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
#!/usr/bin/env python3
import sys
input = sys.stdin.readline
MOD = 10**9 + 7

n = int(input())
x = [int(item) for item in input().split()]
inv = [0] * (n + 10)

n_minus_1_fac = 1
for i in range(1, n):
    n_minus_1_fac *= i
    n_minus_1_fac %= MOD 

for i in range(n + 10):
    inv[i] = pow(i, MOD-2, MOD)
inv_cumsum = [0] * (n + 10)
for i in range(1, n + 10):
    inv_cumsum[i] = (inv_cumsum[i-1] + inv[i]) % MOD

ans = 0
for i, (x1, x2) in enumerate(zip(x, x[1:])):
    ans += (x2 - x1) * inv_cumsum[i+1] * n_minus_1_fac % MOD
    ans %= MOD
print(ans)