Farmer John has installed a new system of N-1 pipes to transport milk between the N stalls in his barn (2 \leq N \leq 50,000), conveniently numbered 1 \ldots N. Each pipe connects a pair of stalls, and all stalls are connected to each-other via paths of pipes.
FJ is pumping milk between K pairs of stalls (1 \leq K \leq 100,000). For the ith such pair, you are told two stalls s_i and t_i, endpoints of a path along which milk is being pumped at a unit rate. FJ is concerned that some stalls might end up overwhelmed with all the milk being pumped through them, since a stall can serve as a waypoint along many of the K paths along which milk is being pumped. Please help him determine the maximum amount of milk being pumped through any stall. If milk is being pumped along a path from s_i to t_i, then it counts as being pumped through the endpoint stalls s_i and t_i, as well as through every stall along the path between them.
Problem credits: Brian Dean
