Description

A N long sequence made up of { 1,2,3, ... , N} have N! different permutations. For example , while N=3 {1,2,3}, there are 6 permutations. Sorting them by lexicographic order,they would be（1）123, （2）132,（3）213,（4）231,（5）312,（6）321. Now , give you a sequence make up of {1,2,3, ... , N}. Can you calculate its lexicographic index(1-based).

Input

Multiple cases. For each case, first line is an integer N (1<=N<=100000), secend line contains N different integers,{ A1,A2, ... An},(1<=Ai<=N).

Output

Output its lexicographic order on a single line for each case. To make this problem easy, just output the result module 9973.

Sample

Input

3
1 2 3
4
4 2 1 3

Output

1
21

Source: MoonLight