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=lambda: sys.stdin.readline().rstrip()
n=int(input())
edge=[]
D=[0]*n
for i in range(n-1):
  u,v=map(int,input().split())
  edge.append((u,v))
  D[u-1]+=1
  D[v-1]+=1
if max(D)<=2:
  for i in range(n-1):
    print(i)
else:
  Ans=[-1]*(n-1)
  for i in range(n):
    if D[i]>=3:
      c=i
      break
  rest=3
  for i in range(n-1):
    u,v=edge[i]
    if rest:
      if u-1==c or v-1==c:
        Ans[i]=rest-1
        rest-=1
  cur=3
  for i in range(n-1):
    if Ans[i]!=-1:
      print(Ans[i])
    else:
      print(cur)
      cur+=1