#include <bits/stdc++.h>
using namespace std;
int32_t main() {
  long long n;
  cin >> n;
  vector<long long> v(n);
  for (long long& i : v) cin >> i;
  vector<long long> p(2000001, 1);
  p[0] = p[1] = 0;
  for (long long i = 2; i <= 2000000; ++i) {
    if (!p[i]) continue;
    for (long long j = 2 * i; j <= 2000000; j += i) p[j] = 0;
  }
  long long ones = 0;
  for (long long i : v)
    if (i == 1) ++ones;
  vector<long long> ans(ones, 1);
  for (long long i : v)
    if (i != 1 && p[i + 1]) {
      ans.push_back(i);
      break;
    }
  if (ans.empty()) {
    for (long long i : v)
      if (p[i]) {
        ans.push_back(i);
        break;
      }
  }
  if (ans.size() < 2) {
    for (long long i = 0; i < n; ++i) {
      for (long long j = 0; j < n; ++j) {
        if (i == j) continue;
        if (p[v[i] + v[j]]) {
          ans.resize(2);
          ans[0] = v[i];
          ans[1] = v[j];
        }
      }
    }
  }
  if (ans.empty()) {
    ans.push_back(v[0]);
  }
  cout << ans.size() << endl;
  for (long long i : ans) cout << i << " ";
  cout << endl;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

A 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.

Input

The 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.

Output

On 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.

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int32_t main() {
  long long n;
  cin >> n;
  vector<long long> v(n);
  for (long long& i : v) cin >> i;
  vector<long long> p(2000001, 1);
  p[0] = p[1] = 0;
  for (long long i = 2; i <= 2000000; ++i) {
    if (!p[i]) continue;
    for (long long j = 2 * i; j <= 2000000; j += i) p[j] = 0;
  }
  long long ones = 0;
  for (long long i : v)
    if (i == 1) ++ones;
  vector<long long> ans(ones, 1);
  for (long long i : v)
    if (i != 1 && p[i + 1]) {
      ans.push_back(i);
      break;
    }
  if (ans.empty()) {
    for (long long i : v)
      if (p[i]) {
        ans.push_back(i);
        break;
      }
  }
  if (ans.size() < 2) {
    for (long long i = 0; i < n; ++i) {
      for (long long j = 0; j < n; ++j) {
        if (i == j) continue;
        if (p[v[i] + v[j]]) {
          ans.resize(2);
          ans[0] = v[i];
          ans[1] = v[j];
        }
      }
    }
  }
  if (ans.empty()) {
    ans.push_back(v[0]);
  }
  cout << ans.size() << endl;
  for (long long i : ans) cout << i << " ";
  cout << endl;
}

```