Maximize This

Algebra Level 2

Subject to \( a, b, c \geq 0 \) and \( a + b + c = 3 \), what is the maximium value of

\[ \big(a^2 - a + 1\big) \big( b^2 - b + 1\big) \big( c^2 - c + 1 \big) ? \]

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