import java.util.*;
import java.io.*;

public class Main {

    static final Reader sc = new Reader();
    static final PrintWriter out = new PrintWriter(System.out,false);
    static public void main(String args[]) {
        int n = sc.nextInt();
        int m = sc.nextInt();
        int[] p = new int[m];
        boolean[][] s = new boolean[m][n];
        for (boolean[] a: s) {
            Arrays.fill(a, false);
        }
        for (int i = 0; i < m; i++) {
            int k = sc.nextInt();
            for (int j = 0; j < k; j++) {
                s[i][sc.nextInt() - 1] = true;
            }
        }
        for (int i = 0; i < m; i++) {
            p[i] = sc.nextInt();
        }
        int count = 0;
        for (int bit = 0; bit < (1<<n); bit++) {
            count++;
            for (int i = 0; i < m; i++) {
                int onNum = 0;
                for (int j = 0; j < n; j++) {
                    if (s[i][j] && (bit & (1<<j)) != 0) {
                        onNum++;
                    }
                }
                if (onNum % 2 != p[i]) {
                    count--;
                    break;
                }
            }
        }
        out.println(count);
        out.flush();
        sc.close();
        out.close();
    }
}

class Reader {
 
    private final InputStream in;
    private final byte[] buf = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
 
    public Reader() { this(System.in);}
    public Reader(InputStream source) { this.in = source;}
 
    private boolean hasNextByte() {
        if (ptr < buflen) return true;
        ptr = 0;
        try{
            buflen = in.read(buf);
        }catch (IOException e) {e.printStackTrace();}
        if (buflen <= 0) return false;
        return true;
    }
 
    private int readByte() { if (hasNextByte()) return buf[ptr++]; else return -1;}
 
    private boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
 
    private void skip() { while(hasNextByte() && !isPrintableChar(buf[ptr])) ptr++;}
 
    public boolean hasNext() {skip(); return hasNextByte();}
 
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
 
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        boolean minus = false;
        long num = readByte();
 
        if(num == '-'){
            num = 0;
            minus = true;
        }else if (num < '0' || '9' < num){
            throw new NumberFormatException();
        }else{
            num -= '0';
        }
 
        while(true){
            int b = readByte();
            if('0' <= b && b <= '9')
                num = num * 10 + (b - '0');
            else if(b == -1 || !isPrintableChar(b))
                return minus ? -num : num;
            else
                throw new NoSuchElementException();
        }
    }
 
    public int nextInt() {
        long num = nextLong();
        if (num < Integer.MIN_VALUE || Integer.MAX_VALUE < num)
            throw new NumberFormatException();
        return (int)num;
    }
 
    public double nextDouble() {
        return Double.parseDouble(next());
    }
 
    public char nextChar() {
        if (!hasNext()) throw new NoSuchElementException();
        return (char)readByte();
    }
 
    public String nextLine() {
        while (hasNextByte() && (buf[ptr] == '\n' || buf[ptr] == '\r')) ptr++;
        if (!hasNextByte()) throw new NoSuchElementException();
 
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (b != '\n' && b != '\r') {
            sb.appendCodePoint(b);
            b = readByte();
        }
 
        return sb.toString();
    }
 
    public int[] nextIntArray(int n) {
        int[] res = new int[n];
        for (int i=0; i<n; i++) res[i] = nextInt();
        return res;
    }
 
    public char[] nextCharArray(int n) {
        char[] res = new char[n];
        for (int i=0; i<n; i++) res[i] = nextChar();
        return res;
    }
 
    public void close() {try{ in.close();}catch(IOException e){ e.printStackTrace();}};
}

Measured memory_bytes: 23124