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.math.*;
import java.lang.*;
 
import static java.lang.Math.*;

public class EhabMex implements Runnable 
{
    static class InputReader 
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream) 
        {
            this.stream = stream;
        }
        
        public int read()
        {
            if (numChars==-1) 
                throw new InputMismatchException();
            
            if (curChar >= numChars) 
            {
                curChar = 0;
                try
                {
                    numChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                
                if(numChars <= 0)               
                    return -1;
            }
            return buf[curChar++];
        }
     
        public String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() 
        {
            int c = read();
            
            while(isSpaceChar(c)) 
                c = read();
            
            int sgn = 1;
        
            if (c == '-') 
            {
                sgn = -1;
                c = read();
            }
            
            int res = 0;
            do
            {
                if(c<'0'||c>'9') 
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c)); 
        
            return res * sgn;
        }
		
        public long nextLong() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            long res = 0;
            
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
                return res * sgn;
        }
		
        public double nextDouble() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') 
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c))
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
    
        public String readString() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = read();
            } 
            while (!isSpaceChar(c));
            
            return res.toString();
        }
     
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        public String next()
        {
            return readString();
        }
        
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
		
    }
	
    public static void main(String args[]) throws Exception 
    {
        new Thread(null, new EhabMex(),"EhabMex",1<<27).start();
    }
	// **just change the name of class from Main to reuquired**
    public void run()
    {
        InputReader sc = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);
		
		int n=sc.nextInt();
		ArrayList<Integer> al[]= new ArrayList[n+1];
		for(int i=0;i<=n;++i) al[i]=new ArrayList<Integer>();
		
		Edge e[]= new Edge[n-1];
		int ans[]= new int[n-1];
		Arrays.fill(ans,-1);
		for(int i=0;i<n-1;++i)
		{
			int u=sc.nextInt();
			int v=sc.nextInt();
			al[u].add(v);
			al[v].add(u);
			e[i]=new Edge(Math.min(u,v),Math.max(u,v));
		}
		
		boolean f=false;
		Edge change[]= new Edge[3];
		for(int i=0;i<=n;++i)
		{
			if(al[i].size()>=3)
			{
				f=true;
				for(int j=0;j<3;++j)
				{
					int u=i;
					int v=al[i].get(j);
					change[j]= new Edge(Math.min(u,v),Math.max(u,v));
				}
				break;
			}
		}
		
		if(f)
		{
			//for(int i=0;i<3;++i) System.out.println(change[i].u+"-->"+change[i].v);
			
			int num=0;
			for(int i=0;i<3;++i)
			{
				for(int j=0;j<n-1;++j)
				{
					if(change[i].equals(e[j]))
					{
						ans[j]=num;
						num++;
						break;
					}
				}
			}
			
			for(int i=0;i<n-1;++i)
			{
				if(ans[i]==-1) 
				{
					ans[i]=num;
					num++;
				}
			}
			
			for(int i=0;i<n-1;++i)
			{
				w.println(ans[i]+" ");
			}
		}
		else
		{
			for(int i=0;i<n-1;++i) w.println(i);
		}
		
        System.out.flush();
        w.close();
    }
}

class Edge
{
	int u,v,index;
	Edge(int u, int v)
	{
		this.u=u;
		this.v=v;
		this.index=index;
	}
	
	public int hashCode()
	{
		return u*31+v*31;
	}
	
	public boolean equals(Object ob)
	{
		if(this==ob) return true;
		
		if(ob instanceof Edge)
		{
			Edge e=(Edge)ob;
			return (e.u==this.u)&&(e.v==this.v);
		}
		else return false;
	}
}