Painting

Problem code: PAINT

All submissions for this problem are available.

Leonardo da Vinci is preparing the background for his new painting. Since this is the computer age, he is using an electronic paper which is initially white. Paper is a MxN rectangular gird having MxN square cells. With paint(i,j) operation, his computer fills the cell(i,j) of the paper with black color. However, at any point in time, he may want to know the size of biggest black segment. Black Segment is defined as the group of cells in which any two vertical or horizontal neighboring cells are black. He asks for your help to complete the above task.

Input

The first line contains two integers, M and N. Next line contains an integer Q, where Q is total number of queries. The following Q lines each have a query Qi containing an integer B. B is either 0 or 1. If B is 1, two integers i and j follow which corresponds to the operation paint(i,j) (1-based index).

Output

For every query with B=0, output the size of biggest black segment.

Example

Input:
3 3
9
1
2 1
0
1
1 3
0
1
3 3
1
2 3
0
1
2 2
0

Output:
1
1
3
5








Figure from Example.


Constraints:

    

  •  1   <=   M,N   <=   1000.
    • 

  •  1   <=   Q   <=   106.
    • 

  •  B will be either 0 or 1.
    • 

  •  1   <=   i   <=   M 
    • 

  •  1   <=   j   <=   N

Author: divij
Date Added: 30-09-2010
Time Limit: 2 sec
Source Limit: 50000 Bytes
Languages: C, C99 strict, CLOJ, CPP 4.0.0-8, CPP 4.3.2, F#, GO, PERL6, PYTH 3.1.2, TEXT


Comments

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