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: Wrong Answer)

N = int(input())
xy = [list(map(int, input().split())) for _ in range(N)]
tmp_x = []
tmp_y = []
x_list = []
x2y_dic = {}
y_list = []
y2x_dic = {}
for p in xy:
    if p[0] in tmp_x:
        x_list.append(p[0])
    if p[1] in tmp_y:
        y_list.append(p[1])
    tmp_x.append(p[0])
    tmp_y.append(p[1])
    if p[0] not in x2y_dic:
        x2y_dic[p[0]] = []
    x2y_dic[p[0]].append(p[1])
    if p[1] not in y2x_dic:
        y2x_dic[p[1]] = []
    y2x_dic[p[1]].append(p[0])
cnt = 0
x_list = list(set(x_list))
y_list = list(set(y_list))
for x in x_list:
    for y in y_list:
        if [x,y] in xy:
            for xx in x2y_dic[x]:
                for yy in y2x_dic[y]:
                    if [xx,yy] not in xy:
                        cnt+=1
print(cnt)