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.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;
import java.util.*;

public class Template implements Runnable {

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine(), " :");
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    int[] readIntArray(int size) throws IOException {
        int[] res = new int[size];
        for (int i = 0; i < size; i++) {
            res[i] = readInt();
        }
        return res;
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    <T> List<T>[] createGraphList(int size) {
        List<T>[] list = new List[size];
        for (int i = 0; i < size; i++) {
            list[i] = new ArrayList<>();
        }
        return list;
    }

    public static void main(String[] args) {
        new Thread(null, new Template(), "", 1l * 200 * 1024 * 1024).start();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    long memoryTotal, memoryFree;

    void memory() {
        memoryFree = Runtime.getRuntime().freeMemory();
        System.err.println("Memory = " + ((memoryTotal - memoryFree) >> 10)
                + " KB");
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            memoryTotal = Runtime.getRuntime().freeMemory();
            init();
            solve();
            out.close();
            if (System.getProperty("ONLINE_JUDGE") == null) {
                time();
                memory();
            }
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    List<Integer>[] graph;
    int[] color;

    boolean failed;

    void dfs(int x, int c) {
        color[x] = c;

        for (int y : graph[x]) {
            if (color[y] == -1) {
                dfs(y, 1 - c);
            } else {
                if (color[y] == c) failed = true;
            }
        }
    }

    void solve() throws IOException {
        int n = readInt();
        int m = readInt();

        graph = createGraphList(n);
        for (int i = 0; i < m; i++) {
            int a = readInt() - 1;
            int b = readInt() - 1;
            graph[a].add(b);
            graph[b].add(a);
        }
        color = new int[n];
        Arrays.fill(color, -1);
        for (int i = 0; i < n; i++) {
            if (color[i] == -1) dfs(i, 0);
        }

        if (failed) {
            out.println(-1);
            return;
        }

        ArrayList<Integer> l = new ArrayList<>();
        ArrayList<Integer> r = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            if (color[i] == 0) l.add(i + 1); else r.add(i + 1);
        }
        out.println(l.size());
        for (int x : l) out.print(x + " ");
        out.println();
        out.println(r.size());
        for (int x : r) out.print(x + " ");

    }

    static final class LongIntHashMap {
        final static class Entry {
            final long key;
            int value;
            Entry next;

            Entry(long key, int value, Entry next) {
                this.key = key;
                this.value = value;
                this.next = next;
            }
        }

        private Entry[] table;
        private int capacity;
        private int threshold;
        private int size;

        public LongIntHashMap() {
            this(16);
        }

        @SuppressWarnings("unchecked")
        public LongIntHashMap(int capacity) {
            this.capacity = capacity;
            this.threshold = capacity * 4 / 3;
            this.table = new Entry[capacity];
        }

        public boolean containsKey(long key) {
            final int index = ((((int) (key >>> 32)) ^ ((int) (key))) & 0x7fffffff) % capacity;

            for (Entry entry = table[index]; entry != null; entry = entry.next) {
                if (entry.key == key) {
                    return true;
                }
            }
            return false;
        }

        public int get(long key) {
            final int index = ((((int) (key >>> 32)) ^ ((int) (key))) & 0x7fffffff) % capacity;
            for (Entry entry = table[index]; entry != null; entry = entry.next) {
                if (entry.key == key) {
                    return entry.value;
                }
            }
            return 0;
        }

        public int put(long key, int value) {
            final int index = ((((int) (key >>> 32)) ^ ((int) (key))) & 0x7fffffff) % capacity;
            final Entry entryOriginal = table[index];
            for (Entry entry = entryOriginal; entry != null; entry = entry.next) {
                if (entry.key == key) {
                    int oldValue = entry.value;
                    entry.value = value;
                    return oldValue;
                }
            }
            table[index] = new Entry(key, value, entryOriginal);
            size++;
            if (size > threshold) {
                setCapacity(2 * capacity);
            }
            return 0;
        }

        public int remove(long key) {
            int index = ((((int) (key >>> 32)) ^ ((int) (key))) & 0x7fffffff) % capacity;
            Entry previous = null;
            Entry entry = table[index];
            while (entry != null) {
                Entry next = entry.next;
                if (entry.key == key) {
                    if (previous == null) {
                        table[index] = next;
                    } else {
                        previous.next = next;
                    }
                    size--;
                    return entry.value;
                }
                previous = entry;
                entry = next;
            }
            return 0;
        }

        long[] getKeys() {
            long[] arr = new long[size()];
            int index = 0;
            for (int i = 0; i < table.length; i++) {
                Entry e = table[i];
                while (e != null) {
                    arr[index++] = e.key;
                    e = e.next;
                }
            }
            return arr;
        }

        public void clear() {
            size = 0;
            Arrays.fill(table, null);
        }

        public int size() {
            return size;
        }

        public void setCapacity(int newCapacity) {
            @SuppressWarnings("unchecked")
            Entry[] newTable = new Entry[newCapacity];
            int length = table.length;
            for (int i = 0; i < length; i++) {
                Entry entry = table[i];
                while (entry != null) {
                    long key = entry.key;
                    int index = ((((int) (key >>> 32)) ^ ((int) (key))) & 0x7fffffff) % newCapacity;

                    Entry originalNext = entry.next;
                    entry.next = newTable[index];
                    newTable[index] = entry;
                    entry = originalNext;
                }
            }
            table = newTable;
            capacity = newCapacity;
            threshold = newCapacity * 4 / 3;
        }

        /**
         * Target load: 0,6
         */
        public void reserveRoom(int entryCount) {
            setCapacity(entryCount * 5 / 3);
        }

    }

}