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.*;
import java.util.*;

public class Main {
    static MyReader in = new MyReader();

    public static void main(String[] args) {
        int N = in.i();
        int M = in.i();

        UnionFind uf = new UnionFind(N);
        for (int i = 0; i < M; i++) {
            uf.unite(in.i() - 1, in.i() - 1);
        }
        System.out.println(uf.ncc - 1);
    }
}

class UnionFind {
    private final int N;
    int[] parent;
    int[] rank;
    int[] size;
    int ncc;

    UnionFind(int n) {
        N = n;
        parent = new int[N];
        Arrays.setAll(parent, i -> i);
        size = new int[N];
        Arrays.fill(size, 1);
        rank = new int[N];
        ncc = n;
    }

    boolean isRoot(int x) {
        return x == parent[x];
    }

    int root(int x) {
        return isRoot(x) ? x : (parent[x] = root(parent[x]));
    }

    boolean same(int x, int y){
        return root(x) == root(y);
    }

    int size(int x) {
        return size[root(x)];
    }

    void unite(int x, int y){
        x = root(x);
        y = root(y);
        if (x != y) {
            if (rank[x] < rank[y]) {
                parent[x] = y;
                size[y] += size[x];
            } else {
                parent[y] = x;
                size[x] += size[y];
                if (rank[x] == rank[y]) {
                    rank[x]++;
                }
            }
            ncc--;
        }
    }

    int ncc() {
        return ncc;
    }
}

class MyReader extends BufferedReader {
    char[] cbuf = new char[1024];
    int head = 0;
    int tail = 0;

    MyReader() {
        super(new InputStreamReader(System.in));
    }

    char next() {
        if (head == tail) {
            try {
                tail = super.read(cbuf, 0, cbuf.length);
            } catch (IOException e) {
                e.printStackTrace();
            }
            head = 0;
        }
        return cbuf[head++];
    }

    int i() {
        int k = next() - '0';
        boolean minus = k == -3;
        int n = minus ? 0 : k;
        while (0 <= (k = next() - '0') && k <= 9) n = 10 * n + k;
        return minus ? -n : n;
    }

    int[] ii(final int N) {
        int[] a = new int[N];
        for (int j = 0; j < a.length; j++) a[j] = i();
        return a;
    }

    long l() {
        int k = next() - '0';
        boolean minus = k == -3;
        long n = minus ? 0 : k;
        while (0 <= (k = next() - '0') && k <= 9) n = 10 * n + k;
        return minus ? -n : n;
    }

    char[] s(final int N) {
        char[] s = new char[N];
        for (int i = 0; i < N; i++) {
            s[i] = next();
        }
        next();
        return s;
    }

    public int read(char[] cbuf) {
        int i;
        char c;
        for (i = 0; (c = next()) != ' ' && c != '\n'; i++) cbuf[i] = c;
        return i;
    }

    public String readLine() {
        try {
            return super.readLine();
        } catch (IOException e) {
            return null;
        }
    }
}