examples/ising-1d.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# COLDER example: the 1D Ising chain\n",
    "\n",
    "In this notebook we will review the simulation of the 1D Ising chain annealing using COLD optimization.\n",
    "\n",
    "First, let us import the essential components that we will need to perform the simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import colder.core.physics as cphys\n",
    "import colder.models.lattice as cll\n",
    "import colder.simulation.cold as ccold\n",
    "\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Build the system hamiltonian and the AGP ansatz\n",
    "\n",
    "Let us focus on the Hamiltonian of the reference paper ([Counterdiabatic Optimized Local Driving](https://link.aps.org/doi/10.1103/PRXQuantum.4.010312)).\n",
    "\n",
    "$$\\mathcal{H} = -J \\sum_j^{N-1} \\sigma_j^z \\sigma_{j+1}^z + Z_0 \\sum_j^N \\sigma_j^z + \\lambda(t)X_f \\sum_j^N \\sigma_j^x$$\n",
    "\n",
    "Looking at the papers, we first have to define some functions and constants that regulate the annealing schedule. In the following, `scale_f` represents $\\lambda(t)$, `f_qoc` the control function $f(t, \\beta)$ (as of Eq. 17). $\\tau$ represents the total annealing time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scale_f(t, tau):\n",
    "    \"\"\"Define the scaling function [0,tau] -> [0,1].\"\"\"\n",
    "    return np.sin( (np.pi/2)*(np.sin(np.pi*t/(2*tau))**2)  )**2\n",
    "\n",
    "def f_qoc(t : float, tau : float, beta : np.ndarray):\n",
    "    \"\"\"control function f(t, beta) to use for qoc\"\"\"\n",
    "    #beta = np.array([beta])\n",
    "    k = np.arange(len(beta)) + 1\n",
    "    \n",
    "    if isinstance(t, np.ndarray):\n",
    "        # fix the sum broadcast when time is an array\n",
    "        t = t.reshape(-1, 1)\n",
    "        return np.sum( beta*np.sin( np.pi*k*t/tau ), axis=1 )\n",
    "    else:\n",
    "        return np.sum( beta*np.sin( np.pi*k*t/tau ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the next step, we define the functions that *drive* our system, namely $J(t)$, $Z(t)$ and $X(t)$, one for each term that composes the hamiltonian $\\mathcal{H}$.\n",
    "This is done using python functions that take some inputs, the first of which *must be* the time value $t$, and that returns the desired coefficient.\n",
    "\n",
    "We will use 5 spins, for simplicity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# parameters of the system\n",
    "Jsys = 1.0\n",
    "Z0sys = 0.02*Jsys\n",
    "Xfsys = 10*Jsys\n",
    "\n",
    "# we use the lattice module to prompt easily the spin indices\n",
    "lattice = cll.chain(nspin = 5)\n",
    "nspin = lattice.nspin\n",
    "\n",
    "# number of frequencies of the control function (will be used later)\n",
    "Nk = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle J \\sum_{i=1}^{4} \\sigma_{ZZ}^{i} + X \\sum_{i=1}^{5} \\sigma_{X}^{i} + Z \\sum_{i=1}^{5} \\sigma_{Z}^{i}$"
      ],
      "text/plain": [
       "J*Sum(sigma_ZZ**i, (i, 1, 4)) + X*Sum(sigma_X**i, (i, 1, 5)) + Z*Sum(sigma_Z**i, (i, 1, 5))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# note: these functions should have same I/O\n",
    "def Jf(t, tau, beta):\n",
    "    return -Jsys*np.ones_like(t)\n",
    "    #            ^^^ trick to avoid issues in vectorialization\n",
    "\n",
    "def xf(t, tau, beta):\n",
    "    return Xfsys*scale_f(t, tau)\n",
    "def zf(t, tau, beta):\n",
    "    return Z0sys*np.ones_like(t) + f_qoc(t, tau, beta)\n",
    "\n",
    "H_J = cphys.hamiltonian('ZZ', lattice.nearest_neighbor, coeff = 'J', coeff_function=Jf)\n",
    "H_Z = cphys.hamiltonian('Z', lattice.single_site, coeff = 'Z', coeff_function=zf)\n",
    "H_X = cphys.hamiltonian('X', lattice.single_site, coeff = 'X', coeff_function=xf)\n",
    "\n",
    "H = H_J + H_Z + H_X\n",
    "H.expression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: In this case $J(t)$ is just a constant. To avoid errors in the vectorialization, I suggest to use `np.ones_like(t)` to be vector-safe.\n",
    "\n",
    "**Important**: All the functions must have the same I/O, i.e. the same input parameters. In this specific case, all the coefficient functions `Jf`, `xf` and `zf` receive the inputs `(t, tau, beta)`, even though not all of them use all the input parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### AGP ansatz\n",
    "\n",
    "It is time to prompt the APG ansatz. We will use the second order LCD potential, as of Eq. 26:\n",
    "$$\\mathcal{A}^{(2)} = \\alpha \\sum_i^N \\sigma_i^y + \\gamma\\sum_i^{N-1} ( \\sigma_i^x\\sigma_{i+1}^y + \\sigma_i^y\\sigma_{i+1}^x ) + \\zeta\\sum_i^{N-1} ( \\sigma_i^z\\sigma_{i+1}^y + \\sigma_i^y\\sigma_{i+1}^z )$$\n",
    "\n",
    "Again, the interface for this is the `physics.hamiltonian` module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\alpha \\sum_{i=1}^{5} \\sigma_{Y}^{i} + \\gamma \\sum_{i=1}^{8} \\sigma_{XY}^{i} + \\zeta \\sum_{i=1}^{8} \\sigma_{ZY}^{i}$"
      ],
      "text/plain": [
       "alpha*Sum(sigma_Y**i, (i, 1, 5)) + gamma*Sum(sigma_XY**i, (i, 1, 8)) + zeta*Sum(sigma_ZY**i, (i, 1, 8))"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ansatz_alpha = cphys.hamiltonian('Y', lattice.single_site, 'alpha')\n",
    "ansatz_gamma = cphys.hamiltonian('XY', lattice.add_invert(lattice.nearest_neighbor), 'gamma')\n",
    "ansatz_zeta = cphys.hamiltonian('ZY', lattice.add_invert(lattice.nearest_neighbor), 'zeta')\n",
    "\n",
    "ansatz = cphys.hamiltonian_collection(ansatz_alpha, ansatz_gamma, ansatz_zeta)\n",
    "ansatz.expression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Explaination of `add_invert` shortcut\n",
    "\n",
    "Let us break down the usage of `lattice.add_invert()`. The `nearest_neighbor` item will return the nearest neighbor interactions\n",
    "```python\n",
    "    >>> lattice.nearest_neighbor\n",
    "    [(0, 1), (1, 2), (2, 3), (3, 4)]\n",
    "```\n",
    "\n",
    "thus, the code\n",
    "```python\n",
    "    cphys.hamiltonian('XY', lattice.nearest_neighbor, 'gamma')\n",
    "```\n",
    "\n",
    "would build the term $\\sum_i^{N-1} \\sigma_i^x\\sigma_{i+1}^y$ of $\\mathcal{A}$.\n",
    "Now one can notice that the following term features interactions in which Y and X are inverted ($\\sigma_i^y\\sigma_{i+1}^x$), therefore we can as well invert each tuple of the spin targets to achieve the same result. Indeed, the method `lattice.add_invert(tl)` inverts the input tuple list `tl` and returns both the original list and the list of inverted tuples.\n",
    "```python\n",
    "    >>> lattice.add_invert(lattice.nearest_neighbor)\n",
    "    [(0, 1), (1, 2), (2, 3), (3, 4), (1, 0), (2, 1), (3, 2), (4, 3)]\n",
    "```\n",
    "\n",
    "<br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## create the COLDER simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[info] caching agp\n"
     ]
    }
   ],
   "source": [
    "tau : float = 0.01   # total annealing time\n",
    "nsteps : int = 200   # number of discrete steps to perform in the annealing simulation\n",
    "backend = 'scipy'\n",
    "\n",
    "csym = ccold.cold(\n",
    "    system = H, ansatz = ansatz, annealing_time = tau, nspin = nspin,\n",
    "    # parameters to be passed at the system coefficient functions\n",
    "    system_fargs = {'tau' : tau, 'beta' : np.zeros(Nk)}, \n",
    "    # name of the parameter to treat as QOC parameter (which will be tweaked during the optimization)\n",
    "    qoc_parameters=['beta'],\n",
    "    # backend\n",
    "    backend = backend\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "### let us take a look at the gauge potential!\n",
    "\n",
    "The `agp` attribute of the colder simulation contains the object that computes and solves the Adiabatic Gauge Potential symbolically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 48.0 J^{2} \\gamma^{2} + 48.0 J^{2} \\zeta^{2} + 64.0 Z^{2} \\gamma^{2} + 20.0 \\left(- X \\alpha - 0.5 dZ\\right)^{2} + 64.0 \\left(- X \\zeta - 0.25 dJ\\right)^{2} + 64.0 \\left(X \\zeta - Z \\gamma\\right)^{2} + 32.0 \\left(J \\alpha - X \\gamma + Z \\zeta\\right)^{2} + 48.0 \\left(J \\zeta + 0.5 Z \\alpha - 0.25 dX\\right)^{2} + 8.0 \\left(J \\zeta + Z \\alpha - 0.5 dX\\right)^{2}$"
      ],
      "text/plain": [
       "48.0*J**2*gamma**2 + 48.0*J**2*zeta**2 + 64.0*Z**2*gamma**2 + 20.0*(-X*alpha - 0.5*dZ)**2 + 64.0*(-X*zeta - 0.25*dJ)**2 + 64.0*(X*zeta - Z*gamma)**2 + 32.0*(J*alpha - X*gamma + Z*zeta)**2 + 48.0*(J*zeta + 0.5*Z*alpha - 0.25*dX)**2 + 8.0*(J*zeta + Z*alpha - 0.5*dX)**2"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csym.agp.compute_square_trace()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here you are! Now you have the AGP without making the math yourself. The computation is instantaneous for small systems, but scales polynomially for bigger systems. However, this is all you need to test an arbitrary AGP on the flight, as the AGP working on smaller systems will work also on bigger ones."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## initialize the simulation\n",
    "\n",
    "The following command is crucial to initialize all the requirements before using the COLD object for simulations.\n",
    "This method computes the AGP and optimizes numerically the interpolation of the schedule functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "csym.be_ready()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you like, you can plot the schedule functions..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAioAAAGdCAYAAAA8F1jjAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAABvGUlEQVR4nO3dd3xUVf7/8dedPpPee0gh9F6kWABFsK6urrpW3OWrWHdd3WJbdS0rP3V3dV13Lfu1fnWtq+6KioiCCEjvJRBISCO9TNrUe39/DAxECBJIcifJ58njPiYzc+bO+96QySfnnnuuommahhBCCCFECDLoHUAIIYQQoiNSqAghhBAiZEmhIoQQQoiQJYWKEEIIIUKWFCpCCCGECFlSqAghhBAiZEmhIoQQQoiQJYWKEEIIIUKWSe8AJ0tVVcrLy4mIiEBRFL3jCCGEEOI4aJpGU1MTqampGAwd95v0+kKlvLycjIwMvWMIIYQQ4gSUlJSQnp7e4fO9vlCJiIgAAhsaGRmpcxohhBBCHA+n00lGRkbw93hHen2hcvBwT2RkpBQqQgghRC/zQ8M2ZDCtEEIIIUKWFCpCCCGECFlSqAghhBAiZEmhIoQQQoiQJYWKEEIIIUKWFCpCCCGECFlSqAghhBAiZEmhIoQQQoiQJYWKEEIIIUKWFCpCCCGECFlSqAghhBAiZEmhIoQQQoiQ1esvSiiEEEIcTtM0vKoXj9+DV/XiVb34VF/w9uDiVb34NT9+1Y9P8+FX/Ue9r2oqqqYe8bWmaaiaioYWfFxDCz6uoqJpWrvHgOD9g/8OPBj8WtO0YLvDbw9/rqedkX4GU1Kn6PLeUqgIIYToEZqm0eZro8XbQquvNXDrbaXVF1javG2BW18bbb423D43Lr+LNl8bLp8Lt98dXFw+Fx6/B4/qwe134/V7cfvdeFQPPtWn96b2OXH2OClUhBBChLaDhYbT46TR3UiDuwGnx4nT7Qzcepw0eZpwepw0e5pp9jbT5Gmi2dtMi7eFFm9LsFehJxkUA2aDGbPBjMlgOrQogVujYgzcGoyYFBMGxdDua4PBgFExBh4/cNtuwYCiKCgowccOvw+goAQfO+IWJdBGOfT1oRul3e3hFKX9Y0dr01VGJ4zutnX/EClUhBCin9I0jRZvC7WuWmrbaqlz1bVbGlwN1LkDt/WuehrcDXhUz0m/r4JCmDkMh9mBw+QI3tpNduwmOw6zA5vRht1kx2ayYTPZsBqt2Iw2rKbArcVowWq0YjVag19bDBbMxkBBYjFagsWJ0WDsgr0l9CKFihBC9DGapuH0OKlqrQou1W3VVLdWU9NWQ3Vb4La2rRaX39Xp9ZsUE1HWqOASaYkMLNZIIiwRRJgjAreWCMIt4USYI3CYHYSbwwkzh2E32Y/oDRCiI1KoCCFEL9PibWF/837KW8qpaKmgoqWCytbK4G1lS2WnChCHyUGsLZY4exyxtth2S7QtmhhrDNG2aKKtgcVhckihIXqMFCpCCBFiWrwtlDaVUtZcRnlzefC2vKWc8uZynB7nca0nyhpFoiORRHsiCY4EEuwJwdt4ezxx9jjibHE4zI5u3iIhTpwUKkII0cM0TaPWVUuxs5iSphKKmwK3ZU1llDaXUueq+8F1RFoiSQlLITksObgkOZICXzuSSXAkYDPZemBrhOheUqgIIUQ3aXA1UOQsYp9zX3Apbiqm2FlMq6/1mK+NtkaTGp5KWnhacEkNTyU1LJXksGTCLeE9tBVC6EsKFSGEOAle1UtJUwmFjYUUNhZS1FhEkTOwNLobO3ydQTGQEpZCekQ6mRGZZERkkBGRQXpEOmnhaURYInpwK4QIXVKoCCHEcWjztVHYWMjexr3sbdgbuG3cS4mzBJ/W8QRjyWHJDIgcQFZkFpkRmWRGBpb08HQsRksPboEQvZMUKkIIcZiDBUlBQwF7GvYEl7LmsnZTmR/ObrKTFZlFdlQ22VHZZEVlkR2ZTUZEhgxUFeIkSaEihOiXvKqXfY37KGgoYFf9LgoaCihoKKC0qbTDgiTGGkNOdA45UYct0TkkOZLkdF0huokUKkKIPk3TNCpaKtjdsJtd9bvYXb+b3Q27KWws7PCaMNHWaAZGDyQ3Ojd4mxudS6wttofTCyGkUBFC9Bkt3hZ21wcKkmBRUr+bJm/TUduHmcMYGD2QgdEDyYvJCxYlcbY46SERIkRIoSJEF9E0DbW5GbWlJbC0tqJYrBijozHGRGOwyMDJrqJqKqVNpeyq30V+fT676gKFSWlz6VHbmxQTWVFZ5MXkMShmEHnReeTF5JESliIFiRAhTgoVIU6Av6GBtq3bMDjsOMaNA0BtaWHXxFM6fE34zLPI+Nvfgvebvv4aS2YmlqwsFKNcNK0jTZ6mYC9Jfn1+sKekzdd21PaJ9sRAQRIbKEgGxQwiJyoHs9Hcw8mFEF1BChUhjpOvuhrnokU0LfyC1jVrQFWJOHtmsFAxOA6c3WEyYQgLw+BwoLnd+BsaQFUPPQ+oLhelt94WeDw8HPu4sTgmTMQxcQL24cNR+mHvy8Fekvz6fPLr8oOHb8qay47a3mKwMDBmIINjBpMXkxe8jbHF9HByIUR3kkJFiGPQVJXGDz+k8cOPaF23DrRDZ4OYB2RiSkkJ3lcMBgZv2ohisbQ7nKCpKmpTE5qqBh/z19djGzkC9+4C1OZmWr5ZRss3ywLrsduJmzuXhNtu7YEt1MfBXpKDPSQ/1EuS5EhiUMwgBscODtzGDCYzMhOTQT7ChOjr5KdciGNRFOrffAvX9u0A2EaPInL2OUTMmoUlPe2I5gar9chVGAwYo6LaPWZOSSH7nXfQ/H7c+fm0rl1L65q1tK5di7++vl17b3k5Nc+/QPi0MwibPBlDWFgXb2T38ak+ip3F7GrYxa66XcFDOOUt5UdtbzVaGRg9kEExg4KFSV50HtG26J4NLoQIGYqmaUefMKCXcDqdREVF0djYSGRkpN5xRC/nys+n7uVXSPr9/RjDA9dSaVq8GE9hIZHnnYc5NbVb31/TNNy7dmNKiMcUGzgVtv7dd6l44MFAA7MZx4TxhJ8xjfDTT8OSmxsSg0E1TaO6rTp4ls3uhsDtnoY9eFTPUV+THJYc7B0ZFDOIQbGDyIyQXhIh+ovj/f0thYoQQNu2bdT84x80f7kYgKR77yH2uut0ThXQtnUbjR99RPPSpXhLSto9Z0pNIf2vz2IfMbzH8jg9TvY07GF3/W4KGgqCtw3uhqO2t5vswbNsDvaU5MXkEWWNOmp7IUT/cLy/v+VPF9GvtW3ZQs1zf6d5yZLAA4pC5Lnn4Jg0Wddch7OPGI59xHC0++7FU1REy7JlNC/9htY1a/BVVGLJSA+2bfjg33jLSgmbMgX76NEnNSi32dPM3sa97GnYE5y1taChgKrWqqO2NygGMiMyyYs5UJREB4qStIg0DIrhhHMIIfo36VER/ZLm81F62+2HChSDgcgLzid+3jysubm6Zjtealsbrh07gmcdARRddTVt69cDoDgcOMaMwTFxAo4JE7CNGnXUMTQNrobgBfb2NOwJXuemsrWyw/dOciQFCpLoPAbGBCZMy4nKwWaydf2GCiH6JOlREeIYFJMJxW4Do5GoCy4g7qZ5WLOz9Y7VKQa7vV2RAhB9+WWYU1JoWbkSf10dLStW0LJiBQBKQhxVbz1GobOIwsZCyqsKyHeXUOeq6/A9Eu2JZEdnkxedF5xOPic6h0iL/FEghOgZ0qMi+jxN02j59ltq//dlkh98IFiQeEpLwe/HMmCAzgm7hqZp1LTVsM+5j+LGImp2bIQN24jaXsaAvU3sSlV48ieHJpb7x998+A2wN1mhJiMS76BMHCNGkJ4+jIHRA8mOypZxJEKIbiM9KqLf03w+nJ99Tu0//4k7Px+AuldeJeXhPwBgSU8/1stDkl/1U9laSWlTKSVNJRQ3FVPSVBL42llMq6+1/QtyDiyakSifhYHRA8iJymGwlkhs82somkZiowb5jfDlFmALpuRkon70I6LuHBNcjep2H/WwkRBCdDcpVESf4y0ro+GDD2h4/wN8VYGBnwaHg+jLLyd2TmicydMRTdOoddVS3lxOeXM5pc2llDeXU9ZcRmlTKeUt5R1e8RcCA1pTwlIYEDmAzIhMsqKyyIrMIisqi2RHMkbDoR4V/5pbcW3dimvbdlzbtuHatg3Pvn34KipQXYcmXvM7neyaNBlzWhqWnGysOblYsrKwDMjEkpmJKTlZLgEghOg2UqiIPkXz+yn66ZX4qqsBMMbFEXvtNcRceeURk67podXbSmVrJRUtFYGlNXBb3lxORUsF+1v24/a7j7kOk8FEWngaGREZZERkkBmRGfg6MoP08HQsxuM708cYHk7Y5MmETT50hpO/uRn3rl3t9pWnsBA0DW9pKd7S0uAMugfFXHMNyfffF3h9UxP1b76FOS0Nc2oKpqRkzIkJ/fKSAEKIriGFiui11NZWmr/5huZvlpHyh4dQzGYUo5Goiy+mbesWYq64gogzz+yRX5Iev4eathqq26qpaQ3cVrVWBW+rWquobK2kydP0g+tSUEh0JJIWnkZaeBop4Smkh6eTHpFORkQGCfaEdj0jXckYHn7EAF3bqFHkLf8W9549ePYW4t67B+++YjzFxXhLS9udHu0p2kf1008fud74eMxJScRcdSXRl14KgL+5hZaVKzDFxWGKjcUYF4chPDwkJrATQoQOKVREr6F5vbi2b6dl9Wpa16yhdfUaNJcLgKgLLyBsyhQAEn51B4rh5ObtUDUVp9tJvbueelc99e566lx11LXVUeeqo95VT42rhtq2WmraanB6nMe97jBzGMmOZJLDkkkKSyI5LJnUsFRSwlJICU8h2ZEcUlf6VRQlUEzExRF2SvurQ2t+P5rv0KEog8NO1MUX4y0rw1tRga+iAs3rxV9TE1gaD+0nT+Feym7/Rfv3MpsxxsRgjIkh5pqribnsMgB89fU0/vtDjNFRGCIjMUZEYoyMOPB1RKDAkcNPQvRJIVGoPPfcczz55JNUVFQwevRonn32WU753gei6F80rxfN78dgC8zL4Vz4BfvvuQe1tf1gUXNGBhGzzm43tf3BIkXVVFq8LTR7mmnyNtHkaaLZ04zT4zy0uAO3je5GGtwNNLobA4unEVVT6QyTwUSCPYEEewLx9ngSHAkkOhKDS5IjiURHIhGWiJPcO6FDMRrbFQjW3FxS5z8evK9pGv76enwVFXgrKrHm5nDYk9hHj8ZXV4e/tha1tRXN68VXVYWvqgq1uSXY1FtSQtWTT3aYI/6Wm0n4RaDo8ZSWUvarOwNXsD5wFWtDmAODI/C1Y+JEwiYFPl/UtjZa167DYLeh2OwY7DYMNhuKzYZitQUelwJICF3pXqi888473HnnnTz//PNMmjSJp59+mtmzZ5Ofn09iYqLe8UQ38jU10bJlE57qKlzlpXhKS/GVlaOWV6CVV+C6/Rqaz59Km68NTdvDgNZWvOE2GoamUj04kbJBMexPttDiK6E1/xFat7YGChNvMy3eFlq8LT8c4gdEmCOItkUTY40h1hZLrD2WWFssMdYY4u3xxNvjibPHEW+PJ9ISKYctvkdRFEyxsZhiY7ENG9buOfuoUWS983bwvtrWhq+2Dn9DA/6GBiwDMoPPGcLDifzRhfgbG1EbnfibmlCdgVvN5cIQFh5s66+vx7VlS4eZ4m6+KVioePdXUHLDDR22jZ1zHUn33BNoW1lF0U9/isFqDVwh22pFsVowWCwoZgvhM6YT89OfBraltZWqvzwdOBxpMQfam83BxZo7kLDJk4BAr1Tz11+DyYRiMgfm+DGbUEwmMJkwRUdjTjt0AUxvZWWgeDIaA22NxsBrjUYwGOT/oOhzdC9U/vznP3PDDTfws5/9DIDnn3+eBQsW8PLLL3P33XfrlmtPfQEFy1biKXCiaSqaqqJpKgSnnVFwnJaKKSVw7rdvVz2+Xc0drs8yIRZDcuCqt/49jXi3Nx61nYaGaUw0xvRwNDTUQiferc4j2hzMYRwZCZkH2pY2oW5sREE71O5AWw0V/+Bw/NlhgccrWjCvrwPUA8/7QfMDKqrmo2VgOM1ZEaiaH2NtM/FrS9A0H4oa6OnAr6KpfjSfn/JBMZTlRODTfNirmpn4+T4MXj9Gjw+j14/Z5cfi9mN1qSyeYmfhJAsev5v0Mjd/fOXoZ7AowNfLXudV25uB+6pG5s+NFCd60ZRioBjagMIf+k4GejoizRFEWMIJN4cTaYkgwhxBpOXQEm2NIsoSSdSB2xhrNNGWqM4dgvG2/nAb0SGDESyJ0ZAYfehBT6DYtKYnkfbog0d9nerxBH4eDrS1pMST/syfUFvbUFtbArctB27bWrEPGxxsi68N65DBaG1tqG0uVJcLze1GcwcGNCsmQ7Ct1lSHb//+DvObU5PQ3IHPALWhlvo33kBDQTWY0IKXEFDQFIXI887FOHgwRpMBo99N6W23oyoGvOYINEUJtEMBBcJOP43ku3+LxWbEFmakYNp0VMVAmz3h0DoPtHWMH0fyvb/DajcSHmNl1/RZaH6VprDUQBFjMKIZDChGI7ZBecTfMg+rw0R0go19c2/C39pKgzn5QDsFRTGAwYA5PZXYa67G6jASl+Kg/MFHUJ1OaokPbNuBdhwoTKMvuQir3URCRhjVz72Ar66OGl9MIKfBgIaCYlAwhEcQdd5sLDYjSQPCqfvXO/iqa6h2RaAe/PWkKGBQMFitRJw1A5PFSGpuBI0LPsdXWUlViwOfZgx8aKCgoIDJRPgZp2EyK6QPiqJpyTd4KyqpbrLi9QdyHtx3ikEhbOpkjEYDGUOiaFm1Bm9FBdWNZtxeQzDCgTfAMX4cislI1vBoWjdtxltWTk2DEZfHgAbtCkX7qJFgNDJgWCQt27bhKSmjpgFaXQR+pyhgMpoxW2zYhg5BUyAy1oW7eB/eigoanQfaHvgu22xh2O2RWAfl4VfAbKrCV1WBr7KKppZA2wANuz2S8PBYrAMHopkMqP5itNoavFWVtLQqtLkO5bTZIoiMjMeakw02Kz5XITTV492/n9Y2hcQRI8mecfph+61n6Trhm8fjweFw8P7773PxxRcHH58zZw4NDQ18/PHHR7zG7Xbjdh86K8LpdJKRkdHlE749s+Yp3M9uxujueNbOPZmwbMQ+AK78ZgK2NjOKMQqDMQ6DKRPFmBT8T7s15m98O2Q3AD9eM5kk35Udrrcg4kW+HLENgAs2jCPdNafDtsX2V/l0zAYAzt4ygtzmjv86rDT/iw8nfAfAGTsGMazh1g7b1hk+4N1J3wBwSkEW46p/BYCi+jCoXgyqF6Pqxeh3U+5Yyr+mBtY7uDSc61acicnXitnbisnXgsXbjMXjxOJpYsGEVv41PfDDH+vUuP9tP04H1EQq1EZBQyQ0Rmo4o8AVoWJFw6Zq2DQNu6ZhVzXsmopd03CoGmFq4OswVcWhaYSrKmGqSriq4VBVwjUNq6Yhf2OGNk0DP2Z8mvXAYjmwWIk27cdmCAxCdvoSKfMMx48Zv2bGjxlVM+HXzKiYyLUtJ9G8F4BqbzYbW36EihFVMx24NaJhRMXIKMcn5NhWA1DpyeNr5y2oGNA044FbAxqBZUL4ewyzLsTdaKbam8vn2u8Pe/5goRC4PzH8X4y3vEftznAaDOksiv9jh9s9NuxDJtneoGRJHC2meJYMfbzDtiMcn3FG2Ivs/CAFjzGCb0/9fx22HWL7irOin2XHOyn4FStLz/hLh21zbcs5J/op8j9Ixu818PX05zpsO8C6lgtiHmP3x0n42owsOf0vqB2cZZZq3sqP437PngWJeJpMLJs6H28Hhz0Tzbu5LO637P08AXeDmRWTH8Zliztq2xhTMVfF/5KiL+Noq7GyauL9tISlHLVthKGK6xLnse/rWBqr7awbfRvN4UmgeQEviiEGxeAAwKyWMME2n5q9YbQ1WdifPBGXNRI0Hxo+TJYRGMwZACi+QqJ9r+FqMuP1GnDZYvAZTQf+2PNjsp+OyToSAL+3BG/zex3uU5P9dEy2iQCovgo8TW912NZom4TZfmqgrb8Wj/O1jttax2N2TANAU524G//ZcVvLKMxhMw+0bcPd+I92z2ebHFzyyitgCetwHSeiV0z4VlNTg9/vJykpqd3jSUlJ7Ny586ivefzxx/nDH/7Q7dmSHYmUGl2HPaIABjjsV14MTYxyBYoms+ZE87vR/OWowVdYMBkSMBkSiItuZvSBtnZzA7amvR2+d1SUk7EHBomGmxqxtR1se+Sv2+jwRia1BdrGGZxYXUUH2h3W9sBfaNG2Bs5qaUUBkg2tmL1VcOCD9uCHLIoRDQOJ5hZ+6mzCqEGE3xNclWYw4TeY8GPHe+CxASYD99fUYdI0cEVTknFWh9s2yv4RPy19E6umofnCKJhyETmGKiYay4k1lRNmqA3EbTqwiJCnaeDRHJgUD0Yl0ENW50unzDMCj+rAo4XhVh14tMDiVe1MiXidZMsuAHa2zeCrxlvROPpYkNnRTzLQFrgMQKV3IF85f3HUdgDRxrJgodLij2WXa3qHbXOsK4Nf+7BQ68vqsK1HdWAwgj3Wi9Xrw1vrONqPY4CmYLRoJI5qwuhthtoOV4umKRjNGlln1+D0KxiqfXCgR1Q50COqKIFbI14UIwy9fD9tajNrqg/9gBxsC6AoGmZDoHcv97wqvKqVNW11gXVx+N+lGopBw64EemzTT61DVRXCtcr269QUFEVDMWmEGeoBSBztRPUpRFKO6v9er6OiYbSoRBoDcxjFDGrG7zYQTRken+PgWwezGm0qUcZAT1XUgFa8iUaiKMXqaQE0NM0PgMFgwGT3Y9f2saMxgdqUMNrizPh8y1CaTGiaD03zEmYegsUYiznMj9+TzzM7p+JLNkIyoH4Kh3VQR5knYDelY4nw43UX8nVlLoQRWNgDh80UYFOtOHxeLBE+POp+9rdFBn6DmgBa4bAhbXb3fsL8DiyRftxaLUe/albgc9nuqSVM3YMlwodXcdJg9EKg3sFnsKEq1oM7C4e3hTBtD5ZwHz5DKy5LG5pHQ/UYcJsi8BkdhzL43IS1BtqqBhceWyuaW8XvMuA2R+ExHjpcavX7CG/dgznMD2YPblsbePz42gy4TZFE2NrQk649KuXl5aSlpbFixQqmHDhjA+C3v/0tS5cuZdWqVUe8pqd6VDRVpdlZj6apGI2mHzyLpLGygup9hTirq6jcW0DZzu14XYcKnZ888CgJA3rXtWQOUlUNv1fF7wvc+rxq4L5Xw+vxExFrJSIu8MPUVOtm58pqPG1+3K0+3K1+XM1e2pp9uFt8nPKjdIafEShMq/Y1s+DZ/HbvZbIaiEqwEZ1kI3dcLGmD9Z/7pL9S/YGPBoMx8Bu5al8z+7Y00OYMfD9dzV5czT5cLT5Uv8bseXmk5gV+BneurGblB8UdrnvGdTlkjYoBYO+GOpa+eegYnmIAk8WAyWzAaDJwykUZDBgRHchQ1MzGL/cHDpmYFAxGBaPJcOBWIXt0LAkDAn/1NdW62belAYMx0E4xcNjXCnFpDqISAoO13a0+aktbUQyBdopBwaAc+toRacYeEfiF7POqtDZ6UZTAcwSOTICioCiB7GZroOg6+LMT2K7A88FDAwrt7/cDfp+PtiYnriYnkQmJWOyBX6zl+TvYvXolrqYmXC3NuJubcbU04W5pxedxc8GvfkfGiFEA7Fi2hCWvvtThe5x90+0MnBiYG2jP2lV88Y+/Bp9TDAbMVismixWz1crky64kZ1ygN6O6qJANn/8Xk8WKyWzBZDFjNFswms2YzBYyho8kLiMwbqrV2UhlwW6MZjMGkwmjyYTBaMJgNGI0mXBERWMLDw9us9flwmA0YjAaUQyGwG0v+77bHREnfTbl9x1vj0qvO/Tzfd11rZ9Wj49hDyw84dcbND9J7ioy2kqJ9DXxZcKZwefGNWygyRTO7rCBuh3z04NBC/wN4T+wyTF+hbFuE1GqQsyBxXDYn6mL7R7WWwN/TcX6Faa4TJSaVEpNKrUHVyZOilWFONVAtKoQ41eIVhUiDyzhmsLb4R7KTIFftKPdRma1dTwnzccON7ssgbbpPgPj3SbcioZbIXCLhkcBjwJlJj/NBz7zzBpYNPAq4ANU+b72OmbVS5i/hWZjGD5DoKDLaCtlaNMOHP5Wwvxt2P2t2NVDf2R+lHwBJfbAoZRhTTs4q2ZJh+v/PGEmu8PzAEhvK2VCw3rcBitugwXP95ZSWxpOc2Qwl83fhtdgxquY8SvGfvWZ25W2Pzwbh6VrD8L0ikM/FouF8ePHs3jx4mChoqoqixcv5rbbbtMz2klTFSP7bSnst7U/dmr1u5nUsAaT5meUcytL4s+g1nL0Y7F9zfd/AdUbNb5yeIP3DRpEqwqxfoUE1cA+06G+1BS/gWFeE8MONG9TNEqNKvvMfgpNKg3GXn1tzW7nUCHRbyDOr1BgVmk8sL+Geo2cfYziI0pVKDvwdYVRZa3VR4ui0WLQaFUOLIbA98N32Pc3UFB6jrrO7/MqgUWEvnh3NTmtRYT7mgn3txDhaybM14JVC3yvP0q+kBJ7YALAcF8Tg1sKjliHikKb0YbxsNP/K62JrIqegMtoo81gw2Ww4TZacRlsuAxWPIZD/0dL7emU2o/vOl1egxmvIXTmJBInRverJ7/zzjvMmTOHF154gVNOOYWnn36ad999l507dx4xduVouqtHRdM02rz+LlvfQe7WFjZ//l82LvgQn8eNYjAw8uzzmXjplcFuUHGkhopWCtdXUbnXSXWRE5+n/RwnZ90wnMyR/aPg+yHuFi8VBY3UFDdRW9ZMXWkLbc5DRcPp1wxm4CmBn63y/Hq+fWsXkQl2IuJtRMTZiYizER5rJSzGij3CEji8IfosTdNoa2ygsaoCZ1UFzqpKnNWVOKsqaKqp4qx5d5A2LDAwdMfSL1nyz78ddT1mm50zb/wFORMDh/Hry0rYt2kdjqgYHNHR2COjDxwS6fpDCKL72c1df7iqV/SoAFxxxRVUV1fzwAMPUFFRwZgxY/j888+Pq0jpToqidHk3F4DDEsW0n17D2JmzWfL6S+xetYLNC//LntXLOeemX5I1ZnyXv2df4MiMJDUz8B/Z71epKW6mNL+Oku11VBQ6yRoSi+3A92vTVyXsL2gge3QCA0bEYQvru39R+f0q1fuacERaiIy3A1C5s4Gv/nd7+4YKRCc6iEsNIybWHvy/PXBkAgMfT/j+akUf5HG1UV9eRl1ZCWlDhhOZEJinavPihSx68dkOX+eqrw7+f0nPHcjIM2cREZdARFw8EXEJhMfFEREbd8QfWo7sbNKye+e4PBFadO9ROVnd1aPSU4o2rmPxK8/TULEfo9nM//z1n4THSs9AZ/g8fkyWQ2eMvDd/LVVFgaH9BqNC+pBYBo5PIHt0Qq8vWnxeP5V7nZTtqqe8oJHKvY34vCoTzs9i0oWBWV9bnR7+88xGkrIiSMiMID4jgtjUMCw23f8uET2kua6Wwk3rqC3ZR01JMbVlJTTX1gSfn33TLxkx42wAirdu5r1H7yMyPoHopGSiEg8uSUQlJRObmo7V0bWnpQoBvWQwbVfo7YUKgM/j4cv//TupeUMYNfMcveP0elX7nOzdWE3hphrqyg/NTmswKGSPiWf2DSN63Yj7VqeHRS9vY/+exuBZJAdZw0yMnJbOpB/ldPBq0RdpmkZTTTWVRXuoLipkwMgxpA0JzP5btHkDHzz2+yNe44iKJjY1nbHnXsigSYH5OPw+H5qqYpIrXIse1msO/QgwWSzMvumX7X55NlZVYAuPxOqQcSudlTggksQBkUy+KJf6ihYK1lWxZ30VtWUtgNJuP+9eW0nGkFhs4aHR06JpGg2VrZTurEdRYMS0wKBBW7iZ6uIm/F4VR6SFtMExpOZFkzIwitjkMBlH0g942lrZt3kjFXt3U7m3gMrCPbiaDk0K4vd5g4VKQmYWmSPHEJ8xgLj0TOLSM4lNS8cefuSEa0aT/BoQoU16VEJQW5OTt+6/C7PFymUPPn7UDxfRefUVLaiqRlxqePD+Ww+tQjEopORGkTUynqxRccQk92w3t7O2jbL8esryGyjNr6elIXAKZ0SsjWsfmxIsrIo21xAZbycmxdHreoRE5/g8Hir27sZkMpM8cBAA9fvLePmOee3aGYxG4jIGkDggm4ETpwTnDxGiN5AelV6sub4Or8tFQ8V+PnriEX5y/yOYLVa9Y/V63y9A2pq9xKWHU1vaTPnuBsp3N7Di3wVEJdrJGBrL8NNTiU/v2iJRVTUMh/V+LHhuE0Vb2k9dajAppORGkzE0BlXVMB6YcC1rVHyXZhGhw93aQtnO7ZTt3Ebpzu1U7tmF3+dj0OTTuPBXgWueRSenkj5sBDEpaSRlDyQpZyDxmVmYzKHRGyhEd5EelRBVU7KPtx/4Le7WFvJOmcoFv/odBoNcbr47OGvaKNpSQ9GWWsry64Mzsl54+2gyhwcGNpftqqc0v57oBDtRiQ6iEuzYwsxHPeTi96q4Wry4Wrw0VrVRV9FCfUUL9ftbcda0cf3/OxWTOfC9XPpWPtu+LScpK4K0wTGkDY4hJSeq3eBg0Xepqp+3H/wdFbt3BS56ehhHVDR5k05l5tybdUonRPeSHpVeLj5jABf95n4+eOz37F69giWv/ZMZ198oXf7dIDLezqgZGYyakYHH5aN0Rz3lBQ0k5Ryavr94Wx3rF+474rVGkwGTxcAlvxlPbEqgx2blh3vY9FVJh+9XXdxMSm5g3RPOz2LKj3Ox2OVHsS/TNI2akn0UbVpPS30t068LXDzUYDAGr8wenZxC+tARpA0ZTtqQYUQnpcjPuxBIoRLSMoaN5Jxb72TBM0+w4fP/EhEXz8QfXap3rD7NYjORMzaBnLHt5xZJzolk2GmpNFa30ljVRnN9YByJ36fi96nB6+FA4CwcRQFrmJmIWBsxKQ5iksOITQ4jJsVBdOKhAdJhUXJIr6/yetyUbN3MnrWr2Lt+Nc31gSuxKwYDU35yVfCU35lzb8EeGUVkvMxnI8TRyKGfXmDtJx+y9I3/JTopheuefBaz1aZ3pH7P5/XjafPj8/rxe1Ui4+0YTYHZNv1+9cAF7eSv4f5q1Yfv8t2H7+A77AKqJouVjGEjyBo9juHTZ8rcJKLfk0M/fciEC36MwWhk8JTTpUgJESazMTjO5PuMRpkevD9xNTdTsPY7sseMJyw6cEVoW3g4Preb8Lh4csdPInf8KWQMGylzlQhxAqRHRQghOsnn9bJ3/Wq2f/M1hRvWovp9nPmzeYw950IgMMWAs6aaxKwcGWciRAekR6WP0jSNbUsX43W7GDv7Ar3jCNFvaJrG/t072bZ0Mfkrl+FuOTTrcVx6ZrtDOfaISOwR8oeTEF1BCpVeZt+m9Sz8x9MYTSbSh44gITNL70hC9AttzkbeeehuVH/gqurhsXEMPW06w06fQbz8HArRbaRQ6WUGjB5HzvhT2LtuNZ8++xRX//EvMuGTEN2gYs9u9m3ZyKSLLwMC85oMnnoGCjDsjLPIGDFS5jYSogfIGJVeqKWhntd+cxttzkYmXHgJ0675ud6RhOgTVNVPwZrvWP/px5Tt3A7Az59+gZiUNCBw+EfGnAjRNWSMSh8WFh3DrBtv5+OnHmXtJx8yZOoZJOUM1DuWEL2W1+Vi8+KFrP/sPzirKwEwGE0Mnno6ymG9JlKkCNHzpFDppQZOnMyQU6exc/lSlrzxTy5/4HH5EBXiBFQU7OLf8x+i7cCViG0RkYw5+1xGn30e4bFxOqcTQkih0oudftUcClavpHT7Vir27CJl4GC9IwnRKxx+CCcuIxMUheikFCb+6FKGnjFDLgIqRAiRMSq93JavvyAuLYPUQUP1jiJEyPO6Xaz/7L/s27Sey37/GIohMDlfbWkxMSlpGIwyOFaIniJjVPqJkTNm6R1BiJDn9/nY+vUXrPzgbVoOXHOnYN0q8iZOAQLzoAghQpMUKn2Is7oKs80mE00JcZjCDWv5+rWXqN9fBkBkQhKnXnENueNP0TmZEOJ4SKHSR2xa9Clfv/YSo846hzN/Nk/vOELoztXSzGd/+xN7168BwB4ZxeRLfsqomefI3ENC9CJSqPQR0cmp+L1eNn6xgNGzziMuLUPvSELoymp30NrYgMFoZNx5FzH5kp9idTj0jiWE6CS5zGsfMWDkGHLGn4Kmqqx45//0jiOELkq2b8Hn8QCgGAzMuumXXPfk35h2zc+lSBGil5JCpQ85/afXAbBr9Qrqyst0TiNEz3G1NLPw+b/y7h/uYeUH/wo+npCZJb2LQvRyUqj0IfGZWeSMmwiaxtpP/q13HCF6xJ51q3jtrlvY+vUXQOAU5F4+64IQ4jAyRqWPmXjRT9i7fg3bly5m6mVXEx4Tq3ckIbqF1+1iyev/ZPOXnwMQk5LKrHm/IH3oCJ2TCSG6khQqfUz6kOGkDh5G1d4C9hfkB+eJEKIvqSnZx3//Mp+6shIAJlx4CVMvv1pmlBWiD5JCpQ+adeNt2CMicURF6x1FiG5hMltorqshLCaWc2+5kwGjxugdSQjRTaRQ6YNklk3RF6mqH8OBKxlHJ6dw0a/vJz4zC0dklM7JhBDdSQbT9nH7C/KDp2sK0VvVlZfxxu9+SfHWTcHHMkeMliJFiH5ACpU+7LO//Ym37ruL7d98pXcUIU7YnnWrefPeX1FTXMSS1/+Jpqp6RxJC9CApVPqwxOyBAKz57weoql/nNEJ0jqZpfPfB23z05CN42lpJHTyMS+99OHjFYyFE/yA/8X3YyLNmYQsLp6FiP0Wb1usdR4jj5vf5WPj8Myx/9/9A0xh99nlc/sBjhEXH6B1NCNHDpFDpwyw2O8OmnQXAlsULdU4jxPHxetx8/OQjbFvyJYpiYOb/3MLM/7kFo0kuJChEfySFSh836qzZQOA4f3N9nc5phPhhJpMZW3gEJouVi35zH6PPPk/vSEIIHUmh0sfFpWeSOmgomqqybeliveMI8YMUg4HZN/+Sqx59itzxk/SOI4TQmRQq/cDIA70qe9et1jmJEEdXV17Gkjf+Nzjo22gykzAgW+dUQohQIBO+9QODJ5+G1e4gZ/wpekcR4gh15aW8+/C9tNTXYbHZmHrZ1XpHEkKEEClU+gGzzUbepKl6xxDiCLWlJbz3yL20NNQTn5nFmFnn6x1JCBFi5NBPP6Oqfnxer94xhKC2tJh3H76HloZ6EjKzuOz3j8n1qYQQR5BCpR/Z8vUX/PP2/2HTF5/qHUX0c/UV5bz78L20NjaQkJXDZQ/8UabDF0IclRQq/Yjf66OpppotXy1E0zS944h+yu/z8eH8PxwqUn7/GPaISL1jCSFClBQq/cjQ06ZhslipLS1m/+6descR/ZTRZGLatT8nPmMAl97zB+zhEXpHEkKEMClU+hGrI4zBU04DYMtXi3ROI/qz3PGTuPaJv8qU+EKIHySFSj8z/MCU+gWrV+D3yaBa0TNU1c+S1/9JQ2VF8DGDwahjIiFEbyGFSj+TNnQ4YdExuFqa2bdlo95xRD/xzf+9zLoFH/Huw/fg83j0jiOE6EWkUOlnDAYjeZNOBWDXym91TiP6g21LF7NuwccAnHH1zzBZLDonEkL0JjLhWz807PQZaKrK0NNn6B1F9HH7C/JZ9NLfAJh86ZUMmXqGzomEEL2NFCr9UEreYFLyBusdQ/RxzfV1/Oepx/B7veROmMzUn1ypdyQhRC8kh36EEF3O5/Xynz89RnN9HXHpmZx7650oBvm4EUJ0nnxy9FOaplG6cxtfv/aSDG4UXc7T2oLqV7GGhXHRb+7H6nDoHUkI0UvJoZ/+StP49K9P0VRbTfqwEeRNnKJ3ItGHOKKiueIP86krKyUmOVXvOEKIXkx6VPopxWBg0IHJ3/JXLNM5jegrDp+bx2yxkpSdq2MaIURfIIVKP3Zwltq961bjdbt0TiN6O7/Py9sP/JZv334Dv8+ndxwhRB8hhUo/lpw7iMiEJLxuF4Ub1uodR/Ryy/71OhV7drNp0ae0NTn1jiOE6CO6rVApKipi7ty5ZGdnY7fbyc3N5cEHH8TzvYGbmzdv5vTTT8dms5GRkcETTzzRXZHE9yiKEuxVyZfJ38RJKNy4jnWffAjA7JvvIDwmVudEQoi+otsKlZ07d6KqKi+88ALbtm3jL3/5C88//zz33ntvsI3T6WTWrFkMGDCAdevW8eSTT/LQQw/x4osvdlcs8T2Dp5wOwN71a/C42nROI3qjloZ6Pv/7XwAYM/sCBk6YpHMiIURf0m1n/Zxzzjmcc845wfs5OTnk5+fzj3/8g6eeegqAN998E4/Hw8svv4zFYmH48OFs3LiRP//5z9x4443dFU0cJjE7l6ikZPxeLw0V+0nMytE7kuhFNE3jixefpbWxgfjMLKZd83O9Iwkh+pgePT25sbGR2NhDXcIrV67kjDPOwHLYtT9mz57N//t//4/6+npiYo68BLzb7cbtdgfvO51yLPxkKIrCT//wBGHRMSiKoncc0cvkr/iGvetWYzCaOP/2X8t1fIQQXa7HBtMWFBTw7LPPMm/evOBjFRUVJCUltWt38H5FRQVH8/jjjxMVFRVcMjIyui90PxEeEytFijghPq8Xs9XG5EuuID4zS+84Qog+qNOFyt13342iKMdcdu7c2e41ZWVlnHPOOVx22WXccMMNJxX4nnvuobGxMbiUlJSc1PrEIarql9OURaeMmD6T6//8d065+Cd6RxFC9FGdPvRz1113cf311x+zTU7OoXEO5eXlzJgxg6lTpx4xSDY5OZnKysp2jx28n5ycfNR1W61WrFZrZ2OLH7D+s//y3Qf/YszsC5h62VV6xxG9SGR8ot4RhBB9WKcLlYSEBBISEo6rbVlZGTNmzGD8+PG88sorGL53UbIpU6Zw33334fV6MZvNACxatIjBgwcfdXyK6D5mq5W2JieFG9ZIoSKOyd3aykdPPMzkS3/KgJFj9I4jhOjjum2MSllZGdOnTyczM5OnnnqK6upqKioq2o09ueqqq7BYLMydO5dt27bxzjvv8Mwzz3DnnXd2VyzRgeyxEwCo2LObloZ6ndOIULbsrVco3bGVL//5nMxAK4Todt121s+iRYsoKCigoKCA9PT0ds9pmgZAVFQUX3zxBbfeeivjx48nPj6eBx54QE5N1kF4TCxJOQOp3FtA4Ya1jJhxtt6RRAjavzufTYs+A2DWjbdjNMl1TYUQ3avbelSuv/56NE076nK4UaNGsWzZMlwuF6Wlpfzud7/rrkjiB2SPnQjA3g1rdE4iQpGmqnz16gsADJ82k4zho3ROJIToD+RaPyIod1ygUNm3eUO7q+AKAbB92ddUFOzCYrdz+lVz9I4jhOgnpFARQUk5A3FEReNpa6N0xza944gQ4mlrZdlbrwIw+ZKfEhYtg92FED1DDjCLIMVgYMys8/F5PUQmyCmn4pAd3y6lpaGemJRUxp33I73jCCH6ESlURDtTfnKl3hFECBo18xwc0dFYbHaMJrPecYQQ/YgUKkKIH6QoCnkTp+gdQwjRD8kYFXEEr9vFnnWr2Ld5o95RhM5qiotoa27SO4YQoh+TQkUcYfOXC/noiUdY898P9I4idKSpKp/+7U+8/MsbKd0pg6uFEPqQQkUcYcCoMQCU7dyOzyunKfdXu1Ytp3pfIarfT1x6pt5xhBD9lBQq4ghx6Zk4oqLxedzs37VD7zhCB6rfz/J33wRgwgU/xh4eoXMiIUR/JYWKOIKiKGSOGA1A8dZNOqcReti+7Gvqy0uxRUQy7ryL9I4jhOjHpFARR3WwUNknhUq/4/d5Wfn+vwA45aKfYHU4dE4khOjPpFARR3WwUKko2IWnrVXnNKInbVn8Bc7qSsKiYxgz6zy94wgh+jkpVMRRRSUmEZWUjKaqlOXLOJX+xFlThaIYmHTJFZitNr3jCCH6OUX7/uWMexmn00lUVBSNjY1ERkbqHadPKdm2mbCYOGJSUlEURe84ogfVlpUQlZiMySyz0Aohusfx/v6WmWlFhzKGj9I7gtBJXFqG3hGEEAKQQz9CiAOKNm+grrxU7xhCCNGOFCrimHatWs5//vxHCtau0juK6EZ+n5eFzz/DK3feTNHmDXrHEUKIIClUxDGV529n96oV7F2/Wu8oohvt+HYpzbU1hEXHkD50hN5xhBAiSAoVcUyZI8YAMvFbX6apKmv+E7iu07hzfyQDaIUQIUUKFXFM6UOHYzAaaaysoLGqUu84ohvsWb+GurISLHYHo88+V+84QgjRjhQq4pgsdgfJuYMA6VXpq9Z8/D4Ao2edh9URpnMaIYRoTwoV8YMyR8p1f/qq0p3bKN+1A6PJxLhzf6R3HCGEOIIUKuIHHX6Bwl4+P6D4nubaGmzhEQybdhbhMbF6xxFCiCPIhG/iB6XkDcHqCCMyIZG2JieOyCi9I4kuMuTUaeSOn4TX49Y7ihBCHJUUKuIHmcxmbn7p/zCa5GyQvshss2G2yTV9hBChSQ79iOMiRUrf0tbcRNHmDWiqqncUIYQ4JilURKd4XS69I4gusPWrL/jgsd/z36fn6x1FCCGOSQoVcVxU1c9b99/Fsz+7HGdNtd5xxEnQVJVNiz4FIHvMBJ3TCCHEsUmhIo6LwWBE9fvRVJXy/O16xxEnoXDTOhqrKrGFhTPk1DP0jiOEEMckhYo4bmmDhwFQulMKld5s48IFAAyfPhOzVQbRCiFCmxQq4rilDR0OQPnObTonESeqobKCwo3rAGS6fCFEryCFijhuB3tUqkv24Wpp1jmNOBGbFn0KmkbW6HHEpKTpHUcIIX6QFCriuIVFxxCdnAKaRvmuHXrHEZ2kaRoVBbsAGD3rfJ3TCCHE8ZEJ30SnpA0eTkPFfsp2bidn7ES944hOUBSFyx98nLId20gdMlTvOEIIcVykUBGdkj12Aj6Pm+TcPL2jiBOgKArpw0boHUMIIY6bFCqiUwZPOY3BU07TO4bopLbmJswWKyaLRe8oQgjRKTJGRYh+YOX7b/H8vGvZ8tUXekcRQohOkUJFdJqmadSWlVBVtFfvKOI4+H1edny7FHdrC+GxcXrHEUKITpFCRXTahs8/4dU7b2b5O2/oHUUch73r1uBqchIeE8uAUWP0jiOEEJ0ihYrotNS8wQCU5++Qq+/2AluXfgnA0DPOxGAw6pxGCCE6RwoV0WmJ2bmYrTZcLc3UlhbrHUccQ0tDPYUb1gIw/IyzdE4jhBCdJ4WK6DSD0UjKgV6VMrlAYUjb8e0SNFUlZeBg4tIz9I4jhBCdJoWKOCFpQwLX/SndIdf9CWXbli4GYPh06U0RQvROMo+KOCGpg4YAsL8gX+ck4lh+dOc9bFv6FYOnnKF3FCGEOCHSoyJOSPLAQQA0VlbQ6mzUOY3oSExKGqf99Fps4eF6RxFCiBMiPSrihNjCwpl27VxiUlIx22x6xxFCCNFHSaEiTtiEC36sdwTRgYI137H9m68YPes8Bowco3ccIYQ4YXLoR4g+aOuSRexevYLiLRv1jiKEECdFChVxwvw+H3vXr2Hl+/+Sid9CiKulmaKN6wAYetp0fcMIIcRJkkM/4qT898+P4/N6GDTlNOLSZJ6OULBn7Sr8Ph9x6ZnEZ2bpHUcIIU6K9KiIE2Y0mUjKHQhARcEundOIg/JXLgNg8JTTdU4ihBAnTwoVcVKSBwZmqN2/e6fOSQRAW3MT+zZvAGDQlNN0TiOEECdPChVxUlKChYr0qISCgtUrUf1+EjKz5FCcEKJPkEJFnJSUvMDEb9XFhXjdLp3TCKvDQWJ2LoOnyky0Qoi+QQbTipMSEZdAWHQMLQ31VBbuIf3ANYCEPgZNPo1Bk0+Ts7CEEH2G9KiIk6IoSvBKyjKgNnQoBvnRFkL0DT3yaeZ2uxkzZgyKorBx48Z2z23evJnTTz8dm81GRkYGTzzxRE9EEl1o6uXXcP2f/s64836kd5R+rWjjOtytrXrHEEKILtUjhcpvf/tbUlNTj3jc6XQya9YsBgwYwLp163jyySd56KGHePHFF3silugiCZlZxKVnYjAY9Y7Sb7U01PPv+X/g+RuvkYtECiH6lG4fo/LZZ5/xxRdf8MEHH/DZZ5+1e+7NN9/E4/Hw8ssvY7FYGD58OBs3buTPf/4zN954Y3dHE6LP2PXdt2iaSsKAbByRUXrHEUKILtOtPSqVlZXccMMNvPHGGzgcjiOeX7lyJWeccQYWiyX42OzZs8nPz6e+vv6o63S73TidznaL0N/O5UtZ8Ncn2bd5o95R+qXgJG9TZZI3IUTf0m2FiqZpXH/99dx0001MmDDhqG0qKipISkpq99jB+xUVFUd9zeOPP05UVFRwyciQuSJCQfHWTexcvpR9WzfqHaXfaaqroWzndgDyJp2qcxohhOhanS5U7r77bhRFOeayc+dOnn32WZqamrjnnnu6NPA999xDY2NjcCkpKenS9YsTc3CG2ord+Ton6X/2rFkFQEreYCLjE3ROI4QQXavTY1Tuuusurr/++mO2ycnJ4auvvmLlypVYrdZ2z02YMIGrr76a1157jeTkZCorK9s9f/B+cnLyUddttVqPWKfQX/AU5b0FqKpfBtb2oIK13wEwcOIUnZMIIUTX63ShkpCQQELCD//V9te//pVHH300eL+8vJzZs2fzzjvvMGnSJACmTJnCfffdh9frxWw2A7Bo0SIGDx5MTExMZ6MJHcWlZ2C22fG62qgtLSFBrtrbI7wuF6XbtwCQO2GSzmmEEKLrddsYlczMTEaMGBFcBg0KTLWem5tLeno6AFdddRUWi4W5c+eybds23nnnHZ555hnuvPPO7ooluonBYCQpJxeAyj27dU7Tf5htNn7+zEvMvvkOubaPEKJP0nX6yqioKL744gsKCwsZP348d911Fw888ICcmtxLJeXkAYHDP6LnRMYnMGL6TL1jCCFEt+ixa/1kZWWhadoRj48aNYply5b1VAzRjZJzBqIoBtwtzXpHEUII0Uco2tGqh17E6XQSFRVFY2MjkZGResfp17weN2gaZqtN7yj9Qsn2Laz5+H2Gnj6DoadN1zuOEEJ0yvH+/pYrl4kuY7ZYpUjpQbtXraBw4zqKt27SO4oQQnQbKVSE6IU0TQuelpw7YbLOaYQQovv02BgV0T/sXrOSNR+9T+rgIUy/7ga94/RZ1fsKaaqpxmSxMmDkaL3jCCFEt5FCRXQp1edjf0E+mqbqHaVPK1gT6E3JGj1WDrcJIfo0OfQjutTBU5Sr9xXi93l1TtN37VkbmDZfDvsIIfo6KVREl4pKTMIWFo7f56OmpFjvOH2Ss6aKqqI9KIqBnHET9Y4jhBDdSgoV0aUURSExZyAAlXtlhtru4GpuJmP4KDKGj8ARGaV3HCGE6FYyRkV0ueScgRRv2Ujl3gI4S+80fU9iVg6XP/BHVNWvdxQhhOh20qMiulxSsEdFptLvTnKFaiFEfyCFiuhySTl5RMQlEJ2UctTLJogT11RXQ2tjg94xhBCix8ihH9HlohKTuPHvr+gdo09a/dH7bFz4CadecS2TL7lC7zhCCNHtpEdFiF6kaNM6AOIzBuicRAgheoYUKqLbaJqGS66k3GXqK8ppqNiPwWgic8QoveMIIUSPkEJFdIvSndv4xw1X897D9+kdpc8o2hjoTUkbMgyL3aFzGiGE6BkyRkV0i8j4BNqanLhbW/B5PJgsFr0j9XqFBwqVrNHjdE4ihBA9R3pURLeIiEvAHhGJ6vdTXVyod5xez+fxULJtCwDZYyfonEYIIXqOFCqiWyiKQlJu4Lo/lXv36Jym9yvdsRWfx014bJwMpBVC9Cty6Ed0m+ScgRRtXCdT6XeBpJyBnHPLr/B7vSiKonccIYToMVKoiG4TvOZPofSonCx7RCTDp8n1CIQQ/Y8c+hHdJikrF4Dakn34vF6d0wghhOiNpEdFdJuI+ARyxp9CTEoaPo8bk9msd6Reae/6NdSWlTBw4mRiklP1jiOEED1KChXRbRRF4ce/fUDvGL3e5sUL2bP2O/xer0ybL4Tod+TQjxAhzO/zUrx1EwDZY8brnEYIIXqeFCqi27mam6nYI2f+nIjy/B14XW04oqJJzMrRO44QQvQ4OfQjulV9RTkv//JGTFYrt7/6LgaDUe9IvcrB3pTMEaNRDPJ3hRCi/5FPPtGtohKTMFmt+Nxu6svL9Y7T6+zbshGAzJGj9Q0ihBA6kUJFdCuDwUjigMAhi6oimU+lM9ytLcFDZgNGjtE3jBBC6EQKFdHtErMDhYpM/NY5NSXFGIxGopNTiIxP1DuOEELoQsaoiG6XeGDit2rpUemUtMFDue3ld3DWVOsdRQghdCM9KqLbJWYHCpWqwr1omqZzmt7FZLEQm5qmdwwhhNCNFCqi28VnZGIwmnC1NOOsrtI7Tq8gBZ0QQgTIoR/R7YwmM5MvvQJHZBQWh0PvOL3CzuVLWf3x+4yccTbjzrtI7zhCCKEbKVREj5hy6ZV6R+hV9m3eSE1xEU11tXpHEUIIXcmhHyFCjKZpwYne5LRkIUR/J4WK6BGq30/Fnt1sW7pY7yghr6GinKbaaowmE2lDhukdRwghdCWHfkSP8Hk9vHnfnaBpZI0eR1h0jN6RQta+LYHelNRBQzFbbTqnEUIIfUmPiugRFpudmJTAabZVRXt1ThPairduBALX9xFCiP5OChXRYw5e/bdKZqjtkKr6Kdm6GYBMGZ8ihBBSqIiekxSc+E0KlY542trInTCJuPRMknPz9I4jhBC6kzEqosccnEpfDv10zBYWzjm3/ErvGEIIETKkR0X0mIMXJ2yo3I+7tUXnNEIIIXoD6VERPcYeEUlEfAJNNdVUFe0lY9hIvSOFFL/PR21pMQmZWSgG+RtCiM7SNA2fz4ff79c7igCMRiMmkwlFUU5qPVKoiB41Y84NWGyO4HgVcUjl3gL+9ftfE5OSys/+8sJJ/3AL0Z94PB72799Pa2ur3lHEYRwOBykpKVgslhNehxQqokflnTJV7wghq2T7FgDiM7KkSBGiE1RVpbCwEKPRSGpqKhaLRX6GdKZpGh6Ph+rqagoLC8nLy8Nwgj3FUqgIESJKDxQq6cNG6JxEiN7F4/GgqioZGRk45MKnIcNut2M2m9m3bx8ejweb7cQmsJQD4aJHqaqfncuX8s1br+LzevWOEzL8Ph9l+TsAZOyOECfoRP9iF92nK74n0qMiepSiGFj8v//A1dLM4Cmny1iVA6oK9+B1tWELjyA+Y4DecYQQImRI+Sl6lKIoJBycobZIJn476OD4lPShw+WMHyGEOIx8Iooed3Aq/eqiQp2ThI6D41PksI8Q/cv111/PxRdfrHeMkCaHfkSPC17zR2aoDTrl4stIys0ja8x4vaMIIURIkUJF9Lhgj8q+vWiqKoc6gPShI0gfKmf7CCHE90mhInpcTGo6RrMZT1sbjVWVRCen6B1JCNGHaJpGm1ef2WntZqPM4dLFpFARPc5oMhGfkUXl3t1U7dvb7wuVzV9+jiM6hswRo7DY7HrHEaLXa/P6GfbAQl3ee/vDs3FY5FdrV5K9KXRx9o23YQsLJzIhUe8oulL9fpb+3//iaWvjmvnPyOnaQgjxPd1aqCxYsICHH36YzZs3Y7PZmDZtGh999FHw+eLiYm6++Wa+/vprwsPDmTNnDo8//jgmk9RPfZ38Qg6oKtqLp60Na1gYCQOy9I4jRJ9gNxvZ/vBs3d5bdK1uqwg++OADbrjhBv74xz9y5pln4vP52Lp1a/B5v9/P+eefT3JyMitWrGD//v1cd911mM1m/vjHP3ZXLCFCysH5U9KGDMdgkA84IbqCoihy+KUP6ZbvpM/n45e//CVPPvkkc+fODT4+bNiw4NdffPEF27dv58svvyQpKYkxY8bwyCOP8Lvf/Y6HHnropK60KEKfpmms/ug9KvcWMPN/bsERFa13JF3I/ClCCHFs3XJe6Pr16ykrK8NgMDB27FhSUlI499xz2/WorFy5kpEjR5KUlBR8bPbs2TidTrZt29bhut1uN06ns90ieh9FUdi2dDG7V6+gqrB/zlCrqn5KdwT+r0uhIkT/pKqqDHf4Ad1SqOzdG5jI66GHHuL+++/nk08+ISYmhunTp1NXVwdARUVFuyIFCN6vqKjocN2PP/44UVFRwSUjI6M7NkH0gODEb/v65wy11UWFeNpasdgdJGRl6x1HCKGDqqoqkpOT9Y4R0jpVqNx9990oinLMZefOnaiqCsB9993HpZdeyvjx43nllVdQFIX33nvvpALfc889NDY2BpeSkpKTWp/QT/CaP/20R2X/7nwA0oYMk/EpQvQz9fX1fPLJJyxZsoSZM2fqHSekdaq/6a677uL6668/ZpucnBz2798PtB+TYrVaycnJobi4GIDk5GRWr17d7rWVlZXB5zpitVqxWq2diS1CVFI/71EZPes8Bowei8/t1juKEKKH/fznP2fNmjXcddddXHTRRXrHCWmdKlQSEhJISEj4wXbjx4/HarWSn5/PaaedBoDX66WoqIgBAwKXsJ8yZQqPPfYYVVVVJCYG5tJYtGgRkZGR7Qoc0Xcd7FGp31+Gx9XW7yY7UxSFmORUvWMIIXTw4Ycf6h2h1+iWMSqRkZHcdNNNPPjgg3zxxRfk5+dz8803A3DZZZcBMGvWLIYNG8a1117Lpk2bWLhwIffffz+33nqr9Jj0E2HRMYTFxIKmUb2vSO84QgghQlC3DTV+8sknMZlMXHvttbS1tTFp0iS++uorYmJiADAajXzyySfcfPPNTJkyhbCwMObMmcPDDz/cXZFECErMyqG4uYmm2mpgqN5xesyO5UvZvWo5Q0+bTt4pU/WOI4QQIUvRNE3TO8TJcDqdREVF0djYSGRkpN5xRCe1OhuxOsIw9rPT8z599il2fLuEyZdeyamXX613HCF6NZfLRWFhIdnZ2dhsNr3jiMMc63tzvL+/+9dvBxFyHJFRekfQRenOwPwp6UOH65xECCFCW7eMURFCdMxZXUVTTTUGo5HUvCF6xxFCiJAmhYrQ3VevvsDrv7mN6uIivaP0iIO9KUnZAzFLN7UQQhyTFCpCd9X7CqkuLqJyb4HeUXpE6Y7ApSTS5LCPEEL8IClUhO6SsnOB/jNDbdkOGZ8ihIAlS5Ycc6b3GTNm6B0xJMhgWqG7xKwDhUpR3y9UfF4v1vBwjCYTqYNlYkMh+rOpU6cGZ3I/3H/+8x9uuukmbrnlFh1ShR4pVITuEg/2qBQVoqkqiqHvdvSZzGaueuQpfB4PJotF7zhCCB1ZLJYjLhmzY8cOfv3rX3PvvfcGJ0jt76RQEbqLTU3HZLbgdbVRX7Gf2NQ0vSN1OylShOhGmgbeVn3e2+wARTmhlzY0NHDRRRcxffp0HnnkkS4O1ntJoSJ0ZzAaiR+QRUXBLqqK9vTpQsXrdmG2ypk+QnQrbyv8UafraN1bDpawTr9MVVWuuuoqTCYTb775JsoJFjt9kRQqIiQk5eThbm1FU1W9o3Qbd2sLf/+fq0kYkMUVD86XU5OFEEH33nsvK1euZPXq1UREROgdJ6RIoSJCwlk/v6nP/wVRnr8D1e/D1dIsRYoQ3cnsCPRs6PXenfT222/z1FNPsWDBAvLy8rohVO8mhYoICX29SIHDps0fMkLnJEL0cYpyQodf9LBx40bmzp3L/PnzmT17tt5xQpIUKiKkaKqKpmkYjEa9o3S50gPzp6QNldOShRBQU1PDxRdfzPTp07nmmmuoqKho97zRaCQhIUGndKFDChURMj7/x9Ps+m455912FwMnTtY7TpfyeTxU7tkFQPpQ6VERQsCCBQvYt28f+/btIyUl5YjnBwwYQFFRUc8HCzF9d8IK0ftoGl5XW5+c+K2iYBd+n4+w6Biik478QBJC9D9z5sxB07QOFylSAqRQESHj4MRvlX1wKv2D41PShgzvF+NxhBCiq8ihHxEyErNyAKgq2qtzkq6XmJXD4KlnkDN2gt5RhBCiV5FCRYSMhAGBQqW5toZWZyOOyCidE3WdnHETyRk3Ue8YQgjR68ihHxEyrA4HMSmB2ST7y5WUhRBCHJsUKiKkJASvpNx3Dv/UFBdRW1qCpml6RxFCiF5HDv2IkJI5fBQ+t4uoxCS9o3SZFe+9xe7VK5h2zc+ZcOElescRQoheRQoVEVJGn30uo88+V+8YXUbTtOAZPyl5Q3ROI4QQvY8c+hGiG9XvL6PN2YjRbCYpV67hIYQQnSWFighJzXW1tDU59Y5x0g5Om58ycDAms1nnNEII0ftIoSJCzuf/eJoXbp7DtqWL9Y5y0sp2bAUCE70JIYToPClURMiJSQ6colyxZ7fOSU5e6c7tAKQPkQsRCiHa8/v9TJ06lUsuaT/IvrGxkYyMDO677z6dkoUWKVREyEnKGQhAZS8vVJpqa3BWV6IoBlIGDdU7jhAixBiNRl599VU+//xz3nzzzeDjt99+O7GxsTz44IM6pgsdctaPCDkHB502VO6nrbkJe3iEzolOjC0igh/f/SAN+8uxOhx6xxFChKBBgwYxf/58br/9ds4880xWr17N22+/zZo1a7BYLHrHCwlSqIiQYw+PIDophYbK/VTu2U3W6HF6RzohZouVnLETYazeSYToXzRNo83Xpst72032Tl949Pbbb+fDDz/k2muvZcuWLTzwwAOMHj26mxL2PlKoiJCUlJsXKFT2FvTaQkUIoY82XxuT3pqky3uvumoVDnPnelAVReEf//gHQ4cOZeTIkdx9993dlK53kjEqIiQlHxinUrFnl85JToyruZllb71K4Ya1MnW+EOIHvfzyyzgcDgoLCyktLdU7TkiRHhURkjJHjmHsuReSMXyU3lFOSOnObaz++H12r/mOn4+doHccIfoVu8nOqqtW6fbenbVixQr+8pe/8MUXX/Doo48yd+5cvvzyy04fQuqrpFARISkxK4czr5+nd4wTVrp9CwAZQ0fonESI/kdRlE4fftFLa2sr119/PTfffDMzZswgOzubkSNH8vzzz3PzzTfrHS8kyKEfIbpByYFCJX34SJ2TCCFC2T333IOmacyfPx+ArKwsnnrqKX77299SVFSkb7gQIYWKCFlel4vSHVspy9+hd5ROcbe2UF1UCEiPihCiY0uXLuW5557jlVdewXHYFAbz5s1j6tSpzJ07V8a4IYd+RAjbuvRLvnr5ebLGjOfSe/6gd5zjVrZzO5qmEp2cQnhsnN5xhBAhatq0afh8vqM+t3Dhwh5OE7qkR0WErOQDE79V7tndq/6qCB72GSqHfYQQ4mRJoSJCVkJmNgajkbYmJ87qKr3jHLfqfQcO+8j4FCGEOGly6EeELJPFQnxmFlWFe6jYs5uoxCS9Ix2XS+99mLqyEsJiYvWOIoQQvZ70qIiQdvDwT2+a+E1RFOLSM7GFhesdRQghej0pVERIS84dBEDl3gKdkwghhNCDHPoRIS04oHZvAZqqohhCu7b++KlHMZotTL3samJT0/SOI4QQvZ4UKiKkxaVnMuP6eSTnDtQ7yg/yuNrYs241mqpy+pVz9I4jhBB9ghQqIqQZjEbGnXuh3jGOS3n+DjRVJTIhsdcM/BVCiFAX2v3oQvQipTu2ApAus9EKIUSXkUJFhDx3awvbli5m1Yfv6h3lmEq2HyhUhkmhIoQ4eUVFRSiKwsaNG4/7Na+++irR0dHdlkkPcuhHhDxXcxOf//0vGIwmxp33I8xWm96RjuB1u6goCJxCnSEz0gohRJeRHhUR8iITkgiPiUX1+6jYs1vvOEdVvmsnqt9HeGwcUUnJescRQog+QwoVEfIURSF1yHAgcMG/UKT6/STlDCRzxGgURdE7jhCil/j888857bTTiI6OJi4ujgsuuIA9e/Ycte2SJUtQFIUFCxYwatQobDYbkydPZuvWrUe0XbhwIUOHDiU8PJxzzjmH/fv3B59bs2YNZ599NvHx8URFRTFt2jTWr1/fbdt4sqRQEb1C2uBhAJTlh2ahkj1mPNc8/jTn3HyH3lGEEAeora0dL2738bd1uY6r7YloaWnhzjvvZO3atSxevBiDwcCPf/xjVFXt8DW/+c1v+NOf/sSaNWtISEjgwgsvxOv1Bp9vbW3lqaee4o033uCbb76huLiYX//618Hnm5qamDNnDt9++y3fffcdeXl5nHfeeTQ1NZ3QNnQ3GaMieoW0IYFCpTx/B6rqx2Aw6pzo6EJ9Qjoh+pP8ceM7fC5s2hlkvvBC8P6uU09Da2s7alvHxIkMeOP14P2Cs2bir68/ot3QnTs6nfHSSy9td//ll18mISGB7du3Ex5+9MtwPPjgg5x99tkAvPbaa6Snp/Phhx9y+eWXA+D1enn++efJzc0F4LbbbuPhhx8Ovv7MM89st74XX3yR6Oholi5dygUXXNDpbehu8qkqeoWEzCwsdjuetlZqivfpHaed1sYGPK6jf8AJIcSx7N69myuvvJKcnBwiIyPJysoCoLi4uMPXTJkyJfh1bGwsgwcPZseOQ0WSw+EIFikAKSkpVFUdugJ9ZWUlN9xwA3l5eURFRREZGUlzc/Mx31NP0qMiegWD0UhK3hD2bd5A9b5CErNy9I4U9N2/32HTos84/crrmHDhJXrHEUIcMHj9uo6fNLbvlR20/NuO236vp3Tg4i9PJlY7F154IQMGDOCll14iNTUVVVUZMWIEHo/nhNdpNpvb3VcUBU3TgvfnzJlDbW0tzzzzDAMGDMBqtTJlypSTes/uJIWK6DXO/Nk8bGHhOKKi9Y7Szr7NG1D9PqIS5WwfIUKJweHQve2x1NbWkp+fz0svvcTpp58OwLffHqNgOuC7774jMzMTgPr6enbt2sXQoUOP+32XL1/O3//+d8477zwASkpKqKmpOYEt6BlSqIheIzY1Xe8IR3DWVFNXXoqiGMgYMUrvOEKIXiQmJoa4uDhefPFFUlJSKC4u5u677/7B1z388MPExcWRlJTEfffdR3x8PBdffPFxv29eXh5vvPEGEyZMwOl08pvf/Aa73X4SW9K9ZIyKECdh35YNQOAqz7awow98E0KIozEYDLz99tusW7eOESNG8Ktf/Yonn3zyB183f/58fvnLXzJ+/HgqKir473//i8ViOe73/d///V/q6+sZN24c1157Lb/4xS9ITEw8mU3pVop2+IGrLrRr1y5+85vfsHz5cjweD6NGjeKRRx5hxowZwTbFxcXcfPPNfP3114SHhzNnzhwef/xxTKbj7+hxOp1ERUXR2NhIZGRkd2yKCCFbvv6Cncu/YfTMcxg0+TS94/DJM0+Qv+IbJl/6U069/Bq94wjRL7lcLgoLC8nOzsZmC72Zq7vKkiVLmDFjBvX19b1mmvxjfW+O9/d3t/WoXHDBBfh8Pr766ivWrVvH6NGjueCCC6ioqADA7/dz/vnn4/F4WLFiBa+99hqvvvoqDzzwQHdFEn1Abck+irdspHjrJr2joKkqxVs2AjBg5BhdswghRF/VLYVKTU0Nu3fv5u6772bUqFHk5eUxf/58WltbgzPoffHFF2zfvp3/+7//Y8yYMZx77rk88sgjPPfccyE78ljoL21w6MxQW7WvkLYmJ2abnZS8IXrHEUKIPqlbCpW4uDgGDx7M66+/TktLCz6fjxdeeIHExETGjw9MwLNy5UpGjhxJUlJS8HWzZ8/G6XSybdu2DtftdrtxOp3tFtF/pA4OjGyvKS3G1dysa5aI2DjO/Nk8TvnRpRg7cbhSCCFOxPTp09E0rdcc9ukq3fLpqigKX375JRdffDEREREYDAYSExP5/PPPiYmJAaCioqJdkQIE7x88PHQ0jz/+OH/4wx+6I7boBcKiY4hJSaV+fznlu3eQM3aiblkcUdGMPedC3d5fCCH6g071qNx9990oinLMZefOnWiaxq233kpiYiLLli1j9erVXHzxxVx44YXtLox0Iu655x4aGxuDS0lJyUmtT/Q+qQev+xMCh3+EEEJ0r071qNx1111cf/31x2yTk5PDV199xSeffEJ9fX1wJO/f//53Fi1axGuvvcbdd99NcnIyq1evbvfayspKAJKTO544y2q1YrVaOxNb9DFpQ4axbcmXuhYqVUV7qdizi6xR44hMCN3T+oQQorfrVKGSkJBAQkLCD7ZrPXAVScP3ph02GAzBK0JOmTKFxx57jKqqquD524sWLSIyMpJhw4Z1JpboZ9IGD8dit2OPiEDTNBRF6fEM25d9zbpPPmT49JlyxWQhhOhG3TJGZcqUKcTExDBnzhweeOAB7HY7L730EoWFhZx//vkAzJo1i2HDhnHttdfyxBNPUFFRwf3338+tt94qPSbimGJSUrn15bd1vYJy8ebARG9Zo8bqlkEIIfqDbjnrJz4+ns8//5zm5mbOPPNMJkyYwLfffsvHH3/M6NGjATAajXzyyScYjUamTJnCNddcw3XXXdfuUtRCHI2iKLoWKS0N9VQXFwGQKfOnCCFEt+q2cyonTJjAwoULj9lmwIABfPrpp90VQfQDTbU1RMTF9+h77t2wBoDE7FwckVE9+t5CCNHfyLV+RK/k83p55c6befGW62muq+3R9y5YvRKAvIlTevR9hRCiP5JCRfRKJrMZqz1wqfXCjet67H3dra3sOzA+JW/S1B57XyGE6K+kUBG9VvbYCQAUbljbY+9ZubcATdOITU0nLj2zx95XCNE3NTU1cfXVVxMWFkZKSgp/+ctfmD59OnfccQcAb7zxBhMmTCAiIoLk5GSuuuoqqqqqgq9fsmQJiqKwcOFCxo4di91u58wzz6SqqorPPvuMoUOHEhkZyVVXXRU8IxcCs9zefvvt3HHHHcTExJCUlMRLL71ES0sLP/vZz4iIiGDgwIF89tlnwdf4/X7mzp1LdnY2drudwYMH88wzz3T7PpJCRfRaBwuVfVs24Pd5e+Q9M0eM4uYX3+T8X/62R95PCHHivG5/h4vP6z/+tp7ja3si7rzzTpYvX85//vMfFi1axLJly1i/fv2h9/J6eeSRR9i0aRMfffQRRUVFR53P7KGHHuJvf/sbK1asoKSkhMsvv5ynn36at956iwULFvDFF1/w7LPPtnvNa6+9Rnx8PKtXr+b222/n5ptv5rLLLmPq1KmsX7+eWbNmce211wYLHFVVSU9P57333mP79u088MAD3Hvvvbz77rsntO3HS9E0TevWd+hmx3uZaNH3aKrK8zddR2tjA5f9/jEyR4zWO5IQQgcul4vCwkKys7Ox2WzBx5+76asOXzNgRBwX3HboM+OFXyzB51GP2jY1L5of3zUueP9/f70MV/ORfxzd+vyZncrd1NREXFwcb731Fj/5yU8AaGxsJDU1lRtuuIGnn376iNesXbuWiRMn0tTURHh4OEuWLGHGjBl8+eWXnHXWWQDMnz+fe+65hz179pCTkwPATTfdRFFREZ9//jkQ6FHx+/0sW7YMCPSWREVFcckll/D6668DgcvZpKSksHLlSiZPnnzUbbjtttuoqKjg/fffP+rzHX1v4Ph/f0uPiui1FIOB7DGBXpW9PXD4R1VP7C8mIYQ4mr179+L1ejnllFOCj0VFRTF48ODg/XXr1nHhhReSmZlJREQE06ZNA6C4uLjdukaNGhX8OikpCYfDESxSDj52+CGj77/GaDQSFxfHyJEj270GaPe65557jvHjx5OQkEB4eDgvvvjiEVm6mlzyVfRq2WMnsG3plxSuX8P0a+d263t98fxfqSsv5bSfXie9N0L0Ajc+M63D55Tv/Zn+8ydP77jt9ya/vu6xnhlI39LSwuzZs5k9ezZvvvkmCQkJFBcXM3v2bDweT7u2ZrM5+LWiKO3uH3zs4MzwR3vN0V53cNbvg697++23+fWvf82f/vQnpkyZQkREBE8++SSrVq06+Y09BilURK82YNQYRp45i+xxE7t1On2/z0fB2u9wt7RgMOo32ZwQ4viZrcf/s9pdbY8lJycHs9nMmjVryMwMDM5vbGxk165dnHHGGezcuZPa2lrmz59PRkYGEDj0o5fly5czdepUbrnlluBje/bs6fb3lUJF9Gq2sHBmzftFt79PybbNuFtacERFkzp4aLe/nxCi74uIiGDOnDn85je/ITY2lsTERB588EEMBgOKopCZmYnFYuHZZ5/lpptuYuvWrTzyyCO65c3Ly+P1119n4cKFZGdn88Ybb7BmzRqys7O79X1ljIoQx2H36hUADJwwWdfp+4UQfcuf//xnpkyZwgUXXMDMmTM59dRTGTp0KDabjYSEBF599VXee+89hg0bxvz583nqqad0yzpv3jwuueQSrrjiCiZNmkRtbW273pXuImf9iF5P0zQqCnaxd8NaTrnoUsxW2w+/qBNU1c8LN82htbGBS+/5A1ljxnfp+oUQJ+dYZ5b0Ni0tLaSlpfGnP/2JuXO7d9xdT+iKs37k0I/oE/779HyaaqpJyRtEztiJXbru8l07aW1swBoWRsaIUT/8AiGEOE4bNmxg586dnHLKKTQ2NgYvzHvRRRfpnCx0yKEf0espikLOgcnf9q7v+oFmu1cFDvvkjjsFo8n8A62FEKJznnrqKUaPHs3MmTNpaWlh2bJlxMf37MVWQ5n0qIg+IWfcKWxa9Bm7vvuW6df9DyZz1xUUueMnUVdeSt7k07psnUIIATB27FjWreu565X1RlKoiD4ha/Q4wuPiaa6tYdd33zLs9Bldtu7MEaPIlEM+QgihCzn0I/oEg9HI6LPOAWDjwk90TiOEEKKrSKEi+oyRZ83GYDSxf3c+lXsLTnp9pTu2suxfr9FUW9MF6YQQQpwIKVREnxEWHcOgyafiiIrGWVt90utb899/s/qj91j10XtdkE4IIcSJkDEqok+Zcf2NWB2Okz47p35/GXvXrwFg3LkXdkU0IYQQJ0AKFdGnOCKjumQ9Gz7/BDSN7LETiE1N75J1CiGE6Dw59CP6JFX1U7hxHdr3rhZ6PFwtzWz9ehEA486TSZeEEEJPUqiIPkfTNN68907+/fiDFG1a3+nXb/16EV63i7j0TAaMHNP1AYUQogtkZWXx9NNP6x2j20mhIvocRVHIGDYCgA2dPFVZ9fvZ8Pl/gUBviqIoXZ5PCCHE8ZNCRfRJo88+D4DCjeuo3ld43K9TFIXh02Zij4xi6OnTuymdEEJAUVERiqIcsUyfPh2Ab7/9ltNPPx273U5GRga/+MUvaGlpAWD69Ons27ePX/3qV8HXAdTW1nLllVeSlpaGw+Fg5MiR/Otf/9JrE7uEFCqiT4pJSSN3wmTQND5+6lFanY3H9TrFYGDqZVdx7f97BrPF2s0phRDdyetydbj4PJ7jbuv1uI+rbWdlZGSwf//+4LJhwwbi4uI444wz2LNnD+eccw6XXnopmzdv5p133uHbb7/ltttuA+Df//436enpPPzww8HXQ+BqxePHj2fBggVs3bqVG2+8kWuvvZbVq1ef4F7Un6JpmqZ3iJNxvJeJFv1Pq7ORt+6/i8bKCtKGDOcn9z/a4TWAnDXV2CMjpTgRohdyuVwUFhaSnZ2NzWYLPv6nKy7o8DXZYydwyd0PBe8/c92l+Nzuo7ZNHzaCKx6cH7z/9/+5irYm5xHt7nrnxGfFdrlcTJ8+nYSEBD7++GNuvPFGjEYjL7zwQrDNt99+y7Rp02hpacFms5GVlcUdd9zBHXfcccx1X3DBBQwZMoSnnnrqhPOdqI6+N3D8v7+lR0X0WY7IKH782wew2B2U7dzG8nfeOGo7T1sr/378Qd5+4Lc4a05+ojghhOisn//85zQ1NfHWW29hMBjYtGkTr776KuHh4cFl9uzZqKpKYWHHh7P9fj+PPPIII0eOJDY2lvDwcBYuXEhxcXEPbk3XknlURJ8Wl57JBXf8jlUfvsOEC358xPOaqvLZc3+htrSY8JhYjCb5kRCir/jFa+93+JxiaP93+i0vvtnxigztB9Xf8LeXTyrX9z366KMsXLiQ1atXExERAUBzczPz5s3jF7/4xRHtMzMzO1zXk08+yTPPPMPTTz/NyJEjCQsL44477sDzvUNdvYl8Kos+L3vMeLJGjwsONtvw+X8p3bkdT1srrY0NVBXuwWgyceGd9xIWHaNzWiFEVzF/71CDHm1/yAcffMDDDz/MZ599Rm5ubvDxcePGsX37dgYOHNjhay0WC36/v91jy5cv56KLLuKaa64BQFVVdu3axbBhw7osc0+TQz+iXzj8NOP9u/PZtXIZRRvXUVW4B4Azf34zqYOG6BVPCNEPbd26leuuu47f/e53DB8+nIqKCioqKqirq+N3v/sdK1as4LbbbmPjxo3s3r2bjz/+ODiYFgLzqHzzzTeUlZVRUxO4eGpeXh6LFi1ixYoV7Nixg3nz5lFZWanXJnYJ6VER/c7Q06aTPHAwVocDi81OTGoa8RkD9I4lhOhn1q5dS2trK48++iiPPvpo8PFp06axZMkSli5dyn333cfpp5+Opmnk5uZyxRVXBNs9/PDDzJs3j9zcXNxuN5qmcf/997N3715mz56Nw+Hgxhtv5OKLL6ax8fjOfAxFctaPEEKIXu1YZ5YIfclZP0IIIYTo06RQEUIIIUTIkkJFCCGEECFLChUhhBBChCwpVIQQQggRsqRQEUII0Seoqqp3BPE9XfE9kXlUhBBC9GoWiwWDwUB5eTkJCQlYLJZ2kzyKnqdpGh6Ph+rqagwGAxaL5YTXJYWKEEKIXs1gMJCdnc3+/fspLy/XO444jMPhIDMzE4PhxA/gSKEihBCi17NYLGRmZuLz+Y64/o3Qh9FoxGQynXTvlhQqQggh+gRFUTCbzZjNZr2jiC4kg2mFEEIIEbKkUBFCCCFEyJJCRQghhBAhq9ePUTl48Wen06lzEiGEEEIcr4O/tw/+Hu9Iry9UmpqaAMjIyNA5iRBCCCE6q6mpiaioqA6fV7QfKmVCnKqqlJeXExER0eUT/DidTjIyMigpKSEyMrJL1y0Okf3cM2Q/9wzZzz1D9nPP6M79rGkaTU1NpKamHnOelV7fo2IwGEhPT+/W94iMjJQfhB4g+7lnyH7uGbKfe4bs557RXfv5WD0pB8lgWiGEEEKELClUhBBCCBGypFA5BqvVyoMPPojVatU7Sp8m+7lnyH7uGbKfe4bs554RCvu51w+mFUIIIUTfJT0qQgghhAhZUqgIIYQQImRJoSKEEEKIkCWFihBCCCFCVp8uVJ577jmysrKw2WxMmjSJ1atXH7P9e++9x5AhQ7DZbIwcOZJPP/203fOapvHAAw+QkpKC3W5n5syZ7N69u12buro6rr76aiIjI4mOjmbu3Lk0Nzd3+baFkp7ez0VFRcydO5fs7Gzsdju5ubk8+OCDeDyebtm+UKHH/+eD3G43Y8aMQVEUNm7c2FWbFJL02s8LFixg0qRJ2O12YmJiuPjii7tys0KOHvt5165dXHTRRcTHxxMZGclpp53G119/3eXbFmq6el//+9//ZtasWcTFxXX4meByubj11luJi4sjPDycSy+9lMrKyhPbAK2PevvttzWLxaK9/PLL2rZt27QbbrhBi46O1iorK4/afvny5ZrRaNSeeOIJbfv27dr999+vmc1mbcuWLcE28+fP16KiorSPPvpI27Rpk/ajH/1Iy87O1tra2oJtzjnnHG306NHad999py1btkwbOHCgduWVV3b79upFj/382Wefaddff722cOFCbc+ePdrHH3+sJSYmanfddVePbLMe9Pr/fNAvfvEL7dxzz9UAbcOGDd21mbrTaz+///77WkxMjPaPf/xDy8/P17Zt26a988473b69etFrP+fl5WnnnXeetmnTJm3Xrl3aLbfcojkcDm3//v3dvs166Y59/frrr2t/+MMftJdeeqnDz4SbbrpJy8jI0BYvXqytXbtWmzx5sjZ16tQT2oY+W6iccsop2q233hq87/f7tdTUVO3xxx8/avvLL79cO//889s9NmnSJG3evHmapmmaqqpacnKy9uSTTwafb2ho0KxWq/avf/1L0zRN2759uwZoa9asCbb57LPPNEVRtLKysi7btlCix34+mieeeELLzs4+mU0JaXru508//VQbMmSItm3btj5fqOixn71er5aWlqb985//7OrNCVl67Ofq6moN0L755ptgG6fTqQHaokWLumzbQk1X7+vDFRYWHvUzoaGhQTObzdp7770XfGzHjh0aoK1cubLT29AnD/14PB7WrVvHzJkzg48ZDAZmzpzJypUrj/qalStXtmsPMHv27GD7wsJCKioq2rWJiopi0qRJwTYrV64kOjqaCRMmBNvMnDkTg8HAqlWrumz7QoVe+/loGhsbiY2NPZnNCVl67ufKykpuuOEG3njjDRwOR1duVsjRaz+vX7+esrIyDAYDY8eOJSUlhXPPPZetW7d29SaGBL32c1xcHIMHD+b111+npaUFn8/HCy+8QGJiIuPHj+/qzQwJ3bGvj8e6devwer3t1jNkyBAyMzM7tZ5g5k6/oheoqanB7/eTlJTU7vGkpCQqKiqO+pqKiopjtj94+0NtEhMT2z1vMpmIjY3t8H17M7328/cVFBTw7LPPMm/evBPajlCn137WNI3rr7+em266qV3x3VfptZ/37t0LwEMPPcT999/PJ598QkxMDNOnT6euru7kNyzE6LWfFUXhyy+/ZMOGDURERGCz2fjzn//M559/TkxMTJdsW6jpjn19PCoqKrBYLERHR5/Ueg7qk4WK6D/Kyso455xzuOyyy7jhhhv0jtOnPPvsszQ1NXHPPffoHaVPU1UVgPvuu49LL72U8ePH88orr6AoCu+9957O6foOTdO49dZbSUxMZNmyZaxevZqLL76YCy+8kP379+sdTxxDnyxU4uPjMRqNR4wwrqysJDk5+aivSU5OPmb7g7c/1Kaqqqrd8z6fj7q6ug7ftzfTaz8fVF5ezowZM5g6dSovvvjiSW1LKNNrP3/11VesXLkSq9WKyWRi4MCBAEyYMIE5c+ac/IaFGL32c0pKCgDDhg0LPm+1WsnJyaG4uPgktig06fn/+ZNPPuHtt9/m1FNPZdy4cfz973/Hbrfz2muvdcm2hZru2NfHIzk5GY/HQ0NDw0mt56A+WahYLBbGjx/P4sWLg4+pqsrixYuZMmXKUV8zZcqUdu0BFi1aFGyfnZ1NcnJyuzZOp5NVq1YF20yZMoWGhgbWrVsXbPPVV1+hqiqTJk3qsu0LFXrtZwj0pEyfPj3416fB0Cf/KwP67ee//vWvbNq0iY0bN7Jx48bgKYrvvPMOjz32WJduYyjQaz+PHz8eq9VKfn5+sI3X66WoqIgBAwZ02faFCr32c2trK8ARnxUGgyHYq9XXdMe+Ph7jx4/HbDa3W09+fj7FxcWdWk9Qp4ff9hJvv/22ZrVatVdffVXbvn27duONN2rR0dFaRUWFpmmadu2112p33313sP3y5cs1k8mkPfXUU9qOHTu0Bx988Kinv0VHR2sff/yxtnnzZu2iiy466unJY8eO1VatWqV9++23Wl5eXp8/Pbmn93Npaak2cOBA7ayzztJKS0u1/fv3B5e+Sq//z4fraIR/X6LXfv7lL3+ppaWlaQsXLtR27typzZ07V0tMTNTq6up6buN7kB77ubq6WouLi9MuueQSbePGjVp+fr7261//WjObzdrGjRt7dgf0oO7Y17W1tdqGDRu0BQsWaID29ttvaxs2bGj3GXzTTTdpmZmZ2ldffaWtXbtWmzJlijZlypQT2oY+W6homqY9++yzWmZmpmaxWLRTTjlF++6774LPTZs2TZszZ0679u+++642aNAgzWKxaMOHD9cWLFjQ7nlVVbXf//73WlJSkma1WrWzzjpLy8/Pb9emtrZWu/LKK7Xw8HAtMjJS+9nPfqY1NTV12zaGgp7ez6+88ooGHHXpy/T4/3y4/lCoaJo++9nj8Wh33XWXlpiYqEVERGgzZ87Utm7d2m3bGAr02M9r1qzRZs2apcXGxmoRERHa5MmTtU8//bTbtjFUdPW+7ugz+MEHHwy2aWtr02655RYtJiZGczgc2o9//OMT/mNS0TRN63w/jBBCCCFE9+u7B/aFEEII0etJoSKEEEKIkCWFihBCCCFClhQqQgghhAhZUqgIIYQQImRJoSKEEEKIkCWFihBCCCFClhQqQgghhAhZUqgIIYQQImRJoSKEEEKIkCWFihBCCCFClhQqQgghhAhZ/x9EHUO2uYOiWgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# check the schedules\n",
    "csym.plot_schedules()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... or the spectrum of the system hamiltonian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "csym.plot_spectrum(use_H0=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to access to the hamiltonian as function of time, use the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-3.9 +0.j        ,  0.  +0.08371406j,  0.  +0.16748091j, ...,\n",
       "         0.  +0.j        ,  0.  +0.j        ,  0.  +0.j        ],\n",
       "       [ 0.  -0.08371406j, -1.94+0.j        ,  0.  +0.j        , ...,\n",
       "         0.  +0.j        ,  0.  +0.j        ,  0.  +0.j        ],\n",
       "       [ 0.  -0.16748091j,  0.  +0.j        ,  0.06+0.j        , ...,\n",
       "         0.  +0.j        ,  0.  +0.j        ,  0.  +0.j        ],\n",
       "       ...,\n",
       "       [ 0.  +0.j        ,  0.  +0.j        ,  0.  +0.j        , ...,\n",
       "        -0.06+0.j        ,  0.  +0.j        ,  0.  -0.16758649j],\n",
       "       [ 0.  +0.j        ,  0.  +0.j        ,  0.  +0.j        , ...,\n",
       "         0.  +0.j        , -2.06+0.j        ,  0.  -0.08381964j],\n",
       "       [ 0.  +0.j        ,  0.  +0.j        ,  0.  +0.j        , ...,\n",
       "         0.  +0.16758649j,  0.  +0.08381964j, -4.1 +0.j        ]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H_t = csym.make_timedependent_hamiltonian()\n",
    "\n",
    "H_t(0.0) # let's print it"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Annealing simulation\n",
    "\n",
    "Before using the optimization of the schedule provided by the colder package, let us test the performances of annealing schedules for the Ising model **without any optimization**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import colder.simulation.annealing\n",
    "import colder.quantum.math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `annealing` module provides the tools to simulate any time evolution given an hamiltonian which is function of time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "ann = colder.simulation.annealing.annealing(tau, P = nsteps, backend = backend)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also, we need the initial state of the time evolution and the final groundstate to evaluate the fidelity.\n",
    "\n",
    "In this work, we get the initial state as the ground state of the system hamiltonian at time zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# computing initial state and true ground state\n",
    "psi0 = csym.get_psi_zero()\n",
    "truegs = csym.get_psi_final()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### standard annealing schedule\n",
    "\n",
    "What happens if one simulates the annealing without any form of optimization? In order to do so, we can get the timedependent hamiltonian without any gauge potential using the method \n",
    "```python\n",
    "    H0 = csym.make_timedependent_hamiltonian_nogauge()\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "H0 = csym.make_timedependent_hamiltonian_nogauge()\n",
    "psi_bare = ann.run(H0, psi0=psi0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The method `run` of the annealing object will run the time evolution as specified in the construction of the annealing object itself. The initial state of the evolution is prompted through the `psi0` argument. The method returns the final evolved state, which we can finally use to compute the fidelity wrt the true ground state of $\\mathcal{H}$ at time $\\tau$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03855172461180932"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "colder.quantum.math.fidelity(psi_bare, truegs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the fidelity is not optimal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### LCD annealing\n",
    "\n",
    "What happens if we use Local Counterdiabatic Driving? We can test this running another simulation using the hamiltonian which includes the AGP terms. We have already computed it in `H_t`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.21910167164306396"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "psi = ann.run(H_t, psi0=psi0)\n",
    "colder.quantum.math.fidelity(psi, truegs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, the fidelity improves. But can we do better?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## COLD optimization\n",
    "\n",
    "In this section we will run a COLD optimization. The first step is to **define a loss function**.\n",
    "By default, the loss function must take as input two arguments:\n",
    "- the final evolved state `psi`\n",
    "- the QOC parameters `param` (in this case it is the $\\beta$ of QOC function)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss_infidelity(psi, param):\n",
    "    infidelity = 1 - colder.quantum.math.fidelity(psi, truegs)\n",
    "    print( f'beta = {param}, infidelity = {infidelity}') #add this just to print the progress\n",
    "    return infidelity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The optimization can be achieved using the suggested Powell method through the `run_cold_opti()` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "beta = [0.94499884], infidelity = 0.11119912677783805\n",
      "beta = [0.94499884], infidelity = 0.11119912677783805\n",
      "beta = [1.94499884], infidelity = 0.03895332700879728\n",
      "beta = [3.56303284], infidelity = 0.0034577432633339233\n",
      "beta = [3.32482657], infidelity = 0.004993275223888927\n",
      "beta = [6.18106687], infidelity = 0.00020971002698566554\n",
      "beta = [4.99901195], infidelity = 0.0005463580679356816\n",
      "beta = [10.41713493], infidelity = 0.00011270341733615741\n",
      "beta = [8.36354825], infidelity = 0.00010861290542785174\n",
      "beta = [7.52991457], infidelity = 0.00012272044717931418\n",
      "beta = [9.14794854], infidelity = 0.00010584888082743049\n",
      "beta = [8.96850481], infidelity = 0.00010586822988156719\n",
      "beta = [9.22997804], infidelity = 0.00010593985763018843\n",
      "beta = [9.06591904], infidelity = 0.000105819284546671\n",
      "beta = [17.18683925], infidelity = 0.00024858181345366326\n",
      "beta = [9.06591904], infidelity = 0.000105819284546671\n",
      "beta = [17.18683925], infidelity = 0.00024858181345366326\n",
      "beta = [-4.07400595], infidelity = 0.9999999999107015\n",
      "beta = [4.04691445], infidelity = 0.0017171569541529763\n",
      "beta = [12.16783445], infidelity = 0.00013519968435082852\n",
      "beta = [10.50051597], infidelity = 0.0001134876925632522\n",
      "beta = [8.70328363], infidelity = 0.00010651063211875034\n",
      "beta = [9.12084221], infidelity = 0.00010583216105986004\n",
      "beta = [9.07051759], infidelity = 0.00010581926679820164\n",
      "beta = [9.06862584], infidelity = 0.0001058192495785315\n",
      "beta = [9.06859878], infidelity = 0.00010581924960473277\n",
      "beta = [9.06870453], infidelity = 0.00010581924963071199\n",
      "beta = [9.0686559], infidelity = 0.00010581924958330546\n",
      "beta = [9.06862584], infidelity = 0.0001058192495785315\n",
      "beta = [9.07133264], infidelity = 0.00010581928473507585\n",
      "beta = [9.06424615], infidelity = 0.00010581934127162906\n",
      "beta = [9.06695295], infidelity = 0.00010581926292552168\n",
      "beta = [9.06965975], infidelity = 0.00010581925475472431\n",
      "beta = [9.06862098], infidelity = 0.00010581924957864253\n",
      "beta = [9.06862577], infidelity = 0.00010581924957342448\n",
      "beta = [9.06862341], infidelity = 0.00010581924959773836\n",
      "beta = [9.06862487], infidelity = 0.00010581924958041888\n",
      "beta = [9.06862542], infidelity = 0.00010581924958041888\n",
      "beta = [9.06862564], infidelity = 0.00010581924957420163\n",
      "beta = [9.06862571], infidelity = 0.00010581924957830946\n",
      "beta = [9.0686258], infidelity = 0.00010581924959685018\n",
      "beta = [9.06862575], infidelity = 0.00010581924957708821\n",
      "beta = [9.06862578], infidelity = 0.00010581924957442368\n",
      "beta = [9.06862576], infidelity = 0.00010581924957442368\n",
      "beta = [9.06862577], infidelity = 0.00010581924957819844\n",
      "beta = [9.06862576], infidelity = 0.00010581924958363853\n",
      "beta = [9.06862577], infidelity = 0.00010581924957486777\n",
      "beta = [9.06862577], infidelity = 0.00010581924957131505\n",
      "beta = [9.06862577], infidelity = 0.00010581924957675515\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 0.000106\n",
      "         Iterations: 2\n",
      "         Function evaluations: 49\n"
     ]
    }
   ],
   "source": [
    "x0 = np.random.uniform(size=Nk) # initial guess of parameters\n",
    "\n",
    "optim = csym.run_cold_opti(init_parameters = x0,\n",
    "    loss_function = loss_infidelity, psi0 = psi0, annealer_nsteps=nsteps, \n",
    "    options={'disp': True} # options for the scipy.optimizer function\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After the convergence of the optimizer, the simulation object is updated with the optimal parameters by default. We clearly see that the fidelity is improved by orders of magnitude, in this example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum loss value 0.00010581924957131505 with beta = [9.06862577]\n",
      "fidelity = 0.9998941807504287\n"
     ]
    }
   ],
   "source": [
    "optim_beta = optim.x\n",
    "optim_f = optim.fun\n",
    "print('minimum loss value {} with beta = {}'.format(optim_f, optim_beta))\n",
    "print('fidelity =', 1-optim_f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br><br>\n",
    "\n",
    "### Run manually the optimization using any other tool\n",
    "\n",
    "The *colder* package allows to fetch the function to be optimized and run the optimization using any other tool. \n",
    "In this section we will fetch the optimization function and run inference-based methods to optimize it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "f0_min = csym.make_cold_optimization_function(loss_function = loss_infidelity, psi0 = psi0, annealer_nsteps=nsteps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a first example, we use **Gaussian minimization** from skopt. \n",
    "\n",
    "Ref: https://scikit-optimize.github.io/stable/modules/generated/skopt.gp_minimize.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "beta = [-0.04672667054701307], infidelity = 0.8229494216018249\n",
      "beta = [6.356768822331393], infidelity = 0.00018972820224072429\n",
      "beta = [2.2422378935454184], infidelity = 0.026648192864348497\n",
      "beta = [5.427198377248024], infidelity = 0.00036405017849427956\n",
      "beta = [7.213395427553749], infidelity = 0.0001332139248541031\n",
      "beta = [3.4718773539291377], infidelity = 0.003973977638242365\n",
      "beta = [-10.0], infidelity = 0.9999999999962738\n",
      "beta = [10.0], infidelity = 0.00010932109388406275\n",
      "beta = [8.839526027316534], infidelity = 0.00010608295523817368\n",
      "beta = [2.8646982460803123], infidelity = 0.010380964211278099\n",
      "beta = [4.514514514759366], infidelity = 0.0009391913870580026\n",
      "beta = [8.065330742783164], infidelity = 0.00011193835583500622\n",
      "beta = [9.514293592793056], infidelity = 0.00010669097404480965\n",
      "beta = [-6.308661586303132], infidelity = 0.9999999999943713\n",
      "beta = [4.022286435017344], infidelity = 0.0017763121942927507\n"
     ]
    }
   ],
   "source": [
    "from skopt import gp_minimize\n",
    "\n",
    "skres = gp_minimize(f0_min,           # the function to minimize\n",
    "                  [(-10.0, 10.0)],    # bounds on each dimension of x\n",
    "                  acq_func=\"EI\",      # acquisition function\n",
    "                  n_calls=15,         # number of evaluations of f\n",
    "                  n_random_starts=5,  # number of random initialization points\n",
    "                  random_state=1234   # random seed\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "infidelity 0.00010608295523817368 with beta = [8.839526027316534]\n"
     ]
    }
   ],
   "source": [
    "print('infidelity {} with beta = {}'.format(skres.fun, skres.x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As last example, we use the **bayes_opt** package.\n",
    "\n",
    "Ref: https://github.com/bayesian-optimization/BayesianOptimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|   iter    |  target   |     x     |\n",
      "-------------------------------------\n",
      "| \u001b[0m1        \u001b[0m | \u001b[0m2.004e-05\u001b[0m | \u001b[0m-1.66    \u001b[0m |\n",
      "| \u001b[95m2        \u001b[0m | \u001b[95m0.9989   \u001b[0m | \u001b[95m4.406    \u001b[0m |\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "| \u001b[0m3        \u001b[0m | \u001b[0m3.726e-12\u001b[0m | \u001b[0m-9.998   \u001b[0m |\n",
      "| \u001b[95m4        \u001b[0m | \u001b[95m0.9991   \u001b[0m | \u001b[95m4.566    \u001b[0m |\n",
      "| \u001b[95m5        \u001b[0m | \u001b[95m0.9999   \u001b[0m | \u001b[95m10.0     \u001b[0m |\n",
      "| \u001b[0m6        \u001b[0m | \u001b[0m0.9999   \u001b[0m | \u001b[0m7.869    \u001b[0m |\n",
      "| \u001b[95m7        \u001b[0m | \u001b[95m0.9999   \u001b[0m | \u001b[95m9.01     \u001b[0m |\n",
      "| \u001b[0m8        \u001b[0m | \u001b[0m0.9998   \u001b[0m | \u001b[0m6.384    \u001b[0m |\n",
      "| \u001b[0m9        \u001b[0m | \u001b[0m0.9999   \u001b[0m | \u001b[0m7.096    \u001b[0m |\n",
      "| \u001b[0m10       \u001b[0m | \u001b[0m0.9997   \u001b[0m | \u001b[0m5.535    \u001b[0m |\n",
      "| \u001b[0m11       \u001b[0m | \u001b[0m0.9999   \u001b[0m | \u001b[0m9.569    \u001b[0m |\n",
      "| \u001b[0m12       \u001b[0m | \u001b[0m0.9999   \u001b[0m | \u001b[0m8.428    \u001b[0m |\n",
      "| \u001b[0m13       \u001b[0m | \u001b[0m0.9998   \u001b[0m | \u001b[0m5.96     \u001b[0m |\n",
      "| \u001b[0m14       \u001b[0m | \u001b[0m0.9995   \u001b[0m | \u001b[0m5.031    \u001b[0m |\n",
      "| \u001b[0m15       \u001b[0m | \u001b[0m0.9999   \u001b[0m | \u001b[0m7.482    \u001b[0m |\n",
      "| \u001b[0m16       \u001b[0m | \u001b[0m0.9998   \u001b[0m | \u001b[0m6.747    \u001b[0m |\n",
      "| \u001b[0m17       \u001b[0m | \u001b[0m0.9999   \u001b[0m | \u001b[0m8.718    \u001b[0m |\n",
      "| \u001b[0m18       \u001b[0m | \u001b[0m0.9999   \u001b[0m | \u001b[0m9.283    \u001b[0m |\n",
      "| \u001b[0m19       \u001b[0m | \u001b[0m0.9999   \u001b[0m | \u001b[0m8.147    \u001b[0m |\n",
      "| \u001b[0m20       \u001b[0m | \u001b[0m0.9999   \u001b[0m | \u001b[0m9.774    \u001b[0m |\n",
      "| \u001b[0m21       \u001b[0m | \u001b[0m0.9999   \u001b[0m | \u001b[0m9.996    \u001b[0m |\n",
      "| \u001b[0m22       \u001b[0m | \u001b[0m0.9999   \u001b[0m | \u001b[0m7.666    \u001b[0m |\n",
      "| \u001b[0m23       \u001b[0m | \u001b[0m0.9999   \u001b[0m | \u001b[0m7.265    \u001b[0m |\n",
      "| \u001b[0m24       \u001b[0m | \u001b[0m0.9998   \u001b[0m | \u001b[0m6.197    \u001b[0m |\n",
      "| \u001b[0m25       \u001b[0m | \u001b[0m0.9999   \u001b[0m | \u001b[0m8.838    \u001b[0m |\n",
      "| \u001b[0m26       \u001b[0m | \u001b[0m0.9999   \u001b[0m | \u001b[0m6.872    \u001b[0m |\n",
      "| \u001b[0m27       \u001b[0m | \u001b[0m0.9999   \u001b[0m | \u001b[0m9.345    \u001b[0m |\n",
      "| \u001b[0m28       \u001b[0m | \u001b[0m0.9999   \u001b[0m | \u001b[0m8.34     \u001b[0m |\n",
      "=====================================\n"
     ]
    }
   ],
   "source": [
    "from bayes_opt import BayesianOptimization\n",
    "\n",
    "\n",
    "# this module likes to maximize functions, so we change the loss function!\n",
    "def loss_fidelity(psi, param):\n",
    "    return colder.quantum.math.fidelity(psi, truegs)\n",
    "\n",
    "f0_max = csym.make_cold_optimization_function(loss_function = loss_fidelity, psi0 = psi0, annealer_nsteps=nsteps)\n",
    "\n",
    "\n",
    "optimizer = BayesianOptimization(\n",
    "    f = lambda x: f0_max(np.array([x])), # fix: this module does not input parameters as numpy array, so we force it...\n",
    "    pbounds = {'x': (-10, 10)},\n",
    "    random_state = 1, allow_duplicate_points=True\n",
    ")\n",
    "\n",
    "optimizer.maximize(\n",
    "    init_points=3,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "infidelity 0.00010583602466351927 with beta = {'x': 9.009775723653998}\n"
     ]
    }
   ],
   "source": [
    "print('infidelity {} with beta = {}'.format(1-optimizer.max['target'], optimizer.max['params']))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}