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

using System;
using System.Collections.Generic;
using System.Linq;

namespace atcoder
{
    class Program
    {
        static List<bool> checkList;
        static List<List<int>> list;

        static void Main(string[] args)
        {
            var n = Int32.Parse(Console.ReadLine());
            list = new List<List<int>>();
            for (int i = 0; i < 200000; i++)
            {
                list.Add(new List<int>());
            }
            for (var i = 0; i < n; i++)
            {
                var s = Console.ReadLine();
                var l = s.Split(" ");
                var x = Int32.Parse(l[0]) - 1;
                var y = Int32.Parse(l[1]) + 100000 - 1;

                list[x].Add(y);
                list[y].Add(x);
            }

            checkList = new List<bool>(new bool[200000]);
            checkList = checkList.Select(c => c=false).ToList();
            long sum = 0;

            for (var i = 0; i < 200000; i++)
            {
                var group = new List<int>();
                var b = DFS(group, i);
                int xc = 0, yc = 0;
                foreach (var g in group)
                {
                    if (g < 100000)xc++;
                    else yc++;
                }
                if (xc + yc >= 4)
                {
                    sum += xc * yc - b;
                }
            }

            Console.WriteLine(sum);
        }

        static int DFS(List<int> group, int index)
        {
            int ret = 0;
            if (!checkList[index])
            {
                checkList[index] = true;
                group.Add(index);
                foreach (var l in list[index])
                {
                    ret += DFS(group, l);
                }
                ret++;
            }
            return ret;
        }
    }
}