
# We ignore warnings about stepping the scheduler since we step it ourselves during gradient accumulation

import warnings

from .state import AcceleratorState, GradientState


warnings.filterwarnings("ignore", category=UserWarning, module="torch.optim.lr_scheduler")







class 					lowerCamelCase		:





     def __init__(self				:   str    ,   _A				:   Optional[Any]    ,   _A				:   List[str]    ,   _A				:   bool = True    ,   _A				:   bool = False       )						->						str:
         snake_case								= scheduler
         snake_case								= optimizers if isinstance(_A    ,   (list, tuple)       ) else [optimizers]
         snake_case								= split_batches
         snake_case								= step_with_optimizer
         snake_case								= GradientState()





     def 		UpperCAmelCase(self				:   List[Any]    ,   *_A				:   int    ,   **_A				:   Union[str, Any]       )						->						int:
         if not self.step_with_optimizer:
             # No link between scheduler and optimizer -> just step
             self.scheduler.step(*_A    ,   **_A       )
             return

         # Otherwise, first make sure the optimizer was stepped.
         if not self.gradient_state.sync_gradients:
             if self.gradient_state.adjust_scheduler:
                 self.scheduler._step_count += 1
             return

         for opt in self.optimizers:
             if opt.step_was_skipped:
                 return
         if self.split_batches:
             # Split batches -> the training dataloader batch size is not changed so one step per training step
             self.scheduler.step(*_A    ,   **_A       )
         else:
             # Otherwise the training dataloader batch size was multiplied by `num_processes`, so we need to do
             # num_processes steps per training step
             snake_case								= AcceleratorState().num_processes
             for _ in range(_A       ):
                 # Special case when using OneCycle and `drop_last` was not used
                 if hasattr(self.scheduler    ,   "total_steps"       ):
                     if self.scheduler._step_count <= self.scheduler.total_steps:
                         self.scheduler.step(*_A    ,   **_A       )
                 else:
                     self.scheduler.step(*_A    ,   **_A       )





     def 		UpperCAmelCase(self				:   List[str]       )						->						str:
         return self.scheduler.get_last_lr()





     def 		UpperCAmelCase(self				:   List[str]       )						->						Union[str, Any]:
         return self.scheduler.state_dict()





     def 		UpperCAmelCase(self				:   str    ,   _A				:   Optional[Any]       )						->						Any:
         self.scheduler.load_state_dict(_A       )





     def 		UpperCAmelCase(self				:   Union[str, Any]       )						->						Tuple:
         return self.scheduler.get_lr()





     def 		UpperCAmelCase(self				:   Tuple    ,   *_A				:   int    ,   **_A				:   Union[str, Any]       )						->						str:
         return self.scheduler.print_lr(*_A    ,   **_A       )



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
       )
   )

