#include <bits/stdc++.h>
using namespace std;
bool B[10000000];
void sang() {
  for (int i = 2; i < 10000000; i++) {
    for (int j = i * 2; j <= 10000000; j += i) {
      B[j] = 1;
    }
  }
}
void xet(int n, int A[]) {
  for (int i = 0; i < n - 1; i++) {
    for (int j = i + 1; j < n; j++) {
      if (B[A[i] + A[j]] == 0) {
        cout << 2 << endl << A[i] << " " << A[j];
        return;
      }
    }
  }
  cout << 1 << endl << A[0];
}
int main() {
  int n, kt1 = 0, A[10000];
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> A[i];
    if (A[i] == 1) kt1++;
  }
  sang();
  if (kt1 < 2) {
    xet(n, A);
  } else {
    int t = -1;
    for (int i = 0; i < n; i++) {
      if (B[A[i] + 1] == 0 && A[i] != 1) {
        t = A[i];
        break;
      }
    }
    if (t != -1) {
      cout << kt1 + 1 << endl;
      for (int i = 0; i < kt1; i++) cout << 1 << " ";
      cout << t;
    } else {
      cout << kt1 << endl;
      for (int i = 0; i < kt1; i++) cout << 1 << " ";
    }
  }
}

### Prompt

In CPP, your task is to solve 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 B[10000000];
void sang() {
  for (int i = 2; i < 10000000; i++) {
    for (int j = i * 2; j <= 10000000; j += i) {
      B[j] = 1;
    }
  }
}
void xet(int n, int A[]) {
  for (int i = 0; i < n - 1; i++) {
    for (int j = i + 1; j < n; j++) {
      if (B[A[i] + A[j]] == 0) {
        cout << 2 << endl << A[i] << " " << A[j];
        return;
      }
    }
  }
  cout << 1 << endl << A[0];
}
int main() {
  int n, kt1 = 0, A[10000];
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> A[i];
    if (A[i] == 1) kt1++;
  }
  sang();
  if (kt1 < 2) {
    xet(n, A);
  } else {
    int t = -1;
    for (int i = 0; i < n; i++) {
      if (B[A[i] + 1] == 0 && A[i] != 1) {
        t = A[i];
        break;
      }
    }
    if (t != -1) {
      cout << kt1 + 1 << endl;
      for (int i = 0; i < kt1; i++) cout << 1 << " ";
      cout << t;
    } else {
      cout << kt1 << endl;
      for (int i = 0; i < kt1; i++) cout << 1 << " ";
    }
  }
}

```