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
MOD = 10**9 + 7

def MOD_perm(n, r):
    rtn = 1
    for _ in range(r):
        rtn *= n
        rtn %= MOD
        n -= 1
    return rtn

def MOD_inv(a):
    b = MOD
    u = 1
    v = 0
    while b > 0:
        t = a // b
        a -= t * b
        a, b = b, a
        u -= t * v
        u, v = v, u
    u = u % MOD
    if u < 0:
        u += MOD
    return u

def main():
    n = int(input())
    x = list(map(int, input().split()))
    ans = 0
    inv = 0
    perm = MOD_perm(n-1, n-1)
    for i in range(1, n):
        dif = x[i] - x[i-1]
        inv += MOD_inv(i)
        inv %= MOD
        ans += dif * perm * inv
        ans %= MOD
    print(ans % MOD)

if __name__ == "__main__":
    main()