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:
// Working program using Reader Class

import java.io.BufferedOutputStream;
import java.io.DataInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.OutputStream;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.Map;
import java.util.Queue;
import java.util.stream.Collector;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class NpHardProblem {
    static Output out;
    static Reader in;
    static Exception exception;

    static int pariCount = 0;
    static ArrayList<Node> paris = new ArrayList<>();

    static int ariCount = 0;
    static ArrayList<Node> aris = new ArrayList<>();


    public static void operate() throws IOException {
        int n = in.nextInt();
        int m = in.nextInt();

        Map<Integer, Node> map = new HashMap<>();

        IntStream.rangeClosed(1, n).forEach(i -> {
            map.put(i, new Node(i));
        });

        IntStream.rangeClosed(1, m).forEach(i -> {
            int node1 = in.nextInt();
            int node2 = in.nextInt();

            map.get(node1).siblings.add(map.get(node2));
            map.get(node2).siblings.add(map.get(node1));

        });

        map.forEach((index, node) -> {
            if (node.marked) {
                return;
            }
            Queue<Node> queue = new LinkedList<>();
            queue.add(
                    map.get(index)
                            .setColor(Color.Pari)
                            .setMarked(true)
            );

            while (!queue.isEmpty()) {
                Node poll = queue.poll();

                ArrayList<Node> siblings = poll.siblings;
                for (Node sibling : siblings) {
                    if (!sibling.marked) {
                        queue.add(sibling);
                        sibling
                                .setColor(poll.color == Color.Aria ? Color.Pari : Color.Aria)
                                .setMarked(true);
                    }
                }
            }
        });

        boolean collision = map.entrySet().stream().anyMatch(entry -> {
            if (map.get(entry.getKey()).siblings.isEmpty()) {
                return false;
            }
            return map.get(entry.getKey()).siblings.stream().anyMatch(node -> {
                return map.get(entry.getKey()).color == node.color;
            });
        });

        if (collision) {
            out.println(-1);
        } else {
            out.println(pariCount);
            out.println(
                    paris.stream()
                            .map(node -> node.nodeId + "")
                            .collect(Collectors.joining(" "))
            );


            out.println(ariCount);
            out.println(
                    aris.stream()
                            .map(node -> node.nodeId + "")
                            .collect(Collectors.joining(" "))
            );
        }


    }

    static class Node {
        ArrayList<Node> siblings = new ArrayList<>();
        boolean marked = false;
        Color color;
        Integer nodeId;

        public Node(Integer nodeId) {
            this.nodeId = nodeId;
        }

        public Node setColor(Color color) {
            switch (color) {
                case Aria:
                    ariCount++;
                    aris.add(this);
                    break;
                case Pari:
                    pariCount++;
                    paris.add(this);
                    break;
            }
            this.color = color;
            return this;
        }

        public Node setMarked(boolean marked) {
            this.marked = marked;
            return this;
        }

        public Node setNodeId(Integer nodeId) {
            this.nodeId = nodeId;
            return this;
        }

        public Node setSiblings(ArrayList<Node> siblings) {
            this.siblings = siblings;
            return this;
        }

        @Override
        public String toString() {
            return "Node{" +
                    "nodeId=" + nodeId +
                    ", color=" + color +
                    ", siblings=[" + siblings.stream().map(s -> s.nodeId + "").collect(Collectors.joining(";")) + "]" +
                    ", marked=" + marked +
                    '}';
        }

    }

    static enum Color {
        Pari, Aria
    }

    private static void initReaderWriter() throws Exception {
        in = new Reader();
        out = new Output(System.out);

//            in = new Reader("input.txt");
//            out = new Output(new File("output.txt"));
//
//            in = new Reader();
//            out = new Output(System.out);
    }

    public static void main(String[] args) throws Exception {
        Runnable run = () -> {
            try {
                initReaderWriter();
                operate();
                out.close();
            } catch (Exception ex) {
                exception = ex;
            }
        };
        Thread thread = new Thread(null, run, "", 1 << 26);
        thread.start();
        thread.join();

        if (exception != null) {
            throw exception;
        }
    }

    static class Output extends PrintStream {

        public Output(OutputStream out) {
            super(new BufferedOutputStream(out));
        }

        public Output(File file) throws FileNotFoundException {
            super(new BufferedOutputStream(new FileOutputStream(file)));
        }
    }

    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() {
            try {
                int ret = 0;
                byte c = read();
                while (c <= ' ')
                    c = read();
                boolean neg = (c == '-');
                if (neg)
                    c = read();
                do {
                    ret = ret * 10 + c - '0';
                } while ((c = read()) >= '0' && c <= '9');

                if (neg)
                    return -ret;
                return ret;
            } catch (Exception ex) {
                throw new RuntimeException(ex);
            }

        }

        public long nextLong() {
            try {
                long ret = 0;
                byte c = read();
                while (c <= ' ')
                    c = read();
                boolean neg = (c == '-');
                if (neg)
                    c = read();
                do {
                    ret = ret * 10 + c - '0';
                }
                while ((c = read()) >= '0' && c <= '9');
                if (neg)
                    return -ret;
                return ret;
            } catch (IOException ex) {
                throw new RuntimeException(ex);
            }
        }

        public double nextDouble() {
            try {
                double ret = 0, div = 1;
                byte c = read();
                while (c <= ' ')
                    c = read();
                boolean neg = (c == '-');
                if (neg)
                    c = read();

                do {
                    ret = ret * 10 + c - '0';
                }
                while ((c = read()) >= '0' && c <= '9');

                if (c == '.') {
                    while ((c = read()) >= '0' && c <= '9') {
                        ret += (c - '0') / (div *= 10);
                    }
                }

                if (neg)
                    return -ret;
                return ret;
            } catch (IOException ex) {
                throw new RuntimeException(ex);
            }
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }
}