9036: We are the Lights

 
One day, Bobo was attending an international light exhibition and noticed a grid of n×m  lights arranged in $n$ rows and $m$ columns. Initially, all lights were off.

Bobo noticed that there were two buttons for each row and column, one for turning on and one for turning off. This means that he can perform the following four operations:

1. row  $i$ on: turns on all the lights in row i.
2. row  $i$ off: turns off all the lights in row $i$.
3. column  $i$ on: turns on all the lights in column $i$.
4. column  $i$ off: turns off all the lights in column $i$.

Mischievous Bobo, of course, will not miss this opportunity. You are given q  operations performed by Bobo. You need to determine the number of lights that are on after performing q  operations in sequence.

 
The first line contains three positive integers n , m , and q  (1≤n,m≤106,1≤q≤106) , denoting the number of rows and columns of the lights, and the number of operations that Bobo performs.
The next $q$ lines contain an operation each, with the form of each operation already given in the problem description.

 
Output an integer in one line, denoting the number of lights that are turned on after performing q  operations in order.