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