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
n=int(input())
L=[[]for i in range(n)]
M=dict()
for i in range(n-1):
    a,b=map(int,input().split())
    M[i]=(a,b)
    L[a-1].append(b)
    L[b-1].append(a)
mxnode=-1
mxdeg=0
for j in range(n):
    if len(L[j])>mxdeg:
        mxdeg=len(L[j])
        mxnode=j+1
mxpt=0
normpt=0
mxedge=list(range(mxdeg))
noredg=list(range(mxdeg,n))
for j in range(n-1):
    if mxnode in M[j]:
        print(mxedge[mxpt])
        mxpt+=1
    else:
        print(noredg[normpt])
        normpt+=1