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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