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 collections import defaultdict

N = int(input())
d = defaultdict(list)
cd = set()
D = 100000
used = [0]*(2*D+1)
ans = 0

for _ in range(N):
    x, y = map(int, input().split())
    y += D
    cd.add(x)
    d[x].append(y)
    d[y].append(x)

for x in cd:
    if used[x]:continue
    q = [x]
    used[x] = 1
    cx, sx = 0, 0

    while q:
        a = q.pop()
        if a<=D:
            cx += 1
        sx += 1
        for b in d[a]:
            if used[b]:continue
            used[b] = 1
            q.append(b)
    ans += cx*(sx-cx)

print(ans-N)
