BD-BDMO 2021 Problem 2

Let $u, v$ be real numbers. The minimum value of $\sqrt{u^2+v^2} +\sqrt{(u-1)^2+v^2}+\sqrt {u^2+ (v-1)^2}+ \sqrt{(u-1)^2+(v-1)^2}$ can be written as $\sqrt{n}$ . Find the value of $10n$ .