import java.util.HashMap;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
 
class Graph
{
    private Map<Integer, List<Integer>> adjacencyList;
 
    public Graph(int v)
    {
        adjacencyList = new HashMap<Integer, List<Integer>>();
        for (int i = 1; i <= v; i++)
            adjacencyList.put(i, new LinkedList<Integer>());
    }
 
    public void setEdge(int from, int to)
    {
        if (to > adjacencyList.size() || from > adjacencyList.size())
            System.out.println("The vertices does not exists");
        /*
         * List<Integer> sls = adjacencyList.get(to);
         * sls.add(from);
         */
        List<Integer> dls = adjacencyList.get(from);
        dls.add(to);
    }
 
    public List<Integer> getEdge(int to)
    {
        /*
         * if (to > adjacencyList.size())
         * {
         * System.out.println("The vertices does not exists");
         * return null;
         * }
         */
        return adjacencyList.get(to);
    }
 
    public Graph checkDAG()
    {
        Integer count = 0;
        Iterator<Integer> iteratorI = this.adjacencyList.keySet().iterator();
        Integer size = this.adjacencyList.size() - 1;
        System.out.println("Minimal set of edges: ");
        while (iteratorI.hasNext())
        {
            Integer i = iteratorI.next();
            List<Integer> adjList = this.adjacencyList.get(i);
            if (count == size)
            {
                return this;
            }
            if (adjList.size() == 0)
            {
                count++;
                Iterator<Integer> iteratorJ = this.adjacencyList.keySet()
                        .iterator();
                while (iteratorJ.hasNext())
                {
                    Integer j = iteratorJ.next();
                    List<Integer> li = this.adjacencyList.get(j);
                    if (li.contains(i))
                    {
                        li.remove(i);
                        System.out.println(i + " -> " + j);
                    }
                }
                this.adjacencyList.remove(i);
                iteratorI = this.adjacencyList.keySet().iterator();
            }
        }
        return this;
    }
 
    public Map<Integer, List<Integer>> getFeedbackArcSet(int v)
    {
        int[] visited = new int[v + 1];
        Iterator<Integer> iterator = this.adjacencyList.keySet().iterator();
        Map<Integer, List<Integer>> l = new HashMap<Integer, List<Integer>>();
        while (iterator.hasNext())
        {
            Integer i = iterator.next();
            List<Integer> list = this.adjacencyList.get(i);
            visited[i] = 1;
            if (list.size() != 0)
            {
                for (int j = 0; j < list.size(); j++)
                {
                    if (visited[list.get(j)] == 1)
                    {
                        l.put(i, new LinkedList<Integer>());
                        l.get(i).add(j);
                    }
                    else
                    {
                        visited[list.get(j)] = 1;
                    }
                }
            }
        }
        return l;
    }
 
    public void printAllEdges(Graph copyG, int v)
    {
        Map<Integer, List<Integer>> edges = this.getFeedbackArcSet(v);
        Iterator<Integer> iterator = copyG.adjacencyList.keySet().iterator();
        while (iterator.hasNext())
        {
            Integer i = iterator.next();
            List<Integer> edgeList = this.getEdge(i);
            if (edgeList.size() != 0)
            {
                for (int j = 0; j < edgeList.size(); j++)
                {
                    if (edges.containsKey(i) && edges.get(i).contains(j))
                        continue;
                    else
                    {
                        System.out.print(i + " -> " + edgeList.get(j));
                    }
                }
                System.out.println();
            }
        }
    }
 
    public void printGraph()
    {
        System.out.println("The Graph is: ");
        Iterator<Integer> iterator = this.adjacencyList.keySet().iterator();
        while (iterator.hasNext())
        {
            Integer i = iterator.next();
            List<Integer> edgeList = this.getEdge(i);
            if (edgeList.size() != 0)
            {
                System.out.print(i);
                for (int j = 0; j < edgeList.size(); j++)
                {
                    System.out.print(" -> " + edgeList.get(j));
                }
                System.out.println();
            }
        }
    }
}
 
public class MinimalSetofEdgesforDAG
{
    public static void main(String args[])
    {
        int v, e, count = 1, to, from;
        Scanner sc = new Scanner(System.in);
        Graph glist;
        try
        {
            System.out.println("Enter the number of vertices: ");
            v = sc.nextInt();
            System.out.println("Enter the number of edges: ");
            e = sc.nextInt();
            glist = new Graph(v);
            System.out.println("Enter the edges in the graph : <from> <to>");
            while (count <= e)
            {
                to = sc.nextInt();
                from = sc.nextInt();
                glist.setEdge(to, from);
                count++;
            }
            Graph copyofGlist = new Graph(v);
            copyofGlist = glist;
            glist.printGraph();
            Graph modified = glist.checkDAG();
            modified.printAllEdges(copyofGlist, v);
        }
        catch (Exception E)
        {
            System.out
                    .println("You are trying to access empty adjacency list of a node.");
        }
        sc.close();
    }
}
