Problem:
Score : 300 points

Problem Statement

You are given an integer N.

Find a triple of positive integers h, n and w such that 4/N = 1/h + 1/n + 1/w.

If there are multiple solutions, any of them will be accepted.

Constraints

It is guaranteed that, for the given integer N, there exists a solution such that h,n,w \leq 3500.

Inputs

Input is given from Standard Input in the following format:

N

Outputs

Print a triple of positive integers h, n and w that satisfies the condition, in the following format:

h n w

Sample Input 1

2

Sample Output 1

1 2 2

4/2 = 1/1 + 1/2 + 1/2.

Sample Input 2

3485

Sample Output 2

872 1012974 1539173474040

It is allowed to use an integer exceeding 3500 in a solution.

Sample Input 3

4664

Sample Output 3

3498 3498 3498

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
int main(){
    
    long long n,a,b,c;
    scanf("%lld",&n);
    
    for(a = 1;a <= 3500;a++)
    {
        for (b = a;b <= 3500;b++)
        {
            c = n*a*b/(4*a*b - n*b - n*a);
            if((4*a*b - n*b - n*a)>0){
                if(n*a*b%(4*a*b - n*b - n*a)==0 )
                {
                    printf("%lld %lld %lld\n",a,b,c);
                    return 0;
                }
            }
        }
    }
    
    return 0;
}