Problem:
Problem D: King Slime

There is a grid of size W × H surrounded by walls. Some cells in the grid are occupied by slimes. The slimes want to unite with each other and become a "King Slime".

In each move, a slime can move to east, west, south and north direction until it enters a cell occupied by another slime or hit the surrounding wall. If two slimes come together, they unite and become a new slime.

Your task is write a program which calculates the minimum number of moves that all the slimes unite and become a King Slime. Suppose slimes move one by one and they never move simultaneously.

Input

The first line contains three integers N (2 ≤ N ≤ 40,000), W and H (1 ≤ W, H ≤ 100,000), which denote the
number of slimes, the width and the height of the grid respectively.

The following N lines describe the initial coordinates of the slimes. The i-th line contains two integers xi (1 ≤ xi ≤ W) and yi (1 ≤ yi ≤ H), which indicate the coordinates of the i-th slime . All the coordinates are 1-based.

You may assume that each cell is occupied by at most one slime initially.

Output

Output the minimum number of moves that all the slimes unite and become a King Slime.

Sample Input 1

4 3 3
1 1
1 3
3 1
3 3

Output for the Sample Input 1

3

Sample Input 2

2 3 3
2 2
3 3

Output for the Sample Input 2

2

Sample Input 3

2 4 4
2 2
3 3

Output for the Sample Input 3

3

Sample Input 4

2 4 4
2 2
2 3

Output for the Sample Input 4

1

Solution in C# (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Debug;
using SB = System.Text.StringBuilder;
using System.Numerics;
using static System.Math;
using P = System.Numerics.Complex;
namespace Program {
    public class Solver {
        Random rnd = new Random();
        public void Solve() {
            var n = ri;
            var h = ri; var w = ri;
            var A = Enumerate(h, x => new List<int>());
            var B = Enumerate(w, x => new List<int>());
            for (int i = 0; i < n; i++)
            {
                var x = ri - 1; var y = ri - 1;
                A[x].Add(i); B[y].Add(i);
            }
            par = Enumerate(n, x => x);
            var ans = 0;
            foreach (var x in A.Concat(B))
                for (int i = 0; i < x.Count - 1; i++)
                    if (unite(x[i], x[i + 1])) ans++;
            var cnt = Enumerate(n, x => x).Count(x => find(x) == x);
            if (cnt > 1)
            {
                ans += cnt - 1;
                if (A[0].Count == 0 && A[h - 1].Count == 0 && B[0].Count == 0 && B[w - 1].Count == 0) ans += cnt;
                else ans += cnt - 1;
            }
            Console.WriteLine(ans);
        }
        int[] par;
        bool unite(int i, int j) {
            i = find(i);
            j = find(j);
            if (i == j) return false;
            par[j] = i;
            return true;
        }
        int find(int i) {
            Debug.WriteLine(i);
            if (par[i] == i) return i;
            else return par[i] = find(par[i]);
        }
        const long INF = 1L << 60;
        int ri { get { return sc.Integer(); } }
        long rl { get { return sc.Long(); } }
        double rd { get { return sc.Double(); } }
        string rs { get { return sc.Scan(); } }
        public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());

        static T[] Enumerate<T>(int n, Func<int, T> f) {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f(i);
            return a;
        }
        static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
    }
}

#region main
static class Ex {
    static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }
    static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") {
        return string.Join(st, ie);
    }
    static public void Main() {
        Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = false });
        var solver = new Program.Solver();
        solver.Solve();
        Console.Out.Flush();
    }
}
#endregion
#region Ex
namespace Program.IO {
    using System.IO;
    using System.Text;
    using System.Globalization;

    public class Printer: StreamWriter {
        public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
        public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
    }

    public class StreamScanner {
        public StreamScanner(Stream stream) { str = stream; }

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }

        private byte read() {
            if (isEof) return 0;
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }

        public char Char() {
            byte b = 0;
            do b = read(); while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }
        public string Scan() {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
            return sb.ToString();
        }
        public string ScanLine() {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
        public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
        public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
}

#endregion