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.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.NoSuchElementException;

public class C {
  private static class Task {
    void solve(FastScanner in, PrintWriter out) {
      int N = in.nextInt();
      int M = in.nextInt();
      ArrayList<Integer>[] graph = new ArrayList[N];
      for (int i = 0; i < N; i++) graph[i] = new ArrayList<Integer>();
      for (int i = 0; i < M; i++) {
        int u = in.nextInt() - 1;
        int v = in.nextInt() - 1;
        graph[u].add(v);
        graph[v].add(u);
      }

      ArrayDeque<Integer> que = new ArrayDeque<>();
      int[] color = new int[N];
      for (int i = 0; i < N; i++) {
        if (color[i] != 0) continue;
        if (graph[i].isEmpty()) {
          color[i] = -1;
          continue;
        }

        color[i] = 1;
        que.add(i);
        while (!que.isEmpty()) {
          int v = que.poll();
          for (int u : graph[v]) {
            if (color[u] != 0 && color[u] == color[v]) {
              out.println(-1);
              return;
            }
            if (color[u] == 0) {
              if (color[v] == 1) {
                color[u] = 2;
              } else if (color[v] == 2) {
                color[u] = 1;
              } else {
                assert false;
              }
              que.add(u);
            }
          }
        }
      }

      int cnt1 = 0, cnt2 = 0;
      for (int i = 0; i < N; i++) {
        if (color[i] == 1) cnt1++;
        else if (color[i] == 2) cnt2++;
      }
      out.println(cnt1);
      for (int i = 0; i < N; i++) {
        if (color[i] == 1) {
          out.print(i + 1);
          cnt1--;
          if (cnt1 > 0) out.print(" ");
        }
      }
      out.println();
      out.println(cnt2);
      for (int i = 0; i < N; i++) {
        if (color[i] == 2) {
          out.print(i + 1);
          cnt2--;
          if (cnt2 > 0) out.print(" ");
        }
      }
      out.println();

    }
  }

  // Template
  public static void main(String[] args) {
    OutputStream outputStream = System.out;
    FastScanner in = new FastScanner();
    PrintWriter out = new PrintWriter(outputStream);
    Task solver = new Task();
    solver.solve(in, out);
    out.close();
  }
  private static class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int bufferLength = 0;

    private boolean hasNextByte() {
      if (ptr < bufferLength) {
        return true;
      } else {
        ptr = 0;
        try {
          bufferLength = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (bufferLength <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) return buffer[ptr++];
      else return -1;
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) throw new NoSuchElementException();
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    long nextLong() {
      if (!hasNext()) throw new NoSuchElementException();
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

    double nextDouble() {
      return Double.parseDouble(next());
    }

    double[] nextDoubleArray(int n) {
      double[] array = new double[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextDouble();
      }
      return array;
    }

    double[][] nextDoubleMap(int n, int m) {
      double[][] map = new double[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextDoubleArray(m);
      }
      return map;
    }

    public int nextInt() {
      return (int) nextLong();
    }

    public int[] nextIntArray(int n) {
      int[] array = new int[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextInt();
      }
      return array;
    }
  }
}