In the game of Rhombinoes, you have a board made up entirely of equilateral trianges (see the image), some of which are "live" and some are "dead". Your goal is to place down as many rhombinoes ("rhombus"-shaped pieces) as possible on the board. Each rhombino should exactly cover two "adjacent" livetriangles that have a common side, and no two rhombinoes can use the same triangle.

Given the description of the live and dead triangles of a Rhombino board, what is the maximum number of rhombinoes you can simultaneously place down on the board?

Description of Board

Each triangle in the board has a pair of coordinates (x, y). The bottom-left triangle has coordinates (0, 0) and will always be a triangle with its tip pointed upward. For any given triangle with coordinates (x, y), the triangle adjacent to it on its right-side (if any) has coordinates (x+1, y), and the triangle adjacent to it on its top-side (if any) has coordinates (x, y+1). Left-side and bottom-side adjacency are defined similarly.

Each board has a width W and a height H. A board with width W and height H is the board which consists of all triangles with coordinates (x, y) such that 0 ≤ x < W and 0 ≤ y < H. For example, the game board in the image has width 6 and height 3.

(See the image for clarification.)

The first line of input contains three space-separated integers W, H, and K.

W is the width of the board, H is the height, and K is the number of dead triangles on the board (1 ≤ W ≤ 100, 1 ≤ H ≤ 100, 1 ≤ K ≤ W*H ≤ 1000).

Exactly K lines will follow. Each such line will contain a pair of space-separated integers x and y (0 ≤ x < W, 0 ≤ y < H), indicating that the triangle with coordinates (x,y) is a dead triangle. All other triangles are live.

Output a line containing a single integer, the maximum number of rhombinoes you can simultaneously place down on the board.

This is the board in the image, with cells (1, 1), (2, 2), (4, 1), and (3, 0) dead.