#include <bits/stdc++.h>
using namespace std;
using namespace std;
const int maxn = 1000005;
const int mod = 998244353;
bool isp[maxn * 2];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int c1 = 0;
  int n;
  cin >> n;
  vector<int> v(n);
  for (int i = 2; i < maxn * 2; i++) {
    if (isp[i]) continue;
    for (int j = i * 2; j < maxn * 2; j += i) {
      isp[j] = 1;
    }
  }
  int p = 0;
  for (auto &i : v) {
    cin >> i;
    if (i == 1) {
      c1++;
    }
    if (!isp[i + 1] && i != 1) {
      p = i;
    }
  }
  if (c1 + (p != 0) >= 2) {
    cout << c1 + (p != 0) << '\n';
    for (int i = 0; i < c1; i++) {
      cout << 1 << ' ';
    }
    if (p) cout << p << '\n';
    exit(0);
  }
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      if (!isp[v[i] + v[j]]) {
        cout << 2 << '\n';
        cout << v[i] << ' ' << v[j] << '\n';
        exit(0);
      }
    }
  }
  cout << 1 << '\n';
  cout << v[0] << endl;
}

### 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;
using namespace std;
const int maxn = 1000005;
const int mod = 998244353;
bool isp[maxn * 2];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int c1 = 0;
  int n;
  cin >> n;
  vector<int> v(n);
  for (int i = 2; i < maxn * 2; i++) {
    if (isp[i]) continue;
    for (int j = i * 2; j < maxn * 2; j += i) {
      isp[j] = 1;
    }
  }
  int p = 0;
  for (auto &i : v) {
    cin >> i;
    if (i == 1) {
      c1++;
    }
    if (!isp[i + 1] && i != 1) {
      p = i;
    }
  }
  if (c1 + (p != 0) >= 2) {
    cout << c1 + (p != 0) << '\n';
    for (int i = 0; i < c1; i++) {
      cout << 1 << ' ';
    }
    if (p) cout << p << '\n';
    exit(0);
  }
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      if (!isp[v[i] + v[j]]) {
        cout << 2 << '\n';
        cout << v[i] << ' ' << v[j] << '\n';
        exit(0);
      }
    }
  }
  cout << 1 << '\n';
  cout << v[0] << endl;
}

```