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.ArrayList;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Scanner;
import java.util.TreeSet;

public class Main {

    public static class TopologicalSort_DFS {

        boolean hasCycle;
        LinkedList<Integer> sortedOrder;
        TreeSet<Integer> unmarkedV;
        boolean[] tempMark;

        public TopologicalSort_DFS(WeightedDigraph graph) {
            tempMark = new boolean[graph.numVertex];
            unmarkedV = new TreeSet<Integer>();
            for (int v = 0; v < graph.numVertex; v++) {
                unmarkedV.add(v);
            }
            sortedOrder = new LinkedList<Integer>();

            try {
                while (!unmarkedV.isEmpty()) {
                    int v = unmarkedV.first();
                    dfs(v, graph);
                }
            } catch (Exception ex) {
                hasCycle = true;
                sortedOrder.clear();
            }
        }

        private void dfs(int vert, WeightedDigraph graph) throws Exception {
            if (tempMark[vert]) {
                throw new Exception("cycle deteced v:" + vert);
            }
            if (unmarkedV.contains(vert)) {
                tempMark[vert] = true;
                for (WeightedDigraph.Edge edge : graph.srcEdges[vert]) {
                    dfs(edge.targetVertex, graph);
                }
                unmarkedV.remove(vert);
                tempMark[vert] = false;
                sortedOrder.addFirst(vert);
            }
        }

        public boolean hasCycle() {
            return hasCycle;
        }

        public Iterator<Integer> sortedOrder() {
            return sortedOrder.iterator();
        }
    }

    public static class WeightedDigraph {

        int numVertex;
        int numEdge;

        List<Edge>[] srcEdges;

        @SuppressWarnings("unchecked")
        public WeightedDigraph(int numV, int numE) {
            this.numVertex = numV;
            this.numEdge = numE;
            srcEdges = new List[numV];

            for (int i = 0; i < numV; i++) {
                srcEdges[i] = new ArrayList<Edge>();
            }
        }

        public void addEdge(int srcVertex, int targetVertex, int weight) {
            Edge e = new WeightedDigraph.Edge(srcVertex, targetVertex, weight);
            srcEdges[srcVertex].add(e);
        }

        public static class Edge {

            int srcVertex;
            int targetVertex;
            int weight;

            public Edge(int srcVertex, int targetVertex, int weight) {
                this.srcVertex = srcVertex;
                this.targetVertex = targetVertex;
                this.weight = weight;
            }
        }

    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int v = in.nextInt();
        int e = in.nextInt();
        WeightedDigraph graph = new WeightedDigraph(v, e);
        while (e-- > 0) {
            graph.addEdge(in.nextInt(), in.nextInt(), 1);
        }
        TopologicalSort_DFS topSort = new TopologicalSort_DFS(graph);
        Iterator<Integer> it = topSort.sortedOrder();
        while (it.hasNext()) {
            System.out.println(it.next());
        }
    }
}