Depth-first search (DFS) follows the strategy to search ”deeper” in the graph whenever possible. In DFS, edges are recursively explored out of the most recently discovered vertex $v$ that still has unexplored edges leaving it. When all of $v$'s edges have been explored, the search ”backtracks” to explore edges leaving the vertex from which $v$ was discovered.

This process continues until all the vertices that are reachable from the original source vertex have been discovered. If any undiscovered vertices remain, then one of them is selected as a new source and the search is repeated from that source.

DFS timestamps each vertex as follows:

* $d[v]$ records when $v$ is first discovered.
* $f[v]$ records when the search finishes examining $v$’s adjacency list.



Write a program which reads a directed graph $G = (V, E)$ and demonstrates DFS on the graph based on the following rules:

* $G$ is given in an adjacency-list. Vertices are identified by IDs $1, 2,... n$ respectively.
* IDs in the adjacency list are arranged in ascending order.
* The program should report the discover time and the finish time for each vertex.
* When there are several candidates to visit during DFS, the algorithm should select the vertex with the smallest ID.
* The timestamp starts with 1.

Constraints

* $1 \leq n \leq 100$

Input

In the first line, an integer $n$ denoting the number of vertices of $G$ is given. In the next $n$ lines, adjacency lists of $u$ are given in the following format:

$u$ $k$ $v_1$ $v_2$ ... $v_k$

$u$ is ID of the vertex and $k$ denotes its degree. $v_i$ are IDs of vertices adjacent to $u$.

Output

For each vertex, print $id$, $d$ and $f$ separated by a space character in a line. $id$ is ID of the vertex, $d$ and $f$ is the discover time and the finish time respectively. Print in order of vertex IDs.

Examples

Input

4
1 1 2
2 1 4
3 0
4 1 3


Output

1 1 8
2 2 7
3 4 5
4 3 6


Input

6
1 2 2 3
2 2 3 4
3 1 5
4 1 6
5 1 6
6 0


Output

1 1 12
2 2 11
3 3 8
4 9 10
5 4 7
6 5 6
import java.util.Arrays;
import java.util.Scanner;

/**
 * 深さ優先探索(再帰)
 * @author nobu
 * @see <a href="http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_11_B&lang=ja">ALDS1_11_B</a>
 */
public class Main{

	private static final int N = 100;
	private static final int WHITE = 0;
	private static final int GRAY = 1;
	private static final int BLACK = 2;

	private static int n, tt;
	// 隣接行列
	private static int M[][] = new int[N][N];
	// 頂点の訪問状態
	private static int color[] = new int[N];
	// タイムスタンプ d[v]: v を最初に発見した発見時刻を記録
	private static int d[] = new int[N];
	// タイムスタンプ f[v]: v の隣接リストを調べ終えた完了時刻を記録
	private static int f[] = new int[N];
	// 各頂点の次に訪問する頂点のインデックスを記録
	private static int nt[] = new int[N];

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		for (int x[] : M) {
			Arrays.fill(x, 0);
		}

		for (int i = 0; i < n; i++) {
			int u = sc.nextInt();
			int k = sc.nextInt();
			for (int j = 0; j < k; j++) {
				int v = sc.nextInt();
				M[u - 1][v - 1] = 1;
			}
		}

		initColor();
		for (int i = 0; i < n; i++) {
			if (color[i] == WHITE) dfsRecursion(i);
		}

		for (int i = 0; i < n; i++) {
			System.out.println((i + 1) + " " + d[i] + " " + f[i]);
		}

		sc.close();
	}

	private static void initColor() {
		for (int i = 0; i < n; i++) {
			color[i] = WHITE;
		}
	}

	private static void dfsRecursion(int u) {
		color[u] = GRAY;
		d[u] = ++tt;
		for (int i = 0; i < n; i++) {
			if (M[u][i] == 1 && color[i] == WHITE) {
				dfsRecursion(i);
			}
		}
		color[u] = BLACK;
		f[u] = ++tt;
	}

}

