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 Python (3.4.3) (judge verdict: Runtime Error)

from collections import defaultdict

N = int(input())
V = 100005

to = [[] for _ in range(V*2)]
visited = [False] * (V*2)
cnt = [0, 0]

def dfs(v):
    if visited[v]: return
    visited[v] = True
    cnt[v//V] += 1
    for u in to[v]: dfs(u)

def main():
    ans = 0

    # 二部グラフの作成
    for i in range(N):
        x, y = map(int, input().split())
        y += V
        to[x].append(y)
        to[y].append(x)

    # 
    for i in range(V*2):
        if (visited[i]): continue
        global cnt
        cnt = [0, 0]
        dfs(i)
        ans += cnt[0] * cnt[1]

    ans -= N
    print(ans)
    
if __name__ == '__main__':
    main()