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 Counter

vertexes_number = int(input())
edges = Counter()

ledger = []
for _ in range(vertexes_number - 1):
    _from, to = map(int, input().split())
    ledger.append((_from, to))
    edges[_from] += 1
    edges[to] += 1

(vertex, power), = edges.most_common(1)
if power >=3:
    asc_index = 0
    desc_index = vertexes_number - 2
    for index, (_from, to) in enumerate(ledger):
        if _from == vertex or to == vertex:
            print(asc_index)
            asc_index += 1
        else:
            print(desc_index)
            desc_index -= 1
else:
    for index in range(len(ledger)):
        print(index)