TopCoder Statistics - Problem Statement

Problem Statement

Manao is playing a new game called Reflections. The goal of the game is transferring an artifact in 3-dimensional space from point (0, 0, 0) to point (X, Y, Z). There are two types of moves in the game:

1) The player can move the artifact by 1 unit in the direction of any coordinate axis. So, using this type of move, from point (a, b, c) the artifact can be moved to points (a + 1, b, c), (a - 1, b, c), (a, b + 1, c), (a, b - 1, c), (a, b, c + 1) or (a, b, c - 1).

2) The player can reflect the artifact against any one of the given planes. The reflection works as follows: the artifact disappears at its position before the reflection and appears on the other side of the plane at such a place that the line connecting the old and new positions is perpendicular to the plane and the old and new positions are equidistant from the plane. Reflection against each particular plane can be performed at most once during the game.

The planes are given as int[]s mirrorX, mirrorY and mirrorZ. mirrorX[i] corresponds to a plane perpendicular to the X axis with coordinate X = mirrorX[i]. mirrorY and mirrorZ contain planes perpendicular to the Y and Z axis in the same fashion. The target position is given in int[] finalPosition. finalPosition contains 3 elements, where finalPosition[0] is X, finalPosition[1] is Y and finalPosition[2] is Z.

Return the minimum possible number of moves which Manao will need to transfer the artifact.

Definition

Class:: Reflections
Method:: minimumMoves
Parameters:: int[], int[], int[], int[]
Returns:: long
Method signature:: long minimumMoves(int[] mirrorX, int[] mirrorY, int[] mirrorZ, int[] finalPosition)
(be sure your method is public)

Constraints

finalPosition will contain exactly 3 elements.
Each element of finalPosition will be between -1,000,000,000 and 1,000,000,000, inclusive.
mirrorX will contain between 0 and 20 elements, inclusive.
Each element of mirrorX will be between -1,000,000,000 and 1,000,000,000, inclusive.
All elements of mirrorX will be distinct.
mirrorY will contain between 0 and 20 elements, inclusive.
Each element of mirrorY will be between -1,000,000,000 and 1,000,000,000, inclusive.
All elements of mirrorY will be distinct.
mirrorZ will contain between 0 and 20 elements, inclusive.
Each element of mirrorZ will be between -1,000,000,000 and 1,000,000,000, inclusive.
All elements of mirrorZ will be distinct.

Examples

{}

{}

{}

{901,-15761,10634}

Returns: 27296
{}

{}

{}

{121239174,-169776576,46727479}

Returns: 337743229
{}

{}

{}

{-942375608,890878630,592242030}

Returns: 2425496268
{5016132}

{-4998477}

{4188859}

{4655104,-5038294,2984952}

Returns: 12598717
{}

{}

{}

{-307,569,-611}

Returns: 1487
{1054}

{2233}

{-2108}

{739,750,-25}

Returns: 1514
{67095,-48095}

{57891}

{}

{32270,-8419,-70605}

Returns: 111294
{195288,-186050}

{}

{357326,-21552}

{283253,306317,-24830}

Returns: 431916
{-2}

{1,-7}

{6}

{9,10,-9}

Returns: 26
{-8242,8023}

{}

{-6322,-1688,6576}

{-5509,8054,-4570}

Returns: 14758
{107,115,117}

{63}

{106,-57}

{18,-2,61}

Returns: 67
{948092,599817,-763116}

{194181,775311}

{406179}

{-334613,286793,695784}

Returns: 552758
{-374,-414}

{-687}

{127,-419,-614,-606}

{-304,-413,-412}

Returns: 663
{-17923}

{56770,78359}

{29718,-64070,62012,23655}

{20500,81719,55298}

Returns: 56461
{31,-202}

{-46,104}

{187}

{173,37,53}

Returns: 202
{}

{-101401,-612272,728897}

{-469777}

{-575566,-705597,-560633}

Returns: 1270635
{}

{154076,-144605,-166845,102954,-126829}

{126291,133711,-45877,157277,99200}

{64475,-149640,-116605}

Returns: 66705
{-2,2,-1,0,3}

{0}

{-3,2,0}

{3,-1,2}

Returns: 5
{-7,-19,2,14,0}

{18,-5,7,-16,-2}

{8,-12,15,18,3,-5}

{-4,-5,-9}

Returns: 6
{100802}

{141864,-113919,-226397,380663}

{527228,-227156}

{-428995,-284419,-602675}

Returns: 609140
{-44562122,24517038,54752647,23742263,17507858,66056969}

{-7861052,-35785800,36055272,-67554524}

{1825838,-22485423,57793752,68258651,-38486219}

{23373893,7984493,10770470}

Returns: 1655185
{-39554047,-23223485}

{-60401708,-66395364,-53135415}

{15805586,32151,60072998,16854175}

{59524429,6561527,-18939979}

Returns: 44895987
{-2,1,2,3,0,-4,-1}

{}

{1,4,-5,0}

{5,-3,-1}

Returns: 6
{1728306,4024712,2142456,6808804}

{}

{1891446,8201482,980096,2092759,3219719,-4016644}

{-607065,5750496,7324596}

Returns: 5984075
{1859561,-6817346,-4745054}

{-1799437,2765497,462434,4673124,-4537069,-6503665}

{-1749857,5112334,-3117938,-5816557,-473714,5238063}

{5290725,559358,-5033224}

Returns: 1181109
{-115,-3,123,108,-187}

{-172,101,187,75}

{-177,-10,-156}

{-77,23,-148}

Returns: 117
{2236893,44767328,6054769,-58145165,-47628964,24023834}

{39776951,-52029567,45404266,-58309345,9145845,-9117872}

{-21614662,4388367,30960510,9702068}

{14015214,55137379,-23862890}

Returns: 9806253
{5688,7383,-13512}

{12096,20692,13413}

{}

{13047,18663,-9165}

Returns: 12310
{17,-7,-3,-19,12}

{-4,12,-5,-13,8,-9}

{16,-14,-3,-11,-2}

{-18,-13,-15}

Returns: 11
{31450}

{10969,-9094,-1691,15177,16211,-31056,14994,-37820}

{-29427,-26980,-28391,41444,48186,-36384}

{20910,3223,-41725}

Returns: 21867
{-7}

{39,27,-24,-31,-36,7,-15,-40,8,-22}

{4,37,23,-4}

{-14,-24,0}

Returns: 3
{602161,-234982,562751,432249}

{-867738,181591,-683693}

{-539720,-352233,493077,492693,72632}

{-455545,-599727,702362}

Returns: 337244
{-445208507,-872009877,50590776,-724417868,-699219776,805526643,-231565328,834728622,-999409472}

{449176581,-215949346,565763001,-762316968,-555086600,310687873,-47298569}

{-507493359,-860076529,84718677,866846412,-785232021}

{-318505119,-637396018,-800623906}

Returns: 59901825
{3157,7654,-193,7316,1885,8149,2363,2365,4112,-6054,1389}

{-1038}

{-7573,8092,-5780,6307}

{-3689,6857,7928}

Returns: 7640
{-26,-16,-55,20,-36,37,4,-17,44,-8,35}

{28,41,-17,-1}

{-29,-7,21}

{30,-20,-11}

Returns: 14
{}

{698,-1085,-1951}

{327,881,54,-1265,-964,-1383,1815,-89,-1530,111}

{355,280,1762}

Returns: 636
{110,-225,-3082,2708,-445,2910,-1051,860}

{-734,-546,-2798,1273,-1343,-680,3121}

{-3102,1538}

{830,-1657,1938}

Returns: 1187
{1968,-4747,-31395,38695,1611,-7218}

{31471,32988}

{-1179,-15455,-11649,-20013,24666,33142,17167,-17157,18253,2375}

{5616,-36761,-27578}

Returns: 33779
{-60570140,70077361,-78892330,16994255,46143860,-68751912,-85053385,-66351455,45537618,67876718}

{8776705,41415087,-9878738,-75065093,-10341981,-10012744,-2838199}

{-78664029,9427062,65787451,65361523,-35101963}

{52996198,25667872,-64403938}

Returns: 3986013
{23407,6351,-20387,16933,13162,7415,27418}

{-5092}

{-16781,11224,-26701,-29730,21695,24160,-23584,-12075,27586,6622,6421,16605}

{11932,-10855,25873}

Returns: 765
{-456995624,-443433312,-197325803,998136312,-752856457,233942366,90632142,-79250744,912684857,-812190318}

{-696062088,460922177}

{366261847}

{-977475098,-981409916,-933077988}

Returns: 1343899335
{46025325,-18840482,-78211604,17363807,31040546,-38735129,-24579799,-18477338,42735938,-61657423,-54422081,16067343}

{-2763400,-2765955,65918205,31576997,14200719,27067855,-66055997,-57075662,77940724,-54080182}

{-42811093}

{-18624235,-91403563,48908095}

Returns: 48939216
{-225936,-334334,68691,-448183,-509087,-612278,639314,349352}

{-562522,-232874,-334841,376231,-630854,593560,-200045}

{377056,106635,670861,-483219,-173316,585962,350769,-241431,-537714,-142659,237375,-499915,-270926,-503109}

{-214677,535027,463959}

Returns: 5780
{149851384,12390128,223387626,-53016899}

{-163897982,-441522449,-171818125,167390381,374290098,272624572,-69911466,211622511,-460702856,324384788,386724054,-207962609,206504072}

{-473446269,-74233017,359388164,222385910,116345522,444589879,-10171844}

{8768621,-123960885,479726023}

Returns: 9906228
{118561420,93447014,235687060,-238476350,-217655277,178515694,-68500633,249812037,-41023939,-206725131,-8502951,93490598}

{-162112500,-62360156}

{237166148,129379636,177132750,-3211844,-56400714,-119354021,123752200,145568475,-242390828,194101368}

{-76560735,80796249,-124335057}

Returns: 80817042
{-211625516,569208506,261460326,491199440,-646005318,-199642760,-296096768,-222442353,-222052159,-489026404,-545179480,296884515}

{-371543891}

{-24102962,254761476,39821380,-375802036,137784419,-30836171,-36585412,-105795738,371357695,-141476863}

{214430319,-356058819,-162027415}

Returns: 356176902
{436945268,173640221,773978092,282275459,426506103,-344656784,-368426327,-290882619,-375958171,821676747,505089068,12093717,-743870196}

{-444674761,329740967,-411169456,-625807738,-862363124,343007125}

{84063891,-48314508,-853310047,-310843000}

{-14201650,-297812463,-697325041}

Returns: 100525395
{-1,-3,-2,9,1,-8}

{-4,0}

{}

{-11,11,-6}

Returns: 14
{-84664,53173}

{95214,75985}

{43936,45936,-57126,56204,-19459,-15795,-3279,-23105}

{-9405,54381,-45860}

Returns: 25481
{-5366698,631209}

{5463242,736482,-5456274,-1343942}

{-5131022,-3355094,-6357969,4477612,-2739196,4614115,5086584,675457,4688522,2666984,-3225724,5908486,1083933,-823104}

{3108094,1274329,5463060}

Returns: 1891166
{1655,2240,1859,2995,2616,3367,-673,-1294,-27,-2637,-2800,1952,2628,1917}

{-2521,-580,-2383,2970,1864,-416}

{-3435,1172,175,574,-2120,845,-2246,557,-45,-367,-2079,-2617}

{-1342,2743,590}

Returns: 45
{-197,107,-45,-177,-132,66,-118,92,178,14,137,-167,73,-36}

{-188,-175}

{68,210,186}

{-40,-8,-71}

Returns: 35
{17974,9168,-34406,-36237}

{-22745,-9006}

{8048,-24436,19372,-1992,31631,31778,8879,-24471,24717,22489,24371,-15509,-3788,-26841}

{36669,-4281,9260}

Returns: 5010
{290231854,152212789,-598673411,-73974258,168173373,273074467,615334860,-233212797,856815741,-650975555,-204516607,905786938,709280815,-304450268}

{36207018}

{-65578330,461703569,705717067,-827911944,5742846,173688629,778537319,390241028,-388452036,-375253831,-504280823,359200762,262415506,870667868,762301216}

{117308333,-432062284,657976618}

Returns: 432067165
{601477,-71845,45421,-650946,653147,376655,426591,24427,267629,-38090,23973,-307609,-117098,606341}

{}

{-364810,-529694,-106911,-68208,377545,629725,488964,-423936}

{-375596,78428,-589587}

Returns: 80804
{539,2180,2417,1383,-404,2526,-2938,2756,-984,-2341,1866,-3991,854,3080,-260,-2731,2819}

{-1732,2635,-3089}

{}

{1148,98,308}

Returns: 410
{-206,216}

{-152,-486,604,-240,-451,536,570,-694,-385,-33,394}

{88,-366,-254,-708,-354}

{-579,237,-68}

Returns: 194
{-602,697,475,573,262,600,-873,-718,230,-35,-447,-529,362}

{-499,237,810,-487,28,868,-13,-311}

{256,152,501,247,930,-311,-180,-417,417,465,-870,27,-40,843,495}

{387,-234,797}

Returns: 15
{397827018,680470956,-211832082,-637570972,-122617322,711682775,-298414015,-713852604,473104422,192690396,-746075750}

{-562734863,355619103,308743875,-655252082,619942288,-61601615,240115609,-802502602,5520790,-798789658,-539553019,251419627}

{-201162317,527719640,575419965,-404131191,482991716,377399746,-24134089,331424517,-536327395}

{-124001764,-26301937,-209590343}

Returns: 219321
{63388461,14951852,71131129,-53935159,43817051,80755499,-88770932,-53609530,-60050780,-71244412,88869136,-18323696,-46290048,65212026,44465466,18310597}

{43593834,34057388,-83516030,48977277,-22994400,-20701910,13208153,33125149,-8705586,-83066595,-33971444,-39047641,-49961138,-59213741}

{75501943,80893455,-13560712,72120160,-76016286,82086581,-12738027,-89277232,-84351063,-26864158,32672839,-26276345,93917172,10415557,37541492,-2299981}

{-12686338,-2598401,-44640858}

Returns: 1182
{-16,1,8,3,-55,37,-29,13,-17,57,-4,18,26}

{-12,25,-17,50,-54,-36,-40,-7,54,12}

{12,-51,54,-5,11,-29,44,6,-45,8,-18,-47}

{44,4,-59}

Returns: 7
{3355987,-6226935,830384,-5491263,4710268,-1087239,-527866,5151989,-5614475,3257324,-1071537,2844944,124266,5641285,4294388,4562950,592292,1901391}

{111602,3817428,-2959010,-6376832,-2051525,-3465091,-792145,3402579,4589216,2474249,5942476,-4221294,-2028908,3133114,75548,-1330447,2123593,5834586}

{-5757668,-4835456,2032979,5893881,-4603457,-3951903,1908351}

{-2478774,-2327501,-5334183}

Returns: 11966
{325133,47683,72762,275719,386728,478731,562680,-397569,703766,459627,33876}

{-511109,-51469,445750,122526,164143,-251148}

{-259544,482865,-439128,588391,411493,-613144,-243361}

{-308422,157249,-118768}

Returns: 9422
{}

{}

{}

{1000000000,-1000000000,1000000000}

Returns: 3000000000
{-206,-59,134,-372,-143,-377,171,-290,-24,398,-353,-126,-348,152,119,-268,-197,100,-122,205}

{-275,-37,277,-76,-297,-61,370,-334,-198,-96,194,230,-123,-220,346,-380,217,-182,-131,24}

{365,379,-350,321,299,20,-281,-68,-129,238,-149,87,-252,-370,-178,51,40,-77,-325,-326}

{-2,390,-215}

Returns: 8
{-25472,34197,43786,-28204,112485,-77026,-168540,116995,-176423,-72589,84084,-105570,-55983,153431,-230257,221938,-97205,170514,203529,-74364}

{127237,-141325,137953,50858,-39098,-199741,123503,-93974,163328,113437,219657,155629,107294,27702,-173055,122831,175264,204665,66068,-204603}

{-131307,-227185,-52570,75359,16731,86144,415,143325,-70648,14878,-160305,207943,223981,-192016,30597,221019,164149,-222489,-128008,136490}

{166851,-135630,219591}

Returns: 19
{64,34,-56,22,-15,17,-8,-50,-3,14,-37,-21,66,54,12,-5,-51,-67,61,-19}

{-5,58,-15,-17,47,44,-43,30,-34,24,-53,-49,-33,5,-56,-45,37,29,64,-66}

{-11,-25,-59,20,-38,0,62,56,61,36,16,52,-2,-22,5,64,24,28,-48,-14}

{23,-64,-46}

Returns: 6
{54,-9,33,-21,40,87,-68,-3,59,-19,-57,53,63,31,-32,90,-42,57,-38,-37}

{-3,-77,-46,89,61,7,45,-24,13,70,85,39,-52,-36,-51,-48,-28,-73,-18,-55}

{8,48,-78,30,-25,-47,-37,-16,37,-36,-5,-87,-28,-83,53,-26,7,-11,82,50}

{14,-5,-61}

Returns: 7
{447262649,-707013703,-757325102,621362772,-369506504,237910819,-747104492,-797015958,-79702000,-216552292,-360732765,-720886334,-576633445,-797649853,-989001059,-377134862,895068188,924884114,-159442374,321684608}

{-61780364,485705698,-659466384,-678615035,12077494,240088120,465367799,-16491021,-762840929,-686729600,-135075286,-814600071,185206331,789312806,-198128471,-294596542,841751138,-626742215,446024991,864081731}

{163703734,-628449286,-734166037,93111580,-709969993,313274637,-883687531,-803891035,-166815286,762734874,-978609449,23516591,722286999,245069204,883691842,753833251,-947104804,-752721821,185393808,-859507208}

{-684932077,724892793,-161054802}

Returns: 52
{501678793,-135469857,-104239864,-339018620,507979227,-10537916,-89042004,279323220,-448402822,-107889059,201526633,262198314,-152423257,-391136416,-325926766,154253394,-529481335,-97823265,513489636,145340091}

{376624194,-10432646,-498328473,-507739493,486286609,421905752,-467440639,164874069,247069418,99884686,448187250,-149526684,275443668,-321467957,360920569,425319170,416450631,-304672637,258418403,348199622}

{-190769283,122022110,268615362,36182463,-524780029,-106410850,-439767397,-137307391,57223818,45955668,430191356,-455753227,-263302359,-208245617,491203150,30188081,387711852,10349259,465538518,491251002}

{-251136291,205391403,-405707791}

Returns: 60
{-821373451,319399321,553090180,495979885,87004877,802254369,-900307795,131719575,-799601760,-424297554,-449796294,384086615,21759615,-397664041,523879181,936067614,-613471720,953449139,501874572,807790685}

{163086474,352244804,-36242432,81947991,-290728320,591455149,303639434,-542864265,117436157,-399140735,-895681330,-461623159,-264636616,-722243250,-656650681,-446082523,-71252351,756962325,-463347124,-328746873}

{-785107996,942313985,10539644,-276222190,572373147,467878129,617861348,-294823195,-733463730,419849549,-570685440,92263524,-996969055,-822223175,-861691695,-811590295,769967708,-402985677,389660704,-357241320}

{644262424,756008335,-573048523}

Returns: 65
{-4,2,-2,3,-3,5,0,-5,1,6,4,-1,-6}

{6,-6,3,1,4,-5,-4,0,-1,-2,2,5,-3}

{-4,4,5,-6,2,-5,-2,3,6,1,-1,0,-3}

{-1,6,-1}

Returns: 3
{0,1,-1,-2,2}

{2,1,0,-2,-1}

{2,0,-1,1,-2}

{-2,2,1}

Returns: 3
{846780052,-428764424,-481602613,892666455,-823713222,78653230,-312726090,-612213844,708860654,-750594874,-102713584,-437584820,54957059,578411162,866355630,74749637,366719028,588049770,896721916,-417420803}

{-155869973,-698616213,-331558646,746799461,748055676,502768745,45346295,200073580,-25455940,437309820,627307578,-170796709,581748948,-721193639,554565595,-775045675,-392480440,-182356624,-668655316,527293755}

{524081193,45586662,50338124,824986749,-434778572,133349922,-468190545,331958440,753708389,635013622,-317209619,-625601483,241790858,-704587641,-769310304,-764146698,747711451,180869900,68431072,8167934}

{499370087,753344868,139081675}

Returns: 56
{-561720425,132339570,461291508,744934453,-787433296,-74740736,525909693,934997330,-658199612,-778344911,-159075450,642861132,643333499,713306417,797658620,131806308,523517378,218968499,6162552,362906552}

{-645766854,-953772644,426946703,150787910,-592464645,610073694,-385475084,986430599,-223508334,-147590554,178466314,-182336714,132267416,26177964,673820170,333772528,25401703,-535627151,-940392036,-253563165}

{-413084360,-94949060,-908682902,-699320767,-577146248,896010789,-556717217,17642914,-321703142,929278571,-414587880,538737231,-159922006,-284841778,723599960,-665633974,-931738587,970744279,310364559,-741431111}

{305498172,-82187409,-489835884}

Returns: 50
{87,75,-72,-18,-57,7,-33,77,-67,-28,22,89,8,-60,16,-56,-27,-23,-14,81}

{-17,51,30,53,83,58,17,-91,-6,6,-86,66,12,-52,33,85,-78,76,31,18}

{21,-7,-78,-88,6,-50,-42,-34,-89,-60,-28,57,-4,15,51,-12,18,88,29,75}

{-88,-84,-40}

Returns: 8
{77691416,-56621108,93352240,-38497912,5621186,75442433,12778751,-49213421,31660578,63367753,92256846,-2455690,-25931904,-45087118,69164174,17753074,37412348,39032591,83786704,42109917}

{-68113223,-78871539,63515745,-30879205,-54965018,-14776688,45657282,-55174404,-30036594,23303023,4157162,94305868,38808636,7286194,-4195492,91897621,70772019,-70170864,-81264604,-58356471}

{55652306,-57143669,-33996532,35850068,23674413,22393472,30103309,58294194,59470285,-74253931,-1563604,-56308883,3391500,-48824979,-64459428,76987414,-94149163,-62609039,3254531,51603934}

{-14408681,-71757195,-40952053}

Returns: 35
{-583,604,-127,-183,414,388,1,-69,-626,307,387,-396,-417,68,-243,570,-56,-155,175,-610}

{127,-239,-504,-225,-461,-552,190,91,149,608,388,17,-450,240,544,640,-136,-139,207,396}

{-268,-162,-353,234,391,-465,-259,81,-524,-224,-397,485,275,-326,-21,-66,-567,166,-232,75}

{408,62,-464}

Returns: 7
{554324286,220739823,-879704406,108928370,693742367,185526030,468343903,-937574625,-267033562,346567009,393528571,-190722660,-498749293,538635343,659320897,-373912176,-79456660,-15646545,-84181021,-503910120}

{497221607,-481950714,-340425222,502128821,372838129,-510237009,-934184748,-128735807,-882707598,812673137,-89637426,194125477,-787156652,-747939882,-303106958,-500525807,-724493158,494844290,-413956327,-396561931}

{-675738598,423986980,-813197019,930303540,-25934370,39664994,-550619310,470680583,403070241,-59451585,-128023821,-967614079,402994931,-354534889,-937410922,-521185719,-668741885,-769340441,-741176238,-75094124}

{-489572252,-793143284,-328032650}

Returns: 54
{-100859022,-830626915,813953478,-151046343,-300594477,-866751582,20786206,-173661890,-778260230,-200552737,-868372481,-933729179,-152018178,-816233904,-300770287,109485270,-749716530,933949831,99370055,727426481}

{44981595,203718305,291022679,-220971266,106875658,583380811,-164798678,-685066866,-958888477,-29602590,809132807,-74202275,-958587368,-811538922,-951566503,-913071488,575552494,308043378,152190116,-802771718}

{119048413,-720142773,-573743583,-725866030,906838297,453800732,-692714038,595940543,841167597,-895117246,-965572716,264566384,-177925567,229495120,-19497539,357824373,773472826,-566104048,54382651,-886310963}

{-416852224,-951042025,-302808748}

Returns: 55
{-3086,5514,-33408,-56125,-38071,-9899,44481,-74047,64482,53282,-63091,-8596,75751,-64812,-70210,64348,-57407,12080,65795,9502}

{34213,-61347,-67106,-6436,33190,45339,56858,-49803,54110,64890,-40708,-2317,18687,-46704,-57421,16575,27075,38922,50317,48480}

{50183,-66368,64711,20433,31856,16554,-42559,12610,-26677,-76806,-29003,25866,-13123,70975,-56013,28959,6205,15883,-54842,4222}

{31217,74753,-69104}

Returns: 17
{3013,-834,-1877,-6955,-3904,4978,3369,-1207,6297,-1211,50,-348,-4941,1024,-5060,3883,-3891,3041,-5157,-4792}

{552,2479,-4608,7359,-897,-1110,4339,-5703,7022,-6969,-184,-7198,2257,-1095,1613,2552,3182,-4531,4046,-1068}

{-2597,1653,-3526,2785,-1927,-2966,-5009,-2186,-7018,3317,2852,-209,7213,-5418,-5631,-5584,251,3594,-2418,6250}

{444,1909,2879}

Returns: 13
{-212957,47891,84941,-339238,21505,107494,301877,-246919,-44076,143737,-60663,-330793,3826,150241,-42827,232224,-180224,324272,-4724,226161}

{301439,-255550,312378,52072,-23995,-331387,-349557,-275645,-131094,-77890,-305110,-137212,-93198,-143286,-240789,330995,207108,44205,-251445,-64156}

{198377,268173,128345,79366,72385,41370,-330698,-301497,-147188,-258414,30769,1347,324233,297033,-159690,-141870,4664,-329859,326214,123969}

{342535,-147031,-57755}

Returns: 24
{-6,-23,14,-40,13,-7,-60,3,-71,55,-18,27,28,2,-72,25,-64,-5,-61,-73}

{42,-10,-58,65,37,-30,-54,21,36,41,8,46,-65,9,0,19,-5,58,-71,45}

{66,9,35,-17,-63,-50,-29,-42,55,31,-16,3,33,-4,-56,-41,46,-18,59,32}

{28,22,72}

Returns: 5
{-39,-479,428,498,36,216,396,370,4,495,-186,-516,58,519,65,163,-132,-440,-405,296}

{-125,-503,-109,-330,-443,60,287,514,264,-488,-392,395,-186,-436,-374,230,370,-264,-435,-456}

{-440,122,-400,-419,-549,279,230,-406,377,-430,511,388,301,-294,33,-251,-243,171,-515,366}

{-454,-547,-180}

Returns: 10
{-71,-157,178,-20,94,7,69,64,-189,165,153,-68,164,150,-60,-22,0,-159,-73,-26}

{-57,-159,-86,-201,-219,-167,-181,214,-207,-102,168,-198,-117,-59,155,23,51,209,45,-174}

{88,93,99,-79,-128,-206,72,-2,142,-81,-69,213,10,-107,102,-137,-102,-113,-195,-41}

{-3,138,-213}

Returns: 8
{2,0,4,-2,1,-3,-6,-4,-7,3,7,6,5,-5,-1}

{6,-6,0,-7,5,-5,7,-1,-4,4,2,-2,-3,3,1}

{5,1,2,0,-5,-1,-3,6,7,4,-7,-2,3,-6,-4}

{-1,-3,2}

Returns: 4
{-690263,810034,-1266247,1304490,-713844,-1213737,-823994,-1195201,-1157124,885092,2776,-354874,-438460,-1139721,-989177,-225769,-1241987,-293170,1139440,-626766}

{-1040616,1155199,851061,394776,-988968,1327611,121770,-1204522,146003,417794,389565,-41313,-853570,57423,750624,196452,-1303543,-174343,-622104,463108}

{1291038,424423,-18030,497335,378548,-359330,-1294895,269491,788300,533667,-1184304,122267,579637,-709851,-206632,724847,253002,215777,-308852,500766}

{362811,-196278,322979}

Returns: 21
{4378,-148,-2546,2589,1705,-3418,4145,-5245,-639,-4092,-1213,1053,-5141,3844,-582,2080,5018,3351,2155,-2048}

{1404,-1972,4233,-1102,-1385,1380,1369,-1231,-4789,-4786,-4346,-1059,3450,-303,-746,-2015,5084,1397,-2453,-335}

{1309,-163,1771,-221,-400,-4709,3223,5622,-2173,983,5644,-937,557,-3575,-3741,511,-4550,1397,-3175,4220}

{-81,3541,-4372}

Returns: 14
{575519897,209317732,-241575931,38857950,773283878,916275041,-851210630,-166038962,-819892752,-337922394,-837422924,-929271868,359659266,27448634,879585781,382018909,591745301,-663567891,-143118070,724397928}

{-910179733,999011273,-801418905,627245690,-234536591,326715763,-104797216,-751233377,-863812339,161002667,875006210,960713643,-718336118,377412590,632157964,-53874514,500137502,-216812485,282381709,-364701563}

{-224393452,-586533646,283529371,382518669,-89313126,523266007,273092013,-765237645,-20616663,50935606,-646108138,-154878425,610128524,727301153,-92140769,-785149713,-335997808,686681813,-380540993,-490221416}

{890709063,938785595,40035321}

Returns: 44
{51,77,-19,-26,-49,-72,36,28,55,-82,38,73,-74,81,-3,-89,0,12,-20,29}

{-2,-16,-89,86,-9,-80,65,-61,57,-66,73,-30,-32,-6,-55,31,-52,-18,-12,12}

{-73,-39,11,9,-83,-69,-76,-30,86,-81,82,-65,-50,68,59,84,92,62,50,-4}

{13,54,92}

Returns: 8
{176501449,522428221,-241028076,398427369,-760438045,-310915737,-905311070,116945722,-993401509,439760876,851709233,905275896,168660342,-376485629,874619740,690277511,218865567,860799524,-596513007,615634162}

{134138804,740634049,-710386496,-716665257,-15474920,-140791491,756273795,121165300,-107285970,-425185046,-399055378,-809607374,832431640,445982636,-81066847,239347155,-522077030,65084971,-933473283,779393207}

{108153885,810294196,77502963,-874158261,990769616,840239789,-437093489,792658921,-491214571,868895425,-842340855,-388806062,632526874,778454699,-864370242,-212327840,-278283534,-892544634,-364903134,-971715338}

{490932754,-416876918,745990560}

Returns: 63
{14484,-20478,9259,-19366,-6987,16625,-9982,-19166,5369,4487,-7288,-11292,-19575,-9510,-19041,-9610,11377,9198,-18535,15140}

{-14991,20408,-9534,-14521,-11549,-19531,-20092,-2,-16356,7082,-19877,4985,10478,-2088,-7170,-14058,2148,-16244,-3009,9279}

{-20630,5671,3420,-12888,-21396,3210,-5958,-14118,-11579,3158,6764,15633,-15300,1957,-3289,-8405,-16643,1349,-3264,9064}

{-4634,-21031,18023}

Returns: 14
{66839849,56094974,-122090440,-10176075,91805380,-101250818,152648613,-74354742,-152435684,-125638981,-108186455,79930308,-58670856,85683551,-80782141,-3362260,-77198136,-126142605,-92984231,-99094944}

{107346483,-24795486,92220,122705524,-87892177,-140576866,-29985568,-106658806,-126162135,81914767,151207889,149825322,-45292636,-59700827,121382134,150350282,44025741,-23487616,28394656,61536377}

{139987417,-34766283,-66821121,-126989721,10250074,-150201830,28729270,106084733,-10773878,81039677,-21281361,-112862762,-12697345,-84759682,19408818,71810124,-134656690,-10687272,-159721684,162543606}

{47723965,-49825232,128868518}

Returns: 36
{-120171121,-407380773,614733832,209986408,-514934002,-73684104,-193968145,-714592997,-804625120,-728785919,946032898,-737610771,-214814807,-590374086,-55338382,-528751325,-585696923,-339417186,-518743909,432997774}

{642450641,-124841002,-996970846,373654389,377790965,339058132,72018123,-177846887,-126484696,430401658,80690557,-128064093,343074906,-442013730,101228477,610173077,-889906539,494096905,714762557,-889340135}

{-705837084,974661870,382500987,182939759,680375733,-699935801,-799348797,60911396,494634861,-338810573,445734246,340442802,152449484,668867569,953058027,12724171,-74972561,-842876614,-10680989,-1175739}

{-332702354,8090298,334346458}

Returns: 60
{226136483,-479038683,310955565,997898473,-982938308,722817040,203830419,-963985303,832627979,-505558832,486488847,265095746,467527186,-148970422,-893755550,-17224351,96033131,970819055,521720318,400786888}

{-480875284,-485869034,-695564342,-85074753,-326157194,-452450684,-326144654,-511368664,110388699,188432654,699545191,39332080,832680297,177737302,-319364742,-360679262,-96437993,-363771215,-270619376,-233478635}

{-466544565,-35389655,843371779,213042502,101229726,99816470,-864049600,324672813,882382599,-427654382,223784759,-746172491,-497206570,814550913,620283317,-800362647,-382183814,83715078,902551788,-219310693}

{252133886,-837895081,-558710998}

Returns: 57
{272834789,-963268914,686538457,287848554,-786695846,764078490,-663546409,504776710,815836495,83794003,622469726,587478922,84562111,-63695277,-288243017,-146230107,-67589793,-770428775,366397057,689085497}

{238735679,-998824911,-703116693,-747494255,532093465,810344627,804246924,976566450,568433466,21999842,-334056865,965015242,108885002,860719988,892968286,-622894139,735800634,743861745,-407272647,510100991}

{67715720,442647476,816949427,-407422700,-804290766,-563676402,-189581798,461450450,739276533,-897611126,-369901471,75931984,-814119488,-758200244,-372534760,237002746,223679891,-514468714,246227583,-21439123}

{-501350307,-335593390,-450082611}

Returns: 68
{463457821,-412911559,-90055191,869497560,-34815092,-824020540,303612013,-521981267,234112920,-101821103,876394100,58077970,390681869,-181368606,626368190,404696772,161129729,30026603,-838673591,-753313498}

{-106538739,-351261056,-505133185,757026234,794315095,-577164058,-50477803,519178244,-139595439,-701151454,245112532,257932329,-567081656,150142621,168170869,-57581788,-857698534,922638704,450762916,-541706081}

{573301765,496979495,-570394508,324396442,-527930341,224962840,735799743,211004020,-646778034,519273887,-560695756,-646496994,171625178,716310410,-345689538,-662518693,-826952275,-992860854,381052096,-329965316}

{-363729768,243182711,491793544}

Returns: 48
{-240147222,-539322285,87856068,-740849146,-224318723,-580120739,-827360920,415263180,524533523,-267319109,-873121900,-580212867,-214146202,-515695552,351868176,660113534,568587931,-832989102,559615305,300873225}

{920560283,408761400,-288536449,998288073,-662622729,366729893,493654609,-995055721,-663028099,-610655926,727019232,245887581,-292590736,-690788474,-442689373,726999323,-60835482,-612897223,-742371129,949113608}

{566409667,-683976010,294554688,620124624,968665037,398145238,-248076431,627045628,947486061,497819689,-603788684,-250207888,-732587647,656721926,-708403443,-492555808,-552695738,-414359278,-992219529,-232740117}

{904735045,-665422120,-357160720}

Returns: 54
{159720484,378541498,-93965213,-681214386,-413623722,123555,197195133,227939673,839707086,-105671404,-434617866,294804744,243189709,-373197586,131990889,-109698945,983886356,300787570,-358858544,375388531}

{-200885339,-178933987,317242072,276206822,-553165514,922494171,73319672,-530277397,310091685,-622209591,-619154755,-642378397,170318784,-915595208,353435561,298925233,-198517039,-856590168,932710148,-883448878}

{-343653589,-567733628,156698199,551167606,503036900,-728343016,663939997,-553393037,595707676,-820214595,448726542,-551872099,-540422988,22354378,-357211985,960581544,-935577162,-94441863,91482123,627720599}

{-665863930,595201833,546841087}

Returns: 56
{208288011,-353233749,-221751645,786054822,656966789,690041446,810623235,373261641,947199298,994380218,136448049,-903786570,31955074,434190040,655635705,-699811542,-588975113,-321591994,-882564555,-439726223}

{827569602,-935325638,104036684,-550956406,-939544359,-244523092,-549339439,103915112,-107742948,-400392184,509370602,981144111,-864164190,-78495122,-865948666,107458110,-165108615,974388985,-367267643,477364445}

{539659172,874651167,867394616,976289541,-166368005,-394917955,609762322,678404733,-143721371,415017835,-270657678,127721484,881224088,221144330,-592123053,-628946807,301056498,989128433,139035700,257113747}

{-743163128,-631092632,-894043338}

Returns: 59
{-657900381,332135169,-117593962,45654475,-965553655,335056657,164155395,-803331694,920364055,-492205005,359309149,586165173,-219106436,-239206635,-661467,169444322,-164780880,637186212,990943595,-447381276}

{-115810933,789309743,717460654,-951534371,630368753,407370810,471838437,-494776542,-78857816,70420194,-68517989,41978291,293759306,-728438041,13484085,508154966,-555784107,897527899,439229775,207216463}

{9006688,-78833690,251296837,690816957,-291843735,-847394893,-728574258,909600659,-366547127,107551995,225832642,-869094606,205421640,21253164,-69780484,554002080,219683253,833787482,548947048,-613863378}

{384144753,881409505,-174520306}

Returns: 58
{943162022,333111981,919339774,863043116,-847356828,751318744,-433032985,-39797824,-694298426,283835424,593981861,-147306360,-79787359,572938010,340921676,269835897,137375477,326588310,498601162,408741173}

{919974502,-847006480,122174689,-242667305,-496081740,-234597847,-391450519,574217949,364771609,-671042309,157143879,52248789,181500770,-16262471,949433582,153176450,977627719,218990419,532853763,-549400097}

{803448465,444953518,-891398944,-129714300,636004587,428337898,744886052,-462297966,-109398657,-8047854,-562221536,-350334990,963813908,77554520,-470745528,-188341860,394988415,-394699214,-60040790,242589325}

{-443730008,513805215,141705740}

Returns: 51
{-34037289,216387127,-8538744,744047266,-469281582,-213634596,-962361279,-757140631,3209328,168420409,-612263901,205566383,486276716,175371651,197096687,-681219289,-981505988,29121315,-458157436,61144515}

{-347531297,-469344854,322171532,343295077,197089670,325197973,-900837471,571806917,217429824,932373054,-633142717,-907741821,318504160,313169933,-887202054,612854607,-380752276,123410753,218396235,345658943}

{-153703702,934671933,528454370,216163236,-724089331,-477488628,916869794,-80008771,390683761,571692056,982222509,-264134387,659805811,432106237,-679353647,-42528644,-475513171,-293320070,485161362,-821339749}

{-452950516,-801788208,11972496}

Returns: 66
{600000000,-400000000,200000000,0,-1000000000,1000000000,-600000000,-900000000,800000000,-700000000,-800000000,-300000000,500000000,700000000,900000000,400000000,-100000000,100000000,-500000000,300000000}

{0,-500000000,-900000000,600000000,800000000,500000000,700000000,900000000,1000000000,-600000000,100000000,-100000000,-400000000,-300000000,-200000000,200000000,-800000000,-1000000000,400000000,-700000000}

{1000000000,700000000,-1000000000,900000000,-500000000,-600000000,200000000,-900000000,-800000000,-700000000,500000000,-100000000,100000000,300000000,400000000,0,600000000,-300000000,-400000000,-200000000}

{200000000,1000000000,100000000}

Returns: 100000002
{43,-6,-63,-12,23,67,-35,-69}

{-39,-65,36,29,47,63,-7,8}

{-13,-39,-2,42,-24,-42,48,-1}

{-59,2,-7}

Returns: 8
{81,-32,161,-122,-155,108,-41,181}

{-207,-229,215,128,73,-45,-16,-115}

{-36,-30,-217,150,133,74,78,174}

{133,-219,-116}

Returns: 13
{358,365,127,-240,193,117,182,305,354,241}

{88,-354,-266,-312,1,-342,161,109,197,-329}

{-322,361,13,-95,68,-197,-79,366,-226,-355}

{2,361,-321}

Returns: 12
{-51,78,111,55,-14,142,-59,-103,195,13}

{44,126,71,152,-78,109,-168,178,138,79}

{-100,122,7,-54,105,70,37,44,3,52}

{109,2,146}

Returns: 7
{-275,-176,80,-183,-61,92,-53,-184,21,108,260,-272}

{-247,-64,127,186,82,58,57,94,-19,-152,-120,-223}

{39,-10,179,265,211,128,-226,-92,-62,-102,169,21}

{-242,-244,-100}

Returns: 9
{7979,-2803,-8262,-5102,3537,158,-2291,4199,-3987,5249,7007,7768}

{-804,-8986,2030,-6912,-4579,-1212,-2728,2160,4850,7483,7636,5160}

{-8519,7102,7233,6806,3233,-8222,-2497,-1745,-1564,2268,2854,6487}

{1632,-2761,1175}

Returns: 16
{97,134,-717,496,51,687,-79,254,301,-639,-408,759,-20,-585}

{-282,720,459,144,232,-484,-392,33,-50,-673,461,-608,-591,-557}

{-361,-125,-521,608,689,472,-189,-760,-741,695,-605,499,34,558}

{-194,2,355}

Returns: 9
{-47,-37,-40,43,28,-21,22,-22,41,-31,-64,-28,26,-43}

{60,-34,-41,-68,-46,46,41,-18,15,37,71,-25,-7,24}

{-1,50,-61,-70,68,-40,5,-64,23,60,-44,42,62,-37}

{62,-3,48}

Returns: 8
{282,-163,-169,165,-455,293,-747,-589,-92,753,-221,338,304,-877,141,485}

{-515,-278,-472,-576,446,-800,-629,522,-602,-613,544,864,-428,765,876,-835}

{-87,-859,334,-588,-195,-373,-342,734,-241,-368,351,411,-695,719,158,132}

{678,363,649}

Returns: 11
{-878,-1333,2714,-3351,-1894,-203,2262,3711,-168,-3281,-4372,3081,-2579,-3373,4271,-3254}

{1297,3476,-3604,-3838,892,-1404,-1708,-3704,-3422,4392,2117,-681,1028,-1395,-3359,1685}

{3277,-602,3348,3803,-126,536,4054,-4351,-2677,925,644,-7,-3693,-4159,451,1470}

{2663,-16,-550}

Returns: 13
{103,-440,35,-132,-386,70,-340,217,61,-65,533,-500,28,175,-154,-491,59,-222}

{320,189,-443,260,-430,535,-178,-70,-367,-529,288,64,-441,65,-191,495,-521,17}

{-188,-399,234,-535,-241,-517,-214,-1,150,-105,96,-31,275,-358,-224,230,-94,-155}

{363,-447,3}

Returns: 9
{-323,-556,323,120,-218,-679,-841,793,123,-508,-444,-603,-364,196,337,-422,142,-214}

{-39,204,-436,-623,18,428,683,408,-427,-373,434,314,302,-423,-798,-740,550,-253}

{646,-230,645,36,-329,582,19,228,-346,-724,446,295,172,820,724,-156,-727,-759}

{-207,-852,322}

Returns: 10
{-1128,760,-686,669,-819,628,839,725,524,-212,175,75,-215,-1092,-990,1007,-83,-274,392,965}

{823,-332,-602,-280,319,119,591,489,-581,658,738,342,23,71,-43,-377,251,517,-770,-503}

{-1130,-226,920,-274,143,346,-422,-113,-547,-416,-275,-865,-469,-694,-332,946,-40,96,-512,744}

{-591,-558,-1147}

Returns: 9
{80,141,-103,36,-177,109,-113,143,149,-12,63,-33,12,-175,11,103,-77,-11,48,-92}

{149,29,3,-106,14,-131,-120,-82,-19,-116,157,-34,-160,40,104,-135,154,64,-31,-77}

{27,-6,-12,22,-157,-38,-74,140,121,-33,-109,-18,-29,-143,-21,-62,-56,128,-167,144}

{88,2,-49}

Returns: 7
{-1,12,-2,10,-10,14,-3,-12}

{0,6,-7,-5,-9,-2,8,2}

{12,-9,-4,7,-3,11,2,0}

{8,2,-3}

Returns: 7
{-46,-78,-158,-127,88,156,181,43}

{-24,-174,101,-191,81,-35,-10,-142}

{21,184,169,97,-189,33,40,62}

{3,152,-107}

Returns: 10
{30,-22,-10,22,45,-46,-28,72,-53,91}

{60,-28,1,91,-19,84,24,-70,55,-1}

{50,49,-30,52,53,-81,-39,-83,-71,-66}

{2,9,-22}

Returns: 9
{24,4,33,6,-11,-4,-27,-25,30,-29}

{-27,-14,1,5,31,4,15,-30,7,-29}

{11,-5,-25,-10,-3,27,30,-15,-18,2}

{-31,-32,2}

Returns: 7
{-13,69,26,-22,51,85,17,-75,2,32,-48,43}

{-52,69,-35,43,63,55,-81,32,-14,-29,37,9}

{-30,84,63,74,51,-63,85,-72,68,-77,6,48}

{2,-23,-33}

Returns: 8
{64,-129,-247,-274,70,184,-182,165,214,-113,174,-9}

{-274,-170,-189,180,229,35,182,-128,-243,-65,-120,-271}

{34,72,129,6,-149,190,57,158,266,-142,-239,-119}

{-247,-45,146}

Returns: 11
{29,6,-31,43,-56,-68,-64,-8,-34,13,-14,-28,27,-73}

{-18,-51,0,44,-1,49,-10,45,68,11,-55,54,42,61}

{-68,-60,-20,25,-13,-34,-29,-32,-17,59,58,5,-33,53}

{2,-24,-1}

Returns: 5
{-140,-532,774,-445,330,392,-923,-199,-665,-885,244,-23,718,-240}

{272,-84,-850,380,-557,538,85,-582,394,882,-595,-927,-200,797}

{298,553,-494,738,-669,-325,54,-457,733,-635,58,569,355,437}

{-396,-49,706}

Returns: 10
{-64,-80,63,-50,0,-45,-133,121,93,-76,-120,133,20,77,67,-69}

{128,-120,4,113,123,79,27,-62,6,-18,20,-29,40,-65,-87,-9}

{83,108,-72,-51,2,-106,136,65,-32,89,-115,107,-50,99,-136,-121}

{2,-71,43}

Returns: 8
{19,60,40,22,-34,15,-11,-50,61,-30,-46,35,2,-32,-52,-38}

{55,48,13,-52,-15,-63,-38,-47,19,50,22,24,-45,-24,6,-21}

{62,27,60,13,43,-49,-44,-31,-51,-12,-26,41,-8,-30,-56,55}

{-30,2,22}

Returns: 8
{602,-558,-15,-304,-280,-94,-444,-593,577,263,-159,440,-564,-583,-168,405,-587,-580}

{430,369,81,307,-132,118,30,-474,-418,-86,-618,399,571,301,-476,325,536,-615}

{146,582,483,-152,312,-213,-479,-33,269,174,-373,136,-107,-364,231,422,502,539}

{579,92,294}

Returns: 8
{-1867,-115,-2286,2272,789,-789,243,1518,2374,-1071,-1572,1778,-1390,-991,2133,469,-12,2399}

{-1557,737,-367,-1178,2196,-1976,-442,-331,2206,-2248,-932,-1808,2032,-452,323,-1134,2432,-294}

{1037,241,-1764,52,1460,-2334,1899,-2026,-2173,252,-1224,-2043,2312,-2333,-421,525,-1601,670}

{-2166,406,-1334}

Returns: 12
{117,-443,476,-252,557,-352,3,222,-122,-202,420,487,-50,-41,-505,-189,539,267,527,-482}

{-209,-509,122,-311,-334,-461,352,-177,372,-307,255,-335,-511,-398,506,302,424,-1,-280,325}

{303,328,-270,-345,-38,-243,-514,56,253,233,78,-324,-455,432,43,363,-59,-349,495,103}

{-172,32,2}

Returns: 9
{-426,-462,19,899,585,677,-199,185,648,494,-140,-910,-716,320,279,-539,-44,194,-654,588}

{-615,261,729,774,496,-826,126,-7,-106,231,-419,681,-49,-748,-159,878,256,-435,956,776}

{407,110,-156,-305,908,635,693,-614,188,524,61,-554,-406,-787,-56,-366,874,593,-678,362}

{560,494,-513}

Returns: 10
{-3635,-419,-3244,4451,2127,7506,-7977,-7910}

{7062,-4774,8114,9303,3132,-180,2057,5370}

{-808,4830,1406,1298,-9188,-2492,-1695,-7864}

{-7883,-2111,8206}

Returns: 102
{-50,10,63,2,-43,-5,43,72}

{12,-5,-10,6,34,51,-56,47}

{70,0,-16,-45,-59,4,-55,2}

{-3,-16,-17}

Returns: 11
{855,141,-781,-457,-48,795,-109,-442,-432,-691}

{541,-504,401,224,218,-559,799,461,779,577}

{266,-673,785,603,763,-249,-67,-455,-272,-38}

{779,-765,-80}

Returns: 13
{-62,-49,-85,-155,-203,-128,122,7,54,-58}

{-171,-57,183,-79,-78,-5,-146,-127,189,162}

{-3,36,82,-14,91,-86,180,182,142,-173}

{-101,21,106}

Returns: 11
{-342,52,-82,-265,331,155,-76,296,-41,239,38,-88}

{-120,3,-74,74,-50,-115,-58,-116,-167,133,246,-289}

{77,-171,120,123,-210,291,-71,-13,-305,131,-102,73}

{226,-110,-3}

Returns: 9
{29,49,24,-27,11,-51,16,6,55,37,-10,76}

{36,-54,50,-15,-70,-25,-68,45,47,-35,0,-45}

{30,-41,26,66,22,-57,14,-65,-38,-77,-59,13}

{-3,68,27}

Returns: 8
{-21,-301,-84,230,-75,23,-295,77,-72,-63,6,118,234,-174}

{333,-131,-210,-30,-63,135,-160,-90,220,8,-1,-161,16,-194}

{-330,-50,205,126,-26,21,-241,140,-14,-45,172,33,300,-257}

{315,62,-3}

Returns: 9
{-941,-301,247,1314,1284,273,1175,587,-695,889,-142,905,-998,976}

{-1317,1121,-430,-1152,-173,-809,1214,1288,-767,1229,598,-830,305,-1088}

{1292,-1080,622,-955,-789,1217,1078,751,-9,74,1202,-1248,1113,-971}

{-414,-689,-1031}

Returns: 13
{-71,46,47,83,-24,33,41,-89,-83,-6,52,8,21,48,-44,-46}

{-87,-63,71,-85,87,-81,-26,70,88,32,-46,-66,-91,65,19,38}

{50,78,-60,-40,-49,-86,-20,70,82,-16,0,-77,3,-46,74,-67}

{15,31,-3}

Returns: 8
{33,-78,-72,-57,-65,2,36,-61,40,32,26,39,66,12,-11,76}

{-38,-70,-22,-43,35,26,41,47,32,63,-63,23,69,-7,6,-66}

{55,4,-12,3,43,-43,12,75,-22,-27,26,31,41,-26,-40,27}

{43,-3,-22}

Returns: 9
{-307,412,-116,-14,-26,-315,253,222,-208,41,430,-446,373,158,392,-263,247,-229}

{-350,-113,-49,-426,153,-304,488,49,4,394,148,-20,-149,-236,139,104,198,45}

{-24,234,-462,-361,240,423,-370,471,-201,-465,255,130,211,-298,-142,34,146,-437}

{-3,-147,202}

Returns: 9
{426,720,-747,615,-255,-353,562,427,274,-135,713,656,-291,473,-251,-523,53,-623}

{-721,418,545,290,-495,689,-404,534,-415,184,599,-156,-123,-132,191,-501,103,196}

{-674,-379,510,569,-63,-614,-457,136,11,499,533,-506,116,-164,600,-148,-670,632}

{-701,620,-3}

Returns: 10
{2}

{}

{}

{3, 0, 1}

Returns: 3

Manao can reflect the artifact against the only given plane, making it appear at (4, 0, 0). Afterwards, he can transfer it into the target position by two moves of the first type.
{-5, 1, 4, 2, 3, 6, -6}

{}

{}

{9, 0, 0}

Returns: 2

A possible solution will be moving the artifact to (-1, 0, 0) and then reflecting it against the plane represented by mirrorX[2].
{5, 8}

{}

{}

{4, 0, 0}

Returns: 4

If a reflection against a particular plane was allowed more than once, Manao could transfer the artifact in only three moves.
{5}

{5}

{1, 2, 3}

{10, 12, -1}

Returns: 5

The planes perpendicular to the Z axis are of no use. After performing the reflections against the other two planes, Manao gets the artifact to point (10, 10, 0). Three more moves of the first type are required then.
{8, -3, 21}

{4, 5}

{-7, -2, -1, 7, 14}

{40, -4, 31}

Returns: 10
{0, 315, 1, -5}

{4, 9, 21, -5655}

{-1000000000, 1000000000}

{0, 0, 0}

Returns: 0
{}

{}

{}

{0, 0, 0}

Returns: 0
{5 }

{5 }

{1, 2, 3 }

{10, 12, -1 }

Returns: 5
{8, -3, 21 }

{4, 5 }

{-7, -2, -1, 7, 14 }

{40, -4, 31 }

Returns: 10
{-332174142, -638603452, -23120720, -179572821, -721016033, -257385004, 540831225, -680342386, -192705044, -638363532, 878697594, -184845502, -655088737, 350795696, -245684021, 584386630, -830330346, -759394703, 538975432, 721871889 }

{-332174142, -638603452, -23120720, -179572821, -721016033, -257385004, 540831225, -680342386, -192705044, -638363532, 878697594, -184845502, -655088737, 350795696, -245684021, 584386630, -830330346, -759394703, 538975432, 721871889 }

{-332174142, -638603452, -23120720, -179572821, -721016033, -257385004, 540831225, -680342386, -192705044, -638363532, 878697594, -184845502, -655088737, 350795696, -245684021, 584386630, -830330346, -759394703, 538975432, 721871889 }

{972407554, -411603950, -725275153 }

Returns: 67
{11436, 5740, 12122, 18444, 11279, 8632, 9301, 6938, 10208, 5518, -29431, -575, -3830, -26684, -26910, -2627, -10758, -13205, -25112, -29156 }

{-899994067, -587053738, 176679700, -194750248, -898632744, -223540289, -509387157, -503715892, 654048330, -327587831, -590663083, 365957972, 276306980, -649061451, 626858164, -186023449, -420013810, 117090635, 705877944, 862209862 }

{-900000000, 166410000, 100, 247950000, 176670000, -83790000, -194760000, 30, -898650000, -833670000, 15, -223560000, 209430000, -509400000, 752400000, -503730000, -105660000, 654030000, -820890000, -327600000 }

{1000000000, 918742891, 170 }

Returns: 999464222
{481765933, 85377743, 270216262, 191391529, -187330300, -446524492, -554650248, 344887256, -269582744, 812158119, -852300289, -119731649, 889772843, -313921295, -894245892, -817453607, 949118330, -779862634, 979932169, 89957932 }

{481765933, 85377743, 270216262, 191391529, -187330300, -446524492, -554650248, 344887256, -269582744, 812158119, -852300289, -119731649, 889772843, -313921295, -894245892, -817453607, 949118330, -779862634, 979932169, 89957932 }

{481765933, 85377743, 270216262, 191391529, -187330300, -446524492, -554650248, 344887256, -269582744, 812158119, -852300289, -119731649, 889772843, -313921295, -894245892, -817453607, 949118330, -779862634, 979932169, 89957932 }

{-984065896, 363674760, -95370251 }

Returns: 85
{-83856, -98603, -83222, -92207, -77610, -70391, -73887, -90765, -88549, -99083, -83548, -80687, -94006, -94001, -90206, -76176, -92062, -86299, -71677, -77401 }

{-68366, -78626, -92066, -85504, -78106, -73661, -80979, -89120, -85727, -75714, -86786, -70549, -73396, -72543, -97685, -96094, -93587, -86487, -80821, -79922 }

{-88645, -72699, -86870, -72414, -70223, -81262, -87305, -72548, -88223, -67735, -79875, -84180, -90613, -96613, -96747, -71144, -86802, -92869, -93799, -72289 }

{6654, 17341, 23611 }

Returns: 18
{1244, 3252, 6463463, 4363, 21425, 336, 215, 5748, 24325, 7457 }

{12311, 25325, 2364376, 124124, 43643, 3214, 4363, 124 }

{11, 77, 5346, 8888888, 35235, 12411, 5474587 }

{99955999, 1000000000, 999499798 }

Returns: 2052510170
{-998638045, -792420988, -371854484, -623859538, -116484720, -813030415, -237111365, -673597461, -901847898, -841823428, 61402892, -872139111, -990419362, -429129956, -353860681, -821490978, -515972334, -938736696, -158917445, -441787226 }

{-59436285, 26389629, -420886472, -503852001, -74198828, -162848260, 70301173, -343414725, -714154995, -97928950, -596426277, -272876238, -990532710, -703768338, -368734600, -100625667, -479309751, -201428490, -508252291, -200686628 }

{-356784305, -210795534, -385391552, -837266736, -543482684, -444746569, -193043909, -818542046, -471843294, -248645987, -841601141, -847959590, -256025398, -541999358, 37883250, -835443127, -117735296, -794538811, -122555691, -832964992 }

{-214013462, -699793716, -267446593 }

Returns: 37
{1, 5, 3, 7, 4, 9, 12 }

{7, 12, 4, 2, 87, 5, 6 }

{7, 1, 2, 22, 9, 3, 6 }

{23, 456, 123 }

Returns: 317
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 100564 }

{1234, 314, 51234, 2134, 123, 2, 543, 214, 876, 986, 45 }

{ }

{3213, 1235435, 45236342 }

Returns: 46362202
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 }

{ }

{ }

{100, 100, 100 }

Returns: 205
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

{1 }

{2 }

{1, 2, 3 }

Returns: 4
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

{0, 0, 0 }

Returns: 0
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

{1, 1, 1 }

Returns: 3
{-959666, -859726, -843558, -823507, -768486, -610884, -491067, -415053, -391859, -310011, -111746, 82135, 253154, 312973, 361955, 461087, 573522, 580634, 800710, 882732 }

{-972576, -787505, -597624, -443209, -428889, -266817, -130241, -44312, 113239, 123399, 151322, 215374, 265085, 353638, 402362, 443871, 514839, 578909, 844863, 974231 }

{-999587, -929401, -861004, -854798, -852249, -847947, -735737, -699362, -601220, -482912, -436755, -30508, 34925, 204072, 263274, 373884, 457864, 467286, 747464, 860826 }

{986146, -793866, -446959 }

Returns: 23
{3, 6 }

{3 }

{3 }

{-9, 0, 0 }

Returns: 5
{10, 3 }

{ }

{ }

{14, 0, 0 }

Returns: 2
{10, 19, 8 }

{ }

{ }

{-2, 0, 0 }

Returns: 2
{3, 5 }

{1 }

{1 }

{-4, 0, 0 }

Returns: 2
{1, 2, 3, 4, 5, 6, 7, 8, 9, 123, 1245, 12356, 34534, 5465656, 1234458, 76, 654, 98765, 87654, 45400 }

{123, 34554, 7654, 9876, 9965, 34456, 11123, 12343454, -123324, -324, -123456, -2345677, -4656877, 900887, -7878999, 123123123, 123125415, -1245677, -111111, -111999 }

{111111, 1222222, 33333, 4444, 55555, 66666, 7777, -44444, -33333, -22222, -1111111, 345456, 34554667, -123456, -3456789, -5555556, -8776565, -22211114, -11112321, -1001 }

{-1000000000, 1000000000, -12312124 }

Returns: 1433642732
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

{20, 20, 20 }

Returns: 3

Statistics

Problem Statement for "Reflections"

Problem Statement

Definition

Constraints

Examples