There are N slimes standing on a number line. The i-th slime from the left is at position x_i.

It is guaruanteed that 1 \leq x_1 < x_2 < \ldots < x_N \leq 10^{9}.

Niwango will perform N-1 operations. The i-th operation consists of the following procedures:

* Choose an integer k between 1 and N-i (inclusive) with equal probability.
* Move the k-th slime from the left, to the position of the neighboring slime to the right.
* Fuse the two slimes at the same position into one slime.



Find the total distance traveled by the slimes multiplied by (N-1)! (we can show that this value is an integer), modulo (10^{9}+7). If a slime is born by a fuse and that slime moves, we count it as just one slime.

Constraints

* 2 \leq N \leq 10^{5}
* 1 \leq x_1 < x_2 < \ldots < x_N \leq 10^{9}
* x_i is an integer.

Input

Input is given from Standard Input in the following format:


N
x_1 x_2 \ldots x_N


Output

Print the answer.

Examples

Input

3
1 2 3


Output

5


Input

12
161735902 211047202 430302156 450968417 628894325 707723857 731963982 822804784 880895728 923078537 971407775 982631932


Output

750927044
import java.io.*;
import java.util.*;

class Main {

	static final int M = 1000000007;


	private static long pow(long x, long n) {
		if (x == 0) return 0;
		long a = 1;
		while (n > 0) {
			if (n % 2 == 1) {
				a = a * x % M;
			}
			x = x * x % M;
			n >>= 1;
		}
		return a;
	}

	private static long inv(long x, long M) {
		return pow(x, M - 2);
	}

	public static void main(String[] args) throws Exception {
		final Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		long[] x = new long[N];
		for (int i = 0; i < N; i++) {
			x[i] = sc.nextLong();
		}

		long[] fact = new long[N];
		fact[0] = 1;
		for (int i = 1; i < N; i++) {
			fact[i] = fact[i - 1] * i % M;
		}

		long a = 0;
		long c = 0;
		for (int i = 0; i < N - 1; i++) {
			c = (c + fact[N - 1] * inv(i + 1, M) % M) % M;
			long d = x[i + 1] - x[i];
			a = (a + c * d % M) % M;
		}

		System.out.println(a);
	}
}
