Fragile network

import sys
def topological_sort_dfs(v):
    global result, G, visited, in_use, cyclic
    visited[v] = True
    in_use[v] = True

    for w in G[v]:
        if not visited[w]:
            topological_sort_dfs(w)
        elif in_use[w]:
            cyclic = True
            return

    result.append(v)
    in_use[v] = False


n = int(input())
sys.setrecursionlimit(n + 10)
result = []
visited = [False] * n
in_use = [False] * n
G = [[] for _ in range(n)]
cyclic = False
for _ in range(n - 1):
    a, b = map(int, input().split())
    G[a - 1].append(b - 1)

answer = []
for v in range(n - 1):
    if not visited[v]:
        topological_sort_dfs(v)

for i in range(n - 1):
    if (i + 1) % n not in G[i]:
        answer.append([i + 1, (i + 1) % n + 1])

print(len(answer))
for i in range(len(answer)):
    print(*answer[i])

Test 1

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Test 2

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Test 3

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Test 4

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Test 5

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Test 6

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Test 7

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Test 8

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Test 9

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Test 10

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Test 11

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Test 12

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Test 13

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Test 14

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Test 15

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Test 16

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Test 17

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Test 18

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Test 19

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Test 20

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Test 21

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