#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC optimization("unroll-loops")
const int N = 2e5 + 5;
const long long int mod = 1e9 + 7;
const long long int Mod = 998244353;
const long double Pi = acos(-1);
const long long int Inf = 4e18;
using namespace std;
bool isPrime(int k) {
  for (int i = 2; i <= sqrt(k); i++) {
    if (k % i == 0) return false;
  }
  return true;
}
void TestCase() {
  int n, c1 = 0;
  cin >> n;
  set<int> eve, odd;
  for (int i = 1, x; i <= n; i++) {
    cin >> x;
    if (x == 1)
      c1++;
    else
      (x % 2 ? odd.insert(x) : eve.insert(x));
  }
  if (c1) {
    int ele = 0;
    for (auto &o : eve) {
      if (isPrime(o + 1)) {
        ele = o;
        break;
      }
    }
    if (ele != 0) {
      cout << c1 + 1 << "\n" << ele << " ";
      for (int i = 1; i <= c1; i++) cout << 1 << " ";
    } else {
      int a = 0, b = 0;
      for (auto &o : eve) {
        for (auto &t : odd) {
          if (isPrime(o + t)) {
            a = o;
            b = t;
            break;
          }
        }
      }
      if (c1 < 2 && a != 0)
        cout << 2 << "\n" << a << " " << b;
      else {
        cout << c1 << "\n";
        for (int i = 1; i <= c1; i++) cout << 1 << " ";
      }
    }
  } else {
    int a = 0, b = 0;
    for (auto &o : eve) {
      for (auto &t : odd) {
        if (isPrime(o + t)) {
          a = o;
          b = t;
          break;
        }
      }
    }
    if (a != 0)
      cout << 2 << "\n" << a << " " << b;
    else {
      cout << 1 << "\n";
      if ((int)eve.size() > 0)
        cout << *eve.begin();
      else
        cout << *odd.begin();
    }
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  ;
  int T = 1;
  while (T--) {
    TestCase();
  }
  return 0;
}

### 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>
#pragma GCC optimize("Ofast")
#pragma GCC optimization("unroll-loops")
const int N = 2e5 + 5;
const long long int mod = 1e9 + 7;
const long long int Mod = 998244353;
const long double Pi = acos(-1);
const long long int Inf = 4e18;
using namespace std;
bool isPrime(int k) {
  for (int i = 2; i <= sqrt(k); i++) {
    if (k % i == 0) return false;
  }
  return true;
}
void TestCase() {
  int n, c1 = 0;
  cin >> n;
  set<int> eve, odd;
  for (int i = 1, x; i <= n; i++) {
    cin >> x;
    if (x == 1)
      c1++;
    else
      (x % 2 ? odd.insert(x) : eve.insert(x));
  }
  if (c1) {
    int ele = 0;
    for (auto &o : eve) {
      if (isPrime(o + 1)) {
        ele = o;
        break;
      }
    }
    if (ele != 0) {
      cout << c1 + 1 << "\n" << ele << " ";
      for (int i = 1; i <= c1; i++) cout << 1 << " ";
    } else {
      int a = 0, b = 0;
      for (auto &o : eve) {
        for (auto &t : odd) {
          if (isPrime(o + t)) {
            a = o;
            b = t;
            break;
          }
        }
      }
      if (c1 < 2 && a != 0)
        cout << 2 << "\n" << a << " " << b;
      else {
        cout << c1 << "\n";
        for (int i = 1; i <= c1; i++) cout << 1 << " ";
      }
    }
  } else {
    int a = 0, b = 0;
    for (auto &o : eve) {
      for (auto &t : odd) {
        if (isPrime(o + t)) {
          a = o;
          b = t;
          break;
        }
      }
    }
    if (a != 0)
      cout << 2 << "\n" << a << " " << b;
    else {
      cout << 1 << "\n";
      if ((int)eve.size() > 0)
        cout << *eve.begin();
      else
        cout << *odd.begin();
    }
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  ;
  int T = 1;
  while (T--) {
    TestCase();
  }
  return 0;
}

```