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CSES Problem Set

Permutations


Task | Statistics


CSES - Permutations

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
Example 1

Input:
5

Output:
4 2 5 3 1

Example 2

Input:
3

Output:
NO SOLUTION