TopCoder Statistics - Problem Statement

Problem Statement

Percy is a penguin in charge of the greatest penguin pastime, penguin sledding. It is Percy's job to help design the sledding course. Percy is a very careful penguin and would like to set up the course in a way that no two sledding paths cross.

The sledding course contains some significant locations called checkpoints, and some sledding paths. The checkpoints are numbered 1 through numCheckpoints, inclusive. Each sledding path is a straight line segment that connects two distinct checkpoints. The checkpoints are distinct, and no three of them lie on the same line. (Therefore, no checkpoint will ever lie on a sledding path.)

When designing the course, Percy specifies some pairs of checkpoints that will be connected by sledding paths. Accidents happen when two sledding paths cross, so such designs should be avoided. Unfortunately, Percy does not know the precise locations of all checkpoints. Therefore, Percy's design must not allow two sledding paths to cross, regardless of the locations of the checkpoints. Percy calls a design safe if he is sure that no two sledding paths will cross.

Percy just found an old design that may be unsafe. He would like to change it to a safe design by removing zero or more sledding paths from the original design. Count all different safe designs he may obtain from the old design in this way. Two designs are considered different if there is a pair of checkpoints that is connected by a sledding path in one design and disconnected in the other.

You are given the int numCheckpoints representing the number of checkpoints in the old design. You are also given two int[]s checkpoint1 and checkpoint2 that describe the sledding paths in the old design: For each i, there is a sledding path connecting the checkpoints checkpoint1[i] and checkpoint2[i]. Return the number of safe designs that can be made from the old design.

Definition

Class:: PenguinSledding
Method:: countDesigns
Parameters:: int, int[], int[]
Returns:: long
Method signature:: long countDesigns(int numCheckpoints, int[] checkpoint1, int[] checkpoint2)
(be sure your method is public)

Constraints

numCheckpoints will be between 2 and 50, inclusive.
checkpoint1 will contain between 1 and 50 elements, inclusive.
checkpoint1 and checkpoint2 will contain the same number of elements.
Each element of checkpoint1 will be between 1 and numCheckpoints, inclusive.
Each element of checkpoint2 will be between 1 and numCheckpoints, inclusive.
Each pair of checkpoints will be connected by at most one sledding path.
For each i, element i of checkpoint1 will not be equal to element i of checkpoint2.

Examples

2

{1}

{2}

Returns: 2

There is only one sledding path. Both including it and removing it are safe designs.
4

{1,2,3}

{2,3,4}

Returns: 6

Either sledding path (1,2) or (3,4) needs to be removed to form a safe design. If neither of these is removed the design is unsafe.
6

{1,3,6}

{2,4,4}

Returns: 5

Note that some of the checkpoints may be isolated.
50

{40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 50, 40, 40, 40, 23, 4, 24, 40, 22, 40, 8, 40, 40, 40, 34, 21, 40, 40, 38, 40, 40, 40, 40, 40, 28, 40, 40, 40, 40, 46, 13, 40, 40, 40, 47, 40, 40}

{45, 42, 20, 48, 12, 32, 25, 10, 26, 39, 16, 2, 19, 43, 37, 17, 19, 19, 19, 18, 19, 27, 19, 29, 11, 36, 19, 19, 1, 41, 19, 35, 14, 33, 49, 3, 19, 7, 5, 19, 31, 19, 19, 6, 9, 15, 19, 44, 30}

Returns: 68719493118
36

{13, 24, 24, 20, 31, 16, 10, 36, 34, 32, 28, 5, 20, 29, 23, 2, 14, 4, 9, 5, 19, 21, 8, 1, 26, 27, 25, 15, 22, 30, 30, 6, 11, 7, 2, 35, 13, 29, 4, 12, 33, 18, 13, 14, 17, 35, 3}

{10, 15, 27, 1, 29, 11, 5, 18, 33, 1, 9, 2, 31, 6, 19, 10, 33, 18, 6, 27, 3, 22, 4, 12, 31, 30, 34, 16, 7, 24, 3, 28, 15, 21, 22, 8, 26, 20, 14, 32, 25, 17, 35, 8, 36, 26, 23}

Returns: 162
6

{1,1,1,2,2,2,3,3,3}

{4,5,6,4,5,6,4,5,6}

Returns: 34
12

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

{4,4,4,5,5,5,5}

Returns: 30
3

{1,2,3}

{2,3,1}

Returns: 8
4

{1,3}

{2,4}

Returns: 3
50

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

{14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14}

Returns: 562949953421312
50

{47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47}

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

Returns: 562949953421312
30

{7, 30, 30, 30, 9, 13, 29, 30, 30, 30, 30, 14, 30, 1, 30, 24, 30, 30, 18, 20, 19, 30, 30, 25, 30, 30, 30, 30, 6, 30, 30, 30, 30, 30, 30, 30, 30, 30, 26, 30, 30, 30, 21}

{22, 7, 14, 2, 17, 2, 10, 9, 26, 11, 4, 12, 19, 15, 3, 3, 17, 23, 8, 28, 27, 1, 25, 4, 5, 20, 22, 16, 11, 18, 12, 24, 13, 15, 28, 8, 10, 21, 23, 27, 6, 29, 16}

Returns: 536870968
14

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

{8, 9, 10, 11, 12, 13, 14, 8, 9, 10, 11, 12, 13, 14, 8, 9, 10, 11, 12, 13, 14, 8, 9, 10, 11, 12, 13, 14, 8, 9, 10, 11, 12, 13, 14, 8, 9, 10, 11, 12, 13, 14, 8, 9, 10, 11, 12, 13, 14}

Returns: 1730
10

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

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

Returns: 5186
30

{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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2}

{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, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23}

Returns: 541065256
50

{1, 1, 2, 1, 2, 1, 3, 2, 4, 1, 5, 2, 6, 1, 7, 3, 8, 2, 9, 4, 10, 1, 11, 5, 12, 2, 13, 6, 14, 1, 15, 7, 16, 3, 17, 8, 18, 2, 19, 9, 20, 4, 21, 10, 22, 1, 23, 11, 24}

{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, 49, 50}

Returns: 862
50

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26}

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

Returns: 33554431
50

{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, 2}

{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, 49, 3}

Returns: 281474976710660
50

{1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 8, 8, 8, 8, 8, 8, 9, 11, 11, 12, 14, 15, 15, 15, 15, 18, 18, 19, 20, 22, 24, 25, 25, 25, 28, 29, 30, 31, 34, 35, 36, 37, 39, 41, 43, 45, 48}

{13, 42, 32, 36, 8, 33, 50, 23, 50, 14, 19, 37, 8, 12, 15, 18, 26, 29, 37, 49, 40, 41, 34, 34, 16, 18, 47, 49, 19, 37, 35, 32, 42, 44, 29, 36, 37, 34, 47, 43, 42, 44, 41, 48, 42, 45, 47, 45, 48, 50}

Returns: 440
50

{1, 1, 1, 1, 2, 3, 4, 4, 6, 6, 6, 7, 7, 8, 8, 10, 11, 11, 12, 13, 13, 13, 13, 14, 15, 17, 17, 19, 21, 21, 21, 21, 22, 22, 23, 23, 25, 25, 25, 26, 29, 30, 31, 31, 32, 32, 33, 35, 39, 40}

{23, 39, 40, 41, 14, 27, 16, 29, 8, 15, 40, 32, 38, 16, 43, 21, 23, 46, 50, 24, 42, 45, 47, 26, 42, 18, 23, 36, 31, 33, 39, 40, 30, 46, 24, 33, 37, 40, 42, 46, 31, 42, 35, 37, 40, 47, 42, 50, 50, 47}

Returns: 270
50

{1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 7, 7, 9, 9, 9, 9, 10, 10, 11, 13, 13, 13, 14, 15, 16, 17, 19, 21, 21, 21, 22, 23, 24, 24, 26, 26, 27, 28, 31, 32, 35, 35, 35, 36, 36, 46}

{13, 16, 28, 12, 19, 32, 7, 21, 40, 8, 44, 18, 49, 37, 43, 48, 26, 29, 41, 45, 35, 37, 47, 14, 28, 40, 18, 31, 37, 41, 42, 32, 39, 42, 38, 39, 31, 42, 33, 34, 48, 34, 35, 40, 38, 43, 50, 46, 48, 50}

Returns: 179
50

{2, 3, 3, 3, 4, 4, 4, 5, 6, 6, 7, 8, 8, 8, 9, 9, 10, 10, 10, 12, 13, 13, 13, 14, 15, 16, 16, 16, 17, 17, 19, 20, 20, 20, 20, 21, 21, 23, 23, 26, 27, 28, 29, 30, 30, 31, 33, 40, 41, 46}

{38, 19, 28, 38, 11, 13, 31, 12, 8, 46, 43, 19, 20, 23, 16, 47, 18, 24, 46, 24, 14, 18, 35, 38, 19, 27, 28, 33, 29, 34, 33, 22, 29, 37, 42, 24, 45, 36, 49, 27, 36, 36, 30, 42, 47, 40, 45, 42, 44, 47}

Returns: 191
50

{1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 5, 5, 5, 5, 6, 7, 7, 9, 10, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 17, 18, 18, 21, 22, 22, 22, 22, 22, 23, 24, 25, 25, 26, 28, 29, 31, 35, 36, 36, 39}

{41, 18, 20, 23, 26, 41, 47, 48, 29, 33, 11, 23, 29, 36, 7, 28, 30, 49, 29, 32, 14, 23, 35, 37, 25, 30, 30, 48, 49, 25, 26, 28, 46, 23, 30, 34, 39, 42, 46, 41, 34, 36, 30, 45, 39, 49, 45, 43, 48, 44}

Returns: 354
50

{1, 1, 1, 1, 2, 3, 4, 6, 7, 7, 7, 7, 7, 7, 9, 10, 11, 12, 12, 12, 13, 15, 15, 15, 16, 16, 16, 17, 19, 19, 19, 20, 21, 21, 22, 23, 24, 24, 26, 26, 27, 27, 29, 30, 35, 37, 38, 38, 40, 41}

{3, 26, 27, 32, 38, 35, 11, 50, 9, 10, 11, 35, 41, 43, 12, 18, 21, 18, 45, 50, 43, 24, 26, 49, 17, 39, 49, 29, 36, 39, 44, 39, 29, 41, 39, 43, 29, 43, 36, 43, 41, 46, 44, 49, 48, 50, 42, 44, 48, 42}

Returns: 256
50

{3, 3, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 10, 10, 12, 13, 15, 15, 15, 15, 15, 17, 18, 18, 18, 18, 19, 21, 23, 24, 25, 25, 26, 27, 29, 29, 30, 31, 32, 33, 37, 37, 39, 40, 43, 45}

{8, 20, 44, 16, 37, 12, 16, 10, 24, 32, 34, 16, 24, 41, 44, 40, 23, 49, 15, 43, 20, 31, 34, 44, 45, 26, 28, 31, 48, 50, 38, 47, 25, 35, 41, 50, 44, 34, 42, 50, 38, 46, 37, 49, 38, 44, 47, 46, 50, 50}

Returns: 263
50

{1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 12, 12, 13, 13, 15, 15, 15, 16, 16, 18, 19, 20, 22, 23, 25, 28, 28, 29, 30, 32, 32, 32, 37, 37, 38, 45}

{34, 38, 35, 44, 11, 47, 36, 50, 26, 30, 44, 47, 27, 39, 14, 36, 12, 21, 49, 25, 43, 16, 43, 46, 23, 31, 16, 26, 18, 28, 31, 38, 44, 36, 26, 22, 47, 48, 34, 37, 38, 36, 48, 45, 48, 49, 41, 44, 39, 47}

Returns: 178
50

{1, 1, 1, 2, 3, 3, 6, 6, 8, 8, 10, 11, 13, 14, 15, 16, 16, 16, 16, 17, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 24, 24, 25, 25, 26, 28, 28, 29, 30, 31, 32, 33, 34, 34, 40, 40, 41, 41, 43, 45}

{30, 47, 49, 30, 6, 22, 17, 46, 11, 48, 31, 41, 40, 34, 26, 32, 35, 47, 48, 41, 22, 37, 31, 40, 47, 27, 30, 34, 31, 37, 34, 45, 30, 37, 31, 38, 49, 40, 36, 47, 38, 43, 35, 50, 41, 45, 45, 49, 49, 48}

Returns: 276
50

{1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 10, 10, 10, 11, 11, 13, 15, 17, 18, 18, 19, 19, 20, 20, 21, 22, 22, 23, 23, 28, 29, 32, 32, 32, 33, 33, 33, 36}

{18, 3, 18, 17, 22, 29, 13, 19, 21, 30, 38, 17, 13, 41, 8, 35, 9, 29, 30, 40, 49, 37, 20, 32, 42, 35, 36, 27, 19, 21, 24, 29, 45, 48, 30, 41, 30, 28, 43, 40, 45, 42, 36, 34, 36, 42, 35, 38, 50, 48}

Returns: 261
50

{1, 3, 3, 3, 4, 4, 6, 6, 8, 8, 9, 9, 9, 9, 11, 11, 11, 11, 13, 15, 16, 16, 16, 17, 18, 22, 23, 23, 23, 23, 24, 27, 28, 28, 29, 30, 30, 31, 34, 34, 34, 34, 34, 35, 36, 36, 37, 38, 42, 45}

{9, 45, 48, 50, 6, 36, 12, 17, 17, 44, 21, 25, 30, 44, 12, 14, 27, 33, 25, 29, 24, 25, 41, 34, 21, 40, 25, 28, 42, 43, 31, 44, 31, 34, 37, 47, 48, 40, 35, 39, 41, 42, 43, 40, 40, 50, 48, 47, 43, 47}

Returns: 307
50

{2, 2, 4, 4, 4, 4, 5, 5, 7, 8, 8, 8, 9, 9, 10, 10, 10, 12, 13, 14, 14, 14, 14, 16, 16, 17, 17, 17, 18, 18, 18, 19, 20, 20, 21, 21, 22, 23, 23, 25, 26, 28, 28, 31, 31, 34, 35, 35, 36, 41}

{5, 49, 30, 32, 41, 44, 25, 32, 46, 27, 29, 39, 37, 47, 25, 33, 37, 27, 26, 22, 24, 25, 43, 21, 41, 24, 31, 41, 24, 33, 36, 28, 25, 42, 33, 49, 46, 35, 40, 36, 27, 30, 44, 34, 47, 39, 37, 49, 50, 50}

Returns: 185
50

{1, 1, 3, 3, 4, 6, 6, 6, 6, 6, 6, 7, 7, 8, 8, 9, 10, 10, 12, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 19, 19, 20, 20, 22, 23, 23, 24, 27, 28, 29, 29, 30, 31, 32, 32, 34, 34, 37, 37}

{11, 14, 9, 14, 22, 9, 12, 28, 39, 41, 42, 49, 50, 35, 37, 50, 26, 35, 13, 36, 31, 44, 37, 48, 24, 32, 43, 18, 19, 29, 20, 50, 23, 36, 50, 35, 40, 49, 32, 47, 42, 46, 42, 41, 35, 39, 37, 50, 42, 50}

Returns: 286
50

{1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 5, 6, 6, 6, 7, 8, 9, 10, 10, 10, 11, 12, 12, 14, 15, 16, 16, 17, 17, 17, 18, 18, 19, 19, 20, 20, 20, 22, 23, 24, 25, 28, 28, 29, 30, 31, 32, 38, 41}

{3, 28, 29, 42, 49, 43, 45, 16, 23, 26, 39, 42, 8, 21, 27, 16, 35, 24, 34, 46, 47, 41, 18, 27, 35, 44, 23, 46, 26, 29, 48, 39, 50, 20, 38, 22, 30, 41, 48, 40, 27, 48, 34, 40, 35, 34, 35, 50, 41, 42}

Returns: 205
50

{1, 1, 1, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 9, 9, 9, 10, 11, 12, 12, 13, 13, 13, 14, 15, 15, 15, 17, 17, 18, 18, 19, 25, 27, 28, 29, 29, 30, 31, 31, 34, 34, 41, 43}

{30, 36, 44, 35, 13, 45, 46, 5, 8, 21, 27, 28, 36, 37, 39, 13, 38, 47, 49, 18, 39, 43, 43, 41, 32, 42, 16, 25, 34, 27, 16, 30, 35, 23, 38, 19, 41, 24, 46, 46, 32, 32, 48, 43, 33, 46, 35, 47, 43, 45}

Returns: 198
50

{1, 1, 3, 4, 4, 5, 5, 6, 6, 7, 9, 10, 10, 11, 12, 12, 14, 14, 14, 16, 16, 16, 17, 18, 18, 18, 18, 18, 19, 21, 22, 23, 25, 25, 26, 27, 28, 29, 30, 31, 31, 32, 34, 34, 34, 37, 38, 40, 41, 41}

{35, 44, 16, 13, 39, 9, 17, 27, 43, 41, 27, 39, 40, 27, 21, 39, 17, 21, 45, 25, 33, 45, 28, 23, 26, 31, 38, 49, 44, 24, 26, 47, 41, 44, 42, 30, 41, 35, 33, 32, 38, 36, 39, 40, 41, 44, 40, 49, 46, 47}

Returns: 238
50

{1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 6, 8, 8, 8, 9, 9, 10, 10, 10, 10, 10, 12, 13, 13, 14, 14, 16, 16, 16, 17, 18, 19, 19, 19, 22, 22, 24, 25, 27, 28, 30, 31, 33, 34, 35, 37, 38, 38, 38, 45}

{11, 26, 26, 50, 4, 39, 41, 7, 13, 18, 32, 16, 21, 41, 40, 48, 23, 26, 34, 41, 47, 36, 25, 46, 36, 49, 30, 35, 45, 50, 30, 23, 30, 44, 27, 30, 48, 41, 43, 34, 36, 44, 38, 47, 38, 43, 39, 48, 49, 47}

Returns: 208
50

{1, 1, 1, 1, 2, 2, 2, 4, 4, 5, 6, 6, 7, 7, 7, 8, 8, 10, 10, 11, 12, 13, 17, 17, 18, 18, 19, 19, 19, 20, 20, 20, 23, 23, 23, 26, 26, 27, 28, 29, 29, 31, 32, 34, 35, 36, 36, 36, 40, 44}

{27, 33, 36, 50, 17, 35, 47, 44, 47, 8, 12, 31, 8, 25, 37, 29, 47, 25, 45, 49, 19, 27, 22, 50, 25, 32, 23, 34, 36, 21, 31, 37, 24, 27, 47, 48, 49, 38, 42, 35, 38, 41, 38, 37, 45, 38, 43, 46, 42, 45}

Returns: 206
50

{1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 13, 14, 15, 16, 17, 20, 20, 20, 22, 22, 25, 26, 26, 27, 27, 29, 31, 33, 34, 35, 37}

{15, 21, 7, 11, 27, 33, 41, 9, 23, 39, 45, 21, 22, 31, 8, 10, 14, 18, 38, 41, 47, 34, 36, 49, 47, 48, 49, 23, 43, 14, 38, 50, 19, 28, 21, 42, 47, 47, 48, 32, 31, 33, 38, 39, 36, 34, 38, 47, 40, 39}

Returns: 212
50

{1, 2, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 9, 9, 10, 11, 11, 12, 14, 16, 16, 17, 17, 17, 17, 18, 20, 21, 23, 23, 25, 26, 26, 29, 29, 30, 30, 30, 32, 32, 34, 34, 35, 35, 36, 40, 41, 44, 48}

{12, 30, 50, 6, 11, 20, 17, 19, 47, 22, 33, 23, 24, 26, 45, 50, 13, 30, 15, 48, 38, 47, 18, 25, 33, 48, 31, 27, 34, 36, 42, 47, 43, 48, 35, 47, 36, 40, 47, 34, 49, 36, 40, 38, 39, 46, 42, 49, 46, 50}

Returns: 212
20

{1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 11, 11, 11, 12, 12, 13, 14, 15, 15, 18}

{7, 11, 12, 19, 20, 8, 10, 16, 18, 19, 4, 8, 9, 12, 17, 19, 9, 14, 19, 20, 9, 12, 15, 17, 20, 10, 12, 13, 15, 20, 10, 18, 19, 10, 11, 12, 15, 17, 16, 17, 16, 19, 20, 13, 20, 14, 19, 16, 19, 19}

Returns: 1365
20

{1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 8, 8, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 11, 12, 12, 13, 13, 13, 14, 15, 15, 16, 16, 17, 17, 18}

{2, 5, 7, 9, 17, 3, 6, 8, 11, 12, 13, 4, 11, 12, 18, 11, 16, 19, 6, 9, 11, 9, 10, 15, 12, 13, 16, 20, 11, 19, 20, 13, 17, 13, 14, 16, 19, 17, 20, 14, 16, 17, 17, 18, 20, 19, 20, 18, 19, 19}

Returns: 1307
20

{1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 10, 10, 11, 11, 12, 12, 12, 13, 14, 15, 16, 17}

{2, 3, 6, 13, 14, 17, 18, 19, 10, 14, 4, 9, 16, 18, 7, 9, 11, 13, 17, 18, 6, 11, 12, 18, 20, 10, 20, 8, 13, 14, 20, 9, 10, 11, 12, 15, 19, 18, 15, 20, 15, 16, 16, 18, 20, 18, 19, 17, 19, 19}

Returns: 964
20

{1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 9, 9, 9, 10, 10, 11, 11, 11, 13, 13, 14, 15, 16}

{3, 6, 7, 11, 12, 17, 3, 4, 10, 16, 20, 5, 6, 14, 15, 19, 7, 10, 15, 16, 18, 6, 16, 20, 7, 8, 10, 18, 9, 11, 12, 13, 15, 16, 17, 20, 10, 10, 14, 19, 13, 19, 15, 18, 19, 14, 20, 17, 16, 17}

Returns: 2796
20

{1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 16, 16, 16, 17}

{4, 7, 12, 20, 3, 7, 9, 6, 9, 14, 5, 10, 11, 13, 14, 15, 18, 19, 20, 9, 12, 13, 15, 7, 13, 14, 15, 9, 10, 9, 20, 20, 12, 14, 15, 17, 18, 20, 15, 18, 19, 20, 14, 18, 20, 19, 17, 19, 20, 18}

Returns: 1893
20

{1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 9, 9, 9, 9, 10, 10, 11, 12, 14, 15, 15, 16}

{6, 7, 10, 12, 14, 20, 6, 7, 8, 12, 4, 5, 6, 8, 12, 13, 14, 16, 19, 5, 7, 11, 13, 15, 17, 14, 15, 16, 18, 9, 12, 15, 17, 10, 13, 15, 18, 18, 14, 15, 18, 19, 11, 14, 19, 13, 16, 16, 17, 19}

Returns: 1369
20

{1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 11, 12, 13, 13, 13, 13, 14, 15, 16, 16, 16}

{13, 16, 10, 15, 19, 20, 6, 12, 7, 9, 10, 15, 16, 19, 6, 13, 14, 15, 16, 17, 18, 19, 20, 10, 13, 20, 12, 14, 19, 9, 10, 17, 16, 17, 18, 19, 20, 11, 14, 18, 18, 15, 18, 19, 20, 20, 16, 18, 19, 20}

Returns: 1572
20

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10, 11, 11, 12, 13, 14}

{2, 3, 6, 8, 9, 12, 14, 16, 17, 19, 20, 4, 5, 17, 12, 13, 17, 8, 12, 13, 14, 17, 18, 20, 6, 8, 15, 16, 19, 8, 9, 11, 14, 18, 11, 12, 20, 11, 16, 17, 18, 12, 18, 14, 17, 13, 19, 14, 17, 19}

Returns: 3119
20

{1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 11, 11, 12, 13, 13, 13, 13, 15, 16, 17}

{3, 5, 6, 8, 15, 18, 12, 13, 14, 15, 16, 18, 19, 9, 13, 17, 7, 9, 10, 14, 9, 17, 18, 20, 10, 11, 19, 9, 10, 11, 15, 10, 13, 14, 16, 18, 10, 12, 15, 17, 13, 16, 15, 14, 17, 19, 20, 20, 17, 20}

Returns: 1084
20

{1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 12, 13, 13, 14, 14, 15, 16, 16}

{2, 6, 9, 11, 12, 15, 6, 8, 9, 19, 6, 12, 18, 19, 20, 8, 9, 13, 15, 6, 9, 17, 18, 19, 14, 8, 10, 15, 16, 19, 10, 11, 16, 17, 11, 15, 16, 20, 12, 13, 12, 20, 20, 15, 19, 15, 18, 18, 17, 19}

Returns: 938
20

{1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 12, 13, 13, 13, 13, 14, 14, 15, 15, 15, 16, 17}

{13, 14, 17, 18, 19, 3, 4, 9, 11, 14, 19, 4, 6, 8, 10, 11, 17, 11, 14, 16, 17, 11, 13, 10, 11, 19, 9, 20, 9, 15, 11, 12, 16, 17, 13, 14, 16, 18, 18, 14, 15, 16, 19, 15, 16, 17, 18, 20, 19, 18}

Returns: 1191
20

{1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 18, 18}

{3, 7, 12, 4, 5, 7, 9, 11, 13, 15, 4, 6, 8, 13, 8, 10, 11, 16, 17, 6, 7, 16, 17, 10, 11, 20, 18, 19, 20, 10, 11, 13, 14, 16, 11, 13, 14, 18, 19, 18, 15, 16, 15, 16, 19, 20, 20, 19, 19, 20}

Returns: 971
20

{1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 11, 12, 13, 13, 14, 16, 16, 18}

{4, 6, 9, 11, 13, 20, 3, 4, 11, 12, 16, 17, 19, 8, 11, 14, 19, 7, 12, 14, 15, 16, 9, 12, 17, 18, 20, 12, 13, 8, 18, 20, 14, 15, 16, 18, 10, 13, 15, 20, 11, 12, 12, 17, 16, 18, 17, 18, 20, 19}

Returns: 891
46

{1, 1, 3, 3, 4, 4, 5, 6, 7, 7, 7, 7, 7, 8, 9, 10, 10, 10, 10, 11, 11, 11, 12, 13, 13, 14, 15, 15, 16, 16, 17, 17, 20, 20, 21, 25, 25, 26, 27, 28, 29, 29, 29, 31, 31, 33, 34, 39, 42, 45}

{2, 35, 24, 29, 15, 44, 9, 40, 30, 31, 33, 42, 43, 15, 18, 29, 33, 34, 44, 18, 33, 40, 25, 38, 42, 35, 19, 35, 23, 41, 18, 46, 29, 30, 28, 33, 38, 30, 44, 31, 37, 42, 44, 32, 44, 36, 36, 43, 45, 46}

Returns: 267
42

{1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 7, 7, 7, 8, 8, 9, 11, 12, 12, 12, 14, 14, 14, 14, 15, 15, 15, 17, 18, 19, 19, 20, 23, 23, 24, 24, 27, 28, 28, 30, 31, 31, 35, 39, 40}

{30, 35, 17, 36, 41, 10, 17, 26, 5, 7, 8, 24, 29, 36, 41, 27, 33, 39, 30, 37, 22, 24, 14, 39, 42, 17, 27, 36, 42, 22, 30, 41, 29, 32, 22, 40, 30, 38, 41, 25, 35, 38, 32, 38, 40, 34, 40, 38, 41, 42}

Returns: 294
40

{1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 6, 7, 7, 8, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 14, 14, 14, 15, 16, 17, 17, 17, 19, 21, 21, 22, 25, 26, 27, 28, 28, 28, 30, 30, 36}

{31, 34, 40, 3, 20, 21, 25, 31, 19, 8, 17, 30, 32, 38, 24, 31, 19, 33, 18, 30, 36, 40, 32, 36, 15, 22, 31, 39, 15, 16, 28, 37, 24, 26, 24, 31, 35, 38, 27, 29, 31, 26, 34, 30, 29, 30, 39, 33, 38, 40}

Returns: 280
36

{1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 10, 11, 11, 11, 12, 12, 12, 12, 13, 13, 15, 15, 15, 16, 17, 18, 18, 18, 19, 19, 20, 20, 20, 20, 22, 22, 22, 24, 25, 26, 27, 27, 31}

{16, 3, 11, 28, 33, 23, 32, 15, 18, 22, 30, 16, 32, 33, 16, 36, 20, 26, 15, 22, 26, 23, 25, 26, 31, 24, 33, 16, 20, 29, 30, 20, 20, 26, 36, 28, 31, 23, 24, 25, 35, 33, 35, 36, 33, 26, 32, 28, 30, 34}

Returns: 552
37

{1, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 6, 7, 7, 7, 7, 7, 8, 10, 10, 11, 12, 12, 13, 13, 14, 14, 14, 14, 14, 15, 15, 16, 16, 16, 16, 17, 19, 19, 20, 21, 23, 23, 23, 23, 24, 27, 30, 32, 32}

{31, 32, 12, 24, 25, 30, 32, 22, 23, 8, 18, 32, 10, 12, 23, 24, 32, 10, 18, 28, 35, 27, 31, 24, 34, 15, 19, 22, 27, 34, 27, 34, 17, 20, 23, 25, 35, 26, 35, 22, 32, 27, 30, 31, 33, 31, 32, 37, 35, 37}

Returns: 619
27

{1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 11, 11, 11, 13, 13, 15, 15, 16, 18, 19, 19}

{4, 5, 9, 19, 20, 21, 3, 6, 8, 18, 6, 10, 20, 25, 17, 19, 20, 18, 20, 23, 24, 27, 8, 10, 11, 12, 14, 19, 22, 14, 18, 20, 15, 20, 22, 10, 12, 13, 15, 18, 19, 24, 22, 27, 21, 24, 21, 24, 22, 27}

Returns: 984
14

{1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 8, 8, 8, 8, 9, 9, 10, 10, 11, 11, 11, 12}

{2, 5, 6, 8, 9, 10, 13, 4, 5, 6, 8, 9, 11, 13, 14, 4, 5, 6, 7, 8, 11, 5, 6, 7, 8, 9, 11, 12, 13, 6, 9, 10, 14, 7, 8, 10, 14, 13, 10, 12, 13, 14, 11, 14, 12, 13, 12, 13, 14, 13}

Returns: 3629
26

{1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 12, 13, 13, 13, 13, 15, 15, 15, 15, 16, 16, 17, 17, 17, 18, 20, 23}

{3, 6, 8, 16, 18, 24, 20, 4, 5, 8, 16, 22, 5, 17, 20, 7, 13, 17, 26, 8, 12, 15, 22, 9, 10, 24, 12, 22, 14, 20, 22, 19, 26, 14, 18, 20, 21, 26, 18, 19, 21, 26, 18, 25, 18, 19, 25, 26, 26, 25}

Returns: 566
21

{1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 12, 13, 13, 15, 15, 15, 16, 16, 16, 18, 19}

{7, 9, 20, 16, 20, 10, 12, 16, 18, 9, 16, 10, 12, 17, 20, 10, 17, 15, 16, 18, 9, 10, 11, 13, 21, 11, 12, 15, 17, 12, 14, 19, 20, 12, 19, 13, 14, 19, 20, 21, 18, 20, 17, 18, 19, 18, 19, 21, 19, 20}

Returns: 1997
23

{1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 20, 21}

{5, 10, 12, 18, 22, 4, 17, 19, 9, 13, 15, 22, 15, 9, 11, 12, 13, 21, 8, 16, 17, 20, 9, 19, 20, 17, 12, 14, 23, 17, 18, 15, 18, 19, 21, 21, 23, 16, 16, 21, 23, 18, 19, 23, 19, 21, 20, 23, 21, 23}

Returns: 753
38

{1, 1, 1, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 6, 7, 8, 8, 8, 9, 10, 11, 12, 13, 13, 14, 14, 14, 15, 16, 16, 18, 18, 18, 19, 19, 19, 20, 21, 22, 22, 22, 22, 23, 26, 28, 28, 30, 33, 34}

{7, 22, 23, 27, 19, 24, 8, 13, 29, 32, 35, 37, 20, 25, 19, 10, 12, 16, 22, 19, 38, 38, 31, 19, 36, 30, 32, 33, 32, 21, 32, 23, 29, 32, 20, 21, 34, 37, 37, 31, 33, 34, 37, 27, 34, 31, 33, 34, 37, 36}

Returns: 433
45

{1, 1, 2, 2, 4, 4, 5, 5, 5, 6, 6, 6, 8, 9, 9, 10, 12, 13, 13, 14, 15, 15, 15, 16, 17, 17, 18, 19, 21, 23, 24, 24, 24, 26, 26, 27, 27, 27, 28, 28, 29, 30, 32, 32, 34, 35, 35, 35, 36, 38}

{12, 14, 11, 26, 28, 42, 7, 14, 34, 9, 18, 19, 12, 33, 42, 30, 28, 14, 30, 34, 20, 41, 45, 30, 39, 45, 24, 28, 35, 29, 28, 36, 40, 35, 36, 31, 35, 38, 34, 38, 44, 34, 37, 42, 36, 36, 37, 38, 45, 39}

Returns: 311
9

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

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

Returns: 2344
25

{1, 1, 1, 1, 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 14, 14, 15, 15, 16, 16, 16, 16, 19, 20, 20, 22}

{2, 8, 10, 11, 18, 9, 11, 19, 22, 23, 18, 23, 13, 18, 20, 13, 21, 10, 12, 19, 11, 19, 21, 23, 24, 25, 12, 16, 18, 20, 21, 15, 18, 24, 13, 20, 21, 14, 15, 16, 19, 20, 17, 18, 20, 23, 20, 21, 24, 25}

Returns: 888
42

{1, 1, 2, 2, 2, 2, 4, 4, 5, 6, 6, 8, 8, 8, 8, 8, 9, 10, 10, 11, 11, 12, 12, 13, 13, 13, 14, 15, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18, 19, 21, 21, 22, 23, 24, 27, 28, 29, 32, 35, 39}

{25, 30, 20, 30, 36, 40, 27, 34, 25, 27, 32, 12, 19, 27, 36, 39, 11, 15, 24, 16, 18, 24, 30, 15, 18, 31, 30, 25, 18, 29, 31, 33, 42, 28, 38, 42, 25, 30, 42, 28, 42, 41, 37, 41, 37, 36, 31, 35, 42, 41}

Returns: 298
7

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

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

Returns: 456
33

{1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 11, 11, 11, 11, 12, 12, 13, 13, 15, 15, 15, 15, 16, 16, 16, 17, 19, 21, 21, 26, 26, 27, 32}

{2, 32, 4, 13, 14, 6, 15, 25, 13, 26, 27, 10, 11, 12, 24, 29, 10, 11, 12, 17, 16, 21, 22, 17, 26, 14, 17, 17, 25, 26, 32, 21, 23, 27, 31, 20, 22, 23, 25, 20, 28, 33, 19, 32, 24, 33, 31, 33, 32, 33}

Returns: 372
17

{1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 13, 15, 16}

{2, 3, 7, 10, 17, 3, 4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 5, 8, 9, 11, 17, 5, 8, 14, 16, 17, 6, 8, 10, 15, 13, 14, 15, 10, 14, 9, 11, 14, 13, 14, 17, 11, 12, 13, 15, 12, 13, 16, 16, 17}

Returns: 5103
41

{1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 10, 11, 12, 12, 13, 13, 13, 13, 13, 15, 17, 17, 17, 18, 19, 19, 22, 22, 23, 25, 26, 26, 28, 29, 29, 30, 31, 38, 38}

{4, 26, 8, 22, 41, 18, 20, 31, 14, 11, 18, 19, 26, 31, 20, 28, 11, 12, 20, 34, 36, 39, 35, 24, 30, 19, 22, 23, 25, 39, 22, 27, 35, 40, 19, 26, 30, 25, 32, 37, 39, 28, 34, 34, 32, 35, 32, 36, 39, 40}

Returns: 265
9

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

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

Returns: 19
3

{1, 2, 3 }

{2, 3, 1 }

Returns: 8
36

{13, 24, 24, 20, 31, 16, 10, 36, 34, 32, 28, 5, 20, 29, 23, 2, 14, 4, 9, 5, 19, 21, 8, 1, 26, 27, 25, 15, 22, 30, 30, 6, 11, 7, 2, 35, 13, 29, 4, 12, 33, 18, 13, 14, 17, 35, 3 }

{10, 15, 27, 1, 29, 11, 5, 18, 33, 1, 9, 2, 31, 6, 19, 10, 33, 18, 6, 27, 3, 22, 4, 12, 31, 30, 34, 16, 7, 24, 3, 28, 15, 21, 22, 8, 26, 20, 14, 32, 25, 17, 35, 8, 36, 26, 23 }

Returns: 162
3

{1, 2, 1 }

{2, 3, 3 }

Returns: 8
4

{1, 2, 3, 4 }

{2, 3, 4, 1 }

Returns: 9
3

{1, 1, 2 }

{2, 3, 3 }

Returns: 8
5

{1, 1, 2, 1, 3, 3, 5, 5, 5, 5 }

{2, 4, 4, 3, 4, 2, 1, 2, 3, 4 }

Returns: 76
48

{1, 1, 2, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 9, 9, 10, 10, 10, 11, 11, 14, 14, 17, 17, 19, 21, 24, 25, 26, 26, 26, 27, 27, 27, 27, 29, 30, 32, 35, 36, 36, 37, 37, 38, 40, 41, 42 }

{19, 32, 32, 48, 13, 48, 17, 19, 35, 11, 20, 35, 43, 26, 44, 11, 27, 41, 28, 32, 22, 31, 32, 34, 42, 40, 44, 37, 27, 32, 35, 38, 39, 44, 48, 43, 45, 41, 46, 37, 39, 38, 46, 48, 42, 47, 47 }

Returns: 264
50

{40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 50, 40, 40, 40, 23, 4, 24, 40, 22, 40, 8, 40, 40, 40, 34, 21, 40, 40, 38, 40, 40, 40, 40, 40, 28, 40, 40, 40, 40, 46, 13, 40, 40, 40, 47, 40, 40 }

{45, 42, 20, 48, 12, 32, 25, 10, 26, 39, 16, 2, 19, 43, 37, 17, 19, 19, 19, 18, 19, 27, 19, 29, 11, 36, 19, 19, 1, 41, 19, 35, 14, 33, 49, 3, 19, 7, 5, 19, 31, 19, 19, 6, 9, 15, 19, 44, 30 }

Returns: 68719493118
3

{3, 2 }

{2, 1 }

Returns: 4

Statistics

Problem Statement for "PenguinSledding"

Problem Statement

Definition

Constraints

Examples