#include <bits/stdc++.h>
using namespace std;
int n;
int ok[2000001];
int main() {
  cin >> n;
  int a[n];
  for (long long i = 2; i <= 2000000; i++) {
    if (ok[i] == 0) {
      for (long long j = i * 2; j <= 2000000; j += i) {
        ok[j] = 1;
      }
    }
  }
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  vector<int> ans;
  for (int i = 0; i < n; i++) {
    vector<int> v;
    v.push_back(a[i]);
    for (int j = i + 1; j < n; j++) {
      int yes = 1;
      for (int k = 0; k < v.size(); k++) {
        int y = v[k] + a[j];
        if (ok[y] == 1) yes = 0;
      }
      if (yes == 1) {
        v.push_back(a[j]);
      }
    }
    if (v.size() > ans.size()) {
      ans = v;
    }
  }
  cout << ans.size() << endl;
  for (int i = 0; i < ans.size(); i++) cout << ans[i] << " ";
}

### Prompt

Please formulate 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 ok[2000001];
int main() {
  cin >> n;
  int a[n];
  for (long long i = 2; i <= 2000000; i++) {
    if (ok[i] == 0) {
      for (long long j = i * 2; j <= 2000000; j += i) {
        ok[j] = 1;
      }
    }
  }
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  vector<int> ans;
  for (int i = 0; i < n; i++) {
    vector<int> v;
    v.push_back(a[i]);
    for (int j = i + 1; j < n; j++) {
      int yes = 1;
      for (int k = 0; k < v.size(); k++) {
        int y = v[k] + a[j];
        if (ok[y] == 1) yes = 0;
      }
      if (yes == 1) {
        v.push_back(a[j]);
      }
    }
    if (v.size() > ans.size()) {
      ans = v;
    }
  }
  cout << ans.size() << endl;
  for (int i = 0; i < ans.size(); i++) cout << ans[i] << " ";
}

```