


from __future__ import annotations



def      lowerCAmelCase	(						lowerCAmelCase_	,				lowerCAmelCase_	)->	Optional[Any]:
				lowerCAmelCase_	: Dict      			=			0
				lowerCAmelCase_	: List[Any]      			=			len(lowerCAmelCase_	) - 1
				while left <= right:
								lowerCAmelCase_	: List[str]      			=			(left + right) // 2
								if left == right:
												if sorted_list[middle] < item:
																lowerCAmelCase_	: Optional[int]      			=			middle + 1
												break
								elif sorted_list[middle] < item:
												lowerCAmelCase_	: Tuple      			=			middle + 1
								else:
												lowerCAmelCase_	: List[str]      			=			middle - 1
				sorted_list.insert(lowerCAmelCase_	,				lowerCAmelCase_	)
				return sorted_list



def      lowerCAmelCase	(						lowerCAmelCase_	,				lowerCAmelCase_	)->	Any:
				lowerCAmelCase_	: List[Any]      			=			[]
				while left and right:
								if left[0][0] < right[0][0]:
												result.append(left.pop(0	)	)
								else:
												result.append(right.pop(0	)	)
				return result + left + right



def      lowerCAmelCase	(						lowerCAmelCase_	)->	Union[str, Any]:
				lowerCAmelCase_	: Optional[int]      			=			len(lowerCAmelCase_	)
				if length <= 1:
								return list_ad
				lowerCAmelCase_	: Tuple      			=			length // 2
				return merge(sortlist_ad(list_ad[:middle]	)	,				sortlist_ad(list_ad[middle:]	)	)



def      lowerCAmelCase	(						lowerCAmelCase_	)->	list[int]:

				if len(lowerCAmelCase_	) <= 1:
								return collection
				lowerCAmelCase_	: Optional[int]      			=			[]
				lowerCAmelCase_	: Tuple      			=			False
				for i in range(0	,				len(lowerCAmelCase_	)	,				2	):
								if i == len(lowerCAmelCase_	) - 1:
												lowerCAmelCase_	: Dict      			=			True
								else:
												if collection[i] < collection[i + 1]:
																two_paired_list.append([collection[i], collection[i + 1]]	)
												else:
																two_paired_list.append([collection[i + 1], collection[i]]	)
				lowerCAmelCase_	: int      			=			sortlist_ad(lowerCAmelCase_	)
				lowerCAmelCase_	: List[str]      			=			[i[0] for i in sorted_list_ad]
				result.append(sorted_list_ad[-1][1]	)
				if has_last_odd_item:
								lowerCAmelCase_	: int      			=			collection[-1]
								lowerCAmelCase_	: Union[str, Any]      			=			binary_search_insertion(lowerCAmelCase_	,				lowerCAmelCase_	)
				lowerCAmelCase_	: str      			=			False
				for i in range(len(lowerCAmelCase_	) - 1	):
								if result[i] == collection[-1] and has_last_odd_item:
												lowerCAmelCase_	: Optional[Any]      			=			True
								lowerCAmelCase_	: Optional[int]      			=			sorted_list_ad[i][1]
								# If last_odd_item is inserted before the item's index,
								# you should forward index one more.
								if is_last_odd_item_inserted_before_this_index:
												lowerCAmelCase_	: List[Any]      			=			result[: i + 2] + binary_search_insertion(result[i + 2 :]	,				lowerCAmelCase_	)
								else:
												lowerCAmelCase_	: Union[str, Any]      			=			result[: i + 1] + binary_search_insertion(result[i + 1 :]	,				lowerCAmelCase_	)

				return result


if __name__ == "__main__":
						_UpperCAmelCase     :					Tuple       =input("""Enter numbers separated by a comma:\n""").strip()
						_UpperCAmelCase     :					int       =[int(item) for item in user_input.split(""",""")]
						print(merge_insertion_sort(unsorted))



from typing import List, Optional, Tuple, Union

from . import logging
from .import_utils import is_torch_available, is_torch_version


if is_torch_available():
						import torch

_UpperCAmelCase     :					List[Any]       =logging.get_logger(__name__)  # pylint: disable=invalid-name

try:
						from torch._dynamo import allow_in_graph as maybe_allow_in_graph
except (ImportError, ModuleNotFoundError):



						def      lowerCAmelCase	(						cls	)->	int:
										return cls



def      lowerCAmelCase	(						lowerCAmelCase_	,				lowerCAmelCase_ = None	,				lowerCAmelCase_ = None	,				lowerCAmelCase_ = None	,				lowerCAmelCase_ = None	,				)->	int:
				lowerCAmelCase_	: Tuple      			=			device
				lowerCAmelCase_	: List[str]      			=			shape[0]

				lowerCAmelCase_	: Union[str, Any]      			=			layout or torch.strided
				lowerCAmelCase_	: Union[str, Any]      			=			device or torch.device('''cpu'''	)

				if generator is not None:
								lowerCAmelCase_	: List[str]      			=			generator.device.type if not isinstance(lowerCAmelCase_	,				lowerCAmelCase_	) else generator[0].device.type
								if gen_device_type != device.type and gen_device_type == "cpu":
												lowerCAmelCase_	: Optional[Any]      			=			'''cpu'''
												if device != "mps":
																logger.info(
																    f"""The passed generator was created on 'cpu' even though a tensor on {device} was expected."""
																    f""" Tensors will be created on 'cpu' and then moved to {device}. Note that one can probably"""
																    f""" slighly speed up this function by passing a generator that was created on the {device} device."""	)
								elif gen_device_type != device.type and gen_device_type == "cuda":
												raise ValueError(f"""Cannot generate a {device} tensor from a generator of type {gen_device_type}."""	)

				if isinstance(lowerCAmelCase_	,				lowerCAmelCase_	):
								lowerCAmelCase_	: Dict      			=			(1,) + shape[1:]
								lowerCAmelCase_	: Union[str, Any]      			=			[
								    torch.randn(lowerCAmelCase_	,				generator=generator[i]	,				device=lowerCAmelCase_	,				dtype=lowerCAmelCase_	,				layout=lowerCAmelCase_	)
								    for i in range(lowerCAmelCase_	)
								]
								lowerCAmelCase_	: Tuple      			=			torch.cat(lowerCAmelCase_	,				dim=0	).to(lowerCAmelCase_	)
				else:
								lowerCAmelCase_	: int      			=			torch.randn(lowerCAmelCase_	,				generator=lowerCAmelCase_	,				device=lowerCAmelCase_	,				dtype=lowerCAmelCase_	,				layout=lowerCAmelCase_	).to(lowerCAmelCase_	)

				return latents




def      lowerCAmelCase	(						lowerCAmelCase_	)->	Optional[Any]:
				if is_torch_version('''<'''	,				'''2.0.0'''	) or not hasattr(lowerCAmelCase_	,				'''_dynamo'''	):
								return False
				return isinstance(lowerCAmelCase_	,				torch._dynamo.eval_frame.OptimizedModule	)