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())
E=[[] for i in range(n+1)]
D=dict()
DEG=[0]*(n+1)
for i in range(n-1):
    x,y=map(int,input().split())
    E[x].append(y)
    E[y].append(x)
    D[x,y]=i
    D[y,x]=i
    DEG[x]+=1
    DEG[y]+=1

ANS=[-1]*(n-1)

LIST=[]
for i in range(n+1):
    if DEG[i]==1:
        LIST.append(i)

if len(LIST)==2:
    for i in range(n-1):
        print(i)

else:
    now=0
    for l in LIST:
        k=E[l][0]
        ANS[D[k,l]]=now
        now+=1

    #print(ANS)

    for i in range(n-1):
        if ANS[i]==-1:
            ANS[i]=now
            now+=1

    for a in ANS:
        print(a)