


'''simple docstring'''




from __future__ import annotations





def      _a		(lowercase__ :      list[int]	) -> list[int]:






     """simple docstring"""
     if not list_of_ints:
          return []

     if min(lowercase__	) < 0:
          raise ValueError('All numbers must be positive'	)

     __snake_case    			=	max(len(bin(lowercase__	)[2:]	) for x in list_of_ints	)
     return _msd_radix_sort(lowercase__       ,      lowercase__	)





def      _a		(lowercase__ :      list[int]       ,      lowercase__ :      int	) -> list[int]:






     """simple docstring"""
     if bit_position == 0 or len(lowercase__	) in [0, 1]:
          return list_of_ints

     __snake_case    			=	[]
     __snake_case    			=	[]
     # Split numbers based on bit at bit_position from the right
     for number in list_of_ints:
          if (number >> (bit_position - 1)) & 1:
               # number has a one at bit bit_position
               ones.append(lowercase__	)
          else:
               # number has a zero at bit bit_position
               zeros.append(lowercase__	)

    # recursively split both lists further
     __snake_case    			=	_msd_radix_sort(lowercase__       ,      bit_position - 1	)
     __snake_case    			=	_msd_radix_sort(lowercase__       ,      bit_position - 1	)

     # recombine lists
     __snake_case    			=	zeros
     res.extend(lowercase__	)

     return res





def      _a		(lowercase__ :      list[int]	) -> str:






     """simple docstring"""
     __snake_case    			=	len(lowercase__	)
     if not list_of_ints or length == 1:
          return

     if min(lowercase__	) < 0:
          raise ValueError('All numbers must be positive'	)

     __snake_case    			=	max(len(bin(lowercase__	)[2:]	) for x in list_of_ints	)
     _msd_radix_sort_inplace(lowercase__       ,      lowercase__       ,      0       ,      lowercase__	)





def      _a		(lowercase__ :      list[int]       ,      lowercase__ :      int       ,      lowercase__ :      int       ,      lowercase__ :      int	) -> Any:






     """simple docstring"""
     if bit_position == 0 or end_index - begin_index <= 1:
          return

     bit_position -= 1

     __snake_case    			=	begin_index
     __snake_case    			=	end_index - 1
     while i <= j:
          __snake_case    			=	False
          if not (list_of_ints[i] >> bit_position) & 1:
               # found zero at the beginning
               i += 1
               __snake_case    			=	True
          if (list_of_ints[j] >> bit_position) & 1:
               # found one at the end
               j -= 1
               __snake_case    			=	True

          if changed:
               continue

          __snake_case			,					__snake_case    			=	list_of_ints[j], list_of_ints[i]
          j -= 1
          if j != i:
               i += 1

     _msd_radix_sort_inplace(lowercase__       ,      lowercase__       ,      lowercase__       ,      lowercase__	)
     _msd_radix_sort_inplace(lowercase__       ,      lowercase__       ,      lowercase__       ,      lowercase__	)


if __name__ == "__main__":
   import doctest

   doctest.testmod()








'''simple docstring'''




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      _a		(lowercase__ :      torch.Tensor       ,      lowercase__ :      torch.Tensor       ,      lowercase__ :      bool	) -> torch.Tensor:






     """simple docstring"""
     # The first operation in a checkpoint can't be in-place, but it's
     # nice to have in-place addition during inference. Thus...
     if not inplace:
          __snake_case    			=	ma + ma
     else:
          ma += ma

     return ma





def      _a		(lowercase__ :      torch.Tensor       ,      lowercase__ :      List[int]	) -> torch.Tensor:






     """simple docstring"""
     __snake_case    			=	-1 * len(lowercase__	)
     __snake_case    			=	list(range(len(tensor.shape[:zero_index]	)	)	)
     return tensor.permute(first_inds + [zero_index + i for i in inds]	)





def      _a		(lowercase__ :      torch.Tensor       ,      lowercase__ :      int	) -> torch.Tensor:






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





def      _a		(lowercase__ :      torch.Tensor       ,      lowercase__ :      torch.Tensor       ,      lowercase__ :      int       ,      lowercase__ :      float = 1e-4	) -> torch.Tensor:






     """simple docstring"""
     __snake_case    			=	mask.expand(*value.shape	)
     return torch.sum(mask * value       ,      dim=lowercase__	) / (eps + torch.sum(lowercase__       ,      dim=lowercase__	))





def      _a		(lowercase__ :      torch.Tensor       ,      lowercase__ :      torch.types.Number = 2.31_25       ,      lowercase__ :      torch.types.Number = 21.68_75       ,      lowercase__ :      int = 6_4	) -> torch.Tensor:






     """simple docstring"""
     __snake_case    			=	torch.linspace(lowercase__       ,      lowercase__       ,      no_bins - 1       ,      device=pts.device	)
     __snake_case    			=	torch.sqrt(torch.sum((pts.unsqueeze(-2	) - pts.unsqueeze(-3	)) ** 2       ,      dim=-1	)	)
     return torch.bucketize(lowercase__       ,      lowercase__	)





def      _a		(lowercase__ :      Callable[[list], Any]       ,      lowercase__ :      List[dict]	) -> dict:






     """simple docstring"""
     __snake_case    			=	dicts[0]
     __snake_case    			=	{}
     for k, v in first.items():
          __snake_case    			=	[d[k] for d in dicts]
          if isinstance(lowercase__       ,      lowercase__	):
               __snake_case    			=	dict_multimap(lowercase__       ,      lowercase__	)
          else:
               __snake_case    			=	fn(lowercase__	)

     return new_dict





def      _a		(lowercase__ :      torch.Tensor       ,      lowercase__ :      torch.Tensor	) -> torch.Tensor:






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





def      _a		(lowercase__ :      torch.Tensor       ,      lowercase__ :      torch.Tensor       ,      lowercase__ :      int = 0       ,      lowercase__ :      int = 0	) -> torch.Tensor:






     """simple docstring"""
     __snake_case    			=	[]
     for i, s in enumerate(data.shape[:no_batch_dims]	):
          __snake_case    			=	torch.arange(lowercase__	)
          __snake_case    			=	r.view(*(*((1,) * i), -1, *((1,) * (len(inds.shape	) - i - 1)))	)
          ranges.append(lowercase__	)

     __snake_case    			=	[slice(lowercase__	) for _ in range(len(data.shape	) - no_batch_dims	)]
     __snake_case    			=	inds
     ranges.extend(lowercase__	)
     # 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(lowercase__	)]


_a      :      str       				=      TypeVar("T")





def      _a		(lowercase__ :      Callable[[T], Any]       ,      lowercase__ :      Dict[Any, Union[dict, list, tuple, T]]       ,      lowercase__ :      Type[T]	) -> Dict[Any, Union[dict, list, tuple, Any]]:






     """simple docstring"""
     __snake_case    			=	{}
     for k, v in dic.items():
          if isinstance(lowercase__       ,      lowercase__	):
               __snake_case    			=	dict_map(lowercase__       ,      lowercase__       ,      lowercase__	)
          else:
               __snake_case    			=	tree_map(lowercase__       ,      lowercase__       ,      lowercase__	)

     return new_dict





@overload
def      _a		(lowercase__ :      Callable[[T], Any]       ,      lowercase__ :      T       ,      lowercase__ :      Type[T]	) -> Any:






     """simple docstring"""
     ...





@overload
def      _a		(lowercase__ :      Callable[[T], Any]       ,      lowercase__ :      dict       ,      lowercase__ :      Type[T]	) -> dict:






     """simple docstring"""
     ...





@overload
def      _a		(lowercase__ :      Callable[[T], Any]       ,      lowercase__ :      list       ,      lowercase__ :      Type[T]	) -> list:






     """simple docstring"""
     ...





@overload
def      _a		(lowercase__ :      Callable[[T], Any]       ,      lowercase__ :      tuple       ,      lowercase__ :      Type[T]	) -> tuple:






     """simple docstring"""
     ...





def      _a		(lowercase__ :      str       ,      lowercase__ :      Any       ,      lowercase__ :      Dict	) -> Union[str, Any]:






     """simple docstring"""
     if isinstance(lowercase__       ,      lowercase__	):
          return dict_map(lowercase__       ,      lowercase__       ,      lowercase__	)
     elif isinstance(lowercase__       ,      lowercase__	):
          return [tree_map(lowercase__       ,      lowercase__       ,      lowercase__	) for x in tree]
     elif isinstance(lowercase__       ,      lowercase__	):
          return tuple(tree_map(lowercase__       ,      lowercase__       ,      lowercase__	) for x in tree	)
     elif isinstance(lowercase__       ,      lowercase__	):
          return fn(lowercase__	)
     else:
          print(type(lowercase__	)	)
          raise ValueError('Not supported'	)


_a      :      Union[str, Any]       				=      partial(tree_map, leaf_type=torch.Tensor)




