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.readline
print = sys.stdout.write
# fin = open('input.txt', 'r')
# input = fin.readline

freqs = [0] * 100001
up_index = 0
down_index = 0


def make_number(edge):
    global down_index
    global up_index
    global freqs

    if freqs[edge[0]] == 1 or freqs[edge[1]] == 1:
        num = down_index
        down_index += 1
        return num
    num = up_index
    up_index += 1
    return num


def solve():
    global freqs
    global up_index

    n = int(input())
    lines = sys.stdin.readlines()
    edges = [tuple(map(int, line.split())) for line in lines]
    for edge in edges:
        freqs[edge[0]] += 1
        freqs[edge[1]] += 1
    down_nodes = [node for node in range(n + 1) if freqs[node] == 1]
    start_up_count = len(down_nodes)
    up_index = start_up_count
    ans = '\n'.join([str(make_number(edge)) for edge in edges])
    print(ans)


solve()