27621번 - Sum of Three Cubes 스페셜 저지다국어

Recently, a mathematician has just found three cube numbers that sum up to 42 using over a million hours of computing time. With this breakthrough, we have found three cube numbers that sum up to all non-negative integers less than 100 if it is possible to do so. In other words, for every 0 ≤ N < 100, we have found the triples (X, Y, Z) such that X³ + Y³ + Z³ = N, or we have proved that no such triplet exists.

The following is a table of (X, Y, Z) that satisfies X³ + Y³ + Z³ = N for 0 ≤ N < 50.

Reading a long table is a tedious job, so you would like to create a program that takes N as an input, and produce X, Y, Z as the output. The value of X, Y, and Z must be an integer not less than −10¹⁸ and not more than 10¹⁸.

Input begins with a line containing an integer: N (0 ≤ N < 50).

Output in a line three integers (separated by a single space): X Y Z that satisfies the condition given in the problem statement. If there is more than one solution, you can output any of them. If there is no solution, output 0 instead.