Project Euler #142: Perfect Square Collection

_{This problem is a programming version of Problem 142 from projecteuler.net}

Print triples of integers such that , , and , , , , , are all perfect squares.

Input Format

The input contains a single integer, .

Constraints

Input #00:
Input #01:
Input #02:
Input #03:
Input #04:
Input #05:
Input #06:
Input #07:
Input #08:

Output Format

Output lines, where each line contains three integers separated by single spaces: , and .

Sample Input

Sample Output

472226642633 463877982992 452392145408

Explanation

The problem asks us to output a single triple . The sample output gives:

You can verify that:

You can output other triples aside from this, as long as they satisfy the constraints.