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 collections import defaultdict

n = int(input())
mp = defaultdict(list)
edges = dict()
input_list = []

for i in range(n-1):
    a, b = list(map(int, input().split()))
    a, b = min(a, b), max(a, b)
    edges[(a, b)] = -1
    input_list.append((a, b))
    mp[a].append(b)
    mp[b].append(a)

solved = False
leaves_edges = []

for i in range(1, n+1):
    if len(mp[i]) > 2:
        solved = True
        for j in range(len(mp[i])):
            a, b = min(i, mp[i][j]), max(i, mp[i][j])
            edges[(a, b)] = j
        break
    elif len(mp[i]) == 1:
        leaves_edges.append((min(i, mp[i][0]), max(i, mp[i][0])))

if not solved:
    for i in range(len(leaves_edges)):
        if edges[leaves_edges[i]] == -1:
            edges[leaves_edges[i]] = i

cnt = n-2
for e in edges:
    if edges[e] == -1:
        edges[e] = cnt
        cnt -= 1

for i in input_list:
    print(edges[i])