#include <bits/stdc++.h>
using namespace std;
int n;
int a[1234];
bool isPrime(int x) {
  if (x < 4) return x - 1;
  for (int i = 2; i * i <= x; ++i)
    if (x % i == 0) return false;
  return true;
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; ++i) cin >> a[i];
  int count1 = 0;
  for (int i = 1; i <= n; ++i)
    if (a[i] == 1) ++count1;
  if (count1) {
    for (int i = 1; i <= n; ++i)
      if (isPrime(a[i] + 1) && a[i] > 1) {
        cout << count1 + 1 << endl;
        for (int j = 0; j < count1; ++j) cout << 1 << " ";
        cout << a[i] << endl;
        return 0;
      }
  }
  if (count1 >= 2) {
    cout << count1 << endl;
    for (int i = 0; i < count1; ++i) cout << 1 << " ";
    cout << endl;
    return 0;
  }
  if (count1 < 2) {
    for (int i = 1; i <= n; ++i)
      for (int j = i + 1; j <= n; ++j)
        if (isPrime(a[i] + a[j])) {
          cout << 2 << endl;
          cout << a[i] << " " << a[j] << endl;
          return 0;
        }
  }
  cout << 1 << endl;
  cout << 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 n;
int a[1234];
bool isPrime(int x) {
  if (x < 4) return x - 1;
  for (int i = 2; i * i <= x; ++i)
    if (x % i == 0) return false;
  return true;
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; ++i) cin >> a[i];
  int count1 = 0;
  for (int i = 1; i <= n; ++i)
    if (a[i] == 1) ++count1;
  if (count1) {
    for (int i = 1; i <= n; ++i)
      if (isPrime(a[i] + 1) && a[i] > 1) {
        cout << count1 + 1 << endl;
        for (int j = 0; j < count1; ++j) cout << 1 << " ";
        cout << a[i] << endl;
        return 0;
      }
  }
  if (count1 >= 2) {
    cout << count1 << endl;
    for (int i = 0; i < count1; ++i) cout << 1 << " ";
    cout << endl;
    return 0;
  }
  if (count1 < 2) {
    for (int i = 1; i <= n; ++i)
      for (int j = i + 1; j <= n; ++j)
        if (isPrime(a[i] + a[j])) {
          cout << 2 << endl;
          cout << a[i] << " " << a[j] << endl;
          return 0;
        }
  }
  cout << 1 << endl;
  cout << a[1] << endl;
}

```