#include <bits/stdc++.h>
using namespace std;
int fix[2000001], a[2000001], n, n1;
int main() {
  for (int i = 2; i * i <= 2000000; i++)
    if (fix[i] == 0)
      for (int j = i * i; j <= 2000000; j = j + i) fix[j] = 1;
  cin >> n;
  for (int i = 1; n >= i; i++) cin >> a[i];
  for (int i = 1; n >= i; i++)
    if (a[i] == 1) n1++;
  if (n1 > 0)
    for (int i = 1; n >= i; i++)
      if (fix[a[i] + 1] == 0 && a[i] != 1) {
        cout << n1 + 1 << endl;
        cout << a[i] << " ";
        for (int j = 1; n1 >= j; j++)
          cout << "1"
               << " ";
        return 0;
      }
  if (n1 > 2) {
    cout << n1 << endl;
    for (int i = 1; i <= n1; i++)
      cout << "1"
           << " ";
    return 0;
  }
  for (int i = 1; i < n; i++)
    for (int j = i + 1; j <= n; j++)
      if (fix[a[i] + a[j]] == 0) {
        cout << 2 << endl;
        cout << a[i] << " " << a[j] << endl;
        return 0;
      }
  cout << 1 << endl << a[1] << endl;
}

### 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;
int fix[2000001], a[2000001], n, n1;
int main() {
  for (int i = 2; i * i <= 2000000; i++)
    if (fix[i] == 0)
      for (int j = i * i; j <= 2000000; j = j + i) fix[j] = 1;
  cin >> n;
  for (int i = 1; n >= i; i++) cin >> a[i];
  for (int i = 1; n >= i; i++)
    if (a[i] == 1) n1++;
  if (n1 > 0)
    for (int i = 1; n >= i; i++)
      if (fix[a[i] + 1] == 0 && a[i] != 1) {
        cout << n1 + 1 << endl;
        cout << a[i] << " ";
        for (int j = 1; n1 >= j; j++)
          cout << "1"
               << " ";
        return 0;
      }
  if (n1 > 2) {
    cout << n1 << endl;
    for (int i = 1; i <= n1; i++)
      cout << "1"
           << " ";
    return 0;
  }
  for (int i = 1; i < n; i++)
    for (int j = i + 1; j <= n; j++)
      if (fix[a[i] + a[j]] == 0) {
        cout << 2 << endl;
        cout << a[i] << " " << a[j] << endl;
        return 0;
      }
  cout << 1 << endl << a[1] << endl;
}

```