How many ordered triples of rational numbers $(a, b, c)$ are there such that the cubic polynomial $f(x) = x^3 + ax^2 + bx + c$ has roots $a, b$ and $c$?

**Details and assumptions**

The polynomial is allowed to have repeated roots. The polynomial $(x-1)^2 (x+2)$ has 3 roots which are $1, 1, -2$, while the polynomial $(x-1)(x+2)$ has 2 roots which are $1, -2$.

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