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:
di = {} #Dictionary of int->tuple
edLi = []
n = int(input())
'''for _ in range(n-1):
    liStr = input().split()
    a = int(liStr[0])
    b = int(liStr[1]) 

    tempLi = []
    tempLi.append(a)
    tempLi.append(b) 
    edLi.append(tuple(tempLi)) 
    
    if(a in di):
        tup = di[a] 
        li = list(tup) 
        li.append(b) 
        tup = tuple(li) 
        di[a] = tup 
    else:
        li = []
        li.append(b)
        tup = tuple(li) 
        di[a] = tup 
    
    if(b in di):
        tup = di[b] 
        li = list(tup) 
        li.append(a) 
        tup = tuple(li) 
        di[b] = tup 
    else: 
        li = []
        li.append(a) 
        tup = tuple(li) 
        di[b] = tup 
#print(di)'''

deg = []
for i in range(0,n+1):
    deg.append(0) 

for _ in range(n-1):
    
    liStr = input().split()
    a = int(liStr[0])
    b = int(liStr[1]) 

    tempLi = []
    tempLi.append(a)
    tempLi.append(b) 
    edLi.append(tuple(tempLi))

    deg[a] += 1 
    deg[b] += 1


degree3Node = 0 
x = 3
for i in range(len(deg)):
    if( deg[i] >= 3):
        degree3Node = i
        x = deg[i] 
        break 

p = x
q = 0  
if(n>2):
    if(degree3Node == 0):
        for i in range(0,n-1):
            print(i) 
    else:
        for i in range(0,n-1):
            if( degree3Node in (edLi[i]) ):
                print(q) 
                q += 1 
            else:
                print(p)
                p += 1 
else:
    print(0)