TopCoder Statistics - Problem Statement

Problem Statement

Gogo has been hired by the newly founded TopCoder Security Agency (TSA) and has been tasked to encrypt a signal code generated by a radar.

The signal will consist of several positive integers. The order of integers within the signal is not important and therefore should not be preserved during encryption. However, there may be duplicate integers, and the number of occurrences of each integer is important and must be preserved during encryption.

Gogo's idea is to encrypt these integers into a String that consists only of digits '1' and '0'. The encryption scheme is as follows:

Start with an infinite String consisting solely of '0' characters. The characters within the string are indexed from left to right 1, 2, 3, ... .
For each input integer X in the signal, Gogo will allocate it within the string. To do this, he will select an index 2^p, where p is a non-negative integer that he may choose arbitrarily, but in such way that characters at indices between 2^p and 2^p + X - 1, inclusive, are all equal to '0'. The allocating procedure consists of replacing all these characters with '1's. This newly created sequence of consecutive '1' characters is said to represent the allocated integer X.
In order to allow unique decryption, the following property must hold after all numbers from the signal are allocated. For every two integers from the input signal, there must be at least one '0' character between the sequences of '1's that represent these integers.

After all numbers are allocated within the string properly, the '1' character with the largest index is found and all '0' characters to the right of it are removed. The obtained finite string is the result of the encryption procedure.

Given integers to encrypt in int[] numbers, return the length of the shortest string that encrypts them and can be obtained according to the scheme described above. It is guaranteed that this length will not exceed 2^62.

Definition

Class:: SignalIntelligence
Method:: encrypt
Parameters:: int[]
Returns:: long
Method signature:: long encrypt(int[] numbers)
(be sure your method is public)

Constraints

numbers will contain between 1 and 50 elements, inclusive.
Each element of numbers will be between 1 and 1,000,000,000, inclusive.
The answer will not exceed 2^62.

Examples

{1,2,3}

Returns: 8

The string "11011101" encrypts the given numbers and has a length of 8. There is no shorter string that encrypts these numbers.
{4,4,2,2}

Returns: 19

The elements in numbers might not be distinct.
{1000000000,1000000000,1000000000,1000000000,1000000000, 1000000000,1000000000,1000000000,1000000000,1000000000, 1000000000,1000000000,1000000000,1000000000,1000000000, 1000000000,1000000000,1000000000,1000000000,1000000000}

Returns: 281475976710655

The answer may be very big, but it will not exceed 2^62.
{1,3,7,15,31,63,127,255,511,1023,2047}

Returns: 4094
{1000000000,1}

Returns: 1000000003
{2,3,7,15,5}

Returns: 36
{1000000000,1000000000,1000000000,1000000000,1000000000, 1000000000,1000000000,1000000000,1000000000,1000000000, 1000000000,1000000000,1000000000,1000000000,1000000000, 1000000000,1000000000,1000000000,1000000000,1000000000, 1000000000,1000000000,1000000000,1000000000,1000000000, 1000000000,1000000000,1000000000,1000000000,1000000000, 1000000000,1000000000,1000000000,1000,1000,1000}

Returns: 2305843010213693951
{179658657,1375,16748571,963287546,963287552,23711273,737827135,1,86550454,916920519,28,932660585,963233450,961582520,963287279,61050923,963287551,57487191,963287460,18861753,652860878,21221311,5545151,14271410,961807367,963287481,63252,963283275,963287499,963039512,947814221,184157393,31,214871850,563608185,961707006,1,3671,963267601,963270890,3,468420162,84216335,963264522,963281384,1,67947,963286662,129181990}

Returns: 2305843009219239102
{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

Returns: 1125899906842624
{2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}

Returns: 1125899906842625
{3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}

Returns: 2251799813685250
{5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}

Returns: 2251799813685252
{10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}

Returns: 4503599627370505
{200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200,200}

Returns: 72057594037928135
{5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283,5283}

Returns: 2305843009213699234
{58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282,58282}

Returns: 2305843009213752233
{1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585,1019585}

Returns: 2305843009214713536
{37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373,37373373}

Returns: 2305843009251067324
{270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000,270000000}

Returns: 2305843009483693951
{987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321,987654321}

Returns: 2305843010201348272
{1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

Returns: 2305843010213693951
{1,1,1,1,1,2,2,1,1,2,2,2,1,1,1,2,2,1,1,1,1,2,1,2,2,1,2,1,2,2,2,1,1,2,2,1,2,2,1,1,1,2,2,1,1,1,1,1,1,2}

Returns: 1125899906842624
{1003,1001,1000,1002,1000,1003,1004,1002,1004,1005,1004,1004,1003,1000,1000,1001,1005,1001,1002,1000,1003,1003,1005,1002,1001,1004,1003,1005,1000,1005,1004,1003,1005,1003,1004,1002,1004,1005,1002,1002,1004,1001,1004,1000,1002,1005,1000,1000,1004,1000}

Returns: 288230376151712743
{1000005,1000007,1000003,1000003,1000006,1000007,1000005,1000004,1000003,1000000,1000002,1000004,1000007,1000004,1000003,1000007,1000002,1000003,1000002,1000005,1000007,1000007,1000003,1000000,1000006,1000001,1000001,1000004,1000006,1000006,1000004,1000006,1000004,1000007,1000000,1000001,1000001,1000002,1000001,1000005,1000005,1000000,1000006}

Returns: 2305843009214693951
{999999991,999999997,999999993,999999991,999999990,999999993,999999995,999999998,999999996,999999992,999999991,999999991,999999993,999999996,999999996,999999990,999999998,999999992,999999994,999999996,999999993,999999996,999999996,999999996,999999995,999999998,999999996,999999991,999999990,999999990,999999997,999999997,999999993}

Returns: 2305843010213693941
{235857565,221602550}

Returns: 490038005
{555785557,125740864,863111154,595742977}

Returns: 2703269204
{699941145,339788511,472789281,845483099,959647936,563964808,269415281,647687104}

Returns: 34629153648
{647435249,803314427,101746030,964429523,223737792,68515974,28150428,125939064,319945227,880135873,447607422,8304030,54616924,977496243,200084211,688775573}

Returns: 549824329861
{523956777,870026136,106698929,79274264,626167319,806819344,197171767,220148874,869478997,244529565,945331946,276812202,576132594,748665937,121622204,32295658,330209878,273838685,209464832,501549133,642315585,636167405,778774046,281641907,844060543,976822490,810188417,517044450,801011353,162695609,180175857,532864569}

Returns: 72057594144626864
{453381899,896620462,37990500,217362760,29719649,215773553,739245534,30200886,483496386,505404724,756663654,592389735,372026736,708612244,923864984,776042099,954534621,270858854,675201114,625437329,912463350,458367504,74585147,807894854,974760403,477659282,102437899,447369076,972739094,297881347,985344042,257386203,198147693,399754088,50127358,992970900,590360959}

Returns: 1152921504644837475
{69122726,93541221}

Returns: 203340453
{577407437,736270213}

Returns: 1651149260
{27096035,298594390,460425141,235956357}

Returns: 1309698180
{727312500,521644191,839367970,236040594,189380898,349154372,385330230,397552844}

Returns: 17529023555
{960279467,800243597,537543980,627721315,966332421,403751475,251094527,221083798,988457022,918523234,816380508,954657304,782274915,782224124,559484609,142724240}

Returns: 4398189235343
{528365618,665524313,235143161,4475297,496903020,914280336,138855536,483782301,628087128,243187789,219058790,122584390,422268174,745856404,648707562,695835340,373986475,27861841,709477528,657488096,588097078,895013274,725032201,916747047,705627486,670368540,472580435,855900854,28482944,986502272,24691132,45314335}

Returns: 18014398537343824
{66111822,901323553,120043437,33574315,27918777,466777994,889149,495588311,194492499,381518458,947371899,286397799,487783925,857521141,399205507,105056546,561852370,315342679,437315059,185693701,319305989,804412056,526862732,768844849,107070267,388356354,942340016,102031025,400926077,143966520,68076598,833930512,23317426,203907340,120631317,970233972,801410459,309325868}

Returns: 1152921504640421290
{364490003,715408767}

Returns: 1252279678
{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

Returns: 1125899906842624
{1,2,1,1,2,2,1,2,2,2,1,1,1,1,1,2,1,2,1,1,2,2,2,1,1,1,1,2,1,2,2,1,2,1,1,2,2,2,2,1,2,1,1,2,2,1,2,1,1,1}

Returns: 1125899906842624
{5,10,7,6,5,10,9,10,5,10,8,9,9,8,10,7,6,9,10,6,8,9,6,6,9,6,7,5,9,8,10,6,9,9,6,7,9,8,6,7,8,9,8,10,7,5,7,10,6,10}

Returns: 2251799813685252
{58,48,59,46,29,24,38,37,39,48,44,32,44,29,31,51,51,30,56,39,57,46,32,36,40,40,24,37,29,55,33,46,25,37,23,51,53,57,36,42,55,41,52,26,49,29,44,34,50,43}

Returns: 9007199254741014
{16980,15834,16744,11681,18064,19497,13666,9116,16465,10731,8440,18246,15097,16843,14594,7870,19592,9193,12031,12601,8528,9084,8447,15282,7075,12139,8441,15731,19011,14570,18541,20137,17290,11821,18076,10886,7268,14594,17206,9841,11932,9612,12604,14403,11888,14141,10176,10174,7212,18361}

Returns: 2305843009213701026
{34318,28848,46912,22709,21631,44334,41956,38932,39002,30513,25852,41790,26297,52817,25411,27541,45176,35778,29969,27124,26128,42836,49044,41319,30208,43711,31518,31476,23045,41069,42007,48776,23782,56941,51469,40026,20404,33756,22329,35193,43900,30121,26844,40093,36474,49005,49819,29978}

Returns: 2305843009213714355
{1072901,3859045,995297,3683954,1001850,4039454,1148240,1199431,3585117,3450722,2473474,2183502,2118901,3949789,1444753,823591,1304318,2033975,1510082,2297550,1198529,3342426,2336853,1069029,2966400,3716528,2111794,3716426,1912854,1132818,3271153,1564892,3593606,2980068,597752,3532360,1283917,3518770,1107041,3883017,1739120,3763298,1939012}

Returns: 2305843009214291703
{33603696,38820812,41406487,39732337,38222020,31426393,34110779,43345829,48053538,49807584,28464602,46264000,35772251,43768413,41481020,38217105,33309217,41885036,30054093,43087163,40117670,29125880,30873599,45175806,30041943,35872207,42774909,44300252,40852416,28965274,44256276,34607812,37918868,37885233,44320284,41016379,45575303,32328032}

Returns: 2305843009242158553
{615710367,828121299,663163955,975276184,640537976,998211095,794924189,956921120,620878206,764485506,699578478,669163154,772478680,914119058,940119645,611342962,770619280,598891628,727284047,771372743,716947274,704330816,734356532,861495820,752292939,746935244,864243989,984891734,761041947,995159153,797080726,837868288,790812076}

Returns: 2305843009812585579
{760265624,569282114,696059557,672289975}

Returns: 4864249409
{312071265,188952715,324521323,183187130,252725036,168635937,193748935,104616538,106047928,131220792,192848456,306638149,256899146,92744101}

Returns: 549848557988
{522123452,589830328,315436987,342645637,445303921,804602161,402459443,380454425,267079239,284914380,728120225,322349158,530348969,445323427,718158227,502161837,438351881,479780186,384481599,566123810,547131716,655069057}

Returns: 562950220500550
{719920934,719364707,720115683,638379714,571312262,583881215,715264040,740207673,646199325,722986352,774576651,544411074,650561187,593008245,650823047}

Returns: 8796637433281
{590604882,513531580,658742168,631775470,576602033,717667847,647539264,735794909,698296962,727783750,635566299,491137194,620875805,543096504,512960162,496287897,688221438}

Returns: 17592677181609
{740963613,644726975,826637708,731671419,712478268,872891455,880265042,926080333,954708551,952898372,704899547,788957219,671647499}

Returns: 2199667982526
{497049138,692021067,178694997,355318725,459144763,220782914,506278761,456456222,222989218,396852334,704609550,531667317,227102797,653136762,583430107,197454156,282931480,375578973,839506205,779324918,826704601,348240237}

Returns: 281475155405652
{617063229,636474530,501001020,311603490,671242581,689924923,559427070,517466912,402805381,507403086,519086393,604741412,494917883,488790034,529445518,412895655,680120335,323914265,581593892,369071119,385135646,499211048}

Returns: 562950265024801
{669195871,709593466,663112277,614498463,690450890,682478180,621650747,643766176,703462664,665575011,715523054}

Returns: 550370312350
{762251236,719512653,884461982,855096015,891277775,961757981,978612762,939900781,730424424,866271739,869040161,686042771,892579882,948463500,800138858,742460199,812942158,795042065,919888160,662536117,976068499,860266833,704341276}

Returns: 2251800476221364
{867,7091,197156,2672235,325,3186275,41989,14883,1277,15,136475,132095,155248,11387,6431,7556,1812,20049,14441,7,214779,1896273,4713,1984,885,478,1613640,43,492082,30860,438,157}

Returns: 68719476892
{649888,130363,98069,648754,647363,76817,386758,199668,129147,174642,419586,914315,115950,389364,302501,902001,213989,139291,757490,113286,404945,367453,360549,367626}

Returns: 549755890704
{349,16136,3063}

Returns: 20231
{524,251,381,186,902,516,643,291,635,832,475,193,772,968,1016,974,224,215,217,161,204,767,602,949,843,163,203,217,430,466,169,736,378,192,687,533,207}

Returns: 8796093022368
{122,95,99,119,130,21,23,28,56,76,44,14,86,29,106,67,206,285,10,229,477,46,24,10,289,31,378,20,13,244,215,61,130,83,49,87,104,38}

Returns: 1099511627785
{7272038,14134620,12531546,7940529,5716835,30923886,6614826,8063007,8783064,3172637}

Returns: 2150656284
{7451,6166,4626,4955,4374,7260,4164,5390,6259,5301,7620,4308,5716,4388,5987,5036,6592,5865,8181,4431,4955,8050,7221,6072,4372,4493,8102,6162,5539,7392,5082,6458,4637,6110,5675}

Returns: 70368744181827
{23788,650788,40674,3774,35080,11824,321113,3012,9071,254479,92515,188867,431484,78179,4652,5155,26935,3099,2535,56634,93248,3184,8989,4756,154525,57576,253646,24147,48207,3489,9409,55812,99437,358545,713975,18800,352753,391490,24588,114348,2929,31332,1768777,388845}

Returns: 18014398509484518
{2666,928,2665,2063,3125,176,64,143,56,797,174,1378,642,346,14,110,26,24,23,92,12}

Returns: 8388630
{82,129064,4438046,888970,6,6966,100410,716,30515,769278,2598077,19,165,53334,2,5923,2,724311,8273,3766,354085,2350465,9765299,17384,3,1997,4,30,2,132,102744,18,38,18,123780,8,308648,75230,9335530,3,2287,22,1502509,120,251,3,1257,155437,2851,11838}

Returns: 1125899906842625
{868023,5864,9496529,439885,23504,9179,15181876,538,6977,367,287012,5864606,2217,15510,14901,2044142,114,1845,129,193,619469,14111680,81,4062,919,3551,378,976,4686303,21850,600,652,5834279,2334,4867,2192,28256,3057,558,768,2369326,395,7803737,88,185,29144,6208,270,5586543,223798}

Returns: 36028797018964048
{10284827,305913,17160683,1893793,6185557,5073935,10236,39300,51985,2185285,3679,12949,16937734,3228,14251,5159481,53669,6469016,1775111,116042751,7184229,126928983,277471,7256964,4571300,127105,6698344,50243236,226167,161430,1785120,5166,23348,248727,7056651,888714,27962262,33717443,18771243,7389711,27694520,3402398,216518,7011,44293,48068127,7549558,10193714,3449,58905}

Returns: 1152921504606850203
{399236,399219,99515,1804,204,259914,31237,248,235,16769241,509605,1467,1008120,14701,2300628,48083921,57458864,1918077,1580345,685175,2015,239,1197443,13642,321104,1959766,511,11133,23504145,27779,10661698,8280513,37828664,122659,997,26258,59333,195,1648,124834,344391,14156896,709,537,54644221,217867,196,13196910,5728,7729}

Returns: 72057594037928130
{45,7337,91,623,492,29536,882,787,73304,26620,35,3819,36089,3752,1401,16,4499,476,2574,43128,205,11376,5841,158,1557,10117,16,14007,50443,720,3431,8456,17,3963,4621,38,82,507784,956,1062,54,280,44,25554,940,377,2929,166,9191,766}

Returns: 9007199254741007
{45619,178774,15754,3471,26143,1270,1216,6849,1838,32335,594567,31864,460062,32249,247937,1251,8641,292314,87435,7046,516288,1527,2173,10503,421222,1244,4888,64864,413300,4847,108380,15806,239547,687970,851221,819831,2246,99742,127828,8918,4739,14030,4506,31220,636238,21366,1037,470559,3106,23766}

Returns: 576460752303424524
{636,12694,16061,5968,1048,392,394,254,988,1365,3507,245,2017,1076,1599,568,5915,246,3265,1907,9339,11832,7046,11103,615,3162,3510,482,144,240,225,136,1690,4002,10697,12062,463,3200,222,3197,1619,844,11030,5482,13785,5772,557,3922,716,1754}

Returns: 72057594037928071
{6905315,2043146,18710,23,1701,64,71,12,1367052,87,126569,247,22900,231,651881707,6,6445,45161,122072,31387357,235,457315,1119,48967,317965322,43335,105,24037992,2,278,869436716,5877,8087188,216,423,59147705,121,102612886,6,3153,9,1892390,2391,14509586,686176,2,191,15185052,319,559632}

Returns: 1125899906842629
{2,45714,173,252441159,6971,97766226,20,16,10646,4903780,86420130,2206219,10047,400871,713875,53819,1419684,4,156435,11099652,1973,6,223538236,27,42548,673,66697,3,12090753,89,147342035,529,100584,137434,3760092,820054138,3,14,1733521,62497304,65835879,455,8058,759353,1908,5164145,24849,2438694,12165,64}

Returns: 1125899906842626
{15894,226,4915,27,166804000,190620568,1856139,919,4580,4224710,2499,5,39,199,2643,291683,252,569928701,12404671,375,114020,123401692,115,601005,794747,30710,82,448684,3426761,59627,9429,204552,85,108360234,30,3530105,53673,8,536714218,961367581,13187,57193550,11,106663,814,86640,377060035,50,585947,6661}

Returns: 4503599627370500
{38819,886812880,112863,104429450,597,3,222431,251546,155549,245772,5,2,30,85617,51734210,871962,3,271908,3776,1816,63,9719758,437948,26989,25,132385,4616254,13,464754,70209681,4926739,24992694,14,22825894,97320268,215399529,8075,263289367,704,125,260134586,18,512329993,5986761,12,1827470,18,550466217,71,20320018}

Returns: 1125899906842626
{29,41,49,45,33,43,42,4,17,14,37,8,48,46,24,16,47,31,3,21,26,18,50,28,22,38,7,2,5,40,23,19,36,20,10,34,32,25,6,1,12,30,39,15,35,13,44,9,11,27}

Returns: 1125899906842624
{70,55,40,44,30,60,53,26,32,41,48,62,51,66,54,43,42,39,52,27,50,56,58,34,57,36,31,75,49,37,67,68,65,29,45,64,46,35,74,47,38,72,71,28,61,69,73,59,63,33}

Returns: 9007199254741017
{188,231,228,221,199,184,203,226,222,198,189,217,223,190,201,229,182,224,215,205,212,216,193,227,187,230,197,204,211,194,214,213,200,192,195,220,196,218,185,207,206,219,208,209,186,225,210,202,183,191}

Returns: 72057594037928117
{5954,5934,5946,5944,5967,5953,5963,5956,5929,5957,5974,5969,5975,5938,5952,5958,5932,5973,5978,5964,5933,5965,5943,5945,5931,5935,5960,5930,5971,5977,5940,5951,5936,5942,5966,5947,5939,5941,5955,5961,5972,5950,5976,5949,5948,5937,5968,5970,5962,5959}

Returns: 2305843009213699880
{4923948,4923919,4923946,4923933,4923930,4923950,4923944,4923929,4923936,4923939,4923942,4923935,4923927,4923931,4923917,4923932,4923924,4923922,4923934,4923914,4923926,4923915,4923921,4923937,4923923,4923913,4923928,4923949,4923951,4923945,4923916,4923925,4923941,4923940,4923912,4923920,4923938,4923918,4923943,4923947}

Returns: 2305843009218617863
{582838205,582838202,582838211,582838188,582838186,582838187,582838203,582838190,582838210,582838194,582838213,582838204,582838189,582838192,582838206,582838199,582838207,582838193,582838201,582838197,582838185,582838208,582838214,582838209,582838184,582838183,582838195,582838191,582838198,582838212,582838196,582838200,582838182}

Returns: 2305843009796532133
{999999971,999999961,999999964,999999965,999999982,999999970,999999954,999999969,999999963,999999956,999999962,999999958,999999975,999999973,999999979,999999976,999999967,999999955,999999977,999999953,999999983,999999951,999999952,999999957,999999978,999999966,999999981,999999959,999999972,999999980,999999960,999999968,999999974}

Returns: 2305843010213693902
{2758,2745,2765,2750,2738,2727,2732,2771,2770,2768,2754,2729,2746,2753,2742,2774,2743,2739,2741,2761,2737,2763,2764,2769,2744,2767,2756,2760,2766,2740,2775,2733,2730,2757,2735,2747,2749,2762,2776,2731,2773,2736,2748,2759,2751,2752,2772,2734,2755,2728}

Returns: 1152921504606849702
{128,16,512,256,256,268435456,1024,8192,2097152,128,64,67108864,131072,8,32,2097152,64,268435456,67108864,1048576,4,8,65536,134217728,4194304,134217728,16777216,1024,131072,536870912,256,256,8192,1024,4,64,256,2097152,32,4,268435456,32,512,128,16777216,8192,8,2,256,1048576}

Returns: 2251799813685249
{531441,59049,4782969,6561,129140163,81,387420489,27,81,531441,4782969,387420489,387420489,531441,81,6561,387420489,4782969,177147,43046721,531441,2187,729,243,3,1,1,243,1,387420489,43046721,9,59049,243,6561,81,2187,6561,43046721,177147,6561,2187,43046721,43046721,531441,1,6561,6561,387420489,19683}

Returns: 1125899906842624
{64,4,16,64,65536,4,268435456,268435456,1024,4,16,16,1024,16,16,67108864,16,4,16777216,16777216,1024,65536,268435456,16,65536,256,268435456,262144,67108864,65536,16777216,16384,16,1048576,16384,262144,16777216,256,1048576,1,67108864,1048576,65536,268435456,16777216,256,1048576,4096,1,16777216}

Returns: 1125899906842627
{390625,125,9765625,625,5,390625,625,15625,78125,48828125,15625,25,3125,25,78125,15625,25,1953125,1953125,1953125,244140625,625,390625,1953125,5,25,625,1,625,48828125,48828125,3125,78125,78125,3125,1,625,25,125,125,390625,48828125,78125,125,3125,390625,78125,1953125,1,9765625}

Returns: 1125899906842624
{100000,10,100000,1,10000000,1000,10000,10000,10000,10000,1000000,1000000,100,1,100000,100000000,1000,100000000,1000000000,100,100000,10000000,100000,1000000,1000,10000000,1000,1000,1000000,1000000,100,1000000,1,10,1000,1000000000,1,100000000,10000,1000,10,10000000,100,10000,100,1,100000,100000,100000,100000000}

Returns: 1125899906842624
{8111104,8111104,1,2848,8111104,2848,1,8111104,8111104,8111104,2848,2848,8111104,2848,1,1,1,1,8111104,1,1,8111104,2848,1,1,2848,2848,1,1,1,2848,2848,2848,2848,2848,2848,8111104,8111104,8111104,8111104,8111104,2848,1,2848,2848,1,8111104,1,1,1}

Returns: 1125899906842624
{1,1,394949,1,1,394949,394949,394949,394949,394949,394949,394949,394949,1,394949,1,394949,394949,394949,1,1,1,394949,394949,394949,394949,1,1,394949,1,394949,394949,1,1,394949,1,1,394949,1,394949,394949,1,1,394949,394949,1,394949,394949,1,1}

Returns: 1125899906842624
{4194304,1048576,33554432,67108864,8,32768,256,1024,512,1,2097152,131072,128,524288,2048,16,16777216,8192,8388608,2,4,16384,536870912,268435456,134217728,65536,4096,262144,64,32}

Returns: 1610612735
{81,19683,6561,1,1594323,9,177147,2187,27,729,43046721,387420489,14348907,243,4782969,129140163,59049,3,531441}

Returns: 655855944
{256,4,64,1,4194304,1024,16384,268435456,16777216,4096,1048576,67108864,16,262144,65536}

Returns: 536870911
{625,244140625,1,15625,390625,3125,25,78125,9765625,5,125,1953125,48828125}

Returns: 311249488
{1000000000,1000000,1,10000000,100,100000000,100000,1000,10000,10}

Returns: 1134217727
{2848,8111104,1}

Returns: 8115199
{1,394949}

Returns: 394952
{15,1048575,31,1,32767,2097151,15,7,7,134217727,1,134217727,127,7,8388607,3,127,4194303,4194303,3,8388607,1048575,1023,268435455,7,32767,262143,1023,511,33554431,2097151,131071,536870911,524287,524287,16777215,4194303,2097151,255,7,536870911,1048575,1,67108863,1,63,8388607,15,8388607,65535}

Returns: 1125899906842624
{177146,43046720,26,14348906,43046720,2,8,8,177146,59048,80,59048,2186,129140162,26,129140162,2,14348906,8,387420488,43046720,2,728,19682,19682,14348906,4782968,177146,531440,177146,2186,242,19682,728,129140162,242,19682,387420488,4782968,387420488,14348906,177146,728,1594322,80,43046720,1594322,14348906,4782968,43046720}

Returns: 1125899906842631
{255,4194303,15,268435455,63,16383,1048575,65535,255,16777215,4194303,3,1023,63,4095,1023,1023,1048575,16777215,63,1023,1048575,255,16777215,262143,67108863,1048575,268435455,67108863,262143,15,16383,3,262143,63,16383,268435455,1048575,1023,262143,67108863,1023,15,4095,255,4194303,15,63,4095,16383}

Returns: 2251799813685262
{9765624,244140624,3124,244140624,1953124,624,3124,624,4,390624,48828124,124,1953124,624,244140624,390624,1953124,15624,24,9765624,24,24,244140624,15624,24,1953124,78124,124,3124,48828124,24,78124,244140624,9765624,124,1953124,124,9765624,78124,24,624,9765624,390624,78124,624,624,15624,244140624,24,124}

Returns: 9007199254740995
{9999999,99999999,9,999999,999,99999999,99,99,999,9999999,99999999,99999,9999,99,99,9999,9,999999,9,999,999999,9999999,999999,999999999,999999,999,999999999,99,9999999,9999999,99,999999999,999999,9999,99999,999999,999,9,99999,999999999,9,9999,999999999,99999999,9,99,9,999999,999,99}

Returns: 4503599627370504
{8111103,8111103,8111103,8111103,8111103,2847,8111103,2847,2847,8111103,2847,2847,8111103,8111103,8111103,8111103,8111103,8111103,2847,2847,2847,2847,8111103,8111103,8111103,8111103,2847,2847,2847,2847,2847,2847,8111103,8111103,8111103,8111103,2847,8111103,2847,8111103,8111103,8111103,2847,2847,8111103,8111103,8111103,8111103,2847,2847}

Returns: 1152921504606849822
{394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948,394948}

Returns: 2305843009214088899
{7,8191,131071,2097151,3,1,1048575,262143,1023,63,255,524287,536870911,134217727,32767,268435455,67108863,8388607,2047,33554431,4095,511,65535,4194303,31,15,16777215,127,16383}

Returns: 1073741822
{1594322,59048,177146,4782968,2186,242,80,387420488,129140162,728,43046720,26,2,14348906,19682,531440,6560,8}

Returns: 655855943
{16383,262143,67108863,63,268435455,15,4194303,1048575,255,16777215,1023,65535,3,4095}

Returns: 402653182
{124,24,78124,244140624,4,390624,3124,624,48828124,15624,9765624,1953124}

Returns: 311249487
{999999999,9999,999,9999999,99,9,99999999,999999,99999}

Returns: 1134217726
{8111103,2847}

Returns: 8115198
{1, 2, 3 }

Returns: 8
{1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000 }

Returns: 281475976710655
{53454325, 43534, 4532, 321312, 13213, 5345, 6546, 76575, 98797, 99808, 43543, 4232, 453345, 8756, 456, 54, 54334, 1 }

Returns: 120563188
{29877788, 99999999, 1000000000, 565200300, 1000000, 25678912, 23232323, 15, 2, 800001, 900000055, 1000005, 257, 1025, 1023, 8048, 500000000, 29877788, 99999999, 1000000000, 565200300, 1000000, 25678912, 23232323, 15, 2, 800001, 900000055, 1000005, 257, 1025, 1023, 8048, 500000000, 29877788, 99999999, 1000000000, 565200300, 1000000, 25678912, 23232323, 15, 2, 800001, 900000055, 1000005 }

Returns: 1125899907642624
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 90, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50 }

Returns: 1125899906842624
{123, 2, 4, 525, 6, 4, 34, 567, 8, 65, 43, 24, 567, 8, 8, 65, 432, 2, 456, 789, 87, 654, 3, 456, 78, 9, 7, 6543, 456, 78, 6, 76, 543, 245, 677, 998765, 4345, 657, 54, 35, 43, 7579, 6, 52453, 677, 854, 354676, 213, 5367, 9 }

Returns: 1125899906842625
{1, 2, 3, 4 }

Returns: 16
{1, 6 }

Returns: 8

Statistics

Problem Statement for "SignalIntelligence"

Problem Statement

Definition

Constraints

Examples