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 python3
import sys
from math import *
from collections import defaultdict
from queue import deque                # Queues
from heapq import heappush, heappop    # Priority Queues

# parse
lines = [line.strip() for line in sys.stdin.readlines()]
n = int(lines[0])
ret = [-1 for i in range(n-1)]
edges = []
deg = [0 for i in range(n)]
for i in range(1,n):
  v, u = list(map(int, lines[i].split()))
  v -= 1
  u -= 1
  edges += [(v, u)]
  deg[v] += 1
  deg[u] += 1

cnt = 0
for i in range(n-1):
  if deg[edges[i][0]] == 1 or deg[edges[i][1]] == 1:
    ret[i] = cnt
    cnt += 1

for i in range(n-1):
  if ret[i] == -1:
    ret[i] = cnt
    cnt += 1

for x in ret:
  print(x)