A10457 | Simple Subset

A tuple of positive integers ${x_{1},x_{2},...,x_{k}}$ is called simple if for all pairs of positive integers $(i,j)$ ( $1<=i<j<=k$ ), $x_{i}+x_{j}$ is a prime.

You are given an array $a$ with $n$ positive integers $a_{1},a_{2},...,a_{n}$ (not necessary distinct). You want to find a simple subset of the array $a$ with the maximum size.

A prime number (or a prime) is a natural number greater than $1$ that has no positive divisors other than $1$ and itself.

Let's define a subset of the array $a$ as a tuple that can be obtained from $a$ by removing some (possibly all) elements of it.

The first line contains integer $n$ ( $1<=n<=1000$ ) — the number of integers in the array $a$ .

The second line contains $n$ integers $a_{i}$ ( $1<=a_{i}<=10^{6}$ ) — the elements of the array $a$ .

On the first line print integer $m$ — the maximum possible size of simple subset of $a$ .

On the second line print $m$ integers $b_{l}$ — the elements of the simple subset of the array $a$ with the maximum size.

If there is more than one solution you can print any of them. You can print the elements of the subset in any order.