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:
#!/usr/bin/env python
#-*- coding:utf-8 -*-

# Code by H~$~C

from sys import stdin
input = stdin.readline
import math

n = int(input())
G = [[] for i in range(n + 1)]
for i in range(n - 1):
  u, v = map(int, input().split())
  G[u].append([v, i])
  G[v].append([u, i])

ans = [-1] * (n + 1)

for u in range(1, n + 1):
  if (len(G[u]) >= 3):
    for j in range(len(G[u])):
      ans[G[u][j][1]] = j
    cnt = len(G[u])
    for j in range(n - 1):
      if (ans[j] == -1):
        ans[j] = cnt
        cnt += 1
    for j in range(n - 1):
      print(ans[j])
    exit(0)

for i in range(n - 1):
  print(i)