Cabbage

Sanggeun wants to grow cabbages on the roof of a building. Because it is inconvenient to climb up to the roof every time he needs to water them, he will install N sprinklers on the roof.

All sprinklers are the same model. Each sprinkler can water the circular region of radius 1 centered at its position.

The roof is a rectangle with width X and height Y. On the coordinate plane, it is modeled as an axis-aligned rectangle whose opposite vertices are (0, 0) and (X, Y).

A sprinkler may be installed only at a point whose coordinates are both integers.

Given the size of the roof and the positions of the sprinklers, find the area of the roof that can be watered.

The first line contains X and Y. (1 <= X, Y <= 1000)

The second line contains the number of sprinklers N. (1 <= N <= 10,000)

Each of the next N lines contains the coordinates x and y of one sprinkler. (0 <= x <= X, 0 <= y <= Y)

Print the area that can be watered by the sprinklers. An absolute or relative error of at most 0.01 is accepted.