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++14 (judge verdict: Accepted)

// includes
#include <bits/stdc++.h>

// macros
#define ll long long int
#define pb emplace_back
#define mk make_pair
#define pq priority_queue
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--)
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define FI first
#define SE second
using namespace std;

//  types
typedef pair<int, int> P;
typedef pair<ll, int> Pl;
typedef pair<ll, ll> Pll;
typedef pair<double, double> Pd;
 
// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 1e9 + 7;

// solve
template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;}
template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;}
template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;}

struct Graph{
  int n;
  vector<vector<int> > edge;
  vector<int> in_deg;
  Graph(int n_){
    n = n_;
    edge.resize(n);
    in_deg.resize(n, 0);
  }
  void adde(int at, int to){
    edge[at].push_back(to);
    in_deg[to]++;
  }
  vector<int> topological_sort(){
    stack<int> st;
    for(int i = 0; i < n; i++){
      if(in_deg[i] == 0)st.push(i);
    }
    vector<int> res;
    while(st.size()){
      int at = st.top(); st.pop();
      res.push_back(at);
      for(int j: edge[at]){
        in_deg[j]--;
        if(in_deg[j] == 0)st.push(j);
      }
    }

    return res;
  }
};

int main(int argc, char const* argv[])
{
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int n, m;
  cin >> n >> m;
  Graph graph(n);
  rep(i, m){
    int a, b;
    cin >> a >> b;
    graph.adde(a, b);
  }
  auto v = graph.topological_sort();
  rep(i, sz(v))cout << v[i] << endl;
	return 0;
}