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:
# cook your dish her
from collections import defaultdict
n=int(input())
d2={}
ans={}
d2=defaultdict(lambda: [],d2)
ans=defaultdict(lambda: -1,ans)
if n==2:
    u,v=map(int,input().split(" "))
    print(0)
else:
    b=[]
    for i in range(n-1):
        u,v=map(int,input().split(" "))
        b.append((u,v))
        d2[u].append(v)
        d2[v].append(u)
    
    
    arr=[]
    a=[0]*(n+1)
    for i in range(1,n+1):
        if len(d2[i])==1:
            arr.append(i)
    
    k=0
    for i in arr:
        ans[(d2[i][0],i)]=k
        ans[(i,d2[i][0])]=k
        k+=1
    
    ans1=[0]*(n-1)
    t=0
    for i in b:
        ans1[t]=ans[i]
        t+=1
    
    i=0
    while i<n-1:
        if ans1[i]==-1:
            ans1[i]=k
            k+=1
        i+=1
        
        
    for i in ans1:
        print(i)