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.*;
public class Sol
{
    public static void main(String []Args)throws Exception
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        ArrayList<Pair> edges = new ArrayList<>();
        int degree[] = new int[n+1];
        for(int i = 1;i<=n-1;i++)
        {
            StringTokenizer str =  new StringTokenizer(br.readLine());
            int a = Integer.parseInt(str.nextToken());
            int b = Integer.parseInt(str.nextToken());
            Pair p = new Pair(a,b);
            edges.add(p);
            degree[a]++;
            degree[b]++;
        }
        int ans[] = new int[n-1];
        int num = 0;
        int last= n-2;
        for(int i = 0;i<n-1;i++)
        {
            Pair p = edges.get(i);
            if(degree[p.a]==1||degree[p.b]==1)
            ans[i] = num++;
            else
            ans[i] = last--;
        }
        StringBuilder st =  new StringBuilder();
        for(int i : ans)
        {
            st.append(i+"\n");
        }System.out.println(st.toString());
    }
    
}
class Pair
{
    int a,b;
    Pair(int a, int b)
    {
        this.a = a;
        this.b = b;
    }
}