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:
from collections import defaultdict
import sys
input = sys.stdin.readline
class Graph:
    def __init__(self,v):
        self.graph = defaultdict(list)
        self.min = 0
        self.max = v-2
        self.edgeAns = defaultdict(dict)
    
    def addEdge(self,u,v):
        self.graph[u].append(v)
        self.graph[v].append(u)
    
    def dfs(self,v):
        for i in range(1,v+1):
            if(len(self.graph[i])>2):
                for j in range(3):
                    g.edgeAns[i][self.graph[i][j]] = j
                    g.edgeAns[self.graph[i][j]][i] = j
                break

    def isLinear(self,n):
        cnt = 0
        for i in range(1,n+1):
            if(len(self.graph[i])==2):
                cnt+=1
        if(cnt==n-2):
            m = 0
            for i in range(1,n+1):
                if(len(self.graph[i])==1):
                    self.edgeAns[i][self.graph[i][0]] = m
                    self.edgeAns[i][self.graph[i][0]] = m
                    m+=1
        else:
            self.dfs(n)
    
n = int(input())
g = Graph(n)
temp = []
for _ in range(n-1):
    a,b = map(int,input().split())
    g.addEdge(a,b)
    temp.append((a,b))

g.isLinear(n)
max = n-2
if(n==2):
    print(0)
else:
    for i,j in temp:
        if i in g.edgeAns[j]:
            print(g.edgeAns[j][i])
        else:
            print(max)
            max-=1