A famous inequality problem

Algebra Level 5

5x2+xy+3y2+3x2+xy+5y2+x2+xy+2y2+2x2+xy+y2 \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 xx and yy be positive reals satisfying x+y=2016x+y=2016. Find the minimum value of the expression above.

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