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)

class UnionFind
  def initialize(n)
    @size = Array.new(n, 1)
    @rank = Array.new(n, 0)
    @parent = []

    (0..n).each do |i|
      @parent[i] = i
    end
  end

  def find(x)
    if @parent[x] == x
      x
    else
      @parent[x] = find(@parent[x])
    end
  end

  def unite(x, y)
    x = find(x)
    y = find(y)
    return if x == y

    if @rank[x] < @rank[y]
      @parent[x] = y
      @size[y] += @size[x]
    else
      @parent[y] = x
      @size[x] += @size[y]

      @rank[x] += 1 if @rank[x] == @rank[y]
    end
  end

  def same?(x, y)
    find(x) == find(y)
  end

  def size(x)
    @size[find(x)]
  end
end

N = gets.to_i
P = N.times.map { |i| [i] + gets.split.map(&:to_i) }
P.sort_by! { |id, x, y| x }

uf = UnionFind.new(N + 1)
ans = Array.new(N, 1)
stack = [[-1, -Float::INFINITY]]

P.each do |id, x, y|
  # p [:id, id, :y, y, :x, x, :cnt, cnt]

  while stack.last.last > y
    stack.pop
  end

  uid = stack.last.first

  if uid != -1
    uf.unite(id, uid)
  end

  stack.push([id, y])
end

stack = [[-1, Float::INFINITY]]

P.reverse_each do |id, x, y|
  while stack.last.last < y
    stack.pop
  end

  uid = stack.last.first

  if uid != -1
    uf.unite(id, uid)
  end

  stack.push([id, y])
end

puts (0...N).map { |x| uf.size(x) }