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:
from bisect import *
from collections import *
from math import gcd,ceil,sqrt,floor,inf
from heapq import *
from itertools import *
from operator import add,mul,sub,xor,truediv,floordiv
from functools import *

#------------------------------------------------------------------------
import os
import sys
from io import BytesIO, IOBase
# region fastio

BUFSIZE = 8192
 
class FastIO(IOBase):
    newlines = 0
 
    def __init__(self, file):
        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 = os.read(self._fd, max(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 = os.read(self._fd, max(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:
            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")


#------------------------------------------------------------------------
def RL(): return map(int, sys.stdin.readline().rstrip().split())
def RLL(): return list(map(int, sys.stdin.readline().rstrip().split()))
def N(): return int(input())
#------------------------------------------------------------------------

from types import GeneratorType
 
 
def bootstrap(f, stack=[]):
    def wrappedfunc(*args, **kwargs):
        if stack:
            return f(*args, **kwargs)
        else:
            to = f(*args, **kwargs)
            while True:
                if type(to) is GeneratorType:
                    stack.append(to)
                    to = next(to)
                else:
                    stack.pop()
                    if not stack:
                        break
                    to = stack[-1].send(to)
            return to
 
    return wrappedfunc


farr=[1]
ifa=[]

def fact(x,mod=0):
    if mod:
        while x>=len(farr):
            farr.append(farr[-1]*len(farr)%mod)
    else:
        while x>=len(farr):
            farr.append(farr[-1]*len(farr))
    return farr[x]

def ifact(x,mod):
    global ifa
    ifa.append(pow(farr[-1],mod-2,mod))
    for i in range(x,0,-1):
        ifa.append(ifa[-1]*i%mod)
    ifa=ifa[::-1]

def per(i,j,mod=0):
    if i<j: return 0
    if not mod:
        return fact(i)//fact(i-j)
    return farr[i]*ifa[i-j]%mod
    
def com(i,j,mod=0):
    if i<j: return 0
    if not mod:        
        return per(i,j)//fact(j)
    return per(i,j,mod)*ifa[j]%mod

def catalan(n):
    return com(2*n,n)//(n+1)
    
def linc(f,t,l,r):
    while l<r:
        mid=(l+r)//2
        if t>f(mid):
            l=mid+1
        else:
            r=mid
    return l

def rinc(f,t,l,r):
    while l<r:
        mid=(l+r+1)//2
        if t<f(mid):
            r=mid-1
        else:
            l=mid
    return l

def ldec(f,t,l,r):
    while l<r:
        mid=(l+r)//2
        if t<f(mid):
            l=mid+1
        else:
            r=mid
    return l

def rdec(f,t,l,r):
    while l<r:
        mid=(l+r+1)//2
        if t>f(mid):
            r=mid-1
        else:
            l=mid
    return l

def isprime(n):
    for i in range(2,int(n**0.5)+1):
        if n%i==0:
            return False
    return True

def binfun(x):
    c=0
    for w in arr:
        c+=ceil(w/x)
    return c

def lowbit(n):
    return n&-n

def inverse(a,m):
    a%=m
    if a<=1: return a
    return ((1-inverse(m,a)*m)//a)%m

class BIT:
    def __init__(self,arr):
        self.arr=arr
        self.n=len(arr)-1
        
    def update(self,x,v):
        while x<=self.n:
            self.arr[x]+=v
            x+=x&-x

    def query(self,x):
        ans=0
        while x:
            ans+=self.arr[x]
            x&=x-1
        return ans
'''
class SMT:
    def __init__(self,arr):
        self.n=len(arr)-1
        self.arr=[0]*(self.n<<2)
        self.lazy=[0]*(self.n<<2)
        def Build(l,r,rt):
            if l==r:
                self.arr[rt]=arr[l]
                return
            m=(l+r)>>1
            Build(l,m,rt<<1)
            Build(m+1,r,rt<<1|1)
            self.pushup(rt)
        Build(1,self.n,1)

    def pushup(self,rt):
        self.arr[rt]=self.arr[rt<<1]+self.arr[rt<<1|1]

    def pushdown(self,rt,ln,rn):#lr,rn表区间数字数
        if self.lazy[rt]:
            self.lazy[rt<<1]+=self.lazy[rt]
            self.lazy[rt<<1|1]=self.lazy[rt]
            self.arr[rt<<1]+=self.lazy[rt]*ln
            self.arr[rt<<1|1]+=self.lazy[rt]*rn
            self.lazy[rt]=0
            
    def update(self,L,R,c,l=1,r=None,rt=1):#L,R表示操作区间
        if r==None: r=self.n
        if L<=l and r<=R:
            self.arr[rt]+=c*(r-l+1)
            self.lazy[rt]+=c
            return
        m=(l+r)>>1
        self.pushdown(rt,m-l+1,r-m)
        if L<=m: self.update(L,R,c,l,m,rt<<1)
        if R>m: self.update(L,R,c,m+1,r,rt<<1|1)
        self.pushup(rt)

    def query(self,L,R,l=1,r=None,rt=1):
        if r==None: r=self.n
        #print(L,R,l,r,rt)
        if L<=l and R>=r:
            return self.arr[rt]
        m=(l+r)>>1
        self.pushdown(rt,m-l+1,r-m)
        ans=0
        if L<=m: ans+=self.query(L,R,l,m,rt<<1)
        if R>m: ans+=self.query(L,R,m+1,r,rt<<1|1)
        return ans
'''       
class DSU:#容量+路径压缩
    def __init__(self,n):
        self.c=[-1]*n

    def same(self,x,y):
        return self.find(x)==self.find(y)

    def find(self,x):
        if self.c[x]<0:
            return x
        self.c[x]=self.find(self.c[x])
        return self.c[x]

    def union(self,u,v):
        u,v=self.find(u),self.find(v)
        if u==v:
            return False
        if self.c[u]<self.c[v]:
            u,v=v,u
        self.c[u]+=self.c[v]
        self.c[v]=u
        return True

    def size(self,x): return -self.c[self.find(x)]
    
class UFS:#秩+路径
    def __init__(self,n):
        self.parent=[i for i in range(n)]
        self.ranks=[0]*n

    def find(self,x):
        if x!=self.parent[x]:
            self.parent[x]=self.find(self.parent[x])
        return self.parent[x]

    def union(self,u,v):
        pu,pv=self.find(u),self.find(v)
        if pu==pv:
            return False
        if self.ranks[pu]>=self.ranks[pv]:
            self.parent[pv]=pu
            if self.ranks[pv]==self.ranks[pu]:
                self.ranks[pu]+=1
        else:
            self.parent[pu]=pv

def Prime(n):
    c=0
    prime=[]
    flag=[0]*(n+1)
    for i in range(2,n+1):
        if not flag[i]:
            prime.append(i)
            c+=1
        for j in range(c):
            if i*prime[j]>n: break
            flag[i*prime[j]]=prime[j]
            if i%prime[j]==0: break
    return prime

def dij(s,graph):
    d={}
    d[s]=0
    heap=[(0,s)]
    seen=set()
    while heap:
        dis,u=heappop(heap)
        if u in seen:
            continue
        for v in graph[u]:
            if v not in d or d[v]>d[u]+graph[u][v]:
                d[v]=d[u]+graph[u][v]
                heappush(heap,(d[v],v))
    return d

def GP(it): return [(ch,len(list(g))) for ch,g in groupby(it)]

class DLN:
    def __init__(self,val):
        self.val=val
        self.pre=None
        self.next=None

class Trie:
    def __init__(self,d):
        if d>=0:
            self.left=Trie(d-1)
        else:
            self.right=Trie(d-1)
        self.c=0

    def put(self,x,i):
        if i==-1:
            self.c=1
            return
        if x&1<<i:
            self.left.put(x,i-1)
        else:
            self.right.put(x,i-1)

def con(i,j,x):
    i+=1
    j+=1
    if x==0:
        return [i,j,i,j+1,i+1,j]
    if x==1:
        return [i,j,i,j+1,i+1,j+1]
    if x==2:
        return [i,j,i+1,j,i+1,j+1]
    if x==3:
        return [i,j+1,i+1,j,i+1,j+1]

def f(i,j):
    if i<n-1 and j<m-1:
        res=a[i][j]+a[i][j+1]+a[i+1][j]+a[i+1][j+1]
        if res=='1111':
            for d in range(4):
                ans.append(con(i,j,d))
        elif res=='1110':
           ans.append(con(i,j,0))
        elif res=='1101':
            ans.append(con(i,j,1))
        elif res=='1011':
            ans.append(con(i,j,2))
        elif res=='0111':
            ans.append(con(i,j,3))
        elif res=='1000':
            for d in range(4):
                if d!=3:
                    ans.append(con(i,j,d))
        elif res=='0100':
            for d in range(4):
                if d!=2:
                    ans.append(con(i,j,d))
        elif res=='0010':
            for d in range(4):
                if d!=1:
                    ans.append(con(i,j,d))
        elif res=='0001':
            for d in range(4):
                if d!=0:
                    ans.append(con(i,j,d))
        elif res=='1100':
            ans.append(con(i,j,2))
            ans.append(con(i,j,3))
        elif res=='1010':
            ans.append(con(i,j,1))
            ans.append(con(i,j,3))
        elif res=='0101':
            ans.append(con(i,j,0))
            ans.append(con(i,j,2))
        elif res=='0011':
            ans.append(con(i,j,0))
            ans.append(con(i,j,1))
        elif res=='1001':
            ans.append(con(i,j,0))
            ans.append(con(i,j,3))
        elif res=='0110':
            ans.append(con(i,j,1))
            ans.append(con(i,j,2))
    else:
        if i==n-1 and j==m-1:
            if a[i][j]=='1':
                for d in range(4):
                    if d!=0:
                        ans.append(con(i-1,j-1,d))
        elif i==n-1:
            tmp=a[i][j]+a[i][j+1]
            if tmp=='11':
                ans.append(con(i-1,j,0))
                ans.append(con(i-1,j,1))
            elif tmp=='10':
                for d in range(4):
                    if d!=1:
                        ans.append(con(i-1,j,d))
            elif tmp=='01':
                for d in range(4):
                    if d!=0:
                        ans.append(con(i-1,j,d))
        else:
            tmp=a[i][j]+a[i+1][j]
            if tmp=='11':
                ans.append(con(i,j-1,0))
                ans.append(con(i,j-1,2))
            elif tmp=='10':
                for d in range(4):
                    if d!=2:
                        ans.append(con(i,j-1,d))
            elif tmp=='01':
                for d in range(4):
                    if d!=0:
                        ans.append(con(i,j-1,d))

def rev(i,j):
    if a[i][j]=='1':
        a[i][j]='0'
    else:
        a[i][j]='1'

t=N()
for i in range(t):
    n,m=RL()
    a=[]
    ans=[]
    for i in range(n):
        a.append(list(input()))
    #print(a)
    if n&1 and m&1:
        if a[n-1][m-1]=='1':
            ans.append(con(n-2,m-2,3))
            rev(n-2,m-1)
            rev(n-1,m-2)
            rev(n-1,m-1)
    #print(a,ans)
    if n&1:
        for j in range(0,m-1,2):
            tmp=a[n-1][j]+a[n-1][j+1]
            if tmp=='11':
                ans.append(con(n-2,j,2))
                rev(n-2,j)
                #print(ans)
            elif tmp=='10':
                ans.append(con(n-2,j,0))
                rev(n-2,j)
                rev(n-2,j+1)
            elif tmp=='01':
                ans.append(con(n-2,j,1))
                rev(n-2,j)
                rev(n-2,j+1)
            #print(n-1,j,tmp,a)
    if m&1:
        for i in range(0,n-1,2):
            tmp=a[i][m-1]+a[i+1][m-1]
            if tmp=='11':
                ans.append(con(i,m-2,1))
                rev(i,m-2)
            elif tmp=='10':
                ans.append(con(i,m-2,0))
                rev(i,m-2)
                rev(i+1,m-2)
            elif tmp=='01':
                ans.append(con(i,m-2,2))
                rev(i,m-2)
                rev(i+1,m-2)
            #print(i,m-1,tmp,a)
    #print(a,ans)
    for i in range(0,n-1,2):
        for j in range(0,m-1,2):
            #print(i,j)
            f(i,j)
            #print(i,j,ans)
    print(len(ans))
    for i in range(len(ans)):
        print(*ans[i])
    
            
''' 
sys.setrecursionlimit(200000)
import threading
threading.stack_size(10**8)
t=threading.Thread(target=main)
t.start()
t.join()
'''