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 JAVA):

Solution:
//package educational.round73;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class G2 {
	InputStream is;
	PrintWriter out;
//	String INPUT = "";
//	String INPUT = "";
	String INPUT = "";
	
	void solve()
	{
		// #all-(-#0-#1-#2+#01+#02+#12)
		// 2^n+(1+A+1-B-B)
		// 全部1になる塗り方 2部グラフで2^#CC通り？=A
		// 01の塗り方1が独立集合をなす=B
		// 独立集合の個数を数える
		int n = ni(), m = ni();
		if(m == 0){
			out.println(0);
			return;
		}
		
		DJSet ds = new DJSet(n);
		long[] lg = new long[n];
		int[] from = new int[m];
		int[] to = new int[m];
		for(int i = 0;i < m;i++){
			int a = ni()-1, b = ni()-1;
			lg[a] |= 1L<<b;
			lg[b] |= 1L<<a;
			from[i] = a; to[i] = b;
			ds.union(a, b);
		}
		int[][] g = packU(n, from, to);
		long ans = 1L<<n;
		
		int z = 0;
		for(int i = 0;i < n;i++){
			if(-ds.upper[i] == 1)z++;
		}
		ans += 2L<<z;
		if(isBipartite(g) != null){
			ans += 1L<<ds.count();
		}
		
		// 64 + 2 + 0 - 22*2 - 2^2 = 
		
		ans -= 2L*(countIS(lg, (1L<<n)-1));
		ans -= 1L<<ds.count();
		out.println(ans);
	}
	
	long countIS(long[] g, long mask)
	{
		if(mask == 0)return 1;
		int max = -1;
		int arg = -1;
		for(long k = mask;k > 0;k &= k-1){
			int q = Long.numberOfTrailingZeros(k);
			if(Long.bitCount(mask&g[q]) > max){
				max = Long.bitCount(mask&g[q]);
				arg = q;
			}
		}
		int p = arg;
		if((mask&~g[p]) == mask){
			return 2L*countIS(g, mask&~(1L<<p));
		}else{
			return 
			countIS(g, mask&~g[p]&~(1L<<p)) +
			countIS(g, mask&~(1L<<p));
		}
	}
	
	public static class DJSet {
		public int[] upper;

		public DJSet(int n) {
			upper = new int[n];
			Arrays.fill(upper, -1);
		}

		public int root(int x) {
			return upper[x] < 0 ? x : (upper[x] = root(upper[x]));
		}

		public boolean equiv(int x, int y) {
			return root(x) == root(y);
		}

		public boolean union(int x, int y) {
			x = root(x);
			y = root(y);
			if (x != y) {
				if (upper[y] < upper[x]) {
					int d = x;
					x = y;
					y = d;
				}
				upper[x] += upper[y];
				upper[y] = x;
			}
			return x == y;
		}

		public int count() {
			int ct = 0;
			for (int u : upper)
				if (u < 0)
					ct++;
			return ct;
		}
	}

	
	public static int[] isBipartite(int[][] g)
	{
		int n = g.length;
		int[] color = new int[n];
		int[] q = new int[n];
		for(int i = 0;i < n;i++){
			if(color[i] == 0){
				int p = 0;
				q[p++] = i;
				color[i] = 1;
				for(int r = 0;r < p;r++){
					int cur = q[r];
					for(int e : g[cur]){
						if(color[e] == 0){
							color[e] = -color[cur];
							q[p++] = e;
						}else if(color[e] == color[cur]){
							return null;
						}
					}
				}
			}
		}
		return color;
	}

	
	public static long pow(long a, long n, long mod) {
		//		a %= mod;
		long ret = 1;
		int x = 63 - Long.numberOfLeadingZeros(n);
		for (; x >= 0; x--) {
			ret = ret * ret % mod;
			if (n << 63 - x < 0)
				ret = ret * a % mod;
		}
		return ret;
	}

	
	static int[][] packU(int n, int[] from, int[] to) {
		int[][] g = new int[n][];
		int[] p = new int[n];
		for (int f : from)
			p[f]++;
		for (int t : to)
			p[t]++;
		for (int i = 0; i < n; i++)
			g[i] = new int[p[i]];
		for (int i = 0; i < from.length; i++) {
			g[from[i]][--p[from[i]]] = to[i];
			g[to[i]][--p[to[i]]] = from[i];
		}
		return g;
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new G2().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}