Topological sort P14952

We must perform $n$ tasks, one at a time. Furthermore, some tasks must be done before others: there are $m$ precedence relations between tasks. Write a program to print a way to sort the $n$ tasks satisfying the $m$ given precedences.

Input

Input consists of several cases. Every case begins with $n$, followed by $m$, followed by $m$ distinct pairs $x$ $y$ that indicate that task $x$ must be done before task $y$. You can assume $1 \le n \le 10^4$, $0 \le m \le 10n$, and that the tasks are numbered from 0 to $n - 1$.

Output

For every case, print the lexicographically smallest order of the $n$ tasks that fulfills the $m$ given precedences. There will always be, at least, one solution.