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())
cc, ls = [0]*(n+1), []
for _ in range(n-1):
    a, b = map(int, input().split())
    ls.append((a, b))
    cc[a] += 1; cc[b] += 1

if n == 2: print(0); exit()

r = 0
for k, v in enumerate(cc):
    if v >= 3: r = k; break

idx = 3 if r > 0 else 0
rcc = 0
for a, b in ls:
    if rcc < 3 and (a == r or b == r):
        print(rcc); rcc += 1
    else:
        print(idx); idx += 1