#include <bits/stdc++.h>
using namespace std;
bool prime[30000005];
int main() {
  fill(prime, prime + 30000005, 1);
  for (int i = 2; i < 30000005; i++) {
    if (prime[i]) {
      for (int j = 2 * i; j < 30000005; j += i) {
        prime[j] = 0;
      }
    }
  }
  long long n;
  cin >> n;
  long long a[n], ans = 0, ai = -1;
  bool scs = 0;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] == 1)
      ans++;
    else {
      if (prime[a[i] + 1] && !scs) {
        ai = i;
        ans++;
        scs = 1;
      }
    }
  }
  ans = max(ans, 1ll);
  if (ans < 2) {
    for (int i = 0; i < n; i++) {
      for (int j = i + 1; j < n; j++) {
        if (prime[a[i] + a[j]]) {
          cout << 2 << '\n' << a[i] << ' ' << a[j];
          return 0;
        }
      }
    }
  }
  cout << ans << '\n';
  if (ans == 1)
    cout << a[0];
  else {
    for (int i = 0; i < ans - 1; i++) {
      cout << 1 << ' ';
    }
    if (ai != -1)
      cout << a[ai];
    else
      cout << 1;
  }
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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 prime[30000005];
int main() {
  fill(prime, prime + 30000005, 1);
  for (int i = 2; i < 30000005; i++) {
    if (prime[i]) {
      for (int j = 2 * i; j < 30000005; j += i) {
        prime[j] = 0;
      }
    }
  }
  long long n;
  cin >> n;
  long long a[n], ans = 0, ai = -1;
  bool scs = 0;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] == 1)
      ans++;
    else {
      if (prime[a[i] + 1] && !scs) {
        ai = i;
        ans++;
        scs = 1;
      }
    }
  }
  ans = max(ans, 1ll);
  if (ans < 2) {
    for (int i = 0; i < n; i++) {
      for (int j = i + 1; j < n; j++) {
        if (prime[a[i] + a[j]]) {
          cout << 2 << '\n' << a[i] << ' ' << a[j];
          return 0;
        }
      }
    }
  }
  cout << ans << '\n';
  if (ans == 1)
    cout << a[0];
  else {
    for (int i = 0; i < ans - 1; i++) {
      cout << 1 << ' ';
    }
    if (ai != -1)
      cout << a[ai];
    else
      cout << 1;
  }
  return 0;
}

```