Alice, a well-known scientist in Berland, has a floor of size $N*M$ in his research laboratory, with each tile measuring $1X1$. If a drop of chemical falls on a tile, it will combine to form a larger drop if there is a drop of chemical solution present in the adjacent tile that shares the common sides or edges.
Note: If a chemical solution falls on the same tile, the size does not change and all indexing are 1 based

You will be given $Q$ queries, each of which can be of two types .
Type $1$: Represents coordinates of point on which chemical drop falls
Type $0$: Print total number of large drops formed till now.

query of type $1$ representing the coordinates of a cell on which chemical drop will fall and for each query of type $0$, find the number of connected components in the grid.

Input Format

First line contain $3$ integers $N,M$ and $Q$ representing the number of rows, columns and the number of queries.

Next $Q$ lines contain $1$ integer which represents the type of query that has been asked.

For query of type $1$, there will be $2$ more integer $x$ and $y$ which represent the coordinate of cells on which chemical solution is falling on.

for query of type $0$, you have to output the number of large drops till now

Output Format

For each query of type $0$ output the total number of large drops till now

Constraints

$1 \leq N,M \leq 10^3$

$1 \leq x \leq N$

$1 \leq y \leq M$

$1 \leq Q \leq 101000$