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
SIZE=100010; MOD=10**9+7 #998244353 #ここを変更する

SIZE += 1
inv = [0]*SIZE  # inv[j] = j^{-1} mod MOD
inv[1] = 1
for i in range(2,SIZE):
    inv[i] = MOD - (MOD//i)*inv[MOD%i]%MOD

# coding: utf-8
# Your code here!
import sys
sys.setrecursionlimit(10**6)
readline = sys.stdin.readline
read = sys.stdin.read

n = int(input())
x = [int(i) for i in readline().split()]

dx =[j-i for i,j in zip(x,x[1:])]

from itertools import accumulate
acc = list(accumulate(inv))

#print(dx)
#print(acc[:10])
ans = 0
for i,di in enumerate(dx):
    ans += di*acc[i+1]
    ans %= MOD

#print(ans)

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



    
