Statistics

Problem Statement for "ByteLand"

Problem Statement

The Kingdom of Byteland consists of several cities connected by bidirectional roads. There are castles standing in some of the cities. Byteasar, the King of Byteland is unhappy with his kingdom's defensive power, so he decided to build k additional castles (he can only afford that many).

Whenever one of the cities is attacked by the enemy, the army from the nearest castle must come with help. The enemy is smart, so it will always find and attack the city that is the farthest away from its nearest castle. Therefore, the distance from the attacked city to its nearest castle must be as small as possible. Your job is to calculate and return this distance, assuming that you can decide where to build the k additional castles.

The cities are built in a specific manner. Each city has a main gate and several other gates. Every gate is connected to another gate by a road. It is possible that two gates of the same city are connected (see example 2). For defensive reasons, every road has exactly one main gate on one of its ends. Please note that every road can be traversed in both directions.

The road going out of the main gate of the i-th city leads to the road[i]'th city and is distance[i] miles long. The int[] castles contains the 0-based indices of the cities in which a castle is already built.

Definition

Class:
ByteLand
Method:
buildCastles
Parameters:
int[], int[], int[], int
Returns:
int
Method signature:
int buildCastles(int[] road, int[] distance, int[] castle, int k)
(be sure your method is public)

Constraints

  • road will contain between 2 and 50 elements, inclusive (let's call this number n).
  • road and distance will contain the same number of elements.
  • Each element of road will be between 0 and n-1, inclusive.
  • Each element of distance will be between 1 and 10^6, inclusive.
  • k will be between 1 and n, inclusive.
  • castle will contain between 0 and n-k elements, inclusive.
  • Each element of castle will be between 0 and n-1, inclusive.
  • The elements of castle will be distinct.
  • It will be possible to build the castles in such a way that you can always reach a castle from each city.

Examples

  1. {1,2,3,4,0}

    {1,1,1,1,1}

    {}

    1

    Returns: 2

    Building the castle in any of the cities results in the maximum distance from a city to a castle being 2.

  2. {1,2,0}

    {1,2,3}

    {2}

    1

    Returns: 1

  3. {0,1}

    {1,1}

    {1}

    1

    Returns: 0

  4. {0,4,3,2,3}

    {1,3,1,2,2}

    {0,2}

    1

    Returns: 3

  5. {2,1,4,4,1}

    {1,2,1,2,3}

    {0,1}

    1

    Returns: 2

  6. {3,2,1,2,0}

    {2,1,3,1,3}

    {3,4}

    1

    Returns: 2

  7. {0,2,0,0,2,2,8,3,8,7}

    {10,9,1,8,1,3,7,2,8,1}

    {3,4,6}

    3

    Returns: 3

  8. {0,0,5,8,9,5,0,4,7,0}

    {9,2,1,2,3,8,3,1,8,10}

    {1,3,8}

    3

    Returns: 3

  9. {6,8,0,9,1,6,5,7,6,5}

    {3,8,8,10,8,4,10,9,2,1}

    {2,3,8}

    2

    Returns: 8

  10. {17,10,14,18,10,17,9,0,17,5,2,19,17,11,17,0,8,0,19,0}

    {10,2,4,8,7,10,8,9,9,1,2,6,1,9,4,3,8,5,4,5}

    {5,7,12}

    5

    Returns: 9

  11. {9,19,3,1,7,3,0,19,4,4,4,3,10,13,1,10,12,1,11,19}

    {5,10,6,9,9,10,2,3,2,2,1,3,1,4,4,10,9,7,1,4}

    {6,10,15}

    2

    Returns: 16

  12. {12,0,19,2,4,13,13,4,17,5,9,17,5,8,19,8,12,0,8,4}

    {3,4,9,4,2,5,4,7,7,1,6,9,4,5,1,8,8,4,2,7}

    {10,14,16}

    2

    Returns: 15

  13. {11,5,16,15,17,16,11,9,19,9,4,12,5,9,9,11,10,16,9,3}

    {1,2,3,1,8,5,7,8,7,3,6,10,8,2,5,5,10,7,6,9}

    {7,13,19}

    3

    Returns: 8

  14. {5,9,14,8,11,10,10,6,0,11,18,2,18,4,1,8,1,13,13,12}

    {4,8,8,10,7,6,8,8,5,7,1,2,8,7,1,1,7,3,7,9}

    {1,3,17}

    3

    Returns: 11

  15. {14,1,2,2,14,15,7,7,10,6,6,0,3,3,17,12,7,5,14,1}

    {6,1,2,6,7,4,5,5,9,4,8,3,7,10,7,4,8,5,1,8}

    {0,8,19}

    2

    Returns: 15

  16. {15,3,8,7,2,6,13,3,13,3,14,0,11,9,14,18,8,9,5,12}

    {7,8,10,10,5,6,2,4,8,2,6,4,5,6,3,7,4,9,1,7}

    {6,7,13}

    3

    Returns: 15

  17. {5,8,13,15,8,3,12,0,1,19,11,2,15,8,5,11,6,16,18,11}

    {1,6,6,9,10,4,1,8,8,10,5,5,8,1,10,6,6,4,8,9}

    {0,3,9}

    5

    Returns: 10

  18. {10,9,5,13,15,1,11,18,3,17,14,13,16,7,4,13,6,13,10,10}

    {3,3,2,8,8,6,7,6,1,8,8,1,8,3,7,5,6,8,4,1}

    {4,5,7}

    6

    Returns: 8

  19. {12,6,1,18,13,14,0,15,8,12,17,15,1,14,4,8,14,1,15,16}

    {9,10,3,4,7,1,7,9,7,6,4,2,4,6,2,7,2,2,5,1}

    {11,15,17}

    4

    Returns: 9

  20. {28,28,7,6,14,7,21,24,0,5,29,14,4,1,19,23,3,19,22,22,23,3,8,15,22,19,24,22,22,12}

    {94,73,23,31,9,67,30,63,61,91,80,12,45,4,55,46,87,99,45,51,71,20,34,30,35,6,41,31,60,63}

    {4,12,14,15,25}

    7

    Returns: 94

  21. {23,4,27,26,4,26,19,10,29,14,5,17,12,11,27,2,11,2,23,17,29,4,18,18,28,22,22,5,7,26}

    {1,24,31,10,72,37,46,31,39,37,45,34,66,9,78,45,92,89,57,7,86,78,63,66,6,34,89,90,91,28}

    {0,1,12,18,25}

    4

    Returns: 115

  22. {3,6,8,4,5,14,18,0,29,7,7,3,20,17,1,18,23,28,13,0,5,6,8,4,26,16,21,0,8,9}

    {42,63,49,90,19,14,26,19,16,27,28,44,20,80,11,73,39,16,3,12,87,38,70,45,14,18,83,97,8,24}

    {7,8,10,11,16}

    10

    Returns: 38

  23. {15,21,26,25,26,2,13,9,3,12,2,27,0,17,19,23,3,8,14,20,23,1,14,29,10,9,7,12,16,23}

    {24,4,7,42,30,54,86,83,43,1,67,47,88,38,15,77,23,20,7,78,22,50,1,7,90,84,66,99,18,15}

    {0,1,4,19,24}

    4

    Returns: 96

  24. {8,3,10,2,8,10,9,14,8,8,0,16,22,20,3,21,21,12,14,29,13,17,17,22,24,21,16,17,2,16}

    {25,44,73,45,76,1,17,27,27,77,67,68,14,30,28,9,73,9,1,17,49,87,96,6,71,93,29,77,82,21}

    {1,4,13,15,16}

    9

    Returns: 68

  25. {11,6,28,9,3,24,16,0,29,7,9,7,19,9,20,8,17,16,13,4,26,5,4,14,29,7,18,14,20,5}

    {87,84,44,5,54,9,51,42,41,11,11,52,78,100,72,98,10,91,56,64,16,32,61,72,88,40,49,7,77,42}

    {2,8,16,18,23}

    5

    Returns: 98

  26. {11,9,8,22,21,8,2,13,8,24,14,5,23,24,3,28,1,26,1,13,4,10,23,0,18,16,15,20,3,25}

    {21,15,35,90,90,47,20,74,10,28,58,44,86,4,20,99,64,12,95,85,27,31,98,42,73,86,99,78,89,84}

    {17,18,19,25,29}

    4

    Returns: 149

  27. {18,17,9,4,18,8,21,3,13,16,13,13,10,24,10,4,2,10,23,3,3,9,21,2,7,26,27,25,16,19}

    {6,57,17,27,21,56,75,95,89,61,71,42,96,63,58,26,40,100,39,13,84,24,72,17,86,71,34,46,27,100}

    {14,17,20,23,29}

    4

    Returns: 133

  28. {18,15,5,2,6,25,24,17,13,27,7,18,18,6,18,10,1,21,12,18,19,12,23,14,0,14,28,15,1,18}

    {27,22,57,63,44,53,10,41,42,53,100,89,74,98,88,84,8,69,66,42,19,85,47,2,1,29,36,49,95,30}

    {2,6,10,14,24}

    6

    Returns: 79

  29. {16,26,6,16,0,10,5,18,3,4,5,29,21,24,24,5,14,0,1,6,20,19,3,8,15,2,6,18,13,1}

    {15,80,20,11,18,70,12,55,61,37,89,86,46,82,32,72,17,97,34,98,15,44,60,68,54,15,51,13,95,36}

    {13,14,25,26,29}

    4

    Returns: 125

  30. {0,41,14,45,16,49,46,34,21,12,13,41,17,39,32,36,17,14,31,38,20,3,49,18,0,27,35,12,5,36,44,7,29,10,4,45,12,0,32,33,14,47,27,31,36,9,19,4,25,2}

    {95,96,56,94,64,9,23,1,21,80,89,18,37,18,28,43,16,40,94,98,76,60,45,53,44,33,12,63,89,39,66,83,35,73,29,50,81,51,3,2,31,91,71,19,61,50,62,76,90,7}

    {0,8,15,16,18,21,22,23,31,39}

    10

    Returns: 87

  31. {38,23,5,12,1,7,43,4,11,46,34,1,16,4,13,15,15,38,6,21,12,24,39,32,42,49,33,25,22,24,47,12,49,4,25,3,13,20,7,24,16,43,28,34,47,41,1,13,32,10}

    {87,95,85,26,28,80,26,13,57,48,39,4,63,88,11,38,41,26,58,48,1,76,91,81,62,89,74,13,54,56,75,40,51,60,66,30,91,43,94,47,42,32,51,4,19,13,41,12,38,50}

    {1,2,10,21,26,37,39,41,45,46}

    10

    Returns: 85

  32. {0,26,35,2,37,2,33,27,46,26,24,38,9,26,41,30,40,34,41,27,35,1,19,12,4,40,1,47,37,3,43,38,32,29,42,19,33,28,47,30,4,23,20,14,49,11,46,39,47,37}

    {69,84,91,90,48,46,81,49,93,70,5,39,10,37,18,3,8,3,81,5,85,37,78,5,3,29,19,49,18,66,38,87,1,29,76,100,26,8,1,70,30,5,8,39,93,77,93,100,80,25}

    {5,6,13,14,15,16,20,31,33,38}

    10

    Returns: 93

  33. {3,19,8,33,47,7,10,6,9,30,37,15,37,26,7,16,20,9,45,45,15,12,10,0,32,25,14,22,43,48,30,49,19,38,34,16,47,45,25,9,25,12,24,14,40,32,30,11,43,27}

    {9,9,41,19,9,75,96,76,100,90,74,80,89,93,20,25,62,67,20,87,26,47,1,53,62,92,35,44,3,28,22,11,88,14,81,48,40,76,23,39,65,48,18,5,41,89,30,54,56,1}

    {3,8,20,24,32,34,36,41,47,49}

    3

    Returns: 128

  34. {48,38,39,30,36,29,6,8,19,22,8,39,29,0,27,10,3,34,10,46,17,7,37,3,17,22,26,21,10,27,47,11,16,37,41,4,18,47,14,39,22,22,28,1,22,6,11,27,40,21}

    {74,10,82,64,16,49,88,44,20,48,21,68,11,39,57,53,93,27,52,58,16,74,32,95,75,5,51,36,84,43,10,58,53,91,73,68,39,60,11,11,7,83,30,18,22,38,22,66,64,73}

    {6,10,12,21,22,24,26,28,47,48}

    11

    Returns: 73

  35. {21,4,23,11,28,42,1,37,4,11,46,38,42,15,11,29,36,27,42,10,3,23,8,9,49,33,23,26,43,21,47,14,27,22,27,6,16,28,45,22,42,41,10,34,6,22,14,44,1,8}

    {8,5,32,16,17,32,1,90,10,46,61,9,60,91,81,89,47,49,20,92,71,62,86,81,48,92,53,12,89,56,21,96,61,4,63,29,87,64,18,96,9,31,4,21,21,36,61,19,84,80}

    {1,3,9,23,28,36,38,40,44,46}

    11

    Returns: 84

  36. {23,8,27,37,36,13,2,5,11,11,35,14,33,5,2,43,23,37,25,35,41,15,31,29,5,19,19,9,47,15,32,22,25,11,10,11,25,12,17,36,25,4,2,10,10,4,6,35,44,31}

    {23,86,99,55,17,7,24,86,66,24,54,100,48,79,62,8,43,37,23,62,25,100,66,77,13,28,34,69,14,78,52,36,15,50,90,31,56,66,68,73,41,21,73,88,100,34,48,94,22,22}

    {2,4,8,12,19,20,25,34,37,47}

    4

    Returns: 178

  37. {5,49,3,5,41,35,12,6,3,35,48,23,9,35,24,42,32,17,15,3,23,12,26,43,37,10,42,48,15,4,37,20,3,41,27,46,28,40,2,31,27,2,7,36,38,33,30,22,3,45}

    {29,27,60,7,72,97,69,16,97,84,20,85,7,76,78,34,72,6,74,27,90,3,31,97,89,21,30,21,44,35,16,24,62,27,30,85,24,98,1,72,34,72,56,40,99,33,73,23,91,99}

    {0,1,6,11,27,29,30,41,43,46}

    12

    Returns: 76

  38. {29,19,6,5,0,40,30,47,42,2,32,14,7,21,12,42,46,34,34,46,36,13,48,17,40,39,18,48,3,14,41,32,35,47,39,35,40,20,34,32,22,17,48,31,40,11,25,38,47,9}

    {85,35,25,84,54,15,75,72,14,80,88,7,14,73,57,4,8,47,76,94,81,98,13,80,81,4,93,59,42,42,20,79,28,45,14,81,59,40,52,24,20,91,83,85,63,39,88,22,37,63}

    {2,11,15,18,26,29,32,41,44,47}

    10

    Returns: 92

  39. {33,23,6,10,17,21,43,28,10,44,1,31,35,35,16,49,23,5,23,11,18,38,30,31,17,29,25,2,21,29,30,6,3,36,18,22,7,11,0,19,8,4,3,45,39,19,44,15,24,17}

    {77,45,8,57,77,78,37,4,82,60,86,14,68,41,52,36,13,9,50,14,80,8,18,33,53,59,4,99,24,29,69,1,25,28,9,53,57,97,57,38,56,94,3,23,34,54,11,46,14,60}

    {10,11,13,18,20,27,31,38,40,43}

    10

    Returns: 77

  40. {44,47,25,43,3,49,47,45,32,1,39,7,16,36,10,7,34,33,7,3,0,1,6,48,35,49,42,13,0,28,16,45,27,41,38,32,40,37,27,24,38,17,34,7,5,46,16,42,31,23}

    {927498,646582,436475,872504,889133,824112,857055,432025,246626,997005,502405,84542,510050,578583,322135,719991,607515,727527,774528,288445,151052,633169,565312,76438,648276,244819,39636,422942,712063,570267,619467,639560,216848,572293,28415,622332,396404,885469,570709,159381,882474,73113,760274,908875,651695,82408,628865,775562,326287,919745}

    {1,5,11,12,18,26,30,37,38,39}

    10

    Returns: 872504

  41. {27,48,12,26,40,27,10,45,47,18,26,20,30,1,45,27,9,11,38,47,5,45,36,19,13,12,8,1,25,40,4,2,38,17,30,30,46,40,26,43,8,2,14,41,3,11,18,14,24,8}

    {944162,42833,547704,60248,173452,929419,762812,537963,701620,575137,42953,125427,583841,340594,807694,522124,486824,809540,495964,394400,16433,108775,739054,827199,917316,281060,150712,605986,619176,132189,950346,563338,175021,498049,139937,864824,427467,419101,402786,645438,994237,962091,770864,94430,819036,94909,616553,822211,420800,112516}

    {2,8,12,15,24,34,36,41,43,48}

    10

    Returns: 866013

  42. {38,39,6,38,27,31,6,27,19,44,16,9,9,45,46,20,47,6,19,14,18,5,6,34,40,14,10,38,10,14,24,48,3,32,39,33,13,45,12,32,41,28,43,3,23,39,23,22,48,44}

    {504238,41767,751951,619644,454503,169591,422710,136666,67781,3070,707430,546005,827421,246486,328339,393810,893769,246902,646055,101083,253537,262299,829962,310332,497052,207537,719972,961575,334010,853722,593019,838247,895488,344969,974242,866343,30911,396951,3008,98691,916373,710437,161047,743793,473274,489385,137602,883394,252639,300008}

    {1,5,8,24,25,26,28,32,36,39}

    3

    Returns: 1524484

  43. {3,34,39,23,25,31,34,28,40,26,0,28,23,44,2,7,47,45,47,6,23,21,14,12,29,22,40,9,5,26,11,8,11,2,33,38,33,17,18,25,46,20,3,19,14,7,28,13,5,26}

    {813071,88029,154350,169385,723544,566729,101407,897384,64641,87064,976262,469102,719374,798425,224656,859658,854466,164941,55177,541334,809316,404623,291755,384569,69042,849519,880327,570523,384933,179982,128999,714355,784362,799700,883739,507905,882781,501497,921640,947421,588561,414254,932874,307934,212678,157529,683943,67143,322469,739120}

    {0,3,9,26,29,32,33,34,35,41}

    10

    Returns: 882781

  44. {12,9,38,24,8,28,30,38,25,22,8,35,25,33,20,4,11,15,47,29,34,25,14,27,7,18,14,9,49,25,46,12,34,36,38,45,15,18,33,40,40,44,27,15,27,49,20,41,14,19}

    {139071,670049,483897,324038,982079,608056,25356,539595,514667,156055,913121,588663,412469,748005,60750,62607,360300,814665,130726,632786,868257,571168,996530,293734,281836,417109,431733,475406,535700,482550,768077,191123,668950,768325,31512,651028,892732,56867,190623,407398,729273,620095,512413,141742,368099,573162,204348,244751,904178,851425}

    {4,16,20,26,27,28,34,35,37,42}

    10

    Returns: 768325

  45. {3,12,2,3,36,13,32,17,31,6,16,3,0,28,44,1,41,42,3,20,16,40,5,10,8,25,37,34,32,21,14,35,33,18,40,21,31,23,40,12,29,7,16,32,35,12,35,27,6,38}

    {273200,645724,595529,149856,199584,234637,641733,974224,713973,696917,928695,85590,765253,380131,540608,64745,96854,110540,213718,455245,884954,951850,379052,76772,899234,897039,827735,423969,582368,858541,287157,855568,20616,882685,521775,736552,633673,679859,710775,347645,376776,155821,433234,658380,52303,490194,723124,149157,600733,453194}

    {0,1,3,9,25,37,41,42,43,45}

    10

    Returns: 837839

  46. {26,5,35,2,6,9,10,32,5,37,4,41,16,7,34,40,13,16,33,15,5,27,18,14,4,11,11,49,20,49,0,48,4,37,0,12,46,13,44,1,0,48,42,19,5,26,11,20,44,44}

    {515138,941601,387324,824108,524117,409928,529920,529529,677127,731292,849080,476077,767441,987034,722166,192843,712646,16362,687358,253042,255365,627761,247690,872410,672430,781598,357688,60841,3920,828285,246187,519058,769885,633510,343165,810353,559789,389436,856233,236915,120728,705312,229343,404520,692345,951508,113714,921342,484221,801072}

    {2,10,21,24,31,32,35,36,40,47}

    10

    Returns: 872410

  47. {19,38,49,5,49,14,9,37,1,42,1,28,3,45,47,0,4,11,41,26,34,24,12,15,48,10,27,21,47,31,11,18,19,13,25,18,27,34,5,28,26,8,9,32,3,6,32,9,19,23}

    {530236,902054,924900,871498,811921,172898,373810,339400,173621,878507,545331,898285,246577,675900,382298,731552,397320,485177,660137,753027,596357,404915,979935,836566,154847,340090,126675,118629,784999,580396,217603,315234,482450,142502,703084,810722,831752,76893,150122,5372,471752,695452,903656,718328,887704,802305,449880,285023,287481,110016}

    {2,6,23,24,25,28,29,33,37,49}

    5

    Returns: 1252317

  48. {8,9,23,12,42,46,13,34,17,36,37,19,44,15,22,48,44,46,29,11,45,16,42,31,20,20,6,49,29,31,23,37,40,48,1,34,44,16,19,14,3,8,35,49,23,7,49,19,5,28}

    {649533,320402,609647,734476,697135,291070,521898,948293,819569,614077,858874,808244,744967,776817,739544,57068,888851,424190,898485,788222,12304,790940,946681,715689,154441,598906,422048,274940,678426,416404,956271,327958,253157,82269,578785,950291,373338,617035,898583,709258,747463,273808,33853,492429,50624,773396,65849,455827,197586,480685}

    {4,10,15,25,28,29,31,35,40,47}

    10

    Returns: 898583

  49. {33,26,19,39,45,6,29,32,40,13,40,2,21,42,33,46,40,31,22,27,17,22,17,42,3,48,7,40,29,13,0,12,40,22,2,35,28,33,17,20,47,9,22,20,4,7,16,46,38,41}

    {795324,686008,60366,413941,834000,788621,507192,440759,822862,980771,264873,357864,767433,778963,721586,636687,581650,525516,22471,529919,870336,339718,333029,503509,894940,57535,466518,706056,960481,276157,777949,755804,478516,354666,686096,312516,143287,193287,753274,966148,690409,534498,324011,457842,313460,561949,94528,411461,87464,633350}

    {7,9,15,18,25,26,29,34,45,49}

    10

    Returns: 1043960

  50. {0,0,0,0,0,1,2,2,7,2,5,6,8,9,6,2,3,4,2,12,17,13,10,18,21,21,3,13,19,24,27,2,10,28,29,2,20,16,28,24,4,38,26,14,24,0,26,12,45,9}

    {901248,799129,618730,531690,540159,973332,998390,996131,629399,896680,679159,568995,547243,865539,891503,962247,546835,540293,869112,986195,722036,787926,883703,552604,715840,593438,851585,957512,653737,550017,531499,575631,849146,670876,607321,909952,664854,605710,906082,794254,502390,605888,883896,549633,971427,775398,532526,538908,815691,901639}

    {6,26,42}

    3

    Returns: 3266471

  51. {0,0,0,0,1,2,5,6,5,2,9,5,5,4,8,4,2,7,9,3,2,16,1,5,3,8,5,17,2,18,14,0,28,12,32,32,28,32,7,20,0,6,9,38,21,19,21,46,18,5}

    {988387,858090,713250,608934,737044,520822,782655,675552,644086,858015,639163,846370,664231,552872,659632,896499,530765,997399,553622,747226,889038,687748,757240,724989,969753,668127,915206,564488,626892,886415,766211,635925,765151,500107,765506,522841,520930,548160,698394,685663,926822,858204,532032,611700,911076,712312,528845,962488,730357,603115}

    {29,36,44}

    3

    Returns: 2491633

  52. {0,0,1,2,1,0,3,2,5,4,3,3,1,0,1,10,4,3,3,9,15,12,6,2,6,23,8,5,0,5,6,27,8,5,19,13,30,16,12,35,35,29,22,7,11,42,42,8,0,33}

    {782698,750265,656651,636015,775813,802244,518178,763849,698840,503456,961598,714830,800245,626298,616497,878295,946726,819046,802095,549771,729537,837856,612653,633770,526978,900877,554585,890394,983251,731670,634411,786595,502581,811709,922610,778395,634600,961436,562890,833440,964892,524487,568917,785783,650785,685414,684724,597511,525106,986819}

    {13,16,49}

    3

    Returns: 2569430

  53. {0,0,1,1,2,2,0,3,2,0,3,3,10,9,5,6,11,8,9,11,3,16,10,4,4,3,7,3,0,3,11,12,28,15,25,3,3,26,37,2,34,20,8,16,40,23,7,42,20,14}

    {604262,989572,729236,814166,786612,784301,708793,701810,864471,590239,784937,699284,858301,710586,963805,519307,838340,691969,984302,713390,677389,928988,581037,881352,644426,905184,623546,765219,626619,966863,666098,751528,956434,915981,586340,763692,720928,795133,965502,585399,906020,771085,805330,764320,981671,769134,804274,840657,981750,809223}

    {14,19,46}

    3

    Returns: 3208932

  54. {0,0,1,1,3,2,0,2,2,0,7,6,5,1,7,10,9,9,11,3,17,19,3,2,4,1,20,5,19,24,12,18,24,4,6,10,25,22,0,20,10,18,23,20,39,30,11,46,20,3}

    {724869,903080,654713,849986,993622,922920,647444,603197,794693,892565,769991,667587,693595,844135,543640,797690,937001,551890,887952,611533,904476,511359,840482,614559,541897,653424,757561,535065,792672,860263,910133,517540,783989,564845,867526,798257,508412,535617,901454,803105,948829,692091,970693,642423,536225,534979,960760,993874,586869,848712}

    {2,7,41}

    3

    Returns: 3061627

  55. {0,0,1,2,1,3,2,1,5,8,0,1,3,8,12,6,3,11,11,9,3,20,19,21,13,8,8,24,11,2,22,13,15,12,33,19,5,27,22,19,34,11,12,0,31,42,41,18,45,15}

    {852353,854728,670509,880153,893705,502943,889360,905908,942894,747277,564810,874189,506559,690249,932035,709104,976941,873994,889975,696910,601620,979953,929639,878258,543881,522006,502160,610820,530275,895431,983876,882629,770805,675031,783428,664509,698621,672787,591063,641514,940712,655873,515702,967918,866769,947738,677021,843709,842378,587643}

    {46,47,48}

    3

    Returns: 3265014

  56. {0,0,0,2,1,0,4,6,1,5,0,2,0,0,4,6,7,11,6,15,0,9,0,12,10,15,14,20,6,1,13,19,0,19,25,9,18,1,15,17,8,9,4,12,10,28,43,15,32,8}

    {730555,557142,867493,623300,845155,917759,859754,996191,576315,678120,632518,781819,508037,591101,640093,871512,936040,761957,798819,521471,631285,713880,680140,964405,879477,576556,918641,989043,801781,676802,503936,552982,754591,892076,676282,620392,830482,556683,637230,906797,734803,769748,709262,742841,881496,870002,634999,817536,631958,954465}

    {0,5,27}

    3

    Returns: 2285059

  57. {0,0,0,1,0,4,4,3,6,1,8,7,6,5,10,14,8,7,8,10,12,15,1,19,4,8,12,25,21,22,21,8,15,19,21,6,9,29,32,26,32,35,38,14,12,32,21,5,39,13}

    {618882,739098,888926,924485,849526,720930,865087,777489,705540,780801,585752,974040,885506,954457,532128,558677,960157,777798,810007,966575,929146,664076,506045,720114,512961,796147,812390,687144,872913,843203,614067,991795,602947,523639,916280,952474,744570,802013,750609,950110,603460,836362,944796,988966,811465,997571,568290,792268,796016,878297}

    {9,16,28}

    3

    Returns: 3415112

  58. {0,0,1,2,3,0,1,4,4,6,7,4,2,2,3,12,8,14,12,2,16,12,21,19,22,3,7,19,6,10,18,28,12,10,11,15,0,27,18,12,28,20,21,8,9,20,15,35,37,43}

    {582450,951220,639925,922144,629822,781035,850774,600692,738806,678347,851051,901092,568939,886944,549944,556158,525163,997756,827148,659270,587725,516621,760411,964097,668866,786160,579342,507803,517882,684070,524836,600333,655937,685409,543123,806406,987091,914545,907099,725896,592891,778796,647634,682478,665739,718226,738636,711549,715981,565784}

    {18,21,24}

    3

    Returns: 2630490

  59. {0,0,0,1,2,1,2,0,5,2,7,0,9,2,5,8,13,0,14,10,2,4,20,5,13,19,25,13,5,4,3,1,2,31,29,8,27,34,24,21,2,29,9,5,18,22,7,25,18,11}

    {765922,594236,527750,637798,542661,658503,768958,743929,546530,986548,816016,738264,827837,581273,759740,941045,805215,669655,854620,505721,672725,614046,824422,924887,904733,825085,753194,755063,901608,564743,849639,667530,658979,877390,825975,722287,556539,615579,966217,603070,622774,802879,861981,950611,904800,621720,912302,710014,812022,766921}

    {0,38,42}

    3

    Returns: 2548958

  60. {0,0,0,2,2,3,5,2,0,7,5,10,1,6,3,11,14,16,2,9,7,18,4,1,0,14,3,1,17,3,3,22,12,23,9,34,1,18,12,28,8,22,39,6,33,20,21,18,15,32}

    {966269,786618,675318,539466,651936,689652,524966,706621,516008,777388,518335,827111,972717,870206,568493,974391,649257,972703,578767,715805,625128,635485,799318,684751,521933,725772,894504,815299,610746,761896,618650,597661,548514,793968,637128,700450,504267,682741,927719,540922,980776,946054,868033,953492,836906,957173,927883,986163,929875,527296}

    {11,25,46}

    3

    Returns: 2821587

  61. {0,0,0,0,3,0,2,0,0,6,7,4,3,6,1,13,6,15,0,11,1,18,5,15,7,8,12,15,1,4,2,23,23,1,7,14,3,13,5,36,3,15,11,14,15,16,11,43,30,14}

    {832211,880270,802270,645693,859944,688529,887058,846428,525309,676366,576173,937739,669749,869144,631215,847848,930466,520889,587901,891532,868656,987912,870651,723030,862494,504949,805108,736562,997817,583901,630391,830027,964171,932661,996368,844762,641836,883425,711836,687792,580437,808656,646177,750187,677800,798040,618681,608265,818929,727229}

    {20,42,44}

    3

    Returns: 2365001

  62. {0,0,0,0,3,2,3,1,5,2,7,10,7,4,3,1,13,11,17,16,1,2,12,15,22,2,23,16,0,15,8,29,4,21,21,3,6,16,31,7,4,9,12,30,29,24,2,37,23,12}

    {554953,524752,700956,551196,934833,934634,686767,932532,987240,549566,971322,768723,627506,859912,981468,824374,644545,992522,856083,843685,865138,873671,787358,563488,809799,971931,973629,826950,801475,786746,633561,856428,811498,855164,928271,766978,789797,615037,720156,797683,685251,691478,566405,833404,551389,547873,678424,716582,561041,534506}

    {7}

    1

    Returns: 4322105

  63. {0,0,1,0,0,1,2,6,0,1,3,8,1,8,6,10,7,8,6,9,15,2,5,18,10,8,8,2,17,26,16,5,16,25,5,21,26,8,17,35,36,19,10,37,32,6,1,23,20,9}

    {858847,976153,845786,980854,829633,684427,781284,920342,604756,636867,571316,930618,921276,611209,787439,944307,970657,628203,594850,992426,739655,965175,532944,974587,951737,520483,579328,844332,611375,774036,940643,970222,770835,786429,971722,621114,991503,753005,562102,596259,889873,633419,547523,831795,744628,855609,776101,735931,983812,891598}

    {}

    1

    Returns: 5196097

  64. {0,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

    {919973,768172,977773,631485,790573,507625,929965,625795,848518,864753,613213,573093,584341,787133,791072,654684,648254,919250,696555,642632,779851,500828,953142,586654,532567,800629,723554,952886,572121,696563,902879,512740,964735,880651,644225,775954,908924,574190,901749,757441,959590,535608,830535,564577,822741,642253,719262,970996,561503,936464}

    {}

    1

    Returns: 18312141

  65. {0,0,1,2,3,3,4,5,6,8,7,10,10,11,13,14,13,15,16,16,19,20,20,20,22,22,23,26,27,26,29,29,29,32,33,34,34,34,35,37,37,39,40,41,43,42,43,46,47,47}

    {740015,910923,510043,541018,909830,858566,639571,841956,878820,980791,692945,738967,823879,990758,821263,973748,789202,763360,511567,709395,782294,619008,799340,507376,585547,935611,908844,523933,722507,970291,756726,983169,881213,787416,524186,811689,666628,663758,653644,566095,665195,867237,805062,509720,878641,646971,983468,667842,930978,995035}

    {10}

    2

    Returns: 5745567

  66. {6, 12, 9, 13, 11, 9, 1, 3, 6, 12, 4, 7, 8, 3, 2, 15, 13}

    {206563, 444965, 93414, 507580, 722734, 846444, 921701, 672902, 602092, 682491, 201095, 449076, 286417, 212249, 541291, 930203, 60184}

    {}

    12

    Returns: 212249

  67. {1, 1, 1, 3}

    {716269, 237225, 427671, 464556}

    {2, 1}

    2

    Returns: 0

  68. {1, 0}

    {5, 10}

    {}

    1

    Returns: 5

  69. {6, 10, 13, 15, 6, 21, 24, 17, 15, 22, 2, 19, 9, 1, 12, 3, 23, 13, 11, 12, 6, 1, 6, 21, 12}

    {4, 4, 5, 3, 3, 6, 9, 2, 7, 2, 8, 4, 6, 2, 2, 10, 8, 8, 3, 2, 3, 4, 10, 5, 9}

    {3, 14, 21}

    12

    Returns: 4

  70. {29, 7, 33, 16, 24, 12, 20, 2, 11, 33, 4, 12, 10, 30, 25, 2, 32, 18, 14, 8, 20, 21, 27, 19, 22, 30, 3, 15, 21, 1, 4, 20, 18, 11}

    {7, 1, 4, 4, 5, 6, 10, 3, 8, 7, 5, 6, 10, 8, 2, 1, 10, 2, 4, 8, 5, 8, 1, 6, 4, 1, 4, 4, 9, 10, 6, 4, 2, 1}

    {29, 23, 3, 7, 16, 17, 26, 11, 6, 27}

    20

    Returns: 1

  71. {9, 1, 1, 5, 9, 9, 5, 7, 9, 10, 0, 11}

    {6, 1, 5, 7, 7, 1, 6, 5, 5, 1, 2, 7}

    {1, 0, 2, 9}

    8

    Returns: 0

  72. {7, 9, 4, 17, 2, 1, 27, 31, 35, 8, 13, 3, 9, 11, 32, 28, 2, 27, 15, 0, 1, 35, 14, 3, 9, 4, 24, 4, 26, 35, 30, 29, 1, 31, 28, 1, 31, 24, 2}

    {10, 10, 4, 4, 8, 5, 3, 10, 7, 2, 8, 8, 5, 6, 3, 3, 8, 3, 1, 2, 3, 4, 10, 6, 5, 7, 7, 1, 7, 1, 4, 2, 3, 1, 7, 4, 8, 3, 3}

    {34, 12, 25}

    2

    Returns: 37

  73. {20, 18, 6, 16, 24, 9, 2, 6, 4, 25, 25, 8, 4, 9, 10, 22, 23, 24, 13, 0, 2, 20, 1, 2, 25, 3, 16}

    {10, 9, 6, 8, 8, 9, 9, 4, 8, 9, 2, 8, 10, 9, 4, 2, 6, 1, 8, 1, 9, 7, 6, 6, 4, 3, 2}

    {16, 20, 6, 4, 19, 18, 22, 11}

    8

    Returns: 6

  74. {0, 1, 0}

    {7, 5, 5}

    {0}

    2

    Returns: 0

  75. {7, 10, 13, 31, 27, 1, 24, 11, 20, 7, 18, 19, 27, 14, 18, 26, 21, 1, 4, 21, 16, 26, 4, 18, 29, 28, 8, 31, 25, 19, 28, 29}

    {5, 10, 2, 7, 5, 4, 8, 2, 4, 6, 2, 2, 2, 3, 1, 4, 5, 1, 10, 1, 4, 1, 5, 6, 7, 6, 6, 2, 3, 7, 7, 9}

    {5, 30, 17}

    24

    Returns: 2

  76. {34, 34, 34, 18, 32, 30, 10, 35, 12, 16, 37, 10, 19, 36, 7, 14, 13, 17, 28, 19, 33, 19, 20, 14, 17, 13, 26, 7, 30, 29, 20, 28, 30, 4, 6, 14, 20, 27, 1}

    {8, 5, 5, 1, 6, 7, 5, 6, 6, 6, 7, 10, 7, 4, 2, 6, 3, 10, 1, 10, 3, 6, 7, 8, 3, 1, 7, 6, 2, 3, 5, 4, 2, 2, 7, 5, 1, 7, 5}

    {10, 0, 29, 31, 33}

    33

    Returns: 1

  77. {16, 14, 8, 0, 0, 11, 28, 5, 24, 0, 6, 22, 28, 10, 9, 27, 6, 16, 5, 16, 12, 20, 11, 27, 5, 7, 10, 19, 4}

    {2, 4, 8, 6, 4, 7, 6, 1, 6, 8, 5, 4, 8, 8, 4, 9, 4, 10, 8, 1, 8, 10, 3, 3, 7, 3, 5, 10, 3}

    {18, 16, 24, 14, 10}

    13

    Returns: 5

  78. {25, 13, 13, 0, 21, 19, 4, 23, 26, 16, 7, 23, 26, 3, 17, 8, 8, 14, 1, 25, 11, 5, 11, 5, 13, 5, 5}

    {8, 4, 7, 7, 5, 8, 1, 2, 3, 10, 5, 10, 5, 6, 10, 4, 5, 2, 5, 8, 4, 4, 6, 10, 7, 8, 7}

    {9, 23, 14, 12, 19}

    22

    Returns: 0

  79. {5, 3, 1, 5, 0, 0}

    {8, 6, 1, 8, 6, 10}

    {}

    3

    Returns: 6

  80. {11, 0, 1, 0, 3, 3, 7, 3, 13, 8, 1, 0, 3, 8}

    {9, 1, 4, 6, 7, 7, 9, 1, 5, 10, 2, 4, 6, 5}

    {7}

    10

    Returns: 2

  81. {41, 11, 43, 27, 15, 5, 36, 9, 17, 15, 12, 10, 16, 6, 8, 30, 5, 40, 21, 1, 35, 21, 21, 42, 21, 2, 14, 28, 36, 10, 39, 28, 18, 10, 22, 31, 36, 31, 40, 32, 22, 5, 28, 22}

    {1, 4, 2, 7, 1, 1, 5, 3, 4, 10, 8, 3, 8, 7, 6, 4, 9, 4, 10, 8, 10, 3, 2, 8, 3, 4, 2, 5, 2, 9, 6, 8, 9, 1, 6, 3, 3, 4, 8, 10, 3, 5, 2, 6}

    {7}

    41

    Returns: 1

  82. {44, 41, 19, 17, 17, 5, 36, 31, 20, 30, 3, 2, 23, 20, 31, 18, 2, 7, 23, 20, 21, 11, 5, 29, 16, 28, 19, 33, 15, 24, 9, 23, 8, 40, 35, 19, 11, 19, 32, 15, 21, 1, 41, 9, 39, 19}

    {1, 2, 3, 2, 3, 6, 4, 3, 1, 7, 10, 9, 5, 6, 2, 1, 10, 4, 2, 5, 9, 7, 8, 3, 10, 2, 1, 3, 6, 7, 2, 1, 2, 1, 3, 7, 1, 4, 10, 9, 8, 1, 10, 4, 1, 7}

    {34, 39, 15, 37, 36, 8}

    38

    Returns: 1

  83. {24, 7, 15, 6, 27, 28, 18, 23, 34, 22, 43, 28, 15, 10, 43, 44, 23, 22, 8, 0, 16, 44, 45, 45, 30, 5, 38, 2, 4, 12, 0, 23, 25, 5, 17, 3, 42, 10, 5, 18, 14, 4, 40, 2, 32, 31}

    {3, 4, 5, 7, 7, 1, 7, 9, 6, 8, 3, 4, 10, 6, 10, 7, 6, 2, 2, 3, 7, 6, 9, 8, 5, 4, 2, 8, 5, 9, 6, 8, 9, 7, 4, 8, 9, 5, 6, 2, 8, 5, 7, 4, 3, 2}

    {12, 19, 3}

    43

    Returns: 0

  84. {31, 7, 35, 3, 26, 20, 16, 24, 38, 28, 19, 0, 7, 28, 21, 4, 25, 24, 25, 38, 27, 15, 22, 2, 4, 35, 15, 1, 10, 24, 17, 23, 0, 15, 42, 16, 21, 9, 7, 6, 36, 10, 31}

    {10, 6, 8, 9, 2, 1, 3, 7, 3, 9, 1, 1, 6, 10, 7, 10, 4, 7, 3, 8, 3, 8, 7, 4, 9, 8, 6, 8, 4, 7, 1, 5, 4, 1, 4, 3, 2, 7, 2, 9, 5, 8, 10}

    {21, 13, 11, 8, 41}

    35

    Returns: 1

  85. {47, 17, 12, 45, 45, 20, 42, 9, 44, 42, 15, 4, 14, 11, 23, 2, 22, 0, 7, 20, 15, 12, 2, 14, 11, 20, 43, 12, 3, 3, 38, 32, 11, 7, 5, 3, 0, 35, 18, 1, 8, 17, 24, 4, 3, 40, 8, 15, 31}

    {10, 4, 1, 8, 2, 10, 2, 2, 4, 4, 3, 10, 1, 8, 8, 3, 9, 1, 10, 5, 5, 7, 7, 3, 2, 8, 3, 6, 1, 10, 10, 3, 8, 6, 7, 6, 5, 2, 8, 10, 3, 5, 2, 3, 2, 9, 10, 3, 8}

    {20}

    43

    Returns: 2

  86. {41, 39, 16, 33, 15, 36, 16, 2, 17, 38, 40, 37, 10, 13, 25, 36, 16, 34, 38, 15, 23, 28, 3, 7, 2, 29, 28, 38, 0, 29, 3, 11, 30, 35, 26, 11, 13, 16, 17, 4, 9, 20}

    {7, 1, 9, 4, 2, 9, 10, 2, 2, 6, 9, 2, 2, 7, 1, 4, 8, 8, 8, 1, 3, 10, 7, 3, 4, 5, 6, 1, 1, 8, 3, 4, 1, 7, 4, 8, 7, 7, 2, 1, 2, 3}

    {6, 31, 8, 1}

    38

    Returns: 0

  87. {45, 1, 22, 13, 34, 31, 10, 5, 27, 22, 30, 43, 29, 44, 1, 44, 33, 46, 31, 13, 47, 11, 43, 36, 38, 47, 14, 44, 35, 0, 15, 1, 20, 44, 13, 38, 21, 41, 14, 43, 11, 37, 7, 2, 37, 12, 3, 35, 18, 15}

    {2, 4, 2, 6, 8, 4, 3, 4, 6, 5, 7, 10, 10, 5, 10, 5, 4, 7, 7, 2, 9, 5, 4, 5, 3, 10, 10, 1, 7, 1, 4, 5, 3, 7, 10, 9, 2, 10, 1, 8, 7, 1, 9, 7, 9, 3, 6, 6, 10, 4}

    {}

    49

    Returns: 1

  88. {13, 28, 17, 41, 45, 5, 25, 18, 9, 34, 6, 17, 34, 46, 16, 38, 9, 15, 16, 11, 22, 43, 42, 0, 12, 0, 24, 29, 27, 45, 13, 8, 26, 41, 3, 27, 21, 0, 47, 13, 13, 17, 29, 0, 37, 33, 17, 10, 33}

    {8, 10, 7, 6, 5, 9, 4, 2, 5, 2, 9, 8, 7, 7, 8, 8, 9, 7, 1, 6, 6, 1, 2, 3, 8, 3, 7, 3, 10, 6, 5, 1, 1, 9, 8, 4, 2, 8, 3, 9, 10, 8, 2, 6, 10, 2, 9, 8, 7}

    {}

    49

    Returns: 0

  89. {0,0,0,1}

    {1,1,1,1000000}

    {3}

    1

    Returns: 1

  90. {0,0,1,0}

    {1,1,1,1000000}

    {3}

    1

    Returns: 1

  91. {1, 2, 3, 4, 5, 0, 6, 8, 9, 10, 11, 12, 13, 14, 11, 20, 20, 20, 20, 20, 20 }

    {42, 8468, 6335, 6501, 9170, 5725, 1479, 9359, 6963, 4465, 5706, 8146, 3282, 6828, 9962, 492, 2996, 1943, 4828, 5437, 1 }

    {1, 4, 17, 18 }

    10

    Returns: 5706

  92. {0, 1, 43, 10, 13, 33, 15, 8, 18, 21, 4, 23, 3, 42, 2, 14, 45, 18, 38, 16, 34, 42, 35, 15, 8, 16, 23, 12, 41, 13, 24, 7, 43, 14, 38, 48, 24, 44, 41, 1, 7, 7, 25, 1, 29, 0, 38, 32, 38, 35 }

    {557508, 206031, 681086, 592852, 955457, 644056, 998372, 243781, 676166, 295696, 85891, 772322, 495279, 881684, 509967, 573323, 953194, 684834, 338712, 7608, 705351, 988938, 774046, 749573, 197708, 143648, 913599, 784196, 589281, 864710, 689372, 287834, 93644, 628921, 280026, 877185, 161235, 273189, 543686, 960793, 174365, 157070, 268122, 177458, 576796, 498156, 285190, 155945, 609766, 739690 }

    { }

    20

    Returns: 772322

  93. {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 6, 10, 11, 5, 8, 15, 3, 12, 2, 1, 2, 7, 6, 19, 13, 14, 6, 22, 15, 16, 11, 8, 27, 5, 2, 26, 12, 7, 10, 15, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3 }

    {513929, 979802, 634022, 723058, 133069, 898167, 961393, 18456, 175011, 478042, 176229, 377373, 484421, 544919, 413784, 898537, 575198, 594324, 798315, 664370, 566413, 803526, 776091, 268980, 759956, 241873, 806862, 999170, 906996, 497281, 702305, 420925, 477084, 336327, 660336, 126505, 750846, 621729, 661313, 925857, 616124, 353895, 819582, 100545, 898814, 233367, 515434, 990364, 344043, 313750 }

    {37, 8, 26, 28, 38, 34, 3 }

    15

    Returns: 898814

  94. {22, 9, 12, 49, 28, 5, 41, 1, 17, 10, 26, 47, 13, 32, 25, 38, 25, 29, 9, 22, 32, 40, 10, 12, 46, 13, 6, 13, 33, 0, 4, 48, 13, 2, 27, 4, 40, 6, 38, 29, 4, 41, 19, 31, 12, 6, 8, 45, 17, 27 }

    {85640, 359567, 43681, 489099, 678099, 788971, 463630, 206602, 107262, 646584, 791577, 166680, 821875, 26606, 597112, 576529, 100642, 942055, 758419, 513302, 407623, 151755, 975475, 240205, 196007, 292640, 466320, 889475, 37953, 712689, 29524, 106952, 884278, 881562, 854125, 343913, 82349, 300332, 955298, 309809, 688477, 325429, 47984, 347704, 503969, 283103, 724902, 416062, 462004, 829175 }

    {1, 2, 3, 4, 10, 23, 12, 30, 15 }

    20

    Returns: 463630

  95. {0, 0, 1, 2, 3 }

    {1, 1, 1, 1, 1 }

    {4 }

    1

    Returns: 1

  96. {0, 0, 1, 2, 3, 4, 5 }

    {3, 3, 3, 3, 3, 3, 3 }

    { }

    2

    Returns: 6

  97. {1, 2, 2 }

    {1, 1, 1 }

    { }

    1

    Returns: 1

  98. {33, 36, 27, 15, 43, 35, 36, 42, 49, 21, 12, 27, 40, 9, 13, 26, 40, 26, 22, 36, 11, 18, 17, 29, 32, 30, 12, 23, 17, 35, 29, 2, 22, 8, 19, 17, 43, 6, 11, 42, 29, 23, 21, 19, 34, 37, 48, 24, 15, 49 }

    {566414, 803527, 776092, 268981, 759957, 241874, 806863, 999171, 906997, 497282, 702306, 420926, 477085, 336328, 660337, 126506, 750847, 621730, 661314, 925858, 616125, 353896, 819583, 100546, 898815, 233368, 515435, 990365, 344044, 313751, 171088, 426809, 117277, 947179, 695789, 393585, 705404, 502652, 392755, 612400, 999933, 95061, 549677, 993369, 947740, 210013, 636227, 698587, 348095, 297540 }

    { }

    14

    Returns: 1179391

  99. {2, 2, 3, 3 }

    {2, 2, 3, 1 }

    {3 }

    1

    Returns: 2

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved.
This problem was used for: