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
# 部分点

def main():
    from functools import reduce

    MOD = 10 ** 9 + 7

    n = int(input())
    *x, r = map(int, input().split())

    dist_to_r_edge = [r - x_ for x_ in x]

    ret = reduce(
        lambda a, b: (a + b) % MOD,
        (
            d * pow(i, MOD - 2, MOD)
            for i, d in enumerate(dist_to_r_edge, 1)
        )
    )

    f = 1
    for i in range(1, n):
        f = (f * i) % MOD

    print(ret * f % MOD)


if __name__ == '__main__':
    main()
