Buggy python submission (verdict: Time Limit Exceeded):
import sys
from collections import defaultdict
sys.setrecursionlimit(10**8)

N = int(input())
graph = [[] for _ in range(N)]
numOfEdges = [0 for _ in range(N)]
visited = [0 for _ in range(N)]
color = [[-1 for _ in range(N)] for _ in range(N)]
edges = defaultdict(int)

for i in range(1, N):
    a, b = map(int, input().split())
    a -= 1; b -= 1;
    numOfEdges[a] += 1
    numOfEdges[b] += 1
    edges[(a, b)] = 0
    graph[a].append(b)
    graph[b].append(a)

def dfs(prev, now, col):
    if visited[now]:
        return
    visited[now] = 1
    i = 1
    for adj in graph[now]:
        if adj == prev:
            continue
        if now < adj:
            edges[(now, adj)] = col + i
        else:
            edges[(adj, now)] = col + i
        dfs(now, adj, col+i)
        i += 1

dfs(-1, 0, 1)
maxColor = max(numOfEdges)
print(maxColor)

for k, i in edges.items():
    e = i % maxColor
    if e:
        print(e)
    else:
        print(maxColor)


Fixed submission:
import sys
from collections import defaultdict
sys.setrecursionlimit(10**8)

N = int(input())
graph = [[] for _ in range(N)]
numOfEdges = [0 for _ in range(N)]
visited = [0 for _ in range(N)]
edges = defaultdict(int)

for i in range(1, N):
    a, b = map(int, input().split())
    a -= 1; b -= 1;
    numOfEdges[a] += 1
    numOfEdges[b] += 1
    edges[(a, b)] = 0
    graph[a].append(b)
    graph[b].append(a)

def dfs(prev, now, col):
    if visited[now]:
        return
    visited[now] = 1
    i = 1
    for adj in graph[now]:
        if adj == prev:
            continue
        if now < adj:
            edges[(now, adj)] = col + i
        else:
            edges[(adj, now)] = col + i
        dfs(now, adj, col+i)
        i += 1

dfs(-1, 0, 1)
maxColor = max(numOfEdges)
print(maxColor)

for k, i in edges.items():
    e = i % maxColor
    if e:
        print(e)
    else:
        print(maxColor)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**8)

N = int(input())
graph = [[] for _ in range(N)]
numOfEdges = [0 for _ in range(N)]
visited = [0 for _ in range(N)]
color = [[-1 for _ in range(N)] for _ in range(N)]
edges = []

for i in range(1, N):
    a, b = map(int, input().split())
    a -= 1; b -= 1;
    edges.append((a, b))
    numOfEdges[a] += 1
    numOfEdges[b] += 1
    graph[a].append(b)
    graph[b].append(a)

def dfs(prev, now, col):
    if visited[now]:
        return
    visited[now] = 1
    i = 1
    for adj in graph[now]:
        if adj == prev:
            continue
        color[now][adj] = col + i
        color[adj][now] = col + i
        dfs(now, adj, col+i)
        i += 1

dfs(-1, 0, 1)
maxColor = max(numOfEdges)
print(maxColor)

for e in edges:
    a, b = e
    c = color[a][b] % maxColor
    if c == 0:
        print(maxColor)
    else:
        print(c)


Fixed submission:
import sys
from collections import defaultdict
sys.setrecursionlimit(10**8)

N = int(input())
graph = [[] for _ in range(N)]
numOfEdges = [0 for _ in range(N)]
visited = [0 for _ in range(N)]
edges = defaultdict(int)

for i in range(1, N):
    a, b = map(int, input().split())
    a -= 1; b -= 1;
    numOfEdges[a] += 1
    numOfEdges[b] += 1
    edges[(a, b)] = 0
    graph[a].append(b)
    graph[b].append(a)

def dfs(prev, now, col):
    if visited[now]:
        return
    visited[now] = 1
    i = 1
    for adj in graph[now]:
        if adj == prev:
            continue
        if now < adj:
            edges[(now, adj)] = col + i
        else:
            edges[(adj, now)] = col + i
        dfs(now, adj, col+i)
        i += 1

dfs(-1, 0, 1)
maxColor = max(numOfEdges)
print(maxColor)

for k, i in edges.items():
    e = i % maxColor
    if e:
        print(e)
    else:
        print(maxColor)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**8)

N = int(input())
graph = [[] for _ in range(N)]
numOfEdges = [0 for _ in range(N)]
visited = [0 for _ in range(N)]
color = [[-1 for _ in range(N)] for _ in range(N)]
edges = []

for i in range(1, N):
    a, b = map(int, input().split())
    a -= 1; b -= 1;
    edges.append((a, b))
    graph[a].append(b)
    graph[b].append(a)

def dfs(prev, now, col):
    if visited[now]:
        return
    visited[now] = 1
    numOfEdges[now] = len(graph[now])
    i = 1
    for adj in graph[now]:
        if adj == prev:
            continue
        color[now][adj] = col + i
        color[adj][now] = col + i
        dfs(now, adj, col+i)
        i += 1

dfs(-1, 0, 1)
maxColor = max(numOfEdges)
print(maxColor)

for e in edges:
    a, b = e
    c = color[a][b] % maxColor
    if c == 0:
        print(maxColor)
    else:
        print(c)


Fixed submission:
import sys
from collections import defaultdict
sys.setrecursionlimit(10**8)

N = int(input())
graph = [[] for _ in range(N)]
numOfEdges = [0 for _ in range(N)]
visited = [0 for _ in range(N)]
edges = defaultdict(int)

for i in range(1, N):
    a, b = map(int, input().split())
    a -= 1; b -= 1;
    numOfEdges[a] += 1
    numOfEdges[b] += 1
    edges[(a, b)] = 0
    graph[a].append(b)
    graph[b].append(a)

def dfs(prev, now, col):
    if visited[now]:
        return
    visited[now] = 1
    i = 1
    for adj in graph[now]:
        if adj == prev:
            continue
        if now < adj:
            edges[(now, adj)] = col + i
        else:
            edges[(adj, now)] = col + i
        dfs(now, adj, col+i)
        i += 1

dfs(-1, 0, 1)
maxColor = max(numOfEdges)
print(maxColor)

for k, i in edges.items():
    e = i % maxColor
    if e:
        print(e)
    else:
        print(maxColor)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**8)

N = int(input())
graph = [[] for _ in range(N)]
numOfEdges = [0 for _ in range(N)]
visited = [0 for _ in range(N)]
color = [[-1 for _ in range(N)] for _ in range(N)]
edges = []

for i in range(1, N):
    a, b = map(int, input().split())
    a -= 1; b -= 1;
    edges.append((a, b))
    graph[a].append(b)
    graph[b].append(a)

def dfs(prev, now, col):
    if visited[now]:
        return
    visited[now] = 1
    numOfEdges[now] = len(graph[now])
    i = 1
    for adj in graph[now]:
        if adj == prev:
            continue
        color[now][adj] = col + i
        color[adj][now] = col + i
        dfs(now, adj, col+i)
        i += 1

dfs(-1, 0, 1)
maxColor = max(numOfEdges)
print(maxColor)

for e in edges:
    a, b = e
    c = color[a][b] % maxColor
    if c == 0:
        print(maxColor)
    else:
        print(c)


Fixed submission:
import sys
from collections import defaultdict
sys.setrecursionlimit(10**8)

N = int(input())
graph = [[] for _ in range(N)]
numOfEdges = [0 for _ in range(N)]
visited = [0 for _ in range(N)]
edges = defaultdict(int)

for i in range(1, N):
    a, b = map(int, input().split())
    a -= 1; b -= 1;
    numOfEdges[a] += 1
    numOfEdges[b] += 1
    edges[(a, b)] = 0
    graph[a].append(b)
    graph[b].append(a)

def dfs(prev, now, col):
    if visited[now]:
        return
    visited[now] = 1
    i = 1
    for adj in graph[now]:
        if adj == prev:
            continue
        if now < adj:
            edges[(now, adj)] = col + i
        else:
            edges[(adj, now)] = col + i
        dfs(now, adj, col+i)
        i += 1

dfs(-1, 0, 1)
maxColor = max(numOfEdges)
print(maxColor)

for k, i in edges.items():
    e = i % maxColor
    if e:
        print(e)
    else:
        print(maxColor)

Buggy python submission (verdict: Runtime Error):
N = int(input())
graph = [[] for _ in range(N)]
numOfEdges = [0 for _ in range(N)]
visited = [0 for _ in range(N)]
edges = []

for i in range(1, N):
    a, b = map(int, input().split())
    a -= 1; b -= 1;
    edges.append((a, b))
    graph[a].append(b)
    graph[b].append(a)

def dfs(prev, now):
    if visited[now]:
        return
    visited[now] = 1
    numOfEdges[now] = len(graph[now])
    for adj in graph[now]:
        if adj == prev:
            continue
        dfs(now, adj)

dfs(-1, 0)
maxColor = max(numOfEdges)
print(maxColor)

for e in edges:
    a, b = e
    x, y = numOfEdges[a], numOfEdges[b]

    print(max(x, y))

    if x > y:
        numOfEdges[a] -= 1
    elif y > x:
        numOfEdges[b] -= 1
    else:
        numOfEdges[a] -= 1
        numOfEdges[b] -= 1


Fixed submission:
import sys
from collections import defaultdict
sys.setrecursionlimit(10**8)

N = int(input())
graph = [[] for _ in range(N)]
numOfEdges = [0 for _ in range(N)]
visited = [0 for _ in range(N)]
edges = defaultdict(int)

for i in range(1, N):
    a, b = map(int, input().split())
    a -= 1; b -= 1;
    numOfEdges[a] += 1
    numOfEdges[b] += 1
    edges[(a, b)] = 0
    graph[a].append(b)
    graph[b].append(a)

def dfs(prev, now, col):
    if visited[now]:
        return
    visited[now] = 1
    i = 1
    for adj in graph[now]:
        if adj == prev:
            continue
        if now < adj:
            edges[(now, adj)] = col + i
        else:
            edges[(adj, now)] = col + i
        dfs(now, adj, col+i)
        i += 1

dfs(-1, 0, 1)
maxColor = max(numOfEdges)
print(maxColor)

for k, i in edges.items():
    e = i % maxColor
    if e:
        print(e)
    else:
        print(maxColor)