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 Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"

	rbt "github.com/emirpasic/gods/trees/redblacktree"
)

type Point struct {
	x, y, idx int
}

func main() {
	defer writer.Flush()
	N := ReadInt()
	points := make([]*Point, N)
	for i := 0; i < N; i++ {
		points[i] = &Point{
			idx: i,
			x:   ReadInt(),
			y:   ReadInt(),
		}
	}

	uf := MakeUnionFind(N)

	sort.Slice(points, func(i, j int) bool {
		return points[i].x < points[j].x
	})
	t := rbt.NewWithIntComparator()
	for _, point := range points {
		node, _ := t.Floor(point.y)
		for node != nil {
			uf.Unite(point.idx, node.Value.(*Point).idx)
			node = node.Left
		}
		t.Put(point.y, point)
	}

	sort.Slice(points, func(i, j int) bool {
		return points[i].x > points[j].x
	})
	t = rbt.NewWithIntComparator()
	for _, point := range points {
		node, _ := t.Ceiling(point.y)
		for node != nil {
			uf.Unite(point.idx, node.Value.(*Point).idx)
			node = node.Right
		}
		t.Put(point.y, point)
	}

	for i := 0; i < N; i++ {
		Println(uf.Size(i))
	}
}

type UnionFind []int

func MakeUnionFind(size int) UnionFind {
	uf := make([]int, size)
	for i := 0; i < size; i++ {
		uf[i] = -1
	}
	return uf
}
func (uf UnionFind) Root(x int) int {
	if uf[x] < 0 {
		return x
	}
	uf[x] = uf.Root(uf[x])
	return uf[x]
}
func (uf UnionFind) Unite(x, y int) {
	x, y = uf.Root(x), uf.Root(y)
	if x == y {
		return
	}
	if uf[x] > uf[y] {
		x, y = y, x
	}
	uf[x] += uf[y]
	uf[y] = x
}
func (uf UnionFind) Connected(x, y int) bool { return uf.Root(x) == uf.Root(y) }
func (uf UnionFind) Size(x int) int          { return -uf[uf.Root(x)] }

var reader = bufio.NewReader(os.Stdin)

func Scan(a ...interface{}) {
	if _, err := fmt.Fscan(reader, a...); err != nil {
		panic(err)
	}
}
func ReadInt() (i int)       { Scan(&i); return }
func ReadString() (s string) { Scan(&s); return }
func ReadInts(n int) (a []int) {
	for i := 0; i < n; i++ {
		a = append(a, ReadInt())
	}
	return
}

var writer = bufio.NewWriter(os.Stdout)

func Printf(format string, a ...interface{}) { fmt.Fprintf(writer, format, a...) }
func Println(a ...interface{})               { fmt.Fprintln(writer, a...) }