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

MOD = 10 ** 9 + 7

def make_table(size=10**6, p=MOD):
    fac = [None] * (size + 1)
    fac[0] = 1
    for i in range(size):
        fac[i+1] = fac[i] * (i + 1) % p
    ifac = [None] * (size + 1)
    ifac[size] = pow(fac[size], p-2, p)
    for i in range(size, 0, -1):
        ifac[i-1] = ifac[i] * i % p
    icumsum = [None] * (size + 1)
    icumsum[1] = 1
    for i in range(1, size):
        icumsum[i+1] = (icumsum[i] + fac[i] * ifac[i+1]) % p
    return fac, ifac, icumsum

fac, ifac, icumsum = make_table(10**5)

n, *x = map(int, sys.stdin.read().split())

def main():
    d = [x[i+1] - x[i] for i in range(n-1)]

    res = 0
    for i in range(n-1):
        res += d[i] * icumsum[i+1]
        res %= MOD

    return res * fac[n-1] % MOD

if __name__ == '__main__':
    ans = main()
    print(ans)