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:
//package CodeforcesJava;

import java.io.*;
import java.util.*;
import java.util.stream.Collectors;

public class Main {

    public void solve(InputProvider in, PrintWriter out) throws IOException {
        int nodeCount = in.nextInt();
        Connection[] connections = new Connection[nodeCount - 1];
        Map<Integer, List<Connection>> connectionMap = new HashMap<>(nodeCount);
        for (int i = 0; i < connections.length; i++) {
            int from = in.nextInt();
            int to = in.nextInt();
            connections[i] = new Connection();
            connectionMap.putIfAbsent(from, new ArrayList<>());
            connectionMap.get(from).add(connections[i]);
            connectionMap.putIfAbsent(to, new ArrayList<>());
            connectionMap.get(to).add(connections[i]);
        }
        List<Connection> orderedConnections = connectionMap
                .entrySet()
                .stream()
                .sorted(Comparator.<Map.Entry<Integer, List<Connection>>>comparingInt(
                        entry -> entry.getValue().size()).reversed())
                .flatMap(entry -> entry.getValue().stream())
                .distinct()
                .collect(Collectors.toList());
        for (int i = 0; i < orderedConnections.size(); i++) {
            orderedConnections.get(i).setMark(i);
        }
        for (Connection connection : connections) {
            out.print(connection.getMark() + "\n");
        }
    }

    private static class Connection {

        private int mark;

        public int getMark() {
            return mark;
        }

        public void setMark(int mark) {
            this.mark = mark;
        }

    }

    public static void main(String[] args) throws Exception {
        try (InputProvider input = new InputProvider(System.in);
             PrintWriter output = new PrintWriter(System.out)) {
            new Main().solve(input, output);
        }
    }

    public static class InputProvider implements AutoCloseable {

        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputProvider(Reader reader) {
            this.reader = new BufferedReader(reader);
        }

        public InputProvider(InputStream input) {
            reader = new BufferedReader(new InputStreamReader(input));
        }

        public String next() throws IOException {
            if (Objects.isNull(tokenizer) || !tokenizer.hasMoreTokens())
                tokenizer = new StringTokenizer(reader.readLine());
            return tokenizer.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public String nextLine() throws IOException {
            return reader.readLine();
        }

        @Override
        public void close() throws Exception {
            reader.close();
        }

    }

}