A permutation of integers $1,2,\ldots,n$ is called beautiful if there are no adjacent elements whose difference is $1$.

Given $n$, your task is to count the number of beautiful permutations.

Input

The only input line contains an integer $n$.

Output

Print the number of beautiful permutations of $1,2,\ldots,n$ modulo $10^9+7$.

Constraints

• $1 \le n \le 1000$

Example

Input:

5

Output:

14