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: Accepted)

from collections import deque
N=int(input())
mod=100010
visit=[0]*(2*mod)
table=[[] for i in range(2*mod)]
for i in range(N):
    x,y=map(int,input().split())
    y+=mod
    visit[x]=1
    visit[y]=1
    table[x].append(y)
    table[y].append(x)
H=deque()
num=0
for i in range(mod):
    if visit[i]==1:
        X=0
        Y=0
        H.append(i)
        visit[i]=0
        while H:
            pt=H.popleft()
            if pt>mod:
                Y+=1
            else:
                X+=1
            for x in table[pt]:
                if visit[x]==1:
                    visit[x]=0
                    H.append(x)
        #print(X,Y)
        num+=X*Y
print(num-N)