Problem:
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Connected Components

Write a program which reads relations in a SNS (Social Network Service), and judges that given pairs of users are reachable each other through the network.

Input

In the first line, two integer $n$ and $m$ are given. $n$ is the number of users in the SNS and $m$ is the number of relations in the SNS. The users in the SNS are identified by IDs $0, 1, ..., n-1$.

In the following $m$ lines, the relations are given. Each relation is given by two integers $s$ and $t$ that represents $s$ and $t$ are friends (and reachable each other).

In the next line, the number of queries $q$ is given. In the following $q$ lines, $q$ queries are given respectively. Each query consists of two integers $s$ and $t$ separated by a space character.

Output

For each query, print "yes" if $t$ is reachable from $s$ through the social network, "no" otherwise.

Constraints

$2 \leq n \leq 100,000$

$0 \leq m \leq 100,000$

$1 \leq q \leq 10,000$

Sample Input

10 9
0 1
0 2
3 4
5 7
5 6
6 7
6 8
7 8
8 9
3
0 1
5 9
1 3

Sample Output

yes
yes
no

Solution in JAVA (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

static class QuickUnionUF {

    private int[] id;
    private int[] sz;

    QuickUnionUF(int N) {
        id = new int[N];
        sz = new int[N];
        for (int i = 0; i < N; i++) {
            id[i] = i;
            sz[i] = 0;
        }
    }

    private int root(int i) {
        while (i != id[i]){
            id[i] = id[id[i]]; // Path Compression: node points to grandparent
            i = id[i];
        }
        return i;
    }

    void union(int p, int q) {
        int i = root(p);
        int j = root(q);

        if (i == j) return;
        if (sz[i] < sz[j]){
            id[i] = j;
            sz[j] += sz[i];
        }
        else {
            id[j] = i;
            sz[i] += sz[j];
        }
    }

    boolean connected(int p, int q) {
        return root(p) == root(q);
    }
}



    public static void main(String[] args) {

        Scanner scanner = new Scanner(System.in);

        int N = scanner.nextInt();
        int M = scanner.nextInt();
//        QuickFindUF uf = new QuickFindUF(N);
        QuickUnionUF uf = new QuickUnionUF(N);

        // input
        for (int i = 0; i < M; i++) {
            int p = scanner.nextInt();
            int q = scanner.nextInt();
            uf.union(p, q);
        }

        // Query
        int Q = scanner.nextInt();
        for (int i = 0; i < Q; i++) {
            int p = scanner.nextInt();
            int q = scanner.nextInt();
            if (uf.connected(p,q))
                System.out.print("yes\n");
            else
                System.out.print("no\n");
        }
    }
}