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 javafx.util.Pair;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Template {

    public static void solve(int testCase, Reader in, PrintWriter out){
        int n = in.nextInt();
        ArrayList<Pair<Integer, Integer>> edges = new ArrayList<>();
        int[] degree = new int[n+1];
        for(int i = 1;i<n;i++) {
            int u = in.nextInt();
            int v = in.nextInt();
            edges.add(new Pair<>(u,v));
            degree[u]++;
            degree[v]++;
        }

        int small = 0;
        int large = n-2;
        int[] ans = new int[n-1];
        for(int i = 0;i<n-1;i++) {
            Pair<Integer, Integer> edge = edges.get(i);
            if (degree[edge.getKey()] == 1 || degree[edge.getValue()] == 1) {
                ans[i] = small++;
            } else {
                ans[i] = large--;
            }
        }

        for(int i: ans) {
            out.println(i);
        }
    }

    public static void main(String... args) {
        Reader in = new Reader();
        PrintWriter out = new PrintWriter(System.out);
        int testCase = 1;
        for(int i = 1;i<=testCase;i++) {
            solve(i, in, out);
        }
        out.flush();
        out.close();
    }

    static class Reader {
        private StringTokenizer tokenizer;
        private BufferedReader reader;

        public Reader() {
            tokenizer = null;
            try {
                reader = new BufferedReader(new InputStreamReader(System.in)); // for file IO, replace this with new FileReader ("in.txt")
            } catch (Exception e) {
                e.printStackTrace();
            }
        }
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return tokenizer.nextToken();
        }
        public int nextInt() { return Integer.parseInt(this.next()); }
        public long nextLong() { return Long.parseLong(this.next()); }
        public double nextDouble() { return Double.parseDouble(this.next()); }
        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return "";
        }
    }
}