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 C {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

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

        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;
        }
    }

    static FastReader s = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);

    private static int[] rai(int n) {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextInt();
        }
        return arr;
    }

    private static int[][] rai(int n, int m) {
        int[][] arr = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextInt();
            }
        }
        return arr;
    }

    private static long[] ral(int n) {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextLong();
        }
        return arr;
    }

    private static long[][] ral(int n, int m) {
        long[][] arr = new long[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextLong();
            }
        }
        return arr;
    }

    private static int ri() {
        return s.nextInt();
    }

    private static long rl() {
        return s.nextLong();
    }

    private static String rs() {
        return s.next();
    }

    public static void main(String[] args) {
        StringBuilder ans = new StringBuilder();
//        int t = ri();
        int t=1;
        while (t-- > 0) {
            int n=ri();
            List<Edge> list=new ArrayList<>();
            HashMap<Integer,Integer> map=new HashMap<>();
            for(int i=1;i<=n;i++)
            {
                map.put(i,0);
            }
            boolean[] arr=new boolean[n+1];
            Arrays.fill(arr,true);
            arr[0]=false;
            for(int i=0;i<n-1;i++)
            {
                int a=ri();
                int b=ri();
                map.put(a,map.getOrDefault(a,0)+1);
                map.put(b,map.getOrDefault(b,0)+1);
                list.add(new Edge(a,b));
                if(map.get(a)>1)
                {
                    arr[a]=false;
                }
                if(map.get(b)>1)
                {
                    arr[b]=false;
                }

            }
            int count=0;
            for(boolean b:arr)
            {
                if(b)
                    count++;
            }
            if(count==2)
            {
                for(int i=0;i<n-1;i++)
                {
                    ans.append(i).append("\n");
                }
                continue;
            }

            int val=3;
            int v2=0;
            for(Edge e:list)
            {
                int u=e.u;
                int v=e.v;
                if((arr[u] || arr[v]) && v2<3)
                {
                    ans.append(v2++).append("\n");
                }
                else {
                    ans.append(val++).append("\n");
                }
            }


        }
        out.print(ans.toString());
        out.flush();

    }
}
class Edge
{
    int u,v;

    public Edge(int u, int v) {
        this.u = u;
        this.v = v;
    }
}