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 sys
input = sys.stdin.buffer.readline
def print(val):
    sys.stdout.write(str(val) + '\n')
from collections import OrderedDict
def prog():
    n = int(input())
    adj_list = [[] for i in range(n+1)]
    index_edges = OrderedDict()
    for _ in range(n-1):
        a,b = map(int, input().split())
        adj_list[a].append(b)
        adj_list[b].append(a)
        index_edges[(a,b)] = None
    had3 = False
    for node in range(1,n+1):
        neighbors = adj_list[node]
        if len(neighbors) >= 3:
            for i in range(3):
                if (node,neighbors[i]) in index_edges:
                    index_edges[(node,neighbors[i])] = i
                else:
                    index_edges[(neighbors[i],node)] = i
            had3 = True
            break
    if had3:
        curr = 3
        for value in index_edges.values():
            if value is None:
                print(curr)
                curr += 1
            else:
                print(value)
    else:
        curr = 2
        smallest = 0
        for edge in index_edges:
            if len(adj_list[edge[0]]) + len(adj_list[edge[1]]) > 3:
                print(curr)
                curr += 1
            else:
                print(smallest)
                smallest += 1
prog()