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:
I = lambda : map(int,input().split())

n= int(input())
l=[-1]*(n-1);g=[0]*(10**5+2)
x=[];d={}
for _ in range(n-1):
    a,b=I()
    d[a]=d.get(a,0)+1
    d[b]=d.get(b,0)+1
    x.append([a,b])
for i in d.keys():
    if d[i]==1:
        g[i]=1
k=0
for i in range(n-1):
    if g[x[i][0]] or g[x[i][1]]:
        l[i]=k
        k+=1
for i in range(n-1):
    if l[i]==-1:
        l[i]=k
        k+=1
print(*l)