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
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__


n=int(input())
dic={}
seq={}
for i in range(n-1):
    u,v=list(map(int,input().split()))
    ulist=dic.get(u,[])
    vlist=dic.get(v,[])
    ulist.append(v)
    vlist.append(u)
    dic[u]=ulist
    dic[v]=vlist
    seq[(u,v)]=i

ans=[-1]*(n-1)

curr=0

for lis in dic:
    nodes=dic[lis]
    if len(nodes)==1:
        #print(seq,(lis,dic[lis][0]))
        seqloc=seq.get((lis,dic[lis][0]),False)
        seqloc1=seq.get((dic[lis][0],lis),False)
        if seqloc:
            ans[seqloc]=curr
            curr+=1
        elif seqloc1:
            ans[seqloc1]=curr
            curr+=1
            
for i in range(n-1):
    if ans[i]==-1:
        ans[i]=curr
        curr+=1
for an in ans:
    print(an)