Problem:
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Depth First Search

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.

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.

Constraints

$1 \leq n \leq 100$

Sample Input 1

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

Sample Output 1

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

Sample Input 2

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

Sample Output 2

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

This is example for Sample Input 2 (discover/finish)

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in JAVA (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.NoSuchElementException;
import java.util.Random;
import java.util.Scanner;


class UnionFind{
	int Parent[];
	UnionFind(int n){//Initialize by -1
		Parent=new int[n];
		Arrays.fill(Parent, -1);
	}
	int root(int A) {//In which tree is A?
		if(Parent[A]<0)return A;
		return Parent[A]=root(Parent[A]);
	}
	int size(int A) {//size of tree which is include A
		return -Parent[root(A)];
	}
	boolean connect(int A,int B) {//Connect A and B
		A=root(A);
		B=root(B);
		if(A==B) return false;
		if(size(A)<size(B)) {int C=0;C=B;B=A;A=C;}//SWAP
		Parent[A]+=Parent[B];
		Parent[B]=A;
		return true;
	}
}
public class Main {
	static FastScanner scan=new FastScanner();
	static Scanner scanner=new Scanner(System.in);
	static Random rand=new Random();
	static long mod=1000000007;
	static double eps=1.0E-14;
	static int big=Integer.MAX_VALUE;
	static double PI=3.14159265358979323846262338327950288;
	static long modlcm(long a,long b) {return a*b*modint(gcd(a,b),mod);}
	static long gcd (long a, long b) {return b>0?gcd(b,a%b):a;}
	static long lcm (long a, long b) {return a*b/gcd(a,b);}
	static int max(int a,int b) {return a>b?a:b;}
	static int min(int a,int b) {return a<b?a:b;}
	static long lmax(long a,long b) {return Math.max(a, b);}
	static long lmin(long a,long b) {return Math.min(a, b);}
	static long factorial(int i) {return i==1?1:i*factorial(i-1);}
	static int n=scan.nextInt();
	static List<ArrayList<Integer>>list=new ArrayList<ArrayList<Integer>>();
	static int time=1;
	static int d[]=new int[n];
	static int f[]=new int[n];
	static boolean visited[]=new boolean[n];
	public static void main(String[] args) throws IOException {
		for(int i=0;i<n;i++)visited[i]=false;
		ArrayList<Integer>lis=new ArrayList<Integer>();
		for(int j=0;j<n;j++) {
			lis=new ArrayList<Integer>();
			list.add(lis);
		}
		for(int i=0;i<n;i++) {
			int x=scan.nextInt();
			x=scan.nextInt();
			for(int j=0;j<x;j++) {
				int n=scan.nextInt();
				lis=list.get(i);
				lis.add(n-1);
				list.set(i, lis);
			}
		}
		for(int j=0;j<n;j++) {
			lis=list.get(j);
			Collections.sort(lis);
			list.set(j,lis);
		}
		for(int i=0;i<n;i++) {
			if(!visited[i]) {dfs(i);visited[i]=true;time++;}
		}
		for(int i=0;i<n;i++) {
			System.out.println((i+1)+" "+d[i]+" "+f[i]);
		}
	}
	static void dfs(int i) {
		d[i]=time;
		List<Integer>lis=list.get(i);
		for(int j=0;j<lis.size();j++) {
			if(lis.get(j)==0)continue;
			if(!visited[lis.get(j)]) {
				visited[lis.get(j)]=true;
				time++;
				dfs(lis.get(j));
			}
		}
		time++;
		f[i]=time;
	}
	static int lower_bound(int a[],int key) {
		int ok=a.length;
		int ng=-1;
		while(Math.abs(ok-ng)>1) {
			int mid=(ok+ng)/2;
			if(a[mid]>=key)ok=mid;
			else ng=mid;
		}
		return ok;
	}
	static int upper_bound(int a[],int key) {
		int ok=a.length;
		int ng=-1;
		while(Math.abs(ok-ng)>1) {
			int mid=(ok+ng)/2;
			if(a[mid]>key)ok=mid;
			else ng=mid;
		}
		return ok;
	}
	static boolean isPrime (long n) {
		if (n==2) return true;
		if (n<2 || n%2==0) return false;
		double d = Math.sqrt(n);
		for (int i=3; i<=d; i+=2)if(n%i==0){return false;}
		return true;
	}
	static int upper_division(int a,int b) {
		if(a%b==0) {
			return a/b;
		}
		else {
			return a/b+1;
		}
	}
	static long lupper_division(long a,long b) {
		if(a%b==0) {
			return a/b;
		}
		else {
			return a/b+1;
		}
	}
	static int[] setArray(int a) {
		int b[]=new int[a];
		for(int i=0;i<a;i++) {
			b[i]=scan.nextInt();
		}
		return b;
	}
	static long[] lsetArray(int a) {
		long b[]=new long[a];
		for(int i=0;i<a;i++) {
			b[i]=scan.nextLong();
		}
		return b;
	}
	static String reverse(String str) {
		char ch[]=new char[str.length()];
		char chch[]=str.toCharArray();
		int a=str.length();
		for(int i=0;i<upper_division(a,2);i++) {
			ch[i]=chch[ch.length-i-1];
			ch[ch.length-1-i]=chch[i];
		}
		return String.valueOf(ch);
	}
	public static void printArray(int[] que) {
		for(int i=0;i<que.length-1;i++) {
			System.out.print(que[i]+" ");
		}
		System.out.println(que[que.length-1]);
	}
	public static void lprintArray(long[] que) {
		for(int i=0;i<que.length-1;i++) {
			System.out.print(que[i]+" ");
		}
		System.out.println(que[que.length-1]);
	}
	public static int[][] doublesort(int[][]a) {
		Arrays.sort(a,(x,y)->Integer.compare(x[0],y[0]));
		return a;
	}
	public static long[][] ldoublesort(long[][]a) {
		Arrays.sort(a,(x,y)->Long.compare(x[0],y[0]));
		return a;
	}
	static long modpow(long x,long n,long mo) {
		long sum=1;
		while(n>0) {
			if((n&1)==1) {
				sum=sum*x%mo;
			}
			x=x*x%mo;
			n>>=1;
		}
		return sum;
	}
	public static char[] revch(char ch[]) {
		char ret[]=new char[ch.length];
		for(int i=ch.length-1,j=0;i>=0;i--,j++) {
			ret[j]=ch[i];
		}
		return ret;
	}
	public static int[] revint(int ch[]) {
		int ret[]=new int[ch.length];
		for(int i=ch.length-1,j=0;i>=0;i--,j++) {
			ret[j]=ch[i];
		}
		return ret;
	}
	public static void warshall_floyd(int v[][],int n) {
		for(int k=0;k<n;k++)
			for(int i=0;i<n;i++)
				for(int j=0;j<n;j++)
					v[i][j]=min(v[i][j],v[i][k]+v[k][j]);
	}
	public static long modint(long a,long m) {
		long b=m,u=1,v=0;
		while(b!=0) {
			long t=a/b;
			a-=t*b;
			long x=a;
			a=b;
			b=x;

			u-=t*v;
			x=u;
			u=v;
			v=x;
		}
		u%=m;
		if(u<0)u+=m;
		return u;
	}
}
class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		}else{
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
	private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
	public String next() {
		if (!hasNext()) throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext()) throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while(true){
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			}else if(b == -1 || !isPrintableChar(b)){
				return minus ? -n : n;
			}else{
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
		return (int) nl;
	}
	public double nextDouble() { return Double.parseDouble(next());}
}