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 Python3 (judge verdict: Accepted)

import sys
from collections import defaultdict

def main():
    lines = sys.stdin.readlines()
    n, m = map(int, lines[0].split())
    relation_lines = lines[1:1+m]

    relations = defaultdict(list)

    for idx, relation_line in enumerate(relation_lines):
        s, t = relation_line.split()
        relations[s].append(t)
        relations[t].append(s)

    group = {}
    for key in relations.keys():
        group[key] = -1
    group_num = 0

    # assign a group number for ids
    for key, val in relations.items():
        if group[key] != -1:
            continue

        group[key] = group_num
        group_num += 1

        group_no = group[key]
        friends = [key]

        while len(friends) != 0:
            n_fs = relations[friends.pop()]
            for n_f in n_fs:
                if group[n_f] == -1:
                    group[n_f] = group_no
                    friends.append(n_f)

    q = int(lines[1+m])
    question_lines = lines[1+m+1:]
    answers = [None] * q
    for i, question in enumerate(question_lines):
        s, t = question.split()

        if s not in group or t not in group:
            answers[i] = 'no'
            continue
        elif group[s] == group[t]:
            answers[i] = 'yes'
        else:
            answers[i] = 'no'

    # answer
    [print(ans) for ans in answers]
    return

main()