Buggy python submission (verdict: Runtime Error):
from collections import defaultdict
vertices, edges = map(int, input().split(" "))
connect = defaultdict(set)
for i in range(vertices):
    a, b = map(int, input().split(" "))
    connect[a] |= {b}
    connect[b] |= {a}

answer = 0
queue = [[set(), 1]]
while queue:
    visited, now = queue.pop()
    visited |= {now}
    # print(visited, now, need_visit)
    if len(visited) == vertices:
        answer += 1
    else:
        for conn in connect[now]:
            if conn not in visited:
                queue.append([visited | {conn}, conn])
        # print(visited, now, need_visit)

print(answer)

Fixed submission:
from collections import defaultdict
vertices, edges = map(int, input().split(" "))
connect = defaultdict(set)
for i in range(edges):
    a, b = map(int, input().split(" "))
    connect[a] |= {b}
    connect[b] |= {a}

answer = 0
queue = [[set(), 1]]
while queue:
    visited, now = queue.pop()
    visited |= {now}
    # print(visited, now, need_visit)
    if len(visited) == vertices:
        answer += 1
    else:
        for conn in connect[now]:
            if conn not in visited:
                queue.append([visited | {conn}, conn])
        # print(visited, now, need_visit)

print(answer)

Buggy python submission (verdict: Runtime Error):
from collections import defaultdict
vertices, edges = map(int, input().split(" "))
connect = defaultdict(set)
for i in range(vertices):
    a, b = map(int, input().split(" "))
    connect[a] |= {b}
    connect[b] |= {a}

comb_answers = defaultdict(int)

def bfs(start, connect, visited):
    queue = [start]
    while queue:
        here = queue.pop()
        visited |= {here}
        for conn in connect[here]:
            if conn not in visited:
                visited |= {conn}
                queue.append(conn)
    return visited
    
for e in connect[1]:
    need_visit = bfs(e, connect, {1})
    temp_answer = 0
    queue = [[{1}, e]]
    while queue:
        visited, now = queue.pop()
        visited |= {now}
        # print(visited, now, need_visit)
        for conn in connect[now]:
            if conn not in visited:
                queue.append([visited | {conn}, conn])
        if visited == need_visit:
            for c in comb_answers.keys():
                if c in visited:
                    comb_answers[c] += 1
                    break
            else:
                comb_answers[e] += 1
            # print(visited, now, need_visit)
answer = 1
for v in comb_answers.values():
    answer *= v

print(answer)

Fixed submission:
from collections import defaultdict
vertices, edges = map(int, input().split(" "))
connect = defaultdict(set)
for i in range(edges):
    a, b = map(int, input().split(" "))
    connect[a] |= {b}
    connect[b] |= {a}

answer = 0
queue = [[set(), 1]]
while queue:
    visited, now = queue.pop()
    visited |= {now}
    # print(visited, now, need_visit)
    if len(visited) == vertices:
        answer += 1
    else:
        for conn in connect[now]:
            if conn not in visited:
                queue.append([visited | {conn}, conn])
        # print(visited, now, need_visit)

print(answer)

Buggy python submission (verdict: Runtime Error):
from collections import defaultdict
vertices, edges = map(int, input().split(" "))
connect = defaultdict(set)
for i in range(vertices):
    a, b = map(int, input().split(" "))
    connect[a] |= {b}
    connect[b] |= {a}

answer = 0
queue = [[set(), 1]]
while queue:
    visited, now = queue.pop()
    visited |= {now}
    if len(visited) == vertices:
        answer += 1
        continue
    for conn in connect[now]:
        if conn not in visited:
            queue.append([visited | {conn}, conn])
print(answer)

Fixed submission:
from collections import defaultdict
vertices, edges = map(int, input().split(" "))
connect = defaultdict(set)
for i in range(edges):
    a, b = map(int, input().split(" "))
    connect[a] |= {b}
    connect[b] |= {a}

answer = 0
queue = [[set(), 1]]
while queue:
    visited, now = queue.pop()
    visited |= {now}
    # print(visited, now, need_visit)
    if len(visited) == vertices:
        answer += 1
    else:
        for conn in connect[now]:
            if conn not in visited:
                queue.append([visited | {conn}, conn])
        # print(visited, now, need_visit)

print(answer)