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: Accepted)

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

# define REP(i,n) for (int i=0;i<(n);++i)
# define rep(i,a,b) for(int i=a;i<(b);++i)
# define all(v) v.begin(),v.end()
# define showVector(v) REP(i,v.size()){p(v[i]);p(" ")} pl("")
template<class T> inline bool chmin(T &a, T b){ if(a > b) { a = b; return true;} return false;}
template<class T> inline bool chmax(T &a, T b){ if(a < b) { a = b; return true;} return false;}
typedef long long int ll;
typedef pair<ll,ll> P_ii;
typedef pair<double,double> P_dd;

template<class T>
vector<T> make_vec(size_t a){
    return vector<T>(a);
}

template<class T, class... Ts>
auto make_vec(size_t a, Ts... ts){
  return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}

template<typename T,typename V>
typename enable_if<is_class<T>::value==0>::type
fill_v(T &t,const V &v){t=v;}

template<typename T,typename V>
typename enable_if<is_class<T>::value!=0>::type
fill_v(T &t,const V &v){
  for(auto &e:t) fill_v(e,v);
}

ll gcd(ll a, ll b) {
    if(a < b) swap(a,b);
    
    if(b == 0) return a;
    return gcd(b, a % b);
}

ll lcm(ll a, ll b){
    ll g = gcd(a,b);
    return (a/g)*b;
}

// 素数判定 O(√n)
bool is_prime(int n){
    for(int i = 2; i * i <= n; i++){
        if(n % i == 0) return false;
    }
    return true;
}

// 約数列挙 O(√n)
vector<ll> divisor(ll n){
    vector<ll> res;
    for(ll i = 1; i * i <= n; i++){
        if(n % i == 0){
            res.push_back(i);
            if(i != n / i) res.push_back(n / i);
        }
    }
    return res;
}

vector<pair<ll, ll> > prime_factorize(ll n) {
    vector<pair<ll, ll> > res;
    for (ll p = 2; p * p <= n; ++p) {
        if (n % p != 0) continue;
        ll num = 0;
        while (n % p == 0) { ++num; n /= p; }
        res.push_back(make_pair(p, num));
    }
    if (n != 1) res.push_back(make_pair(n, 1));
    return res;
}

template<int param>
class ModInt{//{{{
    using Z = int;
    using N = unsigned int;
    using ZZ = long long;
    using NN = unsigned long long;
    struct {} constexpr static exact{};

    // Using Z deliberately to avoid Z -> N promotion.
    template<class Ret = Z&>
    static auto modulo() -> std::enable_if_t<(param<=0), Ret> { static Z mod = 0; return mod; }
    template<class Ret = const Z>
    static auto mod() -> std::enable_if_t<(param<=0), Ret> { return modulo(); }
    template<class Ret = const Z>
    static constexpr auto mod() -> std::enable_if_t<(param>0), Ret> { return param; }
    // std::swap is not a constexpr function in C++14
    static constexpr void swap(Z &a, Z &b){ Z tmp = a; a = b; b = tmp; }

    Z val;
    constexpr ModInt(decltype(exact), const N v) : val(v) {}

public:
    template<class Arg = Z>
    static void set_modulo(const std::enable_if_t<(param<=0), Arg> mod) { modulo() = mod; }

    constexpr ModInt() : val(0) {}
    constexpr ModInt(Z v) : val((v%=mod()) < 0 ? v+mod() : v) {}
    constexpr ModInt(ZZ v) : val((v%=mod()) < 0 ? v+mod() : v) {}

    constexpr int get_val() const { return val; }

    constexpr ModInt inv() const {
        Z a = mod(), b = val;
        Z x = 0, u = 1;
        while (b) {
            const Z t = a / b;
            swap(a -= t * b, b);
            swap(x -= t * u, u);
        }
        return ModInt(exact, x < 0 ? x+mod() : x);
    }

    constexpr explicit operator int() const { return val; }
    constexpr ModInt operator+() const { return *this; }
    constexpr ModInt operator-() const { return ModInt(exact, val ? mod() - val : 0); }

    constexpr ModInt operator++(){ if(++val == mod()) val = 0; return *this; }
    constexpr ModInt operator--(){ val = (val == 0 ? mod()-1 : val-1); return *this; }
    constexpr ModInt operator++(int){ const ModInt res(*this); ++*this; return res; }
    constexpr ModInt operator--(int){ const ModInt res(*this); --*this; return res; }

    constexpr bool operator==(const ModInt &rhs) const { return val == rhs.val; }
    constexpr bool operator!=(const ModInt &rhs) const { return val != rhs.val; }
    constexpr ModInt &operator+=(const ModInt &rhs){
        if((val += rhs.val) >= mod()) val -= mod();
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs){
        if(rhs.val && (val += mod()-rhs.val) >= mod()) val -= mod();
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs){ val = (NN)(val) * rhs.val % mod(); return *this; }
    constexpr ModInt &operator/=(const ModInt &rhs){ return *this *= rhs.inv(); }

    constexpr ModInt pow(long long e) const {
        if(e < 0) return pow(-e).inv();
        NN res = 1, b = val;
        for(; e; e >>= 1, (b *= b) %= mod()) if(e&1) (res *= b) %= mod();
        return ModInt(exact, res);
    }
    friend constexpr ModInt operator+(ModInt lhs, const ModInt &rhs){ return lhs += rhs; }
    friend constexpr ModInt operator-(ModInt lhs, const ModInt &rhs){ return lhs -= rhs; }
    friend constexpr ModInt operator*(ModInt lhs, const ModInt &rhs){ return lhs *= rhs; }
    friend constexpr ModInt operator/(ModInt lhs, const ModInt &rhs){ return lhs /= rhs; }

    friend std::ostream &operator<<(std::ostream &os, const ModInt &v) { return os << v.val; }
    friend std::istream &operator>>(std::istream &is, ModInt &v) {
        int val;
        is >> val;
        v = ModInt(val);
        return is;
    }
};//}}}

const int MOD = 1000000007;
const int inf=1e9+7;
const ll longinf=1LL<<60 ;
using mi = ModInt<1000000007>; 

void addM(ll &a, ll b) {
    a += b;
    if (a >= MOD) a -= MOD;
}

void mulM(ll &a, ll b) {
    a = ((a%MOD)*(b%MOD))%MOD ;
}

const int MAX = 100005;
vector<int> g[MAX * 2];
vector<bool> isVisited(MAX * 2, false);

ll N;
vector<ll> cnt;
void dfs(int s){
    if(isVisited[s]) return;
    isVisited[s] = true;
    cnt[s / MAX]++;
    for(int v : g[s]) dfs(v);
}

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

  cin >> N;
  REP(i, N){
      int x, y;
      cin >> x >> y;
      y += MAX;
      g[x].push_back(y);
      g[y].push_back(x);
  }

  ll ans = 0;
  REP(i, MAX * 2){
      if(isVisited[i]) continue;
      cnt = vector<ll>(2, 0);
      dfs(i);
      ans += cnt[0] * cnt[1];
  }
  cout << ans - N << endl;

  return 0;
}