#include <bits/stdc++.h>
using namespace std;
bool era[3000001];
int ans[1000001];
void prime() {
  era[1] = true;
  for (int i = 2; i * i <= 3000000; i++) {
    if (era[i] == 0) {
      for (int j = i + i; j <= 3000000; j += i) {
        era[j] = 1;
      }
    }
  }
}
int main() {
  prime();
  int n;
  cin >> n;
  int Data[1001] = {
      0,
  };
  int cnt = 0;
  for (int i = 0; i < n; i++) {
    cin >> Data[i];
    if (Data[i] == 1) ans[cnt++] = 1;
  }
  int flag = 0;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      if (era[Data[i] + Data[j]] == false) flag = 1;
    }
  }
  if (cnt != 0) {
    for (int i = 0; i < n; i++) {
      for (int j = i + 1; j < n; j++) {
        if (Data[i] == 1 || Data[j] == 1) continue;
        if (era[Data[i] + 1] == false && era[Data[j] + 1] == false &&
            era[Data[i] + Data[j]] == false) {
          cout << cnt + 2 << endl;
          for (int t = 0; t < cnt; t++) {
            cout << "1 ";
          }
          cout << Data[i] << " " << Data[j];
          return 0;
        }
      }
    }
    for (int i = 0; i < n; i++) {
      if (Data[i] == 1) continue;
      if (era[Data[i] + 1] == false) {
        cout << cnt + 1 << endl;
        for (int t = 0; t < cnt; t++) {
          cout << "1 ";
        }
        cout << Data[i];
        return 0;
      }
    }
    if (cnt == 1 && flag == 1) {
      for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
          if (era[Data[i] + Data[j]] == false) {
            cout << "2\n";
            cout << Data[i] << " " << Data[j];
            return 0;
          }
        }
      }
    }
    cout << cnt << endl;
    for (int i = 0; i < cnt; i++) {
      cout << "1 ";
    }
  } else {
    for (int i = 0; i < n; i++) {
      for (int j = i + 1; j < n; j++) {
        if (era[Data[i] + Data[j]] == false) {
          cout << "2" << endl;
          cout << Data[i] << " " << Data[j];
          return 0;
        }
      }
    }
    cout << "1" << endl << Data[0];
  }
  return 0;
}

### Prompt

Generate a cpp solution to 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;
bool era[3000001];
int ans[1000001];
void prime() {
  era[1] = true;
  for (int i = 2; i * i <= 3000000; i++) {
    if (era[i] == 0) {
      for (int j = i + i; j <= 3000000; j += i) {
        era[j] = 1;
      }
    }
  }
}
int main() {
  prime();
  int n;
  cin >> n;
  int Data[1001] = {
      0,
  };
  int cnt = 0;
  for (int i = 0; i < n; i++) {
    cin >> Data[i];
    if (Data[i] == 1) ans[cnt++] = 1;
  }
  int flag = 0;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      if (era[Data[i] + Data[j]] == false) flag = 1;
    }
  }
  if (cnt != 0) {
    for (int i = 0; i < n; i++) {
      for (int j = i + 1; j < n; j++) {
        if (Data[i] == 1 || Data[j] == 1) continue;
        if (era[Data[i] + 1] == false && era[Data[j] + 1] == false &&
            era[Data[i] + Data[j]] == false) {
          cout << cnt + 2 << endl;
          for (int t = 0; t < cnt; t++) {
            cout << "1 ";
          }
          cout << Data[i] << " " << Data[j];
          return 0;
        }
      }
    }
    for (int i = 0; i < n; i++) {
      if (Data[i] == 1) continue;
      if (era[Data[i] + 1] == false) {
        cout << cnt + 1 << endl;
        for (int t = 0; t < cnt; t++) {
          cout << "1 ";
        }
        cout << Data[i];
        return 0;
      }
    }
    if (cnt == 1 && flag == 1) {
      for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
          if (era[Data[i] + Data[j]] == false) {
            cout << "2\n";
            cout << Data[i] << " " << Data[j];
            return 0;
          }
        }
      }
    }
    cout << cnt << endl;
    for (int i = 0; i < cnt; i++) {
      cout << "1 ";
    }
  } else {
    for (int i = 0; i < n; i++) {
      for (int j = i + 1; j < n; j++) {
        if (era[Data[i] + Data[j]] == false) {
          cout << "2" << endl;
          cout << Data[i] << " " << Data[j];
          return 0;
        }
      }
    }
    cout << "1" << endl << Data[0];
  }
  return 0;
}

```