





import math


class 					__magic_name__  :





     """simple docstring"""



     def __init__(							self       :List[Any]			,      snake_case       :Tuple  ):





        '''simple docstring'''




        A_					:				Tuple          =			len(snake_case  )
        A_					:				List[Any]          =			[0] * (
            4 * self.N
        )  # approximate the overall size of segment tree with array N
        self.build(1			,      0			,      self.N - 1  )



     def 						SCREAMING_SNAKE_CASE		(							self       :Union[str, Any]			,      snake_case       :str  ):





        '''simple docstring'''




        return idx * 2



     def 						SCREAMING_SNAKE_CASE		(							self       :Any			,      snake_case       :Tuple  ):





        '''simple docstring'''




        return idx * 2 + 1



     def 						SCREAMING_SNAKE_CASE		(							self       :str			,      snake_case       :str			,      snake_case       :Dict			,      snake_case       :List[str]  ):  # noqa: E741





        '''simple docstring'''




        if l == r:
           A_					:				List[str]          =			A[l]
        else:
           A_					:				str          =			(l + r) // 2
           self.build(self.left(snake_case  )			,      snake_case			,      snake_case  )
           self.build(self.right(snake_case  )			,      mid + 1			,      snake_case  )
           A_					:				List[str]          =			max(self.st[self.left(snake_case  )]			,      self.st[self.right(snake_case  )]  )



     def 						SCREAMING_SNAKE_CASE		(							self       :List[Any]			,      snake_case       :Dict			,      snake_case       :Tuple			,      snake_case       :Optional[Any]  ):





        '''simple docstring'''




        return self.update_recursive(1			,      0			,      self.N - 1			,      a - 1			,      b - 1			,      snake_case  )



     def 						SCREAMING_SNAKE_CASE		(							self       :Optional[int]			,      snake_case       :List[Any]			,      snake_case       :Dict			,      snake_case       :Dict			,      snake_case       :Tuple			,      snake_case       :Any			,      snake_case       :Any  ):  # noqa: E741





        '''simple docstring'''




        if r < a or l > b:
           return True
        if l == r:
           A_					:				Tuple          =			val
           return True
        A_					:				Dict          =			(l + r) // 2
        self.update_recursive(self.left(snake_case  )			,      snake_case			,      snake_case			,      snake_case			,      snake_case			,      snake_case  )
        self.update_recursive(self.right(snake_case  )			,      mid + 1			,      snake_case			,      snake_case			,      snake_case			,      snake_case  )
        A_					:				Optional[int]          =			max(self.st[self.left(snake_case  )]			,      self.st[self.right(snake_case  )]  )
        return True



     def 						SCREAMING_SNAKE_CASE		(							self       :Any			,      snake_case       :int			,      snake_case       :Optional[Any]  ):





        '''simple docstring'''




        return self.query_recursive(1			,      0			,      self.N - 1			,      a - 1			,      b - 1  )



     def 						SCREAMING_SNAKE_CASE		(							self       :int			,      snake_case       :Dict			,      snake_case       :Any			,      snake_case       :Tuple			,      snake_case       :List[Any]			,      snake_case       :Optional[int]  ):  # noqa: E741





        '''simple docstring'''




        if r < a or l > b:
           return -math.inf
        if l >= a and r <= b:
           return self.st[idx]
        A_					:				Any          =			(l + r) // 2
        A_					:				List[Any]          =			self.query_recursive(self.left(snake_case  )			,      snake_case			,      snake_case			,      snake_case			,      snake_case  )
        A_					:				Optional[int]          =			self.query_recursive(self.right(snake_case  )			,      mid + 1			,      snake_case			,      snake_case			,      snake_case  )
        return max(snake_case			,      snake_case  )





     def 						SCREAMING_SNAKE_CASE		(							self       :int  ):





        '''simple docstring'''




        A_					:				Union[str, Any]          =			[]
        for i in range(1			,      N + 1  ):
           show_list += [self.query(snake_case			,      snake_case  )]
        print(snake_case  )


if __name__ == "__main__":
 _lowerCAmelCase							:      Union[str, Any]						=	[1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
 _lowerCAmelCase							:      List[Any]						=	15
 _lowerCAmelCase							:      Union[str, Any]						=	SegmentTree(A)
 print(segt.query(4, 6))
 print(segt.query(7, 11))
 print(segt.query(7, 12))
 segt.update(1, 3, 111)
 print(segt.query(1, 15))
 segt.update(7, 8, 235)
 segt.show_data()







import torch
from torch import autograd


class 					__magic_name__  (							autograd.Function							):





     """simple docstring"""



     @staticmethod
     def 						SCREAMING_SNAKE_CASE		(							snake_case       :Any			,      snake_case       :torch.tensor			,      snake_case       :float			,      snake_case       :bool  ):





        '''simple docstring'''




        A_					:				int          =			inputs.numel()
        A_					:				str          =			int(0.005 * nb_elems  ) + 1
        if sigmoid:
           A_					:				List[Any]          =			(torch.sigmoid(snake_case  ) > threshold).type(inputs.type()  )
        else:
           A_					:				Optional[Any]          =			(inputs > threshold).type(inputs.type()  )
        if mask.sum() < nb_min:
           # We limit the pruning so that at least 0.5% (half a percent) of the weights are remaining
           A_					:				Tuple          =			inputs.flatten().kthvalue(max(nb_elems - nb_min			,      1  )  ).values
           A_					:				Optional[int]          =			(inputs > k_threshold).type(inputs.type()  )
        return mask





     @staticmethod
     def 						SCREAMING_SNAKE_CASE		(							snake_case       :Optional[int]			,      snake_case       :int  ):





        '''simple docstring'''




        return gradOutput, None, None




class 					__magic_name__  (							autograd.Function							):





     """simple docstring"""



     @staticmethod
     def 						SCREAMING_SNAKE_CASE		(							snake_case       :Tuple			,      snake_case       :torch.tensor			,      snake_case       :float  ):





        '''simple docstring'''




        A_					:				Tuple          =			inputs.clone()
        A_      ,						A_					:				Optional[int]          =			inputs.flatten().sort(descending=snake_case  )
        A_					:				Dict          =			int(threshold * inputs.numel()  )

        # flat_out and mask access the same memory.
        A_					:				str          =			mask.flatten()
        A_					:				List[Any]          =			0
        A_					:				List[str]          =			1
        return mask





     @staticmethod
     def 						SCREAMING_SNAKE_CASE		(							snake_case       :List[Any]			,      snake_case       :Optional[Any]  ):





        '''simple docstring'''




        return gradOutput, None




class 					__magic_name__  (							lowerCamelCase__							):





     """simple docstring"""



     @staticmethod
     def 						SCREAMING_SNAKE_CASE		(							snake_case       :torch.tensor			,      snake_case       :float  ):





        '''simple docstring'''




        A_					:				str          =			inputs.clone()
        A_      ,						A_					:				Optional[int]          =			inputs.abs().flatten().sort(descending=snake_case  )
        A_					:				int          =			int(threshold * inputs.numel()  )

        # flat_out and mask access the same memory.
        A_					:				List[str]          =			mask.flatten()
        A_					:				List[str]          =			0
        A_					:				Union[str, Any]          =			1
        return mask
