swithCount, lightCount = map(int, input().split())
swithList = [0] * lightCount

for i in range(swithCount):
    connectedLightList = list(map(int, input().split()))
    for lightIndex in connectedLightList[1:]:
        lightIndex -= 1
        swithList[i] = swithList[i] | 1 << lightIndex

expectedLightStatusList = list(map(int, input().split()))
expectedLightStatus = 0

for i, eachStatus in enumerate(expectedLightStatusList):
    expectedLightStatus = expectedLightStatus | eachStatus << i

resultCount = 0
for eachSwitchSet in range(1 << swithCount):
    actuallyLightStatus = 0
    for switchIndex in range(swithCount):
        if eachSwitchSet >> switchIndex & 1:
            actuallyLightStatus = actuallyLightStatus ^ swithList[switchIndex]

    if expectedLightStatus == actuallyLightStatus:
        resultCount += 1

print(resultCount)
