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 JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.lang.*;

public class Rextester{
    private LinkedList<Integer>[] graph;
    private int V,p;
    private Edges[] edges;
    
    
    static class Edges{
        int src,dest,value;
        public Edges(int src,int dest){
            this.src = src;
            this.dest = dest;
            value = -1;
        }
    }
    
    public Rextester(int V){
        this.V = V;
        p=0;
        graph = new LinkedList[V];
        edges = new Edges[V-1];
        for(int i=0;i<V;i++){
            graph[i]=new LinkedList<Integer>();
        }
    }
    
    public void addEdge(int a,int b){
        graph[a].add(b);
        graph[b].add(a);
        edges[p++]=new Edges(a,b);
    }
    
    public void printMEX(){
        int node = 0,res = 0;
        boolean flag = false;
        for(int i=0;i<V;i++){
            if(graph[i].size()>=3){
                flag = true;
                node = i;
                res = graph[i].size();
                break;
            }
        }
        if(!flag){
            for(int i=0;i<p;i++){
                System.out.println(i);
            }
            return;
        }
        int q = 0,r=res;
        for(int i=0;i<p;i++){
            if(edges[i].src == node || edges[i].dest == node){
                System.out.println(q++);
            }
            else{
                System.out.println(r++);
            }
        }
    }
                
    
    public static void main(String[] args)throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = new Integer(br.readLine());
        Rextester rs = new Rextester(n);
        for(int i=0;i<n-1;i++){
            StringTokenizer st = new StringTokenizer(br.readLine());
            rs.addEdge(new Integer(st.nextToken())-1,new Integer(st.nextToken())-1);
        }
        rs.printMEX();
    }
}