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 <bits/stdc++.h>
using namespace std;

#define For(i,a,b) for(int (i) = (a);(i) < (b);i++)
#define Rep(i,n) For((i),0,(n))
#define All(a) (a).begin(),(a).end()
#define sp " "
#define INF 1e18
#define INT_INF 1e9

typedef long long ll;
const ll MOD = 1000000007;
const ll MOD_9 = 998244353;

int main(){
    ll N;
    cin >> N;
    ll bikkuri[N+1];
    bikkuri[0] = 1;
    ll x[N];
    ll d[N];
    ll t,ans;
    Rep(i,N){
        bikkuri[i+1] = bikkuri[i]*(i+1);
        bikkuri[i+1] %= MOD;
        cin >> x[i];
        if(i != 0)d[i-1] = x[i]-x[i-1];
    }
    t = 0;
    ans = 0;
    Rep(i,N-1){
        ans *= i+1;
        ans %= MOD;
        t = t*(i+1) + bikkuri[i];
        t %= MOD;
        ans += t*d[i];
        ans %= MOD;
        //cout << t << ans << endl;
    }
    cout << ans << endl;
    //cin >> N;
}