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 #FOR READING PURE INTEGER INPUTS (space separation ok)
n=int(input())
adj=[[] for _ in range(n+1)]
for edgeNo in range(n-1):
    u,v=[int(x) for x in input().split()]
    adj[u].append([v,edgeNo])
    adj[v].append([u,edgeNo])
#if there are at least 3 leaves, put 0,1,2 on edges connected to them

allLeafEdges=set()

for node in range(1,n+1):
    if len(adj[node])==1: #node is leaf
        allLeafEdges.add(adj[node][0][1])
allLeafEdges=list(allLeafEdges)
ans=[-1 for __ in range(n-1)]
if len(allLeafEdges)>=3:
    ans[allLeafEdges[0]]=0
    ans[allLeafEdges[1]]=1
    ans[allLeafEdges[2]]=2
    
    idx=0
    for i in range(3,n-1):
        while (idx<n-1 and ans[idx]!=-1):
            idx+=1
        ans[idx]=i
else:
    ans=list(range(n-1))
print('\n'.join([str(x) for x in ans]))