Permutations

A permutation of integers $1,2,\dots ,n1,2,\backslash ldots,n$ is called beautiful if there are no adjacent elements whose difference is $11$.

Given $nn$, construct a beautiful permutation if such a permutation exists.

Input

The only input line contains an integer $nn$.

Output

Print a beautiful permutation of integers $1,2,\dots ,n1,2,\backslash ldots,n$. If there are several solutions, you may print any of them. If there are no solutions, print "NO SOLUTION".