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 os
import sys
from atexit import register
from io import BytesIO

input = BytesIO(os.read(0, os.fstat(0).st_size)).readline
from collections import defaultdict

n = int(input())
Edges = []#defaultdict(list)
Power = defaultdict(int)

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

onecount = sum(value == 1 for value in Power.values())
if onecount == 2:
    for i in range(n-1):
        print(i)
else:
    left = 0
    right = n-2
    for (u,v) in Edges:
        if (Power[u] == 1) or (Power[v] == 1):
            print(left)
            left += 1
        else:
            print(right)
            right -= 1