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
from collections import defaultdict
n=int(sys.stdin.readline())
graph=defaultdict(list)
rem=[]
for _ in range(n-1):
    u,v=map(int,sys.stdin.readline().split())
    graph[u].append(v)
    graph[v].append(u)
    rem.append([min(u,v),max(u,v)])
l=[]
for i in graph:
    l.append([len(graph[i]),i])
l.sort()
#l.reverse()
vis=defaultdict(lambda:-1)
count=0
#print(graph,'graph')
#print(l,'l')
for i in range(len(l)-1,-1,-1):
    node=l[i][1]
    for j in range(len(graph[node])):
        a,b=min(graph[node][j],node),max(graph[node][j],node)
        if vis[(a,b)]==-1:
            vis[(a,b)]=count
            count+=1
for i,j in rem:
    print(vis[(i,j)])