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.*;
import java.io.*;

// This file is a "Hello, world!" in Java language by OpenJDK for wandbox.

class Main
{
    public static void main(String[] args)
    {
        new Main().run();
    }
	
	final long MOD=(long)(1e9+7);

	long pow(long a,long n){
		long ret=1;
		for(;n>0;n>>=1,a=a*a%MOD)if(n%2==1)ret=ret*a%MOD;
		return ret;
	}
	
	long inv(long a){
		return a==0?1:pow(a,MOD-2);
	}
	
	int MAX=(int)(3e5);
	long[] fac=new long[MAX];
	{
		fac[0]=fac[1]=1;
		for(int i=2;i<fac.length;++i)fac[i]=fac[i-1]*i%MOD;
	}
	
	void run(){
        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 cur=0;
		long ans=0;
		for(int i=0;i<N-1;++i){
			cur+=fac[N-1]*inv(i+1)%MOD;
			cur%=MOD;
			ans+=cur*(x[i+1]-x[i])%MOD;
			ans%=MOD;
		}
		System.out.println(ans);
    }
	
	void tr(Object...o){
		System.out.println(Arrays.deepToString(o));
	}
}
// OpenJDK reference:
//   http://openjdk.java.net/

// Java language references:
//   http://docs.oracle.com/javase
