#include <bits/stdc++.h>
using namespace std;
int n, A[1005], n1, n2;
int pr(int x) {
  if (x < 2) return 0;
  if (x == 2) return 1;
  if (x % 2 == 0) return 0;
  for (int d = 3; d * d <= x; d += 2)
    if (x % d == 0) return 0;
  return 1;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.precision(10);
  cout << fixed;
  cin >> n;
  for (int i = 0; i < (int)(n); ++i) cin >> A[i];
  sort(A, A + n);
  for (int i = 0; i < (int)(n); ++i) {
    if (A[i] == 1)
      n1++;
    else if (pr(A[i] + 1))
      n2 = A[i];
  }
  int re = max(1, n1 + (int)((bool)n2));
  if (re >= 2) {
    cout << re << "\n";
    for (int i = 1; i <= (int)(n1); ++i) cout << "1 ";
    if (n2) cout << n2;
    return 0;
  }
  for (int i = 0; i < (int)(n); ++i)
    for (int j = 0; j < (int)(n); ++j)
      if (i != j && pr(A[i] + A[j])) {
        cout << "2\n" << A[i] << " " << A[j];
        return 0;
      }
  cout << re << "\n" << A[0];
  return 0;
}

### Prompt

Generate 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, A[1005], n1, n2;
int pr(int x) {
  if (x < 2) return 0;
  if (x == 2) return 1;
  if (x % 2 == 0) return 0;
  for (int d = 3; d * d <= x; d += 2)
    if (x % d == 0) return 0;
  return 1;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.precision(10);
  cout << fixed;
  cin >> n;
  for (int i = 0; i < (int)(n); ++i) cin >> A[i];
  sort(A, A + n);
  for (int i = 0; i < (int)(n); ++i) {
    if (A[i] == 1)
      n1++;
    else if (pr(A[i] + 1))
      n2 = A[i];
  }
  int re = max(1, n1 + (int)((bool)n2));
  if (re >= 2) {
    cout << re << "\n";
    for (int i = 1; i <= (int)(n1); ++i) cout << "1 ";
    if (n2) cout << n2;
    return 0;
  }
  for (int i = 0; i < (int)(n); ++i)
    for (int j = 0; j < (int)(n); ++j)
      if (i != j && pr(A[i] + A[j])) {
        cout << "2\n" << A[i] << " " << A[j];
        return 0;
      }
  cout << re << "\n" << A[0];
  return 0;
}

```