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:
t=int(input())
lis1=[]
lis2=[]
for _ in range(t-1):
    temp=list(input().split(" "))
    lis1.append(int(temp[0]))
    lis2.append(int(temp[1]))
temp=[]
temp+=lis1+lis2
temp.sort()
ullist=[]
if(temp[0]!=temp[1]):
    ullist.append(temp[0])
len1=len(temp)
for i in range(1,len1-1):
    if(temp[i]!=temp[i-1] and temp[i]!=temp[i+1]):
        ullist.append(temp[i])
if(temp[len(temp)-1]!=temp[len(temp)-2]):
    ullist.append(temp[len(temp)-1])
if(len(ullist)==2):
    for i in range(t-1):
        print(i)
else:
    temp2=[-1]*(t-1)
    for i in range(t-1):
        if(lis1[i]==ullist[0] or lis2[i]==ullist[0]):
            temp2[i]=0
        if(lis1[i]==ullist[1] or lis2[i]==ullist[1]):
            temp2[i]=1
        if(lis1[i]==ullist[2] or lis2[i]==ullist[2]):
            temp2[i]=2
    l=3
    for i in range(t-1):
        if(temp2[i]==-1):
            temp2[i]=l
            l+=1
    for i in temp2:
        print(i)