Problem: Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.

More formally, you are given an odd numer n. Find a set of numbers pi (1 ≤ i ≤ k), such that

  1. 1 ≤ k ≤ 3
  2. pi is a prime
  3. <image>



The numbers pi do not necessarily have to be distinct. It is guaranteed that at least one possible solution exists.

Input

The single line contains an odd number n (3 ≤ n < 109).

Output

In the first line print k (1 ≤ k ≤ 3), showing how many numbers are in the representation you found.

In the second line print numbers pi in any order. If there are multiple possible solutions, you can print any of them.

Examples

Input

27


Output

3
5 11 11

Note

A prime is an integer strictly larger than one that is divisible only by one and by itself.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
template <typename T>
void UpdateMin(T& a, const T b) {
  a = std::min(a, b);
}
template <typename T>
void UpdateMax(T& a, const T b) {
  a = std::max(a, b);
}
static const long double Eps = 1.0e-09;
template <typename T>
bool IsEqual(const T a, const T b) {
  return std::abs(a - b) < Eps;
}
template <typename T>
bool IsGreater(const T a, const T b) {
  return a > b + Eps;
}
template <typename T>
bool IsLess(const T a, const T b) {
  return a + Eps < b;
}
template <typename T>
std::string ToStr(const T& val) {
  std::ostringstream ostr;
  ostr << val;
  return ostr.str();
}
template <typename T>
bool FromStr(const std::string& str, T& val) {
  std::istringstream istr(str);
  istr >> val;
  return !!istr;
}
template <typename T>
std::istream& operator>>(std::istream& ist, std::vector<T>& data) {
  ;
  for (size_t i = 0; i < data.size(); i++) {
    ist >> data[i];
  }
  return ist;
}
template <typename T>
T Read(std::istream& ist) {
  ;
  T val;
  ist >> val;
  return val;
}
template <typename T>
std::ostream& operator<<(std::ostream& ost, const std::vector<T>& data) {
  for (size_t i = 0; i < data.size(); i++) {
    if (i != 0) {
      ost << ' ';
    }
    ost << data[i];
  }
  return ost;
}
template <size_t id>
class StopWatch {};
static std::vector<uint8_t> GetPrimeNumbersMask(const uint32_t MaxValue) {
  std::vector<uint8_t> isPrime(MaxValue + 1, 1);
  isPrime[0] = 0;
  isPrime[1] = 0;
  for (uint32_t i = 2; i <= MaxValue; i++) {
    if (isPrime[i] != 0) {
      if ((uint64_t)i * i > MaxValue) continue;
      for (uint32_t j = i * i; j <= MaxValue; j += i) isPrime[j] = 0;
    }
  }
  return isPrime;
}
const uint32_t MaxBruteForceVal = 1000000;
bool IsPrime(const uint32_t z, const std::vector<uint32_t>& primes) {
  if (z < 2) return false;
  if (z == 2) return true;
  for (size_t i = 0; i < primes.size(); i++) {
    const uint64_t p = primes[i];
    if (z % p == 0) return false;
    if (p * p > z) break;
  }
  const uint64_t lastPrime = *primes.rbegin();
  ;
  return true;
}
bool TryBruteForce(const uint32_t z, const std::vector<uint8_t>&,
                   const std::vector<uint32_t>& primes,
                   std::vector<uint32_t>& numbers) {
  numbers.clear();
  if (IsPrime(z, primes)) {
    numbers.push_back(z);
    return true;
  };
  if (IsPrime(z - 2, primes)) {
    numbers.push_back(2);
    numbers.push_back(z - 2);
    return true;
  }
  const size_t mx = 10;
  for (size_t a = 0; a < mx; a++) {
    const uint32_t va = primes[a];
    for (size_t b = 0; b < mx; b++) {
      const uint32_t vb = primes[b];
      for (size_t c = 0; c < mx; c++) {
        const uint32_t vc = primes[c];
        if (va + vb + vc == z) {
          numbers.push_back(va);
          numbers.push_back(vb);
          numbers.push_back(vc);
          return true;
        }
      }
    }
  }
  return false;
}
std::vector<uint32_t> GetAns(const uint32_t z,
                             const std::vector<uint8_t>& isPrime,
                             const std::vector<uint32_t>& primes) {
  std::vector<uint32_t> numbers;
  if (TryBruteForce(z, isPrime, primes, numbers)) return numbers;
  numbers.clear();
  numbers.push_back(3);
  const uint32_t x = z - 3;
  const uint32_t mid = x / 2;
  for (uint32_t i = 1; i < mid; i++) {
    {
      const uint32_t vb = mid - i;
      const uint32_t vc = mid + i;
      if (IsPrime(vb, primes) && IsPrime(vc, primes)) {
        numbers.push_back(vb);
        numbers.push_back(vc);
        return numbers;
      }
    }
    {
      const uint32_t vb = i;
      const uint32_t vc = x - i;
      if (IsPrime(vb, primes) && IsPrime(vc, primes)) {
        numbers.push_back(vb);
        numbers.push_back(vc);
        return numbers;
      }
    }
  };
  return std::vector<uint32_t>();
}
bool Solve(std::istream& ist, std::ostream& ost, const bool multipleTestMode) {
  StopWatch<1> sw;
  (void)sw;
  uint32_t n;
  ist >> n;
  if (multipleTestMode && !ist) return false;
  const std::vector<uint8_t> isPrime = GetPrimeNumbersMask(MaxBruteForceVal);
  std::vector<uint32_t> primes;
  for (size_t i = 0; i < isPrime.size(); i++) {
    if (isPrime[i]) {
      primes.push_back(i);
    }
  }
  const std::vector<uint32_t> ans = GetAns(n, isPrime, primes);
  ost << ans.size() << std::endl;
  ost << ans << std::endl;
  ;
  for (size_t i = 0; i < ans.size(); i++) {
    ;
  }
  return multipleTestMode;
}
int main(int argc, const char* argv[]) {
  std::ios_base::sync_with_stdio(false);
  std::istream* ist = &std::cin;
  std::ostream* ost = &std::cout;
  std::unique_ptr<std::istream> fileInput;
  if (argc > 1) {
    fileInput.reset(new std::ifstream(argv[1]));
    if (!(*fileInput)) {
      std::cout << "File not found: " << argv[1] << std::endl;
    }
    ist = fileInput.get();
  }
  Solve(*ist, *ost, false);
}