Cyclic Doesn't Mean Symmetric!

Algebra Level 1

Positive reals a,b,ca,b,c satisfy abc=1abc=1. Find the minimum value of

1+ab1+a+1+bc1+b+1+ca1+c.\dfrac{1+ab}{1+a}+\dfrac{1+bc}{1+b}+\dfrac{1+ca}{1+c}.

Enter your answer correct to 3 decimal places.

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