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>
using namespace std;
inline long long int modadd(long long int n, long long int m,
                            long long int p = 1000000007) {
  return ((n + m) % p + p) % p;
}
inline long long int modsub(long long int n, long long int m,
                            long long int p = 1000000007) {
  return ((n - m + p) % p + p) % p;
}
inline long long int modpro(long long int n, long long int m,
                            long long int p = 1000000007) {
  return (((n % p) * (m % p)) % p + p) % p;
}
unsigned long long int powe(long long int first, long long int second) {
  unsigned long long int res = 1;
  while (second > 0) {
    if (second & 1) res = res * first;
    second = second >> 1;
    first = first * first;
  }
  return res;
}
long long int modpow(long long int first, long long int second,
                     long long int p = 1000000007) {
  long long int res = 1;
  while (second > 0) {
    if (second & 1) res = modpro(res, first, p);
    second = second >> 1;
    first = modpro(first, first, p);
  }
  return res;
}
inline long long int modInverse(long long int n, long long int p = 1000000007) {
  if (n == 1) return 1;
  return modpow(n, p - 2, p);
}
inline long long int moddiv(long long int n, long long int m,
                            long long int p = 1000000007) {
  return modpro(n, modInverse(m, p), p);
}
inline long long int modadd3(long long int first, long long int second,
                             long long int z, long long int p = 1000000007) {
  return modadd(modadd(first, second, p), z, p);
}
inline long long int modadd4(long long int first, long long int second,
                             long long int z, long long int w,
                             long long int p = 1000000007) {
  return modadd(modadd(first, second, p), modadd(z, w, p), p);
}
inline long long int modnCr(long long int fac[], int n, int r,
                            long long int p = 1000000007) {
  if (r == 0) return 1;
  return modpro(fac[n], modInverse(modpro(fac[r], fac[n - r], p), p), p);
}
template <typename T>
inline T max3(T first, T second, T z) {
  return max(max(first, second), z);
}
template <typename T>
inline T max4(T first, T second, T z, T w) {
  return max(max3(first, second, w), z);
}
template <typename T>
inline T min3(T first, T second, T z) {
  return min(min(first, second), z);
}
template <typename T>
inline T min4(T first, T second, T z, T w) {
  return min(min3(first, second, w), z);
}
template <typename T>
void printArr(T *arr, int s, int n) {
  for (int i = s; i <= n; i++) {
    cout << arr[i] << " ";
  }
  cout << endl;
}
long long int fac_[1000005];
void fac_init(int n) {
  fac_[0] = 1;
  for (int i = (1); i < (n + 1); i++) fac_[i] = modpro(fac_[i - 1], i);
}
int a[1000005];
int cn[1000005];
int main() {
  std::ios::sync_with_stdio(false);
  cin.tie(NULL);
  int erer = 1;
  for (int erer2 = (1); erer2 < (erer + 1); erer2++) {
    int n;
    cin >> n;
    fac_init(n + 1);
    for (int i = (0); i < (n); i++) cin >> a[i];
    sort(a, a + n);
    cn[0] = 0;
    int hm = 1;
    for (int i = (1); i < (n); i++) {
      if (a[i] == a[i - 1]) {
        cn[i] = cn[i - 1];
        hm++;
      } else {
        cn[i] = cn[i - 1] + hm;
        hm = 1;
      }
    }
    long long int ans = 0;
    for (int i = (0); i < (n - 1); i++) {
      if (a[i] == a[n - 1]) break;
      long long int temp = modpro(a[i], modpro(fac_[n], modInverse(n - cn[i])));
      ans = modadd(ans, temp);
    }
    cout << ans << endl;
  }
  return 0;
}
