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.InputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;
import java.math.BigInteger;

public class Main{

static PrintWriter out;
static InputReader ir;

static void solve(){
 int V=ir.nextInt();
 int E=ir.nextInt();
 G g=new G(V,false);
 for(int i=0;i<E;i++) g.addEdge(ir.nextInt(),ir.nextInt());
 int[] tpo=g.buildTPO();
 for(int i=0;i<V;i++) out.println(tpo[i]);
}

static class G{

 AL[] g;
 private int V;
 private boolean ndir;

 public G(int V,boolean ndir){
  this.V=V;
  this.ndir=ndir;
  g=new AL[V];
  for(int i=0;i<V;i++){
   g[i]=new AL();
  }
 }

 public void addEdge(int u,int v,int t){
  g[u].add(new int[]{v,t});
  if(this.ndir) g[v].add(new int[]{u,t});
 }

 public void addEdge(int u,int v){
  addEdge(u,v,0);
 }

 public int[] dijkstra(int s,int[] prev){
  int[] dist=new int[this.V];
  java.util.PriorityQueue<int[]> pque=new java.util.PriorityQueue<int[]>(11,new Comparator<int[]>(){
   public int compare(int[] a,int[] b){
    return Integer.compare(a[0],b[0]);
   }
  });
  Arrays.fill(dist,1<<26);
  dist[s]=0;
  pque.offer(new int[]{0,s});
  while(!pque.isEmpty()){
   int[] p=pque.poll();
   int v=p[1];
   if(dist[v]<p[0]) continue;
   for(int i=0;i<g[v].size();i++){
    int to=g[v].get(i)[0],cost=g[v].get(i)[1];
    if(dist[to]>dist[v]+cost){
     dist[to]=dist[v]+cost;
     pque.offer(new int[]{dist[to],to});
    }
   }
  }
  return dist;
 }

 public int[] buildTPO(){
  boolean[] vis=new boolean[this.V];
  ArrayList<Integer> ord=new ArrayList<>();
  for(int i=0;i<this.V;i++) if(!vis[i]) ts(i,vis,ord);
  int[] ret=new int[V];
  for(int i=ord.size()-1;i>=0;i--) ret[ord.size()-1-i]=ord.get(i);
  return ret;
 }

 private void ts(int now,boolean[] vis,ArrayList<Integer> ord){
  vis[now]=true;
  int to;
  for(int i=0;i<g[now].size();i++){
   to=g[now].get(i)[0];
   if(!vis[to]) ts(to,vis,ord);
  }
  ord.add(now);
 }

 static class AL extends ArrayList<int[]>{};
}

public static void main(String[] args) throws Exception{
 ir=new InputReader(System.in);
 out=new PrintWriter(System.out);
 solve();
 out.flush();
}

static class InputReader {
 private InputStream in;
 private byte[] buffer=new byte[1024];
 private int curbuf;
 private int lenbuf;

 public InputReader(InputStream in) {this.in=in; this.curbuf=this.lenbuf=0;}
 
 public boolean hasNextByte() {
  if(curbuf>=lenbuf){
   curbuf= 0;
   try{
    lenbuf=in.read(buffer);
   }catch(IOException e) {
    throw new InputMismatchException();
   }
   if(lenbuf<=0) return false;
  }
  return true;
 }

 private int readByte(){if(hasNextByte()) return buffer[curbuf++]; else return -1;}
 
 private boolean isSpaceChar(int c){return !(c>=33&&c<=126);}
 
 private void skip(){while(hasNextByte()&&isSpaceChar(buffer[curbuf])) curbuf++;}
 
 public boolean hasNext(){skip(); return hasNextByte();}
 
 public String next(){
  if(!hasNext()) throw new NoSuchElementException();
  StringBuilder sb=new StringBuilder();
  int b=readByte();
  while(!isSpaceChar(b)){
   sb.appendCodePoint(b);
   b=readByte();
  }
  return sb.toString();
 }
 
 public int nextInt() {
  if(!hasNext()) throw new NoSuchElementException();
  int c=readByte();
  while (isSpaceChar(c)) c=readByte();
  boolean minus=false;
  if (c=='-') {
   minus=true;
   c=readByte();
  }
  int res=0;
  do{
   if(c<'0'||c>'9') throw new InputMismatchException();
   res=res*10+c-'0';
   c=readByte();
  }while(!isSpaceChar(c));
  return (minus)?-res:res;
 }
 
 public long nextLong() {
  if(!hasNext()) throw new NoSuchElementException();
  int c=readByte();
  while (isSpaceChar(c)) c=readByte();
  boolean minus=false;
  if (c=='-') {
   minus=true;
   c=readByte();
  }
  long res = 0;
  do{
   if(c<'0'||c>'9') throw new InputMismatchException();
   res=res*10+c-'0';
   c=readByte();
  }while(!isSpaceChar(c));
  return (minus)?-res:res;
 }

 public double nextDouble(){return Double.parseDouble(next());}

 public BigInteger nextBigInteger(){return new BigInteger(next());}

 public int[] nextIntArray(int n){
  int[] a=new int[n];
  for(int i=0;i<n;i++) a[i]=nextInt();
  return a;
 }

 public long[] nextLongArray(int n){
  long[] a=new long[n];
  for(int i=0;i<n;i++) a[i]=nextLong();
  return a;
 }

 public char[][] nextCharMap(int n,int m){
  char[][] map=new char[n][m];
  for(int i=0;i<n;i++) map[i]=next().toCharArray();
  return map;
 }
}
}