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.Collections.Generic;
using System.Linq;
using System.Text;

//using System.Numerics;
using CS=System.Runtime.CompilerServices;
using PL=System.Threading.Tasks.Parallel;
//using System.Diagnostics;
using static System.Math;
using ll=System.Int64;
using static Contest_C.Lib_IO;
using static Contest_C.Lib_Minifunc;


namespace Contest_C {

public static class Entry
{

	public static void Main() {
		checked{
			long n, m;
			Lib_IO.rm(out n, out m);
			P<long,long>[] ab;
			rl(m, out ab);

			UnionFind uf = new UnionFind(n);
			foreach (var e in ab)
			{
				uf.Unite(e.A-1,e.B-1);
			}


			long ans = uf.Groups().Length-1;


			Lib_IO.wm(ans);
		}
	}


public class UnionFind {
	private long[] data;
 
	public UnionFind(long size) {
		data = Enumerable.Repeat(-1L, (int)size).ToArray();
	}
	public bool Unite(long x, long y) {
		x = Find(x);
		y = Find(y);
 
		if (x != y) {
			if (data[y] < data[x]) { var t = y; y = x; x = t; }
			data[x] += data[y];
			data[y] = x;
		}
		return x != y;
	}
	public bool IsSameGroup(long x, long y) { return Find(x) == Find(y); }
	public long Find(long x) { return data[x] < 0 ? x : data[x] = Find(data[x]); }
	public long Size(long x) { return -data[Find(x)]; }
	public List<long>[] Groups(){
		var idx = new Dictionary<long, int>();
		int k=0;
		var ret = new List<List<long>>();
		for (int i = 0; i < data.Length; i++) {
			var p = Find(i);
			if(!idx.ContainsKey(p)) {
				idx[p] = k++;
				ret.Add(new List<long>());
			}
			ret[idx[p]].Add(i);
		}
		return ret.ToArray();
	}
}












}



#region BaseModule


public static class Lib_Minifunc{
	public const long MOD1 = 1000000007; // 10^9+7
	public const double EPS1 = 1e-8;
	public const long INF1 = 1000000000000000;  // 10^15
	[CS.MethodImpl(256)] public static void swap1<T>(ref T a,ref T b) { T t = a; a = b; b = t; }
	[CS.MethodImpl(256)] public static void swap2<T>(ref T a,ref T b) where T : IComparable { if (a.CompareTo(b)==1) swap1(ref a, ref b); }  // b の方が小さければ交換

	[CS.MethodImpl(256)] public static bool chmin<T>(ref T a,T b) where T : IComparable { bool r; if (r = (a.CompareTo(b)== 1)) a = b; return r; }  // b の方が小さければ a を更新
	[CS.MethodImpl(256)] public static bool chmax<T>(ref T a,T b) where T : IComparable { bool r; if (r = (a.CompareTo(b)==-1)) a = b; return r; }  // b の方が大きければ a を更新
	[CS.MethodImpl(256)] public static bool inside(long i,long n) => (0<=i&&i<n);
	[CS.MethodImpl(256)] public static bool inside(long x,long y,long w,long h) => (inside(x,w)&&inside(y,h));
	[CS.MethodImpl(256)] public static T min<T>(params T[] a) where T : IComparable { T m = a[0]; for (int i=1;i<a.Length;i++) chmin(ref m, a[i]); return m; }
	[CS.MethodImpl(256)] public static T max<T>(params T[] a) where T : IComparable { T m = a[0]; for (int i=1;i<a.Length;i++) chmax(ref m, a[i]); return m; }
	[CS.MethodImpl(256)] public static long mod(long a,long m=MOD1) { var v = a%m; return (v<0?(m<0?v-m:v+m):v); }
	[CS.MethodImpl(256)] public static long ceil(long a,long b) => (a%b==0||(a<0&&0<b)||(0<a&&b<0)?a/b:a/b+1);	// 整数商の切り上げ
	[CS.MethodImpl(256)] public static long round(double a) => Convert.ToInt64(a);	// 四捨五入
	public static string YES(bool a) => a?"YES":"NO";
	public static string yes(bool a) => a?"Yes":"No";
	[CS.MethodImpl(256)] public static P<T,U> initp<T,U>(T a,U b) => new P<T,U>(a,b);
	[CS.MethodImpl(256)] public static P<T,U,V> initp<T,U,V>(T a,U b,V c) => new P<T,U,V>(a,b,c);
	[CS.MethodImpl(256)] public static P<T,U,V,W> initp<T,U,V,W>(T a,U b,V c,W d) => new P<T,U,V,W>(a,b,c,d);
	public static T[] initc<T>(long l1) where T : new() { var m = new T[l1]; PL.For(0, m.Length, i => m[i] = new T() ); return m; }	// new制約は遅い
	public static int[] range(long s, long c) => Enumerable.Range((int)s,(int)c).ToArray();
	[CS.MethodImpl(256)] public static T[] inita<T>(long l1,T v=default(T)) => Enumerable.Repeat(v,(int)l1).ToArray();
	public static T[][] inita<T>(long l1,long l2,T v=default(T)) { var m = new T[l1][]; PL.For(0, m.Length, i => m[i] = inita(l2,v) ); return m; }
	[CS.MethodImpl(256)] public static bool initd<T,U>(this IDictionary<T,U> d, T k, U v=default(U)) { bool f; if(f = !d.ContainsKey(k)) d[k] = v; return f; }
	public static void shift(this IList<int> l,int o) => PL.For(0, l.Count, i => l[i] += o );
	public static void shift(this IList<long> l,long o) => PL.For(0, l.Count, i => l[i] += o );
	public static void shift(this IList<P<int,int>> l,int o1=0,int o2=0) => PL.For(0, l.Count, i => l[i] = new P<int,int>(l[i].A+o1,l[i].B+o2) );
	public static void shift(this IList<P<long,long>> l,long o1=0,long o2=0) => PL.For(0, l.Count, i => l[i] = new P<long,long>(l[i].A+o1,l[i].B+o2) );
	public static void shift(this IList<P<int,int,int>> l,int o1=0,int o2=0,int o3=0) => PL.For(0, l.Count, i => l[i] = new P<int,int,int>(l[i].A+o1,l[i].B+o2,l[i].C+o3) );
	public static void shift(this IList<P<long,long,long>> l,long o1=0,long o2=0,long o3=0) => PL.For(0, l.Count, i => l[i] = new P<long,long,long>(l[i].A+o1,l[i].B+o2,l[i].C+o3) );
	public static void shift(this IList<P<int,int,int,int>> l,int o1=0,int o2=0,int o3=0,int o4=0) => PL.For(0, l.Count, i => l[i] = new P<int,int,int,int>(l[i].A+o1,l[i].B+o2,l[i].C+o3,l[i].D+o4) );
	public static void shift(this IList<P<long,long,long,long>> l,long o1=0,long o2=0,long o3=0,long o4=0) => PL.For(0, l.Count, i => l[i] = new P<long,long,long,long>(l[i].A+o1,l[i].B+o2,l[i].C+o3,l[i].D+o4) );
	public static KeyValuePair<long,T>[] index<T>(this IList<T> l) { var m = new KeyValuePair<long,T>[l.Count]; PL.For(0, l.Count, i => m[i] = new KeyValuePair<long, T>(i,l[i]) ); return m; }
	public static void sort<T>(this T[] a,int o=1, Comparison<T> f=null) where T : IComparable {
		switch(o){
			case  0: Array.Sort(a,f);break;
			case  1: Array.Sort(a,(x,y)=>x.CompareTo(y));break;
			case -1: Array.Sort(a,(x,y)=>y.CompareTo(x));break;
			default: break;
		}
	}
	public static void sort<T,U>(this P<T,U>[] a,int o, Comparison<P<T,U>> f=null) where T : IComparable where U : IComparable {
		switch(o){
			case  0: Array.Sort(a,f);break;
			case  1: Array.Sort(a,(x,y)=>x.A.CompareTo(y.A));break;
			case -1: Array.Sort(a,(x,y)=>y.A.CompareTo(x.A));break;
			case  2: Array.Sort(a,(x,y)=>x.B.CompareTo(y.B));break;
			case -2: Array.Sort(a,(x,y)=>y.B.CompareTo(x.B));break;
			default: break;
		}
	}
	public static void sort<T,U,V>(this P<T,U,V>[] a,int o, Comparison<P<T,U,V>> f=null) where T : IComparable where U : IComparable where V : IComparable {
		switch(o){
			case  0: Array.Sort(a,f);break;
			case  1: Array.Sort(a,(x,y)=>x.A.CompareTo(y.A));break;
			case -1: Array.Sort(a,(x,y)=>y.A.CompareTo(x.A));break;
			case  2: Array.Sort(a,(x,y)=>x.B.CompareTo(y.B));break;
			case -2: Array.Sort(a,(x,y)=>y.B.CompareTo(x.B));break;
			case  3: Array.Sort(a,(x,y)=>x.C.CompareTo(y.C));break;
			case -3: Array.Sort(a,(x,y)=>y.C.CompareTo(x.C));break;
			default: break;
		}
	}
	public static void sort<T,U,V,W>(this P<T,U,V,W>[] a,int o, Comparison<P<T,U,V,W>> f=null) where T : IComparable where U : IComparable where V : IComparable where W : IComparable {
		switch(o){
			case  0: Array.Sort(a,f);break;
			case  1: Array.Sort(a,(x,y)=>x.A.CompareTo(y.A));break;
			case -1: Array.Sort(a,(x,y)=>y.A.CompareTo(x.A));break;
			case  2: Array.Sort(a,(x,y)=>x.B.CompareTo(y.B));break;
			case -2: Array.Sort(a,(x,y)=>y.B.CompareTo(x.B));break;
			case  3: Array.Sort(a,(x,y)=>x.C.CompareTo(y.C));break;
			case -3: Array.Sort(a,(x,y)=>y.C.CompareTo(x.C));break;
			case  4: Array.Sort(a,(x,y)=>x.D.CompareTo(y.D));break;
			case -4: Array.Sort(a,(x,y)=>y.D.CompareTo(x.D));break;
			default: break;
		}
	}
}


public struct P<T,U> {
	public T A; public U B;
	public P(T a,U b) { A = a; B = b; }
	public static implicit operator KeyValuePair<T,U>(P<T,U> a) => new KeyValuePair<T,U>(a.A,a.B);
	public static implicit operator P<T,U>(KeyValuePair<T,U> a) => new P<T,U>(a.Key,a.Value);
}
public struct P<T,U,V> {
	public T A; public U B; public V C;
	public P(T a,U b,V c) { A = a; B = b; C = c; }
}
public struct P<T,U,V,W> {
	public T A; public U B; public V C; public W D;
	public P(T a,U b,V c,W d) { A = a; B = b; C = c; D = d; }
}

public static class Lib_IO {
	class Prt : System.IO.StreamWriter {
		public override IFormatProvider FormatProvider { get { return System.Globalization.CultureInfo.InvariantCulture; } }
		public Prt(System.IO.Stream s) : base(s,new UTF8Encoding(false,true)) {}
		public Prt(System.IO.Stream s,Encoding e) : base(s,e) {}
	}
	static Prt sw = new Prt(Console.OpenStandardOutput());
	static char[] sp = new char[] {' '};
	[CS.MethodImpl(256)] static bool eq<T,U>() => typeof(T).Equals(typeof(U));
	[CS.MethodImpl(256)] static T ct<T,U>(U a) => (T)Convert.ChangeType(a,typeof(T));
	[CS.MethodImpl(256)] static 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,System.Globalization.CultureInfo.InvariantCulture))
	  : eq<T,char>()   ? ct<T,char>(s[0])
					   : ct<T,string>(s);
	public static string[] rm<T>(out T a) {
		var z = Console.ReadLine().Split(sp,StringSplitOptions.RemoveEmptyEntries); 
		a = cv<T>(z[0]);
		return z;
	}
	public static string[] rm<T,U>(out T a,out U b) {
		var z = rm<T>(out a); 
		b = cv<U>(z[1]);
		return z;
	}
	public static string[] rm<T,U,V>(out T a,out U b,out V c) {
		var z = rm<T,U>(out a,out b); 
		c = cv<V>(z[2]);
		return z;
	}
	public static string[] rm<T,U,V,W>(out T a,out U b,out V c,out W d) {
		var z = rm<T,U,V>(out a,out b,out c); 
		d = cv<W>(z[3]);
		return z;
	}
	public static string[] rm<T,U,V,W,X>(out T a,out U b,out V c,out W d,out X e) {
		var z = rm<T,U,V,W>(out a,out b,out c,out d); 
		e = cv<X>(z[4]);
		return z;
	}
	public static string[] rm<T,U,V,W,X,Y>(out T a,out U b,out V c,out W d,out X e,out Y f) {
		var z = rm<T,U,V,W,X>(out a,out b,out c,out d,out e); 
		f = cv<Y>(z[5]);
		return z;
	}
	public static string[] ra<T>(out T[] a) {		
		var z = Console.ReadLine().Split(sp,StringSplitOptions.RemoveEmptyEntries);
		a = new T[z.Length];
		for(int i=0;i<a.Length;i++) a[i] = cv<T>(z[i]);
		return z;
	}
	public static string[][] rl<T>(long n,out T[] a) {
		a = new T[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) y[i] = rm(out a[i]);
		return y;
	}
	public static string[][] rl<T,U>(long n,out P<T,U>[] a) {
		a = new P<T,U>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p;
			y[i] = rm(out o,out p);
			a[i] = new P<T,U>(o,p);
		}
		return y;
	}
	public static string[][] rl<T,U,V>(long n,out P<T,U,V>[] a) {
		a = new P<T,U,V>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p; V q;
			y[i] = rm(out o,out p,out q);
			a[i] = new P<T,U,V>(o,p,q);
		}
		return y;
	}
	public static string[][] rl<T,U,V,W>(long n,out P<T,U,V,W>[] a) {
		a = new P<T,U,V,W>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p; V q; W r;
			y[i] = rm(out o,out p,out q,out r);
			a[i] = new P<T,U,V,W>(o,p,q,r);
		}
		return y;
	}
	public static string[][] rx<T>(long n,out T[][] a) {
		a = new T[n][];
		var y = new string[n][];
		for(int i=0;i<n;i++) y[i] = ra(out a[i]);
		return y;
	}

	static void wwp(Action act){
		sw.AutoFlush = false;
		Console.SetOut(sw);
		act();
		Console.Out.Flush();
		sw.AutoFlush = true;
		Console.SetOut(sw);
	}
	[CS.MethodImpl(256)] static string wfm(Type t) =>t.Equals(typeof(double)) ? "{0:F10}" : "{0}";
	public static void wm(params object[] a) {
		wwp(()=>{
			for(int i=0;i<a.Length-1;i++) Console.Write(wfm(a[i].GetType())+" ",a[i]);
			Console.WriteLine(wfm(a[a.Length-1].GetType()),a[a.Length-1]);
		});
	}
	public static void wa<T>(IList<T> a) { wxa(new IList<T>[]{a}, " "); }
	public static void wl<T>(IList<T> a) {
		wwp(()=>{
			var f = wfm(typeof(T));
			if(a.Count==0){
				Console.WriteLine();
			}else{
				foreach(T x in a) Console.WriteLine(f,x);
			}
		});
	}
	static void wxa<T>(IList<IList<T>> a, string s) {
		wwp(()=>{
			var f = wfm(typeof(T));
			var g = f + s;
			foreach(var b in a) {
				if(b.Count==0){
					Console.WriteLine();
				}else{
					for(int i=0;i<b.Count-1;i++) Console.Write(g,b[i]);
					Console.WriteLine(f,b[b.Count-1]);
				}
			}
		});
	}
	public static void wx<T>(IList<IList<T>> a) { wxa(a, " "); }
	public static void wg<T>(IList<IList<T>> a) { wxa(a, ""); }
}

#endregion



}