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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

implicit none
integer(8) :: i,j,k,n
read(5,*) n
do i = 1,int(3*n/4)
  do j = int(3*n/4), 3500
       if (4*i*j-N*i-N*j<=0) then
            continue
       else if (mod(N*i*j,4*i*j-N*i-N*j)==0) then
            goto 100
             endif
enddo
enddo
100 write(6,"(i0,1x,i0,1x,i0)") i,j,(N*i*j)/(4*i*j-N*i-N*j)
end