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:
import sys
input = iter(sys.stdin.readlines()).__next__

import collections

n = int(input())
edges = collections.defaultdict(set)
e_labels = [None]*(n-1)

for i in range(n-1):
    u, v = map(int, input().split())
    edges[u].add(i)
    edges[v].add(i)

    if len(edges[v]) == 3:
        u = v

    if len(edges[u]) == 3:
        for k, j in enumerate(edges[u]):
            e_labels[j] = k
        k = 3
        for j in range(n-1):
            if e_labels[j] == None:
                e_labels[j] = k
                k += 1
        break
else:
    e_labels = list(range(n-1))

print(*e_labels, sep='\n')