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 Main 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);
        }
    }
    
    static class Pair<U extends Comparable<U>, V extends Comparable<V>> implements Comparable<Pair<U, V>> {
        public U first;
        public V second;
 
        public Pair(U first, V second) {
            this.first = first;
            this.second = second;
        }
 
        public int hashCode() {
            return (first == null ? 0 : first.hashCode() * 31) + (second == null ? 0 : second.hashCode());
        }
 
        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || getClass() != o.getClass()) {
                return false;
            }
            Pair<U, V> p = (Pair<U, V>) o;
            return (first == null ? p.first == null : first.equals(p.first)) &&
                    (second == null ? p.second == null : second.equals(p.second));
        }
 
        public int compareTo(Pair<U, V> b) {
            int cmpU = first.compareTo(b.first);
            return cmpU != 0 ? cmpU : second.compareTo(b.second);
        }
 
        public String toString() {
            return String.format("Pair = (%s, %s)", first.toString(), second.toString());
        }
    }
    
    public static void main(String args[]) throws Exception {
        new Thread(null, new Main(),"Main",1<<26).start();
    }
    public void run() {
        InputReader sc = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);
 
             int n=sc.nextInt();
             HashMap<Pair<Integer,Integer>,Integer> hm=new HashMap<>();
             ArrayList<Integer> al[]=new ArrayList[n+1];
             Arrays.setAll(al,e->new ArrayList());
             int temp1=0,temp2=0;
             int arr[]=new int[n-1];
             Arrays.fill(arr,-1);
             for(int i=0;i<n-1;i++)
             {
                 temp1=sc.nextInt();
                 temp2=sc.nextInt();
                 al[temp1].add(temp2);
                 al[temp2].add(temp1);
                 hm.put(new Pair(temp1,temp2),i);
                 hm.put(new Pair(temp2,temp1),i);
             }
             int ind=0,cnt=0;
             for(int i=1;i<=n;i++)
             {
                 if(al[i].size()>=3)
                 {
                     for(int j=0;j<3;j++)
                     {
                         temp1=al[i].get(j);
                         ind=hm.get(new Pair(i,temp1));
                         arr[ind]=j;
                     }
                     cnt=3;
                     break;
                 }
             }
                 for(int i=0;i<n-1;i++)
                 {
                     if(arr[i]==-1)
                     {
                         arr[i]=cnt;
                         cnt++;
                     }
                     w.println(arr[i]);
                 }
        w.close();
    }
   
}