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

# t=int(input())

# for _ in range(t):
n=int(input())
nodes={i:0 for i in range(1,n+1)}
# arr=[int(c) for c in input().split()]
q=[]
needednode=-1
for i in range(n-1):
    a,b=[int(c) for c in input().split()]
    q.append((a,b))
    nodes[a]+=1
    if nodes[a] >=3:
        needednode=a
    nodes[b]+=1
    if nodes[b] >=3:
        needednode=b

if needednode == -1:
    for i in range(len(q)):
        print(i)
else:
    first=0
    second=3
    for a,b in q:
        if first <  3 and  (a==needednode or b == needednode):
                print(first)
                first+=1
        else:
            print(second)
            second+=1