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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.TreeMap;
import java.util.Map;
import java.util.Scanner;
import java.util.SortedMap;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main
{
    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB
    {
        public void solve(int testNumber, Scanner in, PrintWriter out)
        {
            int T = 1;
            while (T-- > 0)
            {
                solveOne(in, out);
            }
        }

        private void solveOne(Scanner in, PrintWriter out)
        {
            int rows = in.nextInt(), cols = in.nextInt(), Q = in.nextInt();
            int[][] M = CPUtils.readIntMatrix(rows, cols, in);
            SortedMap<Integer, Integer> map = new TreeMap<>();
            int[] row_sum = new int[rows];
            for (int row = 0; row < rows; row++)
            {
                int cnt = maxWindow(M[row]);
                map.merge(cnt, 1, Integer::sum);
                row_sum[row] = cnt;
            }
            while (Q-- > 0)
            {
                int r = in.nextInt() - 1, c = in.nextInt() - 1;
                int max = row_sum[r];
                remove(max, map);
                M[r][c] = invert(M[r][c]);
                max = maxWindow(M[r]);
                row_sum[r] = max;
                map.merge(max, 1, Integer::sum);

                out.println(map.lastKey());
            }
        }

        private int invert(int i)
        {
            if (i == 0) return 1;
            else return 0;
        }

        private int maxWindow(int arr[])
        {
            int max = 0;
            for (int i = 0; i < arr.length; i++)
            {
                int cnt = 0;
                while (i < arr.length && arr[i] == 1)
                {
                    cnt++;
                    i++;
                }
                max = Math.max(max, cnt);
            }
            return max;
        }

        private void remove(int i, SortedMap<Integer, Integer> map)
        {
            int occ = map.get(i);
            occ--;
            if (occ == 0) map.remove(i);
            else map.put(i, occ);
        }

    }

    static class CPUtils
    {
        public static int[] readIntArray(int size, Scanner in)
        {
            int[] array = new int[size];
            for (int i = 0; i < size; i++)
            {
                array[i] = in.nextInt();
            }
            return array;
        }

        public static int[][] readIntMatrix(int rows, int columns, Scanner in)
        {
            int[][] matrix = new int[rows][columns];
            for (int i = 0; i < rows; i++)
            {
                matrix[i] = CPUtils.readIntArray(columns, in);
            }
            return matrix;
        }

    }
}