Problem Statement

出處: cses

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

Input

The only input line contains an integer $n$.

• $1 \le n \le 10^6$

Output

Print a beautiful permutation of integers $1,2,\ldots,n$. If there are several solutions, you may print any of them. If there are no solutions, print "NO SOLUTION".

Example

5

4 2 5 3 1

3

NO SOLUTION