Again, minimum value

Algebra Level 4

x2+y2xy+(1x)2+(2y)2(1x)(2y) \sqrt{x^2+y^2-xy}+\sqrt{(1-x)^2+(2-y)^2-(1-x)(2-y)}

If 0<x<10 < x < 1 and 0<y<2,0 < y < 2, then the minimum value of the expression above is s.s. What is 1000s?\lfloor 1000s\rfloor?

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