There are n children at a Christmas party, and each of them has brought a gift. The idea is that everybody will get a gift brought by someone else.

In how many ways can the gifts be distributed?

Input

The only input line has an integer n: the number of children.

Output

Print the number of ways modulo 10^9+7.

Constraints

• ~1 \leq n \leq 10^6~

Example

Input:

4

Output:

9