Perfect Cubes

Problem Background

Special for beginners, ^_^

Problem Description

An equation of the form $a^3 = b^3 + c^3 + d^3$ is called a perfect cube equation. For example $12^3 = 6^3 + 8^3 + 10^3$.

Write a program that, for a given positive integer $N\ (N \le 100)$, finds all quadruples $(a, b, c, d)$ such that $a^3 = b^3 + c^3 + d^3$, where $a, b, c, d$ are greater than $1$, less than or equal to $N$, and $b \le c \le d$.

Input Format

A positive integer $N\ (N \le 100)$.

Output Format

Output one perfect cube per line, in the following format:

Cube = a, Triple = (b,c,d)

where $a, b, c, d$ are replaced by the actual values of the quadruple.

Output in ascending order of $a$. When two perfect cube equations have the same $a$, output the one with the smaller $b$ first; if still equal, the smaller $c$ first; if still equal, the smaller $d$ first.

Sample Input

24

Sample Output

Cube = 6, Triple = (3,4,5)
Cube = 12, Triple = (6,8,10)
Cube = 18, Triple = (2,12,16)
Cube = 18, Triple = (9,12,15)
Cube = 19, Triple = (3,10,18)
Cube = 20, Triple = (7,14,17)
Cube = 24, Triple = (12,16,20)

Constraints

1s, 1024KiB for each test case.