Statement

Bland Ice is one of the strongest table football player, and he is going around the world playing tournaments to gain the most ranking points possible. The world is made up of N cities, connected by N-1 bidirectional roads. Moving along a single road always take one day, and it is possible to move from any city to any other using the roads. Ice is currently in city 0. Ice knows that there will be M tournaments in the upcoming days, the i-th of which is in city X_i and T_i days in the future. Note that Ice can take part in a tournament on the very same day he arrives in its city. Ice wants to take part in as many tournaments as possible, however he is too busy practicing his "Chinese shot" to plan which tournaments to take part in and he is therefore asking for your help! What's the maximum number of tournaments he can take part in?