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
from bisect import bisect_left
from collections import defaultdict
N = int(input())
points = list(tuple(map(int,input().split())) for _ in range(N))

xty = defaultdict(list)
ytx = defaultdict(list)
for x,y in points:
    xty[x].append(y)
    ytx[y].append(x)

area = 0
X = set()
Y = set()

for x,y in points:
    if x in X or y in Y:
        continue

    stack_x = [x]
    stack_y = [y]

    dx = set()
    dy = set()

    while stack_x or stack_y:

        while stack_x:
            x = stack_x.pop()
            if x not in dx:
                dx.add(x)
                for y in xty[x]:
                    if y not in dy:
                        stack_y.append(y)

        while stack_y:
            y = stack_y.pop()
            if y not in dy:
                dy.add(y)
                for x in ytx[y]:
                    if x not in dx:
                        stack_x.append(x)
    X |= dx
    Y |= dy
    area += len(dx)*len(dy)

print(area-len(points))