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: Accepted)

import heapq
from collections import deque

def bfs(i, c):
    color[i] = c
    cnt[c] += 1
    q = deque()
    q.append(i)
    while q:
        j = q.popleft()
        for k in G[j]:
            if color[k] == -1:
                color[k] = c
                cnt[c] += 1
                q.append(k)
    return

n = int(input())
xy = [0] * n
for i in range(n):
    x, y = map(int, input().split())
    xy[x - 1] = [y, i]
cnt = [0] * n
h = [[n + 1, n + 1]]
G = []
for _ in range(n):
    G.append([])
for i in range(n):
    c = 0
    while h[0][0] < xy[i][0]:
        p = heapq.heappop(h)
        if c == 0:
            minv = p
        c = 1
        G[p[1]].append(xy[i][1])
        G[xy[i][1]].append(p[1])
    if c:
        heapq.heappush(h, minv)
    else:
        heapq.heappush(h, [xy[i][0], xy[i][1]])
color = [-1] * n
c = 0
for i in range(n):
    if color[i] == -1:
        bfs(i, c)
        c += 1
for i in range(n):
    ans = cnt[color[i]]
    print(ans)