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: Time Limit Exceeded)

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

checked = []
checked_gone = []
town.each_with_index do |t, i|
  now = t
  gone = [t]
  can = []
  town_clone = town.clone

  loop do
    town_clone = town_clone - can - gone
    town_clone.each do |xx, yy|
      can << [xx, yy] if (xx < now[0] && yy < now[1]) || (xx > now[0] && yy > now[1])
    end
    can.sort!

    gone << now
    gone.uniq!

    break if can.length == 0

    index = checked.index(now)
    if index
      gone += checked_gone[index]
      can -= checked_gone[index]
    end
    gone.uniq!

    break if can.length == 0
    now = can.shift
  end
  checked[i] = t
  checked_gone[i] = gone
  (gone - checked).each do |g|
    ti = town.index(g)
    if ti
      checked[ti] = town[ti]
      checked_gone[ti] = gone
    end
  end
  puts gone.length
end