What an odd match. People keep saying the div1 medium was too easy. I just can't see it. From what I am looking at it is going to be very hard to explain. Whole match was incompatible with my editorial method. Problems are too hard to explain when they tend to be "obvious".
Now that I understand div1 hard better, I think that the "dirty tricks" solution I used during the match can be shown to have a very low probability to fail. From the analysis it sorts of follows that the number of beacons tends to be high. Except in cases were it should be easy to find the solution through the brute force anyway.