Description

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?

Input

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

x

th row and

y

th column, and the control range of that soldier is

r

.

It is guaranteed that 1 ≤ n

,

m

≤ 100000000，1 ≤

k

≤ 100000

Output

Print the total number of all the controlled grids.

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

10

Source

POJ Monthly--2007.07.08

, Chen, Qifeng