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
input=sys.stdin.readline
n=int(input())
x_list=list(map(int,input().split()))
INF=10**9+7
def modinv(a,m):
    b=m
    (x,lastx)=(0,1)
    (y,lasty)=(1,0)
    while not b==0:
        q=a//b
        (a,b)=(b,a%b)
        (x, lastx) = (lastx - q * x, x)
        (y, lasty) = (lasty - q * y, y)
    return lastx%m
ans=0
s=1
for i in range(n-1):
    s=s*(i+1)
    s=s%INF
for i in range(n-1):
    x=modinv(i+1,INF)
    ans=(ans+s*x*(x_list[n-1]-x_list[n-2-i]))%INF
sumx=[]
isumx=[]
sx=0
isx=0
for i in range(n-1):
    sx=(sx+x_list[i])%INF
    isx=(isx+x_list[n-2-i])%INF
    sumx.append(sx)
    isumx.append(isx)
for i in range(n-2):
    x=modinv(i+1,INF)
    y=modinv(i+2,INF)
    ans=(ans+s*x*y*(isumx[i]-sumx[i]))%INF
print(ans)
    
