Helium-HF.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
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   "source": [
    "<h2 style=\"margin-bottom:0px;\"><center>Restricted Hartree–Fock for Helium</center></h2>\n",
    "\n",
    "<p style=\"text-align: center; margin-top: 10px; margin-bottom: 0px;\">\n",
    "    By <a target=\"_blank\" href=\"https://github.com/yueyericardo\">$Richard\\;Xue$</a>&nbsp;/&nbsp;\n",
    "    <a target=\"_blank\" href=\"https://github.com/yueyericardo/hartree-fock\">$Source\\;code$</a>\n",
    "</p>\n",
    "\n",
    "<p style=\"text-align: center; margin-top: 5px; margin-bottom: 0px;\">\n",
    "    $2018/12/07$\n",
    "</p>\n",
    "\n",
    "<p style=\"text-align: center; margin-top: 5px;\">\n",
    "    <a target=\"_blank\" href=\"https://yyrcd.com/hf/he.html\">$Helium$</a>&nbsp;/&nbsp;\n",
    "    <a target=\"_blank\" href=\"https://yyrcd.com/hf/li.html\">$Lithium$</a>&nbsp;/&nbsp;    \n",
    "    <a target=\"_blank\" href=\"https://yyrcd.com/hf/be.html\">$Beryllium$</a>\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "from sympy import oo\n",
    "import numpy as np\n",
    "from itertools import product\n",
    "from scipy.linalg import eig\n",
    "from sympy import diff\n",
    "import time as time\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy.plotting import plot\n",
    "# %matplotlib notebook \n",
    "%matplotlib inline\n",
    "from IPython.display import Math\n",
    "sp.init_printing()\n",
    "\n",
    "r, r1, r2, zeta, zeta1, zeta2 = sp.symbols(\"r, r1, r2, zeta, zeta1, zeta2\")\n",
    "n = sp.Symbol('n',integer=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<h2><center>Part 1 Function Definition</center></h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define STO function\n",
    "<p><a href=\"https://en.wikipedia.org/wiki/Laplace_operator\">$STO$</a>$ \\; function \\; has \\; format \\; of: \\; Nr^{n-1}e^{-r\\zeta}$</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For example: STO for 1s\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$2 \\zeta^{1.5} e^{- r \\zeta}$$"
      ],
      "text/plain": [
       "   1.5  -r⋅ζ\n",
       "2⋅ζ   ⋅ℯ    "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def STO(zeta, n, r=r):\n",
    "    return (2*zeta)**n*(2*zeta/sp.factorial(2*n))**(1/2)*r**(n-1)*sp.exp(-zeta*r)\n",
    "\n",
    "print(\"For example: STO for 1s\")\n",
    "STO(zeta, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Overlap Integrate\n",
    "\n",
    "$S = \\int_{0}^\\infty f_1^* f_2 \\; r^2dr$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# S Overlap Integrate\n",
    "def S_int(f1, f2):\n",
    "    return sp.integrate(f1*f2*r*r ,(r, 0, +oo))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hamiltonian core\n",
    "\n",
    "H core = kinetics energy + electron and nuclear potential energy\n",
    "\n",
    "$H = \\int_{0}^\\infty f_1 \\hat{H} f_2 \\; r^2dr$\n",
    "\n",
    "$H = \\int_{0}^\\infty f_1 ((-\\dfrac{1}{2}) \\nabla^2 - \\dfrac{Z_{\\alpha}}{r})f_2 \\; r^2 dr$\n",
    "\n",
    "<p><a href=\"https://en.wikipedia.org/wiki/Laplace_operator\">$Laplace \\; operator: $</a> $\\nabla^2$</p>\n",
    "<p><left><img class = \"none\"style=\"text-align: center; margin-left:0px\" src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/b4a3135d1cc01d19309d36c749aaef4a48dc81da\"></left></p>\n",
    "\n",
    "$\\therefore H = \\int_{0}^\\infty f_1 ((-\\dfrac{1}{2}) \\dfrac{1}{r} \\dfrac{\\partial}{\\partial r} \\dfrac{\\partial}{\\partial r} r f_2 - \\dfrac{Z_{\\alpha}}{r}r^2 f_2 )dr$\n",
    "\n",
    "**reminder:** change the Z of nucleus if you want to run for other atom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# H core = kinetics energy + electron and nuclear potential energy\n",
    "def H_int(f1, f2, Z):\n",
    "    return sp.integrate(f1*(-((1/2)*(1/r)*diff(diff(r*f2, r), r))-((Z/r)*f2))*r*r, (r,0,+oo))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Returns the core hamiltonian matrix\n",
    "def H_matrix(fs, Z):\n",
    "\n",
    "    H = np.zeros((len(fs),len(fs)))\n",
    "    for i in range(len(fs)):\n",
    "        for j in range(len(fs)):\n",
    "            H[i, j] =  H_int(fs[i], fs[j], Z)\n",
    "\n",
    "    return H    \n",
    "\n",
    "# Returns the overlap matrix\n",
    "def S_matrix(fs):\n",
    "\n",
    "    S = np.zeros((len(fs),len(fs)))\n",
    "    for i in range(len(fs)):\n",
    "        for j in range(len(fs)):\n",
    "            S[i, j] =  S_int(fs[i], fs[j])\n",
    "\n",
    "    return S  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two elecron repulsion integral\n",
    "$(rs|tu) = \\int \\int \\dfrac{f_r^*(1) f_s(1) f_t^*(2) f_u(2)}{r_{12}} \\; dv_1 dv_2 $\n",
    "\n",
    "For 1s 2s orbital\n",
    "\n",
    "$(rs|tu)  = \\int_{0}^\\infty \\int_{0}^\\infty \\dfrac{f_r^*(1) f_s(1) f_t^*(2) f_u(2)}{r_{12}} \\; r_1^2dr_1\\; r_2^2dr_2  $\n",
    "\n",
    "$(rs|tu) = \\int_{0}^\\infty f_r^*(1) f_s(1)  \\; r_1^2dr_1\\int_{0}^\\infty \\frac{ f_t^*(2) f_u(2)}{r_{12}}\\; r_2^2dr_2  $\n",
    "\n",
    "From problem 9.14 in quantum_chemistry by levine\n",
    "\n",
    "$(rs|tu) = \\int_{0}^\\infty f_r^*(1) f_s(1)  \\; r_1^2dr_1\\int_{0}^\\infty \\frac{ f_t^*(2) f_u(2)}{r_{>}}\\; r_2^2dr_2  $\n",
    "\n",
    "$(rs|tu) = \\int_{0}^\\infty f_r^*(1) f_s(1)  \\; r_1^2dr_1(\\int_{0}^{r_1} \\frac{ f_t^*(2) f_u(2)}{r_{1}}\\; r_2^2dr_2 + \\int_{r_1}^\\infty \\frac{ f_t^*(2) f_u(2)}{r_{2}}\\; r_2^2dr_2)  $\n",
    "\n",
    "$Let \\; B= \\int_{0}^{r_1} \\frac{ f_t^*(2) f_u(2)}{r_{1}}\\; r_2^2dr_2 + \\int_{r_1}^\\infty \\frac{ f_t^*(2) f_u(2)}{r_{2}}\\; r_2^2dr_2$\n",
    "\n",
    "$(rs|tu) = \\int_{0}^\\infty f_r^*(1) f_s(1) B \\; r_1^2 dr_1  $\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "def Repulsion_electron(zetas):\n",
    "    \n",
    "    f1=STO(zetas[0][0], zetas[0][1], r1)\n",
    "    f2=STO(zetas[1][0], zetas[1][1], r1)\n",
    "    f3=STO(zetas[2][0], zetas[2][1], r2)\n",
    "    f4=STO(zetas[3][0], zetas[3][1], r2)\n",
    "    fs = [f1, f2, f3, f4]\n",
    "    \n",
    "    B = (1/r1)*sp.integrate(f3*f4*r2*r2 ,(r2, 0, r1)) + sp.integrate((1/r2)*f3*f4*r2*r2 ,(r2, r1, +oo))\n",
    "    A = sp.integrate(f1*f2*r1*r1*B ,(r1, 0, +oo))\n",
    "    return A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Density matrix\n",
    "$ P_{tu} =2 \\sum_{j=1}^{n/2}c_{tj}^* c_{uj} $\n",
    "\n",
    "**Reminder:** P need to be changed if the atom have unpaired electron"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculates Density matrix\n",
    "def P_matrix(Co):\n",
    "\n",
    "    P = np.zeros([Co.shape[0], Co.shape[0]])\n",
    "\n",
    "    for t in range(Co.shape[0]):\n",
    "        for u in range(Co.shape[0]):\n",
    "            for j in range(int(Co.shape[0]/2)):\n",
    "                P[t][u] += 2* Co[t][j]*Co[u][j]\n",
    "    return P            "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fock matrix\n",
    "$ F_{rs} = H_{rs}^{core} + \\sum_{t=1}^{b} \\sum_{t=1}^{b}P_{tu}[(rs|tu)- \\frac{1}2(ru|ts)] $  \n",
    "\n",
    "$G = \\sum_{t=1}^{b} \\sum_{t=1}^{b}P_{tu}[(rs|tu)- \\frac{1}2(ru|ts)]$ \n",
    "\n",
    "$ F_{rs} = H_{rs}^{core} + G $  \n",
    "\n",
    "$In\\;G \\;one\\;is\\;coulombic\\;repulsion,\\;another\\;is\\;exchange\\;energy$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def R_matrix(zetas):\n",
    "    R = np.zeros((len(zetas), len(zetas), len(zetas), len(zetas)))\n",
    "\n",
    "    rs = list(product(range(len(zetas)),repeat=2))\n",
    "    tu = list(product(range(len(zetas)),repeat=2))\n",
    "\n",
    "    for r, s in rs:\n",
    "        for t, u in tu:\n",
    "            R[r,s,t,u] = Repulsion_electron((zetas[r], zetas[s], zetas[t], zetas[u]))\n",
    "    return R\n",
    "\n",
    "# Caculate G Matrix\n",
    "def G_matrix(zetas, Co, R):\n",
    "\n",
    "    G = np.zeros((Co.shape[0], Co.shape[0]))\n",
    "\n",
    "    P = P_matrix(Co)\n",
    "    \n",
    "    rs = list(product(range( Co.shape[0]),repeat=2))\n",
    "    tu = list(product(range( Co.shape[0]),repeat=2))\n",
    "\n",
    "    for r, s in rs:\n",
    "        g = 0\n",
    "        for t, u in tu:\n",
    "            int1 = R[r, s, t, u]\n",
    "            int2 = R[r, u, t, s]\n",
    "#             print('({0}{1}|{2}{3}): {4}'.format(r, s, t, u, int1))\n",
    "            g+= P[t, u] * (int1 - 0.5 * int2)\n",
    "        G[r, s] = g\n",
    "    return G\n",
    "\n",
    "# Returns the Fock matrix\n",
    "def F_matrix(fs, Z, zetas, Co, R):\n",
    "    return H_matrix(fs, Z) + G_matrix(zetas, Co, R)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solve Hartree-Fork equation\n",
    "\n",
    "$det(F_{rs}-\\epsilon_i S_{rs} = 0)$  \n",
    "\n",
    "$The\\;energy\\;returned\\;is\\;the\\;orbital\\;energy\\;for\\;1\\;electron$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# slove secular equation, return the energy and improved coeffients\n",
    "# the energy here is orbital energy for 1 electron\n",
    "def secular_eqn(F, S):\n",
    "    ei, C = eig(F, S)\n",
    "    \n",
    "    # sort eigvalue and eigvector from lower to higher\n",
    "    idx = ei.argsort()[::1]   \n",
    "    ei = ei[idx]\n",
    "    C = C[:,idx]\n",
    "\n",
    "    # eigvector from scipy.linalg.eig is not normalized, which is a bug\n",
    "    # this is to fix it\n",
    "    Co = np.zeros((C.shape[0],C.shape[0]))\n",
    "    inte = np.matmul(np.matmul(C.T, S), C)\n",
    "    for i in range(C.shape[0]):\n",
    "        for j in range(C.shape[0]):\n",
    "            Co[j][i]=C[j][i]/np.sqrt(inte[i][i])\n",
    "\n",
    "    return ei, Co"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Return atom energy\n",
    "$ E_{HF} = \\sum_{i=1}^{2/n}\\epsilon  +\\frac{1}2 \\sum_{r=1}^{b} \\sum_{s=1}^{b}P_{rs}H_{rs}+V_{NN} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# return energy of atom\n",
    "def get_E0(e, P, H):\n",
    "    \n",
    "    E0 = 0\n",
    "    for i in range(int(e.shape[0]/2)):\n",
    "        E0 += e[i].real \n",
    "    E0 = E0 + 0.5*(P*H).sum()\n",
    "    return E0 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<h2><center>Part 2 Hartree Fork Iteration (Main Process)</center></h2>\n",
    "\n",
    "- Initialization\n",
    "    1. initializing Co (coefficients) without considering electron repulsion\n",
    "    1. Solve Hartree-Fork equation with H_matrix and S_matrix to get initial Co\n",
    "\n",
    "\n",
    "- Iteration\n",
    "\t1. Using Co, we can get P_matrix (electron density)\n",
    "\t2. Using P_matrix, H_matrix, G_matrix => F_matrix\n",
    "\t3. Solve Hartree-Fork equation with F_matrix and S_matrix to get improved orbital energy and Co, which also means improved orbital functions.\n",
    "\t4. Using improved Co, return to step 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------ Initialization ------------------------------\n",
      "------------------------- Ignore repulsion integral ------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Basis \\ Function:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\chi = N r^{n - 1}e^{-r \\zeta} $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 1.450 \\quad \\zeta_2 = 2.910$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = c_{11} \\chi_1 + c_{21} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2 = c_{12} \\chi_1 + c_{22} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = -0.660 \\quad c21 = -0.380 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = -1.702 \\quad c22 = 1.785 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -1.979 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = 1.030 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -3.95867 \\ hartree = -107.71936 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------ Iteration 1 ------------------------------\n",
      "------- Iteration 1 needs more time to caculate Repulsion Integral ------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 1.450 \\quad \\zeta_2 = 2.910$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = c_{11} \\chi_1 + c_{21} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2 = c_{12} \\chi_1 + c_{22} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = -0.834 \\quad c21 = -0.192 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = -1.624 \\quad c22 = 1.815 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -0.838 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = 2.903 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -2.78431 \\ hartree = -75.76376 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 2.4 s\n",
      "------------------------------ Iteration 2 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 1.450 \\quad \\zeta_2 = 2.910$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = c_{11} \\chi_1 + c_{21} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2 = c_{12} \\chi_1 + c_{22} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = -0.842 \\quad c21 = -0.183 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = -1.620 \\quad c22 = 1.816 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -0.915 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = 2.815 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -2.85860 \\ hartree = -77.78526 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 0.5 s\n",
      "------------------------------ Iteration 3 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 1.450 \\quad \\zeta_2 = 2.910$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = c_{11} \\chi_1 + c_{21} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2 = c_{12} \\chi_1 + c_{22} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = -0.842 \\quad c21 = -0.183 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = -1.620 \\quad c22 = 1.816 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -0.918 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = 2.811 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -2.86152 \\ hartree = -77.86483 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 0.5 s\n",
      "------------------------------ Iteration 4 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 1.450 \\quad \\zeta_2 = 2.910$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = c_{11} \\chi_1 + c_{21} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2 = c_{12} \\chi_1 + c_{22} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = -0.842 \\quad c21 = -0.183 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = -1.620 \\quad c22 = 1.816 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -0.918 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = 2.810 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -2.86166 \\ hartree = -77.86869 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 0.6 s\n",
      "------------------------------ Iteration 5 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 1.450 \\quad \\zeta_2 = 2.910$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = c_{11} \\chi_1 + c_{21} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2 = c_{12} \\chi_1 + c_{22} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = -0.842 \\quad c21 = -0.183 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = -1.620 \\quad c22 = 1.816 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Ke0lOTpZDhw6VUkrpcDhkbGyszMrKcvmZ9u3bV95zzz1SSilXrVolExIS5Jw5c+Tzzz8vpZSytLRUxsfHy927d8uYmBh54sQJGRoaKi0Wi8vy9f1v50KjvmM9dkqqEOJVYCKQIaWMc3H9n8DC8h+LgBullLvc1X5JhpY8KH5YAlYrvP02GAzg66v9e8wYiIzUygZ3iSVfbEdmNTz/oCitYcwY99bXmOyedSW8b8z1b7/9lmnTphEeHg5Ahw4dKCioPRKPjo7mjDPOAOCnn35i6tSplfmIL7vsMjZv3sykSZOIiYlhyJAhAAwbNsxlNrbNmzczdepU/Py03CmTJk2qt5+jR4+us95BgwYxf/58Fi5cyMSJEyuzuLnSo0cPwsLC2LlzJydPnmTo0KEucyGUlpaSk5NTmet57ty51eYMAL766ivi4+OJjIwkKCiIzp07YzabcTgcLst7giePzl4LPAusq+N6MnCelDJXCDEBWAOMclfjjlw9pfjQMbInn38Bf/wBS5dCnz4waxZ8+CGUZ7kD384U+RgwFdZxmqqi/AXJOhLeN+a6lBIhGj6SvmpCellPFkiTyVT5b71eX+fjI1dt1tXPlJSUOuvt06cP27dvZ+PGjSxevJjx48dXfpm7MmvWLNauXUt6ejrXXnutyzJ79+5l1KhRGAx1f+3+/vvvDBo0iF27djF48GAyMjIIDAys9jl5msfmFKSUPwI59Vz/RUqZW/7jb0CUO9sXhXqK9CaETs8PP0BAAIwbBz17QkwM/PgjVP43KHTYAp0EWNWuZqVt+v579/5pjHHjxvHBBx+QkZEBQE5ODkeOHGnU9XHjxvHee++RnZ1dea1msvuaRo8ezccff0xJSQnFxcV89NFH9f6G7ur9H330ERaLhcLCQj777LNG3Ycrx48fx8/Pj6uvvpr58+ezY8eOatdr3svUqVP54osv2Lp1KxdddJHLOvfs2cPgwYPrbTcoKIg//viD3bt3M3jwYO67777KSeWWWpLaVpLsXAd87s4KjRawGPVICdu2weDB4FN+2sWIEfD883DgAPTrp72m62AjMKuU7PzjhAVHurMritIu1ZXwPjo6usHrAwcOZMmSJZx33nno9XqGDh3K2rVrqyW7r7mCJiEhgZkzZ1Ymt581axZDhw51+ajIlYSEBK644gqGDBlCdHR0ZUCpq5+dO3eus649e/awYMECdDodRqOR559/vtr1sLCwaveyYsUKxo4dS0hICHq96xWPe/bsqby3ulx99dVMnTqVDRs2EBoayvTp07m1/JHGlClTmDJlCrm5ucyfP5/x48c36nNpssZOPjTnD9ADSGygzFhgPxBWT5nrgW3Atu7du9c7wVJhrv5xOSNkpUxKkrJ/fylfe+3UtZQUKUHKlStPvXbTmGVyKUvlV19/1Kj6FcWT2sJEs9J4DodDxsfHy4MHD7qlvsGDB9c5WX3HHXfI7du31/v+05lobtUlqUKIwcDLwGQpZXZd5aSUa6SUw6WUwyMiIhpVt7/DiiPAwbZtsH8/xMefuhYdDZdcAr9W2asWGas9S9r9y9Hm3IqiKH9R+/bto1evXowbN47eves+kbmxrFYrhYWFtSarZQstSW21x0dCiO7ABmCGlNKtyQwK8vIxUYY+xMD//gcRERBXY/1T587wxRfgcIBeDwPiO7CbTI7uyXdnVxRF8XIDBgwgKSnJbfWZTCaX9T3zzDN8/fXX5Ofnc+jQIW644Qa3tVmVJ5ekvg2MAcKFEKnAfYARQEr5AnAvEAasLl8xYJdSDndH23t/30UqXTF3ymDXLujWDYw1MnKOHg3r1sGhQ9C3L4w8qy+7ySQ/2R09UBRFca92vyRVSnllA9dnAbM80XbSgSSiSKM03MiJYjj//NplEhLAboetW7WgENk3hiJ2YD/Z9rfaK4qieIpXHnNxPEVbCRsYruc//4Eq+20q9e+vbWTbulX7WfhFUWg0Y8xvKwuyFEVRWp5XBoXs49rOZHOQdu5R3761yxgMcNllULnUWO+DxRf8S+reQKMoiuLtvDIo5Gdouxqdem0dcsVehJpCQuD996HicEZnSBlBditlDpVXQVGUvyavDAqWHO22cov7Eh4OPXq4LhcfD0VFkFw+uezb0YoPdvbt39IyHVWUesh6jn1QlLqc7n83XhkUrAXaUqOj6T3x9z+1k7mm+HjQ6WDfPu3n8O7akGH7T2oJktK6zGYz2dnZKjAoTSKlJDs7G7PZ3Ow6vHJW1VloxI6OI6lmynfku9Sv36mg8Le/QewAP9I2FHBoZ1bLdVZRXIiKiiI1NZXMzMzW7orSzpjNZqKimn+UnFcGBYPTSqlBkJICY8fWXS4oSJtXqNgnMnxUD9LYTeZBtSxVaV1Go5GYmJjW7obyF+SVj49kQSA2nZG0tLrnEyrExp6aUxg4qjdlGChNq+N5k6IoipfzyqBgLIMyg7aqqKGgEBNzKigYQ3pQoPND5KigoCjKX5N3BgWHE7uPNkHXmJHCkSPaGUgYAyg26/Etajg5iKIoijfywqAgMTvsOMxOzjwTunevv3RMDJSVQVqa9rM90E6grQxQqz4URfnr8bqgUGazYMKGNDn59VdoaBI+Nlb7u2KyWR9uI1BaSM867NmOKoqitEFeFxTyctIxU4o0OwkPhyopWF2qWOBRMa8QHKUdkfHr5l0e7KWiKErb5HVBIS3tCD6UIU2SyEZk1ezWTdurUDFS6NZb+0j2bUnzYC8VRVHaJq8LCqkpxwFwGGlUUDAatXmHipHCoAQts9vxfcWe6qKiKEqb5XVB4cSxXADKdIZGBQXQHiFVjBRGnaulaCs8olYgKYry1+N1QSHreAkAxXZzo4NC1Q1sQVF9KRK+ODON9b9JURTFC3ldUMjLsgNQbAtu0kghPR1KSgBTOIVGH3wKvPIEEEVRlHp5XVAozNH2F9h0HenSpXHvqViWmpICCIHV34l/qcMj/VMURWnLPBYUhBCvCiEyhBCJdVwXQoinhRCHhBC7hRAJ7mi3NFe7pcNHerhMw+lKzWWpIsxGsMOCzW5zR5cURVHaDU+OFNYCF9dzfQLQu/zP9cDz7mjUWqAHIL+wO2FhjXtPzQ1s5s4WjNjZvn2/O7qkKIrSbngsKEgpfwRy6ikyGVgnNb8BIUKIRj7wqZujWAsKVhnY6KAQEQF+fqdGChE9tHmJnT+VZ99xOmHrVli/Htau1f7tVMdrK4rifVpzNrUrcKzKz6nlr52oWVAIcT3aaILuDRxmJC0GbBhwoic0tHEdEaL6stTeg304DBxNPA6JibB8ORQUQG4uFBdrmxt694abboJzz21cI4qiKO1Aa040u9oI4PIUOinlGinlcCnl8IiIiPorteix6gyEhIBe3/jOVF2WOvwM7XlS1j4rzJqlLUuaPh0++QQ2bYI774TsbJg5UwsYKmWioiheojVHCqlAtyo/RwHHT7dSg01g0+sa/eioQkwMfPed9v3eO/5MssilKLME4jrC6tXQteupwldeCVOmwMKF8MUX2qOku+/WhhyKoijtWGuOFD4FrilfhXQGkC+lrPXoqKkMZWAziCYHhdhYKCrSBgB6U1eE3o4pzweefrp6QKjg6wsrV8KFF8J998GyZafbdUVRlFbnsZGCEOJtYAwQLoRIBe4DjABSyheAjcAlwCGgBPiXO9r1sUvs/tChQ9PeV7EsNSkJwn9+gRKTDlMJ9Wfp0engnnvg8GH45hvo3x+mTWtu1xVFUVqdx4KClPLKBq5L4Ga3Nuosw+RwUGiUzRopACTvKmDk229jC7iCsMxGzBUIAWvWwHnnafMPCQmnKlMURWlnvGtHsy0XkyzD6dP0oFAxIEh+fxuYTOhCrQRKCyUWa8NvNpngvfdg4ED45z/Lc3sqiqK0P14VFAryjmDGit3U9KAQEAAR4U6S9pdCdDT+XazocbJ9697GVdC9O9xyC/z2G7zwQtM7ryiK0gZ4VVA4mpaMETtOo2zynAJAbEAmyalGuO02ImK0zWl7fmtkUABt2epNN8GCBXDkSNM7oCiK0sq8KigcSz4JgN3Q9CWpSElM7g6S/AfBiBHE9vcD4EhiRuPrEEJbpioE3H57EzugKIrS+rwqKJxIywOgTG9selDYsYPY/B0ctURgt0PCSG05Uk6yvWn1dO8OS5bARx9pG90URVHaEa8KClnp2qRwqdO/6UFh/XpiDKnYnXpSU6F/wkjs6ClNb8ZHdOed2jEYc+eCtRET1YqiKG2EVwWF3Axt1U9hWXDT5hQcDtiwgdiJAwDtuAu9fzSFOl/IbcaqXZNJ2/RmNGoH6CmKorQTXhUUinK0YyYKSiOaNlL48Uc4doyYC3oC5Qfj6fQUm/SYi5t5dMXFF0NkpLa5rbi4eXUoiqK0MK8KCiX52gl4xSWdCQxswhs3b4ZBg+h29Xno9acOxrP5S/xtp7Hn4P77ITMTnnuu+XUoiqK0IK8KCrbyvMrSENn4s+mkhFdegZgYDMH+dO9eJQNbqJVAp4VSWzPnBc48UxsxPPYYFBY2rw5FUZQW5FVBwVHsA4BfcFDj35SYCEePwsSJQPW8Cr6dbRhwsGPHaWRgu/9+7ZS9Z59tfh2KoigtxKuCgizWY8VIWEQTbuubb+CMM2DCBKB6XoWIHtqjo12/7nH93vx9cPhVSHxI+3N4HRQerl5m5Ei49FJYsUJL1KMoitKGtWY+BbcTpQasuiYem/3559qXdVQUoI0UTp7U5oZj+/lyBCspe2psYMvdRf72J3nkRV9Sd3ZH5vrRqbiEfP/jWDu/wbmT07j+tqug0xit/P33w/Dh2oqku+92y70qiqJ4gleNFPQ2HVadvvHLUa1WbZJ53LjKlyoOOE1JgaEjogHISbades+hV3hyyRPc+vehFH3SE1O6GQIgL9yEoUxH9/16djycwFV9d7F2yRyw5cOwYTBpEjzxBOTluedmFUVRPMCrgoLRJihryhEXv/0GFku1oFA1r8LAkcNxoMNyojyv58HnmDPzIEkvx+HjdBA6K4QXcm/jjSPzeCX1Tl4o+DfXHrwaObYYU4mRHx4ezvXDVlKU9hssXaoFhJUr3XrPiqIo7uQ9QUFKfOySMgONDwrffKMlyjnvvMqXKoJCcjIYAmMo1PlBjgGS3+CGa9LQ/9qVvHBfHjgwgwdWz8ZgrJ4IumevHrz47Z3cvf8ibF2LsO/vyLy+v3Kw9DBMnQpPPQW5uW66aUVRFPfynqBgL8bH4cDu04SgcPy49kUdElL5UkQE+PtXbGAzUOxjwFSsY8GtP1P2exdsnWy8nHQ9kZEd6626Z8+evHnsdgIusRFZXMTT5x5hy6VnaPMXTz7Z/PtUFEXxIK8JCg5bHmanHadPI4/NLiuDN9+Ebt2qvSyENlo4tYHNSWCpHesXPTHoSnlsz2zMZlOj+/X0p7fhv7AzBUYDb12v57erJ2mb2bKzm3B3iqIoLcNrgkJBcRomynA2NsHO7t1QWgqjRtW6VHVZqgy2EuwsQe+AKz89mw5hwU3u28JHZjPsHjP+Thvr3x7Djv5RapezoihtkkeDghDiYiHEASHEISHEIhfXuwshvhNC7BRC7BZCXNLcttLTj2DA0fhUnFu2aH+7CAoVG9hkcRoy34QOScFFOsZccFZzu8dtd82hw12BlOn0vLDz/8h680UoKWl2fYqiKJ7gsaAghNADzwETgAHAlUKIATWK3Q28J6UcCkwHVje3vaMp6QA4jY3cp7BlC3TseCo5cxWxsdo+hd1frKJrtvbFPeKSiOZ2rdL85bcQdrmNrpYibsu9E8fLL552nYqiKO7kyZHCSOCQlDJJSmkD3gEm1ygjgYozKYKB481t7ESqtv7fYTA0bk5hyxZtlODikKSYGIjqcIwn7/HHjJZk58jek83tWjUPvzmfo4PM9Mks5LpXssHexCQ+iqIoHuTJoNAVOFbl59Ty16paClwthEgFNgK3uqpICHG9EGKbEGJbZmamy8ay0ksBcBhMmM0N9Cw3Fw4ccPnoCLSgMGfCQzgPRJEcEqrVf9h9yXLW7JjPkdBAonf78OD/LXRbvYqiKKfLk0HB1TmlssbPVwJrpZRRwCXAeiFErT5JKddIKYdLKYdHRLh+jJObof3GLQ0BDfcdMUOjAAAgAElEQVRs61bt77qCQmQWf2zrSi9nKucvC8KJwHJc77Jsc+gNepZtn0qO2cjBdwbyw8b/uq1uRVGU0+HJoJAKVF3vGUXtx0PXAe8BSCl/BcxAeHMaK8wp/4dPI96+ZYv22GjECNd1JT5HyJ9BJAWGcs0NV1Ek/JA5xuZ0q06RMTGMm5tLd2c666YdwmIpdWv9iqIozeHJoLAV6C2EiBFC+KBNJH9ao8xRYByAEKI/WlBw/XyoAZZc7Td5vblLw4W3bIF+/SDYxfJSp4NHlmfSwZlLdkIw6H0o8jFiKnLfSKHClAcexDLqON0tecw6Wx2trShK6/NYUJBS2oFbgE3AfrRVRnuFEA8IISaVF7sTmC2E2AW8DcyUUtZ8xNQo1vIEO34hDawSkvLUJLOry+lfU/p9L3IMgSSmXA2AzU/iX+psTrfqZzLxxNSupHbwJXanhWcee839bSiKojSBR/cpSCk3Sin7SCl7SimXl792r5Ty0/J/75NSni2ljJdSDpFSftncthxFBiQQGBZaf8HkZMjK0nIouPDq6nfpYssnO95Iaqoeux1kSBlBjlIsZe7fVyBuuImFXVZTKnzYf1cBGenpbm9DURSlsbxmR7MsMWDFRGiHBpYe7d4N557rej7Blsv3r/clnXAS/nEpDgccOwa+HcvwoYy9fyS6v+PBwfSaOJ0OZ2+jkyOPO899w/1tKIqiNJLXBAVhMWAVPoQ3NM+8dSv88gsMHFjrUvbutXQ9bqe0SzHDhmuJFZKTIay79ujo9188EBQA5s5lsUjncBdfeh4q5pl7n/ZMO4qiKA3wmqCgt+qw6gwN72beswf69gVT7UPtnnwiGV+nnV7TO1Ym20lKgug+ftq/d3vo0U5kJPTtxwPGx8nRBZK03MaJI0c805aiKEo9vCYoGG06bI1JsJOYCHFxtV+3nCT1yx6kio7Me/AKoqJAr9dGCoMTtAxsWYc9uPt4/nx6HMsi8h+HyHOGs3jsu55rS1EUpQ5eExR87GA3iPqPuCgs1L7lBw2qdSl1x5tE5Vgo7VaKv78vBgOcc452BlLcGfFIoDjNgymt+/aFyZNZ9OW7lHbPJibZwnNLX/Bce4qiKC54RVCQUuLjcGJv6ITUffu0v12MFJ554ig+2Bl6zanVSwaDlrHTv1M3bQNbto+be17DggWQk8NDN+aSp/Pnj2UWMjNV3gVFUVqOVwQFS1kJZqcdaZJVk6jVtmeP9nfNkYI1l6TfoskQody4eHrly7Gx5RnY9CaKjUZ8Ct2/ga2as86Cs88m5oU3CLs+l3BHAfPHqr0LiqK0HK8ICrlFJzDLMpw+ktD6tikkJoKf36lEzOUKD26g14lSCjpJfP1OLWmNiYHMTCgqAquvwL+0Wfvqmubf/4YjR7j73AEc7eRP9F4Lb77ynufbVRRFwUuCQk5mKjokmCQ+9T3h2bNHW4qqq37bz76wEzM2ul9SfUVSRexISQEZYifQbqPUnu/eztc0caJ2BMeKx5n3Xm+sGPn+5hOUlZV5tl1FURS8JCicTD2q/cPcwFEUiYm1Hx1JJ/u/6IYDHTfeO7HaparLUk0RZfhi5UDyNjf1ug46nTa38PvvDLL6Yb2kmChrHrddstKz7SqKouAlQSH9mHaGns7X1Wnd5TIytD81J5lzthN4zMjJYCNR0VHVLlWMFJKToVMPbTnqtp/+cFu/6/TPf0KXLvDYYzyx4d8c9Qsm6Gs7W378zfNtK4ryl+YVQSH7eBEAOnM9S0YTy3cj1xgp/PjfD+lYVohjYO3nTuHhEBCgjRS69dROVD20I6dWObczmWDePPj6a/R7/2Ti05BLB1ZPVUFBURTP8oqgkJdhA0DvW3uXcqU6Vh5tWOcAYPR1fWq9RQhttJCcDENH9gAg42ALTDYDzJkDgYGwZg1Tr5uHbUg6sTn5LJv7XMu0ryjKX5JXBIWibO3Rjo9fPVnX9uzRfvXv2PHUa/YSCnd2JE8EcuU1E1y+rWJZ6sAztaBRnFpP4HGn4GBYuBBeegkOHuTxz/5Olj6QrOdKyTzZrJQTiqIoDfKKoFCSq92G2b+eXAoVk8zi1LxDWdr32PODSe7ih9Hgeg9CxUjBFNaddH0HZFYLBQWAWbPAxwceeYSwqDi63phNqLOIBeNeb7k+KIryl+IVQcGar92GT1BH1wWcTjhypNYk84dvfUWs4wRdRtW9aikmBkpKIDPPF4xl+BV4eANbVZ06wezZsH49HDnColVLORwRQPe9Fja89VnL9UNRlL8MrwgKjgI9TgTm0M6uC6SlQXp6reOyv/9EO/102s2us7BB9WWp1kAHQVY70ELzCqAtTxUCHnsMdEbmvtGJMgx8PjsJh8PRcv1QFOUvwSuCgrNETylmgkNc5FwGOHhQ+7t371Ov2S2U7QsjUxfMuHHD6qy76rJUXbiNYFlEVl4LHmvdrRvMnAmvvAInTjB8/NXkn1dCVEke869QexcURXEvjwYFIcTFQogDQohDQohFdZT5hxBinxBirxDirWa1U5F1LbSO5/0VQaHPqRVGJce+o1NhKXmR9ext4FRQSEqCwG429Dj59ftdzelm8y1cCGVl8MQTAKz8dA4nfILRf+hg354DLdsXRVG8mseCghBCDzwHTAAGAFcKIQbUKNMbWAycLaUcCMxrTls6qx6rzlD3YXh//qmdeRQZWfnS2pe/w0QZkefWP0fg56c92k9Ohqh+WtnEX1o4AU7PnnDVVfD885CVhU9QFKPuy8Vi0PHwpf9t2b4oiuLVPDlSGAkcklImSSltwDvA5BplZgPPSSlzAaSUGc1pyGAT2HR6gut4esTBg9qjoypnHu38Qlu+On3euQ3WX7EsNW5kVwDS9lqa083Ts3gxWCywUntk9K9F91IYZafnsUJWP7qu5fujKIpX8mRQ6Aocq/JzavlrVfUB+gghfhZC/CaEuLg5DRnLwGYUBAXVUaAiKFRwlOJMMZFt9CNhZHyD9VcsSz1j7EgkUHSkBVcgVRgwAC67DJ55BvLyQKfngY/iKRR+JN6TTUlJScv3SVEUr+PJoODqYX3NZTsGoDcwBrgSeFkIUeshkBDieiHENiHEtszM2hu38oUfRWaj65FCWZn2a36V+QRb2k90zJHkdmrcl3tMDBw7Bn5h/SjQ+eHMMDbqfW63ZAkUFMBz2q7mHkMmYLw8h05lBcwbr3Y6K4py+jwZFFKBblV+jgKOuyjziZSyTEqZDBxACxLVSCnXSCmHSymHR0TU3qDWtbQQo97qOigkJ4PDUS0ofPzeJrKIIHhk49JrxsZqVRxLM1JgMmAqrH9y2mOGDoVLL4WnntKSPADL1y4gJTCYiJ/L+PHrn1qnX4qieA1PBoWtQG8hRIwQwgeYDnxao8zHwFgAIUQ42uOkpKY04nQ6MUk70sfhOij8+af2d5Wg8MtGHVGkMebKIY1qo+qy1NJAB0FWW1O66F5LlkB2NqxZA4DetwNXPOtAIHntHx4+1ltRFK/nsaAgpbQDtwCbgP3Ae1LKvUKIB4QQk8qLbQKyhRD7gO+ABVLKJiUlLioqRI9EmpyYzS4KuFiOWrA/lAL8mTT57Ea1UXUDG+EWAmUxRfmt9Az/zDPh/PNhxQptqzVw8Yw7OD7UQY/cfO6Zs6p1+qUoilfw6D4FKeVGKWUfKWVPKeXy8tfulVJ+Wv5vKaW8Q0o5QEo5SEr5TlPbyM4sfyJldlQ91uiUgwchNBTCwrSfrTkEZ+k4GeCHj7FxcwpRUWAwaCMFv24WBLCzpfcqVHXffRASUjlaQAhWfjqJLJOZ4ldKOXLkaOv1TVGUdq3d72jOOKbtGdCZ6zjy4eDBaqOElB2fEmK3IGPtjW5Dr4foaG2k0LmfNle+6+f9ze/06Ro9WotUDz0EhYUABEUNoc+teZQ5/Pj3+A9br2+KorRr7T4opKelA6D3reM8ohpB4cM3tbwKsWPqWr/qWsWy1H4jOgBwNLGgGb11o+XLITMTVp16XHTrI0vJj7LQ72AhLzz+dit2TlGU9qrdB4XM43kA6H1d3EpJCaSmVgsKB3/2xYGOy2eNa1I7FUFh+DkjcKCj4EgLHornysiRMGWKNreQXT4Nozdx3/vdKRK+7Fl8ksLC4tbto6Io7U67Dwq5J7XJVqOfi+Wlhw5pf1cJCiQFkK4LY1Bct9rl6xEbq/1iHhF8Jvk6P8oy28BH9+CD2uOjxx6rfKnnGdMxT0+noz2feWNfaMXOKYrSHrWBb7bTU5hdBoDJ37f2xRqno9qLMwgvsJMXrnc9KV2PimWpqcdMFJj1+BS08kgBtPwQ//yntsv5+KktIMtfu4vDoUFEbrfw2btftmIHFUVpb9p9UCjO1RLk+Aa62KRQIyh8/8kbZBOOX1xZk9upuizVEmQnwNaKexWquv9+bdf28uWnXjOFccOresow8J9/7cNhV3kXFEVpnHYfFCzalAL+rrKuHTyonYwaoB1+980nx+nCSUZdElm7bAOqbmATESUESAt5mdbmdtt9YmO17Gxr1pRvpNCcNflWii8oItKSz7yJT7ViBxVFaU/afVCwFWq3EBgaXfvin39Wm0/I/j0QKz5Mu+aiJrcTFgaBgeV5Fbprp6Tu+K4V9ypUdffd2kaKpUtPvSYET344i6MBgQR+WcqP3/7cat1TFKX9aPdBwVGsx4oPIWEuUnGGhMBZZ1X+KFL9yDAGExHh3+R2hDi1Aqn7QO2R1e8/72l2v90qMhJuvRV++QX2nOqTMagHf19ZjJA6XpuyTaXvVBSlQe0+KEiLHhs+hIT6Vb9QWAgbN1JxIJK1KJ2IEiuWjs5mt1URFOLP7ATAscT8ZtfldosXa/d8++0gT02CX3LtEnLOKKFHYR43X/5sK3ZQUZT2oN0HBUr1WIWLrGsVz9fLZ4g3ffAmRhwExzV+J3NNsbFaUDjz3NGUYaDgWBtYgVQhNBTuuQe++QY+rXLuoNDx9GfT2RfUkZCPLHzz9ZbW66OiKG1euw8KOpvOdda1GkFh83+yABg5sWn7E6qKidH2wznKEsjT+yGzWyHZTn1uuEFLxnPnnWA9NQluDI/j2sdTMeDgjSlbKLM3PzAqiuLd2n1QMNigzOAi61qNoJDxeyBlGLjsmkua3VblstRkHUVmHeaiNjRSAG2yeeVKOHy42vEXABfNepDc0YX0KM7l1gnqMZKiKK61+6BgtIPdgOuRQmgoFc+VfI77kuETSFCQi01ujVR1Wao1xEaQrQ0sSa3pwgvhb3/Tdjunp596Xeh4+pN/cdQ/iLCvi9n40Q/NbqK0FE6e1Kq3tsGPQFGU5mv/QcEhcRidroNC+a/29uJMIiwWSjqd3mOTHj1OVW3sbMEXKyePFJ5WnR7xxBPat/WSJdVe1of05ZqXCnGi45OrdmJtZLKgvXvh2We1pG9nnw2+vtCvH3TpAmYzTJgAY8dq++i+/FLbS6coSvvU7oOCj9OBw8eJf81VplWCwufvv4eJMoLjTm8Xsp8fdO6sjRRCYkoB+OWrNpjtrHdvuO02eO012L692qXzpt9D0cXZRJbmM29s3XmdpYT//AfGj4fhw+HddyElBfr21TZPP/ggrF4Ny5ZB//7aXMumTXDRRdCpkxYgdu/28H0qiuJ2jUtS3IaZpB1MNRLsOBzaN/fUqQD8+GkWAcCIiS42uDVRxbLUyWN05H0Aib/tZ+qssaddr9vdfTe8/roWHDZvpvIDEoKV793Ktd0/JvrXfNav+YgZ10+t9ta9e7VN0j4+cPSoNvC47DItINbHYtFGCh9+qAWRpUu1UcSiRXDuuTT5vClFUVpeux4plJZaMOBAmmpsykpL055h9OwJwMldftjRc9k1E0+7zdhYbRAyfHQPAE4cKDrtOj0iOFhLwpOZqX1DV6EPjOb2dwyUCF9+uzmF9JMZADid8OSTMGQIGI0wY4Z2UshNNzUcEEB7rDR5MqxbBz/9pI0mtm2D887TgszWrZ64UUVR3KldB4Xjx7S0k8K3RlCosfLInKEj0+RHUEDgabcZEwPHjsHQYRdRig+WtDb8Ef7rXxAeru12zsysdmnIRTcT9q9Uiu2hzBvxFiUl8I9/wPr12gDro4/guuu0BU3N0aGDNlg5ckSbj/jlFxg1Sls1m92kLNyKorQkj36jCSEuFkIcEEIcEkIsqqfcNCGEFEIMb0r9qUnJABgDaiyBqRIU7CVZhBWVUdTRPWvzY2O136hPZHQj3+CHLqcNBwW9Hl58EfLzYd68WpcXv7AMXc80+h/L5x9jn2XDBm108O672pe6O/j6ws03w2+/aZutX35Zm5d49VXtc1QUpW3x2DeaEEIPPAdMAAYAVwohBrgoFwjMBZq81TYjTXvsIXxq/DqblKR9IXbrxncbPsWMlYD+7lkSU3VZarGvwK+kje1VqCkuTjsC46234L//rX7NGMiDG84h3SeQuP8VsfyBH7jjDs88+w8K0uYmdu7U9tetXavNN5w44f62FEVpPk/+mjsSOCSlTJJS2oB3gMkuyj0IPAaUNrWBrHTt7CGjf42dxUlJEB0NBgM//CcVgEHjOzW1epcqNrAlJ4M91EZQWSlStvHAcNdd2hKhG2/UzkcqV1gIl80+D8OEbASSlAd/Jz/fs3MkgwbBDz/AVVdp89+DB2urnBRFaRs8GRS6Aseq/Jxa/lolIcRQoJuUst6vBSHE9UKIbUKIbZlVno3nZmhHWJv8jdXfUGU56vFdPjjQMfnqCc2+kaq6dtUmYZOSwNTFig92DiT+4Za6PcZkglde0fJVL14MgM2mJW3bvh0umPkg8u/pRNryuHXEyx7vjhDa3ML27drn+be/wS23aKuXFEVpXZ5ckurqIUTlr9RCCB3wFDCzoYqklGuANQDDhw+vrKMg244Z8A2ocULq4cPaGkpAl2oi02AmqlNX3EGvh+7dtZFCj15O2AK/fv0z/Qb1d0v9HnPmmdqE8zPPwJVXcsfbZ7N/v/Zsf/IUHZMvuosZW9bR6898Hrj1Re59Zo7reuwWyN2BNXMPu3YlknbCQmGJP75mG737mokbMAxDSD8IGQx6U71d6t8ftmzR4tRTT8GOHVrs6t/GP0pF8WaeDAqpQNXT56KA41V+DgTigO+F9hC7M/CpEGKSlLJRO8KKc5yYAb+Q0FMvFhRAVhbExiJt+TgtvqR3cu8W24plqRf9I4Sjb+bw546Tbq3fY5Yvh08+4c3LP+a5E2czfz5cc035Nd9OPLmpD0uHJKF/MZcvL/6O8ZeW779wWHEc3cCa5zex8/NuOA+H4WsRhBMBQA4hdCCPfcB74ghHzMXow7+lyxknuPb6SPqOvh58ah5jqzGZtGWwF10Ejz4KI0dqS1qnTnVZXFEUD/Pk46OtQG8hRIwQwgeYDlSe6SylzJdShkspe0gpewC/AY0OCACl5ekMQqsm2EnWViTRsyd//PwF0Y6TBHUvOd17qaZiA9s55w8DIPNQO0leExDAnkVvMvvE/YzunszDD1e/HDFgMhOeyUHafflo6i7SjiST+v1yrr/gHu7ofZz0FTGE7vPF4IS8aDh5QRAFl4cTcJ0fRdMjSB/dgRO9DfgIG92O2fF7P5TVF5r4v86vs+DKBZQcfAfsrg9LuugiLRgMGKAN8pYs0fYgKorSsjw2UpBS2oUQtwCbAD3wqpRyrxDiAWCblPLT+mtoWFmRHnAQ3jnm1ItVlqNufOVjQE/s2QGn21Q1sbHaYKRz7DCK2UzpsfaxMby0FO7/+my6BZ/knQ43Y9h2L5xxRrUyE69/gJ2/zsXxejgP9vmEgDIjTn0UpT6QMz6C2x6fSK9e3Rtsy1Ji4eWnNpDy+kkik0owvxPAovfSKY5/lDsfNDPg4nmg96n2nqgo+PFHbX7hoYe0x0lvvum+5bGKojTMo99mUsqNwMYar91bR9kxTa3fUayjDAPhnSJPvVglKPy53UAXJBdfeWZTq65X5bLUoyZSAkJwFraP8xvuv187guLz9/3psmA/XHmltka0aoYiZxmjzrDxn/UBdLHlk6fzZ/ADocxdPKNJbfn6+XLrkn/CEigpLOaR216l9N0yuu+UvD7RSUbPR7n2ITPnTrsDdKdWj5lM8NJLMGKEFhxGjNByBg0c6K5PQVGU+rThnVcNkxY9VowEh1ZZfVTlyOzSJD/yhT8jE4a6td2qy1IDAgvpUVjg1vo9Yds2WLFC26V88bQAePttbTXS9defSt9ZksaiaXfw7Y0xBDhtpPkEEuwsJjf19Db++QX688Crt7Km+A5iXo0nKVZPt8Ow6QobM/o9wp+bV9fayXb99drS1V69tDnyT097XKkoSmO066AgrDpsOkP1Y7MPH9a+tR1WAnJ15AT4INy8G6tipJCUBLquxQTKYg7uS3JrG+5ktWonXnTurG0gA7THRsuWwfvvw8sv48hJZOYZa0nf2Id8k5mx/zmHpf/rTIYxkNLVJ9nw1rdu6cs1/5rC+4cXcM5no0nr6E+vP+28PLqQm8beRXHajmplzzxTO+i1Xz+YMgUee6xa+mlFUTygXQcFvU2HTa+rnnWtfI9CwZH/EWYvwt7V/Yf7d+igHQ994gREDdbq37Sh+UlrPO3ZZyExUTvxoloAXbAALryQskdvZvaZG4jZY8cZYufBtJlceOm5RMZfxdSX03EKwXczdrF/30G39Wn8xPN47eQ8op4ZTJafGetvnVkQ8wPPLbkDHKf2MUZGaiOGf/wDFi6EmTNVYh9F8aT2HRTKoExf5YvO4dAO/Y+N5dMPf0CHpONg9z/vF0Lbq7BzJ5x5gbby6cDPWW5vxx1SUrSVPHPnaklyqtHpKFu1iJklDxF9UHK8v4nX0m4jPOzUHMOFMx4lct4xSpyBPDryc/Lyct3av+tumcqaglsImy7xtdvJfCiYq2NXkbz91Mmuvr7a064HHtBWKF1wQfWkcoqiuE+7DgpGO9iNEFhx+GnFkdmxsWz7Tvtt84yJfT3S9sCB2m/fYy+9hDIM5B9smx/lwoWg08H8+bWvyaIUrr10C/5ZOpK6SZ4/Jwm9ocaRIUJw2+MrCb7oADHFeczts5YyN6dW0+v1PPb67dzy55UkRQfT62gpz4w4xtJr7gJbfkU3uOce7WmXj4924uqePW7thqIotPeg4HDiMDrRVdxFxcqjnj3J/SOAMgz8bdr5Hmk7Lk77bbXAFkuO0Q9DhrHhN7Wwn36C997TAkO3bjUu2vKZddFL9Eq2Ye0qeHW6Bd3338Mbb9SuSGfgyc/u4chg6JlZwLUDV3vk2X5MzyjWpcwj4uFeWPV6jr3dhf/r+jJ//PxWZZlp07S5BbsdzjpLnZukKO7WroOCSdpxmqqsWqkICjEx+GSYyPQJwNfX1yNtx8Vpf+/dC8XBkpDitpWY2OnUTsuOitKmDqpfdHDvtcuJ+sXEkeBg1uy/Gf3yZdpSn+uu05If1GQM4qXNMzjc3Ydef+Yx+5zVHuv7zYv+ybKsf2GPLyY6q4SXzk3joTl3Vs41DBsG//ufdgT3pEnajmg1Aa0o7tGOg4ITH2nH6VMjKOj1OMMEHYqtlIR57sD+iqCQmAj6KAshsojk5DSPtddU69ZpB8498oiWW7qq91ctoujtMDLNvixLnI7J7KOd8rd+vTZZMmWKNhlRgz4oljW/jialgy9Rv2Qy9zLPHZ4XGhzC69sWEf1UH8r0BsrWBDEjZhXH924CtIP0fvxR2/384ovaAbBqAlpRTl+7DQolxQX4UAbmKmvoDx+G6Gh++m4jfljx7+OexDquREZqe74SEyFyoA2ALz74ymPtNYXFom1SGzVK259W1bHf32Xzv7tQIv25YuM5REZVOSIkLEx7HlNWBhMnaudI1WCOPJvHf+rJCT9/Sj6CxbNf9ei9XDfvCu5N+z8OxwbR81gpj8Yn8uI9i8DpwM9Pezx2zTVaYLjgAsjI8Gh3FMXrtdugcKw865quairO8uWoX3+m5VDoNybCY+0LoeUGSEyEkWO1L9Z9m9tGxpgXX9S+2x95hFPzLQCWE9w14Rgd7IXE3OnPeWNd7PTu2xc++AD++AOmT9ce3tcQ1v/vLP42BKMpH/3LJ1h252ueuxkgvGMH1h2+Hd+FUTicevYt68K18csoyTqATqetrnrnHW2D3ogRsGuXR7ujKF6t3QaFtBQtVYPet8rD5PKgcHSHGYDJV4/1aB/i4rSgcMHkCTjQkXeg9T9Oi0U7bXTMGO1PJSlZcNWT9EovJmVAEAtX/KvuSsaNg+eeg88/d71sCegxaha3/ddInsGX0iePs3LpWjfehWsLH7mO2/ZPJCdCEp0Id3T7nP++/iQAV1yhTaw7HHD22VqOaUVRmq71v8Wa6eRxbV+A3q98H0KVI7OdxwLJ0wUQ0yvao32Ii4O8PMgtjSbHEIA+3afhN3nYSy9pq6Luu6/669+9/ShFn3Yj3d/Ec/+rI1dCVXPmaDPVq1bBateTyv3GzWXmB3by9H5kPnCM1Q+tc8Md1K93316sz5hHyRVBhJZa+HmmlbmXLMFRms+wYbB1q/a/y2WXwYMPqjzQitJU7TYoZB3X0kr6+Jef6VdxZHZMFMF5kBfo+ZNLKyab9yQKigIFwUWt+w1UWqqNEkaPrj5KcBQe4Y0bzAQ6LUx8cxj+/n511lHN44/D3/+unTXx/vsuiwyf/G+mv1FMoc6f1CWpPHGfiyWtHvDoO7dz4Rdnk+nrS9jnPlzb9VX2//IxXbrA99/DjBmwaZO2hNXF1IiiKHVot0EhJ0NbnmgKLP+CK1+OmuKbQwdHEaKb5yaZK1Sc3JmYCLouVkKcxaSecN9REE318stw/DgsXVrlRSlZcOVquhfmkz/ah0snX9j4CvV6WLsWzGYtqfLHH7ssds70u/nH26UU6XzY/UAZ98/z7BxDhfMvGs0zOTdyZLg/0TlFLDsvh8fm3oXZx8Hrr2vx7NNPtcQ9+/e3SJcUpd1rt0GhIEubYPYPKT/4qN5mRakAACAASURBVDwofLrlODokUcPMHu9DWBh06aIFha6DreiQfP5h66xAslq1ieVzz60+Stj71csY/hvGCVMQT395c9MrDgiAjRth+HDtAKL//tdlsXMuv4uZH0sCjTk4VqWy8KrnmncjTWQ2m3h163y6PdWDUAooecbE//V7hLy0Pdx+O3z9NeTmaoHhww9bpEuK0q6126BQkqf9HRTeSfvH4cMQGsre37Q5hjFTh7VIPyomm4eNjiKLDuz8NqdF2q3plVe0Uz7uu09bGQVAWRGPzSjCTCnnPNcFk6mZcx6Bgdqkc3y89rB+0yaXxRL+toDbvjZxwhyI39tZ3HbRU81rrxlmz5vB4qTLORwVSOyfdpbEfs1bTz/GmDHafo24OO1R0r//7XJBlaIo5dptULAWaN98XbqVTyaXrzwq/DMYG0ZGXzKyRfoRFwf79sGFf7+QEPLJ3+35EUpNVis8/LC26ub8Kqd6PDd/ObEZBST1M3P1ddNPr5GQEC0YDBigbW771vVR2r1H38IDv3XicGAIHb4s4IaER3C0UF7Nrt26sv7YHThmhxBgt/HlbRHMGnU/HYPT+f57bYPbihVw7bXqQD1FqUu7DQq2Iu3gtu7RPbQXkpIgNga/DBPZJj8Mxpa5tbg4bRnoifwoMn0CMJ9o+RVIr72m5cupOkooTd/F9he68qehKw99c4V7GurQAb76SjsOY+JE+OYbl8W6xF/Jqt1DONApgC47rVzbfRWFhUXu6UMjPLDmNqb/diEE59Htf3Bzp3f44aPnWb0aXn8dvvtOG/TUMeBRlL+0dhsUHCV67OiIjPKvPDK7qF8Q4bZiHFGWFutH5XEXewXF4WVElFhwtuA6SKtVy2d81lnajl4ApGT+398l2pZNxxnFdI9049Lc8HAtGEyZApdcou0acyG0x3m8/sckDvUzEnu8kBsi1/HHHynu60cDEkYm8Er2XHIn+RFhsfD9lbncctFirroiny++gIgIuPhi7XGSzdZi3VKUNs+jQUEIcbEQ4oAQ4pAQYpGL63cIIfYJIXYLIb4R4v/bO+/wqKq0gf/O3DuTmWTSSUgIvYUA0sRgQ0GxgCCP7iKs6IrIsooisGtZ9FusCAhKk1WwIWLZlbUuirqKZREUWEDpSAkJLYQkpM1kyj3fHycklABxzWQInN/zXDJ3cu65773Afe/7nreIGj+9pNegULhVU/eKktkfSQuXFSC6dWiK4FVH+/bq5/r1EJ1eiotyvlryTZ2d/+23ITv7WCth7afPE/Odmx1RCUx7aXTtnzQ5WSW3XXihqqMxdWq1FenscW14fe2dFPYpIqYE5nR8j/fe+nfty3MSDMNgxgf3c+XiTA5GOUn6zMnvUt9g/6ZXWbkS7rxTid6zZ1UtRY3mXCdkSkEIYQBzgL5Ae+B3Qoj2xw1bA3SXUnYCFgFP13R+u1cgDEsphZ074bLLWLYhgSyakHldm1q6itPjdsMNNygRzuulciP+/fZ/T3NU7RAIwGOPqfNfdSTSNOhj5ohiTIJc93wbbLYQ/RXHxyv/y003qdft0aOVxXY8EQlMXzKRdmM24LJ8rLx5JY+PCl2F1eq4st+VPF9wL/uuctG2oIAvBu3nT30fY/YzhSxaBFu2QJcuqo6SrraqOdcJpaWQCfwspdwhpfQBbwMDjx4gpVwqpSyr2F0BNK7p5HYflJs2TBMVhP7NN+RtSKIp2Vx385W1dQ01IiJCudp/e+s1WAj2rK6bhdVFi5QyuvXWKivh1cmP02yPl6xWsdx067WhFcDpVC3R7rtPWQ6/+Q2UlZ04znAyZvpzXL3AwyF7JPL5gwzv/DReb92VNTXtJi989gC9PuxObpSTlK/hzgav4Sh6jrVrlWIdPFhFKOmieppzmVAqhTQg+6j9nIrvTsYdwCfV/UIIMVIIsUoIsergwYMARPglPnvFk3DzZoiMxL43inzTTXRi3UYAZWYqF04gojt5Zgy27NA33JFSZS+np8PAClUb9OTz6dRUynDx8Ef9Qy4DoCruTZ0Ks2erTLGbb1buvOMRgj63PMqja9LZ0cSk2Y8e7kqYy/JlP9aNnBVcNeAaXjg8mvy+kSR7SnlnuJsnbprA9Ck7mTJFFRLs2BHefbdOxdJozhhCqRSqa45crXEuhLgF6A5Mre73Usp5UsruUsruSUmq8mlEMEDgSKDPli0EzmtFUomP0gZ1b/9nVkS/rlwlKGzswV/mDnkY5uefw9q1qoHOEQ/RoyOeJeNwHsV9A7TNaBnS85/APfeoKnTr10PXriprrBpSO1zL/M3Dye9TjOWN4p89P+WJ0aEtv308pmEy8+P76b+0JyK+gKYrDf7a5H2Mg0+yepVFkybK6Bk6VJXT0mjOJUKpFHKAo5tANgb2Hj9ICNEHeBi4XkpZY3+Cy/ITdFZE+WzezCfntSKWEqLT68Z1czRdu6qKED/8ALGt/LQJ7mHJ+6HNbJ4yRfV0uOUWtV96cCuH/55AnhHN1HdCsLhcEwYOhI8+UqE9V18Njz9ebUU6EZnKzCWT6DflJ8pNG9Zz2dzafAYHDtSt3+biXj2Zf2gc1ohYIqwgJdOCPHnVLGZP+oDHHoPduyEjQ4Wx6rUGzblCKJXCSqCNEKKFEMIBDAE+PHqAEKIrMBelEGr8RPCU5uHEh3RJlSSQlcXS3OYAdL6qYa1dQE2JjIROnZRSuHiAcl0tXRi6rvKrVqncsbFj1XoGwP2DF5IYLCb6NnBHRYfs3KclI0PdiKFDVUhU377VO+kNO4Pvn8GEn9qzvYWd1lmHeSJtIXNnvHni2BAiBDz24lju3z2Yne0icB6I4aNrNpH98ZNMfSqHtm1h2DBVOmTjxjoVTaMJCyFTClLKAHAP8CmwCfiHlHKDEOJxIcT1FcOmAm7gHSHEWiHEhyeZ7hh2b18PgC3Kgm3bQEr2blONbgbcNqCWr6RmZGaqss2/GTYULw5yVxkhO9eUKRAbq6pbA+SsX0rUV25ynLE8MW9MyM5bY6KiVD/QuXPhp5/g8stPWngoKb0vC7bci2NkIU7hZfk4H7ekz2D/3kN1KnJqWhPmb/oL1y+I4oDbSePvg7x5xdtc3eH/eOlFHz/9pBLeHnqo+rV0jeZsIaR5ClLKj6WUbaWUraSUEyu+myCl/LDicx8pZUMpZZeK7fpTz6jYtS0LAMMtVDwhYMuJ5rDhokHjxNBczGnIzFS9FbL2pXEgykX0/uqWVH4927ap5+tdd0FMRS3Av/5uGW7podOEGAwjdMroFyEEjBypFj9cLhXWM2gQHDhw4li7m/Fzp/OHL5tjpR6gzdbDTGryGhPufqXO3TY33jqYFwtHExgRjbD54UU7y8Y9z9QHpzF0qGTSJBWp9Pe/a5eS5uykXmY079qmVv9c8QI2b8YSkFjipzghfDJdfDE0bqy6f1ktPCQFiti2tfbLaE+bBg4HjKkwCFZ+Mp9G623siI9l9PjhtX6+X02HDvD99zBxoopOat8e3nij2idqes+bWZA1itgxeUhhYfwtm98mv8Bnny2vU5ENw+CJF//EY/tHkXOxk/gSH5v+Igh+Mp15U+cjhOpU2qOH6t2g0ZxN1EulsG+X6qUQm+SALVv4uncmibIQZ+u6i3s/nvR0VS7h66+hfW8fQeDN52rkDasx+/erRc9hwyAlBZAWs0bmYRDkxrlta/VctYrdrvwua9ZA27Zqdfz662HXrmrGRjN2xmye3NaNvV2CNMiTfH3NUoZ3n8S+vSfEKYSUuPhYXlz2ICPW9eNgmyDNcj1k359NyrYnmTnxH+zbB717qzJQ69fXqWgaTciol0ohf5+KMEpqFA2bN7PE0R0BZFweEzaZhFCLkUuXwtC7riGIne2f1a5/Ye5cVVniSNvkfz4/mZY5ZexsGsXAQf1q9VwhoX17ZUo9+6xyI7Vvr5TF4cMnDI1pcQVzVz/CzQsLyImPpNlqH9Mav8GYgTPqNOkNIKNTB17b+gDXfn4xO9LcNN1hkfvwNi4zp/LkX97hP/9R6w133AFZWXUqmkZT69RLpVCap/z1TVonw5YtZO1uwn6S6H/bdWGVq3dvlbdVZvQgzxWJe1fttQTNz1euo0aNVJFSgl4+fMiFH5Nxi6447fFnDIYB48ap9p433qhqfrdqBbNmnViZzmZw+dCHeO3ACKLHefE4TGI+LOaumJd58LbZBOq4McKlfXqzMGccFy66gN0pLiJ2JeKZvJX+7mcYO+I1fvhBGUJ/+AP8/HOdiqbR1Br1Uin4C9VianpKApSUYGZH4zRKaNqudVjl6t1b/Vz6laC8VRnJ5UVsWl87fSBnzYKSEvViDTBt/ARaHi7iQFcH3S7oUivnqFOaNYOFC1UHnM6d1SJJRkb1BYjsbv707CRm5d5A4OYSoi0PkQvyGRPzDA8Nn4XP569T0fv9pi8L9v2JQf9IYndaBC33lOGel0W3g5O5c8gUFi60SE9Xyd3araSpb9RLpWCVmHiIIK20DEsIkou9FDQIt1TqLTElRS0+nj9ApXS/NrX6vsa/hKIimDlTRb107Aj+0j1se64B24wmTPzXsF89f1jp1k1lP3/yiQplHTxYVV59770TCuyZMc2Z9MYUnt57NQX9fJgBiHi1gNuj53PPdTM5dOhEN1Qo6TtoAAty7qPv0kvZ1TqKtNwAkQssBos53HHVE3zxaT7nnQejRqlq4zpaSVMfqJdKQXhMvDY78fu28W2n84ilhMj23nCLhRCqPEJhIdw+VuUr7Pry19dhmjNHzfnww2r/gVtm0sjjIeX6QlIanQHa8NcihGpusGYNvPKKKiR1443KcnjhBZWgeBTO5POYsXgik3IGUHpjGXGymKSPC5mcNJc7uk1l/dq6rad0Ua/evLbtz9yxYTAHLxUklHtJ+9RiaOEr3HLeRPbteI8+fZRCf/55ZfFpNGcq9VIpmB4Dr2lg37aRJa4eAHS8Jj7MUikuvFC99G7OakZ2YiRpe4IEgv+777u0VK3L9u0L558P+3/+D+KDJA7YY5n09hmQqFabGAbcfjt8841yI8XFqYSMpk1VjfDjchwik9vz9D+nMCt/EI5RxeRFOWi6poy/d/2AQU1nMXvya3XWChSgVUYbXvr2LzxVPAr/MCdFTpPWPwVI/mwft8ZN5/yGT/DAn/No3LgqGEujOdOol0rB4QOfHdiyhX17m+PHZMjIm8ItFqCakRkGfPABNOiRT4ws5eUZr//P882dq4J0jlgJ4wd9Qawso/X98dgdZ0iiWm1jGCrR7fvvlS+uRw944gmVIXjTTUrrHvWwN9xNGD9nGq8W3kn6TJOsNCcNswX543dxr3MWIy97mnVr6s56cEZG8eSrD/JS6Vg6vdYRb4tSUgp9tFpq8Ufvq1zXYAobVzzD+ef76dIFZsyAiuK/Gk3YEbKeOTq7d+8uL14zlMJ4iwXu2dx54F4C0uQl773hFq2SXr1UtNDCv/2LZ3vtJZBxmIU/3f+L5zl0SAXmXHqpKun83ccvsfi6XPbEuplfeOZcb52wdavyvbz+uroxaWnw+98ry6LNcU2VpGT32sU8ff8KAt82INV3mN2kEYwpJaFPkDHTBtOsxamquNc+RYUFTB43jwPvO2lceJgC4gmaQfJbeTgUm8hXa0YwbJiNnj1VCkdsbJ2Kpzk3qFGZhXppKTgtP5YrQEHBfpK9JQRaFoVbpGMYOFDFq0el9sdwlpGw0fif3BgTJ0JxMUyeDFgBnrvjMAYBfjuvQ+0LfabTti1Mnw5796o6H126qCJQbdsqq2LatKqemkLQtGt/nvv3k7xQ+gfaTLNRlnGIhGIfse8W81LLV7k9YToP3fI0u3bWTR/OmLh4nnr1QV4uGMPA5f0J9CrFb5e02+Ljkh/2caPxKiVfT2TR3GdJTfHQv79KVMzPrxPxNJpK6p2l0K1bdzlgzfXsaAeZrTaRv7gd5bc6eWrBg+EWrZKsLJXhPGEC7Fv2GKUfN6XH0/DH+2+v8Rw7d0K7dir59+WX4ZlxEzg0w0l2Jyevr/tTCKWvR+zdqzq/vfWWCm0FFd56ww1qobpjx6qWdIC/OIe/TZrLyjdiaJgNMbKMfSRT7vZj71rODWO60fc3ddu1b8VXS5n/1xWUroulZfFBbECxiGRfskF5Cy/+uGspLOtGv37KNXncJWk0v4Qa/cupd0qhQ/uO8qZNg9jZLQA+i+j1qdz+XXe6XXRhuEU7hksvVc1v5j37BW9csIydTaNYmPXnGh8/dKiKyty6FVxyI4+3+AQh4cHs35HaqFEIJa+n7Nypbth778GyZZCYqEJc+/RR25VXqj4PFZTl7+SFyQv54SM7ydvsJAZVSFC+4aaopZdGPZ3c9ueBtG1fd7kva75fxfyJn1O4zElavocDpJDGHg64HRSlBilPge15Q+g3sCXnnaeKz6bVrRdMU785O5VCi2atZO/dD2P02oBc2RhXOcz2jwu3WCfw+uvK5f3ddzBz0Eya7ilnTNbNpDU9fRvq1auhe3cYPx6eegqGt3+SZpuCmGPjeHj6WRZxFAr271eJAe++qxpPFBaq77t0UdVa27eHiy6qKCAFBDz86615LH6xEO+aOKI9PhKDZUggzx5DceMgjS61uOGuy8iso5eP4qICXpz0KuveDxKZHSS51Ec+8cRSxH6Xm9JGHnwpAfL8V9K640Vcfjn07AnNm2tLQnNSzk6l0KhhU/nH3DsovPwA7q9TyU4XzN/8f+EW6wRKSqBJE1W8rrnrKQ5N8pPXz+Rvix8+5XGWpRYay8th0SL46OWn2fZnD9sbxrJw/9i6Ef5sIhhUWvbzz1WSnGWpkFeAFi2UcrjoIhVL3LEjRESQv3sd8+d8wLolJuYONymlpTjwU4aTcptJUbyB0dpH+yujGDj8Wlq2ahXyy9i6YSMLZn7E3qU2InabJPuKsSHZSTPcRgEF8SCblOCPd2HGDaBD13QyM1UYc2J4qslrzjzOTqWQHJcm7z48kj3nl5K2OgoxKooJc+4Lt1jV8sADKtxw6+YyHu/wKjFWCU8V3EtkpOukxzz3HIwerRYZ+/bayLh235LiLeL3q6+mU9fOdSj9WYrXC//9LyxfrrbvvoN9+5S/b/lytRjUubNqpde5M3TuTKEs4M0XP2LVZz6Cm6NJOGwRZ1VloB2yRbO/gYPYNA8pXS16XJtBnwFX43T++sTFk5G142femv0BW5f5kVsiaFDsxy09+LBhAAWGm8JYCCR7kA2DOJPaktpqAJ27RNKpkwrYsttDJp7mzOTsVApJ7kbyntI/srmhE0ehk6k7B5Gcemb62HfuhBEjlNciMu9hcha0IHZgLjPef6ja8du3q4XlmBhY8nGQW1o8S9vsMhgVxyNztNsoJEipmjGvWaP6nP74I6xbp747wlVXqXZrbduqrU0LVpcf4OOv89jxvROZ5cJRYictUNUtzo/JNmcKkVHFyGQ/CenltOgcx4VXnU+3CzNrvRlSMBjkP599weeLVrHve5NgtoP4kgBxVilZEbE0Kz+MH5N8eyQlMRJfigfhlrgaRpPUrCPtul5G69Z2WrVSXjVbvYxL1JyGs1MpJEQ0kTf5xuNxBQhEwxsHzux4/TvvhG+/hUV/L2b2BXMpwcGEddfQum36MeO8XhVyv2SJ6mA59Q9/hSUNyEsP8sZmHW1U5xQWVimIgweVy2nrVmVVHKF1a+UnbNYMmjcjq1kUSwqjWP9zNEVZ0XgKo0kt9BEbLMXAqjwshxQcZhkelyCYUI7ZwCKhuSC1XSTpXZpxwaWZJKek1splbN20kU//8W82f1dC8c92jFw7sWUBPFY0jdhfOc6HSZHTxp6oWCIcHkRCOa5ki4hEJwlpTWnZ/hJat0ujSRNITYUQGkGa0BF+pSCEuBaYCRjAS1LKycf9PgJYAJwPHAIGSyl3nWrOBmZjeQv3EhX0I281eGrBX0IjfC2Rm6ve/hs2hJ4Zk1n+SCzexiW8ueM+RMWKoGWpHgmzZlUkqb09gZLX4jiYHOD57aNwu91hvgpNJcXFqifq1q3KFNy+XcUg79qlfiYmqoXuIxg2DrdLZWnLjqyzWrI3N47SwljMXAeuMkGMv5xIVN2ugzQgCdVV0IuDEsNJXqQTu6McGR3AjAsS16icyKQIGjR1kta8AS3btSC9Q0eiY39ZL5G83AN8tfhzflqew95NFr49DswiP6WlDWjhzcNJVRnzXTSlObspI4JSM4Iyh8Cb4EHaTMyYAEQHiUiwEZPoJCE1kUbNWtKqXWdS02JISID4eJWkrgk74VUKQggD2ApcBeQAK4HfSSk3HjVmFNBJSnmnEGIIcIOUcvCp5k2wNZdDGEu5w2Da3iHEJySdavgZwTvvqLWC3r0lOz+aQsqaIPk9BC8ufwi/H+6+W/Weuftui+1fPILtfTcHIiN5fF0/WtTBIqamlrAsZUns2aNyKI7f3G71F52XV1WmQ8Duay7hh0PlbLM3ZX95CsXeRPyFUZhlDsr8TlLKyoiyfEQc9aAuIQo3pZX75dgpFU4ChsBnCnAFKHTZcRoBhCuIERXEFevD4XbgiJVERRtEx0cQm+AiITma+KQYGjRsSFJqIxKTG7J7x1ZWfr2SrWv3s29HgNIcE1lgIIpNnF4wpZ84nw8Hqq5XNo1pQk6lPHtIJYF8vDY7fsPAH+khzx5DpCjHirAwXEEspx8zCgwnREQJnDEmUbEm7rgY3LFu4hskkpSSRGrjpjRIjifKbcPl0mshv4KwK4WLgEellNdU7I8HkFJOOmrMpxVjlgshTGA/kCRPIVSSaCKHiNH4e5bzwtd/DYnstY2UKvl28WLo0T2f3EUvYRyMpLxRGbZu7cjO7Utm6znkfO4jNUeQmyKY8O8BtO2QfvrJNfUPy1LuqYMH1VZYqKyLggKVwmyayhIpLFRd6aKiYPNGck0f6+OS2BmVyv7oZuQXOvCUu/B4Ygl4nQiPHVu5iekXOK0g+VYsTfyHcODHpCqjvoA44ik8RqQj1sAR/JjsdcSQ4PcSEDaCQhCwCfIdkcRRih8b0gALCRLKDZPIoB8sgbAEAWngsoLYLIkpLQyClFqRJMgSDILYCeDHwMGJmf7lOI5RgAAWggJiicRDUNgIYiNggyIjCpf0YtkEluknKO1IA3ymwBABpE2AIbFsEn8ERNi8WNKufBemhc2QSJcfm2VgmIANbHaJYbcQNgGGDdOUCFNgGALDLjHsdmyGwDDBZtgw7ALDYWIYat/uMDAMA7vdhs00sNsd2E0bpt2OYRrYTBumYWIzBabNxGYXmMKO4RDYhA3DNNW8hg3DNDCEDZvdhmHYsdlUD3GbzYZpGtgMA8OwIYQN0zAwTAOBQBg27HYDm7AhbALTNHFFOcOuFH4LXCulHFGxfyvQQ0p5z1Fj1leMyanY314xJu9k8zYUjWUv9z08t2UoSY2ahET2UGBZMG+eUgwiuB/n7peJ/tlNUAiEsDCCNvwm2DuXMH3JaKJjosMtsuZMJBhU6xhFRaqEbkmJ2srLlQIpK1MbKIvE4wGvh3xfKdllRezzSg75BIf9JkV+OyVeB+W+CEoCdqxyB4GAg2C5gRUwCQoLwxMBARsiYMMWFJTaIoj3eyFgw5ASm5QYluSgEU9aMBebBQYWh0gghVxsVD1f9tCINKrvs+3Bges4RXCEEpy4ObY0filOoqi+XL6FOOa8ZzJeHMe46iTVv85X9/3JxvowKy24o3lEPlIjpVB7/SJP5GTX9kvHIIQYCYwEcBgRbGg8n77XL/r1EoYBn0/9Hw4EgMR8yku9WEGB4YTEhjG4fFH0vuLdGs118OBBkpLOfPdZXaDvRRX/870wK7aTLSJLWdUpyLKqPld8v/W4faRESotg0ELKIEHLQloSS1pICZYlkVJtllTHWYC0AOQxp5Oy4sFw5DshkZY4RjSFQEqJQCBR57DZQEqBACypHjpSiqpjZMVxSJACjoyp+BN53GOqYnzVUaLqe8ExTzBx9CHyqAfekakrJT2e4yY66txCHDufFCCOGnoypfioeHS9lLJjNSc7hlAqhRzg6Ff5xnDCa8KRMTkV7qNY4IQSYFLKecA8UFVSV61aFRKB6xvdu3dH3wuFvhdV6HtRhb4XVQghatSJLJTRyCuBNkKIFkIIBzAE+PC4MR8Ct1V8/i3w5anWEzQajUYTWkJmKUgpA0KIe4BPUcs6r0gpNwghHgdWSSk/BF4GXhdC/IyyEIaESh6NRqPRnJ5Quo+QUn4MfHzcdxOO+uwFBv2SOUeOHFk7wp0F6HtRhb4XVeh7UYW+F8cwryaD6l1GM9Wuvmg0Go3mNJy9ndc0Go1GExrqlVIQQlybnp5O69atmTx58ukPOEsZPnw4ycnJdOx42uiys57s7Gx69+5NRkYGHTp0YObMmeEWKWx4vV4yMzPp3LkzHTp04JFHHgm3SGElGAzStWtX+vfvH25Rwk7z5s0RQvwkhFgrhDhlOFa9UQoVZTPmfPLJJ2zcuJG33nqLjRs3nva4s5Fhw4axZMmScItxRmCaJs888wybNm1ixYoVzJkz55z9dxEREcGXX37JunXrWLt2LUuWLGHFihXhFitszJw5k4yMjHCLcSbRW0rZRUrZ/VSD6o1SADKBn1u2bInD4WDIkCF88MEH4ZYpLFx22WUkJCSEW4wzgtTUVLp16wZAdHQ0GRkZ7NmzJ8xShQchRGXxRL/fj9/vryy6eK6Rk5PD4sWLGTFiRLhFqXfUm4XmmpTNOJcQQjQH/lWTDMVzhYp78g3QUUpZFF5pwkOFRb0aaA3MkVI+GGaRwoIQYhEwCYgG7pNSntM+JCHETqAAFagztyIhuFrqk6VQo5IYmnMTIYQb+Ccw9lxVCABSyqCUsguqgkCmEOKce2kQQvQHcqWUq8MtyxnEJVLKbkBf4G4hxGUnG1iflEJNymZozkGEEHaUQnhDSlmzwlFnOVLKQuAr4NowixIOLgGuF0LsAt4GuAt2PAAAAc1JREFUrhBCLAyvSOFFSrm34mcu8B7KHV8t9Ukp1KRshuYcQyin+cvAJinls+GWJ5wIIZKEEHEVn11AH2BzeKWqe6SU46WUjaWUzVHPiS+llLeEWaywIYSIEkJEH/kMXA2sP9n4eqMUpJQB4EjZjE3AP6SUG8IrVXgQQrwFLAfShRA5Qog7wi1TGLkEuBX1Nri2YusXbqHCRCqwVAjxI+ol6nMp5b/CLJMm/DQE/iOEWAf8ACyWUp40fLHeLDRrNBqNJvTUG0tBo9FoNKFHKwWNRqPRVKKVgkaj0Wgq0UpBo9FoNJVopaDRaDSaSrRS0Gg0Gk0lWiloNBqNphKtFDQajeYsRQhxgRDiRyGEsyKzecPp6mHp5DWNRqM5ixFCPAk4AReQI6WcdMrxWiloNBrN2UtFrbiVgBe4WEoZPNV47T7SaDSas5sEwI3qLeE83WBtKWg0Gs1ZjBDiQ1QJ8RZA6ukak5l1IpVGo9Fo6hwhxO+BgJTyzYqufN8JIa6QUn550mO0paDRaDSaI+g1BY1Go9FUopWCRqPRaCrRSkGj0Wg0lWiloNFoNJpKtFLQaDQaTSVaKWg0Go2mEq0UNBqNRlOJVgoajUajqeT/AdCq6/869z0tAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -0.918 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = 2.810 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -2.86167 \\ hartree = -77.86888 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 0.5 s\n",
      "------------------------------ Iteration 6 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 1.450 \\quad \\zeta_2 = 2.910$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = c_{11} \\chi_1 + c_{21} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2 = c_{12} \\chi_1 + c_{22} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = -0.842 \\quad c21 = -0.183 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = -1.620 \\quad c22 = 1.816 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MX9u/nQlmPWOttkqqUuo9YBJwVkTCTZy/GZhb+tcs4F4R2Wep8s+lZqFQDBw2gIIC+OgjUArc3WHVKhg5Etq3N9L2HHwF3niTnppmqeI1zaJGjLBsfubsyFnThvfmnP/xxx+ZPn06rVoZLXU/Pz/Onz9frYzAwEAuu+wyADZv3sy0adPK9yO+5ppr2LRpE5MnTyY4OJjISGMSar9+/UzuxrZp0yamTZuGm5sbAJMnT661nsOGDasx3969ezNnzhzmzp3LpEmTat0WNCgoCH9/f/bs2cOff/5J3759Te6FkJeXx7lz58r3en7ooYcq9RkAbNy4kT59+tC+fXu8vLxo27YtLi4uFBcXm0xvDdZcOns58B/ggxrOxwLDRSRNKTUeWAYMslThmVlZuONJt9Ae/PADJCTA449DWBjcdBN89hk8+qiR1sG7Dd60IjNXD0vVtDJSw4b35pwXEZRSdZZRcUN6qfpetwJnZ+fyP9vb29f4+shUmTXVMy4ursZ8w8LC2LVrF2vXruWpp55izJgx5Q9zU2bNmsXy5cs5c+YMd9xxh8k0hw4dYtCgQTg41PzY3bt3L71792bfvn1ERERw9uxZPD09K31P1ma1PgUR+RWocZqwiGwVkbJfzX8DOlqyfFVoR2uCcXf24IcfwMEBRo+G0FBo0wa+/75C34JSeDj6k1VyFqj5P0xNayo//2zZjznq2vC+tvOjRo3i888/JzU1tfxc1c3uqxo2bBhr1qwhJyeH7OxsVq9eXetv6KauX716Nbm5uWRmZvL111+bdR+mJCYm4ubmxowZM5gzZw67d++udL7qvUybNo1169axY8cOxo4dazLPAwcOEBERUWu5Xl5eHDlyhP379xMREcH8+fPLO5Uba0hqc9lk507gO0tmmFZwBgfliggcOWK8KnJyMs5NmgRPPGEc79HDOObl4U1BWg5xcTEEBXWxZFU0rUWqacP7wMDAOs/36tWLefPmMXz4cOzt7enbty/Lly+vtNl91RE0UVFRzJw5s3xz+1mzZtG3b1+Tr4pMiYqK4vrrrycyMpLAwMDygFJTPdu2bVtjXgcOHOCJJ57Azs4OR0dH3njjjUrn/f39K93LwoULGTlyJD4+Ptjb29eYZ9m91WTGjBlMmzaNVatW4evryw033MCDDz4IGENSp06dSlpaGnPmzGHMmDFmfS/1Zm7nQ0M+QBBwsI40I4E/AP9a0twF7AR2du7cudYOljLe+EugQ5RER4uAyNKlF87FxYnY24v8+98Xjl3d7RoBZMmb75qVv6ZZU3PoaNbMV1xcLH369JFjx45ZJL+IiIgaO6sfe+wx2bVrV63XX0xHc5MOSVVKRQDvAFNEJLWmdCKyTET6i0j/gIAAs/LOIxtHJ1d27IDwcLj88gvnAgNh4kTYs+fCsZBQL9xxZ8uPe6pnpmmaVoPDhw/TtWtXRo0aRWho6EXnl5+fT2ZmZrXOammkIalN9vpIKdUZWAXcIiIWnSCQk5lGPnk4ubqwe7cxN6FXr8pp/Pzgm2+MfgWloN+QIBZ/k03skdOWrIqmaTauZ8+exMTEWCw/Z2dnk/m9/vrrfP/992RkZHDixAnuuecei5VZkTWHpH4CjABaKaUSgPmAI4CIvAk8A/gDS0tHDBSJSH9LlH1w+0EAXL0c2bMHhg0DR8fKaYYMgeXL4dgx6NYNBg4fjhNOpCTp1VI1TWt+WvyQVBG5sY7zs4BZ1ij74PbDAHi3cubAARg3rnqayy4zOpl37jSCQkjk5XjhRVZmhjWqpGma1iLY5DIXRw7GAeDbzgVHR+jXr3qa7t2NZS/K+hUcXZ1xVz7kFegJbJqmXbpsMiicPm2MR/Zr40V8PHTuXD2NgwP07g1791445urgTV6J3oFN07RLl00GheSzxqQST39jobuwMNPpIiONoFA2ic3N1YNczpOentcY1dQ0TWt2bDIonD+fDUCxisDODkJCTKeLjITUVDhdOuDIy88dEDZv/r1xKqpptZBaln3QtJpc7H83NhkUsnOyccCBosLLmDz5wkzmqkrXwSp/hdSus7Es7i8bf2mEWmpazVxcXEhNTdWBQasXESE1NRUXF5cG59FclrmwqLz8XFxxZ+fm1ri71ZwuIsKYo/DHH8bSFz36tIZf4Y+9sY1XWU0zoWPHjiQkJJCcnNzUVdFaGBcXFzp2bPhScrYZFAqzccaNUyftTQ5HLePpafQ3lI1AGnFVP3gdzsTXOLla0xqFo6MjwcHBTV0N7RJkk6+PCopzcFYeJCUZS1rUpnNnOHHC+PPAERNxxpmM1Orrvmuapl0KbDIo5Es2TnbGe6O6gkLXrhe26HT2CsADb3Jz9axmTdMuTbYbFByMTSmCgmpPGxoK6enGKCQAV3sf8ov0BDZN0y5NNhcUiouLySMHZ0dXIiKgU6fa05ctanj8uPHT1cmLHElDD/rQNO1SZHNBITU1GRCcnV3Zvx86dKg9fVlQKOtX8PByJ4dMTsXrmc2apl16bC4oHPpjFwAuLq74+kJdw3WDg8HO7kJLIaCN0Rfx3ZfrrVlNTdO0ZsnmgsIfhw4TSCCubu7UstteOScnozO6LCgEhXoDsHPT7lqu0jRNs002FxSOHz/JSU7i6OhqVlAA4xVS+bDUy43hSiePJlmphpqmac2XzQWFpARjGJG9oyft2pl3TWjohWGp4yeOAiD1jB6WqmnapcfmgkLq2SwAior9zW4pdO0KGRmQkgLtu1yOMy5k6812NE27BNlcUMhIM5a9zs0JrFdLAUr7FRw9cFO+5OXrloKmaZcemwsK2Zn5KBSpmV3r1acAF/oVjM129AQ2TdMuPVYLCkqp95RSZ5VSB2s4r5RSrymlTiil9iuloixRbmFOIc44E3+us9lBISgI7O0vjEByc/Mki3TycgssUSVN07QWw5otheVALWuUMh4ILf3cBbxhiULz8gpwxpmsYh+zXx9VHZbq4+tGDtls3XzAElXSNE1rMawWFETkV6C2acFTgA/E8Bvgo5Qy8zFes8LCApxxoRAHs1sKcGEEEkD7jsa6SZs2bjEOlJTA9u3w7rvw0Ufw++/GMU3TNBvTlPspdADiK/w9ofRYtQkCSqm7MFoTdO7cudZMi4vyccIFR0eFn5/5lQkNhW3bjGGp3Xv48tVmOLrnBBw+DK++CgkJxvAkpYxEgYFw991w1VXmF6JpmtbMNWVHszJxzOQydCKyTET6i0j/gICAWjMtKs7DSRkT15SpEmoQGgrnz0NyMgwdEQZAUswZePhhSEqC66+Hb7+Fb76Bhx6CrCx48UUjYOjV8zRNsxFNGRQSgIprmHYEEi820yLJw0G5mN2fUKZrV+Pn8eMwbJjx239mWipkZ8Obb8Jtt0FAgPGZMQO++AJ694Znn4X583Vg0DTNJjRlUPgKuLV0FNJlQIaIXPTaEoWSh6O9c736E6DyXAUv/14440pWTh588onppVbd3IxWwsMPww8/wPPPX2zVNU3TmpzV+hSUUp8AI4BWSqkEYD7gCCAibwJrgQnACSAHuP1iyywqKaSQXBwcXOjevX7Xlg1LPXECeONd3JQvuYUZtW/dppTRSoiNNVoMffvCpEkXcwuapmlNympBQURurOO8APdbssyzGacopghHe+d6X+voCBMmQPqZXNi5AVdHL3ILzJjAphQsWwa5uXDTTbBnD3Tp0oDaa5qmNT2bmtEcF38EAAdHZ3x96399Vhbs3pACGzbg4epJNunk5xfVfaGzMyxcaPz8+9+huLj+hWuapjUDNhUUTsQYEw0cnZzrNRy1TGD7Qk4m2MP99+Pt504OOWzbtM/MiwPhtdfg/ffh9dfrX7imaVozYFNBIe64MXjJwdG1QS2FwLS9JElbCq6bQdv2pRPYNmwxP4MbboCJE2HePIiLq38FNE3TmphNBYXTJ40J1Mreo/4tBRECD3yDYEd8+0F07+EPwJF9x83PQylYutTY33PuXD1MVdO0FsemgkJKorGXAsqn/i2FHTsIjN8EwMmTMGRoNwAS45Lrl0/nzrBo0YWJbpqmaS2ITQWFtJRcAPIL2ta/pbBqFYGXtQeMoDBylDGBLT2lAZvt3HEHdOwIc+ZAYWH9r9c0TWsiNhUUstKMB/D57OD6tRSKi+GDD+jUthCl4NQp8GoTjgtu5GSfr39FHB2N1sKxY8ZsaE3TtBbCpoJCbpax/0FOQQheXvW4cMsWSErC6fpptGtntBRwcCudwNbAHdgmTjQWy1uwANL0hj2aprUMNhUU8nMKsceeYpf29VoMj6+/BhcXmDSJwMDSoICxA1tuQ3dgUwr+9S9j/YylSxuWh6ZpWiOzqaBQmFeICy64+bmbf5EIrFwJ110HHh6VgoK7mzGBrbDAjAlspkREQEgIvPSSsfyqpmlaM2dbQaEwH2dc8PRzNP+iY8eMOQWXXw4Yc9Di4409dLx83Mgll+3b9ja8Uk8/DTk5RqtB0zStmbOpoFBUlI8Tzvj51+Pd0XffGT/HGTuHBgZCQQGcOQNtO3gA8Mv6zaavPX8Mov8L+5+FQy/B8bcgK65ymh49jElt//mPsUmPpmlaM2ZbQaE4D0dVz9nM69ZB9+7GMqlcWBT15EkIK53AdnhPlQlsaftJ2Xg71427j26R79I+8gOCIj6ha8S7DAi+g/+7czpy5scL6XVrQdO0FsK2goLk4qjqsRhebi788kt5KwEqB4XBQ4wd2E7HVugPiFnOfbc+Rt9xu1i/7SDZ2edwc/DHydmb/OICTqfEsOK9HXQN/htP3TYV8jMutBZef123FjRNa9ZsLCjk4WDvYv7EtW3bwMcHxo4tP1S2BfTJkzC69Hh6SulchWNLGTL6A/73zVEKS7KYMP46onP2cqJgO8dyNhFfsJe1u7+hQ5co0vNief/Dw/RuN5nU6F91a0HTtBbBhoJCAYXk4mhfj5bCr7/C2bPlncwAnp7g62sEBa82PXHFnZzsDIj9iEGjVrE/Zg9ubq3ZfOx7Pln7Gs4uTpWyjOwbztYTq/lhz0Y8XAI4m5ZARNidbIv7VbcWNE1r9mwmKJzPTqGAPBwd6rFs9q+/QmQkeHtXOlw+LNXeBTflS05BBpOv+5CTCbG0ce3OH8mb6RoaUmvWkZERHMveQmT/gZwpiWXGxP+wMipItxY0TWvWbCYoHI8+DggOTk7mtRQKCozXR8OGVTtVaQKbozfZJcn8vPN3nO392Br3DW5urmbXa/2OT7jn5kdJkhhmP/E2X1wzzphBfe6c2XlomqY1FpsJCseiowFwdHQyr6Wwaxfk5cHQodVOlQUFEfBybUUm6fjgzcIPn6Z1a/96123Jhwu5766HySaTB1cf55eEY7BkSb3z0TRNszarBgWl1Dil1FGl1Aml1JMmzndWSv2klNqjlNqvlJrQ0LJORpdusONk5pDUzaVzD2oICllZkH7mDJk5aRRRRHCPy7juhskNrR6L3nqR2bfcRVbJWa6LcyZuxX+MV0mapmnNiNWCglLKHlgCjAd6AjcqpXpWSfZ/wOci0he4AWjwIkEJcakA2Nm7mtdS2LoVRoyAgIBqp8qGpe5Z/QRnCo8CMHpyVEOrVm7JB69x5RXXcFZOMSquI4VvvXHReWqaplmSNVsKA4ETIhIjIgXAp8CUKmkEKFvP1BtIbGhhZ5OMDXaUnZd5LYXffzf2PDAhMBACW8XxyN/j8MLI7Mje6IZWrZI1m/7LgI6T+bMwjsEvfgdFDVxXSdM0zQqsGRQ6APEV/p5QeqyiBcAMpVQCsBZ40FRGSqm7lFI7lVI7k2tYWC492XgVU2LXCte6+oFPn4akJBgwwOTpwEC4aeSzHDuzA2d7H6PycWfryNR8W2NX4u/UiV0pPzJr7EyL5atpmnaxrBkUTC1AVHXT4huB5SLSEZgArFBKVauTiCwTkf4i0j/AxOsegMw0Yy8F7DrVXbPt242fAweaPN3KM5V1m46RTz53PXYjCjvSGrIDWw0cHBxZv+NtPPHj8x+/4bv/fWqxvDVN0y6GNYNCAlDxCd2R6q+H7gQ+BxCRbYAL0KohheVm5gMg9lW7LUzYvh0cHIw5CibE//4WcWeOEeY4mPn/eAoPvMjKtlxQAOgeMYCnbp1EDlnMuvHv5OfmWjR/TdMD2LBNAAAgAElEQVS0hrBmUNgBhCqlgpVSThgdyV9VSXMKGAWglOqBERQatPFAXo7RUnB0DzWjZjuMvQ5cXKqfkxJuv/sX0kjBK2wY2DnipvzILbBsUAB48u1lDAoaTmLxYYZ3m2bx/DVN0+rLakFBRIqAB4D1wB8Yo4wOKaWeU0qVje18HJitlNoHfALMFJGqr5jMUlychTPOeAZ41J6wpMQICjW8Oio5vZ4Dxw/ip9oQk/Q8AK6OPuSUWGGymZMTv947hs4OkWyP38j8x+davgxN07R6sOo8BRFZKyJhItJFRF4oPfaMiHxV+ufDIjJERPqISKSIbGhoWfm5JTjjjE+AU+0Jo6Ohb18YMsTk6flPv4VziR1dOo/g3Dl7cnLAzdWTTDIossJIIft77+OjYV60J5B3XllFbOzxui/SNE2zEpuZ0VxUlIcTLvj61bHBzv79xnLZPXpUP5d/js9XJpPIGabd/VcATp0Cb18PSijmt02/W77inp5cMWgI43oGksgJxkTeYfkyNE3TzGQzQaG4OA8nZcay2QcOgFLQs3qH9Jl9y4nP2ktn53CuuMKYrHbyJLTpZLyS+mn9L5autuHBB3nnxBZ6egzixPnN3HXzo9YpR9M0rQ42ExSKJAcH5VL3xLUDB6BrV0xNZnjgse/JJYehY4dX3oGtuzEM9tDuYxaudal27eDW2/jK5xhe+PH5xys4evSIdcrSNE2rhQ0FhTwc7cxsKfTuXf14TiIHd2USRCivvf8c7duDvX3pDmzDjVZFQlyDBkaZ5/HH6ZKQxq0jh5BBKlMH3m29sjRN02pgM0HBrA12cnPhxAmTQeHEb/8lOu937D3b4OPjhYODsQrGyZMwcvRInHAiLfW89W6ge3eYMoXX920hzOMyjpz/lcfufMJ65WmapplgE0GhpFgoIBeHujbYOXzYWA/bRFB4cv4miijkykmDy4+VLaHt1SoUD3wtPoGtmieegHPnWPXEcNzx4933PiQxvsHLQWmaptWbTQSFM2fOUEwhjo51bLBz4IDxMzy88vGCNHbuOIsrbixa+nT54fLNduzsjR3YCtMtXvdKhgyBwYPp9d/PmDZhAuc5w6T+ejSSpmmNxyaCwvHowwA4ONWxwc6BA8Ys5q5dKx1OO7aa4vx0OrpE4OVzYfJbYKCxdl5hIbg4+pBTYuWgAEZrIS6OFbdMoKfrlew7u5GFzy20frmapmnYSFCIiSnddc3JBR+fWhIePGgMRbW3r3R43rNfkEAs4QP7VToeGGhMgD59GtzcvMghkxxrb4wzeTKEhcHCRfzns9txxpVFC5aQl5dv3XI1TdOwkaAQH3MaMIKCg0MtCQ8cqP7qSErY9MN57LBnwauPVDpVNiz11Cnw8jNaENs3b7NUtU2zs4O5c8HNjZHu7RkWOYKzcpIxkTdZt1xN0zRsJCgkxhu7rjm5utWcKDXV2EOhaifzuZ2cSYuhjV0IEX0rv1aqOFehbUdPAH7e8LOlql2zm24yRkm99BLfbPuYdnZd2X50Ld9++Y31y9Y07ZJmE0HhXLKx65qTq3fNico6masEhf8tf5cUEunQqXu1Szp3Nn6ePAlhvUonsFloB7ZaubjAo4/C99/jcPAY//fs9RRRyAPXPWP9sjVNu6TZRFBITzXe87u417IVw8GDxs8qr4/eescY8vmX2eOrXeLiAm3aGEHh8uG9AIg/abkd2Gp1zz3g7Q3/+Af3/d/zhAcMI65gDzOn3tc45WuadkmyiaCQm1mACy64erStOdGBA+DrC+3bXzhWlE109Gnc8GTO3LtMXlY2LHXYqOG448G5FCtOYKvIywvuvx9WrYIjR/h2yz/xpA2rv/ycU3EnG6cOmqZdcmwiKGRl5ZFHHj7+1V8BlStb3kJdWEU19+RPnCk8Qju3MBwc7E1eVj6BzT8ID3zJzmmkoADw8MPg7AwLF9IhtD/XTR3NeVK55jLdWtA0zTpsIigU5BagULj7djOdQMR4fVSlP+HFlz8lj1zCete8hWdgoDH6SFC42flZfwJbRa1bw513wooVkJDAO1+8R3eXoez5cz2vLVrSePXQNO2SYRtBIb8AZ5zx8K9hOnN8PERFQb/K8xA2rkuhE52476mba8w7MBDy8uDsWXB18SBb0mjg5nANM2eOMVnilVfAzpFX/3sDjjjyj7mvWmXTH03TLm02ERSKCvJxwgVvnxpu59gxY2Od4OAKF2VzKjGWXIqZNGVsjXmHhkKvXhAbC24uvhRSQHKKFVdLrSooyBiiumwZpKYy9ob7uCz0SpJKTnD14Fsarx6apl0SrBoUlFLjlFJHlVInlFJP1pDmOqXUYaXUIaXUxw0pp6i4AEec8a5pROqx0n0QQkPLD2XEbCSlOA5/9+AaLjJ07AiHDhlBwa+1OwDr1n3fkGo23Ny5kJ0N//mPUf72N2itAvl1xzds37ajceuiaZpNs1pQUErZA0uA8UBP4EalVM8qaUKBp4AhItILeKRaRmYoKs7HQbnUHBSOHwc3t0ojj156+XMKKSAsMqzWvMsaF9HREBRiBIXN31thW87a9OoFM2bA1q2QmYmLT2fuvW8suWRz67gHGrcumqbZNGu2FAYCJ0QkRkQKgE+BKVXSzAaWiEgagIg0aBJAcUkeDqqWlsLx48YieBVGHv2y0ZgFfd/c2l/BuLkZG6PFxED/y9oZ2R2Kb0g1L85DD8GGDeWthQWvLaWb12COnt/OXx+Y3/j10TTNJlkzKHQAKj49E0qPVRQGhCmltiilflNKjWtIQUWSj4NdLS2FY8eMRebKL8gmKSkJL/wYd/XIOvMPCTGCwvjJA7DHnuTTjTgCqcyAATBxIixaBJmZYGfP/9Y+ghvevLP0v5w/n9n4ddI0zeZYMygoE8eqDttxAEKBEcCNwDtKqWrrnCql7lJK7VRK7UxOrt7JW0geDvZOeHmZKLGoyOgQqNCfkJewmT+LTuLr0cWsGwkJMV4fdeg+BE+8ycxoxLkKFc2fD+fOlbcWwodMZ8zlw0mTeMZE6k5nTdMunjWDQgLQqcLfOwJVtxFLAL4UkUIRiQWOYgSJSkRkmYj0F5H+AQEB1QoqJA8HhxpeH8XFGYGhQlB4/bVV5HGert1q72Qu06WLsXx2fok/bsqX3Pw0s66zuLLWwr/+ZbQWgP99/x5dHPoTF7uD/330ZdPUS9M0m2HNoLADCFVKBSulnIAbgK+qpFkDjARQSrXCeJ0UU59CSkpKKCAfewcn00Hh+HHjZ4XXR2u/SQLg2lnmva0KCTHmv508pXB18ia3pImCAhithdRUWGJMXnNw8+eZl0eRSjJzbn+GxpxCoWma7bFaUBCRIuABYD3wB/C5iBxSSj2nlJpcmmw9kKqUOgz8BDwhIqn1KSf+VDyC4ODkgKOjiQRVh6OKEH/qDK64M2u2ea9cQkKMn9HR4OHhQTYZpGfk1aealjNgAEyYcKFvAbj10ZeI7DCMU4X7uW6s6TWcNE3TzGHVeQoislZEwkSki4i8UHrsGRH5qvTPIiKPiUhPEektIp/Wt4xjhw8B4OjkbDrB8ePG4nJlr51yTpGSH0srxxDs7WvbkeeCLqVdDzEx4BvgglDCt1/9Wt+qWk6V1gJKsX7zC/jTjnUbP+fQwT+arm6aprVoLX5Gc1x0LABOzk6mExw/brQSSoej/vjVx2SQQtu2nc0uo00bcHU1gkJwqLED25aNv11cxS/GwIHVWgt+QYOYOeNKssjgL0N0a0HTtIZp8UEhKf5PAJxca2kpVOhPePvtnbSlLZePjjS7DKUuDEsdeJnR4jhxILbhlbaEqq0FYNF/36Grx+UcPb+FeY8/14SV0zStpWrxQeFsktHp6+zmXv1kfr6x7nWFkUcH96VwlmQemTerXuV06WL0KYyfOAqAlMRzDa+0JQwcCOPHw6uvQkaGcczBhU9X3o07Hiz795tklB3XNE0zU4sPCueSjdcnru4mgkJMjLHCaFlQKM4nLf1P/GhLcEhQvcopayl07nYlzriQfb4JJrBV9fzz4OhorKBaqt/Y2xg9eCQpksSY3jOasHKaprVELT4oZKQbW3G6eflXP1llOGpO4jbOlcTj7d6x3uWEhEBODpxN98Pdzpe8ppqrUFFUFAwebMxbSEoqP/zFD+8S4tifhPi9LHttRRNWUNO0lqbFB4XszHwAvHzaVT9ZZTjqO2+tIpccArt2qp62DuXDUmMUro5e5Epq85gT8MILxmuyZ58tP2Tn0oqFSyeQQjILHn2OgvzCJqygpmktSYsPCrlZBQD4BphYsuL4cfD3N/ZmBtatNSZUj5k+tN7lVByW6uHhThZpnD7ZRMtdVNS1K9x7L7zzDvxxYSjqNXcuYHCPESSVnOCqPjc2YQU1TWtJWnxQyM81gkJA2/DqJ8uGo5ZKOJGGQnHPQzPrXU5QkPEzJgb827iSSy6/rt/agBpbwdNPG8u5PvXUhWNKseG3pbS3C+P3o1/zyYpVTVc/TdNajBYfFAoKCnDECR+/VtVPVhyOWpxPRtYZfOxa421y5bzaubhAhw7GCKQu3Yzrt/6w62KqbjkBAfDkk/Dll7B5c/lhR68QXnrZWMpjzu1/09t3appWpxYfFAoLC3DCGS+vKouy5uRAQkJ5SyH79A7OSTy+blVX7zZfly5GS2HAFUaesYdPNzgvi3vkEWMToSeeoGJnx62P/5uBIaNILD7K2IE170WtaZoGNhAUiopq2IrzxAnjZ2lQeP+9r8kik04h9e9kLlM2LHX4yEkAnEtqRvMA3Nzguefgt99gVYVXRcqODVtfJsA+jM17vuLr1d80XR01TWv2Wn5QKM7HARMb7JQNRy0NCuu/PQXAiImXN7iskBBITISgkOEE0JHcrGbQ0VzRbbcZW3c++SQUXhhx5NqmNwvmjUUo5v4b5ujXSJqm1ajlB4Wadl1LTDTG8JcOGzp5onT7zUfuaHBZZSOQEk47kWeXS1Zh1e0hmpiDA/zjH0YradmySqfuW/AqA4OHEV9wlAn9b22iCmqa1ty1/KBQko+Dcq6+69qBA0ZrwdsbpIT083/irQJo3br6Jj3mKpurEBMD7s4+ZMuf5OQ0s9+6J06EqVNhzRpjl7Yyyo6Nvy+mk11PjuzbxofvrmxwEbm5xsoaKSlG142mabajxQcFYytOE30KMTHlT/Gi9COklZzC16XhncxQOSh4+3iSTirH9sZdVJ4WpxQsWAA//VR5iCrgGtCL5/85ijMk8te7/kZOTq5ZWR48CG+8YcSbdu1gyBDw8TEGPQ0YYIzKGjUK/vlP+P57KCiwwn1pmtYobCAo5OPg4Iyra5UT0dHl73u++OR/nCedth3bX1RZAQHg7m5k3baTJ3nkseW7LReVp1X06QMPPQRvv210PFdw62OLGdZ7OEklxxnR/YYasxAxHvCXXWZ0Vbz8Mpw6BWPHwg03GCtrvPYa3HgjXHUVZGUZfx89GoYNg9mzYfdua9+opmmWZt4uM81YAXk4ODiWbZdQerDAeILNMBaEW/U/Y6bvZVf2vaiylLowLLVHZFt+2Q47thy+qDyt5tln4bPPjNnOO3YY/Q0ASrFu01t0CZjC7vhveW7eKzzzwmOVLj140Bjh+sMPxgP/L38x3ki1bVt7kdnZ8OOP8PPPRsvinXfg9tvhjjvgiiusc5uapllWi24pZKSdo4giHByr7KVw6pSxOmppS+HEIWPxuvsea3gnc5nyYaljhhhFRf950Xlahaensaz23r2wdGmlUw7ewaz46AZccOPfLy7i1EljZFZJidFP/eijxm/5r78O330H99xTd0AAoxV19dVGKyIx0Sh+wwYYOhSmTbuwFJWmac1Xiw4KRw6WbsXpXGVz5uho42dpJ8C5tLN44kdoWMhFl1kWFIYO+4uRd2q9tpRuXNOnw5gx8H//ZzylKxh27d+4ZuxI0klibO8ZZGYar4LefBP8/IwH+AMPXGhg1JePDzz8MBw9Cn//u/EqqmdPuP9+OHvWAvemaZpVWDUoKKXGKaWOKqVOKKWerCXddKWUKKX61yf/6KPGXAQnlypbccbEGD+7dIG8M6QXxePrXP/lsk3p0gXy8kAVdsQdb7Jyky2Sr1UoZezMVlAAjz9e7fQHX39IN6/LycyMYdKQu1izxpji8Omn0MrEqiEN4e5uxKQTJ+Cuu+Ctt2DmTHj/fZrHKrOaplVitaCglLIHlgDjgZ7AjUqpnibSeQIPAb/Xt4zTp4w9BJyrbsUZHQ3OztCuHT9+8xHppNK6zcV1MpepOALJw9GPnJKzSHN+unXtaoxC+vRT2Lix8jlHT1avn0+eKmH7gQ/562NfcM89VO6fsZA2bYy3WAcPGjFq5ky49lpjR1FN05oPa7YUBgInRCRGRAqAT4EpJtL9HfgnkFffAv5MTAHAxa3K0KOy4ah2dqx431i0LvLyavGoQSoFBQ9vzpNM0ulm3FoAmDvXCA7332/svVAqIwNm3D+WsVdNpoQS3n75cZKTrfuU7t4d1q83RjN99RX07m38XdO05sGaQaEDEF/h7wmlx8oppfoCnUSk1gV5lFJ3KaV2KqV2JidfeACnnDWWmXD39Kh8QXR0+dP70B5jAtcdD97WsLuoIijI+E06OhoC2niRTRab122u87om5eJivEZKTDR6jzFWwbjuOuP1zs0PL2XsZWP4U04yInSa1atjbw9//Sts325sdTFuHDz4oJ4Ip2nNgTWHpJp6CVH+nkUpZQf8G5hZV0YisgxYBtC/f//yPDLSjKeIu7dPxcTGr/EjRgCQmpyCB95cPiSi/ndggpMTdOpkFNG1ZwC/HYFf1u/kulnXWCR/qxkzBm691XiVNGIEjy7vz4YNsHw5TJhox4Qrl9Gt9XQOZ2xi+lV3svL7d03nU5AJabvISz3ITz/v4mhcIbnZmbi5OtEtrDVXXtETp9YDwDcC7F1qrVJkJOzcaVRp8WJITjbm3XXvbvG71zTNXCJilQ9wObC+wt+fAp6q8HdvIAWIK/3kAYlA/9ry7devn5QZFT5NAHlw1pLyY/LnnyIg8uqrIoWZ4ktr6ejQSyxpxAiRwYNF3l76ggByVY+ZFs3fas6dE+nQQZa3nSsg8vjjlU8n7l8jAaqzOOMiy99+/8KJolzJPbJCHr12gvT2HSEBjiHSkc6CEeSlc+mfO9BB7HGSANVZonxHyLVDJ8of6/8pkhlbZ9XWrRNp107E01Pkyy8te9uapomIuc9ucxPW94PRCokBggEnYB/Qq5b0P9cVEKRKULg8eIIA8uy8by/c9rZtxm19/bXs2/KuABLZZrRlvtJSd9wh0qaNSEJCjADSx3eKRfO3poPLtog/Z+X2ntukqKj6+fdeeEiccZEA1UHi447KgW+ekkGdRkkHQsQdX1HYia99J+nhPVwGd58uEwffKdeMul8mDL5DhobdIKFeI6S9Xai0p6MA4oyzdHWKlEkDp8rp7UtFik0UWurUKZH+/Y1/vmeeESkutuIXoWmXnqYNCmI86CcAx4BoYF7pseeAySbS1jsoRLW9SgB5+81TF277ww+N2zp0SB64aYYAcsO4ey3zlZZ64QWjiKwsEVfcpYvjFRbN31ry80UiI0UCXM/LGVqL/PBD9UQlJXL90KvFmzbSVnWREMIEkFC7ATJu0G2yd+9hs8pKPZcmd9z8mHTxGijOuAkgQXSXXgFXysaPnxUpyjN5XW6uyMyZxvc7aZJIWtrF3LGmaRU0fVCwxqdiUAj3GS522Ms335RcuO3nnjNuKydHLg8ZJ4B8tdLEw+8ifPKJUcSBAyKt7TtLO8Ismr+1PPmkUe81n+WJhIWJdOpU/alblCtvPn2r+NFeAPGhlTx814KLKjc7J1tum/qoBDn0FkCccJZwnxHy6wfzRApzqqUvKRFZskTEwUEkNFTk0KGLKl7TNINZz9gWPaO5oHQrTh+fCn3a0dHGtpSurpxNSsENDyZMHWHRcisOS/V1a4MjJeTmNu+hM1u2GMNA77wTplznDCtWGKORHn74QqLsBK4fMZWH/v4pWZwjgE6kk0Jy4sUt5eHm6sby1a8QW7if115cTHvn7hxM/4Urb11I3zZXcXDD4koz2ZSC++4z1lHKyDAW4fvqq4uqgqZp5jI3ejSXT8WWQohzlHjhJwcOVIiFQ4can+JC8ae9dLDvcVGh1ZSUFOM37ldeERkUOFwAWbf227ovbCL5+SJ9+4pcfbXI+fMVTjzzjHEjK1dKQfJe6dd2qNFxbDdAPlqxSo5tflda0VGccJZ/vfSqRev0z38ulQ7OA8QDD/HAS4aHjZXM+N+rpUtIEJk+XUQpkX/8w2hFaJrWILb/+qizQ7j40U5OVehSkPbtRWbOlPgjP4gddtLbb9RFfYumlJSIeHmJ3H+/yM3jrzdGQN3+eN0XNpGXXzb+pb+tGrcKCkRuvVXyerlJL48h4oKnhLj0l/jTSeVJPn3lUXHHU7zwkx9N9UFcpDkP/1Pa2XUVQAJUJ3n8tltECrMqpcnJEbn+euMebr1VJM90d4SmabWz/aDQ3i5UWqtgSU8vPZCTY9zSc8/J/91/l3Sik1wz7M6L/iZNmTRJZNw4kXdeeVkAGRF+rVXKuVgJCSLu7iKTJ5s+n797jXR16y+ARPiOlYLCgsoJSkpkzk03iAMO0tYuRJKSEi1ex4LCArl68M3ijqcA0tVjkOz7/p2q1ZBnnzX+eYcMMUYea5pWL2Y9Y1t0n4KxP7Mznp6lB2JjjZ9durD550TiiWfc9KFWKdvfH/btg2tvuwV7HPgzoXku/TlnDhQVGctYV1V8Pob+V75MWk4yvb1GsntiGxztq8xnVIqFHyxnXNQ4zpTEcEXQNIqKCi1aR0cHR77a8iFb920j1GcYZ7OOMOyqudw8ZioUni+rBs88Y2wRsWsXDBxo7LiqaZplteigUCh5ONi5YFd2FxWWzE48mYoTTtw6+0arlB0eDklJUCjt8KU157OaX1D46SdjHbwnn4Tg4ConCzIY2vsBDqRvo7VvB/Y8fAX2H35g7NZWlb0zX2/5L5GtR5KWn0C/9hOtUt+IiF4cS/uFu+6fgwNOfLzxS7r4DmfnumXlaa67Dn791VhUb/Bg+PZbq1RF0y5d5jYpmsun4usjT7wl2GXghcbRq68a7xfOnpU2dkHSxi7o4hpbtfjuO6OoX34RCXKMEk98rFZWQxQWikyYIBIcbLxVq6S4SG4YfrUo7KSdUy/Jzc0TKSoSGTtWxMlJZMcOk3kWpB2XLq4DBJDBXa+2av0TE5OkT8BIUdiJO15y85gplYavJiSIREWJdOsmsmiR7oDWNDPY+usjKd2Ks8Ky2dHR4OFBnkMWaSVJeLt1qPnyixQebvw8eBB8/XzIJJ3EhMTaL2pEH38Ma9fCokVU27/6lb/dy+pfNuBn14atR77BxcXZWKXuo4+MLdYeeMDkTjiOPl3Z/ce/CHQKZ+uJrxk38Gar1b9du7bsPfsj8x55Dhfc2LxhL6E+Izm23Rib2qGD0WK44grjFdkdd1RaAFbTtIYyN3o0l09ZSyE3+6wolPTwrTC6aOJEkT595I2XnxZARob/5eJjaw1KSkS8vUXuvVdkwgBjBNKLT//TauXVR0GBSJcuxuzlqktFHNr0sbSmowTSVVZ+tqb6xbt3G4sQDRwokp1tMv9Tu1dKO7tQUdjJ9DF3W+EOKkuIT5RePiMFlHgTIH+deWv5chnFxSLz5xuttsGDRc6csXp1NK2lsu2WQuyxAwiCo1OFXddKl8z+bs1hAIaM6W218pUyWgsHDsDQUZ0B2LR+h9XKq48PPjC+imef5UJ/C0BBGlPGvs5ZEhh709X85ToT21v07WvshrNjB9x8MxQXV0vSqe9f2Lj+EVqpDqzZ8C6zbppjvZsBOnRsx8G0H7nnlscooYCFyz8kqt0YzicdxM7OWFn1889hzx4YMMDYllrTtAYyN3o0l09ZS+GrT98SQAYElo61LC4WcXYWmTNHevuPEIWS+FNxlomvNbj7bhEfH5HEY5vFHgfp5T/UquWZIz9fJDDQWFiu0nv2khKZdtkUAaRXq2F1Z7R4sfHr98MP15hky/9eFB8CpB095OHZf7vouptj545dEuQcJYC0VkHy7sIL5e7aJdKxo4ibm8gXXzRKdTStJTHrGdvkD/n6fsqCwusvzTc6PLvdYNxufLxxO0uXSif7XuJLG8t8jbV4/XWjyIT4ImP2tEN3q5dZlzffNOq0dm3l46vfmSeuuIu/6iApKcnmZfbII0Zm//53jUm+efcZ8aaVOOIkj8yaexE1r5/xg26WANqIG+4yuvdEKcwx1nBKTBQZNMio9gsv6A5oTavAtoPC3+57yNjLoN9M43Z/+UUEpOS7L8UTbwlyjrLM11iLn34yvsF160SCnKLEo4lHIOXmGr8pX3555YdhQXqsdLDvLg44yOuL3jA/w6IikWnTjDUmVq6sMdnqZc+IL23EAUe5+6bGm9n90fufSzu7LgJIoFOE/Lb+IxExvodbbjGCw7RpIhkZjVYlTWvOzHrGttg+hT8TswBw9yqduVY6R+HH+GgyySCgbWur16HSCCSfVmSRzoljR61ebk3eeQcSEuC554w+jzITh90NxZkMDp3MA4/fY36G9vbw4YcwciT84x81bqY8dfazrPjvPXjRinc+XszNkx+6yDsxz023Xsvx8/vo32ks8QUHuWrsfdw17WZcnIp5/324/npjIb1Bg+DIkUapkqa1eC02KKSlFNCOdnj7tTIOxMSAnR0ffb0PgD6Dqs7WsrxWrYwRnAcPQlCYPwDL3/jA6uWakpsLL74Iw4bBqFEXjm9Z9S827d9Mnr0LGw58VP+M3dyMXtyiIpgypcbAMHHmAr747F58acunXy9l6oi7G3gn9ePu7s6OU+t46tH5OODI22s+pm/ABP6M2cmjj8L330NqqjEDevXqRqmSprVoLTYopKfnkEQSbdq3Mw5ER9Ef3nQAAB+GSURBVEPnzhzaYyzzfNu9UxulHuHhRlC4cqzRbPj95z8apdyq3nzTmGFdqZVQmMmtt3xCAXk89vRDODvXvmdyjfz9jadrjx5GYNiwwWSyEdc9zbpv59BKdeCbX97lqqjbGlZeAzz/yjNsP7KVcI9R7D23gR6h0/jn3IcZMQJ27zaqfs018Le/GfFN07QamPueqbl8yvoUBgVOEkAWL/rReFs2aJDIqFES4txP3PAUkcbZy/GRR0RcXUXSks+IPY7Sza/xRyBlZYm0bi0yqsqCsE/MnGqMNvK20EqxKSkiffqIuLiIbNhQY7Ijv/5Xgp0uF0D6tRsjhYWFlinfTDeOu0vc8BB77GVgpzGSnXZa8vJEZs8WGT7c2GP79OlGrZKmNQe23aeQl2NMX+3Vp6dxIDoaQoLJyE/Ex6EDjdUICg83Xt2kZrQh2K4HKiuvUcqt6KOPIC/PaCWUyTz9O8ve34o3fnz082uWKaisxRAWBpMnw8aNJpN1GzqT3/Y/R4hLf3YlbaC79wCS/0y1TB3M8PF3b/Hlui9p79CT7fEb6OI/jM/e/DvLlsHtt8P27RAZWWODR9MubeZGj+byKWspdPcaJk44ydEjJcbwEpDoeQ+LHXYSHjDCcrG1Dr/9ZoxAWrNGJMR1gLjh3qi/GefmirRtKzJ+fOXjg7uPkM50likD7rF8ocnJIhERxhTi1atrTJZ/7g+JbDtCAGlrFyybftxm+brUorCwUK7qc6044Sy+tJGRPSZKYU6qHDok0quXMajqb38z1onStEtA07cUlFLjlFJHlVInlFJPmjj/mFLqsFJqv1LqB6VUoLl55xfk4Ywr/q2U0ckMvP3HOUoooWvPtha8i9r1LG2o7N8P7ToFkEM2ny7/uNHKX7ECzpyBxx+/cGzLd0vYeeQ3lPLkf5tft3yhrVoZe2U6OBgv6l83XYaTb3f2xH7OmKirSS6JZ9KVk3jtZROrsFqJg4MDG/d+zrvvvYe3Y2d++uNbAj0Hs//Xf7B9u7Fe0osv/n979x0nVXX/f/x17p2Z7b3vAktZysJSlyICC1gQUYz88BeQINZYEzVqivEbTYy/RGNsURMLatTYk2/sEgu2RBGwgAiGIiBLFViWsnVm3r8/7rDUhUV3d2A5z8djmLkzZ+79zJnlfubee4o3RemKFa0WlmUd3pqaPQ71BrjAMqAzEADmAT33KjMaiI88vgR45mDr3XmkkBfoqzRToGBQXvdV0KiupwnQw/fd0wJJtnEjRnhTRv7i0ksFaMKIaa2y3WBQKiraq/dyOKRuKUNlMPr9L+5q2QB27JBOP907VLrqqn0HWmoItEZXTj1dcSQoljhNPfXylo1rP2pqajW86+nyE1CAGI3odopqd1To6aelrCwpKUl65BHb2c1q05q2725qwUO9AUOBf+22fC1w7QHK9wf+c7D17kwKOU6R8kxn76P+4Q8SqEfCcPnwq6Zm51RsrWPSJKlDB2n10jkyLTQF6P48+6x2TrHc4JZfXS6Do+L4Y1slBgWD0uWXe4FMnLifcbojwmE9ducVKjL9BUZ9ckdr27ZtrRPjbh75y6PKd7oKUBd3oO67+XqtWCGVlXkfYcIEacOGVg/LslpD1JPCGcD03ZbPAu45QPl7gP9p5LULgbnA3A4dOkiS0slXB18v76NedJGUnq5800VZprB5q7EJ/vhHrybXrwsr3eSrndPyw12Ew958At26eftlSQrVblM7t7cCxOjdGe+1eAx7uOMO7yT9lCnac9LsPS2b9Yy6xA0WoBynk/7xzIutGKSnvq5OI4u/p0xy5MOn0vwTtOHrRbr1Vm86iZwc6eWXWz0sy2ppTdp3t+Q1BbOf57TfgsZMBQYCt+7vdUkPSBooaWBWVhYAdVThdyMTBXz1Fdu7FbJZq0lJzGuO2A/JoEHe/Zy5htS4AraHN1Bf37xTVu7trbe89vc/+5nX8Rjg3NMvpTz0Of07jqTspJaZhrRRV14JL70EM2Z4TXsamRKt85Dvs2TD3zmxZDwV4dVMnTSZKSdd2qqh+vx+3ln4PNOfu58Cf08+XvMmxYWjKZ9/PnNmi06d4MIL4cwzYf36Vg3NsqKvqdnjUG808fQRcAKwCMhuynq900dh+QmoR+IwL/917qx7xp4iQKN6NzJDfQvatk1yHG9c/1E9vf4TD9w1/aDv+y6OP17Kz5dqarzlyvXLlEU7JZKqdeuiOKv94sVeXwaQfvpTb3KH/QkFdff/XKAMCry+FIllWrl8ZevGGjFpzLlKJEUFdFaXuMGa8dwj+s1vvKOG1FRp+nR7rcFqE6J++sgHfAV0YteF5l57lemPdzG6a1PXW1paqsqKDQLUJ+N4rz2h6+p7Jd6w0Df8rPVG6txdSYnXLPSmn14lQOMGfb/FtjV7tvfN3XrrrudO6DFBgE4dOaXFtttk1dXe7EPgjc63svGd/ar5L6pr8lC1p73STbau+tH1rRjoLgsXfKGStNFycBRDrIZ1OVGzP1iiESO8jzFqlPTf/0YlNMtqLtFNCvJ2+uOAxZEd/3WR524ETos8fhNYD3wWub14sHWWlpbqvTdf8eZSaH+KtGyZBOqbdpzAaE35kpaq0AP6xS+kMWOkLRuWy0+MipKHtdi2Jk70fsHuHP1z8ZzXlUSKMkx71TX2yzwannnGa9aTlia98ELj5WoqdNbY05VEqsCoW8pwffHFl60X527u+P2dyne6C1CKydO0cWfpwQfqlJrqTdfxu981OiGdZR3uop8UWuJWWlqqe/94mwCVFf8f6Y03JFCh21spZDVrDR6K6dO92ly4UMp3uimTghbZzpdfetdzr7tu13Ol2ScK0OU//FmLbPM7WbJE6t9fGj5cOu88adOmRovOe+Mh9Ug4VoCSSNWUsZcpHIXzNnV1QU0cfZ6y6SqDUYHbQzdc8TNdfbX3HbdrJz3+eOMtcC3rMNV2k8LV51/jnaI5Zpp0330KgVJJV4fYvs1ag4di8WKvNu+/X+qbPVoGo1n/mdvs27ngAm/oofWRywavPXGPAsSonb+k2bfVbKqrpeuvl1zX6xTw5JONn6Sv364rz5ykNHIEqDhmiJ59LDrTqK1ds0ZDCscphlivCWvcQN3xmz+otNT7rgcPlj74ICqhWda30aR97BE59tGa8s0ApGYlw8aNzDhhNFvYTHZuTtRiKiqCnBx4/30YOqo9AQLceWPz9t5dvRoefdTrgZudDSjMlT98gnrq+eXtrTOHwbcSG+tNGP3xx9CxI0yZAuPGwfLl+5b1JXDHk0+zaNHj9M4Zzebar/nBtMn0zzmRJUuXtGrYuXl5zFrxCjPfm0HPlDJWVH/KrTc8wI7FI7jx5w+yahUceyxcdhksXtyqoVlWy2lq9jhcbqWlpRpb+n0BuvqS30rjx+ucvicJ0AWTftisafVQnXGGNz/yyi/elYOrXqmjmnX911zj/dj+6itv+fZrr1IhHVWc0rzbaVHBoDf/c0KC13zq17/2mm/tTzikR26/Rh0C/QQojhQdP2Citm/f3roxRzzx8FMqihssgyMfPhUnD9fVFz+igQO91mdnnWUvRluHtbZ7+mhYF284i7vveEIqKtIxOSerPe31wb9bucPWXv70J69GV64IK8fprCzTvtnWvXmzlJjo9Q2TpHB9tfLdboohVm+9NbPZttNqVq6UfvITr8JycqQ//7nx5qt1W3X596cow+koQEX00cSR56qutrZ1Y4546N771SV2UENy6JM2SpdMvUVxcV5ymDbNO51oWYeZtpsUBuSMEaD3Z86THEed/P2iPj+yJM2f743X/7e/Sf1yRspgNPvD/zTLuu+802v9Mm+et3zu+ImRFlit3y+jWX3wgRrafRYVeWN3NHK9oa5iqcYPOU3ZdBCgTJOr00eererqmlYO2nP/Xfeqa9KxcnFlMCoM9NOUcZcrPj4k1/WSw4IFUQnNsvan7SaFXskj5eJq0/vzJIOSSVPH2N7NWnvfRijk/eg980zpsikXKI32OmP02d95vZWVXqvOyZO95e2bVyrFZCiNbJWXt4HZYsJh6aWXvM4e4A2y9/zzjTbvqVw7Xyf0O02pZAlQAb10Qv/JWrdubSsH7vnHk8+pV+rIhgvSmW6RxgyYpONHrRdIY8dKM2bYDnBW1LXdpNAtbojiSVL4mWc1szgn8ot5XLPW3rc1bZqUni5tWLVUMcSoa8Kg77zOm27yvqk5c7zl4T29OQomDI/uNZRmFwxKf/2rtxcFqXt36cEHvdZL+7F93ec6ZeD3VOB41xwSSdagvLF6743onEb8eO4cDS08RYmky8VVBjnql3WCygY8LJCKi6X77rP9HKyoabtJoaO/j1LJlm68UZN6lgnQj35wVbPW3rf11FNerc6aJRUG+iiBpO806c6WLd5Rwvjx3vL8j15RgBh1MD1VVxtspqgPM/X1XkX27+9VZm6uN+DeunX7LV5X+bWmnTxJeb5uAtSeDiqKHaSrLvpVq08FKkmVFVt1xuizlRsZjdXBUaG/j44vnaoY/3qVlUkXXyx99JE9erBaVdtNCu2cbsoyHaUf/lAlqWVycLVsyfLmrLxvbeNGr3PZ9ddLJ/bzht647oobvvX6fvtb71uaG+nyUJRRKgdHv7jo/zVPwIezcFh6802vq3hpqeTzed25Z8zY/6mlYI1uvvbHKkocKj+BSK/kdhrRZaLeePXtVg9fku697W71TB2pOBIUIKAU0lWcXKaR/X4qqFXPnt7I72vWRCU86+jSdpNCtilQfqC71L278pwiZZkOzVpz39XUqdIxx0jvvPiYEkhUn8xR32o9W7Z4w1mcFrmW/Mjd1wmMesSObsZojxCLFklXXy1lZnp/toWF3t506dJ9y4bDmv/u0xrZbZxy6SIHRwZH7dweGjf4TH25qPWH0Fizeo3OGDVN7Xw95eAIUBo56p17vIb3vVGuG9Ipp0hPPLFr+BLLamZtNykU0EFd40ZoQ5JfscSpewuOM/Rt7JxfYdnSsArcrkoh81udxrjtNu/H8ccfS+FgrXIChYonXk8/coBxhNq6mhrp6ae9YWJHj/YqurRUuuWWXR04dldfpZuvvVw900ZGxlZCfvzqFj9Kpx47RZ9+8mmrf4T3Z76uEd1PU67TWT5i5OIqnVyVpI3WqJKfKCZQpfHjpUcfPeCoIJZ1qNpuUvDjV/eUEbqm9yAZjE4vm9qsNfddLV/ujap5223ScX1OVx5F+vmlvzqkdaxd6/XvOu88b/msk71RUIfmn9H8AR+pVqzwMvDgwd6fMkiDBkm33+613d3rhH31pqW6bNLZ6ho/ROnkNpzvz3O66tii8Xp0+l9b/SM8/fCTGtr5FOU6RTIYAcqnUEXxQzW8eJJOHP6mRo70DooWLLDXIKzvpG0mhV7FxQLUL3eMBmaPFqAZh+E0WcOHSz16SLPfel4+fOqeeGjTY150kXeUsHixtHrJx0oiTZnk6+sDzGp2VPvqK2/PWVYm+f3en3ZBgXT++d58pZs371F8+zfLdMUPzlOvlFEN4ywByqaduicO08RR52jWf+a06kd4840ZOqH/BPWIGSEfMQ1Jq6szUCXpx+nYXhdp4mlf6txzvb4wq9tAa2SrVbXNpNChoL0ADe88Xu3cXkoxec1aa83lwQe9eZtnzZKKEkYqn85a8t+mDev96afSkCHSL3/pLffNOU6Azp3w4xaMuA1Zs0Z6+GFv3JGUFCk+3psxp39/6corpX/+02sRsFPdNv35pus0osvJynd7yI9fgAxGnZxe6pZWptNHnKWX/tF6Pz7Wr9ugS878sXpnjFaXyLzWgFz86uj0VUnacRpRPE2jjvmXLrpIeuwx7/KKPZKwDqBJ+1gj7XeGzMNWVka2Nm3eyLiSU3l9wQy6p5Tx+ZY3ox3WPrZvh4ICOO00SNcF/OmJhygrnsC7C//3gO8Lh2H4cFi6FP77X3jglp/w61vup33CUBZvf6uVom9D6uthzhx44w1491348EOoqYGyMli3DgYP3nXr1w9iYvhm+cf89n/+wntvLKemYitLg58RIghACunkxHYlLTeDgWXduPia8yjp3bvFP8ZH/36P2294gPlzVxLctoNl+gxFZrdNIZd28cXEpsWRmltI+x7n07VnKQMGwIABkcETLWv/UyTvW+hISwopCenaWlXB0Lzj+XDtW0w95Xwef3l6tMPar1/9Ct5+Gx5/tIrju42gIryK8m3LSUhMaPQ906fD7bfDz38OJwz7jN7dTqVWlbww43lOOOn4Voy+jaqthdmzYd48ePNN+OgjLzkAdO4MycnQty/06ePdl5Swdsdabvvdfbz/5nLWrVnPlvqVbGVLwyq7UEIoxpCalkvnnnmMnTCMKef84IDf83f1xfzPufOmv/Dx+8tYu2k1/voqVrFr1Nk0skmOLSQlMY3U7Czyu5ZSVHI+Jb2TKSmBbt3A72+x8KzDU9tMCgmBFFXVb6VnXBkV1cv4aMX7tC/sFO2w9mvlSm9I7Ysvhg1fTObtd2bRr88gXv/suf2WX7rU+7E6YgS8+nKQkvQRVGwtZ9TJY3ny1eYdhtuKkLwxyWfPhiVLvCw+b96uRNGvn/dFdu8OPXp4t26dea18GX97aT4L529ge8V2vqlbQiXekO6FFFLOalJNJom+HJKTMykozKLngHaMmTCa48eciM/XvHvkYDDEP596jmf/OoMlC9awefNa6sN1rAvvGtPbh58EckkPZBOfkEJyRioZ+QV06TGSkkHj6d49QJcukJsLzhE5qL51EG0zKcS6iQqF68mhE7GxcSyt/jTaIR3Qb34Dd98Nb7+1hTMGHsfWYAWvzv07/UtL9yhXXQ1jxkBcHDz0EJwz9nvMXPgiJWnD+Xzz+1GK/ii2YQPMn+9NlPD55/Dll95t3TrviOKrr7xyOTnQqRN06cyXGQEeWbGDT5bUsGbtFrZu38i24Ea2sol8OrIa7z1+/CSRQZavC8F4kZ6SQEZ2Gp16ZFN6bAknnjKWDoWFzfIxPvloFk88+ByfzlrB+tXr2bp9B1uDX7ONiobTTwDxJBBLMvFuGnGxKSQnZZCYHk9adibti4rpO+gUuhV3oqAA8vK8v1PriBP9pGCMGQvcBbjAdEk37/V6DPAYUApsAiZJWnGgdcY48UpTJg4uw0YN5bm3n2yZ4JvJ+vUwaZL3H6lL+mU89OfXSUnKZ1HlOxjjfUfhMFxyCXzyCVx3HTz1p0n88+3n6eTvx+yNr5OSnBLlT2E1qKz0jiiWLvUSw/Ll3v2OHd4kQsHgnuWPHcqmLeU8ld2eDyuT+XpzHRs317KjuhJ/yKFcy6hjxx5viSUeEHEkE+skk+DPwInzkZwYICE5icysJPIKM+hUVECvAT0ZOGQIGZmZh/Qx1q5exbOPPs2H7yxk5bJv2LJxCzuqKqkKbmIbFeSQxSpWNZTPNZ2o1PqGmAIx6cQFHGLikohLiCMpLZmMzFSy2xfQuVsxJf2G065DGunpkJYGrvttK9xqRtFNCsYYF1gMnAiUA3OAMyUt3K3MpUAfSRcbYyYDEyRNOtB6/SZW8SQScBJYsOoDcvILWiT+5vTcc/DHP8LJJ4sZj4xl5dcL6NipHx9+9Qr19XDFFfDEE3DTTWLG4xOZP2cuVY6fmXP/l779+0Y7fKupQiHvCKO8HFat8u4rK70Esm6dd/vmG69MKOS9x4EFXfJ4Ky6D+eFUVm7zsXkHVNdUU1VbTW1wG365rGcV9dQ2bCqDTDaxsWE5QIAMiqilAr+Jxe/G4QTiSPGlEnZDxMQGiEn0kxAfQ2pKArFJAVIy4sjITCYrJ43s3BzyCnJp37ET+e0L+fzTObz9r7dZMPcrvl5ewY5tNVRs3EJN7XZqQ1sJy88WVhKkviGGQgpZycqG5Rx6UM16/MQTcOLwOXEkxmQRMnUEAn58/gDx8fH4EkR8bAJxibEkpSSSkpZCemYa2XnZ5Ba0p7BzEQXtcklINMTFgc/X8l9lGxX1pDAU+LWkkyLL1wJI+v1uZf4VKfOhMcYHrAOydICgfCagRFLo03Uo7y1+sUVibwm/+x3MnAm9e37Da49OoHLrWpKS8+h+zNksWjKVYX1+xQdv/Js1VQvJie3KM+/cw6AhQ6MdttUSQiGoqICNG70ksWmT97iiAjZv9u7j4+GLL7ykUlkJW7ew3NQwp7iERRuqWBmM55saP1tqHKqCdVRXhQmH/VTVbSQYrqE+XE01tWSSyiqWEybUsPm9d94AGWSwiU0Ny6mkUUMNDn58+HDxk0IWVWYbuC4++XHwYTAETDw12kbYCBMOE1YIgyEsUW+qCCtImCAhgsSSQCUbCUZac6WRRgUVDdtNJJHtbG9Y3vm6weBEInHx4cOPiTw2+EgwydSZGgw+XOPD5yYj1eC4BoMPx7jIdfAZB9dxMI6D47g4rsFx/Ti+MK7x4boOxjW4PodAwIcAn+vgui6u38H4DQHXxfX5cAM+fK7B53Nx/S4+vx+f6+CL8eFzXHx+F78/gN/vw+fzEYiJxe93cF0Hf8CH4/rw+1wcv4vf7/O24Tj4AwEcx8H1e+txXe+xcRz8Ph+uz8UxDoGAH8fn4EY+h9/14/hcAgGf937Hxef3Mqjf7ychKT7qSeEMYKykCyLLZwFDJP1otzILImXKI8vLImU27m+dAI5xlUsP5qx4iYLCzi0Se0sIh+G+++Cll0B15axdeD7rNywnGK7BJUCQGgIE6NihJ6988ijpGRnRDtk6HNXXQ1WV1+Z52zbvvqrKe1xV5Z3GqqralXhqaqB6B2t3bGJR5Q5WhR3WbtnGxmrYUisqQ36qq2qprfWxvT5EMCjq60OEg1AXriMYCqFwkFA4SEBx7AhXEHTqIRQmFNnZJ5FKBesJEkIECRMikyzWsAbYc//i4hLaLUHtlE42m9mwz/NJJLONrfs8H0cc1VTv87zB7HGtpC1zcAgTbnJ5SU1KCi15ILa/APb+tppSBmPMhcCFAD7HR3LnOr438fvfPcIoqKvz/h+HAuBm1VC1dRvhcBifzyU5P5765HWMOemkJq3rm2++ISsrq4UjPjLYutjlkOrCARIjt4idO4VAwzMG8IPqSVbCzgFFvJcij7PUbp/n8pREOBwiFAoRCocJh8OEwiHCYREOhwlLhMORTlPhMLHKRIhdnWq9+xjSYOc4Jjt3DzLEEsPOH7WK/KOGhZ2Pw+zczexTxoDCu6WQPdbv/bPHzijyHrRv2jENm93rlYbVaa/yB0te+25BaLftEDl62rtc4+s0xiyQVHKAjQItmxTKgfa7LbcD1jRSpjxy+igFIu36diPpAeABgIEDB2ru3LktEvCRZuDAgdi68Ni62MXWxS62LnYxxtQ0pVxLtkaeA3Q1xnQyxgSAycDeFwFeBM6OPD4DmHmg6wmWZVlWy2qxIwVJQWPMj4B/4TVJfVjSF8aYG4G5kl4EHgIeN8YsxTtCmNxS8ViWZVkH16KNuyS9Cry613PX7/a4Bvi/h7LOCy+8sHmCawNsXexi62IXWxe72LrYwwNNKXTE9WjmQFdSLMuyrMY0qfWRHeHEsizLanBEJQVjzNju3btTVFTEzTfffPA3tFHnnXce2dnZlJQctHVZm7dq1SpGjx5NcXExvXr14q677op2SFFTU1PD4MGD6du3L7169eKGG26IdkhRFQqF6N+/P6eeemq0Q4m6jh07Yoz53BjzmTHmgM2xjpikEBk2497XXnuNhQsX8tRTT7Fw4cKDvq8tOuecc5gxY0a0wzgs+Hw+brvtNhYtWsSsWbO49957j9q/i5iYGGbOnMm8efP47LPPmDFjBrNmzYp2WFFz1113UVxcHO0wDiejJfWTNPBAhY6YpAAMBpZ27tyZQCDA5MmTeeGFF6IdU1SUlZWRnp4e7TAOC3l5eQwYMACApKQkiouLWb16dZSjig5jDImJXi+0+vp66uvrGwZdPNqUl5fzyiuvcMEFF0Q7lCPOEXOhuSnDZhxNjDEdgZeb0kPxaBGpk/eAEkn7jo1wFIgcUX8MFAH3Svp5lEOKCmPM34HfA0nANZKO6nNIxpjlQAVeQ537Ix2C9+tIOlJo0pAY1tHJGJMI/AO48mhNCACSQpL64Y0gMNgYc9T9aDDGnApskPRxtGM5jAyTNAA4GbjMGFPWWMEjKSk0ZdgM6yhkjPHjJYQnJB14EuyjhKQtwDvA2CiHEg3DgNOMMSuAp4HjjDF/i25I0SVpTeR+A/BPvNPx+3UkJYWmDJthHWWMd9L8IWCRpNujHU80GWOyjDGpkcdxwAnAl9GNqvVJulZSO0kd8fYTMyVNjXJYUWOMSTDGJO18DIwBFjRW/ohJCpKCwM5hMxYBz0r6IrpRRYcx5ingQ6C7MabcGHN+tGOKomHAWXi/Bj+L3MZFO6goyQPeNsbMx/sR9Yakl6MckxV9OcC/jTHzgNnAK5Iabb54xFxotizLslreEXOkYFmWZbU8mxQsy7KsBjYpWJZlWQ1sUrAsy7Ia2KRgWZZlNbBJwbIsy2pgk4JlWZbVwCYFy7KsNsoYM8gYM98YExvp2fzFwcbDsp3XLMuy2jBjzE1ALBAHlEv6/QHL26RgWZbVdkXGipsD1ADHSgodqLw9fWRZltW2pQOJeHNLxB6ssD1SsCzLasOMMS/iDSHeCcg72MRkvlaJyrIsy2p1xphpQFDSk5FZ+T4wxhwnaWaj77FHCpZlWdZO9pqCZVmW1cAmBcuyLKuBTQqWZVlWA5sULMuyrAY2KViWZVkNbFKwLMuyGtikYFmWZTWwScGyLMtq8P8B/Owjm6JaXrAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -0.918 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = 2.810 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -2.86167 \\ hartree = -77.86889 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 0.6 s\n",
      "------------------------------ Iteration 7 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 1.450 \\quad \\zeta_2 = 2.910$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = c_{11} \\chi_1 + c_{21} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2 = c_{12} \\chi_1 + c_{22} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = -0.842 \\quad c21 = -0.183 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = -1.620 \\quad c22 = 1.816 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -0.918 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = 2.810 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -2.86167 \\ hartree = -77.86889 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 0.6 s\n",
      "------------------------------ Iteration 8 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 1.450 \\quad \\zeta_2 = 2.910$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = c_{11} \\chi_1 + c_{21} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2 = c_{12} \\chi_1 + c_{22} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = -0.842 \\quad c21 = -0.183 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = -1.620 \\quad c22 = 1.816 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -0.918 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = 2.810 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -2.86167 \\ hartree = -77.86889 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 0.6 s\n",
      "------------------------------ Iteration 9 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 1.450 \\quad \\zeta_2 = 2.910$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = c_{11} \\chi_1 + c_{21} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2 = c_{12} \\chi_1 + c_{22} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = -0.842 \\quad c21 = -0.183 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = -1.620 \\quad c22 = 1.816 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -0.918 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = 2.810 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -2.86167 \\ hartree = -77.86889 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 0.7 s\n",
      "------------------------------ Iteration 10 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 1.450 \\quad \\zeta_2 = 2.910$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = c_{11} \\chi_1 + c_{21} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2 = c_{12} \\chi_1 + c_{22} \\chi_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = -0.842 \\quad c21 = -0.183 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = -1.620 \\quad c22 = 1.816 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -0.918 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = 2.810 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -2.86167 \\ hartree = -77.86889 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 0.7 s\n"
     ]
    }
   ],
   "source": [
    "# input for zeta\n",
    "zetas = [[1.45, 1], [2.91, 1]]\n",
    "# input nuclear charge (element number)\n",
    "Z = 2\n",
    "\n",
    "# build basis function\n",
    "f1=STO(zetas[0][0], zetas[0][1])\n",
    "f2=STO(zetas[1][0], zetas[1][1])\n",
    "fs = [f1, f2]\n",
    "\n",
    "# initialization\n",
    "R = np.zeros((len(zetas), len(zetas), len(zetas), len(zetas)))\n",
    "H = H_matrix(fs, Z)\n",
    "S = S_matrix(fs)\n",
    "e, Co = secular_eqn(H, S)\n",
    "P = P_matrix(Co)\n",
    "scf_H = get_E0(e, P, H)\n",
    "\n",
    "##############################################print information below#################################################\n",
    "print('-'*30, \"Initialization\", '-'*30)\n",
    "print('-'*25, \"Ignore repulsion integral\", '-'*24)\n",
    "display(Math('Basis \\ Function:'))\n",
    "display(Math('\\chi = N r^{n - 1}e^{-r \\zeta} ')) \n",
    "display(Math('\\zeta_1 = {0} \\quad \\zeta_2 = {1}'.format(format(zetas[0][0], '0.3f'), format(zetas[1][0], '0.3f'), ))) \n",
    "display(Math('Orbitals:'))\n",
    "display(Math(' \\phi_1 = c_{11} \\chi_1 + c_{21} \\chi_2 '))\n",
    "display(Math(' \\phi_2 = c_{12} \\chi_1 + c_{22} \\chi_2 '))    \n",
    "display(Math('c11 = {0} \\quad c21 = {1} '.format(format(Co[0][0], '0.3f'), format(Co[1][0], '0.3f')))) \n",
    "display(Math('c12 = {0} \\quad c22 = {1} '.format(format(Co[0][1], '0.3f'), format(Co[1][1], '0.3f'))))  \n",
    "\n",
    "# plot density graph\n",
    "colorlist = ['red', 'orange', 'yellow', 'green', 'blue', 'purple', 'black', 'red', 'orange', 'yellow', 'green', 'blue', 'purple', 'black']\n",
    "phi1 = Co[0,0]*f1+Co[1,0]*f2\n",
    "phi2 = Co[0,1]*f1+Co[1,1]*f2\n",
    "density_1 = phi1*phi1*r*r\n",
    "density_2 = phi2*phi2*r*r    \n",
    "p = plot((density_1, (r, 0, 5)), (density_2, (r, 0, 5)), show = False, legend = True)\n",
    "p[0].label = 'electron density $r^2 \\phi_1^2$ '\n",
    "p[1].label = 'electron density $r^2 \\phi_2^2$ '    \n",
    "p[0].line_color = colorlist[0]\n",
    "p[1].line_color = 'blue'\n",
    "p.show()\n",
    "# print energy result\n",
    "display(Math(' \\epsilon_1 \\; for \\; \\phi_1  = {0} '.format(format(e[0].real, '0.3f'))))    \n",
    "display(Math(' \\epsilon_2 \\; for \\; \\phi_1 = {0} '.format(format(e[1].real, '0.3f'))))        \n",
    "display(Math(' Hartree \\ Fork \\; atom \\; energy = {0} \\ hartree = {1} \\ eV'.format(format(scf_H, '0.5f'), format(scf_H*27.211, '0.5f'))))  \n",
    "##############################################print information above#################################################\n",
    "\n",
    "for i in range(10):\n",
    "    print('-'*30, \"Iteration\", i + 1, '-'*30)\n",
    "    if(i==0):\n",
    "        print('-'*7, \"Iteration 1 needs more time to caculate Repulsion Integral\", '-'*6)\n",
    "        start = time.time()\n",
    "        R = R_matrix(zetas)\n",
    "    else:\n",
    "        start = time.time()\n",
    "    F = F_matrix(fs, Z, zetas, Co, R)\n",
    "    S = S_matrix(fs)\n",
    "    e, Co = secular_eqn(F, S)\n",
    "    P = P_matrix(Co)\n",
    "    scf_H = get_E0(e, P, H)\n",
    "    ##########################################print information below#################################################\n",
    "    # print information\n",
    "    display(Math('\\zeta_1 = {0} \\quad \\zeta_2 = {1}'.format(format(zetas[0][0], '0.3f'), format(zetas[1][0], '0.3f'), ))) \n",
    "    display(Math('Orbitals:'))    \n",
    "    display(Math(' \\phi_1 = c_{11} \\chi_1 + c_{21} \\chi_2 '))\n",
    "    display(Math(' \\phi_2 = c_{12} \\chi_1 + c_{22} \\chi_2 '))    \n",
    "    display(Math('c11 = {0} \\quad c21 = {1} '.format(format(Co[0][0], '0.3f'), format(Co[1][0], '0.3f')))) \n",
    "    display(Math('c12 = {0} \\quad c22 = {1} '.format(format(Co[0][1], '0.3f'), format(Co[1][1], '0.3f'))))      \n",
    "    # plot density graph\n",
    "    phi1 = Co[0,0]*f1+Co[1,0]*f2\n",
    "    phi2 = Co[0,1]*f1+Co[1,1]*f2\n",
    "    density_1 = phi1*phi1*r*r\n",
    "    density_2 = phi2*phi2*r*r    \n",
    "    p1 = plot((density_1, (r, 0, 5)), (density_2, (r, 0, 5)), show = False, legend = True)\n",
    "    p1[0].label = None \n",
    "    p1[1].label = None     \n",
    "    p1[0].line_color = colorlist[i+1]\n",
    "    p1[1].line_color = colorlist[i+1]\n",
    "    p.extend(p1)\n",
    "    p.show() \n",
    "    # print energy result\n",
    "    display(Math(' \\epsilon_1 \\; for \\; \\phi_1  = {0} '.format(format(e[0].real, '0.3f'))))    \n",
    "    display(Math(' \\epsilon_2 \\; for \\; \\phi_1 = {0} '.format(format(e[1].real, '0.3f'))))        \n",
    "    display(Math(' Hartree \\ Fork \\; atom \\; energy = {0} \\ hartree = {1} \\ eV'.format(format(scf_H, '0.5f'), format(scf_H*27.211, '0.5f'))))    \n",
    "    stop = time.time()\n",
    "    print('Time used:',format(stop-start, '0.1f'),'s')\n",
    "    ##########################################print information above#################################################    "
   ]
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    "Reference\n",
    "\n",
    "[1] Levine, Quantum Chemistry, 7th Edition, chapter 14  \n",
    "[2] C. Roetti and E. Clementi, J. Chem. Phys., 60, 4725 (1974)  \n",
    "[3] Acosta C R. Restricted closed shell Hartree Fock Roothaan matrix method applied to Helium atom using   Mathematica[J]. European Journal of Physics Education, 2017, 5(1): 1-14.  \n",
    "[4] [Simple Quantum Chemistry: Hartree-Fock in Python, 2018](http://nznano.blogspot.com/2018/03/simple-quantum-chemistry-hartree-fock.html)  \n",
    "[5] [Helium hartree fork, prtkm, 2015](https://github.com/prtkm/helium-hartree-fock/)"
   ]
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