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:
from sys import stdin
n=int(input())
e=[]
ad=[[] for _ in range(n)]
for _ in range(n-1):
    
    a,b=map(int,stdin.readline().split())
    a-=1
    b-=1
    e.append((a,b))
    ad[a].append(b)
    ad[b].append(a)
three={}
for x in range(n):
    if len(ad[x])>2:
        for i in range(3):
            three[(x,ad[x][i])]=three[(ad[x][i],x)]=i
        break
i=n-2
for x in e:
    if x in three:
        print(three[x])
    else:
        print(i)
        i-=1