Highly Composite Permutations

A positive integer $x$ is called composite if it has strictly more than two positive integer divisors. For example, 4, 30 and 111 are composite, while 1, 7 and 239 are not.

An integer sequence $p = \langle p_1, p_2, \ldots, p_n \rangle$ is called a permutation of length $n$ if it contains every integer from 1 to $n$ inclusive exactly once.

A permutation $p = \langle p_1, p_2, \ldots, p_n \rangle$ is called highly composite if for every $i$ from 1 to $n$ inclusive, the sum of the first $i$ elements of $p$, that is $p_1 + p_2 + \ldots + p_i$, is composite.

Given a single integer $n$, find a highly composite permutation of length $n$.

The only line of the input contains a single integer $n$ ($1 \le n \le 100$).

If no highly composite permutation of length $n$ exists, output a single integer $-1$. Otherwise, output $n$ integers $p_1, p_2, \ldots, p_n$ such that $p = \langle p_1, p_2, \ldots, p_n \rangle$ is a highly composite permutation.

If there are multiple highly composite permutations of length $n$, you may output any of them.

In the first example test case, the first element of the permutation, 9, is composite, the sum of the first two elements, $9 + 13 = 22$, is composite, the sum of the first three elements, $9 + 13 + 6 = 28$, is composite, and so on.

In the second example test case, only two permutations of the required length exist, $\langle 1, 2 \rangle$ and $\langle 2, 1 \rangle$, and neither of them is highly composite.