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.*;
import java.util.*;
import java.math.*;

public class Main { 
    
    static class Pair {
        int a;
        int b;
        Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }
        public String toString() {
            return this.a+"-"+this.b;
        }
    }

    public static void main(String[] args) throws java.lang.Exception { 
        Reader pm =new Reader(); 
        //Scanner pm = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int t = 1;

        while(t-- > 0){
            int n = pm.nextInt();
            int m = pm.nextInt();
            int q = pm.nextInt();

            HashMap<Integer, Integer> hm = new HashMap<>();

            // TreeSet<Pair> ts = new TreeSet<>(new Comparator<Pair>() {
            //     public int compare(Pair p1, Pair p2) {
            //         if(p1.b < p2.b) 
            //             return 1;
            //         else if(p1.b == p2.b && p1.a == p2.a) 
            //             return 0;
            //         return -1; 
            //     }
            // });

            int[][] a = new int[n][m];

            for(int i=0;i<n;i++) {
                for(int j=0;j<m;j++) {
                    a[i][j] = pm.nextInt();
                }
            }
            for(int i=0;i<n;i++) {
                int cnt = 0;
                if(a[i][0] == 1) 
                    cnt = 1;
                int maxi = cnt;

                for(int j=1;j<m;j++) {
                    if(a[i][j-1] == a[i][j] && a[i][j] == 1) 
                        cnt++;
                    else {
                        if(maxi < cnt) 
                            maxi = cnt;
                        if(a[i][j] == 1) 
                            cnt = 1;
                        else
                            cnt = 0;
                    }
                }

                maxi = Math.max(maxi, cnt);
                //System.out.println(i+" "+maxi);

                hm.put(i, maxi);
               // ts.add(new Pair(i, maxi));
            }
            //System.out.println(ts);
            StringBuffer sb = new StringBuffer();

            while(q-- > 0) {
                int i = pm.nextInt()-1;
                int c = pm.nextInt()-1;
                if(a[i][c] == 1) 
                    a[i][c] = 0;
                else
                    a[i][c] = 1;

                int cnt = 0;
                if(a[i][0] == 1) 
                    cnt = 1;
                int maxi = cnt;

                for(int j=1;j<m;j++) {
                    if(a[i][j-1] == a[i][j] && a[i][j] == 1) 
                        cnt++;
                    else {
                        if(maxi < cnt) 
                            maxi = cnt;
                        if(a[i][j] == 1) 
                            cnt = 1;
                        else
                            cnt = 0;
                    }
                }

                maxi = Math.max(maxi, cnt);
                hm.put(i, maxi);

                int maxAns = Integer.MIN_VALUE;
                
                for(int z: hm.keySet()) {
                    maxAns = Math.max(maxAns, hm.get(z));
                }
                // //System.out.println(i+" "+cnt);

                // Pair crt = new Pair(i, hm.get(i));

                // ts.remove(crt);

                
                // ts.add(new Pair(i, maxi));

                // //System.out.println(i+" "+ts);

                sb.append(maxAns+"\n");

            }
            System.out.println(sb);
        }
        //end of tests
        
    }
    //end of main class

    static int countInRange(int arr[], int n, int x, int y) { 
        // initialize result 
        int count = 0; 
        count = upperIndex(arr, n, y) -  
                lowerIndex(arr, n, x) + 1; 
        return count; 
    } 
    
    
    static int lowerIndex(int arr[], int n, int x) { 
        int l = 0, h = n - 1; 
        while (l <= h)  
        { 
            int mid = (l + h) / 2; 
            if (arr[mid] >= x) 
                h = mid - 1; 
            else
                l = mid + 1; 
        } 
        return l; 
    } 
      
    // function to find last index <= y 
    static int upperIndex(int arr[], int n, int y) { 
        int l = 0, h = n - 1; 
        while (l <= h)  
        { 
            int mid = (l + h) / 2; 
            if (arr[mid] <= y) 
                l = mid + 1; 
            else
                h = mid - 1; 
        } 
        return h; 
    }
    
    public static StringBuilder dec_to_bin(long n) {
        // decimal to binary upto 30 binaries
        if(n==0) {
            StringBuilder str=new StringBuilder("");
            for(int i=0;i<30;i++) {
                str.append("0");
            }
            return str;
        }
        StringBuilder str=new StringBuilder("");
        while(n!=0) {
            str.append(n%2L);
            n/=2L;
        }
        str=str.reverse();
        StringBuilder tmp_str=new StringBuilder("");
        int len=str.length();
        while(len!=30) {
            tmp_str.append("0");
            len++;
        }
        tmp_str.append(str);
        return tmp_str;
    }
    
    private static int binarySearchPM(int[] arr, int key){
        int n = arr.length;
        int mid = -1;
        int begin = 0,end=n;
        while(begin <= end){
            mid = (begin+end) / 2;
            if(mid == n){
                return n;
            }
            if(key < arr[mid]){
                end = mid-1;
            } else if(key > arr[mid]){
                begin = mid+1;
            } else {
                return mid;
            }
        }
        //System.out.println(begin+" "+end);
        return -begin; //expected Index
    }
    
    static class Reader { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    }
}