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.Queue;
import java.util.Scanner;
import java.util.Iterator;
import java.util.Stack;

public class Main {
	public static void main(String[] args) {
		Graph g = new Graph();
		g.load_from_edgelist();
		g.helper();
		while(!g.get_order().isEmpty()) {
			System.out.println(g.get_order().pop());
		}
	}
}

class Graph {
	
	private int totalVertex;
	private LinkedList<LinkedList<Integer>> adjList;
	private boolean[] if_visited;
	private int[] discover_time;
	private int[] complete_time;
	private int[] id;
	private static int timestamp = 1;
	private int[] dist;
	private Stack<Integer> order = new Stack<>();
	
	public Stack<Integer> get_order(){
		return order;
	}
	
	public boolean[] getVisited() {
		return if_visited;
	}
	
	public int[] getDistance() {
		return dist;
	}
	
	//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>>();
		if_visited = new boolean[totalVertex];
		discover_time = new int[totalVertex];
		complete_time = new int[totalVertex];
		id = new int[totalVertex];
		dist = new int[totalVertex];
		
		for(int i = 0; i < totalVertex; i ++) {
			LinkedList<Integer> tmp = new LinkedList<Integer>();
			int idx1 = in.nextInt() - 1;
			if_visited[idx1] = false;
			id[idx1] = i;
			dist[idx1] = 0;
			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 load_from_edgelist() {
		Scanner in = new Scanner(System.in);
		totalVertex = in.nextInt();
		int totalEdges = in.nextInt();
		adjList = new LinkedList<LinkedList<Integer>>();
		if_visited = new boolean[totalVertex];
		//discover_time = new int[totalVertex];
		//complete_time = new int[totalVertex];
		id = new int[totalVertex];
		
		for (int i = 0; i < totalVertex; i++) {
			if_visited[i] = false;
			id[i] = i;
			LinkedList<Integer> tmp = new LinkedList<Integer>();
			adjList.add(tmp);
		}
		
		for (int i = 0; i < totalEdges; i++) {
			int idx1 = in.nextInt();
			int v = in.nextInt();
			adjList.get(idx1).add(v);
		}
		
		in.close();
	}
	
	public void printAdjMatrix() {
		Integer[][] adjMatrix = new Integer[totalVertex][totalVertex];
		//complete the following
		for (int i = 0; i < totalVertex; i++) {
			for (int j = 0; j< totalVertex; j++) {
				if (adjList.get(i).contains(j)) {
					adjMatrix[i][j] = 1;
				}else {
					adjMatrix[i][j] = 0;				
				}
				if (j == totalVertex - 1) {
					System.out.println(adjMatrix[i][j]);
					
				}else {
					System.out.print(adjMatrix[i][j] + " ");
				}
			}
		}
	}
	
	public void DFS(int id) {
			if_visited[id] = true;
			//discover_time[id] = timestamp;
			//timestamp += 1;
			Iterator<Integer> i = adjList.get(id).listIterator();
			while(i.hasNext()) {
				int n = i.next();
				if ( !if_visited[n]) {
					DFS(n);
				}
			}
			order.add(id);
			//complete_time[id] = timestamp++;

		
	}
	
	public void helper() {
		for(int i = 0; i < totalVertex; i++) {
			if(!if_visited[i]) {
				DFS(i);
			}
		}
	}
	
	
	public void show_result() {
		for (int i = 0; i < totalVertex; i++) {
			System.out.print(id[i] + 1 + " ");
			System.out.print(discover_time[id[i]] + " ");
			System.out.print(complete_time[id[i]] + " ");
			System.out.println();
		}
	}
	
	public void BFS(int src) {
		if_visited[src] = true;
		Queue<Integer> q = new LinkedList<>();
		q.add(src);
		while(!q.isEmpty()) {
			int u = q.remove();
			//if_visited[u] = true;
			LinkedList<Integer> tmp = adjList.get(u);
			for(int i = 0; i < tmp.size(); i++) {
				if(!if_visited[tmp.get(i)]) {
					if_visited[tmp.get(i)] = true;
					//if(!q.contains(tmp.get(i))){
					q.add(tmp.get(i));
					dist[tmp.get(i)] = dist[u] + 1;
					//}
				}
			}
		}
	}
	
}