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
import sys
from collections import defaultdict,Counter,deque,OrderedDict
import bisect
#sys.setrecursionlimit(1000000)
input = iter(sys.stdin.buffer.read().decode().splitlines()).__next__
ilele = lambda: map(int,input().split())
alele = lambda: list(map(int, input().split()))
def list2d(a, b, c): return [[c] * b for i in range(a)]
#def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
#INF = 10 ** 18
#MOD = 1000000000 + 7
from itertools import accumulate,groupby
import sys
mod = 1000000007

graph = []

def addEdge(a,b):
    graph[a].append(b)
    graph[b].append(a)


N = int(input())
graph =defaultdict(list);G = []
for i in range(N-1):
    u,v = ilele()
    addEdge(u,v)
    G.append((u,v))
Ans = {};maxi =0;a=0
for i,j in graph.items():
    if len(j) > maxi:
        maxi =len(j)
        a = i
k=0
for i in graph[a]:
    Ans[(i,a)] = k
    Ans[(a,i)] = k
    k+=1
#print(Ans)
for i in G:
    x = Ans.get(i,-1)
    if x!=-1:
        print(x)
    else:
        print(k)
        k+=1