# Machine Schedule

Source : ACM ICPC Beijing Regional Contest 2002 |
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Time limit : 1 sec |
Memory limit : 32 M |

**Submitted** : 478, **Accepted** : 262

As we all know, machine scheduling is a very classical problem in computer
science and has been studied for a very long history. Scheduling problems differ
widely in the nature of the constraints that must be satisfied and the type
of schedule desired. Here we consider a 2-machine scheduling problem.

There are two machines A and B. Machine A has n kinds of working modes, which
is called mode_0, mode_1, …, mode_n-1, likewise machine B has m kinds of working
modes, mode_0, mode_1, … , mode_m-1. At the beginning they are both work at
mode_0.

For k jobs given, each of them can be processed in either one of the two machines
in particular mode. For example, job 0 can either be processed in machine A
at mode_3 or in machine B at mode_4, job 1 can either be processed in machine
A at mode_2 or in machine B at mode_4, and so on. Thus, for job i, the constraint
can be represent as a triple (i, x, y), which means it can be processed either
in machine A at mode_x, or in machine B at mode_y.

Obviously, to accomplish all the jobs, we need to change the machine's working
mode from time to time, but unfortunately, the machine's working mode can only
be changed by restarting it manually. By changing the sequence of the jobs and
assigning each job to a suitable machine, please write a program to minimize
the times of restarting machines.

**Input**

The input file for this program consists of several configurations. The first
line of one configuration contains three positive integers: n, m (n, m <
100) and k (k < 1000). The following k lines give the constrains of the k
jobs, each line is a triple: i, x, y.

The input will be terminated by a line containing a single zero.

**Output**

The output should be one integer per line, which means the minimal times of
restarting machine.

**Sample Input**

5 5 10 0 1 1 1 1 2 2 1 3 3 1 4 4 2 1 5 2 2 6 2 3 7 2 4 8 3 3 9 4 3 0

Sample Output

3