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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyScanner in = new MyScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        C solver = new C();
        solver.solve(1, in, out);
        out.close();
    }

    static class C {
        int N;
        int M;

        public void solve(int testNumber, MyScanner in, PrintWriter out) {
            N = in.Int();
            M = in.Int();
            DSU dsu = new DSU(N);
            for (int i = 0; i < M; i++) {
                int A = in.Int() - 1;
                int B = in.Int() - 1;
                dsu.merge(A, B);
            }
            out.println(dsu.groups().size() - 1);
        }

    }

    static class DSU {
        private int n;
        private int[] parentOrSize;

        public DSU(int n) {
            this.n = n;
            this.parentOrSize = new int[n];
            Arrays.fill(parentOrSize, -1);
        }

        int merge(int a, int b) {
            if (!(0 <= a && a < n))
                throw new IndexOutOfBoundsException("a=" + a);
            if (!(0 <= b && b < n))
                throw new IndexOutOfBoundsException("b=" + b);

            int x = leader(a);
            int y = leader(b);
            if (x == y) return x;
            if (-parentOrSize[x] < -parentOrSize[y]) {
                int tmp = x;
                x = y;
                y = tmp;
            }
            parentOrSize[x] += parentOrSize[y];
            parentOrSize[y] = x;
            return x;
        }

        int leader(int a) {
            if (parentOrSize[a] < 0) {
                return a;
            } else {
                parentOrSize[a] = leader(parentOrSize[a]);
                return parentOrSize[a];
            }
        }

        ArrayList<ArrayList<Integer>> groups() {
            int[] leaderBuf = new int[n];
            int[] groupSize = new int[n];
            for (int i = 0; i < n; i++) {
                leaderBuf[i] = leader(i);
                groupSize[leaderBuf[i]]++;
            }
            ArrayList<ArrayList<Integer>> result = new ArrayList<>(n);
            for (int i = 0; i < n; i++) {
                result.add(new ArrayList<>(groupSize[i]));
            }
            for (int i = 0; i < n; i++) {
                result.get(leaderBuf[i]).add(i);
            }
            result.removeIf(ArrayList::isEmpty);
            return result;
        }

    }

    static class MyScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public MyScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String rl = in.readLine();
                    if (rl == null) {
                        return null;
                    }
                    st = new StringTokenizer(rl);
                } catch (IOException e) {
                    return null;
                }
            }
            return st.nextToken();
        }

        public int Int() {
            return Integer.parseInt(next());
        }

    }
}