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:
from collections import defaultdict

class Graph:
    def __init__(self,V):
        self.vertices = V
        self.graph = defaultdict(list)
        self.degree = defaultdict(int)
        self.label = defaultdict(int)
        self.edges = []
        
    def add_edge(self,u,v):
        self.graph[u].append(v)
        self.graph[v].append(u)
        self.degree[u] += 1
        self.degree[v] += 1
        self.label[(u,v)] = -1
        self.edges.append((u,v))
        

n = int(input())
g = Graph(n)

for _ in range(n-1):
    u,v = map(int,input().strip().split())
    g.add_edge(u,v)

g.degree = dict(sorted(g.degree.items(),key = lambda x:x[1]))

ass_label = 0
for key,val in g.degree.items():
    if val>1:
        break
    for node in g.graph[key]:
        if (key,node) in g.label and g.label[((key,node))]==-1:
            g.label[((key,node))] = ass_label
            ass_label += 1
        elif g.label[((node,key))]==-1:
            g.label[((node,key))] = ass_label
            ass_label += 1

for edge in g.edges:
    if g.label[edge]!=-1:
        print(g.label[edge])
    else:
        print(ass_label)
        ass_label += 1