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 PYTHON3):

Solution:
#!/usr/bin/env python3
# GRL_4_B: Path/Cycle - Topological Sort

from collections import namedtuple


DirectedEdge = namedtuple('DirectedEdge', ('src', 'dest'))


def revert(edge):
    return edge._replace(src=edge.dest, dest=edge.src)


class Digraph:
    def __init__(self, v):
        self.v = v
        self._edges = [[] for _ in range(v)]

    def add(self, edge):
        self._edges[edge.src].append(edge)

    def adj(self, v):
        return self._edges[v]

    def edges(self):
        for es in self._edges:
            for e in es:
                yield e

    def reversed(self):
        g = self.__class__(self.v)
        for e in self.edges():
            g.add(revert(e))

        return g


def sorted_topological(graph):
    return reversed(list(reverse_post(graph.reversed())))


def reverse_post(graph):
    def visit(v):
        if not visited[v]:
            visited[v] = True
            return True
        else:
            return False

    def leave(v):
        if not left[v]:
            left[v] = True
            vs.append(v)
        return False

    visited = [False] * graph.v
    left = [False] * graph.v
    vs = []

    for i in range(graph.v):
        if not visited[i]:
            stack = [(i, leave)]
            stack.extend((e.dest, visit) for e in graph.adj(i))
            while stack:
                v, f = stack.pop()
                if f(v):
                    stack.append((v, leave))
                    for e in graph.adj(v):
                        stack.append((e.dest, visit))
    return reversed(vs)


def run():
    v, e = [int(i) for i in input().split()]
    g = Digraph(v)

    for _ in range(e):
        s, t = [int(i) for i in input().split()]
        g.add(DirectedEdge(s, t))

    for v in sorted_topological(g):
        print(v)


if __name__ == '__main__':
    run()