Simple Subset

1000ms

262144K

Description:

A tuple of positive integers {x₁, x₂, ..., 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 a₁, a₂, ..., 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.

Input:

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 ≤ 10⁶) — the elements of the array a.

Output:

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.

Sample Input:

2
2 3

Sample Output:

2
3 2

Sample Input:

2
2 2

Sample Output:

1
2

Sample Input:

3
2 1 1

Sample Output:

3
1 1 2

Sample Input:

2
83 14

Sample Output:

2
14 83

Informação

Provedor Codeforces

Código CF665D