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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main
{
    static final int mod = (int)1e9+7;
    public static void main(String[] args) throws Exception {
        FastReader in = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        int n = in.nextInt();
        int[][] edge = new int[n][2];
        int[] degree = new int[n + 1];
        for(int i = 1; i < n; i++) {
            edge[i][0] = in.nextInt();
            edge[i][1] = in.nextInt();
            degree[edge[i][0]]++;
            degree[edge[i][1]]++;
        }
        int l = 0, r = n - 2, tn = -1;
        for(int i = 1; i < n; i++) {
            if(tn == -1) {
                if(degree[edge[i][0]] > 2) {
                    tn = edge[i][0];
                    out.println(l++);
                }
                else if(degree[edge[i][1]] > 2) {
                    tn = edge[i][1];
                    out.println(l++);
                }
                else {
                    out.println(r--);
                }
            }
            else {
                if(edge[i][0] == tn) {
                    out.println(l++);
                }
                else if(edge[i][1] == tn) {
                    out.println(l++);
                }
                else {
                    out.println(r--);
                }
            }
        }
        out.flush();
    }
}

class FastReader
{
    private BufferedReader br;
    private StringTokenizer st;

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

    public String next() throws IOException
    {
        if(st == null || !st.hasMoreElements())
        {
            st = new StringTokenizer(br.readLine());
        }

        return st.nextToken();
    }

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

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

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