# Maximum value of f(x,y)

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If $$f(x,y) = \sqrt{x^2+(y-1)^2} + \sqrt{(x-3)^2 + (y-4)^2} - \sqrt{x^2+y^2} - \sqrt{(x-1)^2+y^2}$$. If maximum value of $$f(x,y) = a+\sqrt{b}$$, where $$a,b$$ are positive integers and $$x,y\in \mathbb{R}$$. Then $$a+b =$$

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