// 🐋💭
import Foundation

func readInts() -> [Int] {
    return readLine()!.split(separator: " ").map { Int($0)! }
}

func readInt() -> Int {
    return Int(readLine()!)!
}

func readDoubles () -> [Double] {
    return readLine()!.split(separator: " ").map { Double($0)! }
}

func readDouble() -> Double{
    return Double(readLine()!)!
}

func readLines() -> [String] {
    return readLine()!.map { String($0) }
}
///最大公約数を返す
func gcd(_ m:Int, _ n:Int) -> Int {
    if n == 0 {return m}
    return gcd(n, m % n)
}

///最大公約数を返す
func gcd(_ array: [Int]) -> Int {
    var value = array[0]
    if array.count > 1 {
        for i in 1..<array.count {
            value = gcd(value, array[i])
        }
    }
    return value
}

///最小公倍数を返す
func lcm(_ m:Int, _ n:Int) -> Int {
    let g = gcd(m, n)
    return m / g * n
}

///素数判定(試し割り)
func isPrime(_ x:Int) -> Bool {
    if x <= 1 || x % 2 == 0 { return false }
    if x == 2 { return true }
    for i in stride(from: 3, to: Int(ceil(sqrt(Double(x)))), by: 2){
        if x % i == 0 {
            return false
        }
    }
    return true
}

//https://program-life.com/669
///実行速度の計測
func exectionTime(action: () -> Void) {
    let startDate = Date()
    action()
    let endDate = Date()
    print(endDate.timeIntervalSince(startDate))
}

//https://riptutorial.com/ja/swift/example/14738/インデックスを知らずに配列から要素を削除する
extension Array where Element: Equatable {
    
    mutating func remove(_ element: Element) {
        _ = firstIndex(of: element).flatMap {
            self.remove(at: $0)
        }
    }
}

func binarySearch(rifgt:Int, key:Int, ary:[String]) -> Int{
    var left = 0
    var right = rifgt
    
    while abs(right - left) > 1 {
        let mid = left + (right - left) / 2
        
        if Int(ary[mid])! < key {
            left = mid
            
        } else {
            right = mid
        }
    }
    return left
}

func arrangement (prev:String, ary:[String], returnVal:[String]) -> [String] {
    var returnVal = returnVal
    if ary.count == 0 {
        returnVal.append(prev)
        return returnVal
    }
    
    for s in ary {
        let wprev = prev + s
        var wary = ary
        wary.remove(s)
        returnVal = arrangement(prev: wprev, ary: wary, returnVal: returnVal)
    }
    return returnVal
}
// https://algo-logic.info/divisor/
/// 約数の配列を返す
func divisor(_ n:Int) -> [Int] {
    var ret = [Int]()
    var i = 1
    while i * i <= n {
        if n % i == 0 {
            ret.append(i)
            if i * i != n {
                ret.append(n / i)
            }
        }
        i += 1
    }
    return ret.sorted()
}

/// 1〜nまでの数字からなる辞書順列のm番目の順列を返す
func permutation(_ n: Int, _ m: Int) -> [Int] {
    var m = m
    
    var temp = [Int](repeating: 0, count: n)
    var surplus = [Int](repeating: 0, count: n)
    
    for i in 1...n {
        temp[i - 1] = i
        
        surplus[n - i] = m % i
        m = m / i
    }
    
    var order = [Int](repeating: 0, count: n)
    
    for i in 0..<n {
        order[i] = temp[surplus[i]]
        var j = surplus[i]
        while j + 1 < n {
            temp[j] = temp[j + 1]
            j += 1
        }
    }
    return order
}
func mod() -> Int {
    return Int(pow(10.0, 9.0)) + 7
}

func nPk(_ n: Int, _ k: Int) -> Int {
    var (n, k) = (n, k)
    var res = 1
    while k > 0 {
        res *= n
        res %= mod()
        n -= 1
        k -= 1
    }
    return res
}



func main() {
    let input = readInts()
    let (N, M) = (input[0], input[1])
    /// 1であればその添字のスイッチに接続されている
    var pair = [[Int]](repeating: [Int](repeating: 0, count: N), count: M)
    for i in 0..<M {
        let input = readInts()
        // input[0]はk
        for j in 1...input[0] {
            pair[i][input[j] - 1] = 1
        }
    }
    let p = readInts()
    //＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿ここまで入力
    var ans = 0
    for i in 0..<1<<N {
        /// 0…OFF、1…ON
        var stateSwitches = [Int](repeating: 0, count: N)
        for j in 0..<N {
            if (i>>j) & 1 == 1 {
                stateSwitches[j] = 1
            }
        }
        
        var flag = true
        var cnt = 0
        while cnt < M && flag {
            var switchCount = 0
            for j in 0..<N {
                if pair[cnt][j] == 1 && stateSwitches[j] == 1 {
                    switchCount += 1
                }
            }
            if switchCount % 2 != p[cnt] {
                flag = false
            }
            cnt += 1
        }
        if flag {
            ans += 1
        }
    }
    print(ans)
}
main()


Measured memory_bytes: 13588