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
input = sys.stdin.readline

# 1~nまでの逆元(mod m) O(n)
def mod_inv_list(n:int, m:int):
    # inv_t[i]: iの法mの下での逆元
    inv_t = [0] + [1]
    for i in range(2,n):
        inv_t += [inv_t[m % i] * (m - m//i) % m]
    return inv_t

def main():
    N = int(input())
    x = [int(i) for i in input().split()]
    MOD = 10**9 + 7

    inv_acum = mod_inv_list(N,MOD)
    for i in range(1,N):
        inv_acum[i] = (inv_acum[i] + inv_acum[i-1]) % MOD

    ans = 0
    for i in range(1,N):
        ans += (x[i] - x[i-1]) * inv_acum[i]
        ans %= MOD

    for i in range(1,N):
        ans = (ans * i) % MOD

    print(ans)

if __name__ == "__main__":
    main()