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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Annealing Algorithm Evaluation and OpenJij Benchmarking Capabilities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the annealing algorithm is a heuristic algorithm, it cannot always produce the optimal solution every single time.\n",
    "Also, since it is a stochastic algorithm, solutions will differ each time. Therefore, when evaluating an algorithm, various kinds of averages are used to evaluate its solution. Commonly used metrics are:\n",
    "\n",
    "- Time-to-solution (TTS)\n",
    "- Success probability\n",
    "- Residual energy\n",
    "\n",
    "TTS is the computation time it takes to obtain an optimal solution with a certain probability, and this is often used in various evaluations.\n",
    "Success probability is the probability that the optimal solution was obtained.\n",
    "Residual energy is an average value that indicates how close the obtained solution was to the optimal solution.\n",
    "\n",
    "In this note, we discuss the above three evaluation metrics and their measurement methods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time-to-solution\n",
    "Annealing algorithms can produce a solution with any computation time.\n",
    "For example, in simulated annealing, the computation varies by how fast the temperature is varied.\n",
    "However, it is meaningless if the solution is wrong even under fast computation.\n",
    "Therefore, the computation time until the optimal solution is calculated with the required probability (e.g. the time to obtain the optimal solution with a 90% probability) is set as a metric.\n",
    "\n",
    "As we covered in [Introduction to OpenJij](https://openjij.github.io/OpenJij/tutorial/en/000-intro_optimization_and_Ising.html), annealing algorithms search for the optimal solution among multiple runs, so it is necessary to take those multiple runs into account when evaluating the computation time.\n",
    "\n",
    "> For example, even if a short computation time $\\tau_{\\mathrm{short}}$ returns a low probability of finding an optimal solution, annealing multiple times with that computation time $\\tau_{short}$ may require less computation time and still perform as well as the one with a longer computation time $\\tau_{\\mathrm{long}}$.\n",
    "> Therefore, when evaluating the computation time, simply comparing annealing times may not be sufficient.\n",
    "\n",
    "TTS is the amount of time required for the above calculation, taking into account that annealing is performed multiple times.\n",
    "It can be derived as follows."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $p_s(\\tau)$ be the probability that the optimal solution is calculated in one annealing time $\\tau$.\n",
    "This $p_s(\\tau)$ is the success probability, another metric to evaluate the algorithm.\n",
    "The probability of the optimal solution not being calculated in one annealing is:\n",
    "\n",
    "$$1-p_s(\\tau)$$\n",
    "\n",
    "Let us repeat this $R$ times.\n",
    "Then, the probability that the optimal solution is not calculated in all these $R$ times is:\n",
    "\n",
    "$$\\{ 1-p_s(\\tau)\\}^R$$\n",
    "\n",
    "Hence, $p_R$, the probability of obtaining an optimal solution at least once out of $R$ times can be obtained as follows:\n",
    "\n",
    "$$p_R = 1-\\{ 1-p_s(\\tau)\\}^R$$\n",
    "\n",
    "Solving this equation for $R$ yields:\n",
    "\n",
    "$$R = \\frac{\\ln(1-p_R)}{\\ln\\{1-p_s(\\tau)\\}}$$\n",
    "\n",
    "Multiplying this by a single computation time $\\tau$ leads to the total computation time.\n",
    "Here we derived the TTS, the computation time required to obtain a solution.\n",
    "\n",
    "$${\\rm TTS}(\\tau, p_R) = \\tau R = \\tau \\frac{\\ln(1-p_R)}{\\ln\\{1-p_s(\\tau)\\}}$$\n",
    "\n",
    "${\\rm TTS}(\\tau, p_R)$ is the total computation time, which takes into account the number of iterations until an optimal solution is obtained with probability $p_R$ when one annealing takes $\\tau$ computation time and an optimal solution is obtained with probability $p_s(\\tau)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$p_R$ is given as a constant when evaluating actual problems.\n",
    "$p_R=0.99$ is often used for research and other purposes.\n",
    "$p_s(\\tau)$ is calculated for various annealing times $\\tau$, and then ${\\rm TTS}(\\tau, p_R)$ is derived.\n",
    "\n",
    "In real problems, there are many cases where the optimal solution is not known.\n",
    "In such cases, the **Time to Feasible Solution** is used.\n",
    "This is calculated with the probability of obtaining a feasible solution instead of the probability of obtaining an optimal solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Success Probability\n",
    "The success probability simply calculates the probability of obtaining the optimal solution.\n",
    "Assuming that the optimal solution is obtained $n$ times when annealing is repeated $R$ times, the success probability $p_s$ is:\n",
    "\n",
    "$$p_s = \\frac{n}{R}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Residual Energy\n",
    "Instead of time, as in TTS, an **approximation ratio** is another metric used for evaluation.\n",
    "This is a metric that expresses how much cost was reduced compared to the optimal solution.\n",
    "The approximate ratio is calculated as follows:\n",
    "\n",
    "$$\n",
    "r = \\langle E \\rangle / E_{\\min}\n",
    "$$\n",
    "\n",
    "In physics, **residual energy**, the difference between the average energy and the optimal value, is also used for evaluation.\n",
    "\n",
    "$$\n",
    "E_{\\text{res}} = \\langle E \\rangle - E_{\\min}\n",
    "$$\n",
    "In many cases, the cost value of the problem is proportional to the number of variables $N$.\n",
    "Therefore, we can normalize the energy by size as in $(\\langle E \\rangle - E_{\\min})/N$.\n",
    "Another method is to normalize by the optimal value $E_{\\min}$, as in $(\\langle E \\rangle - E_{\\min})/|E_{\\min}|$.\n",
    "\n",
    "Since the annealing algorithm is an algorithm with an asymptotic convergence to the optimal solution, in most cases the residual energy decreases as the annealing time increases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Experiments and Calculations of Evaluation Metrics with 1D Antiferromagnetic Ising Model\n",
    "\n",
    "Let us calculate these evaluation metrics using OpenJij.  \n",
    "In the following, we consider the 1D antiferromagnetic Ising model.\n",
    "Antiferromagnetic is a magnetism that aligns with neighboring spins pointing in opposite directions.\n",
    "This is a model represented by the following Hamiltonian:\n",
    "\n",
    "$$H(\\{\\sigma_i\\}) = \\sum_{i=0}^{N-1} J_{i, i+1}\\sigma_i \\sigma_{i+1} + \\sum_{i=0}^{N-1} h_i \\sigma_i$$\n",
    "\n",
    "Here we set $J_{i, i+1}=1$, $h_0 = -10$, and the other longitudinal magnetic fields to be 0.\n",
    "From $J_{ij} > 0$ (antiferromagnetism), each spin is oriented differently to have lower energy.\n",
    "Also from $h_0=-1$, we know that the 0th spin has $\\sigma_0 =1$.\n",
    "Therefore, the optimal solution $\\{\\sigma_i\\}$ is $1, -1, 1, -1, -1, \\cdots$, with the first one being 1 and the values alternating.\n",
    "\n",
    "In other words, to find the TTS for this problem is to calculate the total computation time to obtain $1, -1, 1, \\cdots$.\n",
    "We solve the Ising model above and see how the TTS and the success probability change with increasing the time per calculation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import openjij as oj "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create an 1D antiferromagnetic Ising model\n",
    "N = 30\n",
    "h = {0: -10}\n",
    "J = {(i, i+1): 1 for i in range(N-1)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TTS Calculation\n",
    "\n",
    "Response class returned from `sample_ising` or `sample_qubo` of OpenJij has a instance variable `info`.\n",
    "It contains different information for each sampler in a dictionary type.\n",
    "Most samplers have a key `'execution_time'` that stores the time (in $\\mu s$) of one execution of each algorithm.\n",
    "For SASampler, it stores the computation time per run of the simulated annealing algorithm.\n",
    "\n",
    "In this section, we will use this computation time to calculate the TTS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the optimal solution.\n",
    "correct_state = [(-1)**i for i in range(N)]\n",
    "# Calculate the optimal value.\n",
    "bqm = oj.BinaryQuadraticModel.from_ising(h, J)\n",
    "minimum_energy = bqm.energy(correct_state)\n",
    "\n",
    "# Define the pR to calculate TTS.\n",
    "pR = 0.99\n",
    "\n",
    "# Define num_sweeps_list.\n",
    "# This will be passed to the sampler argument parameter.\n",
    "# It is the number of divisions to decrease the parameters (temperature, transverse magnetic field) during annealing.\n",
    "# Therefore, the more you increase it, the slower annealing corresponds to and the longer the annealing time will be.\n",
    "num_sweeps_list = [30, 50, 80, 100, 150, 200, 300, 500]\n",
    "\n",
    "TTS_list = []     # Define a list to store the TTS for each computation time.\n",
    "tau_list = []     # Define a list to store computation times.\n",
    "e_mean_list = []  # Define a list to store average energies.\n",
    "e_min_list = []   # Define a list to store minimum energies.\n",
    "\n",
    "ps_list = [] # Define a list to store success probability, which is obtained while calculating.\n",
    "\n",
    "\n",
    "# Define the number of times to perform one annealing to calculate the probability.\n",
    "num_reads = 1000\n",
    "\n",
    "for num_sweeps in num_sweeps_list:\n",
    "    sampler = oj.SASampler(num_sweeps=num_sweeps, num_reads=num_reads)  \n",
    "    response = sampler.sample_ising(h, J)\n",
    "    \n",
    "    # Calculate ps. Count the number of energies below the optimal solution.\n",
    "    energies = response.energies\n",
    "    ps = len(energies[energies <= minimum_energy])/num_reads\n",
    "    \n",
    "    # Avoid TTS diverging to infinity when ps = 0.\n",
    "    if ps == 0.0:\n",
    "        continue\n",
    "    \n",
    "    ps_list.append(ps)\n",
    "    # Calculate TTS.\n",
    "    tau = response.info['execution_time']\n",
    "    TTS_list.append(np.log(1-pR)/np.log(1-ps)*tau if ps < pR else tau)\n",
    "    tau_list.append(tau)\n",
    "    \n",
    "    e_mean_list.append(np.mean(energies))\n",
    "    e_min_list.append(np.min(energies))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us plot the TTS obtained and the dependence of the success probability over the annealing time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Success probability')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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1YcIEvPHGG5g6dWqTzy9ZsgSzZ8/GrFmzEBwcjBUrVsDV1RWrVq2y7NOtWzcAgJ+fHyZOnIjMzMxm36+6uhoGg8Hq1laGB3kBANK44DAREbVCS9q+hvbs2YM77rgDDz30EAIDA3HPPffgwQcfvGGvFzX265lSxH2eBQCYdUcg51ETUauJnmBdT01NDTIyMhAVFWXZplQqERUVhdTUVAD1PWDl5eUAgIqKCvz444+47bbbmj1mYmIidDqd5ebv799m8UdY1sO62GbvQURE9qUlbd+1br/9dmRkZFgSqtOnT2Pr1q2YOHFiu8RsL86VXsbjn+xHVa0JY/p1xiv3BosdEhHJkKSrCJ4/fx5GoxE+Pj5W2318fHD06FEAQGFhoaX3y2g0Yvbs2QgPD2/2mPHx8YiLi7M8NhgMbZZkDenRCQoFkHO+EkWGKnTx0LbJ+xARkbgCAwPx6KOP4pFHHkFAQMAtHaslbd+1HnroIZw/fx4jR46EIAioq6vDk08+ed0hgtXV1aiurrY8bssRHVJlNAlIyylBUXkVPLROeCf5KIrLq9HPxx3LHhwMlZLl2Imo9SSdYLVEz5498euvv7Z4f2dnZzg7O7dhRFfpXJwwwNcD2fkGpOWWYNKgru3yvkRE1L6efvpprFmzBq+99hrGjBmDxx57DFOnTm239mbHjh1YvHgxPvroI0RERODkyZOYN28eXn/9dSxYsKDJ1yQmJmLRokXtEp8UJR/Ox6Jvs5FfZl0IxF2rxsqZw+CudRIpMiKSO0kPEfT29oZKpUJhYaHV9sLCQvj6+t7SsfV6PYKDg6/b22ULDcu1ExGRfXr66aeRlZWFtLQ0DBgwAE899RT8/PwQGxt73XnBTbmZtm/BggX4+9//jscffxwDBw7E1KlTsXjxYiQmJsJkMjX5mvj4eJSVlVluZ86caVWccpZ8OB9zPs1slFwBQHlVHX47VyZCVERkLySdYGk0GgwdOhQpKSmWbSaTCSkpKYiMjLylY8fExCA7Oxvp6em3GuZ1RTDBIiJyGEOGDMGyZctw7tw5JCQkYOXKlQgPD0dYWBhWrVrVonURb6btu3TpEpRK6yZdpVIBQLPv6ezsDA8PD6ubIzCaBCz6NhvN/SYUABZ9mw2jiWtYEtHNEX2IYEVFBU6ePGl5nJOTg6ysLHh6eiIgIABxcXGYOXMmhg0bhuHDh2Pp0qWorKzErFmzRIy65YYF1idYxwrLUXqpBh1duUghEZG9qq2txcaNG7F69Wps374dI0aMwGOPPYY//vgDL730En744QesW7fuhse5Uds3Y8YMdOvWDYmJiQCA6OhoLFmyBIMHD7YMEVywYAGio6MtiRbVS8spabLnykwAkF9WhbScEkT28mq/wIjIboieYO3fvx9jxoyxPDYXoJg5cybWrFmDadOmobi4GAsXLkRBQQHCwsKQnJzcaPJva+n1euj1ehiNxls6zo10dndGz84dcLq4EvtzLyIq+NbiJiIi6cnMzMTq1avx3//+F0qlEjNmzMAHH3yA/v37W/aZOnVqi4el36jty8vLs+qxeuWVV6BQKPDKK6/g7Nmz6Ny5M6Kjo/Hmm2/a9kTtQFF5yxZfbul+RETXUggtGa9gxwwGA3Q6HcrKytpseET81wfx37QzeOLOnoifOKBN3oOI6Fa0x7XQnqlUKtx999147LHHMGXKFDg5NS6QUFlZidjYWKxevVqECG/MUf4GUk9dwINJe2+4339nj2APFpEDssW1UPQeLEcQHuiJ/6adwT7OwyIiskunT59Gjx7XX5C2Q4cOkk2uHMnwIE/46bTNDhNUAPDVaS1FqoiIWkvSRS7shfkiffhsGSqr60SOhoiIbG3MmDG4cOFCo+2lpaXo2bOnCBFRc1RKBRKim15A2LzqVUJ0MNfAIqKb5rAJVnuVaQeA7p1c0a2jC+pMAg7klbb5+xERUfvKzc1tck5vdXU1zp49K0JEdD1De3hC1cQnIF+dFssfHoLxIX7tHxQR2Q2HHSIYExODmJgYyzjLtjY8yBMbD5xFWm4JRvbxbvP3IyKitrd582bL/W3btlm1J0ajESkpKQgMDBQhMrqeLzLOwGgCQrvrMH/CABSVV6GLe/2wQPZcEdGtctgEq72FB15JsHIaDyEhIiJ5mjJlCgBAoVBg5syZVs85OTkhMDAQ77//vgiRUXNMJgH/TcsDADw8ogcLWRCRzTHBaifmeVgH8kpRXWeEs5rrkhARyZ3JZAIABAUFIT09Hd7eHKEgdT+fPI8zJZfhoVVj0qCuYodDRHbIYedgtbdenTvAq4MG1XUmHD5bJnY4RERkQzk5OUyuZOKzvb8DAB4Y2h0uGn7ZSUS257A9WO210LCZQqFAeKAnkn8rwL6cEgztwfKvRERytmzZMvzjH/+AVqvFsmXLrrvv3Llz2ykqup78sstIOVoEAJgeESByNERkr7jQcDsurLhqdw5e+y4bd/XrjDWzhrfpexERtYajLDJrS0FBQdi/fz+8vLwQFBTU7H4KhQKnT59ux8hujiP8DSz94TiW/nACEUGe2PBEpNjhEJEEcaFhmTHPw8rIvQijSWClIiIiGcvJyWnyPklTndGE9WlnAADTR1x/UWgiolvBOVjtaICfB9yd1SivrsORfIPY4RARETmMH48WocBQBa8OGoy7zUfscIjIjrEHqx2plAoMDeyEHceKkZZTgpBubb/+FhERtY24uLgW77tkyZI2jIRa4rN99aXZ/zLMn5V8iahNMcFqZ8ODPC0J1qMjmx+zT0RE0nbgwIEW7adQcDi42PIuXMKuE8UAgAeH+4scDRHZO4dNsNq7iqBZxJV5WOm5JRAEgQ0vEZFM/fTTT2KHQC303/Q8CAIwqo83enh1EDscIrJzDjsHKyYmBtnZ2UhPT2/X9x3YrSOc1UpcqKzBqeLKdn1vIiIiR1NTZ8Ln6VeKW0SwuAURtT2H7cESi0atxOCAjth7ugRpOSXo3cVN7JCIiOgm3H///VizZg08PDxw//33X3ffr7/+up2iomtt+60AFypr4OPhjLEDuogdDhE5ACZYIhge5HUlwbqAh7jQIRGRLOl0Osswb52ORYuk6rN9vwMApoUHwEnlsAN3iKgdMcESwdV5WBdFjoSIiG7W6tWrm7xP0nGyqAJ7T5dAqQD+Fs7iFkTUPphgiWBwQEeolQqcLb2MPy5eQvdOrmKHRERENlBUVIRjx44BAPr164cuXTgkTUzrrpRm/1N/H3Tt6CJyNETkKBy2r1yv1yM4OBjh4eHt/t6uGrVlDay0nJJ2f38iIrItg8GAv//97+jWrRtGjx6N0aNHo1u3bnj44YdRVlYmdngOqarWiC8zrhS3GMHh+ETUfhw2wRKriqBZw3LtREQkb7Nnz8a+ffvw3XffobS0FKWlpfjuu++wf/9+PPHEE2KH55C2HMyHoaoO3Tu54M4+ncUOh4gcCIcIiiQ80BP/b9dp7GMPFhGR7H333XfYtm0bRo4cadk2btw4JCUlYfz48SJG5rjMxS0eHB4AlZJrThJR+3HYHiyxhQd6QqEAThdXori8WuxwiIjoFnh5eTVZSVCn06FTp04iROTYss8ZkJlXCrVSgb8OY3ELImpfTLBEonN1Qj8fdwAcJkhEJHevvPIK4uLiUFBQYNlWUFCA559/HgsWLBAxMse0Lq2+92pciC86uzuLHA0RORoOERRRRJAnjhaUIy2nBBMH+okdDhERtcLgwYMt62ABwIkTJxAQEICAgPqCCnl5eXB2dkZxcTHnYbWjiuo6bMw8CwCYzrUmiUgETLBEFB7kibWpv7OSIBGRDE2ZMkXsEKgJm7POobLGiJ7eHRDZ00vscIjIATHBEtHwwPpKgkcKDCi7XAudi5PIERERUUslJCSIHQJdQxAES3GLhyICrHoYiYjaC+dgiaiLhxZB3h0gCEDm7xfFDoeIiEjWfv2jDL+dM0CjVuKBId3FDoeIHJTDJlhiLjTcUHhgfXUplmsnIpIvo9GI9957D8OHD4evry88PT2tbtQ+Pttb33s1aaAfOnXQiBwNETkqh02wxF5o2Gx4UP348LScC6LGQUREN2/RokVYsmQJpk2bhrKyMsTFxeH++++HUqnEq6++KnZ4DqHsUi2+PXgOADB9BItbEJF4HDbBkoqIoPpvNg/+UYbLNUaRoyEiopvx2WefISkpCc8++yzUajUefPBBrFy5EgsXLsTevXvFDs8hfH3gD1TVmtDf1x1DArj2GBGJhwmWyLp3coGfTos6k4ADZzgPi4hIjgoKCjBw4EAAgJubG8rKygAAkyZNwpYtW8QMzSHUF7fIA1Bfmp3FLYhITEywRKZQKBB+pZogy7UTEclT9+7dkZ+fDwDo1asX/ve//wEA0tPT4ex8cwvd6vV6BAYGQqvVIiIiAmlpadfdv7S0FDExMfDz84OzszP69u2LrVu33tR7y01aTglOFlXAVaPClMHdxA6HiBwcEywJGB7EBIuISM6mTp2KlJQUAMBTTz2FBQsWoE+fPpgxYwYeffTRVh9vw4YNiIuLQ0JCAjIzMxEaGopx48ahqKioyf1rampw9913Izc3F19++SWOHTuGpKQkdOvmGMmGuffqvrCucNdyyRMiEhfXwZIA8zyszLyLqKkzQaNm3ktEJCdvvfWW5f60adMQEBCA1NRU9OnTB9HR0a0+3pIlSzB79mzMmjULALBixQps2bIFq1atwvz58xvtv2rVKpSUlGDPnj1wcqpPMAIDA2/uZGTmQkU1vj9c33v40PAeIkdDRMQeLEno3cUNnVydUFVrwuFzZWKHQ0REtygyMhJxcXE3lVzV1NQgIyMDUVFRlm1KpRJRUVFITU1t8jWbN29GZGQkYmJi4OPjg5CQECxevBhGY/PFk6qrq2EwGKxucvRlxh+oNQoI7a7DwO46scMhImKCJQWch0VEJH/Hjh1DbGwsxo4di7FjxyI2NhbHjh1r9XHOnz8Po9EIHx8fq+0+Pj4oKCho8jWnT5/Gl19+CaPRiK1bt2LBggV4//338cYbbzT7PomJidDpdJabv79/q2MVm8kkYF2aubgFe6+ISBqYYEkE52EREcnXV199hZCQEGRkZCA0NBShoaHIzMxESEgIvvrqqzZ/f5PJhC5duuDf//43hg4dimnTpuHll1/GihUrmn1NfHw8ysrKLLczZ860eZy29sup8/j9wiW4a9WYFOondjhERAA4B0syzAlWem4JjCYBKiVLzBIRycULL7yA+Ph4vPbaa1bbExIS8MILL+CBBx5o8bG8vb2hUqlQWFhotb2wsBC+vr5NvsbPzw9OTk5QqVSWbQMGDEBBQQFqamqg0WgavcbZ2fmmKxxKxWd763uvHhjSHa4afqQhImlgD5ZEBPt5oINGhfKqOhwrKBc7HCIiaoX8/HzMmDGj0faHH37YUr69pTQaDYYOHWqpSgjU91ClpKQgMjKyydfccccdOHnyJEwmk2Xb8ePH4efn12RyZQ8KDVXYfqQ+CX0oIkDkaIiIrnLYBEuv1yM4OBjh4eFihwIAUKuUGNKjfuX5j3efRuqpCzCaBJGjIiKilrjrrrvw888/N9q+e/dujBo1qtXHi4uLQ1JSEtauXYsjR45gzpw5qKystFQVnDFjBuLj4y37z5kzByUlJZg3bx6OHz+OLVu2YPHixYiJibn5k5K4DelnYDQJGB7oib4+7mKHQ0Rk4bD96TExMYiJiYHBYIBOJ37VoeTD+TiQVwoA+CrzLL7KPAs/nRYJ0cEYH8Jx5UREUrN582bL/cmTJ+PFF19ERkYGRowYAQDYu3cvvvjiCyxatKjVx542bRqKi4uxcOFCFBQUICwsDMnJyZbCF3l5eVAqr35H6u/vj23btuGZZ57BoEGD0K1bN8ybNw8vvvjiLZ6lNNUZTfjvleIW7L0iIqlRCILg0N0k5gSrrKwMHh4eosSQfDgfcz7NxLW/CPMsrOUPD2GSRURtSgrXQrlpmOBcj0KhuG65dKmQw9+A0SQgLacEPx4tRNLPOejoosbel6KgdVLd+MVERC1gi2uhw/ZgSYXRJGDRt9mNkisAEFCfZC36Nht3B/uy8AURkYQ0nO9EbS/5cD4WfZuN/LIqy7Zao4Adx4r4JSQRSYrDzsGSirScEqvG4loCgPyyKpZvJyIih2Ue6XFte1lZY8ScTzORfLh1hUSIiNoSEyyRFZU3n1zdzH5ERCSOnTt3Ijo6Gr1790bv3r0xefLkJgtfUOtcb6SH2aJvs1kYiogkgwmWyLq4a226HxERtb9PP/0UUVFRcHV1xdy5czF37ly4uLhg7NixWLdundjhyRpHehCR3LR4Dtb58+dRWVmJHj16WLb99ttveO+991BZWYkpU6bgoYceapMg7dnwIE/46bQoKKtq8ts5BQBfndayEDEREUnPm2++iXfeeQfPPPOMZdvcuXOxZMkSvP7662wfbwFHehCR3LS4B+upp57CsmXLLI+LioowatQopKeno7q6Go888gj+85//tEmQ9kylVCAhOhjA1aqBZubHCdHBLHBBRCRhp0+fRnR0dKPtkydPRk5OjggR2Q+O9CAiuWlxgrV3715MnjzZ8viTTz6Bp6cnsrKy8M0332Dx4sXQ6/VtEqS9Gx/ih+UPD4Gvzrpx8NVpWaKdiEgG/P39kZKS0mj7Dz/8AH9/fxEish/mkR7Nfc2oAODHkR5EJCEtHiJYUFCAwMBAy+Mff/wR999/P9Tq+kNMnjwZiYmJNg/QUYwP8cPdwb74YPsx/OunUwj288C3T41kzxURkQw8++yzmDt3LrKysnD77bcDAH755ResWbMGH374ocjRyZt5pMecTzMbPceRHkQkRS3uwfLw8EBpaanlcVpaGiIiIiyPFQoFqqurbRqco1EpFRjao/4bOKUSbCyIiGRizpw5WL9+PQ4dOoSnn34aTz/9NA4fPowNGzbgiSeeEDs82TOP9PB201ht50gPIpKiFvdgjRgxAsuWLUNSUhK+/vprlJeX409/+pPl+ePHj3MYhA24a+t/JeVVdSJHQkRELVFXV4fFixfj0Ucfxe7du8UOx26ND/FDZ3ctHli+B51cnfDR9KEYHuTJLyOJSHJa3IP12muvYfPmzXBxccG0adPwwgsvoFOnTpbn169fj9GjR7dJkI7EXesEgAkWEZFcqNVqvPPOO6ir43W7rVXVGgEAnd2dEdnLi8kVEUlSi3uwQkNDceTIEfzyyy/w9fW1Gh4IAH/7298QHBxs8wAdzdUerFoIggCFgo0HEZHUjR07Fjt37rSaq0y2V1Fdn8R2cG7xxxcionbX4ivUn/70J3z99de47777mnz+3nvvtVlQjsycYNUaBVTXmaB1UokcERER3ciECRMwf/58HDp0CEOHDkWHDh2snm9YhZduXsWV0R1uTLCISMJafIXasWMHampq2jKWW3Lp0iUMGDAAf/nLX/Dee++JHc5N66BRQ6EABAEwVNUywSIikoF//vOfAIAlS5Y0ek6hUMBoNLZ3SHapsuZKD5aGCRYRSVeL52BJ3ZtvvokRI0aIHcYtUyoVlm/mOA+LiEgeTCZTszcmV7ZjHiLopmWCRUTS1aorVHZ2NgoKCq67z6BBg24poJtx4sQJHD16FNHR0Th8+HC7v7+teWidUF5VxwSLiIiogcpqDhEkIulrVQ/W2LFjERYW1ug2ePBgy7+ttWvXLkRHR6Nr165QKBTYtGlTo330ej0CAwOh1WoRERGBtLQ0q+efe+45u1rk2DwPy3C5VuRIiIiopVJSUjBp0iT06tULvXr1wqRJk/DDDz+IHZZdqayu7w3s4Mzh80QkXa1KsPbt24ecnJxGt9OnT1v+ba3KykqEhoZCr9c3+fyGDRsQFxeHhIQEZGZmIjQ0FOPGjUNRUREA4JtvvkHfvn3Rt2/fFr1fdXU1DAaD1U1qPFiqnYhIVj766COMHz8e7u7umDdvHubNmwcPDw9MnDix2faNWs/cLrKKIBFJWauuUAEBAejSpYtNA5gwYQImTJjQ7PNLlizB7NmzMWvWLADAihUrsGXLFqxatQrz58/H3r17sX79enzxxReoqKhAbW0tPDw8sHDhwiaPl5iYiEWLFtn0HGytYal2IiKSvsWLF+ODDz5AbGysZdvcuXNxxx13YPHixYiJiRExOvthHiLozgSLiCRM0kUuampqkJGRgaioKMs2pVKJqKgopKamAqhPmM6cOYPc3Fy89957mD17drPJFQDEx8ejrKzMcjtz5kybn0drXU2w2INFRCQHpaWlGD9+fKPt99xzD8rKykSIyD5ZqggywSIiCWtxgjV69Oh2L9N+/vx5GI1G+Pj4WG338fG5YbGN5jg7O8PDw8PqJjXuliGC7MEiIpKDyZMnY+PGjY22f/PNN5g0aZIIEdknLjRMRHLQ4ivUrl27oNFo2jKWW/bII4+IHYJNWIpcsAeLiEgWgoOD8eabb2LHjh2IjIwEAOzduxe//PILnn32WSxbtsyy79y5c8UKU/a40DARyUGLr1CCILRlHE3y9vaGSqVCYWGh1fbCwkL4+vre0rH1ej30er0k1ydxZ5ELIiJZ+fjjj9GpUydkZ2cjOzvbsr1jx474+OOPLY8VCgUTrFvAMu1EJAetukIpFIq2iqNJGo0GQ4cORUpKCqZMmQKgfjHHlJQUq4nENyMmJgYxMTEwGAzQ6XQ2iNZ2WOSCiEhecnJyxA7BIXCIIBHJQauuUH379r1hklVSUtKqACoqKnDy5EnL45ycHGRlZcHT0xMBAQGIi4vDzJkzMWzYMAwfPhxLly5FZWWlpaqgPbo6RJAJFhEREVA/kqaypn7UCXuwiEjKWnWFWrRokc17e/bv348xY8ZYHsfFxQEAZs6ciTVr1mDatGkoLi7GwoULUVBQgLCwMCQnJzcqfNFaUh4i6OHCIYJEREQNVdeZYDTVT1fgQsNEJGWtSrD+9re/2XwdrLvuuuuG87tiY2NveUjgtaQ8RNCDZdqJiIisNGwTO2jYg0VE0tXiMu3tPf/KkbFMOxERkTVzgYsOGhWUSn4mISLpanGCJUYVQUfVcKFh/tyJiIhY4IKI5KPFCZbJZLL58EAx6fV6BAcHIzw8XOxQGjH3YNWZBFTVmkSOhoiIbiQ5ORm7d++2PNbr9QgLC8NDDz2EixcvihiZ/WCJdiKSixYnWPYmJiYG2dnZSE9PFzuURjpoVDCPfuAwQSIi6Xv++edhMBgAAIcOHcKzzz6LiRMnIicnx1K8iW4Ne7CISC4cNsGSMoVCYfmGzsBCF0REkpeTk4Pg4GAAwFdffYVJkyZh8eLF0Ov1+P7772/qmHq9HoGBgdBqtYiIiEBaWlqLXrd+/XooFArL+pH2ooI9WEQkE0ywJIqFLoiI5EOj0eDSpUsAgB9++AH33HMPAMDT09PSs9UaGzZsQFxcHBISEpCZmYnQ0FCMGzcORUVF131dbm4unnvuOYwaNar1JyFxldX1y6qwB4uIpI4JlkRdXWyYPVhERFI3cuRIxMXF4fXXX0daWhruvfdeAMDx48fRvXv3Vh9vyZIlmD17NmbNmoXg4GCsWLECrq6uWLVqVbOvMRqNmD59OhYtWoSePXve9LlI1dU5WFwDi4ikzWETLCkXuQAaLjbMHiwiIqn717/+BbVajS+//BLLly9Ht27dAADff/89xo8f36pj1dTUICMjA1FRUZZtSqUSUVFRSE1NbfZ1r732Grp06YLHHnvs5k5C4jgHi4jkwmGvUlJeaBjgYsNERHISEBCA7777rtH2Dz74oNXHOn/+PIxGI3x8fKy2+/j44OjRo02+Zvfu3fj444+RlZXV4veprq5GdXW15fHNDGVsT5Y5WFqH/ehCRDLhsD1YUsc5WERE8pGZmYlDhw5ZHn/zzTeYMmUKXnrpJdTU1LTpe5eXl+Pvf/87kpKS4O3t3eLXJSYmQqfTWW7+/v5tGOWtswwR1DDBIiJpY4IlUe7swSIiko0nnngCx48fBwCcPn0af/vb3+Dq6oovvvgCL7zwQquO5e3tDZVKhcLCQqvthYWF8PX1bbT/qVOnkJubi+joaKjVaqjVanzyySfYvHkz1Go1Tp061eT7xMfHo6yszHI7c+ZMq+JsbxwiSERywQRLophgERHJx/HjxxEWFgYA+OKLL3DnnXdi3bp1WLNmDb766qtWHUuj0WDo0KFISUmxbDOZTEhJSUFkZGSj/fv3749Dhw4hKyvLcps8eTLGjBmDrKysZnumnJ2d4eHhYXWTMi40TERy4bBXKb1eD71eD6PRKHYoTTIPETRwiCARkeQJggCTyQSgvkz7pEmTAAD+/v44f/58q48XFxeHmTNnYtiwYRg+fDiWLl2KyspKzJo1CwAwY8YMdOvWDYmJidBqtQgJCbF6fceOHQGg0XY54xwsIpILh71KSb3IBXuwiIjkY9iwYXjjjTcQFRWFnTt3Yvny5QDqFyC+tlhFS0ybNg3FxcVYuHAhCgoKEBYWhuTkZMux8vLyoFQ61iCUCq6DRUQywauURLHIBRGRfCxduhTTp0/Hpk2b8PLLL6N3794AgC+//BK33377TR0zNjYWsbGxTT63Y8eO6752zZo1N/WeUsZ1sIhILphgSZS5TLvhMnuwiIikbtCgQVZVBM3effddqFRMCGyhkkUuiEgmHGt8gYxYerCq2YNFRCQHpaWlWLlyJeLj41FSUgIAyM7ORlFRkciR2YcKFrkgIpngVUqiuNAwEZF8HDx4EGPHjkXHjh2Rm5uL2bNnw9PTE19//TXy8vLwySefiB2irNUaTaiuqy8iwgSLiKSOPVgSdXUOVh0EQRA5GiIiup64uDjMmjULJ06cgFartWyfOHEidu3aJWJk9sE8PBDgEEEikj6HTbD0ej2Cg4MRHh4udihNMlcRNJoEXK6VZil5IiKql56ejieeeKLR9m7duqGgoECEiOyLeXigRq2Ek8phP7oQkUw47FUqJiYG2dnZSE9PFzuUJrlqVFApFQA4TJCISOqcnZ1hMBgabT9+/Dg6d+4sQkT2pfJKiXYODyQiOXDYBEvqFAqFpSFhqXYiImmbPHkyXnvtNdTW1l+vFQoF8vLy8OKLL+KBBx4QOTr5q7hS8IkJFhHJARMsCTMPEzSwB4uISNLef/99VFRUoEuXLrh8+TJGjx6N3r17w93dHW+++abY4ckeFxkmIjnhlUrC6gtdXIbhMnuwiIikTKfTYfv27fjll1/w66+/oqKiAkOGDEFUVJTYodkFLjJMRHLCBEvCWKqdiEhe7rjjDtxxxx1ih2F3KrjIMBHJCIcISljDUu1ERCRdc+fOxbJlyxpt/9e//oWnn366/QOyM5VcZJiIZIQJloRd7cHiEEEiIin76quvmuy5uv322/Hll1+KEJF9qahigkVE8sEES8LcOUSQiEgWLly4AJ1O12i7h4cHzp8/L0JE9qWihkMEiUg+HDbBkvpCw0DDIYLswSIikrLevXsjOTm50fbvv/8ePXv2FCEi+1LJOVhEJCMOe6WKiYlBTEwMDAZDk986SgF7sIiI5CEuLg6xsbEoLi7Gn/70JwBASkoK3n//fSxdulTc4OyAeaFhdyZYRCQDvFJJmLkHi+tgERFJ26OPPorq6mq8+eabeP311wEAgYGBWL58OWbMmCFydPJn/qKRPVhEJAe8UkmYO4tcEBHJxpw5czBnzhwUFxfDxcUFbm5uYodkN64OEeQ6WEQkfUywJMzDhT1YRERykJOTg7q6OvTp0wedO3e2bD9x4gScnJwQGBgoXnB2oLKGVQSJSD4ctsiFHLAHi4hIHh555BHs2bOn0fZ9+/bhkUceaf+A7AwXGiYiOWGCJWEeLHJBRCQLBw4caHIdrBEjRiArK6v9A7IzXGiYiOSECZaEmYtcVFTXQRAEkaMhIqLmKBQKlJeXN9peVlYGo9EoQkT2hQsNE5GcMMGSMPMQQaNJwKUaNtBERFJ15513IjEx0SqZMhqNSExMxMiRI0WMTP5MJgGVV9pADhEkIjnglUrCXJxUUCkVMJoElFfVsWEhIpKot99+G3feeSf69euHUaNGAQB+/vlnGAwG/PjjjyJHJ2+Xaq8mrezBIiI5YA+WhCkUCha6ICKSgeDgYBw8eBB//etfUVRUhPLycsyYMQNHjx5FSEiI2OHJmnn+lUqpgNaJH1uISPr4VZDEuWvVKL1Uy1LtREQS17VrVyxevFjsMOyOZZFhjQoKhULkaIiIbsxhEyy9Xg+9Xi/5ycfuzk4ALrMHi4hIwnbt2nXd5++88852isT+sIIgEcmNw16tYmJiEBMTA4PBAJ1OJ3Y4zfJwqf8VsQeLiEi67rrrrkbbGva2SP3LPCmr5BpYRCQzHMwsceZS7ezBIiKSrosXL1rdioqKkJycjPDwcPzvf/8TOzxZMy8y7KZlgkVE8sCrlcS5c7FhIiLJa2okxN133w2NRoO4uDhkZGSIEJV9qKzhEEEikhf2YEmcB3uwiIhky8fHB8eOHRM7DFmrsBS5YIJFRPLAq5XEsQeLiEj6Dh48aPVYEATk5+fjrbfeQlhYmDhB2YmKai4yTETywquVxDHBIiKSvrCwMCgUCgiCYLV9xIgRWLVqlUhR2QdzkQt3zsEiIpngEEGJY5ELIiLpy8nJwenTp5GTk4OcnBz8/vvvuHTpEvbs2YP+/fvf1DH1ej0CAwOh1WoRERGBtLS0ZvdNSkrCqFGj0KlTJ3Tq1AlRUVHX3V9OKixVBFUiR0JE1DJMsCTO/I0dy7QTEUlXjx49rG7+/v7QarU3fbwNGzYgLi4OCQkJyMzMRGhoKMaNG4eioqIm99+xYwcefPBB/PTTT0hNTYW/vz/uuecenD179qZjkIoKlmknIplhgiVx5iIXhsvswSIikprU1FR89913Vts++eQTBAUFoUuXLvjHP/6B6urqVh93yZIlmD17NmbNmoXg4GCsWLECrq6uzQ43/Oyzz/DPf/4TYWFh6N+/P1auXAmTyYSUlJSbOi8p4ULDRCQ3TLAkjnOwiIik67XXXsNvv/1meXzo0CE89thjiIqKwvz58/Htt98iMTGxVcesqalBRkYGoqKiLNuUSiWioqKQmpraomNcunQJtbW18PT0bHaf6upqGAwGq5sUWXqwWEWQiGSCCZbEcQ4WEZF0ZWVlYezYsZbH69evR0REBJKSkhAXF4dly5bh888/b9Uxz58/D6PRCB8fH6vtPj4+KCgoaNExXnzxRXTt2tUqSbtWYmIidDqd5ebv79+qONtLJRcaJiKZYYIlcR5XGpSK6rpG1amIiEhcFy9etEqEdu7ciQkTJlgeh4eH48yZM+0a01tvvYX169dj48aN150HFh8fj7KyMsutveNsqcorZdo5RJCI5IIJlsSZe7BMAlBZYxQ5GiIiasjHxwc5OTkA6of2ZWZmYsSIEZbny8vL4eTk1Kpjent7Q6VSobCw0Gp7YWEhfH19r/va9957D2+99Rb+97//YdCgQdfd19nZGR4eHlY3KWKRCyKSGyZYEqd1UkKtVADgMEEiIqmZOHEi5s+fj59//hnx8fFwdXXFqFGjLM8fPHgQvXr1atUxNRoNhg4dalWgwlywIjIystnXvfPOO3j99deRnJyMYcOGtf5kJKrCUuSCZdqJSB5kn2CVlpZi2LBhCAsLQ0hICJKSksQOyaYUCgULXRARSdTrr78OtVqN0aNHIykpCUlJSdBoNJbnV61ahXvuuafVx42Li0NSUhLWrl2LI0eOYM6cOaisrMSsWbMAADNmzEB8fLxl/7fffhsLFizAqlWrEBgYiIKCAhQUFKCiouLWT1JEgiA0qCLYup5AIiKxyL6/3d3dHbt27YKrqysqKysREhKC+++/H15eXmKHZjPuWidcvFTLHiwiIonx9vbGrl27UFZWBjc3N6hU1r0sX3zxBdzc3Fp93GnTpqG4uBgLFy5EQUEBwsLCkJycbJnvlZeXB6Xy6neky5cvR01NDf785z9bHSchIQGvvvpq609MIqrrTKgz1c8/5kLDRCQXsk+wVCoVXF1dAdSXnBUEwe6KQXCxYSIiadPpdE1uv16Z9BuJjY1FbGxsk8/t2LHD6nFubu5Nv4+UmYcHAizTTkTyIfoQwV27diE6Ohpdu3aFQqHApk2bGu2j1+sRGBgIrVaLiIgIpKWlWT1fWlqK0NBQdO/eHc8//zy8vb3bKfr2wcWGiYjIEZmHB7pqVFBemY9MRCR1oidYlZWVCA0NhV6vb/L5DRs2IC4uDgkJCcjMzERoaCjGjRuHoqIiyz4dO3bEr7/+ipycHKxbt65R5SW54xwsIiJyRFcLXLD3iojkQ/QEa8KECXjjjTcwderUJp9fsmQJZs+ejVmzZiE4OBgrVqyAq6srVq1a1WhfHx8fhIaG4ueff272/eSycn1DVxcbZoJFRESOg2tgEZEciZ5gXU9NTQ0yMjKsVqJXKpWIiopCamoqgPp1QcrLywEAZWVl2LVrF/r169fsMeWycn1DV3uwOESQiIgcRyXXwCIiGZJ0gnX+/HkYjUZL1SQzHx8fFBQUAAB+//13jBo1CqGhoRg1ahSeeuopDBw4sNljymXl+oY8OESQiIgcULklwWIFQSKSD9l/JTR8+HBkZWW1eH9nZ2c4Ozu3XUBt4OoQQfZgERGR4+AaWEQkR5LuwfL29oZKpWpUtKKwsBC+vr4iRdX+WOSCiIgc0dUEiz1YRCQfkk6wNBoNhg4dipSUFMs2k8mElJQUREZG3tKx9Xo9goODER4efqthtjkWuSAiIkdUwTlYRCRDoidYFRUVyMrKsgzzy8nJQVZWFvLy8gAAcXFxSEpKwtq1a3HkyBHMmTMHlZWVmDVr1i29b0xMDLKzs5Genn6rp9DmOmjqv7n74+IlpJ66AKPJvhZSJiIiakpFFcu0E5H8iH7F2r9/P8aMGWN5HBcXBwCYOXMm1qxZg2nTpqG4uBgLFy5EQUEBwsLCkJyc3Kjwhb1KPpyPlzceBgCcK6vCg0l74afTIiE6GOND/ESOjoiIqO1U1rAHi4jkR/Qr1l133QVBuH6PTGxsLGJjY236vnq9Hnq9Hkaj0abHtaXkw/mY82kmrv3pFJRVYc6nmVj+8BAmWUREZLcquA4WEcmQ6EMExSL1IYJGk4BF32Y3Sq4AWLYt+jabwwWJiMhuXS1ywQSLiOTDYRMsqUvLKUF+WVWzzwsA8suqkJZT0n5BERERtSMWuSAiOWKCJVFF5c0nVzezHxERkdyYi1xwoWEikhOHTbCkXqa9i7vWpvsRERHJjbnIhXk9SCIiOXDYBEvqc7CGB3nCT6eF4gb7rd2Tg3Oll9slJiKSLqNJQOqpC/gm6yyXcyC7UckhgkQkQ7xiSZRKqUBCdDDmfJoJBWBV7ML8WKkAkn8rxK4T5zFvbB88OjIITiqHzZmJHFby4Xws+jbbat4ml3Mge2CZg6XhxxUikg9+Gpew8SF+WP7wEPjqrIcB+uq0WPHwEGydNwrDenTCpRojEr8/inuX/Yx9py+IFC0RicG8nMO1RXHMyzkkH84XKTKiW1NnNKGq1gSAVQSJSF54xZK48SF+uDvYF2k5JSgqr0IXdy2GB3lCpawfPPj5E5H4KvMPJH5/FMcLKzDt33tx/+BuiJ84AJ3dnUWOnohsSRAEVNeZUHa5FobLtbh4qQbxXx9qdjkHBeqXc7g72NdyzSCSi8rqq+tUcoggEcmJw16x5LDQsJlKqUBkL68mn1MqFfjLMH/cHeyDd7cdw7q0PHx94Cy2HynE8+P6YXpED36wIpKQOqMJhqo6GC7X1idKVbUwXK5rcN+8vfE+hsu1qDGaWvxeDZdzaO4aQiRVFVcKXGjUSmjUHHBDRPLhsAlWTEwMYmJiYDAYoNPpxA7nlnV01eDNqQPx12H+eGXTYRw6W4aF3/yGz/efwRtTBiLMv6NlX6NJaLZHjIiuTxAEVFTXwVBVh7JL9cmPuUfJUFXX4P6Vfy/XWe1TWXPrX+ooFYCHixPUSgXOV9TccH8u50ByxEWGiUiueNWyM6H+HbEp5g6s2/c73tl2DIfPGjD1o1/w4PAAvDCuH/aevsDJ8OTwqmqNliSo7ErPUKNE6UrydHV7nSVpskWBPjdnNTy0ani4ONXftE7wcFFDZ7nvdOX+lW0uV7d10KigUCiQeuoCHkzae8P34nIOJEdXFxnmGlhEJC9MsOyQSqnA3yMDMT7ED4nfH8HXmWexbl8eNmedszRYDZknwy9/eAiTLJKFOqMJ5VV1jZIfc4LU/NC7+v1q6lo+zK45GpXySsKjtiRI9YmQusF96+3m5Mldq4baBhU/zcs5FJRVNTkPS4H6ojjDgzxv+b2I2pt5kWE3ZyeRIyEiah0mWHass7szlvw1DNOG+eOVTYdwoqiyyf04Gd7+SH0YqCAIqKwxXu0xambe0bU9R+bepaa+KGgtpQJwbyL58dA6QefqZOld0jXTu6R1Ev9b9Rst5wAACdHBkvrdE7XU1SGC4v9fIyJqDYdNsORU5OJWRfT0QkL0bXj447Rm9+FkePvRXmsiVdUam+wlMtwgUTInVbYYZtdBo2rce9TEELumEqUOGjWUdpB4mJdzuPZ37suhvyRjRpOAX8+UAgBqjCYYTQK/KCAi2VAIgmCDjznyZS5yUVZWBg8PD7HDaTPfZJ3FvPVZN9zvw7+F4b6wbm0fELUJ85pI1/6nNn8saTgM1GgSUN5M8tMwKWquul21DYbZOakUVkPpmkuKmhp6565Vc2HtBm6119JRroXUPKn8DXDhbCISky2uhQ7bg+VoWjrJfVnKCZRU1iA6tCu83biOlhwYTQIuXqpBcXk1Xtp4uNk1kQAgdt0BdHHPttkwO4UCll4hS/LTXLGGJrY5q5VQKPittC1cbzkHIrlo7ksizhUmIjlhguUgbjQZ3uxUcSUWfZuNN7Ycwag+3pgS1g333OYDV428/1SkPiepoTqjCSWXalBSWYMLFTW4UFmDkorq+seVNdb/VlSj9HItWtoPXWcScK7MumS3q0Z1nQIN1lXurPZxdYKbnQyzIyLxGU0CFn2bzYWziUj25P2pmVqsJZPh33pgEC7V1GHTgbP49Y8y7DhWjB3HiuGqUWHcbb64L6wrRvb2tkn1s/Yk9nCTmjrTlaSoPkkyJ07mbeb75sSp7HLtTb2Pq0aFSy1YYynu7r6IDu0KD60a7lonLuBJRJKQllNidZ2+FucKE5FcMMFyIC2dDD/rjiCcLq7Apqxz2HTgLPJKLmHjgbPYeOAsvN00iA7tiilh3TCou07yw7vaYrhJVa3RKiG60LB3ydzjdCWZulBRg/KbGIqnUACdXDXw7FB/83Yz33eG15VtXh008HTTwKuDMzq5OiE992KL1kQKD/REkHeHVsdERNQWisur8fOJYqzb93uL9ufC2UQkdUywHMz4ED/cHex7w+FyPTu7Ie7uvngmqg8OnCnFpgNn8e2v53C+ogarf8nF6l9y0dO7A6YM7oYpYd0Q4OXa7HuKNTyvpcNN7ujtjdJLtVZJU0lltVXCZEmaKmpQ2YJeomspFbBKjuoTo6uJkpeb89WkqYMGHV01rf4ZcU0kImpvN3N9rzWakPH7Rew6Xoydx4vx2zlDq96TC2cTkdQ5bBXBhmXajx8/LnrVJDmoNZrw84libDxwDtuzC1BVe7WK3JCAjpg6uBvuHdQVnh00lu3tPTzPvL5SSUUNdh4vwoJvfrP5ewCAWqmw9C55uV3tWfKySp6uJk06F6d2matk7rEDmh4Gygni1BypVJCjq/R6Pd59910UFBQgNDQU//d//4fhw4c3u/8XX3yBBQsWIDc3F3369MHbb7+NiRMntvj9Wvs30Jrr+5mSS9h5JaFKPXWhUZGdkG4eGNnbG5/v/wMXK2uu+yXR7hf/xDlYRNRmbNEeOmyCZcYPFTenoroO2w4XYFPWWfxy8rxlTSO1UoHRfTtjyuBuMAkCnl6f1aKS4c0RBAGGqrorvUvVDeYuXZ23dL6i2qr3qeYmyodrVMoGydLVBMnL7eowvYY9TR5atWSHR4o954zkiddCadmwYQNmzJiBFStWICIiAkuXLsUXX3yBY8eOoUuXLo3237NnD+68804kJiZi0qRJWLduHd5++21kZmYiJCSkRe/Zmr+BGy0JsfRvYfDQOmHn8WLsOl6M0+etF7r36qDBqD7eGN2vM0b27ozO7s5WxwX4JRERiYMJlg3wQ8WtKzJUYfOv57Ap6ywOn7061OPaYhrX8uqgwev3heDi5YZzl6yH6ZVU1qDW2Po/Ua2TEm4aNc5X1txw31Uzh2FM/y6STZhuhpyqJpI08FooLREREQgPD8e//vUvAIDJZIK/vz+eeuopzJ8/v9H+06ZNQ2VlJb777jvLthEjRiAsLAwrVqxo0Xu29G/AaBIw8u0fr1uQ4loqpQJDAzphdL/OuLNPZ9zW1aPZXn1+SUREYuI6WCQJXTy0eHxUTzw+qidOFpVj04FzWJ+Wd8Pk5kJlDf65LrNF7+GqUVnNUfJyazCf6dphem4auGrUlg8BN5qTNLqffSVXANdEIpKzmpoaZGRkID4+3rJNqVQiKioKqampTb4mNTUVcXFxVtvGjRuHTZs2Nfs+1dXVqK6utjw2GFo2F+pG1f7MvDtocE+IL+7s0xm39/aCh9apRcdv6VxhIiKpYoJFNtW7izueG9cPvbu44ekNWTfcv4eXK/p0cWtcIe9KdTzzfCatk6rVsbSkNH1CdDAbbSKSlPPnz8NoNMLHx8dqu4+PD44ePdrkawoKCprcv6CgoNn3SUxMxKJFi1odX0ur+C2YFIz7Bndr9fEBfklERPLGBIvahI9Hy6o8vXX/oDZtRFtamp6IyNHEx8db9XoZDAb4+/vf8HUtreLXpYXtABGRvWGCRW1CSiXDOdyEiOTE29sbKpUKhYWFVtsLCwvh6+vb5Gt8fX1btT8AODs7w9nZudXxSen6TkQkRUqxAyD7ZB6eB1wdjmcmxvA883CT+8K6IbKXF5MrIpIsjUaDoUOHIiUlxbLNZDIhJSUFkZGRTb4mMjLSan8A2L59e7P73wqpXd+JiKSGCRa1GfPwPF+d9TARX52WpXaJiK4jLi4OSUlJWLt2LY4cOYI5c+agsrISs2bNAgDMmDHDqgjGvHnzkJycjPfffx9Hjx7Fq6++iv379yM2NrZN4uP1nYioeQ47RLDhQsPUdjg8j4io9aZNm4bi4mIsXLgQBQUFCAsLQ3JysqWQRV5eHpTKq9+R3n777Vi3bh1eeeUVvPTSS+jTpw82bdrU4jWwbgav70RETeM6WFz7hYiI10Li3wAREWxzLeQQQSIiIiIiIhthgkVERERERGQjTLCIiIiIiIhsxGGLXJiZp6AZDAaRIyEiEo/5Gujg03IdGttDIiLbtIcOn2CVl5cDQItWrycisnfl5eXQ6XRih0EiYHtIRHTVrbSHDl9F0GQy4dy5c3B3d4dC0falZQ0GA/z9/XHmzBm7rdLkCOcI8DztiSOcI3D98xQEAeXl5ejatatV+W9yHGwPbc8RzhHgedoTRzhHoO3bQ4fvwVIqlejevXu7v6+Hh4dd/+ECjnGOAM/TnjjCOQLNnyd7rhwb28O24wjnCPA87YkjnCPQdu0hv6YkIiIiIiKyESZYRERERERENsIEq505OzsjISEBzs7OYofSZhzhHAGepz1xhHMEHOc8SR4c4e/REc4R4HnaE0c4R6Dtz9Phi1wQERERERHZCnuwiIiIiIiIbIQJFhERERERkY0wwSIiIiIiIrIRJlhEREREREQ2wgTLBnbt2oXo6Gh07doVCoUCmzZtsnpeEAQsXLgQfn5+cHFxQVRUFE6cOGG1T0lJCaZPnw4PDw907NgRjz32GCoqKtrxLK4vMTER4eHhcHd3R5cuXTBlyhQcO3bMap+qqirExMTAy8sLbm5ueOCBB1BYWGi1T15eHu699164urqiS5cueP7551FXV9eep3Jdy5cvx6BBgywLz0VGRuL777+3PG8P53itt956CwqFAk8//bRlmz2c56uvvgqFQmF169+/v+V5ezhHs7Nnz+Lhhx+Gl5cXXFxcMHDgQOzfv9/yvD1cg0ge2B7Ws4frC9vDevZwnmwPRWgPBbplW7duFV5++WXh66+/FgAIGzdutHr+rbfeEnQ6nbBp0ybh119/FSZPniwEBQUJly9ftuwzfvx4ITQ0VNi7d6/w888/C7179xYefPDBdj6T5o0bN05YvXq1cPjwYSErK0uYOHGiEBAQIFRUVFj2efLJJwV/f38hJSVF2L9/vzBixAjh9ttvtzxfV1cnhISECFFRUcKBAweErVu3Ct7e3kJ8fLwYp9SkzZs3C1u2bBGOHz8uHDt2THjppZcEJycn4fDhw4Ig2Mc5NpSWliYEBgYKgwYNEubNm2fZbg/nmZCQINx2221Cfn6+5VZcXGx53h7OURAEoaSkROjRo4fwyCOPCPv27RNOnz4tbNu2TTh58qRlH3u4BpE8sD2sZw/XF7aH9ezhPNketn97yATLxq5tUEwmk+Dr6yu8++67lm2lpaWCs7Oz8N///lcQBEHIzs4WAAjp6emWfb7//ntBoVAIZ8+ebbfYW6OoqEgAIOzcuVMQhPpzcnJyEr744gvLPkeOHBEACKmpqYIg1De8SqVSKCgosOyzfPlywcPDQ6iurm7fE2iFTp06CStXrrS7cywvLxf69OkjbN++XRg9erSlQbGX80xISBBCQ0ObfM5ezlEQBOHFF18URo4c2ezz9noNIuljeyj/68u12B7K8zzZHtZrz2sQhwi2sZycHBQUFCAqKsqyTafTISIiAqmpqQCA1NRUdOzYEcOGDbPsExUVBaVSiX379rV7zC1RVlYGAPD09AQAZGRkoLa21uo8+/fvj4CAAKvzHDhwIHx8fCz7jBs3DgaDAb/99ls7Rt8yRqMR69evR2VlJSIjI+3uHGNiYnDvvfdanQ9gX7/LEydOoGvXrujZsyemT5+OvLw8APZ1jps3b8awYcPwl7/8BV26dMHgwYORlJRked5er0EkP/b6t8j2sJ6cz5HtoX2co5TaQyZYbaygoAAArP4ozY/NzxUUFKBLly5Wz6vVanh6elr2kRKTyYSnn34ad9xxB0JCQgDUn4NGo0HHjh2t9r32PJv6OZifk4pDhw7Bzc0Nzs7OePLJJ7Fx40YEBwfb1TmuX78emZmZSExMbPScvZxnREQE1qxZg+TkZCxfvhw5OTkYNWoUysvL7eYcAeD06dNYvnw5+vTpg23btmHOnDmYO3cu1q5dC8A+r0EkT/b4t8j2sKPV/nI8R7aH9nGOgLTaQ/WtnAg5ppiYGBw+fBi7d+8WO5Q20a9fP2RlZaGsrAxffvklZs6ciZ07d4odls2cOXMG8+bNw/bt26HVasUOp81MmDDBcn/QoEGIiIhAjx498Pnnn8PFxUXEyGzLZDJh2LBhWLx4MQBg8ODBOHz4MFasWIGZM2eKHB2RfWN7KG9sD9kethX2YLUxX19fAGhUjaWwsNDynK+vL4qKiqyer6urQ0lJiWUfqYiNjcV3332Hn376Cd27d7ds9/X1RU1NDUpLS632v/Y8m/o5mJ+TCo1Gg969e2Po0KFITExEaGgoPvzwQ7s5x4yMDBQVFWHIkCFQq9VQq9XYuXMnli1bBrVaDR8fH7s4z2t17NgRffv2xcmTJ+3mdwkAfn5+CA4Otto2YMAAy/APe7sGkXzZ298i20P5nyPbQ7aH5se2vgYxwWpjQUFB8PX1RUpKimWbwWDAvn37EBkZCQCIjIxEaWkpMjIyLPv8+OOPMJlMiIiIaPeYmyIIAmJjY7Fx40b8+OOPCAoKsnp+6NChcHJysjrPY8eOIS8vz+o8Dx06ZPWHu337dnh4eDT6DyElJpMJ1dXVdnOOY8eOxaFDh5CVlWW5DRs2DNOnT7fct4fzvFZFRQVOnToFPz8/u/ldAsAdd9zRqET08ePH0aNHDwD2cw0i+bOXv0W2h2wP5Xae12J72A7XoFaX6KBGysvLhQMHDggHDhwQAAhLliwRDhw4IPz++++CINSXhOzYsaPwzTffCAcPHhTuu+++JktCDh48WNi3b5+we/duoU+fPpIqSztnzhxBp9MJO3bssCrzeenSJcs+Tz75pBAQECD8+OOPwv79+4XIyEghMjLS8ry5zOc999wjZGVlCcnJyULnzp0lVeZz/vz5ws6dO4WcnBzh4MGDwvz58wWFQiH873//EwTBPs6xKQ2rJgmCfZzns88+K+zYsUPIyckRfvnlFyEqKkrw9vYWioqKBEGwj3MUhPrSwmq1WnjzzTeFEydOCJ999png6uoqfPrpp5Z97OEaRPLA9rCePVxf2B7Ws4fzZHvY/u0hEywb+OmnnwQAjW4zZ84UBKG+LOSCBQsEHx8fwdnZWRg7dqxw7Ngxq2NcuHBBePDBBwU3NzfBw8NDmDVrllBeXi7C2TStqfMDIKxevdqyz+XLl4V//vOfQqdOnQRXV1dh6tSpQn5+vtVxcnNzhQkTJgguLi6Ct7e38Oyzzwq1tbXtfDbNe/TRR4UePXoIGo1G6Ny5szB27FhLYyII9nGOTbm2QbGH85w2bZrg5+cnaDQaoVu3bsK0adOs1sKwh3M0+/bbb4WQkBDB2dlZ6N+/v/Dvf//b6nl7uAaRPLA9rGcP1xe2h/Xs4TzZHl7VXtcghSAIQsv7u4iIiIiIiKg5nINFRERERERkI0ywiIiIiIiIbIQJFhERERERkY0wwSIiIiIiIrIRJlhEREREREQ2wgSLiIiIiIjIRphgERERERER2QgTLKJ28OqrryIsLMzy+JFHHsGUKVNEiWXHjh1QKBQoLS0V5f2JiMhxsT0kR6AWOwAiR/Thhx+iPdb4vuuuuxAWFoalS5datt1+++3Iz8+HTqdr8/cnIiK6HraHZI+YYBGJQMyLuUajga+vr2jvT0REZMb2kOwRhwiSbCUnJ2PkyJHo2LEjvLy8MGnSJJw6dcryfG5uLhQKBb7++muMGTMGrq6uCA0NRWpqqmWfNWvWoGPHjti2bRsGDBgANzc3jB8/Hvn5+VbvtXLlSgwYMABarRb9+/fHRx99ZPX8iy++iL59+8LV1RU9e/bEggULUFtb22zs1w6JuOuuuzB37ly88MIL8PT0hK+vL1599VWr1xw9ehQjR46EVqtFcHAwfvjhBygUCmzatKnZ99i5cyc+/PBDKBQKKBQK5ObmNhoSYf4ZfPfdd+jXrx9cXV3x5z//GZcuXcLatWsRGBiITp06Ye7cuTAajZbjV1dX47nnnkO3bt3QoUMHREREYMeOHc2eMxERtQ22h2wPSVqYYJFsVVZWIi4uDvv370dKSgqUSiWmTp0Kk8lktd/LL7+M5557DllZWejbty8efPBB1NXVWZ6/dOkS3nvvPfznP//Brl27kJeXh+eee87y/GeffYaFCxfizTffxJEjR7B48WIsWLAAa9eutezj7u6ONWvWIDs7Gx9++CGSkpLwwQcftOp81q5diw4dOmDfvn1455138Nprr2H79u0AAKPRiClTpsDV1RX79u3Dv//9b7z88svXPd6HH36IyMhIzJ49G/n5+cjPz4e/v3+T+166dAnLli3D+vXrkZycjB07dmDq1KnYunUrtm7div/85z/4f//v/+HLL7+0vCY2NhapqalYv349Dh48iL/85S8YP348Tpw40arzJiKiW8P2kO0hSYxAZCeKi4sFAMKhQ4cEQRCEnJwcAYCwcuVKyz6//fabAEA4cuSIIAiCsHr1agGAcPLkScs+er1e8PHxsTzu1auXsG7dOqv3ev3114XIyMhmY3n33XeFoUOHWh4nJCQIoaGhlsczZ84U7rvvPsvj0aNHCyNHjrQ6Rnh4uPDiiy8KgiAI33//vaBWq4X8/HzL89u3bxcACBs3bmw2jtGjRwvz5s2z2vbTTz8JAISLFy8KgtD0z+CJJ54QXF1dhfLycsu2cePGCU888YQgCILw+++/CyqVSjh79qzVsceOHSvEx8c3Gw8REbU9toeNsT2k9sQ5WCRbJ06cwMKFC7Fv3z6cP3/e8k1dXl4eQkJCLPsNGjTIct/Pzw8AUFRUhP79+wMAXF1d0atXL6t9ioqKANR/K3jq1Ck89thjmD17tmWfuro6q3HjGzZswLJly3Dq1ClUVFSgrq4OHh4erTqfhnFeG8exY8fg7+9vNVZ8+PDhrTr+9Vz7M/Dx8UFgYCDc3NystpnjOXToEIxGI/r27Wt1nOrqanh5edksLiIiujG2h2wPSVqYYJFsRUdHo0ePHkhKSkLXrl1hMpkQEhKCmpoaq/2cnJws9xUKBQBYDZto+Lx5H+FKRaOKigoAQFJSEiIiIqz2U6lUAIDU1FRMnz4dixYtwrhx46DT6bB+/Xq8//77rTqfpuK4dnhHW2nqva8XT0VFBVQqFTIyMiw/B7OGjRAREbU9toe2w/aQbIEJFsnShQsXcOzYMSQlJWHUqFEAgN27d9v8fXx8fNC1a1ecPn0a06dPb3KfPXv2oEePHlZjwH///XebxtGvXz+cOXMGhYWF8PHxAQCkp6ff8HUajcZqIq6tDB48GEajEUVFRZafPxERtT+2h2wPSXqYYJEsderUCV5eXvj3v/8NPz8/5OXlYf78+W3yXosWLcLcuXOh0+kwfvx4VFdXY//+/bh48SLi4uLQp08f5OXlYf369QgPD8eWLVuwceNGm8Zw9913o1evXpg5cybeeecdlJeX45VXXgFw9VvIpgQGBmLfvn3Izc2Fm5sbPD09bRJP3759MX36dMyYMQPvv/8+Bg8ejOLiYqSkpGDQoEG49957bfI+RER0fWwP2R6S9LCKIMmSUqnE+vXrkZGRgZCQEDzzzDN499132+S9Hn/8caxcuRKrV6/GwIEDMXr0aKxZswZBQUEAgMmTJ+OZZ55BbGwswsLCsGfPHixYsMCmMahUKmzatAkVFRUIDw/H448/bvmGUKvVNvu65557DiqVCsHBwejcuTPy8vJsFtPq1asxY8YMPPvss+jXrx+mTJmC9PR0BAQE2Ow9iIjo+tgesj0k6VEIQjssn01ENvfLL79g5MiROHnypNWEXCIiIkfC9pCkhgkWkUxs3LgRbm5u6NOnD06ePIl58+ahU6dObTLWnoiISKrYHpLUcQ4WkUyUl5fjxRdfRF5eHry9vREVFdXqykxERERyx/aQpI49WERERERERDbCIhdEREREREQ2wgSLiIiIiIjIRphgERERERER2QgTLCIiIiIiIhthgkVERERERGQjTLCIiIiIiIhshAkWERERERGRjTDBIiIiIiIishEmWERERERERDby/wGQC5BRKDZeXAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1000x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set plotting parameters.\n",
    "fig, (axL, axR) = plt.subplots(ncols=2, figsize=(10,3))\n",
    "plt.subplots_adjust(wspace=0.4)\n",
    "fontsize = 10\n",
    "\n",
    "# Plot TTS.\n",
    "axL.plot(tau_list, TTS_list, '-o')\n",
    "axL.set_xlabel('annealing time', fontsize=fontsize)\n",
    "axL.set_yscale(\"log\")\n",
    "axL.set_ylabel('TTS', fontsize=fontsize)\n",
    "\n",
    "# Plot success probability ps.\n",
    "axR.plot(tau_list, ps_list, '-o')\n",
    "axR.set_xlabel('annealing time', fontsize=fontsize)\n",
    "axR.set_ylabel('Success probability', fontsize=fontsize)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For both of the above two figures, the horizontal axis is the computation time per annealing.\n",
    "\n",
    "In the success probability on the right figure, we see that it increases as the annealing time increases.\n",
    "In this figure, the success probability roughly converges at an annealing time of around 200.\n",
    "\n",
    "The TTS on the left shows that it decreases until the annealing time is about 200, i.e., the optimal solution is quickly obtained.\n",
    "When annealing is slower than 200, TTS increases slowly.\n",
    "This indicates a trend that the success probability relative to the annealing time is reaching its limit.\n",
    "\n",
    "Therefore, we can use these as an indicator of when to stop annealing when the required success probability has been accomplished.\n",
    "The smallest point in the TTS is the best computation time of the annealing algorithm for this instance.\n",
    "This minimum TTS is a common metric of the algorithm's computation time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The annealing algorithm is an algorithm for which there exists an asymptotic convergence to the optimal solution.\n",
    "Therefore, in most cases, the residual energy decreases as the annealing time increases.\n",
    "Plotting the dependence of the residual energy on annealing time confirms that the annealing algorithm is working well.\n",
    "Knowing that the above OpenJij test saves the average value of energy, we plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(tau_list, (np.array(e_mean_list) - minimum_energy)/np.abs(minimum_energy), '-o', label='mean')\n",
    "plt.plot(tau_list, (np.array(e_min_list) - minimum_energy)/np.abs(minimum_energy), '-o', label='lowest')\n",
    "plt.xlabel('annealing time', fontsize=fontsize)\n",
    "plt.ylabel('Residual energy', fontsize=fontsize)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The average residual energy decreases as the annealing time increases.\n",
    "Although we previously calculated TTS based on the success probability, residual energy is another useful indicator to check if annealing is going well, especially when the problem is too difficult to obtain the optimal solution.\n",
    "This plot is useful to compare algorithms even when the optimal value is not known since the residual energy is a shift of the obtained energy value by the optimal value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate Evaluation Metrics using OpenJij's Benchmarking Feature\n",
    "Above, we manually scripted and calculated TTS, success probability, and residual energy to understand the principles.\n",
    "However, OpenJij has a benchmark function `openjij.solver_benchmark` which evaluates TTS, success probability, and residual energy by default.  \n",
    "\n",
    "### `solver_benchmark` Function\n",
    "\n",
    "The `solver_benchmark` function calculates TTS, success probability, and residual energy and returns their values and standard errors.\n",
    "The arguments and return values of the `solver_benchmark` function will be explained later.\n",
    "First, we calculate using this benchmark function with the same settings as above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the optimal solution.\n",
    "correct_state = [(-1)**i for i in range(N)]\n",
    "\n",
    "# Define num_sweeps and num_reads (number of iterations)\n",
    "num_sweeps_list = [30, 50, 80, 100, 150, 200,300,500]\n",
    "num_reads = 1000\n",
    "\n",
    "# Calculate TTS, success probability, and residual energy using benchmark function.\n",
    "result = oj.solver_benchmark(\n",
    "            solver=lambda time, **args: oj.SASampler(num_sweeps=time, num_reads=num_reads).sample_ising(h,J),\n",
    "            time_list=num_sweeps_list, solutions=[correct_state], p_r=0.99\n",
    "            )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Residual energy')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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O//vf//Daa6+J2y5cuIBLly5h8+bN+OKLL7B+/XokJCTgySefrPE4MTExUKlU4i0gIKBO8ei/Y/HrFRFZE5tNqtWH7lZOjdU/iYiI6kgQBMz+8R+U6QQM6eCN8BAfqUMiIrI6M2bMgEwmu+PtzJkzBvukpaVh+PDheOqppzB+/Hhxu06ng0ajwRdffIH+/ftj0KBB+Oyzz/D7778jOTm52vNHR0dDrVaLt8uXL9fpdei/YnHQAhFZE66pVge6SiPVZJz1T0REVCfbTqTj4PnrUNqVFycgIiLjTZ06FREREXds07p1a/H+1atXMXjwYPTp0werVq0yaOfn5wc7Ozu0a9dO3BYcHAwASE1NFddZq0ypVEKpVNbjFZTT6Ucu8OsVEVkRJtXqoFJODTKO9SMiIjJagaYM71cUJ3h9UFsEeDhLHBERkXXy8vKCl5dXrdqmpaVh8ODB6NatG9atWwe53PDLTN++fVFWVobz58+jTZs2AICzZ88CAFq1amXawG8jFoIz61mIiEyLSbU60HFNNSIionpZtusssvI1aNXMGa8NbH33HYiIqF7S0tIwaNAgtGrVCosWLUJ2drb4nK+vLwAgPDwc9913H1566SUsW7YMOp0OkZGRGDp0qMHoNXPQsVABEVkhJtXqiZd8IiIi4yRn5GPdwYsAgP+OvBeO9ixOQERkbrt27cK5c+dw7tw5tGjRwuA5fZEAuVyObdu24Y033sCAAQPQpEkTPPjgg1i8eLHZ42OhAiKyRkyq1QFHqhEREdWNIAiY9eMpaHUCht3rg8HtvaUOiYjIJkRERNx17TUAaN68ObZs2WL+gG4jcKQaEVkhrghWB5Wrf/KaT0REVHs/JKbhSEoOHO3lmPVIiNThEBGRhRAqVlXj1ysisiZMqtWBULn6J6/6REREtaK+WYoPfj4DAHjj/nvQwp3FCYiIqJxY/JNfsIjIijCpVgeVR6pxeDIREVHtLN11FtcKNGjt2QSv9A+SOhwiIrIggphUkzYOIiJjMKlWBwYj1SSMg4iIyFr8c1WNL+IvAgDmPnovlHYsTkBERLfop3/K+QWLiKwIk2p1IHCkGhERUa3pdAJm//gPdALwcEc/9L/HS+qQiIjIwogj1ThsgYisCJNqdaDjmmpERES19t3xK0i4dAPODgq8+0iw1OEQEZEF0s8GkvMbKhFZEV6y6qDSQDUupElERHQH6qJSfPhLeXGCyUPugZ/KSeKIiIjIEt1at5rfr4jIejCpVgf6kWqc709ERHRnH+08g5zCEtzj7YKX+rE4ARERVY+FCojIGjWKpFpgYCA6deqELl26YPDgwWY/n8Byz0RENi82NhaBgYFwdHREr169cOTIkTu2X7ZsGdq3bw8nJycEBARgypQpKC4ubqBopXHyihobDqcCAOY9Ggp7RaP42EFERGbAgQtEZI3spA7AVA4ePAgXF5cGOZc+qcYLPhGRbdq0aROioqKwcuVK9OrVC8uWLcOwYcOQnJwMb2/vKu2//vprzJgxA2vXrkWfPn1w9uxZREREQCaTYcmSJRK8AvPT6QS8++MpCALwaJfmCGvTTOqQiIjIgulnf7JQARFZE/5kXAf6X1E4Uo2IyDYtWbIE48ePx7hx4xASEoKVK1fC2dkZa9eurbb9wYMH0bdvXzz33HMIDAzEAw88gNGjR99xdJtGo0FeXp7BzZpsOnYZf1/OhYvSDu88xOIERER0ZwJHqhGRFZI8qbZ//36MGDECzZs3h0wmww8//FClzd2m2MhkMgwcOBA9evTAhg0bzB6zmFQz+5mIiMhUAgMDMW/ePKSmptbrOCUlJUhISEB4eLi4TS6XIzw8HPHx8dXu06dPHyQkJIj914ULF7Bjxw489NBDNZ4nJiYGKpVKvAUEBNQr7oaUU1iCBXHlxQmmDG0Hb1dHiSMiIiJLxyV2iMgaSZ5UKywsROfOnREbG1vt8/opNnPmzMHx48fRuXNnDBs2DFlZWWKbAwcOICEhAT/99BPmz5+PEydO1Hg+U/zyf2v6Jy/4RETW4s0338TWrVvRunVrDB06FBs3boRGozH6ONeuXYNWq4WPj4/Bdh8fH2RkZFS7z3PPPYd58+ahX79+sLe3R5s2bTBo0CDMnDmzxvNER0dDrVaLt8uXLxsdq1Q++vUMcotK0cG3KcaGtZI6HCIisgK3ZgNJHAgRkREkT6o9+OCDeP/99/HYY49V+3xtptj4+/sDAPz8/PDQQw/h+PHjNZ7PFL/8szINEZH1efPNN5GYmIgjR44gODgYb7zxBvz8/DBx4sQ79humsHfvXsyfPx//93//h+PHj2Pr1q34+eef8d5779W4j1KphKurq8HNGvyVegMbj5YnAOc9Ggo7FicgIqJa4JpqRGSNLPqTbm2m2BQWFiI/Px8AUFBQgD179uDee++t8Zim+OVfgH6+Py/4RETW5r777sMnn3yCq1evYs6cOVizZg169OiBLl26YO3ateKaLjXx9PSEQqFAZmamwfbMzEz4+vpWu8+sWbPw4osv4pVXXkHHjh3x2GOPYf78+YiJiYFOpzPZa5OKVicg/vx1fP9XGqZ8mwhBAB6/zx89gzykDo2IiKwEi8ERkTWy6Oqfd5pic+ZM+VotmZmZ4ig3rVaL8ePHo0ePHjUeU6lUQqlU1isuHUeqERFZrdLSUnz//fdYt24ddu3ahd69e+Pll1/GlStXMHPmTPz222/4+uuva9zfwcEB3bp1w+7duzFq1CgAgE6nw+7duzFx4sRq9ykqKoJcbvg7lkKhAIC7JvEsXdypdMzdloR0dbG4TQagVxCrfRIRUe0JnP5JRFbIopNqtdG6dWv8/fffRu8XGxuL2NhYaLVao/dloQIiIutz/PhxrFu3Dt988w3kcjnGjBmDpUuXokOHDmKbxx577I4/zOhFRUVh7Nix6N69O3r27Illy5ahsLAQ48aNAwCMGTMG/v7+iImJAQCMGDECS5YsQdeuXdGrVy+cO3cOs2bNwogRI8TkmjWKO5WOCV8dx+1pQQHAjC0noHKyw/BQPylCIyIiK6PvSzgbiIisiUUn1eoyxaa2IiMjERkZiby8PKhUKqP2FYcmc2wyEZHV6NGjB4YOHYoVK1Zg1KhRsLe3r9ImKCgIzz777F2P9cwzzyA7OxuzZ89GRkYGunTpgri4OHFkdWpqqsHItHfffRcymQzvvvsu0tLS4OXlhREjRuCDDz4w3QtsYFqdgLnbkqok1Cqbuy0JQ0N8oWB/SUREd6ETpwNJGwcRkTEsek21ylNs9PRTbMLCwiSLSz80mb+iEBFZjwsXLiAuLg5PPfVUtQk1AGjSpAnWrVtXq+NNnDgRly5dgkajweHDh9GrVy/xub1792L9+vXiYzs7O8yZMwfnzp3DzZs3kZqaitjYWLi5udXnJUnqSEqOwZTP2wkA0tXFOJKS03BBERFRjS5evIiXX34ZQUFBcHJyQps2bTBnzhyUlJQYtPv111/Ru3dvNG3aFF5eXnjiiSdw8eJFs8fHQgVEZI0kT6oVFBQgMTERiYmJAICUlBQkJiYiNTUVQPkUm9WrV+Pzzz/H6dOnMWHCBIMpNlK4dcEnIiJrMXjwYFy/fr3K9tzcXLRu3VqCiKxbVn7NCbW6tCMiIvM6c+YMdDodPv30U/zzzz9YunQpVq5ciZkzZ4ptUlJS8Oijj+L+++9HYmIifv31V1y7dg2PP/642ePTiQMXzH4qIiKTkXz657FjxzB48GDxcVRUFABg7NixWL9+/V2n2NSVSdZU40g1IiKrcfHixWqv+RqNBmlpaRJEZN28mzqatB0REZnX8OHDMXz4cPFx69atkZycjBUrVmDRokUAgISEBGi1Wrz//vviMgbTpk3Do48+itLS0hpHepuCwGJwRGSFJE+qDRo06K6VzyZOnFhjRbW6qs+aajpd+X95wScisnw//fSTeP/XX381uOZrtVrs3r0bgYGBEkRm3XoGecBP5YgMdXG166rJAPiqHNEzyKOhQyMiolpSq9Xw8Lh1ne7WrRvkcjnWrVuHiIgIFBQU4Msvv0R4eHiNCTWNRgONRiM+zsvLq1MsXGKHiKyR5Ek1aySAQ5OJiKzFqFGjAJSPLh47dqzBc/b29ggMDMTixYsliMy6KeQyzBkRgv98dbzKc/rucc6IEBYpICKyUOfOncP//vc/cZQaUF6wZ+fOnXj66afx2muvQavVIiwsDDt27KjxODExMZg7d2694+ESO0RkjSRfU80aidU/+SsKEZHF0+l00Ol0aNmyJbKyssTHOp0OGo0GycnJeOSRR6QO0yoND/XDk91aVNnuq3LEihfuw/BQPwmiIiKyfAMHDsQXX3yBmzdv1vtYM2bMgEwmu+PtzJkzBvukpaVh+PDheOqppzB+/Hhxe0ZGBsaPH4+xY8fi6NGj2LdvHxwcHPDkk0/WOLsoOjoaarVavF2+fLlOr4NL7BCRNbLZkWomWVPN1EEREZHZpKSkSB1Co1RSVr4mwtPdWqDvPZ7wblo+5ZMj1IiIata1a1dMmzYNb7zxBp5++mm8/PLL6N27d52ONXXqVERERNyxTeWCPFevXsXgwYPRp08frFq1yqBdbGwsVCoVFi5cKG776quvEBAQgMOHD1cbo1KphFKprFPslXFNNSKyRjabVKvPmmq3Lvi84hMRWbJPPvkEr776KhwdHfHJJ5/cse2kSZMaKKrG5cSVXADAI52bY0A7L2mDISKyEsuWLcOiRYvw008/4fPPP8eAAQPQtm1bvPTSS3jxxReNKsrm5eUFL6/aXX/T0tIwePBgdOvWDevWrROLEegVFRVV2aZQKACUj/w2Jx1nAxGRFbLZpFp93BqaLHEgRER0R0uXLsXzzz8PR0dHLF26tMZ2MpmMSbU6yC0qwcXrRQCATi2M+4GKiMjW2dnZ4fHHH8fjjz+OrKwsrFq1CrNmzcLMmTPx0EMPYdKkSbj//vtNdr60tDQMGjQIrVq1wqJFi5CdnS0+5+vrCwB4+OGHsXTpUsybNw+jR49Gfn4+Zs6ciVatWqFr164mi6V6nA1ERNaHSbU60K8mwF9RiIgsW+Upn5z+aXp/X1EDAAKbOcPN2UHiaIiIrNORI0ewbt06bNy4Ed7e3oiIiEBaWhoeeeQRvP766waFBOpj165dOHfuHM6dO4cWLQzXw9Svl3b//ffj66+/xsKFC7Fw4UI4OzsjLCwMcXFxcHJyMkkcNeH0TyKyRjabVKvPmmq3yj2bOioiIiLrceJyLgCgc4CbpHEQEVmbrKwsfPnll1i3bh3+/fdfjBgxAt988w2GDRsmLjETERGB4cOHmyypFhERcde11wDg2WefxbPPPmuScxqDhQqIyBrZbFKtPmuq6bimGhGRVYiKiqp12yVLlpgxksbp74r11Dq1cJM0DiIia9OiRQu0adMGL730EiIiIqpdE61Tp07o0aOHBNFJgyPViMga2WxSrT54wScisg5//fVXrdrxRxLjCYKAxMvl0z+7BHA9NSIiY+zevRv9+/e/YxtXV1f8/vvvDRSR9FiogIisEZNqdaATp3/ygk9EZMls6ctIQ0tXF+NagQYKuQz3NmdSjYjIGHdLqNkigYUKiMgKMalWB+JINWnDICIikszfFeuptfdpCkd7hbTBEBFZma5du1Y7Slomk8HR0RFt27ZFREQEBg8eLEF00hA4Uo2IrBCTanUgcKQaEZFVePzxx7F+/Xq4urri8ccfv2PbrVu3NlBUjUNixXpqLFJARGS84cOHY8WKFejYsSN69uwJADh69ChOnDiBiIgIJCUlITw8HFu3bsWjjz4qcbQNQxALFUgcCBGREWw2qVaf6p86rqlGRGQVVCqVOBLA2KI0dGf6kWpcT42IyHjXrl3D1KlTMWvWLIPt77//Pi5duoSdO3dizpw5eO+992wmqcZicERkjWw2qVaf6p/ifH9e8ImILNq6deuqvU/1o9UJOJWWB4CVP4mI6uLbb79FQkJCle3PPvssunXrhtWrV2P06NE2VZm6IqfGJXaIyKrYbFKtPm5VppE2DiIiMl5WVhaSk5MBAO3bt4e3t7fEEVmfC9kFKNCUwclegXu8XaQOh4jI6jg6OuLgwYNo27atwfaDBw/C0dERAKDT6cT7tuBWMTiJAyEiMgKTanWg43x/IiKrk5eXh8jISGzcuFGc+q9QKPDMM88gNjaW00ONkFgx9bOjvwp2Crm0wRARWaE33ngD//nPf5CQkIAePXoAKF9Tbc2aNZg5cyYA4Ndff0WXLl0kjLKBcfonEVkhJtXqgpVpiIiszvjx4/HXX39h+/btCAsLAwDEx8dj8uTJeO2117Bx40aJI7QeJ66oAQCdWjARSURUF++++y6CgoKwfPlyfPnllwDKR0+vXr0azz33HADgP//5DyZMmCBlmA2KAxeIyBoxqVYH4gVf4jiIiKj2tm/fjl9//RX9+vUTtw0bNgyrV6/G8OHDJYzM+vzNyp9ERHVWVlaG+fPn46WXXsLzzz9fYzsnJ6cGjEp6AkeqEZEVstk5G7GxsQgJCRGHWxuDF3wiIuvTrFmzaqd4qlQquLu7SxCRddKUaXE6vbxIQRcm1YiIjGZnZ4eFCxeirKxM6lAsilgMTuI4iIiMYbNJtcjISCQlJeHo0aNG78tFNImIrM+7776LqKgoZGRkiNsyMjLw1ltvYdasWRJGZl1Op+ejVCvA3dkeLdxtaxQFEZGpDBkyBPv27ZM6DIui4xI7RGSFOP2zDnQcqUZEZBW6du1qcK3+999/0bJlS7Rs2RIAkJqaCqVSiezsbLz22mtShWlV/q4oUtA5wI39IBFRHT344IOYMWMGTp48iW7duqFJkyYGz48cOVKiyKRzazaQtHEQERmDSbU64Ug1IiJrMGrUKKlDaHTEpFoLN0njICKyZq+//joAYMmSJVWek8lkYpVqWyJwNhARWSEm1eqAI9WIiKzDnDlzpA6h0blVpICVP4mI6kqn00kdgsWp+IoFGVdVIyIrYrNrqtWHODRZ2jCIiIgaVF5xKc5nFwIAOnGkGhGRSRQXF0sdgkXQr1vNcQtEZE2YVKuDW4UKeMUnIrIWWq0WixYtQs+ePeHr6wsPDw+DG93dyStqAEALdyd4uigljoaIyHpptVq899578Pf3h4uLCy5cuAAAmDVrFj777DOJo5OGwNlARGSFmFSrA/6KQkRkfebOnYslS5bgmWeegVqtRlRUFB5//HHI5XL897//lTo8qyBO/eQoNSKievnggw+wfv16LFy4EA4ODuL20NBQrFmzxmznHTlyJFq2bAlHR0f4+fnhxRdfxNWrVw3anDhxAv3794ejoyMCAgKwcOFCs8VTmY5rqhGRFWJSrR44Uo2IyHps2LABq1evxtSpU2FnZ4fRo0djzZo1mD17Ng4dOiR1eFbhVuVPrqdGRFQfX3zxBVatWoXnn38eCoVC3N65c2ecOXPGbOcdPHgwvv32WyQnJ2PLli04f/48nnzySfH5vLw8PPDAA2jVqhUSEhLw0Ucf4b///S9WrVpltphux69YRGRNbLZQQWxsLGJjY+tUWYcj1YiIrE9GRgY6duwIAHBxcYFaXT6V8ZFHHsGsWbOkDM1q/H25/D3jSDUiovpJS0tD27Ztq2zX6XQoLS0123mnTJki3m/VqhVmzJiBUaNGobS0FPb29tiwYQNKSkqwdu1aODg44N5770ViYiKWLFmCV1991WxxAZW+Y3HlaiKyIjY7Ui0yMhJJSUk4evSo0fvqi/Vwvj8RkfVo0aIF0tPTAQBt2rTBzp07AQBHjx6FUmn8+mCxsbEIDAyEo6MjevXqhSNHjtyxfW5uLiIjI+Hn5welUol27dphx44dxr8QiWTmFSMjrxhyGRDqz5FqRET1ERISgj/++KPK9u+++w5du3ZtkBhycnKwYcMG9OnTB/b29gCA+Ph4DBgwwGBK6rBhw5CcnIwbN25UexyNRoO8vDyDW13cWlOtTrsTEUnCZkeq1Ye+3DPn+xMRWY/HHnsMu3fvRq9evfDGG2/ghRdewGeffYbU1FSDX+5rY9OmTYiKisLKlSvRq1cvLFu2TPzS4e3tXaV9SUkJhg4dCm9vb3z33Xfw9/fHpUuX4ObmZqJXZ376qZ/3eDdFEyU/PhAR1cfs2bMxduxYpKWlQafTYevWrUhOTsYXX3yB7du3m/Xc06dPx/Lly1FUVITevXsbnC8jIwNBQUEG7X18fMTn3N3dqxwvJiYGc+fOrXdct2YD8UsWEVkPmx2pVh+s/klEZH0+/PBDzJw5EwDwzDPPYP/+/ZgwYQK+++47fPjhh0Yda8mSJRg/fjzGjRuHkJAQrFy5Es7Ozli7dm217deuXYucnBz88MMP6Nu3LwIDAzFw4EB07ty53q+roYhFCrieGhFRvT366KPYtm0bfvvtNzRp0gSzZ8/G6dOnsW3bNgwdOtSoY82YMQMymeyOt8rrtL311lv466+/sHPnTigUCowZMwaCfphYHURHR0OtVou3y5cv1+k4+hA4cIGIrAl/aq4L/dBkaaMgIqJ6CAsLQ1hYmNH7lZSUICEhAdHR0eI2uVyO8PBwxMfHV7vPTz/9hLCwMERGRuLHH3+El5cXnnvuOUyfPt1ggerKNBoNNBqN+Liu02lM5cSV8vXUOnE9NSIik+jfvz927dpV7+NMnToVERERd2zTunVr8b6npyc8PT3Rrl07BAcHIyAgAIcOHUJYWBh8fX2RmZlpsK/+sa+vb7XHViqVdVpG4Xb6tB7XVCMia8KkWh1waDIRkXVKTk7G//73P5w+fRoAEBwcjDfeeAPt27ev9TGuXbsGrVYrTofR8/HxqbFi24ULF7Bnzx48//zz2LFjB86dO4fXX38dpaWlmDNnTrX7mGo6jSnodII4/bNLgJuksRARNSYlJSXIysqCTr9oc4WWLVvW+hheXl7w8vKq0/n159X/iBMWFoZ33nlHLFwAALt27UL79u2rnfppSoI4G8ispyEiMilO/6wDHRfRJCKyOlu2bEFoaCgSEhLQuXNndO7cGcePH0doaCi2bNli1nPrdDp4e3tj1apV6NatG5555hm88847WLlyZY37mGo6jSlcvF6IvOIyONjJ0d63qWRxEBE1Fv/++y/69+8PJycntGrVCkFBQQgKCkJgYGCVNc1M5fDhw1i+fDkSExNx6dIl7NmzB6NHj0abNm3EkdvPPfccHBwc8PLLL+Off/7Bpk2b8PHHHyMqKsosMVXGQgVEZI04Uq0OBPBXFCIia/P2228jOjoa8+bNM9g+Z84cvP3223jiiSdqdRxPT08oFIpqp8fUNDXGz88P9vb2BlM9g4ODkZGRgZKSEoMqa3qmmk5jCvqpn/c2d4W9gr/HERHVV0REBOzs7LB9+3b4+fk1yAwYZ2dnbN26FXPmzEFhYSH8/PwwfPhwvPvuu2J/o1KpsHPnTkRGRqJbt27w9PTE7Nmz8eqrr5o9Ps4GIiJrxKRaHejERTR5wScishbp6ekYM2ZMle0vvPACPvroo1ofx8HBAd26dcPu3bsxatQoAOUj0Xbv3o2JEydWu0/fvn3x9ddfQ6fTQS4vT0qdPXsWfn5+1SbULE1ixdTPzlxPjYjIJBITE5GQkIAOHTo02Dk7duyIPXv23LVdp06d8McffzRARIZuralGRGQ9+HNzHQjirygSB0JERLU2aNCgar8kHDhwAP379zfqWFFRUVi9ejU+//xznD59GhMmTEBhYSHGjRsHABgzZoxBIYMJEyYgJycHkydPxtmzZ/Hzzz9j/vz5iIyMrN+LaiD6yp9cT42IyDRCQkJw7do1qcOwKBy4QETWiCPV6uDWfH9e8ImILNlPP/0k3h85ciSmT5+OhIQE9O7dGwBw6NAhbN682eiCAM888wyys7Mxe/ZsZGRkoEuXLoiLixOLF6Smpooj0gAgICAAv/76K6ZMmYJOnTrB398fkydPxvTp003wKs2rVKvDP1fLK492aqGSOBoiosZhwYIFePvttzF//nx07NhRLAqg5+rqKlFkEuLABSKyQjJBP+zKRuXl5UGlUkGtVte681r3ZwrmbkvCI538sPy5+8wcIRHRndXlOmYrKie27kQmk0Gr1Zo5mvqR6u98Kk2NR/53AK6Odkic/QDkXFCUiOqI/dUt+v7p9h/pBUGwij7pTur6dx7xvwM4mabG2ojuuL+Dz913ICIyE2OuYzY7Ui02NhaxsbF16rAEDk0mIrIKOp1O6hCsmlYnYOvxKwCAVs2cYdO/whERmdDvv/8udQgWR18MjrOBiMia2GxSLTIyEpGRkWIG0hj6yjT8sZ6IiBqruFPpmLstCenqYgDAybQ89FuwB3NGhGB4qJ/E0RERWbeBAwdKHYLF0f8Oxq9YRGRNWKigDrimGhGRddq3bx9GjBiBtm3bom3bthg5cqQkFc4sXdypdEz46riYUNPLUBdjwlfHEXcqXaLIiIgajz/++AMvvPAC+vTpg7S0NADAl19+iQMHDkgcmTT0o6E5G4iIrAmTanVwa2iyxIEQEVGtffXVVwgPD4ezszMmTZqESZMmwcnJCUOGDMHXX38tdXgWQ6sTMHdbUrVTPfXb5m5LglbHyaBERHW1ZcsWDBs2DE5OTjh+/Dg0Gg0AQK1WY/78+RJHJw2BhQqIyAoxqVYHLPdMRGR9PvjgAyxcuBCbNm0Sk2qbNm3Chx9+iPfee0/q8CzGkZScKiPUKhMApKuLcSQlp+GCIiJqZN5//32sXLkSq1evNqj82bdvXxw/flzCyKTDdauJyBrVOql27do1XLp0yWDbP//8g3HjxuHpp5+2qV/5xemf0oZBRERGuHDhAkaMGFFl+8iRI5GSkiJBRJYpK7/mhFpd2hERUVXJyckYMGBAle0qlQq5ubkNH5AFEGcDSRwHEZExap1Ue+ONN/DJJ5+Ij7OystC/f38cPXoUGo0GERER+PLLL80SpKUpq1hF83JOEeLPX+cUGCIiKxAQEIDdu3dX2f7bb78hICBAgogsk3dTR5O2IyKiqnx9fXHu3Lkq2w8cOIDWrVtLEJH0dFy3moisUK2rfx46dAjr168XH3/xxRfw8PBAYmIi7OzssGjRIsTGxuLFF180R5wWI+5UOj7ddwEAcCglB4dWH4KfypHV0IiILNzUqVMxadIkJCYmok+fPgCAP//8E+vXr8fHH38scXSWo2eQB/xUjshQF1e7rpoMgK/KET2DPBo6NCKiRmP8+PGYPHky1q5dC5lMhqtXryI+Ph7Tpk3DrFmzpA5PElxTjYisUa2TahkZGQgMDBQf79mzB48//jjs7MoPMXLkSMTExJg8QEuir4Z2+5cMfTW0FS/cx8QaEZGFmjBhAnx9fbF48WJ8++23AIDg4GBs2rQJjz76qMTRWQ6FXIY5I0Iw4auqa/rov+fMGREChZzfeoiI6mrGjBnQ6XQYMmQIioqKMGDAACiVSkybNg1vvPGG1OFJgmuqEZE1qvX0T1dXV4P5/UeOHEGvXr3ExzKZTKxa0xixGhoRkfUqKyvDvHnz0KNHDxw4cADXr1/H9evXceDAASbUqjE81A+xz91XZbuvypE/IBERmYBMJsM777yDnJwcnDp1CocOHUJ2drZNF87Rf4tiTo2IrEmtk2q9e/fGJ598Ap1Oh++++w75+fm4//77xefPnj3bqNekYTU0IiLrZWdnh4ULF6KsrEzqUKxG55ZuAAC5DFj6dGd8M743Dky/nwk1IiITcnBwQEhICHr27AkXFxepw5GUTmChAiKyPrWe/jlv3jyEh4fjq6++QllZGWbOnAl3d3fx+Y0bN2LgwIFmCdISsBoaEZF1GzJkCPbt22ewlAHV7OK1QgBAYLMmeOy+FhJHQ0REjZ3AQgVEZIVqnVTr3LkzTp8+jT///BO+vr4GUz8B4Nlnn0VISIjJA7QUrIZGRGTdHnzwQcyYMQMnT55Et27d0KRJE4PnR44cKVFklulCRVItyLPJXVoSERHVn46FCojICtU6qXb//fdj69atNa498/DDD5ssKEvEamhERNbt9ddfBwAsWbKkynMymQxarbahQ7Jo4kg1JtWIiKgBsFABEVmjWq+ptnfvXpSUlJgzFoumr4YGVJ3nz2poRESWT6fT1XhjQq0qJtWIiKghCVxTjYisUK1Hqlm6oqIiBAcH46mnnsKiRYvMco7hoX5Y8cJ9mLstyaBoga/KEXNGhHDxZiIiajRS9NM/mzGpRkRkCj/99FOt25prSYKRI0ciMTERWVlZcHd3R3h4OBYsWIDmzZsDKB9IsXTpUhw5cgR5eXm455578NZbb+H55583SzyV6WcDcaQaEVkTo5JqSUlJyMjIuGObTp061Suguvrggw/Qu3dvs59neKgfhob44o2vj2PHqQwMu9cH//d8N45QIyKyArt378bSpUtx+vRpAEBwcDDefPNNhIeHSxyZZSnT6pCaUwQACPJiUo2IyBRGjRpVq3bmXJJg8ODBmDlzJvz8/JCWloZp06bhySefxMGDBwEABw8eRKdOnTB9+nT4+Phg+/btGDNmDFQqFR555BGzxKTHNdWIyBoZlVQbMmSIOCy3MplMBkEQJFuT5t9//8WZM2cwYsQInDp1yuznU8hluD/YBztOZSC3qJQJNSIiK/B///d/mDx5Mp588klMnjwZAHDo0CE89NBDWLp0KSIjIyWO0HKk5d5EmU6A0k4OP1cW4CEiMgWdTid1CJgyZYp4v1WrVpgxYwZGjRqF0tJS2NvbY+bMmQbtJ0+ejJ07d2Lr1q1mTappdQI0peXvz8m0XAT7ufI7FhFZhVqvqQYAhw8fRkpKSpXbhQsXxP8aa//+/RgxYgSaN28OmUyGH374oUqb2NhYBAYGwtHREb169cKRI0cMnp82bRpiYmKMPnd9BPs1BQCcTs+rNtFIRESWZf78+Vi6dCm++eYbTJo0CZMmTcLXX3+NpUuXYv78+VKHZ1H0Uz9bNXOGnF9qiIgapZycHGzYsAF9+vSBvb19je3UajU8PGouxqbRaJCXl2dwM0bcqXT0W7AHuTdLAQDRW0+h34I9iDuVbtRxiIikYNRItZYtW8Lb29ukARQWFqJz58546aWX8Pjjj1d5ftOmTYiKisLKlSvRq1cvLFu2DMOGDUNycjK8vb3x448/ol27dmjXrp04bPlONBoNNBqN+NjYi77ePd5NYa+QIa+4DGm5N9HC3blOxyEiooaRm5uL4cOHV9n+wAMPYPr06RJEZLnE9dRYpICIyGwKCwuxb98+pKamVikIN2nSJLOdd/r06Vi+fDmKiorQu3dvbN++vca23377LY4ePYpPP/20xjYxMTGYO3dunWKJO5WOCV8dx+1DFDLUxZjw1XGseOE+rltNRBbNqJFq5vDggw/i/fffx2OPPVbt80uWLMH48eMxbtw4hISEYOXKlXB2dsbatWsBlE/d2bhxIwIDAzFt2jSsXr0a8+bNq/F8MTExUKlU4i0gIKBOcTvYydHGywUAcDo9v07HICKihjNy5Eh8//33Vbb/+OOPZl8nxtqw8icRkXn99ddfaNu2LUaPHo2JEyfi/fffx5tvvomZM2di2bJlRh1rxowZkMlkd7ydOXNGbP/WW2/hr7/+ws6dO6FQKDBmzJhqZ978/vvvGDduHFavXo177723xvNHR0dDrVaLt8uXL9cqbq1OwNxtSVUSasCtogVztyVBq+OsICKyXLUeqTZw4MAqv6CYW0lJCRISEhAdHS1uk8vlCA8PR3x8PIDyJJl+6uf69etx6tQpzJ49u8ZjRkdHIyoqSnycl5dX58RaiJ8rzmTk43R6HoaG+NTpGERE1DBCQkLwwQcfYO/evQgLCwNQ/sPMn3/+ialTp+KTTz4R25pzhIA1SLleUaSAlT+JiMxiypQpGDFiBFauXAmVSoVDhw7B3t4eL7zwgrjuZ21NnToVERERd2zTunVr8b6npyc8PT3Rrl07BAcHIyAgAIcOHRL7RgDYt28fRowYgaVLl2LMmDF3PLZSqYRSqTQqZgA4kpKDdHVxjc8LANLVxTiSkoOwNs2MPj4RUUOodVJt//79cHBwMGcsVVy7dg1arRY+PoYJKx8fH4NfW4xR14t+dYL9XIG/0nA6vW5TSImIqOF89tlncHd3R1JSEpKSksTtbm5u+Oyzz8THMpnM5pNqHKlGRGReiYmJ+PTTTyGXy6FQKKDRaNC6dWssXLgQY8eOrXZZnJp4eXnBy8urTnHoiydUXh5n7969eOSRR7BgwQK8+uqrdTpubWTl15xQq0s7IiIp1DqpZg2L8d/tFxpTC/ZzBQAm1YiIrEBKSorUIViFkjIdrtwoH6nWmkk1IiKzsLe3h1xevhKPt7c3UlNTERwcDJVKVevpk8Y6fPgwjh49in79+sHd3R3nz5/HrFmz0KZNG3GU2u+//45HHnkEkydPxhNPPIGMjAwAgIODwx2LFdSFd9PaVZeubTsiIikYtaaaTNawFcA8PT2hUCiQmZlpsD0zMxO+vr71OnZsbCxCQkLQo0ePOh9DXwH0Uk4RCjVl9YqHiIjIEqTmFEEnAE0cFPBqapqR3UREZKhr1644evQogPJldmbPno0NGzbgzTffRGhoqFnO6ezsjK1bt2LIkCFo3749Xn75ZXTq1An79u0TZ/J8/vnnKCoqQkxMDPz8/MSbMSPnaqtnkAf8VI6o6RumDICfyhE9g0ybzCMiMiWjkmrt2rWDh4fHHW+m5ODggG7dumH37t3iNp1Oh927dxvM+a+LyMhIJCUliZ1ZXTRzUcK7qRKCAJzJYLECIiKyfvqpn62aNWnwH9OIiGzF/Pnz4edXXtXygw8+gLu7OyZMmIDs7GysWrXKLOfs2LEj9uzZg+vXr6O4uBgpKSlYsWIF/P39xTbr16+HIAhVbnv37jV5PAq5DHNGhABAlcSa/vGcESFQyNkXEZHlqvX0TwCYO3cuVCqVSQMoKCjAuXPnxMcpKSlITEyEh4cHWrZsiaioKIwdOxbdu3dHz549sWzZMhQWFmLcuHEmjaOugv1ckZWfjdPpeejWyl3qcIiIiOolpSKpFsSpn0REZtO9e3fxvre3N+Li4iSMRjrDQ/2w4oX7MHdbkkHRAm9XJeaOvBfDQ/0kjI6I6O6MSqo9++yz8Pb2NmkAx44dw+DBg8XH+sqcY8eOxfr16/HMM88gOzsbs2fPRkZGBrp06YK4uLgqxQuMFRsbi9jYWGi12nodJ9jPFfvOZnNdNSIiahRSrjOpRkREDWd4qB+GhvjiSEoOIr9OQE5hKRY/2Rn92tWt+AIRUUOqdVLNXFNABg0adNciCBMnTsTEiRNNet7IyEhERkYiLy+vXqPv9OuqMalGRESNASt/EhGZX1BQ0B2/X124cKEBo5GeQi5DWJtm6N26GXaczMCp9Dwm1YjIKjSq6p9SCKmoAHomIx86nQA55/wTEVmkuLg4uLi4oF+/fgDKRyyvXr0aISEhiI2Nhbs7p/ADt5JqQZ7OEkdCRNR4vfnmmwaPS0tL8ddffyEuLg5vvfWWNEFZgFB/FXaczMDJNLXUoRAR1Uqtk2o6nc6ccVitIM8mcLCTo6hEi9ScIv6yT0Rkod566y0sWLAAAHDy5ElMnToVUVFR+P333xEVFYV169ZJHKH0bpZocbViTZsgTxeJoyEiarwmT55c7fbY2FgcO3asgaOxHJ383QAAJ68wqUZE1sGo6p+NSWxsLEJCQtCjR496HcdOIUd7H04BJSKydCkpKQgJKa8ytmXLFjzyyCOYP38+YmNj8csvv0gcnWW4lFM+Ss3V0Q7uzvYSR0NEZHsefPBBbNmyReowJNPRv3xZntScIuQWlUgcDRHR3dlsUi0yMhJJSUk4evRovY/FddWIiCyfg4MDioqKAAC//fYbHnjgAQCAh4cH8vKMv37HxsYiMDAQjo6O6NWrF44cOVKr/TZu3AiZTIZRo0YZfU5zu1ip8qe51lIlIqKafffdd/Dw8JA6DMmonO3R0qN8+YFTafxuRUSWz6jqn1S94Ip11ZLS8yWOhIiIatKvXz9ERUWhb9++OHLkCDZt2gQAOHv2LFq0aGHUsTZt2oSoqCisXLkSvXr1wrJlyzBs2DAkJyffsUr2xYsXMW3aNPTv379er8VcUq6VJx25lAERkXl17drV4McLQRCQkZGB7Oxs/N///Z+EkUmvYwsVUnOKcCItF/3u8ZQ6HCKiO2JSzQT0STWOVCMislzLly/H66+/ju+++w4rVqyAv78/AOCXX37B8OHDjTrWkiVLMH78eIwbNw4AsHLlSvz8889Yu3YtZsyYUe0+Wq0Wzz//PObOnYs//vgDubm5dzyHRqOBRqMRH9dlNJ2xUq4VACgfqUZEROZz+2hluVwOLy8vDBo0CB06dJAmKAvR0V+Fn0+kc101IrIKTKqZQLBveVItLfcm1DdLoXLiOjRERJamZcuW2L59e5XtS5cuNeo4JSUlSEhIQHR0tLhNLpcjPDwc8fHxNe43b948eHt74+WXX8Yff/xx1/PExMRg7ty5RsVWXxcrRqoxqUZEZF5z5syROgSL1aliXTVWACUia2Cza6qZqlABUD7339/NCQBwhqPViIgs0vHjx3Hy5Enx8Y8//ohRo0Zh5syZKCmp/WLI165dg1arhY+Pj8F2Hx8fZGRkVLvPgQMH8Nlnn2H16tW1Pk90dDTUarV4u3z5cq33rauU6+VrqgU2Y1KNiMjU8vLyan2zZfdWJNWu3LiJG4UsVkBEls1mk2qmLFQAsFgBEZGle+2113D27FkAwIULF/Dss8/C2dkZmzdvxttvv2228+bn5+PFF1/E6tWr4elZ+7VhlEolXF1dDW7mVKApQ3Z++XRTrqlGRGR6bm5ucHd3r9XNlqmc7BHYrLxYAUerEZGl4/RPEwn2c8Vvp7NwmsUKiIgs0tmzZ9GlSxcAwObNmzFgwAB8/fXX+PPPP/Hss89i2bJltTqOp6cnFAoFMjMzDbZnZmbC19e3Svvz58/j4sWLGDFihLhNp9MBAOzs7JCcnIw2bdrU7UWZkL7yZ7MmDlzGgIjIDH7//Xfx/sWLFzFjxgxEREQgLCwMABAfH4/PP/8cMTExUoVoMTq2cMPF60U4mabGgHZeUodDRFQjJtVMRCxWkMGRakRElkgQBDGZ9dtvv+GRRx4BAAQEBODatWu1Po6DgwO6deuG3bt3iwtN63Q67N69GxMnTqzSvkOHDgbTTgHg3XffRX5+Pj7++GMEBATU8RWZVkpFUo2j1IiIzGPgwIHi/Xnz5mHJkiUYPXq0uG3kyJHo2LEjVq1ahbFjx0oRosXo5K/Ctr+v4sSVXKlDISK6IybVTESfVEvOyEeZVgc7hc3OrCUiskjdu3fH+++/j/DwcOzbtw8rVqwAAKSkpFRZH+1uoqKiMHbsWHTv3h09e/bEsmXLUFhYKFYDHTNmDPz9/RETEwNHR0eEhoYa7O/m5gYAVbZLST9SjeupERGZX3x8PFauXFlle/fu3fHKK69IEJFlCa1YV+1UGgcsEJFls9nMjykLFQBAKw9nODsooCnT4WLFQs9ERGQ5li1bhuPHj2PixIl455130LZtWwDAd999hz59+hh1rGeeeQaLFi3C7Nmz0aVLFyQmJiIuLk5MzqWmpiI9Pd3kr8Gc9CPVWnsxqUZEZG4BAQHVFq9Zs2aNxYxgllKof/mAhbTcm7hWoJE4GiKimskEQRCkDkJKeXl5UKlUUKvV9V4E+rH/+xN/pebik9FdMbJzcxNFSER0Z6a8jtmi4uJiKBQK2Ntb9jpi5v476/uw2Ofuw8Od/Ex+fCIi9le37NixA0888QTatm2LXr16AQCOHDmCf//9F1u2bMFDDz0kcYR1Z6q/8/2L9+JCdiHWjeuBwe29TRghEdGdGXMds9mRauYgrqvGCqBERBYpNzcXa9asQXR0NHJycgAASUlJyMrKkjgy6YnTPz2dJY6EiKjxe+ihh3D27FmMGDECOTk5yMnJwYgRI3D27FmrTqiZUkf9FNArrABKRJaLa6qZEJNqRESW68SJExgyZAjc3Nxw8eJFjB8/Hh4eHti6dStSU1PxxRdfSB2iZHKLSnCjqBQA11QjImooAQEBmD9/foOec+TIkUhMTERWVhbc3d0RHh6OBQsWoHnzqrNszp07h65du0KhUCA3N7dB4wTKk2o/Jl7FiTQm1YjIcnGkmgmF+DUFwKQaEZElioqKwrhx4/Dvv//C0dFR3P7QQw9h//79EkYmPf16aj6uSjRR8vc2IiJzOHHihFiF+sSJE3e8mcvgwYPx7bffIjk5GVu2bMH58+fx5JNPVmlXWlqK0aNHo3///maL5W7EkWpMqhGRBeMnZxNq71s+Ui0zT4OcwhJ4NHGQOCIiItI7evQoPv300yrb/f39kZGRIUFElkNfYIej1IiIzKdLly7IyMiAt7c3unTpAplMhuqWt5bJZNBqtWaJYcqUKeL9Vq1aYcaMGRg1ahRKS0sN1hZ999130aFDBwwZMgQHDx40Syx3c6+/CjIZkK4uRlZ+MbybOt59JyKiBsakmgm5KO3QqpkzLl0vwun0PPRt6yl1SEREVEGpVCIvr+pI4rNnz8LLy0uCiCxHyrUiAECQJ5NqRETmkpKSIvY3KSkpEkcD5OTkYMOGDejTp49BQm3Pnj3YvHkzEhMTsXXr1rseR6PRQKO5VaGzur62LlyUdmjj5YJzWQU4labG/R2YVCMiy2Oz0z9jY2MREhKCHj16mPS4IRXrqiVd5RRQIiJLMnLkSMybNw+lpeVrh8lkMqSmpmL69Ol44oknJI5OWvoiBUyqERGZT6tWrSCTycT7d7qZ0/Tp09GkSRM0a9YMqamp+PHHH8Xnrl+/joiICKxfv77WlTtjYmKgUqnEW0BAgMli1U8BPXmF362IyDLZbFItMjISSUlJOHr0qEmPy2IFRESWafHixSgoKIC3tzdu3ryJgQMHom3btmjatCk++OADqcOTVIpY+ZNJNSKihvD555/j559/Fh+//fbbcHNzQ58+fXDp0iWjjjVjxgzIZLI73s6cOSO2f+utt/DXX39h586dUCgUGDNmjDgNdfz48XjuuecwYMCAWp8/OjoaarVavF2+fNmo+O9ETKql5ZrsmEREpsTpnyamT6olMalGRGRRVCoVdu3ahT///BN///03CgoKcN999yE8PFzq0CQlCAJHqhERNbD58+djxYoVAID4+HgsX74cy5Ytw/bt2zFlypRaTbvUmzp1KiIiIu7YpnXr1uJ9T09PeHp6ol27dggODkZAQAAOHTqEsLAw7NmzBz/99BMWLVoEoLyP0Ol0sLOzw6pVq/DSSy9VObZSqYRSqax1vMbo1KI8qXbiCosVEJFlYlLNxIIrKoCezy5ASZkODnY2OxiQiMgi9e3bF3379pU6DItxvbAE+ZoyyGRASw9nqcMhIrIJly9fRtu2bQEAP/zwA5588km8+uqr6Nu3LwYNGmTUsby8vOq8Nqi+Gql+TbT4+HiDIgk//vgjFixYgIMHD8Lf379O56iPkOaukMuArHwNMvOK4ePKddWIyLIw42Ni/m5OcHW0Q6lWwLmsAqnDISKiCpMmTcInn3xSZfvy5cvx5ptvNnxAFkI/9bO5ygmO9gqJoyEisg0uLi64fv06AGDnzp0YOnQoAMDR0RE3b940yzkPHz6M5cuXIzExEZcuXcKePXswevRotGnTBmFhYQCA4OBghIaGijd/f3/I5XKEhobC3d3dLHHdibODHdp6uwAATnK0GhFZICbVTEwmk6ED11UjIrI4W7ZsqXaEWp8+ffDdd99JEJFlSOHUTyKiBjd06FC88soreOWVV3D27Fk89NBDAIB//vkHgYGBZjmns7Mztm7diiFDhqB9+/Z4+eWX0alTJ+zbt89s0zdNoaO/GwDgRBqTakRkeZhUM4MQJtWIiCzO9evXoVKpqmx3dXXFtWvXJIjIMlwUixRw6icRUUOJjY1FWFgYsrOzsWXLFjRr1gwAkJCQgNGjR5vlnB07dsSePXtw/fp1FBcXIyUlBStWrLjjtM6IiAjk5uaaJZ7a6uhf/t3qFJNqRGSBuKaaGejXVTudwaQaEZGlaNu2LeLi4jBx4kSD7b/88ovBAs625uJ1/Ug1F4kjISKyHW5ubli+fHmV7XPnzpUgGsvWsYUbgPJiBYIgQCaTSRsQEVElNptUi42NRWxsrMFCnKYSLI5Uy+eFn4jIQkRFRWHixInIzs7G/fffDwDYvXs3Fi9ejGXLlkkbnIQuZOuTahypRkTUkP744w98+umnuHDhAjZv3gx/f398+eWXCAoKQr9+/aQOz2KE+LlCIZfhWoEGmXka+KpYrICILIfNTv+MjIxEUlISjh49avJjt/NpCrkMyCksQVa+xuTHJyIi47300ktYvHgxPvvsMwwePBiDBw/GV199hRUrVmD8+PFShycJQRBw6XoRACCwGddUIyJqKFu2bMGwYcPg5OSE48ePi9U31Wo15s+fL3F0lsXJQYF7KooVnLiSK20wRES3sdmkmjk52ivQ2qv8wp/EddWIiCzGhAkTcOXKFWRmZiIvLw8XLlzAmDFjpA5LMpl5Gtws1UIhlyHAgyPViIgayvvvv4+VK1di9erVsLe3F7f37dsXx48flzAyy9TRv3xN1JNcV42ILAyTamYSzGIFREQWJSUlBf/++y8AwMvLCy4u5T9+/Pvvv7h48aKEkUlHX/kzwN0J9gp+JCAiaijJyckYMGBAle0qlUrywgCWqGMLJtWIyDLxE7SZiMUK0vMljoSIiIDyCmYHDx6ssv3w4cOIiIho+IAsQIpY+ZNTP4mIGpKvry/OnTtXZfuBAwdsunhOTcSRahXFCoiILAWTambCkWpERJblr7/+Qt++fats7927NxITExs+IAugr/zJ9dSIiBrW+PHjMXnyZBw+fBgymQxXr17Fhg0bMG3aNEyYMEHq8CxOsJ8r7OQyXC8swVV1sdThEBGJbLb6p7mFVCTVLmQXoLhUC0d7hcQRERHZNplMhvz8qqOH1Wq1WSpBWwP9SLXWXkyqERE1pBkzZkCn02HIkCEoKirCgAEDoFQqMW3aNLzxxhtSh2dxHO0VuMenKU6n5+HkFTX83ZykDomICABHqpmNd1MlPJo4QCcAZzM5BZSISGoDBgxATEyMQQJNq9UiJiYG/fr1kzAy6YjTPzlSjYioQclkMrzzzjvIycnBqVOncOjQIWRnZ+O9997DzZs3pQ7PInUSixXkShsIEVElHKlmJjKZDMF+TfHnues4nZ6HTi3cpA6JiMimLViwAAMGDED79u3Rv39/AMAff/yBvLw87NmzR+LoGp5WJyD1ehEAIIhrqhERScLBwQEhISEAAI1GgyVLlmDhwoXIyMiQODLL07GFCpuOXcbJNC6vQ0SWgyPVzCjYV7+uGkeqERFJLSQkBCdOnMDTTz+NrKws5OfnY8yYMThz5gxCQ0OlDq/BXc29iRKtDg4KOZpzGg0RUYPQaDSIjo5G9+7d0adPH/zwww8AgHXr1iEoKAhLly7FlClTpA3SQt0qVpDLYgVEZDE4Us2M9MUKklisgIjIIjRv3hzz58+XOgyLoC9S0LKZMxRymcTREBHZhtmzZ+PTTz9FeHg4Dh48iKeeegrjxo3DoUOHsGTJEjz11FNQKLgWc3U6+DWFvUKGG0WluHLjJgI8nKUOiYiISTVzqlwBVBAEyGT80kJEJJX9+/ff8fkBAwY0UCSWgeupERE1vM2bN+OLL77AyJEjcerUKXTq1AllZWX4+++/+V3hLpR2CrT3bYpTaXk4laZmUo2ILILNJtViY2MRGxtr1opvbb1dYK+QIb+4DGm5N9HCnRd+IiKpDBo0qMq2yl9gbK0CqD6pFuTJvomIqKFcuXIF3bp1AwCEhoZCqVRiypQpTKjVUkd/FU6l5eFEmhoPdvSTOhwiIttdUy0yMhJJSUk4evSo2c7hYCdHGy8XAFxXjYhIajdu3DC4ZWVlIS4uDj169MDOnTulDq/BXRSTai4SR0JEZDu0Wi0cHBzEx3Z2dnBx4XW4tjr6uwEATl5RSxsIEVEFmx2p1lBC/FxxJiMfp9PzMDTER+pwiIhslkqlqrJt6NChcHBwQFRUFBISEiSISjoXKyp/BnKkGhFRgxEEAREREVAqlQCA4uJi/Oc//0GTJoZT8bdu3SpFeBZPLFaQpubyOkRkEZhUM7NgP1fgrzScZrECIiKL5OPjg+TkZKnDaFClWh1Sc8qTakGeXFONiKihjB071uDxCy+8IFEk1qmdrwscFHKob5bics5NtGzGH4aISFpMqplZ5WIFREQknRMnThg8FgQB6enp+PDDD9GlSxdpgpLIlRs3odUJcLSXw6epo9ThEBHZjHXr1kkdglVT2inQwa8pTlxR42Samkk1IpKcza6p1lCC/ZoCAC7lFKFQUyZxNEREtqtLly7o2rUrunTpIt5/6KGHUFJSgjVr1kgdXoO6WKnyp1zOqTNERLZi5MiRaNmyJRwdHeHn54cXX3wRV69eNWgjCAIWLVqEdu3aQalUwt/fHx988IFEEVcVWjEF9ERarrSBEBGBSTWza+aihHdTJQQBOJPBYgVERFJJSUnBhQsXkJKSgpSUFFy6dAlFRUU4ePAgOnToYPTxYmNjERgYCEdHR/Tq1QtHjhypse3q1avRv39/uLu7w93dHeHh4Xdsb263Kn9y6icRkS0ZPHgwvv32WyQnJ2PLli04f/48nnzySYM2kydPxpo1a7Bo0SKcOXMGP/30E3r27ClRxFV10q+rxmIFRGQBOP2zAQT7uSIrPxun0/PQrZW71OEQEdmkVq1amexYmzZtQlRUFFauXIlevXph2bJlGDZsGJKTk+Ht7V2l/d69ezF69Gj06dMHjo6OWLBgAR544AH8888/8Pf3N1lctaVPqgUyqUZEZFOmTJki3m/VqhVmzJiBUaNGobS0FPb29jh9+jRWrFiBU6dOoX379gCAoKAgqcKtVscWLFZARJaDI9UaANdVIyKSTnx8PLZv326w7YsvvkBQUBC8vb3x6quvQqPRGHXMJUuWYPz48Rg3bhxCQkKwcuVKODs7Y+3atdW237BhA15//XV06dIFHTp0wJo1a6DT6bB79+46v676uHi9YqRaMybViIhsVU5ODjZs2IA+ffrA3t4eALBt2za0bt0a27dvR1BQEAIDA/HKK68gJyenxuNoNBrk5eUZ3MypnU9TONjJkV9chksVlayJiKTCpFoDCGlenlRLYlKNiKjBzZs3D//884/4+OTJk3j55ZcRHh6OGTNmYNu2bYiJian18UpKSpCQkIDw8HBxm1wuR3h4OOLj42t1jKKiIpSWlsLDw6PGNub8kiJO//RiUo2IyNZMnz4dTZo0QbNmzZCamooff/xRfO7ChQu4dOkSNm/ejC+++ALr169HQkJClSmilcXExEClUom3gIAAs8Zvr5CLgxZOpHEKKBFJi0m1BhBSUawgOSMfOp0gcTRERLYlMTERQ4YMER9v3LgRvXr1wurVqxEVFYVPPvkE3377ba2Pd+3aNWi1Wvj4+Bhs9/HxQUZGRq2OMX36dDRv3twgMXc7c31JKS7VIi33JoDyQgVERGTdZsyYAZlMdsfbmTNnxPZvvfUW/vrrL+zcuRMKhQJjxoyBIJR/R9HpdNBoNPjiiy/Qv39/DBo0CJ999hl+//13JCcnV3v+6OhoqNVq8Xb58mWzv2b9umqnmFQjIolxTbUGENisCZR2chSVaHEpp4gLQxMRNaAbN24YJMD27duHBx98UHzco0ePBvkCoPfhhx9i48aN2Lt3LxwdHWtsFx0djaioKPFxXl6eSRJrl3OKIAiAi9IOni4O9T4eERFJa+rUqYiIiLhjm9atW4v3PT094enpiXbt2iE4OBgBAQE4dOgQwsLC4OfnBzs7O7Rr105sHxwcDABITU0V11mrTKlUQqlUmubF1FJHfQXQK7kNel4iotsxqdYA7BRytPdtihNX1DidnsekGhFRA/Lx8UFKSgoCAgJQUlKC48ePY+7cueLz+fn54loyteHp6QmFQoHMzEyD7ZmZmfD19b3jvosWLcKHH36I3377DZ06dbpjW3N9Salc+ZOLOxMRWT8vLy94eXnVaV+dTgcA4tqiffv2RVlZGc6fP482bdoAAM6ePQvAtAV/6ktfrOCftDzodALkcvZnRCQNTv9sIMG+LFZARCSFhx56CDNmzMAff/yB6OhoODs7o3///uLzJ06cEL841IaDgwO6detmUGRAX3QgLCysxv0WLlyI9957D3FxcejevXvdXowJ6IsUsPInEZFtOXz4MJYvX47ExERcunQJe/bswejRo9GmTRux/woPD8d9992Hl156CX/99RcSEhLw2muvYejQoQaj16R2j7cLlHZy5GvKxH6NiEgKTKo1kOCKddWYVCMialjvvfce7OzsMHDgQKxevRqrV6+Gg8OtaY9r167FAw88YNQxo6KisHr1anz++ec4ffo0JkyYgMLCQowbNw4AMGbMGERHR4vtFyxYgFmzZmHt2rUIDAxERkYGMjIyUFBQYJoXaQRxpFoz5wY/NxERScfZ2Rlbt27FkCFD0L59e7z88svo1KkT9u3bJ46Mlsvl2LZtGzw9PTFgwAA8/PDDCA4OxsaNGyWO3pCdQi4WgzvJddWISEKc/tlA9BVqTqfnSxwJEZFt8fT0xP79+6FWq+Hi4gKFQmHw/ObNm+Hi4mLUMZ955hlkZ2dj9uzZyMjIQJcuXRAXFyeu3Zaamgq5/NbvVitWrEBJSUmV6mlz5szBf//737q9sDrSJ9U4Uo2IyLZ07NgRe/bsuWu75s2bY8uWLQ0QUf108lfhr9RcnLyixqNd/KUOh4hslNUn1XJzcxEeHo6ysjKUlZVh8uTJGD9+vNRhVdGhIqmWlnsT6qJSqJxrv34PERHVn0qlqna7h4dHnY43ceJETJw4sdrn9u7da/D44sWLdTqHOVy8VgQAXN+TiIisWqi+WAFHqhGRhKw+qda0aVPs378fzs7OKCwsRGhoKB5//HE0a9ZM6tAMqJzs4e/mhLTcmzidkYferS0rPiIiavyKSsqQkVcMgEk1IiKybp1auAEA/klTs1gBEUnG6tdUUygUcHYuXxdGo9FAEAQIgiBxVNW7NQWU66oREVHD049Sc3O2h5uzw11aExERWa42Xk3gZK9AYYkWF66xWAERSUPypNr+/fsxYsQING/eHDKZDD/88EOVNrGxsQgMDISjoyN69eqFI0eOGDyfm5uLzp07o0WLFnjrrbfg6enZQNEbJ4TFCoiISEL6CmkcpUZERNbOsFhBrrTBEJHNkjypVlhYiM6dOyM2Nrba5zdt2oSoqCjMmTMHx48fR+fOnTFs2DBkZWWJbdzc3PD3338jJSUFX3/9NTIzM2s8n0ajQV5ensGtobBYARERSelW5U8m1YiIyPp1rFhX7eQVDlogImlInlR78MEH8f777+Oxxx6r9vklS5Zg/PjxGDduHEJCQrBy5Uo4Oztj7dq1Vdr6+Pigc+fO+OOPP2o8X0xMDFQqlXgLCAgw2Wu5G31SLTkzH2VaXYOdl4iICGDlTyIialw6tahIqnGkGhFJRPKk2p2UlJQgISEB4eHh4ja5XI7w8HDEx8cDADIzM5GfXz7yS61WY//+/Wjfvn2Nx4yOjoZarRZvly9fNu+LqKSlhzOaOChQUqYTv9gQERE1lItMqhERUSOiH6l2Ki0PWp1lrqtNRI2bRVf/vHbtGrRaLXx8fAy2+/j44MyZMwCAS5cu4dVXXxULFLzxxhvo2LFjjcdUKpVQKpVmjbsmcrkM7X2b4nhqLpLS83CPT1NJ4iAiy6PVCTiSkoOs/GJ4N3VEzyAPKFjFikxMv6ZaaybViIioEWjt5QJnBwWKSrS4kF3A71dE1OAsOqlWGz179kRiYqLR+8XGxiI2NhZardb0Qd1BsJ8rjqfm4nR6Ph7t0qCnJiILFXcqHXO3JSFdXSxu81M5Ys6IEAwP9ZMwMmpM8opLca2gBABHqhERUeOgkMsQ2lyFIxdzcOKKmkk1ImpwFj3909PTEwqFokrhgczMTPj6+tbr2JGRkUhKSsLRo0frdRxjtfctv9DvS85C/PnrHKZMZOPiTqVjwlfHDRJqAJChLsaEr44j7lS6RJFRY6Of+unpooSL0up/UyMiIgIAhOqLFaSpJY6EiGyRRSfVHBwc0K1bN+zevVvcptPpsHv3boSFhUkYWd3EnUrHx7/9CwA4nZGP0asPod+CPfzSTGSjtDoBc7clobrUun7b3G1JTL6TSejX8uTUTyIiakxuFStgUo2IGp7kP1UXFBTg3Llz4uOUlBQkJibCw8MDLVu2RFRUFMaOHYvu3bujZ8+eWLZsGQoLCzFu3DgJozaefjTK7V+N9aNRVrxwH6d5ETVyJWU6XC/UIDu//HY45XqVEWqVCQDS1cU4kpKDsDbNGi5QapQuXisCAAR6OkscCRERkenoR6r9c1WNMq0OdgqLHjdCRI2M5Em1Y8eOYfDgweLjqKgoAMDYsWOxfv16PPPMM8jOzsbs2bORkZGBLl26IC4urkrxAmM15JpqdxuNIkP5aJShIb5cmJzIymh1Am4UlYiJsux8Da4VVNwvMNx2o6i0TufIyq858UZUW/oiBVxPjYiIGpPWnk3gbC9HUakOa/5IQecANxZ8IqIGI3lSbdCgQRCEO09tmjhxIiZOnGjS80ZGRiIyMhJ5eXlQqVQmPfbtjqTkcDQKkRURBAF5xWW3EmUFtyXLKm3PKSwxanqmnVwGTxclvJoqYSeX4a/LuXfdx7upYz1eDVG5CxXTP4OaMalGRESNx86kDJRVfBb7MO4MABZ8IqKGI3lSzRbUdpQJR6MQmVdRSRmu5Zcgu6D4tuRYiZgku1axrUSrq/VxZTLAw9kBXk3Lk2VeLkp4VvxX3FbxWOVkD3nFL6danYB+C/YgQ11c7UhWGQBflSN6BnmY5g0gm6YvVBDkxaQaERE1Dlxih4ikxqRaA6jtKBOORiEyXkmZDtcKqh9Fdvu2whLjpns3dbQTk2H6xJini2GSzLupEh5NHOq0fodCLsOcESGY8NVxyACDD4T6CQtzRoRw+gLV243CEqhvlk8/buXBpBoREVk/LrFDRJbAZpNqDbmmWs8gD/ipHGscjQKUD1HmaBSiclqdgJzC20aPFVS/ZlmukeuUOdrL4d3UEZ4ulUeWOcKzqUOV5JmjvcJMr/CW4aF+WPHCfZi7Lclgmrgvpy2QCaVUrKfmp3KEk4P5/10TERGZG5fYISJLYLNJtYZcU+1Oo1H0woO9+QsKNWqCICDvZhmyC4qRla/BtYKSqiPLKv57vUADI5Ypg51cZjiS7LZpl5VHlzVxUEAms6z/14aH+mFoiC+OpOQgK78Y3k0ducAumVRKdsXUTxYpICKiRoJL7BCRJbDZpFpDq2k0SlNHO+QXl+HbY1fwXK9WCPZzlTBKIuMVlZTVovJlSZ3WKWvWxOFWQqya9ck8q1mnzFop5DL+ikpmw8qfREQEACNHjkRiYiKysrLg7u6O8PBwLFiwAM2bNxfb/Prrr5gzZw7++ecfODo6YsCAAVi8eDECAwOlC7waXGKHiCwBk2oNqLrRKN1buWP8l8ewNzkbkRuO46c3+sFFyT8LSUtTpsX1yiPJqqt+WTGyzNh1ylz165Q1VcKr8jTM29Yqq+s6ZURUVQorfxIREYDBgwdj5syZ8PPzQ1paGqZNm4Ynn3wSBw8eBACkpKTg0UcfRVRUFDZs2AC1Wo0pU6bg8ccfx/HjxyWO3hCX2CEiS2Cz2ZuGXFOtsupGoyx5ugse/uQPXLhWiJlbT+LjZ7tY3PQ0sn5anYDrhZqK6peaO44u0y9oXltO9gqDhFiVBf0rbs2aODTIOmVEZEifVONINSIi2zZlyhTxfqtWrTBjxgyMGjUKpaWlsLe3R0JCArRaLd5//33I5eU/bk6bNg2PPvqo2MZS1GaJnb5tPbmcBhGZlc0m1RpyTbW78WjigOXPdcUznx7CT39fRa/WHni+VytJY6LqaXWCRa17JQgC1DdLq0y3vDWy7NZos5xC49Yps1fIqp16eXv1S6+mSjTh6EoiiyUIAi5e45pqRERkKCcnBxs2bECfPn3EZFm3bt0gl8uxbt06REREoKCgAF9++SXCw8NrTKhpNBpoNBrxcV5eXoPED9x9iZ3vEq6gX1tPjOrq32AxEZFt4TdhC9GtlQfeHt4e83ecwdxtSQhtrkJRidZikjcExJ1Kr9Jh+5mpQmOhpqzGypeVR5ZdKyipwzplSsPKl5WTZpUSZione46YJGoEsgvKp2nLZUBLD2epwyEiIolNnz4dy5cvR1FREXr37o3t27eLzwUFBWHnzp14+umn8dprr0Gr1SIsLAw7duyo8XgxMTGYO3duQ4RereqW2OkR6I4PdpzGuj8vYtrmv6Fytsfg9t6SxUhEjZdMEAQjxq40PvqRamq1Gq6u0hYJEAQB4784ht9OZ0Ehl0FbaViRuZI3VDtxp9Ix4avjVYaV61NOK164765/G02Z1mDk2LXbEmXZBbe2FRm5TpnKyb5iFJkDvJo63jay7FYCzcOZ65Q1RpZ0HSPzqevf+UhKDp7+NB4BHk744+37zRghEdGdsb8yjxkzZmDBggV3bHP69Gl06NABAHDt2jXk5OTg0qVLmDt3LlQqFbZv3w6ZTIaMjAwMGDAAo0aNwujRo5Gfn4/Zs2fDzs4Ou3btqvYH1+pGqgUEBEj+d9bpBEz5NhE/Jl6Fo70cG17pjS4BbhY164SILJMx/RVHqlkQmUyGB0N98dvpLIOEGgBkqIsx4avjtUrekGlpdQLmbkuqdp0G/bZ3fzgFB4Uc1wtLbiXOCjTIzi8WR5TVZZ0yb9eKKpc1Vb6sSJop7bhOGRFVL+VaAQAgkEUKiIgapalTpyIiIuKObVq3bi3e9/T0hKenJ9q1a4fg4GAEBATg0KFDCAsLQ2xsLFQqFRYuXCi2/+qrrxAQEIDDhw+jd+/eVY6tVCqhVCpN9npMRS6X4aMnOyO3qBT7zmbjxc8Ow9lBgWsFJWIbDlwgovpiUs2CaHUCFu08W+1zAspHRc3dloShIb78RaUBCIKA3KJS7DiZbjDlszrXCkrw0ufH7npMe4XsruuTeXKdMiIyEa1OwIFz1wEAzvYKaHUC+w8iokbGy8sLXl5eddpXpytfRkQ/0qyoqEgsUKCnUCgM2loTBzs5VrxwHx76+A9cvF5UZTYIBy4QUX3Z7Ld2qap/3smRlJw7Jm8EAOnqYhxJyalSQZTqprhUiys3inA55yZSc4pwOaeo/L83buJyThEKNGW1PlZzNye09XapGEXmYJA8865IlnGdMiJqKLevA/lrUib6LdjDX+SJiGzU4cOHcfToUfTr1w/u7u44f/48Zs2ahTZt2iAsLAwA8PDDD2Pp0qWYN2+eOP1z5syZaNWqFbp27SrxK6gbpZ0CN2tYWoUDF4iovmw2qWZJ1T/1svLvPBpKLyOvdu2ofJRGRl4xLlckzC5XJMz0CbSsfM1dj+HmZI/cWkzdXPxUZyY7icgi1LQOJH+RJyKyXc7Ozti6dSvmzJmDwsJC+Pn5Yfjw4Xj33XfF6Zv3338/vv76ayxcuBALFy6Es7MzwsLCEBcXBycnJ4lfQd0cSclB5h0+83PgAhHVh80m1SyRd1PHWrX74OckXMvX4OkeAVA5VV/aWkpandBgC4AKggD1zdKKJFlFsuzGrQRaWu5NlGrvXIvDRWmHAA9ntPRwQoC7c8V9ZwR4OKGFuzPsFXL0W7AHGeriatdVkwHwVZW/TiIiqd1tHUj+Ik9EZJs6duyIPXv23LXds88+i2effbYBImoYtR24sOloKpq7OaIV1yAlIiMwqWZBegZ5wE/lWGPyBgBksvL1uz7YcRpLfzuLJ+5rgYi+gWjj5dKgsdbk9ulGQP0XAC2fonmzYpRZEVKv6xNn5dvy7zJF004uQwt3JwR4lCfMyhNnTuWJM3dnuDnffUrmnBEhmPDVccgAg7+NrNLz/HJKRJaASwkQERHdUtuBCz8kXsUPiVfRzscF4cE+CA/xQZcWbpDf5TN+Qw4oICLLw6SaBVHIZXdN3nz8TBcUlWix7s+LSM7Mx5eHLuHLQ5cwqL0XxvUNwoB7PCVbs6uu0420OgGZFVM0K69npn9cmymaXk2VFUkyw+RZy2bO8HV1rHfHNjzUDyteuK9KwtCXFYOIyMLU9hf52rYjIiKyZrUZuODqaIcQP1ccvXQDZzMLcDazAP+39zw8XZQID/ZGeLAP+rb1hJODwmA/cwwoqA4Td0SWi0k1C1Pb5M0zPQIQf/461v6Zgt1nsrA3ORt7k7PRxqsJIvoG4Yn7/OHsUPXPa64Lcm2mG737wymUaQVcyb0pJsyu3LiJKzeK7jpFs4mDotK0zPLkWctm5YmzFu7OVTo4cxge6oehIb7s0IjIotX2F/natiMiIrJmtRm4sPDJThge6gd1USn2ns3CrqRM7EvOxrUCDTYevYyNRy/D0V6Ofm29MDTEG/d38EHCpZwGWb+0oRJ3UmHCkMylof5tyQRBuHM2o5GqXP3z7NmzUKvVcHV1lToskTH/AC5eK8Tn8Rex+dgVsVqlq6MdRvdsiRfDWqGFuzMA812Qy7Q6xJ3KwMRv/qrzMezkMvi731rTLKBifTN9Es29FlM0iWyVvuCKpV3HyLRq+3fW6gT0W7DnjlNA/VSOODD9fn5oJaIGxf7KNljq39nY70IlZTocScnBrqQM/HY6C2m5Nw2et1fIahwYoF9zub59bU0zgfRHtPbCQ409YUjSqe+/LWOuYzabVNOz1It+XeQXl+K7hCtYf/AiLl0vAgDIZcCwe31xb3NXLN551ugLsqZMi0y1Bunqm8jIK0a6uhgZ6uLyx+piZOQVIztfA10t/xUFNnNG5wA3cT2zFhVrm/m6OsJOIa/7iyeyYY3pOmZNYmNj8dFHHyEjIwOdO3fG//73P/Ts2bPG9ps3b8asWbNw8eJF3HPPPViwYAEeeuihWp/PmL9zzI4kfLo/pcbnXxsQhOiHQmp9biIiU2B/ZRss+e9c15ErgiDgdHo+fjudid9OZ+LEFXWtzvdczwC082kKpb0CSjs5lHYV/7Uvv+9gJ6/YLq/Upvw5uQzov/D3Gn8kM1XiTiqNPWFI0jHFvy0m1YxgyRf9utLqBPx+JgvrDqbgz3PXa7WPm5M9XuoXiKx8TUXSrDx5dr2wpFb7y2WoVWLtm/G9uTA2kYk1xuuYpdu0aRPGjBmDlStXolevXli2bBk2b96M5ORkeHt7V2l/8OBBDBgwADExMXjkkUfw9ddfY8GCBTh+/DhCQ0NrdU6OVCMia8f+yjbYwt/584MpmPNTktRhAADaeDWBm7MDFDIZ5PLy6a5ymQwKuaxiW/l/FXL9fVSzTVZpP1Sz7bbnq2yrdK7Kz1d7/vJJuJM2JiLnDt81PV0csC6iJxRyGWSy8oJ9ACCrSI3IZLeSJOXPVbe9YhsM9688AUrcfpe2lU5RQwwyg3hkqLxj7dpWG9dtMVQbJ2d0ie72Obi2yWgm1YzQ2C/6yRn5WBB3GnvOZNf5GEo7OfxUjvBVOcJP5VTxX0f4upY/9lEp4e7kgAEf/V7jAqDW/ksKkSVr7NcxS9SrVy/06NEDy5cvBwDodDoEBATgjTfewIwZM6q0f+aZZ1BYWIjt27eL23r37o0uXbpg5cqV1Z5Do9FAo7lVqCUvLw8BAQF3/TvHn7+O0asP3fU18EcOImpo7K9sgy38nWvb1/a/xxMqJ3toynTlt1LtrftlWmhKK90v06GkTNcA0VNjdtcEXKVkX02JveqSkqjuuHdJYKJKQtAwhur2F7fXMoGJ27bfLClDWu7di3Hd7XOwMdcxFipo5Nr7NsWjXfxrlVTrFeSBXkEe8FU5wVelhK+rE/xUjnCr5Xpmd1sAdM6IECbUiMjqlZSUICEhAdHR0eI2uVyO8PBwxMfHV7tPfHw8oqKiDLYNGzYMP/zwQ43niYmJwdy5c42Oj9U/iYiIzOtuFUX1AwrWj+tp1PcfnU5AibY80Xbw/DVM+Or4XfeZ9kA7tPVuCp0gQKsTxP/eug9oBQE63W3Pi9sqPV+pXeVtWh0Mn69yLtzh/AK0AgzOn1tUgow8zV1fm6ujHZT2CtwaBlR+RxBufd8UBKHS/fLHt1qW36mxbaXjifuI9wWD7bcf11KHJhm+lprKCJIpPwczqWYDalvh7c3wdvUatVDbyqVERNbs2rVr0Gq18PHxMdju4+ODM2fOVLtPRkZGte0zMjJqPE90dLRBIk4/Uu1uWP2TiIjIvGpTUbQuAwrkchkc5Qo42ivwQIhvrRJ3Ewa1tbqBC7Ud6ffpi92tYlS9INScgBMqJekAwzzX7Ym9ysm/2/eHEW2FSpnEmmIwSDTeFtMd2xq0q5qUrLy/eL+aBObt57p7ArO6eKq+/qSrarz382ncjSk/BzOpZgNq+0tKzyCPep9reKgfhob4siwyEVE9KZVKKJVKo/dryGs+ERGRrTL3gAJzJe4sQWP7rCKTGa7TdusvRA2tZ5AH1hxIadB/Wyy3aAP0F2Sg6v/e5rggK+QyhLVphke7+COsTTOrvNATEdXE09MTCoUCmZmZBtszMzPh6+tb7T6+vr5Gta+Phr7mExER2arhoX44MP1+fDO+Nz5+tgu+Gd8bB6bfb7IZOvrEna/KcFSNr8rRqqtj8rMKmYsU/7aYVLMRjfWCTETU0BwcHNCtWzfs3r1b3KbT6bB7926EhYVVu09YWJhBewDYtWtXje3ri9d8IiKihmHuAQXmTtxJhZ9VyFwa+t+WzU7/jI2NRWxsLLRardShNBhOzSQiMo2oqCiMHTsW3bt3R8+ePbFs2TIUFhZi3LhxAIAxY8bA398fMTExAIDJkydj4MCBWLx4MR5++GFs3LgRx44dw6pVq8wWI6/5REREjYM+cdfY8LMKmUtD/tuy2aRaZGQkIiMjxVKptqKxXpCJiBrSM888g+zsbMyePRsZGRno0qUL4uLixGIEqampkMtvDQbv06cPvv76a7z77ruYOXMm7rnnHvzwww8IDQ01a5y85hMREZEl42cVMpeG+rclEwShuvXbbIY+qaZWq+Hq6ip1OERERuN1zDbw70xE1o7XMdvAvzMRWTtjrmNcU42IiIiIiIiIiMhITKoREREREREREREZyWbXVNPTz37Ny8uTOBIiorrRX79sfDZ/o8f+ioisHfsr28D+ioisnTH9lc0n1fLz8wEAAQEBEkdCRFQ/+fn5NlV4xdawvyKixoL9VePG/oqIGova9Fc2X6hAp9Ph6tWraNq0KWQy2yjdm5eXh4CAAFy+fJmLh5oA30/T4vtpPEEQkJ+fj+bNmxtUnKTGhf0Vrwf1xffTtPh+Go/9lW1gf8XrQX3x/TQtvp/GM6a/svmRanK5HC1atJA6DEm4urryfyoT4vtpWnw/jcNf/Bs/9le8HpgK30/T4vtpHPZXjR/7K14PTIXvp2nx/TRObfsr/kRERERERERERERkJCbViIiIiIiIiIiIjMSkmg1SKpWYM2cOlEql1KE0Cnw/TYvvJxHp8XpgWnw/TYvvJxHp8XpgWnw/TYvvp3nZfKECIiIiIiIiIiIiY3GkGhERERERERERkZGYVCMiIiIiIiIiIjISk2pERERERERERERGYlKNiIiIiIiIiIjISEyqNRIxMTHo0aMHmjZtCm9vb4waNQrJyckGbYqLixEZGYlmzZrBxcUFTzzxBDIzMw3apKam4uGHH4azszO8vb3x1ltvoaysrCFfisX58MMPIZPJ8Oabb4rb+F4aLy0tDS+88AKaNWsGJycndOzYEceOHROfFwQBs2fPhp+fH5ycnBAeHo5///3X4Bg5OTl4/vnn4erqCjc3N7z88ssoKCho6JdCRPXA/sq82GfVH/srIgLYX5kb+6v6Y39lGZhUayT27duHyMhIHDp0CLt27UJpaSkeeOABFBYWim2mTJmCbdu2YfPmzdi3bx+uXr2Kxx9/XHxeq9Xi4YcfRklJCQ4ePIjPP/8c69evx+zZs6V4SRbh6NGj+PTTT9GpUyeD7XwvjXPjxg307dsX9vb2+OWXX5CUlITFixfD3d1dbLNw4UJ88sknWLlyJQ4fPowmTZpg2LBhKC4uFts8//zz+Oeff7Br1y5s374d+/fvx6uvvirFSyKiOmJ/ZT7ss+qP/RUR6bG/Mh/2V/XH/sqCCNQoZWVlCQCEffv2CYIgCLm5uYK9vb2wefNmsc3p06cFAEJ8fLwgCIKwY8cOQS6XCxkZGWKbFStWCK6uroJGo2nYF2AB8vPzhXvuuUfYtWuXMHDgQGHy5MmCIPC9rIvp06cL/fr1q/F5nU4n+Pr6Ch999JG4LTc3V1AqlcI333wjCIIgJCUlCQCEo0ePim1++eUXQSaTCWlpaeYLnojMiv2VabDPMg32V0RUE/ZXpsH+yjTYX1kOjlRrpNRqNQDAw8MDAJCQkIDS0lKEh4eLbTp06ICWLVsiPj4eABAfH4+OHTvCx8dHbDNs2DDk5eXhn3/+acDoLUNkZCQefvhhg/cM4HtZFz/99BO6d++Op556Ct7e3ujatStWr14tPp+SkoKMjAyD91SlUqFXr14G76mbmxu6d+8utgkPD4dcLsfhw4cb7sUQkUmxvzIN9lmmwf6KiGrC/so02F+ZBvsry8GkWiOk0+nw5ptvom/fvggNDQUAZGRkwMHBAW5ubgZtfXx8kJGRIbapfIHSP69/zpZs3LgRx48fR0xMTJXn+F4a78KFC1ixYgXuuece/Prrr5gwYQImTZqEzz//HMCt96S696zye+rt7W3wvJ2dHTw8PGzyPSVqDNhfmQb7LNNhf0VE1WF/ZRrsr0yH/ZXlsJM6ADK9yMhInDp1CgcOHJA6FKt0+fJlTJ48Gbt27YKjo6PU4TQKOp0O3bt3x/z58wEAXbt2xalTp7By5UqMHTtW4uiISCrsr+qPfZZpsb8iouqwv6o/9lemxf7KcnCkWiMzceJEbN++Hb///jtatGghbvf19UVJSQlyc3MN2mdmZsLX11dsc3t1Ff1jfRtbkJCQgKysLNx3332ws7ODnZ0d9u3bh08++QR2dnbw8fHhe2kkPz8/hISEGGwLDg5GamoqgFvvSXXvWeX3NCsry+D5srIy5OTk2OR7SmTt2F+ZBvss02J/RUS3Y39lGuyvTIv9leVgUq2REAQBEydOxPfff489e/YgKCjI4Plu3brB3t4eu3fvFrclJycjNTUVYWFhAICwsDCcPHnS4H+sXbt2wdXVtcr/sI3ZkCFDcPLkSSQmJoq37t274/nnnxfv8700Tt++fauUID979ixatWoFAAgKCoKvr6/Be5qXl4fDhw8bvKe5ublISEgQ2+zZswc6nQ69evVqgFdBRKbA/sq02GeZFvsrItJjf2Va7K9Mi/2VBZG4UAKZyIQJEwSVSiXs3btXSE9PF29FRUVim//85z9Cy5YthT179gjHjh0TwsLChLCwMPH5srIyITQ0VHjggQeExMREIS4uTvDy8hKio6OleEkWpXJlGkHge2msI0eOCHZ2dsIHH3wg/Pvvv8KGDRsEZ2dn4auvvhLbfPjhh4Kbm5vw448/CidOnBAeffRRISgoSLh586bYZvjw4ULXrl2Fw4cPCwcOHBDuueceYfTo0VK8JCKqI/ZX5sc+q+7YXxGRHvsr82N/VXfsrywHk2qNBIBqb+vWrRPb3Lx5U3j99dcFd3d3wdnZWXjssceE9PR0g+NcvHhRePDBBwUnJyfB09NTmDp1qlBaWtrAr8by3H7B53tpvG3btgmhoaGCUqkUOnToIKxatcrgeZ1OJ8yaNUvw8fERlEqlMGTIECE5OdmgzfXr14XRo0cLLi4ugqurqzBu3DghPz+/IV8GEdUT+yvzY59VP+yviEgQ2F81BPZX9cP+yjLIBEEQGnp0HBERERERERERkTXjmmpERERERERERERGYlKNiIiIiIiIiIjISEyqERERERERERERGYlJNSIiIiIiIiIiIiMxqUZERERERERERGQkJtWIiIiIiIiIiIiMxKQaERERERERERGRkZhUIyIiIiIiIiIiMhKTakT19N///hddunQRH0dERGDUqFGSxLJ3717IZDLk5uZKcn4iIrJs7LOIiMgasL8ia2EndQBEjc3HH38MQRDMfp5BgwahS5cuWLZsmbitT58+SE9Ph0qlMvv5iYjI+rHPIiIia8D+iiwVk2pEJiblxdbBwQG+vr6SnZ+IiKwL+ywiIrIG7K/IUnH6J1mkuLg49OvXD25ubmjWrBkeeeQRnD9/Xnz+4sWLkMlk2Lp1KwYPHgxnZ2d07twZ8fHxYpv169fDzc0Nv/76K4KDg+Hi4oLhw4cjPT3d4Fxr1qxBcHAwHB0d0aFDB/zf//2fwfPTp09Hu3bt4OzsjNatW2PWrFkoLS2tMfbbhyYPGjQIkyZNwttvvw0PDw/4+vriv//9r8E+Z86cQb9+/eDo6IiQkBD89ttvkMlk+OGHH2o8x759+/Dxxx9DJpNBJpPh4sWLVYYm69+D7du3o3379nB2dsaTTz6JoqIifP755wgMDIS7uzsmTZoErVYrHl+j0WDatGnw9/dHkyZN0KtXL+zdu7fG10xEZMvYZ7HPIiKyBuyv2F+R6TGpRhapsLAQUVFROHbsGHbv3g25XI7HHnsMOp3OoN0777yDadOmITExEe3atcPo0aNRVlYmPl9UVIRFixbhyy+/xP79+5Gamopp06aJz2/YsAGzZ8/GBx98gNOnT2P+/PmYNWsWPv/8c7FN06ZNsX79eiQlJeHjjz/G6tWrsXTpUqNez+eff44mTZrg8OHDWLhwIebNm4ddu3YBALRaLUaNGgVnZ2ccPnwYq1atwjvvvHPH43388ccICwvD+PHjkZ6ejvT0dAQEBFTbtqioCJ988gk2btyIuLg47N27F4899hh27NiBHTt24Msvv8Snn36K7777Ttxn4sSJiI+Px8aNG3HixAk89dRTGD58OP7991+jXjcRkS1gn8U+i4jIGrC/Yn9FZiAQWYHs7GwBgHDy5ElBEAQhJSVFACCsWbNGbPPPP/8IAITTp08LgiAI69atEwAI586dE9vExsYKPj4+4uM2bdoIX3/9tcG53nvvPSEsLKzGWD766COhW7du4uM5c+YInTt3Fh+PHTtWePTRR8XHAwcOFPr162dwjB49egjTp08XBEEQfvnlF8HOzk5IT08Xn9+1a5cAQPj+++9rjGPgwIHC5MmTDbb9/vvvAgDhxo0bgiBU/x689tprgrOzs5Cfny9uGzZsmPDaa68JgiAIly5dEhQKhZCWlmZw7CFDhgjR0dE1xkNEROXYZ1XFPouIyPKwv6qK/RUZi2uqkUX6999/MXv2bBw+fBjXrl0Tfz1JTU1FaGio2K5Tp07ifT8/PwBAVlYWOnToAABwdnZGmzZtDNpkZWUBKP+l5vz583j55Zcxfvx4sU1ZWZnBnP1Nmzbhk08+wfnz51FQUICysjK4uroa9Xoqx3l7HMnJyQgICDCYp9+zZ0+jjn8nt78HPj4+CAwMhIuLi8E2fTwnT56EVqtFu3btDI6j0WjQrFkzk8VFRNRYsM9in0VEZA3YX7G/ItNjUo0s0ogRI9CqVSusXr0azZs3h06nQ2hoKEpKSgza2dvbi/dlMhkAGAxfrvy8vo1QUTWmoKAAALB69Wr06tXLoJ1CoQAAxMfH4/nnn8fcuXMxbNgwqFQqbNy4EYsXLzbq9VQXx+3DrM2lunPfKZ6CggIoFAokJCSI74Ne5U6CiIjKsc8yHfZZRETmw/7KdNhfkR6TamRxrl+/juTkZKxevRr9+/cHABw4cMDk5/Hx8UHz5s1x4cIFPP/889W2OXjwIFq1amUw//7SpUsmjaN9+/a4fPkyMjMz4ePjAwA4evToXfdzcHAwWPjSVLp27QqtVousrCzx/Sciouqxz2KfRURkDdhfsb8i82BSjSyOu7s7mjVrhlWrVsHPzw+pqamYMWOGWc41d+5cTJo0CSqVCsOHD4dGo8GxY8dw48YNREVF4Z577kFqaio2btyIHj164Oeff8b3339v0hiGDh2KNm3aYOzYsVi4cCHy8/Px7rvvArj1y1B1AgMDcfjwYVy8eBEuLi7w8PAwSTzt2rXD888/jzFjxmDx4sXo2rUrsrOzsXv3bnTq1AkPP/ywSc5DRNQYsM9in0VEZA3YX7G/IvNg9U+yOHK5HBs3bkRCQgJCQ0MxZcoUfPTRR2Y51yuvvII1a9Zg3bp16NixIwYOHIj169cjKCgIADBy5EhMmTIFEydORJcuXXDw4EHMmjXLpDEoFAr88MMPKCgoQI8ePfDKK6+Iv9o4OjrWuN+0adOgUCgQEhICLy8vpKammiymdevWYcyYMZg6dSrat2+PUaNG4ejRo2jZsqXJzkFE1Biwz2KfRURkDdhfsb8i85AJ+snPRGQx/vzzT/Tr1w/nzp0zWACTiIjI0rDPIiIia8D+isyBSTUiC/D999/DxcUF99xzD86dO4fJkyfD3d3dLOscEBER1Qf7LCIisgbsr6ghcE01IguQn5+P6dOnIzU1FZ6enggPDze6+g0REVFDYJ9FRETWgP0VNQSOVCMiIiIiIiIiIjISCxUQEREREREREREZiUk1IiIiIiIiIiIiIzGpRkREREREREREZCQm1YiIiIiIiIiIiIzEpBoREREREREREZGRmFQjIiIiIiIiIiIyEpNqRERERERERERERmJSjYiIiIiIiIiIyEj/D+clAgslkZcdAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1500x300 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set plotting parameters.\n",
    "fig, (axL,axC,axR) = plt.subplots(ncols=3, figsize=(15,3))\n",
    "plt.subplots_adjust(wspace=0.4)\n",
    "fontsize = 10\n",
    "\n",
    "# Plot TTS\n",
    "axL.plot(result['time'], result['tts'],'-o')\n",
    "axL.set_xlabel('annealing time', fontsize=fontsize)\n",
    "axL.set_yscale(\"log\")\n",
    "axL.set_ylabel('TTS', fontsize=fontsize)\n",
    "\n",
    "# Plot success probability\n",
    "axC.plot(result['time'], result['success_prob'],'-o')\n",
    "axC.set_xlabel('annealing time', fontsize=fontsize)\n",
    "axC.set_ylabel('Success probability', fontsize=fontsize)\n",
    "\n",
    "# Plot residual energy\n",
    "axR.plot(result['time'], result['residual_energy'],'-o')\n",
    "axR.set_xlabel('annealing time', fontsize=fontsize)\n",
    "axR.set_ylabel('Residual energy', fontsize=fontsize)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same results are reproduced as earlier as we easily benchmarked with this function.\n",
    "\n",
    "Furthermore, the `solver_benchmark` function also calculates the standard error, and plotting the results with error bars can be done easily."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Residual energy')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x300 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set plotting parameters.\n",
    "fig, (axL,axC,axR) = plt.subplots(ncols=3, figsize=(15,3))\n",
    "plt.subplots_adjust(wspace=0.4)\n",
    "fontsize = 10\n",
    "\n",
    "# Plot TTS with error bars.\n",
    "axL.plot(result['time'], result['tts'])\n",
    "axL.errorbar(result['time'], result['tts'], yerr = (result['se_lower_tts'],result['se_upper_tts']), capsize=5, fmt='o', markersize=5, ecolor='black', markeredgecolor = \"black\", color='w')\n",
    "axL.set_xlabel('annealing time', fontsize=fontsize)\n",
    "axL.set_ylabel('TTS', fontsize=fontsize)\n",
    "axL.set_yscale(\"log\")\n",
    "\n",
    "#Plot success probability with error bars.\n",
    "axC.plot(result['time'], result['success_prob'])\n",
    "axC.errorbar(result['time'], result['success_prob'], yerr = result['se_success_prob'], capsize=5, fmt='o', markersize=5, ecolor='black', markeredgecolor = \"black\", color='w')\n",
    "axC.set_xlabel('annealing time', fontsize=fontsize)\n",
    "axC.set_ylabel('Success probability', fontsize=fontsize)\n",
    "\n",
    "#Plot residual energy with error bars\n",
    "axR.plot(result['time'], result['residual_energy'])\n",
    "axR.errorbar(result['time'], result['residual_energy'], yerr = result['se_residual_energy'], capsize=5, fmt='o', markersize=5, ecolor='black', markeredgecolor = \"black\", color='w')\n",
    "axR.set_xlabel('annealing time', fontsize=fontsize)\n",
    "axR.set_ylabel('Residual energy', fontsize=fontsize)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Benchmarking with User-defined Functions\n",
    "\n",
    "Any user-defined function can be put in `solver` as long as it returns a `Response` class and stores the calculation time in `.info['execution_time']`.  \n",
    "\n",
    "Here we create an appropriate user-defined solver function and benchmark it.\n",
    "Let us define a function that returns one state at random from the three spin states of [1, 1, 1, 1, ...], [1, -1, 1, -1, ...], and [-1, 1, -1, 1, ...] and benchmark it. We set the optimal solution to [1, -1, 1, -1,...]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import time \n",
    "\n",
    "def anti_ferro_solver(time_param, num_reads, h, J):\n",
    "#     \"\"\"\n",
    "#     This function randomly selects from three states [1, 1, 1,...], [1,-1,1,...], and [-1,1,-1,...]\n",
    "#     \"\"\"\n",
    "    \n",
    "    # Create a set of indices from h and J.\n",
    "    indices = set(h.keys())\n",
    "    indices = list(indices | set([key for keys in J.keys() for key in keys]))\n",
    "    \n",
    "    # Create the state of [1, 1, 1,...]\n",
    "    ones_state = list(np.ones(len(indices), dtype=int))\n",
    "    \n",
    "    # Create the state of [-1, 1, -1,...]\n",
    "    minus_plus_state = np.ones(len(indices), dtype=int)\n",
    "    minus_plus_state[::2] *= -1\n",
    "    \n",
    "    # Create the state of [1, -1, 1,...]\n",
    "    plus_minus_state = -1 * minus_plus_state\n",
    "    \n",
    "    # Measure the execution time.\n",
    "    start = time.time()\n",
    "    _states = [ones_state, list(minus_plus_state), list(plus_minus_state)]\n",
    "    \n",
    "    # Randomly select one state from the three states.\n",
    "    state_record = [_states[np.random.randint(3)] for _ in range(num_reads)]\n",
    "    # Convert the state_record type to ndarray.\n",
    "    state_record = np.array(state_record)\n",
    "    \n",
    "    # Here we bulk up the computation time suitably.\n",
    "    exec_time = (time.time()-start) * 10**3 * time_param\n",
    "    # Here we calculate energies suitably.\n",
    "    energies = [sum(state) for state in state_record]\n",
    "    \n",
    "    # Tie the subscripts to the list of states.\n",
    "    samples_like = (state_record, indices)\n",
    "        \n",
    "    # Referring to dimod's from_samples, store the state and energy in the response class.\n",
    "    response = oj.Response.from_samples(samples_like=samples_like, energy=energies, vartype='SPIN')\n",
    "    # Substitute the computation time to the 'execution_time' key in response.info.\n",
    "    response.info['execution_time'] = exec_time\n",
    "    \n",
    "    return response"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OpenJij's response is made with reference to dimod's SampleSet.\n",
    "Therefore, being familiar with OpenJij will help use dimod and transit to D-Wave execution.\n",
    "For more information on dimod's SampleSet, please see [dimod's samples page](https://docs.ocean.dwavesys.com/en/stable/docs_dimod/reference/sampleset.html#)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having our own solver function, let us take the benchmark of this function.\n",
    "Since we are returning random states, there is no optimal value, but for the sake of TTS calculation, let `[1, -1, 1,...]` be the optimal solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the optimal solution.\n",
    "correct_state = [(-1)**i for i in range(N)]\n",
    "\n",
    "# Define num_sweeps and num_reads\n",
    "num_sweeps_list = list(range(10, 101, 10))\n",
    "num_reads = 2000\n",
    "\n",
    "# Calculate TTS, success probability, and residual energy using benchmark function.\n",
    "result = oj.solver_benchmark(\n",
    "            solver= lambda time_param, **args: anti_ferro_solver(time_param, num_reads, h, J), \n",
    "            time_list=num_sweeps_list, solutions=[correct_state], p_r=0.99\n",
    "            )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Residual energy')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x300 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set plotting parameters.\n",
    "fig, (axL,axC,axR) = plt.subplots(ncols=3, figsize=(15,3))\n",
    "plt.subplots_adjust(wspace=0.4)\n",
    "fontsize = 10\n",
    "\n",
    "# Plot TTS\n",
    "axL.plot(result['time'], result['tts'],'-o')\n",
    "axL.set_xlabel('annealing time', fontsize=fontsize)\n",
    "axL.set_yscale(\"log\")\n",
    "axL.set_ylabel('TTS', fontsize=fontsize)\n",
    "\n",
    "# Plot success probability\n",
    "axC.plot(result['time'], result['success_prob'],'-o')\n",
    "axC.set_xlabel('annealing time', fontsize=fontsize)\n",
    "axC.set_ylabel('Success probability', fontsize=fontsize)\n",
    "\n",
    "# Plot residual energy\n",
    "axR.plot(result['time'], result['residual_energy'],'-o')\n",
    "axR.set_xlabel('annealing time', fontsize=fontsize)\n",
    "axR.set_ylabel('Residual energy', fontsize=fontsize)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the optimal solution is randomly selected from the three states, the success probability should be about $1/3\\approx 0.33\\cdots$.  \n",
    "Note that the value of the success probability above is around that value.\n",
    "\n",
    "If you create a solver function, you can calculate TTS, success probability, and residual energy for not only OpenJij's solver but also for your own solver. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Details of the `solver_benchmark` Function\n",
    "We finally describe the arguments and the return values of the `solver_benchmark` function.\n",
    "\n",
    "#### Arguments of the `solver_benchmark` Function\n",
    "\n",
    "- solver: function  \n",
    "    A function that returns the `Response` class. It must have the arguments `time` and `num_reads`.\n",
    "    The `time` is a parameter that controls the computation time. In the case of `SASampler`, it corresponds to `num_sweeps`.\n",
    "    The `num_reads` parameter specifies the number of sampling times required to calculate TTS, residual energy, etc. The `num_reads` parameter is the number of reads required to calculate TTS, residual energy, etc.\n",
    "    Also, `Response.info`, the return value of the function, must have a keyword string specified by the argument `time_name`, and the value associated with `time_name` must contain the calculation time per calculation.\n",
    "- time_list: list  \n",
    "    A list of values to put into the `time` argument of the solver.\n",
    "- solutions: list(list: state)  \n",
    "    A list of states that will be the optimal solution. In case of degeneracy (multiple identical states), multiple states should be entered, e.g. [state1, state2].\n",
    "- args: dict\n",
    "    This is an optional parameter for the solver. The default value is `args = {}`.\n",
    "- p_r: 0 < float <= 1  \n",
    "    This is the value needed to calculate TTS. Equivalent to $p_R$ in the TTS description above.\n",
    "- ref_energy: float  \n",
    "    Reference energy. Used in conjunction with the following `measure_with_energy`. The default value is `ref_energy = 0`.\n",
    "- measure_with_energy: bool  \n",
    "    False: counts as a success if the spin state matches the optimal state.  \n",
    "    True: counts as a success if the energy is less than or equal to the `ref_energy`. This is used when the optimal state is not known.  \n",
    "    The default value is False.\n",
    "- time_name: str  \n",
    "    Specifies the key associated with the execution time in `Response.info`. The default value is `'execution_time'`.\n",
    "\n",
    "#### Return Value of the `solver_benchmark` Function\n",
    "The return value is the result of the benchmark calculation, stored in a dictionary type as follows.\n",
    "\n",
    "- time: List of execution times\n",
    "- success_prob: List of success probabilities\n",
    "- tts: List of TTS\n",
    "- residual_energy: List of residual energies\n",
    "- info: (dict) Parameter information of the benchmark function\n",
    "- se_success_prob: List of standard errors of success probability  \n",
    "      The standard deviation of the expected value of success probability for each iteration of annealing\n",
    "      Stored for each step_num\n",
    "      \n",
    "- se_residual_energy: List of standard errors of residual energy  \n",
    "      The standard deviation of the mean of the residual energy for each iteration of annealing\n",
    "      Stored for each step_num\n",
    "\n",
    "- se_lower_tts: List of lower standard errors of TTS\n",
    "\n",
    "- se_upper_tts: List of upper standard errors of TTS"
   ]
  }
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