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:
N=int(input())
FA=[0]*N
edges=[]
for n in range(N-1):
    edges.append(list(map(int,input().split())))
    FA[edges[n][0]-1]+=1 
    FA[edges[n][1]-1]+=1 
leaf={} 
for i in range(N):
    if FA[i]==1:
        leaf.update({i+1:1}) 
val=0 
ans=[]
for e in edges:
    if e[0] in leaf.keys() or e[1] in leaf.keys():
        ans.append(val) 
        val+=1 
    else:
        ans.append(-1) 
for i in range(N-1):
    if ans[i]==-1:
        ans[i]=val 
        val+=1
for i in range(N-1):
    print(ans[i])