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:
import math
from collections import defaultdict
n = int(input())
adj_lis = defaultdict(int)
edges = []
for i in range(n-1):
    x, y = [int(i) for i in input().split()]
    adj_lis[x] += 1
    adj_lis[y] += 1
    edges.append([x, y])
leaves = {}
for i in range(1, n+1):
    if adj_lis[i] == 1:
        leaves[i] = 1
tot_leaves = len(list(leaves.keys()))
high = tot_leaves
low = 0
for i in range(len(edges)):
    x, y = edges[i]
    if (x in leaves) or (y in leaves):
        print(low)
        low += 1
    else:
        print(high)
        high += 1