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
N = int(input())
x = list(map(int,input().split()))
d = [x[i+1]-x[i] for i in range(N-1)]

MOD = 10**9 + 7
def inv(a):
	b = MOD
	u = 1
	v = 0
	while b > 0:
		t = a // b
		a -= t*b
		a,b = b,a
		u -= t*v
		u,v = v,u
	u %= MOD
	return u

facts = [1]
for i in range(1, N+1):
	facts.append((facts[-1] * i) % MOD)

ans = 0
bunshi = 1
bunbo = 1
for i in range(1, N):
	keisu = (facts[N-1] * bunshi * inv(bunbo)) % MOD
	ans = (ans + keisu * d[i-1]) % MOD
	bunshi = (bunshi * (i+1) + bunbo) % MOD
	bunbo = (bunbo * (i+1)) % MOD
print(ans)