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()))
mod = 10**9+7
ans = 0

# ある区間X[3] - X[2]をあるスライムが通過する確率
# 3番目のスライムが通過する確率:1 (必ず通過する。3!=6通り。123, 132, 231, 213, 312, 321)
# 2番目のスライムが通過する確率:1/2 (先に3が選ばれる必要がある。3/6=1/2)
# 1番目のスライムが通過する確率:1/3 (先に3,2が選ばれる必要がある。2/6=1/3)
# ある区間X[i+1] - X[i]についてあるスライムi-jが通過する確率は 1/(j+1)

# 1 = 1
# 2 = 1 + 1/2 = 3/2
# 3 = 1 + 1/2 + 1/3 = 11/6
# 4 = 1 + 1/2 + 1/3 + 1/4 = 25/12
# 5 = 1 + 1/2 + 1/3 + 1/4 + 1/5 = 137/60

# 各区間の確率係数を求めてかけた場合
# for i in range(N-1):
#     d = X[i+1]-X[i]
#     p = 1
#     for j in range(1, i+1):
#         p += 1/(j+1)
#     ans += d * p % mod

# あるスライムから最後までの総距離ごとの確率
# ここがよくわからん。前計算を理解できてない
for i in range(N-1):
    d = X[N-1]-X[i]
    ans += d * pow(i+1, mod-2, mod)

# (N-1)!
a = 1
for i in range(1, N):
    a *= i
    a %= mod

ans *= a
ans %= mod
print(int(ans))