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
from math import *

    
n=int(input())
a=[[] for i in range(n+1)]
b=[]
g=[]
for i in range(n-1):
    x,y=map(int,input().split())
    a[x].append(y)
    a[y].append(x)
    b.append([x,y])
for i in range(1,n+1):    
    g.append([len(a[i]),i,a[i]])
g.sort(reverse=True)

s={}
r=0
for i in range(0,n):
    for j in g[i][2]:
        m1=min(g[i][1],j)
        m2=max(g[i][1],j)
        h=str(m1)+"*"+str(m2)
        if h in s:
            continue
        s[h]=r
        r+=1
for i in range(len(b)):
    m1=min(b[i])
    m2=max(b[i])
    h=str(m1)+"*"+str(m2)
    if h in s:
        print(s[str(m1)+"*"+str(m2)])