Problem: This is the hard version of the problem. The difference between the versions is in the number of possible operations that can be made. You can make hacks if and only if you solved both versions of the problem.

You are given a binary table of size n × m. This table consists of symbols 0 and 1.

You can make such operation: select 3 different cells that belong to one 2 × 2 square and change the symbols in these cells (change 0 to 1 and 1 to 0).

Your task is to make all symbols in the table equal to 0. You are allowed to make at most nm operations. You don't need to minimize the number of operations.

It can be proved, that it is always possible.

Input

The first line contains a single integer t (1 ≤ t ≤ 5000) — the number of test cases. The next lines contain descriptions of test cases.

The first line of the description of each test case contains two integers n, m (2 ≤ n, m ≤ 100).

Each of the next n lines contains a binary string of length m, describing the symbols of the next row of the table.

It is guaranteed, that the sum of nm for all test cases does not exceed 20000.

Output

For each test case print the integer k (0 ≤ k ≤ nm) — the number of operations.

In the each of the next k lines print 6 integers x_1, y_1, x_2, y_2, x_3, y_3 (1 ≤ x_1, x_2, x_3 ≤ n, 1 ≤ y_1, y_2, y_3 ≤ m) describing the next operation. This operation will be made with three cells (x_1, y_1), (x_2, y_2), (x_3, y_3). These three cells should be different. These three cells should belong to some 2 × 2 square.

Example

Input


5
2 2
10
11
3 3
011
101
110
4 4
1111
0110
0110
1111
5 5
01011
11001
00010
11011
10000
2 3
011
101


Output


1
1 1 2 1 2 2
2 
2 1 3 1 3 2
1 2 1 3 2 3
4
1 1 1 2 2 2 
1 3 1 4 2 3
3 2 4 1 4 2
3 3 4 3 4 4
4
1 2 2 1 2 2 
1 4 1 5 2 5 
4 1 4 2 5 1
4 4 4 5 3 4
2
1 3 2 2 2 3
1 2 2 1 2 2

Note

In the first test case, it is possible to make only one operation with cells (1, 1), (2, 1), (2, 2). After that, all symbols will be equal to 0.

In the second test case:

  * operation with cells (2, 1), (3, 1), (3, 2). After it the table will be: 
    
          
    011  
    001  
    000  
    

  * operation with cells (1, 2), (1, 3), (2, 3). After it the table will be: 
    
          
    000  
    000  
    000  
    




In the fifth test case:

  * operation with cells (1, 3), (2, 2), (2, 3). After it the table will be: 
    
          
    010  
    110  
    

  * operation with cells (1, 2), (2, 1), (2, 2). After it the table will be: 
    
          
    000  
    000  
    

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class C {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            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;
        }
    }

    static FastReader s = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);

    private static int[] rai(int n) {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextInt();
        }
        return arr;
    }

    private static int[][] rai(int n, int m) {
        int[][] arr = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextInt();
            }
        }
        return arr;
    }

    private static long[] ral(int n) {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextLong();
        }
        return arr;
    }

    private static long[][] ral(int n, int m) {
        long[][] arr = new long[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextLong();
            }
        }
        return arr;
    }

    private static int ri() {
        return s.nextInt();
    }

    private static long rl() {
        return s.nextLong();
    }

    private static String rs() {
        return s.next();
    }

    static int gcd(int a,int b)
    {
        if(b==0)
        {
            return a;
        }
        return gcd(b,a%b);
    }

    static boolean isPrime(int n) {
        //check if n is a multiple of 2
        if (n % 2 == 0) return false;
        //if not, then just check the odds
        for (int i = 3; i <= Math.sqrt(n); i += 2) {
            if (n % i == 0)
                return false;
        }
        return true;
    }
    static int MOD=1000000007;



    public static HashMap<Long,Integer> primeFactors(long n)
    {
        // Print the number of 2s that divide n
        HashMap<Long,Integer> map=new HashMap<>();

        while (n % 2 == 0) {
            map.put(2L,map.getOrDefault(2L,0)+1);
            n /= 2;
        }

        // n must be odd at this point.  So we can
        // skip one element (Note i = i +2)
        for (long i = 3; i <= Math.sqrt(n); i += 2) {
            // While i divides n, print i and divide n
            while (n % i == 0) {
                map.put(i,map.getOrDefault(i,0)+1);
                n /= i;
            }
        }

        // This condition is to handle the case whien
        // n is a prime number greater than 2
        if (n > 2)
            map.put(n,map.getOrDefault(n,0)+1);

        return map;
    }



    public static void main(String[] args) {
        StringBuilder ans = new StringBuilder();
        int t = ri();
//        int t = 1;
        while (t-- > 0)
        {
            int n=ri();
            int m=ri();
            int[][] arr=new int[n][m];
            for(int i=0;i<n;i++)
            {
                char[] mid= rs().toCharArray();
                for(int j=0;j<m;j++)
                {
                    arr[i][j]=mid[j]-'0';
                }
            }

            int res=0;
            StringBuilder str=new StringBuilder();
            for(int i=0;i<n-2;i++)
            {
                for(int j=0;j<m;)
                {
                    if(arr[i][j]==1 && arr[i][j+1]==1)
                    {
                        res++;
                        int p1=i+1,p2=j+1;
                        str.append(p1).append(" ").append(p2).append(" ").append(p1).append(" ").append(p2+1).append(" ").append(p1 + 1).append(" ").append(p2).append("\n");
                        arr[i][j]=0;
                        arr[i][j+1]=0;
                        if(arr[i+1][j]==1)
                        {
                            arr[i+1][j]=0;

                        }
                        else {
                            arr[i+1][j]=1;
                        }
                    }
                    else if(arr[i][j]==1)
                    {
                        res++;
                        int p1=i+1,p2=j+1;
                        str.append(p1).append(" ").append(p2).append(" ").append(p1+1).append(" ").append(p2+1).append(" ").append(p1 + 1).append(" ").append(p2).append("\n");
                        arr[i][j]=0;

                        if(arr[i+1][j]==1)
                        {
                            arr[i+1][j]=0;

                        }
                        else {
                            arr[i+1][j]=1;
                        }

                        if(arr[i+1][j+1]==1)
                        {
                            arr[i+1][j+1]=0;

                        }
                        else {
                            arr[i+1][j+1]=1;
                        }
                    }
                    else if(arr[i][j+1]==1)
                    {
                        res++;
                        int p1=i+1,p2=j+1;
                        str.append(p1).append(" ").append(p2+1).append(" ").append(p1+1).append(" ").append(p2+1).append(" ").append(p1 + 1).append(" ").append(p2).append("\n");
                        arr[i][j+1]=0;

                        if(arr[i+1][j]==1)
                        {
                            arr[i+1][j]=0;

                        }
                        else {
                            arr[i+1][j]=1;
                        }

                        if(arr[i+1][j+1]==1)
                        {
                            arr[i+1][j+1]=0;

                        }
                        else {
                            arr[i+1][j+1]=1;
                        }
                    }


                    j+=2;
                    if(j==m-1)
                    {
                        j--;
                    }
                }
            }



            int i=n-2;
            for(int j=0;j<m-2;j++)
            {
                if(arr[i][j]==1 && arr[i+1][j]==1)
                {
                    res++;
                    int p1=i+1,p2=j+1;
                    str.append(p1).append(" ").append(p2).append(" ")
                            .append(p1+1).append(" ").append(p2).append(" ")
                            .append(p1 + 1).append(" ").append(p2+1).append("\n");
                    arr[i][j]=0;
                    arr[i+1][j]=0;
                    if(arr[i+1][j+1]==1)
                    {
                        arr[i+1][j+1]=0;

                    }
                    else {
                        arr[i+1][j+1]=1;
                    }
                }
                else if(arr[i][j]==1)
                {
                    res++;
                    int p1=i+1,p2=j+1;
                    str.append(p1).append(" ").append(p2).append(" ").append(p1+1).append(" ").append(p2+1).append(" ").append(p1).append(" ").append(p2+1).append("\n");
                    arr[i][j]=0;

                    if(arr[i][j+1]==1)
                    {
                        arr[i][j+1]=0;

                    }
                    else {
                        arr[i][j+1]=1;
                    }

                    if(arr[i+1][j+1]==1)
                    {
                        arr[i+1][j+1]=0;

                    }
                    else {
                        arr[i+1][j+1]=1;
                    }
                }
                else if(arr[i+1][j]==1)
                {
                    res++;
                    int p1=i+1,p2=j+1;
                    str.append(p1+1).append(" ").append(p2).append(" ")
                            .append(p1+1).append(" ").append(p2+1).append(" ")
                            .append(p1 ).append(" ").append(p2+1).append("\n");
                    arr[i+1][j]=0;

                    if(arr[i][j+1]==1)
                    {
                        arr[i][j+1]=0;

                    }
                    else {
                        arr[i][j+1]=1;
                    }

                    if(arr[i+1][j+1]==1)
                    {
                        arr[i+1][j+1]=0;

                    }
                    else {
                        arr[i+1][j+1]=1;
                    }
                }



            }

//            str.append("yoyo\n");
//            for( i=0;i<n;i++)
//            {
//                for(int j=0;j<m;j++)
//                {
//                    str.append(arr[i][j]).append(" ");
//                }
//                str.append("\n");
//
//            }
//            str.append("yoyo\n");

            i=n-2;
            int j=m-2;
            boolean[] vis=new boolean[4];
            HashSet<Point> set=new HashSet<>();
            int count=0;
            if(arr[i][j]==1)
            {
                count++;
                set.add(new Point(i,j));
                vis[0]=true;
            }
            if(arr[i][j+1]==1)
            {
                count++;
                set.add(new Point(i,j+1));
                vis[1]=true;
            }
            if(arr[i+1][j]==1)
            {
                count++;
                set.add(new Point(i+1,j));
                vis[2]=true;
            }
            if(arr[i+1][j+1]==1)
            {
                count++;
                set.add(new Point(i+1,j+1));
                vis[3]=true;
            }

            if(count==4)
            {
                int v1=i+1;
                int v2=j+1;
                res++;
                count=1;
                str.append(v1).append(" ").append(v2).append(" ").append(v1).append(" ").append(v2 + 1).append(" ").append(v1 + 1).append(" ").append(v2).append("\n");
                vis[0]=false;
                vis[1]=false;
                vis[2]=false;
                arr[i][j]=0;
                arr[i][j+1]=0;
                arr[i+1][j]=0;
            }
            if(count==1)
            {
                res++;
                count=2;
                int p1=i+1,p2=j+1;
                if(vis[0])
                {
                    str.append(p1).append(" ").append(p2).append(" ").append(p1).append(" ").append(p2+1).append(" ").append(p1 + 1).append(" ").append(p2).append("\n");
                    vis[0]=false;
                    vis[1]=true;
                    vis[2]=true;
                    arr[i][j]=1;
                    arr[i][j+1]=0;
                    arr[i+1][j]=0;

                }
                else if(vis[1])
                {
                    p2++;
                    str.append(p1).append(" ").append(p2).append(" ").append(p1).append(" ").append(p2-1).append(" ").append(p1 + 1).append(" ").append(p2).append("\n");
                    vis[1]=false;
                    vis[0]=true;
                    vis[3]=true;
                    arr[i][j+1]=1;
                    arr[i][j]=0;
                    arr[i+1][j+1]=0;
                }
                else if(vis[2])
                {
                    p1++;
                    str.append(p1).append(" ").append(p2).append(" ").append(p1-1).append(" ").append(p2).append(" ").append(p1).append(" ").append(p2+1).append("\n");
                    vis[2]=false;
                    vis[0]=true;
                    vis[3]=true;
                    arr[i+1][j]=1;
                    arr[i][j]=0;
                    arr[i+1][j+1]=0;
                }
                else {
                    p1++;
                    p2++;
                    str.append(p1).append(" ").append(p2).append(" ").append(p1-1).append(" ").append(p2).append(" ").append(p1).append(" ").append(p2-1).append("\n");
                    vis[3]=false;
                    vis[1]=true;
                    vis[2]=true;
                    arr[i+1][j+1]=1;
                    arr[i][j+1]=0;
                    arr[i+1][j]=0;
                }
            }
            if(count==2)
            {
                res++;
                count=3;
                int p1=i+1,p2=j+1;

                if(vis[0]&&vis[1])
                {
                    str.append(p1).append(" ").append(p2).append(" ").append(p1+1).append(" ").append(p2).append(" ").append(p1+1).append(" ").append(p2+1).append("\n");
                    vis[0]=false;
                    vis[2]=true;
                    vis[3]=true;
                    arr[i][j]=1;
                    arr[i+1][j]=0;
                    arr[i+1][j+1]=0;
                }
                else if(vis[0] && vis[2])
                {
                    str.append(p1).append(" ").append(p2).append(" ").append(p1).append(" ").append(p2+1).append(" ").append(p1+1).append(" ").append(p2+1).append("\n");
                    vis[0]=false;
                    vis[1]=true;
                    vis[3]=true;
                    arr[i][j]=1;
                    arr[i][j+1]=0;
                    arr[i+1][j+1]=0;
                }
                else if(vis[0] && vis[3])
                {
                    str.append(p1).append(" ").append(p2).append(" ").append(p1).append(" ").append(p2+1).append(" ").append(p1+1).append(" ").append(p2).append("\n");
                    vis[0]=false;
                    vis[1]=true;
                    vis[2]=true;
                    arr[i][j]=1;
                    arr[i][j+1]=0;
                    arr[i+1][j]=0;
                }
                else if(vis[1] && vis[2])
                {
                    str.append(p1).append(" ").append(p2).append(" ").append(p1).append(" ").append(p2+1).append(" ").append(p1+1).append(" ").append(p2+1).append("\n");
                    vis[1]=false;
                    vis[0]=true;
                    vis[3]=true;
                    arr[i][j+1]=1;
                    arr[i][j]=0;
                    arr[i+1][j+1]=0;
                }
                else if(vis[1] && vis[3])
                {
//                            System.out.println("yoyo");
                    str.append(p1).append(" ").append(p2).append(" ").append(p1).append(" ").append(p2+1).append(" ").append(p1+1).append(" ").append(p2).append("\n");
                    vis[1]=false;
                    vis[0]=true;
                    vis[2]=true;
                    arr[i][j+1]=1;
                    arr[i][j]=0;
                    arr[i+1][j]=0;
                }
                else if(vis[2] && vis[3])
                {
                    str.append(p1).append(" ").append(p2).append(" ").append(p1).append(" ").append(p2+1).append(" ").append(p1+1).append(" ").append(p2).append("\n");
                    vis[2]=false;
                    vis[0]=true;
                    vis[1]=true;
                    arr[i+1][j]=1;
                    arr[i][j]=0;
                    arr[i][j+1]=0;
                }
            }
            if(count==3)
            {
                res+=1;
                int p1=i+1,p2=j+1;
                if(vis[0] && vis[1] && vis[2])
                {
                    str.append(p1).append(" ").append(p2).append(" ").append(p1).append(" ").append(p2+1).append(" ").append(p1+1).append(" ").append(p2).append("\n");

                }
                else if(vis[0] && vis[1] && vis[3])
                {
                    str.append(p1).append(" ").append(p2).append(" ").append(p1).append(" ").append(p2+1).append(" ").append(p1+1).append(" ").append(p2+1).append("\n");

                }
                else if(vis[0] && vis[2] && vis[3])
                {
                    str.append(p1).append(" ").append(p2).append(" ").append(p1+1).append(" ").append(p2+1).append(" ").append(p1+1).append(" ").append(p2).append("\n");

                }
                else if(vis[3] && vis[1] && vis[2])
                {
                    str.append(p1+1).append(" ").append(p2+1).append(" ").append(p1).append(" ").append(p2+1).append(" ").append(p1+1).append(" ").append(p2).append("\n");

                }
                arr[i][j]=0;
                arr[i][j+1]=0;
                arr[i+1][j]=0;
                arr[i+1][j+1]=0;


            }




//
//            str.append("yoyo\n");
//            for( i=0;i<n;i++)
//            {
//                for(int j=0;j<m;j++)
//                {
//                    str.append(arr[i][j]).append(" ");
//                }
//                str.append("\n");
//
//            }
//            str.append("yoyo\n");

            ans.append(res).append("\n");
            ans.append(str.toString()).append("\n");

        }


        out.print(ans.toString());
        out.flush();

    }
    static class Point
    {
        int x,y;

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

}