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
# -*- coding: utf-8 -*-
import sys

mod=10**9+7
N=input()
X=map(int, sys.stdin.readline().split())
L=map(lambda x: pow(x,mod-2,mod), range(1,N))

L_RUISEKI=[]

for i,x in enumerate(L):
    if i==0: L_RUISEKI.append(x)
    else: L_RUISEKI.append(L_RUISEKI[-1]+x)

ans=0
for i in range(N-1):
    value=X[i+1]-X[i]
    ans+=value*L_RUISEKI[i]


fact=[1]
fact_tmp = 1
for i in range(1, N+1):
    fact_tmp *= i
    fact_tmp %= mod
    fact.append(fact_tmp)

print ans*fact[N-1]%mod