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:
''' Ehab and Path-etic MEXs - spoiled by mzy
'''




''' routine '''


N = int(input())
leaves = {}
edges = [0 for i in range(N)]
for edge in range(N - 1):
    a, b = list(map(int, input().split()))
    for node in (a, b):
        edges[node - 1] += 1
        if edges[node - 1] == 1:
            leaves[node] = edge
        elif edges[node - 1] == 2:
            del leaves[node]

if len(leaves) < 3:
    for n in range(N - 1):
        print(n)
else:
    start = 3
    leaf = 0
    specials = list(leaves.values())[:3]
    for edge in range(N - 1):
        if edge in specials:
            print(leaf)
            leaf += 1
        else:
            print(start)
            start += 1
    # print(specials)