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.
import java.util.*;
import java.io.*;

public class E938 {
	static int mod = (int) 1e9 + 7;

	public static long modPow(long a, long e) {
		long res = 1;
		while (e > 0) {
			if ((e & 1) != 0) {
				res = (res * a) % mod;
			}
			a = (a * a) % mod;
			e >>= 1;
		}
		return res;
	}

	public static long modInv(long x) {
		return modPow(x, mod - 2);
	}

	public static void shuffle(int[] arr) {
		for (int i = 0; i < arr.length; i++) {
			int rand = (int) (Math.random() * arr.length);
			int temp = arr[rand];
			arr[rand] = arr[i];
			arr[i] = temp;
		}
	}

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int n = sc.nextInt();
		int[] arr = sc.nextIntArr(n);
		shuffle(arr);
		Arrays.sort(arr);
		int max = arr[n - 1];

		long facn = 1;
		for (int i = 1; i <= n; i++) {
			facn = (facn * i) % mod;
		}
		int l = 0;
		long ans = 0;
		for (int i = 0; i < n; i++) {
			if (arr[i] == max)
				break;
			if (i == 0 || arr[i] != arr[i - 1]) {
				l = i;
			}
			int g = n - 1 - l;

			ans += arr[i] * facn % mod * modInv(g + 1) % mod;
			ans %= mod;
		}
		pw.println(ans);
		pw.close();

	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader f) {
			br = new BufferedReader(f);
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public int[] nextIntArr(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = Integer.parseInt(next());
			}
			return arr;
		}

	}

}
