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.util.*;

public class EhAb {
    public static void main(String []args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String str = br.readLine();
        int t = Integer.parseInt(str);
        int [][]edge_list = new int[t-1][2];
        ArrayList<Integer> []graph = new ArrayList[t+1];
        for(int i = 1; i <= t; i++) graph[i] = new ArrayList<>();
        for(int i=0; i < (t-1); i++){
            String []st = br.readLine().split(" ");
            edge_list[i][0] = Integer.parseInt(st[0]);
            edge_list[i][1] = Integer.parseInt(st[1]);
            graph[edge_list[i][0]].add(edge_list[i][1]);
            graph[edge_list[i][1]].add(edge_list[i][0]);
        }
        int important[][]=new int[3][2];
        outer: for(int i = 1; i <= t; i++ ){
            if(graph[i].size()>2){
                for(int j = 0;j < 3; j++){
                    important[j][0] = i;
                    important[j][1] = graph[i].get(j);
                }
                break outer;
            }
        }
        int k=0;
        int []ans = new int[t-1];
        Arrays.fill(ans, -1);
        for(int i = 0; i < t - 1; i++ ){
            for(int flag=0;flag<3;flag++) {
                if (important[flag][0] == edge_list[i][0] && important[flag][1] == edge_list[i][1]) {
                    ans[i] = k++;
                } else if (important[flag][1] == edge_list[i][0] && important[flag][0] == edge_list[i][1]) {
                    ans[i] = k++;
                }
            }
        }


        for(int i = 0; i < t - 1; i++ ){
            if(ans[i]==-1){
                ans[i] = k++;
            }
            System.out.println(ans[i]);
        }

    }
}