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:
class Graph: #Directed
    def __init__(self, vertices):
        self.no_of_vertices = vertices
        self.graph = dict() #Adjacency
        for i in range(1, self.no_of_vertices+1):
            self.graph[i] = []
    
    def add_edge(self, u, v):
        self.graph[u].append(v)
        self.graph[v].append(u)
    
    

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

edges = []
for _ in range(n-1):
    [l, r] = [int(i) for i in input().split()]
    edges.append((l, r))

for (u,v) in edges:
    g.add_edge(u, v)

labels = [None]*(n-1)

for u in g.graph:
    if(len(g.graph[u])>2):
        break

l = 0
for i in range(n-1):
    if(u in edges[i]):
        labels[i] = l 
        l = l + 1

for i in range(n-1):
    if(labels[i]==None):
        labels[i] = l 
        l = l+1

for i in labels:
    print(i)