**Time limit:**1.00 s**Memory limit:**512 MB

*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`