Maximize This

Algebra Level 3

Subject to a,b,c0 a, b, c \geq 0 and a+b+c=3 a + b + c = 3 , what is the maximium value of

(a2a+1)(b2b+1)(c2c+1)? \big(a^2 - a + 1\big) \big( b^2 - b + 1\big) \big( c^2 - c + 1 \big) ?

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