Buggy python submission (verdict: Time Limit Exceeded):
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**5)

def main():

    """
    # color: 親と自らを繋ぐ辺の色
    # now: 現在地
    """
    def dfs(color,now):
        # 現在地が葉のとき
        if not now in a:
            return

        # 現在地から伸びる辺のインデックス
        index = [i for i in range(N-1) if now == a[i]]

        # 子ノードに伸びる辺を色塗り
        number = 1
        for i in index:
            if number == color:
                number += 1
            K[i] = number
            # 子ノードで色塗り開始
            dfs(number, b[i])
            number += 1

    N = int(input())
    a = [0] * (N-1)
    b = [0] * (N-1)
    for i in range(N-1):
        a[i],b[i] = map(int,input().split())
    # 辺の色
    K = [0] * (N-1)
    dfs(0,min(a))
    print(len(set(K)))
    for i in K:
        print(i)

if __name__ == '__main__':
    main()


Fixed submission:
import sys
input = sys.stdin.readline
 
N = int(input())
AB = [[int(i) for i in input().split()] for _ in range(N-1)]

# graph[i]: 頂点iの親と子の集合
graph = [[] for _ in range(N+1)]
for a,b in AB:
    graph[a].append(b)
    graph[b].append(a)

# 根
root = 1
# parent[i]: 頂点iの親
parent = [0]*(N+1)
# トポロジカル順序
order = []
# 未探索の頂点
stack = [root]

# dfsでparentを求める
while stack:
    # n: 探索する頂点
    n = stack.pop()
    order.append(n)
    for j in graph[n]:
        # jがnの親の場合
        if j == parent[n]:
            continue
        parent[j] = n
        stack.append(j)

# color[i]: 頂点iと親を繋ぐ辺の色
color = [-1] * (N+1)
# dfsで色を塗る
for i in order:
    # 既に使用した色
    ng = color[i]
    # 色
    c = 1
    for j in graph[i]:
        # jがiの親の場合(塗装済みなのでcontinue)
        if j == parent[i]:
            continue
        if c == ng:
            c += 1
        # 頂点iと頂点jの辺に色を塗る
        color[j] = c
        c += 1

# 入力順に辺の色を出力する
answer = [color[a] if parent[a]==b else color[b] for a,b in AB]
print(max(answer))
print("\n".join(map(str,answer)))

Buggy python submission (verdict: Time Limit Exceeded):
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**5)

def main():

    """
    # color: 親と自らを繋ぐ辺の色
    # now: 現在地
    """
    def dfs(color,now):
        # 現在地が葉のとき
        if not now in a:
            return

        # 現在地から伸びる辺のインデックス
        index = [i for i in range(N-1) if now == a[i]]

        # 子ノードに伸びる辺を色塗り
        number = 1
        for i in range(len(index)):
            if number == color:
                number += 1
            K[index[i]] = number
            # 子ノードで色塗り開始
            dfs(number, b[index[i]])
            number += 1

    N = int(input())
    a = [0] * (N-1)
    b = [0] * (N-1)
    for i in range(N-1):
        a[i],b[i] = map(int,input().split())
    # 辺の色
    K = [0] * (N-1)
    dfs(0,min(a))
    print(len(set(K)))
    for i in K:
        print(i)

if __name__ == '__main__':
    main()

Fixed submission:
import sys
input = sys.stdin.readline
 
N = int(input())
AB = [[int(i) for i in input().split()] for _ in range(N-1)]

# graph[i]: 頂点iの親と子の集合
graph = [[] for _ in range(N+1)]
for a,b in AB:
    graph[a].append(b)
    graph[b].append(a)

# 根
root = 1
# parent[i]: 頂点iの親
parent = [0]*(N+1)
# トポロジカル順序
order = []
# 未探索の頂点
stack = [root]

# dfsでparentを求める
while stack:
    # n: 探索する頂点
    n = stack.pop()
    order.append(n)
    for j in graph[n]:
        # jがnの親の場合
        if j == parent[n]:
            continue
        parent[j] = n
        stack.append(j)

# color[i]: 頂点iと親を繋ぐ辺の色
color = [-1] * (N+1)
# dfsで色を塗る
for i in order:
    # 既に使用した色
    ng = color[i]
    # 色
    c = 1
    for j in graph[i]:
        # jがiの親の場合(塗装済みなのでcontinue)
        if j == parent[i]:
            continue
        if c == ng:
            c += 1
        # 頂点iと頂点jの辺に色を塗る
        color[j] = c
        c += 1

# 入力順に辺の色を出力する
answer = [color[a] if parent[a]==b else color[b] for a,b in AB]
print(max(answer))
print("\n".join(map(str,answer)))

Buggy python submission (verdict: Runtime Error):
import sys
input = sys.stdin.readline

def main():

    """
    # color: 親と自らを繋ぐ辺の色
    # now: 現在地
    """
    def dfs(color,now):
        # 現在地が葉のとき
        if not now in a:
            return

        # 現在地から伸びる辺のインデックス
        index = [i for i in range(N-1) if now == a[i]]

        # 子ノードに伸びる辺を色塗り
        number = 1
        for i in range(len(index)):
            if number == color:
                number += 1
            K[index[i]] = number
            # 子ノードで色塗り開始
            dfs(number, b[index[i]])
            number += 1

    N = int(input())
    a = [0] * (N-1)
    b = [0] * (N-1)
    for i in range(N-1):
        a[i],b[i] = map(int,input().split())
    # 辺の色
    K = [0] * (N-1)
    dfs(0,1)
    print(len(set(K)))
    for i in K:
        print(i)

if __name__ == '__main__':
    main()

Fixed submission:
import sys
input = sys.stdin.readline
 
N = int(input())
AB = [[int(i) for i in input().split()] for _ in range(N-1)]

# graph[i]: 頂点iの親と子の集合
graph = [[] for _ in range(N+1)]
for a,b in AB:
    graph[a].append(b)
    graph[b].append(a)

# 根
root = 1
# parent[i]: 頂点iの親
parent = [0]*(N+1)
# トポロジカル順序
order = []
# 未探索の頂点
stack = [root]

# dfsでparentを求める
while stack:
    # n: 探索する頂点
    n = stack.pop()
    order.append(n)
    for j in graph[n]:
        # jがnの親の場合
        if j == parent[n]:
            continue
        parent[j] = n
        stack.append(j)

# color[i]: 頂点iと親を繋ぐ辺の色
color = [-1] * (N+1)
# dfsで色を塗る
for i in order:
    # 既に使用した色
    ng = color[i]
    # 色
    c = 1
    for j in graph[i]:
        # jがiの親の場合(塗装済みなのでcontinue)
        if j == parent[i]:
            continue
        if c == ng:
            c += 1
        # 頂点iと頂点jの辺に色を塗る
        color[j] = c
        c += 1

# 入力順に辺の色を出力する
answer = [color[a] if parent[a]==b else color[b] for a,b in AB]
print(max(answer))
print("\n".join(map(str,answer)))