Problem H: Project File Dependencies

Project managers, such as the UNIX utility make, are used to maintain large software projects made up from many components. Users write a project file specifying which components (called tasks) depend on others and the project manager can automatically update the components in the correct order.

Problem

Write a program that reads a project file and outputs the order in which the tasks should be performed.

Input specification

For simplicity we represent each task by an integer number from $1,2,\ldots,N$ (where $N$ is the total number of tasks). The first line of input specifies the number $N$ of tasks and the number $M$ of rules, such that $N \leq 100,\; M\leq 100$.

The rest of the input consists of $M$ rules, one in each line, specifying dependencies using the following syntax: 


$T_0$    $k$    $T_1$    $T_2$    ...    $T_k$
This rule means that task number $T_0$ depends on $k$ tasks $T_1, T_2, \ldots T_k$ (we say that task $T_0$ is the target and $T_1\ldots T_k$ are dependents).

Note that tasks numbers are separated by single spaces and that rules end with a newline. Rules can appear in any order, but each task can appear as target only once.

Your program can assume that there are no circular dependencies in the rules, i.e. no task depends directly or indirectly on itself.

Output specification

The output should be a single line with the permutation of the tasks $1\ldots N$ to be performed, ordered by dependencies (i.e. no task should appear before others that it depends on).

To avoid ambiguity in the output, tasks that do not depend on each other should be ordered by their number (lower numbers first).

Sample input

5 4
3 2 1 5
2 2 5 3
4 1 3
5 1 1

Sample output

 
1 5 3 2 4

ACM Programming Contest -- SWERC'2001 -- University of Porto, Portugal