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