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 n, k;
vector<int> ans;
void solve() {
  scanf("%d", &n);
  while (n > 3) {
    ans.emplace_back(2);
    n -= 2;
  }
  ans.emplace_back(n);
  printf("%d\n", (int)ans.size());
  for (auto x : ans) printf("%d ", x);
}
int main() {
  int t = 1;
  while (t--) solve();
  return 0;
}