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Did you know that during the ACM-ICPC World Finals a big chessboard is installed every year and is available for the participants to play against each other? In this problem, we will test your basic chess-playing abilities to verify that you would not make a fool of yourself if you advance to the World Finals.
During the yesterday’s Practice Session, you tried to solve the problem of N independent rooks. This time, let’s concentrate on queens. As you probably know, the queens may move not only horizontally and vertically, but also diagonally.
You are given a chessboard with i − 1 queens already placed and your task is to find all squares that may be used to place the i-th queen such that it cannot be captured by any of the others.
The input consists of several tasks. Each task begins with a line containing three integer numbers separated by a space: X, Y , N. X and Y give the chessboard size, 1 ≤ X, Y ≤ 20 000. N = i−1 is the number of queens already placed, 0 ≤ N ≤ X · Y .
After the first line, there are N lines, each containing two numbers xk, yk separated by a space. They give the position of the k-th queen, 1 ≤ xk ≤ X, 1 ≤ yk ≤ Y . You may assume that those positions are distinct, i.e., no two queens share the same square.
The last task is followed by a line containing three zeros.
For each task, output one line containing a single integer number: the number of squares which are not occupied and do not lie on the same row, column, or diagonal as any of the existing queens.
8 8 2 4 5 5 5 0 0 0