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 Kotlin (1.3.71) (judge verdict: Accepted)

import java.io.BufferedReader
import java.io.InputStreamReader
import java.util.*

fun main() {
    val jin = BufferedReader(InputStreamReader(System.`in`))
    val n = jin.readLine().toInt()
    val xs = IntArray(n + 1)
    val ys = IntArray(n + 1)
    for (j in 1..n) {
        val (x, y) = jin.readLine().split(" ").map { it.toInt() }
        xs[j] = x
        ys[j] = y
    }
    val zs = (1..n).sortedBy { xs[it] }
    val union = IntArray(n + 1) { it }
    val uStack = Stack<Int>()
    fun getUnion(u: Int): Int {
        uStack.push(u)
        while (union[uStack.peek()] != union[union[uStack.peek()]]) {
            uStack.push(union[uStack.peek()])
        }
        val v = union[uStack.pop()]
        while (uStack.isNotEmpty()) {
            union[uStack.pop()] = v
        }
        return v
    }
    val stack = Stack<Int>()
    for (z in zs) {
        val m = if (stack.isEmpty() || ys[z] < ys[stack.peek()]) z else stack.peek()
        while (stack.isNotEmpty() && ys[z] > ys[stack.peek()]) {
            union[getUnion(stack.pop())] = getUnion(z)
        }
        stack.push(m)
    }
    val amts = IntArray(n + 1)
    for (j in 1..n) {
        amts[getUnion(j)]++
    }
    val joiner = StringJoiner("\n")
    for (j in 1..n) {
        joiner.add(amts[getUnion(j)].toString())
    }
    println(joiner)
}