


import logging
import math
from functools import partial
from typing import Any, Callable, Dict, Iterable, List, Optional, Sequence, Tuple, Union

import torch

from .tensor_utils import tensor_tree_map, tree_map

def    lowercase_	(	_A    :					Union[dict, list, tuple, torch.Tensor]		):

						"""simple docstring"""




						lowerCamelCase__	:       Optional[Any]					=						[]
						if isinstance(lowerCamelCase_					,      lowerCamelCase_		):
												for v in tree.values():
																		shapes.extend(_fetch_dims(lowerCamelCase_		)		)
						elif isinstance(lowerCamelCase_					,      (list, tuple)		):
												for t in tree:
																		shapes.extend(_fetch_dims(lowerCamelCase_		)		)
						elif isinstance(lowerCamelCase_					,      torch.Tensor		):
												shapes.append(tree.shape		)
						else:
												raise ValueError("Not supported"		)

						return shapes

@torch.jit.ignore
def    lowercase_	(	_A    :					int					,      _A    :					Tuple[int, ...]		):

						"""simple docstring"""




						lowerCamelCase__	:       Dict					=						[]
						for d in reversed(lowerCamelCase_		):
												idx.append(flat_idx % d		)
												lowerCamelCase__	:       Optional[int]					=						flat_idx // d

						return tuple(reversed(lowerCamelCase_		)		)

@torch.jit.ignore
def    lowercase_	(	_A    :					Sequence[int]					,      _A    :					Sequence[int]					,      _A    :					Sequence[int]					,      _A    :					Optional[Sequence[bool]] = None					,      _A    :					Optional[Sequence[bool]] = None					,      ):

						"""simple docstring"""




						def reduce_edge_list(_A    :					List[bool]		) -> None:
												lowerCamelCase__	:       Union[str, Any]					=						True
												for i in range(len(lowerCamelCase_		)		):
																		lowerCamelCase__	:       str					=						-1 * (i + 1)
																		l[reversed_idx] &= tally
																		lowerCamelCase__	:       List[str]					=						l[reversed_idx]

						if start_edges is None:
												lowerCamelCase__	:       int					=						[s == 0 for s in start]
												reduce_edge_list(lowerCamelCase_		)
						if end_edges is None:
												lowerCamelCase__	:       Optional[int]					=						[e == (d - 1) for e, d in zip(lowerCamelCase_					,      lowerCamelCase_		)]
												reduce_edge_list(lowerCamelCase_		)

						# Base cases. Either start/end are empty and we're done, or the final,
						# one-dimensional tensor can be simply sliced
						if len(lowerCamelCase_		) == 0:
												return [()]
						elif len(lowerCamelCase_		) == 1:
												return [(slice(start[0]					,      end[0] + 1		),)]

						lowerCamelCase__	:       List[str]					=						[]
						lowerCamelCase__	:       int					=						[]

						# Dimensions common to start and end can be selected directly
						for s, e in zip(lowerCamelCase_					,      lowerCamelCase_		):
												if s == e:
																		path_list.append(slice(lowerCamelCase_					,      s + 1		)		)
												else:
																		break

						lowerCamelCase__	:       Dict					=						tuple(lowerCamelCase_		)
						lowerCamelCase__	:       List[Any]					=						len(lowerCamelCase_		)

						# start == end, and we're done
						if divergence_idx == len(lowerCamelCase_		):
												return [path]

						def upper() -> Tuple[Tuple[slice, ...], ...]:
												assert start_edges is not None
												assert end_edges is not None

												lowerCamelCase__	:       Optional[int]					=						start[divergence_idx]
												return tuple(
												    path + (slice(lowerCamelCase_					,      sdi + 1		),) + s
												    for s in _get_minimal_slice_set(
												        start[divergence_idx + 1 :]					,      [d - 1 for d in dims[divergence_idx + 1 :]]					,      dims[divergence_idx + 1 :]					,      start_edges=start_edges[divergence_idx + 1 :]					,      end_edges=[True for _ in end_edges[divergence_idx + 1 :]]					,      )		)

						def lower() -> Tuple[Tuple[slice, ...], ...]:
												assert start_edges is not None
												assert end_edges is not None

												lowerCamelCase__	:       Dict					=						end[divergence_idx]
												return tuple(
												    path + (slice(lowerCamelCase_					,      edi + 1		),) + s
												    for s in _get_minimal_slice_set(
												        [0 for _ in start[divergence_idx + 1 :]]					,      end[divergence_idx + 1 :]					,      dims[divergence_idx + 1 :]					,      start_edges=[True for _ in start_edges[divergence_idx + 1 :]]					,      end_edges=end_edges[divergence_idx + 1 :]					,      )		)

						# If both start and end are at the edges of the subtree rooted at
						# divergence_idx, we can just select the whole subtree at once
						if start_edges[divergence_idx] and end_edges[divergence_idx]:
												slices.append(path + (slice(start[divergence_idx]					,      end[divergence_idx] + 1		),)		)
						# If just start is at the edge, we can grab almost all of the subtree,
						# treating only the ragged bottom edge as an edge case
						elif start_edges[divergence_idx]:
												slices.append(path + (slice(start[divergence_idx]					,      end[divergence_idx]		),)		)
												slices.extend(lower()		)
						# Analogous to the previous case, but the top is ragged this time
						elif end_edges[divergence_idx]:
												slices.extend(upper()		)
												slices.append(path + (slice(start[divergence_idx] + 1					,      end[divergence_idx] + 1		),)		)
						# If both sides of the range are ragged, we need to handle both sides
						# separately. If there's contiguous meat in between them, we can index it
						# in one big chunk
						else:
												slices.extend(upper()		)
												lowerCamelCase__	:       Union[str, Any]					=						end[divergence_idx] - start[divergence_idx]
												if middle_ground > 1:
																		slices.append(path + (slice(start[divergence_idx] + 1					,      end[divergence_idx]		),)		)
												slices.extend(lower()		)

						return slices

@torch.jit.ignore
def    lowercase_	(	_A    :					torch.Tensor					,      _A    :					int					,      _A    :					int					,      _A    :					int		):

						"""simple docstring"""




						lowerCamelCase__	:       int					=						t.shape[:no_batch_dims]
						lowerCamelCase__	:       Union[str, Any]					=						list(_flat_idx_to_idx(lowerCamelCase_					,      lowerCamelCase_		)		)
						# _get_minimal_slice_set is inclusive
						lowerCamelCase__	:       Dict					=						list(_flat_idx_to_idx(flat_end - 1					,      lowerCamelCase_		)		)

						# Get an ordered list of slices to perform
						lowerCamelCase__	:       int					=						_get_minimal_slice_set(
						    lowerCamelCase_					,      lowerCamelCase_					,      lowerCamelCase_					,      )

						lowerCamelCase__	:       Union[str, Any]					=						[t[s] for s in slices]

						return torch.cat([s.view((-1,) + t.shape[no_batch_dims:]		) for s in sliced_tensors]		)

def    lowercase_	(	_A    :					Callable					,      _A    :					Dict[str, Any]					,      _A    :					int					,      _A    :					int					,      _A    :					bool = False					,      _A    :					Any = None					,      _A    :					bool = False					,      ):

						"""simple docstring"""




						if not (len(lowerCamelCase_		) > 0):
												raise ValueError("Must provide at least one input"		)

						lowerCamelCase__	:       Tuple					=						[shape[:no_batch_dims] for shape in _fetch_dims(lowerCamelCase_		)]
						lowerCamelCase__	:       Union[str, Any]					=						tuple([max(lowerCamelCase_		) for s in zip(*lowerCamelCase_		)]		)

						def _prep_inputs(_A    :					torch.Tensor		) -> torch.Tensor:
												if not low_mem:
																		if not sum(t.shape[:no_batch_dims]		) == no_batch_dims:
																								lowerCamelCase__	:       Tuple					=						t.expand(orig_batch_dims + t.shape[no_batch_dims:]		)
																		lowerCamelCase__	:       List[str]					=						t.reshape(-1					,      *t.shape[no_batch_dims:]		)
												else:
																		lowerCamelCase__	:       Union[str, Any]					=						t.expand(orig_batch_dims + t.shape[no_batch_dims:]		)
												return t

						lowerCamelCase__	:       Tuple					=						tensor_tree_map(_prep_inputs					,      lowerCamelCase_		)
						lowerCamelCase__	:       Tuple					=						None
						if _out is not None:
												lowerCamelCase__	:       List[str]					=						tensor_tree_map(lambda _A		: t.view([-1] + list(t.shape[no_batch_dims:]		)		)					,      _out		)

						lowerCamelCase__	:       str					=						1
						for d in orig_batch_dims:
												flat_batch_dim *= d

						lowerCamelCase__	:       Dict					=						flat_batch_dim // chunk_size + (flat_batch_dim % chunk_size != 0)

						def _select_chunk(_A    :					torch.Tensor		) -> torch.Tensor:
												return t[i : i + chunk_size] if t.shape[0] != 1 else t

						lowerCamelCase__	:       Union[str, Any]					=						0
						lowerCamelCase__	:       Union[str, Any]					=						prepped_outputs
						for _ in range(lowerCamelCase_		):
												# Chunk the input
												if not low_mem:
																		lowerCamelCase__	:       Optional[int]					=						_select_chunk
												else:
																		lowerCamelCase__	:       int					=						partial(
																		    _chunk_slice					,      flat_start=lowerCamelCase_					,      flat_end=min(lowerCamelCase_					,      i + chunk_size		)					,      no_batch_dims=len(lowerCamelCase_		)					,      )

												lowerCamelCase__	:       Union[str, Any]					=						tensor_tree_map(lowerCamelCase_					,      lowerCamelCase_		)

												# Run the layer on the chunk
												lowerCamelCase__	:       List[Any]					=						layer(**lowerCamelCase_		)

												# Allocate space for the output
												if out is None:
																		lowerCamelCase__	:       List[str]					=						tensor_tree_map(lambda _A		: t.new_zeros((flat_batch_dim,) + t.shape[1:]		)					,      lowerCamelCase_		)

												# Put the chunk in its pre-allocated space
												if isinstance(lowerCamelCase_					,      lowerCamelCase_		):

																		def assign(_A    :					dict					,      _A    :					dict		) -> None:
																								for k, v in da.items():
																														if isinstance(lowerCamelCase_					,      lowerCamelCase_		):
																																				assign(lowerCamelCase_					,      da[k]		)
																														else:
																																				if _add_into_out:
																																										v[i : i + chunk_size] += da[k]
																																				else:
																																										lowerCamelCase__	:       Optional[Any]					=						da[k]

																		assign(lowerCamelCase_					,      lowerCamelCase_		)
												elif isinstance(lowerCamelCase_					,      lowerCamelCase_		):
																		for xa, xa in zip(lowerCamelCase_					,      lowerCamelCase_		):
																								if _add_into_out:
																														xa[i : i + chunk_size] += xa
																								else:
																														lowerCamelCase__	:       Any					=						xa
												elif isinstance(lowerCamelCase_					,      torch.Tensor		):
																		if _add_into_out:
																								out[i : i + chunk_size] += output_chunk
																		else:
																								lowerCamelCase__	:       Tuple					=						output_chunk
												else:
																		raise ValueError("Not supported"		)

												i += chunk_size

						lowerCamelCase__	:       Tuple					=						tensor_tree_map(lambda _A		: t.view(orig_batch_dims + t.shape[1:]		)					,      lowerCamelCase_		)

						return out







class     _lowercase				:


							"""simple docstring"""




							def __init__(     self							:    Dict      ,   __lowerCamelCase							:    List[str] = 512      ,   ):


													'''simple docstring'''



													lowerCamelCase__	:       Tuple					=						max_chunk_size
													lowerCamelCase__	:       int					=						None
													lowerCamelCase__	:       Optional[Any]					=						None





							def 		lowerCAmelCase  (     self							:    Union[str, Any]      ,   __lowerCamelCase							:    Tuple      ,   __lowerCamelCase							:    Any      ,   __lowerCamelCase							:    str ):


													'''simple docstring'''



													logging.info("Tuning chunk size..." )

													if min_chunk_size >= self.max_chunk_size:
																			return min_chunk_size

													lowerCamelCase__	:       List[Any]					=						[2**l for l in range(int(math.log(self.max_chunk_size      ,   2 ) ) + 1 )]
													lowerCamelCase__	:       Dict					=						[c for c in candidates if c > min_chunk_size]
													lowerCamelCase__	:       Dict					=						[min_chunk_size] + candidates
													candidates[-1] += 4

													def test_chunk_size(__lowerCamelCase							:    List[str] ) -> bool:
																			try:
																									with torch.no_grad():
																															fn(*_lowerCamelCase      ,   chunk_size=_lowerCamelCase )
																									return True
																			except RuntimeError:
																									return False

													lowerCamelCase__	:       List[Any]					=						0
													lowerCamelCase__	:       Any					=						len(_lowerCamelCase ) - 1
													while i > min_viable_chunk_size_index:
																			lowerCamelCase__	:       Dict					=						test_chunk_size(candidates[i] )
																			if not viable:
																									lowerCamelCase__	:       Any					=						(min_viable_chunk_size_index + i) // 2
																			else:
																									lowerCamelCase__	:       Union[str, Any]					=						i
																									lowerCamelCase__	:       str					=						(i + len(_lowerCamelCase ) - 1) // 2

													return candidates[min_viable_chunk_size_index]





							def 		lowerCAmelCase  (     self							:    Union[str, Any]      ,   __lowerCamelCase							:    Optional[int]      ,   __lowerCamelCase							:    List[str] ):


													'''simple docstring'''



													lowerCamelCase__	:       List[str]					=						True
													for aa, aa in zip(_lowerCamelCase      ,   _lowerCamelCase ):
																			assert type(_lowerCamelCase ) == type(_lowerCamelCase )
																			if isinstance(_lowerCamelCase      ,   (list, tuple) ):
																									consistent &= self._compare_arg_caches(_lowerCamelCase      ,   _lowerCamelCase )
																			elif isinstance(_lowerCamelCase      ,   _lowerCamelCase ):
																									lowerCamelCase__	:       Any					=						[v for _, v in sorted(aa.items()      ,   key=lambda __lowerCamelCase : x[0] )]
																									lowerCamelCase__	:       int					=						[v for _, v in sorted(aa.items()      ,   key=lambda __lowerCamelCase : x[0] )]
																									consistent &= self._compare_arg_caches(_lowerCamelCase      ,   _lowerCamelCase )
																			else:
																									consistent &= aa == aa

													return consistent





							def 		lowerCAmelCase  (     self							:    Any      ,   __lowerCamelCase							:    str      ,   __lowerCamelCase							:    Dict      ,   __lowerCamelCase							:    Dict      ,   ):


													'''simple docstring'''



													lowerCamelCase__	:       str					=						True
													lowerCamelCase__	:       Optional[int]					=						tree_map(lambda __lowerCamelCase : a.shape if isinstance(_lowerCamelCase      ,   torch.Tensor ) else a      ,   _lowerCamelCase      ,   _lowerCamelCase )
													if self.cached_arg_data is not None:
																			# If args have changed shape/value, we need to re-tune
																			assert len(self.cached_arg_data ) == len(_lowerCamelCase )
																			lowerCamelCase__	:       Dict					=						self._compare_arg_caches(self.cached_arg_data      ,   _lowerCamelCase )
													else:
																			# Otherwise, we can reuse the precomputed value
																			lowerCamelCase__	:       Tuple					=						False

													if not consistent:
																			lowerCamelCase__	:       Union[str, Any]					=						self._determine_favorable_chunk_size(
																			    _lowerCamelCase      ,   _lowerCamelCase      ,   _lowerCamelCase      ,   )
																			lowerCamelCase__	:       Union[str, Any]					=						arg_data

													assert self.cached_chunk_size is not None

													return self.cached_chunk_size






import os

def    lowercase_	(	_A    :					str = "input.txt"		):

      """simple docstring"""




      with open(os.path.join(os.path.dirname(_A		)					,      _A		)		) as input_file:
            lowerCamelCase__	:       List[Any]					=						[
                [int(_A		) for element in line.split(","		)]
                for line in input_file.readlines()
            ]

      lowerCamelCase__	:       Optional[Any]					=						len(_A		)
      lowerCamelCase__	:       Union[str, Any]					=						len(matrix[0]		)

      lowerCamelCase__	:       Union[str, Any]					=						[[-1 for _ in range(_A		)] for _ in range(_A		)]
      for i in range(_A		):
            lowerCamelCase__	:       Optional[Any]					=						matrix[i][0]

      for j in range(1					,      _A		):
            for i in range(_A		):
                  lowerCamelCase__	:       int					=						minimal_path_sums[i][j - 1] + matrix[i][j]

            for i in range(1					,      _A		):
                  lowerCamelCase__	:       Tuple					=						min(
                      minimal_path_sums[i][j]					,      minimal_path_sums[i - 1][j] + matrix[i][j]		)

            for i in range(rows - 2					,      -1					,      -1		):
                  lowerCamelCase__	:       str					=						min(
                      minimal_path_sums[i][j]					,      minimal_path_sums[i + 1][j] + matrix[i][j]		)

      return min(minimal_path_sums_row[-1] for minimal_path_sums_row in minimal_path_sums		)


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


