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;
int main() {
  cin >> n;
  if (n == 2) {
    cout << "1\n2";
  } else if (n == 3) {
    cout << "1\n3";
  } else {
    if (n % 2 == 0) {
      cout << n / 2 << '\n';
      for (int i = 1; i <= n / 2; i++) cout << "2 ";
    } else {
      n -= 3;
      cout << n / 2 + 1 << '\n';
      for (int i = 1; i <= n / 2; i++) cout << "2 ";
      cout << "3";
    }
  }
}