Algorithm


A. Bachgold Problem
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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
Copy
5
output
Copy
2
2 3
input
Copy
6
output
Copy
3
2 2 2

 



 

Code Examples

#1 Code Example with C++ Programming

Code - C++ Programming

#include<bits/stdc++.h>
using namespace std;

int main(){
  int n;
  cin>>n;
  if(n%2 == 0){
    cout<<(n/2)<<endl;
    for(int i = 0; i < n/2; i++){
      cout<<2<<" ";
    }
    cout<<endl;
    return 0;
  }
  cout<<(n/2)<<endl;
  for(int i = 0; i < n/2 - 1; i++){
    cout<<2<<" ";
  }
  cout<<3<<endl;
  return 0;
}
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Input

x
+
cmd
5

Output

x
+
cmd
2
2 3
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Demonstration


Codeforcess Solution 749-A A. Bachgold Problem ,C++, Java, Js and Python ,749-A,Codeforcess Solution

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