Statistics

Problem Statement for "PizzaDivision"

Problem Statement

You want to divide a round pizza (represented by a circle) into two equal halves with one straight cut. The pizza contains several toppings, represented by points strictly inside the circle. The cut is called beautiful if the two halves of the pizza are mirror images of each other: for every topping in one half there is a topping in the other half in the symmetric point (we don't care about the toppings that are exactly on the cut).

For example, the cut represented by the red line in the following picture is the only beautiful cut for that pizza (black dots are toppings):

This pizza has four different beautiful cuts, all shown by red lines:

You are to count the number of different beautiful cuts for a given pizza. You are given a String[] toppings, each element representing a topping in the form "x y", where x and y are the coordinates of that topping. You may assume that the pizza is large enough to have all those toppings inside. The point of origin coincides with the center of the pizza (that is, the center of the pizza has the coordinates "0 0"). Return the number of different beautiful cuts, or -1 if there are infinitely many of them.

Definition

Class:
PizzaDivision
Method:
howMany
Parameters:
String[]
Returns:
int
Method signature:
int howMany(String[] toppings)
(be sure your method is public)

Notes

  • Two points A and B are symmetric with respect to line L, if and only if either A and B coincide and lie on L or L is perpendicular to AB and crosses it in its middle point.

Constraints

  • toppings will contain between 1 and 50 elements, inclusive.
  • Each element of toppings will be formatted as "x y" (quotes for clarity only), where x and y are integers between -500 and 500, inclusive, with no extra leading zeroes.
  • All elements of toppings will be different.

Examples

  1. {"0 110", "0 70", "-75 20", "75 20", "-25 -50", "25 -50"}

    Returns: 1

    The first example from the problem statement.

  2. {"0 70", "70 0", "0 -70", "-70 0"}

    Returns: 4

    The second example from the problem statement.

  3. {"0 0"}

    Returns: -1

    Any cut passing through the center suffices.

  4. {"3 -4"}

    Returns: 1

  5. {"3 -4", "-3 4"}

    Returns: 2

  6. {"1 2", "3 4"}

    Returns: 0

  7. {"-300 100", "-200 100", "-100 100", "100 100", "200 100", "300 100", "-300 -100", "-200 -100", "-100 -100", "100 -100", "200 -100", "300 -100"}

    Returns: 2

  8. {"5 7","-7 6","-6 2","7 -2","-5 5","-4 9","-9 3","2 7","0 -8","-7 -7"}

    Returns: 0

  9. {"2 -9","-2 4","-3 -5","-6 0","-4 -2","-4 0","4 -7","-8 1","-1 1","4 -3","-8 2","-9 3","-8 -3","-6 -4","-7 5","7 -5","-4 7","3 -6","7 4","-1 2","9 1","0 -3","-5 8","4 2","0 -4","7 0","-6 6","-4 -6","-4 9","6 1","-9 -4","0 6","1 3","9 2","-8 -4","-6 3","8 2","-2 -1","-3 -3","-3 1","3 -1","3 -8","-1 -3","-2 -8","-6 -6","5 -3","-3 -7","9 0","-1 9","-8 -2"}

    Returns: 0

  10. {"20 4","71 43","26 60","43 57","-11 20","58 -32","96 -27","47 -44","71 -41","2 94"}

    Returns: 0

  11. {"-96 8","45 -69","86 -18","79 43","-48 55","77 26","-21 70","-34 49","49 10","-86 -41","12 -77","40 36","-54 51","-44 70","75 27","-4 -96","-18 19","21 91","-36 10","-55 -26","-29 3","-70 -46","23 41","48 51","-58 74","39 28","-74 -63","-46 -88","13 -17","92 -8","76 33","45 -73","-33 -34","26 -70","-7 -93","67 -10","48 28","68 22","-17 67","-13 15","9 60","16 -4","-31 -29","7 -4","-8 17","16 36","62 19","28 87","-25 -44","-51 -71"}

    Returns: 0

  12. {"130 32","-158 -65","308 -86","-314 -46","64 438","291 414","161 376","349 253","238 114","-364 140"}

    Returns: 0

  13. {"-15 -477","-362 411","-10 236","426 -355","-174 -213","158 319","-284 -378","-90 -2","-73 176","383 44","-36 -470","-244 -421","267 -120","-146 -33","28 371","302 1","-179 347","-185 -350","-494 -106","-230 377","-58 117","114 270","-129 364","-339 330","385 -494","-488 -155","299 340","-372 334","-171 -302","-279 -8","147 -386","-362 328","-339 40","316 67","-429 197","-377 267","-465 -178","97 -19","407 231","211 330","126 -116","408 -401","42 407","284 58","-445 380","67 492","283 -1","452 -410","-417 -419","-384 235"}

    Returns: 0

  14. {"8 -2","-6 1","4 1","4 -1","3 0","-2 -8","-2 8","-6 -1","8 2"}

    Returns: 1

  15. {"-8 14","-2 -16","12 5","4 -7","18 1","4 19","-1 -8","-14 -8","-17 7","1 -18","-15 -3","8 -14","-7 -4","3 -2","-7 9","-14 5","-17 -6","-2 10","8 12","16 -2","3 -15","-11 16","2 16","6 9","10 -11","-11 -10","13 -13","-6 17","12 -8","-5 -14","14 8","15 -10","11 -3","-15 10","-12 8","0 13","16 11","19 -4","-8 1","-16 -11","-3 2","-10 11","5 14","14 -5","10 2","11 10","-8 -12","-4 -19","-10 -15","-16 2"}

    Returns: 1

  16. {"33 11","-59 -31","-60 -63","90 -25","60 -63","65 34","-65 34","-90 -25","-33 11","59 -31"}

    Returns: 1

  17. {"-54 -83", "-46 54", "-5 -44", "-1 -31", "-14 47", "7 -5", "-45 -63", "-88 47", "-17 -9", "-26 -66", "40 56", "-67 69", "-49 -2", "2 62", "61 78", "-81 -32", "87 33", "-22 -53", "-43 -38", "57 28", "35 12", "-53 -15", "52 -16", "32 -44", "-73 68", "79 44", "3 56", "-66 26", "-87 41", "4 87", "22 53", "59 16", "-3 55", "3 19", "-26 8", "43 38", "54 46", "-16 22", "-3 -93", "45 63", "0 -37", "-7 5", "-40 -56", "40 19", "-8 -63", "-16 -89", "29 11", "-52 -21", "-58 -22", "4 -61"}

    Returns: 1

  18. {"-48 -221","342 296","-125 490","490 125","171 148","125 -490","-490 -125","-317 -394","194 467","-96 -442"}

    Returns: 1

  19. {"127 361","-267 -44","173 215","-365 -115","-321 -382","365 115","309 -344","-198 -263","21 -194","19 -315","-56 -459","-25 -48","-121 2","-190 221","94 -171","284 -392","50 96","482 -129","-96 50","196 142","-117 244","48 -25","244 117","261 -319","-265 77","56 459","-244 -117","267 44","-44 267","-311 223","-31 -411","-246 -238","-8 -484","-242 4","194 21","29 290","165 -269","-171 -94","338 -54","313 -102","6 363","46 -146","-213 294","-286 271","79 386","-309 344","-29 -290","98 71","190 -221"}

    Returns: 1

  20. {"77 15","282 14","-427 186","209 -52","49 -167","107 -324","350 -432","246 370","363 132","68 -353","-407 -26","68 353","-397 -181","-70 411","-397 181","-494 -98","246 -370","-38 -425","30 101","189 -337","-494 98","-319 -193","-427 -186","284 65","-38 425","189 337","314 -359","249 41","-367 -449","30 -101","-367 449","500 -36","107 324","-319 193","284 -65","282 -14","-70 -411","363 -132","355 -355","500 36","-447 -252","249 -41","355 355","-407 26","350 432","77 -15","-447 252","209 52","314 359","49 167"}

    Returns: 1

  21. {"-2 5","-3 1","2 -5","-3 -1","2 5","3 -1","3 1","-2 -5"}

    Returns: 2

  22. {"-16 11","-10 2","-5 -12","5 12","7 9","-11 -16","-3 11","2 -16","14 -8","5 -14","16 -11","-2 -10","9 6","1 -8","-13 0","9 -7","-11 -3","3 15","-14 8","-2 16","-7 -9","11 16","-9 -6","-4 19","13 0","10 -15","-19 -4","-15 -10","3 -11","10 -2","11 3","15 -3","7 -4","11 -10","-3 -15","-7 4","-15 3","-10 15","-1 8","-11 10","-5 14","4 -19","15 10","2 10","19 4","-9 7"}

    Returns: 2

  23. {"-8 -21","12 -19","8 21","82 -12","-82 12","-12 19","-78 -28","78 28"}

    Returns: 2

  24. {"37 12","97 5","61 -62","8 -84","-52 -77","-16 79","-37 -12","-2 -68","-12 37","-85 47","16 -79","-30 -41","44 72","-27 -28","-13 92","82 29","46 51","-46 -51","49 64","-67 36","9 -50","-49 -64","-82 -29","-76 -3","28 62","-9 50","76 3","-28 27","52 77","-28 -62","28 -27","27 28","67 -36","30 41","2 68","19 -66","-61 62","26 -6","85 -47","-44 -72","-26 6","-8 84","12 -37","-19 66","-97 -5","13 -92"}

    Returns: 2

  25. {"262 -16","-256 -58","189 425","-255 389","256 58","255 -389","-189 -425","-262 16"}

    Returns: 2

  26. {"-134 102","254 -278","-200 57","-355 48","49 259","-46 162","-305 211","-250 -106","85 -361","-190 -194","46 -162","-63 -333","305 -211","438 -217","-166 338","190 194","-20 -207","-49 -259","-259 49","366 314","426 226","85 348","283 -226","-283 226","250 106","-370 70","-42 487","-85 361","-438 217","42 -487","-333 63","370 -70","107 -346","355 -48","63 333","333 -63","200 -57","134 -102","-366 -314","-254 278","-107 346","259 -49","20 207","70 370","-85 -348","166 -338","-70 -370","-426 -226"}

    Returns: 2

  27. {"-4 -310","402 55","-45 259","276 52","-402 -55","276 -52","45 259","-276 -52","442 -410","402 -55","461 -145","22 145","-13 -2","318 -144","-402 55","4 -310","236 -123","45 -259","22 -145","-442 -410","282 -94","4 310","-442 410","230 460","13 2","-236 123","318 144","-282 -94","-318 -144","-230 -460","461 145","236 123","-461 -145","-236 -123","-22 -145","-22 145","-4 310","442 410","-13 2","282 94","-230 460","-276 52","-45 -259","-318 144","-282 94","13 -2","230 -460","-461 145"}

    Returns: 2

  28. {"6 0","-6 0","0 6","0 -6"}

    Returns: 4

  29. {"-11 13","0 -10","13 -4","10 -10","10 0","2 14","-11 8","-10 -10","11 -8","-10 10","-13 9","-9 -13","1 -3","-3 -1","8 11","-14 2","14 -2","5 15","13 -9","-6 8","7 14","17 -1","1 17","-10 0","-2 -14","11 -13","0 10","-1 3","-17 1","15 -5","14 -7","6 -8","13 11","4 13","9 13","-8 -11","-14 7","-15 5","-7 -14","8 6","-1 -17","-5 -15","-8 -6","-13 -11","3 1","-4 -13","-13 4","10 10"}

    Returns: 4

  30. {"-63 -9","63 9","-9 63","9 -63"}

    Returns: 4

  31. {"-39 -72","-47 -18","85 -15","33 38","-61 2","58 -19","-38 33","18 -47","47 18","40 28","28 -40","19 58","-16 -41","-44 -1","-85 15","-7 10","16 41","-10 -7","-19 -58","7 -10","72 -39","-81 -12","-40 -28","38 -33","-72 39","2 61","44 1","10 7","12 -81","-2 -61","-28 40","-15 -85","41 -16","61 -2","-12 81","15 85","-33 -38","-18 47","81 12","-1 44","-41 16","-58 19","39 72","1 -44"}

    Returns: 4

  32. {"386 352","446 -272","-446 272","-386 -352","-272 -446","352 -386","272 446","-352 386"}

    Returns: 4

  33. {"-37 -161","290 -287","374 -69","-337 230","230 337","-151 -67","-92 411","37 161","-354 -139","12 421","-290 287","421 -12","69 374","-139 354","67 -151","337 -230","-12 -421","-47 -57","411 92","151 67","32 213","161 -37","-161 37","-72 203","-287 -290","-57 47","57 -47","203 72","139 -354","72 -203","-69 -374","47 57","354 139","-203 -72","-32 -213","287 290","-230 -337","-213 32","-67 151","213 -32","-421 12","92 -411","-374 69","-411 -92"}

    Returns: 4

  34. {"239 274","415 -458","-274 -239","316 241","211 238","-211 238","233 -125","238 -211","238 211","-241 -316","469 -180","-125 233","-125 -233","-469 180","-458 415","458 -415","-241 316","233 125","-458 -415","-239 -274","-415 -458","274 239","241 -316","239 -274","-238 211","241 316","458 415","180 469","-238 -211","-415 458","-233 -125","-316 -241","-180 -469","180 -469","-274 239","-233 125","274 -239","415 458","-239 274","469 180","-211 -238","211 -238","125 233","125 -233","-180 469","-469 -180","316 -241","-316 241"}

    Returns: 4

  35. {"-245 145","-205 -11","100 -390","245 -145","17 420","-98 58","95 440","479 -85","120 -468","-187 243","-430 56","235 -106","118 -136","-468 -120","-451 300","334 -330","-18 -254","470 -212","86 313","-176 38","-450 134","-186 77","-412 310","264 -57","360 217","31 -283","98 -58","391 -66","382 -193","89 -185","-177 204","480 -251","-32 449","246 -311","340 295","320 373","303 -47","-263 -109","233 226","-353 242","409 188","256 -350","-214 -138","-246 311","-390 -100","-206 155","173 460","-391 66","157 -126","-305 379"}

    Returns: 1

  36. {"-230 -165","-236 193","-94 267","230 165","227 344","111 -213","-335 -310","426 222","26 -483","-270 85","28 466","11 412","94 -267","392 114","-26 483","-392 -114","-426 -222","-239 372","335 310","-111 213","-256 318","-97 446","213 111","-409 -168","-11 -412","-298 -381","-244 -398","-222 426","270 -85","-28 -466","-304 -23","97 -446","304 23","239 -372","244 398","236 -193","-227 -344","409 168","-213 -111","222 -426","256 -318","298 381"}

    Returns: 2

  37. {"92 -261","0 0","-411 -352","-371 318","-17 391","-485 -240","315 -355","166 -373","168 111","-147 466","112 74","485 240","278 -299","-278 299","297 -206","36 -298","-297 206","-260 150","-204 187","-447 -54","-57 -279","260 -150","411 352","204 -187","-315 355","371 -318","185 -280","-92 261","-73 354","57 279","-168 -111","-166 373","-203 429","279 -57","-225 -390","-37 56","447 54","353 -169","-112 -74","203 -429","37 -56","-279 57","73 -354","225 390","17 -391","-185 280","-353 169","147 -466","-36 298"}

    Returns: 2

  38. {"-356 360","447 -92","446 -271","180 178","270 267","271 446","90 89","-446 271","448 87","-445 450","-360 -356","179 -1","-270 -267","-449 -266","-177 359","-358 2","0 0","-269 -88","358 -2","-359 -177","449 266","-266 449","92 447","-89 90","357 -181","87 -448","-88 269","-448 -87","266 -449","-179 1","-267 270","-271 -446","-87 448","360 356","-447 92","-92 -447","445 -450","268 -91","-1 -179","356 -360","-181 -357","2 358","89 -90","267 -270","-91 -268","1 179","-2 -358"}

    Returns: 1

  39. {"86 157","-168 44","-186 318","-44 -168","-440 205","37 484","-80 380","97 199","-104 117","-86 -157","51 -148","429 -247","0 0","186 -318","-334 267","24 263","-179 2","144 -307","-77 -294","221 -13","-5 495","254 113","69 -422","-329 -228","-294 77","-84 22","292 -256","-22 -84","77 294","294 -77","369 38","-153 444","-37 -484","-466 -237","-497 -184","-197 276","241 -108","-170 -135","-404 -343","214 303","440 -205","-360 -175","179 -2","312 -351","223 166","-435 -290","-201 -82"}

    Returns: 1

  40. {"-178 -431","-446 72","-371 288","-266 -383","301 -364","188 397","56 469","431 -178","232 373","-469 56","-364 -301","288 371","72 446","156 443","469 -56","-156 -443","-301 364","178 431","266 383","-336 -302","-431 178","-188 -397","-56 -469","-288 -371","364 301","383 -266","-72 -446","373 -232","-443 156","302 -336","397 -188","-383 266","-232 -373","446 -72","336 302","371 -288","-373 232","-397 188","443 -156","-302 336"}

    Returns: 4

  41. {"92 201","-447 -233","-310 385","432 94","184 402","-186 231","-124 154","-263 169","139 -15","17 -494","372 -462","402 -184","-62 77","340 -107","263 -169","109 -293","-94 432","169 263","62 -77","-47 216","370 171","216 47","-107 -340","-293 -109","246 325","494 17","186 -231","293 109","-479 122","124 -154","94 -432","387 -323","171 -370","310 -385","122 479","-372 462","231 186","-169 -263","-32 355","248 -308","-402 184","-325 246","-109 293","15 139","-248 308","0 0","-355 -32","-233 447","201 -92","-323 -387"}

    Returns: 1

  42. {"-158 110","-63 41","198 -258","130 -142","-346 -234","-254 -145","-282 162","282 -162","-411 -50","-49 57","63 -41","322 -84","49 -57","-337 -482","-74 319","-186 -374","326 -31","158 -110","-381 -48","74 -319","-126 308","433 398","186 374","-409 146","-130 142","3 -384","411 50","126 -308","-110 -271","110 271","-433 -398","-326 31","254 145","5 -414","-3 384","-199 386","-198 258","-5 414","346 234","409 -146","337 482","-322 84","199 -386","381 48"}

    Returns: 2

  43. {"-313 79","-24 -227","-361 -375","7 -368","234 -392","31 -141","0 0","-392 -234","172 -110","-117 196","-141 -31","-227 24","-189 -485","227 -24","-86 55","423 93","-375 361","189 485","361 375","-282 -62","79 313","-275 -430","337 148","-368 -7","48 454","-62 282","117 -196","454 -48","-31 141","-203 251","93 -423","275 430","-148 337","368 7","196 117","148 -337","-251 -203","289 -306","399 -134","-485 189","141 31"}

    Returns: 1

  44. {"111 -442","360 335","117 -389","-136 -253","448 164","382 -419","-64 383","-318 36","82 -224","213 459","224 82","248 294","-377 -11","366 388","-466 -323","365 -95","76 -277","-229 348","-276 407","-105 495","318 -36","271 23","-207 -406","-471 107","-201 -353","-130 -200","419 382","-200 130","-400 260","188 -236","483 -1","-176 342","-259 83","-323 466","301 288","-270 460","30 265","148 359","0 0","-135 230","-236 -188","183 194"}

    Returns: 1

  45. {"4 9","5 -1","-2 7","-4 9","9 2","-4 -1","-9 2","2 7","6 0","-6 0"}

    Returns: 0

  46. {"4 2","3 -1","3 -8","-4 6","-3 0","-4 2","-4 3","4 6","4 3","-3 -8"}

    Returns: 0

  47. {"2 7","-2 7","-9 -1","8 1","-2 -7","-9 1","2 -7","9 -1"}

    Returns: 0

  48. {"5 -4","-5 -4","3 0","5 4","5 -6","-5 4","-5 6","5 6","-3 0","-5 -5"}

    Returns: 0

  49. {"4 -5","-5 5","-5 -5","5 5"}

    Returns: 0

  50. {"3 -3","-3 -3","-3 3","3 4"}

    Returns: 0

  51. {"108 -422","9 404","413 -105","499 297","202 386","-413 -105","-9 404","-108 -422","-498 297","-202 386"}

    Returns: 0

  52. {"-242 63","-475 -432","-269 -22","-23 363","475 -432","420 340","231 470","-104 -38","174 -131","104 -38","242 63","-420 340","269 -22","93 414","-174 -132","23 363","0 247","-231 470","-93 414"}

    Returns: 0

  53. {"-285 -280","44 460","-280 481","-296 218","-44 460","406 -411","-437 384","279 -481","44 -460","339 127","406 411","-406 -411","437 384","285 280","437 -384","296 218","-339 -127","-285 280","-280 -481","-296 -218","280 481","-437 -384","-406 411","285 -280","-339 127","339 -127","-44 -460","296 -218"}

    Returns: 0

  54. {"471 241","-471 241","-191 -56","-336 261","191 56","-115 -386","8 -289","-471 -241","-227 149","-342 78","471 -241","491 221","496 337","491 -221","-496 -337","-491 -221","494 -123","-342 -78","8 289","336 261","-494 123","-336 -261","342 -78","-115 386","336 -261","-8 289","342 78","-491 221","115 386","494 123","227 149","-227 -149","115 -386","-191 56","-496 337","-8 -289","-494 -123","227 -149","496 -338","191 -56"}

    Returns: 0

  55. {"95 321","-198 -201","-66 213","95 -404","153 478","-404 95","213 66","-213 66","-201 198","-201 -198","81 -402","201 198","66 213","66 -213","-95 -321","-321 95","-404 -95","-213 -66","198 -201","478 -153","-66 -213","-81 402","81 402","321 95","-321 -95","404 -95","-402 -81","-95 321","404 95","201 -198","-402 81","321 -95","95 -321","198 201","402 -81","402 81","478 153","213 -66","-81 -402","-478 153","153 -478","-153 -478","-95 404","-198 201","-479 -153","95 404","-95 -404","-153 478"}

    Returns: 0

  56. {"-29 338","93 480","311 176","-93 -480","223 213","-195 -205","-195 205","-223 213","195 -205","-213 223","338 29","-29 -338","-205 -195","-311 176","-421 91","421 -90","-421 -91","-311 -176","-213 -223","338 -29","91 -421","213 223","205 -195","-176 311","-205 195","311 -176","176 311","-91 -421","176 -311","480 -93","213 -223","-480 -93","421 91","480 93","-91 421","195 205","91 421","93 -480","-480 93","-223 -213","-338 29","-93 480","-338 -29","29 338","205 195","-176 -311","29 -338","223 -213"}

    Returns: 0

  57. {"-362 296","244 -262","0 0","362 -296","58 -464","-135 -25","157 434","-156 13","324 -317","-253 9","-29 232","29 -232","-157 -434","176 -498","253 -9","-93 -101","96 -443","328 -414","-58 464","92 -346","-72 -139","93 101","127 219","-181 148","-451 98","-176 498","451 -98","-92 346","156 -13","181 -148","114 63","72 139","-324 317","-328 414","-96 443","-127 -219","-244 262","-114 -62","135 25"}

    Returns: 0

  58. {"-302 375","-223 263","477 -72","-459 -85","117 -468","-80 -88","351 -299","207 73","-402 265","-335 405","-327 -426","-167 -250","202 -43","159 197","41 465","233 190","218 -158","-270 366","80 88","381 -266","-350 -164","-53 -213","356 -404","-450 168","-160 -397","394 124","331 -321","-435 295","-337 -216","-121 331","81 -375","381 -45","-210 432","453 432","130 364","62 -197","301 -354","-283 197","393 366","380 197","-387 -492","-181 -177","183 356","-341 89","-390 234","-86 -404"}

    Returns: 0

  59. {"226 -43","-326 188","48 383","29 -126","291 -46","-21 275","186 -350","-212 -262","-49 82","-496 106","238 -294","304 406","-165 221","14 -378","-1 100","93 -175","-142 -181","-446 -149","-288 257","-65 76","-189 -226","-75 54","-375 270","104 -180","429 24","145 246","-17 94","-339 -264","352 278","-448 -22","90 -386","105 450","22 90","332 -58","45 -193","40 -204","122 356","61 -114","434 181","-271 90","-3 8"}

    Returns: 0

  60. {"277 -64","325 -214","386 26","-5 221","-92 -269","5 -221","-386 -26","-273 131","-277 64","-252 337","495 169","-174 239","-325 214","185 -121","10 -390","-153 392","-148 -359","226 314","-166 108","-226 -314","-405 -331","405 331","-383 64","92 269","273 -131","148 359","-33 -301","-111 274","383 -64","174 -239","166 -108","252 -337","4 -198","-495 -169","33 301","-185 121","-10 389","153 -392","111 -274","-4 198"}

    Returns: 0

  61. {"148 -428","221 -463","-284 -218","-500 -113","-39 286","-249 -146","-148 428","247 325","39 -286","140 288","-183 356","428 148","-393 -76","103 395","0 0","4 -358","-220 463","290 -319","397 -282","-397 282","-467 138","-247 -325","218 -284","-430 31","-103 -395","-70 -144","430 -31","393 76","-358 -4","-290 319","358 4","-140 -288","-428 -148","183 -356","467 -138","-4 358","284 218","500 113","-218 284","249 146","70 144"}

    Returns: 0

  62. {"477 144","-347 115","-134 -399","181 -407","-432 205","432 -205","337 -465","-103 73","385 -11","-182 373","-406 -111","-477 -144","-181 408","199 222","171 468","445 -363","-397 204","103 -73","182 -373","-95 353","180 -443","134 399","233 186","-11 -385","406 111","11 385","-362 203","95 -353","347 -115","-171 -468","-445 363","-67 107","-180 443","-233 -186","-199 -222","397 -204","-337 465","-385 11","67 -107","362 -203"}

    Returns: 0

  63. {"285 203","-241 199","-37 114","-207 -294","83 467","207 294","41 244","265 -40","-113 384","113 -384","-76 -393","260 65","-181 265","118 -268","221 221","76 393","-127 457","64 -239","181 -265","92 278","-83 -467","37 -114","26 117","-221 -221","-92 -278","-260 -65","-285 -203","-155 -281","-234 273","-26 -117","234 -273","241 -199","-303 175","303 -175","127 -457","-64 239","155 281","-265 40","-82 -488","-118 268"}

    Returns: 0

  64. {"229 183","-289 -433","-183 229","141 257","493 -39","-479 -123","-153 354","368 -9","-449 2","-72 361","132 -111","14 -162","361 72","-39 -493","90 375","-354 -153","278 -384","-90 -375","220 -185","354 153","-83 -456","-134 -338","257 -141","-396 333","-264 222","9 368","79 -442","331 -53","2 449","-377 -359","-123 479","-109 317","-296 -352","396 -333","-220 185","-435 -160","-162 -14","375 -90","442 79","-310 -190","-426 208"}

    Returns: 0

  65. {"284 -198","328 -391","-329 343","-328 391","-343 -329","343 329","-186 292","391 328","389 280","377 -344","378 -296","198 284","186 -292","329 -343","296 378","-391 -328","-378 296","49 47","-292 -186","-390 -280","-377 344","-475 250","-284 198","-344 -377","0 0","-250 -475","230 -485","-49 -47","47 -49","485 230","344 377","-47 49","-296 -378","250 475","280 -390","-230 485","-485 -230","-280 390","-198 -284","292 186","475 -250"}

    Returns: 0

  66. {"385 -355","-225 65","-473 -34","286 -107","225 -65","-15 370","-385 355","-286 107","-160 290","313 324","191 408","-64 -225","-141 187","-351 -118","-294 -427","-469 233","469 -233","15 -370","294 427","65 225","-263 271","141 -187","-328 46","187 141","-191 -408","-202 229","347 -149","160 -290","328 -46","-313 -324","202 -229","473 34","-347 149","351 118","-187 -141","-137 454","137 -454","263 -271"}

    Returns: 0

  67. {"-100 375","365 -465","-360 145","265 -90","-266 -328","57 -274","32 121","-124 -17","-400 295","92 -104","375 100","295 400","-375 -100","400 -295","-92 104","288 -116","360 -145","-145 -360","244 -433","80 -300","-101 -43","433 244","417 -419","-433 -244","-104 -92","358 224","-295 -400","-244 433","0 0","100 -375","104 92","55 95","145 360"}

    Returns: 1

  68. {"-53 271","-217 -231","161 273","-371 297","-271 -53","81 -417","-177 389","25 -275","-389 273","-423 61","61 423","366 438","-389 -177","177 -389","-275 -25","371 -297","286 -127","-318 -474","-61 -423","389 177","469 -158","275 25","297 371","389 -273","423 -61","202 -239","99 -168","-273 -389","300 -425","162 -334","65 -405","337 -234","273 389","492 -169","283 -406","271 53","-297 -371","-25 275","423 39","319 -258","53 -271","407 51","366 -62","189 -48"}

    Returns: 1

  69. {"-488 -195","120 275","311 378","-311 -378","-297 462","-347 -45","58 156","-59 61","473 126","300 -5","-473 -126","-181 497","166 -12","-58 -156","377 -371","31 -79","-380 -363","297 -462","488 195","185 297","347 45","-166 12","380 363","-185 -297"}

    Returns: 1

  70. {"131 -105","300 19","222 -102","-153 -333","-222 102","247 245","0 0","-374 15","165 -31","-220 -235","-181 240","-131 105","-421 59","421 -59","-319 281","-136 -296","153 333","255 -274","-300 -19","136 296","25 347","-165 31","-35 -320","181 -240","319 -281"}

    Returns: 1

  71. {"138 416","-161 155","-16 -438","205 89","-138 -416","-205 -89","-416 138","-89 205","-333 249","-438 16","438 -16","89 -205","155 161","-131 496","416 -138","399 117","-155 -161","16 438","161 -155","296 419"}

    Returns: 1

  72. {"-358 -34","-47 -456","-40 231","-410 -57","-272 -369","185 144","-242 266","-184 416","-18 -381","40 -231","404 -70","-145 -375","416 184","-398 197","346 -220","47 456","-185 -144","-404 70","145 375","272 369","265 -318","242 -266","-243 -294","358 34","427 -122","-346 220"}

    Returns: 1

  73. {"38 184","-184 38","-19 -92","35 -295","-425 -200","-35 295","-352 -311","-92 19","92 -19","200 -425","-238 241","-3 -479","19 92","-149 -257","-257 149","-200 425","149 257","-295 -35","311 -352","-187 -441","425 200","-311 352","295 35","257 -149","352 311","314 127","0 0","184 -38"}

    Returns: 1

  74. {"-322 -486","70 -9","461 -256","-88 162","368 95","-444 -35","-173 152","22 -480","-90 472","-368 -95","-365 26","0 0","103 150","440 69","218 198","-135 122","48 178","-380 7","-22 480","365 -26","-148 -500","-349 -110","-218 -198","-461 256","-249 -374","-389 -356","349 110","-258 142","389 356","-66 -25","133 188","258 -142","380 -7","260 -452","90 -472","426 -398","329 -306","-440 -69","444 35"}

    Returns: 1

  75. {"346 428","15 -170","-35 -380","-123 -4","-50 -210","-325 -200","-4 123","14 152","112 51","245 330","222 -419","-419 -222","230 500","-222 419","474 -13","187 366","130 80","4 -123","-166 -138","-51 112","-13 -474","13 474","419 222","-112 -51","123 4","-159 -62","51 -112","-474 13"}

    Returns: 1

  76. {"360 174","31 89","-83 478","91 118","265 -242","-2 -149","-362 -323","-54 418","-89 31","174 -360","89 -31","-25 358","-360 -174","-174 360","149 -2","118 -91","-265 242","2 149","54 -418","478 83","83 -478","-91 -118","-31 -89","-294 302","323 -362","25 -358","-149 2","-478 -83","294 -302","-323 362","-118 91","362 323"}

    Returns: 2

  77. {"344 -377","497 116","-497 -116","-377 -344","333 -253","186 341","252 351","-42 -77","-95 -305","-252 -351","105 492","-245 205","-419 -271","341 -186","-499 1","83 165","-116 497","116 -497","25 183","-105 -492","-192 -465","143 393","377 344","-25 -183","-232 -59","9 -432","-83 -165","-404 -8","-140 319","-227 -76","-9 432","55 -344","-337 298","-344 377","-122 -433","192 465","-77 42","-344 -212"}

    Returns: 0

  78. {"360 -20","-348 -336","-124 407","-175 110","348 336","-150 -490","425 -20","240 420","193 74","150 490","-108 344","323 -496","186 -448","480 -70","274 213","-438 -266","-480 70","-240 -420","124 -407","108 -344","74 -193","-231 487","-186 448","-274 -213","-413 -424","139 318","438 266","-425 20","-110 -175","-360 20","-139 -318","321 433"}

    Returns: 0

  79. {"374 -138","-341 -336","-72 243","255 428","-67 -124","-305 325","-249 -250","-447 220","258 -276","138 374","72 -243","341 336","-345 74","469 -96","-114 382","-374 138","-258 276","67 124","-59 128","-124 67","305 -325","128 59","-138 -374","-325 -305","382 114","325 305","345 -74","-128 -59","249 250","-382 -114","-255 -428","66 372","-66 -372","-469 96","59 -128","447 -220","114 -382","124 -67"}

    Returns: 0

  80. {"107 326","499 243","-356 -308","147 -396","-337 441","-147 396","356 308","-441 -337","-309 -288","-338 -59","-415 30","288 -309","-499 -243","396 147","154 -178","-288 309","243 -499","441 337","255 65","30 415","337 -441","-243 499","-396 -147","309 288","-101 -243"}

    Returns: 0

  81. {"313 246","389 407","-179 -370","14 231","231 -14","-451 -337","-231 14","349 -77","407 -389","-14 -231","-281 282","282 281","-313 -246","-246 313","-196 470","19 493","-29 -410","281 -282","-282 -281","-341 107","229 437","-389 -407","-337 451","451 337","404 310","337 -451","-407 389","246 -313"}

    Returns: 0

  82. {"232 -71","424 -218","-195 -275","-103 321","80 -470","275 -195","298 -399","-232 71","218 424","-494 63","470 80","-424 218","494 -63","-298 46","321 103","46 298","-470 -80","-321 -103","176 -167","195 275","-275 195","-46 -298","-298 399","-80 470","298 -46","-218 -424","103 -321","-176 167"}

    Returns: 0

  83. {"-179 -288","179 288","-347 162","243 -422","-39 473","288 -179","-95 -465","378 307","-162 -347","-27 382","-307 378","130 -75","-422 -243","-333 -64","307 -378","27 -382","95 465","0 0","333 64","382 27","-138 -59","64 -333","347 -162","-378 -307","-243 422","-382 -27","138 59","-288 179","422 243","-130 75","162 347","39 -473","-64 333"}

    Returns: 0

  84. {"279 233","-233 279","-255 68","332 131","-180 -193","211 249","57 -359","186 -234","-164 317","164 -317","-311 99","-317 -164","54 -294","-294 -54","-131 332","180 193","359 57","-54 294","294 54","233 -279","131 -332","255 -68","234 186","-359 -57","-279 -233","-57 359","-211 -249","317 164","-332 -131","-234 -186","311 -99","-186 234"}

    Returns: 0

  85. {"-180 445","-40 299","-181 194","445 180","387 284","110 -75","283 226","393 110","-218 -345","-13 -375","13 375","-363 95","-6 133","341 122","-370 -239","-98 475","218 345","363 -95","40 -299","335 286","134 -229","249 -202","-480 5","181 -194","-247 -257","18 -399","275 -124","-335 -286","370 239","98 191","214 -17","-393 -110","427 -230","-317 -163","98 -475","284 -387","-248 -411","-275 124","317 163","-330 225","-41 318","247 257","-427 230","-134 229"}

    Returns: 0

  86. {"-33 -446","89 198","-114 187","63 -259","33 446","322 -196","2 219","257 -366","-322 196","259 63","135 170","-257 366","446 -33","-47 -129","114 -187","-93 -101","219 -2","-259 -63","366 257","-2 -219","-135 -170","-446 33","-219 2","47 129","187 114","-89 -198","-366 -257","93 101","-187 -114","-63 259"}

    Returns: 0

  87. {"-4 12","-86 258","-48 144","-18 54","-54 162","-26 78","-8 24","-62 186","-82 246","-74 222","-32 96","-88 264","-38 114","-70 210","-24 72","-28 84","-14 42","-84 252","-80 240","-68 204","-42 126","-66 198","-6 18","-10 30","-34 102","-30 90","-78 234","-56 168","-90 270","-46 138","-20 60","-2 6","-60 180","-72 216","-22 66","-16 48","-52 156","-36 108","-58 174","-12 36","-40 120","-76 228","-50 150","-44 132","-64 192"}

    Returns: 1

  88. {"-153 0","0 216","-99 0","-90 0","-63 0","0 90","0 126","-135 0","-198 0","0 108","-81 0","0 54","-108 0","-126 0","0 72","0 144","-36 0","-207 0","-216 0","0 81","-171 0","-45 0","0 207","0 162","-162 0","-117 0","-54 0","-180 0","-225 0","-189 0","0 117","0 45","0 36","-144 0","0 9","-27 0","0 135","-72 0","-18 0","-9 0","0 153","0 18","0 225","0 27","0 99","0 189","0 171","0 198","0 63","0 180"}

    Returns: 1

  89. {"96 12","32 4","72 9","56 7","-136 -17","-48 -6","-112 -14","-152 -19","128 16","120 15","24 3","-128 -16","-56 -7","-8 -1","80 10","-16 -2","-144 -18","40 5","-88 -11","160 20","-192 -24","-104 -13","168 21","-96 -12","-184 -23","-72 -9","64 8","152 19","144 18","112 14","-168 -21","192 24","8 1","176 22","104 13","-160 -20","16 2","-176 -22","-32 -4","-120 -15","88 11","-80 -10","136 17","-40 -5","184 23","-24 -3","-64 -8","48 6"}

    Returns: 2

  90. {"33 11","7 -21","3 1","36 12","5 -15","27 9","-9 27","-12 36","6 2","-7 21","24 8","-15 -5","21 7","-1 3","-3 9","30 10","12 4","-10 30","9 -27","9 3","2 -6","18 6","4 -12","-33 -11","12 -36","-18 -6","-24 -8","-2 6","-4 12","-9 -3","-12 -4","-5 15","-3 -1","-27 -9","-6 -2","8 -24","3 -9","1 -3","15 5","-36 -12","-6 18","10 -30","-21 -7","6 -18","-30 -10","11 -33","-11 33","-8 24"}

    Returns: 4

  91. {"0 0","481 0","480 31","-481 0","-480 -31"}

    Returns: 2

  92. {"-31 480","0 481","31 -480","0 -481","0 0"}

    Returns: 2

  93. {"348 359","0 0","-359 348"}

    Returns: 1

  94. {"348 359","359 -348","0 0"}

    Returns: 1

  95. {"499 -500","-500 -499","0 0","500 499","-499 500"}

    Returns: 4

  96. {"500 499","-500 -499","-499 500","499 -500","0 0"}

    Returns: 4

  97. {"-54 -83", "-46 54", "-5 -44", "-1 -31", "-14 47", "7 -5", "-45 -63", "-88 47", "-17 -9", "-26 -66", "40 56", "-67 69", "-49 -2", "2 62", "61 78", "-81 -32", "87 33", "-22 -53", "-43 -38", "57 28", "35 12", "-53 -15", "52 -16", "32 -44", "-73 68", "79 44", "3 56", "-66 26", "-87 41", "4 87", "22 53", "59 16", "-3 55", "3 19", "-26 8", "43 38", "54 46", "-16 22", "-3 -93", "45 63", "0 -37", "-7 5", "-40 -56", "40 19", "-8 -63", "-16 -89", "29 11", "-52 -21", "-58 -22", "4 -61" }

    Returns: 1

  98. {"1 2", "3 4" }

    Returns: 0

  99. {"0 0", "2 0", "0 2", "-2 0", "0 -2", "5 -5", "-5 5" }

    Returns: 2

  100. {"0 110", "0 70", "-75 20", "75 20", "-25 -50", "25 -50" }

    Returns: 1

  101. {"-300 100", "-200 100", "-100 100", "100 100", "200 100", "300 100", "-300 -100", "-200 -100", "-100 -100", "100 -100", "200 -100", "300 -100" }

    Returns: 2

  102. {"0 0" }

    Returns: -1

  103. {"0 1" }

    Returns: 1

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