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

sys.setrecursionlimit(1000000)
input = lambda : sys.stdin.readline().rstrip()

def pow_mod(x, y, mod):
    tmp = x
    ret = 1
    while y > 0:
        if y % 2 == 1:
            ret = ret * tmp % mod
        tmp = tmp * tmp % mod
        y //= 2
    return ret

def inverse(x, mod):
    return pow_mod(x, mod - 2, mod)

N = int(input())
x = list(map(int, input().split()))

MOD = 1000000007

def factorial(x):
    if x <= 1:
        return 1
    else:
        return x * factorial(x - 1) % MOD

f = factorial(N - 1)

h = [0]
for _ in range(N):
    h.append((h[-1] + f * inverse(len(h), MOD)) % MOD)

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

print(ans)