#include <bits/stdc++.h>
#pragma GCC target("avx2")
#pragma GCC optimization("O3")
#pragma GCC optimization("unroll-loops")
using namespace std;
template <class T1, class T2>
inline bool chmax(T1 &a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmin(T1 &a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
const double EPS = 1e-9, PI = acos(-1);
const double pi = 3.141592653589793238462643383279;
template <int mod>
struct ModInt {
  int x;
  ModInt() : x(0) {}
  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }
  ModInt operator-() const { return ModInt(-x); }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }
  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }
  static int get_mod() { return mod; }
};
using modint = ModInt<1000000007>;
template <typename T>
struct Combination {
  vector<T> _fact, _rfact, _inv;
  Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
    _fact[0] = _rfact[sz] = _inv[0] = 1;
    for (int i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;
    _rfact[sz] /= _fact[sz];
    for (int i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);
    for (int i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];
  }
  inline T fact(int k) const { return _fact[k]; }
  inline T rfact(int k) const { return _rfact[k]; }
  inline T inv(int k) const { return _inv[k]; }
  T P(int n, int r) const {
    if (r < 0 || n < r) return 0;
    return fact(n) * rfact(n - r);
  }
  T C(int p, int q) const {
    if (q < 0 || p < q) return 0;
    return fact(p) * rfact(q) * rfact(p - q);
  }
  T H(int n, int r) const {
    if (n < 0 || r < 0) return (0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};
long long GCD(long long a, long long b) { return (b == 0) ? a : GCD(b, a % b); }
long long LCM(long long a, long long b) { return a / GCD(a, b) * b; }
std::vector<int> sieve(int n) {
  std::vector<int> res(n);
  std::iota(res.begin(), res.end(), 0);
  for (int i = 2; i * i < n; ++i) {
    if (res[i] < i) continue;
    for (int j = i * i; j < n; j += i)
      if (res[j] == j) res[j] = i;
  }
  return res;
}
std::vector<int> factor(int n, const std::vector<int> &min_factor) {
  std::vector<int> res;
  while (n > 1) {
    res.push_back(min_factor[n]);
    n /= min_factor[n];
  }
  return res;
}
int cnt[1010101];
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(12);
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < (int)n; ++i) cin >> a[i];
  for (int i = 0; i < (int)n; ++i) cnt[a[i]]++;
  auto s = sieve(2000001);
  if (cnt[1] >= 2) {
    int t = -1;
    for (int i = 0; i < (int)n; ++i) {
      if (a[i] == 1) continue;
      if (s[1 + a[i]] == 1 + a[i]) {
        t = a[i];
      }
    }
    cout << cnt[1] + ((t != -1) ? 1 : 0) << endl;
    for (int i = 0; i < (int)cnt[1]; ++i) {
      if (i) cout << " ";
      cout << 1;
    }
    if (t != -1) cout << " " << t;
    cout << endl;
  } else {
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if (i != j) {
          int sum = a[i] + a[j];
          if (s[sum] == sum) {
            cout << 2 << endl;
            cout << a[i] << " " << a[j] << endl;
            return 0;
          }
        }
      }
    }
    cout << 1 << endl;
    cout << a[0] << endl;
  }
  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>
#pragma GCC target("avx2")
#pragma GCC optimization("O3")
#pragma GCC optimization("unroll-loops")
using namespace std;
template <class T1, class T2>
inline bool chmax(T1 &a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmin(T1 &a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
const double EPS = 1e-9, PI = acos(-1);
const double pi = 3.141592653589793238462643383279;
template <int mod>
struct ModInt {
  int x;
  ModInt() : x(0) {}
  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }
  ModInt operator-() const { return ModInt(-x); }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }
  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }
  static int get_mod() { return mod; }
};
using modint = ModInt<1000000007>;
template <typename T>
struct Combination {
  vector<T> _fact, _rfact, _inv;
  Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
    _fact[0] = _rfact[sz] = _inv[0] = 1;
    for (int i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;
    _rfact[sz] /= _fact[sz];
    for (int i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);
    for (int i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];
  }
  inline T fact(int k) const { return _fact[k]; }
  inline T rfact(int k) const { return _rfact[k]; }
  inline T inv(int k) const { return _inv[k]; }
  T P(int n, int r) const {
    if (r < 0 || n < r) return 0;
    return fact(n) * rfact(n - r);
  }
  T C(int p, int q) const {
    if (q < 0 || p < q) return 0;
    return fact(p) * rfact(q) * rfact(p - q);
  }
  T H(int n, int r) const {
    if (n < 0 || r < 0) return (0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};
long long GCD(long long a, long long b) { return (b == 0) ? a : GCD(b, a % b); }
long long LCM(long long a, long long b) { return a / GCD(a, b) * b; }
std::vector<int> sieve(int n) {
  std::vector<int> res(n);
  std::iota(res.begin(), res.end(), 0);
  for (int i = 2; i * i < n; ++i) {
    if (res[i] < i) continue;
    for (int j = i * i; j < n; j += i)
      if (res[j] == j) res[j] = i;
  }
  return res;
}
std::vector<int> factor(int n, const std::vector<int> &min_factor) {
  std::vector<int> res;
  while (n > 1) {
    res.push_back(min_factor[n]);
    n /= min_factor[n];
  }
  return res;
}
int cnt[1010101];
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(12);
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < (int)n; ++i) cin >> a[i];
  for (int i = 0; i < (int)n; ++i) cnt[a[i]]++;
  auto s = sieve(2000001);
  if (cnt[1] >= 2) {
    int t = -1;
    for (int i = 0; i < (int)n; ++i) {
      if (a[i] == 1) continue;
      if (s[1 + a[i]] == 1 + a[i]) {
        t = a[i];
      }
    }
    cout << cnt[1] + ((t != -1) ? 1 : 0) << endl;
    for (int i = 0; i < (int)cnt[1]; ++i) {
      if (i) cout << " ";
      cout << 1;
    }
    if (t != -1) cout << " " << t;
    cout << endl;
  } else {
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if (i != j) {
          int sum = a[i] + a[j];
          if (s[sum] == sum) {
            cout << 2 << endl;
            cout << a[i] << " " << a[j] << endl;
            return 0;
          }
        }
      }
    }
    cout << 1 << endl;
    cout << a[0] << endl;
  }
  return 0;
}

```