Please subscribe to the official Codeforces channel in Telegram via the link: https://t.me/codeforces_official. ×

E. Max History
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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.

Examples
Input
2
1 3
Output
1
Input
3
1 1 2
Output
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.