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.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

public class TaskC {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;
        PrintWriter pw = new PrintWriter(System.out);

        int n = Integer.parseInt(br.readLine());
        Graph g = new Graph(n);

        for(int i=0 ; i<n-1 ; i++) {
            st = new StringTokenizer(br.readLine());
            int x = Integer.parseInt(st.nextToken())-1;
            int y = Integer.parseInt(st.nextToken())-1;
            g.addEdge(x, y, i);
        }

        g.solve();





        pw.flush();
        pw.close();
    }
}

class Graph {
    int n;
    HashMap<Integer, Integer>[] adj;
    int[] val;

    Graph(int v) {
        n = v;
        adj = new HashMap[n];
        val = new int[n-1];
        Arrays.fill(val, -1);
        for(int i=0 ; i<n ; i++) adj[i] = new HashMap<>();
    }

    void addEdge(int a, int b, int c) {
        adj[a].put(b, c);
        adj[b].put(a, c);
    }

    void solve() {
        PrintWriter pw = new PrintWriter(System.out);
        if(n == 2) {
            pw.println(0);
        }
        else {
            int assign = 0;
            for(int i=0 ; i<n ; i++) {
                if(adj[i].size() == 1) {
                    for(Map.Entry<Integer, Integer> ent: adj[i].entrySet()) {
                        val[ent.getValue()] = assign;
                        assign++;
                    }
                }
            }

            for(int i=0 ; i<n-1 ; i++) {
                if(val[i] == -1) {
                    val[i] = assign++;
                }
            }


            for(int i=0 ; i<n-1 ; i++) pw.println(val[i]);
        }

        pw.flush();
        pw.close();
    }

}