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() {
  ios_base::sync_with_stdio(0), cin.tie(0);
  cin >> n;
  if (n == 2) {
    cout << 1 << '\n';
    cout << 2 << '\n';
    return 0;
  }
  if (n == 3) {
    cout << 1 << '\n';
    cout << 3 << '\n';
    return 0;
  }
  if (n % 2 == 0) {
    cout << n / 2 << '\n';
    for (int i = 0; i <= n / 2 - 1; i += 1) cout << 2 << ' ';
    cout << '\n';
  } else {
    cout << n / 2 << '\n';
    for (int i = 0; i <= n / 2 - 1 - 1; i += 1) cout << 2 << ' ';
    cout << 3 << '\n';
  }
  return 0;
}