apps_445
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.
-----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} ≤ 10^6) — 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.
-----Examples-----
Input 2 2 3
Output 2 3 2
Input 2 2 2
Output 1 2
Input 3 2 1 1
Output 3 1 1 2
Input 2 83 14
Output 2 14 83
Comments