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())
categories_to_nodes = {0: {i for i in range(1,n+1)}, 1: set(), 2:set()}

all_data = []
for edge in range(n-1):
    data = input().split()
    all_data.append(data)
    if int(data[0]) in categories_to_nodes[0]:
        categories_to_nodes[0].remove(int(data[0]))
        categories_to_nodes[1].add(int(data[0]))
    elif int(data[0]) in categories_to_nodes[1]:
        categories_to_nodes[1].remove(int(data[0]))
        categories_to_nodes[2].add(int(data[0]))

    if int(data[1]) in categories_to_nodes[0]:
        categories_to_nodes[0].remove(int(data[1]))
        categories_to_nodes[1].add(int(data[1]))
    elif int(data[1]) in categories_to_nodes[1]:
        categories_to_nodes[1].remove(int(data[1]))
        categories_to_nodes[2].add(int(data[1]))

leaves = categories_to_nodes[1]
if len(leaves) == 2:
    for i in range(n-1):
        print(i)
else:
    i=n-2
    j=0
    for data in all_data:
        if int(data[0]) in leaves or int(data[1]) in leaves:
            print(j)
            j+=1
        else:
            print(i)
            i-=1