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())
e = [[] for _ in range(n+1)]
ec = [0 for _ in range(n+1)]
done = False
for i in range(n-1):
    a,b=map(int,input().split())
    if done: continue
    e[a].append(i)
    e[b].append(i)
    ec[a]+=1
    ec[b]+=1
    soll = []
    if ec[a]>=3:
        soll = e[a]
        done = True
    elif ec[b]>=3:
        soll = e[b]
        done = True
if not done:
    for i in range(n-1):
        print(i)
else:
    x=0
    y=3
    for i in range(n-1):
        if i in soll:
            print(x)
            x+=1
        else:
            print(y)
            y+=1