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.lang.*;
import java.io.*;

public class Solution{
	public static void main(String[] args) {
	    Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
	    int n = in.nextInt();
	    int[][] arr = new int[n-1][2];
	    for (int i = 0; i < n-1; i++) {
	    	arr[i][0] = in.nextInt();
	    	arr[i][1] = in.nextInt();
	    }
	    int[] ans = solve(n, arr);
	    for (int i = 0; i < n-1; i++) System.out.println(ans[i]);
  	}

  	public static int[] solve(int n, int[][] arr){
  		int[] ans = new int[n-1];
  		Arrays.fill(ans, -1);
  		Map<Integer, Integer> degrees = new HashMap<>();
  		for (int i = 0; i < n-1; i++) {
  			degrees.put(arr[i][0], degrees.getOrDefault(arr[i][0], 0) + 1);
  			if (degrees.get(arr[i][0]) == 3) {
  				int t = 0, s = 3;
  				for (int j = 0; j < n-1; j++) {
  					if ((arr[j][0] == arr[i][0] || arr[j][1] == arr[i][0]) && t < 3) {
  						ans[j] = t;
  						t++;
  					} else {
  						ans[j] = s;
  						s++;
  					}
  				}
  				return ans;
  			}
  			degrees.put(arr[i][1], degrees.getOrDefault(arr[i][1], 0) + 1);
  			if (degrees.get(arr[i][1]) == 3) {
  				int t = 0, s = 3;
  				for (int j = 0; j < n-1; j++) {
  					if ((arr[j][0] == arr[i][1] || arr[j][1] == arr[i][1]) && t < 3) {
  						ans[j] = t;
  						t++;
  					} else {
  						ans[j] = s;
  						s++;
  					}
  				}
  				return ans;
  			}
  		}

  		Set<Integer> set = new HashSet<>();
  		for (int k: degrees.keySet()) {
  			if (degrees.get(k) == 1) set.add(k);
  		}

  		int t = 0, s = 2;
  		for (int i = 0; i < n-1; i++) {
  			if (set.contains(arr[i][0]) || set.contains(arr[i][1])) {
  				ans[i] = t;
  				t++;
  			} else {
  				ans[i] = s;
  				s++;
  			}
  		}

  		return ans;
  	}
}