You have been two integers n and m where n is the size of the array and m is the number of the edges. The next line contains an array of size n and next m lines contains two integers x and y each which represents that there exists a bidirectional edge between x and y. We have to output the number of permutations of the array which are lucky. A permutation is said to be lucky if for every Vi in the array there exists an edge between Vi and Vi+1.

I/p: 3 2 1 2 3

1 2

2 3

o/p:

2(1-2-3 and 3-2-1)