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())
from collections import defaultdict
X=dict()
Y=dict()
P=[]
root=[-1]*N
def find(i):
    global root
    if root[i]>=0:
        root[i]=find(root[i])
        return root[i]
    return i
for i in range(N):
    x,y=map(int,input().split())
    P+=[(x,y)]
    if x not in X.keys():
        rx=i
        X[x]=i
    else:
        rx=find(X[x])
        X[x]=rx
    if y not in Y.keys():
        ry=i
        Y[y]=i
    else:
        ry=find(Y[y])
        Y[y]=ry
    if rx==ry:
        if i!=rx:
            root[i]=rx
        continue
    elif root[rx]<=root[ry]:
        root[rx]+=root[ry]
        root[ry]=rx
    else:
        root[ry]+=root[rx]
        root[rx]=ry
cntx=defaultdict(set)
cnty=defaultdict(set)
RP=set()
ans=0
for i in range(N):
    x,y=P[i]
    r=find(i)
    cntx[r]|={x}
    cnty[r]|={y}
    RP|={r}
for k in RP:
    ans+=len(cntx[k])*len(cnty[k])
print(ans-N)