Given an integer ~N~, find any permutation ~p_1, p_2, \dots, p_N~ of ~1, 2, \dots, N~ such that ~p_1 + p_2 + \dots + p_{i-1} + p_i~ is not prime for every integer ~1 \le i \le N~, or report that no such permutation exists.

Constraints

~1 \le N \le 10^6~

Input Specification

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

Output Specification

If there exists no valid permutation, output ~-1~ on a line by itself.

Otherwise, output ~N~ space-separated integers on a single line, representing a permutation ~p_1, p_2, \dots, p_N~ of ~1, 2, \dots, N~ where no prefix sum is prime.

Sample Input

5

Sample Output

4 5 3 2 1

Explanation

The prefix sums are: ~p_1 = 4~, ~p_1 + p_2 = 9~, ~p_1 + p_2 + p_3 = 12~, ~p_1 + p_2 + p_3 + p_4 = 14~, and ~p_1 + p_2 + p_3 + p_4 + p_5 = 15~.

None of ~4~, ~9~, ~12~, ~14~, or ~15~ are prime, so this is a valid permutation.