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:
/**
 * Created by Chirag on 10-12-2016.
 * DA-IICT (B.tech 2nd year)
 */

import java.io.*;
import java.util.*;


public class mikeandfun {
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
      
      
      /*
      int n      = sc.nextInt();        // read input as integer
      long k     = sc.nextLong();       // read input as long
      double d   = sc.nextDouble();     // read input as double
      String str = sc.next();           // read input as String
      String s   = sc.nextLine();       // read whole line as String

      int result = 3*n;
      out.println(result);                    // print via PrintWriter
      */
        //The Code Starts here
        int n=sc.nextInt();
        int m=sc.nextInt();
        int q=sc.nextInt();
        int state[][]=sc.nextInt2DArray(n,m);
        int maximuminrow[]=new int[n];
        for(int r=0;r<n;r++) {
            int maxrow = 0;
            int tempmaxrow = 0;
            for (int c = 0; c < m; c++) {
                tempmaxrow = (state[r][c] == 1) ? 1 + tempmaxrow : 0;
//                    System.out.println(tempmaxrow);
                if (tempmaxrow > maxrow)
                    maxrow = tempmaxrow;
            }
            maximuminrow[r] = maxrow;
        }
        for(int i=0;i<q;i++)
        {
            int row=sc.nextInt();
            int col=sc.nextInt();
            state[row-1][col-1]=state[row-1][col-1]==0 ? 1 : 0;
//            System.out.println(state[row-1][col-1]);
            int max=Integer.MIN_VALUE;
            int maxrow=0;
            int tempmaxrow=0;
            maximuminrow[row-1]=0;
            for (int c = 0; c < m; c++) {
                tempmaxrow = (state[row-1][c] == 1) ? 1 + tempmaxrow : 0;
//                    System.out.println(tempmaxrow);
                if (tempmaxrow > maxrow)
                    maxrow = tempmaxrow;
            }
            maximuminrow[row-1] = maxrow;

            for(int element : maximuminrow)
            {
                max=Math.max(element,max);
            }
            out.println(max);

    }



//The Code ends here
        out.close();
    }


//-----------PrintWriter for faster output---------------------------------
public static PrintWriter out;

//-----------MyScanner class for faster input----------
public static class MyScanner {
    BufferedReader br;
    StringTokenizer st;

    public MyScanner() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }

    public int[] nextIntArray(int n) {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = nextInt();
        }
        return arr;
    }

    public long[] nextLongArray(int n) {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = nextLong();
        }
        return arr;
    }

    public int[][] nextInt2DArray(int m, int n) {
        int[][] arr = new int[m][n];
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++)
                arr[i][j] = nextInt();
        }
        return arr;
    }

    private boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private boolean isEndOfLine(int c) {
        return c == '\n' || c == '\r' || c == -1;
    }

}

public static class Pair implements Comparable<Pair> {
    long u;
    long v;

    public Pair(long u, long v) {
        this.u = u;
        this.v = v;
    }


    public int hashCode() {
        int hu = (int) (u ^ (u >>> 32));
        int hv = (int) (v ^ (v >>> 32));
        return 31 * hu + hv;
    }

    public boolean equals(Object o) {
        Pair other = (Pair) o;
        return u == other.u && v == other.v;
    }

    public int compareTo(Pair other) {
        return Long.compare(u, other.u) != 0 ? Long.compare(u, other.u) : Long.compare(v, other.v);
    }

    public String toString() {
        return "[u=" + u + ", v=" + v + "]";
    }
}
//--------------------------------------------------------
}