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)

n = int(input())
x = list(map(int, input().split()))
d = [x[i+1] - x[i] for i in range(n - 1)]

def pow(x, y):
    if y == 0:
        return 1
    ans = 1
    while y > 1:
        if y % 2 != 0:
            ans *= x
            ans %= 1000000007
        x *= x
        x %= 1000000007
        y //= 2
    return ans * x % 1000000007

def fact(m):
  return m * fact(m-1) % 1000000007 if m != 1 else 1
 
fact_n_1 = fact(n-1)

e = [None] * (n-1)
for i in range(n-1):
  if i == 0:
    e[i] = fact_n_1
  else:
    e[i] = (e[i - 1] + fact_n_1 * pow(i + 1, 1000000005)) % 1000000007

print(sum(e_i * d_i % 1000000007
          for i, (d_i, e_i) 
          in enumerate(zip(d, e))) % 1000000007 ) 