Given an integer ~N~, find the lexicographically smallest permutation ~p_1, p_2, \dots, p_N~ of ~1, 2, \dots, N~ such that ~i+p_i~ is prime for all ~1 \le i \le N~, or report that no such permutation exists.

Constraints

~1 \le N \le 10^6~

Subtask 1 [5%]

~1 \le N \le 10~

Subtask 2 [25%]

~1 \le N \le 100~

Subtask 3 [15%]

~1 \le N \le 10^3~

Subtask 4 [30%]

~1 \le N \le 10^4~

Subtask 5 [25%]

No additional constraints.

Input Specification

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

Output Specification

If no such permutation exists, output ~-1~ on a line by itself. Otherwise, output ~N~ space-separated integers ~p_1, p_2, \dots, p_N~, the lexicographically smallest permutation such that ~i+p_i~ is prime for all ~1 \le i \le N~.

Sample Input

3

Sample Output

1 3 2

Explanation

Note that ~1+p_1 = 1+1 = 2~, ~2+p_2 = 2+3 = 5~, and ~3+p_3 = 3+2 = 5~ are all prime.