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
import math
import heapq
import collections
def inputnum():
    return(int(input()))
def inputnums():
    return(map(int,input().split()))
def inputlist():
    return(list(map(int,input().split())))
def inputstring():
    return([x for x in input()])
def inputmatrixchar(rows):
    arr2d = [[j for j in input().strip()] for i in range(rows)] 
    return arr2d
def inputmatrixint(rows):
    arr2d = []
    for _ in range(rows):
        arr2d.append([int(i) for i in input().split()])
    return arr2d
    
n = inputnum()
a = [0]*(n+1)
us = []
vs = []
ans = [-1]*(n-1)
for i in range(n-1):
    u, v = inputnums()
    us.append(u)
    vs.append(v)
    a[u] += 1 
    a[v] += 1
for i in range(n-1):
    if a[vs[i]] == 1 or a[us[i]] == 1:
        vs[i] = -1
        us[i] = -1
cur = 0
for i in range(n-1):
    if vs[i] == -1 or us[i] == -1:
        ans[i] = cur
        cur += 1
for i in range(n-1):
    if ans[i] == -1:
        ans[i] = cur
        cur += 1
    print(ans[i])