Permutations · CODER HUSC

Time limit: 1.0 s
Memory limit: 256 MB
Points: 10partial
AC rate: 100.0%
Solvers: 1

A permutation of integers $1,2,\ldots,n$ ~1,2,\ldots,n~ is called beautiful if there are no adjacent elements whose difference is 1.

Given $n$ ~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 $1,2,\ldots,n$ ~1,2,\ldots,n~. If there are several solutions, you may print any of them. If there are no solutions, print "NO SOLUTION".

Constraints

$1 \le n \le 10^6$ ~1 \le n \le 10^6~

Example 1

Input:

Output:

4 2 5 3 1

Example 2

Input:

Output:

NO SOLUTION

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