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.