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())

s=[[] for _ in range(n+1)]

inp=[]

for _ in range(n-1):
    a,b=map(int,input().split())
    inp.append(sorted([a,b]))
    s[a].append(b)
    s[b].append(a)

ind0=0 ; ind1=0 ; ind2=0
for i in range(1,n+1):
    if len(s[i])==1 :
        if not ind0:
            ind0=sorted([i,s[i][0]])
        elif not ind1:
            ind1=sorted([i,s[i][0]])
        else:
            ind2=sorted([i,s[i][0]])
            break
ans=[]

j=2
if ind2:
    j=3
for i in inp:
    if i==ind0 :
        ans.append('0')
    elif i==ind1 :
        ans.append('1')
    elif i==ind2:
        ans.append('2')
    else:
        ans.append(str(j))
        j+=1

print('\n'.join(ans))