Description

Prequel: see Luogu P2525.

Uim successfully delivered gifts to $N$ girls in some order and maintained their harmony.

Now Uim wants to know the lexicographic rank of the final order he chose among all gift-giving orders for $N$ girls. The order can be viewed as a permutation of $1,2,\cdots,N$.

Input Format

The first line contains an integer $N$.

The second line contains an integer $X$, representing the given permutation.

Output Format

Output a single integer, indicating its position in lexicographic order.

3
231

4

Hint

$1\le N \le 9$.

Please note that the permutation in the input has no spaces.

Translated by ChatGPT 5