{
  "slug": "erdos",
  "domain": "Mathematics",
  "title": "A witness for minimum overlap.",
  "description": "A step-function construction that reuses published witness data and applies constrained numerical polishing.",
  "metric": "Minimum-overlap bound C₅",
  "unit": "",
  "note": "The witness comes from public artifacts. The selected program retrieves them at runtime before polishing; the visualization uses the frozen validated replay.",
  "task": "Erdos",
  "score": 0.38085905634104616,
  "reference": 0.38086767582732667,
  "direction": "min",
  "outcome": "Improved",
  "model": "GPT-5.6-Luna",
  "budget": 8,
  "seed": 42,
  "best_iteration": 97,
  "last_iteration": 100,
  "cost_usd": 29.5476394,
  "program_id": "d9f6de18-5685-43b5-b8e3-bf80273f1d13",
  "source_sha256": "ac0a66bbae9dfd4ee32884794aa08d50874e8acb4de63db939d558ce057f785b",
  "source": "static/programs/erdos.py",
  "language": "Python",
  "lines": 452,
  "history": {
    "points": [
      {
        "iteration": 0,
        "candidate_score": 2.0602683441977945,
        "best_score": 2.0602683441977945,
        "gate": "unrecorded"
      },
      {
        "iteration": 1,
        "candidate_score": 2.4242423654729124,
        "best_score": 2.4242423654729124,
        "gate": "retrieve"
      },
      {
        "iteration": 2,
        "candidate_score": 2.620172179738075,
        "best_score": 2.620172179738075,
        "gate": "retrieve"
      },
      {
        "iteration": 3,
        "candidate_score": 2.6200523260021304,
        "best_score": 2.620172179738075,
        "gate": "retrieve"
      },
      {
        "iteration": 4,
        "candidate_score": 2.619941317116197,
        "best_score": 2.620172179738075,
        "gate": "retrieve"
      },
      {
        "iteration": 5,
        "candidate_score": 2.6235798685183935,
        "best_score": 2.6235798685183935,
        "gate": "retrieve"
      },
      {
        "iteration": 6,
        "candidate_score": 2.6241024501952186,
        "best_score": 2.6241024501952186,
        "gate": "retrieve"
      },
      {
        "iteration": 7,
        "candidate_score": 2.6222975479497355,
        "best_score": 2.6241024501952186,
        "gate": "retrieve"
      },
      {
        "iteration": 8,
        "candidate_score": 2.6241024501952186,
        "best_score": 2.6241024501952186,
        "gate": "retrieve"
      },
      {
        "iteration": 9,
        "candidate_score": 2.624156156863831,
        "best_score": 2.624156156863831,
        "gate": "retrieve"
      },
      {
        "iteration": 10,
        "candidate_score": 2.6244812161976507,
        "best_score": 2.6244812161976507,
        "gate": "retrieve"
      },
      {
        "iteration": 11,
        "candidate_score": 2.624156156863831,
        "best_score": 2.6244812161976507,
        "gate": "retrieve"
      },
      {
        "iteration": 12,
        "candidate_score": 2.624469847686121,
        "best_score": 2.6244812161976507,
        "gate": "retrieve"
      },
      {
        "iteration": 13,
        "candidate_score": 2.624469847686121,
        "best_score": 2.6244812161976507,
        "gate": "retrieve"
      },
      {
        "iteration": 14,
        "candidate_score": 2.6245570880347433,
        "best_score": 2.6245570880347433,
        "gate": "retrieve"
      },
      {
        "iteration": 15,
        "candidate_score": 2.6245480191788384,
        "best_score": 2.6245570880347433,
        "gate": "retrieve"
      },
      {
        "iteration": 16,
        "candidate_score": 2.6245570880347433,
        "best_score": 2.6245570880347433,
        "gate": "retrieve"
      },
      {
        "iteration": 17,
        "candidate_score": 2.6256406301651345,
        "best_score": 2.6256406301651345,
        "gate": "retrieve"
      },
      {
        "iteration": 18,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431502703275,
        "gate": "lookup"
      },
      {
        "iteration": 19,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.6256431516474303,
        "gate": "retrieve"
      },
      {
        "iteration": 20,
        "candidate_score": 2.624641997657746,
        "best_score": 2.6256431516474303,
        "gate": "retrieve"
      },
      {
        "iteration": 21,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516474303,
        "gate": "lookup"
      },
      {
        "iteration": 22,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516474303,
        "gate": "lookup"
      },
      {
        "iteration": 23,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.6256431516474303,
        "gate": "lookup"
      },
      {
        "iteration": 24,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.6256431516474303,
        "gate": "retrieve"
      },
      {
        "iteration": 25,
        "candidate_score": 2.624641997657746,
        "best_score": 2.6256431516474303,
        "gate": "retrieve"
      },
      {
        "iteration": 26,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516474303,
        "gate": "lookup"
      },
      {
        "iteration": 27,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516474303,
        "gate": "lookup"
      },
      {
        "iteration": 28,
        "candidate_score": 2.624469847686121,
        "best_score": 2.6256431516474303,
        "gate": "retrieve"
      },
      {
        "iteration": 29,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.6256431516474303,
        "gate": "retrieve"
      },
      {
        "iteration": 30,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516474303,
        "gate": "retrieve"
      },
      {
        "iteration": 31,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.6256431516474303,
        "gate": "retrieve"
      },
      {
        "iteration": 32,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516474303,
        "gate": "retrieve"
      },
      {
        "iteration": 33,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516474303,
        "gate": "lookup"
      },
      {
        "iteration": 34,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.6256431516474303,
        "gate": "lookup"
      },
      {
        "iteration": 35,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516474303,
        "gate": "lookup"
      },
      {
        "iteration": 36,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516474303,
        "gate": "lookup"
      },
      {
        "iteration": 37,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516474303,
        "gate": "retrieve"
      },
      {
        "iteration": 38,
        "candidate_score": 2.6256431513015794,
        "best_score": 2.6256431516474303,
        "gate": "retrieve"
      },
      {
        "iteration": 39,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.6256431516474303,
        "gate": "lookup"
      },
      {
        "iteration": 40,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516474303,
        "gate": "lookup"
      },
      {
        "iteration": 41,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516474303,
        "gate": "lookup"
      },
      {
        "iteration": 42,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516474303,
        "gate": "lookup"
      },
      {
        "iteration": 43,
        "candidate_score": 2.624469847686121,
        "best_score": 2.6256431516474303,
        "gate": "lookup"
      },
      {
        "iteration": 44,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.6256431516474303,
        "gate": "retrieve"
      },
      {
        "iteration": 45,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.6256431516474303,
        "gate": "retrieve"
      },
      {
        "iteration": 46,
        "candidate_score": 2.62564315164743,
        "best_score": 2.6256431516474303,
        "gate": "retrieve"
      },
      {
        "iteration": 47,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516474303,
        "gate": "lookup"
      },
      {
        "iteration": 48,
        "candidate_score": 2.6256431516496423,
        "best_score": 2.6256431516496423,
        "gate": "lookup"
      },
      {
        "iteration": 49,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.6256431516496423,
        "gate": "retrieve"
      },
      {
        "iteration": 50,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516496423,
        "gate": "lookup"
      },
      {
        "iteration": 51,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516496423,
        "gate": "lookup"
      },
      {
        "iteration": 52,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.6256431516496423,
        "gate": "lookup"
      },
      {
        "iteration": 53,
        "candidate_score": 2.625643151864436,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 54,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 55,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 56,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 57,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 58,
        "candidate_score": 2.6256431516496423,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 59,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 60,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 61,
        "candidate_score": 2.6256431516495975,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 62,
        "candidate_score": 2.6256431516474255,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 63,
        "candidate_score": 2.625643151864436,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 64,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 65,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 66,
        "candidate_score": 2.6256431516495975,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 67,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 68,
        "candidate_score": 2.625643151864436,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 69,
        "candidate_score": 2.6256431505008986,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 70,
        "candidate_score": 2.625643151647437,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 71,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 72,
        "candidate_score": 2.625643151649605,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 73,
        "candidate_score": 2.625643151864436,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 74,
        "candidate_score": 2.625643151864436,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 75,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 76,
        "candidate_score": 2.6256431516495975,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 77,
        "candidate_score": 2.625643151649598,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 78,
        "candidate_score": 2.625643151864436,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 79,
        "candidate_score": 2.6256431502703275,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 80,
        "candidate_score": 2.625643151647437,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 81,
        "candidate_score": 2.6256431516495975,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 82,
        "candidate_score": 2.6256431513015794,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 83,
        "candidate_score": 2.625643151864436,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 84,
        "candidate_score": 2.625643151301568,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 85,
        "candidate_score": 2.625643151647437,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 86,
        "candidate_score": 2.6256431516495975,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 87,
        "candidate_score": 2.6256431513015794,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 88,
        "candidate_score": 2.6256431513015794,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 89,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 90,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 91,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 92,
        "candidate_score": 2.625643151649596,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 93,
        "candidate_score": 2.625643151864436,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 94,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 95,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.625643151864436,
        "gate": "retrieve"
      },
      {
        "iteration": 96,
        "candidate_score": 2.625643151647437,
        "best_score": 2.625643151864436,
        "gate": "lookup"
      },
      {
        "iteration": 97,
        "candidate_score": 2.625643153534737,
        "best_score": 2.625643153534737,
        "gate": "retrieve"
      },
      {
        "iteration": 98,
        "candidate_score": 2.625643151864436,
        "best_score": 2.625643153534737,
        "gate": "retrieve"
      },
      {
        "iteration": 99,
        "candidate_score": 2.625643151864436,
        "best_score": 2.625643153534737,
        "gate": "lookup"
      },
      {
        "iteration": 100,
        "candidate_score": 2.6256431516474303,
        "best_score": 2.625643153534737,
        "gate": "retrieve"
      }
    ],
    "trace_sha256": "c9b455c238ee68122b89744890be150a306c85454e5c82efd90bd91ef1306658",
    "score_label": "Search-time evaluator score ↑",
    "note": "Best-so-far envelope of recorded, non-migrant programs. If multiple programs share an iteration, the highest recorded score is used. Missing iterations are not invented."
  },
  "run_fingerprint": "cd2826eb0f2440691f4f80911835b6f45f05c306695b2758d4582a7cae1bc2fd",
  "artifact": {
    "views": [
      {
        "image": "static/images/programs/erdos-comparison.webp",
        "thumbnail": "static/images/programs/erdos-comparison-thumb.webp",
        "pdf": "static/figures/programs/erdos-comparison.pdf",
        "paper_pdf": "static/figures/programs/paper-math.pdf",
        "provenance": {
          "source": "figures/supp_figures/sota_objects_math.pdf",
          "source_sha256": "69b06c0cdce6b7745dec28d5fe3c6fa59a1bad2b2f866d2d294359a30af35c5b",
          "clip_points": [
            0.0,
            0.0,
            202.0,
            115.5999984741211
          ],
          "cropped": true,
          "pdf_sha256": "449673a57c497877a07352dcdd43d79a181166ebc27a0d212089d5d515d33f46",
          "image_sha256": "964fadc3c5526449899d20e7c09c985d8ddf871bbee24478bbbeffbca3c0643d",
          "thumbnail_sha256": "c3204c605cb8709cf80c3af81ede08c781bd24d15f96fc6264d989e82cc61717"
        },
        "label": "Witness comparison",
        "caption": "The published 512-step witness located and polished by EvoDuet, compared with the SimpleTES construction. The full-shift overlap is available in the second view."
      },
      {
        "label": "Overlap profile",
        "image": "static/images/programs/erdos-overlap.svg"
      }
    ],
    "kind": "views",
    "data": {
      "h": [
        9.766642310879856e-17,
        2.415093155615709e-16,
        5.551115123125783e-17,
        3.685535659383738e-16,
        1.513483115961578e-16,
        7.796569115886019e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        9.832621216951299e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        2.6637935621914757e-16,
        5.551115123125783e-17,
        5.636244464383393e-17,
        5.657304097158075e-17,
        5.551115123125783e-17,
        1.0690334503390698e-16,
        1.5311377599004257e-16,
        5.551115123125783e-17,
        7.248474591263168e-17,
        6.49099104276808e-16,
        1.2842062483472803e-16,
        1.1152991860763474e-16,
        5.551115123125783e-17,
        5.551115123125783e-17,
        1.8721291489258025e-16,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        2.115756307926277e-16,
        1.7350926516880065e-16,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        7.672908055292371e-17,
        5.551115123125783e-17,
        7.670690022338767e-17,
        7.017372846544241e-17,
        1.183358771630267e-16,
        5.551115123125783e-17,
        5.551115123125783e-17,
        8.575933361503157e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        2.3276493608409896e-16,
        5.551115123125783e-17,
        5.551115123125783e-17,
        2.31519862426931e-16,
        0.006676088755456584,
        0.013742428642901991,
        0.017378107638108445,
        0.15052119945603623,
        0.2786870644937064,
        0.4921619008036,
        0.6344829051959968,
        0.8780436226706172,
        0.8598520858965788,
        0.9133238485740631,
        0.9520324045964244,
        0.6600379581359748,
        0.5746230504982748,
        0.6503555677875104,
        0.6558026879891556,
        0.5599279991318507,
        0.6126305962753291,
        0.635585279923085,
        0.5742458540285134,
        0.8210559947473082,
        0.8242533130572978,
        0.8885483711166853,
        0.9971006997030527,
        0.982628668209955,
        0.9888706598553894,
        0.9627464002543804,
        0.988371615857591,
        1.0,
        0.999999999999895,
        0.9627120742035162,
        0.879240992160979,
        0.7187622635783284,
        0.5244431070750153,
        0.40505582287353853,
        0.38513563490979696,
        0.009269503723529948,
        2.3648553715160553e-16,
        5.233306775124854e-14,
        5.551115123125783e-17,
        6.739778044746854e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        1.6532200669984031e-16,
        5.551115123125783e-17,
        1.2973646648502322e-16,
        1.117687381533367e-16,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        1.0407253535814821e-16,
        1.3202501012431105e-16,
        5.551115123125783e-17,
        1.8521534915585396e-13,
        0.38663556347736633,
        0.5633978359842127,
        0.5882604440829087,
        0.7705383577671812,
        0.8233074143044306,
        0.8298573660703588,
        0.8588221839908263,
        0.9309480405243402,
        0.9812282643571681,
        0.8787815024247614,
        0.7431542548819581,
        0.6987696643155321,
        0.7634193836392458,
        0.6941774379845262,
        0.655507477433906,
        0.6016599368344819,
        0.4017926787205067,
        0.5467946633276064,
        0.46891806138218767,
        0.3897565159187781,
        0.31093769495604767,
        0.39106845577766364,
        0.4308119548844946,
        0.5341973707487733,
        0.4977638002364426,
        0.39348311290734994,
        0.4709845554682996,
        0.4686251026299786,
        0.47237734440630325,
        0.35081191263076394,
        0.489393254820641,
        0.5467197072807943,
        0.6895970268165883,
        0.7333984544722967,
        0.7428789983636976,
        0.7392298903971781,
        0.8415146163601819,
        0.9774122206865055,
        0.9853072416029132,
        1.0,
        0.984024997675663,
        0.9338025907479037,
        0.7489069226032836,
        0.6653804767613816,
        0.4252886174408938,
        0.4480628018467771,
        0.4153946672664811,
        0.48225243065962164,
        0.33875706079583684,
        0.24284470143048753,
        0.2947777227809404,
        0.2941848536083518,
        0.31542602075277265,
        0.27873431631228246,
        0.2852615312990963,
        0.24460845694437974,
        0.3315339102482121,
        0.3920843412112305,
        0.34308750529636683,
        0.3094133929374647,
        0.49073634704392183,
        0.5143193703773554,
        0.7437154683577174,
        0.8899718354854784,
        0.9858141835507448,
        0.991369071698079,
        0.9999999999998366,
        0.9918890222735293,
        0.9999999999999107,
        0.8761116706532215,
        0.5957857512825904,
        0.39212587134260374,
        0.35407963326098923,
        0.35850882165857545,
        0.38454302774621457,
        0.3949933177908519,
        0.5968217158618598,
        0.6234467135991923,
        0.6681818816112757,
        0.7948640137837388,
        0.7592083376126972,
        0.8308161240530085,
        0.9909074786072551,
        1.0,
        0.939354925071606,
        0.992002588980617,
        0.9822532106040187,
        0.9784553072323758,
        0.8952222771417866,
        0.7515313994208948,
        0.8842143143241914,
        0.8501449023498724,
        0.6293332896821582,
        0.5960273165723393,
        0.605734586635468,
        0.6363208686575959,
        0.5521245411038374,
        0.5102686607548454,
        0.5765226929318725,
        0.5718133338161571,
        0.543753389685472,
        0.5731174434269626,
        0.6952887789635853,
        0.6988215308887067,
        0.9889023967997961,
        0.9958005504762544,
        1.0,
        0.9999999999999998,
        1.0,
        1.0,
        1.0,
        1.0,
        0.9915466256952559,
        0.46806033748116543,
        0.33348700551478133,
        0.5102430851550326,
        0.5908774294208357,
        0.7129374287243877,
        0.9484947165423645,
        1.0,
        1.0,
        1.0,
        1.0,
        0.9999999999999998,
        1.0,
        1.0,
        1.0,
        1.0,
        0.9432250888834406,
        0.8837810737873595,
        0.9780774055723407,
        0.8829902036443404,
        1.0,
        0.9408070472541428,
        0.8844424663791601,
        0.8489741975018048,
        0.9869954722793053,
        0.9041785167123937,
        0.8621668484554921,
        0.9797357016070132,
        0.986053658185778,
        0.9828803447617689,
        1.0,
        1.0,
        1.0,
        1.0,
        1.0,
        1.0,
        1.0,
        1.0,
        1.0,
        1.0,
        1.0,
        0.9889090745372249,
        0.9510443499603289,
        0.7814587652315499,
        0.8257217130790568,
        0.9324476677006517,
        0.8577783934834364,
        0.9114740370100745,
        1.0,
        1.0,
        1.0,
        0.9884392999436695,
        0.9496258898523791,
        0.9628328947762343,
        0.6656454329477632,
        0.6991680465067742,
        0.801517831986275,
        0.6969065481601928,
        0.7563513350105409,
        0.6676072352683831,
        0.5108824395037748,
        0.7200098591190296,
        0.9538216236570833,
        0.9297560308146182,
        0.7595251149969948,
        1.0,
        1.0,
        1.0,
        1.0,
        1.0,
        1.0,
        1.0,
        1.0,
        1.0,
        1.0,
        0.9546430772131356,
        0.7037446678944725,
        0.6936582497368031,
        0.6583963284629355,
        0.4551818968705998,
        0.5718133338161242,
        0.5765226929317251,
        0.513558085838179,
        0.5488351160207345,
        0.636320868657597,
        0.605734586635382,
        0.5960273165721575,
        0.5297322706367096,
        0.8709313608220317,
        0.806540580502042,
        0.8801549143904484,
        0.9346116663297477,
        0.9799696528603348,
        1.0,
        1.0,
        0.9230741800880666,
        0.9689275021732187,
        0.9994775656121384,
        0.8308161240533478,
        0.7592083376125254,
        0.7948640137837601,
        0.6681818816111418,
        0.6234467135994357,
        0.5968217158616818,
        0.3834432412937088,
        0.39456114189092356,
        0.3600407840111099,
        0.35407963326094277,
        0.3921258713425813,
        0.595785751282538,
        0.8761116706533114,
        1.0,
        0.9918890222733323,
        1.0,
        0.9913690716978116,
        0.9858141835508987,
        0.8899718354856709,
        0.7437154683574654,
        0.5143193703774178,
        0.4907363470438573,
        0.309413392937673,
        0.3430875052963736,
        0.3920843412113742,
        0.331533910248154,
        0.24460845694429906,
        0.2852615312989309,
        0.2787343163125208,
        0.31542602075270687,
        0.2941848536083039,
        0.2921155591034876,
        0.2455068651078871,
        0.33875706079572854,
        0.48225243065975637,
        0.4153946672664957,
        0.4480628018468326,
        0.42528861744075214,
        0.6653804767615079,
        0.7489069226034384,
        0.9338025907476084,
        0.9840249976756612,
        1.0,
        0.9853072416030304,
        0.9774122206865354,
        0.841514616360227,
        0.7392298903971566,
        0.7428789983634283,
        0.7333984544723993,
        0.6895970268166385,
        0.5467197072804795,
        0.48939325482077556,
        0.35081191263089356,
        0.47237734440627466,
        0.4686251026299998,
        0.4709845554684698,
        0.39348311290732896,
        0.497763800236238,
        0.5341973707488861,
        0.4308119548843676,
        0.39106845577750665,
        0.31093769495619844,
        0.38975651591896815,
        0.4689180613821666,
        0.5467946633275804,
        0.4017926787204672,
        0.6016599368344671,
        0.6555074774340448,
        0.6941774379844401,
        0.7634193836389418,
        0.6987696643158781,
        0.7431542548817531,
        0.8787815024247867,
        0.9812282643572212,
        0.9309480405243031,
        0.8588221839908294,
        0.829857366070607,
        0.8233074143041128,
        0.7705383577671843,
        0.5882604440829815,
        0.5633978359842597,
        0.3866355634775681,
        1.3530093557426114e-16,
        3.662935393915189e-16,
        5.551115123125783e-17,
        5.551115123125783e-17,
        4.186825318202049e-14,
        5.551115123125783e-17,
        5.551115123125783e-17,
        1.277528277249312e-16,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        1.2028238947503764e-16,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        6.716548358420179e-17,
        5.551115123125783e-17,
        0.009269503723636411,
        0.38513563490960195,
        0.4050558228736158,
        0.5244431070751736,
        0.7187622635781634,
        0.8792409921609643,
        0.9627120742035074,
        1.0,
        0.999999999999988,
        0.9883716158576459,
        0.9627464002542991,
        0.9888706598552568,
        0.9826286682100744,
        0.9971006997030147,
        0.8885483711168196,
        0.8242533130573078,
        0.8210559947471163,
        0.5742458540287461,
        0.6355852799229145,
        0.6126305962754246,
        0.559927999131764,
        0.65580268798922,
        0.6503555677873802,
        0.5746230504983121,
        0.6600379581361779,
        0.9520324045962296,
        0.9133238485741315,
        0.8598520858964436,
        0.8780436226706447,
        0.6344829051960179,
        0.4921619008037015,
        0.2786870644936511,
        0.15052119945602965,
        0.017378107638062697,
        0.013742428643001766,
        0.00667608875543723,
        5.551115123125783e-17,
        5.551115123125783e-17,
        9.468342710216537e-17,
        5.551115123125783e-17,
        7.377435068809894e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        7.377435070456877e-17,
        1.2928550198794067e-16,
        1.223466079214708e-16,
        5.551115123125783e-17,
        6.683545654446185e-17,
        7.377435040750574e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        1.296920776680692e-16,
        5.551115123125783e-17,
        1.1540771420071043e-16,
        7.418092737511676e-17,
        5.551115123125783e-17,
        2.2683659210843836e-16,
        1.0846881994977252e-16,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        8.80587146627785e-17,
        7.50482875578406e-17,
        5.551115123125783e-17,
        7.418092621174676e-17,
        8.071324400958638e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        1.2275318440387822e-16,
        1.5744765374577033e-16,
        1.435698660030114e-16,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17,
        5.551115123125783e-17
      ],
      "shift": [
        -1.99609375,
        -1.9921875,
        -1.98828125,
        -1.984375,
        -1.98046875,
        -1.9765625,
        -1.97265625,
        -1.96875,
        -1.96484375,
        -1.9609375,
        -1.95703125,
        -1.953125,
        -1.94921875,
        -1.9453125,
        -1.94140625,
        -1.9375,
        -1.93359375,
        -1.9296875,
        -1.92578125,
        -1.921875,
        -1.91796875,
        -1.9140625,
        -1.91015625,
        -1.90625,
        -1.90234375,
        -1.8984375,
        -1.89453125,
        -1.890625,
        -1.88671875,
        -1.8828125,
        -1.87890625,
        -1.875,
        -1.87109375,
        -1.8671875,
        -1.86328125,
        -1.859375,
        -1.85546875,
        -1.8515625,
        -1.84765625,
        -1.84375,
        -1.83984375,
        -1.8359375,
        -1.83203125,
        -1.828125,
        -1.82421875,
        -1.8203125,
        -1.81640625,
        -1.8125,
        -1.80859375,
        -1.8046875,
        -1.80078125,
        -1.796875,
        -1.79296875,
        -1.7890625,
        -1.78515625,
        -1.78125,
        -1.77734375,
        -1.7734375,
        -1.76953125,
        -1.765625,
        -1.76171875,
        -1.7578125,
        -1.75390625,
        -1.75,
        -1.74609375,
        -1.7421875,
        -1.73828125,
        -1.734375,
        -1.73046875,
        -1.7265625,
        -1.72265625,
        -1.71875,
        -1.71484375,
        -1.7109375,
        -1.70703125,
        -1.703125,
        -1.69921875,
        -1.6953125,
        -1.69140625,
        -1.6875,
        -1.68359375,
        -1.6796875,
        -1.67578125,
        -1.671875,
        -1.66796875,
        -1.6640625,
        -1.66015625,
        -1.65625,
        -1.65234375,
        -1.6484375,
        -1.64453125,
        -1.640625,
        -1.63671875,
        -1.6328125,
        -1.62890625,
        -1.625,
        -1.62109375,
        -1.6171875,
        -1.61328125,
        -1.609375,
        -1.60546875,
        -1.6015625,
        -1.59765625,
        -1.59375,
        -1.58984375,
        -1.5859375,
        -1.58203125,
        -1.578125,
        -1.57421875,
        -1.5703125,
        -1.56640625,
        -1.5625,
        -1.55859375,
        -1.5546875,
        -1.55078125,
        -1.546875,
        -1.54296875,
        -1.5390625,
        -1.53515625,
        -1.53125,
        -1.52734375,
        -1.5234375,
        -1.51953125,
        -1.515625,
        -1.51171875,
        -1.5078125,
        -1.50390625,
        -1.5,
        -1.49609375,
        -1.4921875,
        -1.48828125,
        -1.484375,
        -1.48046875,
        -1.4765625,
        -1.47265625,
        -1.46875,
        -1.46484375,
        -1.4609375,
        -1.45703125,
        -1.453125,
        -1.44921875,
        -1.4453125,
        -1.44140625,
        -1.4375,
        -1.43359375,
        -1.4296875,
        -1.42578125,
        -1.421875,
        -1.41796875,
        -1.4140625,
        -1.41015625,
        -1.40625,
        -1.40234375,
        -1.3984375,
        -1.39453125,
        -1.390625,
        -1.38671875,
        -1.3828125,
        -1.37890625,
        -1.375,
        -1.37109375,
        -1.3671875,
        -1.36328125,
        -1.359375,
        -1.35546875,
        -1.3515625,
        -1.34765625,
        -1.34375,
        -1.33984375,
        -1.3359375,
        -1.33203125,
        -1.328125,
        -1.32421875,
        -1.3203125,
        -1.31640625,
        -1.3125,
        -1.30859375,
        -1.3046875,
        -1.30078125,
        -1.296875,
        -1.29296875,
        -1.2890625,
        -1.28515625,
        -1.28125,
        -1.27734375,
        -1.2734375,
        -1.26953125,
        -1.265625,
        -1.26171875,
        -1.2578125,
        -1.25390625,
        -1.25,
        -1.24609375,
        -1.2421875,
        -1.23828125,
        -1.234375,
        -1.23046875,
        -1.2265625,
        -1.22265625,
        -1.21875,
        -1.21484375,
        -1.2109375,
        -1.20703125,
        -1.203125,
        -1.19921875,
        -1.1953125,
        -1.19140625,
        -1.1875,
        -1.18359375,
        -1.1796875,
        -1.17578125,
        -1.171875,
        -1.16796875,
        -1.1640625,
        -1.16015625,
        -1.15625,
        -1.15234375,
        -1.1484375,
        -1.14453125,
        -1.140625,
        -1.13671875,
        -1.1328125,
        -1.12890625,
        -1.125,
        -1.12109375,
        -1.1171875,
        -1.11328125,
        -1.109375,
        -1.10546875,
        -1.1015625,
        -1.09765625,
        -1.09375,
        -1.08984375,
        -1.0859375,
        -1.08203125,
        -1.078125,
        -1.07421875,
        -1.0703125,
        -1.06640625,
        -1.0625,
        -1.05859375,
        -1.0546875,
        -1.05078125,
        -1.046875,
        -1.04296875,
        -1.0390625,
        -1.03515625,
        -1.03125,
        -1.02734375,
        -1.0234375,
        -1.01953125,
        -1.015625,
        -1.01171875,
        -1.0078125,
        -1.00390625,
        -1.0,
        -0.99609375,
        -0.9921875,
        -0.98828125,
        -0.984375,
        -0.98046875,
        -0.9765625,
        -0.97265625,
        -0.96875,
        -0.96484375,
        -0.9609375,
        -0.95703125,
        -0.953125,
        -0.94921875,
        -0.9453125,
        -0.94140625,
        -0.9375,
        -0.93359375,
        -0.9296875,
        -0.92578125,
        -0.921875,
        -0.91796875,
        -0.9140625,
        -0.91015625,
        -0.90625,
        -0.90234375,
        -0.8984375,
        -0.89453125,
        -0.890625,
        -0.88671875,
        -0.8828125,
        -0.87890625,
        -0.875,
        -0.87109375,
        -0.8671875,
        -0.86328125,
        -0.859375,
        -0.85546875,
        -0.8515625,
        -0.84765625,
        -0.84375,
        -0.83984375,
        -0.8359375,
        -0.83203125,
        -0.828125,
        -0.82421875,
        -0.8203125,
        -0.81640625,
        -0.8125,
        -0.80859375,
        -0.8046875,
        -0.80078125,
        -0.796875,
        -0.79296875,
        -0.7890625,
        -0.78515625,
        -0.78125,
        -0.77734375,
        -0.7734375,
        -0.76953125,
        -0.765625,
        -0.76171875,
        -0.7578125,
        -0.75390625,
        -0.75,
        -0.74609375,
        -0.7421875,
        -0.73828125,
        -0.734375,
        -0.73046875,
        -0.7265625,
        -0.72265625,
        -0.71875,
        -0.71484375,
        -0.7109375,
        -0.70703125,
        -0.703125,
        -0.69921875,
        -0.6953125,
        -0.69140625,
        -0.6875,
        -0.68359375,
        -0.6796875,
        -0.67578125,
        -0.671875,
        -0.66796875,
        -0.6640625,
        -0.66015625,
        -0.65625,
        -0.65234375,
        -0.6484375,
        -0.64453125,
        -0.640625,
        -0.63671875,
        -0.6328125,
        -0.62890625,
        -0.625,
        -0.62109375,
        -0.6171875,
        -0.61328125,
        -0.609375,
        -0.60546875,
        -0.6015625,
        -0.59765625,
        -0.59375,
        -0.58984375,
        -0.5859375,
        -0.58203125,
        -0.578125,
        -0.57421875,
        -0.5703125,
        -0.56640625,
        -0.5625,
        -0.55859375,
        -0.5546875,
        -0.55078125,
        -0.546875,
        -0.54296875,
        -0.5390625,
        -0.53515625,
        -0.53125,
        -0.52734375,
        -0.5234375,
        -0.51953125,
        -0.515625,
        -0.51171875,
        -0.5078125,
        -0.50390625,
        -0.5,
        -0.49609375,
        -0.4921875,
        -0.48828125,
        -0.484375,
        -0.48046875,
        -0.4765625,
        -0.47265625,
        -0.46875,
        -0.46484375,
        -0.4609375,
        -0.45703125,
        -0.453125,
        -0.44921875,
        -0.4453125,
        -0.44140625,
        -0.4375,
        -0.43359375,
        -0.4296875,
        -0.42578125,
        -0.421875,
        -0.41796875,
        -0.4140625,
        -0.41015625,
        -0.40625,
        -0.40234375,
        -0.3984375,
        -0.39453125,
        -0.390625,
        -0.38671875,
        -0.3828125,
        -0.37890625,
        -0.375,
        -0.37109375,
        -0.3671875,
        -0.36328125,
        -0.359375,
        -0.35546875,
        -0.3515625,
        -0.34765625,
        -0.34375,
        -0.33984375,
        -0.3359375,
        -0.33203125,
        -0.328125,
        -0.32421875,
        -0.3203125,
        -0.31640625,
        -0.3125,
        -0.30859375,
        -0.3046875,
        -0.30078125,
        -0.296875,
        -0.29296875,
        -0.2890625,
        -0.28515625,
        -0.28125,
        -0.27734375,
        -0.2734375,
        -0.26953125,
        -0.265625,
        -0.26171875,
        -0.2578125,
        -0.25390625,
        -0.25,
        -0.24609375,
        -0.2421875,
        -0.23828125,
        -0.234375,
        -0.23046875,
        -0.2265625,
        -0.22265625,
        -0.21875,
        -0.21484375,
        -0.2109375,
        -0.20703125,
        -0.203125,
        -0.19921875,
        -0.1953125,
        -0.19140625,
        -0.1875,
        -0.18359375,
        -0.1796875,
        -0.17578125,
        -0.171875,
        -0.16796875,
        -0.1640625,
        -0.16015625,
        -0.15625,
        -0.15234375,
        -0.1484375,
        -0.14453125,
        -0.140625,
        -0.13671875,
        -0.1328125,
        -0.12890625,
        -0.125,
        -0.12109375,
        -0.1171875,
        -0.11328125,
        -0.109375,
        -0.10546875,
        -0.1015625,
        -0.09765625,
        -0.09375,
        -0.08984375,
        -0.0859375,
        -0.08203125,
        -0.078125,
        -0.07421875,
        -0.0703125,
        -0.06640625,
        -0.0625,
        -0.05859375,
        -0.0546875,
        -0.05078125,
        -0.046875,
        -0.04296875,
        -0.0390625,
        -0.03515625,
        -0.03125,
        -0.02734375,
        -0.0234375,
        -0.01953125,
        -0.015625,
        -0.01171875,
        -0.0078125,
        -0.00390625,
        0.0,
        0.00390625,
        0.0078125,
        0.01171875,
        0.015625,
        0.01953125,
        0.0234375,
        0.02734375,
        0.03125,
        0.03515625,
        0.0390625,
        0.04296875,
        0.046875,
        0.05078125,
        0.0546875,
        0.05859375,
        0.0625,
        0.06640625,
        0.0703125,
        0.07421875,
        0.078125,
        0.08203125,
        0.0859375,
        0.08984375,
        0.09375,
        0.09765625,
        0.1015625,
        0.10546875,
        0.109375,
        0.11328125,
        0.1171875,
        0.12109375,
        0.125,
        0.12890625,
        0.1328125,
        0.13671875,
        0.140625,
        0.14453125,
        0.1484375,
        0.15234375,
        0.15625,
        0.16015625,
        0.1640625,
        0.16796875,
        0.171875,
        0.17578125,
        0.1796875,
        0.18359375,
        0.1875,
        0.19140625,
        0.1953125,
        0.19921875,
        0.203125,
        0.20703125,
        0.2109375,
        0.21484375,
        0.21875,
        0.22265625,
        0.2265625,
        0.23046875,
        0.234375,
        0.23828125,
        0.2421875,
        0.24609375,
        0.25,
        0.25390625,
        0.2578125,
        0.26171875,
        0.265625,
        0.26953125,
        0.2734375,
        0.27734375,
        0.28125,
        0.28515625,
        0.2890625,
        0.29296875,
        0.296875,
        0.30078125,
        0.3046875,
        0.30859375,
        0.3125,
        0.31640625,
        0.3203125,
        0.32421875,
        0.328125,
        0.33203125,
        0.3359375,
        0.33984375,
        0.34375,
        0.34765625,
        0.3515625,
        0.35546875,
        0.359375,
        0.36328125,
        0.3671875,
        0.37109375,
        0.375,
        0.37890625,
        0.3828125,
        0.38671875,
        0.390625,
        0.39453125,
        0.3984375,
        0.40234375,
        0.40625,
        0.41015625,
        0.4140625,
        0.41796875,
        0.421875,
        0.42578125,
        0.4296875,
        0.43359375,
        0.4375,
        0.44140625,
        0.4453125,
        0.44921875,
        0.453125,
        0.45703125,
        0.4609375,
        0.46484375,
        0.46875,
        0.47265625,
        0.4765625,
        0.48046875,
        0.484375,
        0.48828125,
        0.4921875,
        0.49609375,
        0.5,
        0.50390625,
        0.5078125,
        0.51171875,
        0.515625,
        0.51953125,
        0.5234375,
        0.52734375,
        0.53125,
        0.53515625,
        0.5390625,
        0.54296875,
        0.546875,
        0.55078125,
        0.5546875,
        0.55859375,
        0.5625,
        0.56640625,
        0.5703125,
        0.57421875,
        0.578125,
        0.58203125,
        0.5859375,
        0.58984375,
        0.59375,
        0.59765625,
        0.6015625,
        0.60546875,
        0.609375,
        0.61328125,
        0.6171875,
        0.62109375,
        0.625,
        0.62890625,
        0.6328125,
        0.63671875,
        0.640625,
        0.64453125,
        0.6484375,
        0.65234375,
        0.65625,
        0.66015625,
        0.6640625,
        0.66796875,
        0.671875,
        0.67578125,
        0.6796875,
        0.68359375,
        0.6875,
        0.69140625,
        0.6953125,
        0.69921875,
        0.703125,
        0.70703125,
        0.7109375,
        0.71484375,
        0.71875,
        0.72265625,
        0.7265625,
        0.73046875,
        0.734375,
        0.73828125,
        0.7421875,
        0.74609375,
        0.75,
        0.75390625,
        0.7578125,
        0.76171875,
        0.765625,
        0.76953125,
        0.7734375,
        0.77734375,
        0.78125,
        0.78515625,
        0.7890625,
        0.79296875,
        0.796875,
        0.80078125,
        0.8046875,
        0.80859375,
        0.8125,
        0.81640625,
        0.8203125,
        0.82421875,
        0.828125,
        0.83203125,
        0.8359375,
        0.83984375,
        0.84375,
        0.84765625,
        0.8515625,
        0.85546875,
        0.859375,
        0.86328125,
        0.8671875,
        0.87109375,
        0.875,
        0.87890625,
        0.8828125,
        0.88671875,
        0.890625,
        0.89453125,
        0.8984375,
        0.90234375,
        0.90625,
        0.91015625,
        0.9140625,
        0.91796875,
        0.921875,
        0.92578125,
        0.9296875,
        0.93359375,
        0.9375,
        0.94140625,
        0.9453125,
        0.94921875,
        0.953125,
        0.95703125,
        0.9609375,
        0.96484375,
        0.96875,
        0.97265625,
        0.9765625,
        0.98046875,
        0.984375,
        0.98828125,
        0.9921875,
        0.99609375,
        1.0,
        1.00390625,
        1.0078125,
        1.01171875,
        1.015625,
        1.01953125,
        1.0234375,
        1.02734375,
        1.03125,
        1.03515625,
        1.0390625,
        1.04296875,
        1.046875,
        1.05078125,
        1.0546875,
        1.05859375,
        1.0625,
        1.06640625,
        1.0703125,
        1.07421875,
        1.078125,
        1.08203125,
        1.0859375,
        1.08984375,
        1.09375,
        1.09765625,
        1.1015625,
        1.10546875,
        1.109375,
        1.11328125,
        1.1171875,
        1.12109375,
        1.125,
        1.12890625,
        1.1328125,
        1.13671875,
        1.140625,
        1.14453125,
        1.1484375,
        1.15234375,
        1.15625,
        1.16015625,
        1.1640625,
        1.16796875,
        1.171875,
        1.17578125,
        1.1796875,
        1.18359375,
        1.1875,
        1.19140625,
        1.1953125,
        1.19921875,
        1.203125,
        1.20703125,
        1.2109375,
        1.21484375,
        1.21875,
        1.22265625,
        1.2265625,
        1.23046875,
        1.234375,
        1.23828125,
        1.2421875,
        1.24609375,
        1.25,
        1.25390625,
        1.2578125,
        1.26171875,
        1.265625,
        1.26953125,
        1.2734375,
        1.27734375,
        1.28125,
        1.28515625,
        1.2890625,
        1.29296875,
        1.296875,
        1.30078125,
        1.3046875,
        1.30859375,
        1.3125,
        1.31640625,
        1.3203125,
        1.32421875,
        1.328125,
        1.33203125,
        1.3359375,
        1.33984375,
        1.34375,
        1.34765625,
        1.3515625,
        1.35546875,
        1.359375,
        1.36328125,
        1.3671875,
        1.37109375,
        1.375,
        1.37890625,
        1.3828125,
        1.38671875,
        1.390625,
        1.39453125,
        1.3984375,
        1.40234375,
        1.40625,
        1.41015625,
        1.4140625,
        1.41796875,
        1.421875,
        1.42578125,
        1.4296875,
        1.43359375,
        1.4375,
        1.44140625,
        1.4453125,
        1.44921875,
        1.453125,
        1.45703125,
        1.4609375,
        1.46484375,
        1.46875,
        1.47265625,
        1.4765625,
        1.48046875,
        1.484375,
        1.48828125,
        1.4921875,
        1.49609375,
        1.5,
        1.50390625,
        1.5078125,
        1.51171875,
        1.515625,
        1.51953125,
        1.5234375,
        1.52734375,
        1.53125,
        1.53515625,
        1.5390625,
        1.54296875,
        1.546875,
        1.55078125,
        1.5546875,
        1.55859375,
        1.5625,
        1.56640625,
        1.5703125,
        1.57421875,
        1.578125,
        1.58203125,
        1.5859375,
        1.58984375,
        1.59375,
        1.59765625,
        1.6015625,
        1.60546875,
        1.609375,
        1.61328125,
        1.6171875,
        1.62109375,
        1.625,
        1.62890625,
        1.6328125,
        1.63671875,
        1.640625,
        1.64453125,
        1.6484375,
        1.65234375,
        1.65625,
        1.66015625,
        1.6640625,
        1.66796875,
        1.671875,
        1.67578125,
        1.6796875,
        1.68359375,
        1.6875,
        1.69140625,
        1.6953125,
        1.69921875,
        1.703125,
        1.70703125,
        1.7109375,
        1.71484375,
        1.71875,
        1.72265625,
        1.7265625,
        1.73046875,
        1.734375,
        1.73828125,
        1.7421875,
        1.74609375,
        1.75,
        1.75390625,
        1.7578125,
        1.76171875,
        1.765625,
        1.76953125,
        1.7734375,
        1.77734375,
        1.78125,
        1.78515625,
        1.7890625,
        1.79296875,
        1.796875,
        1.80078125,
        1.8046875,
        1.80859375,
        1.8125,
        1.81640625,
        1.8203125,
        1.82421875,
        1.828125,
        1.83203125,
        1.8359375,
        1.83984375,
        1.84375,
        1.84765625,
        1.8515625,
        1.85546875,
        1.859375,
        1.86328125,
        1.8671875,
        1.87109375,
        1.875,
        1.87890625,
        1.8828125,
        1.88671875,
        1.890625,
        1.89453125,
        1.8984375,
        1.90234375,
        1.90625,
        1.91015625,
        1.9140625,
        1.91796875,
        1.921875,
        1.92578125,
        1.9296875,
        1.93359375,
        1.9375,
        1.94140625,
        1.9453125,
        1.94921875,
        1.953125,
        1.95703125,
        1.9609375,
        1.96484375,
        1.96875,
        1.97265625,
        1.9765625,
        1.98046875,
        1.984375,
        1.98828125,
        1.9921875,
        1.99609375
      ],
      "overlap": [
        3.8150946526874436e-19,
        1.3249052291811306e-18,
        1.5417456636782314e-18,
        2.981408030625004e-18,
        3.5726123727974954e-18,
        3.877165853886793e-18,
        4.0940062883838935e-18,
        4.3108467228809944e-18,
        4.527687157378095e-18,
        4.744527591875196e-18,
        5.128614358162357e-18,
        5.3454547926594576e-18,
        5.5622952271565585e-18,
        6.602839587387604e-18,
        6.8196800218847046e-18,
        7.03984582127468e-18,
        7.260834262569917e-18,
        7.477674697067018e-18,
        7.895265888605717e-18,
        8.49336657606682e-18,
        8.710207010563921e-18,
        8.99335054928514e-18,
        1.1528893925366422e-17,
        1.2030536991127077e-17,
        1.2466200735688151e-17,
        1.2683041170185252e-17,
        1.2899881604682353e-17,
        1.3631182053481492e-17,
        1.3848022487978593e-17,
        1.4064862922475694e-17,
        1.4281703356972795e-17,
        1.44985437914699e-17,
        1.53250110992536e-17,
        1.6002781666319228e-17,
        1.621962210081633e-17,
        1.643646253531343e-17,
        1.665330296981053e-17,
        1.6870143404307632e-17,
        1.716986637521749e-17,
        1.738670680971459e-17,
        1.76863431387122e-17,
        1.7960459265530333e-17,
        1.8422708785698407e-17,
        1.8639549220195508e-17,
        1.885638965469261e-17,
        1.9191387051626327e-17,
        1.9408227486123425e-17,
        1.9625067920620525e-17,
        1.9841908355117626e-17,
        2.0058748789614727e-17,
        2.0275589224111828e-17,
        2.049242965860893e-17,
        2.070927009310603e-17,
        2.161850812468454e-17,
        2.183534855918164e-17,
        2.2052188993678742e-17,
        2.295656345628394e-17,
        2.6078471701025235e-05,
        7.975983358736113e-05,
        0.00014764306654872224,
        0.0007356165019238637,
        0.001824237847602404,
        0.0037467452726164664,
        0.0062251941210383285,
        0.009655052022095425,
        0.013013849232628936,
        0.01658152051612137,
        0.020300397096576155,
        0.022878670370544807,
        0.025123291661553693,
        0.027663743098223656,
        0.030225472348181296,
        0.03241269109479008,
        0.03480577936149058,
        0.03728853436119013,
        0.03953168222848902,
        0.04273893220797069,
        0.04595867171210076,
        0.049429563786775314,
        0.053324488394990356,
        0.05716288163018549,
        0.061025657645245604,
        0.06478638577123928,
        0.068647212395683,
        0.072553462395683,
        0.07645971239568258,
        0.08022030643554007,
        0.08365484156116888,
        0.08646250665327172,
        0.0885111125402835,
        0.09009336184838328,
        0.09159779792224967,
        0.09163400692116971,
        0.09163400692116971,
        0.09163400692116992,
        0.09163400692116992,
        0.09163400692116992,
        0.09163400692116992,
        0.09163400692116991,
        0.09163400692116991,
        0.09163400692116991,
        0.09163400692116991,
        0.09163400692116991,
        0.09163400692116991,
        0.09163400692116991,
        0.09163400692116991,
        0.09163400692116991,
        0.09163400692116991,
        0.09163400692116992,
        0.09163400692117064,
        0.0931443020910041,
        0.09534507488781743,
        0.0976429672475163,
        0.10065288270754434,
        0.10386875319247935,
        0.10710984086781045,
        0.11046368768583585,
        0.11409213108374489,
        0.11790289496450286,
        0.12129148472786191,
        0.12405818567425131,
        0.12649156988348775,
        0.12887473415104247,
        0.13061692840548456,
        0.1316297477570207,
        0.13198148609960147,
        0.1310492371637951,
        0.13035818480601438,
        0.12932517855235567,
        0.128277319772912,
        0.12727161548318622,
        0.12689710216378897,
        0.12729115633128296,
        0.12813166963421457,
        0.1288548898479216,
        0.12934413095311523,
        0.12967896924784664,
        0.1294899121368145,
        0.12904588000864275,
        0.1278612830482188,
        0.1262721652170836,
        0.12476186945339689,
        0.12367038104698912,
        0.1223316872626137,
        0.12152081571345862,
        0.12085245029458241,
        0.12063144564045934,
        0.12124607531126069,
        0.12241723924343527,
        0.12406161727598329,
        0.12633934126863117,
        0.12943534530970172,
        0.13269985950317395,
        0.13659267639526046,
        0.14031319307566917,
        0.14430188037586741,
        0.14860943306168956,
        0.15259929398551694,
        0.15588055604723902,
        0.15882017274049282,
        0.16107844291427156,
        0.1630066263096804,
        0.16525541410207176,
        0.16753072484341533,
        0.16981453679369005,
        0.17249063274518187,
        0.17595000475897232,
        0.17971242730074358,
        0.18417624620001444,
        0.18860128952996918,
        0.1935058021770547,
        0.19824494905319062,
        0.203014088866877,
        0.20744243585607403,
        0.21089312277199734,
        0.2135992979188856,
        0.21560254211191202,
        0.21655126693714222,
        0.2176882634192179,
        0.2183665524306077,
        0.21728208795290044,
        0.21526174043613835,
        0.21346065953410948,
        0.2119340003744928,
        0.21012049447213776,
        0.20901104074187588,
        0.2085001878715277,
        0.20785448831189585,
        0.2072048787715962,
        0.20645708221435927,
        0.20608319198642674,
        0.20562340381159797,
        0.20579131004041562,
        0.20568844684319398,
        0.2046425703330034,
        0.20386658203113092,
        0.2032925442729248,
        0.2027331313758968,
        0.2021639232899386,
        0.20270113470202894,
        0.2044852717143047,
        0.20684536603737846,
        0.21005124372485304,
        0.21328780686999937,
        0.2166067677249061,
        0.2207882769179796,
        0.22442334342643122,
        0.22710206608497904,
        0.22982666665392237,
        0.23217374787019343,
        0.2341953796738825,
        0.2359703194092344,
        0.23776042866987795,
        0.23953206854318937,
        0.24325563309684775,
        0.2477826227596326,
        0.2526801903153484,
        0.257557241111135,
        0.26214448580867944,
        0.2669474364878656,
        0.27085025835923066,
        0.27396572563265387,
        0.2764018786534815,
        0.27614550379200653,
        0.27482788861705737,
        0.27444959660840007,
        0.2735215620229893,
        0.27213887413528104,
        0.2720128005482365,
        0.272753604847921,
        0.2744840416062876,
        0.27627885731267454,
        0.2786111429491257,
        0.28094140234995646,
        0.2835674937000938,
        0.28665812276634683,
        0.289902540722666,
        0.29300584828807885,
        0.2965547279341048,
        0.3008538077090357,
        0.30586820401108183,
        0.31122479240298484,
        0.3175057386580839,
        0.3234531661048234,
        0.32907950466344704,
        0.3346885198353523,
        0.3392504860352719,
        0.34296479099800686,
        0.3447424493877297,
        0.3455412020107819,
        0.34465756383783924,
        0.34256886015419097,
        0.3397079772248467,
        0.3359172535858787,
        0.33193550108036596,
        0.32757268517751725,
        0.3232425194686026,
        0.319196870711856,
        0.3154865462737778,
        0.3125292182464563,
        0.31053429167559926,
        0.3099118254394358,
        0.31099938161600904,
        0.3133955922699581,
        0.31763952279134877,
        0.3218524516387867,
        0.3278619117170238,
        0.3339149948031201,
        0.33960505693310183,
        0.3453510070193907,
        0.3506621514870372,
        0.35512781465934135,
        0.3591786348488093,
        0.3623156815594311,
        0.3642678822701666,
        0.3664283937959302,
        0.3675163490819287,
        0.36816735124105204,
        0.3691670785493852,
        0.37004681175391496,
        0.37093978569908975,
        0.3722352143233922,
        0.3723544572388195,
        0.3730235446714586,
        0.373964498557914,
        0.37528824309460856,
        0.37626200102367896,
        0.37775179861988595,
        0.377969225462725,
        0.37792551621571624,
        0.37782791604591726,
        0.3773547559790846,
        0.37740345541203135,
        0.37767612777253656,
        0.37800727931445677,
        0.37893005969046256,
        0.3802724979117976,
        0.38085905634104517,
        0.3808590563410454,
        0.38085905634104505,
        0.38085905634104505,
        0.38085905634104544,
        0.38085905634104533,
        0.38085905634104544,
        0.38085905634104533,
        0.38085905634104555,
        0.38085905634104605,
        0.38085905634104533,
        0.3808590563410451,
        0.38046998986039865,
        0.3805511869638055,
        0.38024777394106263,
        0.38073355482690086,
        0.38081997588101085,
        0.3808590563410451,
        0.3808590563410453,
        0.3808590563410455,
        0.38063784645414217,
        0.3808255794386821,
        0.3808590563410454,
        0.3808590563410456,
        0.3808590563410452,
        0.3808590563410455,
        0.380859056341045,
        0.38085905634104583,
        0.3808590563410451,
        0.3808139388547283,
        0.38085307211310593,
        0.38085905634104544,
        0.3808590563410452,
        0.38085905634104567,
        0.38085905634104505,
        0.38085905634104533,
        0.38085905634104544,
        0.38085905634104517,
        0.38085905634104533,
        0.3808590563410455,
        0.3808590563410451,
        0.3808590563410458,
        0.38085905634104517,
        0.3808590563410455,
        0.38085905634104567,
        0.3808590563410457,
        0.3808590563410457,
        0.38085905634104567,
        0.38085905634104583,
        0.3808590563410456,
        0.38085905634104544,
        0.3808590563410457,
        0.38085905634104555,
        0.3808590563410454,
        0.3808486572641805,
        0.3808590563410455,
        0.38085905634104483,
        0.3808590563410458,
        0.3808590563410454,
        0.3808590563410458,
        0.38085905634104555,
        0.3808590563410455,
        0.38085905634104605,
        0.3808590563410451,
        0.38085905634104533,
        0.3808590563410456,
        0.38085905634104544,
        0.3808590563410455,
        0.38085905634104544,
        0.3808590563410454,
        0.38085905634104555,
        0.38085905634104533,
        0.38085905634104567,
        0.38085905634104456,
        0.3808590563410448,
        0.3808590563410452,
        0.3808590563410451,
        0.3808590563410453,
        0.38085905634104594,
        0.38085905634104555,
        0.38085905634104517,
        0.3808590563410451,
        0.3808590563410449,
        0.38085905634104494,
        0.3808590563410451,
        0.38085905634104567,
        0.38085905634104555,
        0.38085905634104544,
        0.3808590563410456,
        0.3808590563410453,
        0.3808590563410456,
        0.38085905634104555,
        0.3808590563410449,
        0.38085905634104555,
        0.3808590563410452,
        0.3808590563410454,
        0.3808590563410454,
        0.3808590563410451,
        0.38085905634104517,
        0.38085905634104555,
        0.3808590563410447,
        0.3808590563410451,
        0.3808590563410453,
        0.3808590563410451,
        0.38085905634104555,
        0.3808590563410455,
        0.3808590563410451,
        0.38085905634104555,
        0.38085905634104517,
        0.3808590563410458,
        0.3808590563410454,
        0.38085905634104494,
        0.3808590563410454,
        0.38085905634104517,
        0.3808590563410454,
        0.3808590563410453,
        0.38085905634104567,
        0.3808590563410458,
        0.380859056341045,
        0.3808590563410456,
        0.38085905634104567,
        0.3808590563410451,
        0.3808590563410458,
        0.3808590563410455,
        0.38085905634104517,
        0.38085905634104583,
        0.38085905634104517,
        0.3808590563410452,
        0.3808590563410451,
        0.38085905634104544,
        0.3808590563410454,
        0.38085905634104544,
        0.38085905634104544,
        0.38085905634104517,
        0.38085905634104544,
        0.3808590563410454,
        0.3808590563410455,
        0.3808590563410457,
        0.3808590563410452,
        0.38085905634104594,
        0.38085905634104567,
        0.38085905634104494,
        0.3808590563410455,
        0.3808590563410455,
        0.3808590563410454,
        0.38085905634104544,
        0.38085905634104567,
        0.3808590563410449,
        0.3808590563410454,
        0.38085905634104494,
        0.380859056341045,
        0.3808590563410452,
        0.3808590563410453,
        0.38085905634104544,
        0.38085905634104583,
        0.380859056341045,
        0.3808590563410454,
        0.38085905634104533,
        0.3808590563410452,
        0.38085905634104544,
        0.38085905634104533,
        0.3808590563410455,
        0.38085905634104583,
        0.3808590563410451,
        0.38085905634104555,
        0.38085905634104544,
        0.3808590563410452,
        0.380859056341045,
        0.38085905634104544,
        0.3808590563410451,
        0.3808590563410452,
        0.38085905634104567,
        0.3808590563410451,
        0.38080917487681687,
        0.38085905634104544,
        0.38085905634104567,
        0.38085905634104533,
        0.3808590563410452,
        0.3808590563410451,
        0.38085905634104544,
        0.380859056341045,
        0.3808590563410455,
        0.38085905634104533,
        0.38085905634104494,
        0.380840309352523,
        0.38085905634104567,
        0.38085905634104517,
        0.38085905634104567,
        0.38085905634104544,
        0.38085905634104533,
        0.38084265485752744,
        0.3808590563410449,
        0.3806106290699735,
        0.38085905634104544,
        0.3808174476469678,
        0.3808590563410452,
        0.38056194578577857,
        0.37827856874451804,
        0.37695679950777683,
        0.3742753612769557,
        0.371578718479705,
        0.36865736357374623,
        0.36441631441788647,
        0.35810624978805694,
        0.3494787642813736,
        0.33861813697665544,
        0.3259122025090131,
        0.3099286284971434,
        0.291793919103542,
        0.2732625101947408,
        0.253948155618716,
        0.23595931483034088,
        0.22136313144647413,
        0.20880858680605321,
        0.1999789773309743,
        0.20880858680605324,
        0.22136313144647413,
        0.23595931483034088,
        0.253948155618716,
        0.2732625101947408,
        0.291793919103542,
        0.3099286284971434,
        0.3259122025090131,
        0.33861813697665544,
        0.3494787642813736,
        0.35810624978805694,
        0.36441631441788647,
        0.3686573635737463,
        0.3715787184797049,
        0.3742753612769557,
        0.37695679950777683,
        0.378278568744518,
        0.38056194578577857,
        0.3808590563410452,
        0.38081744764696773,
        0.3808590563410455,
        0.3806106290699735,
        0.38085905634104494,
        0.38084265485752744,
        0.38085905634104533,
        0.3808590563410454,
        0.38085905634104567,
        0.38085905634104517,
        0.38085905634104567,
        0.380840309352523,
        0.3808590563410449,
        0.3808590563410454,
        0.38085905634104544,
        0.380859056341045,
        0.38085905634104544,
        0.3808590563410451,
        0.3808590563410452,
        0.38085905634104533,
        0.38085905634104567,
        0.3808590563410454,
        0.38080917487681687,
        0.3808590563410451,
        0.38085905634104567,
        0.3808590563410452,
        0.3808590563410451,
        0.38085905634104533,
        0.380859056341045,
        0.3808590563410452,
        0.38085905634104533,
        0.38085905634104555,
        0.38085905634104505,
        0.3808590563410458,
        0.38085905634104544,
        0.3808590563410453,
        0.38085905634104544,
        0.38085905634104517,
        0.3808590563410453,
        0.3808590563410452,
        0.3808590563410452,
        0.3808590563410459,
        0.38085905634104555,
        0.3808590563410451,
        0.38085905634104544,
        0.38085905634104533,
        0.38085905634104533,
        0.3808590563410452,
        0.380859056341045,
        0.38085905634104505,
        0.38085905634104567,
        0.3808590563410457,
        0.3808590563410453,
        0.38085905634104555,
        0.38085905634104467,
        0.3808590563410458,
        0.38085905634104544,
        0.38085905634104555,
        0.38085905634104533,
        0.38085905634104517,
        0.38085905634104555,
        0.38085905634104555,
        0.3808590563410458,
        0.38085905634104555,
        0.3808590563410452,
        0.3808590563410454,
        0.3808590563410453,
        0.38085905634104544,
        0.38085905634104555,
        0.3808590563410454,
        0.38085905634104544,
        0.38085905634104533,
        0.380859056341046,
        0.38085905634104544,
        0.3808590563410452,
        0.3808590563410458,
        0.38085905634104555,
        0.3808590563410449,
        0.38085905634104567,
        0.38085905634104555,
        0.3808590563410452,
        0.3808590563410452,
        0.38085905634104505,
        0.3808590563410453,
        0.38085905634104483,
        0.3808590563410453,
        0.3808590563410457,
        0.3808590563410452,
        0.38085905634104555,
        0.38085905634104517,
        0.3808590563410456,
        0.3808590563410449,
        0.3808590563410452,
        0.38085905634104555,
        0.3808590563410458,
        0.3808590563410454,
        0.3808590563410449,
        0.38085905634104555,
        0.3808590563410455,
        0.38085905634104555,
        0.38085905634104583,
        0.3808590563410458,
        0.38085905634104533,
        0.380859056341046,
        0.38085905634104555,
        0.3808590563410451,
        0.38085905634104533,
        0.3808590563410456,
        0.38085905634104533,
        0.3808590563410453,
        0.3808590563410455,
        0.38085905634104567,
        0.3808590563410461,
        0.38085905634104533,
        0.3808590563410451,
        0.38085905634104555,
        0.3808590563410452,
        0.38085905634104544,
        0.38085905634104555,
        0.38085905634104544,
        0.38085905634104544,
        0.38085905634104544,
        0.3808590563410457,
        0.38085905634104555,
        0.38085905634104544,
        0.38085905634104605,
        0.38085905634104483,
        0.3808590563410449,
        0.38085905634104505,
        0.3808590563410451,
        0.3808590563410457,
        0.38085905634104544,
        0.3808590563410452,
        0.380859056341045,
        0.38085905634104505,
        0.38085905634104567,
        0.38085905634104533,
        0.3808590563410451,
        0.3808590563410455,
        0.3808590563410451,
        0.38085905634104533,
        0.3808590563410452,
        0.380859056341045,
        0.380859056341045,
        0.3808590563410449,
        0.38085905634104555,
        0.38085905634104505,
        0.38085905634104505,
        0.38085905634104456,
        0.3808590563410452,
        0.3808590563410452,
        0.380859056341046,
        0.3808590563410456,
        0.38085905634104555,
        0.3808590563410451,
        0.3808590563410452,
        0.38085905634104616,
        0.380859056341045,
        0.38085905634104555,
        0.3808590563410451,
        0.38085905634104533,
        0.38085905634104533,
        0.3808590563410458,
        0.38085905634104533,
        0.38085905634104533,
        0.38085905634104533,
        0.38085905634104544,
        0.38085905634104533,
        0.38085905634104533,
        0.3808590563410454,
        0.38085905634104544,
        0.3808590563410452,
        0.380859056341045,
        0.380859056341046,
        0.3808590563410456,
        0.38054994641186984,
        0.3807075596386812,
        0.3807387995254754,
        0.3808081229215533,
        0.3807749578741282,
        0.3808424016215337,
        0.3808590563410452,
        0.3808590563410454,
        0.38085905634104544,
        0.38085905634104567,
        0.3808590563410451,
        0.3808590563410455,
        0.38085905634104494,
        0.38084620702431393,
        0.3808590563410458,
        0.3808590563410451,
        0.3808590563410451,
        0.3805130739472366,
        0.38084619459190844,
        0.38083982533711663,
        0.3808590563410452,
        0.38013867244466226,
        0.37881263832302925,
        0.37788985794702346,
        0.37755870640510336,
        0.37728603404459804,
        0.3772373346116513,
        0.377710494678484,
        0.377808094848283,
        0.3778848250886697,
        0.37974528755254483,
        0.3808590563410458,
        0.38085905634104544,
        0.38085905634104544,
        0.3808590563410458,
        0.37929744993409686,
        0.3772675915479812,
        0.37467375368644584,
        0.3728290271436559,
        0.3707653351428769,
        0.3689902868657401,
        0.3671641598882839,
        0.3647701320747375,
        0.3624644365441937,
        0.36031546196569403,
        0.3573550332670262,
        0.3537581932580764,
        0.3493781652202552,
        0.34452409026962305,
        0.33843233564040476,
        0.33241794283163123,
        0.32655238006319703,
        0.3204520899676836,
        0.3154362833583404,
        0.3113754224980745,
        0.30947429866475706,
        0.3084658999037815,
        0.3091428440376568,
        0.3112046442617881,
        0.31416197228910975,
        0.31787229672718786,
        0.32191794548393443,
        0.32624811119284913,
        0.33061092709569784,
        0.33459267960121064,
        0.33838340324017857,
        0.34124428616952296,
        0.3432661161998968,
        0.3440952764751277,
        0.3432173664364779,
        0.34094462122612323,
        0.3370472466022635,
        0.3332881581642493,
        0.3277699730096203,
        0.3219561141333346,
        0.3163330173653869,
        0.3103978756532172,
        0.30458421774429995,
        0.2994841863077707,
        0.2947311263523217,
        0.2910056286943417,
        0.28809909499669306,
        0.2849998610451541,
        0.28321530450644894,
        0.2817643379746445,
        0.2802093995426173,
        0.2790610727024154,
        0.27821800959364357,
        0.2777859820725098,
        0.27895579324351377,
        0.2799743858048682,
        0.28041611980612063,
        0.2800204098548369,
        0.2794249439344241,
        0.27813899272466536,
        0.2763174782794261,
        0.2738483042652206,
        0.2707328369917974,
        0.2668300151204323,
        0.2620270644412462,
        0.25743981974370167,
        0.2525627689479151,
        0.2476652013921993,
        0.24312180762971236,
        0.23953206854318934,
        0.23774119766594917,
        0.23595745766009774,
        0.23384939728007403,
        0.23217374787019307,
        0.22982666665392215,
        0.2271020660849794,
        0.22441049410969982,
        0.22078827691797903,
        0.21660676772490556,
        0.21328780686999918,
        0.21005124372485356,
        0.20723443251802523,
        0.20479314109154464,
        0.2033124171020116,
        0.20227277008457145,
        0.20268811336901416,
        0.20324161085343298,
        0.20374632521556107,
        0.20449107363063906,
        0.2056005468009216,
        0.2058247869427791,
        0.20562340381159863,
        0.2060831919864261,
        0.20645708221435932,
        0.20720487877159616,
        0.20785448831189632,
        0.2085001878715272,
        0.2090110407418761,
        0.21016561195845493,
        0.21193998460243219,
        0.21346065953410925,
        0.21526174043613833,
        0.2172820879529005,
        0.21836655243060799,
        0.21768826341921782,
        0.21655126693714177,
        0.21560254211191235,
        0.21359929791888532,
        0.21089312277199807,
        0.2074424358560742,
        0.20301408886687639,
        0.198244949053191,
        0.19350580217705482,
        0.18860128952996955,
        0.184176246200014,
        0.1797124273007431,
        0.1759500047589713,
        0.17249063274518106,
        0.16981453679368957,
        0.1675307248434155,
        0.165255414102071,
        0.16300662630967988,
        0.1610784429142712,
        0.15883057181735755,
        0.15588055604723894,
        0.15259929398551728,
        0.14860943306168933,
        0.1443018803758672,
        0.1403131930756687,
        0.13659267639526054,
        0.13269985950317353,
        0.1294353453097007,
        0.12633934126863128,
        0.12406161727598339,
        0.1224172392434354,
        0.12124607531126036,
        0.12063144564045888,
        0.1208524502945818,
        0.12152081571345807,
        0.12233168726261423,
        0.12367038104698924,
        0.12476186945339682,
        0.12627216521708476,
        0.12786128304821945,
        0.12904588000864287,
        0.1294899121368147,
        0.1296789692478468,
        0.12934413095311476,
        0.12885488984792118,
        0.12813166963421496,
        0.1272911563312829,
        0.1268971021637894,
        0.12727161548318727,
        0.12827731977291246,
        0.12932517855235537,
        0.13035818480601413,
        0.13104923716379502,
        0.13198148609960153,
        0.13162974775702077,
        0.1306169284054841,
        0.12887473415104234,
        0.1264915698834888,
        0.12405818567425103,
        0.12129148472786244,
        0.11790289496450329,
        0.1140921310837451,
        0.1104636876858362,
        0.10710984086781078,
        0.10386875319247874,
        0.10065288270754497,
        0.0976429672475169,
        0.09534507488781777,
        0.09314430209100424,
        0.09163400692116999,
        0.09163400692116999,
        0.09163400692116999,
        0.09163400692116999,
        0.09163400692116999,
        0.09163400692116982,
        0.09163400692116982,
        0.09163400692116984,
        0.09163400692116984,
        0.09163400692116982,
        0.09163400692116982,
        0.09163400692116984,
        0.09163400692116982,
        0.09163400692116984,
        0.09163400692116982,
        0.09163400692116982,
        0.09163400692116982,
        0.09163400692116984,
        0.09159779792224937,
        0.09009336184838374,
        0.08851111254028368,
        0.08646250665327128,
        0.08365484156116908,
        0.08022030643554032,
        0.07645971239568286,
        0.07255346239568286,
        0.06864721239568292,
        0.06478638577123898,
        0.06102565764524563,
        0.057162881630186034,
        0.05332448839499043,
        0.04942956378677553,
        0.045958671712100455,
        0.04273893220797035,
        0.03953168222848943,
        0.03728853436118963,
        0.034805779361490756,
        0.03241269109478988,
        0.030225472348181424,
        0.02766374309822353,
        0.025123291661554078,
        0.022878670370545043,
        0.020300397096575603,
        0.01658152051612158,
        0.013013849232628879,
        0.009655052022095899,
        0.006225194121038694,
        0.0037467452726167466,
        0.0018242378476022911,
        0.0007356165019239666,
        0.0001476430665488509,
        7.975983358766848e-05,
        2.6078471700942856e-05,
        1.6172874218909097e-17,
        1.5956033784411996e-17,
        1.5739193349914895e-17,
        1.536933621279706e-17,
        1.515249577829996e-17,
        1.4864314720924575e-17,
        1.4647474286427474e-17,
        1.4430633851930373e-17,
        1.4142452794490647e-17,
        1.3637431302350257e-17,
        1.315951486515701e-17,
        1.2942674430659911e-17,
        1.2681598428533107e-17,
        1.2393417372253788e-17,
        1.2176576937756688e-17,
        1.1959736503259585e-17,
        1.1742896068762484e-17,
        1.1526055634265385e-17,
        1.1309215199768284e-17,
        1.0802605521377387e-17,
        1.0585765086880286e-17,
        1.0134953703283761e-17,
        9.845184455724713e-18,
        9.628344021227612e-18,
        8.742263583304025e-18,
        8.318557255375225e-18,
        8.101716820878124e-18,
        7.884876386381023e-18,
        7.668035951883923e-18,
        7.451195517386822e-18,
        7.107216163235343e-18,
        6.814058789962529e-18,
        6.597218355465428e-18,
        6.307449112450792e-18,
        5.992163003038345e-18,
        5.7753225685412446e-18,
        5.558482134044144e-18,
        5.341641699547043e-18,
        5.124801265049941e-18,
        4.907960830552841e-18,
        4.69112039605574e-18,
        4.47427996155864e-18,
        4.257439527061539e-18,
        4.0405990925644375e-18,
        3.8237586580673366e-18,
        3.606918223570236e-18,
        3.390077789073135e-18,
        3.173237354576034e-18,
        2.956396920078933e-18,
        2.4768922935012838e-18,
        1.8618623960568682e-18,
        1.3010426069826051e-18,
        1.0842021724855042e-18,
        8.673617379884034e-19,
        6.505213034913026e-19,
        4.336808689942017e-19,
        2.1684043449710086e-19
      ]
    }
  },
  "related_trajectories": [
    {
      "slug": "erdos-cross-domain",
      "title": "From radar codes to a mathematical bound.",
      "same_run": false
    },
    {
      "slug": "erdos-artifact-reuse",
      "title": "Start from a witness. Then improve it.",
      "same_run": true
    }
  ]
}
