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;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace Tasks
{
    public class C
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var (N, M) = Scanner.Scan<int, int>();
            var dsu = new DisjointSetUnion(N);
            for (var i = 0; i < M; i++)
            {
                var (A, B) = Scanner.Scan<int, int>();
                A--; B--;
                dsu.Merge(A, B);
            }
            Console.WriteLine(dsu.GetGroups().Count() - 1);
        }

        public class DisjointSetUnion
        {
            private readonly int _n;
            private readonly int[] _parentOrSize;
            public DisjointSetUnion(int n = 0)
            {
                _n = n;
                _parentOrSize = Enumerable.Repeat(-1, n).ToArray();
            }
            public int Merge(int a, int b)
            {
                if (a < 0 || _n <= a) throw new IndexOutOfRangeException(nameof(a));
                if (b < 0 || _n <= b) throw new IndexOutOfRangeException(nameof(b));
                var (x, y) = (LeaderOf(a), LeaderOf(b));
                if (x == y) return x;
                if (-_parentOrSize[x] < -_parentOrSize[y]) (x, y) = (y, x);
                _parentOrSize[x] += _parentOrSize[y];
                _parentOrSize[y] = x;
                return x;
            }
            public bool IsSame(int a, int b)
            {
                if (a < 0 || _n <= a) throw new IndexOutOfRangeException(nameof(a));
                if (b < 0 || _n <= b) throw new IndexOutOfRangeException(nameof(b));
                return LeaderOf(a) == LeaderOf(b);
            }
            public int LeaderOf(int a)
            {
                if (a < 0 || _n <= a) throw new IndexOutOfRangeException(nameof(a));
                if (_parentOrSize[a] < 0) return a;
                return _parentOrSize[a] = LeaderOf(_parentOrSize[a]);
            }
            public int SizeOf(int a)
            {
                if (a < 0 || _n <= a) throw new IndexOutOfRangeException(nameof(a));
                return -_parentOrSize[LeaderOf(a)];
            }
            public IEnumerable<IEnumerable<int>> GetGroups()
            {
                var leaders = new int[_n];
                var groupSize = new int[_n];
                for (var i = 0; i < _n; i++)
                {
                    leaders[i] = LeaderOf(i);
                    groupSize[leaders[i]]++;
                }
                var ret = new List<int>[_n].Select(x => new List<int>()).ToArray();
                for (var i = 0; i < _n; i++) ret[leaders[i]].Add(i);
                return ret.Where(x => x.Any());
            }
        }

        public static class Scanner
        {
            private static Queue<string> queue = new Queue<string>();
            public static T Next<T>()
            {
                if (!queue.Any()) foreach (var item in Console.ReadLine().Trim().Split(" ")) queue.Enqueue(item);
                return (T)Convert.ChangeType(queue.Dequeue(), typeof(T));
            }
            public static T Scan<T>() => Next<T>();
            public static (T1, T2) Scan<T1, T2>() => (Next<T1>(), Next<T2>());
            public static (T1, T2, T3) Scan<T1, T2, T3>() => (Next<T1>(), Next<T2>(), Next<T3>());
            public static (T1, T2, T3, T4) Scan<T1, T2, T3, T4>() => (Next<T1>(), Next<T2>(), Next<T3>(), Next<T4>());
            public static (T1, T2, T3, T4, T5) Scan<T1, T2, T3, T4, T5>() => (Next<T1>(), Next<T2>(), Next<T3>(), Next<T4>(), Next<T5>());
            public static IEnumerable<T> ScanEnumerable<T>() => Console.ReadLine().Trim().Split(" ").Select(x => (T)Convert.ChangeType(x, typeof(T)));
        }
    }
}