Again, minimum value

Algebra Level 4

\[ \sqrt{x^2+y^2-xy}+\sqrt{(1-x)^2+(2-y)^2-(1-x)(2-y)}\]

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

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