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.util.*;

class Main{
    public static void main(String[] args){
        long mod=1_000_000_007l;
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        long[] x=new long[n+1];
        for(int i=1;i<=n;x[i++]=sc.nextLong());
        sc.close();
        long ans=0;
        for(int i=1;i<n;i++){
            ans+=((x[n]-x[i])*modinv(i, mod))%mod;
        }
        ans%=mod;
        for(int i=2;i<n;ans=(ans*i++)%mod);
        System.out.println(ans);
    }
    static long modinv(long a, long mod) {
        long b = mod;
        long u = 1, v = 0;
        while (b >= 1) {
            long t = a / b;
            a -= t * b;
            long tmp1 = a;
            a = b;
            b = tmp1;
            u -= t * v;
            long tmp2 = u;
            u = v;
            v = tmp2;
        }
        u %= mod;
        return u >= 0 ? u : u + mod;
    }
}
