Problem: <image>


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.

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 $G$

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).

Example

Input

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


Output

0
3
1
4
5
2

Solution (in JAVA):

Solution:
import java.util.LinkedList;
import java.util.Stack;
import java.util.Queue;
import java.util.ArrayList;
import java.util.Scanner;
import java.util.Iterator;

class Graph {
	private int totalVertex;
	private ArrayList<LinkedList<Integer>> adjList;
	private int[][] adjMatrix;
	//adjacency list of edges
	public Graph() { totalVertex = 0; }
	/*
	public void loadAdjList() {
		Scanner in = new Scanner(System.in);
		totalVertex = in.nextInt();
		adjList = new LinkedList<LinkedList<Integer>>();
		for(int i = 0; i < totalVertex; i ++) {
			LinkedList<Integer> tmp = new LinkedList<Integer>();
			int idx1 = in.nextInt() - 1;
			int degree = in.nextInt();
			//System.out.println("mark idx1 = " + idx1 + " degree = " + degree);
			for(int j = 0; j < degree; j ++) {
				int idx2 = in.nextInt() - 1;
				tmp.add(idx2);
			}	
			adjList.add(tmp);
		}
		in.close();
	}

	public void BfsSP() {
		int[] distances = new int[totalVertex];
		boolean[] visited = new boolean[totalVertex];
		for (int i = 1; i < distances.length; i++) {
			distances[i] = -1;
		}

		Queue<Integer> unvisitedNodes = new LinkedList<>();
		unvisitedNodes.add(0);

		while (!unvisitedNodes.isEmpty()) {
			int currVertex = unvisitedNodes.poll();
			visited[currVertex] = true;
			LinkedList<Integer> neighborList = adjList.get(currVertex);
			for (Integer neighbor : neighborList) {
				if (!visited[neighbor]) {
					unvisitedNodes.add(neighbor);
					int newDistance = distances[currVertex] + 1;
					distances[neighbor] = distances[neighbor] == -1 ? newDistance : Math.min(distances[neighbor], newDistance);
				}
			}
		}

		for (int i = 0; i < distances.length; i++) {
			System.out.println((i + 1) + " " + distances[i]);
		}
	}
	*/

	public void loadAdjList() {
		Scanner input = new Scanner(System.in);
		totalVertex = input.nextInt();
		int totalEdges = input.nextInt();

		adjList = new ArrayList<>(totalVertex);
		for (int i = 0; i < totalVertex; i++) {
			adjList.add(new LinkedList<>());
		}

		for (int i = 0; i < totalEdges; i++) {
			int src = input.nextInt();
			int dest = input.nextInt();
			adjList.get(src).add(dest);
		}
		input.close();
	}

	public void loadAdjMatrix() {
		adjMatrix = new int[totalVertex][totalVertex];

		for (int i = 0; i < totalVertex; i++) {
			LinkedList<Integer> neighborList = adjList.get(i);
			for (Integer neighbor : neighborList) {
				adjMatrix[i][neighbor] = 1;
			}
		}
	}

	public void topologicalSort() {
		int[] indegree = new int[totalVertex];
		Queue<Integer> eligibleNodes = new LinkedList<>();

		for (int i = 0; i < adjList.size(); i++) {
			LinkedList<Integer> neighborList = adjList.get(i);
			for (Integer neighbor : neighborList) {
				indegree[neighbor]++;
			}
		}

		for (int i = 0; i < totalVertex; i++) {
			if (indegree[i] == 0) {
				eligibleNodes.add(i);
			}
		}

		while (!eligibleNodes.isEmpty()) {
			int currVertex = eligibleNodes.poll();
			System.out.println(currVertex);

			for (int i = 0; i < totalVertex; i++) {
				if (adjMatrix[currVertex][i] == 1) {
					indegree[i]--;
					if (indegree[i] == 0) {
						eligibleNodes.add(i);
					}
				}
			}
		}
	}

	public void recursiveTopological() {
		Stack<Integer> output = new Stack<>();
		boolean[] visited = new boolean[totalVertex];
		
		for (int i = 0 ; i < totalVertex; i++) {
			if (!visited[i]) {
				helperRecursiveTop(i, visited, output);
			}
		}

		while (!output.isEmpty()) {
			System.out.println(output.pop());
		}
	}

	public void helperRecursiveTop(int vertex, boolean[] visited, Stack<Integer> output) {
		visited[vertex] = true;
		LinkedList<Integer> neighborList = adjList.get(vertex);

		for (Integer neighbor : neighborList) {
			if (!visited[neighbor]) {
				helperRecursiveTop(neighbor, visited, output);
			}
		}

		output.push(vertex);
	}
}

//change class name GraphRepresentation to Main() for submission to AIZU
public class Main {
	public static void main(String argv[]) {
		Graph g = new Graph();
		g.loadAdjList();
		g.loadAdjMatrix();
		// g.BfsSP();
		// g.topologicalSort();
		g.recursiveTopological();
	}
}