#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e6;
int a[maxn];
bool tub[maxn + 1];
int main() {
  for (int i = 2; i * i <= maxn; i++) {
    if (!tub[i]) {
      for (int j = i * i; j <= maxn; j += i) tub[j] = 1;
    }
  }
  int n;
  cin >> n;
  int ans = 0, ans1 = 1, ans_x = a[0];
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    if (a[i] == 1) ans++;
  }
  for (int i = 1; i <= n; i++) {
    for (int j = i + 1; j <= n; j++) {
      if (!tub[a[i] + a[j]]) {
        if (ans < 2) {
          cout << 2 << endl;
          cout << a[i] << " " << a[j];
          return 0;
        }
      }
    }
  }
  if (ans > 0) {
    int ok = 0;
    for (int i = 1; i <= n; i++) {
      if (a[i] != 1 && !tub[a[i] + 1]) {
        ok = a[i];
        break;
      }
    }
    if (ok) {
      cout << ans + 1 << endl;
      for (int i = 1; i <= ans; i++) cout << 1 << " ";
      cout << ok;
    } else {
      cout << ans << endl;
      for (int i = 1; i <= ans; i++) cout << 1 << " ";
    }
  } else {
    cout << 1 << endl << a[1];
  }
}

### Prompt

Develop a solution in cpp 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 maxn = 2e6;
int a[maxn];
bool tub[maxn + 1];
int main() {
  for (int i = 2; i * i <= maxn; i++) {
    if (!tub[i]) {
      for (int j = i * i; j <= maxn; j += i) tub[j] = 1;
    }
  }
  int n;
  cin >> n;
  int ans = 0, ans1 = 1, ans_x = a[0];
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    if (a[i] == 1) ans++;
  }
  for (int i = 1; i <= n; i++) {
    for (int j = i + 1; j <= n; j++) {
      if (!tub[a[i] + a[j]]) {
        if (ans < 2) {
          cout << 2 << endl;
          cout << a[i] << " " << a[j];
          return 0;
        }
      }
    }
  }
  if (ans > 0) {
    int ok = 0;
    for (int i = 1; i <= n; i++) {
      if (a[i] != 1 && !tub[a[i] + 1]) {
        ok = a[i];
        break;
      }
    }
    if (ok) {
      cout << ans + 1 << endl;
      for (int i = 1; i <= ans; i++) cout << 1 << " ";
      cout << ok;
    } else {
      cout << ans << endl;
      for (int i = 1; i <= ans; i++) cout << 1 << " ";
    }
  } else {
    cout << 1 << endl << a[1];
  }
}

```