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 = lambda: sys.stdin.readline().rstrip()
n=int(input())
tree=[[] for i in range(n)] ; s=[]
for _ in range(n-1):
    a,b=map(int,input().split())
    s.append([a-1,b-1])
    tree[a-1].append(b-1)
    tree[b-1].append(a-1)
ans=[-1]*(n-1) ; maxx=0 ; ind=-1
for i in range(len(tree)):
    if len(tree[i])>maxx:
        maxx=len(tree[i])
        ind=i
k=0
st=set([int(i) for i in range(n-1)])
for i in range(len(s)):
    if ind in s[i]:
        ans[i]=k
        st.remove(k)
        k+=1
st=list(st)
for i in range(len(ans)):
    if ans[i]==-1:
        ans[i]=st[-1]
        st.pop()
for i in range(len(ans)):
    print(ans[i])