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 tr0 {
	static PrintWriter out;
	static StringBuilder sb;
	static int mod = 1000000007;
	static long inf = (long) 1e18 + 1;
	static int[] col;
	static int n, m;
	static ArrayList<pair>[] ad;
	static Boolean[][] memo;
	static HashSet<Integer> h;
	static int[] a;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		n = sc.nextInt();
		long[] fac = new long[n + 1];
		fac[0] = 1;
		long[] invfac = new long[n + 1];
		invfac[0] = modPow(1, mod - 2);
		for (int i = 1; i < fac.length; i++) {
			fac[i] = i * 1l * fac[i - 1] % mod;
			invfac[i] = modPow(i, mod - 2);
		}
		Integer[] a = new Integer[n];
		for (int i = 0; i < n; i++)
			a[i] = sc.nextInt();
		Arrays.sort(a);
		TreeMap<Integer, Integer> hm = new TreeMap<>();
		TreeMap<Integer, Integer> hk = new TreeMap<>();
		for (int i = 0; i < n; i++) {
			hm.put(a[i], hm.getOrDefault(a[i], 0) + 1);
			hk.put(a[i], i);
		}
		int[] l = new int[n];
		for (int i = 0; i < n; i++)
			l[i] = hk.get(a[i]) + 1 - hm.get(a[i]);
		long ans = 0;
		for (int i = 0; i < n; i++)
			if (a[i] == hm.lastKey())
				break;
			else {
				ans = (ans + (a[i] * fac[n] % mod) * invfac[n - l[i]] % mod);
				if (ans >= mod)
					ans -= mod;
			}
		System.out.println(ans);
		out.flush();
	}

	static long modPow(long a, long e)

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

	static class pair implements Comparable<pair> {
		int to;
		long number;

		pair(int t, long n) {
			number = n;
			to = t;
		}

		public String toString() {
			return to + " " + number;
		}

		@Override
		public int compareTo(pair o) {
			return Long.compare(number, o.number);
		}

	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

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

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

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

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

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

		public int[] nextArrInt(int n) throws IOException {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextArrLong(int n) throws IOException {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}