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: Time Limit Exceeded)

from bisect import bisect_left
from collections import Counter
import sys

input = sys.stdin.readline

N = int(input().rstrip())
# 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

def main():
    XYs = []
    XYs2 = []
    for i in range(N):
        x, y = map(int, input().rstrip().split())
        XYs.append([x, y, i])
        XYs2.append([N-x, N-y, i])
    XYs.sort()
    XYs2.sort()
    
    BL = (200001).bit_length()
    WIDTH = pow(2, BL)
    BUFSIZE = pow(2, BL+1) - 1
    BASE = BUFSIZE - WIDTH
     
    def update(buf, i, x):
        buf[BASE + i] = x
        i += BASE
        i = (i-1) // 2
        while i >= 0:
            buf[i] = compare(buf[2*i+1], buf[2*i+2])
            i = (i-1) // 2
     
    # [q_left, q_right]
    def search(buf, l, width, i, q_left, q_right):
        if q_right < l or l + width - 1 < q_left:
            return set()
        if q_left <= l and l + width - 1 <= q_right:
            return buf[i]
        nwidth = width // 2
        c1 = search(buf, l, nwidth, 2*i+1, q_left, q_right)
        c2 = search(buf, l+nwidth, nwidth, 2*i+2, q_left, q_right)
        return compare(c1, c2)
     
    def compare(c1, c2):
        if not c1:
            return c2
        if not c2:
            return c1
        return c1 | c2
     
    buf1 = [set() for _ in range(BUFSIZE)]
    prevX = None
    for x, y, k in XYs:
        nodes = search(buf1, 0, WIDTH, 0, 0, y-1)
        if nodes:
            for k2 in nodes:
                union(k, k2)
        else:
            update(buf1, y, set([k]))
        prevX = x
    
    buf1 = [set() for _ in range(BUFSIZE)]
    for x, y, k in XYs2:
        nodes = search(buf1, 0, WIDTH, 0, 0, y-1)
        if nodes:
            for k2 in nodes:
                union(k, k2)
        else:
            update(buf1, y, set([k]))
        prevX = x
     
    for i in range(N):
        get_root(i)
    
    ct = Counter(parent)
    for i in range(N):
        print(ct[parent[i]])

main()