192 lines
6.1 KiB
Plaintext
192 lines
6.1 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "google",
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"metadata": {},
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"source": [
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"##### Copyright 2022 Google LLC."
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]
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},
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{
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"cell_type": "markdown",
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"id": "apache",
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"metadata": {},
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"source": [
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"Licensed under the Apache License, Version 2.0 (the \"License\");\n",
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"you may not use this file except in compliance with the License.\n",
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"You may obtain a copy of the License at\n",
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"\n",
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" http://www.apache.org/licenses/LICENSE-2.0\n",
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"\n",
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"Unless required by applicable law or agreed to in writing, software\n",
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"distributed under the License is distributed on an \"AS IS\" BASIS,\n",
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"WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
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"See the License for the specific language governing permissions and\n",
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"limitations under the License.\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "basename",
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"metadata": {},
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"source": [
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"# all_interval"
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]
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},
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{
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"cell_type": "markdown",
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"id": "link",
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"metadata": {},
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"source": [
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"<table align=\"left\">\n",
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"<td>\n",
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"<a href=\"https://colab.research.google.com/github/google/or-tools/blob/master/examples/notebook/contrib/all_interval.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
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"</td>\n",
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"<td>\n",
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"<a href=\"https://github.com/google/or-tools/blob/master/examples/contrib/all_interval.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/tools/github_32px.png\"/>View source on GitHub</a>\n",
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"</td>\n",
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"</table>"
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]
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},
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{
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"cell_type": "markdown",
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"id": "doc",
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"metadata": {},
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"source": [
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"First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "install",
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"metadata": {},
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"outputs": [],
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"source": [
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"!pip install ortools"
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]
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},
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{
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"cell_type": "markdown",
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"id": "description",
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"metadata": {},
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"source": [
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"\n",
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"\n",
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" All interval problem in Google CP Solver.\n",
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"\n",
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" CSPLib problem number 7\n",
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" http://www.cs.st-andrews.ac.uk/~ianm/CSPLib/prob/prob007/index.html\n",
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" '''\n",
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" Given the twelve standard pitch-classes (c, c , d, ...), represented by\n",
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" numbers 0,1,...,11, find a series in which each pitch-class occurs exactly\n",
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" once and in which the musical intervals between neighbouring notes cover\n",
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" the full set of intervals from the minor second (1 semitone) to the major\n",
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" seventh (11 semitones). That is, for each of the intervals, there is a\n",
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" pair of neigbhouring pitch-classes in the series, between which this\n",
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" interval appears. The problem of finding such a series can be easily\n",
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" formulated as an instance of a more general arithmetic problem on Z_n,\n",
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" the set of integer residues modulo n. Given n in N, find a vector\n",
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" s = (s_1, ..., s_n), such that (i) s is a permutation of\n",
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" Z_n = {0,1,...,n-1}; and (ii) the interval vector\n",
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" v = (|s_2-s_1|, |s_3-s_2|, ... |s_n-s_{n-1}|) is a permutation of\n",
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" Z_n-{0} = {1,2,...,n-1}. A vector v satisfying these conditions is\n",
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" called an all-interval series of size n; the problem of finding such\n",
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" a series is the all-interval series problem of size n. We may also be\n",
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" interested in finding all possible series of a given size.\n",
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" '''\n",
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"\n",
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" Compare with the following models:\n",
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" * MiniZinc: http://www.hakank.org/minizinc/all_interval.mzn\n",
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" * Comet : http://www.hakank.org/comet/all_interval.co\n",
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" * Gecode/R: http://www.hakank.org/gecode_r/all_interval.rb\n",
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" * ECLiPSe : http://www.hakank.org/eclipse/all_interval.ecl\n",
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" * SICStus : http://www.hakank.org/sicstus/all_interval.pl\n",
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"\n",
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"\n",
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" This model was created by Hakan Kjellerstrand (hakank@gmail.com)\n",
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" Also see my other Google CP Solver models:\n",
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" http://www.hakank.org/google_or_tools/\n",
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"\n",
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"\n",
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"\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "code",
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"metadata": {},
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"outputs": [],
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"source": [
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"import sys\n",
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"\n",
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"from ortools.constraint_solver import pywrapcp\n",
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"\n",
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"\n",
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"def main(n=12):\n",
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"\n",
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" # Create the solver.\n",
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" solver = pywrapcp.Solver(\"All interval\")\n",
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"\n",
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" #\n",
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" # data\n",
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" #\n",
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" print(\"n:\", n)\n",
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"\n",
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" #\n",
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" # declare variables\n",
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" #\n",
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" x = [solver.IntVar(1, n, \"x[%i]\" % i) for i in range(n)]\n",
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" diffs = [solver.IntVar(1, n - 1, \"diffs[%i]\" % i) for i in range(n - 1)]\n",
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"\n",
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" #\n",
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" # constraints\n",
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" #\n",
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" solver.Add(solver.AllDifferent(x))\n",
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" solver.Add(solver.AllDifferent(diffs))\n",
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"\n",
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" for k in range(n - 1):\n",
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" solver.Add(diffs[k] == abs(x[k + 1] - x[k]))\n",
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"\n",
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" # symmetry breaking\n",
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" solver.Add(x[0] < x[n - 1])\n",
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" solver.Add(diffs[0] < diffs[1])\n",
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"\n",
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" #\n",
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" # solution and search\n",
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" #\n",
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" solution = solver.Assignment()\n",
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" solution.Add(x)\n",
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" solution.Add(diffs)\n",
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"\n",
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" db = solver.Phase(x, solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_MIN_VALUE)\n",
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"\n",
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" solver.NewSearch(db)\n",
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" num_solutions = 0\n",
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" while solver.NextSolution():\n",
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" print(\"x:\", [x[i].Value() for i in range(n)])\n",
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" print(\"diffs:\", [diffs[i].Value() for i in range(n - 1)])\n",
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" num_solutions += 1\n",
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" print()\n",
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"\n",
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" print(\"num_solutions:\", num_solutions)\n",
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" print(\"failures:\", solver.Failures())\n",
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" print(\"branches:\", solver.Branches())\n",
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" print(\"WallTime:\", solver.WallTime())\n",
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"\n",
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"\n",
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"n = 12\n",
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"if len(sys.argv) > 1:\n",
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" n = int(sys.argv[1])\n",
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"main(n)\n",
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"\n"
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]
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}
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],
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"metadata": {},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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