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.Diagnostics.CodeAnalysis;
using System.IO;
using System.Linq;
using System.Runtime.InteropServices;

public static class Ex
{
    public static bool IsNullOrEmpty(this string s) { return string.IsNullOrEmpty(s); }
    public static List<string> FastSort(this List<string> s) { s.Sort(StringComparer.OrdinalIgnoreCase); return s.ToList(); }
    public static void yesno(this bool b) { Console.WriteLine(b ? "yes" : "no"); }
    public static void YesNo(this bool b) { Console.WriteLine(b ? "Yes" : "No"); }
    public static void YESNO(this bool b) { Console.WriteLine(b ? "YES" : "NO"); }
    public static int PopCount(this uint bits)
    {
        bits = (bits & 0x55555555) + (bits >> 1 & 0x55555555);
        bits = (bits & 0x33333333) + (bits >> 2 & 0x33333333);
        bits = (bits & 0x0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f);
        bits = (bits & 0x00ff00ff) + (bits >> 8 & 0x00ff00ff);
        return (int)((bits & 0x0000ffff) + (bits >> 16 & 0x0000ffff));
    }
}



partial class Program
{
    string GetStr() { return Console.ReadLine().Trim(); }
    char GetChar() { return Console.ReadLine().Trim()[0]; }
    int GetInt() { return int.Parse(Console.ReadLine().Trim()); }
    long GetLong() { return long.Parse(Console.ReadLine().Trim()); }
    double GetDouble() { return double.Parse(Console.ReadLine().Trim()); }
    string[] GetStrArray() { return Console.ReadLine().Trim().Split(' '); }
    string[][] GetStrArray(int N)
    {
        var res = new string[N][];
        for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ');
        return res;
    }
    int[] GetIntArray() { return Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray(); }
    int[][] GetIntArray(int N)
    {
        var res = new int[N][];
        for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
        return res;
    }
    public long[] GetLongArray() { return Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray(); }
    long[][] GetLongArray(int N)
    {
        var res = new long[N][];
        for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray();
        return res;
    }
    char[] GetCharArray() { return Console.ReadLine().Trim().Split(' ').Select(char.Parse).ToArray(); }
    double[] GetDoubleArray() { return Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray(); }
    double[][] GetDoubleArray(int N)
    {
        var res = new double[N][];
        for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray();
        return res;
    }
    char[][] GetGrid(int H)
    {
        var res = new char[H][];
        for (int i = 0; i < H; i++) res[i] = Console.ReadLine().Trim().ToCharArray();
        return res;
    }
    T[] CreateArray<T>(int N, T value)
    {
        var res = new T[N];
        for (int i = 0; i < N; i++) res[i] = value;
        return res;
    }
    T[][] CreateArray<T>(int H, int W, T value)
    {
        var res = new T[H][];
        for (int i = 0; i < H; i++)
        {
            res[i] = new T[W];
            for (int j = 0; j < W; j++) res[i][j] = value;
        }
        return res;
    }
    T[][][] CreateArray<T>(int H, int W, int R, T value)
    {
        var res = new T[H][][];
        for (int i = 0; i < H; i++)
        {
            res[i] = new T[W][];
            for (int j = 0; j < W; j++)
            {
                res[i][j] = new T[R];
                for (int k = 0; k < R; k++) res[i][j][k] = value;
            }
        }
        return res;
    }

    Dictionary<int, List<int>> GetUnweightedAdjacencyList(int N, int M, bool isDirected, bool isNode_0indexed)
    {
        var dic = new Dictionary<int, List<int>>();
        foreach (var e in Enumerable.Range(0, N)) { dic.Add(e, new List<int>()); }
        for (int i = 0; i < M; i++)
        {
            var input = GetIntArray();
            var a = isNode_0indexed ? input[0] : input[0] - 1;
            var b = isNode_0indexed ? input[1] : input[1] - 1;
            dic[a].Add(b);
            if (isDirected == false) dic[b].Add(a);
        }
        return dic;
    }
    //Dictionary<int, List<(int node, long cost)>> GetWeightedAdjacencyList(int N, int M, bool isDirected, bool isNode_0indexed)
    //{
    //    var dic = new Dictionary<int, List<(int, long)>>();
    //    foreach (var e in Enumerable.Range(0, N)) { dic.Add(e, new List<(int, long)>()); }
    //    for (int i = 0; i < M; i++)
    //    {
    //        var input = GetIntArray();
    //        var a = isNode_0indexed ? input[0] : input[0] - 1;
    //        var b = isNode_0indexed ? input[1] : input[1] - 1;
    //        var c = input[2];
    //        dic[a].Add((b, c));
    //        if (isDirected == false) dic[b].Add((a, c));
    //    }
    //    return dic;
    //}

    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);
    void Multi<T>(out T a) => a = cv<T>(GetStr());
    void Multi<T, U>(out T a, out U b)
    {
        var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]);
    }
    void Multi<T, U, V>(out T a, out U b, out V c)
    {
        var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]);
    }
    void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    {
        var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]);
    }
    void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    {
        var ar = GetStrArray(); 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]);
    }
    void Multi<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 ar = GetStrArray(); 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]); f = cv<Y>(ar[5]);
    }

    void Swap<T>(ref T a, ref T b) { T temp = a; a = b; b = temp; }

    int[] dx = new int[] { 1, 0, -1, 0, 1, 1, -1, -1 };
    int[] dy = new int[] { 0, 1, 0, -1, 1, -1, 1, -1 };
    long mod = 1000000007;
}

class Pair : IComparable<Pair>
{
    public Pair(int _node, long _cost)
    {
        node = _node; cost = _cost;
    }
    public int node;
    public long cost;
    public int CompareTo(Pair p)
    {
        return p.cost > cost ? 1 : -1;
    }
}

class Comparable : IComparable<Comparable>
{
    public Comparable(int x, int id)
    {
        X = x;
        Id = id;
    }

    public int X;
    public int Id;
    public int CompareTo(Comparable c)
    {
        return X >= c.X ? -1 : 1;
    }
}

class Comparer<T> : IComparer<T>
{
    public int Compare(T t1, T t2)
    {
        return 1;
    }
}





partial class Program
{
    static void Main()
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        new Program().Solve();
        Console.Out.Flush();
        Console.Read();
    }

    public void Solve()
    {
        int N, M;
        Multi(out N, out M);
        var uf = new UnionFind(N);
        for(int i = 0; i < M; i++)
        {
            int a, b;
            Multi(out a, out b);
            uf.Union(a - 1, b - 1);
        }

        var gro = uf.parents.Count(e => e < 0);
        Console.WriteLine(gro - 1);
    }

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

        public int Find(int x)
        {
            if (parents[x] < 0) return x;
            return parents[x] = Find(parents[x]);
        }

        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;

            if (Size(x) < Size(y))
            {
                var tmp = x;
                x = y;
                y = tmp;
            }
            parents[x] += parents[y];
            parents[y] = x;
            return true;
        }
    }
}