Your friend Ashley enjoys art inspired by mathematics and you would like to make them a cute birthday card. You have seen the variety of patterns (rays, parabolas, partial symmetry, oh my) in this plot of pythagorean triplets and think you could make something neat with them.
The next step on your creative journey is to find some pythagorean triplets!
A Pythagorean triplet is a set of three natural numbers, {a, b, c}, for which,
a² + b² = c²
and such that,
a < b < c
For example,
3² + 4² = 5².
Given an input integer N, find all Pythagorean triplets for which a + b + c = N.
For example, with N = 1000, there is exactly one Pythagorean triplet for which a + b + c = 1000: {200, 375, 425}.
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