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)                        
    raise SystemExit                
                                    
arr = [None for _ in range(n)]      
                                    
for i in range(n-1):                
    a, b = map(int, input().split())
    a -= 1                          
    b -= 1                          
                                    
    if arr[a] == None:              
        arr[a] = i                  
    else:                           
        arr[a] = False              
                                    
    if arr[b] == None:              
        arr[b] = i                  
    else:                           
        arr[b] = False              
                                    
ret = [-1 for _ in range(n-1)]      
i = 0                               
for e in arr:                       
    if type(e) == int:              
        ret[e] = i                  
        i += 1                      
                                    
for j in range(n-1):                
    if ret[j] == -1:                
        ret[j] = i                  
        i += 1                      
                                    
print("\n".join(map(str, ret)))