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

def inv_mod(n,mod):
    inv_mod = [0]*(n+1)
    inv_mod[1] = 1
    for i in range(2,n+1):
        inv_mod[i] = mod - inv_mod[mod%i] * (mod//i ) % mod
    
    return inv_mod

n = int(input())
x = list(map(int,input().split()))

x_dif = [x2-x1 for x1,x2 in zip(x,x[1:])]

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

inv = inv_mod(n,MOD) 
    
ans = 0
count = 0
for i,dist in enumerate(x_dif,1):
    count += (fac * inv[i]) %MOD
    count %= MOD
    
    ans += (dist * count)%MOD
    ans %= MOD

print(ans)