Let $P(x) = x^3 + ax^2 + bx + c$ be a polynomial where $a, b, c$ are integers and $c$ is odd. Let $p_i$ be the value of $P(x)$ at $x = i$. Given that $p_1^3 + p_2^3 + p_3^3 = 3p_1p_2p_3$, find the value of $p_2 + 2p_1 - 3p_0$.

Let's think step by step and output the final answer within \boxed{}.
user