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())
graph = {}
values = {}
order = []
for i in range(n):
    graph[i+1] = []
    values[i] = -1
val = -1
for i in range(n-1):
    a = input().split(' ')
    a[0] = int(a[0])
    a[1] = int(a[1])
    order.append(a)
    graph[a[0]].append(a[1])
    graph[a[1]].append(a[0])
    if len(graph[a[0]]) >= 3:
        val = a[0]
    if len(graph[a[1]]) >= 3:
        val = a[1]
if val == -1:
    for i in range(n-1):
        print(i)
else:
    count = 0
    for i in range(n-1):
        if order[i][0] == val or order[i][1] == val:
            values[i] = count
            count = count + 1
    for i in range(n):
        if values[i] == -1:
            values[i] = count
            count = count + 1
    for i in range(n-1):
        print(values[i])