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)

END { load __FILE__ unless $stdin.eof? }

class DSU
  def initialize(n = 0)
    @n = n
    @parent_or_size = Array.new(n, -1)
  end

  def merge(a, b)
    x, y = leader(a), leader(b)
    return x if x == y

    x, y = y, x if -@parent_or_size[x] < -@parent_or_size[y]
    @parent_or_size[x] += @parent_or_size[y]
    @parent_or_size[y] = x
  end

  def same(a, b)
    leader(a) == leader(b)
  end

  def leader(a)
    return a if @parent_or_size[a] < 0

    @parent_or_size[a] = leader(@parent_or_size[a])
  end

  def size(a)
    -@parent_or_size[leader(a)]
  end

  def groups
    @n.times.group_by { |i| leader(i) }.values
  end
end

n = gets.to_i
towns = Array.new(n) { |i| gets.split.map!(&:to_i) << i }.sort!

graph = DSU.new(n)
while (tx, ty, tid = towns.shift)
  tymax = n
  loop do
    town = towns.find { |x, y| y > ty && y <= tymax }
    break unless town
    graph.merge(tid, town[2])
    tymax = town[1] - 1
  end
end

leaders = n.times.map(&graph.method(:leader))
histogram = leaders.tally

n.times { |i| puts histogram[leaders[i]] }