Given an array perm of length n representing a permutation of the integers from $1$ to n, return the $0$ based index of perm in the lexicographically sorted list of all permutations of $[1, 2, \dots,$ n$]$.

Constraints:

• $1 \leq$ n $==$ perm.length $\leq 10^5$

• perm is a permutation of $[1, 2, \dots,$ n$]$.

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