Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

3
1 1
5 1
5 5

Sample Output 1

1

By choosing a = 1, b = 1, c = 5, d = 5, we can add a dot at (1, 5). We cannot do the operation any more, so the maximum number of operations is 1.

Sample Input 2

2
10 10
20 20

Sample Output 2

0

There are only two dots, so we cannot do the operation at all.

Sample Input 3

9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5

Sample Output 3

16

We can do the operation for all choices of the form a = 1, b = 1, c = i, d = j (2 \leq i,j \leq 5), and no more. Thus, the maximum number of operations is 16.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

/* Aa^~ kokoro ga pyonpyon suru n jaa^~
// ZZZXXkXkkkZ!``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ```?Wfpppbpbbpbbpbbbkbkk
// ppbbbpbbpVr`` `` ` ` ` ` ```` `` ` ` ``  ` ` ` ` ` ` ` ` `  dppbbkkkkkkkkkkqkqkk
// HkqqqqqkkWr`` ` ` ``` ``` `?G, ` ` ``.JC!```` ` ` `` `` ````(Wpbkkkkkkkkqkkkkkqk
// mmmmmqqqqpr` `` `` ```````.+zT=`` `` 7TO-.```````` `` `` ```(yppbkkkkkkkkkkkkkkk
// ggmgmmqqqH$ ``````````....````` `  ````````.`````` `` ``````.yfpppbbbbkkkkqqqqqH
// gmmmmmqqqkW<```` `````...`````  .,.`  ````....````` ``````` (Wbqqmgmmgmggggggggg
// qmmmqqqqkkWk.``````````````````` ;:<`` `````.`````````````-_<-?WHHqmmmmmmgmmgggg
// @@@@@@@gggHH6- ``````````````` `` _ `` ```````````````` ._~~_.`-?Wkqmmmmmmmggg@g
// @@@@g@gggHY~.-<_- `````````````````````````````````` ._~~(<-``.`.(WHqqqmmggggmmm
// @@g@gggHH=.`..._<-___..```````````````````````. .-_~~~_(!``-.``.`` OHHWUWHmqHWXW
// gggggmqK1.``..~.. _<<+-(____..  ````````  ..__~~_((<<!.`.``` .``.`` j0C1XUHmHIdW
// ggmmqH0!,_``.>`````` _<<;<v<<<++((((((((((<<<<<<~_. (-.``~``.>..```  jOuWHHqHIdH
// gmmqkW!`(_ J>`    `` ` _~<`_~~~~<<<<<<<~~__````````` ?1. ._`(__```    zXWHg@HkXH
// gHHWS{``(lJ<!``.``.```(:+>`._`````.` <..`` - ``. `   _ ?&._.I`_`````` .XyVfppppW
// HHHSv``.(X:_..... _..(;+<!.(<..-.....-.-_..+_`..<.`.`..`_IJd}  .`..````jqg@@@@@@
// XHWZ{..<Jk~!.`.. (<.-(+>(_.(1.(_..`.`.`.<_.+<_..<<-..._..-zy>.`_`...```.WH@HHHHH
// bkWt~.-jCz(_..`.(+<.(;< ._-<=_(<_..-....(_.<1<..(<<.`._..-JUS-._.`...```dHmH9VUH
// WUUO..(f.(c...__+z<-(+~` _-+<_(><..__.`.(<._.z_.(1;_..__.(C(zT-(..`...``(WHR<+Xk
// kkkk._(_.->..._(z;:_><.._>_+_<(1>_._<...(v<<.(<.(+z<..-_(Z~_<_j+_..`...`(WHKz1ZW
// @@gR._+_..~..-<+z<<?<>```_.<_.(+1><_;_..(1_:`.<<??1z--(+Z!..<_.j<....`..(bgHAAQX
// @@mR.(j:..~.._<z!`.(>~``` ~(_.(+<1><><_.(((_`.<__`.<_.(X>...<_.(<.....`.JUWWWyWW
// @gmH_(zl..(.._+>```<+_````.~>``(+.<?>>_._(<```(<<``(__<>....<.._<.......dXkkkHHH
// mmqHl(dk_.(_.-=~`.`.1-..._~-1.``_:`(??<_~(`.--.&_.`.<(;<...._.._<..`..._Xg@@@@@@
// qHkpk(dX<.(;..j_```.(((JJ&a&-~``````.1<_```-(((e+.-(/`(>...._..(<......(Wmggg@@g
// HVHbWcz><__+_.(_.(dWWHHH@HHc~````````.+~`` (jHMMMHHHm&.?..._<..(<_..._.(WqqHHmHg
// 0>vWWkzZwl~<o.__`__~X@@HM@Hb ```.`.``. ```` d@@HHH@@K?76...(<..(<_...(_(ppWWWWHq
// X0XWHKXXw$<(z<.( `` WHHMHHHH_``````````````.WHHMNMHHH_`(...(<_.(z_..._<(fWVC174W
// XuXWHHWWz>__+z+.!`..??CZYCOX_`````````````.`~.OvTUZUS_`~.._+?_.(_~_.._zjO=1+~+jy
// kkkkkkkkX:._<z=1(_`` << ``->``.``.``.``.```` ?<`` (v!`._..(??_.(1._.._=dUOOzzzwX
// @@@@@@@@H<...1O=v<_...__ -_````````````````.`` `` ~.`` :.~+=?~.(;_(...jdQQQQQkkk
// H@@@@@@@H~...(==>.~~~~~....`.`````````.`````.`........->.(===~~<<.(...(dg@@@@@@@
// @@@H@@HHH_.__(=l>~.~~~~~....``.``.``.```..`......~~~~~(<_+=l=~_<.->..~_dqggggg@g
// @H@@@@MHH_._<(=l>...........```````````````.`...~~~~~~+<(=lz=~((j=z_..~jWqmmgggm
// @@H@@HHWH_._<(lll-.......```.````.``.`..`````........_z<+llZz~(lOO=<...(VYUUUW9Y
// @@HMMHWZf>~_=:=llw+.`````````.`.```__~~_``.`````.....(z+llOOz_zllOlz~..~<<1+dW>_
// MMM#MHHWXl~_=>1ltwOl&.`.``.`````.``````````````.````.(llttwtz(OltwOz<..__zwOwwOz
// HM#HMHUUI<._1z+ttOZttlt&....``.``.`.````.``...``...(zZtttOktzjttttwlz_._<(Xkkkkk
// HHHmHSZu:(_~+OztttXtttOZZttO+-..............-(+ztOttwttttd0tOZttttwOl<~.(_dMMHHH
// rvuuXuuI~~<~(uttttwvOwwwkQQHMMHHHHHHHHHMMMNmgey?OwwwrtttwXOtwttttttXtO-~.((wZyyy
// HHHHHHK>(~(-(dOrtrrl(QgMHMMMHHHHHHHHHHHHHHHH##HMNkX0rrrrXXrd%`` (Ctwwtz_~.<(Wg@H
// NNNNNHD(~(zo~zXrrrQdHHMMNMHHHHHHHHHHHHHHHHHHHHHH##HNmyrdKkwZ ` _``-zwrt1~~_<(MNM
// MMMMM#<<_jwr:(Z4QHHMMHMHHHHHHHHHHHHHHHHHHHHHHHHHHHH###NHSXZ>` ~````.OXtt>~._<?MM
*/

#include <bits/stdc++.h>
using namespace std;

using VI = vector<int>;
using VVI = vector<VI>;
using PII = pair<int, int>;
using LL = long long;
using VL = vector<LL>;
using VVL = vector<VL>;
using PLL = pair<LL, LL>;
using VS = vector<string>;

#define ALL(a)  begin((a)),end((a))
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define EB emplace_back
#define MP make_pair
#define MT make_tuple
#define SZ(a) int((a).size())
#define SORT(c) sort(ALL((c)))
#define RSORT(c) sort(RALL((c)))
#define UNIQ(c) (c).erase(unique(ALL((c))), end((c)))

#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)  FOR(i,0,n)

#define FF first
#define SS second

template<class S, class T>
istream& operator>>(istream& is, pair<S,T>& p){
  return is >> p.FF >> p.SS;
}
template<class T>
istream& operator>>(istream& is, vector<T>& xs){
  for(auto& x: xs)
	is >> x;
  return is;
}
template<class S, class T>
ostream& operator<<(ostream& os, const pair<S,T>& p){
  return os << p.FF << " " << p.SS;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T>& xs){
  for(unsigned int i=0;i<xs.size();++i)
	os << (i?" ":"") << xs[i];
  return os;
}
template<class T>
void maxi(T& x, T y){
  if(x < y) x = y;
}
template<class T>
void mini(T& x, T y){
  if(x > y) x = y;
}
void debug(istringstream&){}
template <char sep=',', class Head, class... Tail>
void debug(istringstream& iss, Head&& head, Tail&&... tail)
{
  string name;
  getline(iss, name, ',');
  cout << sep << name << "=" << head;
  debug(iss, forward<Tail>(tail)...);
}

#ifdef PYONPOI
#define DEBUG(...) \
  do{ \
    istringstream ss(#__VA_ARGS__); \
    debug<' '>(ss, __VA_ARGS__); \
    cout<<endl; \
  }while(0)
#else
#define DEBUG
#endif


const double EPS = 1e-10;
const double PI  = acos(-1.0);
const LL MOD = 1e9+7;

int main(){
  cin.tie(0);
  ios_base::sync_with_stdio(false);

  int N;
  cin >> N;

  const int MX = 1e5+10;
  vector<vector<PII>> Gx(MX);
  vector<vector<PII>> Gy(MX);
  vector<PII> ps(N);
  REP(i,N){
    int x, y;
    cin >> x >> y;
    Gx[x].EB(y, i);
    Gy[y].EB(x, i);
    ps[i] = MP(x, y);
  }

  LL ans = 0;
  vector<bool> vis(N);
  REP(i,N){
    if(vis[i]) continue;
    queue<int> qx, qy;
    set<int> sx, sy;
    qx.push(ps[i].FF);
    qy.push(ps[i].SS);
    sx.insert(ps[i].FF);
    sy.insert(ps[i].SS);
    set<int> crt;
    crt.insert(i);

    while(!qx.empty() || !qy.empty()){
      if(!qx.empty()){
        int x = qx.front();
        qx.pop();
        for(auto v : Gx[x]){
          int yy = v.FF;
          if(!sy.count(yy)){
            qy.push(yy);
            sy.insert(yy);
            vis[v.SS] = true;
            crt.insert(v.SS);
          }
        }
      }
      if(!qy.empty()){
        int y = qy.front();
        qy.pop();
        for(auto v : Gy[y]){
          int xx = v.FF;
          if(!sx.count(xx)){
            qx.push(xx);
            sx.insert(xx);
            vis[v.SS] = true;
            crt.insert(v.SS);
          }
        }
      }
    }

    if(SZ(sx) > 1 && SZ(sy) > 1)
      ans += (LL)SZ(sy) * (LL)SZ(sx);
    else
      ans += SZ(crt);
  }
  cout << ans - N << endl;

  return 0;
}