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
# sys.setrecursionlimit(20000)


N = int(input())
COR = [tuple((map(int, input().split()))) for _ in range(N)]


class Group:
    
    def __init__(self):
        self.n = 0
        self.x = 0
        self.y = 0
        self.xy = {}
        
    def new_cor_n(self):
        return self.x * self.y - self.n
        

def grouping(group, x, xcor, ycor):
    x_list = []
    group.x += 1
    for y in xcor[x][0]:
        if (x, y) not in group.xy:
            group.n += 1
            group.xy[(x, y)] = None
        if ycor[y][1]:
            continue
        ycor[y][1] = True
        group.y += 1
        for x_ in ycor[y][0]:
            if (x_, y) not in group.xy:
                group.n += 1
                group.xy[(x_, y)] = None
            if xcor[x_][1]:
                continue
            xcor[x_][1] = True
            x_list.append(x_)
    return x_list

if N <= 2:
    print(0)
else:
    xcor, ycor = {}, {}
    for xi, yi in COR:
        if xi in xcor:
            xcor[xi][0].append(yi)
        else:
            xcor[xi] = [[yi], False]
        if yi in ycor:
            ycor[yi][0].append(xi)
        else:
            ycor[yi] = [[xi], False]
    group_list = []
    for i, v in xcor.items():
        if v[1]:
            continue
        group = Group()
        group_list.append(group)
        xcor[i][1] = True
        x_list = [i]
        while True:
            new_x_list = []
            for x in x_list:
                new_x_list += grouping(group, x, xcor, ycor)
            if new_x_list == []:
                break
            x_list = new_x_list
    s = 0
    for group in group_list:
        s += group.new_cor_n()
    print(s)
