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)

def a(input)
  x = {}
  y = {}
  x_list = input.map{|v| v[0]}
  y_list = input.map{|v| v[1]}

  x_max = x_list.max
  y_max = y_list.max

  1.upto(x_max) do |v|
    x[v] = []
  end
  1.upto(y_max) do |v|
    y[v] = []
  end

  input.each.with_index(1) do |v, idx|
    x[v[0]] << idx
    y[v[1]] << idx
  end
  res = []
  input.each.with_index(1) do |v, idx|
    val = 1
    target_x = 1.upto(v[0] - 1).map do |t|
      x[t]
    end.flatten
    target_y = 1.upto(v[1] - 1).map do |t|
      y[t]
    end.flatten

    val += (target_x & target_y).size
    target_x = (v[0] +1).upto(x_max).map do |t|
      x[t]
    end.flatten
    target_y = (v[1] +1).upto(y_max).map do |t|
      y[t]
    end.flatten

    val += (target_x & target_y).size

    res << val
  end
  res
end

line = $stdin.gets
values = Array.new
while line = $stdin.gets
  values << line.chomp.split(' ').map(&:to_i)
end

puts a(values)