CSES - Permutations II
  • Time limit: 1.00 s
  • Memory limit: 512 MB
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