101315: [AtCoder]ABC131 F - Must Be Rectangular!

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 $16$.