HMMT November 2015 U12

Let $a$ and $b$ be positive real numbers. Determine the minimum possible value of

$$\sqrt{a^{2}+b^{2}}+\sqrt{(a-1)^{2}+b^{2}}+\sqrt{a^{2}+(b-1)^{2}}+\sqrt{(a-1)^{2}+(b-1)^{2}}$$