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 PYTHON3):

Solution:
#If FastIO not needed, used this and don't forget to strip 
#import sys, math   
#input = sys.stdin.readline   
import os 
import sys 
from io import BytesIO, IOBase  
import heapq as h 
import bisect 
 
from types import GeneratorType  
BUFSIZE = 8192
class SortedList: 
    def __init__(self, iterable=[], _load=200):
        """Initialize sorted list instance."""
        values = sorted(iterable)
        self._len = _len = len(values)
        self._load = _load
        self._lists = _lists = [values[i:i + _load] for i in range(0, _len, _load)]
        self._list_lens = [len(_list) for _list in _lists]
        self._mins = [_list[0] for _list in _lists]
        self._fen_tree = []
        self._rebuild = True
 
    def _fen_build(self):
        """Build a fenwick tree instance."""
        self._fen_tree[:] = self._list_lens
        _fen_tree = self._fen_tree
        for i in range(len(_fen_tree)):
            if i | i + 1 < len(_fen_tree):
                _fen_tree[i | i + 1] += _fen_tree[i]
        self._rebuild = False
 
    def _fen_update(self, index, value):
        """Update `fen_tree[index] += value`."""
        if not self._rebuild:
            _fen_tree = self._fen_tree
            while index < len(_fen_tree):
                _fen_tree[index] += value
                index |= index+1
 
    def _fen_query(self, end):
        """Return `sum(_fen_tree[:end])`."""
        if self._rebuild:
            self._fen_build()
 
        _fen_tree = self._fen_tree
        x = 0
        while end:
            x += _fen_tree[end - 1]
            end &= end - 1
        return x
 
    def _fen_findkth(self, k):
        """Return a pair of (the largest `idx` such that `sum(_fen_tree[:idx]) <= k`, `k - sum(_fen_tree[:idx])`)."""
        _list_lens = self._list_lens
        if k < _list_lens[0]:
            return 0, k
        if k >= self._len - _list_lens[-1]:
            return len(_list_lens) - 1, k + _list_lens[-1] - self._len
        if self._rebuild:
            self._fen_build()
 
        _fen_tree = self._fen_tree
        idx = -1
        for d in reversed(range(len(_fen_tree).bit_length())):
            right_idx = idx + (1 << d)
            if right_idx < len(_fen_tree) and k >= _fen_tree[right_idx]:
                idx = right_idx
                k -= _fen_tree[idx]
        return idx + 1, k
 
    def _delete(self, pos, idx):
        """Delete value at the given `(pos, idx)`."""
        _lists = self._lists
        _mins = self._mins
        _list_lens = self._list_lens
 
        self._len -= 1
        self._fen_update(pos, -1)
        del _lists[pos][idx]
        _list_lens[pos] -= 1
 
        if _list_lens[pos]:
            _mins[pos] = _lists[pos][0]
        else:
            del _lists[pos]
            del _list_lens[pos]
            del _mins[pos]
            self._rebuild = True
 
    def _loc_left(self, value):
        """Return an index pair that corresponds to the first position of `value` in the sorted list."""
        if not self._len:
            return 0, 0
 
        _lists = self._lists
        _mins = self._mins
 
        lo, pos = -1, len(_lists) - 1
        while lo + 1 < pos:
            mi = (lo + pos) >> 1
            if value <= _mins[mi]:
                pos = mi
            else:
                lo = mi
 
        if pos and value <= _lists[pos - 1][-1]:
            pos -= 1
 
        _list = _lists[pos]
        lo, idx = -1, len(_list)
        while lo + 1 < idx:
            mi = (lo + idx) >> 1
            if value <= _list[mi]:
                idx = mi
            else:
                lo = mi
 
        return pos, idx
 
    def _loc_right(self, value):
        """Return an index pair that corresponds to the last position of `value` in the sorted list."""
        if not self._len:
            return 0, 0
 
        _lists = self._lists
        _mins = self._mins
 
        pos, hi = 0, len(_lists)
        while pos + 1 < hi:
            mi = (pos + hi) >> 1
            if value < _mins[mi]:
                hi = mi
            else:
                pos = mi
 
        _list = _lists[pos]
        lo, idx = -1, len(_list)
        while lo + 1 < idx:
            mi = (lo + idx) >> 1
            if value < _list[mi]:
                idx = mi
            else:
                lo = mi
 
        return pos, idx
 
    def add(self, value):
        """Add `value` to sorted list."""
        _load = self._load
        _lists = self._lists
        _mins = self._mins
        _list_lens = self._list_lens
 
        self._len += 1
        if _lists:
            pos, idx = self._loc_right(value)
            self._fen_update(pos, 1)
            _list = _lists[pos]
            _list.insert(idx, value)
            _list_lens[pos] += 1
            _mins[pos] = _list[0]
            if _load + _load < len(_list):
                _lists.insert(pos + 1, _list[_load:])
                _list_lens.insert(pos + 1, len(_list) - _load)
                _mins.insert(pos + 1, _list[_load])
                _list_lens[pos] = _load
                del _list[_load:]
                self._rebuild = True
        else:
            _lists.append([value])
            _mins.append(value)
            _list_lens.append(1)
            self._rebuild = True
 
    def discard(self, value):
        """Remove `value` from sorted list if it is a member."""
        _lists = self._lists
        if _lists:
            pos, idx = self._loc_right(value)
            if idx and _lists[pos][idx - 1] == value:
                self._delete(pos, idx - 1)
 
    def remove(self, value):
        """Remove `value` from sorted list; `value` must be a member."""
        _len = self._len
        self.discard(value)
        if _len == self._len:
            raise ValueError('{0!r} not in list'.format(value))
 
    def pop(self, index=-1):
        """Remove and return value at `index` in sorted list."""
        pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
        value = self._lists[pos][idx]
        self._delete(pos, idx)
        return value
 
    def bisect_left(self, value):
        """Return the first index to insert `value` in the sorted list."""
        pos, idx = self._loc_left(value)
        return self._fen_query(pos) + idx
 
    def bisect_right(self, value):
        """Return the last index to insert `value` in the sorted list."""
        pos, idx = self._loc_right(value)
        return self._fen_query(pos) + idx
 
    def count(self, value):
        """Return number of occurrences of `value` in the sorted list."""
        return self.bisect_right(value) - self.bisect_left(value)
 
    def __len__(self):
        """Return the size of the sorted list."""
        return self._len
 
    def __getitem__(self, index):
        """Lookup value at `index` in sorted list."""
        pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
        return self._lists[pos][idx]
 
    def __delitem__(self, index):
        """Remove value at `index` from sorted list."""
        pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
        self._delete(pos, idx)
 
    def __contains__(self, value):
        """Return true if `value` is an element of the sorted list."""
        _lists = self._lists
        if _lists:
            pos, idx = self._loc_left(value)
            return idx < len(_lists[pos]) and _lists[pos][idx] == value
        return False
 
    def __iter__(self):
        """Return an iterator over the sorted list."""
        return (value for _list in self._lists for value in _list)
 
    def __reversed__(self):
        """Return a reverse iterator over the sorted list."""
        return (value for _list in reversed(self._lists) for value in reversed(_list))
 
    def __repr__(self):
        """Return string representation of sorted list."""
        return 'SortedList({0})'.format(list(self))
 
class FastIO(IOBase):
    newlines = 0
 
    def __init__(self, file):
        import os
        self.os = os
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
 
    def read(self):
        while True:
            b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
 
    def readline(self):
        while self.newlines == 0:
            b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
 
    def flush(self):
        if self.writable:
            self.os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)
 
 
class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")
 
 
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
 
import collections as col
import math, string
 
def getInts():
    return [int(s) for s in input().split()]
 
def getInt():
    return int(input())
 
def getStrs():
    return [s for s in input().split()]
 
def getStr():
    return input()
 
def listStr():
    return list(input())
 
MOD = 10**9+7
mod=10**9+7
t=int(input())
#t=1
p=10**9+7
def ncr_util():
    
    inv[0]=inv[1]=1
    fact[0]=fact[1]=1
    for i in range(2,300001):
        inv[i]=(inv[i%p]*(p-p//i))%p
    for i in range(1,300001):
        inv[i]=(inv[i-1]*inv[i])%p
        fact[i]=(fact[i-1]*i)%p

def z_array(s1):
    n = len(s1)
    z=[0]*(n)
    l, r, k = 0, 0, 0
    for i in range(1,n): 
  
        # if i>R nothing matches so we will calculate. 
        # Z[i] using naive way. 
        if i > r: 
            l, r = i, i 
  
            # R-L = 0 in starting, so it will start 
            # checking from 0'th index. For example, 
            # for "ababab" and i = 1, the value of R 
            # remains 0 and Z[i] becomes 0. For string 
            # "aaaaaa" and i = 1, Z[i] and R become 5 
            while r < n and s1[r - l] == s1[r]: 
                r += 1
            z[i] = r - l 
            r -= 1
        else: 
  
            # k = i-L so k corresponds to number which 
            # matches in [L,R] interval. 
            k = i - l 
  
            # if Z[k] is less than remaining interval 
            # then Z[i] will be equal to Z[k]. 
            # For example, str = "ababab", i = 3, R = 5 
            # and L = 2 
            if z[k] < r - i + 1: 
                z[i] = z[k] 
  
            # For example str = "aaaaaa" and i = 2,  
            # R is 5, L is 0 
            else: 
  
                # else start from R and check manually 
                l = i 
                while r < n and s1[r - l] == s1[r]: 
                    r += 1
                z[i] = r - l 
         
                r -= 1  
    return z
def solve3(ans,d,i,j):
    ans1=[]
    for i1 in range(i,i+2):
        for j1 in range(j,j+2):
            #print(i1,j1,d[i1][j1])
            if d[i1][j1]==1:
                d[i1][j1]^=1
                ans1.append(i1)
                ans1.append(j1)
    #print('solve 3',ans1)            
    ans.append(ans1)
    
def solve2(ans,d,i,j):
    cnt=0
    ans1=[]
    for i1 in range(i,i+2):
        for j1 in range(j,j+2):
            #print(200000,i1,j1,d[i1][j1])
            if d[i1][j1]==0:
                ans1.append(i1)
                ans1.append(j1)
                
                d[i1][j1]^=1
            elif cnt==0 and d[i1][j1]==1:
                cnt=1
                ans1.append(i1)
                ans1.append(j1)
                d[i1][j1]^=1
        #print()
    ans.append(ans1) 
    #print('solve 2',ans1)
    solve3(ans,d,i,j)
                               
def solve1(ans,d,i,j):
    cnt=0
    ans1=[]
    for i1 in range(i,i+2):
        for j1 in range(j,j+2):
            #print('solve 1',d[i1][j1])
            if d[i1][j1]==1:
                ans1.append(i1)
                ans1.append(j1)
                d[i1][j1]^=1
            elif d[i1][j1]==0 and cnt<2:
                cnt+=1
                ans1.append(i1)
                ans1.append(j1)
                d[i1][j1]^=1
    #print('solve 1',ans1)            
    ans.append(ans1)
    solve2(ans,d,i,j)
def solve4(ans,d,i,j):
    d[i][j]^=1
    d[i][j+1]^=1
    d[i+1][j]^=1
    ans.append([i,j,i,j+1,i+1,j])
    solve1(ans,d,i,j)
def solve_util(ans,d,i,j):
    x1,y=0,0
    for i1 in range(i,i+2):
        for j1 in range(j,j+2):
            if d[i1][j1]==1:
                x1+=1
    #print(144,x1)
    if x1==4:
        solve4(ans,d,i,j)
        
    elif x1==3:
        solve3(ans,d,i,j)
        #ans.append(l1)
    elif x1==2:
        
        solve2(ans,d,i,j)
        #ans.append(l1)
    elif x1==1:
        solve1(ans,d,i,j)
        #ans.append(l1)
        
def solve():
    ans=[]
    d={}
    for i in range(n):
        d[i]=[]
        for j in range(m):
            if l[i][j]=='0':
                d[i].append(0)
            else:
                d[i].append(1)
    i1,j1=0,0
    #print(123,d)
    for i1 in range(n-2):
        for j1 in range(m):
            #print(i1,j1,d[i1][j1])
            if d[i1][j1]==1:
                if j1==m-1:
                    ans.append([i1,j1,i1+1,j1,i1+1,j1-1])
                    d[i1][j1]^=1
                    d[i1+1][j1]^=1
                    d[i1+1][j1-1]^=1
                else:
                    ans.append([i1,j1,i1+1,j1,i1,j1+1])
                    d[i1][j1]^=1
                    d[i1+1][j1]^=1
                    d[i1][j1+1]^=1
    #print(1233,ans,len(ans))
    if m%2!=0:
        if d[n-2][m-1]==1 and d[n-1][m-1]==1:
            ans.append([n-2,m-1,n-1,m-1,n-2,m-2])
            d[n-2][m-1]^=1
            d[n-1][m-1]^=1
            d[n-2][m-2]^=1
            
        elif d[n-2][m-1]==1:
            ans.append([n-2,m-1,n-2,m-2,n-1,m-2])
            d[n-2][m-1]^=1
            d[n-2][m-2]^=1
            d[n-1][m-2]^=1
        elif d[n-1][m-1]==1:
            ans.append([n-1,m-1,n-1,m-2,n-2,m-2])
            d[n-1][m-1]^=1
            d[n-1][m-2]^=1
            d[n-2][m-2]^=1
    j1=0
    cnt1=m//2
    #print('pre',ans,len(ans))
    while cnt1:
        solve_util(ans,d,n-2,j1)
        j1+=2
        cnt1-=1
    print(len(ans))
    for i in range(len(ans)):
        for j in range(6):
            print(ans[i][j]+1,end=" ")
        print()

for _ in range(t):
    #n=int(input())
    #n=int(input())
    n,m=(map(int,input().split()))
    #n1=n
    #x=int(input())
    #b=int(input())
    #d={}
    #r,g=map(int,input().split())
    #n=int(input())
    #s=input()
    #p=input()
    #l=list(map(int,input().split()))
    l=[]
    
    for i in range(n):
        l.append(input())
        
    #l.sort()
    
    #l.sort(revrese=True)
    #l2=list(map(int,input().split()))
    #l=str(n)
    #l.sort(reverse=True)
    #l2.sort(reverse=True)
    #l1.sort(reverse=True)
    (solve())