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 math
from bisect import bisect_left, bisect_right
from sys import stdin, stdout, setrecursionlimit
from collections import Counter
input = lambda: stdin.readline().strip()
print = stdout.write

n = int(input())
graph = [0]
edge = [0]
for i in range(1, n+1):
    graph.append(0)
    edge.append(0)
for i in range(n-1):
    a, b = map(int, input().split())
    graph[a]+=1
    graph[b]+=1
    edge[a] = i
    edge[b] = i
ans = []
for i in range(n-1):
    ans.append(-1)
i = 0
for k in range(1, n+1):
    v = graph[k]
    if v==1 and i<min(3, n-1):
        ans[edge[k]] = i
        i+=1
for k in range(len(ans)):
    if ans[k]==-1:
        ans[k] = i
        i+=1
for i in ans:
    print(str(i)+'\n')