From left to right: d, ZQFMGB12, jlsajfj, ChaSiu and nathanl3

During the last DMOPC, d did great and scored 4^th place! (Only to be beaten by Thornhill of course.) ZQFMGB12 is so happy for d that he decided to throw a LAN party with the entire school. The party is organized into ~R~ rows of seats. Each row has ~C~ seats. Initially, there is one player in each seat. As the event goes on, a person's laptop battery might run dry, which causes them to pack up and go home.

ZQFMGB12 will host ~M~ games. Before each game, a single player's laptop battery runs out and they leave the party. Specifically, before the ~i^\text{th}~ game, the player sitting at the ~u_i^\text{th}~ row and the ~v_i^\text{th}~ column leaves the party. After this person leaves, ZQFMGB12 needs to choose players to play in the upcoming game, so he chooses a square of seats such that all seats in the square are occupied by a player.

Before each game, ZQFMGB12 wants to know the side length of the greatest square of players he can invite for that game. Can you help him?

Constraints

For all subtasks:

~1 \le R, C \le 350~

~1 \le M \le R \cdot C~

~1 \le u \le R~

~1 \le v \le C~

Subtask 1 [20%]

~R, C \le 10~

Subtask 2 [20%]

~R, C \le 50~

Subtask 3 [60%]

No additional constraints.

Input Specification

The first line will contain ~R~ and ~C~, the number of rows and columns respectively.

The second line will contain ~M~, the players that will leave throughout the event.

The next ~M~ lines will contain integers ~u~ and ~v~, indicating that the person at the ~u^\text{th}~ row and the ~v^\text{th}~ column leaves because his or her battery dies. It is guaranteed that the player sitting at ~(u,v)~ has not already left.

Output Specification

For each of the ~M~ lines, output the side length of the largest square of players that ZQFMGB12 can still invite to his game. If there are no players remaining, print 0.

Sample Input

3 3
3
3 3
3 2
2 2

Sample Output

2
2
1