URI Online Judge | 1677
# The Bottom of a Graph

**Timelimit: 3**

Local Contest, University of Ulm Germany

We will use the following standard definitions from graph theory. Let V be a nonempty and finite set, its elements being called vertices (or nodes). Let E be a subset of the Cartesian product V×V, its elements being called edges. Then G = (V, E) is called a directed graph.

Let N be a positive integer, and let P = (e_{1},...,e_{n}) be a sequence of length N of edges, e_{i} ∈ E such that e_{i} = (v_{i} ,v_{i+1}) for a sequence of vertices (v_{1},...,v_{n+1}). Then P is called a path from vertex v_{1} to vertex v_{n+1} in G and we say that v_{n+1} is reachable from v_{1}, writing (v_{1}→v_{n+1}).

Here are some new definitions. A node V in a graph G = (V, E) is called a sink, if for every node W in G that is reachable from v, v is also reachable from W. The bottom of a graph is the subset of all nodes that are sinks, i.e., bottom(G) = {v ∈ V|∀w ∈ V:(v→W) ⇒ (W→v)}. You have to calculate the bottom of certain graphs.

The input contains several test cases, each of which corresponds to a directed graph **G**. Each test case starts with an integer number **v**, denoting the number of vertices of **G** = (**V**, **E**), where the vertices will be identified by the integer numbers in the set **V **= {1,...,**v**}. You may assume that **v**(1 ≤ **v** ≤ 5000). That is followed by a non-negative integer * e* and, thereafter,

For each test case output the bottom of the specified graph on a single line. To this end, print the numbers of all nodes that are sinks in sorted order separated by a single space character. If the bottom is empty, print an empty line.

Sample Input | Sample Output |

3 3 1 3 2 3 3 1 2 1 1 2 0 |
1 3 2 |