Buggy python submission (verdict: Time Limit Exceeded):
import sys,os,io
input = sys.stdin.readline
#input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split())) for _ in range(N)]
y_to_i = [0]*(N+1)
for i,(x,y) in enumerate(A):
  y_to_i[y] = i
A.sort()
ans = [0]*N
from bisect import *
lis = []
cum_max = N

for x,y in A:
  insort(lis,y)
  lis_max,lis_min = lis[-1],lis[0]
  if lis_max==cum_max and len(lis)==lis_max-lis_min+1:
    for y1 in lis:
      ans[y_to_i[y1]] = len(lis)
    cum_max = lis_min-1
    lis = []
print(*ans, sep='\n')


Fixed submission:
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n
    self.min_y = [N]*n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.min_y[x] = min(self.min_y[x],self.min_y[y])
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
uf.min_y = [y for x,y,i in A]
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from heapq import *
heap = []
for u,y in Y:
  atode = []
  for _ in range(len(heap)):
    y1,v = heappop(heap)
    if y<y1:
      heappush(heap,(y1,v))
      break
    uf.union(u,v)
    if uf.parents[v]<0:
      atode.append((uf.min_y[v],v))
  if uf.parents[u]<0:
    heappush(heap,(uf.min_y[u],u))
  for y1,v in atode:
    heappush(heap,(y1,v))
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = [list(map(int, input().split())) for _ in range(N)]
y_to_i = [0]*(N+1)
for i,(x,y) in enumerate(A):
  y_to_i[y] = i
A.sort()
ans = [0]*N
from bisect import *
lis = []
cum_max = N

for x,y in A:
  insort(lis,y)
  lis_max,lis_min = lis[-1],lis[0]
  if lis_max==cum_max and len(lis)==lis_max-lis_min+1:
    for y1 in lis:
      ans[y_to_i[y1]] = len(lis)
    cum_max = lis_min-1
    lis = []
print(*ans, sep='\n')


Fixed submission:
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n
    self.min_y = [N]*n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.min_y[x] = min(self.min_y[x],self.min_y[y])
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
uf.min_y = [y for x,y,i in A]
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from heapq import *
heap = []
for u,y in Y:
  atode = []
  for _ in range(len(heap)):
    y1,v = heappop(heap)
    if y<y1:
      heappush(heap,(y1,v))
      break
    uf.union(u,v)
    if uf.parents[v]<0:
      atode.append((uf.min_y[v],v))
  if uf.parents[u]<0:
    heappush(heap,(uf.min_y[u],u))
  for y1,v in atode:
    heappush(heap,(y1,v))
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
A.sort()
ans = [0]*N
from bisect import *
lis = []
cum_max = N
for x,y,i in A:
  insort(lis,(y,i))
  if lis[-1][0]==cum_max and len(lis)==lis[-1][0]-lis[0][0]+1:
    for y1,i1 in lis:
      ans[i1] = len(lis)
    cum_max = lis[0][0]-1
    lis = []
print(*ans, sep='\n')


Fixed submission:
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n
    self.min_y = [N]*n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.min_y[x] = min(self.min_y[x],self.min_y[y])
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
uf.min_y = [y for x,y,i in A]
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from heapq import *
heap = []
for u,y in Y:
  atode = []
  for _ in range(len(heap)):
    y1,v = heappop(heap)
    if y<y1:
      heappush(heap,(y1,v))
      break
    uf.union(u,v)
    if uf.parents[v]<0:
      atode.append((uf.min_y[v],v))
  if uf.parents[u]<0:
    heappush(heap,(uf.min_y[u],u))
  for y1,v in atode:
    heappush(heap,(y1,v))
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')

Buggy python submission (verdict: Runtime Error):
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from heapq import *
heap = []
for u,y in Y:
  for _ in range(len(heap)):
    y1,v = heappop(heap)
    if y<y1:
      heappush(heap,(y1,v))
      break
    if uf.parents[v]>=0:
      continue
    uf.union(u,v)
    if uf.parents[v]<0:
      deq.append(v)
  if uf.parents[u]<0:
    heappush(heap,(y,u))
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')



Fixed submission:
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n
    self.min_y = [N]*n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.min_y[x] = min(self.min_y[x],self.min_y[y])
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
uf.min_y = [y for x,y,i in A]
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from heapq import *
heap = []
for u,y in Y:
  atode = []
  for _ in range(len(heap)):
    y1,v = heappop(heap)
    if y<y1:
      heappush(heap,(y1,v))
      break
    uf.union(u,v)
    if uf.parents[v]<0:
      atode.append((uf.min_y[v],v))
  if uf.parents[u]<0:
    heappush(heap,(uf.min_y[u],u))
  for y1,v in atode:
    heappush(heap,(y1,v))
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')

Buggy python submission (verdict: Runtime Error):
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n
    self.min_y = [N]*n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.min_y[x] = min(self.min_y[x],self.min_y[y])
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
uf.min_y = [y for x,y,i in A]
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from heapq import *
heap = []
for u,y in Y:
  for _ in range(len(heap)):
    y1,v = heappop(heap)
    if y<y1:
      heappush(heap,(y1,v))
      break
    if uf.parents[v]>=0:
      continue
    uf.union(u,v)
    if uf.parents[v]<0:
      deq.append(v)
  if uf.parents[u]<0:
    heappush(heap,(y,u))
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')



Fixed submission:
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n
    self.min_y = [N]*n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.min_y[x] = min(self.min_y[x],self.min_y[y])
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
uf.min_y = [y for x,y,i in A]
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from heapq import *
heap = []
for u,y in Y:
  atode = []
  for _ in range(len(heap)):
    y1,v = heappop(heap)
    if y<y1:
      heappush(heap,(y1,v))
      break
    uf.union(u,v)
    if uf.parents[v]<0:
      atode.append((uf.min_y[v],v))
  if uf.parents[u]<0:
    heappush(heap,(uf.min_y[u],u))
  for y1,v in atode:
    heappush(heap,(y1,v))
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')

Buggy python submission (verdict: Time Limit Exceeded):
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n
    self.min_y = [N]*n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.min_y[x] = min(self.min_y[x],self.min_y[y])
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
uf.min_y = [y for x,y,i in A]
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from collections import deque
deq = deque([])
for u,y in Y:
  for _ in range(len(deq)):
    v = deq.popleft()
    if uf.parents[v]>=0:
      continue
    if y>uf.min_y[v]:
      uf.union(u,v)
    if uf.parents[v]<0:
      deq.append(v)
  if uf.parents[u]<0:
      deq.append(u)
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')



Fixed submission:
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n
    self.min_y = [N]*n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.min_y[x] = min(self.min_y[x],self.min_y[y])
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
uf.min_y = [y for x,y,i in A]
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from heapq import *
heap = []
for u,y in Y:
  atode = []
  for _ in range(len(heap)):
    y1,v = heappop(heap)
    if y<y1:
      heappush(heap,(y1,v))
      break
    uf.union(u,v)
    if uf.parents[v]<0:
      atode.append((uf.min_y[v],v))
  if uf.parents[u]<0:
    heappush(heap,(uf.min_y[u],u))
  for y1,v in atode:
    heappush(heap,(y1,v))
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')

Buggy python submission (verdict: Time Limit Exceeded):
# Binary Indexed Tree (Fenwick Tree)
class BIT:
  def __init__(self, n):
    self.n = n
    self.bit = [0]*(n+1)
    self.el = [0]*(n+1)
  def sum(self, i):
    s = 0
    while i > 0:
      s += self.bit[i]
      i -= i & -i
    return s
  def add(self, i, x):
    # assert i > 0
    self.el[i] += x
    while i <= self.n:
      self.bit[i] += x
      i += i & -i
  def get(self, i, j=None):
    if j is None:
      return self.el[i]
    return self.sum(j) - self.sum(i-1)
  def lower_bound(self,x):
    w = i = 0
    k = 1<<((self.n).bit_length())
    while k:
      if i+k <= self.n and w + self.bit[i+k] < x:
        w += self.bit[i+k]
        i += k
      k >>= 1
    return i+1

class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split())) for i in range(N)]
y_to_i = [0]*(N+1)
for i,(x,y) in enumerate(A):
  y_to_i[y] = i

ans = [1]*N
A.sort()
bit = BIT(N)
uf = UnionFind(N)
cnt = 0
y_lis = []
import bisect
for j,(x,y) in enumerate(A):
  p = bit.sum(y)
  for i in range(1,p+1):
    if i<p:
      y2 = y_lis[i-1]
    else:
      y2 = bit.lower_bound(i)
    if not uf.same(y_to_i[y],y_to_i[y2]):
      uf.union(y_to_i[y],y_to_i[y2])
      cnt += 1
      if cnt>=j:
        break
  bisect.insort_right(y_lis,y)
  bit.add(y,1)
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')



Fixed submission:
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n
    self.min_y = [N]*n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.min_y[x] = min(self.min_y[x],self.min_y[y])
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
uf.min_y = [y for x,y,i in A]
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from heapq import *
heap = []
for u,y in Y:
  atode = []
  for _ in range(len(heap)):
    y1,v = heappop(heap)
    if y<y1:
      heappush(heap,(y1,v))
      break
    uf.union(u,v)
    if uf.parents[v]<0:
      atode.append((uf.min_y[v],v))
  if uf.parents[u]<0:
    heappush(heap,(uf.min_y[u],u))
  for y1,v in atode:
    heappush(heap,(y1,v))
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')

Buggy python submission (verdict: Runtime Error):
# Binary Indexed Tree (Fenwick Tree)
class BIT:
  def __init__(self, n):
    self.n = n
    self.bit = [0]*(n+1)
    self.el = [0]*(n+1)
  def sum(self, i):
    s = 0
    while i > 0:
      s += self.bit[i]
      i -= i & -i
    return s
  def add(self, i, x):
    # assert i > 0
    self.el[i] += x
    while i <= self.n:
      self.bit[i] += x
      i += i & -i
  def get(self, i, j=None):
    if j is None:
      return self.el[i]
    return self.sum(j) - self.sum(i-1)
  def lower_bound(self,x,p):
    i = p
    w = self.bit[i]
    k = 1<<((self.n).bit_length())
    while k:
      if i+k <= self.n and w + self.bit[i+k] < x:
        w += self.bit[i+k]
        i += k
      k >>= 1
    return i+1

class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split())) for i in range(N)]
y_to_i = [0]*(N+1)
for i,(x,y) in enumerate(A):
  y_to_i[y] = i

ans = [1]*N
A.sort()
bit = BIT(N)
uf = UnionFind(N)
cnt = 0
for j,(x,y) in enumerate(A):
  p = bit.sum(y)
  y2 = 0
  for i in range(1,p+1):
    y2 = bit.lower_bound(i,y2)
    if not uf.same(y_to_i[y],y_to_i[y2]):
      uf.union(y_to_i[y],y_to_i[y2])
      cnt += 1
      if cnt>=j:
        break
  bit.add(y,1)
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')



Fixed submission:
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n
    self.min_y = [N]*n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.min_y[x] = min(self.min_y[x],self.min_y[y])
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
uf.min_y = [y for x,y,i in A]
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from heapq import *
heap = []
for u,y in Y:
  atode = []
  for _ in range(len(heap)):
    y1,v = heappop(heap)
    if y<y1:
      heappush(heap,(y1,v))
      break
    uf.union(u,v)
    if uf.parents[v]<0:
      atode.append((uf.min_y[v],v))
  if uf.parents[u]<0:
    heappush(heap,(uf.min_y[u],u))
  for y1,v in atode:
    heappush(heap,(y1,v))
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')

Buggy python submission (verdict: Runtime Error):
# Binary Indexed Tree (Fenwick Tree)
class BIT:
  def __init__(self, n):
    self.n = n
    self.bit = [0]*(n+1)
    self.el = [0]*(n+1)
  def sum(self, i):
    s = 0
    while i > 0:
      s += self.bit[i]
      i -= i & -i
    return s
  def add(self, i, x):
    # assert i > 0
    self.el[i] += x
    while i <= self.n:
      self.bit[i] += x
      i += i & -i
  def get(self, i, j=None):
    if j is None:
      return self.el[i]
    return self.sum(j) - self.sum(i-1)
  def lower_bound(self,x,p):
    i = p
    w = self.bit[i]
    k = 1<<((self.n-p).bit_length())
    while k:
      if i+k <= self.n and w + self.bit[i+k] < x:
        w += self.bit[i+k]
        i += k
      k >>= 1
    return i+1

class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split())) for i in range(N)]
y_to_i = [0]*(N+1)
for i,(x,y) in enumerate(A):
  y_to_i[y] = i

ans = [1]*N
A.sort()
bit = BIT(N)
uf = UnionFind(N)
cnt = 0
for j,(x,y) in enumerate(A):
  p = bit.sum(y)
  y2 = 0
  for i in range(1,p+1):
    y2 = bit.lower_bound(i,y2)
    if not uf.same(y_to_i[y],y_to_i[y2]):
      uf.union(y_to_i[y],y_to_i[y2])
      cnt += 1
      if cnt>=j:
        break
  bit.add(y,1)
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')



Fixed submission:
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n
    self.min_y = [N]*n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.min_y[x] = min(self.min_y[x],self.min_y[y])
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
uf.min_y = [y for x,y,i in A]
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from heapq import *
heap = []
for u,y in Y:
  atode = []
  for _ in range(len(heap)):
    y1,v = heappop(heap)
    if y<y1:
      heappush(heap,(y1,v))
      break
    uf.union(u,v)
    if uf.parents[v]<0:
      atode.append((uf.min_y[v],v))
  if uf.parents[u]<0:
    heappush(heap,(uf.min_y[u],u))
  for y1,v in atode:
    heappush(heap,(y1,v))
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')

Buggy python submission (verdict: Time Limit Exceeded):
# Binary Indexed Tree (Fenwick Tree)
class BIT:
  def __init__(self, n):
    self.n = n
    self.bit = [0]*(n+1)
    self.el = [0]*(n+1)
  def sum(self, i):
    s = 0
    while i > 0:
      s += self.bit[i]
      i -= i & -i
    return s
  def add(self, i, x):
    # assert i > 0
    self.el[i] += x
    while i <= self.n:
      self.bit[i] += x
      i += i & -i
  def get(self, i, j=None):
    if j is None:
      return self.el[i]
    return self.sum(j) - self.sum(i-1)
  def lower_bound(self,x):
    w = i = 0
    k = 1<<((self.n).bit_length())
    while k:
      if i+k <= self.n and w + self.bit[i+k] < x:
        w += self.bit[i+k]
        i += k
      k >>= 1
    return i+1

class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
# input = sys.stdin.readline
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split())) for i in range(N)]
y_to_i = [0]*(N+1)
for i,(x,y) in enumerate(A):
  y_to_i[y] = i

ans = [1]*N
A.sort()
bit = BIT(N)
uf = UnionFind(N)
cnt = 0
for j,(x,y) in enumerate(A):
  p = bit.sum(y)
  for i in range(1,p+1):
    y2 = bit.lower_bound(i)
    if not uf.same(y_to_i[y],y_to_i[y2]):
      uf.union(y_to_i[y],y_to_i[y2])
      cnt += 1
      if cnt>=j:
        break
  bit.add(y,1)
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')



Fixed submission:
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n
    self.min_y = [N]*n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.min_y[x] = min(self.min_y[x],self.min_y[y])
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
uf.min_y = [y for x,y,i in A]
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from heapq import *
heap = []
for u,y in Y:
  atode = []
  for _ in range(len(heap)):
    y1,v = heappop(heap)
    if y<y1:
      heappush(heap,(y1,v))
      break
    uf.union(u,v)
    if uf.parents[v]<0:
      atode.append((uf.min_y[v],v))
  if uf.parents[u]<0:
    heappush(heap,(uf.min_y[u],u))
  for y1,v in atode:
    heappush(heap,(y1,v))
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')

Buggy python submission (verdict: Runtime Error):
# Binary Indexed Tree (Fenwick Tree)
class BIT:
  def __init__(self, n):
    self.n = n
    self.bit = [0]*(n+1)
    self.el = [0]*(n+1)
  def sum(self, i):
    s = 0
    while i > 0:
      s += self.bit[i]
      i -= i & -i
    return s
  def add(self, i, x):
    # assert i > 0
    self.el[i] += x
    while i <= self.n:
      self.bit[i] += x
      i += i & -i
  def get(self, i, j=None):
    if j is None:
      return self.el[i]
    return self.sum(j) - self.sum(i-1)
  def lower_bound(self,x,p):
    w = 0
    i = p
    k = 1<<((self.n).bit_length())
    while k:
      if i+k <= self.n and w + self.bit[i+k] < x:
        w += self.bit[i+k]
        i += k
      k >>= 1
    return i+1

class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys
input = sys.stdin.readline
N = int(input())
A = [list(map(int, input().split())) for i in range(N)]
y_to_i = [0]*(N+1)
for i,(x,y) in enumerate(A):
  y_to_i[y] = i

ans = [1]*N
A.sort()
bit = BIT(N)
uf = UnionFind(N)
cnt = 0
for j,(x,y) in enumerate(A):
  p = bit.sum(y)
  y2 = 0
  for i in range(1,p+1):
    y2 = bit.lower_bound(1,y2)
    if not uf.same(y_to_i[y],y_to_i[y2]):
      uf.union(y_to_i[y],y_to_i[y2])
      cnt += 1
      if cnt>=j:
        break
  bit.add(y,1)
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')


Fixed submission:
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n
    self.min_y = [N]*n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.min_y[x] = min(self.min_y[x],self.min_y[y])
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
uf.min_y = [y for x,y,i in A]
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from heapq import *
heap = []
for u,y in Y:
  atode = []
  for _ in range(len(heap)):
    y1,v = heappop(heap)
    if y<y1:
      heappush(heap,(y1,v))
      break
    uf.union(u,v)
    if uf.parents[v]<0:
      atode.append((uf.min_y[v],v))
  if uf.parents[u]<0:
    heappush(heap,(uf.min_y[u],u))
  for y1,v in atode:
    heappush(heap,(y1,v))
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')

Buggy python submission (verdict: Time Limit Exceeded):
# Binary Indexed Tree (Fenwick Tree)
class BIT:
  def __init__(self, n):
    self.n = n
    self.bit = [0]*(n+1)
    self.el = [0]*(n+1)
  def sum(self, i):
    s = 0
    while i > 0:
      s += self.bit[i]
      i -= i & -i
    return s
  def add(self, i, x):
    # assert i > 0
    self.el[i] += x
    while i <= self.n:
      self.bit[i] += x
      i += i & -i
  def get(self, i, j=None):
    if j is None:
      return self.el[i]
    return self.sum(j) - self.sum(i-1)
  def lower_bound(self,x):
    w = i = 0
    k = 1<<((self.n).bit_length())
    while k:
      if i+k <= self.n and w + self.bit[i+k] < x:
        w += self.bit[i+k]
        i += k
      k >>= 1
    return i+1

class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys
input = sys.stdin.readline
N = int(input())
A = [list(map(int, input().split())) for i in range(N)]
y_to_i = [0]*(N+1)
for i,(x,y) in enumerate(A):
  y_to_i[y] = i

ans = [1]*N
A.sort()
bit = BIT(N)
uf = UnionFind(N)
cnt = 0
for j,(x,y) in enumerate(A):
  p = bit.sum(y)
  for i in range(1,p+1):
    y2 = bit.lower_bound(i)
    if not uf.same(y_to_i[y],y_to_i[y2]):
      uf.union(y_to_i[y],y_to_i[y2])
      cnt += 1
      if cnt>=j:
        break
  bit.add(y,1)
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')



Fixed submission:
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n
    self.min_y = [N]*n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.min_y[x] = min(self.min_y[x],self.min_y[y])
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
uf.min_y = [y for x,y,i in A]
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from heapq import *
heap = []
for u,y in Y:
  atode = []
  for _ in range(len(heap)):
    y1,v = heappop(heap)
    if y<y1:
      heappush(heap,(y1,v))
      break
    uf.union(u,v)
    if uf.parents[v]<0:
      atode.append((uf.min_y[v],v))
  if uf.parents[u]<0:
    heappush(heap,(uf.min_y[u],u))
  for y1,v in atode:
    heappush(heap,(y1,v))
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')

Buggy python submission (verdict: Time Limit Exceeded):
# Binary Indexed Tree (Fenwick Tree)
class BIT:
  def __init__(self, n):
    self.n = n
    self.bit = [0]*(n+1)
    self.el = [0]*(n+1)
  def sum(self, i):
    s = 0
    while i > 0:
      s += self.bit[i]
      i -= i & -i
    return s
  def add(self, i, x):
    # assert i > 0
    self.el[i] += x
    while i <= self.n:
      self.bit[i] += x
      i += i & -i
  def get(self, i, j=None):
    if j is None:
      return self.el[i]
    return self.sum(j) - self.sum(i-1)
  def lower_bound(self,x):
    w = i = 0
    k = 1<<((self.n).bit_length())
    while k:
      if i+k <= self.n and w + self.bit[i+k] < x:
        w += self.bit[i+k]
        i += k
      k >>= 1
    return i+1

class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

N = int(input())
A = [list(map(int, input().split())) for i in range(N)]
y_to_i = [0]*(N+1)
for i,(x,y) in enumerate(A):
  y_to_i[y] = i

ans = [1]*N
A.sort()
bit = BIT(N)
uf = UnionFind(N)
cnt = 0
for j,(x,y) in enumerate(A):
  p = bit.sum(y)
  for i in range(1,p+1):
    y2 = bit.lower_bound(i)
    if not uf.same(y_to_i[y],y_to_i[y2]):
      uf.union(y_to_i[y],y_to_i[y2])
      cnt += 1
      if cnt>=j:
        break
  bit.add(y,1)
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')


Fixed submission:
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n
    self.min_y = [N]*n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.min_y[x] = min(self.min_y[x],self.min_y[y])
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
uf.min_y = [y for x,y,i in A]
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from heapq import *
heap = []
for u,y in Y:
  atode = []
  for _ in range(len(heap)):
    y1,v = heappop(heap)
    if y<y1:
      heappush(heap,(y1,v))
      break
    uf.union(u,v)
    if uf.parents[v]<0:
      atode.append((uf.min_y[v],v))
  if uf.parents[u]<0:
    heappush(heap,(uf.min_y[u],u))
  for y1,v in atode:
    heappush(heap,(y1,v))
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')

Buggy python submission (verdict: Time Limit Exceeded):
# Binary Indexed Tree (Fenwick Tree)
class BIT:
  def __init__(self, n):
    self.n = n
    self.bit = [0]*(n+1)
    self.el = [0]*(n+1)
  def sum(self, i):
    s = 0
    while i > 0:
      s += self.bit[i]
      i -= i & -i
    return s
  def add(self, i, x):
    # assert i > 0
    self.el[i] += x
    while i <= self.n:
      self.bit[i] += x
      i += i & -i
  def get(self, i, j=None):
    if j is None:
      return self.el[i]
    return self.sum(j) - self.sum(i-1)
  def lower_bound(self,x):
    w = i = 0
    k = 1<<((self.n).bit_length())
    while k:
      if i+k <= self.n and w + self.bit[i+k] < x:
        w += self.bit[i+k]
        i += k
      k >>= 1
    return i+1

class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

N = int(input())
A = [list(map(int, input().split())) for i in range(N)]
y_to_i = [0]*(N+1)
for i,(x,y) in enumerate(A):
  y_to_i[y] = i

ans = [1]*N
A.sort()
bit = BIT(N)
uf = UnionFind(N)
for x,y in A:
  p = bit.sum(y)
  for i in range(1,p+1):
    y2 = bit.lower_bound(i)
    uf.union(y_to_i[y],y_to_i[y2])
  bit.add(y,1)
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')


Fixed submission:
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n
    self.min_y = [N]*n

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

  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.min_y[x] = min(self.min_y[x],self.min_y[y])
    self.parents[y] = x

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

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

  def num_roots(self):
    return len([i for i, x in enumerate(self.parents) if x < 0])

  def members(self, x):
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys,os,io
input = sys.stdin.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
N = int(input())
A = [list(map(int, input().split()))+[i] for i in range(N)]
uf = UnionFind(N)
uf.min_y = [y for x,y,i in A]
ans = [1]*N
A.sort()
Y = [(i,y) for x,y,i in A]
from heapq import *
heap = []
for u,y in Y:
  atode = []
  for _ in range(len(heap)):
    y1,v = heappop(heap)
    if y<y1:
      heappush(heap,(y1,v))
      break
    uf.union(u,v)
    if uf.parents[v]<0:
      atode.append((uf.min_y[v],v))
  if uf.parents[u]<0:
    heappush(heap,(uf.min_y[u],u))
  for y1,v in atode:
    heappush(heap,(y1,v))
for i in range(N):
  ans[i] = uf.num_members(i)
print(*ans, sep='\n')