Peter has recently been fascinated by numbers that can be expressed in the form $f(a, b, c) = a(b-c)^3+b(c-a)^3+c(a-b)^3$ for some integers $a,b$ and $c$. He thinks that we should use this system to do arithmetic in future.

How many positive integers $N \leq 1000$ can be expressed in the form of $f(a, b, c)$?

**Details and assumptions**

As a specific example, since $f(-1, 2, 3) = 48$, hence $48$ can be expressed in the form of $f(a, b, c)$.

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