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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Collection;
import java.util.HashMap;
import java.io.IOException;
import java.util.Deque;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;
import java.util.Map;
import java.io.BufferedReader;
import java.util.ArrayDeque;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyScanner in = new MyScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TopologicalSort solver = new TopologicalSort();
        solver.solve(1, in, out);
        out.close();
    }

    static class TopologicalSort {
        public void solve(int testNumber, MyScanner in, PrintWriter out) {
            int V = in.Int();
            int E = in.Int();
            TopologicalSort.Topological top = new TopologicalSort.Topological(V);
            for (int i = 0; i < E; i++) {
                int s = in.Int();
                int t = in.Int();
                top.addEdge(s, t);
            }
            top.sort();
            top.list.forEach(out::println);
        }

        static class Topological {
            int n;
            List<Integer> list = new ArrayList<>();
            int[] in;
            Map<Integer, List<Integer>> out;

            Topological(int n) {
                this.n = n;
                this.in = new int[n];
                this.out = new HashMap<>();
                for (int i = 0; i < n; i++) {
                    out.put(i, new ArrayList<>());
                }
            }

            public void addEdge(int x, int y) {
                in[y]++;
                out.get(x).add(y);
            }

            public void sort() {
                list.clear();
                Deque<Integer> que = new ArrayDeque<>();
                for (int i = 0; i < n; i++) {
                    if (in[i] == 0) {
                        que.add(i);
                    }
                }
                while (!que.isEmpty()) {
                    int i = que.poll();
                    list.add(i);
                    for (int j : out.get(i)) {
                        in[j]--;
                        if (in[j] == 0) {
                            que.add(j);
                        }
                    }
                }
            }

        }

    }

    static class MyScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public MyScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String rl = in.readLine();
                    if (rl == null) {
                        return null;
                    }
                    st = new StringTokenizer(rl);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        public int Int() {
            return Integer.parseInt(next());
        }

    }
}