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.IO;
using System.Linq;

public static class Ex
{
    public static bool IsNullOrEmpty(this string s) { return string.IsNullOrEmpty(s); }
    public static List<string> FastSort(this List<string> s) { s.Sort(StringComparer.OrdinalIgnoreCase); return s.ToList(); }
    public static void yesno(this bool b) { Console.WriteLine(b ? "yes" : "no"); }
    public static void YesNo(this bool b) { Console.WriteLine(b ? "Yes" : "No"); }
    public static void YESNO(this bool b) { Console.WriteLine(b ? "YES" : "NO"); }
    public static int PopCount(this uint bits)
    {
        bits = (bits & 0x55555555) + (bits >> 1 & 0x55555555);
        bits = (bits & 0x33333333) + (bits >> 2 & 0x33333333);
        bits = (bits & 0x0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f);
        bits = (bits & 0x00ff00ff) + (bits >> 8 & 0x00ff00ff);
        return (int)((bits & 0x0000ffff) + (bits >> 16 & 0x0000ffff));
    }
}



partial class Program
{
    string GetStr() { return Console.ReadLine().Trim(); }
    char GetChar() { return Console.ReadLine().Trim()[0]; }
    int GetInt() { return int.Parse(Console.ReadLine().Trim()); }
    long GetLong() { return long.Parse(Console.ReadLine().Trim()); }
    double GetDouble() { return double.Parse(Console.ReadLine().Trim()); }
    string[] GetStrArray() { return Console.ReadLine().Trim().Split(' '); }
    string[][] GetStrArray(int N)
    {
        var res = new string[N][];
        for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ');
        return res;
    }
    int[] GetIntArray() { return Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray(); }
    int[][] GetIntArray(int N)
    {
        var res = new int[N][];
        for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
        return res;
    }
    public long[] GetLongArray() { return Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray(); }
    long[][] GetLongArray(int N)
    {
        var res = new long[N][];
        for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray();
        return res;
    }
    char[] GetCharArray() { return Console.ReadLine().Trim().Split(' ').Select(char.Parse).ToArray(); }
    double[] GetDoubleArray() { return Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray(); }
    double[][] GetDoubleArray(int N)
    {
        var res = new double[N][];
        for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray();
        return res;
    }
    char[][] GetGrid(int H)
    {
        var res = new char[H][];
        for (int i = 0; i < H; i++) res[i] = Console.ReadLine().Trim().ToCharArray();
        return res;
    }
    T[] CreateArray<T>(int N, T value)
    {
        var res = new T[N];
        for (int i = 0; i < N; i++) res[i] = value;
        return res;
    }
    T[][] CreateArray<T>(int H, int W, T value)
    {
        var res = new T[H][];
        for (int i = 0; i < H; i++)
        {
            res[i] = new T[W];
            for (int j = 0; j < W; j++) res[i][j] = value;
        }
        return res;
    }
    T[][][] CreateArray<T>(int H, int W, int R, T value)
    {
        var res = new T[H][][];
        for (int i = 0; i < H; i++)
        {
            res[i] = new T[W][];
            for (int j = 0; j < W; j++)
            {
                res[i][j] = new T[R];
                for (int k = 0; k < R; k++) res[i][j][k] = value;
            }
        }
        return res;
    }

    Dictionary<int, List<int>> GetUnweightedAdjacencyList(int N, int M, bool isDirected, bool isNode_0indexed)
    {
        var dic = new Dictionary<int, List<int>>();
        foreach (var e in Enumerable.Range(0, N)) { dic.Add(e, new List<int>()); }
        for (int i = 0; i < M; i++)
        {
            var input = GetIntArray();
            var a = isNode_0indexed ? input[0] : input[0] - 1;
            var b = isNode_0indexed ? input[1] : input[1] - 1;
            dic[a].Add(b);
            if (isDirected == false) dic[b].Add(a);
        }
        return dic;
    }
    //Dictionary<int, List<(int node, long cost)>> GetWeightedAdjacencyList(int N, int M, bool isDirected, bool isNode_0indexed)
    //{
    //    var dic = new Dictionary<int, List<(int, long)>>();
    //    foreach (var e in Enumerable.Range(0, N)) { dic.Add(e, new List<(int, long)>()); }
    //    for (int i = 0; i < M; i++)
    //    {
    //        var input = GetIntArray();
    //        var a = isNode_0indexed ? input[0] : input[0] - 1;
    //        var b = isNode_0indexed ? input[1] : input[1] - 1;
    //        var c = input[2];
    //        dic[a].Add((b, c));
    //        if (isDirected == false) dic[b].Add((a, c));
    //    }
    //    return dic;
    //}

    bool eq<T, U>() => typeof(T).Equals(typeof(U));
    T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    T cv<T>(string s) => eq<T, int>() ? ct<T, int>(int.Parse(s))
                       : eq<T, long>() ? ct<T, long>(long.Parse(s))
                       : eq<T, double>() ? ct<T, double>(double.Parse(s))
                       : eq<T, char>() ? ct<T, char>(s[0])
                                         : ct<T, string>(s);
    void Multi<T>(out T a) => a = cv<T>(GetStr());
    void Multi<T, U>(out T a, out U b)
    {
        var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]);
    }
    void Multi<T, U, V>(out T a, out U b, out V c)
    {
        var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]);
    }
    void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    {
        var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]);
    }
    void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    {
        var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]);
    }
    void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
    {
        var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]);
    }

    void Swap<T>(ref T a, ref T b) { T temp = a; a = b; b = temp; }

    int[] dx = new int[] { 1, 0, -1, 0, 1, 1, -1, -1 };
    int[] dy = new int[] { 0, 1, 0, -1, 1, -1, 1, -1 };
    long mod = 1000000007;
}

class Pair : IComparable<Pair>
{
    public Pair(int _node, long _cost)
    {
        node = _node; cost = _cost;
    }
    public int node;
    public long cost;
    public int CompareTo(Pair p)
    {
        return p.cost > cost ? 1 : -1;
    }
}

class Comparable : IComparable<Comparable>
{
    public Comparable(int x, int id)
    {
        X = x;
        Id = id;
    }

    public int X;
    public int Id;
    public int CompareTo(Comparable c)
    {
        return X >= c.X ? -1 : 1;
    }
}

class Comparer<T> : IComparer<T>
{
    public int Compare(T t1, T t2)
    {
        return 1;
    }
}





partial class Program
{
    static void Main()
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        new Program().Solve();
        Console.Out.Flush();
        Console.Read();
    }

    public void Solve()
    {
        int N = GetInt();
        var pos = GetIntArray(N).Select((s, index) => new { x = s[0], y = s[1], n = index }).OrderBy(o => o.x).ToArray();
        var uf = new UnionFind(N);
        var pq = new PriorityQueue<(int n, int y)>((a, b) => a.y < b.y);

        for(int i = 0; i < N; i++)
        {
            int nowy = pos[i].y;
            while(pq.Count()>0 && pq.Peek().y < nowy)
            {
                uf.Union(pos[i].n, pq.Peek().n);
                pq.Dequeue();
            }
            pq.Enqueue((pos[i].n, pos[i].y));
        }

        for(int i = 0; i < N; i++)
        {
            Console.WriteLine(uf.Size(i));
        }
    }

    class PriorityQueue<T>
    {
        public PriorityQueue(Func<T, T, bool> func)
        {
            elements = new List<T>();
            compare = func;
        }

        Func<T, T, bool> compare; //T1がT2より優先度が高いか否か
        List<T> elements;
        public void Enqueue(T elem)
        {
            int n = elements.Count;
            elements.Add(elem);
            while (n != 0)
            {
                int i = (n - 1) / 2;
                //T1がT2より優先度が高ければ交換
                if (compare(elements[n], elements[i]))
                {
                    T temp = elements[n];
                    elements[n] = elements[i];
                    elements[i] = temp;
                }
                n = i;
            }
        }

        public T Dequeue()
        {
            var t = Peek();
            Pop();
            return t;
        }

        void Pop()
        {
            int n = elements.Count - 1;
            elements[0] = elements[n];
            elements.RemoveAt(n);
            for (int i = 0, j; (j = 2 * i + 1) < n;)
            {
                //左の子と右の子で右の子の方が優先度が高いなら右の子を処理したい
                if ((j != n - 1) && compare(elements[j], elements[j + 1]) == false) { j++; }
                //親より子が優先度が高いなら親子を入れ替える
                if (compare(elements[i], elements[j]) == false)
                {
                    T temp = elements[j];
                    elements[j] = elements[i];
                    elements[i] = temp;
                }
                i = j;
            }
        }

        public T Peek()
        {
            return elements[0];
        }

        public int Count()
        {
            return elements.Count;
        }
    }

    class UnionFind
    {
        int[] parents;
        public UnionFind(int n)
        {
            parents = new int[n];
            for (int i = 0; i < n; i++)
            {
                parents[i] = -1;
            }
        }

        public int Find(int x)
        {
            if (parents[x] < 0) return x;
            return parents[x] = Find(parents[x]);
        }

        public int Size(int x)
        {
            return -parents[Find(x)];
        }

        public bool Same(int x, int y)
        {
            return Find(x) == Find(y);
        }

        public bool Union(int x, int y)
        {
            x = Find(x);
            y = Find(y);
            if (x == y) return false;

            if (Size(x) < Size(y))
            {
                var tmp = x;
                x = y;
                y = tmp;
            }
            parents[x] += parents[y];
            parents[y] = x;
            return true;
        }
    }
}