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:
n = int(input())
inputEdges = []
adjList = [[] for i in range(0,n+1)]
for i  in range(0,n-1):
    edge = list(map(lambda x: int(x), input().split()))
    inputEdges.append(edge)
    adjList[edge[0]].append(edge[1])
    adjList[edge[1]].append(edge[0])

isLinear = True
junction = 0
for i in range(1,n+1):
    if len(adjList[i]) >= 3:
        junction = i
        isLinear = False
        break

high=n-2
low=0
if(isLinear):
    for i in range(0,n-1):
        print(i)
else:
    for e in inputEdges:
        if e[0]==junction or e[1]==junction:
            print(low)
            low+=1
        else:
            print(high)
            high-=1