want help in discuss
mutations
Problem Description
Mr. X is teaching number theory in his class. He is discussing about factors and permutations in his class. A factor of a positive integer N is a positive integer that divides n precisely (without leaving a remainder). The set of factors always includes 1 and N.

Mr. X likes combinatorics a lot. He asked his students find out all the factors of the number Y, and sort them in an ascending order. He asks them to list all permutations of the factors. They then need to cross out all permutations where two adjacent numbers are adjacent in the same order in the original list. The number of uncrossed (valid) permutations are to be given to him.

Illustration:

Integer 9 has 3 factors [1,3,9].

The permutations of these factors of number 9 are [1,3,9],[1,9,3],[3,9,1],[3,1,9],[9,1,3],[9,3,1].

Of these 6 permutations, we need to cross out [1,3,9] (1 3 adjacent in same order), [3,9,1] (3 9 in same order) and[9,1,3] (1 3 in same order)

The remaining (valid) permutations are:

[1,9,3] ,[9,3,1],[3,1,9]

Hence the number of valid permutations =3, which is the answer.