Problem:
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Topological Sort

A directed acyclic graph (DAG) can be used to represent the ordering of tasks. Tasks are represented by vertices and constraints where one task can begin before another, are represented by edges. For example, in the above example, you can undertake task B after both task A and task B are finished. You can obtain the proper sequence of all the tasks by a topological sort.

Given a DAG $G$, print the order of vertices after the topological sort.

Input

A directed graph $G$ is given in the following format:

$|V|\;|E|$

$s_0 \; t_0$

$s_1 \; t_1$

:

$s_{|E|-1} \; t_{|E|-1}$

$|V|$ is the number of vertices and $|E|$ is the number of edges in the graph. The graph vertices are named with the numbers $0, 1,..., |V|-1$ respectively.

$s_i$ and $t_i$ represent source and target nodes of $i$-th edge (directed).

Output

Print the vertices numbers in order. Print a number in a line.

If there are multiple possible solutions, print any one of them (the solution is judged by a special validator).

Constraints

$1 \leq |V| \leq 10,000$

$0 \leq |E| \leq 100,000$

There are no parallel edges in $G$

There are no self loops in $G$

Sample Input

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

Sample Output

0
3
1
4
5
2

Solution in JAVA (judge verdict: Time Limit Exceeded)

import java.util.Scanner;
import java.util.List;
import java.util.ArrayList;
import java.util.Set;
import java.util.HashSet;
import java.util.Map;
import java.util.HashMap;
import java.util.Queue;
import java.util.ArrayDeque;

public class Main {
	static class Vertex {
		int id;
		Set<Integer> adj;

		public Vertex(int id) {
			this.id = id;
			this.adj = new HashSet<>();
		}

		public void addEdge(int v) {
			adj.add(v);
		}

		public List<Integer> getAdjacentVertices() {
			List<Integer> vs = new ArrayList<>(adj);

			vs.sort((x, y) -> x-y);

			return vs;
		}
	}

	static class Graph {
		private List<Vertex> vertices;
		private int n;

		public Graph(int n) {
			this.n = n;

			this.vertices = new ArrayList<>();
			for (int i = 0; i < n; i++)
				vertices.add(new Vertex(i));
		}

		public int getNumVertices() {
			return n;
		}

		public int getIndegree(int v) {
			if (v < 0 || v >= n)
				throw new IllegalArgumentException("invalid vertex");

			int d = 0;
			for (int i = 0; i < n; i++) {
				if (vertices.get(i).getAdjacentVertices().contains(v))
					d++;
			}

			return d;
		}

		public List<Integer> getAdjacentVertices(int v) {
			return vertices.get(v).getAdjacentVertices();
		}

		public void addEdge(int v1, int v2) {
			if (v1 < 0 || v2 < 0 || v1 >= n|| v2 >= n)
				throw new IllegalArgumentException("invalid vertex");

			vertices.get(v1).addEdge(v2);
		}							
	}

	public static List<Integer> sort(Graph g) {
		Queue<Integer> q = new ArrayDeque<>();
		Map<Integer, Integer> m = new HashMap<>();

		int n = g.getNumVertices();
		for (int i = 0; i < n; i++) {
			int d = g.getIndegree(i);
			m.put(i, d);

			if (d == 0)
				q.add(i);
		}

		List<Integer> vs = new ArrayList<>();
		while (!q.isEmpty()) {
			int v = q.remove();

			vs.add(v);
			List<Integer> adj = g.getAdjacentVertices(v);
			for (int a : adj) {
				m.replace(a, m.get(a)-1);
				if (m.get(a) == 0)
					q.add(a);
			}
		}

		if (vs.size() != n)
			throw new IllegalStateException("cycle detected!");

		return vs;
	}														

	public static void main(String[] args) {
		try (Scanner in = new Scanner(System.in)) {
			int n = in.nextInt();
			int m = in.nextInt();
			Graph g = new Graph(n);

			for (int i = 0; i < m; i++) {
				int x = in.nextInt();
				int y = in.nextInt();

				g.addEdge(x, y);
			}

			List<Integer> vs = sort(g);
			for (int v : vs)
				System.out.println(v);
		} catch (Exception ex) {
			throw new RuntimeException(ex);
		}
	}
}