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())
A=[]
B=[0]*(n-1)
G=[[] for i in range(n)]
GG=[[0]*2 for i in range(n-1)]
for i in range(n-1):
    a,b=map(int,input().split())
    c=a
    a=min(b,c)
    b=max(b,c)
    GG[i]=[a,b]
    G[a-1].append(b-1)
    G[b-1].append(a-1)
    A.append(a*10**6+b)
D=dict(zip(A,B))
a=10**6
b=10**6
c=10**6
for i in range(n):
    if len(G[i])>=3:
        a=i
        break
if a==10**6:
    for i in range(n-1):
        print(i)
else:
    B=[]
    for i in range(3):
        D[min(a+1,G[a][i]+1)*10**6+max(a+1,G[a][i]+1)]=i
        B.append(min(a+1,G[a][i]+1)*10**6+max(a+1,G[a][i]+1))
    f=3
    x=3
    for i in range(n-1):
        if GG[i][0]*10**6+GG[i][1] not in B:
            print(x)
            x=x+1
        else:
            print(D[GG[i][0]*10**6+GG[i][1]])