Problem: Bachgold problem is very easy to formulate. Given a positive integer n represent it as a sum of maximum possible number of prime numbers. One can prove that such representation exists for any integer greater than 1.

Recall that integer k is called prime if it is greater than 1 and has exactly two positive integer divisors — 1 and k. 

Input

The only line of the input contains a single integer n (2 ≤ n ≤ 100 000).

Output

The first line of the output contains a single integer k — maximum possible number of primes in representation.

The second line should contain k primes with their sum equal to n. You can print them in any order. If there are several optimal solution, print any of them.

Examples

Input

5


Output

2
2 3


Input

6


Output

3
2 2 2

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int64_t n;
  cin >> n;
  multiset<int64_t> S;
  if (n & 1) {
    n--;
    cout << n / 2 << endl;
    while (n) {
      S.insert(2);
      n = n - 2;
    }
    auto itr = S.end();
    itr--;
    S.erase(itr);
    S.insert(3);
  } else {
    cout << n / 2 << endl;
    while (n) {
      S.insert(2);
      n = n - 2;
    }
  }
  for (auto itr = S.begin(); itr != S.end(); itr++) {
    cout << (*itr) << " ";
  }
}