Problem: We had a really tough time generating tests for problem D. In order to prepare strong tests, we had to solve the following problem.

Given an undirected labeled tree consisting of n vertices, find a set of segments such that:

  1. both endpoints of each segment are integers from 1 to 2n, and each integer from 1 to 2n should appear as an endpoint of exactly one segment; 
  2. all segments are non-degenerate; 
  3. for each pair (i, j) such that i ≠ j, i ∈ [1, n] and j ∈ [1, n], the vertices i and j are connected with an edge if and only if the segments i and j intersect, but neither segment i is fully contained in segment j, nor segment j is fully contained in segment i. 



Can you solve this problem too?

Input

The first line contains one integer n (1 ≤ n ≤ 5 ⋅ 10^5) — the number of vertices in the tree.

Then n - 1 lines follow, each containing two integers x_i and y_i (1 ≤ x_i, y_i ≤ n, x_i ≠ y_i) denoting the endpoints of the i-th edge.

It is guaranteed that the given graph is a tree.

Output

Print n pairs of integers, the i-th pair should contain two integers l_i and r_i (1 ≤ l_i < r_i ≤ 2n) — the endpoints of the i-th segment. All 2n integers you print should be unique.

It is guaranteed that the answer always exists.

Examples

Input


6
1 2
1 3
3 4
3 5
2 6


Output


9 12
7 10
3 11
1 5
2 4
6 8


Input


1


Output


1 2

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
public class TestD {

	static BufferedReader br;
	static StringTokenizer tokenizer;

	public static void main(String[] args) throws Exception {
		br = new BufferedReader(new InputStreamReader(System.in));
		int n = nextInt();
		ArrayList<Integer>[] adj = new ArrayList[n];
		for(int i = 0; i < n; i++)
			adj[i] = new ArrayList<Integer>();
		for(int i = 0; i < n - 1; i++) {
			int a = nextInt() - 1;
			int b = nextInt() - 1;
			adj[a].add(b);
			adj[b].add(a);
		}
		ArrayList<Integer> ans = new ArrayList<Integer>();
		ans.add(0);
		DFS(ans, 0, adj, new boolean[n]);
		int[] start = new int[n];
		int[] end = new int[n];
		for(int i = 0; i < 2 * n; i++) {
			if(start[ans.get(i)] != 0) end[ans.get(i)] = i + 1;
			else start[ans.get(i)] = i + 1;
		}
		PrintWriter out = new PrintWriter(System.out);
		for(int i = 0; i < n; i++)
			out.println(start[i] + " " + end[i]);
		out.close();
	}
	public static void DFS(ArrayList<Integer> ans, int curr, ArrayList<Integer>[] adj, boolean[] visited) {
		visited[curr] = true;
		for(int e: adj[curr]) if(!visited[e]) ans.add(e);
		ans.add(curr);
		for(int i = adj[curr].size() - 1; i >= 0; i--)
			if(!visited[adj[curr].get(i)])
				DFS(ans, adj[curr].get(i), adj, visited);
	}
	public static String next() throws IOException {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			String line = br.readLine();
			if (line == null)
				throw new IOException();
			tokenizer = new StringTokenizer(line);
		}
		return tokenizer.nextToken();
	}

	public static int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	public static long nextLong() throws IOException {
		return Long.parseLong(next());
	}

	public static double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}
}