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
input = sys.stdin.readline
n=int(input())
adj_list=[[] for _ in range(n)];intial_arr=[]
for _ in range(n-1):
   a,b=map(int,input().split())
   #print('he')
   intial_arr.append([a-1,b-1])
   adj_list[a-1].append(b-1)
   adj_list[b-1].append(a-1)
l=0;ans={}
#print(adj_list)
for i in range(n):
   if len(adj_list[i])>=3:
     for k in adj_list[i]:
       ans[(k,i)]=l
       ans[(i,k)]=l
       l+=1
     break
#print(ans)
for a in intial_arr:
 # print('k')     
  if (a[0],a[1]) in ans:
      print(ans[(a[0],a[1])])
  elif (a[1],a[0]) in ans:
       print(ans[(a[1],a[0])])
  else:print(l);l+=1