Problem:
Score : 600 points

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.

Solution in Python (3.4.3) (judge verdict: Accepted)

def main():
    MAX = 10 ** 5 + 1

    data = [-1] * (2 * MAX)

    def find(x):
        if data[x] < 0:
            return x
        else:
            data[x] = find(data[x])
            return data[x]

    def union(x, y):
        x, y = find(x), find(y)
        if x != y:
            if data[y] < data[x]:
                x, y = y, x
            data[x] += data[y]
            data[y] = x
        return (x != y)


    N, *XY = map(int, open(0).read().split())

    for x, y in zip(*[iter(XY)] * 2):
        union(x, y + MAX)

    X = [0] * (MAX * 2)
    Y = [0] * (MAX * 2)

    for i in range(MAX):
        X[find(i)] += 1
    for i in range(MAX, MAX * 2):
        Y[find(i)] += 1

    res = sum(X[i] * Y[i] for i in range(MAX * 2))

    print(res - N)


if __name__ == '__main__':
    main()