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:
from collections import Counter, defaultdict, deque
from heapq import heapify, heappush, heappop, heappushpop
from sys import stdin

# int input
int_inp = lambda : int(stdin.readline().strip())
# int array input
lst_inp = lambda : [int(i) for i in stdin.readline().strip().split(" ")]
# string input
str_inp = lambda : stdin.readline().strip()

n = int_inp()
G = Counter()
edges = []
for _ in range(n-1):
    u, v = lst_inp()
    G[u] += 1
    G[v] += 1
    edges.append((u, v))

for u in G:
    if G[u] >= 3:
        deg_3 = u
        break
else:
    deg_3 = 0

cntr = 0 if deg_3 == 0 else 3
spec = 0

for u, v in edges:
    if deg_3 in {u, v}:
        print(spec)
        spec += 1
        if spec >= 3:
            deg_3 = -1
    else:
        print(cntr)
        cntr += 1