

import math




def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       )->		bool:



    """simple docstring"""






    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
        return False

    # All primes number are in format of 6k +/- 1
    for i in range(5       ,		int(math.sqrt(SCREAMING_SNAKE_CASE_       ) + 1       )       ,		6       ):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True




def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_ = 6_0_0_8_5_1_4_7_5_1_4_3       )->		int:



    """simple docstring"""






    try:
        UpperCamelCase_          =		int(SCREAMING_SNAKE_CASE_       )
    except (TypeError, ValueError):
        raise TypeError("Parameter n must be int or castable to int."       )
    if n <= 0:
        raise ValueError("Parameter n must be greater than or equal to one."       )
    UpperCamelCase_          =		0
    if is_prime(SCREAMING_SNAKE_CASE_       ):
        return n
    while n % 2 == 0:
        n //= 2
    if is_prime(SCREAMING_SNAKE_CASE_       ):
        return n
    for i in range(3       ,		int(math.sqrt(SCREAMING_SNAKE_CASE_       )       ) + 1       ,		2       ):
        if n % i == 0:
            if is_prime(n // i       ):
                UpperCamelCase_          =		n // i
                break
            elif is_prime(SCREAMING_SNAKE_CASE_       ):
                UpperCamelCase_          =		i
    return max_number


if __name__ == "__main__":
 print(F'''{solution() = }''')



from functools import partial
from typing import Any, Callable, Dict, List, Type, TypeVar, Union, overload

import torch
import torch.nn as nn
import torch.types




def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )->		torch.Tensor:



    """simple docstring"""






    if not inplace:
        UpperCamelCase_          =		ma + ma
    else:
        ma += ma

    return ma




def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )->		torch.Tensor:



    """simple docstring"""






    UpperCamelCase_          =		-1 * len(SCREAMING_SNAKE_CASE_       )
    UpperCamelCase_          =		list(range(len(tensor.shape[:zero_index]       )       )       )
    return tensor.permute(first_inds + [zero_index + i for i in inds]       )




def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )->		torch.Tensor:



    """simple docstring"""






    return t.reshape(t.shape[:-no_dims] + (-1,)       )




def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_ = 1E-4       )->		torch.Tensor:



    """simple docstring"""






    UpperCamelCase_          =		mask.expand(*value.shape       )
    return torch.sum(mask * value       ,		dim=SCREAMING_SNAKE_CASE_       ) / (eps + torch.sum(SCREAMING_SNAKE_CASE_       ,		dim=SCREAMING_SNAKE_CASE_       ))




def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_ = 2.3125       ,		SCREAMING_SNAKE_CASE_ = 21.6875       ,		SCREAMING_SNAKE_CASE_ = 6_4       )->		torch.Tensor:



    """simple docstring"""






    UpperCamelCase_          =		torch.linspace(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		no_bins - 1       ,		device=pts.device       )
    UpperCamelCase_          =		torch.sqrt(torch.sum((pts.unsqueeze(-2       ) - pts.unsqueeze(-3       )) ** 2       ,		dim=-1       )       )
    return torch.bucketize(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )




def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )->		dict:



    """simple docstring"""






    UpperCamelCase_          =		dicts[0]
    UpperCamelCase_          =		{}
    for k, v in first.items():
        UpperCamelCase_          =		[d[k] for d in dicts]
        if isinstance(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ):
            UpperCamelCase_          =		dict_multimap(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )
        else:
            UpperCamelCase_          =		fn(SCREAMING_SNAKE_CASE_       )

    return new_dict




def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )->		torch.Tensor:



    """simple docstring"""






    UpperCamelCase_          =		v_bins.view(((1,) * len(x.shape       )) + (len(SCREAMING_SNAKE_CASE_       ),)       )
    UpperCamelCase_          =		x[..., None] - reshaped_bins
    UpperCamelCase_          =		torch.argmin(torch.abs(SCREAMING_SNAKE_CASE_       )       ,		dim=-1       )
    return nn.functional.one_hot(SCREAMING_SNAKE_CASE_       ,		num_classes=len(SCREAMING_SNAKE_CASE_       )       ).float()




def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_ = 0       ,		SCREAMING_SNAKE_CASE_ = 0       )->		torch.Tensor:



    """simple docstring"""






    UpperCamelCase_          =		[]
    for i, s in enumerate(data.shape[:no_batch_dims]       ):
        UpperCamelCase_          =		torch.arange(SCREAMING_SNAKE_CASE_       )
        UpperCamelCase_          =		r.view(*(*((1,) * i), -1, *((1,) * (len(inds.shape       ) - i - 1)))       )
        ranges.append(SCREAMING_SNAKE_CASE_       )

    UpperCamelCase_          =		[slice(SCREAMING_SNAKE_CASE_       ) for _ in range(len(data.shape       ) - no_batch_dims       )]
    UpperCamelCase_          =		inds
    ranges.extend(SCREAMING_SNAKE_CASE_       )
    # Matt note: Editing this to get around the behaviour of using a list as an array index changing
    # in recent Numpy versions
    return data[tuple(SCREAMING_SNAKE_CASE_       )]


SCREAMING_SNAKE_CASE						:Dict      =			TypeVar("""T""")




def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )->		Dict[Any, Union[dict, list, tuple, Any]]:



    """simple docstring"""






    UpperCamelCase_          =		{}
    for k, v in dic.items():
        if isinstance(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ):
            UpperCamelCase_          =		dict_map(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )
        else:
            UpperCamelCase_          =		tree_map(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )

    return new_dict




@overload
def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )->		Any:



    """simple docstring"""






    ...




@overload
def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )->		dict:



    """simple docstring"""






    ...




@overload
def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )->		list:



    """simple docstring"""






    ...




@overload
def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )->		tuple:



    """simple docstring"""






    ...




def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )->		Optional[int]:



    """simple docstring"""






    if isinstance(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ):
        return dict_map(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )
    elif isinstance(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ):
        return [tree_map(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ) for x in tree]
    elif isinstance(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ):
        return tuple(tree_map(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ) for x in tree       )
    elif isinstance(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ):
        return fn(SCREAMING_SNAKE_CASE_       )
    else:
        print(type(SCREAMING_SNAKE_CASE_       )       )
        raise ValueError("Not supported"       )
SCREAMING_SNAKE_CASE						:Dict      =			partial(tree_map, leaf_type=torch.Tensor)
