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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.IO;
using System.Linq;
using System.Collections.Generic;
using static System.Math;
using static System.Console;
using static System.Linq.Enumerable;
using static System.Numerics.BitOperations;

namespace ACLB{
    class SolverC{
        static void Main(){
            SetOut(new StreamWriter(Console.OpenStandardOutput()){AutoFlush = false});
            new SolverC().Solve();
            Out.Flush();
        }

        public void Solve(){
            checked{

                (int N, int M) = Get.Tuple<int,int>();
                UnionFind uf = new UnionFind(N);
                for(int i=0; i<M; i++){
                    (int a, int b) = Get.Tuple<int,int>();
                    a--; b--;
                    uf.Union(a,b);
                }
                int groupNum = 0;
                for(int i=0; i<N; i++){
                    if(uf.Parents[i] < 0){
                        groupNum++;
                    }
                }
                WriteLine(groupNum-1);
            }
        }


class UnionFind{
        // 自分が親であるとき、その集合の要素数に-1を掛けた値を保持する。
        // そうでなければ親のidを保持する。
        public int[] Parents {get; set;}

        public UnionFind(int n){
            Parents = new int[n];
            for(int i=0; i<n; i++){
                Parents[i] = -1;
            }
        }

        // 要素xのルートを返す
        public int Find(int x){
            if (Parents[x] < 0) return x;
            // ルートまで再帰的に探し、ルートにつなぎ替える
            Parents[x] = Find(Parents[x]);
            return Parents[x];
        }

        // 要素xの属するグループの要素数
        public int Size(int x){
            return -Parents[Find(x)];
        }

        public bool Same(int x, int y){
            return Find(x) == Find(y);
        }

        public bool Union(int x, int y){
            x = Find(x);
            y = Find(y);
            if (x == y) return false;

            // 要素数が少ないグループを多いほうに書き換えたい
            if (Size(x) < Size(y)){
                var tmp = x;
                x = y;
                y = tmp;
            }

            // まとめる先の要素数を更新
            Parents[x] += Parents[y];
            // まとめられるグループのルートの親を書き換え
            Parents[y] = x;
            return true;
        }
        
    }


        static class Mod{
            public static long Pow(long x, long e, long mod = long.MaxValue){
                long res = 1;
                while (e > 0){
                    if ((e & 1) == 1) res = res * x % mod;
                    x = x * x % mod;
                    e >>= 1;
                }
                return res;
            }

            // 逆元を求める。前提：modが素数、aがpの倍数でない。フェルマーの小定理に基づく。
            public static long Inv(long a, long mod){
                return Pow(a, mod-2, mod);
            }
        }
        
        static class Debug{
            public static void Put(object obj, int padLeft = 0, bool newline = true){

                if (obj is Array arr){
                    if( arr.Rank == 1 ){
                        Write("[");
                        for(int i=0; i<arr.Length; i++){
                            Put(arr.GetValue(i), padLeft, false);
                            if( i < arr.Length - 1 ) Write(", ");
                        }
                        Write("]");
                    }
                    else if( arr.Rank == 2 ){
                        Write("[\n");
                        for(int i=0; i<arr.GetLength(0); i++){
                            Write(" [");
                            for(int j=0; j<arr.GetLength(1); j++){
                                Put(arr.GetValue(i,j), padLeft, false);
                                if (j < arr.GetLength(1) - 1) Write(", ");
                            }
                            if (i < arr.GetLength(0) - 1 ) Write("],\n");
                            else Write("]\n");
                        }
                        Write("]");
                    }
                }
                else if( obj is ValueType val ){
                    Write(val.ToString().PadLeft(padLeft));
                }
                else if( obj is string str ){
                    Write(str.PadLeft(padLeft));
                }
                else{
                    Write(obj.ToString().PadLeft(padLeft));
                }

                if(newline) Write("\n");
            }

            public static void Put(object obj, string label, int padLeft = 0, bool newline = true){
                Write("\u001b[32m{0}:\u001b[0m ", label);
                Put(obj, padLeft, newline);
            }
            public static void Put(params object[] args){
                if (args.Length % 2 != 0){
                    WriteLine("Debug.Put(params): arg length shall be multiple of 2.");
                }
                for(int i=0; i<args.Length; i += 2){
                    Put(args[i], (string)args[i+1],0, false);
                    Write("   ");
                }
                Write("\n");
            }
        }

        
        private static class Get
        {
            public static string Str() => ReadLine().Trim();
            public static int Int() => int.Parse(Str());
            public static long Long() => long.Parse(Str());
            public static double Double() => double.Parse(Str());
            public static string[] Strs() => Str().Split(' ', StringSplitOptions.RemoveEmptyEntries);
            public static int[] Ints() => Strs().Select(int.Parse).ToArray();
            public static long[] Longs() => Strs().Select(long.Parse).ToArray();
            public static double[] Doubles() => Strs().Select(double.Parse).ToArray();
            static bool TypeEq<T,U>() => typeof(T).Equals(typeof(U));
            static T TypeConv<T,U>(U u) => (T)Convert.ChangeType(u, typeof(T));
            static T TypeConv<T>(string s) => TypeEq<T, int>() ?   TypeConv<T, int>(int.Parse(s))
                                        : TypeEq<T, long>() ?       TypeConv<T, long>(long.Parse(s))
                                        : TypeEq<T, double>() ?     TypeConv<T, double>(long.Parse(s))
                                        : TypeConv<T, string>(s);
            public static (T,U) Tuple<T,U>() {string[] strs = Strs(); T t = TypeConv<T>(strs[0]); U u = TypeConv<U>(strs[1]); return(t,u);}
            public static (T,U,V) Tuple<T,U,V>() {string[] strs = Strs(); T t = TypeConv<T>(strs[0]); U u = TypeConv<U>(strs[1]); V v = TypeConv<V>(strs[2]); return(t,u,v);}
        }
    }
}