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() {
  int k, b = 0, s = 0, i, c = 0, m;
  cin >> k;
  b = k % 2;
  if (b == 1) {
    c++;
    k = k - 3;
    s++;
  }
  c = c + k / 2;
  cout << c << endl;
  for (i = 0; i = k; k = k - 2) {
    cout << "2 ";
    if (k == 0) {
      break;
    }
  }
  if (s == 1) {
    cout << "3";
  }
  return 0;
}