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

"""
Performs topological sorting of the given DAG using Kahn's algorithm.

Verification: []()
"""

import heapq


class TopologicalSortError(Exception):
    """This exception is raised when something gets wrong while performing `topological_sort`.
    """    
    pass


def topological_sort(num_vs, adj_vs):
    """Performs topological sorting of the given DAG.

    This function computes the lexicographically least
    topological order of the given DAG.

    Parameters:

    - `num_vs`: The number of vertices of the DAG.
    - `adj_vs` The adjacency list of the DAG.

    Returns: the lexicographically least topological order as a list.
    
    Raises `TopologicalSortError` if the given graph is not a DAG.
    """
    
    in_deg = [0 for _ in range(num_vs)]
    for dests in adj_vs:
        for dest in dests:
            in_deg[dest] += 1
    sorted_vs = []
    pq = []
    for s in range(num_vs):
        if in_deg[s] == 0:
            heapq.heappush(pq, s)
    while pq:
        u = heapq.heappop(pq)
        sorted_vs.append(u)
        for v in adj_vs[u]:
            in_deg[v] -= 1
            if in_deg[v] == 0:
                heapq.heappush(pq, v)
    if all(x == 0 for x in in_deg):
        return sorted_vs
    else:
        raise TopologicalSortError("The graph has a cycle")


def main():
    v, e = map(int, input().split())
    adj_vs = [set() for _ in range(v)]
    for _ in range(e):
        s, t = map(int, input().split())
        adj_vs[s].add(t)
    for u in topological_sort(v, adj_vs):
        print(u)


if __name__ == "__main__":
    main()