#include <bits/stdc++.h>
using namespace std;
int a[1002];
int n;
bool use[2000002];
map<int, int> mp;
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    mp[a[i]]++;
  }
  for (int i = 2; i < 2000002; i++) {
    if (use[i] == false) {
      for (int j = i * 2; j < 2000002; j += i) {
        use[j] = true;
      }
    }
  }
  for (auto it = mp.begin(); it != mp.end(); it++) {
    if ((*it).first >= 2) {
      (*it).second = 1;
    }
  }
  int ans = 0;
  int id = 0;
  if (mp.count(2)) {
    for (auto it = mp.begin(); it != mp.end(); it++) {
      if (use[(*it).first + 2] == false) {
        if (ans < (*it).second + 1) {
          ans = (*it).second + 1;
          id = (*it).first;
        }
      }
    }
  }
  if (mp.count(1)) {
    int anss = 0;
    int id = -1;
    for (auto it = mp.begin(); it != mp.end(); it++) {
      if (use[1 + (*it).first] == false && (*it).first != 1) {
        id = (*it).first;
      }
    }
    anss = mp[1];
    if (id != -1) {
      anss++;
    }
    if (ans < anss && anss > 1) {
      printf("%d\n", anss);
      for (int i = 0; i < mp[1]; i++) {
        if (i) {
          printf(" ");
        }
        printf("1");
      }
      if (id != -1) {
        printf(" %d", id);
      }
      puts("");
      return 0;
    }
  }
  if (ans > 1) {
    cout << ans << endl;
    for (int i = 0; i < mp[2]; i++) {
      if (i) {
        printf(" ");
      }
      printf("2");
    }
    for (int i = 0; i < mp[id]; i++) {
      printf(" %d", id);
    }
    puts("");
    return 0;
  }
  for (auto it = mp.begin(); it != mp.end(); it++) {
    for (auto itt = mp.begin(); itt != mp.end(); itt++) {
      if (it != itt) {
        if (use[(*it).first + (*itt).first] == false) {
          printf("2\n");
          printf("%d %d\n", (*it).first, (*itt).first);
          return 0;
        }
      }
    }
  }
  for (auto it = mp.begin(); it != mp.end(); it++) {
    if (1 || use[(*it).first] == false) {
      puts("1");
      printf("%d\n", (*it).first);
      return 0;
    }
  }
  puts("0");
  puts("");
  return 0;
}

### Prompt

Your task is to create 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 a[1002];
int n;
bool use[2000002];
map<int, int> mp;
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    mp[a[i]]++;
  }
  for (int i = 2; i < 2000002; i++) {
    if (use[i] == false) {
      for (int j = i * 2; j < 2000002; j += i) {
        use[j] = true;
      }
    }
  }
  for (auto it = mp.begin(); it != mp.end(); it++) {
    if ((*it).first >= 2) {
      (*it).second = 1;
    }
  }
  int ans = 0;
  int id = 0;
  if (mp.count(2)) {
    for (auto it = mp.begin(); it != mp.end(); it++) {
      if (use[(*it).first + 2] == false) {
        if (ans < (*it).second + 1) {
          ans = (*it).second + 1;
          id = (*it).first;
        }
      }
    }
  }
  if (mp.count(1)) {
    int anss = 0;
    int id = -1;
    for (auto it = mp.begin(); it != mp.end(); it++) {
      if (use[1 + (*it).first] == false && (*it).first != 1) {
        id = (*it).first;
      }
    }
    anss = mp[1];
    if (id != -1) {
      anss++;
    }
    if (ans < anss && anss > 1) {
      printf("%d\n", anss);
      for (int i = 0; i < mp[1]; i++) {
        if (i) {
          printf(" ");
        }
        printf("1");
      }
      if (id != -1) {
        printf(" %d", id);
      }
      puts("");
      return 0;
    }
  }
  if (ans > 1) {
    cout << ans << endl;
    for (int i = 0; i < mp[2]; i++) {
      if (i) {
        printf(" ");
      }
      printf("2");
    }
    for (int i = 0; i < mp[id]; i++) {
      printf(" %d", id);
    }
    puts("");
    return 0;
  }
  for (auto it = mp.begin(); it != mp.end(); it++) {
    for (auto itt = mp.begin(); itt != mp.end(); itt++) {
      if (it != itt) {
        if (use[(*it).first + (*itt).first] == false) {
          printf("2\n");
          printf("%d %d\n", (*it).first, (*itt).first);
          return 0;
        }
      }
    }
  }
  for (auto it = mp.begin(); it != mp.end(); it++) {
    if (1 || use[(*it).first] == false) {
      puts("1");
      printf("%d\n", (*it).first);
      return 0;
    }
  }
  puts("0");
  puts("");
  return 0;
}

```