Given an integer $N$, find any permutation $p_1,p_2,\dots ,p_N$ of $1,2,\dots ,N$ such that $p_1+p_2+\cdots +p_{i-1}+p_i$ 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.