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
MOD = 10**9 + 7
N = int(input())
X = list(map(int, input().split()))
D = [dj - di for di, dj in zip(X, X[1:])]

def power(n, r, mod=10**9+7):
    if r == 0: return 1
    if r%2 == 0:
        return power(n*n % mod, r//2, mod) % mod
    if r%2 == 1:
        return n * power(n, r-1, mod) % mod

def framod(n, a=1, mod=10**9+7):
    for i in range(1,n+1):
        a = a * i % mod
    return a

count_d = []
frac_Nm1 = framod(N-1)
for i in range(1, N):
  count_d.append(frac_Nm1 * power(i, MOD-2) % MOD)

for i in range(1, N-1):
  count_d[i] += count_d[i-1]


ans = sum([d*c % MOD for d, c in zip(D, count_d)]) % MOD
print(ans)