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 sun.reflect.generics.tree.Tree;

import java.lang.reflect.Array;
import java.util.*;
import java.io.*;
import java.lang.*;
import java.math.*;


public class cf1 implements Runnable {

    public long gcd(long a,long b){
        if (a==0)
            return b;
        return gcd(b % a, a);
    }


    public void run(){

        InputReader in =  new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);
        int n=in.nextInt();
        ArrayList<Integer>[] al=new ArrayList[n+1];
        HashMap<String,Integer> hm=new HashMap<>();

        for (int i = 1; i <=n ; i++) {
            al[i]=new ArrayList<Integer>();
        }

        for (int i = 0; i <n-1; i++) {
            int a=in.nextInt();
            int b=in.nextInt();
            al[a].add(b);
            al[b].add(a);

            String ab=String.valueOf(a)+String.valueOf(b);
            String ba=String.valueOf(b)+String.valueOf(a);

            hm.put(ab,i);
            hm.put(ba,i);
        }

        int nxt=0;
        int[] ans=new int[n];
        Arrays.fill(ans,-1);
        for (int i = 1; i <=n ; i++) {
            if(al[i].size()>=3){
                int a=al[i].get(0);
                int b=al[i].get(1);
                int c=al[i].get(2);

                String ia=String.valueOf(i)+String.valueOf(a);
                String ib=String.valueOf(i)+String.valueOf(b);
                String ic=String.valueOf(i)+String.valueOf(c);
                //w.println(ia+" "+ib+" "+ic);
                //w.println(hm.get(ia)+" "+hm.get(ib)+" "+hm.get(ic));
                ans[hm.get(ia)]=0;
                ans[hm.get(ib)]=1;
                ans[hm.get(ic)]=2;

                nxt=3;
                break;
            }
        }

        for (int i = 0; i <n-1 ; i++) {
            if(ans[i]!=-1)
                w.println(ans[i]);
            else{
                w.println(nxt);
                nxt++;
            }
        }
        w.close();
    }

    static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        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()
        {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            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 cf1(),"cf1",1<<26).start();
    }
}