Time Limit: Java: 10000 ms / Others: 10000 ms

Memory Limit: Java: 32768 KB / Others: 32768 KB

For hundreds of years Fermat's Last Theorem, which stated simply that for n >
2 there exist no integers a, b, c > 1 such that a^n = b^n + c^n, has remained
elusively unproven. (A recent proof is believed to be correct, though it is still
undergoing scrutiny.) It is possible, however, to find integers greater than 1
that satisfy the ``perfect cube'' equation a^3 = b^3 + c^3 + d^3 (e.g. a quick
calculation will show that the equation 12^3 = 6^3 + 8^3 + 10^3 is indeed true).
This problem requires that you write a program to find all sets of numbers {a,
b, c, d} which satisfy this equation for a <= 200.

The output should be listed as shown below, one perfect cube per line, in non-decreasing order of a (i.e. the lines should be sorted by their a values). The values of b, c, and d should also be listed in non-decreasing order on the line itself. There do exist several values of a which can be produced from multiple distinct sets of b, c, and d triples. In these cases, the triples with the smaller b values should be listed first.

The first part of the output is shown here:

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)

Note: The programmer will need to be concerned with an efficient implementation.
The official time limit for this problem is 2 minutes, and it is indeed possible
to write a solution to this problem which executes in under 2 minutes on a 33
MHz 80386 machine. Due to the distributed nature of the contest in this region,
judges have been instructed to make the official time limit at their site the
greater of 2 minutes or twice the time taken by the judge's solution on the
machine being used to judge this problem.

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