#include <bits/stdc++.h>
using namespace std;
const int MAX = 1e4 + 9, N = 2e6 + 9;
int n, a[MAX], pr[N], s, a1, a2;
int main() {
  pr[1] = 1;
  for (int i = 1; i < N; i++)
    if (!pr[i])
      for (int j = i * 2; j < N; j += i) pr[j] = 1;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i], s += (a[i] == 1);
  for (int i = 0; i < n; i++) {
    if (!pr[a[i] + 1] && s && a[i] != 1) {
      cout << s + 1 << '\n';
      for (int i = 0; i < s; i++) cout << 1 << ' ';
      cout << a[i] << '\n';
      return 0;
    }
    for (int j = i + 1; j < n; j++)
      if (!pr[a[i] + a[j]]) a1 = a[i], a2 = a[j];
  }
  if (s > 2) {
    cout << s << '\n';
    for (int i = 0; i < s; i++) cout << 1 << ' ';
    return 0;
  }
  if (a1) return cout << 2 << '\n' << a1 << " " << a2, 0;
  cout << 1 << '\n' << a[0];
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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;
const int MAX = 1e4 + 9, N = 2e6 + 9;
int n, a[MAX], pr[N], s, a1, a2;
int main() {
  pr[1] = 1;
  for (int i = 1; i < N; i++)
    if (!pr[i])
      for (int j = i * 2; j < N; j += i) pr[j] = 1;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i], s += (a[i] == 1);
  for (int i = 0; i < n; i++) {
    if (!pr[a[i] + 1] && s && a[i] != 1) {
      cout << s + 1 << '\n';
      for (int i = 0; i < s; i++) cout << 1 << ' ';
      cout << a[i] << '\n';
      return 0;
    }
    for (int j = i + 1; j < n; j++)
      if (!pr[a[i] + a[j]]) a1 = a[i], a2 = a[j];
  }
  if (s > 2) {
    cout << s << '\n';
    for (int i = 0; i < s; i++) cout << 1 << ' ';
    return 0;
  }
  if (a1) return cout << 2 << '\n' << a1 << " " << a2, 0;
  cout << 1 << '\n' << a[0];
}

```