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Experimental Emergency Teleportation

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2018-12-23

Day 23: Experimental Emergency Teleportation

Description:
--- Day 23: Experimental Emergency Teleportation ---

Using your torch to search the darkness of the rocky cavern, you finally locate the man's friend: a small reindeer.

You're not sure how it got so far in this cave. It looks sick - too sick to walk - and too heavy for you to carry all the way back. Sleighs won't be invented for another 1500 years, of course.

The only option is experimental emergency teleportation.

You hit the "experimental emergency teleportation" button on the device and push I accept the risk on no fewer than 18 different warning messages. Immediately, the device deploys hundreds of tiny nanobots which fly around the cavern, apparently assembling themselves into a very specific formation. The device lists the X,Y,Z position (pos) for each nanobot as well as its signal radius (r) on its tiny screen (your puzzle input).

Each nanobot can transmit signals to any integer coordinate which is a distance away from it less than or equal to its signal radius (as measured by Manhattan distance). Coordinates a distance away of less than or equal to a nanobot's signal radius are said to be in range of that nanobot.

Before you start the teleportation process, you should determine which nanobot is the strongest (that is, which has the largest signal radius) and then, for that nanobot, the total number of nanobots that are in range of it, including itself.

For example, given the following nanobots:

pos=<0,0,0>, r=4
pos=<1,0,0>, r=1
pos=<4,0,0>, r=3
pos=<0,2,0>, r=1
pos=<0,5,0>, r=3
pos=<0,0,3>, r=1
pos=<1,1,1>, r=1
pos=<1,1,2>, r=1
pos=<1,3,1>, r=1

The strongest nanobot is the first one (position 0,0,0) because its signal radius, 4 is the largest. Using that nanobot's location and signal radius, the following nanobots are in or out of range:

The nanobot at 0,0,0 is distance 0 away, and so it is in range.
The nanobot at 1,0,0 is distance 1 away, and so it is in range.
The nanobot at 4,0,0 is distance 4 away, and so it is in range.
The nanobot at 0,2,0 is distance 2 away, and so it is in range.
The nanobot at 0,5,0 is distance 5 away, and so it is not in range.
The nanobot at 0,0,3 is distance 3 away, and so it is in range.
The nanobot at 1,1,1 is distance 3 away, and so it is in range.
The nanobot at 1,1,2 is distance 4 away, and so it is in range.
The nanobot at 1,3,1 is distance 5 away, and so it is not in range.

In this example, in total, 7 nanobots are in range of the nanobot with the largest signal radius.

Find the nanobot with the largest signal radius. How many nanobots are in range of its signals?

--- Part Two ---

Now, you just need to figure out where to position yourself so that you're actually teleported when the nanobots activate.

To increase the probability of success, you need to find the coordinate which puts you in range of the largest number of nanobots. If there are multiple, choose one closest to your position (0,0,0, measured by manhattan distance).

For example, given the following nanobot formation:

pos=<10,12,12>, r=2
pos=<12,14,12>, r=2
pos=<16,12,12>, r=4
pos=<14,14,14>, r=6
pos=<50,50,50>, r=200
pos=<10,10,10>, r=5

Many coordinates are in range of some of the nanobots in this formation. However, only the coordinate 12,12,12 is in range of the most nanobots: it is in range of the first five, but is not in range of the nanobot at 10,10,10. (All other coordinates are in range of fewer than five nanobots.) This coordinate's distance from 0,0,0 is 36.

Find the coordinates that are in range of the largest number of nanobots. What is the shortest manhattan distance between any of those points and 0,0,0?

Input:
pos=<35736475,5268315,44141623>, r=68945144
pos=<98249648,35180107,46324866>, r=99363158
pos=<-33547541,25677708,29822965>, r=91044586
pos=<18997357,27435558,22203548>, r=51976657
pos=<9999306,44070497,46228534>, r=60389933
pos=<-11232017,15711495,38725419>, r=69792763
pos=<69735987,47669658,46708342>, r=57976671
pos=<108348247,48092549,46991236>, r=95882854
pos=<29616366,30343943,25580230>, r=56310558
pos=<55771892,34986939,14417116>, r=88986230
pos=<-4076452,46003840,-27660246>, r=98730882
pos=<37806127,35544433,26100531>, r=58779554
pos=<28537325,-29968211,43996784>, r=97127437
pos=<175944061,22745049,18215615>, r=83019610
pos=<-7518172,50302588,20566683>, r=51741591
pos=<32973385,102732735,26399661>, r=93414748
pos=<27566699,32225307,2735607>, r=75224145
pos=<90765957,45380919,68169326>, r=99066859
pos=<17439378,-23734545,29591571>, r=94200997
pos=<37348398,35907697,1171310>, r=82887984
pos=<16668596,17585024,30949266>, r=50752838
pos=<43294910,55011497,6547354>, r=75867319
pos=<-39687235,73312930,41074953>, r=86412726
pos=<77600061,52837446,45466783>, r=69078996
pos=<79847020,47470311,46895275>, r=68099888
pos=<41161959,-11459287,37418030>, r=97821876
pos=<55243809,26266628,37349576>, r=74246269
pos=<28554372,56539455,11790628>, r=57411682
pos=<35376754,77309282,68931747>, r=68620223
pos=<80333063,47281103,44270109>, r=71400211
pos=<26282613,18846337,19865708>, r=70189108
pos=<81162185,36811904,29601881>, r=97366760
pos=<76518508,39246657,43222325>, r=76667967
pos=<49483399,13072223,23782144>, r=95247770
pos=<75407008,32771443,67266045>, r=95414250
pos=<20396216,32874538,18115050>, r=52025144
pos=<47518497,34143968,14694996>, r=81297906
pos=<58121018,46842064,20052637>, r=73844744
pos=<-25482904,58405932,58752491>, r=60023043
pos=<2414899,74909973,18437390>, r=68545229
pos=<93399797,56430242,41827270>, r=92111574
pos=<22057772,29819687,42910507>, r=84744225
pos=<58887283,37744860,27213147>, r=76547677
pos=<20511261,12176609,40616709>, r=50336418
pos=<27531206,5567327,11585926>, r=92996314
pos=<-11888301,36803758,23995873>, r=64086479
pos=<55138614,6254749,54369165>, r=88765526
pos=<27689879,48020738,33552377>, r=70404742
pos=<17399375,22091331,11617566>, r=66308859
pos=<-30063622,12388637,40670912>, r=90001755
pos=<35362839,37222182,9170045>, r=71588990
pos=<203530720,40857437,31304618>, r=97936573
pos=<71684320,41513849,32460452>, r=80328463
pos=<6832912,17923279,-10870456>, r=99111947
pos=<70541337,40514901,23109870>, r=89534942
pos=<-22356418,22728990,45454279>, r=67170798
pos=<21116887,35329043,40481972>, r=74431257
pos=<31626078,42426499,2331845>, r=69486096
pos=<64317834,61658521,38180749>, r=71903858
pos=<-52795703,46719036,38718342>, r=80355995
pos=<52774899,78131860,28428556>, r=86586505
pos=<32215639,16811727,25393141>, r=72629218
pos=<21974048,46228429,-17810448>, r=76175002
pos=<59234315,42744200,40747201>, r=58361302
pos=<50620475,95139824,34221129>, r=95647436
pos=<31524663,83545637,36393296>, r=62785299
pos=<-43702001,60251514,32749670>, r=85692014
pos=<47014566,71579815,66754620>, r=72351399
pos=<71588604,22705912,35843016>, r=95658127
pos=<88518450,40216724,54752646>, r=88566919
pos=<-60378893,29488684,44404684>, r=99483294
pos=<-11101653,79245668,34873217>, r=69961698
pos=<44936915,20055145,71895444>, r=82289701
pos=<-44992958,47946287,40495699>, r=69548743
pos=<46823746,44888999,1056656>, r=83496494
pos=<-36025436,54507898,22026426>, r=82994433
pos=<20587527,-24964792,34210791>, r=93959974
pos=<-147275777,18337543,40032704>, r=74216227
pos=<41111909,-13140154,40504911>, r=96365562
pos=<28252618,41639354,43825267>, r=79119691
pos=<64777674,43642375,38465261>, r=65289045
pos=<50314871,48086008,33304117>, r=51543138
pos=<52803279,52187826,33480017>, r=55619426
pos=<42764327,22650241,12311998>, r=90420773
pos=<36024431,23059804,20110184>, r=75472847
pos=<65070465,24199205,24785446>, r=98704248
pos=<21614823,44943481,40873083>, r=78906127
pos=<42135803,45316305,7170286>, r=72267592
pos=<60338695,24596400,68535461>, r=89790637
pos=<91847494,36602917,44174167>, r=93688975
pos=<42617883,45456599,2364062>, r=77415614
pos=<-17900452,26264040,46075639>, r=58558593
pos=<23065024,54683026,44912280>, r=79925134
pos=<7393618,13065147,24339203>, r=68199956
pos=<66409579,61821152,55522004>, r=70755419
pos=<-16465303,31827246,46650925>, r=50984786
pos=<63652634,35204424,42567838>, r=68499244
pos=<-33503704,33700462,30229837>, r=82571056
pos=<28323023,71484327,26373493>, r=57542097
pos=<28638640,42039332,41138992>, r=52702802
pos=<71640578,37211073,21580686>, r=95467266
pos=<-41000570,46965324,40040080>, r=66992886
pos=<76894429,46086205,25958626>, r=87468098
pos=<-2104680,19136731,39740387>, r=56225317
pos=<-24197801,50664690,29123122>, r=60226968
pos=<78990123,45644865,29732704>, r=86230964
pos=<-75727029,44926164,44902145>, r=98896354
pos=<31308722,45558616,9895068>, r=58473693
pos=<4366402,38123986,47281720>, r=95230204
pos=<95625327,59551444,-77297749>, r=57341892
pos=<62785679,81502394,31308615>, r=97087863
pos=<-15796059,72916646,38179244>, r=65020985
pos=<18491161,-132636,19831409>, r=81410854
pos=<23872265,29672987,5867691>, r=70950377
pos=<70800264,78761297,46375689>, r=87294333
pos=<29356716,5693454,18985832>, r=87296130
pos=<24908148,26208701,2213603>, r=79104220
pos=<66837058,30632466,35443185>, r=83379848
pos=<34758918,14455953,51851302>, r=57666779
pos=<54033957,17306737,38736710>, r=80609003
pos=<48708931,41607919,37147697>, r=52571767
pos=<-589665,74402116,82826728>, r=75200417
pos=<104827312,44510775,45564490>, r=97370611
pos=<16914008,-5653659,34384768>, r=70801459
pos=<20021121,-10501160,45627107>, r=67513655
pos=<26852275,85491857,44735094>, r=51717310
pos=<17505657,7026134,65101229>, r=61093244
pos=<-55850355,27721263,54572745>, r=98593809
pos=<90722224,39374348,46408572>, r=87557755
pos=<75712788,47079590,41284423>, r=69967135
pos=<-20098667,80444558,16622292>, r=98408534
pos=<-6183342,53541207,-17315146>, r=91527240
pos=<74050808,67317078,33746975>, r=91729179
pos=<54343750,38615989,93193128>, r=94433797
pos=<-5682328,86361229,20285787>, r=86245296
pos=<62616200,14021719,39538183>, r=91674704
pos=<18076520,56782799,72306919>, r=99500690
pos=<25035042,46689028,-14950654>, r=75915233
pos=<44009109,28898114,41196461>, r=56532945
pos=<-37907339,58047707,13717933>, r=96724811
pos=<-187456522,36438102,43373346>, r=67272291
pos=<42609408,29331524,12947311>, r=82949011
pos=<-34091899,66998918,59222950>, r=77695659
pos=<21320292,30995210,18116462>, r=54827457
pos=<-35162362,37777932,13653808>, r=96728256
pos=<-28240962,57549303,36590434>, r=63687396
pos=<53576376,36200124,36144896>, r=63849798
pos=<45336817,45251822,18873424>, r=63830112
pos=<-22707479,37411073,35715277>, r=62578849
pos=<40230216,57454752,95174584>, r=79862068
pos=<59394402,27523746,18638104>, r=95851003
pos=<88516125,41197150,40930949>, r=89006386
pos=<67918123,48121345,6145417>, r=96269722
pos=<52126865,27095082,86460873>, r=97005363
pos=<27227299,-18178187,62306972>, r=93225082
pos=<-52776428,19141315,50163425>, r=99690435
pos=<7041041,73555120,46658718>, r=70803069
pos=<57128675,96955462,56836215>, r=97922737
pos=<54449598,39543556,42204757>, r=55319856
pos=<64335579,45020796,21767560>, r=80165742
pos=<-10953426,35883853,72893055>, r=63854399
pos=<-4190893,64549410,77887691>, r=64009634
pos=<63151021,45773096,45935136>, r=54061174
pos=<34548926,20300660,27453916>, r=69412731
pos=<51843539,38693218,34049205>, r=61719484
pos=<44387978,51031179,8721243>, r=70806158
pos=<59223378,44844401,59074782>, r=58966408
pos=<61304375,46368851,54526663>, r=54974690
pos=<68152456,22248517,46227589>, r=82294719
pos=<18339974,-5788972,63757444>, r=73398926
pos=<57538247,45718816,28488332>, r=65949533
pos=<8913814,-12458905,33265853>, r=83277038
pos=<16791601,13698532,12465629>, r=73245867
pos=<73788319,54065233,38631376>, r=73330460
pos=<107019791,47183191,46696404>, r=95758626
pos=<27086216,46495998,2060349>, r=61148476
pos=<84492299,48203216,39343804>, r=79563639
pos=<49703995,33106963,44981015>, r=54234420
pos=<41387363,71321738,39509986>, r=57307429
pos=<-3676647,73532276,29728496>, r=61968152
pos=<32178381,21984325,84180197>, r=79886828
pos=<-7069263,47417372,21236800>, r=51412727
pos=<30301905,45665804,85726216>, r=55875295
pos=<49297738,17850032,57142847>, r=74103135
pos=<41561820,8727671,33335040>, r=82117473
pos=<-43781510,33486286,38940865>, r=84352561
pos=<64076551,42015352,-101902867>, r=50498200
pos=<-19931867,48178934,33747288>, r=51003449
pos=<48825639,37857409,83237873>, r=79718665
pos=<52754055,54074845,30871190>, r=60065992
pos=<23710745,38605907,-4774784>, r=72497986
pos=<20100858,45307027,-19905476>, r=77317736
pos=<51989289,39999030,27113427>, r=67495320
pos=<13124305,40302301,-2002745>, r=61573777
pos=<67333830,64297659,37758704>, r=77981081
pos=<-6206707,30586474,26208321>, r=62409597
pos=<43829193,6417845,33763264>, r=86266460
pos=<17441312,-3276117,46331101>, r=57004923
pos=<-5811539,67444586,34653790>, r=53090097
pos=<68574352,40336927,40977103>, r=69878682
pos=<41825475,46893199,42551899>, r=65263400
pos=<42543839,30413383,21732752>, r=73016846
pos=<54017489,43310312,43147046>, r=50178577
pos=<21356984,45064785,45699790>, r=95382140
pos=<56047348,39293098,44816599>, r=54556172
pos=<31012313,-810216,35010177>, r=79430729
pos=<20548415,23427947,50386534>, r=55974101
pos=<83730679,35320880,35929550>, r=95098682
pos=<-31137295,40318031,44440067>, r=59376839
pos=<28766416,51774559,1709817>, r=62939486
pos=<-14625904,24101034,41655322>, r=61867183
pos=<38852614,90776048,36288511>, r=77448703
pos=<32782342,38841848,-3575742>, r=80134716
pos=<93144002,43891300,33538220>, r=98333022
pos=<31170005,42947708,37646677>, r=64444426
pos=<21097695,37432740,45253045>, r=67959464
pos=<34685485,25162272,41906424>, r=50235239
pos=<57801108,28735238,65912151>, r=80490652
pos=<66008687,22000710,46643748>, r=79982873
pos=<75031283,42124842,65292374>, r=83711450
pos=<4314807,21493748,37255215>, r=49933897
pos=<30191609,11668271,6324880>, r=94816823
pos=<17367539,65981694,57542607>, r=95842811
pos=<-28473549,42977346,35446488>, r=63048072
pos=<37223961,67290016,81894566>, r=73410945
pos=<79638394,38789373,36923054>, r=86544333
pos=<55426104,14105266,42298311>, r=81640923
pos=<-21879323,106239503,44120331>, r=98486095
pos=<-125107,39446044,11813301>, r=61863422
pos=<25471056,28888510,14288615>, r=64912401
pos=<26040713,-937694,33260097>, r=76336814
pos=<26146255,5138662,13390128>, r=90236012
pos=<-31600050,46188373,24574225>, r=73835185
pos=<38701928,50721403,-15619730>, r=89151831
pos=<-62241067,45831496,32278384>, r=97129012
pos=<20062556,37906685,-793875>, r=65568196
pos=<82392638,51991373,45837286>, r=72655021
pos=<96740744,55028844,43580747>, r=92297164
pos=<36356721,29153145,13541303>, r=76280665
pos=<3079865,36558003,4307974>, r=69051802
pos=<80867329,62476685,53187768>, r=83534175
pos=<42484950,25640433,47378396>, r=52084513
pos=<75958750,40394046,37982939>, r=80200200
pos=<29644031,40847960,56546097>, r=51384581
pos=<38435552,3322493,34653481>, r=83077941
pos=<-31221495,46982605,44374419>, r=52862427
pos=<-28423714,36081949,52968024>, r=61201574
pos=<28016904,22899945,20572393>, r=67162992
pos=<86298312,43104046,38408210>, r=87405045
pos=<60693649,74876518,46712644>, r=72965794
pos=<22566696,48065309,56798978>, r=58303861
pos=<22859392,32036957,-13067634>, r=86508478
pos=<28179535,8102799,45263720>, r=57431406
pos=<59144734,38297774,44640215>, r=58825116
pos=<25398427,83962413,12916227>, r=80552853
pos=<55592927,37186002,42591816>, r=58433808
pos=<-10125545,53516203,-17317432>, r=95447056
pos=<75808705,37788820,58643982>, r=82176381
pos=<41582059,39353159,27704214>, r=57143154
pos=<36803982,39355205,-3606646>, r=83673791
pos=<-47369219,53669223,52952969>, r=71373292
pos=<173669415,26884632,8820116>, r=71245061
pos=<64230471,11859745,45688728>, r=89300367
pos=<-27995389,46478149,44011250>, r=50504006
pos=<64473597,40967985,29294451>, r=76829606
pos=<25626639,2500140,63776164>, r=72415149
pos=<40692851,779372,32287262>, r=90244577
pos=<42543510,50835442,77328557>, r=57710094
pos=<53123916,88806838,38591588>, r=87447575
pos=<16755624,94346153,37553592>, r=57656465
pos=<73517767,51897005,44233258>, r=65289793
pos=<42254027,44801184,43191862>, r=91192046
pos=<-15181467,39110959,-1260032>, r=90328480
pos=<35670950,45587984,-8157326>, r=80858652
pos=<34184905,72353269,33496591>, r=57149825
pos=<32484778,19554133,947384>, r=94601902
pos=<30709295,45482776,34168006>, r=83608882
pos=<-35663744,67855128,71173420>, r=92073973
pos=<73290429,44934629,24008003>, r=86966267
pos=<22676200,70440578,5275779>, r=71949242
pos=<41520507,14891289,20432424>, r=88815486
pos=<59842801,43646981,44363468>, r=54450816
pos=<-4916364,38616567,42725884>, r=64463717
pos=<48351155,1597262,37357878>, r=92014388
pos=<63495534,34021892,28309017>, r=83783006
pos=<25250062,47123617,62396321>, r=53909007
pos=<62790330,20464052,37883023>, r=87061827
pos=<71971005,23513326,33376228>, r=97700266
pos=<10528816,46412160,-23305683>, r=79362401
pos=<33637997,29425119,23496000>, r=63335252
pos=<57419524,68187124,36263879>, r=73451039
pos=<53254197,44600779,61357054>, r=55523521
pos=<40827842,3720677,21472120>, r=98253647
pos=<-17748085,18576383,64823922>, r=79887411
pos=<78665184,45003396,44757601>, r=71522560
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pos=<51451105,-360679,53170686>, r=90494961
pos=<86002985,43075618,39182127>, r=86363642
pos=<63451473,47897170,35010139>, r=63162531
pos=<45765295,53618906,46572448>, r=54105448
pos=<67982431,29563806,36215213>, r=84822022
pos=<7252558,21459622,13715670>, r=70569819
pos=<39155542,9628304,23450909>, r=88694703
pos=<69564813,55081791,67433902>, r=79083210
pos=<67109709,45181504,47428433>, r=57118272
pos=<26525614,21687012,22790961>, r=64666018
pos=<-15535104,65300544,25315798>, r=70007382
pos=<65487693,48063533,39034482>, r=61008092
pos=<49970856,18435302,59964573>, r=77012725
pos=<85282321,44036760,60372854>, r=87130962
pos=<42412226,21638106,78745610>, r=85032224
pos=<65945066,31842198,35733778>, r=80987451
pos=<56940122,58392056,44183826>, r=55256842

Part 1: 
var input = File.ReadAllLines(Path.Combine(Path.GetDirectoryName(Util.CurrentQueryPath), @"23_input.txt"))
	.Where(p => !string.IsNullOrWhiteSpace(p))
	.Select(p => new
	{
		X = int.Parse(p.Split(' ')[0].Substring(5).Split(',')[0].Trim(new[] { ' ', '<', '>', ',' })),
		Y = int.Parse(p.Split(' ')[0].Substring(5).Split(',')[1].Trim(new[] { ' ', '<', '>', ',' })),
		Z = int.Parse(p.Split(' ')[0].Substring(5).Split(',')[2].Trim(new[] { ' ', '<', '>', ',' })),
		R = int.Parse(p.Split(' ')[1].Substring(2).Trim(new[] { ' ', '<', '>', ',' })),
	})
	.ToList();
	
	var max = input.OrderByDescending(p => p.R).First();
	
	input.Count(i => Math.Abs(i.X-max.X) + Math.Abs(i.Y-max.Y) + Math.Abs(i.Z-max.Z) <= max.R).Dump();
Result: 417

Part 2: 
class C3 { public long X, Y, Z; }

void Main()
{
	var input = File.ReadAllLines(Path.Combine(Path.GetDirectoryName(Util.CurrentQueryPath), @"23_input.txt"))
		.Where(p => !string.IsNullOrWhiteSpace(p))
		.Select(p => new
		{
			X = long.Parse(p.Split(' ')[0].Substring(5).Split(',')[0].Trim(new[] { ' ', '<', '>', ',' })),
			Y = long.Parse(p.Split(' ')[0].Substring(5).Split(',')[1].Trim(new[] { ' ', '<', '>', ',' })),
			Z = long.Parse(p.Split(' ')[0].Substring(5).Split(',')[2].Trim(new[] { ' ', '<', '>', ',' })),
			R = long.Parse(p.Split(' ')[1].Substring(2).Trim(new[] { ' ', '<', '>', ',' })),
		})
		.ToList();

	var x_min = input.Min(i => i.X);
	var x_max = input.Max(i => i.X);
	var y_min = input.Min(i => i.Y);
	var y_max = input.Max(i => i.Y);
	var z_min = input.Min(i => i.Z);
	var z_max = input.Max(i => i.Z);

	long dist = 1;
	for (; dist < x_max - x_min; dist *= 2) ;

	long target_count = 0;
	C3 best = null;
	long? best_val = null;

	for (; dist > 0;)
	{
		target_count = 0;
		best = null;
		best_val = null;

		for (long x = x_min; x <= x_max; x += dist)
		{
			for (long y = y_min; y <= y_max; y += dist)
			{
				for (long z = z_min; z <= z_max; z += dist)
				{
					var count = 0;
					foreach (var b in input)
					{
						var calc = Math.Abs(x - b.X) + Math.Abs(y - b.Y) + Math.Abs(z - b.Z);
						if ((calc - b.R) / dist <= 0) count++;
					}
					if (count > target_count)
					{
						target_count = count;
						best_val = Math.Abs(x) + Math.Abs(y) + Math.Abs(z);
						best = new C3 { X = x, Y = y, Z = z };
					}
					else if (count == target_count)
					{
						if (Math.Abs(x) + Math.Abs(y) + Math.Abs(z) < best_val)
						{
							best_val = Math.Abs(x) + Math.Abs(y) + Math.Abs(z);
							best = new C3 { X = x, Y = y, Z = z };
						}
					}
				}
			}
		}

		x_min = best.X - dist;
		x_max = best.X + dist;
		y_min = best.Y - dist;
		y_max = best.Y + dist;
		z_min = best.Z - dist;
		z_max = best.Z + dist;
		dist /= 2;
	}
	best_val.Dump();
}
Result: 112997634

made with vanilla PHP and MySQL, no frameworks, no bootstrap, no unnecessary* javascript