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.lang.*;
public class Main{
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        solve(in, out);
        out.close();
    }
    static int L,R,top,bottom;
    // static int ans;
    public static void solve(InputReader sc, PrintWriter pw) {
        // int iter=sc.nextInt();
        int iter=1;
        // int a=0,b=0;
        u:while(iter-->0){
            int n=sc.nextInt();
            int u,v;
            top=n-2;
            bottom=0;
            Pair []arr=new Pair[n-1];
            HashMap<Integer,HashMap<Integer,Integer>> hmap=new HashMap<>();
            for(int i=0;i<n-1;i++){
                u=sc.nextInt();
                v=sc.nextInt();
                arr[i]=new Pair(u,v);
                hmap.putIfAbsent(u,new HashMap<>());
                hmap.putIfAbsent(v,new HashMap<>());
                hmap.get(u).put(v,-1);
                hmap.get(v).put(u,-1);
            }
            // System.out.println(hmap);
            boolean []vis=new boolean [n];
            Arrays.fill(vis,false);
            dfs(hmap,1,-1,vis);
            // System.out.println(hmap);
            for(int i=0;i<n-1;i++)
                // System.out.println(arr[i].u+" "+arr[i].v);
                pw.println(Math.max(hmap.get(arr[i].u).get(arr[i].v),hmap.get(arr[i].v).get(arr[i].u)));
        }
    }
    public static void dfs(HashMap<Integer,HashMap<Integer,Integer>> hmap, int i,int par, boolean []vis){
        vis[i-1]=true;
        boolean isEnd=true;
        for(int j:hmap.get(i).keySet()){
            if(!vis[j-1]){
                dfs(hmap,j,i,vis);
                isEnd=false;
            }
        }
        if(isEnd)
            hmap.get(par).put(i,bottom++);
        else if(par!=-1)
            hmap.get(par).put(i,top--);
    }
    public static void swap(char []chrr, int i, int j){
        char temp=chrr[i];
        chrr[i]=chrr[j];
        chrr[j]=temp;
    }
    public static int num(int n){
        int a=0;
        while(n>0){
            a+=(n&1);
            n>>=1;
        }
        return a;
    }
    static class Pair{
        int u, v;
        Pair(int a,int b){
            this.u=a;
            this.v=b;
        }   
    }
        // public int compareTo(Pair p){
        //     return (b-p.b);
        // }
        // public int hashCode(){
        //     int hashcode = (a+" "+b).hashCode();
        //     return hashcode;
        // }
         
        // public boolean equals(Object obj){
        //     if (obj instanceof Pair) {
        //         Pair p = (Pair) obj;
        //         return (p.a==this.a && p.b == this.b);
        //     }
        //     return false;
        // }
 
    static boolean isPrime(int n) { 
        if (n <= 1) 
            return false; 
        if (n <= 3) 
            return true; 
        if (n % 2 == 0 || n % 3 == 0) 
            return false; 
        for (int i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
                return false; 
        return true; 
    } 
    static int gcd(int a, int b) { 
        if (b == 0) 
            return a; 
        return gcd(b, a % b);  
    } 
    static long fast_pow(long base,long n,long M){
        if(n==0)
           return 1;
        if(n==1)
        return base;
        long halfn=fast_pow(base,n/2,M);
        if(n%2==0)
            return ( halfn * halfn ) % M;
        else
            return ( ( ( halfn * halfn ) % M ) * base ) % M;
    }
    static long modInverse(long n,long M){
        return fast_pow(n,M-2,M);
    }
    public static void feedArr(long []arr,InputReader sc){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.nextLong();
    }
    public static void feedArr(double []arr,InputReader sc){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.nextDouble();
    }
    public static void feedArr(int []arr,InputReader sc){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.nextInt();
    }
    public static void feedArr(String []arr,InputReader sc){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.next();
    }
    public static String printArr(int []arr){
        StringBuilder sbr=new StringBuilder();
        for(int i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public  static String printArr(long []arr){
        StringBuilder sbr=new StringBuilder();
        for(long i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public static String printArr(String []arr){
        StringBuilder sbr=new StringBuilder();
        for(String i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public static String printArr(double []arr){
        StringBuilder sbr=new StringBuilder();
        for(double i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
 
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
 
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}