Beautiful Permutation II

A permutation of integers 1,2,\ldots,n is called beautiful if there are no adjacent elements whose difference is 1. Given n, construct the lexicographically minimal beautiful permutation if such a permutation exists.

Input

The only line contains an integer n.

Output

Print the lexicographically minimal beautiful permutation of integers 1,2,\ldots,n. If there is no such permutation, print "NO SOLUTION".

Constraints

$1 \le n \le 10^6$

Example

Input

5

Output

1 3 5 2 4
```Example 2
## Input

3

## Output

NO SOLUTION