Must Be Rectangular!

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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N x_1 y_1 : x_N y_N

outputFormat

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

样例

3
1 1
5 1
5 5

1