





"""simple docstring"""






from collections import defaultdict



class 	lowerCAmelCase					:






       def __init__(   self    ,  a__    ,  a__     ):
              _UpperCAmelCase     =     total  # total no of tasks (N)

              # DP table will have a dimension of (2^M)*N
              # initially all values are set to -1
              _UpperCAmelCase     =     [
                  [-1 for i in range(total + 1     )] for j in range(2 ** len(a__     )     )
              ]

              _UpperCAmelCase     =     defaultdict(a__     )  # stores the list of persons for each task

              # final_mask is used to check if all persons are included by setting all bits
              # to 1
              _UpperCAmelCase     =     (1 << len(a__     )) - 1






       def 							__A (   self    ,  a__    ,  a__     ):
              # if mask == self.finalmask all persons are distributed tasks, return 1
              if mask == self.final_mask:
                     return 1

              # if not everyone gets the task and no more tasks are available, return 0
              if task_no > self.total_tasks:
                     return 0

              # if case already considered
              if self.dp[mask][task_no] != -1:
                     return self.dp[mask][task_no]

              # Number of ways when we don't this task in the arrangement
              _UpperCAmelCase     =     self.count_ways_until(a__    ,  task_no + 1     )

              # now assign the tasks one by one to all possible persons and recursively
              # assign for the remaining tasks.
              if task_no in self.task:
                     for p in self.task[task_no]:
                            # if p is already given a task
                            if mask & (1 << p):
                                   continue

                            # assign this task to p and change the mask value. And recursively
                            # assign tasks with the new mask value.
                            total_ways_util += self.count_ways_until(mask | (1 << p)    ,  task_no + 1     )

        # save the value.
              _UpperCAmelCase     =     total_ways_util

              return self.dp[mask][task_no]






       def 							__A (   self    ,  a__     ):
              # Store the list of persons for each task
              for i in range(len(a__     )     ):
                     for j in task_performed[i]:
                            self.task[j].append(a__     )

        # call the function to fill the DP table, final answer is stored in dp[0][1]
              return self.count_ways_until(0    ,  1     )


if __name__ == "__main__":
    lowerCAmelCase_			=							5  # total no of tasks (the value of N)

    # the list of tasks that can be done by M persons.
    lowerCAmelCase_			=							[[1, 3, 4], [1, 2, 5], [3, 4]]
    print(
        AssignmentUsingBitmask(task_performed, total_tasks).count_no_of_ways(
            task_performed
        )
    )









"""simple docstring"""






def       __lowerCamelCase    (       SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE							)		->       str:






       """simple docstring"""




       if a < 0 or b < 0:
              raise ValueError('the value of both inputs must be positive'							)

       _UpperCAmelCase     =     str(bin(SCREAMING_SNAKE_CASE							)							)[2:]  # remove the leading "0b"
       _UpperCAmelCase     =     str(bin(SCREAMING_SNAKE_CASE							)							)[2:]  # remove the leading "0b"

       _UpperCAmelCase     =     max(len(SCREAMING_SNAKE_CASE							),len(SCREAMING_SNAKE_CASE							)							)

       return "0b" + "".join(
           str(int(char_a == '1' and char_b == '1'							)							)
           for char_a, char_b in zip(a_binary.zfill(SCREAMING_SNAKE_CASE							),b_binary.zfill(SCREAMING_SNAKE_CASE							)							)							)


if __name__ == "__main__":
    import doctest

    doctest.testmod()






