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

readline = sys.stdin.readline
MOD = 10 ** 9 + 7
INF = float('INF')
sys.setrecursionlimit(10 ** 5)


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

    mul_mod = [0] * N

    cur = 1
    for i in range(1, N):
        cur *= i
        cur %= MOD
    mul_mod[1] = cur

    for i in range(2, N):
        mul_mod[i] = (mul_mod[1] * pow(i, MOD - 2, MOD)) % MOD

    p = [0] * (N - 1)
    p[-1] = sum(mul_mod[1:N]) % MOD

    for i in range(2, N):
        p[-i] = p[-i + 1] - mul_mod[N - i + 1]
        p[-i] %= MOD

    ans = 0

    for i in range(N - 1):
        ans += (X[i + 1] - X[i]) * p[i]
        ans %= MOD

    print(ans)


if __name__ == '__main__':
    main()
