**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