Problem:
Score : 300 points

Problem Statement

There are N cities on a 2D plane. The coordinate of the i-th city is (x_i, y_i). Here (x_1, x_2, \dots, x_N) and (y_1, y_2, \dots, y_N) are both permuations of (1, 2, \dots, N).

For each k = 1,2,\dots,N, find the answer to the following question:

Rng is in City k.
Rng can perform the following move arbitrarily many times:

move to another city that has a smaller x-coordinate and a smaller y-coordinate, or a larger x-coordinate and a larger y-coordinate, than the city he is currently in.

How many cities (including City k) are reachable from City k?

Constraints

1 \leq N \leq 200,000

(x_1, x_2, \dots, x_N) is a permutation of (1, 2, \dots, N).

(y_1, y_2, \dots, y_N) is a permutation of (1, 2, \dots, N).

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print N lines. In i-th line print the answer to the question when k = i.

Sample Input 1

4
1 4
2 3
3 1
4 2

Sample Output 1

1
1
2
2

Rng can reach City 4 from City 3, or conversely City 3 from City 4.

Sample Input 2

7
6 4
4 3
3 5
7 1
2 7
5 2
1 6

Sample Output 2

3
3
1
1
2
3
2

Solution in PyPy3 (7.3.0) (judge verdict: Wrong Answer)

from bisect import bisect_left
from collections import Counter
N = int(input())
XYs = []
XYs2 = []
for i in range(N):
    x, y = map(int, input().split())
    XYs.append([x, y, i])
    XYs2.append([N-x, N-y, i])
XYs.sort()
XYs2.sort()

# Union-Find
parent = [i for i in range(N)]
rank = [1] * N
def get_root(node):
  global parent
  if parent[node] == node:
    return node
  root = get_root(parent[node])
  parent[node] = root
  return root

def union(a, b):
  global parent
  global rank
  root_a = get_root(a)
  rank_a = rank[root_a]
  root_b = get_root(b)
  rank_b = rank[root_b]
  if root_a == root_b:
    return
  if rank_a < rank_b:
    parent[root_a] = root_b
  else:
    parent[root_b] = root_a
    if rank_a == rank_b:
      rank[root_a] += 1

INF = float('inf')
LIS = [[INF, 0] for _ in range(N)]
for x, y, k in XYs:
    idx = bisect_left(LIS, [y, k])
    LIS[idx] = [y, k]
    if idx > 0:
        union(LIS[idx-1][1], k)

LIS = [[INF, 0] for _ in range(N)]
for x, y, k in XYs2:
    idx = bisect_left(LIS, [y, k])
    LIS[idx] = [y, k]
    if idx > 0:
        union(LIS[idx-1][1], k)

for i in range(N):
    get_root(i)

ct = Counter(parent)
for i in range(N):
    print(ct[parent[i]])