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
#include<iostream>
#include<cstdio>

using namespace std;

inline int read()
{
	int f = 1,x = 0;
	char ch;
	do
	{
		ch = getchar();
		if(ch == '-') f = -1;
	}while(ch < '0' || ch > '9');
	do
	{
		x = (x<<3) + (x<<1) + ch - '0';
		ch = getchar();
	}while(ch>='0'&&ch<='9');
	return f*x;
}

const int MAXN = 100000 + 10;
const int MOD = 1e9 + 7;

inline long long Pow(long long a,long long b)
{
	long long  ans = 1,mul = a;
	while(b)
	{
		if(b&1) ans = (ans * mul) % MOD;
		mul = (mul *mul)%MOD;
		b>>=1;	
	}
	return ans;
}

int n;
long long a[MAXN],x[MAXN];
long long inv[MAXN];

int main()
{
	n = read();
	for(register int i=1;i<=n;i++) a[i] = read();
	for(register int i=1;i<n;i++) x[i] = a[i+1] - a[i];
	for(register int i=1;i<=n;i++) inv[i] = (inv[i-1] + Pow(i,MOD-2))%MOD;
	long long ans = 0;
	for(register int i=1;i<n;i++) ans = (ans + x[i]*inv[i]%MOD)%MOD;
	for(register int i=1;i<n;i++) ans = (ans * i)%MOD;
	cout<<ans<<endl;
}