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ACM ICPC 2018 World Finals
Time Limit: 5000MSMemory Limit: 65536K
Total Submissions: 484Accepted: 96


There are k soldiers placed on an n-row and m-column chessboard. It is allowed that more than one soldier are placed on the same grid.

If the Manhattan distance between a grid(in ath row and bth column) and a soldier(in xth row and yth column), |x-a|+|y-b|, is not larger than the control range of that soldier, then the grid will be controlled.

Could you tell the total number of all the controlled grids?


The input contains only one case.
The input begins with three positive integers, n, m and k, indicating the length of row and column, and the number of soldiers.
In the next k lines each line contains three non-negative integers, x, y, r, indicating a soldier is placed on the xth row and yth column, and the control range of that soldier is r.
It is guaranteed that 1 ≤ n, m ≤ 100000000,1 ≤ k ≤ 100000


Print the total number of all the controlled grids.

Sample Input

4 4 3
1 1 1
3 1 1
3 3 1

Sample Output



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