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.*;
import java.util.*;
public class R628C {
    public static void main(String[] args) throws Exception {
        BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
        int N=Integer.parseInt(in.readLine());
        List<List<Integer>> //neighbors=new ArrayList<>(),
                edgeidxs=new ArrayList<>();
        for (int i=0; i<N; i++) {
            //neighbors.add(new ArrayList<>());
            edgeidxs.add(new ArrayList<>());
        }
        int[] deg=new int[N];
        for (int i=0; i<N-1; i++) {
            StringTokenizer tok=new StringTokenizer(in.readLine());
            int u=Integer.parseInt(tok.nextToken())-1,
                    v=Integer.parseInt(tok.nextToken())-1;
            //neighbors.get(u).add(v);
            edgeidxs.get(u).add(i);
            //neighbors.get(v).add(u);
            edgeidxs.get(v).add(i);
            deg[u]++;
            deg[v]++;
        }
        int rt=0;
        while (rt<N && deg[rt]<3)
            rt++;
        int[] labels=new int[N-1];
        Arrays.fill(labels,-1);
        if (rt==N) {
            //path tree
            for (int i=0; i<N-1; i++)
                labels[i]=i;
        }
        else {
            for (int ni = 0; ni < 3; ni++)
                labels[edgeidxs.get(rt).get(ni)] = ni;
            for (int e = 0, l = 3; e < N - 1; e++) {
                if (labels[e] == -1) {
                    labels[e] = l;
                    l++;
                }
            }
        }
        StringBuilder s=new StringBuilder();
        for (int l:labels)
            s.append(l).append("\n");
        System.out.println(s);
    }
}