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()))
y=[x[i+1]-x[i] for i in range(N-1)]
 
upp=[1]*(N+1)
for i in range(2, N+1):
  upp[i]=upp[i-1]*i
  upp[i]%=MOD
  
a=[0]*(N-1)
a[0]=upp[N-1]
for i in range(1, N-1):
  a[i]=a[0]*pow(i+1, MOD-2, MOD)
  a[i]%=MOD

b=[0]*(N-1)
b[0]=a[0]
for i in range(1, N-1):
  b[i]=b[i-1]+a[i]
  b[i]%=MOD
  
def moddot(v1, v2):
  n=len(v1)
  out=0
  for i in range(n):
    out+=v1[i]*v2[i]%MOD
    out%=MOD
  return out
 
ex=moddot(b, y)
print(ex)