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.util.*;
import java.io.*;
import java.math.*;
 
public class Main
{
    static class Edge{
        int u , v, label;
        public Edge(int u, int v){
            this.u = u;
            this.v = v;
            label = -1;
        }
    }
    public static void process()throws IOException
    {
        int n = ni(), deg[] = new int[n+1], cnt = 0;
        ArrayList<Edge> l[] = new ArrayList[n+1];
        ArrayList<Edge> li = new ArrayList<>();
        for(int i = 0 ; i <= n; i++) l[i] = new ArrayList<>();

        for(int i = 1; i <= n-1; i++){
            int u = ni(), v = ni();

            Edge e = new Edge(u, v);
            li.add(e);
            l[u].add(e);
            l[v].add(e);

            deg[u]++;
            deg[v]++;
        }

        boolean taken[] = new boolean[n+1];

        for(int i = 1; i <= n; i++){
            if(deg[i] >= 3){
                for(int j = 0; j < 3; j++){
                    Edge e = l[i].get(j);
                    e.label = cnt;
                    cnt++;
                }

                break;
            }
        }

        for(Edge e : li){
            if(e.label == -1){
                pn(cnt);
                cnt++;
            }
            else
                pn(e.label);
        }
    }
 
 
    static FastReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        out = new PrintWriter(System.out);
        sc=new FastReader();
 
        long s = System.currentTimeMillis();
        int t=1;
        //t=ni();
        while(t-->0)
            process();
 
        out.flush();
        System.err.println(System.currentTimeMillis()-s+"ms");
    }
    
    
    static void pn(Object o){out.println(o);}
    static void p(Object o){out.print(o);}
    static int ni()throws IOException{return Integer.parseInt(sc.next());}
    static long nl()throws IOException{return Long.parseLong(sc.next());}
    static double nd()throws IOException{return Double.parseDouble(sc.next());}
    static String nln()throws IOException{return sc.nextLine();}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
    
    static long mod=(long)1e9+7l;
 
/////////////////////////////////////////////////////////////////////////////////////////////////////////
    static class FastReader{ 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader(){ 
            br = new BufferedReader(new InputStreamReader(System.in)); 
        } 
  
        String next(){ 
            while (st == null || !st.hasMoreElements()){ 
                try{ st = new StringTokenizer(br.readLine()); } catch (IOException  e){ e.printStackTrace(); } 
            } 
            return st.nextToken(); 
        } 
  
        String nextLine(){ 
            String str = ""; 
            try{ str = br.readLine(); } catch (IOException e) { e.printStackTrace(); } 
            return str; 
        } 
    } 
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
}