1 - packing equal circles in a square
2 - packing equal circles in a circle
3 - packing equal spheres in a cube
4 - packing equal spheres in a sphere
As you probably know, the problems of packing are all NP and are of a great theoretical and practical interest.
The natural question is, how the Critticall would handle them. Since
there is a huge academic and hobbyist tradition for solving this kind of
riddles, it was not hard to find some challenges and to do some
comparisons how good we really are with this method.
It turns out that the Critticall's engine is just fine! What was
accomplished by many different people with many different
algorithms/programs and (super)computers throughout the decades, is
quite easily matched and/or surpassed by the program you may download
and try.
The 256 circles inside a square, an example from www.packomania.com has been solved (from scratch) in a matter of hours. Now as the task is mechanized, get your own machine at www.algit.eu
and contribute to the packing saga, which has just begun. Be an
explorer at the packing frontier, have fun and do science yourself!
The record dense packing of 256 equal circles inside a square, obtained by the Packntail software:
Hide the X Y coordinates for the 256 circles
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The record dense packing of 72 equal spheres inside a cube, obtained by the Packntail software:
Hide the X Y Z coordinates for the 72 spheres
radius=0.122962655
1 0.377887609551165238000000000000 -0.204717978629842451000000000000 -0.319661403550345224000000000000
2 0.203236858012899813000000000000 -0.377854023520164783000000000000 -0.318531969606450194000000000000
3 -0.033654961597472318700000000000 -0.325571755416378505000000000000 -0.375846993848794719000000000000
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23 0.377934344207443762000000000000 -0.377910300167629443000000000000 -0.144561027433984940000000000000
24 -0.319471007807960894000000000000 -0.377866902873566446000000000000 0.204036181660689930000000000000
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26 0.204392992959712499000000000000 -0.030013119953430297800000000000 0.377695041537969400000000000000
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30 -0.202114828137401781000000000000 0.202143467138951455000000000000 -0.028105306222799806400000000000
31 -0.375977424207564581000000000000 0.376097070754190910000000000000 -0.376114964247285410000000000000
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37 0.378084868755264814000000000000 -0.377911729534018304000000000000 0.203958532913694729000000000000
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49 -0.201913906510135771000000000000 0.028266088805026307700000000000 0.145917077184899296000000000000
50 -0.375989157611347880000000000000 0.376070090559220638000000000000 -0.028165938595013855600000000000
51 0.204466425730286061000000000000 0.320200823339759244000000000000 0.377945775216207425000000000000
52 0.204790938964640595000000000000 0.144216475269445532000000000000 0.203219189380391851000000000000
53 0.145808198853692284000000000000 0.376143768443657267000000000000 0.145753692949102065000000000000
54 -0.375977923333384423000000000000 0.202006008746781596000000000000 0.145866791027081472000000000000
55 0.204275777629805005000000000000 -0.029963187483982564600000000000 0.029407829510539246200000000000
56 0.030178238697175469700000000000 -0.377911733228669611000000000000 -0.143716485370326857000000000000
57 -0.207545674938640373000000000000 -0.377911732506829468000000000000 -0.206697426585482152000000000000
58 -0.375946562783121496000000000000 -0.146039918630861132000000000000 -0.201736252962081614000000000000
59 0.378084140730331919000000000000 -0.203963989554060032000000000000 0.029488248009535734900000000000
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61 -0.201994086307083154000000000000 0.028170359287504873100000000000 -0.201938132349402194000000000000
62 0.204041788494765536000000000000 -0.203985888119280423000000000000 -0.144440806265492633000000000000
63 0.030643950735331881900000000000 -0.029528932521027312400000000000 0.203633539558734505000000000000
64 -0.028067606630779954500000000000 0.028399683964562074500000000000 -0.028059000946414784000000000000
65 -0.375948231489703133000000000000 0.027860752857515398000000000000 -0.375783368242216864000000000000
66 0.145927093203444325000000000000 0.202211857309024079000000000000 -0.028409938412949746500000000000
67 -0.028109047880728182900000000000 0.202255094513276640000000000000 0.145933746105262802000000000000
68 -0.375989820020900700000000000000 0.028224428135860464600000000000 -0.028142596697428988400000000000
69 0.145595492966165058000000000000 0.376162956728872677000000000000 -0.202286163473567732000000000000
70 0.319790503386776836000000000000 0.376162955946386879000000000000 -0.028690782093732838900000000000
71 -0.028190606567476843300000000000 0.376152912901318193000000000000 -0.028281421278628246500000000000
72 -0.202155158694682952000000000000 0.376110541064776649000000000000 -0.202125565638570509000000000000
The record dense packing of 72 equal spheres inside a sphere, obtained by the Packntail software:
Hide the X Y Z coordinates for the 72 spheres
radius=0.196078624
1 -0.365142892803682839000000000000 0.368988570632518387000000000000 -0.613846624222014858000000000000
2 0.050320587481783155000000000000 -0.531136876629041299000000000000 -0.601374289611330215000000000000
3 0.712648540781815831000000000000 -0.332161893929239838000000000000 -0.167601052736207706000000000000
4 -0.311366006101928217000000000000 -0.592947909590187061000000000000 -0.444694906864035178000000000000
5 -0.691995879685380788000000000000 -0.404442600547515518000000000000 -0.062108485607051851200000000000
6 -0.252045885532391933000000000000 -0.302164614519069175000000000000 -0.701041365649105464000000000000
7 0.219733155253111462000000000000 -0.131470599487650941000000000000 -0.393287546668305787000000000000
8 -0.145715460803957891000000000000 0.092770681526746168200000000000 -0.785143416229040381000000000000
9 0.035575387080422474200000000000 -0.399640337658212053000000000000 0.164753931293529304000000000000
10 0.129162232729993498000000000000 -0.186578513127819534000000000000 -0.771229636005407060000000000000
11 0.505195478444795509000000000000 -0.379546822212735280000000000000 -0.497002331335563263000000000000
12 -0.382604723388845436000000000000 0.647551197972866310000000000000 -0.283867311717188597000000000000
13 -0.070578117058970490900000000000 0.609870328681016649000000000000 -0.519005289509013923000000000000
14 -0.012098914965412351300000000000 0.037661903340762081800000000000 -0.041888612602723057600000000000
15 0.145346935034737584000000000000 0.345030095067422160000000000000 -0.711419763736948263000000000000
16 -0.168359283737344351000000000000 0.319222543882309584000000000000 -0.274567127275713307000000000000
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18 -0.595234746200556497000000000000 -0.322606603273001280000000000000 -0.433293307210191769000000000000
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21 -0.728833947087550449000000000000 -0.201444546911113520000000000000 0.272966575924076471000000000000
22 -0.057793530017871998200000000000 -0.774647338259847107000000000000 -0.207053105622638400000000000000
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29 -0.290351777570426128000000000000 0.744861912476579180000000000000 0.084653145421028572200000000000
30 -0.659750626677549246000000000000 0.258255471283862226000000000000 -0.379898397356358719000000000000
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36 -0.416569831202107055000000000000 -0.683154469346673676000000000000 -0.077840384768356807300000000000
37 -0.120914969257860674000000000000 -0.774126981802794822000000000000 0.179990459952169113000000000000
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39 -0.531255585854838341000000000000 -0.540167282363147816000000000000 0.268842683808440841000000000000
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48 -0.303402480572859123000000000000 0.352991744455802725000000000000 0.092052953002371346000000000000
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52 -0.764570155727782419000000000000 0.176541672736697464000000000000 0.174800146449135496000000000000
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58 -0.319212312977379509000000000000 -0.315046183675845637000000000000 0.020677154692941113900000000000
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61 -0.607551005240175912000000000000 0.077248823091312326900000000000 0.520772477978292847000000000000
62 0.410032038593905523000000000000 -0.393332657946550090000000000000 0.568729045164089064000000000000
63 0.049833948602119974800000000000 0.249432517439114904000000000000 0.762620202288114002000000000000
64 0.603471764809066169000000000000 -0.047366913107012992300000000000 0.529025315150935316000000000000
65 -0.556722798398451624000000000000 0.439223902343028882000000000000 0.378723736701544245000000000000
66 -0.327200430203272996000000000000 -0.003457538356428875150000000000 0.258708850509407062000000000000
67 0.011984035030897078800000000000 -0.107616595928592324000000000000 0.425718120503987052000000000000
68 0.416210507152887321000000000000 0.283007197831244506000000000000 0.626869451991908355000000000000
69 0.074856974931970660100000000000 0.767967891835186878000000000000 0.225635385084888923000000000000
70 -0.054928033258031180900000000000 0.276712320841883130000000000000 0.385701050314073257000000000000
71 -0.220429137227870831000000000000 0.627123099039437637000000000000 0.452125189853263998000000000000
72 -0.326082659577084266000000000000 0.307659394611485448000000000000 0.667312050783284594000000000000
28-March-2010
The record dense packing of 257 equal circles inside a square, obtained by the Packntail software:
Hide the X Y coordinates for the 257 circles
1 -0.434709965982162240000000000000 -0.412546512445044288000000000000
2 -0.401434706058495808000000000000 -0.468147633796452160000000000000
3 -0.339708501597092416000000000000 -0.448434599093466816000000000000
4 -0.277982300236140192000000000000 -0.468147633850033152000000000000
5 -0.213184709294916832000000000000 -0.468147633546786944000000000000
6 -0.148375222021306336000000000000 -0.468147633788618048000000000000
7 -0.083577631828799552000000000000 -0.468147633848698304000000000000
8 -0.018780008243720646400000000000 -0.468147178420937088000000000000
9 0.046017864163058387200000000000 -0.468147432790823616000000000000
10 0.110816143618941312000000000000 -0.468147557465563392000000000000
11 0.175614134786659616000000000000 -0.468147552605216320000000000000
12 0.240416242827840576000000000000 -0.468147627284518016000000000000
13 0.305216002565226880000000000000 -0.468147610821793152000000000000
14 0.434829313779377984000000000000 -0.468146680065615872000000000000
15 0.370027801552188672000000000000 -0.468147272537548864000000000000
16 -0.467985233672736192000000000000 -0.356945396505699648000000000000
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12-April-2010
The record dense packing of 258 equal circles inside a square, obtained by the Packntail software:
Hide the X Y coordinates for the 258 circles
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153 -0.353278581368708672000000000000 0.101773660421968128000000000000
154 -0.270957420988720288000000000000 0.129899282647400144000000000000
155 -0.199340734839446592000000000000 0.133466798987818512000000000000
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190 0.113110475056797120000000000000 0.208150221213390272000000000000
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203 0.028589596206698144000000000000 0.302403167776762688000000000000
204 0.093390901727941107200000000000 0.302464711723639360000000000000
205 0.145473054847929088000000000000 0.264153522872748064000000000000
206 0.210128424036374816000000000000 0.264153985844255360000000000000
207 0.274783756230022816000000000000 0.264153631352020288000000000000
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209 0.404248853652614080000000000000 0.265378165553573792000000000000
210 0.468591085951183104000000000000 0.271777216912838112000000000000
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224 0.370755950260200448000000000000 0.320682221276252480000000000000
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228 -0.294807467383389440000000000000 0.414356289025027072000000000000
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230 -0.165496795116183232000000000000 0.414356344224370880000000000000
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232 -0.036103254568403763200000000000 0.414367977088101120000000000000
233 0.028605602489401932800000000000 0.414375517015338240000000000000
234 0.093298057938332710400000000000 0.414358489443366272000000000000
235 0.158083364935463232000000000000 0.414429296338082240000000000000
236 0.210220299291109760000000000000 0.376192694124377216000000000000
237 0.293497086106620544000000000000 0.392139652104464896000000000000
238 0.356706325776884800000000000000 0.405747075441812224000000000000
239 0.411273662479957376000000000000 0.371066882614563136000000000000
240 0.468594174772360064000000000000 0.400977822624642816000000000000
241 -0.427956570209588288000000000000 0.412140731044473216000000000000
242 -0.399812760578710208000000000000 0.470349275311730496000000000000
243 -0.327136062443850944000000000000 0.470349108238506368000000000000
244 -0.262479764119794848000000000000 0.470349288727531328000000000000
245 -0.197824564792663424000000000000 0.470349294041399744000000000000
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247 -0.068452208357729408000000000000 0.470349138444553920000000000000
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250 0.125629566139770032000000000000 0.470349290121617088000000000000
251 0.190537205797226240000000000000 0.470349297476284544000000000000
252 0.242674207435047328000000000000 0.432112629819550912000000000000
253 0.294811348869083648000000000000 0.470349053766478848000000000000
254 0.359466719815345600000000000000 0.470349274644747456000000000000
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257 0.468594151152310592000000000000 0.470349236441741376000000000000
258 -0.464654940407738496000000000000 0.465781668939667520000000000000
12-April-2010
The record dense packing of 53 equal spheres inside a sphere, obtained by the Packntail software:
Hide the X Y Z coordinates for the 53 spheres
radius=0.216249512
1 -0.457512621666683605000000000000 -0.409318053229394685000000000000 -0.487243018927405902000000000000
2 0.055663595922053686600000000000 -0.595726614626344575000000000000 -0.506237288236563332000000000000
3 0.640808939689632040000000000000 -0.172589222691599459000000000000 -0.416943269593091248000000000000
4 -0.453642009572810700000000000000 -0.002066575960651449630000000000 -0.638967825039066684000000000000
5 -0.124695277432806853000000000000 -0.269369895025402872000000000000 -0.725365958884737316000000000000
6 0.303814627841285267000000000000 -0.277103072540210493000000000000 -0.667208955558021621000000000000
7 0.753731112382332036000000000000 0.150855924474388253000000000000 -0.152959887560912833000000000000
8 -0.269872752485708689000000000000 0.403079878990742158000000000000 -0.615597381303632063000000000000
9 0.028879874389578130000000000000 0.132249261428019849000000000000 -0.771972093363322398000000000000
10 0.438581428875529866000000000000 0.142283578481249395000000000000 -0.633771678778513148000000000000
11 -0.615932959409701275000000000000 0.307932408480475150000000000000 -0.374257997284677735000000000000
12 -0.126396188688897154000000000000 0.697885244793288506000000000000 -0.333534129751712205000000000000
13 0.164123106642269034000000000000 0.497143133135770743000000000000 -0.583247064211424915000000000000
14 -0.609264050429307868000000000000 -0.484849868669396888000000000000 -0.089346230027021397700000000000
15 -0.263070224472765679000000000000 -0.700451170357854314000000000000 -0.233296039667159977000000000000
16 0.448685073986750671000000000000 -0.550526697559622580000000000000 -0.331461742379635604000000000000
17 -0.762075907441790434000000000000 -0.138453698562848254000000000000 0.119731832494683513000000000000
18 0.740213724012181551000000000000 -0.255863974438282793000000000000 -0.004164591506924549690000000000
19 0.101075521491408041000000000000 -0.286145042744100353000000000000 -0.207653274344074545000000000000
20 0.592127892510437737000000000000 0.507911640411213616000000000000 0.074392781946611391500000000000
21 -0.712099212918956725000000000000 -0.108633468950237941000000000000 -0.308833786567041191000000000000
22 -0.117034637108937190000000000000 0.049667022150512302200000000000 -0.371504518999713873000000000000
23 0.332416817912459694000000000000 0.079096119188767341500000000000 -0.219293903221175784000000000000
24 -0.727873705847453922000000000000 0.286656591670131411000000000000 0.042988250297387287100000000000
25 -0.321850126842260664000000000000 0.126023981776648725000000000000 0.016542234912311035200000000000
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28 -0.479383349629910138000000000000 0.612123439119372947000000000000 -0.098799421658553668300000000000
29 0.258947348466578964000000000000 0.726512544608769795000000000000 -0.139250208400751113000000000000
30 -0.271197616832258959000000000000 -0.707877578481592940000000000000 0.199062838845616652000000000000
31 0.145804727607417278000000000000 -0.762594682878638741000000000000 -0.106515880565014986000000000000
32 0.493036234693885356000000000000 -0.601681493380924692000000000000 0.095705165920759796600000000000
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34 -0.244002262905636313000000000000 -0.301843562539085897000000000000 0.052597154281203067900000000000
35 0.208607034902579397000000000000 -0.286566737224880297000000000000 0.211264620076202420000000000000
36 0.730624658028558360000000000000 0.077942799793108238900000000000 0.272722122917826659000000000000
37 -0.638362014869514716000000000000 0.129510067696850639000000000000 0.435873729039838620000000000000
38 -0.106589969397134096000000000000 -0.030155931296103253400000000000 0.359776415450491716000000000000
39 0.256778472462966922000000000000 0.143134761879762346000000000000 0.201696950457848578000000000000
40 -0.489356621508787171000000000000 0.519696241836464568000000000000 0.323590389940387524000000000000
41 -0.074342432194179922100000000000 0.398502453687684166000000000000 0.312158231184512136000000000000
42 0.250504189561342350000000000000 0.683251957390706210000000000000 0.290996977767957687000000000000
43 0.494696951560821219000000000000 0.378011694044983026000000000000 0.476074482238496799000000000000
44 -0.124638855322423858000000000000 0.768140991589862932000000000000 0.093216913614878826900000000000
45 0.141338838380155346000000000000 -0.697396993707418700000000000000 0.328520308367764802000000000000
46 -0.174992457152478020000000000000 -0.508176308682207645000000000000 0.570437819420438696000000000000
47 0.240080237384449335000000000000 -0.401566456998044108000000000000 0.628785088338723375000000000000
48 0.596592909795447879000000000000 -0.312890424140267243000000000000 0.400551257307985020000000000000
49 -0.393549110717131723000000000000 -0.146317343813297002000000000000 0.661796917182722599000000000000
50 0.014301393087310146000000000000 -0.065490710151835995800000000000 0.780878519681986960000000000000
51 0.425334619190795071000000000000 -0.009923310957758746730000000000 0.657339554767270795000000000000
52 -0.305166457715773942000000000000 0.286326684748217208000000000000 0.662687915727345089000000000000
53 0.122353171286892742000000000000 0.344071346742989614000000000000 0.693476340706684513000000000000
26-April-2010
The record dense packing of 66 equal spheres inside a cube, obtained by the Packntail software:
Hide the X Y Z coordinates for the 66 spheres
radius=0.125735995
1 -0.306083699916466612000000000000 -0.374206375248205214000000000000 0.374088452876670086000000000000
2 0.365744342947252832000000000000 -0.374206374558543775000000000000 0.374088452676877348000000000000
3 0.035051059135188522600000000000 -0.374206373828158245000000000000 0.374088449997977079000000000000
4 0.200397718542613235000000000000 -0.374206376716467615000000000000 0.184619045970691092000000000000
5 0.365744330407917817000000000000 0.004729716125844809530000000000 0.372468861823137098000000000000
6 0.200400108418556211000000000000 -0.184734866753239607000000000000 0.374088444861129910000000000000
7 0.029829193597821764700000000000 0.000047475725329096652400000000 0.374088452630235269000000000000
8 -0.382783665334970213000000000000 0.116755236081600711000000000000 0.374088452877342881000000000000
9 0.195182461662057077000000000000 0.189511179828242948000000000000 0.374088337411570437000000000000
10 -0.135516323659568810000000000000 -0.189422899233719189000000000000 0.374088450368488368000000000000
11 0.019625122916081722700000000000 -0.007137032783911720880000000000 0.007415391418104490610000000000
12 -0.329736316563641774000000000000 0.368938595022069771000000000000 0.371866109969664516000000000000
13 -0.140708927147159796000000000000 0.184857980263915617000000000000 0.374088452781731529000000000000
14 0.016176364527695223000000000000 0.177911546701831430000000000000 0.177678352632667125000000000000
15 -0.345899000037022841000000000000 0.125731381991270402000000000000 0.125498202808311005000000000000
16 0.365729708261277209000000000000 0.374319133479360078000000000000 0.374081675406028158000000000000
17 -0.140708926250452643000000000000 0.374321623739795051000000000000 0.184624804160769374000000000000
18 0.024644297496593754700000000000 0.374321628968405429000000000000 0.374088451514475895000000000000
19 -0.382783665644555349000000000000 -0.374206376875570457000000000000 0.134598833856402145000000000000
20 0.365744342935256872000000000000 -0.373217983602755432000000000000 -0.004847782816934778640000000000
21 -0.135516325275898686000000000000 -0.374206373086322763000000000000 0.189304977039169375000000000000
22 0.029830321381603026900000000000 -0.374206376713078881000000000000 -0.000164410380193065052000000000
23 -0.382783664240463006000000000000 -0.134716755486695483000000000000 0.374088432239233493000000000000
24 0.197229508256167613000000000000 -0.186569674970193666000000000000 -0.003017984179235416470000000000
25 0.032446103551799734800000000000 -0.187056633344494738000000000000 0.186940841001002472000000000000
26 -0.382783665509996207000000000000 -0.123007183684912119000000000000 0.122888689222946712000000000000
27 0.196872674331382752000000000000 0.003224957199684828220000000000 0.186140210449372040000000000000
28 -0.147727135920053071000000000000 -0.196529240963514623000000000000 0.011766537927875433300000000000
29 0.016541385971717042400000000000 -0.177447676337904647000000000000 -0.177679859689689801000000000000
30 0.365744244811521624000000000000 0.189532985869864223000000000000 0.189299495945753654000000000000
31 0.196872641618881183000000000000 0.186373387706088578000000000000 0.002991728715098541940000000000
32 -0.147728824332386238000000000000 -0.011883985353511806300000000000 0.196411913183493492000000000000
33 0.365744338477700937000000000000 0.372701737353804630000000000000 0.004496560318155725860000000000
34 0.195182401473003170000000000000 0.374321624839894285000000000000 0.189277955332362607000000000000
35 -0.147728851218221047000000000000 0.196645092212234945000000000000 -0.012117203527086461300000000000
36 0.029829163468450947000000000000 0.374321632209428490000000000000 -0.000185699734311809219000000000
37 -0.382783665551283570000000000000 -0.374206375664487556000000000000 -0.116873157074698350000000000000
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39 -0.140708910748873095000000000000 -0.373553071914281387000000000000 -0.184972705348823013000000000000
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49 -0.147727057021040498000000000000 0.011999660223772046600000000000 -0.196762311016484226000000000000
50 -0.140708908812402000000000000000 -0.184739525575648267000000000000 -0.373785596728203773000000000000
51 0.200400130617253480000000000000 0.374321631009421951000000000000 -0.184968031840291869000000000000
52 -0.382783665800229433000000000000 0.374321632262406889000000000000 0.116522064811088372000000000000
53 -0.135516308883802478000000000000 0.374321631010015643000000000000 -0.189656111633274782000000000000
54 0.032446132923770236400000000000 0.187174022666166590000000000000 -0.187289793033349167000000000000
55 -0.323602754708209039000000000000 -0.366040117928176922000000000000 -0.369335019452531277000000000000
56 0.365744343349778178000000000000 0.374321631933850041000000000000 -0.374439549852594034000000000000
57 0.024639351623429978100000000000 -0.374206376873635949000000000000 -0.374439556294916598000000000000
58 0.365739159563483129000000000000 -0.374204434403022756000000000000 -0.374432312800462630000000000000
59 0.365744343151293894000000000000 0.000065764493441411418000000000 -0.000167441605016795098000000000
60 0.029830310648156652100000000000 0.000068778702376702004300000000 -0.374439553259169611000000000000
61 0.195179855368300736000000000000 -0.374206376753774439000000000000 -0.189631280189378748000000000000
62 -0.382783664766097542000000000000 -0.116639986481648458000000000000 -0.374439555825819725000000000000
63 0.365744343246575510000000000000 -0.004614609608794436290000000000 -0.373450137439911678000000000000
64 -0.135516343046472448000000000000 0.189538160625265462000000000000 -0.374439487296653162000000000000
65 -0.306083722700014937000000000000 0.374321632079483602000000000000 -0.374439555453884687000000000000
66 -0.382783665763577308000000000000 0.374321568517077485000000000000 -0.134949926854574548000000000000
30-April-2010
The record dense packing of 251 equal circles inside a square, obtained by the Packntail software:
Hide the X Y coordinates for the 251 circles
1 -0.464977976326911846000000000000 -0.471992483231039983000000000000
2 -0.399439394111786694000000000000 -0.471992484077577767000000000000
3 -0.333900811730481861000000000000 -0.471992484166328663000000000000
4 -0.272790885439983533000000000000 -0.448309522671398231000000000000
5 -0.211680958841981653000000000000 -0.471992483586142098000000000000
6 -0.146142376563323795000000000000 -0.471992345344969644000000000000
7 -0.080603794079835075500000000000 -0.471992482643908862000000000000
8 -0.015065211345505971300000000000 -0.471992483257403228000000000000
9 0.047298600099344043100000000000 -0.451841533109572591000000000000
10 0.109662412768214729000000000000 -0.471992483191994050000000000000
11 0.175200995046934427000000000000 -0.471992483053438161000000000000
12 0.240735744076221642000000000000 -0.471283652524748631000000000000
13 0.306270493760995410000000000000 -0.471992484098037846000000000000
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