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:
import sys, math
input = sys.stdin.readline

def getInts():
    return [int(s) for s in input().split()]

def getInt():
    return int(input())

def getStrs():
    return [s for s in input().split()]

def getStr():
    return input()

def listStr():
    return list(input())

import collections as col
import math

def solve():
    #find the longest path
    #first priority: keep 0 and 1 apart
    #second priority: get 2 on an edge that isn't between 0 and 1
    #if N == 2, then just print 0
    #0 and 1 will *always* meet as there is a path between every pair of nodes
    #if there is only one path, then print the numbers in order
    #otherwise, there must be a node with 3 edges: assign 0, 1 and 2 to the 3 corners of the node
    N = getInt()
    if N == 2:
        print(0)
        return
    graph = col.defaultdict(set)
    edges = dict()
    edge_list = []
    for n in range(N-1):
        U, V = getInts()
        graph[U].add(V)
        graph[V].add(U)
        edges[(U,V)] = -1
        edge_list.append((U,V))
    max_size = 0
    flag = False
    for node in graph:
        if len(graph[node]) > 2:
            flag = True
            break
    next_ind = 0
    if flag:
        ns = []
        for neighbour in graph[node]:
            ns.append(neighbour)
            if len(ns) == 3:
                break
        for j in range(3):
            if (node,ns[j]) in edges:
                edges[(node,ns[j])] = j
            else:
                edges[(ns[j],node)] = j
        next_ind = 3
    for edge in edge_list:
        if edges[edge] == -1:
            print(next_ind)
            next_ind += 1
        else:
            print(edges[edge])
    return
        
    
    
solve()