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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long double EPS = 1e-10;
const long long MOD = 1e9 + 7;
const long double PI = 3.1415926535897932384626433832795028841;
long long powmod(long long a, long long b) {
  long long res = 1;
  a %= MOD;
  for (; b; b >>= 1) {
    if (b & 1) res = res * a % MOD;
    a = a * a % MOD;
  }
  return res;
}
ostream& operator<<(std::ostream& stream, const long long* arr) {
  int i = 0;
  cout << "{";
  while (arr[i] != INT_MAX) {
    cout << arr[i];
    if (arr[i + 1] != INT_MAX) cout << ",";
    i++;
  }
  cout << "}";
  return stream;
}
ostream& operator<<(std::ostream& stream, const vector<int> vec) {
  cout << "{";
  for (int i = 0; i < vec.size(); i++) {
    cout << vec[i];
    if (i != vec.size() - 1) cout << ",";
  }
  cout << "}";
  return stream;
}
ostream& operator<<(std::ostream& stream,
                    const pair<long long, long long>& vec) {
  cout << "(" << vec.first << ',' << vec.second << ")";
  return stream;
}
template <class T>
struct segtree_t {
  vector<T> t, lazy, flag_equal;
  int st, sz;
  T (*addition_fun)(T, T);
  T invalid_value;
  segtree_t() {}
  segtree_t(int start, int finish, T* arr, T (*add_fun)(T, T), T invalid_val) {
    int size = (finish + 1) * 2;
    int tree_size = 2;
    while (tree_size < size) tree_size *= 2;
    t = vector<T>(tree_size);
    lazy = vector<T>(tree_size);
    flag_equal = vector<T>(tree_size);
    st = start;
    sz = finish;
    addition_fun = add_fun;
    invalid_value = invalid_val;
    build(1, start, finish, arr);
  }
  void build(int i, int l, int r, T* arr) {
    if (l > r) return;
    lazy[i] = 0;
    flag_equal[i] = 0;
    if (l == r) {
      t[i] = arr[l];
    } else {
      build(i * 2, l, (l + r) / 2, arr);
      build(i * 2 + 1, (l + r) / 2 + 1, r, arr);
      t[i] = addition_fun(t[i * 2], t[i * 2 + 1]);
    }
  }
  void inc_range(int l, int r, T value) {
    if (l > r) return;
    inc_range_rec(1, st, sz, l, r, value);
  }
  void set_values(int l, int r, T value) {
    set_values_rec(1, st, sz, l, r, value);
  }
  void inc_range_rec(int i, int l, int r, int tl, int tr, T value) {
    if (lazy[i] != 0) {
      t[i] += lazy[i];
      if (l != r) {
        lazy[i * 2] += lazy[i];
        lazy[i * 2 + 1] += lazy[i];
      }
      lazy[i] = 0;
    }
    if (r < tl or l > tr) return;
    if (l > r) return;
    if (l >= tl and r <= tr) {
      if (l != r) {
        lazy[i * 2] += value;
        lazy[i * 2 + 1] += value;
      }
      t[i] += value;
    } else {
      inc_range_rec(i * 2, l, (l + r) / 2, tl, tr, value);
      inc_range_rec(i * 2 + 1, (l + r) / 2 + 1, r, tl, tr, value);
      t[i] = addition_fun(t[i * 2], t[i * 2 + 1]);
    }
  }
  T query_rec(int i, int l, int r, int tl, int tr) {
    if (flag_equal[i] != 0) {
      if (l != r) {
        t[i * 2] = t[i];
        t[i * 2 + 1] = t[i];
        flag_equal[i * 2] = 1;
        flag_equal[i * 2 + 1] = 1;
      }
      flag_equal[i] = 0;
    }
    if (r < tl or l > tr) return invalid_value;
    if (l > r) return invalid_value;
    if (lazy[i] != 0) {
      t[i] += lazy[i];
      if (l != r) {
        lazy[i * 2] += lazy[i];
        lazy[i * 2 + 1] += lazy[i];
      }
      lazy[i] = 0;
    }
    if (l >= tl and r <= tr) {
      return t[i];
    } else {
      T m1 = query_rec(i * 2, l, (l + r) / 2, tl, tr);
      T m2 = query_rec(i * 2 + 1, (l + r) / 2 + 1, r, tl, tr);
      if (m1 == invalid_value && m2 == invalid_value) return invalid_value;
      if (m1 == invalid_value) return m2;
      if (m2 == invalid_value) return m1;
      return addition_fun(m1, m2);
    }
  }
  T query(int l, int r) { return query_rec(1, st, sz, l, r); }
  void set_values_rec(int i, int l, int r, int tl, int tr, T value) {
    if (flag_equal[i] != 0) {
      if (l != r) {
        t[i * 2] = t[i];
        t[i * 2 + 1] = t[i];
        flag_equal[i * 2] = 1;
        flag_equal[i * 2 + 1] = 1;
      }
      flag_equal[i] = 0;
    }
    if (r < tl || l > tr) return;
    if (l > r) return;
    if (l >= tl and r <= tr) {
      t[i] = value;
      flag_equal[i] = 1;
    } else {
      set_values_rec(i * 2, l, (l + r) / 2, tl, tr, value);
      set_values_rec(i * 2 + 1, (l + r) / 2 + 1, r, tl, tr, value);
      t[i] = addition_fun(t[i * 2], t[i * 2 + 1]);
    }
  }
  ~segtree_t() {}
};
const int maxn = 24;
const int maxm = 1e5 + 5;
const int maxk = 1e5 + 5;
const int maxq = 1e5 + 5;
vector<int> CONN[maxn];
const int max_mask = (1 << 22);
int CONN_MASK[maxn];
int DP[max_mask];
int prv[max_mask];
int last[max_mask];
int main() {
  int n, m;
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    int u, v;
    cin >> u >> v;
    u--;
    v--;
    CONN[u].push_back(v);
    CONN[v].push_back(u);
    CONN_MASK[u] |= (1 << v);
    CONN_MASK[v] |= (1 << u);
  }
  int max_value = (1 << n) - 1;
  for (int i = 1; i <= max_value; i++) DP[i] = INT_MAX;
  for (int i = 0; i < n; i++) {
    DP[1 << i] = 0;
    prv[1 << i] = 0;
  }
  for (int i = 1; i <= max_value; i++) {
    if (DP[i] == INT_MAX) continue;
    for (int j = 0; j < n; j++) {
      if (i & (1 << j)) {
        int new_mask = i;
        int cost = 0;
        for (int k = 0; k < CONN[j].size(); k++) {
          if ((CONN_MASK[CONN[j][k]] & new_mask) != new_mask) cost = 1;
          new_mask |= (1 << CONN[j][k]);
        }
        if (DP[i] + cost < DP[new_mask]) {
          DP[new_mask] = DP[i] + cost;
          if (cost > 0) {
            prv[new_mask] = j;
          } else {
            prv[new_mask] = -1;
          }
          last[new_mask] = i;
        }
      }
    }
  }
  vector<int> seq;
  int i = max_value;
  while (last[i] != 0) {
    if (prv[i] != -1) seq.push_back(prv[i]);
    i = last[i];
  }
  cout << DP[max_value] << '\n';
  for (int i = seq.size() - 1; i >= 0; i--) {
    cout << seq[i] + 1 << ' ';
  }
  cout << '\n';
}