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
from collections import defaultdict
input = stdin.readline
def read_tuple(): return map(int,input().split())
def read_int(): return int(input())
def read_list(): return list(map(int,input().split()))
def read_str_list(): return list(input().split())

n = read_int()
tree = defaultdict(list)
queries = []
for _ in range(n-1):
    u,v = read_tuple()
    tree[u].append(v)
    tree[v].append(u)
    if u>v: u,v = v,u
    queries.append( (u,v) )

ans = defaultdict(int)
    
mex = 0
for u in range(1,n+1):
    if len(tree[u]) == 1 and mex < n-1:
        v = tree[u][0]
        if u>v: ans[ (v,u) ] = mex
        else: ans[ (u,v) ] = mex
        mex+=1
        
for u,v in queries:
    val = ans.get( (u,v), -1 )
    if val==-1:
        print(mex)
        mex+=1
    else:
        print(val)