Buggy python submission (verdict: Time Limit Exceeded):
import math

class UnionFind(): # 0インデックス
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        '''
        xとyは-=1して使う
        '''
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

if __name__ == "__main__":
    N, M = map(int, input().split()) # N人、M個の関係
    union_find = UnionFind(N)
    for _ in range(M):
        A, B = map(int, input().split())
        A -= 1
        B -= 1
        union_find.union(A, B)

    group_dict = union_find.all_group_members()

    answer = 0
    count = 0
    for v in group_dict.values():
        answer = max(answer, len(v))
        count + 1
        if count >=  math.log2(N) + 1:
            break
    print(answer)
   

Fixed submission:
import math

class UnionFind(): # 0インデックス
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        '''
        xとyは-=1して使う
        '''
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

if __name__ == "__main__":
    N, M = map(int, input().split()) # N人、M個の関係
    union_find = UnionFind(N)
    for _ in range(M):
        A, B = map(int, input().split())
        A -= 1
        B -= 1
        union_find.union(A, B)

    answer = 0
    for i in range(N):
        answer = max(answer, union_find.size(i))

    print(answer)

Buggy python submission (verdict: Time Limit Exceeded):
class UnionFind(): # 0インデックス
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        '''
        xとyは-=1して使う
        '''
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

if __name__ == "__main__":
    N, M = map(int, input().split()) # N人、M個の関係
    union_find = UnionFind(N)
    for _ in range(M):
        A, B = map(int, input().split())
        A -= 1
        B -= 1
        union_find.union(A, B)

    group_dict = union_find.all_group_members()
    answer = 0
    for v in group_dict.values():
        answer = max(answer, len(v))
        
    print(answer)

Fixed submission:
import math

class UnionFind(): # 0インデックス
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        '''
        xとyは-=1して使う
        '''
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

if __name__ == "__main__":
    N, M = map(int, input().split()) # N人、M個の関係
    union_find = UnionFind(N)
    for _ in range(M):
        A, B = map(int, input().split())
        A -= 1
        B -= 1
        union_find.union(A, B)

    answer = 0
    for i in range(N):
        answer = max(answer, union_find.size(i))

    print(answer)

Buggy python submission (verdict: Time Limit Exceeded):
class UnionFind(): # 0インデックス
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        '''
        xとyは-=1して使う
        '''
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

if __name__ == "__main__":
    N, M = map(int, input().split()) # N人、M個の関係
    union_find = UnionFind(N)
    for _ in range(M):
        A, B = map(int, input().split())
        A -= 1
        B -= 1
        union_find.union(A, B)

    group_dict = union_find.all_group_members()
    answer = 0
    for v in group_dict.values():
        answer = max(answer, len(v))
        
    print(answer)

Fixed submission:
import math

class UnionFind(): # 0インデックス
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        '''
        xとyは-=1して使う
        '''
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

if __name__ == "__main__":
    N, M = map(int, input().split()) # N人、M個の関係
    union_find = UnionFind(N)
    for _ in range(M):
        A, B = map(int, input().split())
        A -= 1
        B -= 1
        union_find.union(A, B)

    answer = 0
    for i in range(N):
        answer = max(answer, union_find.size(i))

    print(answer)