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 PYTHON):

Solution:
from collections import defaultdict

n = int(raw_input())
m = n-1
deg = defaultdict(int)
adj = defaultdict(list)
for i in range(m):
    a, b = map(int, raw_input().split())
    deg[a] += 1
    deg[b] += 1
    adj[a].append((b, i))
    adj[b].append((a, i))
sor = sorted(deg.items(), key=lambda x: -x[1])
res = [-1]*(n-1)
cnt = 0
# print(sor)
for x, y in sor:
    for b in adj[x]:
        # print(b, cnt, res)
        if res[b[1]] != -1:
            continue
        res[b[1]] = cnt
        cnt += 1
for x in res:
    print(x)