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

class UnionFind:
    def __init__(self, n):
        self.root = [i for i in range(n)]
        self.rank = [0] * n

    def find(self, x):
        if self.root[x] == x:
            return x
        else:
            y = self.find(self.root[x])
            self.root[x] = y
            return self.root[x]

    def unite(self, x, y):
        if self.is_same(x, y):
            return
        rx = self.find(x)
        ry = self.find(y)
        if self.rank[rx] < self.rank[ry]:
            self.root[rx] = ry
        else:
            self.root[ry] = rx
            if self.rank[rx] == self.rank[ry]:
                self.rank[rx] += 1

    def is_same(self, x, y):
        return self.find(x) == self.find(y)
    

def main():
    input = sys.stdin.readline
    V = 10**5  # max size of x
    N = int(input())
    uft = UnionFind(2*V)
    for _ in range(N):
        x, y = map(int, input().split())
        x -= 1
        y += V - 1
        uft.unite(x, y)

    cnt_x = defaultdict(lambda: 0)
    cnt_y = defaultdict(lambda: 0)
    for i in range(2*V):
        root = uft.find(i)
        if i < V:  # node of x coordinate.
            cnt_x[root] += 1
        else:
            cnt_y[root] += 1

    ans = 0
    for root in cnt_x.keys():
        ans += cnt_x[root] * cnt_y[root]

    return ans - N


if __name__ == '__main__':
    print(main())
