Max History
Description
You are given an array a of length n. We define fa the following way:
- Initially fa = 0, M = 1;
- for every 2 ≤ i ≤ n if aM < ai then we set fa = fa + aM and then set M = i.
Calculate the sum of fa over all n! permutations of the array a modulo 109 + 7.
Note: two elements are considered different if their indices differ, so for every array a there are exactly n! permutations.
The first line contains integer n (1 ≤ n ≤ 1 000 000) — the size of array a.
Second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109).
Print the only integer, the sum of fa over all n! permutations of the array a modulo 109 + 7.
Input
The first line contains integer n (1 ≤ n ≤ 1 000 000) — the size of array a.
Second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109).
Output
Print the only integer, the sum of fa over all n! permutations of the array a modulo 109 + 7.
Samples
2
1 3
1
3
1 1 2
4
Note
For the second example all the permutations are:
- p = [1, 2, 3] : fa is equal to 1;
- p = [1, 3, 2] : fa is equal to 1;
- p = [2, 1, 3] : fa is equal to 1;
- p = [2, 3, 1] : fa is equal to 1;
- p = [3, 1, 2] : fa is equal to 0;
- p = [3, 2, 1] : fa is equal to 0.
Where p is the array of the indices of initial array a. The sum of fa is equal to 4.