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
import math
input=sys.stdin.readline
#t=int(input())
t=1
for _ in range(t):
    n=int(input())
    #x,y=map(int,input().split())
    #a=list(map(int,input().split()))
    d={}
    fr=[]
    to=[]
    for i in range(1,n+1):
        d[i]=[]
    for i in range(n-1):
        u,v=map(int,input().split())
        d[u].append(v)
        d[v].append(u)
        fr.append(u)
        to.append(v)
    weight={}
    k=0
    for i in range(1,n+1):
        if len(d[i])==1:
            weight[i]=k
            k+=1
    if n==2:
        weight[1]=0
        weight[2]=0
    for i in range(n-1):
        if weight.get(fr[i],-1)!=-1 :
            print(weight[fr[i]])
        elif  weight.get(to[i],-1)!=-1 :
            print(weight[to[i]])
        else:
            print(k)
            k+=1