P3489 [POI 2009] WIE-Hexer

Byteasar has become a hexer - a conqueror of monsters. Currently he is to return to his hometown Byteburg. The way home, alas, leads through a land full of beasts. Fortunately the habitants, forced to fight the monsters for centuries, have mastered the art of blacksmithery - they are now capable of making special swords that are very efficient against the beasts. The land Byteasar wanders through is quite vast: many towns lie there, and many roads connect them. These roads do not cross outside the towns (mostly because some of them are underground passages). Byteasar has gathered all practical information about the land (all hexers like to know these things). He knows what kind of monsters he may come across each of the roads and how much time he needs to walk it down. He also knows in which villages there are blacksmiths and against what kinds of monsters the swords that they make work. Byteasar wants to get back to Byteburg as soon as possible. As a hexer he is quite ashamed that he does not know the best route, and that he has no sword on him at the moment. Help him find the shortest path to Byteburg such that whenever he could meet some king of monster, previously he would have a chance to get an appropriate sword to fight the beast. You need not worry about the number or weight of the swords - every hexer is as strong as an ox, so he can carry (virtually) unlimited number of equipment, swords in particular.

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