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