p02370 Topological Sort
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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
```python
from collections import deque
from typing import List, Optional


def topological_sort(
    graph: List[List[int]], in_degrees: List[int], first_index: int = 0
) -> Optional[List[int]]:
    """Topological sort that uses Kahn's algorithm and is able to detect cycles.
    Returns:
        If the given graph is DAG, a list of sorted vertices is returned.
        Otherwise, if loops are detected, None is returned.
    """
    V = len(graph) + first_index
    order = [i for i in range(first_index, V) if not in_degrees[i]]
    queue = deque(order)

    while queue:
        u = queue.popleft()
        for v in graph[u]:
            in_degrees[v] -= 1
            if not in_degrees[v]:
                queue.append(v), order.append(v)

    return order if len(order) + first_index == V else None


def grl_4_b():
    # https://onlinejudge.u-aizu.ac.jp/courses/library/5/GRL/4/GRL_4_B
    V, _, *ST = map(int, open(0).read().split())
    graph = [[] for _ in range(V)]
    in_degrees = [0] * V
    for s, t in zip(*[iter(ST)] * 2):
        graph[s].append(t)
        in_degrees[t] += 1

    res = topological_sort(graph, in_degrees)
    print("\n".join(map(str, res)))


if __name__ == "__main__":
    grl_4_b()


```