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

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