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 collections import defaultdict, deque
from sys import stdin,stdout
n,A=int(input()),[]
for _i in range(n-1):
    A.append(tuple(int(x) for x in stdin.readline().strip().split(" ")))
    
hmap=defaultdict(list)
for a,b in A:
    hmap[a].append(b)
    hmap[b].append(a)

res=dict()
label=0
for i in range(1,n+1):
    if len(hmap[i])>=3:
        for x in hmap[i]:
            res[i,x]=label
            res[x,i]=label
            label+=1
        break
for x in A:
    if x not in res.keys():
        stdout.write(str(label)+"\n")
        label+=1
    else:
        stdout.write(str(res[x])+"\n")