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.
#include <bits/stdc++.h>
const long long MOD = 1e9 + 7;
const int ms = 2e6 + 10;
long long fexp(long long x, long long e) {
  long long ans = 1;
  for (; e > 0; e /= 2) {
    if (e & 1) {
      ans = ans * x % MOD;
    }
    x = x * x % MOD;
  }
  return ans;
}
long long fat[ms], ifat[ms];
int a[ms];
int p[ms];
long long comb(int n, int k) {
  return fat[n] * ifat[k] % MOD * ifat[n - k] % MOD;
}
int main() {
  srand(time(0));
  fat[0] = 1;
  for (int i = 1; i < ms; i++) {
    fat[i] = fat[i - 1] * i % MOD;
    ifat[i] = fexp(fat[i], MOD - 2);
  }
  ifat[0] = 1;
  int n;
  std::cin >> n;
  std::map<int, int> freq;
  for (int i = 0; i < n; i++) {
    int temp;
    scanf("%lli", &temp);
    freq[temp]++;
    p[i] = i;
    a[i] = temp;
  }
  int lesser = 0;
  long long ans = 0;
  for (auto a : freq) {
    int greater = n - lesser - a.second;
    if (greater != 0) {
      long long count = fat[lesser] * fat[n - lesser - 1] % MOD;
      count = count * a.first % MOD;
      count = count * a.second % MOD;
      count = count * comb(n, lesser);
      ans = (ans + count) % MOD;
    }
    lesser += a.second;
  }
  std::cout << ans << '\n';
}
