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-----
3
1 1
5 1
5 5

-----Sample Output-----
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.

见题面

见题面