TopCoder Statistics - Problem Statement

Problem Statement

You have an undirected graph G with n vertices and m edges. The vertices are numbered 0 through n-1. You are given the int n. You are also given the int[]s a and b, each with m elements. For each valid i, the graph G contains the edge between a[i] and b[i].

The graph G is guaranteed to have the following properties:

G is simple: there are no self-loops and no multiple edges.
G is connected: each vertex is reachable from each other vertex by following a sequence of edges.
The number of edges is between n+1 and n+5, inclusive.

An automorphism of a graph is an isomorphism between two copies of the graph. Formally, an automorphism of a graph is a permutation p of {0, 1, ..., n-1} with the following property: For each i and j, vertices i and j are connected by an edge if and only if vertices p[i] and p[j] are connected by an edge.

Compute the number of automorphisms of the given graph, and return that value modulo 10^9 + 7.

Definition

Class:: AutomorphicGraph
Method:: count
Parameters:: int, int[], int[]
Returns:: int
Method signature:: int count(int n, int[] a, int[] b)
(be sure your method is public)

Constraints

n will be between 4 and 100, inclusive.
m will be between n+1 and n+5, inclusive.
a and b will contain exactly m elements.
All elements in a and b will be between 0 and n-1, inclusive.
The graph G will be simple and connected.

Examples

5

{0,0,0,0,1,1,1,2,2,3}

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

Returns: 120

The graph is G5, so all 5! = 120 permutations are good.
4

{0,0,0,2,2}

{1,2,3,1,3}

Returns: 4

This time we have 4 permutations: {0, 1, 2, 3} {0, 3, 2, 1} {2, 1, 0, 3} {2, 3, 0, 1}
6

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

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

Returns: 6

The graph looks like this: /\ /__\ /\ /\ /__\/__\
12

{0,1,2,3,4,5,6,7,8,0,3,6,1,4,7}

{1,2,3,4,5,6,7,8,0,3,6,0,9,10,11}

Returns: 3
7

{0,1,2,3,1,2,5,1}

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

Returns: 1
27

{0,1,2,3,0,0,7,6,5,1,8,8,2,11,11,3,7,6,18,18,5,15,15,22,22,0,0,23,4,4,25}

{1,2,3,4,4,7,6,5,4,8,9,10,11,12,13,14,21,18,19,20,15,16,17,0,4,23,24,24,25,26,26}

Returns: 128
67

{0,1,2,3,1,2,5,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66}

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

Returns: 73741817

The answer is (2^30) % (10^9+7).
8

{0,0,0,1,1,2,0,0,1,1}

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

Returns: 16
10

{0,0,0,1,1,2,0,0,1,1,4,4}

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

Returns: 8
10

{0,0,0,1,1,2,0,0,1,1,4,6}

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

Returns: 4
10

{0,0,0,1,1,2,0,0,1,1,4,8}

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

Returns: 4
100

{0,0,0,0,1,1,1,2,2,3,5, 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, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99}

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

Returns: 941431496
22

{0,1,11,1,3,12,13,21,3,2,3,10,17,7,21,17,11,17,8,21,5,5,20,15,21}

{5,0,6,7,13,7,2,18,9,16,16,18,14,19,17,4,0,6,6,12,9,3,4,12,3}

Returns: 2
20

{19,3,10,18,17,12,0,7,3,8,12,12,12,13,5,5,2,5,18,6,7,8,3,7,14}

{8,0,9,6,14,5,10,4,11,14,1,19,8,14,15,4,6,11,8,4,14,1,5,18,16}

Returns: 12
31

{23,3,22,6,13,20,17,28,7,17,5,11,7,8,14,21,24,4,27,30,23,28,10,12,9,28,7,9,0,15,18,0,13,10}

{9,26,13,17,29,24,12,18,6,19,9,23,17,27,21,19,9,24,20,23,7,22,1,18,26,24,29,25,24,28,16,2,14,22}

Returns: 4
21

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

{12,9,3,13,16,6,1,17,12,8,4,0,11,17,10,2,10,20,13,0,14,5,6,11,6}

Returns: 24
23

{9,3,5,18,5,1,21,16,20,4,13,15,14,8,22,10,19,8,0,1,17,21,2,15,13}

{8,14,7,6,9,16,15,13,8,12,4,19,22,2,21,18,4,19,12,10,6,16,16,22,11}

Returns: 1
32

{16,16,0,31,0,16,17,3,8,14,25,30,18,19,10,8,21,26,10,27,16,22,8,28,5,5,14,26,10,24,21,8,20}

{4,17,3,13,20,23,29,11,22,22,11,0,8,16,5,9,22,25,31,12,25,31,2,30,6,1,15,3,27,9,17,7,22}

Returns: 144
22

{17,20,6,6,8,8,9,17,6,11,20,14,21,0,7,3,14,19,19,10,20,11,10,18,9,2,16}

{12,21,5,3,14,10,8,11,4,15,4,4,11,7,13,5,12,8,0,21,14,1,12,1,14,7,11}

Returns: 8
34

{2,13,21,31,28,26,10,27,12,24,21,7,32,9,27,17,19,0,5,23,8,25,19,6,15,21,2,29,1,31,30,17,14,31,2,1,19,25,5}

{22,17,31,6,17,18,29,11,4,26,22,1,16,23,9,20,23,11,33,8,31,18,1,28,31,14,10,5,0,27,17,3,12,33,9,30,16,22,17}

Returns: 6
32

{10,16,11,28,31,0,23,30,19,12,0,15,27,31,27,30,6,10,26,12,25,24,27,22,5,25,27,26,16,4,16,9,14,28}

{27,1,8,24,30,14,12,11,13,10,19,21,3,20,30,15,27,29,1,0,18,30,29,31,13,16,7,2,30,14,27,16,17,13}

Returns: 48
29

{19,0,17,20,16,14,3,0,8,7,28,10,20,25,3,8,6,26,5,21,21,24,27,0,11,18,23,8,15,9,5,20,7}

{4,23,22,1,4,17,4,24,13,25,9,1,10,1,15,23,3,4,2,6,5,16,10,17,16,7,12,28,2,13,17,4,16}

Returns: 16
28

{7,11,24,26,8,19,10,5,14,16,9,13,15,9,19,11,25,16,11,0,17,3,16,14,19,27,16,9,17,13,2}

{23,21,7,11,25,1,9,7,25,0,4,24,9,22,16,13,20,18,6,4,8,23,11,21,0,23,1,12,5,17,21}

Returns: 96
30

{18,10,23,6,5,18,27,23,14,0,17,19,6,5,17,3,4,7,17,6,16,9,16,20,11,28,16,1,29,9,21,15,27,7}

{26,14,21,14,12,24,10,25,2,26,6,23,2,1,21,27,16,21,2,3,0,24,26,2,23,23,13,21,23,6,8,10,22,24}

Returns: 240
33

{7,4,13,15,3,0,10,32,14,2,28,6,1,5,28,29,29,15,19,11,29,5,12,24,15,16,17,3,28,27,19,18,32,5,11,0}

{15,21,21,10,1,22,28,25,8,27,1,15,12,26,7,30,19,12,18,23,9,32,20,32,27,21,27,8,25,6,13,1,31,12,1,23}

Returns: 32
23

{12,5,17,10,0,6,8,13,19,13,18,12,9,7,19,16,3,20,12,11,9,7,18,18,2}

{8,19,4,5,4,0,22,21,20,20,9,15,5,5,18,17,17,21,6,12,4,10,14,1,8}

Returns: 64
28

{24,14,3,25,24,14,13,23,0,2,24,21,25,21,23,24,19,21,16,22,17,0,24,4,27,16,24,13,19,12,1,0}

{5,19,10,24,26,10,27,11,18,17,8,4,7,11,21,15,23,0,13,13,14,19,1,10,15,10,9,14,13,5,6,20}

Returns: 72
22

{12,14,20,20,16,18,13,7,0,15,9,12,16,20,20,11,12,14,19,11,21,12,12}

{8,19,19,6,14,11,3,15,21,6,20,1,3,4,2,3,15,17,0,14,10,5,10}

Returns: 36
21

{19,17,19,20,1,4,4,0,14,5,3,8,6,1,10,6,13,0,17,20,20,18,19,0}

{6,19,11,4,20,15,10,9,15,0,11,0,2,12,20,0,0,11,7,19,15,11,3,16}

Returns: 120
25

{21,20,9,21,6,0,16,16,23,16,24,13,2,0,11,11,6,20,0,14,12,0,8,16,4,16,4,3}

{3,10,12,12,14,18,0,7,16,4,12,10,12,15,5,21,8,8,1,19,11,5,12,22,6,12,17,13}

Returns: 216
30

{18,22,14,29,20,3,28,18,29,28,8,6,8,14,23,28,8,18,15,14,8,29,25,29,7,0,0,10,25,14,26,20,27}

{3,29,2,7,5,24,1,22,14,19,12,8,21,19,15,17,11,14,14,26,9,23,22,16,3,26,12,3,23,13,5,4,12}

Returns: 192
26

{4,14,11,10,5,21,18,5,20,19,2,19,10,9,0,15,20,25,13,17,16,7,18,4,6,8,2}

{23,16,16,12,2,0,17,10,0,9,3,4,24,4,1,0,9,13,16,0,5,13,15,16,20,20,22}

Returns: 256
24

{8,17,16,21,14,11,15,0,9,20,14,6,16,17,18,9,22,18,4,20,10,16,0,14,11}

{16,23,18,5,1,21,20,2,23,14,3,20,12,13,23,4,4,11,0,7,16,19,13,4,17}

Returns: 288
21

{9,11,14,5,15,4,14,17,8,14,3,2,14,5,9,14,10,4,8,7,1,1,17,20,1,15}

{8,8,19,14,0,5,6,16,1,17,17,9,12,17,4,20,14,13,5,14,4,15,18,15,9,3}

Returns: 480
39

{25,8,22,26,22,20,7,12,26,4,16,20,35,10,2,30,12,20,32,18,20,17,29,32,16,37,28,24,29,16,0,3,16,12,23,26,1,31,10,28,16,18,33,31}

{16,9,15,6,16,2,19,9,5,37,36,24,9,29,27,5,26,37,19,13,14,10,12,22,27,2,27,31,6,21,26,22,38,37,34,31,5,16,11,37,34,0,19,28}

Returns: 768
30

{9,13,14,20,6,24,21,29,25,15,16,11,5,1,20,8,7,27,26,22,29,10,4,24,14,0,20,8,18,16,24}

{6,4,12,22,7,28,24,9,11,6,2,24,4,0,24,22,0,24,29,0,23,16,19,29,18,5,3,5,25,5,17}

Returns: 384
22

{7,16,0,10,14,9,18,1,6,15,19,0,3,7,6,11,8,18,20,21,19,5,21,2,11,11}

{0,7,16,0,19,5,20,5,13,11,11,11,5,4,14,17,11,13,11,5,13,13,7,5,6,12}

Returns: 1152
35

{16,8,15,29,4,0,32,28,29,12,15,6,19,18,3,25,4,26,1,29,3,22,3,26,24,19,29,29,15,12,24,4,11,17,1,1,24,20,13,3}

{4,4,31,9,25,5,33,12,10,19,27,20,1,15,26,12,21,22,34,7,30,32,31,0,0,14,14,17,2,23,28,12,17,6,23,0,29,29,0,14}

Returns: 432
34

{20,21,1,22,10,29,16,15,33,15,18,21,20,20,30,30,1,30,28,17,3,7,24,8,32,3,9,1,22,0,2,32,29,0,0,23,5}

{24,3,24,19,11,32,15,33,29,22,20,31,7,26,13,21,11,17,11,11,18,6,3,18,27,12,30,33,25,32,21,4,30,22,14,15,7}

Returns: 128
24

{4,23,11,16,2,23,18,22,4,6,1,9,2,2,0,7,5,4,3,19,6,6,5,21,1,2}

{15,22,2,20,15,13,2,20,1,12,3,2,14,10,4,2,22,23,0,22,15,8,6,13,7,17}

Returns: 1440
22

{7,2,10,1,16,19,20,14,5,14,2,13,12,10,14,21,9,17,14,7,2,20,14,7}

{16,8,20,4,12,9,1,9,7,0,3,17,7,4,6,2,12,14,18,17,4,19,11,15}

Returns: 576
33

{3,23,9,9,27,30,10,7,9,6,25,30,24,0,15,9,31,30,30,28,10,8,28,19,12,10,10,32,15,17,13,21,4,26}

{29,26,1,23,4,5,23,9,24,10,26,20,28,29,2,15,10,1,23,16,15,1,14,4,24,29,11,23,22,25,24,10,1,18}

Returns: 1536
55

{42,50,45,35,9,19,11,44,36,10,15,27,1,5,40,40,33,52,42,6,46,16,20,33,42,21,13,12,14,34,20,45,53,29,50,47,41,44,36,36,6,42,3,2,52,52,5,36,38,16,25,15,53,8,25,10,43}

{17,24,40,7,54,1,27,51,30,2,45,49,39,31,34,0,0,26,37,47,39,32,24,50,4,19,52,45,6,23,22,26,48,25,7,19,10,28,39,18,54,38,44,27,9,15,16,51,22,18,45,4,42,54,15,48,33}

Returns: 8
50

{12,5,9,13,45,33,15,6,11,0,46,17,25,8,18,31,14,7,37,43,48,4,6,4,39,42,19,26,12,36,25,1,38,49,31,33,24,32,33,27,33,24,39,43,22,27,45,42,7,47,14,43,14,16}

{4,10,32,1,26,40,44,27,9,33,48,44,28,44,34,44,2,28,16,42,18,5,29,22,34,21,23,1,34,11,8,2,43,27,28,41,20,7,29,23,21,6,3,35,39,13,48,27,23,28,24,41,16,30}

Returns: 16
55

{0,46,47,43,32,50,19,22,8,14,35,18,17,40,47,33,34,36,50,52,48,28,16,2,17,12,35,31,6,42,31,49,34,30,16,43,44,4,36,52,21,1,40,43,32,0,10,46,0,5,39,2,27,38,21,41,28}

{3,15,45,21,24,20,9,53,38,13,0,50,50,26,3,9,49,11,42,18,2,44,23,49,13,35,42,50,38,29,48,3,19,49,47,54,7,15,27,2,6,43,4,39,26,5,19,37,41,51,46,25,26,46,50,53,54}

Returns: 2
58

{51,8,34,34,12,17,23,29,7,18,46,32,41,7,41,6,16,47,41,1,43,35,28,5,49,52,3,17,7,24,51,53,44,48,50,30,23,16,42,55,0,48,22,21,28,57,55,20,12,19,13,19,55,2,29,10,52,37,15,4,41,26,29}

{20,4,39,53,30,45,31,56,27,5,21,16,13,25,20,26,33,24,23,28,22,18,56,21,35,0,40,43,52,20,33,36,38,41,18,9,10,4,15,45,38,3,46,50,54,39,14,11,23,7,57,6,56,37,2,33,10,48,27,22,25,46,14}

Returns: 4
52

{20,19,0,6,2,31,47,46,21,19,10,5,7,43,34,27,22,29,2,4,1,16,25,12,41,38,26,34,26,24,14,34,6,40,5,14,25,4,1,43,19,31,15,38,11,8,0,42,12,23,28,13,2,34,39,16,1}

{48,30,38,32,47,1,45,38,45,3,8,34,6,27,15,50,19,12,8,9,11,48,8,17,42,13,35,44,34,7,5,37,15,18,41,4,1,51,34,18,36,33,49,31,41,39,11,12,25,21,44,40,14,23,30,40,18}

Returns: 48
50

{46,28,47,39,9,44,14,35,25,21,6,1,7,23,49,26,18,16,42,26,27,28,11,37,46,39,48,40,10,46,44,15,18,27,33,33,2,19,4,0,27,18,10,27,34,36,41,10,21,34,40}

{5,42,27,18,46,30,12,21,44,40,42,39,6,33,21,3,1,1,22,46,19,11,48,16,45,34,45,38,37,20,48,27,8,12,13,36,9,33,45,9,40,4,17,32,24,16,9,31,43,38,29}

Returns: 3456
50

{8,31,19,1,24,20,40,15,21,10,16,14,16,48,16,22,35,30,32,30,24,12,46,10,5,38,36,8,46,35,27,30,47,25,29,28,27,19,29,7,48,40,23,9,10,45,2,18,41,19,12,17,43,47,19}

{25,34,28,7,29,47,10,41,10,33,2,4,35,24,11,1,12,5,47,40,34,3,39,4,13,0,45,35,35,49,47,2,23,42,44,6,29,40,3,38,26,6,43,46,30,24,43,16,33,45,38,39,45,37,49}

Returns: 24
57

{32,10,28,29,1,3,40,18,38,14,4,6,43,11,17,21,12,20,22,4,53,31,49,54,24,22,21,18,19,14,12,4,35,44,15,38,25,46,1,46,39,13,13,15,12,34,7,33,47,3,39,39,52,23,22,13,21,41,30,45,26,47}

{39,17,44,22,19,27,31,39,55,26,2,3,24,45,44,51,15,56,48,42,39,54,56,0,13,20,37,21,0,56,40,24,16,55,23,9,23,49,45,20,17,38,8,16,35,25,13,0,7,35,38,36,24,22,55,39,5,4,0,12,20,50}

Returns: 6912
54

{53,2,6,22,45,2,49,26,18,52,10,31,12,13,50,27,6,49,12,14,43,16,36,51,22,24,12,52,15,28,20,30,51,16,37,42,44,29,48,46,24,36,42,19,9,26,20,44,19,43,2,37,8,21,17,35,41,47,32}

{42,52,50,17,41,36,43,28,10,49,33,29,40,12,23,46,23,10,38,31,18,17,13,24,28,7,30,13,40,6,39,5,4,12,3,0,53,1,46,37,12,34,16,4,10,11,46,52,39,36,1,25,44,13,9,53,51,11,44}

Returns: 32
51

{17,41,22,15,25,46,42,48,5,1,37,33,4,14,6,42,14,49,38,39,0,11,31,44,26,43,12,0,25,12,49,36,38,40,1,50,6,11,16,46,40,30,46,50,5,10,40,20,14,36,1,19,18}

{3,14,20,33,31,33,16,31,14,9,2,30,47,23,1,9,36,3,35,36,45,41,47,25,13,28,29,39,26,25,8,40,17,34,38,7,28,21,43,14,47,2,27,6,32,13,16,4,44,24,48,33,15}

Returns: 1
52

{50,31,49,5,15,16,25,35,18,28,29,35,39,15,17,49,1,46,51,23,27,40,26,34,19,30,17,20,3,44,23,33,20,4,34,48,0,28,46,32,17,14,17,41,6,45,14,10,50,34,24,15,14,49,49,50,29}

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

Returns: 12
52

{1,1,11,20,47,16,41,39,10,14,2,50,3,15,48,20,0,6,7,8,48,12,17,28,44,29,35,49,50,39,49,44,21,1,21,51,41,37,28,29,45,49,18,12,18,48,22,30,25,42,12,2,22,23,21}

{15,45,40,38,48,15,24,50,1,50,4,40,39,5,19,43,42,42,30,4,40,22,3,4,33,28,45,31,26,27,7,24,20,30,42,12,25,21,5,25,46,32,38,27,17,51,17,13,9,34,36,27,33,37,29}

Returns: 96
52

{4,30,30,20,18,21,33,29,39,9,17,13,7,6,38,13,51,26,32,17,24,33,17,33,17,13,29,37,21,0,32,13,37,12,48,35,44,19,42,3,46,33,49,12,38,5,47,0,27,43,17,34,27,35,2,7,40}

{46,4,16,43,2,19,15,2,0,24,10,8,22,4,42,37,25,1,11,45,28,1,49,31,24,46,40,50,41,34,12,25,26,8,43,19,26,11,1,27,14,42,32,17,30,50,13,46,51,47,44,37,36,5,23,45,13}

Returns: 64
52

{20,43,23,28,10,12,8,12,41,43,31,2,43,36,18,41,24,47,38,1,45,17,7,17,29,5,50,23,16,45,21,18,21,24,19,29,34,51,35,2,22,35,23,21,10,49,3,2,8,48,12,40,26,40,46,26,37}

{44,41,50,47,48,23,27,14,29,46,17,45,23,33,41,36,21,1,27,30,7,1,23,42,32,15,7,39,24,0,31,48,6,44,15,0,22,15,25,35,20,39,38,15,8,22,22,25,4,37,42,13,11,23,9,15,9}

Returns: 36
50

{31,32,30,6,4,14,35,45,11,10,28,17,39,15,19,17,19,25,40,34,29,0,2,12,46,1,25,38,47,6,48,33,34,45,10,24,43,10,1,8,12,42,31,22,9,20,44,45,13,44,13,24,36,22,8}

{1,36,38,19,32,19,21,37,23,5,15,7,24,3,26,45,2,42,49,2,49,29,47,28,4,18,0,45,18,33,37,0,28,3,11,16,31,25,33,41,6,27,33,40,24,47,35,46,49,31,14,40,25,2,10}

Returns: 72
52

{47,34,9,3,39,20,47,27,14,44,7,24,0,43,43,10,20,32,3,0,50,4,10,1,11,20,1,45,13,47,13,17,27,3,47,18,6,31,23,5,48,19,44,39,32,31,21,5,45,46,12,48,13,18,26,51}

{35,27,23,25,6,10,16,33,8,27,49,40,42,6,30,21,28,36,42,1,46,8,43,44,0,22,38,36,33,27,49,36,26,35,18,2,0,17,47,29,41,4,9,24,37,12,39,14,38,17,15,20,19,15,25,20}

Returns: 6
61

{10,47,54,60,4,0,34,1,23,41,9,6,15,10,29,48,4,21,32,18,57,18,20,10,27,27,57,31,6,45,47,42,36,55,47,40,21,26,10,13,19,52,25,13,2,34,13,50,17,44,43,46,10,12,43,44,51,37,46,33,14,39,39,39,28,31}

{49,53,59,55,28,40,24,50,25,40,28,20,45,40,21,31,29,17,10,36,22,37,49,38,9,59,17,3,32,55,49,52,35,44,29,16,26,8,58,42,17,7,30,5,23,2,40,23,32,47,33,26,56,31,34,36,43,38,1,37,55,43,1,11,10,21}

Returns: 144
54

{30,49,5,52,45,34,45,0,10,42,10,30,29,15,39,10,26,43,51,13,6,22,24,53,42,52,42,4,45,34,39,11,33,2,48,7,19,37,47,19,24,36,8,50,15,42,29,42,24,7,35,16,9,9,22,2,1,41}

{8,21,20,11,46,9,52,25,38,29,27,21,38,22,1,2,16,40,5,36,31,37,45,42,3,40,12,31,44,14,18,10,15,0,28,49,0,51,1,17,23,32,20,8,28,5,50,36,52,2,24,42,29,31,43,13,2,51}

Returns: 192
50

{17,18,39,25,31,8,31,20,37,1,38,19,21,0,37,30,42,16,32,2,26,26,26,14,0,12,44,35,21,8,46,32,41,5,16,18,14,23,23,30,28,12,35,30,15,25,48,14,33,40,15,19,33}

{5,43,4,12,11,22,18,47,15,47,24,13,24,43,49,2,12,18,44,39,38,27,14,34,27,6,5,3,4,44,3,9,26,20,4,19,10,8,37,7,5,5,5,29,21,26,47,45,29,8,0,36,30}

Returns: 384
96

{81,60,9,16,76,39,68,39,22,51,86,49,21,44,24,85,37,68,23,29,16,14,14,84,54,94,77,41,6,74,85,10,66,43,89,63,28,31,58,2,89,92,18,67,33,27,9,77,85,22,56,59,54,59,61,39,16,22,14,68,49,47,10,5,29,82,50,8,82,45,49,85,90,48,34,23,12,9,75,40,32,47,80,81,90,36,13,49,57,65,72,54,28,85,65,7,89}

{6,75,56,49,54,7,6,58,60,7,35,50,38,0,27,49,76,61,4,42,51,71,30,9,70,95,19,51,28,32,54,11,23,63,6,32,44,9,66,78,17,83,69,62,47,30,26,25,69,17,66,83,43,28,39,55,94,1,40,67,91,42,62,9,40,18,52,10,80,10,38,40,20,21,38,73,42,46,15,87,53,77,35,64,51,32,90,78,32,23,9,3,79,88,93,77,37}

Returns: 3317760
94

{68,57,71,39,40,58,33,25,74,45,58,35,79,66,43,49,79,65,52,81,6,62,42,35,25,4,59,12,53,73,5,46,25,2,41,30,15,68,39,53,57,81,91,18,12,46,42,72,84,11,64,57,16,50,21,93,60,24,76,35,62,60,18,82,8,34,44,2,46,3,74,51,11,17,89,0,0,23,63,22,42,26,4,36,46,70,52,69,11,52,88,54,90,54,74,84,2}

{66,8,45,66,55,67,11,3,83,63,80,58,63,8,7,15,62,13,80,68,85,10,30,76,50,3,36,77,55,82,1,84,55,91,45,3,14,38,36,62,73,48,78,74,28,20,43,50,36,32,50,25,91,47,8,15,46,21,74,37,65,14,12,74,85,85,25,85,54,86,27,74,85,63,30,39,9,5,31,45,87,80,5,92,29,46,56,50,75,61,22,19,40,91,41,43,37}

Returns: 1327104
91

{75,76,75,29,27,33,2,43,25,28,16,20,18,56,25,40,43,48,65,62,81,68,44,5,29,23,83,37,59,9,42,48,76,76,54,85,67,23,66,83,47,87,26,78,84,13,54,89,83,32,50,84,79,72,6,48,36,60,51,35,1,42,21,71,3,6,76,31,61,40,41,4,50,59,12,77,13,62,2,81,82,0,65,71,23,89,78,64,27,7,78,86,71}

{70,18,5,62,63,15,47,81,67,2,25,87,88,81,19,24,67,72,90,52,69,59,52,22,88,43,24,56,5,76,89,5,30,73,18,5,2,74,81,34,45,79,47,20,53,38,43,37,29,47,27,41,0,47,8,71,59,58,86,83,76,17,67,33,90,53,11,72,81,86,48,68,53,14,21,56,88,55,49,57,22,52,74,39,10,60,80,13,46,25,73,54,50}

Returns: 2654208
99

{15,24,39,13,13,74,7,68,36,96,59,90,2,6,93,29,69,26,16,50,34,50,29,47,33,81,68,53,86,84,17,62,37,98,95,14,53,51,70,26,39,98,76,27,60,77,68,19,5,89,70,13,68,89,74,9,24,70,63,50,9,21,13,27,0,79,38,17,81,38,89,30,45,38,44,23,92,64,42,94,34,80,55,62,65,9,73,32,1,56,46,19,11,95,10,31,8,82,74,3}

{24,86,52,80,18,81,14,71,91,44,50,25,67,63,97,7,21,47,70,4,94,63,50,62,50,29,52,33,74,61,93,60,24,44,81,83,40,7,9,80,12,69,26,82,63,49,81,57,12,21,17,78,94,67,57,81,22,28,84,25,88,56,72,75,47,20,27,49,35,70,5,76,47,20,41,70,14,57,14,3,85,48,13,36,5,87,48,13,29,58,64,66,8,43,21,34,43,54,61,59}

Returns: 1658880
98

{89,28,40,31,54,79,78,59,92,75,26,56,77,21,65,90,32,75,47,88,54,35,42,25,85,91,60,25,25,30,21,63,77,21,29,91,71,12,73,89,87,34,10,19,26,92,43,13,85,51,58,16,40,4,69,63,24,8,40,65,5,79,62,85,57,47,14,52,15,61,47,7,45,72,0,64,87,84,24,37,53,81,16,36,2,65,35,93,83,39,9,79,95,82,38,7,18,30,54,72,24,7}

{69,47,58,97,65,50,6,80,89,27,21,9,5,76,96,13,91,7,70,44,70,34,74,11,48,4,5,33,87,3,61,21,10,74,5,44,75,59,91,87,20,67,31,96,4,71,82,82,59,68,89,85,55,25,90,1,43,80,23,31,22,31,40,69,54,21,36,91,27,6,35,49,7,96,51,74,41,54,3,79,82,36,0,80,40,18,95,87,7,45,82,46,66,17,52,86,94,17,3,62,13,39}

Returns: 1990656
94

{5,90,3,55,67,92,32,18,42,50,20,29,22,58,43,60,56,65,44,42,90,22,30,25,62,68,66,48,28,80,3,77,52,84,8,71,32,71,59,11,15,13,73,45,35,42,79,30,92,17,81,42,35,2,16,76,31,70,28,63,64,1,77,26,28,66,83,74,33,92,8,54,11,13,65,70,87,38,23,6,0,40,72,88,36,55,36,36,79,9,60,79,28,43,55}

{69,3,66,66,93,80,24,22,1,22,67,42,26,22,77,36,36,89,75,57,52,49,71,29,13,82,88,77,14,67,45,52,22,76,32,58,73,25,22,73,91,51,43,7,44,10,43,34,86,92,55,93,80,13,82,23,51,61,63,84,40,13,41,39,5,28,36,55,50,27,65,5,12,37,91,22,81,22,85,37,30,33,89,46,10,4,19,82,78,3,53,47,21,90,25}

Returns: 1769472
99

{50,69,25,31,36,29,13,20,74,84,96,58,53,80,34,8,75,46,56,89,28,23,46,90,66,93,89,14,63,20,80,45,32,74,52,74,13,73,48,46,7,9,1,63,38,91,82,10,21,76,61,58,87,60,3,47,18,39,64,27,69,7,4,84,33,37,58,48,14,47,30,59,87,66,59,57,70,55,36,79,78,85,46,12,68,6,48,98,7,3,86,35,1,84,42,77,95,86,63,53}

{71,19,79,41,6,48,32,36,54,30,53,23,14,98,94,79,11,71,18,98,0,50,62,10,93,33,13,30,70,26,66,79,21,88,89,39,64,39,28,17,3,24,48,79,70,66,98,52,83,9,36,82,34,56,63,79,47,21,51,21,92,37,65,9,65,51,61,67,13,22,69,22,26,16,31,64,75,78,1,72,54,48,49,79,89,5,43,15,44,40,91,47,2,81,46,71,38,97,6,22}

Returns: 1105920
98

{30,68,71,64,24,85,73,29,33,57,70,55,79,70,6,50,2,94,37,13,39,72,56,29,57,50,70,13,49,88,84,19,68,87,67,60,26,71,15,37,44,59,25,23,63,28,25,4,30,24,90,69,13,12,85,92,91,26,59,34,80,69,12,31,60,27,18,48,51,35,13,58,97,80,85,91,88,45,66,83,81,10,20,61,82,97,40,3,52,36,87,95,76,57,17,17,41,76,20,23,23}

{59,13,41,68,86,0,46,80,18,8,78,60,4,8,59,67,75,74,46,43,12,57,57,47,63,73,77,5,26,48,38,42,76,93,85,69,9,60,86,64,33,38,92,10,89,4,14,34,67,57,85,42,14,93,11,35,57,41,19,29,20,89,74,12,54,33,62,61,62,16,1,87,75,96,88,74,51,57,96,4,47,50,51,53,87,15,52,23,15,26,65,73,22,7,20,21,32,71,33,16,54}

Returns: 1492992
97

{93,55,71,46,35,33,26,78,78,75,3,88,24,5,27,31,72,52,56,72,78,41,1,6,35,11,15,52,43,74,32,7,18,91,82,87,45,52,24,43,4,75,18,19,15,79,1,83,77,21,39,21,4,46,40,6,20,67,14,18,20,5,69,89,64,83,69,66,36,66,23,70,94,61,70,7,44,2,59,91,17,34,81,78,53,38,35,13,5,51,22,18,49,58,57,3,49,7}

{2,75,67,37,50,60,54,35,77,71,83,30,12,47,95,78,46,4,35,63,0,82,96,93,11,27,48,5,65,15,78,95,71,86,91,26,85,54,5,37,33,4,65,60,79,29,71,19,46,50,90,92,64,15,60,90,89,9,22,10,90,84,71,62,42,90,68,41,72,19,35,45,45,5,64,73,33,25,78,34,14,16,50,80,46,24,30,78,28,56,6,76,4,35,34,8,78,72}

Returns: 53084160
92

{64,3,34,91,73,62,46,74,9,87,69,45,10,83,52,36,81,14,17,46,61,25,69,46,77,91,1,76,90,79,53,58,11,68,61,38,55,78,77,52,13,91,2,64,60,6,51,68,53,69,58,36,38,38,33,16,11,42,90,82,15,43,86,62,35,76,51,29,38,69,85,26,25,39,8,12,30,71,39,47,12,48,24,73,14,91,32,54,11,12,10,7,87,2}

{7,53,91,7,16,19,81,81,59,44,38,21,56,21,0,67,62,4,16,14,78,56,53,28,56,5,91,19,86,10,31,70,28,7,4,19,52,65,9,82,3,50,69,8,17,8,56,23,75,45,7,37,37,80,8,91,16,87,59,33,21,80,40,87,81,63,22,86,66,29,28,28,49,80,84,86,48,10,41,24,57,25,16,27,20,72,24,28,89,88,18,10,47,19}

Returns: 2211840
96

{72,92,15,71,18,48,92,41,87,81,8,94,21,22,6,60,9,72,79,80,53,2,29,84,90,18,75,22,62,22,86,23,71,0,62,9,62,37,80,13,2,78,34,0,22,95,70,71,73,95,88,50,68,24,35,51,21,37,63,59,78,6,0,84,27,26,16,30,68,62,49,28,74,83,66,94,85,76,14,6,6,36,88,91,33,42,78,10,93,61,39,18,71,68,40,57,83,6}

{84,43,23,70,68,70,52,58,62,18,73,77,75,32,2,95,14,75,74,56,69,90,65,44,71,92,5,86,38,11,44,62,44,12,70,85,63,61,22,62,65,53,37,67,47,46,81,0,34,63,50,4,79,26,77,85,45,77,53,32,73,33,3,41,88,78,69,77,64,50,29,62,55,27,77,20,95,79,89,1,7,62,19,65,25,69,31,58,10,82,47,57,17,54,69,43,84,48}

Returns: 1244160
98

{25,1,49,59,34,59,56,65,44,59,59,19,40,31,88,65,55,50,36,24,45,89,18,52,11,33,78,8,72,22,41,63,39,21,22,36,59,11,88,88,34,62,4,42,47,60,38,0,55,67,82,23,62,62,40,44,29,83,50,79,18,12,90,59,27,85,28,7,65,49,11,73,43,47,76,87,6,62,35,16,67,44,91,50,53,91,60,1,16,45,62,1,75,91,20,74,16,67,3}

{79,9,48,6,38,84,8,66,85,58,44,85,22,39,13,39,87,93,25,21,6,96,33,1,41,86,49,41,63,60,96,1,2,10,2,70,64,42,87,97,0,59,10,67,0,14,42,32,90,66,1,31,14,95,12,72,71,69,10,60,85,54,26,4,25,29,45,49,83,71,76,88,60,88,5,94,3,77,89,5,37,61,52,57,4,46,51,81,80,15,17,30,40,92,25,31,68,71,8}

Returns: 3981312
94

{5,90,74,70,27,93,32,51,54,80,88,57,73,52,51,48,62,73,84,28,53,58,15,10,9,42,34,79,90,21,46,89,57,4,50,21,30,61,3,92,18,89,58,40,82,89,5,21,17,67,56,1,45,42,68,36,41,32,6,35,53,59,13,32,11,84,31,88,23,26,27,50,58,38,86,72,24,86,14,90,44,56,7,90,20,85,82,87,83,8,12,33,6,19,19,0}

{6,60,37,18,16,52,48,0,34,59,24,2,34,81,63,65,74,17,49,57,27,40,89,48,37,54,75,81,64,28,2,62,89,21,62,52,76,90,77,58,49,54,43,30,28,25,37,49,55,24,47,93,6,23,57,7,1,34,77,79,45,74,72,69,13,0,91,13,71,19,22,58,91,23,90,30,19,24,57,78,50,59,46,29,90,46,66,89,24,34,13,18,39,4,58,37}

Returns: 4423680
97

{21,72,51,43,82,80,2,62,47,6,6,84,50,55,49,47,54,45,77,79,31,20,49,30,54,24,8,20,24,78,68,96,90,79,42,15,22,69,44,73,53,11,42,92,81,95,84,95,95,15,13,6,6,20,65,24,89,27,44,39,83,40,42,0,68,68,46,14,57,30,91,15,13,14,17,66,25,95,27,67,19,1,64,42,75,87,10,30,16,62,45,94,72,36,86,52,6,23,84,77}

{71,71,42,84,64,79,93,76,49,76,61,15,56,10,62,25,94,59,95,44,63,56,96,19,79,14,91,7,2,46,70,94,79,26,35,5,62,62,43,37,65,37,0,46,10,79,56,12,38,10,43,29,85,21,74,54,24,79,18,58,53,39,34,31,10,11,56,63,43,32,77,19,3,40,49,82,23,60,48,46,53,0,3,88,68,47,9,41,17,33,17,28,4,84,76,17,18,93,90,15}

Returns: 2985984
100

{91,95,92,46,23,37,62,68,72,31,33,77,60,33,12,55,97,41,49,56,19,5,20,19,51,56,75,82,71,86,56,12,85,22,63,33,11,5,8,74,5,55,80,32,42,97,83,60,55,13,19,44,18,0,56,68,0,67,62,42,19,24,93,98,76,63,65,64,50,39,33,24,77,33,56,21,82,17,44,63,7,84,38,44,58,33,99,73,56,61,93,40,83,29,16,73,99,70,31,49,56}

{23,33,10,65,80,44,22,5,49,66,89,14,48,83,15,10,66,82,30,45,12,0,76,25,52,1,71,50,43,78,26,96,81,69,47,94,95,81,31,50,12,25,19,93,87,51,60,9,8,98,44,56,52,46,49,16,83,24,83,83,17,45,55,86,71,92,53,90,96,7,4,71,98,36,79,90,78,54,39,2,90,11,0,3,50,28,49,44,6,77,27,29,35,23,59,57,34,81,88,38,69}

Returns: 2949120
92

{3,14,75,74,29,27,31,7,62,26,4,20,20,64,49,58,74,49,0,19,7,83,83,2,41,16,61,57,15,7,67,50,15,78,56,2,80,26,82,24,61,17,91,54,51,14,6,10,3,60,19,41,51,90,29,45,81,90,67,61,14,26,80,10,29,20,20,56,52,29,6,20,6,55,88,13,33,66,32,16,37,86,36,53,55,76,78,47,59,22,43,14,62,37}

{56,28,1,91,44,58,55,77,82,9,26,49,12,79,79,72,83,77,69,15,1,90,34,70,30,87,30,11,28,18,80,26,84,73,46,65,8,34,70,43,25,26,15,26,84,24,40,66,62,1,69,6,39,67,38,71,35,11,72,5,85,35,82,89,23,42,29,21,58,8,48,45,52,63,19,61,43,81,10,7,91,19,30,55,21,73,10,20,80,90,68,84,51,14}

Returns: 4976640
90

{14,18,74,7,29,15,29,26,33,32,85,27,65,31,27,71,55,23,64,26,77,87,20,61,27,16,77,7,19,41,85,43,0,13,43,35,45,76,26,27,72,86,83,69,33,41,18,40,43,39,23,56,53,65,32,38,37,61,41,73,47,72,52,41,18,12,67,46,36,22,6,6,31,15,76,4,89,18,78,29,11,27,59,62,21,9,41,55,59,15,11}

{28,27,41,58,60,69,66,55,14,5,63,54,6,77,20,35,81,78,10,53,89,66,80,86,2,57,84,80,57,39,55,76,52,74,56,60,31,40,15,25,35,64,43,82,75,19,66,44,89,38,60,28,23,86,76,76,43,60,64,24,27,24,49,68,34,6,76,18,64,31,50,3,42,88,49,23,17,1,48,79,74,8,64,64,87,86,70,30,51,84,41}

Returns: 2488320
98

{4,40,81,83,39,26,84,21,78,56,61,17,86,4,77,57,90,22,73,22,32,2,67,33,46,56,30,68,96,7,90,40,91,65,73,15,32,4,76,73,81,78,64,82,5,25,15,64,85,26,56,45,89,77,75,96,69,28,40,77,41,74,81,31,65,23,65,46,42,17,23,1,89,65,64,51,43,64,73,58,63,6,28,69,54,12,11,34,68,36,80,59,71,15,24,42,14,36,74}

{59,17,42,66,53,7,27,42,61,1,42,64,76,35,73,45,70,4,41,6,25,65,57,41,28,39,32,27,94,90,78,62,33,48,88,52,93,96,77,19,67,8,18,65,0,17,95,9,41,5,67,76,97,30,93,8,56,27,83,58,65,41,55,38,29,84,10,44,15,31,72,92,25,60,50,19,89,13,68,49,55,79,87,47,33,77,1,33,37,93,81,3,62,20,64,16,39,12,44}

Returns: 199065600
94

{75,64,37,73,89,49,91,30,85,36,87,38,15,31,30,12,76,21,63,17,21,29,30,12,3,17,92,91,90,9,59,8,52,22,11,92,92,31,5,76,45,32,46,4,85,88,11,8,9,29,87,70,2,11,37,2,32,43,55,87,68,57,82,68,65,47,45,82,93,12,30,41,73,54,32,68,9,42,40,1,58,74,89,76,73,7,6,34,61,25,78,19,81,76,36,45,63}

{32,92,15,31,44,14,15,18,35,21,93,28,53,25,11,84,52,73,23,31,29,39,32,23,87,30,13,1,13,0,13,65,69,53,51,27,49,71,11,56,55,83,58,9,33,45,89,91,30,72,86,62,37,67,31,48,24,13,76,56,50,84,85,66,26,66,32,20,60,10,62,89,63,8,79,70,16,50,89,92,70,46,77,20,28,76,61,71,57,80,11,85,47,45,20,25,60}

Returns: 23887872
99

{57,97,11,29,90,76,91,52,60,20,1,38,14,69,62,66,50,5,56,23,93,39,3,93,22,9,76,74,76,8,23,46,72,30,20,82,1,69,78,42,85,16,19,53,14,80,55,10,44,88,64,88,59,89,15,18,75,17,60,95,4,22,88,39,23,6,33,44,75,61,63,15,75,27,50,73,39,19,38,40,40,58,86,89,10,79,84,54,30,6,2,34,8,93,50,1,66,2,15,38}

{94,94,36,69,62,52,13,82,32,67,62,65,67,49,21,8,92,16,32,28,98,69,79,31,52,64,24,59,81,13,31,72,6,65,23,85,71,61,88,44,95,12,25,17,42,75,88,89,79,0,71,43,94,47,61,38,45,60,11,23,85,59,59,16,68,31,88,47,60,82,64,53,62,44,43,22,8,7,14,89,37,5,37,87,41,77,17,94,51,7,16,53,48,83,35,26,70,96,69,44}

Returns: 1179648
90

{14,32,9,6,88,82,87,34,70,64,73,55,23,35,66,45,76,39,3,71,79,39,49,50,35,82,43,53,8,58,13,83,89,77,58,46,8,28,18,42,19,84,65,81,34,79,57,35,20,8,38,56,80,57,64,81,86,18,41,88,60,50,35,30,67,87,77,81,64,11,69,38,9,68,63,22,88,85,5,2,31,23,23,44,51,39,66,66,71,75,44}

{23,15,37,23,36,37,35,40,82,26,16,81,59,1,61,71,19,52,50,38,45,26,46,13,7,89,76,62,51,87,65,40,21,33,75,64,62,39,40,74,25,7,71,13,54,74,45,13,19,74,66,1,35,10,25,24,40,3,8,72,58,19,85,70,77,88,37,12,82,24,18,15,16,81,66,81,48,27,8,7,40,52,0,36,29,78,17,4,47,23,14}

Returns: 5308416
96

{54,66,4,22,41,55,24,0,17,39,46,38,86,23,16,56,81,13,54,5,13,21,14,33,71,89,0,46,7,58,88,34,79,65,34,24,34,30,58,52,83,21,26,13,65,34,44,11,74,82,44,34,27,26,23,80,8,82,69,25,14,29,66,1,48,32,82,16,67,57,34,83,10,61,34,26,12,28,36,49,75,28,57,91,45,74,35,18,46,82,79,85,68,79,20,60,31}

{46,87,66,29,95,22,80,64,95,46,37,1,79,63,46,82,92,0,38,34,90,35,46,55,74,53,19,86,92,46,17,82,57,61,38,59,6,77,66,57,23,17,46,62,9,78,69,88,93,30,54,19,30,72,57,44,82,74,17,30,31,60,40,47,93,83,29,7,53,84,42,53,63,30,94,70,43,3,44,41,15,93,2,23,30,75,12,84,76,73,51,75,45,50,48,40,23}

Returns: 6635520
97

{62,29,25,46,77,45,30,43,50,4,63,84,12,42,37,66,35,77,37,57,45,92,18,85,4,18,63,58,12,29,6,59,41,94,2,45,61,8,32,6,49,32,88,18,91,35,22,5,83,81,76,16,40,5,34,73,8,41,93,70,88,78,65,58,23,17,83,51,23,60,44,17,12,15,28,91,95,24,1,68,41,54,10,17,21,18,96,79,81,69,55,60,36,40,14,87,88,47,22,86}

{18,26,84,23,11,51,16,86,29,52,26,20,45,30,66,58,42,75,93,31,91,94,38,90,94,59,23,75,67,3,90,15,82,84,92,14,85,0,42,92,18,74,25,36,23,92,9,9,88,33,59,31,11,86,40,16,70,45,57,19,3,42,8,19,22,71,72,64,39,37,70,45,48,75,36,47,46,59,43,30,80,35,60,53,30,56,83,14,94,36,22,7,89,27,13,75,44,23,36,10}

Returns: 3538944
98

{35,22,90,71,4,39,79,79,71,23,97,69,58,43,91,71,32,40,32,84,39,1,45,30,2,14,83,72,7,37,24,15,7,82,20,12,58,82,89,75,60,17,50,82,82,47,48,63,45,55,28,5,53,61,1,84,28,31,91,4,19,68,74,22,44,59,87,62,94,26,40,82,20,72,24,10,65,84,28,75,39,27,84,31,27,75,3,76,80,82,90,32,55,32,83,73,21,52,28,90}

{81,62,29,89,69,8,14,59,7,48,5,56,56,49,44,36,50,67,85,35,49,16,97,24,97,25,18,67,26,82,27,66,64,42,94,38,25,33,73,78,84,49,48,17,71,93,51,48,15,89,77,4,5,7,86,96,56,27,28,35,84,55,17,73,16,93,76,86,24,12,41,41,73,11,50,31,55,92,83,39,13,54,95,52,6,46,16,86,50,57,4,88,0,70,34,9,17,64,68,43}

Returns: 13271040
95

{35,17,11,67,5,2,5,92,70,55,10,17,27,54,79,75,53,57,22,31,92,49,68,85,56,77,79,41,70,52,39,83,79,9,45,49,75,78,41,7,83,72,37,74,76,90,34,10,78,68,7,13,69,88,81,93,19,48,12,54,50,22,23,39,81,80,88,72,84,90,32,62,67,74,67,43,22,23,75,84,46,31,33,29,29,25,87,67,30,40,8,43,80,38,38,75,49}

{50,24,54,14,16,92,57,18,59,92,67,1,50,60,82,42,83,6,28,53,4,70,91,63,79,29,85,60,5,57,58,8,16,72,88,25,57,54,64,48,3,64,83,24,29,9,65,17,67,88,50,45,79,32,1,24,72,54,64,43,44,16,80,7,61,79,28,56,36,21,94,61,92,53,15,86,65,51,0,17,87,47,57,73,20,20,85,89,43,16,26,71,66,10,12,84,79}

Returns: 17915904
99

{87,17,40,69,96,79,56,26,91,23,64,31,80,93,45,82,74,37,17,25,91,78,26,28,4,13,72,9,54,36,54,13,44,8,45,36,71,54,0,7,64,13,12,19,9,6,45,65,42,96,86,6,3,20,79,88,44,98,54,70,65,52,12,63,38,22,5,88,6,24,22,95,18,14,63,71,6,25,19,10,7,65,36,76,15,42,1,81,29,65,73,54,61,41,50,54,61,12,94,25,46,66,86}

{95,68,62,77,35,25,61,80,63,36,59,0,31,65,11,20,31,82,98,16,13,1,46,62,48,50,36,51,35,80,43,49,62,53,3,75,52,32,95,59,50,82,95,13,6,21,69,88,34,70,39,55,39,55,51,8,23,34,33,63,97,4,13,94,53,93,33,41,48,36,70,84,61,1,39,90,57,58,61,36,92,73,47,13,65,63,86,64,63,2,66,30,85,60,27,89,67,83,19,48,34,34,52}

Returns: 26542080
97

{89,6,28,83,94,49,71,94,37,48,19,1,19,40,63,91,72,18,40,6,30,75,2,86,23,65,0,62,26,31,89,55,60,83,10,10,5,82,96,4,16,51,31,60,85,75,41,33,80,22,34,40,89,66,63,12,28,81,92,25,2,8,77,53,47,28,65,19,11,73,20,79,93,54,84,80,74,89,87,35,46,54,44,69,24,64,43,47,6,39,58,80,75,26,56,24,52,19}

{6,96,22,95,89,23,53,77,73,71,28,55,88,96,91,55,59,96,1,78,82,13,38,54,3,10,89,11,1,19,50,29,26,80,87,52,74,6,61,28,69,83,63,3,68,80,89,26,76,13,85,44,37,27,32,7,36,6,47,87,42,6,70,66,96,85,28,21,3,48,38,4,53,13,86,15,6,57,17,20,82,2,12,35,26,93,65,14,9,65,89,72,90,45,10,67,21,1}

Returns: 5898240
91

{86,21,41,47,62,74,14,85,38,59,20,3,14,43,80,77,67,90,37,78,42,51,52,70,56,12,24,30,17,47,34,85,77,67,84,78,77,51,83,88,0,28,40,90,14,88,69,88,5,84,8,10,84,74,9,90,34,38,86,35,4,45,44,58,5,29,80,75,59,64,87,63,82,27,75,31,56,81,21,6,72,15,73,59,39,30,88,50,26,1,85,32,49}

{47,68,66,54,34,77,18,41,48,8,83,25,46,61,70,13,69,2,68,57,25,32,16,36,76,52,4,90,47,43,27,13,55,52,88,71,22,68,41,23,74,4,4,44,69,62,25,57,42,48,11,44,4,25,46,69,61,11,19,88,89,27,4,17,79,66,57,38,1,56,79,67,75,33,65,4,80,70,17,14,47,17,42,39,53,7,60,8,78,49,48,12,47}

Returns: 1474560
95

{2,51,53,63,50,17,17,50,48,33,50,75,31,24,79,63,82,26,67,88,89,78,42,46,41,50,87,35,47,91,86,46,73,82,15,12,48,88,73,17,63,1,54,28,46,90,83,0,50,69,26,10,25,63,31,80,36,85,66,72,13,58,82,52,72,48,27,6,41,37,41,78,11,75,49,2,1,39,64,42,81,43,70,26,92,3,55,55,11,44,45,54,68,14,0,82,23,0,87}

{26,65,61,9,80,34,36,61,57,88,13,43,16,38,20,92,81,86,69,76,71,0,71,20,20,67,56,29,9,21,89,38,5,51,69,41,63,91,23,19,78,23,18,19,42,82,4,20,66,93,88,27,41,22,75,0,78,54,32,90,8,24,35,24,91,60,50,13,84,73,62,85,30,53,63,77,24,48,86,40,4,56,65,11,94,65,74,50,7,6,41,59,86,4,85,65,36,7,75}

Returns: 8847360
93

{25,12,39,75,43,65,61,56,44,61,50,62,88,54,88,32,13,66,54,34,80,38,46,49,48,7,15,11,88,58,80,61,57,67,10,91,60,57,18,36,2,59,18,20,23,54,71,48,14,73,34,1,92,1,17,78,65,26,72,81,3,37,16,50,85,59,49,85,11,12,12,57,51,63,5,53,7,31,77,57,35,34,58,64,86,30,10,87,29,68,11,50,24,70}

{54,78,36,36,66,55,19,87,48,91,92,65,74,9,38,66,52,21,87,2,65,56,17,8,18,49,37,6,49,40,66,38,18,25,71,17,4,17,76,14,13,31,69,9,8,80,27,85,25,3,92,36,90,27,89,44,0,53,65,75,78,1,11,19,47,80,45,86,12,83,60,64,57,42,37,36,41,70,65,63,65,82,36,84,28,40,22,33,65,18,24,79,39,28}

Returns: 11612160
98

{40,62,73,66,15,42,21,23,23,34,3,50,25,41,5,83,97,96,88,0,26,42,13,90,10,41,77,21,17,61,38,81,48,25,27,74,73,63,61,77,41,54,31,67,19,47,96,32,31,58,72,67,4,59,81,79,64,7,73,95,6,50,97,69,41,47,77,59,74,8,18,29,10,52,50,44,85,86,75,51,82,43,38,24,21,31,74,79,24,56,47,59,36,28,37,11,12,32,87,29,93,19}

{41,22,35,70,31,40,45,70,15,64,38,64,45,48,66,47,80,66,71,39,66,92,86,41,76,1,39,93,18,53,96,79,9,5,81,24,0,42,81,71,39,41,79,85,50,50,42,62,46,24,86,20,44,94,94,18,20,77,64,57,41,55,95,41,14,62,49,84,91,79,78,15,40,79,24,60,80,51,97,0,53,75,16,33,87,60,2,89,65,41,68,30,68,68,5,85,45,4,34,7,9,55}

Returns: 92897280
93

{20,76,18,85,85,52,1,90,90,5,5,39,52,13,5,11,62,36,91,64,10,58,85,69,2,72,46,12,11,77,80,23,48,46,17,91,56,13,86,14,92,72,58,36,28,35,20,88,92,13,63,28,20,63,38,2,48,32,51,28,48,29,42,78,41,71,91,54,66,48,34,16,55,74,26,77,26,57,53,64,4,36,31,22,11,87,49,68,76,11,32,5,64,35,10,22,48}

{87,25,11,26,54,49,49,5,21,6,43,82,0,5,50,45,74,27,86,17,41,20,11,92,44,37,75,19,15,73,47,5,39,58,1,62,28,75,3,0,70,22,37,88,2,52,79,39,13,85,25,25,59,35,1,59,53,69,49,88,30,26,92,33,81,61,27,83,65,80,28,76,86,40,71,90,84,21,60,19,60,8,28,78,89,65,10,33,9,24,7,67,58,72,22,29,27}

Returns: 1382400
98

{2,47,83,4,58,2,37,87,14,53,27,69,16,31,12,78,55,73,82,49,73,4,88,48,81,11,96,87,46,32,94,64,0,32,10,11,21,73,73,55,76,97,32,67,20,42,49,24,71,68,49,38,94,42,17,31,75,77,68,18,71,17,12,68,7,25,1,15,58,55,75,42,7,70,18,1,4,11,37,94,65,10,87,72,47,15,6,74,10,66,74,95,33,20,12,76,23,92,85}

{45,89,85,11,16,18,95,24,49,76,45,87,92,62,10,2,62,78,7,84,10,85,71,32,78,49,5,3,4,0,97,40,71,26,96,72,4,1,93,36,54,87,90,89,53,72,63,8,64,42,58,3,29,43,7,93,55,20,53,40,30,11,66,80,93,73,61,0,95,94,79,52,13,4,39,22,57,91,47,41,45,86,19,9,60,50,76,22,34,59,56,35,32,44,51,28,76,12,33}

Returns: 10616832
100

{95,88,3,58,40,99,49,26,24,63,60,32,30,42,75,82,12,8,19,96,32,60,32,90,62,82,58,14,54,9,10,79,99,49,88,26,35,83,46,8,8,31,55,3,72,84,84,64,94,0,90,40,31,62,13,47,84,26,70,41,52,57,56,7,68,56,60,32,46,59,1,28,80,73,13,28,33,64,46,93,48,60,89,30,7,38,1,67,89,1,4,58,21,23,97,3,14,96,42,5,86}

{65,23,94,29,88,32,15,18,88,12,10,53,61,22,20,73,90,60,84,10,42,69,81,75,20,54,90,20,99,16,25,23,25,65,67,57,54,26,74,17,16,98,95,30,69,92,54,88,42,42,49,25,70,81,61,26,6,34,69,96,34,9,33,90,96,48,51,36,86,10,61,43,1,39,56,12,76,45,18,73,50,91,88,2,78,99,85,87,44,11,63,5,32,71,42,66,77,27,37,14,43}

Returns: 5971968
99

{6,92,94,42,86,89,21,35,52,49,82,59,71,20,7,21,13,34,58,32,37,42,77,25,33,58,76,47,82,44,1,59,31,88,62,32,58,25,25,15,24,29,80,18,6,8,81,30,93,5,46,6,56,8,31,82,41,81,10,79,54,74,30,9,25,13,57,41,5,16,7,33,37,26,65,72,57,76,26,52,15,60,69,62,55,27,63,85,45,37,52,0,91,62,95,96,61,12,35,57}

{38,23,35,39,62,19,25,49,24,71,6,25,92,66,82,32,51,31,14,85,98,65,94,73,68,19,94,56,74,78,49,24,22,72,44,26,84,40,67,10,39,69,41,77,3,94,26,65,82,68,58,36,87,48,26,76,70,3,43,52,63,56,37,25,75,74,97,71,15,36,64,55,53,83,28,13,37,55,17,89,11,31,70,4,20,82,33,2,37,62,50,21,68,90,65,29,76,69,59,35}

Returns: 9953280
100

{24,59,27,19,76,1,44,7,52,5,74,94,52,6,97,57,92,56,89,74,42,66,79,0,50,30,39,49,95,85,60,85,69,77,0,14,72,15,32,63,27,69,32,98,47,12,13,91,69,86,55,20,32,15,69,88,18,98,98,97,93,41,15,41,40,35,35,46,57,45,20,95,40,84,79,75,79,39,88,87,31,60,60,74,66,11,29,74,33,31,64,38,16,5,94,80,27,9,15,70,97}

{66,53,22,45,96,25,88,0,27,47,36,96,41,58,91,45,3,70,33,52,3,75,2,97,79,47,5,94,8,3,48,22,56,74,61,22,67,10,83,3,0,26,17,72,37,84,32,47,66,88,69,96,62,13,46,13,15,93,75,70,1,15,8,51,45,74,6,59,34,68,0,23,7,71,52,54,84,28,4,84,35,47,33,82,73,69,30,90,81,65,53,7,55,43,21,41,99,14,78,50,66}

Returns: 47775744
100

{4,65,35,14,15,30,65,16,96,52,27,29,51,67,12,12,76,54,95,13,30,97,24,52,99,66,34,23,26,3,53,79,4,70,81,23,23,14,46,4,35,35,89,25,77,65,5,56,53,4,46,26,26,6,38,20,38,46,57,84,2,34,69,25,94,92,6,62,1,42,47,85,29,48,76,33,35,11,99,2,39,22,94,71,15,86,63,41,93,78,16,48,31,46,59,19,21,74,18,25,2,67,35,14}

{65,73,73,45,47,23,49,76,45,6,67,80,56,17,83,24,72,7,67,96,68,76,20,33,67,26,32,25,33,1,56,97,50,42,10,61,97,26,36,37,0,90,10,88,55,20,44,93,88,8,16,69,54,4,7,99,80,18,32,77,99,24,79,10,51,1,98,30,10,1,10,56,75,46,28,77,91,49,9,60,1,34,87,60,5,35,3,82,41,76,58,64,1,43,20,46,35,57,40,94,73,88,81,70}

Returns: 7464960
90

{17,51,78,39,25,51,12,15,44,70,61,83,25,53,56,44,22,74,27,79,52,52,44,27,54,1,79,81,32,1,55,58,69,79,82,23,53,78,25,49,47,81,62,69,78,54,38,51,27,82,62,23,2,47,77,57,57,60,7,28,80,21,16,53,40,48,44,78,68,76,42,4,57,77,18,32,30,33,51,15,12,43,52,77,74,35,12,46,31,41,55}

{10,89,17,85,57,8,79,6,0,55,86,74,61,50,51,55,89,19,84,63,49,82,66,21,5,19,64,59,42,29,74,10,67,61,22,26,51,85,19,24,29,57,32,37,34,57,52,11,32,26,37,75,65,62,25,78,38,28,53,62,60,36,1,72,55,56,88,65,51,58,73,14,14,45,61,20,80,79,9,10,87,44,71,13,3,89,41,86,86,34,87}

Returns: 7962624
14

{0,9,1,11,13,2,3,11,0,6,12,10,7,7,0,5,5,6,0}

{2,10,4,5,1,4,8,4,3,0,5,13,11,4,1,2,6,12,13}

Returns: 1
12

{0,5,1,1,7,9,0,8,8,11,3,6,6,11,7,0}

{10,2,4,6,5,8,5,5,1,5,0,0,4,6,9,2}

Returns: 2
4

{0,0,2,2,1}

{3,1,3,0,3}

Returns: 4
4

{1,2,2,1,0,0}

{2,3,0,3,1,3}

Returns: 24
13

{11,12,0,1,8,3,5,8,7,9,6,7,6,8}

{8,7,7,10,2,8,12,7,6,0,4,10,8,1}

Returns: 12
13

{10,9,11,9,0,8,6,0,3,11,1,7,8,7}

{9,4,2,0,3,1,9,12,5,1,5,11,5,12}

Returns: 6
6

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

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

Returns: 8
5

{0,0,0,1,2,4,4,1,2,2}

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

Returns: 120
6

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

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

Returns: 16
8

{0,2,6,0,0,0,0,7,0}

{7,4,0,5,4,1,3,4,2}

Returns: 48
6

{2,4,4,2,1,0,5,1,0}

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

Returns: 72
6

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

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

Returns: 10
11

{4,10,7,4,6,3,8,2,0,10,10,6}

{10,1,9,7,9,10,10,10,7,5,7,0}

Returns: 240
13

{5,1,1,2,6,8,4,1,1,5,5,0,6,4}

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

Returns: 36
15

{10,12,6,3,13,8,6,7,7,6,13,1,7,13,5,4}

{7,4,2,12,3,6,14,0,11,0,0,7,9,5,12,8}

Returns: 96
14

{3,11,13,8,7,0,4,10,1,7,5,11,9,8,3,9}

{13,12,4,4,6,8,12,7,8,4,2,5,2,7,4,4}

Returns: 32
10

{5,6,5,1,6,2,2,9,8,1,3,7,0,0,1}

{3,4,6,4,2,7,0,0,9,5,1,6,8,4,8}

Returns: 3
7

{2,0,5,4,0,3,2,1,3,6,3,2}

{5,1,4,6,5,4,1,4,2,0,0,6}

Returns: 144
15

{6,1,12,1,3,8,1,1,1,5,3,2,1,1,12,10}

{14,0,1,13,13,6,8,11,7,1,10,1,9,4,6,0}

Returns: 2880
9

{0,4,5,5,5,2,6,8,6,5,6,3,2}

{1,7,3,0,7,5,2,0,4,4,5,7,3}

Returns: 20
15

{14,3,0,7,12,8,3,1,8,3,14,3,3,3,14,12,12}

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

Returns: 288
10

{8,9,4,2,2,2,3,7,0,2,9,2,9}

{9,5,2,9,6,1,9,2,9,3,6,0,1}

Returns: 192
13

{4,8,4,10,4,4,3,0,2,11,0,11,5,5,0}

{7,4,9,0,0,12,5,1,5,5,6,0,10,4,5}

Returns: 384
14

{7,2,7,13,3,3,7,2,0,2,7,7,9,3,0}

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

Returns: 480
15

{2,9,0,10,2,9,5,1,9,3,7,9,14,5,4,14,0}

{0,13,8,12,5,12,9,0,6,0,0,4,10,11,10,9,11}

Returns: 576
15

{14,14,14,9,3,0,13,5,8,3,10,11,4,14,5,1,14}

{9,2,12,0,1,1,14,10,14,10,11,6,14,7,6,14,0}

Returns: 1440
12

{8,7,10,2,10,6,4,5,11,0,9,10,8}

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

Returns: 864
14

{0,13,7,10,13,13,13,13,12,3,11,2,0,10,6}

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

Returns: 720
8

{0,1,3,2,4,5,7,6,0,1,2,3}

{1,3,2,0,5,7,6,4,4,5,6,7}

Returns: 48
95

{0, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 32, 33, 34, 35, 36, 37, 38, 39, 40, 1, 41, 42, 43, 44, 45, 46, 47, 48, 49, 1, 50, 51, 52, 53, 54, 55, 56, 57, 58, 1, 59, 60, 61, 62, 63, 64, 65, 66, 67, 2, 68, 69, 70, 71, 72, 73, 74, 75, 76, 2, 77, 78, 79, 80, 81, 82, 83, 84, 85, 3, 86, 87, 88, 89, 90, 91, 92, 93, 94}

{5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 14, 15, 16, 17, 18, 19, 20, 21, 22, 2, 23, 24, 25, 26, 27, 28, 29, 30, 31, 3, 32, 33, 34, 35, 36, 37, 38, 39, 40, 4, 41, 42, 43, 44, 45, 46, 47, 48, 49, 2, 50, 51, 52, 53, 54, 55, 56, 57, 58, 3, 59, 60, 61, 62, 63, 64, 65, 66, 67, 4, 68, 69, 70, 71, 72, 73, 74, 75, 76, 3, 77, 78, 79, 80, 81, 82, 83, 84, 85, 4, 86, 87, 88, 89, 90, 91, 92, 93, 94, 4}

Returns: 120
94

{0, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 0, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 1, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 1, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 2, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93}

{4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 2, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 3, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 2, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 3, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 3}

Returns: 24
100

{0, 0, 0, 1, 1, 2, 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, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99}

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

Returns: 594355750

Statistics

Problem Statement for "AutomorphicGraph"

Problem Statement

Definition

Constraints

Examples