D. On Sum of Number of Inversions in Permutations
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a permutation p. Calculate the total number of inversions in all permutations that lexicographically do not exceed the given one.

As this number can be very large, print it modulo 1000000007 (109 + 7).

Input

The first line contains a single integer n (1 ≤ n ≤ 106) — the length of the permutation. The second line contains n distinct integers p1, p2, ..., pn (1 ≤ pi ≤ n).

Output

Print a single number — the answer to the problem modulo 1000000007 (109 + 7).

Examples
Input
22 1
Output
1
Input
32 1 3
Output
2
Note

Permutation p of length n is the sequence that consists of n distinct integers, each of them is from 1 to n.

An inversion of permutation p1, p2, ..., pn is a pair of indexes (i, j), such that i < j and pi > pj.

Permutation a do not exceed permutation b lexicographically, if either a = b or there exists such number i, for which the following logical condition fulfills: AND (ai < bi).