Problem:
Score : 300 points

Problem Statement

There are N cities numbered 1 through N, and M bidirectional roads numbered 1 through M.
Road i connects City A_i and City B_i.

Snuke can perform the following operation zero or more times:

Choose two distinct cities that are not directly connected by a road, and build a new road between the two cities.

After he finishes the operations, it must be possible to travel from any city to any other cities by following roads (possibly multiple times).

What is the minimum number of roads he must build to achieve the goal?

Constraints

2 \leq N \leq 100,000

1 \leq M \leq 100,000

1 \leq A_i < B_i \leq N

No two roads connect the same pair of cities.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
:
A_M B_M

Output

Print the answer.

Sample Input 1

3 1
1 2

Sample Output 1

1

Initially, there are three cities, and there is a road between City 1 and City 2.

Snuke can achieve the goal by building one new road, for example, between City 1 and City 3.
After that,

We can travel between 1 and 2 directly.

We can travel between 1 and 3 directly.

We can travel between 2 and 3 by following both roads (2 - 1 - 3).

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
#define ll long long
#define int long long int
#define MOD 1000000007
#define mkp make_pair
#define maxn 10000500000000000
#define pb push_back
#define ff first
#define ss second
#define all(x) x.begin(),x.end()
#define debug1(a) cout<<a<<endl;
#define debug2(a,b) cout<<a<<' '<<b<<endl;
#define debug3(a,b,c) cout<<a<<' '<<b<<' '<<c<<endl;
#define rep(i,n) for(int i=0;i<n;i++)
#define repl(i,a,b) for(int i=a;i<b;i++)
#define pi pair<int,int>
#define pii pair<int,pi>
#define mp map<int,int>
#define ump unordered_map<int,int>
#define  vi vector<int>
#define st set<int>
#define mst multiset<int>
#define pq priority_queue
#define mpq priority_queue<int,vector<int>,greater<int> >
#define fastio ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define in cin>>
#define out cout<<
using namespace std;
const int infi=1e15+7;
void printVector(vector<int> v){
    for(int i=0;i<(int)v.size();i++)
        cout<<v[i]<<" ";
    out endl;
}

void printArray(int arr[],int n)
{
   for(int i=0;i<n;i++)cout<<arr[i]<<' ';
cout<<endl;
}
 set<pair<int,int>> primeset;
 vi prime_number;
void SieveOfEratosthenes(int n)
{
    bool prime[n+1];
    memset(prime, true, sizeof(prime));

    for (int p=2; p*p<=n; p++)
    {
        if (prime[p] == true)
        {
        for (int i=p*p; i<=n; i += p)
                prime[i] = false;
        }
    }
    for (int p=2; p<=n; p++)
       if (prime[p])
           primeset.insert(mkp(p,1));
}
ll modExp(ll base, ll power) {
    if (power == 0) {
        return 1;
    } else {
        ll cur = modExp(base, power / 2); cur = cur * cur; cur = cur % MOD;
        if (power % 2 == 1) cur = cur * base;
        cur = cur % MOD;
        return cur;
    }
}
//for making unordered_map with pair
struct hash_pair {
    template <class T1, class T2>
    size_t operator()(const pair<T1, T2>& p) const
    {
        auto hash1 = hash<T1>{}(p.first);
        auto hash2 = hash<T2>{}(p.second);
        return hash1 ^ hash2;
    }
};
int root(int a,int id[]){
    while(id[a]!=a){
        id[a]=id[id[a]];
        a=id[a];
    }
    return a;
}
void Union(int a,int b,int id[]){
    int x=root(a,id);
    int y=root(b,id);
    id[x]=id[y];
}
int32_t main()
{
    fastio;
   
    int t=1;
    //in t;
    int tt=0;
    while(t--){
            int n;in n;
            int q;in q;
            int id[n+1];
            for(int i=1;i<=n;i++) id[i]=i;
            while(q--){
                int a,b;
                cin>>a>>b;
                if(root(a,id)!=root(b,id))
                    Union(a,b,id);
            }
            set<int> roots;
            for(int i=1;i<=n;i++){
                roots.insert(root(i,id));
            }
             n=roots.size();
            cout<<(n*(n-1))/2<<endl;
    }

        return 0;
}

/*
google kick start
  cout << "Case #" << tt << ": "<<ans<<endl;
*/