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.