Bachgold 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.

Example

Input

5

Output

2
2 3

Input

6

Output

3
2 2 2
代码

#include <stdio.h>
#include <stdlib.h>

int main()
{
    int n,j;
    while(scanf("%d",&n)!=EOF)
    {
        if(n%2==0)
        {
            printf("%d
",n/2);
            printf("2");
            for(j=1;j<n/2;j++)
            {
                printf(" 2");
            }
            printf("
");
        }
        else if(n==3)
        {
            printf("1
3
");
        }
        else
        {
            printf("%d
",n/2);
            printf("2");
            for(j=2;j<n/2;j++)
            {
                printf(" 2");
            }
            printf(" 3
");
        }

    }
    return 0;
}