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.io.*;
import java.util.*;

public class CF1278E extends PrintWriter {
	CF1278E() { super(System.out); }
	Scanner sc = new Scanner(System.in);
	public static void main(String[] $) {
		CF1278E o = new CF1278E(); o.main(); o.flush();
	}

	int[] oo, oj; int __ = 1;
	int link(int o, int j) {
		oo[__] = o; oj[__] = j;
		return __++;
	}
	int[] ae, dd, ll, rr;
	void init(int n, int m) {
		oo = new int[1 + m * 2]; oj = new int[1 + m * 2];
		ae = new int[n]; dd = new int[n]; ll = new int[n]; rr = new int[n];
	}
	int x;
	void dfs(int p, int i, int l) {
		ll[i] = l;
		rr[i] = x += dd[i];
		int x_ = x;
		for (int o = ae[i]; o != 0; o = oo[o]) {
			int j = oj[o];
			if (j != p)
				dfs(i, j, --x_);
		}
	}
	void main() {
		int n = sc.nextInt();
		init(n, n - 1);
		for (int h = 0; h < n - 1; h++) {
			int i = sc.nextInt() - 1;
			int j = sc.nextInt() - 1;
			ae[i] = link(ae[i], j); dd[i]++;
			ae[j] = link(ae[j], i); dd[j]++;
		}
		dd[0]++;
		dfs(-1, 0, ++x);
		for (int i = 0; i < n; i++)
			println(ll[i] + " " + rr[i]);
	}
}