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.

<image>

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.*;
import java.util.*;

public class Main {
    
public static int countones(int [][] ar,int r,int m){

   {ArrayList<Integer> ls = new ArrayList<>();
    int c = 0; 
    int max = 0 ;
   for(int cels = 0 ; cels < m ;cels++ ){
                  if(ar[r][cels]==1)c++;
                  else {
                      ls.add(c);
                      c=0;
                  }
              }
    if( ls.size()>0){
    return Math.max(c,Collections.max(ls));
    }
   return c ;}
  
}
public static ArrayList<Integer> score(int [][] ar,int m)
{
    ArrayList<Integer> ls  = new ArrayList<>();
    for (int i = 0; i < ar.length; i++) {
        ls.add(countones(ar, i, m));
    }
    return ls;
}

    public static void main(String args[]) throws IOException {
            Reader.init(System.in);
          int n = Reader.nextInt();
          int m = Reader.nextInt();
          int q = Reader.nextInt();
          boolean once = true;
          int [][] ar = new int [n][m];
          Integer [] ars = new Integer [n]; 
          int rowindex [] = new int [q];
          int celindex [] = new int [q];
          for(int rows = 0 ; rows < ar.length;rows++){
              for(int cels = 0 ; cels < m ;cels++ ){
                  ar[rows][cels]=Reader.nextInt();
              }
          }
          for (int i = 0; i < q; i++) {
            rowindex[i] = Reader.nextInt();
            celindex [i] = Reader.nextInt();
            
        }
        ArrayList<Integer> ls  =  score(ar, m);
         for (int i = 0; i < ls.size(); i++) {
            ars[i]=ls.get(i);
        }
          int ans [] = new int [q];
          for (int i = 0; i < q; i++) {
            if(ar[rowindex[i]-1][celindex[i]-1]==1){
                ar[rowindex[i]-1][celindex[i]-1]=0;
                ars[rowindex[i]-1] = countones(ar, rowindex[i]-1, m);
         ans[i]=Collections.max(Arrays.asList(ars));
            }
            else{
                ar[rowindex[i]-1][celindex[i]-1]=1;
                ars[rowindex[i]-1] = countones(ar, rowindex[i]-1, m);
         ans[i]=Collections.max(Arrays.asList(ars));
                
            }
        }
          for(int i : ans){
              System.out.println(i);
          }
    }
          
          
          
}
class dragons implements Comparable<dragons>{
        int power ,bounes; 
    
        public dragons (int p , int b)
        {
            this.power = p ; 
            this.bounes = b ;
        }

        @Override
        public int compareTo(dragons o) {
            return Integer.compare(this.power, o.power);
        }
        
    }

 

class Reader {

    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /**
     * call this method to initialize reader for InputStream
     */
    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
    }

    /**
     * get next word
     */
    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

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

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
   static public void nextIntArrays(int[]... arrays) throws IOException {
        for (int i = 1; i < arrays.length; ++i) {
            if (arrays[i].length != arrays[0].length) {
                throw new InputMismatchException("Lengths are different");
            }
        }
        for (int i = 0; i < arrays[0].length; ++i) {
            for (int[] array : arrays) {
                array[i] = nextInt();
            }
        }}
    static public void nextLineArrays(String[]... arrays) throws IOException {
        for (int i = 1; i < arrays.length; ++i) {
            if (arrays[i].length != arrays[0].length) {
                throw new InputMismatchException("Lengths are different");
            }
        }
        for (int i = 0; i < arrays[0].length; ++i) {
            for (String[] array : arrays) {
                array[i] = reader.readLine();
            }
        }}
}