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
#coding:utf-8
import sys
sys.setrecursionlimit(10**6)
write = sys.stdout.write
dbg = lambda *something : print(*something) if DEBUG else 0
DEBUG = False
def main(given = sys.stdin.readline):
    input = lambda : given().rstrip()
    LMIIS = lambda : list(map(int,input().split()))
    II = lambda : int(input())
    XLMIIS = lambda x : [LMIIS() for _ in range(x)]
    MOD = 10**9+7
    from math import factorial
    N = II()
    X = LMIIS()
    f = factorial(N-1) % MOD
    def calc(k,slimes):
        r = 0
        for k in range(N-1):
            r += (slimes[-1]-slimes[-2-k]) * f * pow((N-k-1),MOD-2,MOD)
            r %= MOD
        return r
    print(calc(0,X))


if __name__ == '__main__':
    main()