# Hello IMOment 3

Algebra Level 5

$\large (a^2-bc)(b^2-ca)(c^2-ab)$

Let $$a$$, $$b$$ and $$c$$ are real numbers such that $$a^2+b^2+c^2=1$$.

Let $$M$$ be the maximum value of above expression. Find $$\left\lfloor 1000M\right\rfloor$$.

Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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