Minimizing Sum Of Roots

Algebra Level 5

x2+4+(x2)2+(y2)2+4+(3y)2\sqrt{x^2+4}+\sqrt{(x-2)^2+(y-2)^2}+\sqrt{4+(3-y)^2}

Let xx and yy be real numbers. And Let ss be the minimum value of the above expression. Find the value of 1000s\lfloor 1000s\rfloor.

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