{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pricing Basket Options"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Introduction\n",
    "<br>\n",
    "Suppose a <a href=\"https://www.investopedia.com/terms/b/basketoption.asp\">basket option</a> with strike price $K$ and two underlying assets whose spot price at maturity $S_T^1$, $S_T^2$ follow given random distributions.\n",
    "The corresponding payoff function is defined as:\n",
    "<br>\n",
    "<br>\n",
    "$$\\max\\{S_T^1 + S_T^2 - K, 0\\}$$\n",
    "<br>\n",
    "In the following, a quantum algorithm based on amplitude estimation is used to estimate the expected payoff, i.e., the fair price before discounting, for the option:\n",
    "<br>\n",
    "<br>\n",
    "$$\\mathbb{E}\\left[ \\max\\{S_T^1 + S_T^2 - K, 0\\} \\right].$$\n",
    "<br>\n",
    "The approximation of the objective function and a general introduction to option pricing and risk analysis on quantum computers are given in the following papers:\n",
    "\n",
    "- [Quantum Risk Analysis. Woerner, Egger. 2018.](https://arxiv.org/abs/1806.06893)\n",
    "- [Option Pricing using Quantum Computers. Stamatopoulos et al. 2019.](https://arxiv.org/abs/1905.02666)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-07-13T20:39:54.949868Z",
     "start_time": "2020-07-13T20:39:51.957621Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from scipy.interpolate import griddata\n",
    "\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "\n",
    "from qiskit import QuantumRegister, QuantumCircuit, AncillaRegister, transpile\n",
    "from qiskit_algorithms import IterativeAmplitudeEstimation, EstimationProblem\n",
    "from qiskit.circuit.library import WeightedAdder, LinearAmplitudeFunction\n",
    "from qiskit_aer.primitives import Sampler\n",
    "from qiskit_finance.circuit.library import LogNormalDistribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Uncertainty Model\n",
    "\n",
    "We construct a circuit to load a multivariate log-normal random distribution into a quantum state on $n$ qubits.\n",
    "For every dimension $j = 1,\\ldots,d$, the distribution is truncated to a given interval $[\\text{low}_j, \\text{high}_j]$ and discretized using $2^{n_j}$ grid points, where $n_j$ denotes the number of qubits used to represent dimension $j$, i.e., $n_1+\\ldots+n_d = n$.\n",
    "The unitary operator corresponding to the circuit implements the following: \n",
    "\n",
    "$$\\big|0\\rangle_{n} \\mapsto \\big|\\psi\\rangle_{n} = \\sum_{i_1,\\ldots,i_d} \\sqrt{p_{i_1\\ldots i_d}}\\big|i_1\\rangle_{n_1}\\ldots\\big|i_d\\rangle_{n_d},$$\n",
    "\n",
    "where $p_{i_1\\ldots i_d}$ denote the probabilities corresponding to the truncated and discretized distribution and where $i_j$ is mapped to the right interval using the affine map:\n",
    "\n",
    "$$ \\{0, \\ldots, 2^{n_j}-1\\} \\ni i_j \\mapsto \\frac{\\text{high}_j - \\text{low}_j}{2^{n_j} - 1} * i_j + \\text{low}_j \\in [\\text{low}_j, \\text{high}_j].$$\n",
    "\n",
    "For simplicity, we assume both stock prices are independent and identically distributed.\n",
    "This assumption just simplifies the parametrization below and can be easily relaxed to more complex and also correlated multivariate distributions.\n",
    "The only important assumption for the current implementation is that the discretization grid of the different dimensions has the same step size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-07-13T20:39:54.963598Z",
     "start_time": "2020-07-13T20:39:54.951907Z"
    }
   },
   "outputs": [],
   "source": [
    "# number of qubits per dimension to represent the uncertainty\n",
    "num_uncertainty_qubits = 2\n",
    "\n",
    "# parameters for considered random distribution\n",
    "S = 2.0  # initial spot price\n",
    "vol = 0.4  # volatility of 40%\n",
    "r = 0.05  # annual interest rate of 4%\n",
    "T = 40 / 365  # 40 days to maturity\n",
    "\n",
    "# resulting parameters for log-normal distribution\n",
    "mu = (r - 0.5 * vol**2) * T + np.log(S)\n",
    "sigma = vol * np.sqrt(T)\n",
    "mean = np.exp(mu + sigma**2 / 2)\n",
    "variance = (np.exp(sigma**2) - 1) * np.exp(2 * mu + sigma**2)\n",
    "stddev = np.sqrt(variance)\n",
    "\n",
    "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n",
    "low = np.maximum(0, mean - 3 * stddev)\n",
    "high = mean + 3 * stddev\n",
    "\n",
    "# map to higher dimensional distribution\n",
    "# for simplicity assuming dimensions are independent and identically distributed)\n",
    "dimension = 2\n",
    "num_qubits = [num_uncertainty_qubits] * dimension\n",
    "low = low * np.ones(dimension)\n",
    "high = high * np.ones(dimension)\n",
    "mu = mu * np.ones(dimension)\n",
    "cov = sigma**2 * np.eye(dimension)\n",
    "\n",
    "# construct circuit\n",
    "u = LogNormalDistribution(num_qubits=num_qubits, mu=mu, sigma=cov, bounds=list(zip(low, high)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-07-13T20:39:55.563010Z",
     "start_time": "2020-07-13T20:39:54.966704Z"
    },
    "tags": [
     "nbsphinx-thumbnail"
    ]
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot PDF of uncertainty model\n",
    "x = [v[0] for v in u.values]\n",
    "y = [v[1] for v in u.values]\n",
    "z = u.probabilities\n",
    "# z = map(float, z)\n",
    "# z = list(map(float, z))\n",
    "resolution = np.array([2**n for n in num_qubits]) * 1j\n",
    "grid_x, grid_y = np.mgrid[min(x) : max(x) : resolution[0], min(y) : max(y) : resolution[1]]\n",
    "grid_z = griddata((x, y), z, (grid_x, grid_y))\n",
    "plt.figure(figsize=(10, 8))\n",
    "ax = plt.axes(projection=\"3d\")\n",
    "ax.plot_surface(grid_x, grid_y, grid_z, cmap=plt.cm.Spectral)\n",
    "ax.set_xlabel(\"Spot Price $S_T^1$ (\\$)\", size=15)\n",
    "ax.set_ylabel(\"Spot Price $S_T^2$ (\\$)\", size=15)\n",
    "ax.set_zlabel(\"Probability (\\%)\", size=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Payoff Function\n",
    "\n",
    "The payoff function equals zero as long as the sum of the spot prices at maturity $(S_T^1 + S_T^2)$ is less than the strike price $K$ and then increases linearly.\n",
    "The implementation first uses a weighted sum operator to compute the sum of the spot prices into an ancilla register, and then uses a comparator, that flips an ancilla qubit from $\\big|0\\rangle$ to $\\big|1\\rangle$ if $(S_T^1 + S_T^2) \\geq K$.\n",
    "This ancilla is used to control the linear part of the payoff function.\n",
    "\n",
    "The linear part itself is approximated as follows.\n",
    "We exploit the fact that $\\sin^2(y + \\pi/4) \\approx y + 1/2$ for small $|y|$.\n",
    "Thus, for a given approximation rescaling factor $c_\\text{approx} \\in [0, 1]$ and $x \\in [0, 1]$ we consider\n",
    "$$ \\sin^2( \\pi/2 * c_\\text{approx} * ( x - 1/2 ) + \\pi/4) \\approx \\pi/2 * c_\\text{approx} * ( x - 1/2 ) + 1/2 $$ for small $c_\\text{approx}$.\n",
    "\n",
    "We can easily construct an operator that acts as \n",
    "$$\\big|x\\rangle \\big|0\\rangle \\mapsto \\big|x\\rangle \\left( \\cos(a*x+b) \\big|0\\rangle + \\sin(a*x+b) \\big|1\\rangle \\right),$$\n",
    "using controlled Y-rotations.\n",
    "\n",
    "Eventually, we are interested in the probability of measuring $\\big|1\\rangle$ in the last qubit, which corresponds to\n",
    "$\\sin^2(a*x+b)$.\n",
    "Together with the approximation above, this allows to approximate the values of interest.\n",
    "The smaller we choose $c_\\text{approx}$, the better the approximation.\n",
    "However, since we are then estimating a property scaled by $c_\\text{approx}$, the number of evaluation qubits $m$ needs to be adjusted accordingly.\n",
    "\n",
    "For more details on the approximation, we refer to:\n",
    "[Quantum Risk Analysis. Woerner, Egger. 2018.](https://arxiv.org/abs/1806.06893)\n",
    "\n",
    "Since the weighted sum operator (in its current implementation) can only sum up integers, we need to map from the original ranges to the representable range to estimate the result, and reverse this mapping before interpreting the result. The mapping essentially corresponds to the affine mapping described in the context of the uncertainty model above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-07-13T20:39:55.570350Z",
     "start_time": "2020-07-13T20:39:55.565874Z"
    }
   },
   "outputs": [],
   "source": [
    "# determine number of qubits required to represent total loss\n",
    "weights = []\n",
    "for n in num_qubits:\n",
    "    for i in range(n):\n",
    "        weights += [2**i]\n",
    "\n",
    "# create aggregation circuit\n",
    "agg = WeightedAdder(sum(num_qubits), weights)\n",
    "n_s = agg.num_sum_qubits\n",
    "n_aux = agg.num_qubits - n_s - agg.num_state_qubits  # number of additional qubits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-07-13T20:39:55.579531Z",
     "start_time": "2020-07-13T20:39:55.572709Z"
    }
   },
   "outputs": [],
   "source": [
    "# set the strike price (should be within the low and the high value of the uncertainty)\n",
    "strike_price = 3.5\n",
    "\n",
    "# map strike price from [low, high] to {0, ..., 2^n-1}\n",
    "max_value = 2**n_s - 1\n",
    "low_ = low[0]\n",
    "high_ = high[0]\n",
    "mapped_strike_price = (\n",
    "    (strike_price - dimension * low_) / (high_ - low_) * (2**num_uncertainty_qubits - 1)\n",
    ")\n",
    "\n",
    "# set the approximation scaling for the payoff function\n",
    "c_approx = 0.25\n",
    "\n",
    "# setup piecewise linear objective fcuntion\n",
    "breakpoints = [0, mapped_strike_price]\n",
    "slopes = [0, 1]\n",
    "offsets = [0, 0]\n",
    "f_min = 0\n",
    "f_max = 2 * (2**num_uncertainty_qubits - 1) - mapped_strike_price\n",
    "basket_objective = LinearAmplitudeFunction(\n",
    "    n_s,\n",
    "    slopes,\n",
    "    offsets,\n",
    "    domain=(0, max_value),\n",
    "    image=(f_min, f_max),\n",
    "    rescaling_factor=c_approx,\n",
    "    breakpoints=breakpoints,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         ┌───────┐┌────────┐      \n",
      "state_0: ┤0      ├┤0       ├──────\n",
      "         │       ││        │      \n",
      "state_1: ┤1      ├┤1       ├──────\n",
      "         │  P(X) ││        │      \n",
      "state_2: ┤2      ├┤2       ├──────\n",
      "         │       ││        │      \n",
      "state_3: ┤3      ├┤3       ├──────\n",
      "         └───────┘│        │┌────┐\n",
      "    obj: ─────────┤        ├┤3   ├\n",
      "                  │        ││    │\n",
      "  sum_0: ─────────┤4 adder ├┤0   ├\n",
      "                  │        ││    │\n",
      "  sum_1: ─────────┤5       ├┤1   ├\n",
      "                  │        ││    │\n",
      "  sum_2: ─────────┤6       ├┤2 F ├\n",
      "                  │        ││    │\n",
      " work_0: ─────────┤7       ├┤4   ├\n",
      "                  │        ││    │\n",
      " work_1: ─────────┤8       ├┤5   ├\n",
      "                  │        ││    │\n",
      " work_2: ─────────┤9       ├┤6   ├\n",
      "                  └────────┘└────┘\n",
      "objective qubit index 4\n"
     ]
    }
   ],
   "source": [
    "# define overall multivariate problem\n",
    "qr_state = QuantumRegister(u.num_qubits, \"state\")  # to load the probability distribution\n",
    "qr_obj = QuantumRegister(1, \"obj\")  # to encode the function values\n",
    "ar_sum = AncillaRegister(n_s, \"sum\")  # number of qubits used to encode the sum\n",
    "ar = AncillaRegister(max(n_aux, basket_objective.num_ancillas), \"work\")  # additional qubits\n",
    "\n",
    "objective_index = u.num_qubits\n",
    "\n",
    "basket_option = QuantumCircuit(qr_state, qr_obj, ar_sum, ar)\n",
    "basket_option.append(u, qr_state)\n",
    "basket_option.append(agg, qr_state[:] + ar_sum[:] + ar[:n_aux])\n",
    "basket_option.append(basket_objective, ar_sum[:] + qr_obj[:] + ar[: basket_objective.num_ancillas])\n",
    "\n",
    "print(basket_option.draw())\n",
    "print(\"objective qubit index\", objective_index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-07-13T20:39:55.869583Z",
     "start_time": "2020-07-13T20:39:55.581673Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot exact payoff function (evaluated on the grid of the uncertainty model)\n",
    "x = np.linspace(sum(low), sum(high))\n",
    "y = np.maximum(0, x - strike_price)\n",
    "plt.plot(x, y, \"r-\")\n",
    "plt.grid()\n",
    "plt.title(\"Payoff Function\", size=15)\n",
    "plt.xlabel(\"Sum of Spot Prices ($S_T^1 + S_T^2)$\", size=15)\n",
    "plt.ylabel(\"Payoff\", size=15)\n",
    "plt.xticks(size=15, rotation=90)\n",
    "plt.yticks(size=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-07-13T20:39:55.878255Z",
     "start_time": "2020-07-13T20:39:55.872521Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "exact expected value:\t0.4870\n"
     ]
    }
   ],
   "source": [
    "# evaluate exact expected value\n",
    "sum_values = np.sum(u.values, axis=1)\n",
    "exact_value = np.dot(\n",
    "    u.probabilities[sum_values >= strike_price],\n",
    "    sum_values[sum_values >= strike_price] - strike_price,\n",
    ")\n",
    "print(\"exact expected value:\\t%.4f\" % exact_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluate Expected Payoff\n",
    "\n",
    "We first verify the quantum circuit by simulating it and analyzing the resulting probability to measure the $|1\\rangle$ state in the objective qubit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-07-13T20:39:56.199909Z",
     "start_time": "2020-07-13T20:39:56.086824Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "state qubits:  5\n",
      "circuit width: 11\n",
      "circuit depth: 415\n"
     ]
    }
   ],
   "source": [
    "num_state_qubits = basket_option.num_qubits - basket_option.num_ancillas\n",
    "print(\"state qubits: \", num_state_qubits)\n",
    "transpiled = transpile(basket_option, basis_gates=[\"u\", \"cx\"])\n",
    "print(\"circuit width:\", transpiled.width())\n",
    "print(\"circuit depth:\", transpiled.depth())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "basket_option_measure = basket_option.measure_all(inplace=False)\n",
    "sampler = Sampler()\n",
    "job = sampler.run(basket_option_measure)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-07-13T20:40:02.503868Z",
     "start_time": "2020-07-13T20:40:02.471459Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exact Operator Value:  0.4209\n",
      "Mapped Operator value: 0.6350\n",
      "Exact Expected Payoff: 0.4870\n"
     ]
    }
   ],
   "source": [
    "# evaluate the result\n",
    "value = 0\n",
    "probabilities = job.result().quasi_dists[0].binary_probabilities()\n",
    "for i, prob in probabilities.items():\n",
    "    if prob > 1e-4 and i[-num_state_qubits:][0] == \"1\":\n",
    "        value += prob\n",
    "\n",
    "\n",
    "# map value to original range\n",
    "mapped_value = (\n",
    "    basket_objective.post_processing(value) / (2**num_uncertainty_qubits - 1) * (high_ - low_)\n",
    ")\n",
    "print(\"Exact Operator Value:  %.4f\" % value)\n",
    "print(\"Mapped Operator value: %.4f\" % mapped_value)\n",
    "print(\"Exact Expected Payoff: %.4f\" % exact_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we use amplitude estimation to estimate the expected payoff."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-07-13T20:40:03.034186Z",
     "start_time": "2020-07-13T20:40:03.030226Z"
    }
   },
   "outputs": [],
   "source": [
    "# set target precision and confidence level\n",
    "epsilon = 0.01\n",
    "alpha = 0.05\n",
    "\n",
    "problem = EstimationProblem(\n",
    "    state_preparation=basket_option,\n",
    "    objective_qubits=[objective_index],\n",
    "    post_processing=basket_objective.post_processing,\n",
    ")\n",
    "# construct amplitude estimation\n",
    "ae = IterativeAmplitudeEstimation(\n",
    "    epsilon_target=epsilon, alpha=alpha, sampler=Sampler(run_options={\"shots\": 100, \"seed\": 75})\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-07-13T20:40:49.786497Z",
     "start_time": "2020-07-13T20:40:11.062354Z"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "result = ae.estimate(problem)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-07-13T20:40:49.793418Z",
     "start_time": "2020-07-13T20:40:49.788189Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exact value:        \t0.4870\n",
      "Estimated value:    \t0.4945\n",
      "Confidence interval:\t[0.4821, 0.5069]\n"
     ]
    }
   ],
   "source": [
    "conf_int = (\n",
    "    np.array(result.confidence_interval_processed)\n",
    "    / (2**num_uncertainty_qubits - 1)\n",
    "    * (high_ - low_)\n",
    ")\n",
    "print(\"Exact value:        \\t%.4f\" % exact_value)\n",
    "print(\n",
    "    \"Estimated value:    \\t%.4f\"\n",
    "    % (result.estimation_processed / (2**num_uncertainty_qubits - 1) * (high_ - low_))\n",
    ")\n",
    "print(\"Confidence interval:\\t[%.4f, %.4f]\" % tuple(conf_int))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-07-13T20:40:50.292936Z",
     "start_time": "2020-07-13T20:40:50.150321Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "<h3>Version Information</h3><table><tr><th>Software</th><th>Version</th></tr><tr><td><code>qiskit</code></td><td>None</td></tr><tr><td><code>qiskit-terra</code></td><td>0.45.0.dev0+c626be7</td></tr><tr><td><code>qiskit_finance</code></td><td>0.4.0</td></tr><tr><td><code>qiskit_ibm_provider</code></td><td>0.6.1</td></tr><tr><td><code>qiskit_aer</code></td><td>0.12.0</td></tr><tr><td><code>qiskit_algorithms</code></td><td>0.2.0</td></tr><tr><th colspan='2'>System information</th></tr><tr><td>Python version</td><td>3.9.7</td></tr><tr><td>Python compiler</td><td>GCC 7.5.0</td></tr><tr><td>Python build</td><td>default, Sep 16 2021 13:09:58</td></tr><tr><td>OS</td><td>Linux</td></tr><tr><td>CPUs</td><td>2</td></tr><tr><td>Memory (Gb)</td><td>5.778430938720703</td></tr><tr><td colspan='2'>Fri Aug 18 16:17:28 2023 EDT</td></tr></table>"
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       "<div style='width: 100%; background-color:#d5d9e0;padding-left: 10px; padding-bottom: 10px; padding-right: 10px; padding-top: 5px'><h3>This code is a part of Qiskit</h3><p>&copy; Copyright IBM 2017, 2023.</p><p>This code is licensed under the Apache License, Version 2.0. You may<br>obtain a copy of this license in the LICENSE.txt file in the root directory<br> of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.<p>Any modifications or derivative works of this code must retain this<br>copyright notice, and modified files need to carry a notice indicating<br>that they have been altered from the originals.</p></div>"
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   "source": [
    "import tutorial_magics\n",
    "\n",
    "%qiskit_version_table\n",
    "%qiskit_copyright"
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