


'''simple docstring'''



from typing import Dict

import numpy as np
import torch

from . import residue_constants as rc
from .tensor_utils import tensor_tree_map, tree_map







def 			_UpperCamelCase					(						UpperCamelCase__    ):
			UpperCAmelCase__     :    List[Any]         =   []
			UpperCAmelCase__     :    Any         =   []
			UpperCAmelCase__     :    Any         =   []

			for rt in rc.restypes:
						UpperCAmelCase__     :    Tuple         =   rc.restype_name_to_atomaa_names[rc.restype_atoa[rt]]
						restype_atomaa_to_atomaa_list.append([(rc.atom_order[name] if name else 0) for name in atom_names]    )
						UpperCAmelCase__     :    List[str]         =   {name: i for i, name in enumerate(UpperCamelCase__    )}
						restype_atomaa_to_atomaa_list.append(
						    [(atom_name_to_idxaa[name] if name in atom_name_to_idxaa else 0) for name in rc.atom_types]    )

						restype_atomaa_mask_list.append([(1.0 if name else 0.0) for name in atom_names]    )

			# Add dummy mapping for restype 'UNK'
			restype_atomaa_to_atomaa_list.append([0] * 1_4    )
			restype_atomaa_to_atomaa_list.append([0] * 3_7    )
			restype_atomaa_mask_list.append([0.0] * 1_4    )

			UpperCAmelCase__     :    int         =   torch.tensor(
			    UpperCamelCase__       ,					dtype=torch.intaa       ,					device=protein["""aatype"""].device       ,					)
			UpperCAmelCase__     :    int         =   torch.tensor(
			    UpperCamelCase__       ,					dtype=torch.intaa       ,					device=protein["""aatype"""].device       ,					)
			UpperCAmelCase__     :    Any         =   torch.tensor(
			    UpperCamelCase__       ,					dtype=torch.floataa       ,					device=protein["""aatype"""].device       ,					)
			UpperCAmelCase__     :    List[str]         =   protein["""aatype"""].to(torch.long    )

			# create the mapping for (residx, atom14) --> atom37, i.e. an array
			# with shape (num_res, 14) containing the atom37 indices for this protein
			UpperCAmelCase__     :    Optional[Any]         =   restype_atomaa_to_atomaa[protein_aatype]
			UpperCAmelCase__     :    int         =   restype_atomaa_mask[protein_aatype]

			UpperCAmelCase__     :    Any         =   residx_atomaa_mask
			UpperCAmelCase__     :    int         =   residx_atomaa_to_atomaa.long()

			# create the gather indices for mapping back
			UpperCAmelCase__     :    Optional[Any]         =   restype_atomaa_to_atomaa[protein_aatype]
			UpperCAmelCase__     :    Optional[int]         =   residx_atomaa_to_atomaa.long()

			# create the corresponding mask
			UpperCAmelCase__     :    str         =   torch.zeros([2_1, 3_7]       ,					dtype=torch.floataa       ,					device=protein["""aatype"""].device    )
			for restype, restype_letter in enumerate(rc.restypes    ):
						UpperCAmelCase__     :    List[Any]         =   rc.restype_atoa[restype_letter]
						UpperCAmelCase__     :    int         =   rc.residue_atoms[restype_name]
						for atom_name in atom_names:
									UpperCAmelCase__     :    Optional[int]         =   rc.atom_order[atom_name]
									UpperCAmelCase__     :    str         =   1

			UpperCAmelCase__     :    int         =   restype_atomaa_mask[protein_aatype]
			UpperCAmelCase__     :    Any         =   residx_atomaa_mask

			return protein







def 			_UpperCamelCase					(						UpperCamelCase__    ):
			UpperCAmelCase__     :    Union[str, Any]         =   tree_map(lambda UpperCamelCase__    : torch.tensor(UpperCamelCase__       ,					device=batch["""aatype"""].device    )       ,					UpperCamelCase__       ,					np.ndarray    )
			UpperCAmelCase__     :    Optional[Any]         =   tensor_tree_map(lambda UpperCamelCase__    : np.array(UpperCamelCase__    )       ,					make_atomaa_masks(UpperCamelCase__    )    )
			return out







import math
def 						_a    (      a :int )							->			list:
 a		  =      [True] * n
 a		  =      False
 a		  =      False
 a		  =      True

 for i in range(3	,							int(n**0.5 + 1 )	,							2 ):
  a		  =      i * 2
  while index < n:
   a		  =      False
   a		  =      index + i

 a		  =      [2]

 for i in range(3	,							a	,							2 ):
  if is_prime[i]:
   primes.append(a )

 return primes
def 						_a    (      a :int = 999_966_663_333 )							->			int:
 a		  =      math.floor(math.sqrt(a ) ) + 100
 a		  =      prime_sieve(a )

 a		  =      0
 a		  =      0
 a		  =      primes[prime_index]

 while (last_prime**2) <= limit:
  a		  =      primes[prime_index + 1]

  a		  =      last_prime**2
  a		  =      next_prime**2

  # Get numbers divisible by lps(current)
  a		  =      lower_bound + last_prime
  while upper_bound > current <= limit:
   matches_sum += current
   current += last_prime

  # Reset the upper_bound
  while (upper_bound - next_prime) > limit:
   upper_bound -= next_prime

  # Add the numbers divisible by ups(current)
  a		  =      upper_bound - next_prime
  while current > lower_bound:
   matches_sum += current
   current -= next_prime

  # Remove the numbers divisible by both ups and lps
  a		  =      0
  while upper_bound > current <= limit:
   if current <= lower_bound:
    # Increment the current number
    current += last_prime * next_prime
    continue

   if current > limit:
    break

   # Remove twice since it was added by both ups and lps
   matches_sum -= current * 2

   # Increment the current number
   current += last_prime * next_prime

  # Setup for next pair
  a		  =      next_prime
  prime_index += 1

 return matches_sum


if __name__ == "__main__":
     print(solution())


