Given an integer n, consider a $1$ indexed array nums representing a permutation of the integers from $1$ to n.

A permutation nums is defined as self divisible if $\gcd($nums[i], i$) = 1$ for every index i satisfying $1 \le$ i $\le$ n, where $\gcd(a, b)$ denotes the greatest common divisor of $a$ and $b$.

Return the total number of self divisible permutations of length n.

Constraints:

• $1 \le$ n $\le 12$

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