#include <bits/stdc++.h>
using namespace std;
const int intf = 0x3f3f3f3f;
int a[1005];
bool pr(int x) {
  for (int i = 2; i * i <= x; i++) {
    if (x % i == 0) {
      return false;
    }
  }
  return true;
}
int main() {
  int n;
  cin >> n;
  int y = 0;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] == 1) {
      y++;
    }
  }
  sort(a, a + n);
  if (n == 1) {
    cout << 1 << endl;
    cout << a[0] << endl;
  } else if (n == 2) {
    if (pr(a[0] + a[1])) {
      cout << 2 << endl;
      cout << a[0] << ' ' << a[1] << endl;
    } else {
      cout << 1 << endl;
      cout << a[0] << endl;
    }
  } else {
    int q = -1, w = -1;
    if (y > 1) {
      int x = -1;
      for (int i = y; i < n; i++) {
        if (pr(1 + a[i])) {
          x = a[i];
          break;
        }
      }
      if (x != -1) {
        cout << y + 1 << endl;
        for (int i = 0; i < y; i++) {
          cout << 1 << ' ';
        }
        cout << x << endl;
      } else {
        cout << y << endl;
        for (int i = 0; i < y; i++) {
          cout << 1;
          if (i != y - 1) cout << ' ';
        }
      }
    } else if (y == 1) {
      for (int i = y; i < n - 1; i++) {
        for (int j = i + 1; j < n; j++) {
          if (pr(a[i] + a[j])) {
            q = a[i];
            w = a[j];
            if (pr(1 + a[i]) && pr(1 + a[j])) {
              cout << 3 << endl;
              cout << 1 << ' ' << a[i] << ' ' << a[j] << endl;
              return 0;
            }
          }
        }
      }
      if (q != -1 && w != -1) {
        cout << 2 << endl;
        cout << q << ' ' << w << endl;
      } else {
        cout << 1 << endl;
        cout << a[0] << endl;
      }
    } else {
      for (int i = y; i < n - 1; i++) {
        for (int j = i + 1; j < n; j++) {
          if (pr(a[j] + a[i])) {
            q = a[i];
            w = a[j];
          }
        }
      }
      if (q != -1 && w != -1) {
        cout << 2 << endl;
        cout << q << ' ' << w << endl;
      } else {
        cout << 1 << endl;
        cout << a[0] << endl;
      }
    }
  }
  return 0;
}

### Prompt

Your challenge is to write 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;
const int intf = 0x3f3f3f3f;
int a[1005];
bool pr(int x) {
  for (int i = 2; i * i <= x; i++) {
    if (x % i == 0) {
      return false;
    }
  }
  return true;
}
int main() {
  int n;
  cin >> n;
  int y = 0;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] == 1) {
      y++;
    }
  }
  sort(a, a + n);
  if (n == 1) {
    cout << 1 << endl;
    cout << a[0] << endl;
  } else if (n == 2) {
    if (pr(a[0] + a[1])) {
      cout << 2 << endl;
      cout << a[0] << ' ' << a[1] << endl;
    } else {
      cout << 1 << endl;
      cout << a[0] << endl;
    }
  } else {
    int q = -1, w = -1;
    if (y > 1) {
      int x = -1;
      for (int i = y; i < n; i++) {
        if (pr(1 + a[i])) {
          x = a[i];
          break;
        }
      }
      if (x != -1) {
        cout << y + 1 << endl;
        for (int i = 0; i < y; i++) {
          cout << 1 << ' ';
        }
        cout << x << endl;
      } else {
        cout << y << endl;
        for (int i = 0; i < y; i++) {
          cout << 1;
          if (i != y - 1) cout << ' ';
        }
      }
    } else if (y == 1) {
      for (int i = y; i < n - 1; i++) {
        for (int j = i + 1; j < n; j++) {
          if (pr(a[i] + a[j])) {
            q = a[i];
            w = a[j];
            if (pr(1 + a[i]) && pr(1 + a[j])) {
              cout << 3 << endl;
              cout << 1 << ' ' << a[i] << ' ' << a[j] << endl;
              return 0;
            }
          }
        }
      }
      if (q != -1 && w != -1) {
        cout << 2 << endl;
        cout << q << ' ' << w << endl;
      } else {
        cout << 1 << endl;
        cout << a[0] << endl;
      }
    } else {
      for (int i = y; i < n - 1; i++) {
        for (int j = i + 1; j < n; j++) {
          if (pr(a[j] + a[i])) {
            q = a[i];
            w = a[j];
          }
        }
      }
      if (q != -1 && w != -1) {
        cout << 2 << endl;
        cout << q << ' ' << w << endl;
      } else {
        cout << 1 << endl;
        cout << a[0] << endl;
      }
    }
  }
  return 0;
}

```