Problem: You are given a tree consisting of n nodes. You want to write some labels on the tree's edges such that the following conditions hold:

  * Every label is an integer between 0 and n-2 inclusive. 
  * All the written labels are distinct. 
  * The largest value among MEX(u,v) over all pairs of nodes (u,v) is as small as possible. 



Here, MEX(u,v) denotes the smallest non-negative integer that isn't written on any edge on the unique simple path from node u to node v.

Input

The first line contains the integer n (2 ≤ n ≤ 10^5) — the number of nodes in the tree.

Each of the next n-1 lines contains two space-separated integers u and v (1 ≤ u,v ≤ n) that mean there's an edge between nodes u and v. It's guaranteed that the given graph is a tree.

Output

Output n-1 integers. The i^{th} of them will be the number written on the i^{th} edge (in the input order).

Examples

Input


3
1 2
1 3


Output


0
1


Input


6
1 2
1 3
2 4
2 5
5 6


Output


0
3
2
4
1

Note

The tree from the second sample:

<image>

Solution (in PYTHON3):

Solution:
from sys import stdin, exit
from itertools import combinations
from collections import deque
input = stdin.readline
lmi = lambda: list(map(int, input().split()))
mi = lambda: map(int, input().split())
si = lambda: input().strip('\n')
ssi = lambda: input().strip('\n').split()


# def dfs(u, p, s):
#     for i in graph[u]:
#         if i != p:
#             dfs(i, u, s+1)
#     global diameter
#     diameter = max(s, diameter)


n = int(input())
graph = [[] for i in range(n+1)]
edges = []
edges2 = {}
for i in range(n-1):
    a, b = mi()
    graph[a].append(b)
    graph[b].append(a)
    edges.append((a, b))
    edges2[(a, b)] = -1

if all(len(i) <= 2 for i in graph):
    for i in range(n-2, -1, -1):
        print(i)
else:
    for idx, i in enumerate(graph):
        if len(i) >= 3:
            for j in range(3):
                a, b = idx, graph[idx][j]
                if (a, b) not in edges2:
                    a, b = b, a
                edges2[(a, b)] = j
            break
    cnt = 3
    for a, b in edges2:
        if edges2[(a, b)] == -1:
            edges2[(a, b)] = cnt
            cnt += 1
    for a, b in edges:
        print(edges2[(a, b)])

# diameter = 0
# dfs(1, -1, 0)
# mex = n-diameter-1
# print(mex)