac{21 eps^{2}}{256} - \\frac{3 eps}{8} + 1\\right) \\right)}}{32} - \\frac{\\cos{\\left(3 t \\left(- \\frac{21 eps^{2}}{256} - \\frac{3 eps}{8} + 1\\right) \\right)}}{32}\\right) + \\cos{\\left(t \\left(- \\frac{21 eps^{2}}{256} - \\frac{3 eps}{8} + 1\\right) \\right)}$"
      ],
      "text/plain": [
       "eps*(cos(t*(-21*eps**2/256 - 3*eps/8 + 1))/32 - cos(3*t*(-21*eps**2/256 - 3*eps/8 + 1))/32) + cos(t*(-21*eps**2/256 - 3*eps/8 + 1))"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "asymp_exp_1=soltot1.subs('tau',tau_exp)\n",
    "asymp_exp_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\cos{\\left(t \\left(- \\frac{21 eps^{2}}{256} - \\frac{3 eps}{8} + 1\\right) \\right)}$"
      ],
      "text/plain": [
       "cos(t*(-21*eps**2/256 - 3*eps/8 + 1))"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Second order??"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prepare for print\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [],
   "source": [
    "eps_use=0.05\n",
    "t_max=50\n",
    "time=np.linspace(0,t_max,num=100)\n",
    "\n",
    "solexp0=sp.lambdify(t,asymp_exp_0.subs('eps',eps_use))\n",
    "\n",
    "solexp1=sp.lambdify(t,asymp_exp_1.subs('eps',eps_use))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numerical solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rhs(t,u,eps):\n",
    "    x,y= u\n",
    "    x_dot = y\n",
    "    y_dot = -x +eps* x**3\n",
    "    return [x_dot, y_dot]\n",
    "eps=0.01\n",
    "sol = solve_ivp(rhs,[0,np.max(time)],[0,1],t_eval=time,args=([eps_use]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc999e6ddf0>"
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sol.t,sol.y[1])\n",
    "plt.plot(sol.t,solexp0(sol.t))\n",
    "plt.plot(sol.t,solexp1(sol.t))\n",
    "plt.legend(['numerical','O(1)','O($\\epsilon$)'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc999dac610>"
      ]
     },
     "execution_count": 225,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sol.t,sol.y[1]-solexp0(sol.t))\n",
    "plt.plot(sol.t,sol.y[1]-solexp1(sol.t))\n",
    "\n",
    "plt.legend(['Diff num O(1)','Diff num O($\\epsilon$)'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc999d25490>]"
      ]
     },
     "execution_count": 226,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Z6RhNGVgGUw+EJEa/phhE2XcRRjH8KEbXYxITYLblBnfkWo6NlZ5XSTaca7noJgyirrGjjYG4CcxKXft+iJ5XD4NIJSbXwmLHTWMMMmyNmH7ccixYxKzENPBZCwgepOaPiXBpY4Qgorj76DwAdiOZZRDTh4nquximDIJpyPUwCAtLXa9Sbctc2yk1wjrAHZClrpsyL5Wkde7aDs4cngOAWmIQxftU1mKeKwBdz8btSx24NjFaC8ENY9u1sNrzSrMbd8as20HGIBqJad9inJMjqlBXnh2RMQiDBiInRyx23NICnK1hiIW2A0IIOm61PPabBfeS8gxC5gnxx+cSj8lzzDKIycNEfdD5SWfNbmL0TRfL5WVDxiDUBmJrFGC+7WZG2CAr5BLmYofVQQByoz/wQ7y4OcKZQ8xDN10HwSQmtqZuycHKnYGu58C2CE6udGthEG3HxmqvVcogUompVW6EdaIxEDcBJjGxC85zLDgWkWqClNJUr+61HHQ9u54YhGdjqcskJlWGDWcQ7G8coxITP9hWul4ag5AdJtkNy57XciyjswMm9Wr1wcrX1kkOE9PFcqkc4dqMQfTLJaaFtlMLK+QMYqGTMQjZvfBsmsHEGIRXY5prp2RPB4Xr7fRqzyiDGAVsbZZFsDLnVQ9SJ9/xTsMg9i/yhwnALj7ZQedHTJPlXumhObPFcunhlTCIKKbK7o9bwyANZnY92+jYURGDkH1vfM3ckNTCIJLDpOVYIEQ+PnOQVJvzw+S2pY7RYrlRTmJa7nrYHofKiuDtUYD5hBV2PceoHMElzKWOWyobXlxnLOvUCgsCtwwXyo0FrFB2fXOjxg3JHauMQZhKXx4FEVouW9tqjyUeqGI3nEF0KsQ8daIxEDeBcZAdJgA/WCWHyXjSMzk0V6437gbFLCZAXVi1NQqx0HHSv6mFQfRyMQjJhc5v5I7L1tZybAQRNZab7ocxWi5bEyEEXYXc1i/s6bHFttFiuVEQwyIsUL/c43sqZxE74xDzrZzRN9g+hU+TW+y4qRwoYxCpbNjO9tSs0Y+y1GW3hLEGk3t656EeBn5kjO2PwwjtZE2rPZb+rrpPt0ch5lsOPMeCZ1u1tfxuDMRNwI/i1PoDLC1SSl1zhWsAq3A2GqTmGS+ejcUOy0xSZTLlGYSKCenAWiKNrHS9TI4oOYTzDAKAsQNlHBaMfsuRHqx5vRoAbl80Wyw3CthhQgjBUpftaelhkhzCVQoSd4PNiRhECSvke7oHsqFtEbQcS+7IFSSmkwnLOb9uRmYaBaz3FwCsJLFJmczkhzHGYZwa4F7LbmIQ+xl+4TDpeLbUEx4UqCuTmMynubYcK2UQSgORj0G4ttF5EOt9H7ZFMN92cgFNdVZJJ3eYADAmSeTlCEB9sPI1ZwwiK5YzgWGQeZvLXbZXslTXMJkXMd/O4komJSaeBMF6MSWBYMmepoY1l3hQVwwCUO9pkbFmtTBm1jcKIrSTOOahJMVcVgvBGdlcavSdmYZb7QaNgbgJzHaYTHrCh+dZxoKp0Z6jIEIn8TZTAyE5TMZhhFEQY6Emb3Nt4GO568KySKlezQ0rv1H59z2OzKwvL0cAUGZ0FY0Xr4V40VAm0yiIU4lkOWEQskwmfnBwBtEzLDFtDgPMtRw4tpUxCIlB6qeHMDf6NsKYGulMGkYxYorCfSqfQVJkEBljNXO95WMQK3OJgZC02+B7OsEgmiD1/oU/ZSDkElO/4JnwVNcqYwZvBrwFBMBy0wE5g+BV1JxBtD3DMYi+nx5wbcdOAsESBpELtgPmGUQx8WCWuBI3EJcNZTKNwuww4e081iXXD99T7m2alg03h0HqiJQxiIHPnBfeWoV/JhO1EFyKLCaTyIxl0UC4NjG2NoA5mZxB8CJV2ZmwPSoaiPKKdV1oDMRNYJxLcwUSz1sabJ1mEIC5YrlhwiAAlEpMPAMlzWJy5YeiDqz1/fSAsywWCJbFIAZ+iI5rw0oOE9MxiGk5Qj7akT/O2Q3v12MqUD3yMzmiTGLivbUmWKFBb3NzkBmI0sy0cZgewEDO6BuoheAHe3WJSSxp+pHZuBLAYnKAXGLaKUhMPQUT0o3GQNwExkU5ooLE1M3FIADgmqFMJqZXZ/n8jkWkxXJbKYOoR2JaTyQmjq5ivi7vX8XBDbIJBiGSI1R7OixITF2Xz/M2JBuGGSvsuDY8x5IGqbm3yWMQLIHCrMTEDYTnWHBtItXHWVfjbE9T2dAEgwgFDEIlGxYSDzzbnngd3cgHqR3bYv2YpBITu385g+h6dtOLaT9jWmKSSzP8AOwkF94Rwwxi5GeeCct6kfdjKjII0xLTWj9I6TRQHrvpCLxNEwxCJEdUiStN6dWGDpOhnxl9QoiymnpnNBmD6CikMh3gjfo4up6jkA3DlHUBZo3+WGAglLJhMhbYLjJWUwYijNK0aoClupZJTGlcqZGY9i8opROtoQFO+dTaZq/AIEzVQuQlJoDFF6QGYpRVwQLME/ZDdbO1mwWlNGEQeQMhz7CZPkx4DMKcHNGqaiCSA5DLPqb16nyQGkDS0VUSV0q8zflc8aPpLCbOIAB2nctlw0goMZkIBHOj35oKUsuyDSfXxvfUVDLJOMhiEACw2pNnN2ZB6oQVNkHq/YswpqAUU2musi6Wg4K22fFszLUcXN82FKQOJj3vxY4rzWLaGha9TSt9Dd3YGoWIYjrBIHqePJ+7yCBMxiBEckTXc+SN3ZKDjsdHHJu1tDCWmVbwNpe6bgWJKUuJHAaRkQJDSumExASoZUMWg5g2+iakOVEMQsWm+FhgDuMMIicFA1B2dN0ZTccgmjTXfQoZdQXEB+vAD+FYRBAsM7PBw5zEBLAWCKUMIpczz9esGzzrZoJBtOTBtv54D+SI4h4FkbD4bRBMepuA2VYg+SA1UMIgpgwE+7uRgUDwKIjhhzEWuwUGIWWFk99b3TEIvqciDIOwNocEmAxSAyw7TZaZtjMOQQhLIgGY0R+HsdHJlByNgZgRIjlCdbD2x8wTZmO2GUweJuNwUo5QzYTYGgawczUJ/O9GBoqD1nJtNjhYO4u9ZxAio9/xbFAqPryGhbUBgGtwZvYojFN2B0DZ8ntrFMBzrNSglnUx3Q02c0VyHCoZp++HaTdSIGf0TWQxSdJcVXGlCYnJMme8ALaneQax0HawLWEF26MQc56TMta00aXh8cBAYyBmRuaZZBcTjy+IdMFhMrs4D88xd5gM/WjKQKgOE97qG8h3MTXIIPIGoqX2NnsCvdpkSuSEXq3o3dMfh2nmUn59Rr3NCQbBJgWK2A3v2cORNakzZyCWOjnZULGnw2IMwmQdhIgVKmJsg8J9Y1kErk2MyIZB0sAznyrfa7G1ib4L3qgv/1xAXpCoE42BmBH8gBJJTMLDxA+n5QiD3uZUDCLp/inSoLeGYRqgBsobmu0GXF9d6eZjEOrgfqcmTVicxSRnhcNgMl0TMLenlNKJVhsAY2FhTIUeZ74PE2DW6HPHozKDGEcFBlG/xARI9tQXyIaG9jQ/LIhD1eiQt/rm4OusIw7RGIgZoZKYRFWaQ19wmDiWsYBm8TBZ7LigNNOm82AMImcguF5twEAUay4AxiBU/Y7EDMKkt5m9n2pEZVGOAADXECv0oxiUYsLo8z0T7el2MiyIo1OzxNRribOYophOZdiZ3FOZbAiI2dTAnwygA+b2NGvfnn0X3ACIDv0pBmEwVlhEYyBmhOjC65UxiIIcYWq+chRT+IIYBJC1Zc5jaxhMHtgVxqfeLIQenSsOtsXJYSIKaBqVIyqyQiZHTO+pCaPPM3zyDgk/LLZH07GlnQKD4B67CYlpIzdulENWB8ETOMTFj3Wlucr3VBRXMreniYEoSEyAuE3J9rjAIFrmjH4RjYGYESrPRLRhdQY0s2lyuYCmot3G1iicZBCuPBtrt+A3Wl4TlgXbRmEESrOun0A+oGnCS8864HJ0FHLEQCQb7oW3KWQQkwYikw31e5tbw8k6GiBJXRak1XKjIUpzNZq6nGOFSqMvy0wzsqeJ8XKnjb5oT3eSAVDpc2scO9oYiBkhLqqSS0zFlhEAz2LSn5c+FBwmi4qGfflZEICagu8WfsiG3ji24HsrvF+xUhnICpeMyBGBiBXKPW/RnrqGWGF+ABRHyiCEMYhJickkK9wcBrAIJoPiLQeUTqfVFrsaA2ZTl4WtNkru06LE5DkWxiYZxITRl8cVdooMwpPLUbrRGIgZMSt1FcoRhjwTfpiJvE2xXh1OSEwmGYQfxXDtycstS8GcXFvWLTVbGyHE2JB7WasNQCFH1LSn3NvM7+n8DAwiG3JvQGIasFkiPP0y/35FNl3sagyYroOonkwSRix7SBSkDozER6bvU9n3BvAg9WScBzCzp0U0BmJGKKmrYHMHfjjNIGwrvYB1QuRtzkv0aj+MMQyiCQZR1o1zNyj2r2LvJ77QizOfOUwdwqJCORmbopQKJSZTaa5DgWyYyhEFwxrHFDt+KAxSm5AjikFnIB+PKxh9AYPIDMTeGn0ucdZV/Jga/XxcKQ1ST96nfKb8XHuaQdTRsK8xEDNCnOYqP1j7ouCXYyEwKDFNGghxxgs3GHlvk7MiUwyiVTAQPUlqX3Hmc7Y+22gWk0g2LB5045B1fq07rpQPaMpiEDt+CEoLko/B1OUgEhl9CYMQxCDspNagtjoIiWxYbPXNYSrNVZ3FJGZe+T3tKWKeutEYiBkhOkxsi8BzrKlcc05dpwrlDF14ogudX3hbhcOE/55vk2BZBB3XlvYg2g2CUC4xFYPUxZnPHC1TqaSqLKbC2orNFzlMZbykI2TzcoTngJDpGESxzQbAYj6eY5ljhXbR6FdnEAD73kwafR67AhQMQhDzYn9rODMtP9de4iwV+zABbE9bjtUEqfcjRIcJkIx2rEhdXcdMheYonNarbYtgruVMeZvFVt8cpmZCFCe2sfcSV4Ryr0kk45jJYpre05ZjJRPviofJtCfM/9aI/CVghZZFMOdN7+lOYRYEB2tzrf8w8YVGn6drygxrwei7thGJaZxcb/kWNzK5bSCIjwAmJc1pVugmh35RNiyOG+Woq+V3YyBmhCjNFRC3rpZ5wp5tm2UQBV14vu1MxSCKrb452q6ZmRAibzMNUhcu9KHEo2M3rMEajdz6CCFJr6hqcoQ5iWm66hZgHmVRrxbJhgCUk/t2A5HRTxlEMfEgnYsiMPqGsphaxeuNJ2FI9lR0vZlwSESJBwAzAlID0S4aiHpafjcGYkaIJCZAPO82010FF57JlEhPZCCKDCKpbBZ6m2b06qK3KSvi4gaj15qWmEzJEbZFJlJwAZayWdxTmRxRZ+oyID5MtmQGouUYS12eZtJiBsGdpykGYSgQLFqbY1vwbEsqGwpbbRhNc502+jKJab7IIGpq+d0YiBkhkiMAsTRTnAXB4SVNwETN1nYDUZAaYJLD9ljGICYvvI6hqXJjRRaTjEGIgvumKH+R3fD1Ffe0r/CE68pMA9hhUjT6afO8XL8rwFx7eVHigTR12Wctq4uHomeQQRSvN0A8E0J6nxpqiTMSpLkCyaFflA0lDML0eGAOLQaCEPIQIeQpQshZQsi7BP/eIoT8ZvLvnyWEnM79208kjz9FCHlL7vH3E0KuEkKe0LFGXeCasEguKVK+tL2AQK+mlA0f0gm1xFQtBqGa27sbiG7YlsMG7UzFIHgWk1s8hM1lMQkPE4XEVNxT1yZmUyIrMAg+GGqxM72nJiQmFSssGv3+OEqC62Ticban9chfgNhYcpZYVzKJqH0KIJGYRrd4DIIQYgN4L4C3ArgXwDsIIfcWnvZDANYppXcB+DkA70n+9l4AbwdwH4CHAPxC8noA8KvJY/sKouAXkPSgkUhMIr0a0N9XKJUjvMltnW+70wZiNDkLgoNNxzOUElk4TAgh6HnTF/ogCOE51pTkYyyLSXGYVKnyBsynLhcPk/n2tLe5kRr96cPEmMQk2COR0R8G07Uj/PnGjL6AFXYEI1GVsqGhxIOW4AyZa0/fC6ls2Jo0+j3PuWViEA8COEspPUcp9QF8EMDDhec8DOADyc8fBvAdhH07DwP4IKV0TCl9FsDZ5PVAKf0UgDUN69MKUfALEA8jSb1NQasNQP+IylEQgZBpdiMMUg/DiVkQHHVmMQGs8djUITyOptJIAR40NCR/CSWm6dbV8px5G1FMtc/z5odJvloZkDCIYYD5ljNlWDumJCYB85IZ/f54utcRwFI9TaUuVzb6Y3nigQmjX5wmx9ETZBum7Uym4kr2LRODOA7gfO73C8ljwudQSkMAmwBWK/6tEoSQdxJCHiOEPHbt2rUZlz47RFo6IE5z5Z7KVDdXQ51J+bCg4qE/33YEdRDBVAYTkGQx1eRtAkn2l8CjK2Z+AWbrIIoeOiA2+n1JmqvrkPS1dEJ2mMy1XOFhItpTUTaWDgQRnZKYgKSNuyA9WLSnxuogZA6JO230MwZRX/sU0fU217KnCuXWBz4WC+1MAPUsFZ245YPUlNL3UUofoJQ+cPjwYePvJztMWJpr0dtMDhNBYzdAfw8aUesDgGVA+GE84X0XG/VxdA0FqYOIwpVpwoKApsjbNJV2qPI2qxZVceOnOw4h29O5toMdf3IQ1NYwmIo/AMwzNWEg5M6SmEEUmTRgLgYhY4XCIHUiadqFQ5i32tCdTDIKZUZ/OnV5fRBMJR0AyTTGWyRIfRHAydzvJ5LHhM8hhDgAFgHcqPi3+wrK7IhAwiAEGS+AfompOCyIQ9RuY6vQqI9DNRFsN5AxCGEMQjCQB2CHiakYhNjoi2VDi0zHBFqGWOEoiKcyfwBm9CmdDAZvDMQGQnQo6oAfRuLvTTAISsYgWu7eG33RNDmAZRsC0C4zjSV72ms5GAWT81E2Bv7EvA2OOY85faYGj3HoMBCfB3A3IeROQogHFnR+tPCcRwE8kvz8fQD+kDKz/CiAtydZTncCuBvA5zSsyRikF55rI4joxAHBL8R8xSRgztscBdN9n4B8w76cgZAwiLZrYxTEwhGluwHzNsnU48IYhEyOMMQgxoHsMHGmKpC5/FWU8VyDeyr0NgUN+zaHgfAw6Xk2/Ej/YcIkJsGeCti03OjvvWw48KOpjDkgJwXr3lMFgwAma0jW+wGWhQyinrnUuzYQSUzh7wP4GICvAvgQpfRJQshPEUK+O3naLwNYJYScBfAPAbwr+dsnAXwIwFcA/B6AH6OURgBACPkNAJ8GcA8h5AIh5Id2u1YdGIeRJNg6XfQ1GDOppKgfmspiGgWxWGJKGURGX4vjRjn4TVzs579biLKY+PuJYxA1HiaqlMggmpAYBn4oNMJp4oEB2VB1mOTjEJsSiYnPQdAtM8m+t57sEK7R6Csz0wS9v4R7auw+jaacRkA8dlRl9AHxBDqdmN6xmwCl9CMAPlJ47J/mfh4B+H7J374bwLsFj79Dx9p0g8kR05ubHw6/CDf5WUJdTUlMviQGIZhWtTUUS0ydXDsC0Q19s5BT/ukRlQM/mpgmx8E14TimU0Z3t2srpoYCzNuklLEffkgPfHmGFaDf25TJEaKhQTIDkTWpC4X/fjPgGVv5tvfp+7Uc9NcGE4/1BW3vgSQGUVNrF0AsocoZK1uv/mzDeCorCRA37Fsf+GoGYdhA3PJB6rohv/CmO0UyBiE+6AAzQeq2QmLimUyiWRAcHcHn0AHRwCAgG1GZx8APhYcwN8y6D2GVbMjWk9tTP0o98jxM1rYI40oFBjEKIozDWJzFZGBP026pAtmwJygaHYwVmWk1tdoAmANUlFAHEgbB5bP6MtMmGcQ4jDDwIyyrGMR+l5heapBlbuQ9bw6ZVGJOYorQEXibCwWJaVvSqA8wM1Uu9TYl0pzoMFHJOLoNK5MjRKxw2kuTFXwZ06sVWUxAdphkbTZEBkI+PvVmkbacERn9QpVvEMXwo1hq9INIf/2ISmICJq/vYaBmhbqvtzwjzaM4l3pjIG6dkl+bCeOaR2MgZoQs+CWih0OJxJRlMenvxaSSmHiQmjMJcRaTuOPlbsApusxL95O5GUAysS2IptoeAOYyhVRVt8DkdyEt+DJl9EsCmvww4QZCJTHpnEAma1oJ8Bz9LHYj63UEmKsJYnuqkIIn9lSSYWUsMy2amCbHkTY6TPZpfeADgFBiMhUfKaIxEDNCleYKTA6YkV14JgvlVIdJaiAkfZgAMxKTaKQnRzG4Pw5jRDEtYRB6abWMFWbNBHPepowVGttTWZprwgrHk96mMgahkRVyz1VWKBfFNN13zsCK3XmB7BDWvafy+3SaTcmC1Pyzmeh40BLtaYEVrvfZnookJlNnSBGNgZgRZYfJTBJTpPemkOnVjm2h69mptJS1hZZLTDr7MakYRDrDOOljJZvYBpjz6MayfH6BxDQI5BXBgP7DZFyW5lqJQeiXmHi2lmhPV3vM4722PQYgHyELZFPVdO4ppbRUYsr3TStLJtEvG8bCLKZeIQaxkTCIRYWBMJEBlkdjIGbEOBRnMRXpISA3EFlKpOYKTUkdBDDZ0TWdBSEplAPMBDRVDIIfIrKJbUDe29QvR8gK5YBq3qYpj04mMfFGi7zyNo1BdAQZLyYkJoXRv22xAwB4cWMIIMcghHvK1qZzT/naZHUQbE3FxIN60lwppRhL9pRnefF94s0XRRJTq4lB7E/Iqkc7guCXLOOFX3g6hwYFUYwgosIYBMBkJj4TIp0FoWAQOoPU2XxgeaYQvynSVhaSlMj86+lAJW+zyAoF37GJQrmwwp4Wg9QiBmHiMFHt6e1LbQDApc0RADWDMCEbKh2SQjJJFLPi1mK/NCAnG2q9TyliOj0XA2DXt2dbaT8mdQxC/70gQmMgZkSZxDR5mIjTNVM5QuPmygbLcORbfqcxCElbBgBTFcS7gUpiWp2blCNkvY7yf6/T2wxjCkrFh0kxSB3HVFnEB+i9YbMZ4+LbND80aHPggwi6fgJm2E0lBrHJGASftyCqbeHf20jj0CDZ3HhgmiFnjLUeBiEbFsTRa2WscGMQoOVYtTLWIhoDMQO4tyliEFxTHOQOE1kWkwltM5sFIZeYttIsJtZCWGS8RExot5DN8QaAUytdAMDzSWEVL5pTS0wGvM0KMQh+c8uK+AC9e5qNppTsaYFBzLccYQGhEQPBs5gkaa4LbQeXCwxCGVfSyW4UxiuTmNj3JmvfPrE2A45cS2ogstn2631xkRyQ39OmDmLfQOVtWokmzA+4URiB0pLDROOFx8c2yhjEQtvN1UGEWOi4U/2E8n+vNQahyJlf6XmYazl44UZ/4n2VhtXAQacOaHJvU742E7Ut/PCSGYi53NAg1pJBcpgYWFtWKCc+Qm5f6uDFDWYgUi9dyCCSGIQJBqEoaB365XtqouMB/5yiNFdgUjZknVzFle9NHcQ+hOowAbLePQDSm+PQXGvqebZFYBG9F55sHjXHZJBa3IeJr81zrNoyXgghOLXSxQsJg5DNWwDMBjRFa2NTv7KGaLKRrvm/13qYlMgRxRiErI2GY7Mpbzq/t0Bh9AHgtsU2LiUSk4pBGI1BVJCC6zb6ZaxwLjc0aEPSZgNo6iD2JVRSCTDZVvnpK9sAgHuOzgufq3sYSUaVxWvLj6iUtfrmaGtuoKY6hAHgjtVuKjEN94hBiDLTCCETw3ZUxsuIXl3qbWZxpQ2FgQCyPla6UOYs3bbUSYPUqfOikHF0Xm+q+zRN+U3WlMZHVPVKWmVDHldSSEx+tqfLPfGemmoDUkRjIGaA6jABktkGiUf31OVtEALcdWRO+FxX8yStYZle3XYxDCIEUaxkEABrUmbC2xRlvAAsDnFhbYgopmlRmqqSWqe3yV9LygpbTnqIqL3N5IbVWB2vOliBxOhXYBAAM2B1BakB4PbFNtb6PkZBhP44hGMRIdtoG6iDUK3Ncyw4FkllryoZViaC1KI4JjApG24MfCwK0pYB5rx4tqU1E1KExkDMgDKvKT806Okr27hjpSu9uVuOVbvEBLDCKlmr7/za6ko7BIBTq134UYzLW6M0e6quzA1VlTcwOWDm7JUdAMDJlc7U8/gNW7scMQ5BKWXT5CR6NaDf6JftKc9kurQ5SjO/RDEvI7KhIoAOTM6EULYBMZC6XLqnXranG4NAWEWdrs9Q+/s8GgMxA0q9zdyF99SVbbxcIi8B+j26UUlAMz9VTtbqm0P33IUyae6OlR4A4IUbA/T9CK5NpDGB/OvpgKqnEMAMLt/Tzz+3huWui5cdFrNCU7KhqOoWYN5mlKTeljEI3XtaxiBu47UQG0P0x6GwzUb+7+uKQQDJTAi/gsRkQDZMg9SS1GWWxRRiexwijKk0BgE0BmLfYVx6mLAmZaMgwnPX+7jnmNxAuJo14aoMYmsUlDII3Rceb0oo8zbvWGWpri+s9aUzLfi6ADMGosph8tjz63jg9IrQEwaYzKSTFfI6CFlciffYuro9RhDRvYlBlDCIF3MMQoTU6NdUBwHwmRBsT3kPK1EA3bIIHIvUWgcx13bQ9yOs7bAiOVkWE8C++1th5OhLBmVeU69lY+CHOHetj5iilEFoPUxKgl/cQGwMAgz8SFgkl66t7oDmYhuORfD8jYHa27QNGIiSPeUDZq5tj/Hs9T5ee3pZ+lq6DWuaMy9hEHxPL66zbKFyBqG/v5YszfW2xYxByAbysHUlFcE11UEAk6zw95+8gtOrXRyen842BFjczMh9KmOFSQcB3qakYRC3ELiXI9M2ucSUZjApGITuzR2XBL84Y7i4MUh+l0tMnm1p9ujU0pxjWzi+3MHzawMMFP2kCCHav7cyT5jr1Y8/vwYAeOD0ivS1dBvWKjEIINvTpTKjX+P31nZtrPQ8vLg5Ql/BIDyTDEJxnw6DEOfXBvj0uRv43teckLJCU0ZfWh2fdOm9kBh9WRZTuraGQewfpE3AJJvbcR0M/QhPXdmGaxOcXu1JX0t3FlOZl54eJsmFp2IQLVfvhcclJtGAe45TK12cXxtgMA6FGUzp2kwF0EviSp9/bh0tx8L9ty9KX8u1zRgImcEs7mlpFpORXkzyPb1tsY3Lm4xByFihncg4de4pN/q/82cXAQDf+5rj0tcyZfTlldTs8QvridFXMQjNcUwRGgMxAzLPRLy5Xc9G3w/x1OVtnDk0J71AAXbh6S2qUsdHuBxxIaGuyhhEzSmRQFILcWMg7azJYSqALvveuIF47Lk1vPrkknpPtWcxldRB8D2tYPS1M4iIwrMtqecNsDjEpc1RMm5Uvada6yBKZUM2EvW3//QCXndmFSeWu9LXYnuqL3WZf045g5jc0zKJqWn3vY9Q6m222JD7L13YxMsV8hJgIKskjGERJteIwLOYqjAI/fKXmvIDLJNpcxjg0uZIGDDkaJlK11TEILZGAZ54cQuvVchLbG2as5gCltEl21Nu5LnRLw1Sa/7eVMYSYF1dX9wYou+Lx7RytFzbUJ8omSPn4Oy1HTx3Y4C/+k0nlK9lgkEQIr8XuIE4v15BCm5iEPsLZTo/byV8fWeMe46KUyE5dMsRbOiN/Cb0HAstx8JFziAUaa6eY2uWmGK4NlF6mydXeCbTQBrQZGvTbLwqeJt+yKbcPaAIUAMmApqRNJgJTEtMZRkveoP7UamBuG2xg61RiPV+oNzTumXDjscm3nU9G2+9/5jytRiD0Le2URAlLVzE90IvxyAW2o7UOQASh6SJQewfVPE2OVQZTECSxaSRulbx6Obbbtphs0xiGmueB6FiD0CW6gqIq1o5TB0mMm+Ty12EAK+5Q20gTDAvWbwLyA6Ty1sj2BZJDYZ0bZpjEKr4A5DNhfCjONXWZWurlRUmjtxD9x+Txkbya9M5O34UxNKkAyAz+pe3RljuyeUloIlB7DuUpkTmbgJVBhN/Dd2pfWUGYqHtIIzZxV5nkNoPY2k6JAdv+w2oDYSxbJySw+QVxxaURjVdm+bvrQorjGKKhbajZGgmaluqMAiOUgahM4spimBbBLag9TlbC/tOv+81ankJYEF43dmGSlaYSEqUqgPUQD0Sk9p8NphAmuaqkCMAFoA6qQh8AYnEpLlCU7YuDh6ols2C4NAtRwRROYPotRwcmmvh+s5Y2BaaQ3dAsyorVNU/cGjf00qs0MF4x1fGHwAzMa+yPeW1EID6emtpljTL1vbGbziKtYGPbzmzWvpa+tNcY2mAGsAEC1S12UjXZlhiagzEDCgvwGFf591H5oWDW/LQvbnjCgyCB6plsyA4jBwmJWsDmMx0fWcsHOnJ4dXsbXKJSVX/kF+b1j0NxONt85hrObhewUDoNvrjMJY2X+Q4ttgGIcwbrjsGobreXn1yCa8+uVTptTzHTse56sAoEM+j5mg5FmyLICppswE0EtO+Q5XGbkB5/AEwkK4ZqOUIIGMQVaUSSvVor+MKDALIZCY1g9CbxTQO1Gt7zR3LeOMrjuDb7j5U+lotA+nBpQYi2dPFmuWIoMLaXNvC4WQeimjGeH5teo1+NYekClisUG/7FFkNBMCKQTmLUCUdAEm7nsZA7B+Mw0iZ+80DcfccU2cwAfr79lS5KVIDochgApjxohTagnNBRQbBDUSZ/KX9EFZQ/uNLHbz/B15bqgcD+rOYxkH598YPk1IGYSA+UmVPucxUXvyoWZqr4JBUgeeQPWGFgLoGAmgYxL4DCxrKv7LTqz38ndefxl9+1e2lr6U/2BpJW4BwpBJTBQYB6OuPU9Wj45lMykI514Acoe0w0d8+pYwV8tYMiyVG37NZamcU6zH6flQuMQFZoFqdmaa/DqLsEK4K3YfwOFRnMQGZo1kWg2g5zTyIfYUyr8mxLfzkX75vIntDBs+2EcYUsaYbtiwlEphBYtLc5tivoFcD2XClFUV6n3YGUdETrgL91crVWWEVBgHo29OgotHnbb/LalvqjEHMAhMdD6oyiKqyoS4pWITGQMyAKlklVeE6fAKZvkO4zBPmF16ZxOTxDps6D5MKBuKVJ5bwoR95HV7/MrnezxhEvcH9qmASk8a2DBUy01K9WjJ5jEO3gajKvG7nDEIRg9CemaZ5T3WzwrK19VKJqZojF2pyMkVoDMQM0E1dAX0GogqDWJhRYtLl1c3i0T1454oyA8yz9csRWiUmjcH9mYLUFRnEONK3p2W1LQDwhlccxkP3HcOJZTmr1m3097VsOEM6emkMQrPRF0HLt0gIeYgQ8hQh5Cwh5F2Cf28RQn4z+ffPEkJO5/7tJ5LHnyKEvKXqa+4FdFNX/po6UOWmyILU5dqmzrVVSYmsChOHiS6jn35vuoz+DEHquvfUj+LSmBcA3HVkHv/xb32TMpZiIgahVTbULjGVxCC8allMt4SBIITYAN4L4K0A7gXwDkLIvYWn/RCAdUrpXQB+DsB7kr+9F8DbAdwH4CEAv0AIsSu+Zu3QnT4HQJu+WbXVBqBuAAbon9xWJSWyKnjbam1euk7ZMGk9oUtmqhKkrhqD0G4gNB/CWmMQmu9TrSnfYXkWU69qFpNmh0QEHd/igwDOUkrPUUp9AB8E8HDhOQ8D+EDy84cBfAdhuaIPA/ggpXRMKX0WwNnk9aq8pjZ88HMv4P/68JdKn1flhq0K3dZ/lsOkzNvcqyymKuAyWpnx+vxza+mQHxW07qmB4H5VOaLU29QsaWrd06TfUVmG1dYoqPTdapWYbJbyrUvn9ytIwXcdmcOJ5Y4y84uvjb+mKej4Fo8DOJ/7/ULymPA5lNIQwCaAVcXfVnlNAAAh5J2EkMcIIY9du3btpj7AU1e28ZEvXyp9ns4LzzVwmJTdsHcfncNb7z+GB+9UVwW3jGQxqSvLq6LqQfczH/0a3vPRp8rXptPb1Bzcr5IU8aZvOIr/52334hUVen/pXFugUzas+L1997/7Y/zCH50tfT0TUrAOpk8prSQx/Y1vPoVP/Z9vUHY7yK/N5EyIWz5ITSl9H6X0AUrpA4cPH76p11hou9geh6UejJEYhM4gdcnaup6D//A3v0k5ICW/Nn0SU3ljt6rgVahllbdbwwAbQ7/09fQafS4x7f57i2KKMKYVWKGLH/rWOysfJjpjEDoZBKBeG6UU59eHeP7GoPT1dGYb6vze0omUJWsjhJS26sm/zn5nEBcBnMz9fiJ5TPgcQogDYBHADcXfVnlNbeA0fWccKp9X5RCuCp0XXpwcJvpuWL2eMDuE9cg4rYoMYnsUVuqhY8Lo6zCsZU0EZ4VOOSKOKTP6GjOFAHXW3ChgMzk2BhWMvsaY1yxM/4UbAwx8+RlSNr1wVtwqMYjPA7ibEHInIcQDCzo/WnjOowAeSX7+PgB/SFnU51EAb0+ynO4EcDeAz1V8TW3gmvxWyYGi9TDReMNWGek5C0xkWPG6j90ijUGUzKvYGYfYGqoNPl9bnZ5wVZQNp5oVWZrr7tcWxHqvt1YFw8qdt42qRl+78VJ/b5RS/OV//8f4xU89K31OWTfomddm63XkRNh1N1dKaUgI+fsAPgbABvB+SumThJCfAvAYpfRRAL8M4NcIIWcBrIEd+Eie9yEAXwEQAvgxSmkEAKLX3O1aZeBZPdujcgahX9vcffAru/A0B9A15MxTSiunRFZBlRhEFNP0QCkzALqLqoBqEtM/e/RJLHc9/Pib7havi3ubJQHNqkgPOg1N8VJ2oy11OZENFQyC7+fmoF5W2HKq7en6IMDmMMC1nZH0OZnR35+JLiJoafdNKf0IgI8UHvunuZ9HAL5f8rfvBvDuKq9pCjz9c2ukvvi0Skx29UP46vYIa30frzi2IF5X8hr7kUFwA6g9i0lx0PVzNH9rFOBQ0lFUBL2N3apT/t9/8jLuWO3hxyE2EFXmeM8CnTUauuWvSgxiNAODMGD0y763K1vMMAzG8vt5rNno85iXDkdOhls+SK0DvLK4jEH4GlMiZ9E23/PRp/Ajv/a49N91U9cqN2xVcM9LV8ZLSqsVN+xObh/L4hBGjH7J9xZEMS5vjUr06sTbLGnsVn1t+uQIbvS17eksEtPAV/Yv4w0JdcW8qu7p5cRA9FV7qltiukWC1Lc85lOJqSQGoTUlknsm5RLT01e2sd6XB+eqZkfMvDbFhffHz1zHH3zlSulrafc2KzCIvKFXxZUopVorqd2KXvrlzRFiCgz8Ct7mPjxMjDEIxZ5yAxFTYEdxCGsP7leUmK4ks97Ve6pXYtLpyMnQTJRDtSA1z2HWTvkrBL/OXdtRXgS6NWH+Oqr3fO8nz+LixhBvuveo8rW0B9ArSHM742wfVQxCt/xV1du8sD4EUM1A6JcNdy9H+JolTX5gqmMQuT0dBNJ+YroNhFvhXgByDEKRCenrNvo1BKkbBoE8g5BvbhhTUKpvc6sGNK9uj9H3I4QxlV4IurXNKgfdwA/xwtqgNGjIX0NnLyZA7W1uVZSYdBuvqkb/wjrL5d8TOUJxvX3wcy/g889VqT7nDommzLQK31teNtxQXHN7FY+7sjUGUJEVak480NlBuIjGQIAdXm3XUgapTVHXsgvv69d20p+HkosvYxB6qKtlEbg2UXpN/EZ48sVN5Wtpl78qBA3zh8mWwujrZl5Vjf7FjXIGYex7U+zpv/rYU/jXv19efa498SB5nZEyBpF9V6oCyNRL18z0yw7hK1ViECmD0J3F1ASpjWOh7SoZxF4ZiGev99OfZRdfFtDUt51lHTb54fbliyUGwlRKpIYYRLan9aYdconJD2OpMeF1HvqSIkjp2vp+iMeeWy+PxWl2SNrpnlaTmNYVDCJlrJrqbqru6eXNKllMhtjNPi+UOxCYbztKA6Hb+mcpaurNPXctMxAyj1P3IQzwNsfyi32Y3MxPvLilfB39WUzlBV/8MCGkqoGo94blEhOg2FPNDIIQwrqmStYWxxSjIEYYU/zJ2evK18pkQ73Fj0oGkZcNFdXUqWyoyXi5FdPRr27vQRbTLdKs70BgoePWKzFV3NxzOYlJlhape21A+WhPvpYnqjII7VlM8ht2exSCEODQXKskBqHXo6uauswlJkAuG/LDROeethz5ng5z3+cnv6Zuehlojt1UYxARDs+zehZVDMJYFlMol5j8MMb1HR+uTdKWICIYczIbA2Ee821XrVdrPkwIIWmveRXOXe9jNZnRLPM2dadEAupJWlHibXZcG89e71cyrLoZhOp72x6FmGs5WCox+qNAL/OqUowWxRSXNkbphDW5bKj3MOHrk+0pv7YIAf7o6avK+Qe6M6zayWeUGUuAscKVroeuZyuL5Uw5cirGytnDqRXWBFPmyOlun1LGCnWgMRAJ5tsOthUX3kgzPQSYBxAorP84jHB+bYD7ji8CqBCk1uxtyoLU3Nv8xlNLAICvKGQmU5lCZTGI+ZaDhY5bKYtJX2VrOYO4sjVCGFO8/Chrzy3TrH3NhwmgZoX82vrmO1dwZWuMr17alr5OJuPoqwi2CDAqabUx12ZGvxKD0O2QlOwpAJw5PAeggiOnM1aoeWZ2EY2BSLBQyiAMyDiOmkGcXxsgpsD9ty8AqBCk1uhtqhgE95D4XAmVzKQ795t7TerDJMB828VimYHQnPFiWwS2RZRZTDxAnRqIEgZR1/U2CNg63nr/bQAYi5Ah0Lw2Qgjarp06YSLsjCP0Wg4Wux42FVlMY911NxWC1DzF9cyhHgB5LcRYM2Pl62sMRA1YaDuVpBJdhwnAPE7V5n49CVDfnzCIMs+krsOEe5snl7u4bbGtzGTyNQepAaDj2qUMYq7tsD1VdHTdi9jNxQ0WoH750YreZk2yIV/HqdUu7rt9AX+kiEOYcJY6ro2RKgYxCjDfqs4gdNePqIw+z2A6c5gZCHniQQTHInAaA3HrYaHjwg9jaTWnCXpYxiB4BtP9tycGQuKZ6M54AdhBJ5OY+A3Q9Wzcf3xRySB0BzQBoO1a6sNkHGK+7VRmENoNq+KGvbDGGMRdR9QGwg9jWATaDxOpbMj31LXxhnuO4PEX1qXfne64EoAKDCKJK3XdWmMQnBWWSUyeY+H4EotBqBiEznsUKD9DdovGQCQoq6bWnfsNlB8m567t4PB8C0cWWPbGQHIomqKucgPBvqOOZ+PPHV/Euet96bAlE4dwx7Unsm6K4EHqxY6L7VEgbe5mwhN2bUvZX+vixhCH5lrpQHqVbKhTMgTU7CYz+g6+/Z7DiGKKP35GnO5qwui3XLVs2E8kpqVuvTEIgMVIVIfwla0Rji600Gux/VKxQl3NFznKGOtu0RiIBNxAyPLm90KOOHe9jzOHemg5FiyiCFJHbOZzlTGFVaEqlMsfJvcfXwCl8kC17px5gHmbqoyX7VGI+baLhY6rbO5m4jBRZQoBLAZxYrmDXotdb1JWGJYPt58VVeJKHc/Gq08uYbHj4lNPi2Um3a3IAZbJJEtzjZP5HnNtB4sdFoOQZVkZiRWW3KeXt0Y4Ot9O91Rl9HV+Z0C5TL1bNAYiQVnLb91VkPy1VNrms9f7OHN4DoQQdD0HfUnGC6Ouej0TdtCJ368oMQHyimruTbc0Mq+2a5e0ZQgw33ZKmzCa2lOVt3lxY4jjyx10vcTblLFCjY0hs7XZ0pTI/J46toVTK11c2RYPvzFhWJlsKF4bP3DnEwYRRLS8aFTrntolDGKMo4vtbE9l96kpo99ITOZRNjSIX7z8ItABVR3ExsDHWt9PMyM6no1hIItBRFpvCKBakLrr2Tgy38bRhRaelBkIQxLTSHJABFGMURCzNNdkT8u0dJ3GVZW6HMcUFxMGwVlhrYdJJYnJTv8vO4SDKIZj6WWsbUWQmjtGvSRIDcgHB5lh+vIYBKUUV7ZGOLbQRs8rYRCGYhAm2303BiLBQkcdg+AUvK1RQ1TRQ57BxDMjep4tZRA6Z/ByVNWrAeC+2xfxlUv1SUwdz5bq1bwlw1wSpAbkBqLu7K9rO2P4UYwTSx0QQtDzHOlhwuZU1McKhzmJCWAGQlV3o9shYaxQsqdJ65S5NmMQAHOghGvTXKMBqJn+9jjEwI9wdKGFbmkMQn9cqUzS3C0aA5FgPpWYZAyCbXpHo4Fgh4lYS+UtNnjxTcdzSoJf9Xkmg8JhcmjOkwYOg0h/Nk7btaSHFzfwLAbB40r1Zn/JblheA3FimWW7dFvyQ9iEXq2sg/Aj2BZJ37OrMl4aB2dxVNrTFotBAPLZ1CbiI6rYDR8UdHShDc+24FhEWduinUHYapl6t2gGBiXIgtTizR0G7AbS6QmrLrxz1/twLIKTSUuGnkpiMsAgqrRlyOQIR94nyshhIs9i2ubeZitjEKWJB7prWyQ3LG/SdzzZU3YI7x+JqevaIIRd3x0FgwiiWGuKK8CC1NIYRE5i4vepSmLSnbChYvp8UNCxhXYSK1Qz/ToTD3SgYRAJ5jwHhMgZxNCPJ24gHVBZ/+dv9HFqpZt63h3FhWcs+KU4TDzbSg8JFh+R3xTaDxNFzjz3NhfyQWrJnvqhfi1d9b3xJn3Hl7iBsKVZTGaC1OpWG1wiSdemMF6619b2bGkN0k7O6GcSk3xP62RevIr62GIbADNiagahOc21CVLXA8simGs50nYbwyBCW2OAGlDfsFvDML0ZgAqasIGbIoypsIZg6IepvAQwdhNE4ol3fqSfVquqbvMxiDnPgUXkMYhhEGmNKQFq5nVhfYjlrpumQ5Ydwtpz5lVGP4jSmBKgZhA653hzqBhEJhs6WEokJtnQICMJGwoGwfswHV1gBqLr2QpWGBmRmBoGURNYPyYZgwi1xh8A9eb2/TA9SADUHtBUzTYY+NFENlcnOVhEB4oJ46UqlOMS03zbhWUR1sZdZiD8aMLQ6YCrYIUsg6mb/q6U5kzo1crMtMnru+c58KMYoeD5RiQmRXU8r0yeazlouxY8x5LGIEwE0FXf2+XNERY7bupo9FqOmhWaWFtjIOrBvKJ3zzCItBsI15E3dhv6k++n8ujGoX6vKR0kL/DqBoWDNcvpn/7u/DCGayCgGcVU+N2lDCIxrgttebuNoqHTAdVhcnFjmMpLANBrqRiEGU84iMSssPhdqOo0TGUxhTEVGiRepd9rOSCEYFlRTW3EQJQwiGMJewBKGISpVhuNgagHbOyoTI6I9UtMtrxaeYpBtNRZTCY8EyAbAp/HwA+Fh4koRhJEBvTqxHCKWMRWTo4AoOzHNPD1G33VYbI1DLDcy2TDjqvYUwOHCY9TyVhhx5t0SAAJKzSUxQSIp8ptj0N4jpW+51LHU0hMZuRWmSN3ZWuUtsIBGPNSzYMwwfSbeRA1YaEjHzs6SrI8dEK1ucOijJPIKiLvz4QcwbvWig475m1mxqtbJjHpjkEk34tIktgZh3Btkn4fCx1VXCnUziBcxWHCDFLe6NvKVFITejV/7SKK11tm9CWsUGM2H5AZfdGe9sdsvgfHYimDqC92c7nAIDqerS5+NHCf+mGsHPC0GzQGIod5VQwi0K9XezaTmESb2x+Lb1iR12ySQYhujGEgkSMEh51vKCUSAEa+wNscBZhLpAignEHkDZ0OyLrgUkoTVpj/3lQMwkxRFSAx+kE4GaRODJlofX5EtR/C6Z6KjP5okk0vKfZ0HMYpG9EFWZprFFNc2x6nGUyAOlZoKtsQAAJFg8jdoDEQOSy05QxiYCJI7VigFAgLrCCOaXII57x0RSMw5m2aCVKLDjupXl0zgxAZy52kUR/HQrveILXM2xwFMShFgXkxiVHEOIwwCMWeFr8LlUNipO6GS0wSVjiXNxAKBtEfh2nLC12QFbTujELEFFhKOvMCrPhRxCDCiM2qrjOZRAcaA5HDfBKDEHn0oyDWnhIpG1HJb8qJQ9iVa8LM29RfKCdaG8A6kOalEn7oib1NAymRisOEt/rmUDGIIhPSAVltCzfsvVa5YaWU1s4K++NJCVXVutoPI3iOKYlJHKSea+cNhDwGYSTxwBa3KOF7OpfbU84gimeIiap9vjZAPfFuN2gMRA7zbQcxhTALwchhIplWlVYqtyb16vy/5WEiaKhMc51BYjKTEin3breTYUEcCx0X4zAWGhNTWUwxxVQ2Dvcq8wyCyyZFox9EFJSaOEzYZy0eJhljzce8+NpEe0qNpC4D1RjEYsfFKBDvaTG5QwdkmWk8PjPJ9G3EdJqljQ3MtAeQZgg2BqIGqNpDm5IjgOnN5QdtdyLN1Zn4Nw7ubdbpmQwEVbf88SJM1UEAKolp0kAA4mrqYSForAOuJBCcMghRILiwp5m3Wc/1xpvkdQryF1CfbKhkEKNpiQkQF0AauU+T9OAiuCPZKzAIYDq4nzWG1L82oDEQtUA2VY57WKYkpqK3kfWeKT+Ew5h5myZS+4DpCy+KWcV0t6rEZPAwEQ2Y2R4HEzEIWT8mSulUuq4OpKwwnDxQRKxQlv3FP5c5Vjj5fgPBQZcZLzFjNVEoB8gYRDQpMfFqakEcoj+OJoywDngOq7uJCrFCXhDXq2BYeRsRU3Gl4p7qwq5WSwhZIYR8nBDyTPL/ZcnzHkme8wwh5JHc499ECPkyIeQsIeTnSZJ6Qgj5fkLIk4SQmBDywG7WOAsWJB1d+QGuO0jdkkhMvClfMaAJTNcapDMNNGdHpIVyYfEw4WvLvou2a4EQuRyh+zApYxB5b3MhOVg2h9MeXUxhjBUW60cGKgYh8TZNscKiQ8INVLEwk/2bYE9NMgiB1r8zDoQMotjyOxIkd+iAzFnKF/BxyKbKmZhpD+Rjhfszi+ldAD5BKb0bwCeS3ydACFkB8JMAvhnAgwB+MmdI/gOAHwZwd/LfQ8njTwD4XgCf2uX6ZkLa0bVgIPhB1DHQXRMQyBGpXj2ZEsnWIqGuhhhE8TDhnlH+YCWEoOuKK0hNBFuzOojJtVFKk3Gjk3o1MM0g8kOPdMJL6gOKh0lfEIOQeZsmht7kX29a0hStTc4KxyYK5RzxnobJAKhiDAKY7ujK79M8E9IBWTJJsatx/ueiI5fFIF5aWUwPA/hA8vMHAHyP4DlvAfBxSukapXQdwMcBPEQIuQ3AAqX0M5SF/P8T/3tK6VcppU/tcm0zY14ydjTLKjKkV1e6YcsOk3py5kU3BSCfV+GHUXpo6gI/TKakmTBGGNMJOUIWgxgE016zDsjy0kXMK51LLfgcgP7DRL6n02uzLVZsWPyOKaVG4koyiYkftMIYREFiyj6HIQYhiysJGEQxVmhMYpIkHujCbld7lFJ6Kfn5MoCjguccB3A+9/uF5LHjyc/Fx2cCIeSdhJDHCCGPXbsmHrJeFdmAGbG3aaKbKyDKYpq+YWXzbs1rm7K1Td6ErNusJONFt7fpsdcrSkzcCIhiEMWAZnGCmi7Ibth+GoOYrI5n/1YIUpuSmCR7OhSwQkDcbZbX7OivgxBnMeXne3DwuoNiqutAwLy1rE3C9Ae5ORUcUgZhek8NGYhSU0sI+QMAxwT/9E/yv1BKKSHEjBCmAKX0fQDeBwAPPPDArt5/IZ1LXWAQAo1WB8pknG5rWmKqTY6Q1WhIGISsSZmRFFybxTyKQeqd3OQxjnRPh0Vv0xQrFEtMooBm6m1OxSAMBalnkErY79Os0NT1JmMQXOfPs8KeZ8OxyFSQum+IQbiOeE/52opdcAEFgzB0hpgKUpd+k5TSN8n+jRByhRByG6X0UiIZXRU87SKAb8/9fgLAHyWPnyg8frHCmo2h5VjwbEsqMWnv5iq9YacPE075py88M54JD6ZJjZfAQBTlCJ75oTtITQgRtvzeLjTqA9gN1HHtKQYh+xy7hVyOmL6GZB1T6/Y2B4LCTCDpKyRhNyaMl0WmYxD5Vt8chBBWTS3ZU90xCM4KRUy/49qwcwOnZHOpjbHCfZ7m+igAnpX0CIDfFTznYwDeTAhZToLTbwbwsUSa2iKEfEuSvfS3JX9fGwghrOW3LEitm7pK9GpOT4sGSUT5xzUziOI86mxt0z1o+A2le20AHxok9ujmCoVSC53pNu4yWWW3kB7CY5ZSm59e13LYoViUDbPMtHqMVya3TcuGxeuN76kJo98WDILiRr9Y/LYgqJAXFa7pgGxP+340ZYzkDMKs0ZfNj98tdrvanwHwnYSQZwC8KfkdhJAHCCG/BACU0jUAPw3g88l/P5U8BgA/CuCXAJwF8HUAH03+/q8QQi4AeB2A/0YI+dgu11kZ84J+TKYlJlGrjY5rT43CrJPyO4lHJ5Mjiv1uRAzCVIYVIJ5LvS2IQQDidhvGGIS0UG46/ZIQImzulkpMNdW2pN9F4fruuIo9NWD02649lebKjX6eFbLf3VRS5BiaYhAyKXg8XbWdxpUkWUz657bscQxCBUrpDQDfIXj8MQB/N/f7+wG8X/K8+wWP/w6A39nN2m4WoglkI0MMgnthReraH4sLuLoCyp8FqfWuDRC3GFBJTHUZL4Bp1lUkJkBmIHi1uhlvM5iK3YTCg6vbkh/CpnLmq6QuA8xrv7o9mnjMVE8hAGg71jQrHIlZ4XzLmapXShMBtFfHM0eteJ/ujKeNvmWRWu/T/Z7meuDAGITY26yNQRRaWXCoDmETN6xnW1OBYJk00xEMSkklJgMMouPZU2uTGQjRVDlTsqEqBiGSPpg0Vw/zkhXKDfwQFpm+hjo1SkwAhBKTqBgNYAZjpxDcT42+ZgahSg8WVW2r9lR7u+99HoM4cGBzqesJUqc3rCC/WuQFiWYYm/ToWq6tYBCT6+vVzSCcaYlJdpgsdNw0XZLDlMSkSjwQHybT6cGmDhNCiHDi3cCP0POyGRrp2gQSk29QNmzNEFeabztTElPaokb7jA956rKoMWCvZQsy027NNNfGQBQgYhCmJCZ+kxXliGIzPA5hkNqQtsnXJ/I2PceayNzgaytOvPMNepuiGd07Y5ZVUnw/UVzJGCtUVMeLrp+uZ8vbp5iSDQWMVba2umXDYmuXnRGTW4vX25wwVhiCEGgfGMS/m2KsiMUgKjII3l9L870gc0h0oTEQBbCZENPBL9si2scsyovRIqEXJKL8vsFMoZbgMGFrm74pOp4DSid76Zg8TFrOtLe5PQom8uU5FpI9zffoH/oh2q41lQiw+3WpGEQ1Vmiq+BHgcaVinyhx23ORbGjS6LedaYlJ1r57vu1ixw8nHJJ+Mha4yIR2i7SAdoqxhBLZUBSDYB2Xda8trbtpYhD1YKHtYuBHEwEpnlWke3Ol6XPjUOjRiQaic8+kLm9TNqZTNK/CpPHqeOKUyGL8AWAMIorpxNpMNHUD5B5dfyxmhb2WghUaOIRlElMxxRVgB10Q0Yl7YS8SD+ZFBqLFHJK8Vz/ww4luubogK7bsS5wlESs00ZIfSGRDyRRDHWgMRAGLgnYbA19/q2+AFb9ZRNTNVeal188gpjp/BmLjlXZY9QUMwoTE5FpiAyHxNvm/cwz8SLu8BKjbpwhZoStIXY5YryPd7IavbzqtWp41BxSMvsGkCGb0p2MQIlbIH8sHqk20+gZY8LzlWIJqfDG7ETpyYay9roWjJZmDrgONgShgQdC7Z2RgmhyH6IZlerUk+OVHE1KJ0SwmKYMQ667ApEdnslBOVAexMw6naiCAvESQ7enQwDQ5QJ4z35fElXote7oOItDfniS/PpGkqdrToYAV1iYxFabJcXCmuDMqMAgDrBBgqdL562ccRggiKjQQ3ZaIQURGHCWA7alozK0ONAaigLQ9dO7CGxryNgF2o03355enz0UxnbjBx2EMQgDHlLcpaFAm+i5ELQbMMghxoZz4MJme82Fi3CjA9rPj2hPeZhjF8MNYEYOYPkxMGHxALDHJrm/RKFmTRl+UxbQ9EnvpfJ+3CqxQd5EcB6uPyr2XojGgnEEYNPoNg6gHou6fwyDS3smVo1Ww/pTSqZnPHPwmzrdm4K2XdcdHAIleHYhv2K5CYjLhbfLDJM+mNgZB2go6j2zOx6TRNyEbAsBy18V6rpGcrNcRf8wP4ymd3ySDEBXKiYPUCqNvKotJxAoVRn9CYpLEUnRgoe1MnAnZCFkJgxDElUzECQH5zGwdaAxEAaK51MzDqsejY4cehMG2NBCcu4lMBb8AucQkTomcnsVrNEjNx44m66OUYmMYYFFgIERBxoFEd9eBxa6HzVwralFbaA6Rzr83e1ptbZnR1++QiFpt9CUxiGw8cG5Px2LmrQNFiSlrDCiOQRSNft2sUBcaA1GAjEEYk5gK1l803J6jk2rC2SHMJraZYjf2VF76MEklnF5bwiCCmgKaicHmjGUUMBmHzyvOY0Ewa1yWjaUDRQaRtaGuqPOH5rzNlsDbHEpmc4skJj9pLNmyDQSDHZY1xWc/U0qxI+h3BGQS005Ne1pswcOZi6xeia+Ho26jrwuNgSiAe5tFA2Hqwut6zkRAi3ubwiC1YBiJvwfeplB3VaS5mmrLAGR1F3x4jEhiEk2VkxWH6cBS152YlzwQjBvl4N9bf8LoR+YkpoK3ySVNWcwLkGSmGZKYgKwwdRiwQPCCIPFgXpDFNJD0u9KBYruWgaJqWzRVzmQWUyMx1Yi2y2ZCFA8TU3r1as/DWn+c/j4IVAxC5JkYpK7CjJdQLEe40xJTYPAwSRlL8l3w4TFLnenDpOVYcG0iYBCmDIQ3McxGxQpFh3Cd3uY4ZJLmfpGYgMxArPWZkV3tTbNC1hpkMq7UN2j0mcSUFVtm40blDCLvyI0DsxJTk+ZaEwghU3RyFEToeGa+qtU5Dzf6mbeZzoJQHCYTlN9kQLNw4QVRzFL7FMZLlBJpKs0VyAbMpAaiO32YsDkf7oRebZJBLCfDbPhhkjWRkx/CE7Eb0xkveUlzLJe/UockJxsGUQyLsHbwupEyiOSaW++z/VoWGAjLIpjzsn5MgSJTTAcWOiyDkAefRUO9OEQzIfyokZgODIoDZkwVVQHASs/D2k5mIIbK4Fe92mbLnTQQsrbQALtIXZtMHCZ1eJs85sElHZHEBLA4BN/TMIrhR7H2ttAcSx0PUUyxnRy+WRO56nq1sZx520ortfPvq3JIhoWDzpRD0i5kwq0le7rSE+/pXK5vmqnmixzFRIcdLhtKWrgDRQZh7nsTtcTRhcZACJCfH0ApZUFqQ57JobkWtsdhSqtVAU2hl26QQbQSvZp7wtk8avF30XEnu1iOAlajYaoOgr0Hj0FwBiE+TPIMQpV2qgN8DRt9fnjJGUSmVxdlQ0NBaneSQQwV34Vo+I0fxkZiSoBIYmLS67KAFQKTLb9Tj95Aqw0gXx+V7KlgxjiHiEGMDSYeNDGImpE3ENyDNskggExvVR3C/MLrT1FXcxcekI1EHSiMF3t8sujr2vYYh+ZaRmo0igHNLAYhPkzyHV1NjRvl4DIXD5xnU/gUh3BtsqE94W2qPG8+B30iM82gVNJOU5e5gWB7uiKQmICk5XdqIAwzCJ7dmFxnfT8CIeJzQZSw0aS5HiCwmRDsQsjGjRqKQRQMhDrNVXzhmSyqArJYgkqOABi1zktMV7dHOLrQMrK2TlFiGvrwHEva6jm/p6YPk+WEQfBUV9kMDSDHIMZFb7MevTqdMS6R23otZzrmZYpBONzo8xiED9siwiwmAJjLzW5RZYrpQCoxjbhsGKIrGAucX8N0FpOZ781tDES9yDMIU5PHOFbnmIG4vsPo9EARpE6H3Nd0wxanVcnmUXN0vUmJ6crWGEfm20bWVtSrNwcBljqulK3kGUQZE9otUgaRaOj9cQjXJkJD3hUEgusIUk/LhuLvouNONog0yW6mJKaBj+WuK21ayIYGcY9e7ljpwGKhgFbVOTZl+sm9TCk1WtvSSEw1gwWpWRYKvznMpbkyD5szCJW3yYfcTwWpDR0mrQLlT71NGYModCY1ySCyOojE2xz40vgDMFnolElMhoLUPAaRYxAyiTI1+uPJPfUMFKLx9wOmWaFcNpwczDQKzDHWYmbaet+Xxh8A1vK7GIMw0e4byBo+csdR1Tk2Y/psTaamyXE0WUw1Y7HjIqasCGcUmKWuKwmDuLHDDUSIlmBiG0dxklqdDKLM2+y2sgZ6QRTjRt83xiD4TTjK1UGIUlw55ttsyld+LoQxBtHhElPGIGTBU270i4VyxhiEZE+lRr/QYv7K1ghHF0yxwsm40o2+L0xx5Zhr5VmhPM6jA/PtQpBa0uobYAe2Z1tpSmwtBqJhEPUh327D1DxqjvmWA8+2cD3J2BhI5txy9FqT4wxNyxH8PfjaALW3yfPqr++MQSnMHSbO5GGyOQyERXIcaXO3UWh8Tx3bwnzLmWAQKmOUN/pxTBFE1OhhAuT3lMttksy0gkNyYX2IE8tdI2srVsev932sKI0+G+4VxTSLQRhiELZFMN/KGvbtjMXzPTi6ubnU6YRAg/Mg8tmGOtEYCAGynOcw52GZ+aoIIVidy2oh+pK+OBwdd3LIvUk5ojjboExi6rhO+n1d2WIG78i8GYnJsVndxTDIMwiFxJR2dA1KmZAOLPWydhuysZkceaNvsrgw/7qpxFSS8tvNsZuBH+JG38eJ5Y6RtbWdgsQ0KGEQuZkQaXq4oUMYmGz5LZsbz7HYcbGWOAhpTzKD8yCALNtQJxoDIUCeQZiOQQAsje9GLs1VdXAVxxmabg0NTOvVMs+pl8tiuro1AmCOQQCTQ4M2hn6JxJRJBGXZWDqw3PXS2ozBuHxPudHnRWzGApoCickicvkjzyAurg8BwJyB8DJWGMcU64NAWiQH5Dq6jrM9VR3au8VCrqOrSjYEgJPLXbywNgCQk5hMM30DMlNjIATIT5UzHYMAgNW5Vmog+iUdKbstJz2E42R4kLFKas4ggkKaq8RYdjw7pfpXthmDMBWkBpL20EGMURBhFMSpYRchnSo3DDNZxVAlNcCcjDTNNSiRI3JGfxyx/xs3+jnZsOs50uyvXi4GcSE1EGYkJjbXhBmI7VGIKKZY6cmvHz4nYmccoj8O4VjEWDwOmJwJMZDMo+Y4udLFeW4gAsMxCMkcdB1oDIQA+apJ03o1wGohbqRprmqJqZuTmEzLEcWMl2EQoe3KZyV3XQd+FCOMYlzdGsEizPiZQsdlIyqzPkwqiSmbKme6UA5IGEQiMQ3GkVIbX2i7aUDb+GEyJRuqe1J1c9PRLqyzA++kIQZBCEnHjt5IYnIqBjGXa+PO4zwmijI58plwO2P1eNM7VrtY6/vYHgVZDMJYmit73cZA1IT80KBhidesA6yja5bmqmYQmbfJD25znsnkhVc28zc/0OjqFquilmVj6QCLx0RpxbIyJTJ/mAQR8zYNfW9sLW5quPqSEbIcdx2Zw7lr/bRHFGDeQGSyYUnMy8tkvAvrQ3iOhUMGjX7btTAK4tRgqvc0SzwwOY+aY7HjYjvp6Fo23vTUCmNZL6wNasliAhoDURvmW0kr4VwWU9tQkBpgqa4DP8LAD0tv2G7uhq3L20wNhGQeNUea/z2OcGXbXDokR9u1MAojZatvjoVcDMJkJ1eOxa6HrVGQZtio3u+eY/PwoxjP3egb39OWoPhRtaddlw3x8cMYFzaGOLHUkTJIHWgnrLCszQaQn0sdMGnWYPwByGZCjMMYUUyVMYjUQNwY1BiDiEqeOTsaAyGAlUtp40E8k9rmoURnvbHjl3omC21Gc0dBVJvElBXKqdeWn0B2ZWtsNP4AJEFqPzMQonGjHJNyhLlxoxzLXReUsjgWYxDyw+SeY/MAgK9d3q5BjpgOUpcxCP68C+tDHDckL3GwsaMx1vvlDGIhNzRoUJJ2qgMLHVaYxwPVqvc7tZpjEIHhPbUnZUOdaAyEBItdN62DUAXxdCDfsK9MYvrGU8sIY4o/e2HD/IVXZBAlXW2zHjQRrm2PcNhQkRxHx2OHyWY6TU5+mLi2hY5rYzvJYjItR/B4yOXNEWKqzq552eE52BbBU5e3jU5sy7/uuKJsmO5pEOLi+sBYBhNHy7EYg0hbfVdLczU5AIqDxyavbLL4iOr9Ftoulrsunq9BYmo1ElP9WEgagbHArNkLj/djutEfl3q3D965AosAnz53o/ac+aEfKvPM+bq3hgGu7/jmGYRjY+RXk5iAbM7H0OB8Dw5urC5usMwflbfZdm2cXu0mDKJm2bBEbuOM8caOj+s7vrEMJo5MYvLRcqzSmiDbImmQ2lSrbw4uU764mexpyfudWu3h/NogN5u9HkdOJxoDIQFv2DfyzU2T4+BBv4sbibepOEwWOy7uu30Rnzl3I3fhmT9MRkGEc9f6OKQofOM3M8//Nh2D4AHU9UEA1yalHuR8201z5s1LTMxAvJgYiLL3e8WxBTw1YSBM9WJKEg+ibO5z2SEMAGev7gAwVwPB0XbZQKO1vo+Vnqdk7oSQdCZE3w+Nx5V48srlTVbjU2ogVrp4PheDqMuR04ldrZgQskII+Tgh5Jnk/8uS5z2SPOcZQsgjuce/iRDyZULIWULIz5PkaiCE/CtCyNcIIV8ihPwOIWRpN+u8GSwmKW3DwLy3yWk0z5suO0xe97JVfOGFjTQn2+TIUYDJER9+/AJu9H2848GT0udzw/bsjT4AszUQAM94ibA59LHYUR8mQDZVjkllhhlEcphwA1F2mNxzbB4vrA3S1Nh66yDUaa4A8PSVbQDmDUQnKX4sa9THMddyWPGjonmeLnCJKWUQJe93x0oXFzeGaZqwKUduuevhDfccVtYB3Sx2u+J3AfgEpfRuAJ9Ifp8AIWQFwE8C+GYADwL4yZwh+Q8AfhjA3cl/DyWPfxzA/ZTSVwJ4GsBP7HKdM4NnLDAKbpa6dj0bbdeqbiDOrMKPYnz66zcAmAug8wt66Ef4xf9xDq86sYjXnVmVPp+v+9lrzECYatTHwSupNwZBOoNBBT5VblhLkHpSYip7Px6ofvLFLQDmi6oGfoRPf/0GtkeBkrFyQ/r0Fc4gapKYBr4y/sDBWn6HSYsa80FqALi0wRhE2fudWukiiinOXWf3g6kspruOzOFX/s6DeOWJJe2vvdsVPwzgA8nPHwDwPYLnvAXAxymla5TSdbDD/yFCyG0AFiiln6Gsy9R/4n9PKf19SilvOPQZACd2uc6ZkQ9SmxoWxEEIwWqvhfPr3ECoL7wHTi/Dtgj++9PXAJhrAkYIq0z9b1++hOdvDPC//sWXKb10fpg8lzCII4YZRL5QTlUkx8FnQtQRpJ5vO7BILgZRwiBekRiIL17YAGA+JfKn/+tX8I5f/AxiCnzjqSXp87upgdiGZ1s4bLAGAuBZTAmDqGggtkcsrqTKsNMBHoPIJCb1+/FMprOJcTWZCWkKu71LjlJKLyU/XwZwVPCc4wDO536/kDx2PPm5+HgRPwjgN2ULIIS8E8A7AeDUqVOVF16GhbaDcRhjcxDg9iWznjDAAtXP30gMRMmFN992cf/xRXzx/AYAsxee51h49nofdx7q4c33HVM+lwdin78xgG2RdNaFKbSTHP0b/TFOrfRKn8976VBqtooaYKnSix037V9UxiBOLnfRcW18JWEQpvZ0vuXgofuOoevZePN9R/EX7j6sNF583efXBzi92jNaAwFkhXKjIMJKBaM/13Lw4sYIYUxrKZQDZghSJ7UQT1/dhmMROAfRQBBC/gCA6GT4J/lfKKWUEKK1nSAh5J8ACAH8uuw5lNL3AXgfADzwwAPa3j9Nadse4WVHyg+f3WKl5+FLFzYBqDNeOF53ZjU1EKa8TSDxOMfAj3zbmdKqaB6rGYcxji20jVZR59/v8uaoEr2ebzvYGoWwCTHa9ZNjueul8Ziyw8uyCF5+dA5fTK4BU6zQsgj+49/6psrP5+um1Hz8AWBBdN6SXdWHiWO+7eLK9gYAs915+evbFsGVpBFl2X16bKENz7GwMQiMx0dMofRkoZS+iVJ6v+C/3wVwJZGKkPz/quAlLgLIRzZPJI9dxKR0xB9H8no/AOBtAP4GNdHovAQ8Y2FjEBhPcwUw4W1XudBf97IsFmCSQbQcC0fmW/grrxGRu0lYFkmHvpiWlwCgzdNqR2FpiivAJAI/jEszd3RhMSmWA6oNsuFxCGD/yBH576kOA5Hv0Kvqw8Qx187mbpgulCOEYKHtIIgoLALp/HMOyyJp3ypTBt80dnsVPgqAZyU9AuB3Bc/5GIA3E0KWk+D0mwF8LJGmtggh35JkL/1t/veEkIcA/GMA300pHexyjTeFhdyBU8dhwmshqr7fA3csw0k8dFMBTQD4wdffiZ/+nvsrp13ym9R0gBrIhgYB6kZ9HLzyFsiMi0nks3CqDLK559gCAIAQwLXNsq+qyGfwHV+qw0Bke1o1BsFhutUGkCkLvYrFs1xmMnmPmsRuV/0zAL6TEPIMgDclv4MQ8gAh5JcAgFK6BuCnAXw++e+nkscA4EcB/BKAswC+DuCjyeP/HsA8gI8TQr5ACPmPu1znzMinjJlOcwVYwz6OKlpqr+XgVSeXAJjLmQeAH/62M3hLSewhD67tm05xzb8XoK6i5uDN3QCzg2U4lma8hniguuVYRiv3Z0GeFZrOYAIm566opslxzOcMr2kGAWSOY1VjdMcqk6dNNoY0iV19o5TSGwC+Q/D4YwD+bu739wN4v+R59wsev2s369KB2g1ELjuk6sX3+rsO4csXNo3GIGZFNzUQdTCIvIGowCA6OW+zhsOEGy1e8VsGLjHtF3mJo+s5GAXmJsnlkb/XqjCIuZyBMJ14AEwyiCo4eYszCPN3yS2KhZy3WYccMcEgKhqkv/cXX4Y3fcORWmIkVdFNJaaaGURnNgZRx2HCazOqpl8emmvh0Fx5wV/d4Id2PQwiO0ir1UFke1oLg2jPyCBSA7F/7tFZcGuatRow4W3WwiDYzeA5VuV0uI5nGymO2Q1qZRDubAxiQq+uwUDwNc3CVl5+dH7fMYhey4Zrk1qM/qx7OldzDIKfC1WNEa+FaBjEAUPLsdOc7Dq8Te4t3arpcBz84K0liynnbVZpM7BQM4PgEtMsxuiH/8KZtGByv6DjOThueA4EB/e051tOJa87b/TrjEFUbQyYBqn3kQw8CxoDocBix8UoGNea5lqHNm4S3RqzmDq7YhB1xCBmO0wA4A2vOGJqOTeNe2+bRxjVk2nOjX6V+AMAzLdyiQd1MAguMVU0+m3XxtGF1i0rMd3ap5FhLHZcXNka1xKk7ng2usl/tzJ4MdFqxRt8N+AswLHIRLBSBpaayIq+6viel2+CQexH/MvvfWVt78WdsaoGYkJiquE+XZgxSA0Aj/z508ZblJhCYyAU4N5CHXIEwOIQt/ph8oZXHIFrW7XIETyLaanrVgrs8kmBW6OwFqOfxSBu7T2tE9xAVGmzAWSscJbY3W6wOKPEBAA/+u17npR502gMhAL8YqjrBj+20DbeOdY03nLfsZnqJnYDbrhnaXM8nwyCqidIzeNKt/ae1olZJSbOHOuK3fFiS9ONAfcLmitXAX7w1JVG+i+/95WowfE+MOCZIVWK5DgWOi4ubgxriUH0PJb9U4c2flDAWWGVIjmA3ZuebdUWu0sL5V4iRv+l8SlvEvxiqEOOAFhf9wbVQQir8q3Sh4ljvs3iEGV9dHSAEIIf/fa78M1nVoy/10EBZ4Urc9WN/lzbqc2j507j3EvE6DcGQoHUQDQa8r5Fx7WxWFGvBphE0HHt2orR/vfvfHkt73NQsNrz8JdeeRu+7e7Dlf9mruXUJs2eWO7gTd9wBK+986Vh9BsDocBti214tjVRrdlgf+F/e+PduPf2hcrPX2i7TdB4H8OxLbz3r79mpr+Zbzu1xSBajo1feuS1tbzXfkBjIBT4q685gdeeXqmUQtlgb/CD33rnTM9/5M+fxre9vLp32mD/48fecFctkuFLEc3Jp4DnWE1c4IDhVSeX0i64DQ4GvuvP3bbXSziwaMxugwYNGjQQojEQDRo0aNBAiMZANGjQoEEDIRoD0aBBgwYNhGgMRIMGDRo0EKIxEA0aNGjQQIjGQDRo0KBBAyEaA9GgQYMGDYQglNYzKaoOEEKuAXj+Jv/8EIDrGpdzK6D5zC8NNJ/5pYHdfOY7KKVTLQYOlIHYDQghj1FKH9jrddSJ5jO/NNB85pcGTHzmRmJq0KBBgwZCNAaiQYMGDRoI0RiIDO/b6wXsAZrP/NJA85lfGtD+mZsYRIMGDRo0EKJhEA0aNGjQQIjGQDRo0KBBAyEaAwGAEPIQIeQpQshZQsi79no9JkAIeT8h5Coh5IncYyuEkI8TQp5J/r+8l2vUCULISULIJwkhXyGEPEkI+fHk8YP8mduEkM8RQr6YfOZ/njx+JyHks8n1/ZuEEG+v16obhBCbEPJnhJD/mvx+oD8zIeQ5QsiXCSFfIIQ8ljym/dp+yRsIQogN4L0A3grgXgDvIITcu7erMoJfBfBQ4bF3AfgEpfRuAJ9Ifj8oCAH8I0rpvQC+BcCPJft6kD/zGMAbKaWvAvBqAA8RQr4FwHsA/Byl9C4A6wB+aO+WaAw/DuCrud9fCp/5DZTSV+dqH7Rf2y95AwHgQQBnKaXnKKU+gA8CeHiP16QdlNJPAVgrPPwwgA8kP38AwPfUuSaToJReopT+afLzNtjhcRwH+zNTSulO8qub/EcBvBHAh5PHD9RnBgBCyAkAfwnALyW/ExzwzyyB9mu7MRDs0Dif+/1C8thLAUcppZeSny8DOLqXizEFQshpAN8I4LM44J85kVq+AOAqgI8D+DqADUppmDzlIF7f/wbAPwYQJ7+v4uB/Zgrg9wkhjxNC3pk8pv3adnb7Ag0OBiillBBy4HKeCSFzAH4LwD+glG4x55LhIH5mSmkE4NWEkCUAvwPgFXu7IrMghLwNwFVK6eOEkG/f4+XUiW+llF4khBwB8HFCyNfy/6jr2m4YBHARwMnc7yeSx14KuEIIuQ0Akv9f3eP1aAUhxAUzDr9OKf3t5OED/Zk5KKUbAD4J4HUAlggh3Bk8aNf36wF8NyHkOTB5+I0A/i0O9mcGpfRi8v+rYI7AgzBwbTcGAvg8gLuTrAcPwNsBPLrHa6oLjwJ4JPn5EQC/u4dr0YpEh/5lAF+llP5s7p8O8mc+nDAHEEI6AL4TLPbySQDflzztQH1mSulPUEpPUEpPg927f0gp/Rs4wJ+ZENIjhMzznwG8GcATMHBtN5XUAAgh3wWmY9oA3k8pffferkg/CCG/AeDbwVoCXwHwkwD+C4APATgF1ib9f6GUFgPZtyQIId8K4H8A+DIybfr/BotDHNTP/Eqw4KQN5vx9iFL6U4SQM2De9QqAPwPwNyml471bqRkkEtP/QSl920H+zMln+53kVwfA/0spfTchZBWar+3GQDRo0KBBAyEaialBgwYNGgjRGIgGDRo0aCBEYyAaNGjQoIEQjYFo0KBBgwZCNAaiQYMGDRoI0RiIBg0aNGggRGMgGjRo0KCBEP8/CtfNCg+9xTkAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sol.t,solexp0(sol.t)-solexp1(sol.t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv",
   "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": "3.8.5"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}