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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.List;
import java.util.Arrays;
import java.io.StringReader;
import java.io.IOException;
import java.io.Reader;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Denis Nedelyaev
 */
public class Main {
    public static void main(String[] args) throws Exception {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA(in, out);
        solver.solve(1);
        out.close();
    }

    static class TaskA {
        private final FastScanner in;
        private final PrintWriter out;
        private List<Integer>[] adj;
        private int[] sides;

        public TaskA(FastScanner in, PrintWriter out) {
            this.in = in;
            this.out = out;
        }

        public void solve(int testNumber) throws IOException {
            int n = in.nextInt();
            int m = in.nextInt();

            adj = new List[n];
            for (int i = 0; i < n; i++) {
                adj[i] = new ArrayList<>();
            }
            for (int i = 0; i < m; i++) {
                int u = in.nextInt() - 1;
                int v = in.nextInt() - 1;
                adj[u].add(v);
                adj[v].add(u);
            }

            sides = new int[n];
            Arrays.fill(sides, -1);

            for (int i = 0; i < n; i++) {
                if (!adj[i].isEmpty() && sides[i] == -1) {
                    if (!dfs(i, -1, 0)) {
                        out.println(-1);
                        return;
                    }
                }
            }

            int[] count = {0, 0};

            for (int side : sides) {
                if (side != -1) {
                    count[side]++;
                }
            }

            for (int side = 0; side < 2; side++) {
                out.println(count[side]);

                for (int i = 0; i < n; i++) {
                    if (sides[i] == side) {
                        out.print((i + 1) + " ");
                    }
                }

                out.println();
            }
        }

        private boolean dfs(int u, int parent, int side) {
            if (sides[u] != -1) {
                return sides[u] == side;
            }

            sides[u] = side;

            for (int v : adj[u]) {
                if (v != parent) {
                    if (!dfs(v, u, 1 - side)) {
                        return false;
                    }
                }
            }

            return true;
        }

    }

    static class FastScanner {
        private final BufferedReader br;
        private String line;
        private int pos;

        public FastScanner(String s) throws IOException {
            this(new StringReader(s));
        }

        public FastScanner(InputStream is) throws IOException {
            this(new InputStreamReader(is, "UTF-8"));
        }

        public FastScanner(Reader reader) throws IOException {
            this(new BufferedReader(reader));
        }

        public FastScanner(BufferedReader reader) throws IOException {
            br = reader;
            line = br.readLine();
            pos = 0;
        }

        public String next() throws IOException {
            if (!skipWhitespace()) {
                return null;
            }

            int start = pos;

            while (pos < line.length()) {
                char c = line.charAt(pos);

                if (c == ' ' || c == '\t') {
                    break;
                }

                pos++;
            }

            return line.substring(start, pos);
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        private boolean skipWhitespace() throws IOException {
            while (line != null) {
                while (pos < line.length()) {
                    char c = line.charAt(pos);

                    if (c != ' ' && c != '\t') {
                        return true;
                    }

                    pos++;
                }

                line = br.readLine();
                pos = 0;
            }

            return false;
        }

    }
}