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

• $1 \le n \le 10^6$

Example

Input:

4

Output:

9