Buggy python submission (verdict: Runtime Error):
import sys
sys.setrecursionlimit(10**6)
n = int(input())
edges = []
nodes = [[] for _ in range(n)]
i: int
for i in range(n - 1):
    a, b = map(int, input().split())
    a, b = a - 1, b - 1
    edges.append({a: b, b: a, 'color': 0})
    nodes[a].append(i)
    nodes[b].append(i)


def paint_edge(edge, node, root=False):
    if not root:
        color = edges[edge]["color"]
        i = 1
        max_color = len(nodes[node])
        for n_edge in nodes[node]:
            if n_edge != edge:
                if i == color:
                    i += 1
                edges[n_edge]["color"] = i
                max_color = max(max_color, paint_edge(n_edge, edges[n_edge][node]))
                i += 1
        return max_color

    else:
        connect = len(nodes[node])
        max_color = connect
        for i in range(connect):
            n_edge = nodes[node][i]
            edges[n_edge]["color"] = i + 1
            max_color = max(max_color, paint_edge(n_edge, edges[n_edge][node]))
        return max_color


print(paint_edge(-1, 0, True))
for i in range(n - 1):
    print(edges[i]["color"])


Fixed submission:
import sys
sys.setrecursionlimit(1000000)
n = int(input())
edges = []
nodes = [[] for _ in range(n)]
for i in range(n - 1):
    a, b = map(int, input().split())
    a, b = a - 1, b - 1
    edges.append({a: b, b: a, 'color': 0})
    nodes[a].append(i)
    nodes[b].append(i)
 
 
def paint_edge(edge, node, root=False):
    if not root:
        color = edges[edge]["color"]
        i = 1
        max_color = len(nodes[node])
        for n_edge in nodes[node]:
            if n_edge != edge:
                if i == color:
                    i += 1
                edges[n_edge]["color"] = i
                max_color = max(max_color, paint_edge(n_edge, edges[n_edge][node]))
                i += 1
        return max_color
 
    else:
        connect = len(nodes[node])
        max_color = connect
        for i in range(connect):
            n_edge = nodes[node][i]
            edges[n_edge]["color"] = i + 1
            max_color = max(max_color, paint_edge(n_edge, edges[n_edge][node]))
        return max_color
 
 
print(paint_edge(-1, 0, True))
for i in range(n - 1):
    print(edges[i]["color"])

Buggy python submission (verdict: Runtime Error):
import sys 
sys.setrecursionlimit(10**7)
n = int(input())
edges = []
nodes = [[] for _ in range(n)]
i: int
for i in range(n - 1):
    a, b = map(int, input().split())
    a, b = a - 1, b - 1
    edges.append({a: b, b: a, 'color': 0})
    nodes[a].append(i)
    nodes[b].append(i)


def paint_edge(edge, node, root=False):
    if not root:
        color = edges[edge]["color"]
        i = 1
        max_color = len(nodes[node])
        for n_edge in nodes[node]:
            if n_edge != edge:
                if i == color:
                    i += 1
                edges[n_edge]["color"] = i
                max_color = max(max_color, paint_edge(n_edge, edges[n_edge][node]))
                i += 1
        return max_color

    else:
        connect = len(nodes[node])
        max_color = connect
        for i in range(connect):
            n_edge = nodes[node][i]
            edges[n_edge]["color"] = i + 1
            max_color = max(max_color, paint_edge(n_edge, edges[n_edge][node]))
        return max_color


print(paint_edge(-1, 0, True))
for i in range(n - 1):
    print(edges[i]["color"])


Fixed submission:
import sys
sys.setrecursionlimit(1000000)
n = int(input())
edges = []
nodes = [[] for _ in range(n)]
for i in range(n - 1):
    a, b = map(int, input().split())
    a, b = a - 1, b - 1
    edges.append({a: b, b: a, 'color': 0})
    nodes[a].append(i)
    nodes[b].append(i)
 
 
def paint_edge(edge, node, root=False):
    if not root:
        color = edges[edge]["color"]
        i = 1
        max_color = len(nodes[node])
        for n_edge in nodes[node]:
            if n_edge != edge:
                if i == color:
                    i += 1
                edges[n_edge]["color"] = i
                max_color = max(max_color, paint_edge(n_edge, edges[n_edge][node]))
                i += 1
        return max_color
 
    else:
        connect = len(nodes[node])
        max_color = connect
        for i in range(connect):
            n_edge = nodes[node][i]
            edges[n_edge]["color"] = i + 1
            max_color = max(max_color, paint_edge(n_edge, edges[n_edge][node]))
        return max_color
 
 
print(paint_edge(-1, 0, True))
for i in range(n - 1):
    print(edges[i]["color"])

Buggy python submission (verdict: Runtime Error):
n = int(input())
edges = []
nodes = [[] for _ in range(n)]
for i in range(n - 1):
    a, b = map(int, input().split())
    a, b = a - 1, b - 1
    edges.append({a: b, b: a, 'color': 0})
    nodes[a].append(i)
    nodes[b].append(i)


def paint_edge(edge, node, root=False):
    if not root:
        color = edges[edge]["color"]
        i = 1
        max_color = len(nodes[node])
        for n_edge in nodes[node]:
            if n_edge != edge:
                if i == color:
                    i += 1
                edges[n_edge]["color"] = i
                max_color = max(max_color, paint_edge(n_edge, edges[n_edge][node]))
                i += 1
        return max_color

    else:
        connect = len(nodes[node])
        max_color = connect
        for i in range(connect):
            n_edge = nodes[node][i]
            edges[n_edge]["color"] = i + 1
            max_color = max(max_color, paint_edge(n_edge, edges[n_edge][node]))
        return max_color


print(paint_edge(-1, 0, True))
for i in range(n - 1):
    print(edges[i]["color"])

Fixed submission:
import sys
sys.setrecursionlimit(1000000)
n = int(input())
edges = []
nodes = [[] for _ in range(n)]
for i in range(n - 1):
    a, b = map(int, input().split())
    a, b = a - 1, b - 1
    edges.append({a: b, b: a, 'color': 0})
    nodes[a].append(i)
    nodes[b].append(i)
 
 
def paint_edge(edge, node, root=False):
    if not root:
        color = edges[edge]["color"]
        i = 1
        max_color = len(nodes[node])
        for n_edge in nodes[node]:
            if n_edge != edge:
                if i == color:
                    i += 1
                edges[n_edge]["color"] = i
                max_color = max(max_color, paint_edge(n_edge, edges[n_edge][node]))
                i += 1
        return max_color
 
    else:
        connect = len(nodes[node])
        max_color = connect
        for i in range(connect):
            n_edge = nodes[node][i]
            edges[n_edge]["color"] = i + 1
            max_color = max(max_color, paint_edge(n_edge, edges[n_edge][node]))
        return max_color
 
 
print(paint_edge(-1, 0, True))
for i in range(n - 1):
    print(edges[i]["color"])