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 = [tuple(map(int, input().split())) for _ in range(n - 1)]
ans = {e: -1 for e in edges}
gs = [[] for _ in range(n + 1)]
for u, v in edges:
    gs[u].append(v)
    gs[v].append(u)

g = max(range(1, n + 1), key=lambda x: len(gs[x]))

cnt = 0
for v in gs[g]:
    uv = g, v
    if uv not in ans:
        uv = v, g
    ans[uv] = cnt
    cnt += 1

for a in ans.values():
    if a == -1:
        print(cnt)
        cnt += 1
    else:
        print(a)