Coding of Permutations

A permutation $P=(p_1, p_2, \ldots, p_n)$ uses each integer from $1$ to $n$ exactly once. List every permutation of length $n$ in lexicographic order and let $d(P)$ be the position of $P$ in that list. The first one, $(1, 2, \ldots, n)$, has number $1$.

Write a program that computes $d(P)$ without generating all permutations of length $n$. Here $n$ is at most $50$.

For $n=4$, the permutations in lexicographic order and their numbers are shown below.

If $P=(2,3,4,1)$ then $d(P)=10$, and if $P=(4,2,1,3)$ then $d(P)=21$.

The input has several lines. Each line holds one query in the form $(n,(p_1,p_2,\ldots,p_n))$ and contains no spaces. The last line holds only $-1$, and the input ends there. At least one query is given.

Print $d(P)$ for every query on a single line, in the order the queries are given. Separate two values with one comma, and put no space before or after the comma.