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
input = sys.stdin.readline


def main():
    N = int(input())
    XY = [list(map(int, input().split())) for _ in range(N)]

    MAX = 10**5
    Xs = [[] for _ in range(MAX+1)]
    Ys = [[] for _ in range(MAX+1)]
    for i, (x, y) in enumerate(XY):
        Xs[x].append(i)
        Ys[y].append(i)

    ans = 0
    checked = [False]*N
    for i in range(N):
        if checked[i]: continue
        q = [i]
        checked[i] = True
        X = set()
        Y = set()
        c = 0
        while q:
            qq = []
            for p in q:
                x, y = XY[p]
                X.add(x)
                Y.add(y)
                c += 1
                for ni in Xs[x]:
                    if not checked[ni]:
                        checked[ni] = True
                        qq.append(ni)
                for ni in Ys[y]:
                    if not checked[ni]:
                        checked[ni] = True
                        qq.append(ni)
            q = qq
        ans += len(X)*len(Y)-c

    print(ans)


if __name__ == "__main__":
    main()