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 types import GeneratorType
 
def bootstrap(f, stack=[]):
    def wrappedfunc(*args, **kwargs):
        if stack:
            return f(*args, **kwargs)
        else:
            to = f(*args, **kwargs)
            while True:
                if type(to) is GeneratorType:
                    stack.append(to)
                    to = next(to)
                else:
                    stack.pop()
                    if not stack:
                        break
                    to = stack[-1].send(to)
            return to
 
    return wrappedfunc
######################
 
import math
from bisect import bisect_left, bisect_right
from sys import stdin, stdout, setrecursionlimit
from collections import Counter
input = lambda: stdin.readline().strip()

#print = stdout.write
import heapq
##################
##################

n=int(input())
degree=[0 for i in range(n+1)]
adj=[[] for i in range(n+1)]
ans=[-1 for i in range(n+1)]
edges=[[] for i in range(n+1)]
vis_nodes=[False for i in range(n+1)]
vis_edges=[False for i in range(n+1)]
for _ in range(n-1):
    u,v=map(int,input().split())
    adj[u].append(v)
    adj[v].append(u)
    degree[u]+=1
    degree[v] += 1
    edges[u].append(_+1)
    edges[v].append(_+1)
node=[(-1*degree[i],i) for i in range(1,n+1)]
heapq.heapify(node)
cnt=0
while cnt<n-1 and len(node)>0:
    k=heapq.heappop(node)
    x=k[1]
    for i in edges[x]:
        if ans[i]==-1:
            ans[i]=cnt
            cnt += 1
for i in range(1,n):
    print(str(ans[i]))