

'''simple docstring'''

from __future__ import annotations

def      __magic_name__							(			A				)      ->		list[int]:
	if not list_of_ints:
		return []

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

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

def      __magic_name__							(			A       , A				)      ->		list[int]:
	if bit_position == 0 or len(A				) 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(A				)
		else:
			# number has a zero at bit bit_position
			zeros.append(A				)

    # recursively split both lists further
	snake_case							=					_msd_radix_sort(A       , bit_position - 1				)
	snake_case							=					_msd_radix_sort(A       , bit_position - 1				)

	# recombine lists
	snake_case							=					zeros
	res.extend(A				)

	return res

def      __magic_name__							(			A				)      ->		Any:
	snake_case							=					len(A				)
	if not list_of_ints or length == 1:
		return

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

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

def      __magic_name__							(			A       , A       , A       , A				)      ->		Any:
	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(A       , A       , A       , A				)
	_msd_radix_sort_inplace(A       , A       , A       , A				)


if __name__ == "__main__":
						import doctest

						doctest.testmod()













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   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      torch.Tensor:
 # 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:
  lowerCamelCase_							:    Tuple							=     ma + ma
 else:
  ma += ma

 return ma




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__				)  ->      torch.Tensor:
 lowerCamelCase_							:    Union[str, Any]							=     -1 * len(lowerCamelCase__				)
 lowerCamelCase_							:    Optional[Any]							=     list(range(len(tensor.shape[:zero_index]				)				)				)
 return tensor.permute(first_inds + [zero_index + i for i in inds]				)




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__				)  ->      torch.Tensor:
 return t.reshape(t.shape[:-no_dims] + (-1,)				)




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__ = 1e-4				)  ->      torch.Tensor:
 lowerCamelCase_							:    Optional[int]							=     mask.expand(*value.shape				)
 return torch.sum(mask * value ,			dim=lowerCamelCase__				) / (eps + torch.sum(lowerCamelCase__ ,			dim=lowerCamelCase__				))




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ = 2.3125 ,			lowerCamelCase__ = 21.6875 ,			lowerCamelCase__ = 64				)  ->      torch.Tensor:
 lowerCamelCase_							:    int							=     torch.linspace(lowerCamelCase__ ,			lowerCamelCase__ ,			no_bins - 1 ,			device=pts.device				)
 lowerCamelCase_							:    Tuple							=     torch.sqrt(torch.sum((pts.unsqueeze(-2				) - pts.unsqueeze(-3				)) ** 2 ,			dim=-1				)				)
 return torch.bucketize(lowerCamelCase__ ,			lowerCamelCase__				)




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__				)  ->      dict:
 lowerCamelCase_							:    Optional[Any]							=     dicts[0]
 lowerCamelCase_							:    Optional[Any]							=     {}
 for k, v in first.items():
  lowerCamelCase_							:    Tuple							=     [d[k] for d in dicts]
  if isinstance(lowerCamelCase__ ,			lowerCamelCase__				):
   lowerCamelCase_							:    Optional[int]							=     dict_multimap(lowerCamelCase__ ,			lowerCamelCase__				)
  else:
   lowerCamelCase_							:    List[Any]							=     fn(lowerCamelCase__				)

 return new_dict




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__				)  ->      torch.Tensor:
 lowerCamelCase_							:    str							=     v_bins.view(((1,) * len(x.shape				)) + (len(lowerCamelCase__				),)				)
 lowerCamelCase_							:    List[Any]							=     x[..., None] - reshaped_bins
 lowerCamelCase_							:    List[Any]							=     torch.argmin(torch.abs(lowerCamelCase__				) ,			dim=-1				)
 return nn.functional.one_hot(lowerCamelCase__ ,			num_classes=len(lowerCamelCase__				)				).float()




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__ = 0 ,			lowerCamelCase__ = 0				)  ->      torch.Tensor:
 lowerCamelCase_							:    List[Union[slice, torch.Tensor]]							=     []
 for i, s in enumerate(data.shape[:no_batch_dims]				):
  lowerCamelCase_							:    int							=     torch.arange(lowerCamelCase__				)
  lowerCamelCase_							:    Any							=     r.view(*(*((1,) * i), -1, *((1,) * (len(inds.shape				) - i - 1)))				)
  ranges.append(lowerCamelCase__				)

 lowerCamelCase_							:    List[Union[slice, torch.Tensor]]							=     [slice(lowerCamelCase__				) for _ in range(len(data.shape				) - no_batch_dims				)]
 lowerCamelCase_							:    Optional[int]							=     inds
 ranges.extend(lowerCamelCase__				)
 # 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(lowerCamelCase__				)]


UpperCamelCase											=      TypeVar('''T''')




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      Dict[Any, Union[dict, list, tuple, Any]]:
 lowerCamelCase_							:    Dict[Any, Union[dict, list, tuple, Any]]							=     {}
 for k, v in dic.items():
  if isinstance(lowerCamelCase__ ,			lowerCamelCase__				):
   lowerCamelCase_							:    Optional[Any]							=     dict_map(lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)
  else:
   lowerCamelCase_							:    Dict							=     tree_map(lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)

 return new_dict




@overload
def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      Any:
 ...




@overload
def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      dict:
 ...




@overload
def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      list:
 ...




@overload
def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      tuple:
 ...




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      Any:
 if isinstance(lowerCamelCase__ ,			lowerCamelCase__				):
  return dict_map(lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)
 elif isinstance(lowerCamelCase__ ,			lowerCamelCase__				):
  return [tree_map(lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				) for x in tree]
 elif isinstance(lowerCamelCase__ ,			lowerCamelCase__				):
  return tuple(tree_map(lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				) for x in tree				)
 elif isinstance(lowerCamelCase__ ,			lowerCamelCase__				):
  return fn(lowerCamelCase__				)
 else:
  print(type(lowerCamelCase__				)				)
  raise ValueError('Not supported'				)





UpperCamelCase											=      partial(tree_map, leaf_type=torch.Tensor)
