Problem: Arseny likes to organize parties and invite people to it. However, not only friends come to his parties, but friends of his friends, friends of friends of his friends and so on. That's why some of Arseny's guests can be unknown to him. He decided to fix this issue using the following procedure.

At each step he selects one of his guests A, who pairwise introduces all of his friends to each other. After this action any two friends of A become friends. This process is run until all pairs of guests are friends.

Arseny doesn't want to spend much time doing it, so he wants to finish this process using the minimum number of steps. Help Arseny to do it.

Input

The first line contains two integers n and m (1 ≤ n ≤ 22; <image>) — the number of guests at the party (including Arseny) and the number of pairs of people which are friends.

Each of the next m lines contains two integers u and v (1 ≤ u, v ≤ n; u ≠ v), which means that people with numbers u and v are friends initially. It's guaranteed that each pair of friends is described not more than once and the graph of friendship is connected.

Output

In the first line print the minimum number of steps required to make all pairs of guests friends.

In the second line print the ids of guests, who are selected at each step.

If there are multiple solutions, you can output any of them.

Examples

Input

5 6
1 2
1 3
2 3
2 5
3 4
4 5


Output

2
2 3 

Input

4 4
1 2
1 3
1 4
3 4


Output

1
1 

Note

In the first test case there is no guest who is friend of all other guests, so at least two steps are required to perform the task. After second guest pairwise introduces all his friends, only pairs of guests (4, 1) and (4, 2) are not friends. Guest 3 or 5 can introduce them.

In the second test case guest number 1 is a friend of all guests, so he can pairwise introduce all guests in one step.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Jialin Ouyang (Jialin.Ouyang@gmail.com)
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    QuickScanner in = new QuickScanner(inputStream);
    QuickWriter out = new QuickWriter(outputStream);
    TaskC solver = new TaskC();
    solver.solve(1, in, out);
    out.close();
  }

  static class TaskC {
    int n;
    int m;
    int[] adjMask;
    static int INF = Integer.MAX_VALUE;
    int[] dp;
    int[] idx;
    int[] fromDP;

    public void solve(int testNumber, QuickScanner in, QuickWriter out) {
      n = in.nextInt();
      m = in.nextInt();
      adjMask = new int[n];
      for (int i = 0; i < n; ++i) adjMask[i] = 1 << i;
      for (int i = 0; i < m; ++i) {
        int u = in.nextInt() - 1;
        int v = in.nextInt() - 1;
        adjMask[u] |= 1 << v;
        adjMask[v] |= 1 << u;
      }
      int res = calc();
      if (res == 0) {
        out.println(0);
        return;
      }
      out.println(calc());
      boolean first = true;
      for (int mask = (1 << n) - 1; mask > 0; mask = fromDP[mask]) {
        if (!first) out.print(' ');
        first = false;
        out.print(idx[mask] + 1);
      }
      out.println();
    }

    int calc() {
      if ((m << 1) == n * (n - 1)) return 0;
      dp = new int[1 << n];
      idx = new int[1 << n];
      fromDP = new int[1 << n];
      Arrays.fill(dp, 1, 1 << n, INF);
      for (int i = 0; i < n; ++i) {
        dp[adjMask[i]] = 1;
        idx[adjMask[i]] = i;
      }
      for (int mask = 1; mask < 1 << n; ++mask)
        if (dp[mask] != INF) {
          for (int i = 0; i < n; ++i)
            if ((mask & (1 << i)) > 0) {
              int nxtMask = mask | adjMask[i];
              if (dp[nxtMask] > dp[mask] + 1) {
                fromDP[nxtMask] = mask;
                idx[nxtMask] = i;
                dp[nxtMask] = dp[mask] + 1;
              }
            }
        }
      return dp[(1 << n) - 1];
    }

  }

  static class QuickScanner {
    private static final int BUFFER_SIZE = 1024;
    private InputStream stream;
    private byte[] buffer;
    private int currentPosition;
    private int numberOfChars;

    public QuickScanner(InputStream stream) {
      this.stream = stream;
      this.buffer = new byte[BUFFER_SIZE];
      this.currentPosition = 0;
      this.numberOfChars = 0;
    }

    public int nextInt() {
      int c = nextNonSpaceChar();
      boolean positive = true;
      if (c == '-') {
        positive = false;
        c = nextChar();
      }
      int res = 0;
      do {
        if (c < '0' || '9' < c) throw new RuntimeException();
        res = res * 10 + (c - '0');
        c = nextChar();
      } while (!isSpaceChar(c));
      return positive ? res : -res;
    }

    public int nextNonSpaceChar() {
      int res = nextChar();
      for (; isSpaceChar(res) || res < 0; res = nextChar()) ;
      return res;
    }

    public int nextChar() {
      if (numberOfChars == -1) {
        throw new RuntimeException();
      }
      if (currentPosition >= numberOfChars) {
        currentPosition = 0;
        try {
          numberOfChars = stream.read(buffer);
        } catch (Exception e) {
          throw new RuntimeException(e);
        }
        if (numberOfChars <= 0) {
          return -1;
        }
      }
      return buffer[currentPosition++];
    }

    public boolean isSpaceChar(int c) {
      return c == ' ' || c == '\t' || isEndOfLineChar(c);
    }

    public boolean isEndOfLineChar(int c) {
      return c == '\n' || c == '\r' || c < 0;
    }

  }

  static class QuickWriter {
    private final PrintWriter writer;

    public QuickWriter(OutputStream outputStream) {
      this.writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public QuickWriter(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();
    }

  }
}