Problem:
Score : 300 points

Problem Statement

You are given an undirected unweighted graph with N vertices and M edges that contains neither self-loops nor double edges.

Here, a self-loop is an edge where a_i = b_i (1≤i≤M), and double edges are two edges where (a_i,b_i)=(a_j,b_j) or (a_i,b_i)=(b_j,a_j) (1≤i<j≤M).

How many different paths start from vertex 1 and visit all the vertices exactly once?

Here, the endpoints of a path are considered visited.

For example, let us assume that the following undirected graph shown in Figure 1 is given.

Figure 1: an example of an undirected graph

The following path shown in Figure 2 satisfies the condition.

Figure 2: an example of a path that satisfies the condition

However, the following path shown in Figure 3 does not satisfy the condition, because it does not visit all the vertices.

Figure 3: an example of a path that does not satisfy the condition

Neither the following path shown in Figure 4, because it does not start from vertex 1.

Figure 4: another example of a path that does not satisfy the condition

Constraints

2≦N≦8

0≦M≦N(N-1)/2

1≦a_i<b_i≦N

The given graph contains neither self-loops nor double edges.

Input

The input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print the number of the different paths that start from vertex 1 and visit all the vertices exactly once.

Sample Input 1

3 3
1 2
1 3
2 3

Sample Output 1

2

The given graph is shown in the following figure:

The following two paths satisfy the condition:

Sample Input 2

7 7
1 3
2 7
3 4
4 5
4 6
5 6
6 7

Sample Output 2

1

This test case is the same as the one described in the problem statement.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.List;
import java.util.Set;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            Vertex[] vertices = new Vertex[n];
            for (int i = 0; i < n; i++)
                vertices[i] = new Vertex();

            for (int i = 0; i < m; i++) {
                int cf = in.nextInt() - 1;
                int ct = in.nextInt() - 1;
                vertices[cf].setEdge(vertices[ct]);
                vertices[ct].setEdge(vertices[cf]);
            }

            out.println(bfs(vertices[0], new HashSet<>(), n));

        }

        static int bfs(Vertex v, Set<Vertex> visited, int max) {
            Set<Vertex> nextSet = new HashSet<>();
            nextSet.addAll(visited);
            nextSet.add(v);
            if (nextSet.size() == max)
                return 1;
            int ans = 0;
            for (int i = 0; i < v.getDegree(); i++) {
                Vertex next = v.getEdge(i).getVertex();
                if (nextSet.contains(next))
                    continue;
                ans += bfs(next, nextSet, max);
            }
            return ans;
        }

    }

    static class Vertex {
        private long value;
        private List<Edge> edges = new ArrayList<Edge>();

        public Vertex() {
        }

        public Vertex(long v) {
            this.value = v;
        }

        public void setEdge(Vertex v) {
            this.edges.add(new Edge(v));
        }

        public long getDegree() {
            return this.edges.size();
        }

        public Edge getEdge(int index) {
            return this.edges.get(index);
        }

    }

    static class Edge {
        private Vertex from;
        private Vertex to;
        private long cost;

        public Edge() {
        }

        public Edge(Vertex to) {
            this.to = to;
        }

        public Edge(Vertex to, long c) {
            this.to = to;
            this.cost = c;
        }

        public Edge(Vertex from, Vertex to, long c) {
            this.from = from;
            this.to = to;
            this.cost = c;
        }

        public Vertex getVertex() {
            return this.to;
        }

    }

    static class FastScanner {
        private InputStream in;
        private byte[] buffer = new byte[1024];
        private int bufPointer;
        private int bufLength;

        public FastScanner(InputStream in) {
            this.in = in;
        }

        private int readByte() {
            if (bufPointer >= bufLength) {
                if (bufLength == -1)
                    throw new InputMismatchException();

                bufPointer = 0;
                try {
                    bufLength = in.read(buffer);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (bufLength <= 0)
                    return -1;
            }
            return buffer[bufPointer++];
        }

        private static boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public long nextLong() {
            long n = 0;

            int b = readByte();
            while (isSpaceChar(b))
                b = readByte();

            boolean minus = (b == '-');
            if (minus)
                b = readByte();

            while (b >= '0' && b <= '9') {
                n *= 10;
                n += b - '0';
                b = readByte();
            }

            if (!isSpaceChar(b))
                throw new NumberFormatException();

            return minus ? -n : n;
        }

        public int nextInt() {
            long n = nextLong();

            if (n < Integer.MIN_VALUE || n > Integer.MAX_VALUE)
                throw new NumberFormatException();

            return (int) n;
        }

    }
}