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>
#pragma GCC optimize("Ofast")
using namespace std;
void *wmem;
char memarr[96000000];
template <class S, class T>
inline S max_L(S a, T b) {
  return a >= b ? a : b;
}
template <class T>
inline void walloc1d(T **arr, int x, void **mem = &wmem) {
  static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1};
  (*mem) = (void *)(((char *)(*mem)) + skip[((unsigned long long)(*mem)) & 15]);
  (*arr) = (T *)(*mem);
  (*mem) = ((*arr) + x);
}
template <class T1, class T2>
void sortA_L(int N, T1 a[], T2 b[], void *mem = wmem) {
  int i;
  pair<T1, T2> *arr;
  walloc1d(&arr, N, &mem);
  for (i = (0); i < (N); i++) {
    arr[i].first = a[i];
    arr[i].second = b[i];
  }
  sort(arr, arr + N);
  for (i = (0); i < (N); i++) {
    a[i] = arr[i].first;
    b[i] = arr[i].second;
  }
}
inline void rd(int &x) {
  int k;
  int m = 0;
  x = 0;
  for (;;) {
    k = getchar();
    if (k == '-') {
      m = 1;
      break;
    }
    if ('0' <= k && k <= '9') {
      x = k - '0';
      break;
    }
  }
  for (;;) {
    k = getchar();
    if (k < '0' || k > '9') {
      break;
    }
    x = x * 10 + k - '0';
  }
  if (m) {
    x = -x;
  }
}
inline void wt_L(char a) { putchar(a); }
inline void wt_L(long long x) {
  int s = 0;
  int m = 0;
  char f[20];
  if (x < 0) {
    m = 1;
    x = -x;
  }
  while (x) {
    f[s++] = x % 10;
    x /= 10;
  }
  if (!s) {
    f[s++] = 0;
  }
  if (m) {
    putchar('-');
  }
  while (s--) {
    putchar(f[s] + '0');
  }
}
template <class S, class T>
inline S chmin(S &a, T b) {
  if (a > b) {
    a = b;
  }
  return a;
}
struct unionFind {
  int *d;
  int N;
  int M;
  inline void malloc(const int n) {
    d = (int *)std::malloc(n * sizeof(int));
    M = n;
  }
  inline void free(void) { std::free(d); }
  inline void walloc(const int n, void **mem = &wmem) {
    walloc1d(&d, n, mem);
    M = n;
  }
  inline void init(const int n) {
    int i;
    N = n;
    for (i = (0); i < (n); i++) {
      d[i] = -1;
    }
  }
  inline void init(void) { init(M); }
  inline int get(int a) {
    int t = a;
    int k;
    while (d[t] >= 0) {
      t = d[t];
    }
    while (d[a] >= 0) {
      k = d[a];
      d[a] = t;
      a = k;
    }
    return a;
  }
  inline int connect(int a, int b) {
    if (d[a] >= 0) {
      a = get(a);
    }
    if (d[b] >= 0) {
      b = get(b);
    }
    if (a == b) {
      return 0;
    }
    if (d[a] < d[b]) {
      d[a] += d[b];
      d[b] = a;
    } else {
      d[b] += d[a];
      d[a] = b;
    }
    return 1;
  }
  inline int operator()(int a) { return get(a); }
  inline int operator()(int a, int b) { return connect(a, b); }
  inline int &operator[](const int a) { return d[a]; }
  inline int size(int a) {
    a = get(a);
    return -d[a];
  }
  inline int sizeList(int res[]) {
    int i;
    int sz = 0;
    for (i = (0); i < (N); i++) {
      if (d[i] < 0) {
        res[sz++] = -d[i];
      }
    }
    return sz;
  }
};
struct graph {
  int N;
  int *es;
  int **edge;
  void setEdge(int N__, int M, int A[], int B[], void **mem = &wmem) {
    int i;
    N = N__;
    walloc1d(&es, N, mem);
    walloc1d(&edge, N, mem);
    for (i = (0); i < (N); i++) {
      es[i] = 0;
    }
    for (i = (0); i < (M); i++) {
      es[A[i]]++;
      es[B[i]]++;
    }
    for (i = (0); i < (N); i++) {
      walloc1d(&edge[i], es[i], mem);
    }
    for (i = (0); i < (N); i++) {
      es[i] = 0;
    }
    for (i = (0); i < (M); i++) {
      edge[A[i]][es[A[i]]++] = B[i];
      edge[B[i]][es[B[i]]++] = A[i];
    }
  }
  graph reduce(int tn, int ind[], int self_e = 0, int dep_e = 0,
               void **mem = &wmem) {
    int i;
    int j;
    int k;
    int M = 0;
    int x;
    int y;
    graph g;
    void *tmem;
    pair<int, int> *A;
    for (i = (0); i < (N); i++) {
      M += es[i];
    }
    tmem = ((char *)(*mem)) + sizeof(int **) * N + sizeof(int *) * N +
           sizeof(int) * M + 16 * (N + 2);
    walloc1d(&A, M, &tmem);
    M = 0;
    for (i = (0); i < (N); i++) {
      x = ind[i];
      if (x < 0) {
        continue;
      }
      for (j = (0); j < (es[i]); j++) {
        y = ind[edge[i][j]];
        if (y < 0) {
          continue;
        }
        if (self_e == 0 && x == y) {
          continue;
        }
        A[M++] = make_pair(x, y);
      }
    }
    if (dep_e == 0) {
      sort(A, A + M);
      k = 0;
      for (i = (0); i < (M); i++) {
        if (k && A[k - 1] == A[i]) {
          continue;
        }
        A[k++] = A[i];
      }
      M = k;
    }
    g.N = tn;
    walloc1d(&g.es, tn, mem);
    walloc1d(&g.edge, tn, mem);
    for (i = (0); i < (tn); i++) {
      g.es[i] = 0;
    }
    for (i = (0); i < (M); i++) {
      g.es[A[i].first]++;
    }
    for (i = (0); i < (tn); i++) {
      walloc1d(&g.edge[i], g.es[i], mem);
    }
    for (i = (0); i < (tn); i++) {
      g.es[i] = 0;
    }
    for (i = (0); i < (M); i++) {
      j = A[i].first;
      k = A[i].second;
      g.edge[j][g.es[j]++] = k;
    }
    return g;
  }
  void articulationDFS(int n, int b, int &k, int od[], int lw[], int vs[],
                       int &ress, int res[]) {
    int i;
    int j;
    int a = 0;
    int c = 0;
    vs[n] = 1;
    lw[n] = od[n] = k++;
    for (i = (0); i < (es[n]); i++) {
      j = edge[n][i];
      if (j == b) {
        continue;
      }
      if (!vs[j]) {
        c++;
        articulationDFS(j, n, k, od, lw, vs, ress, res);
        chmin(lw[n], lw[j]);
        if (b != -1 && od[n] <= lw[j]) {
          a = 1;
        }
      } else {
        chmin(lw[n], od[j]);
      }
    }
    if (b == -1 && c >= 2) {
      a = 1;
    }
    if (a) {
      res[ress++] = n;
    }
  }
  int articulation(int res[], void *mem = wmem) {
    int i;
    int k = 0;
    int ress = 0;
    int *od;
    int *lw;
    int *vs;
    walloc1d(&od, N, &mem);
    walloc1d(&lw, N, &mem);
    walloc1d(&vs, N, &mem);
    for (i = (0); i < (N); i++) {
      vs[i] = 0;
    }
    for (i = (0); i < (N); i++) {
      if (!vs[i]) {
        articulationDFS(i, -1, k, od, lw, vs, ress, res);
      }
    }
    return ress;
  }
  long long countIndependenceSet(void *mem = wmem, int skip = 0) {
    int i;
    int j;
    int k;
    int x;
    long long res;
    int *deg;
    int *ind;
    long long *pr;
    graph g;
    unionFind uf;
    void *tmem;
    if (N == 0) {
      return 1;
    }
    if (N == 1) {
      return 2;
    }
    walloc1d(&deg, N, &mem);
    walloc1d(&ind, N, &mem);
    walloc1d(&pr, N, &mem);
    if (!skip) {
      k = 0;
      uf.walloc(N, &mem);
      uf.init(N);
      for (i = (0); i < (N); i++) {
        for (j = (0); j < (es[i]); j++) {
          k += uf(i, edge[i][j]);
        }
      }
      if (k < N - 1) {
        res = 1;
        for (i = (0); i < (N); i++) {
          deg[i] = 0;
        }
        for (i = (0); i < (N); i++) {
          deg[uf(i)]++;
        }
        for (x = (0); x < (N); x++) {
          if (deg[x]) {
            k = 0;
            for (i = (0); i < (N); i++) {
              if (uf(i) != x) {
                ind[i] = -1;
                continue;
              }
              ind[i] = k++;
            }
            tmem = mem;
            g = reduce(k, ind, 1, 1, &mem);
            res *= g.countIndependenceSet(mem, 1);
            mem = tmem;
          }
        }
        return res;
      }
    }
    k = articulation(ind);
    for (i = (0); i < (N); i++) {
      pr[i] = 0;
    }
    for (i = (0); i < (k); i++) {
      pr[ind[i]] += (1LL << 40);
    }
    for (i = (0); i < (N); i++) {
      for (j = (0); j < (es[i]); j++) {
        pr[i] += (1LL << 20) - es[edge[i][j]];
      }
    }
    {
      int cTE1_r3A;
      int RZTsC2BF = 0;
      long long FmcKpFmN;
      long long xr20shxY;
      int WYIGIcGE;
      for (cTE1_r3A = (0); cTE1_r3A < (((N)-1) + 1); cTE1_r3A++) {
        xr20shxY = pr[cTE1_r3A];
        if (RZTsC2BF == 0 || FmcKpFmN < xr20shxY) {
          FmcKpFmN = xr20shxY;
          RZTsC2BF = 1;
          WYIGIcGE = cTE1_r3A;
        }
      }
      x = WYIGIcGE;
    }
    res = 0;
    k = 0;
    for (i = (0); i < (N); i++) {
      if (i == x) {
        ind[i] = -1;
        continue;
      }
      ind[i] = k++;
    }
    tmem = mem;
    g = reduce(k, ind, 1, 1, &mem);
    res += g.countIndependenceSet(mem);
    mem = tmem;
    k = 0;
    for (i = (0); i < (N); i++) {
      deg[i] = 0;
    }
    deg[x] = 1;
    for (j = (0); j < (es[x]); j++) {
      deg[edge[x][j]] = 1;
    }
    for (i = (0); i < (N); i++) {
      if (deg[i]) {
        ind[i] = -1;
        continue;
      }
      ind[i] = k++;
    }
    g = reduce(k, ind, 1, 1, &mem);
    res += g.countIndependenceSet(mem);
    return res;
  }
  int bipartite(int res[] = NULL, void *mem = wmem) {
    int i;
    int j;
    int k;
    int *st;
    int sts;
    if (res == NULL) {
      walloc1d(&res, N, &mem);
    }
    walloc1d(&st, N, &mem);
    for (i = (0); i < (N); i++) {
      res[i] = -1;
    }
    for (i = (0); i < (N); i++) {
      if (res[i] == -1) {
        res[i] = 0;
        sts = 0;
        st[sts++] = i;
        while (sts) {
          i = st[--sts];
          for (j = (0); j < (es[i]); j++) {
            k = edge[i][j];
            if (res[k] == -1) {
              res[k] = 1 - res[i];
              st[sts++] = k;
            }
            if (res[i] + res[k] != 1) {
              return 0;
            }
          }
        }
      }
    }
    return 1;
  }
};
int N;
int M;
int A[1000];
int B[1000];
int ind[40];
long long dp[8];
long long nx[8];
long long now[8];
int main() {
  int x;
  wmem = memarr;
  int i;
  int j;
  int k;
  unionFind uf;
  graph og;
  graph g;
  rd(N);
  rd(M);
  {
    int Lj4PdHRW;
    for (Lj4PdHRW = (0); Lj4PdHRW < (M); Lj4PdHRW++) {
      rd(A[Lj4PdHRW]);
      A[Lj4PdHRW] += (-1);
      rd(B[Lj4PdHRW]);
      B[Lj4PdHRW] += (-1);
    }
  }
  og.setEdge(N, M, A, B);
  uf.malloc(N);
  uf.init(N);
  for (i = (0); i < (M); i++) {
    uf(A[i], B[i]);
  }
  dp[0] = 1;
  for (x = (0); x < (N); x++) {
    k = 0;
    for (i = (0); i < (N); i++) {
      if (uf(i) != x) {
        ind[i] = -1;
      } else {
        ind[i] = k++;
      }
    }
    if (!k) {
      continue;
    }
    if (k == 1) {
      for (i = (0); i < (8); i++) {
        now[i] = 0;
      }
      now[0] = 2;
    } else {
      g = og.reduce(k, ind, 1, 1);
      now[0] = now[5] = 0;
      now[1] = now[4] = 1;
      now[2] = 2 * g.bipartite();
      now[3] = now[6] = g.countIndependenceSet() - 1 - now[2];
      {
        int KL2GvlyY;
        long long Q5VJL1cS;
        if (7 == 0) {
          Q5VJL1cS = 0;
        } else {
          Q5VJL1cS = now[0];
          for (KL2GvlyY = (1); KL2GvlyY < (7); KL2GvlyY++) {
            Q5VJL1cS += now[KL2GvlyY];
          }
        }
        now[7] = (1LL << k) - Q5VJL1cS;
      }
    }
    for (i = (0); i < (8); i++) {
      nx[i] = 0;
    }
    for (i = (0); i < (8); i++) {
      for (j = (0); j < (8); j++) {
        nx[i | j] += dp[i] * now[j];
      }
    }
    for (i = (0); i < (8); i++) {
      dp[i] = nx[i];
    }
  }
  wt_L(dp[7]);
  wt_L('\n');
  return 0;
}