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
from itertools import accumulate
MOD = 10 ** 9 + 7
N = int(input())
Xs = list(map(int, input().split()))
Ds = []
for i in range(1, N):
    Ds.append(Xs[i] - Xs[i-1])
S = list(accumulate(Xs))

factorials = [1]
for i in range(1, N):
    factorials.append(factorials[-1]*i % MOD)

def div(a, b):
    return a * pow(b, MOD-2, MOD)

ans = 0
prev = 0
fact = factorials[N-1]
for i, d in enumerate(Ds):
    n = i+1
    tmp = prev + div(fact, n)
    prev = tmp
    ans += tmp * Ds[i]
    ans %= MOD

print(ans)