Problem 461: Almost Pi

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Let f(k, n) = $e^\frac{k}{n} - 1$, for all non-negative integers k.

Remarkably, f(6, 200) + f(75, 200) + f(89, 200) + f(226, 200) = 3.1415926… ≈ π.

In fact, it is the best approximation of π of the form f(a, 200) + f(b, 200) + f(c, 200) + f(d, 200).

Let almostPi(n) = a2 + b2 + c2 + d2 for a, b, c, d that minimize the error: $\lvert f(a,n) + f(b,n) + f(c,n) + f(d,n) - \Pi\rvert$

You are given almostPi(200) = 62 + 752 + 892 + 2262 = 64658.