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)

import sys
sys.setrecursionlimit(10**7)
INF = 10 ** 18
MOD = 10 ** 9 + 7
def YesNo(x): return 'Yes' if x else 'No'
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x) - 1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def II(): return int(sys.stdin.readline())
def SI(): return input()
from collections import defaultdict

def main():
    N = II()
    xy = []
    for _ in range(N):
        xy.append(LI())
    x2g = defaultdict(int)
    y2g = defaultdict(int)
    g2y = defaultdict(set)
    g2x = defaultdict(set)
    g2c = defaultdict(int)
    for x, y in xy:
        gx = x2g[x]
        gy = y2g[y]
        if gx > 0 and gy > 0:  # merge
            if len(g2x[gx]) + len(g2y[gx]) < len(g2x[gy]) + len(g2y[gy]):
                gx, gy = gy, gx
            for x in g2x[gy]:
                x2g[x] = gx
            for y in g2y[gy]:
                y2g[y] = gx
            g2y[gx] |= g2y[gy]
            g2x[gx] |= g2x[gy]
            g2y[gy] = set()
            g2x[gy] = set()
            g2c[gx] += g2c[gy] + 1
            g2c[gy] = 0
        else:
            g = gx or gy or x
            x2g[x] = g
            y2g[y] = g
            g2x[g].add(x)
            g2y[g].add(y)
            g2c[g] += 1
    ans = 0
    for g in g2x.keys():
        if g2x[g]:
            ans += len(g2x[g]) * len(g2y[g]) - g2c[g]
    return ans

print(main())