Problem: You are given an undirected graph with n vertices and m edges. You have to write a number on each vertex of this graph, each number should be either 0 or 1. After that, you write a number on each edge equal to the sum of numbers on vertices incident to that edge.

You have to choose the numbers you will write on the vertices so that there is at least one edge with 0 written on it, at least one edge with 1 and at least one edge with 2. How many ways are there to do it? Two ways to choose numbers are different if there exists at least one vertex which has different numbers written on it in these two ways.

Input

The first line contains two integers n and m (1 ≤ n ≤ 40, 0 ≤ m ≤ (n(n - 1))/(2)) — the number of vertices and the number of edges, respectively.

Then m lines follow, each line contains two numbers x_i and y_i (1 ≤ x_i, y_i ≤ n, x_i ≠ y_i) — the endpoints of the i-th edge. It is guaranteed that each pair of vertices is connected by at most one edge.

Output

Print one integer — the number of ways to write numbers on all vertices so that there exists at least one edge with 0 written on it, at least one edge with 1 and at least one edge with 2.

Examples

Input


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


Output


20


Input


4 4
1 2
2 3
3 4
4 1


Output


4


Input


35 29
1 2
2 3
3 1
4 1
4 2
3 4
7 8
8 9
9 10
10 7
11 12
12 13
13 14
14 15
15 16
16 17
17 18
18 19
19 20
20 21
21 22
22 23
23 24
24 25
25 26
26 27
27 28
28 29
29 30


Output


34201047040

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-8;
const double pi = acos(-1.0);
template <class T>
long long chkmin(T &a, T b) {
  return a > b ? a = b, 1 : 0;
}
template <class T>
long long chkmax(T &a, T b) {
  return a < b ? a = b, 1 : 0;
}
template <class T>
T sqr(T a) {
  return a * a;
}
template <class T>
T mmin(T a, T b) {
  return a < b ? a : b;
}
template <class T>
T mmax(T a, T b) {
  return a > b ? a : b;
}
template <class T>
T aabs(T a) {
  return a < 0 ? -a : a;
}
template <class T>
long long dcmp(T a, T b) {
  return a > b;
}
template <long long *a>
long long cmp_a(long long first, long long second) {
  return a[first] < a[second];
}
namespace io {
const long long SIZE = (1 << 21) + 1;
char ibuf[SIZE], *iS, *iT, obuf[SIZE], *oS = obuf, *oT = oS + SIZE - 1, c,
                                       qu[55];
long long f, qr;
inline void flush() {
  fwrite(obuf, 1, oS - obuf, stdout);
  oS = obuf;
}
inline void putc(char first) {
  *oS++ = first;
  if (oS == oT) flush();
}
inline bool read(signed &first) {
  for (f = 1, c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                              (iS == iT ? EOF : *iS++))
                            : *iS++);
       c < '0' || c > '9';
       c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                       (iS == iT ? EOF : *iS++))
                     : *iS++))
    if (c == '-')
      f = -1;
    else if (c == EOF)
      return 0;
  for (first = 0; c <= '9' && c >= '0';
       c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                       (iS == iT ? EOF : *iS++))
                     : *iS++))
    first = first * 10 + (c & 15);
  first *= f;
  return 1;
}
inline bool read(long long &first) {
  for (f = 1, c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                              (iS == iT ? EOF : *iS++))
                            : *iS++);
       c < '0' || c > '9';
       c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                       (iS == iT ? EOF : *iS++))
                     : *iS++))
    if (c == '-')
      f = -1;
    else if (c == EOF)
      return 0;
  for (first = 0; c <= '9' && c >= '0';
       c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                       (iS == iT ? EOF : *iS++))
                     : *iS++))
    first = first * 10 + (c & 15);
  first *= f;
  return 1;
}
inline bool read(char &first) {
  first = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                       (iS == iT ? EOF : *iS++))
                    : *iS++);
  return first != EOF;
}
inline bool read(char *first) {
  while ((*first = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                                (iS == iT ? EOF : *iS++))
                             : *iS++)) == '\n' ||
         *first == ' ' || *first == '\r')
    if (*first == EOF) return 0;
  while (!(*first == '\n' || *first == ' ' || *first == '\r' || *first == EOF))
    *(++first) = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                              (iS == iT ? EOF : *iS++))
                           : *iS++);
  *first = 0;
  return 1;
}
template <typename A, typename... B>
inline bool read(A &first, B &...second) {
  return read(first) && read(second...);
}
inline bool write(signed first) {
  if (!first) putc('0');
  if (first < 0) putc('-'), first = -first;
  while (first) qu[++qr] = first % 10 + '0', first /= 10;
  while (qr) putc(qu[qr--]);
  return 0;
}
inline bool write(long long first) {
  if (!first) putc('0');
  if (first < 0) putc('-'), first = -first;
  while (first) qu[++qr] = first % 10 + '0', first /= 10;
  while (qr) putc(qu[qr--]);
  return 0;
}
inline bool write(char first) {
  putc(first);
  return 0;
}
inline bool write(const char *first) {
  while (*first) {
    putc(*first);
    ++first;
  }
  return 0;
}
inline bool write(char *first) {
  while (*first) {
    putc(*first);
    ++first;
  }
  return 0;
}
template <typename A, typename... B>
inline bool write(A first, B... second) {
  return write(first) || write(second...);
}
struct Flusher_ {
  ~Flusher_() { flush(); }
} io_flusher_;
}  // namespace io
using io ::putc;
using io ::read;
using io ::write;
long long inf;
struct _init_ {
  _init_() { memset(&inf, 0x3f, sizeof(inf)); }
};
_init_ ___INIT__;
long long s[25], e[45], s1[25], s2[25];
long long f[1 << 20];
long long g[1 << 20], lg[1 << 20];
long long ms[1 << 20];
long long cnt[9];
long long eu[405], ev[405];
long long fa[45];
long long find(long long first) {
  return first == fa[first] ? first : fa[first] = find(fa[first]);
}
vector<long long> to[45];
long long col[45];
long long chk(long long first, long long c) {
  if (~col[first]) return col[first] == c;
  col[first] = c;
  for (auto i : to[first])
    if (!chk(i, c ^ 1)) return 0;
  return 1;
}
signed main() {
  long long n, m, u, v;
  read(n, m);
  if (m == 0) return write("0\n");
  for (long long i = 0; i < n; ++i) fa[i] = i, col[i] = -1;
  long long hfn = n >> 1, ans = 1LL << n, ahf = n - hfn;
  for (long long i = 1; i <= m; ++i) {
    read(u, v);
    if (u > v) swap(u, v);
    --u;
    --v;
    e[u] = 1;
    e[v] = 1;
    fa[find(u)] = find(v);
    to[u].push_back(v);
    to[v].push_back(u);
    if (u < hfn && v < hfn) {
      s1[u] |= 1 << v;
    } else if (u >= hfn && v >= hfn) {
      u -= hfn;
      v -= hfn;
      s2[u] |= 1 << v;
    } else {
      v -= hfn;
      s[u] |= 1 << v;
    }
  }
  long long w0 = 1;
  for (long long i = 0; i < n; ++i)
    if (fa[i] == i) w0 <<= 1;
  for (long long i = 0; i < n; ++i)
    if (!~col[i]) {
      if (!chk(i, 0)) {
        ans -= w0;
        break;
      }
    }
  long long w2 = 2;
  for (long long i = 0; i < n; ++i)
    if (!e[i]) w2 <<= 1;
  ans += w2;
  for (long long i = 0; i < hfn; ++i) lg[1 << i] = i;
  ms[0] = (1 << ahf) - 1;
  for (long long i = 0; i < 1 << hfn; ++i) {
    f[i] = 1;
    for (long long j = 0; j < hfn; ++j)
      if (i & (1 << j))
        if (i & s1[j]) {
          f[i] = 0;
          break;
        }
    if (i) {
      ms[i] = ms[i & (i - 1)] & ~s[lg[i & (-i)]];
    }
  }
  for (long long i = 0; i < 1 << ahf; ++i) {
    g[i] = 1;
    for (long long j = 0; j < ahf; ++j)
      if (i & (1 << j))
        if (i & s2[j]) {
          g[i] = 0;
          break;
        }
  }
  for (long long i = 0; i < ahf; ++i)
    for (long long j = 0; j < 1 << ahf; ++j)
      if (!(j & (1 << i))) {
        g[j | (1 << i)] += g[j];
      }
  for (long long i = 0; i < 1 << hfn; ++i) ans -= f[i] * 2 * g[ms[i]];
  write(ans, '\n');
  return 0;
}