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
input=stdin.readline
#import bisect
#i = bisect.bisect_left(a, k)
#list=input().split(maxsplit=1)
for xoxo in range(1):
    #a=[]a
    for _ in range (1):
        n=int(input())
        t=[]
        for i in range(n):
            t.append([])
        a=[]    
        for i in range(n-1):
            l,r=map(int, input().split())
            t[l-1].append(r-1)
            t[r-1].append(l-1)
            a.append([min(l,r)-1,max(l,r)-1])
        ans=[]    
        k=-1
        for i in range(n):
            if len(t[i])>2:
                for j in range(3):
                    ans.append([min(i,t[i][j]),max(i,t[i][j])])
                
                k=0
                break
        if k==-1:
            for i in range(n-1):
                print(i)
            exit()    
        k,p=3,0
        for i in range(n-1):            
            if a[i] in ans:
                print(p)
                p+=1
            else:
                print(k)
                k+=1
        #print(ans,t,a)
            
    #ans=[]
    #n,k=map(int, input().split())
    #a=list(map(int, input().split()))
    #ans=0