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())
edge=[[] for i in range(n+1)]
matrix=[]
for i in range(n-1):
    u,v=list(map(int,input().split()))
    edge[u].append(v)
    edge[v].append(u)
    matrix.append([u,v])
lis=[]
for i in range(1,n+1):
    lis.append(len(edge[i]))
a=max(lis)
if a<=2:
    for i in range(n-1):
        print(i)
else:
    b=lis.index(a)
    arr=[]
    for i in range(3):
        arr.append(edge[b+1][i])
    ans=[-1]*(n-1)
    p=0
    for i in range(n-1):
        if (matrix[i]==[b+1,arr[0]] or matrix[i]==[arr[0],b+1]) or (matrix[i]==[b+1,arr[1]] or matrix[i]==[arr[1],b+1]) or (matrix[i]==[b+1,arr[2]] or matrix[i]==[arr[2],b+1]):
            ans[i]=p
            p+=1
    p=3
    for i in range(n-1):
        if ans[i]==-1:
            ans[i]=p
            p+=1
    for i in range(n-1):
        print(ans[i])