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 Ruby (2.7.1) (judge verdict: Wrong Answer)

n = gets.strip.to_i
town = []
n.times do
  x, y = gets.strip.split.map(&:to_i)
  town << [x, y]
end

town.each do |t|
  gone = []
  can = []
  gone << t
  now = t

  loop do
    town.each do |tt|
      next if tt == now
      can << tt if !gone.include?(tt) && ((tt[0] < now[0] && tt[1] < now[1]) || (tt[0] > now[0] && tt[1] > now[1]))
    end

    break if can.length == 0

    now = can.shift
    gone << now
  end
  puts gone.length
end