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: Wrong Answer)

#region インクルード
using System;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
using System.IO;
using System.Threading;
using System.Text;
using System.Text.RegularExpressions;
using System.Diagnostics;
using static util;
using P = pair<int, int>;
using static System.Math;
#endregion

class Solver
{
    #region Template
    StreamWriter sw;
    Scan sc;
    void Prt(string a) => sw.WriteLine(a);
    void Prt<T>(IEnumerable<T> a) => Prt(string.Join(" ", a));
    void Prt(params object[] a) => Prt(string.Join(" ", a));
    public Solver(StreamWriter sw)
    {
        this.sw = sw;
        this.sc = new Scan();
    }
    #endregion 
    public void solve()
    {
        var NM = sc.LongArr;
        var N = NM[0];
        var M = NM[1];
        var UF = new UnionFind(N + 1);
        for (int i = 0; i < M; i++)
        {
            var AB = sc.LongArr;
            var A = AB[0];
            var B = AB[1];

            UF.Union(A, B);

        }
        long ans = 0;
        for (int i = 1; i <= N; i++)
        {
            if(UF.Size(i) < 2)
            {
                ans++;
            }
        }
        Prt(ans);
    }
}
class UnionFind



{



    // 親要素のインデックスを保持する



    // 親要素が存在しない(自身がルートである)とき、マイナスでグループの要素数を持つ



    public long[] Parents { get; set; }



    public UnionFind(long n)



    {



        this.Parents = new long[n];



        for (int i = 0; i < n; i++)



        {



            // 初期状態ではそれぞれが別のグループ(ルートは自分自身)



            // ルートなのでマイナスで要素数(1個)を保持する



            this.Parents[i] = -1;



        }



    }







    // 要素xのルート要素はどれか



    public long Find(long x)



    {



        // 親がマイナスの場合は自分自身がルート



        if (this.Parents[x] < 0) return x;



        // ルートが見つかるまで再帰的に探す



        // 見つかったルートにつなぎかえる



        this.Parents[x] = Find(this.Parents[x]);



        return this.Parents[x];



    }







    // 要素xの属するグループの要素数を取得する



    public long Size(long x)



    {



        // ルート要素を取得して、サイズを取得して返す



        return -this.Parents[this.Find(x)];



    }







    // 要素x, yが同じグループかどうか判定する



    public bool Same(long x, long y)



    {



        return this.Find(x) == this.Find(y);



    }







    // 要素x, yが属するグループを同じグループにまとめる



    public bool Union(long x, long y)



    {



        // x, y のルート



        x = this.Find(x);



        y = this.Find(y);



        // すでに同じグループの場合処理しない



        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 (this.Size(x) < this.Size(y))



        {



            var tmp = x;



            x = y;



            y = tmp;



        }



        // まとめる先のグループの要素数を更新



        this.Parents[x] += this.Parents[y];



        // まとめられるグループのルートの親を書き換え



        this.Parents[y] = x;



        return true;



    }



}
#region メインクラス
class Program
{
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        var solver = new Solver(sw);
        // var t = new Thread(solver.solve, 1 << 26); // 64 MB
        // t.Start();
        // t.Join();
        solver.solve();
        sw.Flush();
    }
}
#endregion
#region pair
class pair<T, U> : IComparable<pair<T, U>>
{
    public T v1;
    public U v2;
    public pair() : this(default(T), default(U)) { }
    public pair(T v1, U v2) { this.v1 = v1; this.v2 = v2; }
    public int CompareTo(pair<T, U> a)
    {
        int c = Comparer<T>.Default.Compare(v1, a.v1);
        return c != 0 ? c : Comparer<U>.Default.Compare(v2, a.v2);
    }
    public override string ToString() => v1 + " " + v2;
    public void Deconstruct(out T a, out U b) { a = v1; b = v2; }
}
#endregion
#region util:使える小技集
static class util
{
    public static readonly int M = 1000000007;
    // public static readonly int M = 998244353;
    public static readonly long LM = 1L << 60;
    public static readonly double eps = 1e-11;
    public static void DBG(string a) => Console.Error.WriteLine(a);
    public static void DBG<T>(IEnumerable<T> a) => DBG(string.Join(" ", a));
    public static void DBG(params object[] a) => DBG(string.Join(" ", a));
    public static void Assert(params bool[] conds)
    {
        if (conds.Any(x => !x)) throw new Exception();
    }
    public static pair<T, U> make_pair<T, U>(T v1, U v2) => new pair<T, U>(v1, v2);
    public static int CompareList<T>(IList<T> a, IList<T> b) where T : IComparable<T>
    {
        for (int i = 0; i < a.Count && i < b.Count; i++)
            if (a[i].CompareTo(b[i]) != 0) return a[i].CompareTo(b[i]);
        return a.Count.CompareTo(b.Count);
    }
    public static bool inside(int i, int j, int h, int w) => i >= 0 && i < h && j >= 0 && j < w;
    static readonly int[] dd = { 0, 1, 0, -1 };
    // static readonly string dstring = "RDLU";
    public static P[] adjacents(int i, int j)
        => Enumerable.Range(0, dd.Length).Select(k => new P(i + dd[k], j + dd[k ^ 1])).ToArray();
    public static P[] adjacents(int i, int j, int h, int w)
        => Enumerable.Range(0, dd.Length).Select(k => new P(i + dd[k], j + dd[k ^ 1]))
                                         .Where(p => inside(p.v1, p.v2, h, w)).ToArray();
    public static P[] adjacents(this P p) => adjacents(p.v1, p.v2);
    public static P[] adjacents(this P p, int h, int w) => adjacents(p.v1, p.v2, h, w);
    public static Dictionary<T, int> compress<T>(this IEnumerable<T> a)
        => a.Distinct().OrderBy(v => v).Select((v, i) => new { v, i }).ToDictionary(p => p.v, p => p.i);
    public static Dictionary<T, int> compress<T>(params IEnumerable<T>[] a) => compress(a.Aggregate(Enumerable.Union));
    public static T[] inv<T>(this Dictionary<T, int> dic)
    {
        var res = new T[dic.Count];
        foreach (var item in dic) res[item.Value] = item.Key;
        return res;
    }
    public static void swap<T>(ref T a, ref T b) where T : struct { var t = a; a = b; b = t; }
    public static void swap<T>(this IList<T> a, int i, int j) where T : struct { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a)
    {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
    public static void Deconstruct<T>(this IList<T> v, out T a)
    {
        a = v[0];
    }
    public static void Deconstruct<T>(this IList<T> v, out T a, out T b)
    {
        a = v[0]; b = v[1];
    }
    public static void Deconstruct<T>(this IList<T> v, out T a, out T b, out T c)
    {
        a = v[0]; b = v[1]; c = v[2];
    }
    public static void Deconstruct<T>(this IList<T> v, out T a, out T b, out T c, out T d)
    {
        a = v[0]; b = v[1]; c = v[2]; d = v[3];
    }
    public static void Deconstruct<T>(this IList<T> v, out T a, out T b, out T c, out T d, out T e)
    {
        a = v[0]; b = v[1]; c = v[2]; d = v[3]; e = v[4];
    }
}
#endregion
#region スキャナー
class Scan
{
    StreamReader sr;
    public Scan() { sr = new StreamReader(Console.OpenStandardInput()); }
    public Scan(string path) { sr = new StreamReader(path); }
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public string Str => sr.ReadLine().Trim();
    public pair<T, U> Pair<T, U>()
    {
        T a; U b;
        Multi(out a, out b);
        return new pair<T, U>(a, b);
    }
    public P P => Pair<int, int>();
    public int[] IntArr => StrArr.Select(int.Parse).ToArray();
    public long[] LongArr => StrArr.Select(long.Parse).ToArray();
    public double[] DoubleArr => StrArr.Select(double.Parse).ToArray();
    public string[] StrArr => Str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
    bool eq<T, U>() => typeof(T).Equals(typeof(U));
    T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    T cv<T>(string s) => eq<T, int>() ? ct<T, int>(int.Parse(s))
                       : eq<T, long>() ? ct<T, long>(long.Parse(s))
                       : eq<T, double>() ? ct<T, double>(double.Parse(s))
                       : eq<T, char>() ? ct<T, char>(s[0])
                                         : ct<T, string>(s);
    public void Multi<T>(out T a) => a = cv<T>(Str);
    public void Multi<T, U>(out T a, out U b)
    {
        var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]);
    }
    public void Multi<T, U, V>(out T a, out U b, out V c)
    {
        var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]);
    }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    {
        var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]);
    }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    {
        var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]);
    }
}
#endregion