In the mathematics of sums of powers, it is an open problem to characterize the numbers that can be expressed as a sum of three cubes of integers, allowing both positive and negative cubes in the sum. A necessary condition for an integer \(k\) to equal such a sum is that \(k\) cannot equal 4 or 5 modulo 9, because the cubes modulo 9 are 0, 1, and −1, and no three of these numbers can sum to 4 or 5 modulo 9. It is unknown whether this necessary condition is sufficient.
Provided an integer \(k\) on standard input, write a solution to the sum of three cubes problem to stdout. The output should consist of three lines, representing the non-zero integers \(x\), \(y\) and \(z\) in the formula \(x^3+y^3+z^3 = k\).
You may assume that only \(k\) for which such a representation exists will be given as an input.
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