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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.net.ConnectException;
import java.rmi.dgc.Lease;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.NoSuchElementException;
import java.util.Objects;
import java.util.Set;
import java.util.Stack;
import java.util.TreeMap;
import java.util.TreeSet;

import static java.util.Comparator.*;

public class Main {
	public static void main(String[] args) {
		Main main = new Main();
		main.solve();
		main.out.close();
	}
	// ======================================================================
	List<PP> list = new ArrayList<>();
	UnionFind UF;
	int[] ans;
	public void solve() {
		int N = ni();
		UF = new UnionFind(N);
		int x, y;
		for (int i = 0; i < N; i++) {
			x = ni();
			y = ni();
			list.add(new PP(x, y, i));
		}
		list.sort(comparing(PP::getKey));
		for(PP pp1 : list) {
			for(PP pp2 : list) {
				if(pp2.key == pp1.key)	break;
				if(pp2.val < pp1.val) {
					UF.connect(pp1.no, pp2.no);
				}
			}
		}
		for (int i = 0; i < N; i++) {
			out.println(UF.size(i));
		}
	}
	class UnionFind {
		int gcnt;	// グループ数
		int[] par; 	// [子番号] = 親番号(親の場合、メンバ数のマイナス値)
		// [1]=3 [2]=-1 [3]=-2  なら　１　と　３　は　同じグループ
		
		public UnionFind(int n) {
			gcnt = n;
			par = new int[n];
			Arrays.fill(par, -1); // 全部が親で、メンバ数を　１　とする
		}
		
		// 親の番号を返す（この中で親に直接つなぎ変えている）
		int root(int x) {
			if (par[x] < 0)
				return x; // 親の場合はマイナスが入っている
			else
				return par[x] = root(par[x]);
		}
		
		// 同じグループなら true を返す
		boolean same(int x, int y) {
			return root(x) == root(y);
		}
		
		// グループ数を返す
		int groupCnt() {
			return gcnt;
		}
		
		// メンバ数を返す
		int size(int x) {
			return -par[root(x)];
		}
		
		// メンバのリストを返す
		List<Integer> member(int x) {
			List<Integer> ans = new ArrayList<>();
			int root = root(x);
			for (int i = 0; i < par.length; i++) {
				if (root(i) == root) {
					ans.add(i);
				}
			}
			return ans;
		}
		
		// 同じ親につなげる
		void connect(int x, int y) {
			int xP = root(x); 				// 親を取得する
			int yP = root(y); 				// 親を取得する
			if (xP == yP)		return; 	// 同じなので処理しない
			if (size(xP) > size(yP)) { 		// メンバ数が多い方にくっつける
				par[xP] += par[yP]; 		//   メンバ数を更新する
				par[yP] = xP; 				//   親番号を設定する
			} else {
				par[yP] += par[xP];
				par[xP] = yP;
			}
			gcnt--;
		}
		
		void dump(PrintWriter out) {
			for (int i = 0; i < par.length; i++) {
				out.println("par[" + i + "] = " + par[i]);
			}
			out.println("");
		}
	}
		
	class PP {
		public int key, val, no;
		public PP(int key, int val, int no) {
			this.key = key;
			this.val = val;
			this.no = no;
		}
		public int getKey() {			return key;		}
		public void setKey(int key) {	this.key = key;	}
		public int getVal() {			return val;		}
		public void setVal(int val) {	this.val = val;	}
	}

	// ------------------------------------------
	// ライブラリ
	// ------------------------------------------
	// Print
	private PrintWriter out = new PrintWriter(System.out);
	
	// Scanner
	private FastScanner scan = new FastScanner();
	int ni(){ return scan.nextInt();}
	int[] ni(int n){int[] a = new int[n]; for(int i = 0; i < n; i++){a[i] = ni();} return a;}
	int[][] ni(int y, int x){int[][] a = new int[y][x];
	for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = ni();}} return a;}
	long nl(){return scan.nextLong();}
	long[] nl(int n){long[] a = new long[n]; for(int i = 0; i < n; i++){a[i] = nl();} return a;}
	long[][] nl(int y, int x){long[][] a = new long[y][x];
	for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = nl();}} return a;}
	String ns(){return scan.next();}
	String[] ns(int n){String[] a = new String[n]; for(int i = 0; i < n; i++){a[i] = ns();} return a;}
	String[][] ns(int y, int x){String[][] a = new String[y][x];
	for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = ns();}} return a;}
}
class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		}else{
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
	private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
	public String next() {
		if (!hasNext()) throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext()) throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while(true){
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			}else if(b == -1 || !isPrintableChar(b)){
				return minus ? -n : n;
			}else{
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
		return (int) nl;
	}
	public double nextDouble() { return Double.parseDouble(next());}
}