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 C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Threading;
using System.Runtime.CompilerServices;
using System.Text;
using System.Diagnostics;
using System.Numerics;
using static System.Console;
using static System.Convert;
using static System.Math;
using static Template;
using SC = Scanner;

public partial class Solver
{
    public void Solve()
    {
        var N = sc.Int;
        var res = new int[N];
        int[] X = new int[N], Y = new int[N];
        var rev = new int[N];
        for (int i = 0; i < N; i++)
        {
            sc.ArrInt.Out(out X[i], out Y[i]);
            X[i]--;Y[i]--;rev[Y[i]] = i;
        }
        var uf = new UnionFind(N);
        var idx = Enumerable.Range(0, N).ToArray();
        Array.Sort(idx, (a, b) => X[a] - X[b]);
        var seg = new SegmentTree<int>(N, 0, (a, b) => a + b);
        for (int i = 0; i < N; i++)
        {
            var y = Y[idx[i]];
            int ix = 0;
            while ((ix=seg.MaxRight(0, a => a < 1)) < y)
            {
                seg.Update(ix, 0);
                uf.Union(idx[i], rev[ix]);
            }
            seg.Update(y, 1);
        }
        Console.WriteLine(Enumerable.Range(0,N).Select(v=>uf.Size(v)).Concat("\n"));
    }
}

public class SegmentTree<T>
{
    protected readonly T[] dat;
    protected readonly int _N, sz;
    protected readonly Func<T, T, T> merge;
    protected readonly Func<T, T, T> update;
    protected readonly T id;
    private bool finished = true;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    protected int Left(int i)
        => i << 1;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    protected int Right(int i)
        => (i << 1) | 1;
    public T this[int i]
    {
        get { return dat[i + sz]; }
        set { finished = false; dat[i + sz] = value; }
    }

    public SegmentTree(int N, T id, Func<T, T, T> merge, Func<T, T, T> update = null)
    {
        _N = N;
        this.sz = 1;
        while (sz < N) sz <<= 1;
        this.id = id;
        this.merge = merge;
        this.update = update ?? ((T val1, T val2) => val2);
        dat = Create(sz << 1, () => id);
    }

    public void Update(int i, T value)
    {
        i += sz;
        dat[i] = update(dat[i], value);
        while (i > 1)
        {
            i >>= 1;
            dat[i] = merge(dat[Left(i)], dat[Right(i)]);
        }
    }

    public void Build()
    {
        for (int i = sz - 1; i > 0; i--)
            dat[i] = merge(dat[Left(i)], dat[Right(i)]);
        finished = true;
    }

    public virtual T Query(int left, int right)
    {
        if (!finished) throw new Exception("You need to Execute \"Build()\"");
        T l = id, r = id;
        for (left += sz, right += sz; left < right; left >>= 1, right >>= 1)
        {
            if ((left & 1) == 1) l = merge(l, dat[left++]);
            if ((right & 1) == 1) r = merge(dat[--right], r);
        }
        return merge(l, r);
    }
    public int MaxRight(int l, Func<T, bool> f)
    {
        if (l == _N) return _N;
        l += sz;
        var sm = id;
        do
        {
            while ((l & 1) == 0) l >>= 1;
            if (!f(merge(sm, dat[l])))
            {
                while (l < sz)
                {
                    l <<= 1;
                    if (f(merge(sm, dat[l])))
                    {
                        sm = merge(sm, dat[l]);
                        l++;
                    }
                }
                return l - sz;
            }
            sm = merge(sm, dat[l]);
            l++;
        } while ((l & -l) != l);
        return _N;
    }
    public int MinLeft(int r, Func<T, bool> f)
    {
        if (r == 0) return 0;
        r += sz;
        var sm = id;
        do
        {
            r--;
            while (r > 1 && (r & 1) == 1) r >>= 1;
            if (!f(merge(dat[r], sm)))
            {
                while (r < sz)
                {
                    r = (r << 1) | 1;
                    if (f(merge(dat[r], sm)))
                    {
                        sm = merge(dat[r], sm); r--;
                    }
                }
                return r + 1 - sz;
            }
            sm = merge(dat[r], sm);
        } while ((r & -r) != r);
        return 0;
    }
}
public class UnionFind
{
    public int GroupCount { get; private set; }
    protected int[] data;
    public virtual int this[int i] => Find(i);
    public UnionFind(int size)
    {
        data = Create(size, () => -1);
        GroupCount = size;
    }
    protected int Find(int i) => data[i] < 0 ? i : (data[i] = Find(data[i]));
    public int Size(int i) => -data[Find(i)];
    public virtual bool Union(int u, int v)
    {
        u = Find(u); v = Find(v);
        if (u == v) return false;
        if (data[u] > data[v]) swap(ref u, ref v);
        GroupCount--;
        data[u] += data[v];
        data[v] = u;
        return true;
    }
}
#region Template
public partial class Solver
{
    public SC sc = new SC();
    static void Main(string[] args)
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        var sol = new Solver();
        int testcase = 1;
        //testcase = sol.sc.Int;
        //var th = new Thread(sol.Solve, 1 << 26);th.Start();th.Join();
        while (testcase-- > 0)
            sol.Solve();
        Console.Out.Flush();
    }
}
public static class Template
{
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) > 0) { a = b; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(ref T a, ref T b) { var t = b; b = a; a = t; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(this IList<T> A, int i, int j) { var t = A[i]; A[i] = A[j]; A[j] = t; }
    public static T[] Create<T>(int n, Func<T> f) { var rt = new T[n]; for (var i = 0; i < rt.Length; ++i) rt[i] = f(); return rt; }
    public static T[] Create<T>(int n, Func<int, T> f) { var rt = new T[n]; for (var i = 0; i < rt.Length; ++i) rt[i] = f(i); return rt; }
    public static void Out<T>(this IList<T> A, out T a) => a = A[0];
    public static void Out<T>(this IList<T> A, out T a, out T b) { a = A[0]; b = A[1]; }
    public static void Out<T>(this IList<T> A, out T a, out T b, out T c) { A.Out(out a, out b); c = A[2]; }
    public static void Out<T>(this IList<T> A, out T a, out T b, out T c, out T d) { A.Out(out a, out b, out c); d = A[3]; }
    public static string Concat<T>(this IEnumerable<T> A, string sp) => string.Join(sp, A);
    public static char ToChar(this int s, char begin = '0') => (char)(s + begin);
    public static IEnumerable<T> Shuffle<T>(this IEnumerable<T> A) => A.OrderBy(v => Guid.NewGuid());
    public static int CompareTo<T>(this T[] A, T[] B, Comparison<T> cmp = null) { cmp = cmp ?? Comparer<T>.Default.Compare; for (var i = 0; i < Min(A.Length, B.Length); i++) { int c = cmp(A[i], B[i]); if (c > 0) return 1; else if (c < 0) return -1; } if (A.Length == B.Length) return 0; if (A.Length > B.Length) return 1; else return -1; }
    public static string ToStr<T>(this T[][] A) => A.Select(a => a.Concat(" ")).Concat("\n");
    public static int ArgMax<T>(this IList<T> A, Comparison<T> cmp = null) { cmp = cmp ?? Comparer<T>.Default.Compare; T max = A[0]; int rt = 0; for (int i = 1; i < A.Count; i++) if (cmp(max, A[i]) < 0) { max = A[i]; rt = i; } return rt; }
    public static T PopBack<T>(this List<T> A) { var v = A[A.Count - 1]; A.RemoveAt(A.Count - 1); return v; }
    public static void Fail<T>(T s) { Console.WriteLine(s); Console.Out.Close(); Environment.Exit(0); }
}
public class Scanner
{
    public string Str => Console.ReadLine().Trim();
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public int[] ArrInt => Str.Split(' ').Select(int.Parse).ToArray();
    public long[] ArrLong => Str.Split(' ').Select(long.Parse).ToArray();
    public char[][] Grid(int n) => Create(n, () => Str.ToCharArray());
    public int[] ArrInt1D(int n) => Create(n, () => Int);
    public long[] ArrLong1D(int n) => Create(n, () => Long);
    public int[][] ArrInt2D(int n) => Create(n, () => ArrInt);
    public long[][] ArrLong2D(int n) => Create(n, () => ArrLong);
    private Queue<string> q = new Queue<string>();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public T Next<T>() { if (q.Count == 0) foreach (var item in Str.Split(' ')) q.Enqueue(item); return (T)Convert.ChangeType(q.Dequeue(), typeof(T)); }
    public void Make<T1>(out T1 v1) => v1 = Next<T1>();
    public void Make<T1, T2>(out T1 v1, out T2 v2) { v1 = Next<T1>(); v2 = Next<T2>(); }
    public void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3) { Make(out v1, out v2); v3 = Next<T3>(); }
    public void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4) { Make(out v1, out v2, out v3); v4 = Next<T4>(); }
    public void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5) { Make(out v1, out v2, out v3, out v4); v5 = Next<T5>(); }
    public void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6) { Make(out v1, out v2, out v3, out v4, out v5); v6 = Next<T6>(); }
    public void Make<T1, T2, T3, T4, T5, T6, T7>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6, out T7 v7) { Make(out v1, out v2, out v3, out v4, out v5, out v6); v7 = Next<T7>(); }
    public (T1, T2) Make<T1, T2>() { Make(out T1 v1, out T2 v2); return (v1, v2); }
    public (T1, T2, T3) Make<T1, T2, T3>() { Make(out T1 v1, out T2 v2, out T3 v3); return (v1, v2, v3); }
    public (T1, T2, T3, T4) Make<T1, T2, T3, T4>() { Make(out T1 v1, out T2 v2, out T3 v3, out T4 v4); return (v1, v2, v3, v4); }
}

#endregion