At the Phoenix Wonderland carnival, you found a mysterious booth that proposes an interesting challenge. The operator (some strange floating nuigurumi) will give you an integer ~N~, and you are to find any permutation ~p_1, p_2, \dots, p_N~ of ~1, 2, \dots, N~ wherein every adjacent sum in the permutation is non-prime. That is, for all ~1 \le i < N~, we must have ~p_i + p_{i + 1}~ be non-prime. Can you find any such permutation, or determine that none exists?

Constraints

~1 \le N \le 10^6~

Subtask 1 [10%]

~1 \le N \le 4~

Subtask 2 [20%]

~1 \le N \le 10~

Subtask 3 [30%]

~1 \le N \le 3 \times 10^3~

Subtask 4 [40%]

No additional constraints.

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~ wherein every adjacent sum in the permutation is non-prime.

Sample Input 1

7

Sample Output 1

7 2 4 6 3 5 1

Explanation for Sample 1

Note that the adjacent pairs have sums of ~9, 6, 10, 9, 8, 6~, none of which are prime.

Sample Input 2

2

Sample Output 2

-1

Explanation for Sample 2

Note that ~1 + 2 = 3~ which is prime, so regardless of order the sum of the one pair is prime.