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 PYTHON):

Solution:
import atexit, io, sys 
 
  
# A stream implementation using an in-memory bytes  
# buffer. It inherits BufferedIOBase. 
 
buffer = io.BytesIO() 
 
sys.stdout = buffer
 
  
# print via here 
 
@atexit.register 
 
def write(): 
 
    sys.__stdout__.write(buffer.getvalue()) 






n=input()
adj=[[] for j in range(n+1)]
deg=[[0,j] for j in range(n+1)]
edge=[-1 for j in range(n-1)]

for _ in range(n-1):
    a,b=map(int,raw_input().split())
    deg[a][0]+=1
    deg[b][0]+=1
    adj[a].append([b,_]);adj[b].append([a,_])
deg=sorted(deg)
v=0
for i in range(1,n+1):
    if v==n-1:
        break
    p=deg[i][1]
    
    k=adj[p]
    for h in k:
        if v==(n-1):
            break
        if edge[h[1]]==-1:
            edge[h[1]]=v;v+=1
for i in edge:
    print i