12. As shown in the figure, rectangle $ABCD$ is a cargo yard with a length of 1000 meters and a width of 600 meters, with entrances at $A$ and $D$. A toll booth $P$ is to be built inside the cargo yard, and a loading platform $H$ is to be built on the railway segment $BC$. The minimum sum of the lengths of the three roads $AP$, $DP$, and $PH$ is $\qquad$ meters.
Answer: $500 \sqrt{3}+600$