

import dataclasses
import re
import string
from typing import Any, Dict, Iterator, List, Mapping, Optional, Sequence, Tuple

import numpy as np

from . import residue_constants


lowerCAmelCase							:  Any   	=						Mapping[str, np.ndarray]
lowerCAmelCase							:  int   	=						Mapping[str, Any]  # Is a nested dict.
lowerCAmelCase							:  Optional[Any]   	=						0.01



@dataclasses.dataclass(frozen=UpperCAmelCase_	)
class   __lowercase				:




			"""simple docstring"""







			_UpperCAmelCase   :							np.ndarray  # [num_res, num_atom_type, 3]

			# Amino-acid type for each residue represented as an integer between 0 and
			# 20, where 20 is 'X'.
			_UpperCAmelCase   :							np.ndarray  # [num_res]

			# Binary float mask to indicate presence of a particular atom. 1.0 if an atom
			# is present and 0.0 if not. This should be used for loss masking.
			_UpperCAmelCase   :							np.ndarray  # [num_res, num_atom_type]

			# Residue index as used in PDB. It is not necessarily continuous or 0-indexed.
			_UpperCAmelCase   :							np.ndarray  # [num_res]

			# B-factors, or temperature factors, of each residue (in sq. angstroms units),
			# representing the displacement of the residue from its ground truth mean
			# value.
			_UpperCAmelCase   :							np.ndarray  # [num_res, num_atom_type]

			# Chain indices for multi-chain predictions
			_UpperCAmelCase   :							Optional[np.ndarray]										=     None

			# Optional remark about the protein. Included as a comment in output PDB
			# files
			_UpperCAmelCase   :							Optional[str]										=     None

			# Templates used to generate this protein (prediction-only)
			_UpperCAmelCase   :							Optional[Sequence[str]]										=     None

			# Chain corresponding to each parent
			_UpperCAmelCase   :							Optional[Sequence[int]]										=     None







def 			A_      (    _UpperCAmelCase    ):
						SCREAMING_SNAKE_CASE_: Optional[Any]  		=       R"(\[[A-Z]+\]\n)"
						SCREAMING_SNAKE_CASE_: List[str]  		=       [tag.strip() for tag in re.split(_UpperCAmelCase				,	_UpperCAmelCase    ) if len(_UpperCAmelCase    ) > 0]
						SCREAMING_SNAKE_CASE_: Iterator[Tuple[str, List[str]]]  		=       zip(tags[0::2]				,	[l.split("\n"    ) for l in tags[1::2]]    )

						SCREAMING_SNAKE_CASE_: List[str]  		=       ["N", "CA", "C"]
						SCREAMING_SNAKE_CASE_: Any  		=       None
						SCREAMING_SNAKE_CASE_: Optional[Any]  		=       None
						SCREAMING_SNAKE_CASE_: List[str]  		=       None
						for g in groups:
												if "[PRIMARY]" == g[0]:
																		SCREAMING_SNAKE_CASE_: Optional[int]  		=       g[1][0].strip()
																		for i in range(len(_UpperCAmelCase    )    ):
																								if seq[i] not in residue_constants.restypes:
																														SCREAMING_SNAKE_CASE_: Union[str, Any]  		=       "X"  # FIXME: strings are immutable
																		SCREAMING_SNAKE_CASE_: Tuple  		=       np.array(
																		    [residue_constants.restype_order.get(_UpperCAmelCase				,	residue_constants.restype_num    ) for res_symbol in seq]    )
												elif "[TERTIARY]" == g[0]:
																		SCREAMING_SNAKE_CASE_: List[List[float]]  		=       []
																		for axis in range(3    ):
																								tertiary.append(list(map(_UpperCAmelCase				,	g[1][axis].split()    )    )    )
																		SCREAMING_SNAKE_CASE_: List[Any]  		=       np.array(_UpperCAmelCase    )
																		SCREAMING_SNAKE_CASE_: int  		=       np.zeros((len(tertiary[0]    ) // 3, residue_constants.atom_type_num, 3)    ).astype(np.floataa    )
																		for i, atom in enumerate(_UpperCAmelCase    ):
																								SCREAMING_SNAKE_CASE_: str  		=       np.transpose(tertiary_np[:, i::3]    )
																		atom_positions *= PICO_TO_ANGSTROM
												elif "[MASK]" == g[0]:
																		SCREAMING_SNAKE_CASE_: Optional[int]  		=       np.array(list(map({"-": 0, "+": 1}.get				,	g[1][0].strip()    )    )    )
																		SCREAMING_SNAKE_CASE_: Any  		=       np.zeros(
																		    (
																		        len(_UpperCAmelCase    ),
																		        residue_constants.atom_type_num,
																		    )    ).astype(np.floataa    )
																		for i, atom in enumerate(_UpperCAmelCase    ):
																								SCREAMING_SNAKE_CASE_: str  		=       1
																		atom_mask *= mask[..., None]

						assert aatype is not None

						return Protein(
						    atom_positions=_UpperCAmelCase				,	atom_mask=_UpperCAmelCase				,	aatype=_UpperCAmelCase				,	residue_index=np.arange(len(_UpperCAmelCase    )    )				,	b_factors=_UpperCAmelCase				,	)







def 			A_      (    _UpperCAmelCase				,	_UpperCAmelCase = 0    ):
						SCREAMING_SNAKE_CASE_: List[str]  		=       []

						SCREAMING_SNAKE_CASE_: Any  		=       prot.remark
						if remark is not None:
												pdb_headers.append(f"REMARK {remark}"    )

						SCREAMING_SNAKE_CASE_: Any  		=       prot.parents
						SCREAMING_SNAKE_CASE_: Dict  		=       prot.parents_chain_index
						if parents is not None and parents_chain_index is not None:
												SCREAMING_SNAKE_CASE_: Optional[int]  		=       [p for i, p in zip(_UpperCAmelCase				,	_UpperCAmelCase    ) if i == chain_id]

						if parents is None or len(_UpperCAmelCase    ) == 0:
												SCREAMING_SNAKE_CASE_: Optional[int]  		=       ["N/A"]

						pdb_headers.append(f"PARENT {' '.join(_UpperCAmelCase    )}"    )

						return pdb_headers







def 			A_      (    _UpperCAmelCase				,	_UpperCAmelCase    ):
						SCREAMING_SNAKE_CASE_: List[str]  		=       []
						SCREAMING_SNAKE_CASE_: List[str]  		=       pdb_str.split("\n"    )

						SCREAMING_SNAKE_CASE_: Optional[int]  		=       prot.remark
						if remark is not None:
												out_pdb_lines.append(f"REMARK {remark}"    )

						SCREAMING_SNAKE_CASE_: List[List[str]]
						if prot.parents is not None and len(prot.parents    ) > 0:
												SCREAMING_SNAKE_CASE_: Optional[int]  		=       []
												if prot.parents_chain_index is not None:
																		SCREAMING_SNAKE_CASE_: Dict[str, List[str]]  		=       {}
																		for p, i in zip(prot.parents				,	prot.parents_chain_index    ):
																								parent_dict.setdefault(str(_UpperCAmelCase    )				,	[]    )
																								parent_dict[str(_UpperCAmelCase    )].append(_UpperCAmelCase    )

																		SCREAMING_SNAKE_CASE_: List[str]  		=       max([int(_UpperCAmelCase    ) for chain_idx in parent_dict]    )
																		for i in range(max_idx + 1    ):
																								SCREAMING_SNAKE_CASE_: List[str]  		=       parent_dict.get(str(_UpperCAmelCase    )				,	["N/A"]    )
																								parents_per_chain.append(_UpperCAmelCase    )
												else:
																		parents_per_chain.append(list(prot.parents    )    )
						else:
												SCREAMING_SNAKE_CASE_: List[Any]  		=       [["N/A"]]

						def make_parent_line(_UpperCAmelCase    ) -> str:
												return f"PARENT {' '.join(_UpperCAmelCase    )}"

						out_pdb_lines.append(make_parent_line(parents_per_chain[0]    )    )

						SCREAMING_SNAKE_CASE_: Union[str, Any]  		=       0
						for i, l in enumerate(_UpperCAmelCase    ):
												if "PARENT" not in l and "REMARK" not in l:
																		out_pdb_lines.append(_UpperCAmelCase    )
												if "TER" in l and "END" not in lines[i + 1]:
																		chain_counter += 1
																		if not chain_counter >= len(_UpperCAmelCase    ):
																								SCREAMING_SNAKE_CASE_: Any  		=       parents_per_chain[chain_counter]
																		else:
																								SCREAMING_SNAKE_CASE_: Union[str, Any]  		=       ["N/A"]

																		out_pdb_lines.append(make_parent_line(_UpperCAmelCase    )    )

						return "\n".join(_UpperCAmelCase    )







def 			A_      (    _UpperCAmelCase    ):
						SCREAMING_SNAKE_CASE_: int  		=       residue_constants.restypes + ["X"]

						def res_atoa(_UpperCAmelCase    ) -> str:
												return residue_constants.restype_atoa.get(restypes[r]				,	"UNK"    )

						SCREAMING_SNAKE_CASE_: int  		=       residue_constants.atom_types

						SCREAMING_SNAKE_CASE_: List[str]  		=       []

						SCREAMING_SNAKE_CASE_: Optional[int]  		=       prot.atom_mask
						SCREAMING_SNAKE_CASE_: Optional[Any]  		=       prot.aatype
						SCREAMING_SNAKE_CASE_: Optional[Any]  		=       prot.atom_positions
						SCREAMING_SNAKE_CASE_: int  		=       prot.residue_index.astype(np.intaa    )
						SCREAMING_SNAKE_CASE_: Dict  		=       prot.b_factors
						SCREAMING_SNAKE_CASE_: str  		=       prot.chain_index

						if np.any(aatype > residue_constants.restype_num    ):
												raise ValueError("Invalid aatypes."    )

						SCREAMING_SNAKE_CASE_: Optional[int]  		=       get_pdb_headers(_UpperCAmelCase    )
						if len(_UpperCAmelCase    ) > 0:
												pdb_lines.extend(_UpperCAmelCase    )

						SCREAMING_SNAKE_CASE_: List[Any]  		=       aatype.shape[0]
						SCREAMING_SNAKE_CASE_: str  		=       1
						SCREAMING_SNAKE_CASE_: List[Any]  		=       0
						SCREAMING_SNAKE_CASE_: List[Any]  		=       string.ascii_uppercase
						SCREAMING_SNAKE_CASE_: int  		=       None
						# Add all atom sites.
						for i in range(_UpperCAmelCase    ):
												SCREAMING_SNAKE_CASE_: List[str]  		=       res_atoa(aatype[i]    )
												for atom_name, pos, mask, b_factor in zip(_UpperCAmelCase				,	atom_positions[i]				,	atom_mask[i]				,	b_factors[i]    ):
																		if mask < 0.5:
																								continue

																		SCREAMING_SNAKE_CASE_: List[Any]  		=       "ATOM"
																		SCREAMING_SNAKE_CASE_: Optional[Any]  		=       atom_name if len(_UpperCAmelCase    ) == 4 else f" {atom_name}"
																		SCREAMING_SNAKE_CASE_: List[str]  		=       ""
																		SCREAMING_SNAKE_CASE_: Optional[int]  		=       ""
																		SCREAMING_SNAKE_CASE_: List[str]  		=       1.0_0
																		SCREAMING_SNAKE_CASE_: int  		=       atom_name[0]  # Protein supports only C, N, O, S, this works.
																		SCREAMING_SNAKE_CASE_: Optional[Any]  		=       ""

																		SCREAMING_SNAKE_CASE_: Dict  		=       "A"
																		if chain_index is not None:
																								SCREAMING_SNAKE_CASE_: int  		=       chain_tags[chain_index[i]]

																		# PDB is a columnar format, every space matters here!
																		SCREAMING_SNAKE_CASE_: Tuple  		=       (
																		    f"{record_type:<6}{atom_index:>5} {name:<4}{alt_loc:>1}"
																		    f"{res_name_a:>3} {chain_tag:>1}"
																		    f"{residue_index[i]:>4}{insertion_code:>1}   "
																		    f"{pos[0]:>8.3f}{pos[1]:>8.3f}{pos[2]:>8.3f}"
																		    f"{occupancy:>6.2f}{b_factor:>6.2f}          "
																		    f"{element:>2}{charge:>2}"
																		)
																		pdb_lines.append(_UpperCAmelCase    )
																		atom_index += 1

												SCREAMING_SNAKE_CASE_: Optional[Any]  		=       i == n - 1
												if chain_index is not None:
																		if i != n - 1 and chain_index[i + 1] != prev_chain_index:
																								SCREAMING_SNAKE_CASE_: Dict  		=       True
																								SCREAMING_SNAKE_CASE_: List[str]  		=       chain_index[i + 1]

												if should_terminate:
																		# Close the chain.
																		SCREAMING_SNAKE_CASE_: int  		=       "TER"
																		SCREAMING_SNAKE_CASE_: int  		=       (
																		    f"{chain_end:<6}{atom_index:>5}      {res_atoa(aatype[i]    ):>3} {chain_tag:>1}{residue_index[i]:>4}"
																		)
																		pdb_lines.append(_UpperCAmelCase    )
																		atom_index += 1

																		if i != n - 1:
																								# "prev" is a misnomer here. This happens at the beginning of
																								# each new chain.
																								pdb_lines.extend(get_pdb_headers(_UpperCAmelCase				,	_UpperCAmelCase    )    )

						pdb_lines.append("END"    )
						pdb_lines.append(""    )
						return "\n".join(_UpperCAmelCase    )







def 			A_      (    _UpperCAmelCase    ):
						return residue_constants.STANDARD_ATOM_MASK[prot.aatype]







def 			A_      (    _UpperCAmelCase				,	_UpperCAmelCase				,	_UpperCAmelCase = None				,	_UpperCAmelCase = None				,	_UpperCAmelCase = None				,	_UpperCAmelCase = None				,	_UpperCAmelCase = None				,	):
						return Protein(
						    aatype=features["aatype"]				,	atom_positions=result["final_atom_positions"]				,	atom_mask=result["final_atom_mask"]				,	residue_index=features["residue_index"] + 1				,	b_factors=b_factors if b_factors is not None else np.zeros_like(result["final_atom_mask"]    )				,	chain_index=_UpperCAmelCase				,	remark=_UpperCAmelCase				,	parents=_UpperCAmelCase				,	parents_chain_index=_UpperCAmelCase				,	)








"""simple docstring"""



from math import sqrt
def 					_UpperCAmelCase      ( __lowerCamelCase   :       int = 1_00_00_00		)     ->					int:
  _snake_case					     =       0
  _snake_case					     =       0
  _snake_case					     =       42

  while num_cuboids <= limit:
    max_cuboid_size += 1
    for sum_shortest_sides in range(2 ,					2 * max_cuboid_size + 1		):
      if sqrt(sum_shortest_sides**2 + max_cuboid_size**2		).is_integer():
        num_cuboids += (
            min(__lowerCamelCase ,					sum_shortest_sides // 2		)
            - max(1 ,					sum_shortest_sides - max_cuboid_size		)
            + 1
        )

  return max_cuboid_size


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



