TopCoder Statistics - Problem Statement

Problem Statement

You are given an undirected graph with n vertices numbered 0 through n-1. For each valid i, there is an undirected edge connecting two different vertices x[i] and y[i]. No two edges connect the same pair of vertices.
A triangle is a set of three distinct vertices such that each pair of those vertices is connected by an edge. Formally, three distinct vertices u,v,w are a triangle if the graph contains the edges (u,v), (v,w), and (w,u).
The graph has 2^n subsets of vertices (including the empty set). A subset S of vertices is called triangle-free if and only if no three vertices in S form a triangle.
You are given the description of the graph: the int n and the int[]s x and y. Compute and return the number of triangle-free subsets of vertices of the given graph.

Definition

Class:: TriangleFree
Method:: count
Parameters:: int, int[], int[]
Returns:: long
Method signature:: long count(int n, int[] x, int[] y)
(be sure your method is public)

Constraints

n will be between 1 and 60, inclusive.
x will have between 0 and 60 elements, inclusive.
y will have the same number of elements as x.
Each element of x and y will be between 0 and n-1, inclusive.
For each valid i, x[i] != y[i].
No two edges will connect the same pair of vertices.

Examples

4

{0,1,2,3}

{1,2,0,2}

Returns: 14

There are 2^4 = 16 subsets in total. Two of them are not triangle-free: {0,1,2} and {0,1,2,3}.
5

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

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

Returns: 16

This is a complete graph. Any subset having more than two vertices is not triangle-free.
6

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

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

Returns: 40
60

{10,20,30}

{20,30,10}

Returns: 1008806316530991104
60

{14,18,14,9,15,17,18,14,10,6,17,19,19,5,3,17,5,19,15,1,13,13,16,4,12,11,19,12,9,16,8,11,16,13,13,14,14,14,2,15,12,17,4,6,18,16,12,13,11,16,19,19,19,17,10,17,19,14,5,9}

{8,16,13,4,5,14,11,5,6,2,10,3,17,4,0,12,3,10,6,0,6,5,9,1,2,2,2,8,1,7,4,1,10,4,11,9,1,0,1,7,9,8,2,3,3,8,3,8,10,0,4,7,5,13,8,11,0,11,1,8}

Returns: 209857187323838464
60

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

{14,6,7,8,15,3,0,4,0,0,0,13,11,3,10,0,3,11,15,0,5,7,0,12,6,3,2,2,20,12,4,5,8,6,16,9,7,3,1,4,8,9,0,6,17,2,1,16,6,3,11,3,1,1,0,13,7,12,6,8}

Returns: 181135744583073792
60

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

{1,4,2,2,16,14,9,19,1,15,3,4,11,13,12,7,13,5,11,4,0,13,14,9,14,3,3,3,7,15,17,10,5,1,2,5,0,0,16,12,6,2,5,16,11,18,3,7,8,1,18,9,7,5,7,5,19,3,9,3}

Returns: 363806407398522880
60

{12,9,9,3,17,21,25,17,24,24,22,18,22,23,13,12,24,13,10,13,20,25,25,22,22,15,23,22,11,19,17,14,8,25,17,13,23,11,11,15,16,15,20,20,8,21,25,10,18,13,21,21,23,20,18,20,24,20,19,18}

{10,7,0,1,15,10,3,4,22,4,19,10,3,17,5,7,5,9,9,6,13,11,22,8,17,12,9,13,1,2,0,2,5,9,7,3,14,9,6,9,15,14,10,6,4,1,0,8,1,8,9,14,8,7,4,14,3,19,5,14}

Returns: 507780857986023424
60

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

{23,0,7,14,14,9,0,17,7,16,0,6,11,7,0,6,16,7,2,21,13,14,16,18,13,19,4,3,0,9,26,8,21,2,2,3,5,22,2,4,2,6,5,16,1,1,8,15,16,12,8,14,5,13,1,5,6,15,6,12}

Returns: 423338364972826624
60

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

{0,3,23,7,24,4,16,10,9,7,22,8,15,9,15,16,19,3,0,12,3,19,14,26,3,6,3,1,7,4,0,16,0,21,18,3,19,3,5,13,25,18,7,4,0,7,1,27,1,2,7,2,5,15,2,12,7,13,5,20}

Returns: 689613692941107200
60

{22,8,23,13,19,28,21,23,28,31,26,25,16,21,29,29,24,25,26,27,31,27,28,27,12,30,18,19,26,30,18,20,14,24,22,25,29,31,30,15,6,21,27,23,22,21,28,27,8,10,29,26,23,23,16,30,29,26,16,13}

{4,1,18,9,14,25,15,6,26,25,19,4,7,17,8,18,21,22,22,19,2,24,8,1,0,10,14,7,8,23,13,14,7,22,11,21,19,29,24,9,0,14,21,16,6,10,10,6,4,7,25,7,20,14,15,15,3,4,10,7}

Returns: 380334266187251712
60

{26,12,20,24,25,25,28,8,32,30,24,15,28,17,24,31,15,23,20,29,18,26,9,32,27,32,26,21,15,29,21,5,22,8,16,31,24,27,8,32,32,17,17,28,30,28,21,26,32,27,12,23,19,33,9,20,20,27,19,26}

{7,3,14,17,18,10,5,0,28,9,11,13,20,5,5,13,2,22,10,18,0,13,6,31,3,21,6,10,5,20,13,3,0,5,15,19,4,5,7,6,15,8,6,4,15,19,20,11,19,12,0,19,12,0,8,2,3,15,7,17}

Returns: 465858678642180096
60

{17,28,26,19,19,19,7,22,16,34,23,30,31,33,8,32,33,7,35,19,26,22,20,28,15,16,34,11,34,35,24,31,22,11,25,16,20,27,31,30,16,23,30,31,28,29,32,19,31,1,6,14,23,12,19,31,32,20,32,20}

{15,16,17,0,2,12,4,8,6,17,18,7,1,14,6,14,8,3,7,15,18,6,2,2,3,13,19,3,23,9,0,4,18,2,22,11,5,17,7,20,7,10,12,6,12,26,7,7,29,0,3,10,6,5,10,3,12,1,30,16}

Returns: 630503947831869440
60

{23,23,23,29,20,11,19,18,37,11,33,21,29,34,34,37,28,27,21,30,31,35,32,24,24,19,28,5,14,32,12,21,34,28,15,34,31,30,31,3,32,26,9,13,34,33,24,27,33,14,7,18,23,25,35,34,36,15,29,26}

{8,7,1,5,14,10,15,17,19,8,32,3,27,2,23,3,26,25,9,20,3,0,9,22,4,17,24,3,3,29,7,12,0,7,11,19,17,28,27,1,11,14,7,7,25,10,20,1,20,2,5,2,3,0,21,21,13,0,8,24}

Returns: 772367336094040064
60

{12,35,7,30,24,21,19,30,37,39,36,23,34,30,14,14,18,31,28,16,36,27,30,36,11,27,24,34,37,16,32,25,28,37,32,37,12,24,20,28,9,38,33,37,12,32,24,33,18,8,39,21,34,38,25,25,32,30,17,38}

{2,1,4,2,20,16,0,4,36,26,23,6,16,9,12,3,17,9,15,10,21,18,23,24,8,3,13,15,13,5,15,6,6,31,29,10,3,6,10,8,5,22,17,26,9,31,9,7,16,1,17,0,24,15,15,23,21,1,5,27}

Returns: 882705526964617216
60

{41,35,29,15,7,33,14,18,5,19,30,35,17,30,37,31,33,24,16,28,32,36,41,31,24,22,39,25,39,17,37,14,10,27,18,21,38,36,34,37,40,19,40,28,40,13,23,18,39,39,41,16,27,39,12,16,26,23,13,9}

{30,34,11,5,1,24,12,1,4,4,16,29,15,18,16,1,4,11,12,16,12,6,20,26,12,13,6,12,26,7,1,0,7,0,5,18,9,9,21,32,9,5,30,22,34,2,5,17,22,23,2,10,8,32,1,11,0,8,6,4}

Returns: 1008806316530991104
60

{34,40,28,5,22,35,36,41,24,33,32,42,40,25,24,27,30,25,26,43,2,24,19,15,20,27,24,43,29,25,17,14,18,32,37,15,19,22,31,32,43,34,42,22,37,14,37,27,15,41,30,38,40,40,40,37,23,23,27,32}

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

Returns: 717198240658751488
60

{29,8,32,20,33,25,23,31,14,13,45,41,43,42,31,31,15,34,41,20,42,40,38,20,39,39,45,42,23,33,25,30,43,32,31,41,24,18,40,1,10,44,27,26,38,43,36,30,34,42,15,45,23,30,30,35,45,21,34,33}

{17,6,22,7,25,7,22,11,0,6,5,33,21,40,2,17,7,27,20,3,27,33,16,11,28,17,0,16,4,29,20,21,12,3,8,12,3,2,34,0,3,28,9,24,9,7,19,3,33,5,2,8,9,29,24,4,23,19,6,22}

Returns: 772367336094040064
60

{47,15,20,40,44,47,25,47,39,35,22,16,29,46,39,43,43,24,16,40,9,12,39,15,36,46,15,44,46,42,33,25,18,47,39,13,32,45,28,23,42,34,34,37,35,25,32,41,12,28,43,46,34,36,39,39,28,42,24,39}

{7,5,12,35,29,22,1,45,29,29,3,8,0,12,4,18,19,12,9,17,7,1,8,11,23,44,14,9,11,32,14,19,2,2,36,6,19,42,13,9,4,3,12,14,2,4,27,29,7,15,31,16,32,8,25,24,3,7,14,15}

Returns: 900719925474099200
60

{23,48,43,28,30,35,44,20,30,32,49,49,16,41,33,21,48,28,26,23,34,16,37,35,5,35,14,35,34,48,49,26,9,20,43,24,43,11,29,48,47,31,17,46,43,48,37,21,41,45,38,40,35,35,30,42,44,49,27,24}

{14,42,11,15,1,8,21,19,22,22,17,38,5,0,5,8,36,26,13,15,23,0,36,16,1,29,9,24,21,19,0,5,7,4,18,3,31,10,10,34,29,24,9,7,39,1,14,2,34,41,25,6,22,7,9,27,20,5,21,2}

Returns: 1152921504606846976
60

{18,26,14,21,32,50,14,38,35,37,36,37,37,44,43,29,39,33,45,17,51,44,46,39,51,22,34,17,24,47,23,45,35,3,33,20,28,43,23,28,45,18,43,30,25,34,44,44,40,32,40,43,37,24,47,18,21,47,25,42}

{4,4,0,20,2,28,5,9,4,36,8,27,13,27,34,17,16,8,8,10,22,33,32,27,6,9,14,11,12,26,22,37,29,0,27,5,3,7,14,22,15,7,38,6,12,7,41,11,6,31,19,13,28,14,34,11,12,25,4,25}

Returns: 882705526964617216
60

{36,20,27,43,19,37,49,24,35,50,7,43,35,47,51,27,47,44,48,34,48,14,49,53,10,48,51,36,37,21,41,29,44,51,50,11,36,50,52,38,49,51,36,26,50,46,40,31,28,13,22,51,26,45,33,7,43,51,48,52}

{15,19,21,35,2,35,36,19,30,38,3,22,2,22,0,0,27,16,32,10,24,12,18,38,5,37,36,9,10,20,30,24,4,21,48,9,7,9,18,20,47,25,14,16,35,15,24,28,15,10,2,37,8,26,30,2,40,28,42,19}

Returns: 1152921504606846976
60

{31,39,15,32,39,35,55,34,46,53,46,39,21,37,34,48,23,24,22,53,36,41,40,29,50,51,28,34,54,29,39,18,29,43,39,51,54,41,35,44,46,49,32,37,40,54,24,19,22,3,36,33,40,51,54,54,48,50,41,35}

{2,33,3,5,23,13,30,32,44,43,3,1,2,10,10,37,3,17,13,28,27,2,16,4,28,37,7,15,4,25,36,7,7,9,12,18,38,33,5,19,28,2,13,33,37,51,15,0,18,0,5,30,28,6,48,15,16,26,37,6}

Returns: 1008806316530991104
60

{36,20,49,9,31,14,48,19,40,49,54,44,22,37,53,15,6,28,53,35,56,52,12,29,44,55,12,2,26,54,42,25,42,44,52,51,13,38,52,20,21,56,17,47,54,54,40,57,23,13,32,43,38,46,23,35,55,44,19,53}

{16,14,14,7,30,0,23,15,4,35,28,36,17,6,36,10,2,23,21,14,28,0,10,16,8,41,3,0,17,26,11,9,23,25,34,34,1,0,6,7,9,17,7,10,40,10,18,0,0,2,5,7,16,33,14,11,52,7,16,26}

Returns: 900719925474099200
60

{47,39,59,39,28,45,49,14,38,11,57,42,47,36,34,39,57,37,42,56,51,10,46,35,16,13,42,30,44,55,16,56,48,48,32,24,49,16,44,52,34,39,38,43,30,58,31,41,51,59,45,34,42,58,58,24,25,15,43,51}

{19,19,44,14,0,0,12,0,16,5,36,35,15,25,19,13,46,4,22,34,40,1,13,29,14,12,39,26,12,47,5,45,3,46,14,15,4,7,31,32,24,27,1,27,3,18,16,35,44,13,9,1,26,56,22,23,1,8,9,25}

Returns: 1152921504606846976
60

{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59}

{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,0}

Returns: 1152921504606846976
60

{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,0}

{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,0,2}

Returns: 1008806316530991104
60

{3,8,9,11,12,13,17,20,21,24,26,28,30,32,33,34,35,36,37,38,40,42,44,45,46,48,49,50,51,55,57}

{4,9,10,12,13,14,18,21,22,25,27,29,31,33,34,35,36,37,38,39,41,43,45,46,47,49,50,51,52,56,58}

Returns: 1152921504606846976
60

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

{1,2,3,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,49,50,51,52,53,54,56,57,58,59}

Returns: 1152921504606846976
1

{}

{}

Returns: 2
2

{}

{}

Returns: 4
2

{0}

{1}

Returns: 4
3

{0,1,2}

{2,0,1}

Returns: 7
60

{0,0,1,3,3,4,6,6,7,9,9,10,12,12,13,15,15,16,18,18,19,21,21,22,24,24,25,27,27,28,30,30,31,33,33,34,36,36,37,39,39,40,42,42,43,45,45,46,48,48,49,51,51,52,54,54,55,57,57,58}

{1,2,2,4,5,5,7,8,8,10,11,11,13,14,14,16,17,17,19,20,20,22,23,23,25,26,26,28,29,29,31,32,32,34,35,35,37,38,38,40,41,41,43,44,44,46,47,47,49,50,50,52,53,53,55,56,56,58,59,59}

Returns: 79792266297612001
60

{0,0,0,1,1,2,4,4,4,5,5,6,8,8,8,9,9,10,12,12,12,13,13,14,16,16,16,17,17,18,20,20,20,21,21,22,24,24,24,25,25,26,28,28,28,29,29,30,32,32,32,33,33,34,36,36,36,37,37,38}

{1,2,3,2,3,3,5,6,7,6,7,7,9,10,11,10,11,11,13,14,15,14,15,15,17,18,19,18,19,19,21,22,23,22,23,23,25,26,27,26,27,27,29,30,31,30,31,31,33,34,35,34,35,35,37,38,39,38,39,39}

Returns: 27197360938418176
60

{0,0,0,0,1,1,1,2,2,3,5,5,5,5,6,6,6,7,7,8,10,10,10,10,11,11,11,12,12,13,15,15,15,15,16,16,16,17,17,18,20,20,20,20,21,21,21,22,22,23,25,25,25,25,26,26,26,27,27,28}

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

Returns: 18014398509481984
60

{0,0,0,0,0,1,1,1,1,2,2,2,3,3,4,6,6,6,6,6,7,7,7,7,8,8,8,9,9,10,12,12,12,12,12,13,13,13,13,14,14,14,15,15,16,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22}

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

Returns: 16097949742268416
60

{0,0,0,0,0,0,1,1,1,1,1,2,2,2,2,3,3,3,4,4,5,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12,14,14,14,14,14,14,15,15,15,15,15,16,16,16,16,17,17,17}

{1,2,3,4,5,6,2,3,4,5,6,3,4,5,6,4,5,6,5,6,6,8,9,10,11,12,13,9,10,11,12,13,10,11,12,13,11,12,13,12,13,13,15,16,17,18,19,20,16,17,18,19,20,17,18,19,20,18,19,20}

Returns: 21267853416071168
60

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

{1,2,3,4,5,6,7,2,3,4,5,6,7,3,4,5,6,7,4,5,6,7,5,6,7,6,7,7,9,10,11,12,13,14,15,10,11,12,13,14,15,11,12,13,14,15,12,13,14,15,13,14,15,14,15,15,17,18,19,20}

Returns: 24083702694805504
60

{0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,6,6,7,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12}

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

Returns: 35404274414387200
60

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

{1,2,3,4,5,6,7,8,9,2,3,4,5,6,7,8,9,3,4,5,6,7,8,9,4,5,6,7,8,9,5,6,7,8,9,6,7,8,9,7,8,9,8,9,9,11,12,13,14,15,16,17,18,19,12,13,14,15,16,17}

Returns: 47534086692012032
60

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

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

Returns: 37717646879227904
60

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

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

Returns: 48413695994232832
60

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

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

Returns: 80924055804313600
60

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

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

Returns: 129619226775257088
60

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

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

Returns: 216524625834672128
60

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

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

Returns: 218530135043735552
60

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

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

Returns: 252254355690881024
60

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

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

Returns: 360353940887306240
60

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

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

Returns: 360716779724472320
60

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

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

Returns: 363668968445050880
60

{0,0,1,3,3,4,0,6,6,7,3,9,9,10,6,12,12,13,9,15,15,16,12,18,18,19,15,21,21,22,18,24,24,25,21,27,27,28,24,30,30,31,27,33,33,34,30,36,36,37,33,39,39,40,36,42,42,43,39,45}

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

Returns: 155568095557812224
60

{0,0,0,1,1,2,4,4,4,5,5,6,0,8,8,8,9,9,10,4,12,12,12,13,13,14,8,16,16,16,17,17,18,12,20,20,20,21,21,22,16,24,24,24,25,25,26,20,28,28,28,29,29,30,24,32,32,32,33,33}

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

Returns: 46752488224718848
60

{0,0,0,0,1,1,1,2,2,3,5,5,5,5,6,6,6,7,7,8,0,10,10,10,10,11,11,11,12,12,13,5,15,15,15,15,16,16,16,17,17,18,10,20,20,20,20,21,21,21,22,22,23,15,25,25,25,25,26,26}

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

Returns: 29273397577908224
60

{0,0,0,0,0,1,1,1,1,2,2,2,3,3,4,6,6,6,6,6,7,7,7,7,8,8,8,9,9,10,0,12,12,12,12,12,13,13,13,13,14,14,14,15,15,16,6,18,18,18,18,18,19,19,19,19,20,20,20,21}

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

Returns: 21220024660262912
60

{0,0,0,0,0,0,1,1,1,1,1,2,2,2,2,3,3,3,4,4,5,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12,0,14,14,14,14,14,14,15,15,15,15,15,16,16,16,16,17,17}

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

Returns: 22654887334510592
60

{0,0,1,3,3,4,0,6,6,7,3,9,9,10,0,12,12,13,3,15,15,16,9,18,18,19,9,21,21,22,9,24,24,25,3,27,27,28,18,30,30,31,6,33,33,34,21,36,36,37,3,39,39,40,3,42,42,43,21,45}

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

Returns: 155568095557812224
60

{0,0,0,1,1,2,4,4,4,5,5,6,0,8,8,8,9,9,10,4,12,12,12,13,13,14,0,16,16,16,17,17,18,8,20,20,20,21,21,22,0,24,24,24,25,25,26,0,28,28,28,29,29,30,24,32,32,32,33,33}

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

Returns: 46752488224718848
60

{0,0,0,0,1,1,1,2,2,3,5,5,5,5,6,6,6,7,7,8,0,10,10,10,10,11,11,11,12,12,13,0,15,15,15,15,16,16,16,17,17,18,10,20,20,20,20,21,21,21,22,22,23,5,25,25,25,25,26,26}

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

Returns: 29273397577908224
60

{0,0,0,0,0,1,1,1,1,2,2,2,3,3,4,6,6,6,6,6,7,7,7,7,8,8,8,9,9,10,0,12,12,12,12,12,13,13,13,13,14,14,14,15,15,16,6,18,18,18,18,18,19,19,19,19,20,20,20,21}

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

Returns: 21220024660262912
60

{0,0,0,0,0,0,1,1,1,1,1,2,2,2,2,3,3,3,4,4,5,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12,0,14,14,14,14,14,14,15,15,15,15,15,16,16,16,16,17,17}

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

Returns: 22654887334510592
60

{0,0,1,3,3,4,0,6,6,7,3,9,9,10,0,12,12,13,3,15,15,16,9,18,18,19,9,21,21,22,9,24,24,25,3,27,27,28,18,30,30,31,6,33,33,34,21,36,36,37,3,39,39,40,3,42,42,43,21,45}

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

Returns: 155568095557812224
60

{0,0,0,1,1,2,4,4,4,5,5,6,0,8,8,8,9,9,10,4,12,12,12,13,13,14,0,16,16,16,17,17,18,8,20,20,20,21,21,22,0,24,24,24,25,25,26,0,28,28,28,29,29,30,24,32,32,32,33,33}

{1,2,3,2,3,3,5,6,7,6,7,7,4,9,10,11,10,11,11,8,13,14,15,14,15,15,12,17,18,19,18,19,19,16,21,22,23,22,23,23,20,25,26,27,26,27,27,24,29,30,31,30,31,31,28,33,34,35,34,0}

Returns: 50348833472774144
60

{0,0,0,0,1,1,1,2,2,3,5,5,5,5,6,6,6,7,7,8,0,10,10,10,10,11,11,11,12,12,13,0,15,15,15,15,16,16,16,17,17,18,10,20,20,20,20,21,21,21,22,22,23,5,25,25,25,25,26,26}

{1,2,3,4,2,3,4,3,4,4,6,7,8,9,7,8,9,8,9,9,5,11,12,13,14,12,13,14,13,14,14,10,16,17,18,19,17,18,19,18,19,19,15,21,22,23,24,22,23,24,23,24,24,20,26,27,28,29,27,0}

Returns: 31525197391593472
60

{0,0,0,0,0,1,1,1,1,2,2,2,3,3,4,6,6,6,6,6,7,7,7,7,8,8,8,9,9,10,0,12,12,12,12,12,13,13,13,13,14,14,14,15,15,16,6,18,18,18,18,18,19,19,19,19,20,20,20,21}

{1,2,3,4,5,2,3,4,5,3,4,5,4,5,5,7,8,9,10,11,8,9,10,11,9,10,11,10,11,11,6,13,14,15,16,17,14,15,16,17,15,16,17,16,17,17,12,19,20,21,22,23,20,21,22,23,21,22,23,0}

Returns: 25610374589972480
60

{0,0,0,0,0,0,1,1,1,1,1,2,2,2,2,3,3,3,4,4,5,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12,0,14,14,14,14,14,14,15,15,15,15,15,16,16,16,16,17,17}

{1,2,3,4,5,6,2,3,4,5,6,3,4,5,6,4,5,6,5,6,6,8,9,10,11,12,13,9,10,11,12,13,10,11,12,13,11,12,13,12,13,13,7,15,16,17,18,19,20,16,17,18,19,20,17,18,19,20,18,0}

Returns: 25428955171389440
60

{0,0,1,3,3,4,0,0,6,6,7,3,3,9,9,10,6,6,12,12,13,9,9,15,15,16,12,12,18,18,19,15,15,21,21,22,18,18,24,24,25,21,21,27,27,28,24,24,30,30,31,27,27,33,33,34,30,30,36,36}

{1,2,2,4,5,5,3,4,7,8,8,6,7,10,11,11,9,10,13,14,14,12,13,16,17,17,15,16,19,20,20,18,19,22,23,23,21,22,25,26,26,24,25,28,29,29,27,28,31,32,32,30,31,34,35,35,33,34,37,38}

Returns: 122111830100279296
60

{0,0,0,1,1,2,4,4,4,5,5,6,0,0,8,8,8,9,9,10,4,4,12,12,12,13,13,14,8,8,16,16,16,17,17,18,12,12,20,20,20,21,21,22,16,16,24,24,24,25,25,26,20,20,28,28,28,29,29,30}

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

Returns: 47491088969105408
60

{0,0,0,0,1,1,1,2,2,3,5,5,5,5,6,6,6,7,7,8,0,0,10,10,10,10,11,11,11,12,12,13,5,5,15,15,15,15,16,16,16,17,17,18,10,10,20,20,20,20,21,21,21,22,22,23,15,15,25,25}

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

Returns: 33380176586866688
60

{0,0,0,0,0,1,1,1,1,2,2,2,3,3,4,6,6,6,6,6,7,7,7,7,8,8,8,9,9,10,0,0,12,12,12,12,12,13,13,13,13,14,14,14,15,15,16,6,6,18,18,18,18,18,19,19,19,19,20,20}

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

Returns: 26417828441620480
60

{0,0,0,0,0,0,1,1,1,1,1,2,2,2,2,3,3,3,4,4,5,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12,0,0,14,14,14,14,14,14,15,15,15,15,15,16,16,16,16,17}

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

Returns: 25217299183042560
29

{1,0,0,3,2,2,5,2,2,7,7,7,8,8,9,2,2,2,2,5,5,5,5,2,12,12,13,3,3,3,0,16,3,3,2,2,18,18,19,8,8,8,21,21,22,2,2,2,11,11,11,19,8,25,25,25,26,26,27,2}

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

Returns: 31397520
60

{0,0,1,2,2,3,1,1,5,6,6,7,4,4,9,6,6,11,0,0,13,9,9,15,14,14,17,8,8,19,9,9,21,4,4,23,13,13,25,24,24,27,8,8,29,16,16,31,21,21,33,8,8,35,31,31,37,5,5,39}

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

Returns: 121267495472988160
60

{0,0,1,0,0,3,1,1,5,0,0,7,2,2,9,3,3,11,4,4,13,6,6,15,16,16,17,16,16,19,14,14,21,15,15,23,4,4,25,3,3,27,16,16,29,14,14,31,3,3,33,27,27,35,31,31,37,0,0,39}

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

Returns: 128830589485711360
60

{0,0,1,0,0,3,2,2,5,0,0,7,6,6,9,2,2,11,0,0,13,5,5,15,16,16,17,2,2,19,10,10,21,7,7,23,23,23,25,4,4,27,21,21,29,18,18,31,28,28,33,2,2,35,27,27,37,7,7,39}

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

Returns: 127681404237512704
60

{0,0,1,2,2,3,4,4,5,6,6,7,8,8,9,10,10,11,12,12,13,14,14,15,16,16,17,18,18,19,20,20,21,22,22,23,24,24,25,26,26,27,28,28,29,30,30,31,32,32,33,34,34,35,36,36,37,38,38,39}

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

Returns: 111392341090631680
60

{0,0,1,0,0,3,0,0,5,0,0,7,0,0,9,0,0,11,0,0,13,0,0,15,0,0,17,0,0,19,0,0,21,0,0,23,0,0,25,0,0,27,0,0,29,0,0,31,0,0,33,0,0,35,0,0,37,0,0,39}

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

Returns: 578288831523454976
60

{0,0,1,1,2,0,2,2,3,2,5,2,5,2,5,1,2,0,4,0,10,2,4,4,12,2,7,5,8,2,14,2,7,5,15,1,2,0,4,2,17,3,5,2,5,2,16,0,11,2,16,11,25,2,4,0,4,2,19,4}

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

Returns: 251052864359628800
60

{0,0,1,1,2,0,1,0,1,0,2,1,2,0,1,0,6,6,9,6,10,6,10,1,2,6,11,6,14,6,14,2,13,2,6,9,10,6,16,1,8,1,3,0,5,0,9,6,12,2,7,0,23,2,26,26,28,8,21,1}

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

Returns: 174543347740835840
60

{0,0,1,0,2,0,1,2,3,1,4,0,1,0,2,1,7,2,3,0,7,0,8,1,9,1,6,0,4,0,7,0,4,1,14,0,1,0,12,0,16,0,17,3,5,0,8,1,13,3,23,0,2,7,11,1,7,1,13,1}

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

Returns: 231227570199199744
60

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

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

Returns: 864691128992006144
60

{0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,29}

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

Returns: 97709218030682112
60

{0,0,1,0,1,2,2,4,0,3,3,3,7,3,8,5,5,10,0,0,12,5,10,0,12,7,7,16,2,2,18,4,4,20,10,10,22,16,17,8,8,25,19,19,27,1,3,21,21,30,8,9,11,11,33,14,14,35,3,3}

{1,2,2,3,3,4,5,5,6,6,7,8,8,9,9,10,11,11,12,13,13,14,14,15,15,16,17,17,18,19,19,20,21,21,22,23,23,24,24,25,26,26,27,28,28,29,29,30,31,31,32,32,33,34,34,35,36,36,37,38}

Returns: 129492398270054400
60

{31,0,31,1,31,2,31,3,31,4,31,5,31,6,31,7,31,8,31,9,31,10,31,11,31,12,31,13,31,14,31,15,31,16,31,17,31,18,31,19,31,20,31,21,31,22,31,23,31,24,31,25,31,26,31,27,31,28,31,29}

{0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,29,0}

Returns: 577459599561457664
60

{0,2,3,0,2,4,6,7,4,6,8,10,11,8,10,12,14,15,12,14,16,18,19,16,18,20,22,23,20,22,24,26,27,24,26,28,30,31,28,30,32,34,35,32,34,36,38,39,36,38,40,42,43,40,42,44,46,47,44,46}

{1,1,1,3,3,5,5,5,7,7,9,9,9,11,11,13,13,13,15,15,17,17,17,19,19,21,21,21,23,23,25,25,25,27,27,29,29,29,31,31,33,33,33,35,35,37,37,37,39,39,41,41,41,43,43,45,45,45,47,47}

Returns: 95428956661682176
60

{0,2,2,3,3,3,5,5,6,6,6,8,8,9,9,9,11,11,12,12,12,14,14,15,15,15,17,17,18,18,18,20,20,21,21,21,23,23,24,24,24,26,26,27,27,27,29,29,30,30,30,32,32,33,33,33,35,35,36,36}

{1,1,0,1,2,4,4,3,4,5,7,7,6,7,8,10,10,9,10,11,13,13,12,13,14,16,16,15,16,17,19,19,18,19,20,22,22,21,22,23,25,25,24,25,26,28,28,27,28,29,31,31,30,31,32,34,34,33,34,35}

Returns: 102279555426811904
60

{0,0,2,2,3,4,4,0,3,5,5,7,7,8,9,9,5,8,10,10,12,12,13,14,14,10,13,15,15,17,17,18,19,19,15,18,20,20,22,22,23,24,24,20,23,25,25,27,27,28,29,29,25,28,30,32,30,32,32,31}

{1,3,1,3,1,1,3,5,5,6,8,6,8,6,6,8,10,10,11,13,11,13,11,11,13,15,15,16,18,16,18,16,16,18,20,20,21,23,21,23,21,21,23,25,25,26,28,26,28,26,26,28,30,30,31,31,32,1,0,0}

Returns: 131051176253718528
60

{0,0,0,4,4,4,5,5,5,9,9,9,10,10,10,14,14,14,15,15,15,19,19,19,20,20,20,24,24,24,25,25,25,29,29,29,30,30,30,34,34,34,35,35,35,39,39,39,40,40,40,44,44,44,45,45,45,49,49,49}

{1,2,3,1,2,3,6,7,8,6,7,8,11,12,13,11,12,13,16,17,18,16,17,18,21,22,23,21,22,23,26,27,28,26,27,28,31,32,33,31,32,33,36,37,38,36,37,38,41,42,43,41,42,43,46,47,48,46,47,48}

Returns: 1152921504606846976
60

{0,0,1,0,0,3,0,0,5,0,0,7,0,0,9,0,0,11,0,0,13,0,0,15,0,0,17,0,0,19,0,0,21,0,0,23,0,0,25,0,0,27,0,0,29,5,2,23,5,20,27,26,22,19,18,13,15,12,7,9}

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

Returns: 578333426763956224
60

{0,0,1,0,0,3,0,0,5,0,0,7,0,0,9,0,0,11,0,0,13,0,0,15,0,0,17,0,0,19,0,0,21,0,0,23,0,0,25,0,0,27,0,0,29,10,20,4,28,5,11,7,9,5,8,30,5,2,13,4}

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

Returns: 451892312578981888
60

{0,0,1,0,0,3,0,0,5,0,0,7,0,0,9,0,0,11,0,0,13,0,0,15,0,0,17,0,0,19,0,0,21,0,0,23,0,0,25,0,0,27,0,0,29,11,8,26,4,14,21,23,28,25,15,19,14,26,19,2}

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

Returns: 578017309654777856
60

{0,0,0,1,1,1,2,2,2,3,3,3,4,4,4,5,6,6,6,7,7,7,8,8,8,9,9,9,10,10,10,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,18,19,20,21,22,6,7,8,9,10,12,13}

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

Returns: 81310534141476864
60

{0,0,0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9,10,10,10,11,11,11,12,13,14,15,16,17,18,19,20,21,22,23,24,13,14,15,16,17,18,19,20,21,22,23}

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

Returns: 57718003906641920
60

{0,1,2,3,5,5,6,6,7,7,8,8,10,10,11,11,12,12,13,13,15,15,16,16,17,17,18,18,20,21,22,23,0,0,1,1,2,2,3,3,4,5,5,6,6,7,7,8,8,9,10,10,11,11,12,12,13,13,14,15}

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

Returns: 121405874915770368
60

{0,1,2,3,4,6,6,7,7,8,8,9,9,10,10,12,12,13,13,14,14,15,15,16,16,18,19,20,21,22,0,0,1,1,2,2,3,3,4,4,5,6,6,7,7,8,8,9,9,10,10,11,12,12,13,13,14,14,15,15}

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

Returns: 108055604731314176
60

{0,0,1,1,1,2,2,3,3,3,4,4,4,5,5,6,6,6,7,7,7,8,8,8,9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,15,16,17,18,19,15,16,16,17,17,18,18,19,19,20,21,22,23,24,21}

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

Returns: 99489429898395648
60

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

{0,2,0,1,4,1,2,6,2,3,8,3,4,10,4,5,12,5,6,14,6,7,16,7,8,18,8,9,20,9,10,22,10,11,24,11,12,26,12,13,28,13,14,30,14,15,32,15,16,34,16,17,36,17,18,38,18,19,40,19}

Returns: 109452255607914496
60

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

{0,2,0,1,4,1,2,6,2,3,8,3,4,10,4,5,12,5,6,14,6,7,16,7,8,18,8,9,20,9,10,22,10,11,24,11,12,26,12,13,28,13,14,30,14,15,32,15,16,34,16,17,36,17,18,38,18,0,40,0}

Returns: 109200548880711680
60

{}

{}

Returns: 1152921504606846976
60

{0,0,2,2,4,4,6,6,8,8,10,10,12,12,14,14,16,16,18,18,20,20,22,22,24,24,26,26,28,28,30,30,32,32,34,34,36,36,38,38,40,40,42,42,44,44,46,46,48,48,50,50,52,52,54,54,56,56,58,58}

{2,4,4,6,6,8,8,10,10,12,12,14,14,16,16,18,18,20,20,22,22,24,24,26,26,28,28,30,30,32,32,34,34,36,36,38,38,40,40,42,42,44,44,46,46,48,48,50,50,52,52,54,54,56,56,58,58,59,59,57}

Returns: 97709218030682112
60

{0,0,30,30,1,1,31,31,2,2,32,32,3,3,33,33,4,4,34,34,5,5,35,35,6,6,36,36,7,7,37,37,8,8,38,38,9,9,39,39,10,10,40,40,11,11,41,41,12,12,42,42,13,13,43,43,14,14,44,44}

{30,1,1,31,31,2,2,32,32,3,3,33,33,4,4,34,34,5,5,35,35,6,6,36,36,7,7,37,37,8,8,38,38,9,9,39,39,10,10,40,40,11,11,41,41,12,12,42,42,13,13,43,43,14,14,44,44,15,15,45}

Returns: 97709218030682112
60

{0,2,2,3,3,5,5,6,6,8,8,9,9,11,11,12,12,14,14,15,15,17,17,18,18,20,20,21,21,23,23,24,24,26,26,27,27,29,29,30,30,32,32,33,33,35,35,36,36,38,38,39,39,41,41,42,42,44,44,45}

{1,1,0,0,4,4,3,3,7,7,6,6,10,10,9,9,13,13,12,12,16,16,15,15,19,19,18,18,22,22,21,21,25,25,24,24,28,28,27,27,31,31,30,30,34,34,33,33,37,37,36,36,40,40,39,39,43,43,42,42}

Returns: 155568095557812224
60

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

{1,1,0,3,4,4,3,6,7,7,6,9,10,10,9,12,13,13,12,15,16,16,15,18,19,19,18,21,22,22,21,24,25,25,24,27,28,28,27,30,31,31,30,33,34,34,33,36,37,37,36,39,40,40,39,42,43,43,42,45}

Returns: 155568095557812224
60

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

{1,1,0,3,4,4,3,6,7,7,6,9,10,10,9,12,13,13,12,15,16,16,15,18,19,19,18,21,22,22,21,24,25,25,24,27,28,28,27,30,31,31,30,33,34,34,33,36,37,37,36,39,40,40,39,42,43,43,42,43}

Returns: 155568095557812224
1

{}

{}

Returns: 2
2

{}

{}

Returns: 4
2

{0}

{1}

Returns: 4
60

{0, 0, 1, 0, 0, 3, 0, 0, 5, 0, 0, 7, 0, 0, 9, 0, 0, 11, 0, 0, 13, 0, 0, 15, 0, 0, 17, 0, 0, 19, 0, 0, 21, 0, 0, 23, 0, 0, 25, 0, 0, 27, 0, 0, 29, 5, 2, 23, 5, 20, 27, 26, 22, 19, 18, 13, 15, 12, 7, 9 }

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

Returns: 578333426763956224
60

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

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

Returns: 577695395413491712

Statistics

Problem Statement for "TriangleFree"

Problem Statement

Definition

Constraints

Examples