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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

from sys import stdin
import math
import copy

n = int(stdin.readline().rstrip())

m = []

for i in range(n):
    x, y = [int(x) for x in stdin.readline().rstrip().split()]
    m.append((x,y))

m.sort()

mm = copy.copy(m)
#print(m)

ans=0

for x,y in m:
  for x2,y2 in [(x2,y2) for x2,y2 in m if x2==x and y < y2]:
    for x3,y3 in [(x3,y3) for x3,y3 in m if y==y3]:
      if not (x3,y2) in mm:
          ans +=1
          mm.append((x3,y2))
    for x4,y4 in [(x4,y4) for x4,y4 in m if y2==y4]:
      if not (x4,y) in mm:
          ans +=1
          mm.append((x4,y))

print(ans)