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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