D. Simple Subsettime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputA tuple of positive integers {x1, x2, ..., xk} is called simple if for all pairs of positive integers (i,  j) (1  ≤ i  <  j ≤ k), xi  +  xj is a prime.You are given an array a with n positive integers a1,  a2,  ...,  an (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.InputThe first line contains integer n (1 ≤ n ≤ 1000) — the number of integers in the array a.The second line contains n integers ai (1 ≤ ai ≤ 106) — the elements of the array a.OutputOn the first line print integer m — the maximum possible size of simple subset of a.On the second line print m integers bl — 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.ExamplesInput22 3Output23 2Input22 2Output12Input32 1 1Output31 1 2Input283 14Output214 83
Input22 3
Output23 2
['constructive algorithms', 'greedy', 'number theory', '*1800']