Permutations

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

Input

5

Output

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

3

## Output

NO SOLUTION