Fuad’s challenge

With the launch of the “Technest” Scholarship Program in 2023 at the International Olympiad training camp, after hard trainings Fuad and Aykhan are playing a permutation puzzle game. Fuad challenges Aykhan to create a special sequence of numbers.

To win the challenge, Aykhan must generate a “composite sum permutation”, a sequence where for every $i$ between $1$ and $n$ inclusive, the sum of the first $i$ numbers of the permutation $p$ of size $n$ is always composite.

A positive integer $x$ is considered composite if it has more than two positive integer divisors. For instance, integers like $10,25$, and $222$ are composite, while $1,3,31,89,97$, and $13$ are not.

A sequence of positive integers $p=p_1,p_2,...,p_n$ is defined as a permutation of length $n$ if it contains every integer between $1$ and $n$ inclusive exactly once.

We’ll call a permutation $p=p_1,p_2,...,p_n$ a “composite sum permutation” if, for every index $i$ between $1$ and $n$ inclusive, the sum of the first $i$ elements of $p$, denoted as $p_1+p_2+...+p_i$, is a composite number.

Help Aykhan to generate the required permutation by writing a program.

Input

One single integer $n(1\le n\le 100)$.

Output

If no composite sum permutation of length $n$ exists, print a single integer $-1$.

Otherwise, print $n$ integers $p_1,p_2,...,p_n$ such that $p=p_1,p_2,...,p_n$ is a “composite sum permutation”.

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

Examples

In the first example for $n=3$, there is no answer.

In the second example for $n=4$, we can generate permutation “$4231$”. Compute the prefix sums: “$4,6,9,10$”. Each of these sums is composite: $4=2\cdot 2,6=2\cdot 3,9=3\cdot 3,10=2\cdot 5$".

Scoring

This task consists of the following subtasks. If all tests of a subtask are passed, you will earn points for that subtask.

1. ($25$ points): $n\le 10$;

2. ($75$ points): $noadditionalconstrains$;