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;
typedef long long ll;
#define rep(i, srt, end) for (long long i = (srt); i < (long long)(end); i++)

struct union_find{
    vector<ll> parent;
    vector<ll> nums;
    union_find(ll n){
        parent.resize(n);
        nums.resize(n, 1LL);
        rep(i, 0, n) parent[i] = i;
    }

    ll root(ll x){
        if(parent[x] == x) return x;
        parent[x] = root(parent[x]);
        return parent[x];
    }

    void unite(ll x, ll y){
        ll rx = root(x);
        ll ry = root(y);
        if(rx != ry){
            parent[rx] = ry;
            nums[ry] += nums[rx];
        }
    }

    bool same(ll x, ll y){
        ll rx = root(x);
        ll ry = root(y);
        if(rx == ry) return true;
        return false;
    }

    ll size(ll x){
        return nums[root(x)];
    }
};  

int main(){
    ll N;
    cin >> N;
    vector<ll> x(N), y(N);
    ll stride = 1e5+100;
    union_find t(2*stride);
    rep(i, 0, N){
        cin >> x[i] >> y[i];
        t.unite(x[i], y[i] + stride);
    }
    map<ll, ll> mpx, mpy;
    rep(i, 0, stride) mpx[t.root(i)]++;
    rep(i, stride, 2*stride) mpy[t.root(i)]++;
    ll ans = 0;
    rep(i, 0, stride*2) ans += mpx[i] * mpy[i];
    cout << ans - N << endl;
    return 0;
}