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.