#include <bits/stdc++.h>
using namespace std;
int n, cnt1, a[1002];
bool prim(int n) {
  for (int i = 2; i * i <= n; i++)
    if (n % i == 0) return 0;
  return 1;
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    cnt1 += (a[i] == 1);
  }
  if (cnt1)
    for (int i = 1; i <= n; i++)
      if (a[i] != 1 && prim(a[i] + 1)) {
        cout << cnt1 + 1 << "\n";
        while (cnt1--) cout << "1 ";
        cout << a[i];
        return 0;
      }
  if (cnt1 > 1) {
    cout << cnt1 << "\n";
    while (cnt1--) cout << "1 ";
    return 0;
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j < i; j++)
      if (prim(a[i] + a[j])) {
        cout << 2 << "\n";
        cout << a[i] << " " << a[j];
        return 0;
      }
  }
  cout << "1 \n" << a[1];
  return 0;
}

### Prompt

Your task is to create 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, cnt1, a[1002];
bool prim(int n) {
  for (int i = 2; i * i <= n; i++)
    if (n % i == 0) return 0;
  return 1;
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    cnt1 += (a[i] == 1);
  }
  if (cnt1)
    for (int i = 1; i <= n; i++)
      if (a[i] != 1 && prim(a[i] + 1)) {
        cout << cnt1 + 1 << "\n";
        while (cnt1--) cout << "1 ";
        cout << a[i];
        return 0;
      }
  if (cnt1 > 1) {
    cout << cnt1 << "\n";
    while (cnt1--) cout << "1 ";
    return 0;
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j < i; j++)
      if (prim(a[i] + a[j])) {
        cout << 2 << "\n";
        cout << a[i] << " " << a[j];
        return 0;
      }
  }
  cout << "1 \n" << a[1];
  return 0;
}

```