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.io.*;

public class File {
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }

            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
	
	
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
		
		
		
		
		
		
		
		int n = sc.nextInt();
		
		Map<Integer, List<Integer>> tree = new HashMap<>();
		for (int i = 0; i <= n; i++) {
			tree.put(i, new ArrayList<Integer>());
		}
		
		List<int[]> edges = new ArrayList<>();
		
		for (int i = 0; i < n-1; i++) {
			int u = sc.nextInt();
			int v = sc.nextInt();
			
			tree.get(u).add(i);
			tree.get(v).add(i);
			
			edges.add(new int[] {u, v});
		}
		
		
		int maxEdges = 0;
		for (int i = 1; i <= n; i++) {
			maxEdges = Math.max(maxEdges, tree.get(i).size());
		}
		
		if (maxEdges <= 2) {
			// If the max number of edges to a node is <= 2,
			// MEX is always n-1, because there's only a single path.
			for (int i = 0; i < n-1; i++) {
				out.println(i);
			}
		}
		else {
			// If for any node has > 2 edges from it, smallest MEX is always 2
				// set the node's edges to 0, 1, 2. There will never be
				// path with 0, 1 and 2 in it as a result.
				// The rest of edges can be anything.
			int tripleNode = -1;
			for (int i = 1; i <= n; i++) {
				if (tree.get(i).size() >= 3) {
					tripleNode = i;
					break;
				}
			}
			
			int[] edgeVal = new int[n-1];
			int val = 0;
            Set<Integer> set = new HashSet<Integer>();
            
			for (int edge : tree.get(tripleNode)) {
				edgeVal[edge] = val++;
				set.add(edge);
			}
			
			for (int edge = 0; edge < n-1; edge++) {
				if (!set.contains(edge)) {
					edgeVal[edge] = val++;
					set.add(edge);
				}
			}
			
			for (int res : edgeVal) {
				out.println(res);
			}
		}
		
		
		
		out.close();
	}
}