Statement

William, after playing a lot of soccer games on his smartphone, wanted to get involved in an actual soccer team; right now he is helping to manage his local one. There are N players the team would like to buy. For this reason, for the i-th player a meeting has been scheduled on day D_i. Of course, at every meeting there must be at least one representative of the team to negotiate the terms of the contracts. However, the team manager would like to minimize the number of representatives needed. Since the players might live in different cities, it takes C_ij days to go from the city of the i-th player to the city of the j-th one. This means that a team representative can attend the j-th player's meeting after attending the meeting for the i-th player only if D_i + C_ij < D_j. What is the minimum number of representatives needed in order to be able to attend all the meetings?