HMMT 2006 U44

On the Euclidean plane are given 14 points:

$$\begin{array}{rlrr} A=(0,428) & B=(9,85) & C=(42,865) & D=(192,875) \\ E=(193,219) & F=(204,108) & G=(292,219) & H=(316,378) \\ I=(375,688) & J=(597,498) & K=(679,766) & L=(739,641) \\ & M=(772,307) & & N=(793,0) \\ & \end{array}$$

A fly starts at $A$, visits all the other points, and comes back to $A$ in such a way as to minimize the total distance covered. What path did the fly take? Give the names of the points it visits in order. Your score will be

$$20+\lfloor\text { the optimal distance }\rfloor-\lfloor\text { your distance }\rfloor$$

or 0 , whichever is greater.