#include <bits/stdc++.h>
using namespace std;
vector<int> solve() {
  const int N = 3e6;
  vector<bool> isPrime(N, true);
  isPrime[0] = isPrime[1] = false;
  for (int i = 0; i * i < N; i++) {
    if (isPrime[i]) {
      for (int j = i * 2; j < N; j += i) {
        isPrime[j] = false;
      }
    }
  }
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  int one = count(a.begin(), a.end(), 1);
  vector<int> ans;
  ans.push_back(a[0]);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i == j) continue;
      vector<int> cand;
      if (isPrime[a[i] + a[j]]) {
        cand.push_back(a[i]);
        cand.push_back(a[j]);
        if (isPrime[a[i] + 1] && isPrime[a[j] + 1] && a[i] != 1 && a[j] == 1) {
          for (int k = 0; k < one - 1; k++) cand.push_back(1);
          return cand;
        }
        if (ans.size() < cand.size()) ans = cand;
      }
    }
  }
  if (one >= 2) {
    ans.assign(one, 1);
  }
  return ans;
}
int main() {
  auto ans = solve();
  cout << ans.size() << endl;
  for (int x : ans) cout << x << " ";
  cout << endl;
}

### Prompt

Create a solution in Cpp for the following problem:

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;
vector<int> solve() {
  const int N = 3e6;
  vector<bool> isPrime(N, true);
  isPrime[0] = isPrime[1] = false;
  for (int i = 0; i * i < N; i++) {
    if (isPrime[i]) {
      for (int j = i * 2; j < N; j += i) {
        isPrime[j] = false;
      }
    }
  }
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  int one = count(a.begin(), a.end(), 1);
  vector<int> ans;
  ans.push_back(a[0]);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i == j) continue;
      vector<int> cand;
      if (isPrime[a[i] + a[j]]) {
        cand.push_back(a[i]);
        cand.push_back(a[j]);
        if (isPrime[a[i] + 1] && isPrime[a[j] + 1] && a[i] != 1 && a[j] == 1) {
          for (int k = 0; k < one - 1; k++) cand.push_back(1);
          return cand;
        }
        if (ans.size() < cand.size()) ans = cand;
      }
    }
  }
  if (one >= 2) {
    ans.assign(one, 1);
  }
  return ans;
}
int main() {
  auto ans = solve();
  cout << ans.size() << endl;
  for (int x : ans) cout << x << " ";
  cout << endl;
}

```