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source: branches/MemPRAlgorithm/HeuristicLab.Problems.GraphColoring/3.3/GraphColoringProblem.cs @ 14471

Last change on this file since 14471 was 14471, checked in by abeham, 7 years ago

#2701:

  • Updated GraphColoringProblem and Problems.Instances
    • Added new fitness function from literature
    • Added DIMACS benchmark instances
  • Updated LinearLinkageEncoding
    • Added HammingSimilarityCalculator
File size: 26.2 KB
Line 
1#region License Information
2/* HeuristicLab
3 * Copyright (C) 2002-2016 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
4 *
5 * This file is part of HeuristicLab.
6 *
7 * HeuristicLab is free software: you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation, either version 3 of the License, or
10 * (at your option) any later version.
11 *
12 * HeuristicLab is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
15 * GNU General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License
18 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
19 */
20#endregion
21
22using System;
23using System.Linq;
24using HeuristicLab.Analysis;
25using HeuristicLab.Common;
26using HeuristicLab.Core;
27using HeuristicLab.Data;
28using HeuristicLab.Encodings.LinearLinkageEncoding;
29using HeuristicLab.Optimization;
30using HeuristicLab.Optimization.Operators;
31using HeuristicLab.Parameters;
32using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
33using HeuristicLab.Problems.Instances;
34
35namespace HeuristicLab.Problems.GraphColoring {
36  public enum FitnessFunction { Prioritized, Penalized }
37  [Item("Graph Coloring Problem (GCP)", "Attempts to find a coloring using a minimal number of colors that doesn't produce a conflict.")]
38  [Creatable(CreatableAttribute.Categories.CombinatorialProblems, Priority = 135)]
39  [StorableClass]
40  public sealed class GraphColoringProblem : SingleObjectiveBasicProblem<LinearLinkageEncoding>, IProblemInstanceConsumer<GCPData> {
41
42    public override bool Maximization {
43      get { return false; }
44    }
45
46    [Storable]
47    private IValueParameter<IntMatrix> adjacencyListParameter;
48    public IValueParameter<IntMatrix> AdjacencyListParameter {
49      get { return adjacencyListParameter; }
50    }
51    [Storable]
52    private IValueParameter<EnumValue<FitnessFunction>> fitnessFunctionParameter;
53    public IValueParameter<EnumValue<FitnessFunction>> FitnessFunctionParameter {
54      get { return fitnessFunctionParameter; }
55    }
56
57    [StorableConstructor]
58    private GraphColoringProblem(bool deserializing) : base(deserializing) { }
59    private GraphColoringProblem(GraphColoringProblem original, Cloner cloner)
60      : base(original, cloner) {
61      adjacencyListParameter = cloner.Clone(original.adjacencyListParameter);
62      fitnessFunctionParameter = cloner.Clone(original.fitnessFunctionParameter);
63      RegisterEventHandlers();
64    }
65    public GraphColoringProblem() {
66      Encoding = new LinearLinkageEncoding("lle");
67      Parameters.Add(adjacencyListParameter = new ValueParameter<IntMatrix>("Adjacency List", "The adjacency list that describes the (symmetric) edges in the graph with nodes from 0 to N-1."));
68      Parameters.Add(fitnessFunctionParameter = new ValueParameter<EnumValue<FitnessFunction>>("Fitness Function", "The function to use for evaluating the quality of a solution.", new EnumValue<FitnessFunction>(FitnessFunction.Prioritized)));
69
70      var imat = new IntMatrix(defaultInstance.Length, 2);
71      for (var i = 0; i < defaultInstance.Length; i++) {
72        imat[i, 0] = defaultInstance[i].Item1 - 1;
73        imat[i, 1] = defaultInstance[i].Item2 - 1;
74      }
75      Encoding.Length = defaultInstanceNodes;
76      AdjacencyListParameter.Value = imat;
77      BestKnownQuality = 7;
78
79      InitializeOperators();
80      RegisterEventHandlers();
81    }
82
83    public override IDeepCloneable Clone(Cloner cloner) {
84      return new GraphColoringProblem(this, cloner);
85    }
86
87    protected override void OnEncodingChanged() {
88      base.OnEncodingChanged();
89
90      Parameterize();
91    }
92
93    [StorableHook(HookType.AfterDeserialization)]
94    private void AfterDeserialization() {
95      RegisterEventHandlers();
96    }
97
98    private void RegisterEventHandlers() {
99      fitnessFunctionParameter.ValueChanged += FitnessFunctionParameterOnValueChanged;
100      fitnessFunctionParameter.Value.ValueChanged += FitnessFunctionOnValueChanged;
101    }
102
103    private void FitnessFunctionParameterOnValueChanged(object sender, EventArgs eventArgs) {
104      fitnessFunctionParameter.Value.ValueChanged += FitnessFunctionOnValueChanged;
105      OnReset();
106    }
107
108    private void FitnessFunctionOnValueChanged(object sender, EventArgs eventArgs) {
109      BestKnownQualityParameter.Value = null;
110      OnReset();
111    }
112
113    public override double Evaluate(Individual individual, IRandom random) {
114      var fitFun = FitnessFunctionParameter.Value.Value;
115      var adjList = adjacencyListParameter.Value;
116      var lle = individual.LinearLinkage(Encoding.Name).ToLLEe(); // LLE-e encoding uses the highest indexed member as group number
117
118      switch (fitFun) {
119        case FitnessFunction.Prioritized: {
120            var conflicts = 0;
121            var colors = lle.Distinct().Count();
122            for (var r = 0; r < adjList.Rows; r++) {
123              if (lle[adjList[r, 0]] == lle[adjList[r, 1]]) conflicts++; // both nodes are adjacent and have the same color (are in the same group)
124            }
125            // number of conflicts is the integer part of the quality
126            // number of colors constitutes the fractional part
127            // the number of fractional digits is defined by the maximum number of possible colors (each node its own color)
128            var mag = Math.Pow(10, -(int)Math.Ceiling(Math.Log10(lle.Length)));
129            // the value is e.g. 4.03 for 4 conflicts with 3 colors (and less than 100 nodes)
130            return conflicts + colors * mag;
131          }
132        case FitnessFunction.Penalized: {
133            // Fitness function from
134            // David S. Johnson, Cecilia R. Aragon, Lyle A. McGeoch, and Catherine Schevon. 1991.
135            // Optimization by simulated annealing: An experimental evaluation; part II, graph coloring and number partitioning.
136            // Operations Research 39(3), pp. 378–406.
137            // All local optima of this function correspond to legal colorings.
138            var colors = lle.GroupBy(x => x).ToDictionary(x => x.Key, x => new EvaluationHelper() { ColorCount = x.Count() });
139            for (var r = 0; r < adjList.Rows; r++) {
140              var color1 = lle[adjList[r, 0]];
141              var color2 = lle[adjList[r, 1]];
142              if (color1 == color2) colors[color1].ConflictCount++;
143            }
144            return 2 * colors.Sum(x => x.Value.ColorCount * x.Value.ConflictCount) - colors.Sum(x => x.Value.ColorCount * x.Value.ColorCount);
145          }
146        default: throw new InvalidOperationException(string.Format("Unknown fitness function {0}.", fitFun));
147      }
148    }
149
150    private class EvaluationHelper {
151      public int ColorCount { get; set; }
152      public int ConflictCount { get; set; }
153    }
154
155    public override void Analyze(Individual[] individuals, double[] qualities, ResultCollection results, IRandom random) {
156      var orderedIndividuals = individuals.Zip(qualities, (i, q) => new { Individual = i, Quality = q }).OrderBy(z => z.Quality);
157      var best = Maximization ? orderedIndividuals.Last().Individual.LinearLinkage(Encoding.Name) : orderedIndividuals.First().Individual.LinearLinkage(Encoding.Name);
158
159      var adjList = AdjacencyListParameter.Value;
160      var lle = best.ToLLEe();
161      var conflicts = 0;
162      var colors = lle.Distinct().Count();
163      for (var r = 0; r < adjList.Rows; r++) {
164        if (lle[adjList[r, 0]] == lle[adjList[r, 1]]) conflicts++; // both nodes are adjacent and have the same color (are in the same group)
165      }
166
167      IResult res;
168      if (!results.TryGetValue("Best Solution Colors", out res)) {
169        res = new Result("Best Solution Colors", new IntValue(colors));
170        results.Add(res);
171      } else ((IntValue)res.Value).Value = colors;
172      if (!results.TryGetValue("Best Solution Conflicts", out res)) {
173        res = new Result("Best Solution Conflicts", new IntValue(conflicts));
174        results.Add(res);
175      } else ((IntValue)res.Value).Value = conflicts;
176    }
177
178    public void Load(GCPData data) {
179      Encoding.Length = data.Nodes;
180      AdjacencyListParameter.Value = new IntMatrix(data.Adjacencies);
181      if (FitnessFunctionParameter.Value.Value == FitnessFunction.Prioritized && data.BestKnownColors.HasValue) {
182        var mag = Math.Pow(10, -(int)Math.Ceiling(Math.Log10(data.Nodes)));
183        // the value is e.g. 4.03 for 4 conflicts with 3 colors (and less than 100 nodes)
184        BestKnownQuality = data.BestKnownColors.Value * mag;
185      } else BestKnownQualityParameter.Value = null;
186      Name = data.Name;
187      Description = data.Description;
188      OnReset();
189    }
190
191    private void InitializeOperators() {
192      Operators.Add(new HammingSimilarityCalculator());
193      Operators.Add(new QualitySimilarityCalculator());
194      Operators.Add(new PopulationSimilarityAnalyzer(Operators.OfType<ISolutionSimilarityCalculator>()));
195
196      Parameterize();
197    }
198
199    private void Parameterize() {
200      foreach (var simCalc in Operators.OfType<ISolutionSimilarityCalculator>()) {
201        simCalc.SolutionVariableName = Encoding.Name;
202        simCalc.QualityVariableName = Evaluator.QualityParameter.ActualName;
203      }
204    }
205
206    #region Default Instance (myciel6.col)
207    private static readonly int defaultInstanceNodes = 95;
208    private static readonly Tuple<int, int>[] defaultInstance = {
209Tuple.Create(1, 2),
210Tuple.Create(1, 4),
211Tuple.Create(1, 7),
212Tuple.Create(1, 9),
213Tuple.Create(1, 13),
214Tuple.Create(1, 15),
215Tuple.Create(1, 18),
216Tuple.Create(1, 20),
217Tuple.Create(1, 25),
218Tuple.Create(1, 27),
219Tuple.Create(1, 30),
220Tuple.Create(1, 32),
221Tuple.Create(1, 36),
222Tuple.Create(1, 38),
223Tuple.Create(1, 41),
224Tuple.Create(1, 43),
225Tuple.Create(1, 49),
226Tuple.Create(1, 51),
227Tuple.Create(1, 54),
228Tuple.Create(1, 56),
229Tuple.Create(1, 60),
230Tuple.Create(1, 62),
231Tuple.Create(1, 65),
232Tuple.Create(1, 67),
233Tuple.Create(1, 72),
234Tuple.Create(1, 74),
235Tuple.Create(1, 77),
236Tuple.Create(1, 79),
237Tuple.Create(1, 83),
238Tuple.Create(1, 85),
239Tuple.Create(1, 88),
240Tuple.Create(1, 90),
241Tuple.Create(2, 3),
242Tuple.Create(2, 6),
243Tuple.Create(2, 8),
244Tuple.Create(2, 12),
245Tuple.Create(2, 14),
246Tuple.Create(2, 17),
247Tuple.Create(2, 19),
248Tuple.Create(2, 24),
249Tuple.Create(2, 26),
250Tuple.Create(2, 29),
251Tuple.Create(2, 31),
252Tuple.Create(2, 35),
253Tuple.Create(2, 37),
254Tuple.Create(2, 40),
255Tuple.Create(2, 42),
256Tuple.Create(2, 48),
257Tuple.Create(2, 50),
258Tuple.Create(2, 53),
259Tuple.Create(2, 55),
260Tuple.Create(2, 59),
261Tuple.Create(2, 61),
262Tuple.Create(2, 64),
263Tuple.Create(2, 66),
264Tuple.Create(2, 71),
265Tuple.Create(2, 73),
266Tuple.Create(2, 76),
267Tuple.Create(2, 78),
268Tuple.Create(2, 82),
269Tuple.Create(2, 84),
270Tuple.Create(2, 87),
271Tuple.Create(2, 89),
272Tuple.Create(3, 5),
273Tuple.Create(3, 7),
274Tuple.Create(3, 10),
275Tuple.Create(3, 13),
276Tuple.Create(3, 16),
277Tuple.Create(3, 18),
278Tuple.Create(3, 21),
279Tuple.Create(3, 25),
280Tuple.Create(3, 28),
281Tuple.Create(3, 30),
282Tuple.Create(3, 33),
283Tuple.Create(3, 36),
284Tuple.Create(3, 39),
285Tuple.Create(3, 41),
286Tuple.Create(3, 44),
287Tuple.Create(3, 49),
288Tuple.Create(3, 52),
289Tuple.Create(3, 54),
290Tuple.Create(3, 57),
291Tuple.Create(3, 60),
292Tuple.Create(3, 63),
293Tuple.Create(3, 65),
294Tuple.Create(3, 68),
295Tuple.Create(3, 72),
296Tuple.Create(3, 75),
297Tuple.Create(3, 77),
298Tuple.Create(3, 80),
299Tuple.Create(3, 83),
300Tuple.Create(3, 86),
301Tuple.Create(3, 88),
302Tuple.Create(3, 91),
303Tuple.Create(4, 5),
304Tuple.Create(4, 6),
305Tuple.Create(4, 10),
306Tuple.Create(4, 12),
307Tuple.Create(4, 16),
308Tuple.Create(4, 17),
309Tuple.Create(4, 21),
310Tuple.Create(4, 24),
311Tuple.Create(4, 28),
312Tuple.Create(4, 29),
313Tuple.Create(4, 33),
314Tuple.Create(4, 35),
315Tuple.Create(4, 39),
316Tuple.Create(4, 40),
317Tuple.Create(4, 44),
318Tuple.Create(4, 48),
319Tuple.Create(4, 52),
320Tuple.Create(4, 53),
321Tuple.Create(4, 57),
322Tuple.Create(4, 59),
323Tuple.Create(4, 63),
324Tuple.Create(4, 64),
325Tuple.Create(4, 68),
326Tuple.Create(4, 71),
327Tuple.Create(4, 75),
328Tuple.Create(4, 76),
329Tuple.Create(4, 80),
330Tuple.Create(4, 82),
331Tuple.Create(4, 86),
332Tuple.Create(4, 87),
333Tuple.Create(4, 91),
334Tuple.Create(5, 8),
335Tuple.Create(5, 9),
336Tuple.Create(5, 14),
337Tuple.Create(5, 15),
338Tuple.Create(5, 19),
339Tuple.Create(5, 20),
340Tuple.Create(5, 26),
341Tuple.Create(5, 27),
342Tuple.Create(5, 31),
343Tuple.Create(5, 32),
344Tuple.Create(5, 37),
345Tuple.Create(5, 38),
346Tuple.Create(5, 42),
347Tuple.Create(5, 43),
348Tuple.Create(5, 50),
349Tuple.Create(5, 51),
350Tuple.Create(5, 55),
351Tuple.Create(5, 56),
352Tuple.Create(5, 61),
353Tuple.Create(5, 62),
354Tuple.Create(5, 66),
355Tuple.Create(5, 67),
356Tuple.Create(5, 73),
357Tuple.Create(5, 74),
358Tuple.Create(5, 78),
359Tuple.Create(5, 79),
360Tuple.Create(5, 84),
361Tuple.Create(5, 85),
362Tuple.Create(5, 89),
363Tuple.Create(5, 90),
364Tuple.Create(6, 11),
365Tuple.Create(6, 13),
366Tuple.Create(6, 15),
367Tuple.Create(6, 22),
368Tuple.Create(6, 25),
369Tuple.Create(6, 27),
370Tuple.Create(6, 34),
371Tuple.Create(6, 36),
372Tuple.Create(6, 38),
373Tuple.Create(6, 45),
374Tuple.Create(6, 49),
375Tuple.Create(6, 51),
376Tuple.Create(6, 58),
377Tuple.Create(6, 60),
378Tuple.Create(6, 62),
379Tuple.Create(6, 69),
380Tuple.Create(6, 72),
381Tuple.Create(6, 74),
382Tuple.Create(6, 81),
383Tuple.Create(6, 83),
384Tuple.Create(6, 85),
385Tuple.Create(6, 92),
386Tuple.Create(7, 11),
387Tuple.Create(7, 12),
388Tuple.Create(7, 14),
389Tuple.Create(7, 22),
390Tuple.Create(7, 24),
391Tuple.Create(7, 26),
392Tuple.Create(7, 34),
393Tuple.Create(7, 35),
394Tuple.Create(7, 37),
395Tuple.Create(7, 45),
396Tuple.Create(7, 48),
397Tuple.Create(7, 50),
398Tuple.Create(7, 58),
399Tuple.Create(7, 59),
400Tuple.Create(7, 61),
401Tuple.Create(7, 69),
402Tuple.Create(7, 71),
403Tuple.Create(7, 73),
404Tuple.Create(7, 81),
405Tuple.Create(7, 82),
406Tuple.Create(7, 84),
407Tuple.Create(7, 92),
408Tuple.Create(8, 11),
409Tuple.Create(8, 13),
410Tuple.Create(8, 16),
411Tuple.Create(8, 22),
412Tuple.Create(8, 25),
413Tuple.Create(8, 28),
414Tuple.Create(8, 34),
415Tuple.Create(8, 36),
416Tuple.Create(8, 39),
417Tuple.Create(8, 45),
418Tuple.Create(8, 49),
419Tuple.Create(8, 52),
420Tuple.Create(8, 58),
421Tuple.Create(8, 60),
422Tuple.Create(8, 63),
423Tuple.Create(8, 69),
424Tuple.Create(8, 72),
425Tuple.Create(8, 75),
426Tuple.Create(8, 81),
427Tuple.Create(8, 83),
428Tuple.Create(8, 86),
429Tuple.Create(8, 92),
430Tuple.Create(9, 11),
431Tuple.Create(9, 12),
432Tuple.Create(9, 16),
433Tuple.Create(9, 22),
434Tuple.Create(9, 24),
435Tuple.Create(9, 28),
436Tuple.Create(9, 34),
437Tuple.Create(9, 35),
438Tuple.Create(9, 39),
439Tuple.Create(9, 45),
440Tuple.Create(9, 48),
441Tuple.Create(9, 52),
442Tuple.Create(9, 58),
443Tuple.Create(9, 59),
444Tuple.Create(9, 63),
445Tuple.Create(9, 69),
446Tuple.Create(9, 71),
447Tuple.Create(9, 75),
448Tuple.Create(9, 81),
449Tuple.Create(9, 82),
450Tuple.Create(9, 86),
451Tuple.Create(9, 92),
452Tuple.Create(10, 11),
453Tuple.Create(10, 14),
454Tuple.Create(10, 15),
455Tuple.Create(10, 22),
456Tuple.Create(10, 26),
457Tuple.Create(10, 27),
458Tuple.Create(10, 34),
459Tuple.Create(10, 37),
460Tuple.Create(10, 38),
461Tuple.Create(10, 45),
462Tuple.Create(10, 50),
463Tuple.Create(10, 51),
464Tuple.Create(10, 58),
465Tuple.Create(10, 61),
466Tuple.Create(10, 62),
467Tuple.Create(10, 69),
468Tuple.Create(10, 73),
469Tuple.Create(10, 74),
470Tuple.Create(10, 81),
471Tuple.Create(10, 84),
472Tuple.Create(10, 85),
473Tuple.Create(10, 92),
474Tuple.Create(11, 17),
475Tuple.Create(11, 18),
476Tuple.Create(11, 19),
477Tuple.Create(11, 20),
478Tuple.Create(11, 21),
479Tuple.Create(11, 29),
480Tuple.Create(11, 30),
481Tuple.Create(11, 31),
482Tuple.Create(11, 32),
483Tuple.Create(11, 33),
484Tuple.Create(11, 40),
485Tuple.Create(11, 41),
486Tuple.Create(11, 42),
487Tuple.Create(11, 43),
488Tuple.Create(11, 44),
489Tuple.Create(11, 53),
490Tuple.Create(11, 54),
491Tuple.Create(11, 55),
492Tuple.Create(11, 56),
493Tuple.Create(11, 57),
494Tuple.Create(11, 64),
495Tuple.Create(11, 65),
496Tuple.Create(11, 66),
497Tuple.Create(11, 67),
498Tuple.Create(11, 68),
499Tuple.Create(11, 76),
500Tuple.Create(11, 77),
501Tuple.Create(11, 78),
502Tuple.Create(11, 79),
503Tuple.Create(11, 80),
504Tuple.Create(11, 87),
505Tuple.Create(11, 88),
506Tuple.Create(11, 89),
507Tuple.Create(11, 90),
508Tuple.Create(11, 91),
509Tuple.Create(12, 23),
510Tuple.Create(12, 25),
511Tuple.Create(12, 27),
512Tuple.Create(12, 30),
513Tuple.Create(12, 32),
514Tuple.Create(12, 46),
515Tuple.Create(12, 49),
516Tuple.Create(12, 51),
517Tuple.Create(12, 54),
518Tuple.Create(12, 56),
519Tuple.Create(12, 70),
520Tuple.Create(12, 72),
521Tuple.Create(12, 74),
522Tuple.Create(12, 77),
523Tuple.Create(12, 79),
524Tuple.Create(12, 93),
525Tuple.Create(13, 23),
526Tuple.Create(13, 24),
527Tuple.Create(13, 26),
528Tuple.Create(13, 29),
529Tuple.Create(13, 31),
530Tuple.Create(13, 46),
531Tuple.Create(13, 48),
532Tuple.Create(13, 50),
533Tuple.Create(13, 53),
534Tuple.Create(13, 55),
535Tuple.Create(13, 70),
536Tuple.Create(13, 71),
537Tuple.Create(13, 73),
538Tuple.Create(13, 76),
539Tuple.Create(13, 78),
540Tuple.Create(13, 93),
541Tuple.Create(14, 23),
542Tuple.Create(14, 25),
543Tuple.Create(14, 28),
544Tuple.Create(14, 30),
545Tuple.Create(14, 33),
546Tuple.Create(14, 46),
547Tuple.Create(14, 49),
548Tuple.Create(14, 52),
549Tuple.Create(14, 54),
550Tuple.Create(14, 57),
551Tuple.Create(14, 70),
552Tuple.Create(14, 72),
553Tuple.Create(14, 75),
554Tuple.Create(14, 77),
555Tuple.Create(14, 80),
556Tuple.Create(14, 93),
557Tuple.Create(15, 23),
558Tuple.Create(15, 24),
559Tuple.Create(15, 28),
560Tuple.Create(15, 29),
561Tuple.Create(15, 33),
562Tuple.Create(15, 46),
563Tuple.Create(15, 48),
564Tuple.Create(15, 52),
565Tuple.Create(15, 53),
566Tuple.Create(15, 57),
567Tuple.Create(15, 70),
568Tuple.Create(15, 71),
569Tuple.Create(15, 75),
570Tuple.Create(15, 76),
571Tuple.Create(15, 80),
572Tuple.Create(15, 93),
573Tuple.Create(16, 23),
574Tuple.Create(16, 26),
575Tuple.Create(16, 27),
576Tuple.Create(16, 31),
577Tuple.Create(16, 32),
578Tuple.Create(16, 46),
579Tuple.Create(16, 50),
580Tuple.Create(16, 51),
581Tuple.Create(16, 55),
582Tuple.Create(16, 56),
583Tuple.Create(16, 70),
584Tuple.Create(16, 73),
585Tuple.Create(16, 74),
586Tuple.Create(16, 78),
587Tuple.Create(16, 79),
588Tuple.Create(16, 93),
589Tuple.Create(17, 23),
590Tuple.Create(17, 25),
591Tuple.Create(17, 27),
592Tuple.Create(17, 34),
593Tuple.Create(17, 46),
594Tuple.Create(17, 49),
595Tuple.Create(17, 51),
596Tuple.Create(17, 58),
597Tuple.Create(17, 70),
598Tuple.Create(17, 72),
599Tuple.Create(17, 74),
600Tuple.Create(17, 81),
601Tuple.Create(17, 93),
602Tuple.Create(18, 23),
603Tuple.Create(18, 24),
604Tuple.Create(18, 26),
605Tuple.Create(18, 34),
606Tuple.Create(18, 46),
607Tuple.Create(18, 48),
608Tuple.Create(18, 50),
609Tuple.Create(18, 58),
610Tuple.Create(18, 70),
611Tuple.Create(18, 71),
612Tuple.Create(18, 73),
613Tuple.Create(18, 81),
614Tuple.Create(18, 93),
615Tuple.Create(19, 23),
616Tuple.Create(19, 25),
617Tuple.Create(19, 28),
618Tuple.Create(19, 34),
619Tuple.Create(19, 46),
620Tuple.Create(19, 49),
621Tuple.Create(19, 52),
622Tuple.Create(19, 58),
623Tuple.Create(19, 70),
624Tuple.Create(19, 72),
625Tuple.Create(19, 75),
626Tuple.Create(19, 81),
627Tuple.Create(19, 93),
628Tuple.Create(20, 23),
629Tuple.Create(20, 24),
630Tuple.Create(20, 28),
631Tuple.Create(20, 34),
632Tuple.Create(20, 46),
633Tuple.Create(20, 48),
634Tuple.Create(20, 52),
635Tuple.Create(20, 58),
636Tuple.Create(20, 70),
637Tuple.Create(20, 71),
638Tuple.Create(20, 75),
639Tuple.Create(20, 81),
640Tuple.Create(20, 93),
641Tuple.Create(21, 23),
642Tuple.Create(21, 26),
643Tuple.Create(21, 27),
644Tuple.Create(21, 34),
645Tuple.Create(21, 46),
646Tuple.Create(21, 50),
647Tuple.Create(21, 51),
648Tuple.Create(21, 58),
649Tuple.Create(21, 70),
650Tuple.Create(21, 73),
651Tuple.Create(21, 74),
652Tuple.Create(21, 81),
653Tuple.Create(21, 93),
654Tuple.Create(22, 23),
655Tuple.Create(22, 29),
656Tuple.Create(22, 30),
657Tuple.Create(22, 31),
658Tuple.Create(22, 32),
659Tuple.Create(22, 33),
660Tuple.Create(22, 46),
661Tuple.Create(22, 53),
662Tuple.Create(22, 54),
663Tuple.Create(22, 55),
664Tuple.Create(22, 56),
665Tuple.Create(22, 57),
666Tuple.Create(22, 70),
667Tuple.Create(22, 76),
668Tuple.Create(22, 77),
669Tuple.Create(22, 78),
670Tuple.Create(22, 79),
671Tuple.Create(22, 80),
672Tuple.Create(22, 93),
673Tuple.Create(23, 35),
674Tuple.Create(23, 36),
675Tuple.Create(23, 37),
676Tuple.Create(23, 38),
677Tuple.Create(23, 39),
678Tuple.Create(23, 40),
679Tuple.Create(23, 41),
680Tuple.Create(23, 42),
681Tuple.Create(23, 43),
682Tuple.Create(23, 44),
683Tuple.Create(23, 45),
684Tuple.Create(23, 59),
685Tuple.Create(23, 60),
686Tuple.Create(23, 61),
687Tuple.Create(23, 62),
688Tuple.Create(23, 63),
689Tuple.Create(23, 64),
690Tuple.Create(23, 65),
691Tuple.Create(23, 66),
692Tuple.Create(23, 67),
693Tuple.Create(23, 68),
694Tuple.Create(23, 69),
695Tuple.Create(23, 82),
696Tuple.Create(23, 83),
697Tuple.Create(23, 84),
698Tuple.Create(23, 85),
699Tuple.Create(23, 86),
700Tuple.Create(23, 87),
701Tuple.Create(23, 88),
702Tuple.Create(23, 89),
703Tuple.Create(23, 90),
704Tuple.Create(23, 91),
705Tuple.Create(23, 92),
706Tuple.Create(24, 47),
707Tuple.Create(24, 49),
708Tuple.Create(24, 51),
709Tuple.Create(24, 54),
710Tuple.Create(24, 56),
711Tuple.Create(24, 60),
712Tuple.Create(24, 62),
713Tuple.Create(24, 65),
714Tuple.Create(24, 67),
715Tuple.Create(24, 94),
716Tuple.Create(25, 47),
717Tuple.Create(25, 48),
718Tuple.Create(25, 50),
719Tuple.Create(25, 53),
720Tuple.Create(25, 55),
721Tuple.Create(25, 59),
722Tuple.Create(25, 61),
723Tuple.Create(25, 64),
724Tuple.Create(25, 66),
725Tuple.Create(25, 94),
726Tuple.Create(26, 47),
727Tuple.Create(26, 49),
728Tuple.Create(26, 52),
729Tuple.Create(26, 54),
730Tuple.Create(26, 57),
731Tuple.Create(26, 60),
732Tuple.Create(26, 63),
733Tuple.Create(26, 65),
734Tuple.Create(26, 68),
735Tuple.Create(26, 94),
736Tuple.Create(27, 47),
737Tuple.Create(27, 48),
738Tuple.Create(27, 52),
739Tuple.Create(27, 53),
740Tuple.Create(27, 57),
741Tuple.Create(27, 59),
742Tuple.Create(27, 63),
743Tuple.Create(27, 64),
744Tuple.Create(27, 68),
745Tuple.Create(27, 94),
746Tuple.Create(28, 47),
747Tuple.Create(28, 50),
748Tuple.Create(28, 51),
749Tuple.Create(28, 55),
750Tuple.Create(28, 56),
751Tuple.Create(28, 61),
752Tuple.Create(28, 62),
753Tuple.Create(28, 66),
754Tuple.Create(28, 67),
755Tuple.Create(28, 94),
756Tuple.Create(29, 47),
757Tuple.Create(29, 49),
758Tuple.Create(29, 51),
759Tuple.Create(29, 58),
760Tuple.Create(29, 60),
761Tuple.Create(29, 62),
762Tuple.Create(29, 69),
763Tuple.Create(29, 94),
764Tuple.Create(30, 47),
765Tuple.Create(30, 48),
766Tuple.Create(30, 50),
767Tuple.Create(30, 58),
768Tuple.Create(30, 59),
769Tuple.Create(30, 61),
770Tuple.Create(30, 69),
771Tuple.Create(30, 94),
772Tuple.Create(31, 47),
773Tuple.Create(31, 49),
774Tuple.Create(31, 52),
775Tuple.Create(31, 58),
776Tuple.Create(31, 60),
777Tuple.Create(31, 63),
778Tuple.Create(31, 69),
779Tuple.Create(31, 94),
780Tuple.Create(32, 47),
781Tuple.Create(32, 48),
782Tuple.Create(32, 52),
783Tuple.Create(32, 58),
784Tuple.Create(32, 59),
785Tuple.Create(32, 63),
786Tuple.Create(32, 69),
787Tuple.Create(32, 94),
788Tuple.Create(33, 47),
789Tuple.Create(33, 50),
790Tuple.Create(33, 51),
791Tuple.Create(33, 58),
792Tuple.Create(33, 61),
793Tuple.Create(33, 62),
794Tuple.Create(33, 69),
795Tuple.Create(33, 94),
796Tuple.Create(34, 47),
797Tuple.Create(34, 53),
798Tuple.Create(34, 54),
799Tuple.Create(34, 55),
800Tuple.Create(34, 56),
801Tuple.Create(34, 57),
802Tuple.Create(34, 64),
803Tuple.Create(34, 65),
804Tuple.Create(34, 66),
805Tuple.Create(34, 67),
806Tuple.Create(34, 68),
807Tuple.Create(34, 94),
808Tuple.Create(35, 47),
809Tuple.Create(35, 49),
810Tuple.Create(35, 51),
811Tuple.Create(35, 54),
812Tuple.Create(35, 56),
813Tuple.Create(35, 70),
814Tuple.Create(35, 94),
815Tuple.Create(36, 47),
816Tuple.Create(36, 48),
817Tuple.Create(36, 50),
818Tuple.Create(36, 53),
819Tuple.Create(36, 55),
820Tuple.Create(36, 70),
821Tuple.Create(36, 94),
822Tuple.Create(37, 47),
823Tuple.Create(37, 49),
824Tuple.Create(37, 52),
825Tuple.Create(37, 54),
826Tuple.Create(37, 57),
827Tuple.Create(37, 70),
828Tuple.Create(37, 94),
829Tuple.Create(38, 47),
830Tuple.Create(38, 48),
831Tuple.Create(38, 52),
832Tuple.Create(38, 53),
833Tuple.Create(38, 57),
834Tuple.Create(38, 70),
835Tuple.Create(38, 94),
836Tuple.Create(39, 47),
837Tuple.Create(39, 50),
838Tuple.Create(39, 51),
839Tuple.Create(39, 55),
840Tuple.Create(39, 56),
841Tuple.Create(39, 70),
842Tuple.Create(39, 94),
843Tuple.Create(40, 47),
844Tuple.Create(40, 49),
845Tuple.Create(40, 51),
846Tuple.Create(40, 58),
847Tuple.Create(40, 70),
848Tuple.Create(40, 94),
849Tuple.Create(41, 47),
850Tuple.Create(41, 48),
851Tuple.Create(41, 50),
852Tuple.Create(41, 58),
853Tuple.Create(41, 70),
854Tuple.Create(41, 94),
855Tuple.Create(42, 47),
856Tuple.Create(42, 49),
857Tuple.Create(42, 52),
858Tuple.Create(42, 58),
859Tuple.Create(42, 70),
860Tuple.Create(42, 94),
861Tuple.Create(43, 47),
862Tuple.Create(43, 48),
863Tuple.Create(43, 52),
864Tuple.Create(43, 58),
865Tuple.Create(43, 70),
866Tuple.Create(43, 94),
867Tuple.Create(44, 47),
868Tuple.Create(44, 50),
869Tuple.Create(44, 51),
870Tuple.Create(44, 58),
871Tuple.Create(44, 70),
872Tuple.Create(44, 94),
873Tuple.Create(45, 47),
874Tuple.Create(45, 53),
875Tuple.Create(45, 54),
876Tuple.Create(45, 55),
877Tuple.Create(45, 56),
878Tuple.Create(45, 57),
879Tuple.Create(45, 70),
880Tuple.Create(45, 94),
881Tuple.Create(46, 47),
882Tuple.Create(46, 59),
883Tuple.Create(46, 60),
884Tuple.Create(46, 61),
885Tuple.Create(46, 62),
886Tuple.Create(46, 63),
887Tuple.Create(46, 64),
888Tuple.Create(46, 65),
889Tuple.Create(46, 66),
890Tuple.Create(46, 67),
891Tuple.Create(46, 68),
892Tuple.Create(46, 69),
893Tuple.Create(46, 94),
894Tuple.Create(47, 71),
895Tuple.Create(47, 72),
896Tuple.Create(47, 73),
897Tuple.Create(47, 74),
898Tuple.Create(47, 75),
899Tuple.Create(47, 76),
900Tuple.Create(47, 77),
901Tuple.Create(47, 78),
902Tuple.Create(47, 79),
903Tuple.Create(47, 80),
904Tuple.Create(47, 81),
905Tuple.Create(47, 82),
906Tuple.Create(47, 83),
907Tuple.Create(47, 84),
908Tuple.Create(47, 85),
909Tuple.Create(47, 86),
910Tuple.Create(47, 87),
911Tuple.Create(47, 88),
912Tuple.Create(47, 89),
913Tuple.Create(47, 90),
914Tuple.Create(47, 91),
915Tuple.Create(47, 92),
916Tuple.Create(47, 93),
917Tuple.Create(48, 95),
918Tuple.Create(49, 95),
919Tuple.Create(50, 95),
920Tuple.Create(51, 95),
921Tuple.Create(52, 95),
922Tuple.Create(53, 95),
923Tuple.Create(54, 95),
924Tuple.Create(55, 95),
925Tuple.Create(56, 95),
926Tuple.Create(57, 95),
927Tuple.Create(58, 95),
928Tuple.Create(59, 95),
929Tuple.Create(60, 95),
930Tuple.Create(61, 95),
931Tuple.Create(62, 95),
932Tuple.Create(63, 95),
933Tuple.Create(64, 95),
934Tuple.Create(65, 95),
935Tuple.Create(66, 95),
936Tuple.Create(67, 95),
937Tuple.Create(68, 95),
938Tuple.Create(69, 95),
939Tuple.Create(70, 95),
940Tuple.Create(71, 95),
941Tuple.Create(72, 95),
942Tuple.Create(73, 95),
943Tuple.Create(74, 95),
944Tuple.Create(75, 95),
945Tuple.Create(76, 95),
946Tuple.Create(77, 95),
947Tuple.Create(78, 95),
948Tuple.Create(79, 95),
949Tuple.Create(80, 95),
950Tuple.Create(81, 95),
951Tuple.Create(82, 95),
952Tuple.Create(83, 95),
953Tuple.Create(84, 95),
954Tuple.Create(85, 95),
955Tuple.Create(86, 95),
956Tuple.Create(87, 95),
957Tuple.Create(88, 95),
958Tuple.Create(89, 95),
959Tuple.Create(90, 95),
960Tuple.Create(91, 95),
961Tuple.Create(92, 95),
962Tuple.Create(93, 95),
963Tuple.Create(94, 95)
964    };
965    #endregion
966  }
967}
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