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

def input():
    return sys.stdin.readline()[:-1]

def main():
    N = int(input())
    T = []
    G = [[] for k in range(N+1)]
    for k in range(N-1):
        a, b = map(int,input().split())
        G[a].append(b)
        G[b].append(a)
        T.append(str(a)+"0"+str(b))

    V = [0 for k in range(N+1)]
    C = [set() for k in range(N+1)]
    ans = dict()
    m = 0
    V[1] = 1
    Q = [1]
    while len(Q) > 0:
        ima = Q.pop()
        for tsugi in G[ima]:
            t = 1
            if V[tsugi] == 0:
                V[tsugi] = 1
                while t in C[ima] or t in C[tsugi]:
                    t += 1
                m = max(m,t)
                C[ima].add(t)
                C[tsugi].add(t)
                ans[str(ima)+"0"+str(tsugi)] = t
                Q.append(tsugi)
    print(m)
    for e in T:
        print(ans[e])

if __name__ == '__main__':
    main()


Fixed submission:
import sys, math

def input():
    return sys.stdin.readline()[:-1]

def main():
    N = int(input())
    T = []
    G = [[] for k in range(N+1)]
    for k in range(N-1):
        a, b = map(int,input().split())
        G[a].append(b)
        G[b].append(a)
        T.append(str(a)+"0"+str(b))

    V = [0 for k in range(N+1)]
    C = [set() for k in range(N+1)]
    ans = dict()
    m = 0
    V[1] = 1
    Q = [1]
    while len(Q) > 0:
        ima = Q.pop()
        t = 1
        for tsugi in G[ima]:
            if V[tsugi] == 0:
                V[tsugi] = 1
                while t in C[ima] or t in C[tsugi]:
                    t += 1
                m = max(m,t)
                C[ima].add(t)
                C[tsugi].add(t)
                ans[str(ima)+"0"+str(tsugi)] = t
                Q.append(tsugi)
    print(m)
    for e in T:
        print(ans[e])

if __name__ == '__main__':
    main()

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

def input():
    return sys.stdin.readline()[:-1]

def main():
    N = int(input())
    T = []
    G = [[] for k in range(N+1)]
    for k in range(N-1):
        a, b = map(int,input().split())
        G[a].append(b)
        G[b].append(a)
        T.append(str(a)+"0"+str(b))

    V = [0 for k in range(N+1)]
    C = [set() for k in range(N+1)]
    ans = dict()
    m = 0
    V[1] = 1
    Q = [1]
    while len(Q) > 0:
        ima = Q.pop()
        for tsugi in G[ima]:
            if V[tsugi] == 0:
                V[tsugi] = 1
                t = 1
                while t in C[ima] or t in C[tsugi]:
                    t += 1
                m = max(m,t)
                C[ima].add(t)
                C[tsugi].add(t)
                ans[str(ima)+"0"+str(tsugi)] = t
                Q.append(tsugi)
    print(m)
    for e in T:
        print(ans[e])

if __name__ == '__main__':
    main()


Fixed submission:
import sys, math

def input():
    return sys.stdin.readline()[:-1]

def main():
    N = int(input())
    T = []
    G = [[] for k in range(N+1)]
    for k in range(N-1):
        a, b = map(int,input().split())
        G[a].append(b)
        G[b].append(a)
        T.append(str(a)+"0"+str(b))

    V = [0 for k in range(N+1)]
    C = [set() for k in range(N+1)]
    ans = dict()
    m = 0
    V[1] = 1
    Q = [1]
    while len(Q) > 0:
        ima = Q.pop()
        t = 1
        for tsugi in G[ima]:
            if V[tsugi] == 0:
                V[tsugi] = 1
                while t in C[ima] or t in C[tsugi]:
                    t += 1
                m = max(m,t)
                C[ima].add(t)
                C[tsugi].add(t)
                ans[str(ima)+"0"+str(tsugi)] = t
                Q.append(tsugi)
    print(m)
    for e in T:
        print(ans[e])

if __name__ == '__main__':
    main()