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:
"""    Arnab Chanda    """

from collections import defaultdict, deque
from itertools import permutations
from sys import stdin,stdout
from bisect import bisect_left, bisect_right
from copy import deepcopy
import heapq

int_input=lambda : int(stdin.readline())
string_input=lambda : stdin.readline().split()
multi_int_input =lambda : map(int, stdin.readline().split())
multi_input = lambda : stdin.readline().split()
list_input=lambda : list(map(int,stdin.readline().split()))
string_list_input=lambda: list(string_input())
MOD = pow(10,9)+7

n = int_input()
mini = 0
graph = []
for i in range(n+5):
    graph.append([])
inputorder = []
ans = []
frequency = {}

if n == 2:
    u,v = multi_int_input()
    print(0)

elif n == 3:
    a,b= multi_int_input()
    b,c = multi_int_input()
    print(0)
    print(1)

else:
    count = 0
    for _ in range(n-1):
        u,v = multi_int_input()
        inputorder.append([u,v])
        graph[u].append(v)
        graph[v].append(u)

    threeDegreePoint = -1
    for i in range(1,n+1):
        if len(graph[i]) >= 3:
            threeDegreePoint = i

    if threeDegreePoint == -1:
        for i in range(0,n-1):
            print(i)

    else:
        a = 0
        b = 3
        count = 0
        for x in inputorder:
            if (x[0] == threeDegreePoint or x[1] == threeDegreePoint) and count<3:
                print(a)
                count+=1
                a+=1
            else:
                print(b)
                b+=1