Problem Statement

Vil is 160cm tall, but all of his classmates are at least 170km tall. Since he cannot see the blackboard if he sits behind such a tall classmate, the seats Vil can sit in within the classroom are limited.

In the classroom, a total of $H \times W$ desks are arranged in $H$ rows and $W$ columns, and initially nobody is there. From now on, $Q$ students will arrive at school one after another. Denoting the desk in the $y$-th row from the front and the $x$-th column from the left as $(y,x)$, the $i$-th student sits at $(Y_i,X_i)$.

Find the number of seats Vil can sit in immediately after each student takes a seat. Here, Vil can sit at $(y,x)$ if and only if, at that moment, no student is sitting at any of $(h,x)(1 \le h \le y)$.

Input

$H\ W\ Q$
$Y_1\ X_1$
$Y_2\ X_2$
$\vdots$
$Y_Q\ X_Q$

• All inputs are integers.
• $1 \le H,W \le 10^9$
• $1 \le Q \le \min(H \times W,10^5)$
• $1 \le Y_i \le H$
• $1 \le X_i \le W$
• If $i \neq j $, then $(Y_i,X_i) \neq (Y_j,X_j)$

Output

Output $Q$ lines.

On the $i(1 \le i \le Q)$-th line, output the number of seats Vil can sit in immediately after the $i$-th student takes a seat, followed by a newline.

Sample

3 3 3
1 1
2 3
3 1

6
4
4

#..
#..
#..

#..
#.#
#.#

#..
#.#
#.#

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

67
64
57
54
54
53
52