Problem: Recently, Pari and Arya did some research about NP-Hard problems and they found the minimum vertex cover problem very interesting.

Suppose the graph G is given. Subset A of its vertices is called a vertex cover of this graph, if for each edge uv there is at least one endpoint of it in this set, i.e. <image> or <image> (or both).

Pari and Arya have won a great undirected graph as an award in a team contest. Now they have to split it in two parts, but both of them want their parts of the graph to be a vertex cover.

They have agreed to give you their graph and you need to find two disjoint subsets of its vertices A and B, such that both A and B are vertex cover or claim it's impossible. Each vertex should be given to no more than one of the friends (or you can even keep it for yourself).

Input

The first line of the input contains two integers n and m (2 ≤ n ≤ 100 000, 1 ≤ m ≤ 100 000) — the number of vertices and the number of edges in the prize graph, respectively.

Each of the next m lines contains a pair of integers ui and vi (1 ≤ ui, vi ≤ n), denoting an undirected edge between ui and vi. It's guaranteed the graph won't contain any self-loops or multiple edges.

Output

If it's impossible to split the graph between Pari and Arya as they expect, print "-1" (without quotes).

If there are two disjoint sets of vertices, such that both sets are vertex cover, print their descriptions. Each description must contain two lines. The first line contains a single integer k denoting the number of vertices in that vertex cover, and the second line contains k integers — the indices of vertices. Note that because of m ≥ 1, vertex cover cannot be empty.

Examples

Input

4 2
1 2
2 3


Output

1
2 
2
1 3 


Input

3 3
1 2
2 3
1 3


Output

-1

Note

In the first sample, you can give the vertex number 2 to Arya and vertices numbered 1 and 3 to Pari and keep vertex number 4 for yourself (or give it someone, if you wish).

In the second sample, there is no way to satisfy both Pari and Arya.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.StreamTokenizer;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.List;
import java.util.Queue;

/**
 * User: dmitryt
 * Date: 04/07/2015
 */
public class CF688C {
    public static class Graph {
        private static final String NEWLINE = System.getProperty("line.separator");

        private final int V;
        private int E;
        private List<Integer>[] adj;

        /**
         * Initializes an empty graph with {@code V} vertices and 0 edges.
         * param V the number of vertices
         *
         * @param  V number of vertices
         * @throws IllegalArgumentException if {@code V < 0}
         */
        public Graph(int V) {
            if (V < 0) throw new IllegalArgumentException("Number of vertices must be nonnegative");
            this.V = V;
            this.E = 0;
            adj = (List<Integer>[]) new List[V];
            for (int v = 0; v < V; v++) {
                adj[v] = new ArrayList<>();
            }
        }

        /**
         * Returns the number of vertices in this graph.
         *
         * @return the number of vertices in this graph
         */
        public int V() {
            return V;
        }

        /**
         * Returns the number of edges in this graph.
         *
         * @return the number of edges in this graph
         */
        public int E() {
            return E;
        }

        // throw an IllegalArgumentException unless {@code 0 <= v < V}
        private void validateVertex(int v) {
            if (v < 0 || v >= V)
                throw new IllegalArgumentException("vertex " + v + " is not between 0 and " + (V-1));
        }

        /**
         * Adds the undirected edge v-w to this graph.
         *
         * @param  v one vertex in the edge
         * @param  w the other vertex in the edge
         * @throws IllegalArgumentException unless both {@code 0 <= v < V} and {@code 0 <= w < V}
         */
        public void addEdge(int v, int w) {
            validateVertex(v);
            validateVertex(w);
            E++;
            adj[v].add(w);
            adj[w].add(v);
        }


        /**
         * Returns the vertices adjacent to vertex {@code v}.
         *
         * @param  v the vertex
         * @return the vertices adjacent to vertex {@code v}, as an iterable
         * @throws IllegalArgumentException unless {@code 0 <= v < V}
         */
        public Iterable<Integer> adj(int v) {
            validateVertex(v);
            return adj[v];
        }

        /**
         * Returns the degree of vertex {@code v}.
         *
         * @param  v the vertex
         * @return the degree of vertex {@code v}
         * @throws IllegalArgumentException unless {@code 0 <= v < V}
         */
        public int degree(int v) {
            validateVertex(v);
            return adj[v].size();
        }

    }

    private static int nextInt(StreamTokenizer st) throws Exception {
        int token = st.nextToken();
        while (token != StreamTokenizer.TT_NUMBER) token = st.nextToken();
        return (int)st.nval;
    }

    private static class Node {
        final int v;
        final int color;

        public Node(int v, int color) {
            this.v = v;
            this.color = color;
        }
    }

    private static Node getStart(int[] colors, int prevStart) {
        for (int i = prevStart; i < colors.length; i++) {
            if (colors[i] == 0) return new Node(i, 1);
        }
        return null;
    }

    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StreamTokenizer st = new StreamTokenizer(in);

        int n = nextInt(st);
        int m = nextInt(st);

        Graph G = new Graph(n);
        for (int i = 0; i < m; i++) {
            G.addEdge(nextInt(st) - 1, nextInt(st) - 1);
        }

        int[] colors = new int[n];

        Node start = getStart(colors, 0);
        while (start != null) {
            Queue<Node> q = new ArrayDeque<>();
            q.add(start);
            while (q.size() > 0) {
                Node v = q.poll();
                if (colors[v.v] == 0) {
                    colors[v.v] = v.color;
                }
                for (int neighbour : G.adj(v.v)) {
                    int neighbourColor = v.color == 1 ? 2 : 1;
                    if (colors[v.v] == colors[neighbour]) {
                        System.out.println("-1");
                        System.exit(0);
                    }
                    if (colors[neighbour] == 0)
                        q.add(new Node(neighbour, neighbourColor));
                }
            }

            start = getStart(colors, start.v);
        }

        List<String> l1 = new ArrayList<>();
        List<String> l2 = new ArrayList<>();

        for (int i = 0; i < n; i++) {
            if (colors[i] == 1)
                l1.add(String.valueOf(i+1));
            else
                l2.add(String.valueOf(i+1));
        }
        System.out.println(l1.size());
        System.out.println(String.join(" ", l1));
        System.out.println(l2.size());
        System.out.println(String.join(" ", l2));
   }
}