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.util.*;
import java.io.*;
import static java.lang.Math.*;
import java.math.BigInteger;

public class C {

    public static void main(String[] args) throws Exception {
        FastScanner scanner = new FastScanner();

        int n = scanner.nextInt();
        //ArrayList<Pair> oe = new ArrayList <>();
        int[] m = new int[n + 5];
        Pair[] oe = new Pair[n + 5];

        for (int i = 0; i < n - 1; i++) {
            int[] tmp = scanner.nextIntArray();
            oe[i] = new Pair(tmp[0], tmp[1]);
            m[tmp[0]]++; m[tmp[1]]++;
        }
        int c = 1;
        int v = 2;
        for (int i = 1; i <= n; i++) {
            if (m[i] > 2) {
                c = i;
                v = m[i];
                break;
            }
        }
        int cnt = 0;
        int cnt2 = v;
        for (int i = 0; i < n - 1; i++) {
            if (oe[i].x == c || oe[i].y == c) {
                // oe.get(i).val = cnt;

                System.out.println(cnt);
                cnt++;
            } else {
                // oe.get(i).val = cnt2;

                System.out.println(cnt2);
                cnt2++;
            }
            // System.out.println(oe.get(i).val);
        }
    }

    public static class Pair {
        int x, y;
        //int val;
        public Pair(int x, int y) {
            this.x = x;
            this.y = y;
            //this.val = -1;
        }
    }

    private static class FastScanner {
        private BufferedReader br;

        public FastScanner() { br = new BufferedReader(new InputStreamReader(System.in)); }
        public FastScanner(String input) throws Exception { br = new BufferedReader(new FileReader(input)); }
        public int[] nextIntArray() throws IOException {
            String line = br.readLine();
            String[] strings = line.trim().split("\\s+");
            int[] array = new int[strings.length];
            for (int i = 0; i < array.length; i++)
                array[i] = Integer.parseInt(strings[i]);
            return array;
        }
        public int nextInt() throws IOException { return Integer.parseInt(br.readLine()); }
        public long[] nextLongArray() throws IOException {
            String line = br.readLine();
            String[] strings = line.trim().split("\\s+");
            long[] array = new long[strings.length];
            for (int i = 0; i < array.length; i++)
                array[i] = Long.parseLong(strings[i]);
            return array;
        }
        public ArrayList<Integer> nextIntegerArrayList() throws IOException {
            String line = br.readLine();
            String[] strings = line.trim().split("\\s+");
            ArrayList<Integer> array = new ArrayList<Integer>();
            for (int i = 0; i < strings.length; i++)
                array.add(Integer.parseInt(strings[i]));
            return array;
        }
        public ArrayList<Long> nextLongArrayList() throws IOException {
            String line = br.readLine();
            String[] strings = line.trim().split("\\s+");
            ArrayList<Long> array = new ArrayList<Long>();
            for (int i = 0; i < strings.length; i++)
                array.add(Long.parseLong(strings[i]));
            return array;
        }
        public long nextLong() throws IOException { return Long.parseLong(br.readLine()); }
        public double nextDouble() throws IOException { return Double.parseDouble(br.readLine()); }
        public String nextLine() throws IOException { return br.readLine(); }


        public ArrayList<BigInteger> nextBigIntegers() throws IOException {
            String line = br.readLine();
            String[] strings = line.trim().split("\\s+");
            ArrayList<BigInteger> array = new ArrayList<BigInteger>();
            for (int i = 0; i < strings.length; i++)
                array.add(BigInteger.valueOf(Long.valueOf(strings[i])));
            return array;
        }
    }
}