Let f_n(k) = e^k/n - 1, for all non-negative integers k.

Remarkably, f₂₀₀(6) + f₂₀₀(75) + f₂₀₀(89) + f₂₀₀(226) = 3.141592644529… ≈ π.

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

Let g(n) = a² + b² + c² + d² for a, b, c, d that minimize the error: | f_n(a) + f_n(b) + f_n(c) + f_n(d) - π|
(where |x| denotes the absolute value of x).

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

Find g(10000).