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())
if n==2:
    print(0)
    exit()
E=[[] for _ in range(n)]
E_=[0]*n
ans=[-1]*(n-1)
for i in range(n-1):
    a,b=map(int,input().split())
    E[a-1].append([b-1,i])
    E[b-1].append([a-1,i])
    E_[a-1]+=1
    E_[b-1]+=1
if max(E_)<=2:
    x=0
    for i in range(n):
        if E_[i]==1:
            ans[E[i][0][1]]=x
            x+=1
    for i in range(n-1):
        if ans[i]==-1:
            ans[i]=x
            x+=1
else:
    for i in range(n):
        if E_[i]>=3:
            ans[E[i][0][1]]=0
            ans[E[i][1][1]]=1
            ans[E[i][2][1]]=2
            break
    x=3
    for i in range(n-1):
        if ans[i]==-1:
            ans[i]=x
            x+=1
for i in range(n-1):
    print(ans[i])