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 sys import stdin

d = {}
pair = []
l = int(stdin.readline())
v = [-1]*(l-1)
for _ in range(l-1):
    
    #n = int(stdin.readline())
    n = [int(i) for i in stdin.readline().split(" ")]
    pair.append(n)
    key1, key2 = str(n[0]), str(n[1])
    if key1 not in d:
        d[key1] = 1
    else:
        d[key1] += 1 
    if key2 not in d:
        d[key2] = 1
    else:
        d[key2] += 1

#print(pair)
#print(d)
values = list(d.values())
values = list(sorted(set(values)))
#print(values)

flag = 0

for key, value in d.items(): 
    if value>2:
        flag = 1
        temp1 = 0
        temp2 = 3
        key = int(key)
        for i in range(l): 
            if pair[i][0]==key or pair[i][1]==key:
                v[i] = temp1
                temp1 += 1
                if(temp1>2):
                    break
                    
        for i in range(l-1):
            if v[i]!=-1:
                print(v[i])
            else:
                print(temp2)
                temp2 += 1
        break


if flag==0:
    for i in range(0,l-1):
        print(i)