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())
edges = []
in_node = [0]*N

for _ in range(N-1):
    a, b = map(int, input().split())
    in_node[a-1] += 1
    in_node[b-1] += 1
    edges.append([a-1, b-1])
leaf = {i for i, v in enumerate(in_node) if v == 1}

num = 0
ids = [-1]*(N-1)
for i in range(N-1):
    a, b = edges[i]
    if a in leaf or b in leaf:
        ids[i] = num
        num += 1
for i in range(N-1):
    a, b = edges[i]
    if ids[i] == -1:
        ids[i] = num
        num += 1
print("\n".join(map(str, ids)))