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.*;

public class a {
    public static void main(String[] args) throws IOException {
        FastReader scan = new FastReader();
        //PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("taming.out")));
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        Task solver = new Task();
        //int t = scan.nextInt();
        int t = 1;
        for(int i = 1; i <= t; i++) solver.solve(i, scan, out);
        out.close();
    }
    static class Task {
        public void solve(int testNumber, FastReader sc, PrintWriter pw) {
        	int n = sc.nextInt();
        	ArrayList<ArrayList<tup>> adjl = new ArrayList<>();
        	tup[] arr = new tup[n-1];
        	for(int i=0;i<=n;i++){
        		adjl.add(new ArrayList<tup>());
        	}
        	for(int i=0;i<n-1;i++){
        		int a =sc.nextInt();
        		int b = sc.nextInt();
        		arr[i]=new tup(a,b);
        		adjl.get(a).add(new tup(b,i));
        		adjl.get(b).add(new tup(a,i));
        	}
        	int[] ans = new int[n-1];
        	int ct = 0;
        	ArrayList<Integer> lea = new ArrayList<Integer>();
        	for(int i=1;i<=n;i++){
        		if(adjl.get(i).size()==1){
        			ct++;
        			lea.add(adjl.get(i).get(0).b);}
        	
        	}if(ct == 2){
        		for(int i=0;i<n-1;i++){
        			pw.println(i);
        		}
        		return;
        	}
        	Arrays.fill(ans,-1);
        	ans[lea.get(0)]=0;
        	ans[lea.get(1)]=1;
        	ans[lea.get(2)]=2;
        	int ctr = 2;
        	for(int i=0;i<n-1;i++){
        		if(ans[i]==-1)ans[i]=++ctr;
        	}
        	for(int x : ans){
        		pw.println(x);
        	}
        	
        }

    }
    static class tup implements Comparable<tup>{
        int a, b;
        tup(){};
        tup(int a, int b){
            this.a=a;
            this.b=b;
        }

        @Override
        public int compareTo( tup o2) {
            return o2.b!=b?Integer.compare(o2.b,b):Integer.compare(o2.a,a);
        }
    }
    static void shuffle(long[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            long temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }
    static void shuffle(int[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(new File(s)));
        }

        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;
        }
    }

}