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.io.OutputStream;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Set;
import java.util.StringTokenizer;

public class C {

	static int crossroad = -1;
	static int crossroadSize = -1;

	static class Graph {
		int V;

		LinkedList<Integer> adjListArray[];

		Graph(int V) {
			this.V = V;
			adjListArray = new LinkedList[V];

			for (int i = 0; i < V; i++) {
				adjListArray[i] = new LinkedList<>();
			}
		}
	}

	static void addEdge(Graph graph, int src, int dest) {

		graph.adjListArray[src].add(dest);
		graph.adjListArray[dest].add(src);

		if (graph.adjListArray[src].size() >= 3) {
			crossroad = src;
			crossroadSize = graph.adjListArray[src].size();
		}

		if (graph.adjListArray[dest].size() >= 3) {
			crossroad = dest;
			crossroadSize = graph.adjListArray[dest].size();
		}
	}

	static LinkedList<Integer> neigh(Graph g, int i) {
		return g.adjListArray[i];
	}

	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);

		int nodes = in.nextInt();
		Graph g = new Graph(nodes);
		int u, v;
		int[][] inputs = new int[nodes - 1][2];

		for (int i = 0; i < nodes - 1; i++) {
			u = in.nextInt();
			v = in.nextInt();
			inputs[i][0] = u - 1;
			inputs[i][1] = v - 1;
			addEdge(g, inputs[i][0], inputs[i][1]);

		}

		int counter = 0;
		if (crossroad == -1)
			 counter = 0;
		else
			 counter = crossroadSize;

		for (int i = 0; i < nodes - 1; i++) {
			if (inputs[i][0] == crossroad || inputs[i][1] == crossroad) {
				out.println(--crossroadSize);
				out.flush();
			} else {
				out.println(counter);
				counter++;
				out.flush();

			}
		}

		out.close();
	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 64000);
			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());
		}

	}
}