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 {

    public static void main(String[] args) {
        FastReader scan = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        Task solver = new Task();
        int t = 1;
        for(int tt = 1; tt <= t; tt++) solver.solve(tt, scan, out);
        out.close();
    }

    static class Task {
        static int n;
        static ArrayList<Edge>[] adj;
        static int[] ans;
        static int[] parity;
        static boolean[] visited;

        public void solve(int testNumber, FastReader scan, PrintWriter out) {
            n = scan.nextInt();
            adj = new ArrayList[n];
            ans = new int[n - 1];
            Arrays.fill(ans, -1);
            parity = new int[n];
            visited = new boolean[n];
            for(int i = 0; i < n; i++) adj[i] = new ArrayList<>();
            for(int i = 0; i < n - 1; i++) {
                int a = scan.nextInt() - 1, b = scan.nextInt() - 1;
                adj[a].add(new Edge(b, i));
                adj[b].add(new Edge(a, i));
            }
            int at = 0;
            outer:
            for(int i = 0; i < n; i++) {
                if(adj[i].size() >= 3) {
                    for(int j = 0; j < 3; j++) {
                        ans[adj[i].get(j).index] = at++;
                    }
                    break outer;
                }
            }
            for(int i = 0; i < n; i++) {
                for(Edge e : adj[i]) {
                    if(ans[e.index] == -1) ans[e.index] = at++;
                }
            }
            for(int i : ans) out.println(i);
        }

        static class Edge {
            int to;
            int index;

            public Edge(int a, int b) {
                to = a;
                index = b;
            }
        }

    }

    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 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 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;
        }
    }

}