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

Sample input 1

5

4 2 5 3 1

Sample input 2

3

NO SOLUTION