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
# (x,a), (x,b) → (s,a)と(t,b)は同値になる → aとbを同一視
# 連結成分を作る
N = int(input())
U = 10 ** 5
root_x = [None] * (U+1)
root_y = [None] * (U+1)
size_x = [0] * (U+1) # 連結成分のxの個数
size_y = [0] * (U+1) # 連結成分のyの個数
cnt_x = [0] * (U+1) # 生成時に登場した点
cnt_y = [0] * (U+1) # 生成時に登場した点
x_to_y = [None] * (U+1)
y_to_x = [None] * (U+1)

def find_root(root,size,x):
  y = root[x]
  if y is None:
    root[x] = x
    size[x] = 1
    return x
  if x == y:
    return y
  z = find_root(root,size,y)
  root[x] = z
  return z

def merge(root,size,cnt,x,y):
  rx = find_root(root,size,x)
  ry = find_root(root,size,y)
  if rx == ry:
    return
  sx = size[rx]
  sy = size[ry]
  if sx > sy:
    root[ry] = rx
    size[rx] += sy
    cnt[rx] += cnt[ry]
  else:
    root[rx] = ry
    size[ry] += sx
    cnt[ry] += cnt[rx]
  return

for _ in range(N):
  x,y = map(int,input().split())
  rx = find_root(root_x,size_x,x)
  ry = find_root(root_y,size_y,y)
  cnt_x[rx] += 1
  cnt_y[ry] += 1
  if x_to_y[rx] is None:
    x_to_y[rx] = ry
  if y_to_x[ry] is None:
    y_to_x[ry] = rx
  merge(root_y, size_y, cnt_y, x_to_y[rx], ry)
  merge(root_x, size_x, cnt_x, y_to_x[ry], rx)
  x_to_y[root_x[rx]] = root_y[ry]
  y_to_x[root_y[ry]] = root_x[rx]

  
answer = 0

for x in range(1,U+1):
  if root_x[x] is None:
    continue
  rx = find_root(root_x,size_x,x)
  if x != rx:
    continue
  y = x_to_y[x]
  ry = find_root(root_y,size_y,y)
  sx = size_x[rx]
  sy = size_y[ry]
  cnt = cnt_x[rx]
  answer += (sx * sy - cnt)
print(answer)
