Buggy python submission (verdict: Time Limit Exceeded):
import sys
f = sys.stdin

def mix(a,b):
    return (min(a[0],b[0]),min(a[1],b[1]),max(a[2],b[2]),max(a[3],b[3]))

s = {}

n, d = map(int, f.readline().split())
for _ in range(n):
    x, y, b = map(int, f.readline().split())
    s[b] = mix(s[b],(x,y,x,y)) if b in s else (x,y,x,y)

max_size = 0
b = sorted(s.keys())
for i in range(len(b)):
    xy = s[b[i]]
    for j in range(i + 1,len(b)):
        if b[i] + d < b[j]:
            break
        xy = mix(xy,s[b[j]])
    max_size = max(max_size,((xy[2] - xy[0]) * (xy[3] - xy[1])))
print(max_size)

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
f = sys.stdin

def mix(a,b):
    return (min(a[0],b[0]),min(a[1],b[1]),max(a[2],b[2]),max(a[3],b[3]))

s = {}

n, d = map(int, f.readline().split())
for _ in range(n):
    x, y, b = map(int, f.readline().split())
    s[b] = mix(s[b],(x,y,x,y)) if b in s else (x,y,x,y)

max_size = 0
b = sorted(s.keys())
i = j = 0
while j < len(b) - 1:
    for k in range(j,-1,-1):
        if b[k] + d < b[j]:
            break
        i = k
    for k in range(i,len(b)):
        if b[i] + d < b[k]:
            break
        j = k
    
    xy = s[b[i]]
    for k in range(i + 1, j + 1):
        xy = mix(xy,s[b[k]])
    
    max_size = max(max_size,((xy[2] - xy[0]) * (xy[3] - xy[1])))
    j+=1
    
print(max_size)

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

x,y = {},{}
for line in f:
    xi, yi, bi = map(int, line.split())
    if bi not in x:
        x[bi],y[bi] = [],[]
    x[bi].append(xi)
    y[bi].append(yi)

b = sorted(x.keys())

xmin,xmax,ymin,ymax = [None for _ in range(len(b))],[None for _ in range(len(b))],[None for _ in range(len(b))],[None for _ in range(len(b))]
for i in range(len(b)):
    xmin[i],xmax[i],ymin[i],ymax[i] = min(x[b[i]]),max(x[b[i]]),min(y[b[i]]),max(y[b[i]])

max_size = i = j = 0
while j < len(b) - 1:
    for k in range(j,-1,-1):
        if b[k] + d < b[j]:
            break
        i = k
    for k in range(i,len(b)):
        if b[i] + d < b[k]:
            break
        j = k
    size = (max(xmax[i:j + 1]) - min(xmin[i:j + 1])) * (max(ymax[i:j + 1]) - min(ymin[i:j + 1]))
    max_size = max(max_size,size)
    j+=1
    
print(max_size)

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

x,y,b = [],[],set()
for line in f:
    xi, yi, bi = map(int, line.split())
    x.append((xi,bi))
    y.append((yi,bi))
    b.update([bi])    
x = sorted(x)
y = sorted(y)
b = sorted(b)


def search(target,bmin,bmax):
    tmax,tmin = None,None
    for i in range(len(target)):
        if bmin <= target[i][1] <= bmax:
            tmin = target[i][0]
            break
    for i in range(len(target) - 1, -1, -1):
        if bmin <= target[i][1] <= bmax:
            tmax = target[i][0]
            break
    return tmax,tmin
    

max_size = i = j = 0
while j < len(b) - 1:
    for k in range(j,-1,-1):
        if b[k] + d < b[j]:
            break
        i = k
    for k in range(i,len(b)):
        if b[i] + d < b[k]:
            break
        j = k

    xmax,xmin = search(x,b[i],b[j])
    ymax,ymin = search(y,b[i],b[j])
    
    max_size = max(max_size,(xmax - xmin) * (ymax - ymin))
    j+=1
    
print(max_size)

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import math
class SegmentTree:
    def __init__(self, dat, func, sentinel):
        self.pad = 2 ** math.ceil(math.log(len(dat),2)) - 1
        self.dat = [None] * self.pad + dat + [sentinel] * (self.pad + 1 - len(dat))
        self.func = func
        self.sentinel = sentinel
        for i in range(self.pad - 1, -1, -1):
            self.dat[i] = self.func(self.dat[i * 2 + 1],self.dat[i * 2 + 2])
        
    def q(self,s,e):
        return self._q(self.pad + s,self.pad + e,0,self.pad,len(self.dat) - 1)
    def _q(self,a,b,k,l,r):
        if b < l or r < a:
            return self.sentinel
        elif a <= l and r <= b:
            return self.dat[k]
        else:
            vl = self._q(a,b,k * 2 + 1,l,(l+r)//2)
            vr = self._q(a,b,k * 2 + 2,(l+r)//2 + 1,r)
            return self.func(vl,vr)
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

b = []
for line in f:
    xi, yi, bi = map(int, line.split())
    b.append((bi,xi,yi))
b = sorted(b)
x = [xi for _,xi,_ in b]
y = [yi for _,_,yi in b]


        
minx = SegmentTree(x,min,sentinel = 2000001)
maxx = SegmentTree(x,max,sentinel = -1)
miny = SegmentTree(y,min,sentinel = 2000001)
maxy = SegmentTree(y,max,sentinel = -1)


max_size = i = j = 0
while j < len(b) - 1:
    for k in range(j,-1,-1):
        if b[k][0] + d < b[j][0]:
            break
        i = k
    for k in range(i,len(b)):
        if b[i][0] + d < b[k][0]:
            break
        j = k
    
    max_size = max(max_size,(maxx.q(i,j) - minx.q(i,j)) * (maxy.q(i,j) - miny.q(i,j)))
    j+=1
    
print(max_size)

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
f = sys.stdin

def q(t,s,e,func):
    if s == e:
        return t[s]
    else:
        return func(q(t,s,(s+e)//2,func),q(t,(s+e)//2 + 1,e,func))

_, d = map(int, f.readline().split())

b = []
for line in f:
    xi, yi, bi = map(int, line.split())
    b.append((bi,xi,yi))
b = sorted(b)
x = tuple(xi for _,xi,_ in b)
y = tuple(yi for _,_,yi in b)

max_size = i = j = 0
while j < len(b) - 1:
    for k in range(j,-1,-1):
        if b[k][0] + d < b[j][0]:
            break
        i = k
    for k in range(i,len(b)):
        if b[i][0] + d < b[k][0]:
            break
        j = k

    max_size = max(max_size,(q(x,i,j,max) - q(x,i,j,min)) * (q(y,i,j,max) - q(y,i,j,min)))
    j+=1
    
print(max_size)

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
f = sys.stdin


def memoize(f):
  memo = {}
  def inner(v1,v2,v3,v4):
      if not (v1,v2,v3,v4) in memo:
        memo[v1,v2,v3,v4] = f(v1,v2,v3,v4)
      return memo[v1,v2,v3,v4]
  return inner

@memoize
def q(t,s,e,func):
    if s == e:
        return t[s]
    else:
        return func(q(t,s,(s+e)//2,func),q(t,(s+e)//2 + 1,e,func))

_, d = map(int, f.readline().split())

b = []
for line in f:
    xi, yi, bi = map(int, line.split())
    b.append((bi,xi,yi))
b = sorted(b)
x = tuple(xi for _,xi,_ in b)
y = tuple(yi for _,_,yi in b)

max_size = i = j = 0
while j < len(b) - 1:
    for k in range(j,-1,-1):
        if b[k][0] + d < b[j][0]:
            break
        i = k
    for k in range(i,len(b)):
        if b[i][0] + d < b[k][0]:
            break
        j = k

    max_size = max(max_size,(q(x,i,j,max) - q(x,i,j,min)) * (q(y,i,j,max) - q(y,i,j,min)))
    j+=1
    
print(max_size)

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
f = sys.stdin

def q(t,i,s,e,func):
    if s == e:
        return t[s][i]
    else:
        return func(q(t,i,s,(s+e)//2,func),q(t,i,(s+e)//2 + 1,e,func))

_, d = map(int, f.readline().split())

b = []
for line in f:
    xi, yi, bi = map(int, line.split())
    b.append((bi,xi,yi))
b = sorted(b)

max_size = i = j = 0
while j < len(b) - 1:
    for k in range(j,-1,-1):
        if b[k][0] + d < b[j][0]:
            break
        i = k
    for k in range(i,len(b)):
        if b[i][0] + d < b[k][0]:
            break
        j = k

    max_size = max(max_size,(q(b,1,i,j,max) - q(b,1,i,j,min)) * (q(b,2,i,j,max) - q(b,2,i,j,min)))
    j+=1
    
print(max_size)

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import math
class SegmentTree:
    def __init__(self, dat, func, sentinel):
        self.pad = 2 ** math.ceil(math.log(len(dat),2)) - 1
        self.dat = [None] * self.pad + dat + [sentinel] * (self.pad + 1 - len(dat))
        self.func = func
        self.sentinel = sentinel
        for i in range(self.pad - 1, -1, -1):
            self.dat[i] = self.func(self.dat[i * 2 + 1],self.dat[i * 2 + 2])
        
    def q(self,s,e):
        return self._q(self.pad + s,self.pad + e,0,self.pad,len(self.dat) - 1)
    def _q(self,a,b,k,l,r):
        if b < l or r < a:
            return self.sentinel
        elif a <= l and r <= b:
            return self.dat[k]
        else:
            vl = self._q(a,b,k * 2 + 1,l,(l+r)//2)
            vr = self._q(a,b,k * 2 + 2,(l+r)//2 + 1,r)
            return self.func(vl,vr)
import sys
f = sys.stdin


_, d = map(int, f.readline().split())

#内包表記にしないと速度不足
b = sorted([list(map(int, line.split()))[::-1] for line in f])
x = [bi[2] for bi in b]
y = [bi[1] for bi in b]


        
minx = SegmentTree(x,min,sentinel = 2000001)
maxx = SegmentTree(x,max,sentinel = -1)
miny = SegmentTree(y,min,sentinel = 2000001)
maxy = SegmentTree(y,max,sentinel = -1)

max_size = i = j = 0
while j < len(b) - 1:
    for k in range(j,-1,-1):
        if b[k][0] + d < b[j][0]:
            break
        i = k
    for k in range(i,len(b)):
        if b[i][0] + d < b[k][0]:
            break
        j = k
    
    max_size = max(max_size,(maxx.q(i,j) - minx.q(i,j)) * (maxy.q(i,j) - miny.q(i,j)))
    j+=1
    
print(max_size)

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
from math import ceil
class sqrt_tree:
    def __init__(self,dat,f):
        self.dat = dat
        self.sq = int(len(dat) ** 0.5)
        self.baqet = {}
        for fi in f:
            self.baqet[fi] = [fi(dat[i * self.sq:(i + 1) * self.sq]) for i in range(self.sq)]
    
    #query
    def q(self,f,l,r):
        r += 1
        if ceil(l / self.sq) >= r // self.sq:
            return f(self.dat[l:r])
        ret = f(self.baqet[f][ceil(l / self.sq):r // self.sq])
        if l % self.sq:
            ret = f(ret,f(self.dat[l:l + self.sq]))
        if r % self.sq:
            ret = f(ret,f(self.dat[r - r % self.sq:r]))
        return ret

import sys
f = sys.stdin

_, d = map(int, f.readline().split())

b = sorted([tuple(map(int,line.split()))[::-1] for line in f])

x = sqrt_tree([bi[2] for bi in b],[min,max])
y = sqrt_tree([bi[1] for bi in b],[min,max])

max_size = i = j = 0
while j < len(b) - 1:
    for k in range(j,-1,-1):
        if b[k][0] + d < b[j][0]:
            break
        i = k
    for k in range(i,len(b)):
        if b[i][0] + d < b[k][0]:
            break
        j = k

    max_size = max(max_size,(x.q(max,i,j) - x.q(min,i,j)) * (y.q(max,i,j) - y.q(min,i,j)))
    j+=1
    
print(max_size)

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Runtime Error):
from math import ceil
class sqrt_tree:
    def __init__(self,dat,f):
        self.dat = dat
        self.sq = int(len(dat) ** 0.5)
        self.f = f
        self.baqet = [self.f(dat[i * self.sq:(i + 1) * self.sq]) for i in range(self.sq)]
    
    #query
    def q(self,l,r):
        r += 1
        if ceil(l / self.sq) >= r // self.sq:
            return self.f(self.dat[l:r])
        ret = self.f(self.baqet[ceil(l / self.sq):r // self.sq])
        if l % self.sq:
            ret = self.f(ret,self.f(self.dat[l:l + self.sq]))
        if r % self.sq:
            ret = self.f(ret,self.f(self.dat[r - r % self.sq:r]))
        return ret

import sys
f = sys.stdin

_, d = map(int, f.readline().split())

x,y = {},{}
for line in f:
    xi, yi, bi = map(int, line.split())
    if bi not in x:
        x[bi],y[bi] = [],[]
    x[bi].append(xi)
    y[bi].append(yi)

b = sorted(x.keys())

xmax = sqrt_tree([max(x[bi]) for bi in b],max)
xmin = sqrt_tree([min(x[bi]) for bi in b],min)
ymax = sqrt_tree([max(y[bi]) for bi in b],max)
ymin = sqrt_tree([min(y[bi]) for bi in b],min)

def get_lr(b,d):
    l = r = 0
    while r < len(b) - 1:
        for k in range(r,-1,-1):
            if b[k] + d < b[r]:
                break
            l = k
        for k in range(l,len(b)):
            if b[l] + d < b[k]:
                break
            r = k
        yield l,r
        r += 1
   
max_size = max((xmax.q(l,r) - xmin.q(l,r)) * (ymax.q(l,r) - ymin.q(l,r)) for l,r in get_lr(b,d))
print(max_size)

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Runtime Error):
from math import ceil
class sqrt_tree:
    def __init__(self,dat,f):
        self.dat = dat
        self.sq = int(len(dat) ** 0.5)
        self.f = f
        self.baqet = [self.f(dat[i * self.sq:(i + 1) * self.sq]) for i in range(self.sq)]
    
    #query
    def q(self,l,r):
        r += 1
        if ceil(l / self.sq) >= r // self.sq:
            return self.f(self.dat[l:r])
        ret = self.f(self.baqet[ceil(l / self.sq):r // self.sq])
        if l % self.sq:
            ret = self.f(ret,self.f(self.dat[l:l + self.sq]))
        if r % self.sq:
            ret = self.f(ret,self.f(self.dat[r - r % self.sq:r]))
        return ret

import sys
f = sys.stdin

_, d = map(int, f.readline().split())

x,y = {},{}
for line in f:
    xi, yi, bi = map(int, line.split())
    if bi not in x:
        x[bi],y[bi] = [],[]
    x[bi].append(xi)
    y[bi].append(yi)

b = sorted(x.keys())

xmax = sqrt_tree([max(x[bi]) for bi in b],max)
xmin = sqrt_tree([min(x[bi]) for bi in b],min)
ymax = sqrt_tree([max(y[bi]) for bi in b],max)
ymin = sqrt_tree([min(y[bi]) for bi in b],min)

def get_lr(b,d):
    l = r = 0
    while r < len(b) - 1:
        while b[l] + d < b[r]:
            l += 1
        for k in range(l,len(b)):
            if b[l] + d < b[k]:
                break
            r = k
        yield l,r
        r += 1
        l += 1
   
max_size = max((xmax.q(l,r) - xmin.q(l,r)) * (ymax.q(l,r) - ymin.q(l,r)) for l,r in get_lr(b,d))
print(max_size)

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import math
class sqrt_tree:
    def __init__(self,dat,f):
        self.dat = dat
        self.sq = int(len(dat) ** 0.5)
        self.f = f
        self.baqet = [self.f(dat[i * self.sq:(i + 1) * self.sq]) for i in range(len(dat) // self.sq)]
    
    #query
    def q(self,l,r):
        r += 1
        if math.ceil(l / self.sq) >= r // self.sq:
            return self.f(self.dat[l:r])
        ret = []
        if math.ceil(l / self.sq) < len(self.baqet):
            ret.append(self.f(self.baqet[math.ceil(l / self.sq):r // self.sq]))
        if l % self.sq:
            ret.append(self.f(self.dat[l:l + self.sq]))
        if r % self.sq:
            ret.append(self.f(self.dat[r - r % self.sq:r]))
        return self.f(ret)

import sys
f = sys.stdin

_, d = map(int, f.readline().split())

x,y = {},{}
for line in f:
    xi, yi, bi = map(int, line.split())
    if bi not in x:
        x[bi],y[bi] = [],[]
    x[bi].append(xi)
    y[bi].append(yi)

b = sorted(x.keys())

xmax = sqrt_tree([max(x[bi]) for bi in b],max)
xmin = sqrt_tree([min(x[bi]) for bi in b],min)
ymax = sqrt_tree([max(y[bi]) for bi in b],max)
ymin = sqrt_tree([min(y[bi]) for bi in b],min)

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for k in range(r,len(b)):
            if b[l] + d < b[k]:
                break
            r = k
        yield l,r
        r += 1
        l += 1
    
max_size = max((xmax.q(l,r) - xmin.q(l,r)) * (ymax.q(l,r) - ymin.q(l,r)) for l,r in get_lr(b,d))
print(max_size)

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import math
class SegmentTree:
    def __init__(self, dat, f, sentinel):
        self.pad = 2 ** math.ceil(math.log(len(dat),2))
        self.dat = [None] * self.pad + dat + [sentinel] * (self.pad - len(dat))
        self.f = f
        self.sentinel = sentinel
        for i in range(self.pad - 1, 0, -1):
            self.dat[i] = self.f(self.dat[i * 2:i * 2 + 2])
        
    def q(self,l,r):
        return self._q(self.pad + l,self.pad + r,1,self.pad,len(self.dat) - 1)
    def _q(self,a,b,k,l,r):
        if b < l or r < a:
            return self.sentinel
        elif a <= l and r <= b:
            return self.dat[k]
        else:
            vl = self._q(a,b,k * 2,l,(l+r)//2)
            vr = self._q(a,b,k * 2 + 1,(l+r)//2 + 1,r)
            return self.f(vl,vr)
        
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

x,y = {},{}
for line in f:
    xi, yi, bi = map(int, line.split())
    if bi not in x:
        x[bi],y[bi] = [],[]
    x[bi].append(xi)
    y[bi].append(yi)

b = sorted(x.keys())

xmax = SegmentTree([max(x[bi]) for bi in b],max,sentinel = -1)
xmin = SegmentTree([min(x[bi]) for bi in b],min,sentinel = 2000001)
ymax = SegmentTree([max(y[bi]) for bi in b],max,sentinel = -1)
ymin = SegmentTree([min(y[bi]) for bi in b],min,sentinel = 2000001)

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        yield l,r
        l += 1
        r += 1
    
max_size = max((xmax.q(l,r) - xmin.q(l,r)) * (ymax.q(l,r) - ymin.q(l,r)) for l,r in get_lr(b,d))
print(max_size)

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import math
class SegmentTree:
    def __init__(self, dat, f, sentinel):
        self.pad = 2 ** math.ceil(math.log(len(dat),2))
        self.dat = [None] * self.pad + dat + [sentinel] * (self.pad - len(dat))
        self.f = f
        self.sentinel = sentinel
        for i in range(self.pad - 1, 0, -1):
            self.dat[i] = self.f(self.dat[i * 2:i * 2 + 2])
        
    def q(self,l,r):
        return self.f(self.dat[i] for i in self.get_index(l,r))
        
    def get_index(self,l,r):
        l += self.pad 
        r += self.pad + 1
        while l < r:
            if r & 1:
                r -= 1
                yield r
            if l & 1:
                yield l
                l += 1
            l >>= 1
            r >>= 1
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

x,y = {},{}
for line in f:
    xi, yi, bi = map(int, line.split())
    if bi not in x:
        x[bi],y[bi] = [],[]
    x[bi].append(xi)
    y[bi].append(yi)

b = sorted(x.keys())

xmax = SegmentTree([max(x[bi]) for bi in b],max,sentinel = -1)
xmin = SegmentTree([min(x[bi]) for bi in b],min,sentinel = 2000001)
ymax = SegmentTree([max(y[bi]) for bi in b],max,sentinel = -1)
ymin = SegmentTree([min(y[bi]) for bi in b],min,sentinel = 2000001)

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        yield l,r
        l += 1
        r += 1
    
max_size = max((xmax.q(l,r) - xmin.q(l,r)) * (ymax.q(l,r) - ymin.q(l,r)) for l,r in get_lr(b,d))
print(max_size)

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import math
class SegmentTree:
    def __init__(self, dat, f, sentinel):
        self.pad = 2 ** math.ceil(math.log(len(dat),2))
        self.dat = [None] * self.pad + dat + [sentinel] * (self.pad - len(dat))
        self.f = f
        self.sentinel = sentinel
        for i in range(self.pad - 1, 0, -1):
            self.dat[i] = self.f(self.dat[i * 2:i * 2 + 2])
        
    def q(self,l,r):
        return self.f(self.dat[i] for i in self.get_index(l,r))
    #[l,r)
    def get_index(self,l,r):
        l += self.pad 
        r += self.pad
        while l < r:
            if r & 1:
                r -= 1
                yield r
            if l & 1:
                yield l
                l += 1
            l >>= 1
            r >>= 1
    def q2(self,index):
        return self.f(self.dat[i] for i in index)

    def get_index2(self,l,r):
        l += self.pad 
        r += self.pad
        ret = []
        while l < r:
            if r & 1:
                r -= 1
                ret.append(r)
            if l & 1:
                ret.append(l)
                l += 1
            l >>= 1
            r >>= 1
        return ret
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

x,y = {},{}
for line in f:
    xi, yi, bi = map(int, line.split())
    if bi not in x:
        x[bi],y[bi] = [],[]
    x[bi].append(xi)
    y[bi].append(yi)

b = sorted(x.keys())

xmax = SegmentTree([max(x[bi]) for bi in b],max,sentinel = -1)
xmin = SegmentTree([min(x[bi]) for bi in b],min,sentinel = 2000001)
ymax = SegmentTree([max(y[bi]) for bi in b],max,sentinel = -1)
ymin = SegmentTree([min(y[bi]) for bi in b],min,sentinel = 2000001)

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
#max_size = max((xmax.q(l,r) - xmin.q(l,r)) * (ymax.q(l,r) - ymin.q(l,r)) for l,r in get_lr(b,d))
size = []
for l,r in get_lr(b,d):
    index = xmax.get_index2(l,r)
    size.append((xmax.q2(index) - xmin.q2(index)) * (ymax.q2(index) - ymin.q2(index)))
print(max(size))

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import math
class SegmentTree:
    def __init__(self, dat, f, sentinel):
        self.pad = 2 ** math.ceil(math.log(len(dat),2))
        self.dat = [None] * self.pad + dat + [sentinel] * (self.pad - len(dat))
        self.f = f
        self.sentinel = sentinel
        for i in range(self.pad - 1, 0, -1):
            self.dat[i] = self.f(self.dat[i * 2:i * 2 + 2])
        
    def q(self,index):
        return self.f(self.dat[i] for i in index)

    def get_index(self,l,r):
        l += self.pad 
        r += self.pad
        ret = []
        while l < r:
            if r & 1:
                r -= 1
                ret.append(r)
            if l & 1:
                ret.append(l)
                l += 1
            l >>= 1
            r >>= 1
        return ret
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

x,y = {},{}
for line in f:
    xi, yi, bi = map(int, line.split())
    if bi not in x:
#        x[bi],y[bi] = [],[]
#    x[bi].append(xi)
#    y[bi].append(yi)
        x[bi],y[bi] = set(),set()
    x[bi].update([xi])
    y[bi].update([yi])

b = sorted(x.keys())

xmax = SegmentTree([max(x[bi]) for bi in b],max,sentinel = -1)
xmin = SegmentTree([min(x[bi]) for bi in b],min,sentinel = 2000001)
ymax = SegmentTree([max(y[bi]) for bi in b],max,sentinel = -1)
ymin = SegmentTree([min(y[bi]) for bi in b],min,sentinel = 2000001)

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
size = []
for l,r in get_lr(b,d):
    index = xmax.get_index(l,r)
    size.append((xmax.q(index) - xmin.q(index)) * (ymax.q(index) - ymin.q(index)))
print(max(size))

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [None] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2:i * 2 + 2])
        return dat

import sys
f = sys.stdin

_, d = map(int, f.readline().split())

x,y = {},{}
for line in f:
    xi, yi, bi = map(int, line.split())
    if bi not in x:
        x[bi],y[bi] = [],[]
    x[bi].append(xi)
    y[bi].append(yi)

b = sorted(x.keys())

xmax = segmentTree([max(x[bi]) for bi in b],max,sentinel = -1)
xmin = segmentTree([min(x[bi]) for bi in b],min,sentinel = 2000001)
ymax = segmentTree([max(y[bi]) for bi in b],max,sentinel = -1)
ymin = segmentTree([min(y[bi]) for bi in b],min,sentinel = 2000001)

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
size = []
pad = len(xmax) // 2
for l,r in get_lr(b,d):
    # 参照するsegmentのindexを生成　※速度のためインライン展開
    l += pad 
    r += pad
    index = []
    while l < r:
        if r & 1:
            r -= 1
            index.append(r)
        if l & 1:
            index.append(l)
            l += 1
        l >>= 1
        r >>= 1

    size.append((max(xmax[i] for i in index)
                 - min(xmin[i] for i in index))
                * (max(ymax[i] for i in index)
                   - min(ymin[i] for i in index)))
print(max(size))

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [None] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2:i * 2 + 2])
        return dat
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

x,y = {},{}
for line in f:
    xi, yi, bi = map(int, line.split())
    try:#if key not in dict よりtry exceptの方が早い
        x[bi].append(xi)
        y[bi].append(yi)
    except KeyError:
        x[bi],y[bi] = [xi],[yi]

b = sorted(x.keys())

xmax = segmentTree([max(x[bi]) for bi in b],max,sentinel = -1)
xmin = segmentTree([min(x[bi]) for bi in b],min,sentinel = 2000001)
ymax = segmentTree([max(y[bi]) for bi in b],max,sentinel = -1)
ymin = segmentTree([min(y[bi]) for bi in b],min,sentinel = 2000001)

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1

size = []
sa = size.append #万単位で呼び出す場合は若干早くなる
pad = len(xmax) // 2
for l,r in get_lr(b,d):
    # 参照するsegmentのindexを生成　※速度のためインライン展開
    l += pad 
    r += pad
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1

    sa((max(xmax[i] for i in index)
                 - min(xmin[i] for i in index))
                * (max(ymax[i] for i in index)
                   - min(ymin[i] for i in index)))
print(max(size))    

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import math
import array
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = array.array('L',[0] * pad + dat + [sentinel] * (pad - len(dat)))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2:i * 2 + 2])
        return dat

import sys
f = sys.stdin


_, d = map(int, f.readline().split())

x,y = {},{}
for line in f:
    xi, yi, bi = map(int, line.split())
    try:#if key not in dict よりtry exceptの方が早い
        x[bi].append(xi)
        y[bi].append(yi)
    except KeyError:
        x[bi],y[bi] = [xi],[yi]

b = sorted(x.keys())

xmax = segmentTree([max(x[bi]) for bi in b],max,sentinel = 0)
xmin = segmentTree([min(x[bi]) for bi in b],min,sentinel = 2000000)
ymax = segmentTree([max(y[bi]) for bi in b],max,sentinel = 0)
ymin = segmentTree([min(y[bi]) for bi in b],min,sentinel = 2000000)

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
size = []
sa = size.append #万単位で呼び出す場合は若干早くなる
pad = len(xmax) // 2
for l,r in get_lr(b,d):
    # 参照するsegmentのindexを生成　※速度のためインライン展開
    l += pad 
    r += pad
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1

    sa((max(xmax[i] for i in index)
                 - min(xmin[i] for i in index))
                * (max(ymax[i] for i in index)
                   - min(ymin[i] for i in index)))
print(max(size))

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2:i * 2 + 2])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


size = []
sa = size.append #万単位で呼び出す場合は若干早くなる
pad = len(xmax) // 2
for l,r in get_lr(b,d):
    # 参照するsegmentのindexを生成　※速度のためインライン展開
    l += pad 
    r += pad
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1

    sa((max(xmax[i] for i in index)
                 - min(xmin[i] for i in index))
                * (max(ymax[i] for i in index)
                   - min(ymin[i] for i in index)))
print(max(size))

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)

Buggy python submission (verdict: Time Limit Exceeded):
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2:i * 2 + 2])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


size = []
sa = size.append #万単位で呼び出す場合は若干早くなる
pad = len(xmax) // 2
max_size = 0
m = pad
pre_xmax,pre_xmin,pre_ymax,pre_ymin=0,0,0,0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(m,r)

    now_xmax = max(xmax[i] for i in index)
    now_xmin = min(xmin[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    now_ymin = min(ymin[i] for i in index)
    
    if pre_xmax < now_xmax or pre_xmin > now_xmin or pre_ymax < now_ymax or pre_ymin > now_ymin:
        if l < m:
            index = create_index(l,m)
            now_xmax = max(now_xmax,max(xmax[i] for i in index))
            now_xmin = min(now_xmin,min(xmin[i] for i in index))
            now_ymax = max(now_ymax,max(ymax[i] for i in index))
            now_ymin = min(now_ymin,min(ymin[i] for i in index))

        sa((now_xmax - now_xmin) * (now_ymax - now_ymin))
    pre_xmax,pre_xmin,pre_ymax,pre_ymin=now_xmax,now_xmin,now_ymax,now_ymin
    m = r
print(max(size))

Fixed submission:
import math
def segmentTree(dat, f, sentinel):
        pad = 2 ** math.ceil(math.log(len(dat),2))
        dat = [0] * pad + dat + [sentinel] * (pad - len(dat))
        for i in range(pad - 1, 0, -1):
            dat[i] = f(dat[i * 2],dat[i * 2 + 1])
        return dat

def get_lr(b,d):
    l = r = 0
    while r < len(b):
        while b[l] + d < b[r]:
            l += 1
        for r in range(r,len(b)):
            if b[l] + d < b[r]:
                r -= 1
                break
        r += 1
        yield l,r
        l += 1
    
import sys
f = sys.stdin

_, d = map(int, f.readline().split())

xyb = []
for line in f:
    xyb.append(tuple(map(int, line.split())))
from operator import itemgetter
xyb.sort(key=itemgetter(2))

x = [xybi[0] for xybi in xyb]
y = [xybi[1] for xybi in xyb]
b = [xybi[2] for xybi in xyb]

xmax = segmentTree(x,max,sentinel = 0)
xmin = segmentTree(x,min,sentinel = 2000000)
ymax = segmentTree(y,max,sentinel = 0)
ymin = segmentTree(y,min,sentinel = 2000000)


pad = len(xmax) // 2
max_size = 0
def create_index(l,r):
    index = []
    ia = index.append
    while l < r:
        if r & 1:
            r -= 1
            ia(r)
        if l & 1:
            ia(l)
            l += 1
        l >>= 1
        r >>= 1
    return index

for l,r in get_lr(b,d):
    l += pad 
    r += pad
    index = create_index(l,r)

    now_xmax = max(xmax[i] for i in index)
    now_ymax = max(ymax[i] for i in index)
    if max_size < now_xmax * now_ymax:
        max_size = max(max_size,((now_xmax - min(xmin[i] for i in index)) * (now_ymax - min(ymin[i] for i in index))))
print(max_size)