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Description

A permutation of integers 1,2,…,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 Format

The only input line contains an integer n.

Output Format

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

5

4 2 5 3 1

Hint

1≤n≤10⁶

Example 2

Input:

3

Output:

NO SOLUTION

Source

CSES