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:
/*
 * Remember a 6.72 student can know more than a 10.0 student.
 * Grades don't determine intelligence, they test obedience. 
 * I Never Give Up.
 * I will become Candidate Master.
 * I will defeat Saurabh Anand.
 * Skills are Cheap,Passion is Priceless.
 * Obsession is necessary.
 * Author : Sameer Raj
 */
import java.util.*;
import java.util.Map.Entry;
import java.io.*;
import java.lang.Math.*;

import static java.lang.System.out;
import static java.util.Arrays.fill;
 
public class ContestMain implements Runnable{
	private static Reader in=new Reader();
	private static StringBuilder ans=new StringBuilder();
	private static long MOD=(long)1e9+7;
	private static final int N=(int) (1e5+7); // 1e5+7
    private static ArrayList<Integer> v[]=new ArrayList[N];
	private static boolean mark[]=new boolean[N];
//    private static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	/*Not try to hack the sort function*/
	public static void sort(long arr[]){
		for(int i=arr.length-1;i>=2;i--){
			int x=new Random().nextInt(i-1);
			long temp=arr[x];
			arr[x]=arr[i];
			arr[i]=temp;
		}
		Arrays.sort(arr);
	}
	public static void sort(int arr[]){
		for(int i=arr.length-1;i>=2;i--){
			int x=new Random().nextInt(i-1);
			int temp=arr[x];
			arr[x]=arr[i];
			arr[i]=temp;
		}
		Arrays.sort(arr);
	}
    private static long gcd(long a, long b){
        if(b==0)return a;
        return gcd(b,a%b);
    }
    /*Code lies here*/
    @Override
	public void run() {
    	int n=in.nextInt();
    	int x,y;
    	for(int i=1;i<=n;i++)
    		v[i]=new ArrayList();
    	int maxdeg=0,ind=0;
    	Pair<Integer> pair[]=new Pair[n-1];
    	for(int i=0;i<n-1;i++){
    		x=in.nextInt();
    		y=in.nextInt();
    		pair[i]=new Pair(x,y);
    		v[x].add(y);
    		v[y].add(x);
    		if(v[x].size()>maxdeg){maxdeg=v[x].size();ind=x;}
    		if(v[y].size()>maxdeg){maxdeg=v[y].size();ind=y;}
    	}
    	int res[]=new int[n-1];
    	fill(res,-1);
    	int c=0;
    	for(int i=0;i<n-1;i++){
    		if(pair[i].l==ind||pair[i].r==ind){
    			res[i]=c++;
    		}
    	}
    	for(int i=0;i<n-1;i++)
    		if(res[i]==-1)res[i]=c++;
    	for(int i=0;i<n-1;i++)
    		appn(res[i]);
    	pn(ans);
	}
	public static void main(String[] args) throws IOException{
		new Thread(null,new ContestMain(),"Accepted",1<<26).start();
	}
	static class Pair<T> implements Comparable<Pair>{
		int l;
		int r;
		Pair(){
			l=0;
			r=0;
		}
		Pair(int k,int v){
			l=k;
			r=v;
		}
		@Override
		public int compareTo(Pair o){
			if(l!=o.l)return (int)(l-o.l);
			return (int)(r-o.r);
		}
		// Fenwick tree question comparator
//        @Override
//        public int compareTo(Pair o) {
//            if(o.r!=r)return (int) (r-o.r);
//            else return (int)(l-o.l);
//        }
	}
	/* BINARY SEARCH FUNCTIONS */
	public static int ceilSearch(int l,int r,int val,int ar[]){
		int mid;
		while(l+1!=r&&l<r){
			mid=(l+r)/2;
			if(ar[mid]<val)l=mid;
			else r=mid;
		}
		if(ar[l]>=val)return l;
		else if(ar[r]>=val)return r;
		else return -1;
	}
	public static int ceilSearch(int l,int r,long val,long ar[]){
		int mid;
		while(l+1!=r&&l<r){
			mid=(l+r)/2;
			if(ar[mid]<val)l=mid;
			else r=mid;
		}
		if(ar[l]>=val)return l;
		else if(ar[r]>=val)return r;
		else return -1;
	}
	public static int floorSearch(int l,int r,int val,int ar[]){
		int mid;
		while(l+1!=r&&l<r){
			mid=(l+r)/2;
			if(ar[mid]>val)r=mid;
			else l=mid;
		}
		if(ar[r]<=val)return r;
		else if(ar[l]<=val)return l;
		else return -1;
	}
	public static int floorSearch(int l,int r,long val,long ar[]){
		int mid;
		while(l+1!=r&&l<r){
			mid=(l+r)/2;
			if(ar[mid]>val)r=mid;
			else l=mid;
		}
		if(ar[r]<=val)return r;
		else if(ar[l]<=val)return l;
		else return -1;
	}
	/* MODULAR OPERATIONS */
	private static long mod(long a,long b){
	    	return (b+a%b)%b;
	}
	private static long modInv(long a){
	    	return powmod(a,MOD-2);
	}
	private static long powmod(long x,long n){
		if(n==0||x==0)return 1;
		else if(n%2==0)return(powmod((x*x)%MOD,n/2));
		else return (x*(powmod((x*x)%MOD,(n-1)/2)))%MOD;
	}
	public static long mul(long a,long b){
		return mod(mod(a,MOD)*mod(b,MOD),MOD);
	}
	public static long add(long a,long b){
		return mod(mod(a,MOD)+mod(b,MOD),MOD);
	}
	/* MAX-MIN FUNCTIONS */
	public static long min(long a,long b){
		return Math.min(a, b);
	}
	public static int min(int a,int b){
		return Math.min(a, b);
	}
	public static long max(long a,long b){
		return Math.max(a, b);
	}
	public static int max(int a,int b){
		return Math.max(a, b);
	}
	public static long min(long ar[]){
		return Arrays.stream(ar).min().getAsLong();
	}
	public static int min(int ar[]){
		return Arrays.stream(ar).min().getAsInt();
	}
	public static long max(long ar[]){
		return Arrays.stream(ar).max().getAsLong();
	}
	public static int max(int ar[]){
		return Arrays.stream(ar).max().getAsInt();
	}
	//Reader Class
	static class Reader{
		BufferedReader br;
		StringTokenizer st;
		public Reader(){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();
		}
		int nextInt(){return Integer.parseInt(next());}
		long nextLong(){return Long.parseLong(next());}
		double nextDouble(){return Double.parseDouble(next());}
		String nextLine(){
			String str="";
			try{
				str=br.readLine();
			}catch(IOException e){
				e.printStackTrace();
			}
			return str;
		}
	}
	//Looping methods
	static void rep(int ar[],int start,int end){
		for(int i=start;i<end;i++)
			ar[i]=in.nextInt();
	}
	static void rep(long ar[],int start,int end){
		for(int i=start;i<end;i++)
			ar[i]=in.nextLong();
	}
	static void rep(String ar[],int start,int end){
		for(int i=start;i<end;i++)
			ar[i]=in.next();
	}
	//Printer Methods
	static void pn(Object o){out.print(o);}
	static void pln(Object o){out.println(o);}
	static void pln(){out.println();}
	static void pf(String format,Object o){out.printf(format,o);}
	//Appenders
	static void app(Object o){ans.append(o);}
	static void appn(Object o){ans.append(o+"\n");}
}