#include <bits/stdc++.h>
using namespace std;
bool sieve[20000006];
int n, a[1002];
int main() {
  sieve[0] = sieve[1] = true;
  for (int i = 2; i <= 20000006; i++)
    if (sieve[i] == false) {
      for (int j = 2 * i; j <= 20000006; j += i) sieve[j] = true;
    }
  cin >> n;
  int cnt1 = 0;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    if (a[i] == 1) cnt1++;
  }
  int sol = max(cnt1, 1), x = 1, y = 1;
  for (int i = 1; i <= n; i++) {
    if (sieve[a[i] + 1] == false && a[i] != 1 && cnt1 + 1 > sol) {
      sol = cnt1 + 1;
      x = a[i];
      y = 1;
    }
    for (int j = i + 1; j <= n; j++)
      if (sieve[a[i] + a[j]] == false && sol < 2) {
        sol = 2;
        x = a[i];
        y = a[j];
      }
  }
  cout << sol << '\n';
  if (sol == 1) cout << a[1] << ' ';
  if (sol == 2) {
    cout << x << ' ' << y << '\n';
  } else if (sol >= 2) {
    cout << x << ' ' << y << ' ';
    for (int i = 3; i <= sol; i++) cout << 1 << ' ';
  }
  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 sieve[20000006];
int n, a[1002];
int main() {
  sieve[0] = sieve[1] = true;
  for (int i = 2; i <= 20000006; i++)
    if (sieve[i] == false) {
      for (int j = 2 * i; j <= 20000006; j += i) sieve[j] = true;
    }
  cin >> n;
  int cnt1 = 0;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    if (a[i] == 1) cnt1++;
  }
  int sol = max(cnt1, 1), x = 1, y = 1;
  for (int i = 1; i <= n; i++) {
    if (sieve[a[i] + 1] == false && a[i] != 1 && cnt1 + 1 > sol) {
      sol = cnt1 + 1;
      x = a[i];
      y = 1;
    }
    for (int j = i + 1; j <= n; j++)
      if (sieve[a[i] + a[j]] == false && sol < 2) {
        sol = 2;
        x = a[i];
        y = a[j];
      }
  }
  cout << sol << '\n';
  if (sol == 1) cout << a[1] << ' ';
  if (sol == 2) {
    cout << x << ' ' << y << '\n';
  } else if (sol >= 2) {
    cout << x << ' ' << y << ' ';
    for (int i = 3; i <= sol; i++) cout << 1 << ' ';
  }
  return 0;
}

```