You are given a matrix of size $n\times m$. Initally, the matrix contains $0s$. There are $q$ queries and you must process them sequentially by performing the following operations:

1. $toggle(x,y)$: If the value of $(x,y)$ is $0$, then change it to $1$ and vice versa.
2. For each pair $(x,y)$, perform the first query.

Your task is to count the remaining number of $1s$ that are available after the $q$ queries.

Input format

• First line: Three integers $n$, $m$, and $q$ ($1\leq n,m\leq 10^9,1\leq q\leq 10^5$)
• Each $q$ line contains the following:
  • $1\ x\ y$ that denotes the first operation ($1\leq x_i\leq n,1\leq y_i\leq m$)
  • $2$ denotes the second operation