Score : 400 points
Joisino is planning to record N TV programs with recorders.
The TV can receive C channels numbered 1 through C.
The i-th program that she wants to record will be broadcast from time s_i to time t_i (including time s_i but not t_i) on Channel c_i.
Here, there will never be more than one program that are broadcast on the same channel at the same time.
When the recorder is recording a channel from time S to time T (including time S but not T), it cannot record other channels from time S-0.5 to time T (including time S-0.5 but not T).
Find the minimum number of recorders required to record the channels so that all the N programs are completely recorded.
Input is given from Standard Input in the following format:
N C s_1 t_1 c_1 : s_N t_N c_N
When the minimum required number of recorders is x, print the value of x.
3 2 1 7 2 7 8 1 8 12 1
2
Two recorders can record all the programs, for example, as follows:
3 4 1 3 2 3 4 4 1 4 3
3
There may be a channel where there is no program to record.
9 4 56 60 4 33 37 2 89 90 3 32 43 1 67 68 3 49 51 3 31 32 3 70 71 1 11 12 3
2