Problem: Mike and some bears are playing a game just for fun. Mike is the judge. All bears except Mike are standing in an n × m grid, there's exactly one bear in each cell. We denote the bear standing in column number j of row number i by (i, j). Mike's hands are on his ears (since he's the judge) and each bear standing in the grid has hands either on his mouth or his eyes.

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They play for q rounds. In each round, Mike chooses a bear (i, j) and tells him to change his state i. e. if his hands are on his mouth, then he'll put his hands on his eyes or he'll put his hands on his mouth otherwise. After that, Mike wants to know the score of the bears.

Score of the bears is the maximum over all rows of number of consecutive bears with hands on their eyes in that row.

Since bears are lazy, Mike asked you for help. For each round, tell him the score of these bears after changing the state of a bear selected in that round. 

Input

The first line of input contains three integers n, m and q (1 ≤ n, m ≤ 500 and 1 ≤ q ≤ 5000).

The next n lines contain the grid description. There are m integers separated by spaces in each line. Each of these numbers is either 0 (for mouth) or 1 (for eyes).

The next q lines contain the information about the rounds. Each of them contains two integers i and j (1 ≤ i ≤ n and 1 ≤ j ≤ m), the row number and the column number of the bear changing his state.

Output

After each round, print the current score of the bears.

Examples

Input

5 4 5
0 1 1 0
1 0 0 1
0 1 1 0
1 0 0 1
0 0 0 0
1 1
1 4
1 1
4 2
4 3


Output

3
4
3
3
4

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class Test
{
    private static int[][] input = new int[600][600];     // 输入数组
    private static int[] max = new int[600];              // 每一行的最大值
    
    public static void main(String[] args)
    {   
        Scanner scan = new Scanner(System.in);
        int i , j , n , m , q;
        n = scan.nextInt();
        m = scan.nextInt();
        q = scan.nextInt();
        
        for (i = 1;i <= n;i ++)
        {    
            for (j = 1;j <= m;j ++)
                input[i][j] = scan.nextInt();
            // 获得一行的最大值
            max[i] = getMax(i , m);
        }
        
        // 判断每次查询
        for (i = 0;i < q;i ++)
        {
            int x , y , result = 0;
            x = scan.nextInt();
            y = scan.nextInt();
            // 更新一个位置的值
            if (input[x][y] == 1)
                input[x][y] = 0;
            else
                input[x][y] = 1;
            // 获得一行的最大值
            max[x] = getMax(x , m);
            // 获得最大值
            for (j = 1;j <= n;j ++)
            {
                if (max[j] > result)
                    result = max[j];
            }
            System.out.println(result);
        }
    }
    
    // 获得一行的最大值
    private static int getMax(int rowNum , int m)
    {
        int i , j , result = 0;
        for (i = 1;i <= m;i ++)
        {
            if (input[rowNum][i] == 1)
            {
                j = i;
                while (j <= m && input[rowNum][j] == 1)
                    j ++;
                if (j - i > result)
                    result = j - i;
                i = j - 1;
            }
        }
        return result;
    }
    
}