Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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 C# (judge verdict: Accepted)

using System;
using System.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using System.Diagnostics;
using Enu = System.Linq.Enumerable;

public class Program
{
    public void Solve()
    {
        int N = Reader.Int(), M = Reader.Int();
        var E = Enu.Range(0, N).Select(i => new List<int>()).ToArray();
        for (int i = 0; i < M; i++)
        {
            int a = Reader.Int(), b = Reader.Int();
            E[a].Add(b);
        }
        var sorted = TopologicalSort(E);
        foreach (int a in sorted) Console.WriteLine(a);
        Console.ReadLine();
    }


    int[] TopologicalSort(List<int>[] E)
    {
        var seen = new bool[E.Length];
        var sorted = new List<int>();
        Action<int> DFS = null;
        DFS = a =>
        {
            if (seen[a]) return;
            seen[a] = true;
            for (int i = E[a].Count - 1; i >= 0; i--)
                DFS(E[a][i]);
            sorted.Add(a);
        };
        for (int a = E.Length - 1; a >= 0; a--)
            DFS(a);

        sorted.Reverse();
        return sorted.ToArray();
    }

}


class Entry { static void Main() { new Program().Solve(); } }
class Reader
{
    static TextReader reader = Console.In;
    static readonly char[] separator = { ' ' };
    static readonly StringSplitOptions op = StringSplitOptions.RemoveEmptyEntries;
    static string[] A = new string[0];
    static int i;
    static void Init() { A = new string[0]; }
    public static void Set(TextReader r) { reader = r; Init(); }
    public static void Set(string file) { reader = new StreamReader(file); Init(); }
    public static bool HasNext() { return CheckNext(); }
    public static string String() { return Next(); }
    public static int Int() { return int.Parse(Next()); }
    public static long Long() { return long.Parse(Next()); }
    public static double Double() { return double.Parse(Next()); }
    public static int[] IntLine() { return Array.ConvertAll(Split(Line()), int.Parse); }
    public static int[] IntArray(int N) { return Range(N, Int); }
    public static int[][] IntTable(int H) { return Range(H, IntLine); }
    public static string[] StringArray(int N) { return Range(N, Next); }
    public static string[][] StringTable(int N) { return Range(N, () => Split(Line())); }
    public static string Line() { return reader.ReadLine().Trim(); }
    static string[] Split(string s) { return s.Split(separator, op); }
    static T[] Range<T>(int N, Func<T> f) { var r = new T[N]; for (int i = 0; i < N; r[i++] = f()) ; return r; }
    static string Next() { CheckNext(); return A[i++]; }
    static bool CheckNext()
    {
        if (i < A.Length) return true;
        string line = reader.ReadLine();
        if (line == null) return false;
        if (line == "") return CheckNext();
        A = Split(line);
        i = 0;
        return true;
    }
}