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 10^5~

Subtask 1 [30%]

~1 \le N \le 10^3~

Subtask 2 [30%]

~1 \le N \le 10^4~

Subtask 3 [40%]

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~.