
from collections import defaultdict







class 					lowerCamelCase		:





     def __init__(self				:   Tuple    ,   _A				:   Optional[int]    ,   _A				:   List[str]       )						->						Union[str, Any]:
         snake_case								= total  # total no of tasks (N)

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

         snake_case								= 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
         snake_case								= (1 << len(_A       )) - 1





     def 		UpperCAmelCase(self				:   str    ,   _A				:   Optional[Any]    ,   _A				:   List[Any]       )						->						str:
         # 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
         snake_case								= 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.
         snake_case								= total_ways_util

         return self.dp[mask][task_no]





     def 		UpperCAmelCase(self				:   Any    ,   _A				:   Dict       )						->						Optional[Any]:
         # 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__":
   _A   =			5  # total no of tasks (the value of N)

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



from __future__ import annotations

from decimal import Decimal

from numpy import array



def 						lowercase_      (       A__		)							->							list[list[float]]:
    """simple docstring"""

    snake_case								= Decimal

    # Check if the provided matrix has 2 rows and 2 columns
    # since this implementation only works for 2x2 matrices
    if len(A__		) == 2 and len(matrix[0]		) == 2 and len(matrix[1]		) == 2:
        # Calculate the determinant of the matrix
        snake_case								= float(
            d(matrix[0][0]		) * d(matrix[1][1]		) - d(matrix[1][0]		) * d(matrix[0][1]		)		)
        if determinant == 0:
            raise ValueError("This matrix has no inverse."		)

        # Creates a copy of the matrix with swapped positions of the elements
        snake_case								= [[0.0, 0.0], [0.0, 0.0]]
        snake_case					,							snake_case								= matrix[1][1], matrix[0][0]
        snake_case					,							snake_case								= -matrix[1][0], -matrix[0][1]

        # Calculate the inverse of the matrix
        return [
            [(float(d(A__		)		) / determinant) or 0.0 for n in row] for row in swapped_matrix
        ]
    elif (
        len(A__		) == 3
        and len(matrix[0]		) == 3
        and len(matrix[1]		) == 3
        and len(matrix[2]		) == 3
    ):
        # Calculate the determinant of the matrix using Sarrus rule
        snake_case								= float(
            (
                (d(matrix[0][0]		) * d(matrix[1][1]		) * d(matrix[2][2]		))
                + (d(matrix[0][1]		) * d(matrix[1][2]		) * d(matrix[2][0]		))
                + (d(matrix[0][2]		) * d(matrix[1][0]		) * d(matrix[2][1]		))
            )
            - (
                (d(matrix[0][2]		) * d(matrix[1][1]		) * d(matrix[2][0]		))
                + (d(matrix[0][1]		) * d(matrix[1][0]		) * d(matrix[2][2]		))
                + (d(matrix[0][0]		) * d(matrix[1][2]		) * d(matrix[2][1]		))
            )		)
        if determinant == 0:
            raise ValueError("This matrix has no inverse."		)

        # Creating cofactor matrix
        snake_case								= [
            [d(0.0		), d(0.0		), d(0.0		)],
            [d(0.0		), d(0.0		), d(0.0		)],
            [d(0.0		), d(0.0		), d(0.0		)],
        ]
        snake_case								= (d(matrix[1][1]		) * d(matrix[2][2]		)) - (
            d(matrix[1][2]		) * d(matrix[2][1]		)
        )
        snake_case								= -(
            (d(matrix[1][0]		) * d(matrix[2][2]		)) - (d(matrix[1][2]		) * d(matrix[2][0]		))
        )
        snake_case								= (d(matrix[1][0]		) * d(matrix[2][1]		)) - (
            d(matrix[1][1]		) * d(matrix[2][0]		)
        )
        snake_case								= -(
            (d(matrix[0][1]		) * d(matrix[2][2]		)) - (d(matrix[0][2]		) * d(matrix[2][1]		))
        )
        snake_case								= (d(matrix[0][0]		) * d(matrix[2][2]		)) - (
            d(matrix[0][2]		) * d(matrix[2][0]		)
        )
        snake_case								= -(
            (d(matrix[0][0]		) * d(matrix[2][1]		)) - (d(matrix[0][1]		) * d(matrix[2][0]		))
        )
        snake_case								= (d(matrix[0][1]		) * d(matrix[1][2]		)) - (
            d(matrix[0][2]		) * d(matrix[1][1]		)
        )
        snake_case								= -(
            (d(matrix[0][0]		) * d(matrix[1][2]		)) - (d(matrix[0][2]		) * d(matrix[1][0]		))
        )
        snake_case								= (d(matrix[0][0]		) * d(matrix[1][1]		)) - (
            d(matrix[0][1]		) * d(matrix[1][0]		)
        )

        # Transpose the cofactor matrix (Adjoint matrix)
        snake_case								= array(A__		)
        for i in range(3		):
            for j in range(3		):
                snake_case								= cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
        snake_case								= array(A__		)
        for i in range(3		):
            for j in range(3		):
                inverse_matrix[i][j] /= d(A__		)

        # Calculate the inverse of the matrix
        return [[float(d(A__		)		) or 0.0 for n in row] for row in inverse_matrix]
    raise ValueError("Please provide a matrix of size 2x2 or 3x3."		)

