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 sys
sys.setrecursionlimit(10000000)
MOD = 10 ** 9 + 7
INF = 10 ** 15

def main():
    N = int(input())
    X = list(map(int,input().split()))

    ans = 0
    fact = [1]
    for i in range(1,N):
        fact.append(fact[-1]*i%MOD)
    inv_fact = [1] * N
    inv_fact[-1] = pow(fact[N - 1],MOD - 2,MOD)
    for i in range(N - 1,0,-1):
        inv_fact[i - 1] = inv_fact[i]*i%MOD
    
    cum = 0
    for i in range(N - 1):
        cum += fact[N - 1] * inv_fact[i + 1] * fact[i] % MOD
        cum %= MOD
        ans += cum * (X[i + 1] - X[i])
        ans %= MOD
    print(ans)
if __name__ == '__main__':
    main()