## 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
`22 3`
input
Copy
`6`
output
Copy
`32 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;
}``````
Copy The Code &

Input

cmd
5

Output

cmd
2
2 3