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 ques3
{
	public static void main(String[] args)throws Exception{ new ques3().run();} 
	long mod=1000000000+7;
	
	void solve() throws Exception
	{
		for(int ii=ni();ii>0;ii--)
		{
			int n=ni();
			int m=ni();
			int a[][]=new int[n+1][m+1];
			for(int i=1;i<=n;i++)
			{
				for(int j=1;j<=m;j++)
				{
					a[i][j]=nc()-'0';
				}
			}
			ArrayList<int []> arr = new ArrayList<>();
			for(int i=1;i<=n-2;i++)
			{
				for(int j=1;j<=m;j=j+2)
				{
					if(j+1>m)continue;
					if(a[i][j]==0&&a[i][j+1]==0) continue;
					int s[]=new int[6]; int in=0;
					if(a[i][j]==1)
						{s[in++]=i;s[in++]=j;   a[i][j]=0;}
					if(a[i][j+1]==1)
						{s[in++]=i;s[in++]=j+1;  a[i][j+1]=0;}

						s[in++]=i+1; s[in++]=j;  a[i+1][j]=a[i+1][j]^1;
					if(in==4)
					{
						s[in++]=i+1; s[in++]=j+1;  a[i+1][j+1]=a[i+1][j+1]^1;
					}
					arr.add(s);
				}
				
				if(a[i][m-1]!=0||a[i][m]!=0)
				{
				int s[]=new int[6]; int in=0;
				if(a[i][m-1]==1)
					{s[in++]=i;s[in++]=m-1;  a[i][m-1]=0; }
				if(a[i][m]==1)
					{s[in++]=i;s[in++]=m;    a[i][m]=0;}

					s[in++]=i+1; s[in++]=m-1;  a[i+1][m-1]=a[i+1][m-1]^1;
				if(in==4)
				{
					s[in++]=i+1; s[in++]=m;   a[i+1][m]=a[i+1][m]^1;
				}
				arr.add(s);
				}
			}
			
			for(int j=1;j<=m;j++)
			{
				if(j+1>m)continue;
				if(a[n-1][j]==0&&a[n][j]==0) continue;
				int s[]=new int[6]; int in=0;
				if(a[n-1][j]==1)
					{s[in++]=n-1;s[in++]=j;   a[n-1][j]=0;}
				if(a[n][j]==1)
					{s[in++]=n;s[in++]=j;   a[n][j]=0;}

					s[in++]=n-1; s[in++]=j+1;  a[n-1][j+1]=a[n-1][j+1]^1;
				if(in==4)
				{
					s[in++]=n; s[in++]=j+1;  a[n][j+1]=a[n][j+1]^1;
				}
				arr.add(s);
			}
			
			if(a[n-1][m]==0&&a[n][m]==1)
			{
				int s1[]= {n-1,m-1,n,m-1,n,m};
				arr.add(s1);
				int s2[]= {n-1,m-1,n-1,m,n,m};
				arr.add(s2);
				int s3[]= {n,m-1,n-1,m,n,m};
				arr.add(s3);
			}
			else if(a[n-1][m]==1&&a[n][m]==0)
			{
				int s1[]= {n-1,m-1,n,m-1,n-1,m};
				arr.add(s1);
				int s2[]= {n-1,m-1,n-1,m,n,m};
				arr.add(s2);
				int s3[]= {n,m-1,n-1,m,n,m};
				arr.add(s3);
			}
			else if(a[n-1][m]==1&&a[n][m]==1)
			{
				int s1[]= {n-1,m-1,n,m-1,n-1,m};
				arr.add(s1);
				int s2[]= {n-1,m-1,n,m-1,n,m};
				arr.add(s2);
			}
			out.println(arr.size());
			for(int i=0;i<arr.size();i++)
			{
				for(int j:arr.get(i))
					out.print(j+" ");
				out.println();
			}
		}
	}
	int[] shuffle(int a[]) {
		ArrayList<Integer> al = new ArrayList<>();
		for(int i=0;i<a.length;i++) {
			al.add(a[i]);
		}
		Collections.sort(al);
		for(int i=0;i<a.length;i++) {
			a[i]=al.get(i);
		}
		return a;
	}
	/*IMPLEMENTATION BY AMAN KOTIYAL, FAST INPUT OUTPUT & METHODS BELOW*/
	
	private byte[] buf=new byte[1024];
	private int index;
	private InputStream in;
	private int total;
	private SpaceCharFilter filter;
	PrintWriter out;
	
	int gcd(int a, int b) 
	{ 
		if (a == 0) 
			return b; 
		return gcd(b%a, a); 
	} 
	long gcd(long a, long b) 
	{ 
		if (a == 0) 
			return b; 
		return gcd(b%a, a); 
	}
	/* for (1/a)%mod = ( a^(mod-2) )%mod  ----> use expo to calc -->(a^(mod-2)) */
	long expo(long p,long q)  /*  (p^q)%mod   */
	{
		long z = 1;
		while (q>0) {
			if (q%2 == 1) {
				z = (z * p)%mod;
			}
			p = (p*p)%mod;
			q >>= 1;
		}
		return z;
	}
	void run()throws Exception
	{
		in=System.in; out = new PrintWriter(System.out);
		solve();
		out.flush();
	}
	private int scan()throws IOException
	{
		if(total<0)
			throw new InputMismatchException();
		if(index>=total)
		{
			index=0;
			total=in.read(buf);
			if(total<=0)
				return -1;
		}
		return buf[index++];
	}
	private int ni() throws IOException 
	{
		int c = scan();
		while (isSpaceChar(c))
			c = scan();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = scan();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = scan();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
	private long nl() throws IOException 
	{
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = scan()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = scan();
		}
		
		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = scan();
		}
	}
	private double nd() throws IOException{
		return Double.parseDouble(ns());
	}
	private String ns() throws IOException {
		int c = scan();
		while (isSpaceChar(c))
			c = scan();
		StringBuilder res = new StringBuilder();
		do {
			if (Character.isValidCodePoint(c))
				res.appendCodePoint(c);
			c = scan();
		} while (!isSpaceChar(c));
		return res.toString();
	}
	private String nss() throws IOException
	{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		return br.readLine();
	}
	private char nc() throws IOException 
	{
		int c = scan();
		while (isSpaceChar(c))
			c = scan();
		return (char) c;
	}
	private boolean isWhiteSpace(int n)
	{
		if(n==' '||n=='\n'||n=='\r'||n=='\t'||n==-1)
			return true;
		return false;
	}
	private boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhiteSpace(c);
	}
	private interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}