3973: Smile House
Description
A smile house is created to raise the mood. It has n rooms. Some of the rooms are connected by doors. For each two rooms (number i and j), which are connected by a door, Petya knows their value cij − the value which is being added to his mood when he moves from room i to room j.
Petya wondered whether he can raise his mood infinitely, moving along some cycle? And if he can, then what minimum number of rooms he will need to visit during one period of a cycle?
The first line contains two positive integers n and m (
), where n is the number of rooms, and m is the number of doors in the Smile House. Then follows the description of the doors: m lines each containing four integers i, j, cij , cji (1≤i,j≤n,i≠j,-104≤cij,cji≤104). It is guaranteed that no more than one door connects any two rooms. No door connects the room with itself.
Print the minimum number of rooms that one needs to visit during one traverse of the cycle that can raise mood infinitely. If such cycle does not exist, print number 0.
4 4
1 2 -10 3
1 3 1 -10
2 4 -10 -1
3 4 0 -3
4
Cycle is such a sequence of rooms a1, a2, ..., ak, that a1 is connected with a2, a2 is connected with a3, ..., ak-1 is connected with ak, ak is connected with a1. Some elements of the sequence can coincide, that is, the cycle should not necessarily be simple. The number of rooms in the cycle is considered as k, the sequence's length. Note that the minimum possible length equals two.