Problem:
Score : 600 points

Problem Statement

There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).

We will repeat the following operation as long as possible:

Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.

We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.

Constraints

1 \leq N \leq 10^5

1 \leq x_i, y_i \leq 10^5

If i \neq j, x_i \neq x_j or y_i \neq y_j.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the maximum number of times we can do the operation.

Sample Input 1

3
1 1
5 1
5 5

Sample Output 1

1

By choosing a = 1, b = 1, c = 5, d = 5, we can add a dot at (1, 5). We cannot do the operation any more, so the maximum number of operations is 1.

Sample Input 2

2
10 10
20 20

Sample Output 2

0

There are only two dots, so we cannot do the operation at all.

Sample Input 3

9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5

Sample Output 3

16

We can do the operation for all choices of the form a = 1, b = 1, c = i, d = j (2 \leq i,j \leq 5), and no more. Thus, the maximum number of operations is 16.

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Diagnostics;

namespace AtCoder
{
    class Program
    {
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        static int Solve(int N, Tuple<int, int>[] points)
        {
            var xs = new Dictionary<int, List<int>>();
            var ys = new Dictionary<int, List<int>>();
            foreach (var p in points)
            {
                int x = p.Item1;
                int y = p.Item2;
                if (!xs.ContainsKey(y)) { xs[y] = new List<int>(); }
                if (!ys.ContainsKey(x)) { ys[x] = new List<int>(); }
                xs[y].Add(x);
                ys[x].Add(y);
            }
            var set = new HashSet<Tuple<int, int>>();
            var X = new HashSet<int>();
            var Y = new HashSet<int>();
            foreach (var p in points)
            {
                if (xs[p.Item2].Count >= 2 && ys[p.Item1].Count >= 2)
                {
                    foreach (int x in xs[p.Item2])
                    {
                        set.Add(new Tuple<int, int>(x, p.Item2));
                        X.Add(x);
                    }
                    foreach (int y in ys[p.Item1])
                    {
                        set.Add(new Tuple<int, int>(p.Item1, y));
                        Y.Add(y);
                    }
                }
            }
            return X.Count * Y.Count - set.Count;
        }

        static void Main(string[] args)
        {
            int N = ReadInt();
            var points = new Tuple<int, int>[N];
            for (int i = 0; i < N; ++i)
            {
                var V = ReadInts();
                points[i] = new Tuple<int, int>(V[0], V[1]);
            }
            Console.WriteLine(Solve(N, points));
        }
    }
}