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,n,h,w,sign;
	while(~scanf("%lld",&N))
	{
		getchar();
		sign=0;
		for(n=1;n<=3500;n++)
		{
			for(h=1;h<=3500;h++)
			{
				w=(N*h*n)/(4*h*n-n*N-h*N);
				if((4*h*n-n*N-h*N)>0&&(N*h*n)%(4*h*n-n*N-h*N)==0) 
				{
					printf("%lld %lld %lld\n",n,h,w);
					
					sign=1;break;
				}
			}
			if(sign) break;
		}
	}
}