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;
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
const int MAXN = 40;
int n, m;
vector<int> adj[MAXN];
int col[MAXN];
bool been[MAXN];
bool dfscol(int at, int c) {
  if (col[at] != -1)
    return col[at] == c;
  else
    col[at] = c;
  for (int i = (0); i < (((int)(adj[at]).size())); ++i) {
    int to = adj[at][i];
    if (!dfscol(to, 1 - c)) return false;
  }
  return true;
}
void dfsbeen(int at) {
  if (been[at])
    return;
  else
    been[at] = true;
  for (int i = (0); i < (((int)(adj[at]).size())); ++i) {
    int to = adj[at][i];
    dfsbeen(to);
  }
}
long long calcany() { return 1LL << n; }
long long calcindep() {
  int n1 = n / 2, n2 = n - n1;
  vector<long long> adjmask(n, 0LL);
  for (int at = (0); at < (n); ++at)
    for (int i = (0); i < (((int)(adj[at]).size())); ++i) {
      int to = adj[at][i];
      adjmask[at] |= 1LL << to;
    }
  vector<int> ways(1 << n2, 0);
  for (int mask = (0); mask < (1 << n1); ++mask) {
    bool ok = true;
    int othmask = 0;
    for (int i = (0); i < (n1); ++i)
      if ((mask & (1 << i)) != 0) {
        if ((adjmask[i] & mask) != 0) ok = false;
        othmask |= adjmask[i] >> n1;
      }
    if (!ok) continue;
    assert(othmask >= 0 && othmask < (1 << n2));
    ++ways[(1 << n2) - 1 - othmask];
  }
  for (int bit = (0); bit < (n2); ++bit)
    for (int mask = (0); mask < (1 << n2); ++mask)
      if ((mask & (1 << bit)) != 0) ways[mask ^ (1 << bit)] += ways[mask];
  long long ret = 0;
  for (int mask = (0); mask < (1 << n2); ++mask) {
    bool ok = true;
    for (int i = (0); i < (n2); ++i)
      if ((mask & (1 << i)) != 0) {
        if ((adjmask[n1 + i] & (((long long)mask) << n1)) != 0) ok = false;
      }
    if (!ok) continue;
    ret += ways[mask];
  }
  return ret;
}
long long calcmono() {
  for (int i = (0); i < (n); ++i) been[i] = false;
  long long ret = 1;
  for (int i = (0); i < (n); ++i)
    if (!been[i]) dfsbeen(i), ret *= 2;
  return ret;
}
long long calcbipartite() {
  for (int i = (0); i < (n); ++i) col[i] = -1;
  long long ret = 1;
  for (int i = (0); i < (n); ++i)
    if (col[i] == -1)
      if (!dfscol(i, 0))
        return 0;
      else
        ret *= 2;
  return ret;
}
long long calcsingle() {
  long long ret = 1;
  for (int i = (0); i < (n); ++i)
    if (((int)(adj[i]).size()) == 0) ret *= 2;
  return ret;
}
long long calcnone() {
  long long ret = 1;
  for (int i = (0); i < (n); ++i)
    if (((int)(adj[i]).size()) > 0)
      return 0;
    else
      ret *= 2;
  return ret;
}
long long solve() {
  long long ret = 0;
  ret += calcany();
  ret -= 2 * calcindep();
  ret -= calcmono();
  ret += calcbipartite();
  ret += 2 * calcsingle();
  ret -= calcnone();
  return ret;
}
void run() {
  scanf("%d%d", &n, &m);
  for (int i = (0); i < (m); ++i) {
    int a, b;
    scanf("%d%d", &a, &b);
    --a, --b;
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
  printf("%lld\n", solve());
}
int main() {
  run();
  return 0;
}