B. Destroy them all!
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

The grandson of Professor R. Vanya downloaded the game 'Destroy them all!' and plays it all day long.

The game has a checkered field of size $$$n \times m$$$. It contains $$$k$$$ cells. The player can select any unmarked cell of the field and destroy all the marked cells exactly in one of the directions (left, right, above, below it). The grandson really wants to know the maximum number of cells he can destroy in one move at the current state of the field, but he is still too young to calculate this number. Help him – find the maximum number of cells that can be destroyed in one move if the coordinates of the $$$k$$$ marked cells are known.

Input

The first line contains the numbers $$$n$$$, $$$m$$$ and $$$k$$$ $$$(1 \le n, m \le 10^9, 1 \le k \le min(n \cdot m, 2 \cdot 10^5))$$$ - the size of the playing field and the number of marked cells.

The next $$$k$$$ lines contain pairs of numbers $$$x_i$$$ and $$$y_i$$$ $$$(1 \le x_i \le n, 1 \le y_i \le m)$$$ – the coordinates of the $$$i$$$-th marked cell.

Output

In the first line, print one number – the maximum number of cells that can be destroyed in one move. In the second line, print two numbers – the coordinates of an empty cell from which the maximum number of cells can be destroyed.

If there are no unmarked points, print «0» (without quotes) in the first line and «0 0» (without quotes) in the second line.

If there are multiple solutions print any of them.

Example
Input
12 12 4
3 7
3 11
6 4
12 4
Output
2
3 4
Note

From a point with coordinates $$$(3, 4)$$$, either two points above or two points to the right can be destroyed.