Statistics

Problem Statement

NOTE: This problem statement contains images that may not display properly if viewed outside of the applet.

A city has imposed new safety measures for its buildings. An emergency staircase is going to be built between the only two tall buildings in Linear Kingdom. These buildings are side-by-side and are infinitely tall. The lowest floor is floor 0 on the ground. The distance between two adjacent floors is two meters. The sides of the buildings are parallel and the distance between the buildings is Width meters, where Width is an even integer. The illustration below shows the bottom of the buildings when the buildings are separated by 4 meters (note that for simplicity only the first six floors are labeled):

Normally a staircase is a structure composed of "flights" (or "flights of stairs") and "landings." A flight is a continious sequence of stairs (steps), usually the same size and in the same direction, which begins and ends on flat areas called landings. For this problem we will use an idealized staircase where landings are a single points and flights are straight line segments.

Each flight that is going to be built is a straight line segment whose slope is either 1 or -1. The picture below illustrates two examples of flights.

Some floors of the buildings have emergency exits. These exits are going to be connected to the ground through the staircase. You are given Strings leftBuilding and rightBuilding. The i-th character (1-based indexing) of leftBuilding (rightBuilding) will be 'Y' if there is an emergency exit on floor i of the left building (right building). Note that this implies that no emergency exit will be on floor 0.

Initially, all floors except floor 0 are not connected to the ground. The procedure for building the staircase will be as follows:

• You pick a point that is connected to the ground (this point must be located on the staircase or on floor 0).
• Then, you pick one of the two possible slopes for the flight and extend a line segment from your chosen point until the first time you hit the edge of a building or another flight. This segment must not end in the middle of the ground (though segments that end at floor 0 are allowed). This line segment is the new flight that you are going to build.
• Flights must be built only in the space between the buildings.
• All points on the new flight become connected to the ground and if this flight ends at the edge of a building, that floor of that building becomes connected to the ground.

For simplicity, you are only allowed to create flights whose length is a multiple of the square root of 2. That is, a flight connects a vertex of the grid in the first image to another vertex there. Below is an example of a final staircase configuration of valid flights:

The cost of a flight is determined by its length. You are given int[] cost containing Width elements. The i-th element in cost (0-based indexing) is the actual cost to build a flight whose length is (i+1) * SQRT(2). Note that the cost of the flight is the cost of the original length at the time it is built. Starting a new flight at some non-endpoint of an existing flight (for the purposes of this problem) does not divide the existing flight into two and does not affect the cost of the existing flight.

Return the minimum cost required to connect all the emergency exits to the ground.

Definition

Class:

KingdomXEmergencyStaircase

Method:

determineCost

Parameters:

String, String, int[]

Returns:

long

Method signature:

long determineCost(String leftBuilding, String rightBuilding, int[] cost)

(be sure your method is public)

Constraints

• leftBuilding will contain between 1 and 50 characters, inclusive.
• rightBuilding will contain between 1 and 50 characters, inclusive.
• Each character in leftBuilding and rightBuilding will be 'Y' or 'N'.
• There will be at least one 'Y' in leftBuilding, or, there will be at least one 'Y' in rightBuilding.
• cost will contain between 2 and 10 elements, inclusive.
• cost will contain an even number of elements.
• Each element of cost will be between 1 and 1,000,000,000, inclusive.

Examples

1. "YNYY"

   "NNNY"

   {10, 40, 18, 25}

   Returns: 98

   The optimal solution corresponds to the last image in the statement. Note that the black squares on some of the floors represent the ones with exits.

2. "N"

   "Y"

   {1, 1000}

   Returns: 1000

3. "NNNNNNNY"

   "NNNNNNNY"

   {1, 2}

   Returns: 17

4. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

   "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

   {800000000,800000000,800000000,800000000,800000000,800000000,800000000,800000000}

   Returns: 6400000000

   The answer may not fit into a 32-bit integer.

5. "YNYNYYNYNYYNYNYYNYNYYNYNYYNYNYYNYNYYNYNYYNYNYYNYNY"

   "YNYNYYNYNYYNYNYYNYNYYNYNYYNYNYYNYNYYNYNYYNYNYYNYNY"

   {958231113, 959939939, 999999999, 954321321, 1000000000, 998998998, 987987987, 999888777, 1000000000, 1000000000}

   Returns: 58212305211

   A huge test case @Ivan the intended solution is really quick :)

6. "NNY"

   "NNYYY"

   {10000, 10, 40, 10000, 80, 80}

   Returns: 220

7. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

   "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

   {1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000}

   Returns: 100000000000

   Upperbound on the answer

8. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

   "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

   {1, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000}

   Returns: 100000

   A tower.

9. "N"

   "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

   {1, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 1}

   Returns: 100

   A curious case.

10. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    "N"

    {1, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 1}

    Returns: 100

    Reversed curious case.

11. "NNNNNNNNNNNNNNNNNNNN"

    "YNNNYYNNNN"

    {96023230,163690201}

    Returns: 1078164436

12. "YYYY"

    "NYYNNNNNYYYYYNNYNNYYYYYNYYNNYNYY"

    {989583534,990560251,985387828,977245020,343664912,972489206}

    Returns: 20529738990

13. "NNNNNNNNNYNNNNNNYNYNNNNNYNNNN"

    "NYNYYYYYNNNNNNYYYNNNNYNYY"

    {580402295,553591508,708724209,634644078,697169587,659453250,628060281,687360846,697850075,604551699}

    Returns: 9785884314

14. "YNYNYYNY"

    "NNNNNNNYNNNNNNNNNYYYNNNNNNNNNNYNNNNN"

    {502928602,581095003}

    Returns: 20025659501

15. "NNNNNNNYNNNNNNNNNYNNNNNNNNNNNNNNNNNNN"

    "NNNNNNNNYNNNNNNNNNNNNNNNN"

    {449386691,437564512,465230251,430895616,498543778,432090319,458795523,450679284}

    Returns: 2741467472

16. "YYNYNNNYNNNYYY"

    "NYYYNNYNNYYNYYYYNYYYNNYYYYYY"

    {734359722,811163980,507608624,507992981}

    Returns: 17046879788

17. "YYNYYYYYYYYNYYYYYYYYYYYYYNNYYYYYYYNYYYYYYYYYY"

    "YYYYYYYYYNNYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {30324387,10696603,30072744,25071338,18071925,10852577}

    Returns: 1177259453

18. "YNYYY"

    "YYYYYYNNNNYNNYYYYYYYYNNNNYYYYYYNYYYYYYYYNYYNYYYN"

    {269858868,198863374,426679028,214731620}

    Returns: 11601925496

19. "NNNNNNNNNYNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "YYYYYYYYY"

    {26703361,377183164,909470895,856975545,483383631,487875870,700767084,468256964,468265132,744338963}

    Returns: 4650850115

20. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    "NNNNNNYYNNNNNN"

    {459813926,573179902}

    Returns: 23519426048

21. "NNNNNNNNNNNNNNNNNNNNNNNNN"

    "YNNYNYNYNNNYNYNNYNYNYNNNNNNNNNYNYYNYNNYNNNNNYYYYYN"

    {586938057,636475137}

    Returns: 34708910055

22. "NNNNNNNYNNYNN"

    "NNNYYNYNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNYYN"

    {567164826,834495514,822596428,904805856,787810200,352982110,381068918,658227264}

    Returns: 8379239522

23. "NN"

    "NYYNYYYYYN"

    {906419950,594819953,901044342,619462802,909750161,905541879,906334287,592513630}

    Returns: 6284590810

24. "YYYYYYYYYYYNYYYNNY"

    "YYYNNYNNYYYNYNNYNNNNYNNYNYYYYNYNNNYYNYNYNYN"

    {642744532,499567004,953634879,627581562}

    Returns: 27122006293

25. "NNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "YNYNYYYNYNYNNYNNNNYYNNYYNYNYNYYYYNNNYNNYY"

    {9075220,606084997,7231445,659380318}

    Returns: 1041234093

26. "NNNNNNNYNN"

    "NNNNNNNNNYNNNNNNNNNN"

    {331690215,549668165,492491890,343204049,470841409,433227283,380500328,350699830,481672938,437421429}

    Returns: 1168621587

27. "YNNN"

    "NNYNYNYNYNNYYNNNYYNNYNNYNYNYNNNNYNNYYYNYYNNN"

    {312384312,235781852,562419329,235199978,296111345,482837892,542217049,481647274,291160089,523655994}

    Returns: 6951197237

28. "NNYYNYNYYNYNYNYYYYNNYYYYYNYYYNYNNNNY"

    "YYYYYYYYYYNYYNNYNYYYYYYYNYYY"

    {63143818,38147816,442805675,38088921,73005397,61673731,24193110,866660191}

    Returns: 2556616378

29. "NNNN"

    "YYYYYYY"

    {298542636,395087728,368639324,304857658,565522785,376686626,243959591,598260612}

    Returns: 2773669395

30. "N"

    "Y"

    {721918845,602721939,642162410,887148176,100814683,843677612,923579321,92155490,201550116,650885822}

    Returns: 944591428

31. "N"

    "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

    {168126041,55892163,932419108,164603702,111991051,45436029,140946155,59357025,927387527,89955006}

    Returns: 899550060

32. "N"

    "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

    {915844611,932068381,938901263,931501842,495302747,918212306,923987875,928505919}

    Returns: 36119240166

33. "N"

    "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    {917852328,926430785,932949091,913416060,981478402,961400632,953904089,954956246,148422747,248713219}

    Returns: 645849185

34. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {153540898,4872413}

    Returns: 4082143100

35. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

    {85953195,431066715}

    Returns: 21981800985

36. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {466904225,794451517}

    Returns: 51395181475

37. "Y"

    "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

    {289292679,362963320}

    Returns: 18148166000

38. "Y"

    "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

    {964883197,965831046,964451246,964844699}

    Returns: 51129793914

39. "Y"

    "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    {16292054,99861481,150330815,129488601,14959603,15658648,15669441,14985100}

    Returns: 177057809

40. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

    {568776171,371147052}

    Returns: 36758190072

41. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {53456581,42215391}

    Returns: 4783598600

42. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

    "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

    {413488333,359333504}

    Returns: 25409465194

43. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

    "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    {710267415,973020597}

    Returns: 48651029850

44. "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

    "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {874487153,421412557,706816220,31797367,315891332,322122056}

    Returns: 23764137553

45. "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

    "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    {245329544,406070152,290130858,230634278,455225804,307105311,230884404,448430389}

    Returns: 11961375996

46. "N"

    "Y"

    {1,1000000000,1000000000,1,1,1,1,1000000000,1000000000,1000000000}

    Returns: 1000000001

47. "N"

    "Y"

    {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

    Returns: 2000000000

48. "N"

    "Y"

    {1,1,1,1,1,1,1,1,1,1}

    Returns: 2

49. "N"

    "Y"

    {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1,1000000000,1000000000}

    Returns: 2000000000

50. "N"

    "Y"

    {1,1,1,1,1,1,1,1,1,1000000000}

    Returns: 1000000001

51. "N"

    "Y"

    {1000000000,999999999,999999999,1000000000,1000000000,999999999,1000000000,999999999,1000000000,999999999}

    Returns: 1999999999

52. "N"

    "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

    {1,1000000000,1,1,1,1,1000000000,1000000000,1000000000,1000000000}

    Returns: 1000000045

53. "N"

    "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

    {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

    Returns: 10000000000

54. "N"

    "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

    {1,1,1,1,1,1,1,1,1,1}

    Returns: 10

55. "N"

    "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

    {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1,1000000000}

    Returns: 2000000010

56. "N"

    "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

    {1,1000000000,1,1,1,1,1,1,1,1}

    Returns: 10

57. "N"

    "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

    {1000000000,999999999,1000000000,999999999,999999999,1000000000,1000000000,999999999,1000000000,999999999}

    Returns: 9999999990

58. "N"

    "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

    {1,1,1000000000,1000000000,1000000000,1,1000000000,1,1,1000000000}

    Returns: 1000000044

59. "N"

    "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

    {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

    Returns: 43000000000

60. "N"

    "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

    {1,1,1,1,1,1,1,1,1,1}

    Returns: 43

61. "N"

    "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

    {1000000000,1,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

    Returns: 24000000027

62. "N"

    "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

    {1,1000000000,1,1,1,1,1,1,1,1}

    Returns: 43

63. "N"

    "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

    {999999999,1000000000,1000000000,1000000000,999999999,1000000000,1000000000,999999999,999999999,999999999}

    Returns: 42999999963

64. "N"

    "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    {1000000000,1,1000000000,1,1,1000000000,1,1,1000000000,1000000000}

    Returns: 1000000001

65. "N"

    "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

    Returns: 2000000000

66. "N"

    "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    {1,1,1,1,1,1,1,1,1,1}

    Returns: 2

67. "N"

    "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1,1000000000,1000000000,1000000000}

    Returns: 2000000000

68. "N"

    "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    {1,1,1,1,1000000000,1,1,1,1,1}

    Returns: 2

69. "N"

    "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    {999999999,1000000000,1000000000,1000000000,999999999,1000000000,999999999,999999999,999999999,1000000000}

    Returns: 1999999999

70. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {1,1,1,1000000000,1000000000,1,1000000000,1000000000,1000000000,1}

    Returns: 55

71. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

    Returns: 55000000000

72. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {1,1,1,1,1,1,1,1,1,1}

    Returns: 55

73. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1,1000000000,1000000000}

    Returns: 43000000014

74. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {1,1,1,1000000000,1,1,1,1,1,1}

    Returns: 55

75. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {1000000000,1000000000,999999999,1000000000,999999999,999999999,999999999,1000000000,1000000000,999999999}

    Returns: 54999999970

76. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

    {1000000000,1,1000000000,1000000000,1,1000000000,1000000000,1,1,1}

    Returns: 36

77. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

    {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

    Returns: 32000000000

78. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

    {1,1,1,1,1,1,1,1,1,1}

    Returns: 32

79. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

    {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1,1000000000,1000000000}

    Returns: 20000000014

80. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

    {1,1,1,1,1,1,1,1000000000,1,1}

    Returns: 32

81. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

    {1000000000,999999999,999999999,999999999,999999999,1000000000,1000000000,1000000000,999999999,1000000000}

    Returns: 31999999971

82. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {1,1000000000,1000000000,1,1,1,1000000000,1,1000000000,1000000000}

    Returns: 2000000056

83. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

    Returns: 55000000000

84. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {1,1,1,1,1,1,1,1,1,1}

    Returns: 55

85. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {1000000000,1000000000,1000000000,1000000000,1000000000,1,1000000000,1000000000,1000000000,1000000000}

    Returns: 28000000044

86. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {1,1,1,1,1,1,1,1,1000000000,1}

    Returns: 55

87. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

    "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

    {999999999,1000000000,999999999,1000000000,1000000000,999999999,999999999,1000000000,999999999,1000000000}

    Returns: 54999999952

88. "Y"

    "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

    {1,1000000000,1000000000,1,1,1000000000,1000000000,1000000000,1,1}

    Returns: 11

89. "Y"

    "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

    {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

    Returns: 11000000000

90. "Y"

    "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

    {1,1,1,1,1,1,1,1,1,1}

    Returns: 11

91. "Y"

    "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

    {1000000000,1000000000,1000000000,1000000000,1,1000000000,1000000000,1000000000,1000000000,1000000000}

    Returns: 10000000004

92. "Y"

    "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

    {1,1,1,1,1,1,1,1,1,1000000000}

    Returns: 1000000013

93. "Y"

    "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

    {999999999,1000000000,999999999,1000000000,1000000000,1000000000,999999999,999999999,1000000000,999999999}

    Returns: 10999999990

94. "Y"

    "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

    {1,1000000000,1,1,1000000000,1000000000,1000000000,1000000000,1,1}

    Returns: 44

95. "Y"

    "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

    {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

    Returns: 44000000000

96. "Y"

    "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

    {1,1,1,1,1,1,1,1,1,1}

    Returns: 44

97. "Y"

    "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

    {1000000000,1000000000,1000000000,1000000000,1,1000000000,1000000000,1000000000,1000000000,1000000000}

    Returns: 32000000022

98. "Y"

    "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

    {1000000000,1,1,1,1,1,1,1,1,1}

    Returns: 44

99. "Y"

    "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

    {1000000000,999999999,999999999,1000000000,1000000000,999999999,999999999,1000000000,999999999,1000000000}

    Returns: 43999999973

100. "Y"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1000000000,1000000000,1000000000,1,1,1,1,1000000000,1,1000000000}

     Returns: 1000000003

101. "Y"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

     Returns: 3000000000

102. "Y"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1,1,1,1,1,1,1,1,1,1}

     Returns: 3

103. "Y"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1,1000000000,1000000000}

     Returns: 3000000000

104. "Y"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1,1,1,1,1000000000,1,1,1,1,1}

     Returns: 3

105. "Y"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {999999999,1000000000,1000000000,999999999,999999999,999999999,1000000000,1000000000,999999999,1000000000}

     Returns: 2999999998

106. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

     {1,1,1,1,1000000000,1000000000,1000000000,1000000000,1,1000000000}

     Returns: 1000000076

107. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

     {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

     Returns: 76000000000

108. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

     {1,1,1,1,1,1,1,1,1,1}

     Returns: 76

109. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

     {1,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

     Returns: 36000000042

110. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

     {1,1000000000,1,1,1,1,1,1,1,1}

     Returns: 76

111. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

     {999999999,999999999,999999999,1000000000,999999999,1000000000,999999999,1000000000,1000000000,1000000000}

     Returns: 75999999930

112. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     {1,1000000000,1000000000,1,1,1000000000,1000000000,1,1000000000,1}

     Returns: 1000000101

113. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

     Returns: 100000000000

114. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     {1,1,1,1,1,1,1,1,1,1}

     Returns: 100

115. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1,1000000000,1000000000}

     Returns: 55000000045

116. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     {1,1,1,1,1,1000000000,1,1,1,1}

     Returns: 100

117. "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     {999999999,999999999,1000000000,1000000000,999999999,999999999,1000000000,1000000000,999999999,1000000000}

     Returns: 99999999902

118. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

     "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

     {1000000000,1000000000,1,1000000000,1,1,1000000000,1000000000,1,1}

     Returns: 1000000053

119. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

     "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

     {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

     Returns: 44000000000

120. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

     "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

     {1,1,1,1,1,1,1,1,1,1}

     Returns: 44

121. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

     "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

     {1,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

     Returns: 26000000019

122. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

     "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

     {1,1,1,1,1,1000000000,1,1,1,1}

     Returns: 44

123. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

     "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

     {999999999,999999999,1000000000,1000000000,999999999,1000000000,1000000000,999999999,999999999,1000000000}

     Returns: 43999999962

124. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1000000000,1000000000,1000000000,1000000000,1000000000,1,1,1,1,1}

     Returns: 12

125. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

     Returns: 11000000000

126. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1,1,1,1,1,1,1,1,1,1}

     Returns: 11

127. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1000000000,1000000000,1000000000,1,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

     Returns: 10000000001

128. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1,1,1,1,1,1,1000000000,1,1,1}

     Returns: 11

129. "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1000000000,1000000000,1000000000,999999999,1000000000,1000000000,999999999,999999999,999999999,999999999}

     Returns: 10999999989

130. "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

     "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     {1000000000,1,1,1,1,1000000000,1000000000,1000000000,1,1000000000}

     Returns: 2000000075

131. "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

     "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

     Returns: 76000000000

132. "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

     "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     {1,1,1,1,1,1,1,1,1,1}

     Returns: 76

133. "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

     "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1,1000000000,1000000000}

     Returns: 51000000025

134. "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

     "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     {1,1,1,1,1,1,1000000000,1,1,1}

     Returns: 76

135. "NNNYNNNYYNYNYYNNYYNYYYNYYYYNYYNNNYNYYNNYYNYYYNNNYN"

     "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY"

     {1000000000,1000000000,1000000000,1000000000,1000000000,999999999,999999999,999999999,999999999,999999999}

     Returns: 75999999954

136. "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1000000000,1,1,1,1000000000,1,1000000000,1000000000,1,1000000000}

     Returns: 1000000048

137. "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

     Returns: 44000000000

138. "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1,1,1,1,1,1,1,1,1,1}

     Returns: 44

139. "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1000000000,1000000000,1000000000,1000000000,1,1000000000,1000000000,1000000000,1000000000,1000000000}

     Returns: 32000000022

140. "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1,1,1,1,1,1,1,1,1,1000000000}

     Returns: 1000000045

141. "YYYYNNNYYYYNYYYYYYNYYYNYYYYNYYNYYYNYYYYYYNYYYNNYYY"

     "YNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN"

     {1000000000,999999999,1000000000,999999999,999999999,1000000000,999999999,1000000000,999999999,1000000000}

     Returns: 43999999976

142. "Y"

     "N"

     {5,1}

     Returns: 1

143. "NNNNY"

     "NNNNN"

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

     Returns: 1

144. "NNNNN"

     "NNNNY"

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

     Returns: 1

145. "N"

     "Y"

     {5,1}

     Returns: 1

146. "NNYNNNNYYYNNYNNNNYYYNNYNNNNYYYNNYNNNNYYYNNYNNNNYYY"

     "NNYYYNNYNNNNYYYNNYNNNNYYYNNYNNNNYYYNNYNNNNYYYNNYNN"

     {10000, 10, 40, 10000, 80, 80}

     Returns: 2200

147. "NNYYYYYYYYYYYYYYYYY"

     "NNNNY"

     {1,1,1,1,1000000,1000000,1,1000000,1000000,1}

     Returns: 20

148. "YY"

     "YY"

     {371,44,298,9}

     Returns: 521

149. "Y"

     "Y"

     {496,35,454,109}

     Returns: 819

150. "YNYY"

     "NNNY"

     {10, 40, 18, 25 }

     Returns: 98

151. "NYYYYYYYNYYYYYYYNYYYNYYYYYYYYNNYYNNYNYYYYYYYNYYYYY"

     "YNYNYYNYYYYYYYYNNNYYYYNYYYYYNYNYYYYYYNYYNNYYYNYYYY"

     {746211362, 427778473, 609181022, 421252720, 634126555, 142390490, 741434962, 845183368, 401105843, 212290473 }

     Returns: 27880738415