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)

# Disjoint Set Union
class DSU
  def initialize(n = 0)
    # root node: -1 * component size
    # otherwise: parent
    @parent_or_size = Array.new(n) { -1 }
  end

  def merge(a, b)
    x = leader(a)
    y = 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
    x
  end

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

  def leader(a)
    @parent_or_size[a] < 0 ? a : (@parent_or_size[a] = leader(@parent_or_size[a]))
  end

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

  def groups_with_leader
    h = Hash.new { |hash, key| hash[key] = [] }
    @parent_or_size.each_with_index do |parent_or_size, i|
      leader = parent_or_size < 0 ? i : parent_or_size
      h[leader] << i
    end
    h
  end

  def groups
    groups_with_leader.values
  end

  alias root leader
  alias find leader
  alias unite merge
  alias union merge
  alias same? same
end

UnionFind        = DSU
UnionFindTree    = DSU
DisjointSetUnion = DSU

n   = gets.to_s.to_i
xys = Array.new(n) { |i| gets.to_s.split.map{ |e| e.to_i } << i }.sort_by{ |(x, _, _)| x }

d = DSU.new(n)

n.times do |i|
  i.times do |j|
    if xys[i][1] > xys[j][1]
      d.merge(xys[i][2], xys[j][2])
    end
  end
end

ans = Array.new(n)
d.groups.each do |group|
  s = group.size
  group.each { |e| ans[e] = s }
end

puts ans