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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
 
public class ProblemC {
	public static void main(String[] args) throws IOException {
		InputStream in = System.in;
		InputReader scan = new InputReader(in);
		int n = scan.nextInt();
		ArrayList<ArrayList<Integer>> tree = new ArrayList<>();
		for(int i=0;i<=n;i++) {
			tree.add(new ArrayList<>());
		}
		int[][] edges = new int[n-1][2];
		for(int i=0;i<n-1;i++) {
			int u = scan.nextInt();
			int v = scan.nextInt();
			edges[i][0] = u;
			edges[i][1] = v;
			tree.get(u).add(v);
			tree.get(v).add(u);
		}
		//Find leaf nodes, which has degree 1. Put their edges least values
		int[] weight = new int[n-1];
		int minAvailable = 0;
		int maxAvailable = n-2;
		for(int i=0;i<n-1;i++) {
			//If the edge has one leaf node put minimum, else maximum available
			boolean isAnyLeaf = false;
			if(tree.get(edges[i][0]).size()==1) {
				isAnyLeaf = true;
			}
			if(tree.get(edges[i][1]).size()==1) {
				isAnyLeaf = true;
			}
			if(isAnyLeaf) {
				weight[i]=minAvailable;
				minAvailable++;
			} else {
				weight[i] = maxAvailable;
				maxAvailable--;
			}
		}
		StringBuilder sb = new StringBuilder();
		for(int i=0;i<n-1;i++) {
			sb.append(weight[i]);
			sb.append("\n");
		}
		System.out.println(sb.toString());
	}
	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;
 
		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}
 
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
 
		public int nextInt() {
			return Integer.parseInt(next());
		}
		
		public long nextLong() {
			return Long.parseLong(next());
		}
	}
}