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(10000000)
MOD = 10 ** 9 + 7
INF = 10 ** 15

def main():
    MAXS = 100005
    N = int(input())
    X = [set() for _ in range(MAXS)]
    Y = [set() for _ in range(MAXS)]
    for _ in range(N):
        x,y = map(int,input().split())
        X[x].add(y)
        Y[y].add(x)
    
    used_x = [0] * MAXS
    used_y = [0] * MAXS
    ans = -N
    for i in range(MAXS):
        if used_x[i]:
            continue
        used_x[i] = 1
        if not X[i]:
            continue
        max_height = set(X[i])
        max_width = {i}
        stack = [(i,0)]
        while stack:
            v,typ = stack.pop()
            if typ == 0:
                for y in X[v]:
                    if used_y[y]:
                        continue
                    used_y[y] = 1
                    if Y[y]:
                        max_width |= Y[y]
                        stack.append((y,1))
            else:
                for x in Y[v]:
                    if used_x[x]:
                        continue
                    used_x[x] = 1
                    if X[x]:
                        max_height |= X[x]
                        stack.append((x,0))
        ans += len(max_width) * len(max_height)
    print(ans)
if __name__ == '__main__':
    main()