A famous inequality problem

Algebra Level 4

\[ \sqrt{5x^2+xy+3y^2}+\sqrt{3x^2+xy+5y^2}+\sqrt{x^2+xy+2y^2} +\sqrt{2x^2+xy+y^2}\]

Let \(x\) and \(y\) be positive reals satisfying \(x+y=2016\). Find the minimum value of the expression above.

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