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;
vector<int> colour[10000];
list<int> l;
long long int n, m, k, a, b, c, cnt, cnt1, res, sum, mx, mn, T, testcase;
bool flag;
int main() {
  cin >> n;
  cout << n / 2 << endl;
  if (n % 2) {
    for (int i = 1; i < n / 2; i++) cout << " 2";
    cout << " 3" << endl;
  } else {
    for (int i = 1; i <= n / 2; i++) cout << " 2";
    cout << endl;
  }
  return 0;
}