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
def inp():
    return sys.stdin.readline()
n=int(inp())
el=[]
deg=[0]*(n+1)
edge={}
ans_edge={}
for _ in range(n-1):
    u,v=map(int,inp().split())
    el.append((u,v))
    deg[u]+=1 
    deg[v]+=1
    if u not in edge:
        edge[u]=set()
    if v not in edge:
        edge[v]=set()
ll=[(min(deg[i[1]],deg[i[0]]),max(deg[i[1]],deg[i[0]]),i) for i in el]
ll.sort(reverse=True)
val=0
#print(ll)
while val<n-1:
    rmv=ll.pop()
    vtx=rmv[1]
    ans_edge[rmv[2]]=val 
    val+=1
    #del edge[vtx]
for i in el:
    print(ans_edge[i])