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 Main {
  public static void main(String[] args) throws IOException {
    InputStreamReader in = new InputStreamReader(System.in);
    BufferedReader br = new BufferedReader(in);

    int n = Integer.parseInt(br.readLine());
    
    int[][] edges = new int[n-1][3];

    ArrayList<ArrayList<Integer>> adjEdge = new ArrayList<>();
    int[][] nodeSize = new int[n][2];

    for (int i = 0; i < n; i++) {
      nodeSize[i][0] = i;
      adjEdge.add(new ArrayList<Integer>());
    }

    

    for (int i = 0; i < n-1; i++) {
      StringTokenizer st = new StringTokenizer(br.readLine());

      int u = Integer.parseInt(st.nextToken())-1;
      int v = Integer.parseInt(st.nextToken())-1;

      edges[i][0] = u;
      edges[i][1] = v;
      edges[i][2] = -1; //not visited

      adjEdge.get(u).add(i);
      adjEdge.get(v).add(i);

      nodeSize[u][1]++;
      nodeSize[v][1]++;
    }

    Arrays.sort(nodeSize, new Comparator<int[]>(){
      public int compare(int[] x, int[] y) {
        return x[1]-y[1];
      }
    });

    int currentVal = 0;

    for (int[] node : nodeSize) {
      int index = node[0];
      for (int edge : adjEdge.get(index)) {
        if (edges[edge][2] == -1) {
          edges[edge][2] = currentVal;
          currentVal++;
        }
      }
    }

    for (int[] edge : edges) {
      System.out.println(edge[2]);
    }
  }
}