question-permutations.md

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 $n$, construct a beautiful permutation if such a permutation exists.

Input

The only input line contains an integer $n$.

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".

Constraints

• 1 $\le$ n $\le$ $10^{6}$

Example 1

Input:
5

Output:
4 2 5 3 1

Example 2
Input:
3

Output:
NO SOLUTION

Solution