The primeness of any permutation $p_1,p_2,\dots ,p_N$ of $1,2,\dots ,N$ is defined as the sum of all prime absolute differences of consecutive elements. Given an integer $N$, find any permutation $p_1,p_2,\dots ,p_N$ of $1,2,\dots ,N$ with the maximum primeness over all length $N$ permutations.

Constraints

$1\le N\le 100$

Subtask 1 [20%]

$1\le N\le 20$

Subtask 2 [60%]

$1\le N\le 50$

Subtask 3 [20%]

No additional constraints.

Input Specification

The first and only line of input contains a single integer $N$.

Output Specification

Output $N$ space-separated integers on a single line, representing a permutation $p_1,p_2,\dots ,p_N$ of $1,2,\dots ,N$ with the maximum primeness over all length $N$ permutations.

Sample Input 1

3

Sample Output 1

2 3 1

Explanation for Sample 1

There are $2$ absolute differences of consecutive elements, namely $|2-3|=1$ and $|3-1|=2$. Out of these, only $2$ is prime, so the primeness of this permutation is $2$.

Sample Input 2

6

Sample Output 2

3 6 1 4 2 5

Explanation for Sample 2

The absolute differences of consecutive elements are $3,5,3,2,3$. All of these are prime, so the primeness of this permutation is $3+5+3+2+3=16$.