P80 · Extremal configurations · Formed here · Hard

The sofa in a hairpin · wall thickness w = 1/10

Find the planar region of largest area that can be moved continuously through a hairpin hallway of width 1: two right-angled corners the same way round, with a wall of thickness w between the legs.

Instancewall thickness w = 1/10

ObjectiveMaximize the area of the sofa

Formal definition

ContainerA closed set; touching a wall is allowed. The forbidden regions are four open sets: the left wall x < 0, the floor y < 0, the wall strip {x > 1, 1 < y < 1 + w} and the roof y > 2 + w $H = {x \geq 0, 0 \leq y \leq 1} \cup {0 \leq x \leq 1, 0 \leq y \leq 2 + w} \cup {x \geq 0, 1 + w \leq y \leq 2 + w}$
SubmissionA simple polygon (its vertices in the sofa's own frame, at most 800) and its consecutive placements (at most 1500), with vertices × placements at most 300,000
MotionBetween consecutive placements the sofa moves by the unique rigid displacement taking one to the other: a translation when the turns agree, otherwise (Chasles) one rotation about a fixed pivot, by at most 90°
EndsThe first placement lies inside the lower leg with a vertex at x > 1; the last lies inside the upper leg with a vertex at x > 1
Exact verificationEach placement's turn gives a rational rotation matrix and the pivot between placements is solved exactly; the region swept by each edge is compared with the four open forbidden regions through its boundary — a parallelogram for a translation, the two endpoint arcs, the inner arc and the first and last segments for a rotation. All arithmetic is rational; the arcs enter only through the sign of a + b√D. No sampling and no epsilon
ScoreThe area of the polygon, cut down to nine decimals; larger is better $A (S) = area (S)$
ObjectiveMaximise the area over every sofa that gets through the hairpin $\max_{S} A (S)$

Open the full editor ↗

VERIFIED CONSTRUCTIONsofa area 1.67923101

Getting a feel for it

Why this is not the L

The hairpin adds a roof and a second corner, so a motion valid in the L may collide here. The supplied baseline uses a shortened Hammersley-family sofa along a planned two-corner path that must clear the roof. This explains that construction, not an optimality bound for all shapes and motions. A half-turn is not required: a unit square can pass by translation alone.

Where the frontier is

U-shaped and other multi-corner corridors have appeared in prior work, but the site has not verified directly comparable external best values for these wall thicknesses. The starting constructions are shortened Hammersley-family shapes with planner-generated, verifier-checked motions, bylined MinMax Arena. They are baselines, not known optima.

Source

Current leader

1.67923101

the area of the sofa

Record holderTmrg

Solution methodHuman

Challenge this record ↗Submit a proof / idea ↓Share a proof or idea in the discussion. Accepted contributions can earn proof points.

Record holder's solver noteNo solver note yet (expand)＋

The record holder has not shared a solver note yet.

Record history (4 changes)

TmrgHuman
1.675825244→1.67923101
2026-09-06
iqyHuman
1.672819358→1.675825244
2026-09-06
NUE_13Human
1.655546662→1.672819358
2026-09-06
NUE_13Human
1.647809337→1.655546662
2026-09-06

ANSWER FORMAT

How to write your answer

The hallway is H = {x ≥ 0, 0 ≤ y ≤ 1} ∪ {0 ≤ x ≤ 1, 0 ≤ y ≤ 2 + w} ∪ {x ≥ 0, 1 + w ≤ y ≤ 2 + w}: the lower leg comes in from the right, the vertical leg is on the left, the upper leg goes back out to the right. Between the horizontal legs is the wall {x > 1, 1 < y < 1 + w}; above everything is the outer wall y > 2 + w.

Submit polygon (the vertices in the sofa's own frame, either orientation) and poses (consecutive placements {x,y,turn}: turn by θ about the origin with turn = tan(θ/2), then shift by (x,y)). The first placement must lie inside the lower leg (0 ≤ y ≤ 1) reaching past x = 1, the last inside the upper leg (1 + w ≤ y ≤ 2 + w) reaching past x = 1, and consecutive placements may differ by at most 90°. The turn parameter cannot represent exactly 180°; a finite turn may approach it (|turn| ≤ 10⁶). A motion need not accumulate a half-turn. The editor also attaches outline (its arc model); the verifier ignores it and judges polygon and poses alone. In the editor the motion is planned automatically for the drawn shape.

The current leader's answer

{
  "outline": {
    "nodes": [
      {
        "bulge": "-0.292491578",
        "x": "0.368449069",
        "y": "0.276987329"
      },
      {
        "bulge": "-0.11915481",
        "x": "0.995694687",
        "y": "1.241018351"
      },
      {
        "bulge": "0.35370257",
        "x": "0.065820249",
        "y": "1.180264571"
      },
      {
        "bulge": "-0.098310876",
        "x": "-0.168863212",
        "y": "1.193144574"
      },
      {
        "bulge": "-0.306846957",
        "x": "-1.09965324",
        "y": "1.251439987"
      },
      {
        "bulge": "0",
        "x": "-0.484371174",
        "y": "0.283428022"
      }
    ],
    "step": "1"
  },
  "polygon": [
    [
      "0.368449069",
      "0.276987329"
    ],
    [
      "0.385150352",
      "0.284717339"
    ],
    [
      "0.401715849",
      "0.292734211"
    ],
    [
      "0.418140632",
      "0.301035561"
    ],
    [
      "0.434419818",
      "0.309618919"
    ],
    [
      "0.450548564",
      "0.318481732"
    ],
    [
      "0.466522074",
      "0.327621366"
    ],
    [
      "0.482335597",
      "0.337035101"
    ],
    [
      "0.49798443",
      "0.346720139"
    ],
    [
      "0.513463918",
      "0.356673598"
    ],
    [
      "0.528769459",
      "0.366892518"
    ],
    [
      "0.5438965",
      "0.377373861"
    ],
    [
      "0.558840543",
      "0.388114508"
    ],
    [
      "0.573597142",
      "0.399111266"
    ],
    [
      "0.58816191",
      "0.410360865"
    ],
    [
      "0.602530514",
      "0.421859958"
    ],
    [
      "0.616698681",
      "0.433605125"
    ],
    [
      "0.630662198",
      "0.445592874"
    ],
    [
      "0.644416911",
      "0.457819638"
    ],
    [
      "0.65795873",
      "0.470281783"
    ],
    [
      "0.671283628",
      "0.482975601"
    ],
    [
      "0.684387641",
      "0.495897318"
    ],
    [
      "0.697266873",
      "0.50904309"
    ],
    [
      "0.709917492",
      "0.522409007"
    ],
    [
      "0.722335737",
      "0.535991095"
    ],
    [
      "0.734517914",
      "0.549785314"
    ],
    [
      "0.7464604",
      "0.563787562"
    ],
    [
      "0.758159644",
      "0.577993674"
    ],
    [
      "0.769612165",
      "0.592399425"
    ],
    [
      "0.780814559",
      "0.607000531"
    ],
    [
      "0.791763493",
      "0.621792649"
    ],
    [
      "0.802455711",
      "0.636771381"
    ],
    [
      "0.812888032",
      "0.65193227"
    ],
    [
      "0.823057355",
      "0.66727081"
    ],
    [
      "0.832960655",
      "0.682782436"
    ],
    [
      "0.842594987",
      "0.698462538"
    ],
    [
      "0.851957485",
      "0.71430645"
    ],
    [
      "0.861045365",
      "0.730309461"
    ],
    [
      "0.869855924",
      "0.746466811"
    ],
    [
      "0.878386541",
      "0.762773695"
    ],
    [
      "0.886634681",
      "0.779225264"
    ],
    [
      "0.894597888",
      "0.795816625"
    ],
    [
      "0.902273796",
      "0.812542842"
    ],
    [
      "0.909660122",
      "0.829398942"
    ],
    [
      "0.916754668",
      "0.846379912"
    ],
    [
      "0.923555325",
      "0.863480701"
    ],
    [
      "0.93006007",
      "0.880696224"
    ],
    [
      "0.936266968",
      "0.898021359"
    ],
    [
      "0.942174174",
      "0.915450956"
    ],
    [
      "0.947779931",
      "0.932979829"
    ],
    [
      "0.953082571",
      "0.950602767"
    ],
    [
      "0.958080518",
      "0.968314527"
    ],
    [
      "0.962772285",
      "0.986109842"
    ],
    [
      "0.967156477",
      "1.00398342"
    ],
    [
      "0.97123179",
      "1.021929944"
    ],
    [
      "0.974997011",
      "1.039944078"
    ],
    [
      "0.978451021",
      "1.058020464"
    ],
    [
      "0.981592793",
      "1.076153726"
    ],
    [
      "0.984421393",
      "1.094338471"
    ],
    [
      "0.986935979",
      "1.11256929"
    ],
    [
      "0.989135802",
      "1.130840762"
    ],
    [
      "0.99102021",
      "1.149147453"
    ],
    [
      "0.992588642",
      "1.167483918"
    ],
    [
      "0.993840631",
      "1.185844703"
    ],
    [
      "0.994775804",
      "1.204224349"
    ],
    [
      "0.995393884",
      "1.222617388"
    ],
    [
      "0.995694687",
      "1.241018351"
    ],
    [
      "0.962548264",
      "1.246485836"
    ],
    [
      "0.929313972",
      "1.25139099"
    ],
    [
      "0.896001349",
      "1.255732403"
    ],
    [
      "0.862619957",
      "1.259508829"
    ],
    [
      "0.829179377",
      "1.262719185"
    ],
    [
      "0.795689209",
      "1.26536255"
    ],
    [
      "0.762159065",
      "1.267438163"
    ],
    [
      "0.72859857",
      "1.268945431"
    ],
    [
      "0.695017355",
      "1.26988392"
    ],
    [
      "0.661425061",
      "1.27025336"
    ],
    [
      "0.627831329",
      "1.270053646"
    ],
    [
      "0.594245801",
      "1.269284834"
    ],
    [
      "0.560678118",
      "1.267947147"
    ],
    [
      "0.527137915",
      "1.266040967"
    ],
    [
      "0.49363482",
      "1.263566842"
    ],
    [
      "0.460178447",
      "1.260525481"
    ],
    [
      "0.426778401",
      "1.256917759"
    ],
    [
      "0.393444269",
      "1.25274471"
    ],
    [
      "0.360185618",
      "1.248007532"
    ],
    [
      "0.327011994",
      "1.242707585"
    ],
    [
      "0.29393292",
      "1.23684639"
    ],
    [
      "0.260957891",
      "1.23042563"
    ],
    [
      "0.228096371",
      "1.223447147"
    ],
    [
      "0.195357792",
      "1.215912944"
    ],
    [
      "0.162751552",
      "1.207825185"
    ],
    [
      "0.13028701",
      "1.199186191"
    ],
    [
      "0.097973484",
      "1.18999844"
    ],
    [
      "0.065820249",
      "1.180264571"
    ],
    [
      "0.063161339",
      "1.178380787"
    ],
    [
      "0.060469992",
      "1.176543643"
    ],
    [
      "0.057747026",
      "1.174753698"
    ],
    [
      "0.054993269",
      "1.173011496"
    ],
    [
      "0.052209559",
      "1.171317566"
    ],
    [
      "0.04939674",
      "1.169672423"
    ],
    [
      "0.046555668",
      "1.168076567"
    ],
    [
      "0.043687206",
      "1.166530484"
    ],
    [
      "0.040792227",
      "1.165034643"
    ],
    [
      "0.03787161",
      "1.163589498"
    ],
    [
      "0.034926244",
      "1.162195489"
    ],
    [
      "0.031957022",
      "1.160853041"
    ],
    [
      "0.028964848",
      "1.15956256"
    ],
    [
      "0.025950632",
      "1.158324439"
    ],
    [
      "0.022915289",
      "1.157139054"
    ],
    [
      "0.019859741",
      "1.156006766"
    ],
    [
      "0.016784919",
      "1.154927919"
    ],
    [
      "0.013691755",
      "1.153902841"
    ],
    [
      "0.010581191",
      "1.152931843"
    ],
    [
      "0.007454172",
      "1.15201522"
    ],
    [
      "0.004311649",
      "1.151153251"
    ],
    [
      "0.001154575",
      "1.150346199"
    ],
    [
      "-0.002016088",
      "1.149594307"
    ],
    [
      "-0.005199377",
      "1.148897806"
    ],
    [
      "-0.008394325",
      "1.148256906"
    ],
    [
      "-0.011599961",
      "1.147671803"
    ],
    [
      "-0.014815309",
      "1.147142673"
    ],
    [
      "-0.018039394",
      "1.146669679"
    ],
    [
      "-0.021271234",
      "1.146252964"
    ],
    [
      "-0.024509849",
      "1.145892654"
    ],
    [
      "-0.027754252",
      "1.145588859"
    ],
    [
      "-0.031003459",
      "1.145341671"
    ],
    [
      "-0.034256481",
      "1.145151166"
    ],
    [
      "-0.03751233",
      "1.145017401"
    ],
    [
      "-0.040770016",
      "1.144940417"
    ],
    [
      "-0.044028549",
      "1.144920238"
    ],
    [
      "-0.047286939",
      "1.144956869"
    ],
    [
      "-0.050544195",
      "1.145050299"
    ],
    [
      "-0.053799327",
      "1.145200501"
    ],
    [
      "-0.057051345",
      "1.145407428"
    ],
    [
      "-0.060299263",
      "1.145671017"
    ],
    [
      "-0.063542091",
      "1.145991189"
    ],
    [
      "-0.066778845",
      "1.146367845"
    ],
    [
      "-0.07000854",
      "1.146800873"
    ],
    [
      "-0.073230195",
      "1.147290139"
    ],
    [
      "-0.076442832",
      "1.147835495"
    ],
    [
      "-0.079645472",
      "1.148436776"
    ],
    [
      "-0.082837144",
      "1.149093799"
    ],
    [
      "-0.086016876",
      "1.149806363"
    ],
    [
      "-0.089183702",
      "1.150574253"
    ],
    [
      "-0.092336661",
      "1.151397235"
    ],
    [
      "-0.095474792",
      "1.152275059"
    ],
    [
      "-0.098597144",
      "1.153207458"
    ],
    [
      "-0.101702766",
      "1.154194148"
    ],
    [
      "-0.104790714",
      "1.155234831"
    ],
    [
      "-0.10786005",
      "1.156329188"
    ],
    [
      "-0.110909842",
      "1.157476889"
    ],
    [
      "-0.113939162",
      "1.158677583"
    ],
    [
      "-0.116947089",
      "1.159930907"
    ],
    [
      "-0.119932709",
      "1.161236479"
    ],
    [
      "-0.122895115",
      "1.162593901"
    ],
    [
      "-0.125833406",
      "1.164002763"
    ],
    [
      "-0.128746689",
      "1.165462635"
    ],
    [
      "-0.131634079",
      "1.166973074"
    ],
    [
      "-0.134494698",
      "1.16853362"
    ],
    [
      "-0.137327676",
      "1.170143799"
    ],
    [
      "-0.140132153",
      "1.171803123"
    ],
    [
      "-0.142907276",
      "1.173511086"
    ],
    [
      "-0.145652202",
      "1.175267169"
    ],
    [
      "-0.148366096",
      "1.177070839"
    ],
    [
      "-0.151048133",
      "1.178921548"
    ],
    [
      "-0.153697498",
      "1.180818732"
    ],
    [
      "-0.156313386",
      "1.182761816"
    ],
    [
      "-0.158895002",
      "1.184750208"
    ],
    [
      "-0.161441561",
      "1.186783305"
    ],
    [
      "-0.16395229",
      "1.188860488"
    ],
    [
      "-0.166426424",
      "1.190981126"
    ],
    [
      "-0.168863212",
      "1.193144574"
    ],
    [
      "-0.208403073",
      "1.203241554"
    ],
    [
      "-0.248109264",
      "1.212663231"
    ],
    [
      "-0.287970253",
      "1.221406869"
    ],
    [
      "-0.327974462",
      "1.229469928"
    ],
    [
      "-0.368110271",
      "1.236850067"
    ],
    [
      "-0.408366023",
      "1.243545141"
    ],
    [
      "-0.448730027",
      "1.249553206"
    ],
    [
      "-0.489190558",
      "1.254872517"
    ],
    [
      "-0.529735864",
      "1.259501529"
    ],
    [
      "-0.57035417",
      "1.263438897"
    ],
    [
      "-0.611033677",
      "1.266683479"
    ],
    [
      "-0.65176257",
      "1.269234331"
    ],
    [
      "-0.692529021",
      "1.271090713"
    ],
    [
      "-0.733321187",
      "1.272252085"
    ],
    [
      "-0.774127222",
      "1.27271811"
    ],
    [
      "-0.814935272",
      "1.272488653"
    ],
    [
      "-0.855733486",
      "1.271563781"
    ],
    [
      "-0.896510013",
      "1.269943762"
    ],
    [
      "-0.93725301",
      "1.267629066"
    ],
    [
      "-0.977950643",
      "1.264620366"
    ],
    [
      "-1.018591092",
      "1.260918536"
    ],
    [
      "-1.059162552",
      "1.256524651"
    ],
    [
      "-1.09965324",
      "1.251439987"
    ],
    [
      "-1.100017243",
      "1.233796161"
    ],
    [
      "-1.100076684",
      "1.21614868"
    ],
    [
      "-1.099831544",
      "1.198502803"
    ],
    [
      "-1.099281896",
      "1.180863784"
    ],
    [
      "-1.098427905",
      "1.163236878"
    ],
    [
      "-1.097269824",
      "1.145627337"
    ],
    [
      "-1.095807999",
      "1.128040405"
    ],
    [
      "-1.094042865",
      "1.110481322"
    ],
    [
      "-1.091974948",
      "1.092955318"
    ],
    [
      "-1.089604863",
      "1.075467614"
    ],
    [
      "-1.086933317",
      "1.058023418"
    ],
    [
      "-1.083961106",
      "1.040627929"
    ],
    [
      "-1.080689115",
      "1.023286326"
    ],
    [
      "-1.077118319",
      "1.006003777"
    ],
    [
      "-1.073249781",
      "0.988785429"
    ],
    [
      "-1.069084653",
      "0.971636411"
    ],
    [
      "-1.064624177",
      "0.954561832"
    ],
    [
      "-1.059869682",
      "0.937566778"
    ],
    [
      "-1.054822582",
      "0.920656311"
    ],
    [
      "-1.049484383",
      "0.903835469"
    ],
    [
      "-1.043856673",
      "0.887109262"
    ],
    [
      "-1.03794113",
      "0.870482673"
    ],
    [
      "-1.031739516",
      "0.853960655"
    ],
    [
      "-1.025253678",
      "0.83754813"
    ],
    [
      "-1.018485547",
      "0.821249985"
    ],
    [
      "-1.011437141",
      "0.805071077"
    ],
    [
      "-1.004110558",
      "0.789016225"
    ],
    [
      "-0.996507981",
      "0.773090211"
    ],
    [
      "-0.988631676",
      "0.757297779"
    ],
    [
      "-0.980483987",
      "0.741643633"
    ],
    [
      "-0.972067342",
      "0.726132438"
    ],
    [
      "-0.963384249",
      "0.710768812"
    ],
    [
      "-0.954437293",
      "0.695557333"
    ],
    [
      "-0.945229141",
      "0.680502533"
    ],
    [
      "-0.935762534",
      "0.665608894"
    ],
    [
      "-0.926040294",
      "0.650880855"
    ],
    [
      "-0.916065315",
      "0.636322803"
    ],
    [
      "-0.905840569",
      "0.621939073"
    ],
    [
      "-0.895369103",
      "0.607733951"
    ],
    [
      "-0.884654035",
      "0.593711668"
    ],
    [
      "-0.873698557",
      "0.579876401"
    ],
    [
      "-0.862505933",
      "0.566232272"
    ],
    [
      "-0.851079497",
      "0.552783344"
    ],
    [
      "-0.839422652",
      "0.539533624"
    ],
    [
      "-0.827538872",
      "0.52648706"
    ],
    [
      "-0.815431695",
      "0.513647536"
    ],
    [
      "-0.803104728",
      "0.501018878"
    ],
    [
      "-0.790561644",
      "0.488604848"
    ],
    [
      "-0.777806179",
      "0.476409144"
    ],
    [
      "-0.764842132",
      "0.464435398"
    ],
    [
      "-0.751673365",
      "0.452687178"
    ],
    [
      "-0.738303801",
      "0.441167982"
    ],
    [
      "-0.724737423",
      "0.429881243"
    ],
    [
      "-0.710978271",
      "0.418830322"
    ],
    [
      "-0.697030445",
      "0.408018512"
    ],
    [
      "-0.682898099",
      "0.397449033"
    ],
    [
      "-0.668585443",
      "0.387125033"
    ],
    [
      "-0.65409674",
      "0.377049588"
    ],
    [
      "-0.639436307",
      "0.367225699"
    ],
    [
      "-0.62460851",
      "0.357656292"
    ],
    [
      "-0.609617767",
      "0.348344219"
    ],
    [
      "-0.594468542",
      "0.339292252"
    ],
    [
      "-0.579165349",
      "0.330503089"
    ],
    [
      "-0.563712747",
      "0.321979348"
    ],
    [
      "-0.548115337",
      "0.313723567"
    ],
    [
      "-0.532377767",
      "0.305738206"
    ],
    [
      "-0.516504725",
      "0.298025643"
    ],
    [
      "-0.500500938",
      "0.290588177"
    ],
    [
      "-0.484371174",
      "0.283428022"
    ]
  ],
  "poses": [
    {
      "turn": "0",
      "x": "2.150076684",
      "y": "-0.276987329"
    },
    {
      "turn": "0",
      "x": "1.100126684",
      "y": "-0.276987329"
    },
    {
      "turn": "-0.004363351",
      "x": "1.089514595",
      "y": "-0.273534634"
    },
    {
      "turn": "-0.008726868",
      "x": "1.078797276",
      "y": "-0.258953043"
    },
    {
      "turn": "-0.013090717",
      "x": "1.068135188",
      "y": "-0.26719754"
    },
    {
      "turn": "-0.017455065",
      "x": "1.057450692",
      "y": "-0.263882529"
    },
    {
      "turn": "-0.021820078",
      "x": "1.046817849",
      "y": "-0.260602176"
    },
    {
      "turn": "-0.026185922",
      "x": "1.036093433",
      "y": "-0.236915844"
    },
    {
      "turn": "-0.030552763",
      "x": "1.025415203",
      "y": "-0.245910493"
    },
    {
      "turn": "-0.034920769",
      "x": "1.014732007",
      "y": "-0.250560894"
    },
    {
      "turn": "-0.039290107",
      "x": "1.004092418",
      "y": "-0.247147579"
    },
    {
      "turn": "-0.043660943",
      "x": "0.993372919",
      "y": "-0.219969521"
    },
    {
      "turn": "-0.048033444",
      "x": "0.982695235",
      "y": "-0.240347856"
    },
    {
      "turn": "-0.052407779",
      "x": "0.972022678",
      "y": "-0.231564229"
    },
    {
      "turn": "-0.056784115",
      "x": "0.961371588",
      "y": "-0.233447196"
    },
    {
      "turn": "-0.06116262",
      "x": "0.950687785",
      "y": "-0.229941717"
    },
    {
      "turn": "-0.065543463",
      "x": "0.940061994",
      "y": "-0.22647541"
    },
    {
      "turn": "-0.069926812",
      "x": "0.929374741",
      "y": "-0.202379639"
    },
    {
      "turn": "-0.074312837",
      "x": "0.91872226",
      "y": "-0.219434622"
    },
    {
      "turn": "-0.078701707",
      "x": "0.908090037",
      "y": "-0.207913769"
    },
    {
      "turn": "-0.083093592",
      "x": "0.897463786",
      "y": "-0.212326978"
    },
    {
      "turn": "-0.087488664",
      "x": "0.886840158",
      "y": "-0.198201054"
    },
    {
      "turn": "-0.091887092",
      "x": "0.876223118",
      "y": "-0.205154641"
    },
    {
      "turn": "-0.096289048",
      "x": "0.865631576",
      "y": "-0.198065174"
    },
    {
      "turn": "-0.100694705",
      "x": "0.855058524",
      "y": "-0.197919797"
    },
    {
      "turn": "-0.105104235",
      "x": "0.844470753",
      "y": "-0.181325735"
    },
    {
      "turn": "-0.109517812",
      "x": "0.833897245",
      "y": "-0.190624649"
    },
    {
      "turn": "-0.113935608",
      "x": "0.823364133",
      "y": "-0.182544103"
    },
    {
      "turn": "-0.1183578",
      "x": "0.812839411",
      "y": "-0.18327142"
    },
    {
      "turn": "-0.122784561",
      "x": "0.802318148",
      "y": "-0.169640615"
    },
    {
      "turn": "-0.127216068",
      "x": "0.791805856",
      "y": "-0.17586235"
    },
    {
      "turn": "-0.131652498",
      "x": "0.781339206",
      "y": "-0.172108297"
    },
    {
      "turn": "-0.136094027",
      "x": "0.770893024",
      "y": "-0.168399681"
    },
    {
      "turn": "-0.140540835",
      "x": "0.7604337",
      "y": "-0.164619551"
    },
    {
      "turn": "-0.144993099",
      "x": "0.750024401",
      "y": "-0.160885728"
    },
    {
      "turn": "-0.149451001",
      "x": "0.739607997",
      "y": "-0.14592984"
    },
    {
      "turn": "-0.153914721",
      "x": "0.729205485",
      "y": "-0.152338352"
    },
    {
      "turn": "-0.15838444",
      "x": "0.718868441",
      "y": "-0.14952358"
    },
    {
      "turn": "-0.162860342",
      "x": "0.70854261",
      "y": "-0.145683457"
    },
    {
      "turn": "-0.167342609",
      "x": "0.69822135",
      "y": "-0.132712114"
    },
    {
      "turn": "-0.171831427",
      "x": "0.687911748",
      "y": "-0.138058922"
    },
    {
      "turn": "-0.176326981",
      "x": "0.677674249",
      "y": "-0.134186333"
    },
    {
      "turn": "-0.180829457",
      "x": "0.667439142",
      "y": "-0.13036271"
    },
    {
      "turn": "-0.185339045",
      "x": "0.657229688",
      "y": "-0.120632467"
    },
    {
      "turn": "-0.189855932",
      "x": "0.647033039",
      "y": "-0.122626841"
    },
    {
      "turn": "-0.194380309",
      "x": "0.636897605",
      "y": "-0.118626471"
    },
    {
      "turn": "-0.198912367",
      "x": "0.626775484",
      "y": "-0.11485357"
    },
    {
      "turn": "-0.203452299",
      "x": "0.616682956",
      "y": "-0.106131471"
    },
    {
      "turn": "-0.208000299",
      "x": "0.60660424",
      "y": "-0.107045297"
    },
    {
      "turn": "-0.212556562",
      "x": "0.596592942",
      "y": "-0.103099019"
    },
    {
      "turn": "-0.217121284",
      "x": "0.586587598",
      "y": "-0.099204372"
    },
    {
      "turn": "-0.221694663",
      "x": "0.576630552",
      "y": "-0.093408183"
    },
    {
      "turn": "-0.226276898",
      "x": "0.566688984",
      "y": "-0.09112018"
    },
    {
      "turn": "-0.230868191",
      "x": "0.556805067",
      "y": "-0.086957129"
    },
    {
      "turn": "-0.235468743",
      "x": "0.546937711",
      "y": "-0.082653304"
    },
    {
      "turn": "-0.240078759",
      "x": "0.537121276",
      "y": "-0.078342774"
    },
    {
      "turn": "-0.244698443",
      "x": "0.527325655",
      "y": "-0.073866065"
    },
    {
      "turn": "-0.249328003",
      "x": "0.517585696",
      "y": "-0.069379528"
    },
    {
      "turn": "-0.253967646",
      "x": "0.507863257",
      "y": "-0.064731282"
    },
    {
      "turn": "-0.258617584",
      "x": "0.498205037",
      "y": "-0.060070121"
    },
    {
      "turn": "-0.263278028",
      "x": "0.488554162",
      "y": "-0.055251728"
    },
    {
      "turn": "-0.267949192",
      "x": "0.478985204",
      "y": "-0.050417389"
    },
    {
      "turn": "-0.272631292",
      "x": "0.469404252",
      "y": "-0.045430289"
    },
    {
      "turn": "-0.277324544",
      "x": "0.459938418",
      "y": "-0.040424271"
    },
    {
      "turn": "-0.282029168",
      "x": "0.450428734",
      "y": "-0.030938286"
    },
    {
      "turn": "-0.286745386",
      "x": "0.441053863",
      "y": "-0.030093811"
    },
    {
      "turn": "-0.29147342",
      "x": "0.431632718",
      "y": "-0.018416389"
    },
    {
      "turn": "-0.296213495",
      "x": "0.422338788",
      "y": "-0.019429156"
    },
    {
      "turn": "-0.300965839",
      "x": "0.413016654",
      "y": "-0.009052663"
    },
    {
      "turn": "-0.305730681",
      "x": "0.40381793",
      "y": "-0.008433553"
    },
    {
      "turn": "-0.310508253",
      "x": "0.394586212",
      "y": "-0.002787364"
    },
    {
      "turn": "-0.315298789",
      "x": "0.385496725",
      "y": "0.002889647"
    },
    {
      "turn": "-0.320102524",
      "x": "0.376347007",
      "y": "0.008696495"
    },
    {
      "turn": "-0.324919696",
      "x": "0.36735353",
      "y": "0.014536997"
    },
    {
      "turn": "-0.329750547",
      "x": "0.358304594",
      "y": "0.02050269"
    },
    {
      "turn": "-0.33459532",
      "x": "0.349409885",
      "y": "0.026504948"
    },
    {
      "turn": "-0.339454259",
      "x": "0.34046447",
      "y": "0.049822856"
    },
    {
      "turn": "-0.344327613",
      "x": "0.331641491",
      "y": "0.04273265"
    },
    {
      "turn": "-0.349215633",
      "x": "0.32283207",
      "y": "0.045037638"
    },
    {
      "turn": "-0.354118573",
      "x": "0.314143137",
      "y": "0.051387976"
    },
    {
      "turn": "-0.359036687",
      "x": "0.305412766",
      "y": "0.075257286"
    },
    {
      "turn": "-0.363970234",
      "x": "0.296800789",
      "y": "0.072630054"
    },
    {
      "turn": "-0.368919477",
      "x": "0.288211863",
      "y": "0.070847831"
    },
    {
      "turn": "-0.373884679",
      "x": "0.279739251",
      "y": "0.077508419"
    },
    {
      "turn": "-0.378866109",
      "x": "0.271234601",
      "y": "0.084240223"
    },
    {
      "turn": "-0.383864035",
      "x": "0.26287396",
      "y": "0.091022783"
    },
    {
      "turn": "-0.388878732",
      "x": "0.254486153",
      "y": "0.097901856"
    },
    {
      "turn": "-0.393910476",
      "x": "0.246240141",
      "y": "0.104834452"
    },
    {
      "turn": "-0.398959546",
      "x": "0.237971621",
      "y": "0.129829253"
    },
    {
      "turn": "-0.404026226",
      "x": "0.229812912",
      "y": "0.127788581"
    },
    {
      "turn": "-0.409110801",
      "x": "0.221696035",
      "y": "0.126076349"
    },
    {
      "turn": "-0.414213562",
      "x": "0.213686915",
      "y": "0.133332786"
    },
    {
      "turn": "-0.419334802",
      "x": "0.205664353",
      "y": "0.158895966"
    },
    {
      "turn": "-0.424474816",
      "x": "0.197747349",
      "y": "0.152573472"
    },
    {
      "turn": "-0.429633906",
      "x": "0.189881459",
      "y": "0.167582574"
    },
    {
      "turn": "-0.434812375",
      "x": "0.182088947",
      "y": "0.164464336"
    },
    {
      "turn": "-0.440010531",
      "x": "0.174352161",
      "y": "0.170521668"
    },
    {
      "turn": "-0.445228685",
      "x": "0.166716529",
      "y": "0.178205262"
    },
    {
      "turn": "-0.450467154",
      "x": "0.15908119",
      "y": "0.203361352"
    },
    {
      "turn": "-0.455726256",
      "x": "0.151544748",
      "y": "0.202006418"
    },
    {
      "turn": "-0.461006314",
      "x": "0.144073197",
      "y": "0.220402726"
    },
    {
      "turn": "-0.466307658",
      "x": "0.136668254",
      "y": "0.219178189"
    },
    {
      "turn": "-0.471630619",
      "x": "0.129332755",
      "y": "0.237717662"
    },
    {
      "turn": "-0.476975533",
      "x": "0.122061566",
      "y": "0.236621177"
    },
    {
      "turn": "-0.482342741",
      "x": "0.114864354",
      "y": "0.252763293"
    },
    {
      "turn": "-0.487732589",
      "x": "0.107729133",
      "y": "0.241795159"
    },
    {
      "turn": "-0.493145426",
      "x": "0.1006724",
      "y": "0.257408262"
    },
    {
      "turn": "-0.498581608",
      "x": "0.093681125",
      "y": "0.258334195"
    },
    {
      "turn": "-0.504041494",
      "x": "0.086761219",
      "y": "0.266685533"
    },
    {
      "turn": "-0.509525449",
      "x": "0.079934391",
      "y": "0.275120446"
    },
    {
      "turn": "-0.515033843",
      "x": "0.073135046",
      "y": "0.302095374"
    },
    {
      "turn": "-0.520567051",
      "x": "0.066420594",
      "y": "0.292146176"
    },
    {
      "turn": "-0.526125451",
      "x": "0.059798033",
      "y": "0.309031407"
    },
    {
      "turn": "-0.531709432",
      "x": "0.053230828",
      "y": "0.309408822"
    },
    {
      "turn": "-0.537319382",
      "x": "0.046754244",
      "y": "0.326063963"
    },
    {
      "turn": "-0.5429557",
      "x": "0.040334573",
      "y": "0.32690225"
    },
    {
      "turn": "-0.548618787",
      "x": "0.03400765",
      "y": "0.343141625"
    },
    {
      "turn": "-0.554309051",
      "x": "0.027738066",
      "y": "0.344621132"
    },
    {
      "turn": "-0.560026908",
      "x": "0.021562136",
      "y": "0.360455382"
    },
    {
      "turn": "-0.565772778",
      "x": "0.015444502",
      "y": "0.36256007"
    },
    {
      "turn": "-0.571547087",
      "x": "0.009421492",
      "y": "0.37158807"
    },
    {
      "turn": "-0.577350269",
      "x": "0.003478661",
      "y": "0.380730039"
    },
    {
      "turn": "-0.583182763",
      "x": "-0.002410583",
      "y": "0.398864657"
    },
    {
      "turn": "-0.589045016",
      "x": "-0.008229043",
      "y": "0.399076193"
    },
    {
      "turn": "-0.594937482",
      "x": "-0.013930486",
      "y": "0.408311093"
    },
    {
      "turn": "-0.600860619",
      "x": "-0.019563631",
      "y": "0.417672481"
    },
    {
      "turn": "-0.606814896",
      "x": "-0.025134706",
      "y": "0.426978682"
    },
    {
      "turn": "-0.612800788",
      "x": "-0.030610437",
      "y": "0.436436374"
    },
    {
      "turn": "-0.618818777",
      "x": "-0.036019831",
      "y": "0.445841233"
    },
    {
      "turn": "-0.624869352",
      "x": "-0.041336477",
      "y": "0.455392365"
    },
    {
      "turn": "-0.630953011",
      "x": "-0.046582545",
      "y": "0.47301983"
    },
    {
      "turn": "-0.637070261",
      "x": "-0.05176518",
      "y": "0.474504394"
    },
    {
      "turn": "-0.643221614",
      "x": "-0.05681842",
      "y": "0.484128184"
    },
    {
      "turn": "-0.649407593",
      "x": "-0.061816925",
      "y": "0.493857501"
    },
    {
      "turn": "-0.655628729",
      "x": "-0.066727968",
      "y": "0.5060009"
    },
    {
      "turn": "-0.661885561",
      "x": "-0.071565984",
      "y": "0.513324572"
    },
    {
      "turn": "-0.668178638",
      "x": "-0.076439869",
      "y": "0.523125304"
    },
    {
      "turn": "-0.674508517",
      "x": "-0.081269086",
      "y": "0.533021514"
    },
    {
      "turn": "-0.680875765",
      "x": "-0.086131218",
      "y": "0.542875363"
    },
    {
      "turn": "-0.687280959",
      "x": "-0.090947325",
      "y": "0.55285077"
    },
    {
      "turn": "-0.693724684",
      "x": "-0.095796313",
      "y": "0.562785083"
    },
    {
      "turn": "-0.700207538",
      "x": "-0.100597853",
      "y": "0.572836663"
    },
    {
      "turn": "-0.706730127",
      "x": "-0.10543221",
      "y": "0.582848401"
    },
    {
      "turn": "-0.713293068",
      "x": "-0.110217728",
      "y": "0.592973102"
    },
    {
      "turn": "-0.719896989",
      "x": "-0.115035973",
      "y": "0.603059206"
    },
    {
      "turn": "-0.726542528",
      "x": "-0.119804022",
      "y": "0.613253954"
    },
    {
      "turn": "-0.733230336",
      "x": "-0.124604679",
      "y": "0.62341134"
    },
    {
      "turn": "-0.739961075",
      "x": "-0.129353814",
      "y": "0.633673042"
    },
    {
      "turn": "-0.746735418",
      "x": "-0.134135411",
      "y": "0.643898606"
    },
    {
      "turn": "-0.75355405",
      "x": "-0.138864194",
      "y": "0.654224145"
    },
    {
      "turn": "-0.76041767",
      "x": "-0.143625266",
      "y": "0.664514762"
    },
    {
      "turn": "-0.767326988",
      "x": "-0.148332267",
      "y": "0.674901003"
    },
    {
      "turn": "-0.774282728",
      "x": "-0.153071355",
      "y": "0.68525353"
    },
    {
      "turn": "-0.781285627",
      "x": "-0.157755147",
      "y": "0.695697316"
    },
    {
      "turn": "-0.788336435",
      "x": "-0.162470799",
      "y": "0.706108592"
    },
    {
      "turn": "-0.795435917",
      "x": "-0.167129965",
      "y": "0.716606751"
    },
    {
      "turn": "-0.802584852",
      "x": "-0.171820736",
      "y": "0.727073596"
    },
    {
      "turn": "-0.809784033",
      "x": "-0.176453864",
      "y": "0.737622937"
    },
    {
      "turn": "-0.81703427",
      "x": "-0.181118317",
      "y": "0.748142155"
    },
    {
      "turn": "-0.824336386",
      "x": "-0.185724004",
      "y": "0.758739472"
    },
    {
      "turn": "-0.831691221",
      "x": "-0.19036071",
      "y": "0.769307853"
    },
    {
      "turn": "-0.839099631",
      "x": "-0.194937563",
      "y": "0.779949924"
    },
    {
      "turn": "-0.846562489",
      "x": "-0.199545101",
      "y": "0.790564243"
    },
    {
      "turn": "-0.854080685",
      "x": "-0.204091732",
      "y": "0.801247831"
    },
    {
      "turn": "-0.861655127",
      "x": "-0.20866869",
      "y": "0.811904849"
    },
    {
      "turn": "-0.869286738",
      "x": "-0.213183724",
      "y": "0.822626706"
    },
    {
      "turn": "-0.876976463",
      "x": "-0.2177287",
      "y": "0.833323171"
    },
    {
      "turn": "-0.884725265",
      "x": "-0.222210769",
      "y": "0.844080036"
    },
    {
      "turn": "-0.892534124",
      "x": "-0.226722371",
      "y": "0.854812686"
    },
    {
      "turn": "-0.900404044",
      "x": "-0.231170118",
      "y": "0.865601285"
    },
    {
      "turn": "-0.908336046",
      "x": "-0.235646962",
      "y": "0.876366848"
    },
    {
      "turn": "-0.916331174",
      "x": "-0.240059041",
      "y": "0.887183898"
    },
    {
      "turn": "-0.924390492",
      "x": "-0.244499756",
      "y": "0.89797909"
    },
    {
      "turn": "-0.932515086",
      "x": "-0.24887483",
      "y": "0.9088213"
    },
    {
      "turn": "-0.940706067",
      "x": "-0.253278055",
      "y": "0.91964283"
    },
    {
      "turn": "-0.948964567",
      "x": "-0.2576148",
      "y": "0.930506898"
    },
    {
      "turn": "-0.957291742",
      "x": "-0.261979187",
      "y": "0.94135147"
    },
    {
      "turn": "-0.965688775",
      "x": "-0.266276289",
      "y": "0.952234089"
    },
    {
      "turn": "-0.974156871",
      "x": "-0.270600499",
      "y": "0.963098395"
    },
    {
      "turn": "-0.982697263",
      "x": "-0.274856659",
      "y": "0.973996251"
    },
    {
      "turn": "-0.991311211",
      "x": "-0.279139367",
      "y": "0.984876983"
    },
    {
      "turn": "-1",
      "x": "-0.276937329",
      "y": "0.997849259"
    },
    {
      "turn": "-1",
      "x": "-0.276937329",
      "y": "0.999873316"
    },
    {
      "turn": "-1.008764946",
      "x": "-0.273684632",
      "y": "1.01048606"
    },
    {
      "turn": "-1.017607393",
      "x": "-0.246504693",
      "y": "1.021202724"
    },
    {
      "turn": "-1.026528714",
      "x": "-0.26719754",
      "y": "1.031868487"
    },
    {
      "turn": "-1.035530314",
      "x": "-0.260050181",
      "y": "1.042549308"
    },
    {
      "turn": "-1.044613628",
      "x": "-0.260602176",
      "y": "1.053194693"
    },
    {
      "turn": "-1.053780125",
      "x": "-0.246273161",
      "y": "1.063906567"
    },
    {
      "turn": "-1.063031307",
      "x": "-0.253927414",
      "y": "1.074580411"
    },
    {
      "turn": "-1.07236871",
      "x": "-0.243652507",
      "y": "1.085267993"
    },
    {
      "turn": "-1.081793905",
      "x": "-0.247175289",
      "y": "1.095930281"
    },
    {
      "turn": "-1.091308501",
      "x": "-0.231869106",
      "y": "1.106627081"
    },
    {
      "turn": "-1.100914143",
      "x": "-0.240347856",
      "y": "1.117304297"
    },
    {
      "turn": "-1.110612515",
      "x": "-0.226106926",
      "y": "1.127977322"
    },
    {
      "turn": "-1.120405341",
      "x": "-0.233447196",
      "y": "1.138646271"
    },
    {
      "turn": "-1.130294386",
      "x": "-0.219112879",
      "y": "1.149312215"
    },
    {
      "turn": "-1.140281458",
      "x": "-0.22647541",
      "y": "1.159973443"
    },
    {
      "turn": "-1.150368407",
      "x": "-0.214191086",
      "y": "1.170625259"
    },
    {
      "turn": "-1.160557129",
      "x": "-0.219434622",
      "y": "1.181268512"
    },
    {
      "turn": "-1.170849566",
      "x": "-0.205093846",
      "y": "1.191909963"
    },
    {
      "turn": "-1.181247708",
      "x": "-0.212326978",
      "y": "1.202545442"
    },
    {
      "turn": "-1.191753593",
      "x": "-0.201020976",
      "y": "1.213159842"
    },
    {
      "turn": "-1.202369311",
      "x": "-0.205154641",
      "y": "1.223767654"
    },
    {
      "turn": "-1.213097004",
      "x": "-0.196655197",
      "y": "1.234368424"
    },
    {
      "turn": "-1.223938869",
      "x": "-0.197919797",
      "y": "1.24494609"
    },
    {
      "turn": "-1.234897157",
      "x": "-0.188493151",
      "y": "1.255529247"
    },
    {
      "turn": "-1.245974177",
      "x": "-0.190624649",
      "y": "1.266085767"
    },
    {
      "turn": "-1.257172299",
      "x": "-0.186926023",
      "y": "1.276635867"
    },
    {
      "turn": "-1.268493953",
      "x": "-0.18327142",
      "y": "1.287146249"
    },
    {
      "turn": "-1.279941632",
      "x": "-0.165258695",
      "y": "1.297681852"
    },
    {
      "turn": "-1.291517897",
      "x": "-0.17586235",
      "y": "1.308196544"
    },
    {
      "turn": "-1.303225373",
      "x": "-0.170806566",
      "y": "1.318660794"
    },
    {
      "turn": "-1.315066758",
      "x": "-0.168399695",
      "y": "1.329111236"
    },
    {
      "turn": "-1.327044822",
      "x": "-0.153725377",
      "y": "1.3395663"
    },
    {
      "turn": "-1.339162408",
      "x": "-0.160885728",
      "y": "1.350009384"
    },
    {
      "turn": "-1.351422438",
      "x": "-0.15666726",
      "y": "1.360392003"
    },
    {
      "turn": "-1.363827914",
      "x": "-0.153322739",
      "y": "1.370762598"
    },
    {
      "turn": "-1.37638192",
      "x": "-0.149493974",
      "y": "1.381131559"
    },
    {
      "turn": "-1.389087628",
      "x": "-0.145713031",
      "y": "1.391457584"
    },
    {
      "turn": "-1.401948294",
      "x": "-0.137331291",
      "y": "1.40177865"
    },
    {
      "turn": "-1.414967272",
      "x": "-0.138058922",
      "y": "1.412073135"
    },
    {
      "turn": "-1.428148007",
      "x": "-0.134186279",
      "y": "1.422326988"
    },
    {
      "turn": "-1.441494043",
      "x": "-0.130362733",
      "y": "1.432557149"
    },
    {
      "turn": "-1.455009029",
      "x": "-0.12646989",
      "y": "1.442770312"
    },
    {
      "turn": "-1.468696716",
      "x": "-0.122626832",
      "y": "1.452947858"
    },
    {
      "turn": "-1.482560969",
      "x": "-0.112789031",
      "y": "1.463102395"
    },
    {
      "turn": "-1.496605763",
      "x": "-0.11485357",
      "y": "1.473243619"
    },
    {
      "turn": "-1.510835194",
      "x": "-0.110923924",
      "y": "1.483315904"
    },
    {
      "turn": "-1.525253479",
      "x": "-0.107045265",
      "y": "1.493383496"
    },
    {
      "turn": "-1.539864964",
      "x": "-0.101703521",
      "y": "1.503408102"
    },
    {
      "turn": "-1.554674125",
      "x": "-0.099204403",
      "y": "1.513413838"
    },
    {
      "turn": "-1.569685577",
      "x": "-0.094533616",
      "y": "1.523369448"
    },
    {
      "turn": "-1.584904077",
      "x": "-0.09112018",
      "y": "1.533307333"
    },
    {
      "turn": "-1.600334529",
      "x": "-0.086957129",
      "y": "1.543195001"
    },
    {
      "turn": "-1.615981993",
      "x": "-0.082653305",
      "y": "1.553062084"
    },
    {
      "turn": "-1.631851687",
      "x": "-0.077582739",
      "y": "1.562878724"
    },
    {
      "turn": "-1.647948997",
      "x": "-0.073895946",
      "y": "1.57267693"
    },
    {
      "turn": "-1.664279482",
      "x": "-0.069379528",
      "y": "1.58241341"
    },
    {
      "turn": "-1.680848881",
      "x": "-0.064731271",
      "y": "1.592139426"
    },
    {
      "turn": "-1.697663119",
      "x": "-0.060070121",
      "y": "1.601794069"
    },
    {
      "turn": "-1.71472832",
      "x": "-0.055251716",
      "y": "1.61144852"
    },
    {
      "turn": "-1.732050808",
      "x": "-0.050417389",
      "y": "1.621013237"
    },
    {
      "turn": "-1.74963712",
      "x": "-0.045430275",
      "y": "1.630598507"
    },
    {
      "turn": "-1.767494016",
      "x": "-0.040424271",
      "y": "1.640053981"
    },
    {
      "turn": "-1.785628485",
      "x": "-0.027453899",
      "y": "1.649571266"
    },
    {
      "turn": "-1.804047755",
      "x": "-0.030093811",
      "y": "1.658957539"
    },
    {
      "turn": "-1.822759308",
      "x": "-0.024563473",
      "y": "1.668367282"
    },
    {
      "turn": "-1.841770886",
      "x": "-0.019429156",
      "y": "1.677641095"
    },
    {
      "turn": "-1.861090505",
      "x": "-0.006888627",
      "y": "1.686983346"
    },
    {
      "turn": "-1.880726465",
      "x": "-0.008433553",
      "y": "1.696189152"
    },
    {
      "turn": "-1.900687369",
      "x": "-0.000489295",
      "y": "1.705413788"
    },
    {
      "turn": "-1.920982127",
      "x": "0.002889647",
      "y": "1.714510796"
    },
    {
      "turn": "-1.941619979",
      "x": "0.015761194",
      "y": "1.723652993"
    },
    {
      "turn": "-1.962610506",
      "x": "0.014536997",
      "y": "1.732669589"
    },
    {
      "turn": "-1.983963644",
      "x": "0.023852088",
      "y": "1.741695406"
    },
    {
      "turn": "-2.005689708",
      "x": "0.026504948",
      "y": "1.750601076"
    },
    {
      "turn": "-2.027799402",
      "x": "0.039705541",
      "y": "1.75953553"
    },
    {
      "turn": "-2.050303842",
      "x": "0.038789855",
      "y": "1.76835191"
    },
    {
      "turn": "-2.073214574",
      "x": "0.045067684",
      "y": "1.77716793"
    },
    {
      "turn": "-2.096543599",
      "x": "0.051387976",
      "y": "1.785856961"
    },
    {
      "turn": "-2.12030339",
      "x": "0.075257286",
      "y": "1.794587234"
    },
    {
      "turn": "-2.144506921",
      "x": "0.064295475",
      "y": "1.803199211"
    },
    {
      "turn": "-2.169167685",
      "x": "0.075692914",
      "y": "1.811788137"
    },
    {
      "turn": "-2.194299731",
      "x": "0.077508419",
      "y": "1.820276605"
    },
    {
      "turn": "-2.219917683",
      "x": "0.091040809",
      "y": "1.828765399"
    },
    {
      "turn": "-2.246036774",
      "x": "0.091022783",
      "y": "1.837148295"
    },
    {
      "turn": "-2.272672879",
      "x": "0.104221783",
      "y": "1.845513847"
    },
    {
      "turn": "-2.299842547",
      "x": "0.104834452",
      "y": "1.853780541"
    },
    {
      "turn": "-2.327563039",
      "x": "0.118348244",
      "y": "1.862028379"
    },
    {
      "turn": "-2.355852366",
      "x": "0.118939218",
      "y": "1.870178476"
    },
    {
      "turn": "-2.384729328",
      "x": "0.133320879",
      "y": "1.878303965"
    },
    {
      "turn": "-2.414213562",
      "x": "0.133332786",
      "y": "1.886336793"
    },
    {
      "turn": "-2.444325587",
      "x": "0.140640855",
      "y": "1.894335647"
    },
    {
      "turn": "-2.475086853",
      "x": "0.14801077",
      "y": "1.902222774"
    },
    {
      "turn": "-2.506519797",
      "x": "0.172161973",
      "y": "1.910118541"
    },
    {
      "turn": "-2.538647896",
      "x": "0.166754036",
      "y": "1.917911053"
    },
    {
      "turn": "-2.571495734",
      "x": "0.170521668",
      "y": "1.925647839"
    },
    {
      "turn": "-2.605089065",
      "x": "0.178205262",
      "y": "1.933283471"
    },
    {
      "turn": "-2.639454881",
      "x": "0.195286321",
      "y": "1.94091881"
    },
    {
      "turn": "-2.674621494",
      "x": "0.193931387",
      "y": "1.948455252"
    },
    {
      "turn": "-2.710618609",
      "x": "0.21382113",
      "y": "1.955926803"
    },
    {
      "turn": "-2.747477419",
      "x": "0.212596593",
      "y": "1.963331746"
    },
    {
      "turn": "-2.785230695",
      "x": "0.224480688",
      "y": "1.970667245"
    },
    {
      "turn": "-2.823912886",
      "x": "0.225507501",
      "y": "1.977931485"
    },
    {
      "turn": "-2.863560231",
      "x": "0.233612529",
      "y": "1.985135646"
    },
    {
      "turn": "-2.904210878",
      "x": "0.241795159",
      "y": "1.992240912"
    },
    {
      "turn": "-2.945905005",
      "x": "0.259030599",
      "y": "1.9993276"
    },
    {
      "turn": "-2.988684963",
      "x": "0.258334195",
      "y": "2.006324184"
    },
    {
      "turn": "-3.032595423",
      "x": "0.277224079",
      "y": "2.013238781"
    },
    {
      "turn": "-3.077683537",
      "x": "0.275808433",
      "y": "2.02009559"
    },
    {
      "turn": "-3.123999113",
      "x": "0.283566624",
      "y": "2.026864954"
    },
    {
      "turn": "-3.171594802",
      "x": "0.29217627",
      "y": "2.03354924"
    },
    {
      "turn": "-3.220526311",
      "x": "0.310029847",
      "y": "2.040201967"
    },
    {
      "turn": "-3.270852618",
      "x": "0.309537111",
      "y": "2.04677202"
    },
    {
      "turn": "-3.322636226",
      "x": "0.321793106",
      "y": "2.053245756"
    },
    {
      "turn": "-3.375943423",
      "x": "0.32690225",
      "y": "2.059651451"
    },
    {
      "turn": "-3.430844574",
      "x": "0.344389729",
      "y": "2.06599235"
    },
    {
      "turn": "-3.487414444",
      "x": "0.344621132",
      "y": "2.072266018"
    },
    {
      "turn": "-3.545732543",
      "x": "0.353543032",
      "y": "2.078437864"
    },
    {
      "turn": "-3.605883509",
      "x": "0.362571806",
      "y": "2.084532839"
    },
    {
      "turn": "-3.667957531",
      "x": "0.377216888",
      "y": "2.090578508"
    },
    {
      "turn": "-3.732050808",
      "x": "0.3807136",
      "y": "2.096539814"
    },
    {
      "turn": "-3.798266061",
      "x": "0.393158235",
      "y": "2.102410583"
    },
    {
      "turn": "-3.866713095",
      "x": "0.399076193",
      "y": "2.108210369"
    },
    {
      "turn": "-3.937509419",
      "x": "0.408311093",
      "y": "2.113930486"
    },
    {
      "turn": "-4.010780934",
      "x": "0.417672481",
      "y": "2.119563631"
    },
    {
      "turn": "-4.086662697",
      "x": "0.43207234",
      "y": "2.125134706"
    },
    {
      "turn": "-4.16529977",
      "x": "0.436406128",
      "y": "2.130627205"
    },
    {
      "turn": "-4.24684816",
      "x": "0.449862689",
      "y": "2.136019831"
    },
    {
      "turn": "-4.331475874",
      "x": "0.455362099",
      "y": "2.141349736"
    },
    {
      "turn": "-4.419364096",
      "x": "0.466915422",
      "y": "2.146582545"
    },
    {
      "turn": "-4.510708504",
      "x": "0.474504394",
      "y": "2.151745203"
    },
    {
      "turn": "-4.605720746",
      "x": "0.489123244",
      "y": "2.15681963"
    },
    {
      "turn": "-4.704630109",
      "x": "0.49382718",
      "y": "2.16182974"
    },
    {
      "turn": "-4.807685394",
      "x": "0.504027724",
      "y": "2.166727968"
    },
    {
      "turn": "-4.915157031",
      "x": "0.513324572",
      "y": "2.171559527"
    },
    {
      "turn": "-5.027339492",
      "x": "0.523125304",
      "y": "2.176442022"
    },
    {
      "turn": "-5.144554016",
      "x": "0.533021485",
      "y": "2.181262629"
    },
    {
      "turn": "-5.267151723",
      "x": "0.542875363",
      "y": "2.18613337"
    },
    {
      "turn": "-5.395517174",
      "x": "0.552850742",
      "y": "2.190940868"
    },
    {
      "turn": "-5.530072445",
      "x": "0.562785083",
      "y": "2.195798465"
    },
    {
      "turn": "-5.67128182",
      "x": "0.572836634",
      "y": "2.200591396"
    },
    {
      "turn": "-5.819657198",
      "x": "0.582848401",
      "y": "2.205434362"
    },
    {
      "turn": "-5.975764364",
      "x": "0.592973074",
      "y": "2.210211272"
    },
    {
      "turn": "-6.140230267",
      "x": "0.603059206",
      "y": "2.215038126"
    },
    {
      "turn": "-6.313751515",
      "x": "0.613253926",
      "y": "2.219797566"
    },
    {
      "turn": "-6.497104326",
      "x": "0.62341134",
      "y": "2.224606831"
    },
    {
      "turn": "-6.691156238",
      "x": "0.633673014",
      "y": "2.229347358"
    },
    {
      "turn": "-6.896879945",
      "x": "0.643898606",
      "y": "2.234137535"
    },
    {
      "turn": "-7.115369722",
      "x": "0.654224117",
      "y": "2.238857821"
    },
    {
      "turn": "-7.347861045",
      "x": "0.664552899",
      "y": "2.243627307"
    },
    {
      "turn": "-7.595754113",
      "x": "0.674866475",
      "y": "2.248326381"
    },
    {
      "turn": "-7.860642258",
      "x": "0.68525353",
      "y": "2.253073279"
    },
    {
      "turn": "-8.144346428",
      "x": "0.695697291",
      "y": "2.257749374"
    },
    {
      "turn": "-8.44895734",
      "x": "0.706129197",
      "y": "2.262472678"
    },
    {
      "turn": "-8.776887357",
      "x": "0.716576167",
      "y": "2.267124494"
    },
    {
      "turn": "-9.130934819",
      "x": "0.727073596",
      "y": "2.271822526"
    },
    {
      "turn": "-9.514364454",
      "x": "0.737622913",
      "y": "2.276448494"
    },
    {
      "turn": "-9.931008767",
      "x": "0.748172647",
      "y": "2.28112004"
    },
    {
      "turn": "-10.38539708",
      "x": "0.758704909",
      "y": "2.285719047"
    },
    {
      "turn": "-10.88292144",
      "x": "0.769307853",
      "y": "2.290362325"
    },
    {
      "turn": "-11.430052303",
      "x": "0.779949903",
      "y": "2.294932718"
    },
    {
      "turn": "-12.034622321",
      "x": "0.790582958",
      "y": "2.299546675"
    },
    {
      "turn": "-12.706204736",
      "x": "0.801216567",
      "y": "2.304087174"
    },
    {
      "turn": "-13.456625313",
      "x": "0.811904849",
      "y": "2.308670176"
    },
    {
      "turn": "-14.300666257",
      "x": "0.822626687",
      "y": "2.313179269"
    },
    {
      "turn": "-15.257051688",
      "x": "0.833323171",
      "y": "2.317730131"
    },
    {
      "turn": "-16.349855476",
      "x": "0.844080017",
      "y": "2.322206477"
    },
    {
      "turn": "-17.610558829",
      "x": "0.854844396",
      "y": "2.326723732"
    },
    {
      "turn": "-19.081136688",
      "x": "0.86556463",
      "y": "2.331166257"
    },
    {
      "turn": "-20.818827605",
      "x": "0.876366848",
      "y": "2.335648209"
    },
    {
      "turn": "-22.903765548",
      "x": "0.887183882",
      "y": "2.3400553"
    },
    {
      "turn": "-25.451699579",
      "x": "0.897987796",
      "y": "2.344500984"
    },
    {
      "turn": "-28.636253283",
      "x": "0.908799212",
      "y": "2.348871247"
    },
    {
      "turn": "-32.730263715",
      "x": "0.91964283",
      "y": "2.353279219"
    },
    {
      "turn": "-38.188459297",
      "x": "0.930506883",
      "y": "2.357611309"
    },
    {
      "turn": "-45.829351174",
      "x": "0.941375587",
      "y": "2.361980287"
    },
    {
      "turn": "-57.289961631",
      "x": "0.952198646",
      "y": "2.366273181"
    },
    {
      "turn": "-76.390009311",
      "x": "0.963102279",
      "y": "2.370601492"
    },
    {
      "turn": "-114.588650129",
      "x": "0.973984588",
      "y": "2.374853731"
    },
    {
      "turn": "-229.181663609",
      "x": "0.984876983",
      "y": "2.37914033"
    },
    {
      "turn": "-666666.666644453",
      "x": "0.995762021",
      "y": "2.376938434"
    },
    {
      "turn": "-666666.666644453",
      "x": "3.045690964",
      "y": "2.376938434"
    }
  ]
}

Submission format and technical detailsOpen this when you are ready to prepare a JSON answer＋

Instance parameters

{
  "w": "0.1"
}

The current leader's answer

{
  "outline": {
    "nodes": [
      {
        "bulge": "-0.292491578",
        "x": "0.368449069",
        "y": "0.276987329"
      },
      {
        "bulge": "-0.11915481",
        "x": "0.995694687",
        "y": "1.241018351"
      },
      {
        "bulge": "0.35370257",
        "x": "0.065820249",
        "y": "1.180264571"
      },
      {
        "bulge": "-0.098310876",
        "x": "-0.168863212",
        "y": "1.193144574"
      },
      {
        "bulge": "-0.306846957",
        "x": "-1.09965324",
        "y": "1.251439987"
      },
      {
        "bulge": "0",
        "x": "-0.484371174",
        "y": "0.283428022"
      }
    ],
    "step": "1"
  },
  "polygon": [
    [
      "0.368449069",
      "0.276987329"
    ],
    [
      "0.385150352",
      "0.284717339"
    ],
    [
      "0.401715849",
      "0.292734211"
    ],
    [
      "0.418140632",
      "0.301035561"
    ],
    [
      "0.434419818",
      "0.309618919"
    ],
    [
      "0.450548564",
      "0.318481732"
    ],
    [
      "0.466522074",
      "0.327621366"
    ],
    [
      "0.482335597",
      "0.337035101"
    ],
    [
      "0.49798443",
      "0.346720139"
    ],
    [
      "0.513463918",
      "0.356673598"
    ],
    [
      "0.528769459",
      "0.366892518"
    ],
    [
      "0.5438965",
      "0.377373861"
    ],
    [
      "0.558840543",
      "0.388114508"
    ],
    [
      "0.573597142",
      "0.399111266"
    ],
    [
      "0.58816191",
      "0.410360865"
    ],
    [
      "0.602530514",
      "0.421859958"
    ],
    [
      "0.616698681",
      "0.433605125"
    ],
    [
      "0.630662198",
      "0.445592874"
    ],
    [
      "0.644416911",
      "0.457819638"
    ],
    [
      "0.65795873",
      "0.470281783"
    ],
    [
      "0.671283628",
      "0.482975601"
    ],
    [
      "0.684387641",
      "0.495897318"
    ],
    [
      "0.697266873",
      "0.50904309"
    ],
    [
      "0.709917492",
      "0.522409007"
    ],
    [
      "0.722335737",
      "0.535991095"
    ],
    [
      "0.734517914",
      "0.549785314"
    ],
    [
      "0.7464604",
      "0.563787562"
    ],
    [
      "0.758159644",
      "0.577993674"
    ],
    [
      "0.769612165",
      "0.592399425"
    ],
    [
      "0.780814559",
      "0.607000531"
    ],
    [
      "0.791763493",
      "0.621792649"
    ],
    [
      "0.802455711",
      "0.636771381"
    ],
    [
      "0.812888032",
      "0.65193227"
    ],
    [
      "0.823057355",
      "0.66727081"
    ],
    [
      "0.832960655",
      "0.682782436"
    ],
    [
      "0.842594987",
      "0.698462538"
    ],
    [
      "0.851957485",
      "0.71430645"
    ],
    [
      "0.861045365",
      "0.730309461"
    ],
    [
      "0.869855924",
      "0.746466811"
    ],
    [
      "0.878386541",
      "0.762773695"
    ],
    [
      "0.886634681",
      "0.779225264"
    ],
    [
      "0.894597888",
      "0.795816625"
    ],
    [
      "0.902273796",
      "0.812542842"
    ],
    [
      "0.909660122",
      "0.829398942"
    ],
    [
      "0.916754668",
      "0.846379912"
    ],
    [
      "0.923555325",
      "0.863480701"
    ],
    [
      "0.93006007",
      "0.880696224"
    ],
    [
      "0.936266968",
      "0.898021359"
    ],
    [
      "0.942174174",
      "0.915450956"
    ],
    [
      "0.947779931",
      "0.932979829"
    ],
    [
      "0.953082571",
      "0.950602767"
    ],
    [
      "0.958080518",
      "0.968314527"
    ],
    [
      "0.962772285",
      "0.986109842"
    ],
    [
      "0.967156477",
      "1.00398342"
    ],
    [
      "0.97123179",
      "1.021929944"
    ],
    [
      "0.974997011",
      "1.039944078"
    ],
    [
      "0.978451021",
      "1.058020464"
    ],
    [
      "0.981592793",
      "1.076153726"
    ],
    [
      "0.984421393",
      "1.094338471"
    ],
    [
      "0.986935979",
      "1.11256929"
    ],
    [
      "0.989135802",
      "1.130840762"
    ],
    [
      "0.99102021",
      "1.149147453"
    ],
    [
      "0.992588642",
      "1.167483918"
    ],
    [
      "0.993840631",
      "1.185844703"
    ],
    [
      "0.994775804",
      "1.204224349"
    ],
    [
      "0.995393884",
      "1.222617388"
    ],
    [
      "0.995694687",
      "1.241018351"
    ],
    [
      "0.962548264",
      "1.246485836"
    ],
    [
      "0.929313972",
      "1.25139099"
    ],
    [
      "0.896001349",
      "1.255732403"
    ],
    [
      "0.862619957",
      "1.259508829"
    ],
    [
      "0.829179377",
      "1.262719185"
    ],
    [
      "0.795689209",
      "1.26536255"
    ],
    [
      "0.762159065",
      "1.267438163"
    ],
    [
      "0.72859857",
      "1.268945431"
    ],
    [
      "0.695017355",
      "1.26988392"
    ],
    [
      "0.661425061",
      "1.27025336"
    ],
    [
      "0.627831329",
      "1.270053646"
    ],
    [
      "0.594245801",
      "1.269284834"
    ],
    [
      "0.560678118",
      "1.267947147"
    ],
    [
      "0.527137915",
      "1.266040967"
    ],
    [
      "0.49363482",
      "1.263566842"
    ],
    [
      "0.460178447",
      "1.260525481"
    ],
    [
      "0.426778401",
      "1.256917759"
    ],
    [
      "0.393444269",
      "1.25274471"
    ],
    [
      "0.360185618",
      "1.248007532"
    ],
    [
      "0.327011994",
      "1.242707585"
    ],
    [
      "0.29393292",
      "1.23684639"
    ],
    [
      "0.260957891",
      "1.23042563"
    ],
    [
      "0.228096371",
      "1.223447147"
    ],
    [
      "0.195357792",
      "1.215912944"
    ],
    [
      "0.162751552",
      "1.207825185"
    ],
    [
      "0.13028701",
      "1.199186191"
    ],
    [
      "0.097973484",
      "1.18999844"
    ],
    [
      "0.065820249",
      "1.180264571"
    ],
    [
      "0.063161339",
      "1.178380787"
    ],
    [
      "0.060469992",
      "1.176543643"
    ],
    [
      "0.057747026",
      "1.174753698"
    ],
    [
      "0.054993269",
      "1.173011496"
    ],
    [
      "0.052209559",
      "1.171317566"
    ],
    [
      "0.04939674",
      "1.169672423"
    ],
    [
      "0.046555668",
      "1.168076567"
    ],
    [
      "0.043687206",
      "1.166530484"
    ],
    [
      "0.040792227",
      "1.165034643"
    ],
    [
      "0.03787161",
      "1.163589498"
    ],
    [
      "0.034926244",
      "1.162195489"
    ],
    [
      "0.031957022",
      "1.160853041"
    ],
    [
      "0.028964848",
      "1.15956256"
    ],
    [
      "0.025950632",
      "1.158324439"
    ],
    [
      "0.022915289",
      "1.157139054"
    ],
    [
      "0.019859741",
      "1.156006766"
    ],
    [
      "0.016784919",
      "1.154927919"
    ],
    [
      "0.013691755",
      "1.153902841"
    ],
    [
      "0.010581191",
      "1.152931843"
    ],
    [
      "0.007454172",
      "1.15201522"
    ],
    [
      "0.004311649",
      "1.151153251"
    ],
    [
      "0.001154575",
      "1.150346199"
    ],
    [
      "-0.002016088",
      "1.149594307"
    ],
    [
      "-0.005199377",
      "1.148897806"
    ],
    [
      "-0.008394325",
      "1.148256906"
    ],
    [
      "-0.011599961",
      "1.147671803"
    ],
    [
      "-0.014815309",
      "1.147142673"
    ],
    [
      "-0.018039394",
      "1.146669679"
    ],
    [
      "-0.021271234",
      "1.146252964"
    ],
    [
      "-0.024509849",
      "1.145892654"
    ],
    [
      "-0.027754252",
      "1.145588859"
    ],
    [
      "-0.031003459",
      "1.145341671"
    ],
    [
      "-0.034256481",
      "1.145151166"
    ],
    [
      "-0.03751233",
      "1.145017401"
    ],
    [
      "-0.040770016",
      "1.144940417"
    ],
    [
      "-0.044028549",
      "1.144920238"
    ],
    [
      "-0.047286939",
      "1.144956869"
    ],
    [
      "-0.050544195",
      "1.145050299"
    ],
    [
      "-0.053799327",
      "1.145200501"
    ],
    [
      "-0.057051345",
      "1.145407428"
    ],
    [
      "-0.060299263",
      "1.145671017"
    ],
    [
      "-0.063542091",
      "1.145991189"
    ],
    [
      "-0.066778845",
      "1.146367845"
    ],
    [
      "-0.07000854",
      "1.146800873"
    ],
    [
      "-0.073230195",
      "1.147290139"
    ],
    [
      "-0.076442832",
      "1.147835495"
    ],
    [
      "-0.079645472",
      "1.148436776"
    ],
    [
      "-0.082837144",
      "1.149093799"
    ],
    [
      "-0.086016876",
      "1.149806363"
    ],
    [
      "-0.089183702",
      "1.150574253"
    ],
    [
      "-0.092336661",
      "1.151397235"
    ],
    [
      "-0.095474792",
      "1.152275059"
    ],
    [
      "-0.098597144",
      "1.153207458"
    ],
    [
      "-0.101702766",
      "1.154194148"
    ],
    [
      "-0.104790714",
      "1.155234831"
    ],
    [
      "-0.10786005",
      "1.156329188"
    ],
    [
      "-0.110909842",
      "1.157476889"
    ],
    [
      "-0.113939162",
      "1.158677583"
    ],
    [
      "-0.116947089",
      "1.159930907"
    ],
    [
      "-0.119932709",
      "1.161236479"
    ],
    [
      "-0.122895115",
      "1.162593901"
    ],
    [
      "-0.125833406",
      "1.164002763"
    ],
    [
      "-0.128746689",
      "1.165462635"
    ],
    [
      "-0.131634079",
      "1.166973074"
    ],
    [
      "-0.134494698",
      "1.16853362"
    ],
    [
      "-0.137327676",
      "1.170143799"
    ],
    [
      "-0.140132153",
      "1.171803123"
    ],
    [
      "-0.142907276",
      "1.173511086"
    ],
    [
      "-0.145652202",
      "1.175267169"
    ],
    [
      "-0.148366096",
      "1.177070839"
    ],
    [
      "-0.151048133",
      "1.178921548"
    ],
    [
      "-0.153697498",
      "1.180818732"
    ],
    [
      "-0.156313386",
      "1.182761816"
    ],
    [
      "-0.158895002",
      "1.184750208"
    ],
    [
      "-0.161441561",
      "1.186783305"
    ],
    [
      "-0.16395229",
      "1.188860488"
    ],
    [
      "-0.166426424",
      "1.190981126"
    ],
    [
      "-0.168863212",
      "1.193144574"
    ],
    [
      "-0.208403073",
      "1.203241554"
    ],
    [
      "-0.248109264",
      "1.212663231"
    ],
    [
      "-0.287970253",
      "1.221406869"
    ],
    [
      "-0.327974462",
      "1.229469928"
    ],
    [
      "-0.368110271",
      "1.236850067"
    ],
    [
      "-0.408366023",
      "1.243545141"
    ],
    [
      "-0.448730027",
      "1.249553206"
    ],
    [
      "-0.489190558",
      "1.254872517"
    ],
    [
      "-0.529735864",
      "1.259501529"
    ],
    [
      "-0.57035417",
      "1.263438897"
    ],
    [
      "-0.611033677",
      "1.266683479"
    ],
    [
      "-0.65176257",
      "1.269234331"
    ],
    [
      "-0.692529021",
      "1.271090713"
    ],
    [
      "-0.733321187",
      "1.272252085"
    ],
    [
      "-0.774127222",
      "1.27271811"
    ],
    [
      "-0.814935272",
      "1.272488653"
    ],
    [
      "-0.855733486",
      "1.271563781"
    ],
    [
      "-0.896510013",
      "1.269943762"
    ],
    [
      "-0.93725301",
      "1.267629066"
    ],
    [
      "-0.977950643",
      "1.264620366"
    ],
    [
      "-1.018591092",
      "1.260918536"
    ],
    [
      "-1.059162552",
      "1.256524651"
    ],
    [
      "-1.09965324",
      "1.251439987"
    ],
    [
      "-1.100017243",
      "1.233796161"
    ],
    [
      "-1.100076684",
      "1.21614868"
    ],
    [
      "-1.099831544",
      "1.198502803"
    ],
    [
      "-1.099281896",
      "1.180863784"
    ],
    [
      "-1.098427905",
      "1.163236878"
    ],
    [
      "-1.097269824",
      "1.145627337"
    ],
    [
      "-1.095807999",
      "1.128040405"
    ],
    [
      "-1.094042865",
      "1.110481322"
    ],
    [
      "-1.091974948",
      "1.092955318"
    ],
    [
      "-1.089604863",
      "1.075467614"
    ],
    [
      "-1.086933317",
      "1.058023418"
    ],
    [
      "-1.083961106",
      "1.040627929"
    ],
    [
      "-1.080689115",
      "1.023286326"
    ],
    [
      "-1.077118319",
      "1.006003777"
    ],
    [
      "-1.073249781",
      "0.988785429"
    ],
    [
      "-1.069084653",
      "0.971636411"
    ],
    [
      "-1.064624177",
      "0.954561832"
    ],
    [
      "-1.059869682",
      "0.937566778"
    ],
    [
      "-1.054822582",
      "0.920656311"
    ],
    [
      "-1.049484383",
      "0.903835469"
    ],
    [
      "-1.043856673",
      "0.887109262"
    ],
    [
      "-1.03794113",
      "0.870482673"
    ],
    [
      "-1.031739516",
      "0.853960655"
    ],
    [
      "-1.025253678",
      "0.83754813"
    ],
    [
      "-1.018485547",
      "0.821249985"
    ],
    [
      "-1.011437141",
      "0.805071077"
    ],
    [
      "-1.004110558",
      "0.789016225"
    ],
    [
      "-0.996507981",
      "0.773090211"
    ],
    [
      "-0.988631676",
      "0.757297779"
    ],
    [
      "-0.980483987",
      "0.741643633"
    ],
    [
      "-0.972067342",
      "0.726132438"
    ],
    [
      "-0.963384249",
      "0.710768812"
    ],
    [
      "-0.954437293",
      "0.695557333"
    ],
    [
      "-0.945229141",
      "0.680502533"
    ],
    [
      "-0.935762534",
      "0.665608894"
    ],
    [
      "-0.926040294",
      "0.650880855"
    ],
    [
      "-0.916065315",
      "0.636322803"
    ],
    [
      "-0.905840569",
      "0.621939073"
    ],
    [
      "-0.895369103",
      "0.607733951"
    ],
    [
      "-0.884654035",
      "0.593711668"
    ],
    [
      "-0.873698557",
      "0.579876401"
    ],
    [
      "-0.862505933",
      "0.566232272"
    ],
    [
      "-0.851079497",
      "0.552783344"
    ],
    [
      "-0.839422652",
      "0.539533624"
    ],
    [
      "-0.827538872",
      "0.52648706"
    ],
    [
      "-0.815431695",
      "0.513647536"
    ],
    [
      "-0.803104728",
      "0.501018878"
    ],
    [
      "-0.790561644",
      "0.488604848"
    ],
    [
      "-0.777806179",
      "0.476409144"
    ],
    [
      "-0.764842132",
      "0.464435398"
    ],
    [
      "-0.751673365",
      "0.452687178"
    ],
    [
      "-0.738303801",
      "0.441167982"
    ],
    [
      "-0.724737423",
      "0.429881243"
    ],
    [
      "-0.710978271",
      "0.418830322"
    ],
    [
      "-0.697030445",
      "0.408018512"
    ],
    [
      "-0.682898099",
      "0.397449033"
    ],
    [
      "-0.668585443",
      "0.387125033"
    ],
    [
      "-0.65409674",
      "0.377049588"
    ],
    [
      "-0.639436307",
      "0.367225699"
    ],
    [
      "-0.62460851",
      "0.357656292"
    ],
    [
      "-0.609617767",
      "0.348344219"
    ],
    [
      "-0.594468542",
      "0.339292252"
    ],
    [
      "-0.579165349",
      "0.330503089"
    ],
    [
      "-0.563712747",
      "0.321979348"
    ],
    [
      "-0.548115337",
      "0.313723567"
    ],
    [
      "-0.532377767",
      "0.305738206"
    ],
    [
      "-0.516504725",
      "0.298025643"
    ],
    [
      "-0.500500938",
      "0.290588177"
    ],
    [
      "-0.484371174",
      "0.283428022"
    ]
  ],
  "poses": [
    {
      "turn": "0",
      "x": "2.150076684",
      "y": "-0.276987329"
    },
    {
      "turn": "0",
      "x": "1.100126684",
      "y": "-0.276987329"
    },
    {
      "turn": "-0.004363351",
      "x": "1.089514595",
      "y": "-0.273534634"
    },
    {
      "turn": "-0.008726868",
      "x": "1.078797276",
      "y": "-0.258953043"
    },
    {
      "turn": "-0.013090717",
      "x": "1.068135188",
      "y": "-0.26719754"
    },
    {
      "turn": "-0.017455065",
      "x": "1.057450692",
      "y": "-0.263882529"
    },
    {
      "turn": "-0.021820078",
      "x": "1.046817849",
      "y": "-0.260602176"
    },
    {
      "turn": "-0.026185922",
      "x": "1.036093433",
      "y": "-0.236915844"
    },
    {
      "turn": "-0.030552763",
      "x": "1.025415203",
      "y": "-0.245910493"
    },
    {
      "turn": "-0.034920769",
      "x": "1.014732007",
      "y": "-0.250560894"
    },
    {
      "turn": "-0.039290107",
      "x": "1.004092418",
      "y": "-0.247147579"
    },
    {
      "turn": "-0.043660943",
      "x": "0.993372919",
      "y": "-0.219969521"
    },
    {
      "turn": "-0.048033444",
      "x": "0.982695235",
      "y": "-0.240347856"
    },
    {
      "turn": "-0.052407779",
      "x": "0.972022678",
      "y": "-0.231564229"
    },
    {
      "turn": "-0.056784115",
      "x": "0.961371588",
      "y": "-0.233447196"
    },
    {
      "turn": "-0.06116262",
      "x": "0.950687785",
      "y": "-0.229941717"
    },
    {
      "turn": "-0.065543463",
      "x": "0.940061994",
      "y": "-0.22647541"
    },
    {
      "turn": "-0.069926812",
      "x": "0.929374741",
      "y": "-0.202379639"
    },
    {
      "turn": "-0.074312837",
      "x": "0.91872226",
      "y": "-0.219434622"
    },
    {
      "turn": "-0.078701707",
      "x": "0.908090037",
      "y": "-0.207913769"
    },
    {
      "turn": "-0.083093592",
      "x": "0.897463786",
      "y": "-0.212326978"
    },
    {
      "turn": "-0.087488664",
      "x": "0.886840158",
      "y": "-0.198201054"
    },
    {
      "turn": "-0.091887092",
      "x": "0.876223118",
      "y": "-0.205154641"
    },
    {
      "turn": "-0.096289048",
      "x": "0.865631576",
      "y": "-0.198065174"
    },
    {
      "turn": "-0.100694705",
      "x": "0.855058524",
      "y": "-0.197919797"
    },
    {
      "turn": "-0.105104235",
      "x": "0.844470753",
      "y": "-0.181325735"
    },
    {
      "turn": "-0.109517812",
      "x": "0.833897245",
      "y": "-0.190624649"
    },
    {
      "turn": "-0.113935608",
      "x": "0.823364133",
      "y": "-0.182544103"
    },
    {
      "turn": "-0.1183578",
      "x": "0.812839411",
      "y": "-0.18327142"
    },
    {
      "turn": "-0.122784561",
      "x": "0.802318148",
      "y": "-0.169640615"
    },
    {
      "turn": "-0.127216068",
      "x": "0.791805856",
      "y": "-0.17586235"
    },
    {
      "turn": "-0.131652498",
      "x": "0.781339206",
      "y": "-0.172108297"
    },
    {
      "turn": "-0.136094027",
      "x": "0.770893024",
      "y": "-0.168399681"
    },
    {
      "turn": "-0.140540835",
      "x": "0.7604337",
      "y": "-0.164619551"
    },
    {
      "turn": "-0.144993099",
      "x": "0.750024401",
      "y": "-0.160885728"
    },
    {
      "turn": "-0.149451001",
      "x": "0.739607997",
      "y": "-0.14592984"
    },
    {
      "turn": "-0.153914721",
      "x": "0.729205485",
      "y": "-0.152338352"
    },
    {
      "turn": "-0.15838444",
      "x": "0.718868441",
      "y": "-0.14952358"
    },
    {
      "turn": "-0.162860342",
      "x": "0.70854261",
      "y": "-0.145683457"
    },
    {
      "turn": "-0.167342609",
      "x": "0.69822135",
      "y": "-0.132712114"
    },
    {
      "turn": "-0.171831427",
      "x": "0.687911748",
      "y": "-0.138058922"
    },
    {
      "turn": "-0.176326981",
      "x": "0.677674249",
      "y": "-0.134186333"
    },
    {
      "turn": "-0.180829457",
      "x": "0.667439142",
      "y": "-0.13036271"
    },
    {
      "turn": "-0.185339045",
      "x": "0.657229688",
      "y": "-0.120632467"
    },
    {
      "turn": "-0.189855932",
      "x": "0.647033039",
      "y": "-0.122626841"
    },
    {
      "turn": "-0.194380309",
      "x": "0.636897605",
      "y": "-0.118626471"
    },
    {
      "turn": "-0.198912367",
      "x": "0.626775484",
      "y": "-0.11485357"
    },
    {
      "turn": "-0.203452299",
      "x": "0.616682956",
      "y": "-0.106131471"
    },
    {
      "turn": "-0.208000299",
      "x": "0.60660424",
      "y": "-0.107045297"
    },
    {
      "turn": "-0.212556562",
      "x": "0.596592942",
      "y": "-0.103099019"
    },
    {
      "turn": "-0.217121284",
      "x": "0.586587598",
      "y": "-0.099204372"
    },
    {
      "turn": "-0.221694663",
      "x": "0.576630552",
      "y": "-0.093408183"
    },
    {
      "turn": "-0.226276898",
      "x": "0.566688984",
      "y": "-0.09112018"
    },
    {
      "turn": "-0.230868191",
      "x": "0.556805067",
      "y": "-0.086957129"
    },
    {
      "turn": "-0.235468743",
      "x": "0.546937711",
      "y": "-0.082653304"
    },
    {
      "turn": "-0.240078759",
      "x": "0.537121276",
      "y": "-0.078342774"
    },
    {
      "turn": "-0.244698443",
      "x": "0.527325655",
      "y": "-0.073866065"
    },
    {
      "turn": "-0.249328003",
      "x": "0.517585696",
      "y": "-0.069379528"
    },
    {
      "turn": "-0.253967646",
      "x": "0.507863257",
      "y": "-0.064731282"
    },
    {
      "turn": "-0.258617584",
      "x": "0.498205037",
      "y": "-0.060070121"
    },
    {
      "turn": "-0.263278028",
      "x": "0.488554162",
      "y": "-0.055251728"
    },
    {
      "turn": "-0.267949192",
      "x": "0.478985204",
      "y": "-0.050417389"
    },
    {
      "turn": "-0.272631292",
      "x": "0.469404252",
      "y": "-0.045430289"
    },
    {
      "turn": "-0.277324544",
      "x": "0.459938418",
      "y": "-0.040424271"
    },
    {
      "turn": "-0.282029168",
      "x": "0.450428734",
      "y": "-0.030938286"
    },
    {
      "turn": "-0.286745386",
      "x": "0.441053863",
      "y": "-0.030093811"
    },
    {
      "turn": "-0.29147342",
      "x": "0.431632718",
      "y": "-0.018416389"
    },
    {
      "turn": "-0.296213495",
      "x": "0.422338788",
      "y": "-0.019429156"
    },
    {
      "turn": "-0.300965839",
      "x": "0.413016654",
      "y": "-0.009052663"
    },
    {
      "turn": "-0.305730681",
      "x": "0.40381793",
      "y": "-0.008433553"
    },
    {
      "turn": "-0.310508253",
      "x": "0.394586212",
      "y": "-0.002787364"
    },
    {
      "turn": "-0.315298789",
      "x": "0.385496725",
      "y": "0.002889647"
    },
    {
      "turn": "-0.320102524",
      "x": "0.376347007",
      "y": "0.008696495"
    },
    {
      "turn": "-0.324919696",
      "x": "0.36735353",
      "y": "0.014536997"
    },
    {
      "turn": "-0.329750547",
      "x": "0.358304594",
      "y": "0.02050269"
    },
    {
      "turn": "-0.33459532",
      "x": "0.349409885",
      "y": "0.026504948"
    },
    {
      "turn": "-0.339454259",
      "x": "0.34046447",
      "y": "0.049822856"
    },
    {
      "turn": "-0.344327613",
      "x": "0.331641491",
      "y": "0.04273265"
    },
    {
      "turn": "-0.349215633",
      "x": "0.32283207",
      "y": "0.045037638"
    },
    {
      "turn": "-0.354118573",
      "x": "0.314143137",
      "y": "0.051387976"
    },
    {
      "turn": "-0.359036687",
      "x": "0.305412766",
      "y": "0.075257286"
    },
    {
      "turn": "-0.363970234",
      "x": "0.296800789",
      "y": "0.072630054"
    },
    {
      "turn": "-0.368919477",
      "x": "0.288211863",
      "y": "0.070847831"
    },
    {
      "turn": "-0.373884679",
      "x": "0.279739251",
      "y": "0.077508419"
    },
    {
      "turn": "-0.378866109",
      "x": "0.271234601",
      "y": "0.084240223"
    },
    {
      "turn": "-0.383864035",
      "x": "0.26287396",
      "y": "0.091022783"
    },
    {
      "turn": "-0.388878732",
      "x": "0.254486153",
      "y": "0.097901856"
    },
    {
      "turn": "-0.393910476",
      "x": "0.246240141",
      "y": "0.104834452"
    },
    {
      "turn": "-0.398959546",
      "x": "0.237971621",
      "y": "0.129829253"
    },
    {
      "turn": "-0.404026226",
      "x": "0.229812912",
      "y": "0.127788581"
    },
    {
      "turn": "-0.409110801",
      "x": "0.221696035",
      "y": "0.126076349"
    },
    {
      "turn": "-0.414213562",
      "x": "0.213686915",
      "y": "0.133332786"
    },
    {
      "turn": "-0.419334802",
      "x": "0.205664353",
      "y": "0.158895966"
    },
    {
      "turn": "-0.424474816",
      "x": "0.197747349",
      "y": "0.152573472"
    },
    {
      "turn": "-0.429633906",
      "x": "0.189881459",
      "y": "0.167582574"
    },
    {
      "turn": "-0.434812375",
      "x": "0.182088947",
      "y": "0.164464336"
    },
    {
      "turn": "-0.440010531",
      "x": "0.174352161",
      "y": "0.170521668"
    },
    {
      "turn": "-0.445228685",
      "x": "0.166716529",
      "y": "0.178205262"
    },
    {
      "turn": "-0.450467154",
      "x": "0.15908119",
      "y": "0.203361352"
    },
    {
      "turn": "-0.455726256",
      "x": "0.151544748",
      "y": "0.202006418"
    },
    {
      "turn": "-0.461006314",
      "x": "0.144073197",
      "y": "0.220402726"
    },
    {
      "turn": "-0.466307658",
      "x": "0.136668254",
      "y": "0.219178189"
    },
    {
      "turn": "-0.471630619",
      "x": "0.129332755",
      "y": "0.237717662"
    },
    {
      "turn": "-0.476975533",
      "x": "0.122061566",
      "y": "0.236621177"
    },
    {
      "turn": "-0.482342741",
      "x": "0.114864354",
      "y": "0.252763293"
    },
    {
      "turn": "-0.487732589",
      "x": "0.107729133",
      "y": "0.241795159"
    },
    {
      "turn": "-0.493145426",
      "x": "0.1006724",
      "y": "0.257408262"
    },
    {
      "turn": "-0.498581608",
      "x": "0.093681125",
      "y": "0.258334195"
    },
    {
      "turn": "-0.504041494",
      "x": "0.086761219",
      "y": "0.266685533"
    },
    {
      "turn": "-0.509525449",
      "x": "0.079934391",
      "y": "0.275120446"
    },
    {
      "turn": "-0.515033843",
      "x": "0.073135046",
      "y": "0.302095374"
    },
    {
      "turn": "-0.520567051",
      "x": "0.066420594",
      "y": "0.292146176"
    },
    {
      "turn": "-0.526125451",
      "x": "0.059798033",
      "y": "0.309031407"
    },
    {
      "turn": "-0.531709432",
      "x": "0.053230828",
      "y": "0.309408822"
    },
    {
      "turn": "-0.537319382",
      "x": "0.046754244",
      "y": "0.326063963"
    },
    {
      "turn": "-0.5429557",
      "x": "0.040334573",
      "y": "0.32690225"
    },
    {
      "turn": "-0.548618787",
      "x": "0.03400765",
      "y": "0.343141625"
    },
    {
      "turn": "-0.554309051",
      "x": "0.027738066",
      "y": "0.344621132"
    },
    {
      "turn": "-0.560026908",
      "x": "0.021562136",
      "y": "0.360455382"
    },
    {
      "turn": "-0.565772778",
      "x": "0.015444502",
      "y": "0.36256007"
    },
    {
      "turn": "-0.571547087",
      "x": "0.009421492",
      "y": "0.37158807"
    },
    {
      "turn": "-0.577350269",
      "x": "0.003478661",
      "y": "0.380730039"
    },
    {
      "turn": "-0.583182763",
      "x": "-0.002410583",
      "y": "0.398864657"
    },
    {
      "turn": "-0.589045016",
      "x": "-0.008229043",
      "y": "0.399076193"
    },
    {
      "turn": "-0.594937482",
      "x": "-0.013930486",
      "y": "0.408311093"
    },
    {
      "turn": "-0.600860619",
      "x": "-0.019563631",
      "y": "0.417672481"
    },
    {
      "turn": "-0.606814896",
      "x": "-0.025134706",
      "y": "0.426978682"
    },
    {
      "turn": "-0.612800788",
      "x": "-0.030610437",
      "y": "0.436436374"
    },
    {
      "turn": "-0.618818777",
      "x": "-0.036019831",
      "y": "0.445841233"
    },
    {
      "turn": "-0.624869352",
      "x": "-0.041336477",
      "y": "0.455392365"
    },
    {
      "turn": "-0.630953011",
      "x": "-0.046582545",
      "y": "0.47301983"
    },
    {
      "turn": "-0.637070261",
      "x": "-0.05176518",
      "y": "0.474504394"
    },
    {
      "turn": "-0.643221614",
      "x": "-0.05681842",
      "y": "0.484128184"
    },
    {
      "turn": "-0.649407593",
      "x": "-0.061816925",
      "y": "0.493857501"
    },
    {
      "turn": "-0.655628729",
      "x": "-0.066727968",
      "y": "0.5060009"
    },
    {
      "turn": "-0.661885561",
      "x": "-0.071565984",
      "y": "0.513324572"
    },
    {
      "turn": "-0.668178638",
      "x": "-0.076439869",
      "y": "0.523125304"
    },
    {
      "turn": "-0.674508517",
      "x": "-0.081269086",
      "y": "0.533021514"
    },
    {
      "turn": "-0.680875765",
      "x": "-0.086131218",
      "y": "0.542875363"
    },
    {
      "turn": "-0.687280959",
      "x": "-0.090947325",
      "y": "0.55285077"
    },
    {
      "turn": "-0.693724684",
      "x": "-0.095796313",
      "y": "0.562785083"
    },
    {
      "turn": "-0.700207538",
      "x": "-0.100597853",
      "y": "0.572836663"
    },
    {
      "turn": "-0.706730127",
      "x": "-0.10543221",
      "y": "0.582848401"
    },
    {
      "turn": "-0.713293068",
      "x": "-0.110217728",
      "y": "0.592973102"
    },
    {
      "turn": "-0.719896989",
      "x": "-0.115035973",
      "y": "0.603059206"
    },
    {
      "turn": "-0.726542528",
      "x": "-0.119804022",
      "y": "0.613253954"
    },
    {
      "turn": "-0.733230336",
      "x": "-0.124604679",
      "y": "0.62341134"
    },
    {
      "turn": "-0.739961075",
      "x": "-0.129353814",
      "y": "0.633673042"
    },
    {
      "turn": "-0.746735418",
      "x": "-0.134135411",
      "y": "0.643898606"
    },
    {
      "turn": "-0.75355405",
      "x": "-0.138864194",
      "y": "0.654224145"
    },
    {
      "turn": "-0.76041767",
      "x": "-0.143625266",
      "y": "0.664514762"
    },
    {
      "turn": "-0.767326988",
      "x": "-0.148332267",
      "y": "0.674901003"
    },
    {
      "turn": "-0.774282728",
      "x": "-0.153071355",
      "y": "0.68525353"
    },
    {
      "turn": "-0.781285627",
      "x": "-0.157755147",
      "y": "0.695697316"
    },
    {
      "turn": "-0.788336435",
      "x": "-0.162470799",
      "y": "0.706108592"
    },
    {
      "turn": "-0.795435917",
      "x": "-0.167129965",
      "y": "0.716606751"
    },
    {
      "turn": "-0.802584852",
      "x": "-0.171820736",
      "y": "0.727073596"
    },
    {
      "turn": "-0.809784033",
      "x": "-0.176453864",
      "y": "0.737622937"
    },
    {
      "turn": "-0.81703427",
      "x": "-0.181118317",
      "y": "0.748142155"
    },
    {
      "turn": "-0.824336386",
      "x": "-0.185724004",
      "y": "0.758739472"
    },
    {
      "turn": "-0.831691221",
      "x": "-0.19036071",
      "y": "0.769307853"
    },
    {
      "turn": "-0.839099631",
      "x": "-0.194937563",
      "y": "0.779949924"
    },
    {
      "turn": "-0.846562489",
      "x": "-0.199545101",
      "y": "0.790564243"
    },
    {
      "turn": "-0.854080685",
      "x": "-0.204091732",
      "y": "0.801247831"
    },
    {
      "turn": "-0.861655127",
      "x": "-0.20866869",
      "y": "0.811904849"
    },
    {
      "turn": "-0.869286738",
      "x": "-0.213183724",
      "y": "0.822626706"
    },
    {
      "turn": "-0.876976463",
      "x": "-0.2177287",
      "y": "0.833323171"
    },
    {
      "turn": "-0.884725265",
      "x": "-0.222210769",
      "y": "0.844080036"
    },
    {
      "turn": "-0.892534124",
      "x": "-0.226722371",
      "y": "0.854812686"
    },
    {
      "turn": "-0.900404044",
      "x": "-0.231170118",
      "y": "0.865601285"
    },
    {
      "turn": "-0.908336046",
      "x": "-0.235646962",
      "y": "0.876366848"
    },
    {
      "turn": "-0.916331174",
      "x": "-0.240059041",
      "y": "0.887183898"
    },
    {
      "turn": "-0.924390492",
      "x": "-0.244499756",
      "y": "0.89797909"
    },
    {
      "turn": "-0.932515086",
      "x": "-0.24887483",
      "y": "0.9088213"
    },
    {
      "turn": "-0.940706067",
      "x": "-0.253278055",
      "y": "0.91964283"
    },
    {
      "turn": "-0.948964567",
      "x": "-0.2576148",
      "y": "0.930506898"
    },
    {
      "turn": "-0.957291742",
      "x": "-0.261979187",
      "y": "0.94135147"
    },
    {
      "turn": "-0.965688775",
      "x": "-0.266276289",
      "y": "0.952234089"
    },
    {
      "turn": "-0.974156871",
      "x": "-0.270600499",
      "y": "0.963098395"
    },
    {
      "turn": "-0.982697263",
      "x": "-0.274856659",
      "y": "0.973996251"
    },
    {
      "turn": "-0.991311211",
      "x": "-0.279139367",
      "y": "0.984876983"
    },
    {
      "turn": "-1",
      "x": "-0.276937329",
      "y": "0.997849259"
    },
    {
      "turn": "-1",
      "x": "-0.276937329",
      "y": "0.999873316"
    },
    {
      "turn": "-1.008764946",
      "x": "-0.273684632",
      "y": "1.01048606"
    },
    {
      "turn": "-1.017607393",
      "x": "-0.246504693",
      "y": "1.021202724"
    },
    {
      "turn": "-1.026528714",
      "x": "-0.26719754",
      "y": "1.031868487"
    },
    {
      "turn": "-1.035530314",
      "x": "-0.260050181",
      "y": "1.042549308"
    },
    {
      "turn": "-1.044613628",
      "x": "-0.260602176",
      "y": "1.053194693"
    },
    {
      "turn": "-1.053780125",
      "x": "-0.246273161",
      "y": "1.063906567"
    },
    {
      "turn": "-1.063031307",
      "x": "-0.253927414",
      "y": "1.074580411"
    },
    {
      "turn": "-1.07236871",
      "x": "-0.243652507",
      "y": "1.085267993"
    },
    {
      "turn": "-1.081793905",
      "x": "-0.247175289",
      "y": "1.095930281"
    },
    {
      "turn": "-1.091308501",
      "x": "-0.231869106",
      "y": "1.106627081"
    },
    {
      "turn": "-1.100914143",
      "x": "-0.240347856",
      "y": "1.117304297"
    },
    {
      "turn": "-1.110612515",
      "x": "-0.226106926",
      "y": "1.127977322"
    },
    {
      "turn": "-1.120405341",
      "x": "-0.233447196",
      "y": "1.138646271"
    },
    {
      "turn": "-1.130294386",
      "x": "-0.219112879",
      "y": "1.149312215"
    },
    {
      "turn": "-1.140281458",
      "x": "-0.22647541",
      "y": "1.159973443"
    },
    {
      "turn": "-1.150368407",
      "x": "-0.214191086",
      "y": "1.170625259"
    },
    {
      "turn": "-1.160557129",
      "x": "-0.219434622",
      "y": "1.181268512"
    },
    {
      "turn": "-1.170849566",
      "x": "-0.205093846",
      "y": "1.191909963"
    },
    {
      "turn": "-1.181247708",
      "x": "-0.212326978",
      "y": "1.202545442"
    },
    {
      "turn": "-1.191753593",
      "x": "-0.201020976",
      "y": "1.213159842"
    },
    {
      "turn": "-1.202369311",
      "x": "-0.205154641",
      "y": "1.223767654"
    },
    {
      "turn": "-1.213097004",
      "x": "-0.196655197",
      "y": "1.234368424"
    },
    {
      "turn": "-1.223938869",
      "x": "-0.197919797",
      "y": "1.24494609"
    },
    {
      "turn": "-1.234897157",
      "x": "-0.188493151",
      "y": "1.255529247"
    },
    {
      "turn": "-1.245974177",
      "x": "-0.190624649",
      "y": "1.266085767"
    },
    {
      "turn": "-1.257172299",
      "x": "-0.186926023",
      "y": "1.276635867"
    },
    {
      "turn": "-1.268493953",
      "x": "-0.18327142",
      "y": "1.287146249"
    },
    {
      "turn": "-1.279941632",
      "x": "-0.165258695",
      "y": "1.297681852"
    },
    {
      "turn": "-1.291517897",
      "x": "-0.17586235",
      "y": "1.308196544"
    },
    {
      "turn": "-1.303225373",
      "x": "-0.170806566",
      "y": "1.318660794"
    },
    {
      "turn": "-1.315066758",
      "x": "-0.168399695",
      "y": "1.329111236"
    },
    {
      "turn": "-1.327044822",
      "x": "-0.153725377",
      "y": "1.3395663"
    },
    {
      "turn": "-1.339162408",
      "x": "-0.160885728",
      "y": "1.350009384"
    },
    {
      "turn": "-1.351422438",
      "x": "-0.15666726",
      "y": "1.360392003"
    },
    {
      "turn": "-1.363827914",
      "x": "-0.153322739",
      "y": "1.370762598"
    },
    {
      "turn": "-1.37638192",
      "x": "-0.149493974",
      "y": "1.381131559"
    },
    {
      "turn": "-1.389087628",
      "x": "-0.145713031",
      "y": "1.391457584"
    },
    {
      "turn": "-1.401948294",
      "x": "-0.137331291",
      "y": "1.40177865"
    },
    {
      "turn": "-1.414967272",
      "x": "-0.138058922",
      "y": "1.412073135"
    },
    {
      "turn": "-1.428148007",
      "x": "-0.134186279",
      "y": "1.422326988"
    },
    {
      "turn": "-1.441494043",
      "x": "-0.130362733",
      "y": "1.432557149"
    },
    {
      "turn": "-1.455009029",
      "x": "-0.12646989",
      "y": "1.442770312"
    },
    {
      "turn": "-1.468696716",
      "x": "-0.122626832",
      "y": "1.452947858"
    },
    {
      "turn": "-1.482560969",
      "x": "-0.112789031",
      "y": "1.463102395"
    },
    {
      "turn": "-1.496605763",
      "x": "-0.11485357",
      "y": "1.473243619"
    },
    {
      "turn": "-1.510835194",
      "x": "-0.110923924",
      "y": "1.483315904"
    },
    {
      "turn": "-1.525253479",
      "x": "-0.107045265",
      "y": "1.493383496"
    },
    {
      "turn": "-1.539864964",
      "x": "-0.101703521",
      "y": "1.503408102"
    },
    {
      "turn": "-1.554674125",
      "x": "-0.099204403",
      "y": "1.513413838"
    },
    {
      "turn": "-1.569685577",
      "x": "-0.094533616",
      "y": "1.523369448"
    },
    {
      "turn": "-1.584904077",
      "x": "-0.09112018",
      "y": "1.533307333"
    },
    {
      "turn": "-1.600334529",
      "x": "-0.086957129",
      "y": "1.543195001"
    },
    {
      "turn": "-1.615981993",
      "x": "-0.082653305",
      "y": "1.553062084"
    },
    {
      "turn": "-1.631851687",
      "x": "-0.077582739",
      "y": "1.562878724"
    },
    {
      "turn": "-1.647948997",
      "x": "-0.073895946",
      "y": "1.57267693"
    },
    {
      "turn": "-1.664279482",
      "x": "-0.069379528",
      "y": "1.58241341"
    },
    {
      "turn": "-1.680848881",
      "x": "-0.064731271",
      "y": "1.592139426"
    },
    {
      "turn": "-1.697663119",
      "x": "-0.060070121",
      "y": "1.601794069"
    },
    {
      "turn": "-1.71472832",
      "x": "-0.055251716",
      "y": "1.61144852"
    },
    {
      "turn": "-1.732050808",
      "x": "-0.050417389",
      "y": "1.621013237"
    },
    {
      "turn": "-1.74963712",
      "x": "-0.045430275",
      "y": "1.630598507"
    },
    {
      "turn": "-1.767494016",
      "x": "-0.040424271",
      "y": "1.640053981"
    },
    {
      "turn": "-1.785628485",
      "x": "-0.027453899",
      "y": "1.649571266"
    },
    {
      "turn": "-1.804047755",
      "x": "-0.030093811",
      "y": "1.658957539"
    },
    {
      "turn": "-1.822759308",
      "x": "-0.024563473",
      "y": "1.668367282"
    },
    {
      "turn": "-1.841770886",
      "x": "-0.019429156",
      "y": "1.677641095"
    },
    {
      "turn": "-1.861090505",
      "x": "-0.006888627",
      "y": "1.686983346"
    },
    {
      "turn": "-1.880726465",
      "x": "-0.008433553",
      "y": "1.696189152"
    },
    {
      "turn": "-1.900687369",
      "x": "-0.000489295",
      "y": "1.705413788"
    },
    {
      "turn": "-1.920982127",
      "x": "0.002889647",
      "y": "1.714510796"
    },
    {
      "turn": "-1.941619979",
      "x": "0.015761194",
      "y": "1.723652993"
    },
    {
      "turn": "-1.962610506",
      "x": "0.014536997",
      "y": "1.732669589"
    },
    {
      "turn": "-1.983963644",
      "x": "0.023852088",
      "y": "1.741695406"
    },
    {
      "turn": "-2.005689708",
      "x": "0.026504948",
      "y": "1.750601076"
    },
    {
      "turn": "-2.027799402",
      "x": "0.039705541",
      "y": "1.75953553"
    },
    {
      "turn": "-2.050303842",
      "x": "0.038789855",
      "y": "1.76835191"
    },
    {
      "turn": "-2.073214574",
      "x": "0.045067684",
      "y": "1.77716793"
    },
    {
      "turn": "-2.096543599",
      "x": "0.051387976",
      "y": "1.785856961"
    },
    {
      "turn": "-2.12030339",
      "x": "0.075257286",
      "y": "1.794587234"
    },
    {
      "turn": "-2.144506921",
      "x": "0.064295475",
      "y": "1.803199211"
    },
    {
      "turn": "-2.169167685",
      "x": "0.075692914",
      "y": "1.811788137"
    },
    {
      "turn": "-2.194299731",
      "x": "0.077508419",
      "y": "1.820276605"
    },
    {
      "turn": "-2.219917683",
      "x": "0.091040809",
      "y": "1.828765399"
    },
    {
      "turn": "-2.246036774",
      "x": "0.091022783",
      "y": "1.837148295"
    },
    {
      "turn": "-2.272672879",
      "x": "0.104221783",
      "y": "1.845513847"
    },
    {
      "turn": "-2.299842547",
      "x": "0.104834452",
      "y": "1.853780541"
    },
    {
      "turn": "-2.327563039",
      "x": "0.118348244",
      "y": "1.862028379"
    },
    {
      "turn": "-2.355852366",
      "x": "0.118939218",
      "y": "1.870178476"
    },
    {
      "turn": "-2.384729328",
      "x": "0.133320879",
      "y": "1.878303965"
    },
    {
      "turn": "-2.414213562",
      "x": "0.133332786",
      "y": "1.886336793"
    },
    {
      "turn": "-2.444325587",
      "x": "0.140640855",
      "y": "1.894335647"
    },
    {
      "turn": "-2.475086853",
      "x": "0.14801077",
      "y": "1.902222774"
    },
    {
      "turn": "-2.506519797",
      "x": "0.172161973",
      "y": "1.910118541"
    },
    {
      "turn": "-2.538647896",
      "x": "0.166754036",
      "y": "1.917911053"
    },
    {
      "turn": "-2.571495734",
      "x": "0.170521668",
      "y": "1.925647839"
    },
    {
      "turn": "-2.605089065",
      "x": "0.178205262",
      "y": "1.933283471"
    },
    {
      "turn": "-2.639454881",
      "x": "0.195286321",
      "y": "1.94091881"
    },
    {
      "turn": "-2.674621494",
      "x": "0.193931387",
      "y": "1.948455252"
    },
    {
      "turn": "-2.710618609",
      "x": "0.21382113",
      "y": "1.955926803"
    },
    {
      "turn": "-2.747477419",
      "x": "0.212596593",
      "y": "1.963331746"
    },
    {
      "turn": "-2.785230695",
      "x": "0.224480688",
      "y": "1.970667245"
    },
    {
      "turn": "-2.823912886",
      "x": "0.225507501",
      "y": "1.977931485"
    },
    {
      "turn": "-2.863560231",
      "x": "0.233612529",
      "y": "1.985135646"
    },
    {
      "turn": "-2.904210878",
      "x": "0.241795159",
      "y": "1.992240912"
    },
    {
      "turn": "-2.945905005",
      "x": "0.259030599",
      "y": "1.9993276"
    },
    {
      "turn": "-2.988684963",
      "x": "0.258334195",
      "y": "2.006324184"
    },
    {
      "turn": "-3.032595423",
      "x": "0.277224079",
      "y": "2.013238781"
    },
    {
      "turn": "-3.077683537",
      "x": "0.275808433",
      "y": "2.02009559"
    },
    {
      "turn": "-3.123999113",
      "x": "0.283566624",
      "y": "2.026864954"
    },
    {
      "turn": "-3.171594802",
      "x": "0.29217627",
      "y": "2.03354924"
    },
    {
      "turn": "-3.220526311",
      "x": "0.310029847",
      "y": "2.040201967"
    },
    {
      "turn": "-3.270852618",
      "x": "0.309537111",
      "y": "2.04677202"
    },
    {
      "turn": "-3.322636226",
      "x": "0.321793106",
      "y": "2.053245756"
    },
    {
      "turn": "-3.375943423",
      "x": "0.32690225",
      "y": "2.059651451"
    },
    {
      "turn": "-3.430844574",
      "x": "0.344389729",
      "y": "2.06599235"
    },
    {
      "turn": "-3.487414444",
      "x": "0.344621132",
      "y": "2.072266018"
    },
    {
      "turn": "-3.545732543",
      "x": "0.353543032",
      "y": "2.078437864"
    },
    {
      "turn": "-3.605883509",
      "x": "0.362571806",
      "y": "2.084532839"
    },
    {
      "turn": "-3.667957531",
      "x": "0.377216888",
      "y": "2.090578508"
    },
    {
      "turn": "-3.732050808",
      "x": "0.3807136",
      "y": "2.096539814"
    },
    {
      "turn": "-3.798266061",
      "x": "0.393158235",
      "y": "2.102410583"
    },
    {
      "turn": "-3.866713095",
      "x": "0.399076193",
      "y": "2.108210369"
    },
    {
      "turn": "-3.937509419",
      "x": "0.408311093",
      "y": "2.113930486"
    },
    {
      "turn": "-4.010780934",
      "x": "0.417672481",
      "y": "2.119563631"
    },
    {
      "turn": "-4.086662697",
      "x": "0.43207234",
      "y": "2.125134706"
    },
    {
      "turn": "-4.16529977",
      "x": "0.436406128",
      "y": "2.130627205"
    },
    {
      "turn": "-4.24684816",
      "x": "0.449862689",
      "y": "2.136019831"
    },
    {
      "turn": "-4.331475874",
      "x": "0.455362099",
      "y": "2.141349736"
    },
    {
      "turn": "-4.419364096",
      "x": "0.466915422",
      "y": "2.146582545"
    },
    {
      "turn": "-4.510708504",
      "x": "0.474504394",
      "y": "2.151745203"
    },
    {
      "turn": "-4.605720746",
      "x": "0.489123244",
      "y": "2.15681963"
    },
    {
      "turn": "-4.704630109",
      "x": "0.49382718",
      "y": "2.16182974"
    },
    {
      "turn": "-4.807685394",
      "x": "0.504027724",
      "y": "2.166727968"
    },
    {
      "turn": "-4.915157031",
      "x": "0.513324572",
      "y": "2.171559527"
    },
    {
      "turn": "-5.027339492",
      "x": "0.523125304",
      "y": "2.176442022"
    },
    {
      "turn": "-5.144554016",
      "x": "0.533021485",
      "y": "2.181262629"
    },
    {
      "turn": "-5.267151723",
      "x": "0.542875363",
      "y": "2.18613337"
    },
    {
      "turn": "-5.395517174",
      "x": "0.552850742",
      "y": "2.190940868"
    },
    {
      "turn": "-5.530072445",
      "x": "0.562785083",
      "y": "2.195798465"
    },
    {
      "turn": "-5.67128182",
      "x": "0.572836634",
      "y": "2.200591396"
    },
    {
      "turn": "-5.819657198",
      "x": "0.582848401",
      "y": "2.205434362"
    },
    {
      "turn": "-5.975764364",
      "x": "0.592973074",
      "y": "2.210211272"
    },
    {
      "turn": "-6.140230267",
      "x": "0.603059206",
      "y": "2.215038126"
    },
    {
      "turn": "-6.313751515",
      "x": "0.613253926",
      "y": "2.219797566"
    },
    {
      "turn": "-6.497104326",
      "x": "0.62341134",
      "y": "2.224606831"
    },
    {
      "turn": "-6.691156238",
      "x": "0.633673014",
      "y": "2.229347358"
    },
    {
      "turn": "-6.896879945",
      "x": "0.643898606",
      "y": "2.234137535"
    },
    {
      "turn": "-7.115369722",
      "x": "0.654224117",
      "y": "2.238857821"
    },
    {
      "turn": "-7.347861045",
      "x": "0.664552899",
      "y": "2.243627307"
    },
    {
      "turn": "-7.595754113",
      "x": "0.674866475",
      "y": "2.248326381"
    },
    {
      "turn": "-7.860642258",
      "x": "0.68525353",
      "y": "2.253073279"
    },
    {
      "turn": "-8.144346428",
      "x": "0.695697291",
      "y": "2.257749374"
    },
    {
      "turn": "-8.44895734",
      "x": "0.706129197",
      "y": "2.262472678"
    },
    {
      "turn": "-8.776887357",
      "x": "0.716576167",
      "y": "2.267124494"
    },
    {
      "turn": "-9.130934819",
      "x": "0.727073596",
      "y": "2.271822526"
    },
    {
      "turn": "-9.514364454",
      "x": "0.737622913",
      "y": "2.276448494"
    },
    {
      "turn": "-9.931008767",
      "x": "0.748172647",
      "y": "2.28112004"
    },
    {
      "turn": "-10.38539708",
      "x": "0.758704909",
      "y": "2.285719047"
    },
    {
      "turn": "-10.88292144",
      "x": "0.769307853",
      "y": "2.290362325"
    },
    {
      "turn": "-11.430052303",
      "x": "0.779949903",
      "y": "2.294932718"
    },
    {
      "turn": "-12.034622321",
      "x": "0.790582958",
      "y": "2.299546675"
    },
    {
      "turn": "-12.706204736",
      "x": "0.801216567",
      "y": "2.304087174"
    },
    {
      "turn": "-13.456625313",
      "x": "0.811904849",
      "y": "2.308670176"
    },
    {
      "turn": "-14.300666257",
      "x": "0.822626687",
      "y": "2.313179269"
    },
    {
      "turn": "-15.257051688",
      "x": "0.833323171",
      "y": "2.317730131"
    },
    {
      "turn": "-16.349855476",
      "x": "0.844080017",
      "y": "2.322206477"
    },
    {
      "turn": "-17.610558829",
      "x": "0.854844396",
      "y": "2.326723732"
    },
    {
      "turn": "-19.081136688",
      "x": "0.86556463",
      "y": "2.331166257"
    },
    {
      "turn": "-20.818827605",
      "x": "0.876366848",
      "y": "2.335648209"
    },
    {
      "turn": "-22.903765548",
      "x": "0.887183882",
      "y": "2.3400553"
    },
    {
      "turn": "-25.451699579",
      "x": "0.897987796",
      "y": "2.344500984"
    },
    {
      "turn": "-28.636253283",
      "x": "0.908799212",
      "y": "2.348871247"
    },
    {
      "turn": "-32.730263715",
      "x": "0.91964283",
      "y": "2.353279219"
    },
    {
      "turn": "-38.188459297",
      "x": "0.930506883",
      "y": "2.357611309"
    },
    {
      "turn": "-45.829351174",
      "x": "0.941375587",
      "y": "2.361980287"
    },
    {
      "turn": "-57.289961631",
      "x": "0.952198646",
      "y": "2.366273181"
    },
    {
      "turn": "-76.390009311",
      "x": "0.963102279",
      "y": "2.370601492"
    },
    {
      "turn": "-114.588650129",
      "x": "0.973984588",
      "y": "2.374853731"
    },
    {
      "turn": "-229.181663609",
      "x": "0.984876983",
      "y": "2.37914033"
    },
    {
      "turn": "-666666.666644453",
      "x": "0.995762021",
      "y": "2.376938434"
    },
    {
      "turn": "-666666.666644453",
      "x": "3.045690964",
      "y": "2.376938434"
    }
  ]
}

DISCUSSION

Discussion

Talk strategy, share methods, ask why you are stuck. Every signed-in user can post. Posts carry your public byline, the same name your records use; the #number after it is the account's signup ordinal, so a name cannot be worn by someone else. New posts appear after an automated review.

有亿点难NUE_13#310 replies1h ago