#include <bits/stdc++.h>
using namespace std;
bool f[2000005] = {};
int a[1000005];
vector<int> ans;
int main() {
  for (int i = 2; i <= 2000005; i++) {
    if (f[i] == 0)
      for (int j = 2 * i; j <= 2000005; j += i) f[j] = 1;
  }
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  if (a[0] == 1 and a[1] == 1) {
    ans.push_back(1);
    ans.push_back(1);
    int i = 2;
    for (; i < n; i++)
      if (a[i] == 1)
        ans.push_back(1);
      else
        break;
    for (int i1 = i; i1 < n; i1++)
      if (f[a[i1] + 1] == 0) {
        ans.push_back(a[i1]);
        break;
      }
  } else {
    bool f1 = 1;
    for (int i = 0; i < n and f1 == 1; i++)
      for (int j = i + 1; j < n and f1 == 1; j++)
        if (f[a[i] + a[j]] == 0) {
          ans.push_back(a[i]);
          ans.push_back(a[j]);
          f1 = 0;
        }
    if (f1 == 1) ans.push_back(a[0]);
  }
  cout << ans.size() << endl;
  for (int i = 0; i < ans.size(); i++) cout << ans[i] << " ";
  return 0;
}

### Prompt

Please create a solution in Cpp 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;
bool f[2000005] = {};
int a[1000005];
vector<int> ans;
int main() {
  for (int i = 2; i <= 2000005; i++) {
    if (f[i] == 0)
      for (int j = 2 * i; j <= 2000005; j += i) f[j] = 1;
  }
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  if (a[0] == 1 and a[1] == 1) {
    ans.push_back(1);
    ans.push_back(1);
    int i = 2;
    for (; i < n; i++)
      if (a[i] == 1)
        ans.push_back(1);
      else
        break;
    for (int i1 = i; i1 < n; i1++)
      if (f[a[i1] + 1] == 0) {
        ans.push_back(a[i1]);
        break;
      }
  } else {
    bool f1 = 1;
    for (int i = 0; i < n and f1 == 1; i++)
      for (int j = i + 1; j < n and f1 == 1; j++)
        if (f[a[i] + a[j]] == 0) {
          ans.push_back(a[i]);
          ans.push_back(a[j]);
          f1 = 0;
        }
    if (f1 == 1) ans.push_back(a[0]);
  }
  cout << ans.size() << endl;
  for (int i = 0; i < ans.size(); i++) cout << ans[i] << " ";
  return 0;
}

```