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 = {}

maxi = 1
for i in range(n-1):
    u, v = map(int, input().split())
    if u not in graph:
        graph[u] = {i}
    else:
        graph[u].add(i)
    if v not in graph:
        graph[v] = {i}
    else:
        graph[v].add(i)
    if len(graph[u]) >= 3:
        maxi = u
        break
    if len(graph[v]) >= 3:
        maxi = v
        break
w = 0
t = n-2
temp = ""
for j in range(n-1):
    if j in graph[maxi]:
        temp += str(w) + "\n"
        w += 1
    else:
        temp += str(t) + "\n"
        t -= 1
print(temp)