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
import sys
from collections import defaultdict, deque
readline = sys.stdin.readline
N = int(readline())
P = defaultdict(list); Q = defaultdict(list)
for i in range(N):
    x, y = map(int, readline().split())
    P[x].append(y)
    Q[y].append(x)
X = set(); Y = set()

res = 0
que = deque()
for x in P:
    que.append((0, x))
    X.add(x)
    cx = 1; cy = 0
    while que:
        t, v = que.popleft()
        if t:
            for x in Q[v]:
                if x in X:
                    continue
                X.add(x)
                que.append((0, x))
                cx += 1
        else:
            for y in P[v]:
                if y in Y:
                    continue
                Y.add(y)
                que.append((1, y))
                cy += 1
    res += cx * cy
print(res - N)