output_description: Print the number of combinations of "on" and "off" states of the switches that
  light all the bulbs.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N M
      k_1 s_{11} s_{12} ... s_{1k_1}
      :
      k_M s_{M1} s_{M2} ... s_{Mk_M}
      p_1 p_2 ... p_M
attempt: list = input().split(" ")
  n = int(list[0])
  m = int(list[1])
  
  denkyu = []
  
  for i in range(m):
      info = input().split(" ")
      for j in range(len(info)):
          info[j] = int(info[j])
      list = []
      for i in range(n):
          list.append(0)
  
      # print(info)
      for j in range(len(info) - 1):
          list[info[j + 1] - 1] = 1
      denkyu.append(list)
  
  # print(denkyu)
  
  shogo = []
  
  for x in range(2**n):
      shinsu = []
      for y in range(n):
          if x % 2 == 1:
              shinsu.append(1)
              x = int((x - 1) / 2)
          else:
              shinsu.append(0)
              x = int((x) / 2)
      shogo.append(shinsu)
  
  # print(shogo)
  
  plist = input().split(" ")
  for j in range(len(plist)):
      plist[j] = int(plist[j])
  
  # print(plist)
  
  # print("")
  kosu = 0
  for s in shogo:
      switch = 1
      now = 0
      complete = 0
      while switch == 1:
          match = 0
          for i in range(n):
              if s[i] == denkyu[now][i] and s[i] == 1:
                  # print("X", s[i], denkyu[now][i], s, denkyu[now])
                  match += 1
          if match % 2 == plist[now]:
              now += 1
          else:
              switch = 0
          if now == (m):
              if switch == 1:
                  complete = 1
                  switch = 0
                  # print(s)
      if complete == 1:
          kosu += 1
          # print("y", s)
  print(kosu)
  
problem_description: Statement
  
  We have N switches with "on" and "off" state, and M bulbs. The switches are
  numbered 1 to N, and the bulbs are numbered 1 to M.
  
  Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}.
  It is lighted when the number of switches that are "on" among these switches
  is congruent to p_i modulo 2.
  
  How many combinations of "on" and "off" states of the switches light all the
  bulbs?
samples: [{"input": "2 2\n    2 1 2\n    1 2\n    0 1", "output": "1\n    \n\n  * Bulb 1 is lighted when there is an even number of switches that are \"on\" among the following: Switch 1 and 2.\n  * Bulb 2 is lighted when there is an odd number of switches that are \"on\" among the following: Switch 2.\n\nThere are four possible combinations of states of (Switch 1, Switch 2): (on,\non), (on, off), (off, on) and (off, off). Among them, only (on, on) lights all\nthe bulbs, so we should print 1.\n\n* * *"}, {"input": "2 3\n    2 1 2\n    1 1\n    1 2\n    0 0 1", "output": "0\n    \n\n  * Bulb 1 is lighted when there is an even number of switches that are \"on\" among the following: Switch 1 and 2.\n  * Bulb 2 is lighted when there is an even number of switches that are \"on\" among the following: Switch 1.\n  * Bulb 3 is lighted when there is an odd number of switches that are \"on\" among the following: Switch 2.\n\nSwitch 1 has to be \"off\" to light Bulb 2 and Switch 2 has to be \"on\" to light\nBulb 3, but then Bulb 1 will not be lighted. Thus, there are no combinations\nof states of the switches that light all the bulbs, so we should print 0.\n\n* * *"}, {"input": "5 2\n    3 1 2 5\n    2 2 3\n    1 0", "output": "8"}]