import java.io.PrintWriter
import java.util.*
import java.math.*
import java.lang.*

val pw = PrintWriter(System.out)
val MOD: Long = (1e+9 + 7).toLong()

fun main(args: Array<String>) {
    val (n, m) = readListOfInt()
    
    val k = mutableListOf<Int>()
    val s = mutableListOf<List<Int>>()
    for(i in 0 until m) {
        val row = readListOfInt() 
        val k_ = row[0] 
        val s_ = row.slice(1..k_).map { it - 1 }
        k.add(k_)
        s.add(s_)
    }
    val p = readListOfInt()

    var allBrightCount = 0
    val combNum = Math.pow(2.0, n.toDouble()).toInt()
    for(switchStateNum in 0 until combNum) { // switch states
        var isBrightAllLight = true
        for(i in 0 until m) { // about each lights
            val cs = s[i]
            var switchCount = 0
            cs.forEach { cs_ ->
                val switchState = (switchStateNum shr cs_) % 2
                if(switchState == 1) {
                    switchCount++
                }
            }
            val cp = p[i]
            if(switchCount % 2 != cp) {
                isBrightAllLight = false
            }
        }
        if(isBrightAllLight) {
            allBrightCount++
        }
    }
    println(allBrightCount)

    pw.flush()
}

/****** Decrared Functions and Data Structures ******/
// IO
fun read() = readLine()!!
fun readInt() = read().toInt()
fun readLong() = read().toLong()
fun readDouble() = read().toDouble()
fun readListOfString() = read().split(" ")
fun readListOfInt() = readListOfString().map { it.toInt() }
fun readListOfLong() = readListOfString().map { it.toLong() }
fun readListOfDouble() = readListOfString().map { it.toDouble() }

fun Double.format(digits: Int) = String.format("%.${digits}f", this)
fun Float.format(digits: Int) = String.format("%.${digits}f", this)

fun print(value: Any) { pw.print(value) }
fun println(value : Any) { pw.println(value) }

fun<T> permutations(src: List<T>): List<List<T>> {
    if(src.size == 1) return listOf(src)
    val perms = mutableListOf<List<T>>()
    val insertElement = src[0]
    permutations(src.drop(1)).forEach { perm ->
        for(i in 0..perm.size) {
            val newPerm = perm.toMutableList()
            newPerm.add(i, insertElement)
            perms.add(newPerm.toList())
    }
    }
    return perms
}

// return nCr, if you want nCr, please access v[n][r]
fun combinations(n: Long): List<List<Long>> {
    val v = (0..n).map { (0..n).map{0L}.toMutableList() }.toMutableList()
    for(i in 0 until v.size) {
        v[i][0] = 1L
        v[i][i] = 1L
    }
    for(i in 0 until v.size) {
        for(j in 1 until i) {
            v[i][j] = (v[i-1][j-1] + v[i-1][j] % MOD)
        }
    }
    return v.map { it.toList() }.toList()
}

fun gcd(a: Long, b: Long): Long = 
    if(b != 0L) a else gcd(b, a % b)

fun lcm(a: Long, b: Long) = 
    (a * b) / gcd(a, b)

fun sumDigits(num_: Long): Long {
    var num = num_
    var rtn: Long = 0
    while(num != 0.toLong()) {
        val tmp = num % 10
        rtn += tmp
        num /= 10
    }
    return rtn
}

fun isDecimal(v: Double): Boolean = ((v - Math.floor(v)) != 0.0)

// Data Structures
class Stack<T>(private var st: MutableList<T> = mutableListOf<T>()) {
    fun isEmpty() = st.isEmpty()
    fun top(): T = st.last()
    fun push(e: T) { st.add(e) }
    fun pop() { st = st.dropLast(1).toMutableList() }
}

class Queue<T>(private var que: MutableList<T> = mutableListOf<T>()) {
    fun isEmpty() = que.isEmpty()
    fun top(): T = que.first()
    fun push(e: T) { que.add(e) }
    fun pop() { que = que.drop(1).toMutableList() }
}
