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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();

	}

	static class TaskC {
		public void solve(int testNumber, InputReader in, PrintWriter out) {
			int n = in.nextInt() ; 
			int m = in.nextInt() ; 
			int q = in.nextInt() ; 
			int mat[][] = new int [n][m] ; 
			int ii[] =  new int[q] ; 
			int jj[] =  new int[q] ;
			for (int i = 0; i < n; i++)
				for (int j = 0; j <m; j++)
					mat[i][j] = in.nextInt() ; 
			for (int i = 0; i < q; i++)
			{
				ii[i]=in.nextInt()-1 ; 
				jj[i] = in.nextInt()-1 ;
			}
			int max[] = new int [n] ; 
			int maxx=Integer.MIN_VALUE ; 
			for (int i = 0; i < n; i++)
			{
				int sum=0 ;
				for (int j = 0; j < m; j++)
				{
					if(mat[i][j]==0)
						sum= 0 ; 
					else
						sum++ ;
					max[i]=Math.max(sum, max[i]) ;

				}
				maxx = Math.max(maxx , max[i]) ;
			}
			for (int i = 0; i <q; i++)
			{
				if(mat[ii[i]][jj[i]] == 1)
				{
					mat[ii[i]][jj[i]]=0;
				}else{
					mat[ii[i]][jj[i]]=1;
				}
				int sum=0 ;
				max[ii[i]]= Integer.MIN_VALUE ;
				for (int j = 0; j < m; j++)
				{
					if(mat[ii[i]][j]==0)
						sum= 0 ; 
					else
						sum++ ; 
					max[ii[i]]=Math.max(sum, max[ii[i]]);
				}
				maxx = Integer.MIN_VALUE ;
				for (int j = 0; j < n; j++)
					maxx = Math.max(max[j] , maxx) ;

				out.println(maxx);
			}

		}
		public static int binarySearch(int []arr , int target) {
			int low = 0, high = arr.length;
			while (low != high) {
				int mid = (low + high) / 2;
				if (arr[mid] <= target) {
					low = mid + 1;
				}
				else {
					high = mid;
				}
			}
			return arr[low] ;
		}



		public static boolean isPrime (long num){
			if (num < 2) return false;
			if (num == 2) return true;
			if (num % 2 == 0) return false;
			for (long i = 3*1l; i * i <= num; i += 2)
				if (num % i == 0) return false;
			return true;
		}
	}
	static class InputReader {
		public BufferedReader	reader;
		public StringTokenizer	tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens())
			{
				try
				{
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e)
				{
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

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

	}
	static class Vertix{
		int x ; 
		ArrayList<Vertix> children; 
		Vertix parent; 

		public Vertix(int x){
			this.x = x ;
			this.children= new ArrayList<Vertix>();
		}

	}

	static class Pair implements Comparable<Pair> {
		int x ; 
		int y ; 

		public Pair(int x, int y) {
			this.x = x ;
			this.y = y ; 

		}

		@Override
		public int compareTo(Pair p) {
			if (this.x < p.x)
				return -1;
			else if (this.x > p.x)
				return 1;
			else
				return 0;

		}
		//
	}

}