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.

Examples

Input

3
1 1
5 1
5 5

Output

1

Input

2
10 10
20 20

Output

0

Input

9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5

Output

16

见题面

见题面