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.util.ArrayDeque;
import java.util.InputMismatchException;
import java.util.LinkedList;

public class Cf2906C {
    private static InputReader in = new InputReader(System.in);
    private static OutputWriter out = new OutputWriter(System.out);
    private static int n;
    private static int m;
    private static int[] colors;
    private static LinkedList<Integer>[] adj;
    private static boolean[] isVisited;
    private static int color;
    private static void solve() throws Exception{
        n = in.readInt();
        m = in.readInt();
        colors = new int[n+1];
        adj  = new LinkedList[n+1];
        isVisited = new boolean[n+1];
        for(int i=0; i<=n; ++i){
            adj[i] = new LinkedList<>();
        }
        for(int i=0; i<m; ++i){
            int u = in.readInt();
            int v = in.readInt();
            adj[u].add(v);
            adj[v].add(u);
        }
        boolean flag = false;
        for(int i=1; i<=n; ++i){
            color = 1;
            if(adj[i].size()==0){
                continue;
            }
            if(isVisited[i]){
                continue;
            }
            colors[i] = 1;
            isVisited[i] = true;
            ArrayDeque<Integer> arrayDeque = new ArrayDeque();
            arrayDeque.add(i);
            while(!arrayDeque.isEmpty()){
                int item = arrayDeque.remove();
                for(int x: adj[item]){
                     if(isVisited[x]){
                         if(colors[x]==colors[item]){
                             flag = true;
                         }
                     }
                     else{
                         if(colors[item]==1){
                             colors[x] =  2;
                         }
                         else{
                             colors[x] = 1;
                         }
                         arrayDeque.add(x);
                         isVisited[x] = true;
                     }
                 }
            }
        }
        if(flag){
            out.println(-1);
        }
        else{
            StringBuilder line1 = new StringBuilder();
            StringBuilder line2 = new StringBuilder();
            int count1 =0 ;
            int count2 =0;
            for(int i=1; i<=n; ++i){
                if(colors[i]==1){
                    count1++;
                    line1.append(i+" ");

                }
                else if(colors[i]==2){
                    count2++;
                    line2.append(i+" ");

                }
            }
            out.println(count1);
            out.println(line1);
            out.println(count2);
            out.println(line2);
        }


    }



    public static void main(String[] args) throws Exception {
        solve();
        out.close();
    }


    private static class InputReader {
        private InputStream stream;
        private byte[] buffer;
        private int currentIndex;
        private int bytesRead;

        public InputReader(InputStream stream) {
            this.stream = stream;
            buffer = new byte[131072];
        }


        public InputReader(InputStream stream, int bufferSize) {
            this.stream = stream;
            buffer = new byte[bufferSize];
        }


        private int read() throws IOException {
            if (currentIndex >= bytesRead) {
                currentIndex = 0;
                bytesRead = stream.read(buffer);
                if (bytesRead <= 0) {
                    return -1;
                }
            }
            return buffer[currentIndex++];
        }

        public String readString() throws IOException {
            int c = read();
            while (!isPrintable(c)) {
                c = read();
            }
            StringBuilder result = new StringBuilder();
            do {
                result.appendCodePoint(c);
                c = read();
            } while (isPrintable(c));
            return result.toString();
        }

        public int readInt() throws Exception {
            int c = read();
            int sign = 1;
            while (!isPrintable(c)) {
                c = read();
            }
            if (c == '-') {
                sign = -1;
                c = read();
            }
            int result = 0;
            do {
                if ((c < '0') || (c > '9')) {
                    throw new InputMismatchException();
                }
                result *= 10;
                result += (c - '0');
                c = read();
            } while (isPrintable(c));
            return sign * result;
        }

        public long readLong() throws Exception {
            int c = read();
            int sign = 1;
            while (!isPrintable(c)) {
                c = read();
            }
            if (c == '-') {
                sign = -1;
                c = read();
            }
            long result = 0;
            do {
                if ((c < '0') || (c > '9')) {
                    throw new InputMismatchException();
                }
                result *= 10;
                result += (c - '0');
                c = read();
            } while (isPrintable(c));
            return sign * result;
        }

        public double readDouble() throws Exception {
            int c = read();
            int sign = 1;
            while (!isPrintable(c)) {
                c = read();
            }
            if (c == '-') {
                sign = -1;
                c = read();
            }
            boolean fraction = false;
            double multiplier = 1;
            double result = 0;
            do {
                if ((c == 'e') || (c == 'E')) {
                    return sign * result * Math.pow(10, readInt());
                }
                if ((c < '0') || (c > '9')) {
                    if ((c == '.') && (!fraction)) {
                        fraction = true;
                        c = read();
                        continue;
                    }
                    throw new InputMismatchException();
                }
                if (fraction) {
                    multiplier /= 10;
                    result += (c - '0') * multiplier;
                    c = read();
                } else {
                    result *= 10;
                    result += (c - '0');
                    c = read();
                }
            } while (isPrintable(c));
            return sign * result;
        }

        private boolean isPrintable(int c) {
            return ((c > 32) && (c < 127));
        }
    }

    private static class OutputWriter {
        private PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void println(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void flush() {
            writer.flush();
        }
    }
}