





from collections import defaultdict
from math import gcd

def   a_   (			lowerCAmelCase_				:      int = 150_0000     ):
   __lowerCAmelCase							     =     defaultdict(lowerCAmelCase_     )
   __lowerCAmelCase							     =     2
   while 2 * euclid_m * (euclid_m + 1) <= limit:
      for euclid_n in range((euclid_m % 2) + 1,     lowerCAmelCase_,     2     ):
         if gcd(lowerCAmelCase_,     lowerCAmelCase_     ) > 1:
            continue
         __lowerCAmelCase							     =     2 * euclid_m * (euclid_m + euclid_n)
         for perimeter in range(lowerCAmelCase_,     limit + 1,     lowerCAmelCase_     ):
            frequencies[perimeter] += 1
      euclid_m += 1
   return sum(1 for frequency in frequencies.values() if frequency == 1     )


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








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   a_   (			lowerCAmelCase_				:      Dict[str, torch.Tensor]     ):
   __lowerCAmelCase							     =     []
   __lowerCAmelCase							     =     []
   __lowerCAmelCase							     =     []

   for rt in rc.restypes:
      __lowerCAmelCase							     =     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]     )
      __lowerCAmelCase							     =     {name: i for i, name in enumerate(lowerCAmelCase_     )}
      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] * 14     )
   restype_atomaa_to_atomaa_list.append([0] * 37     )
   restype_atomaa_mask_list.append([0.0] * 14     )

   __lowerCAmelCase							     =     torch.tensor(
       lowerCAmelCase_,     dtype=torch.intaa,     device=protein['aatype'].device,     )
   __lowerCAmelCase							     =     torch.tensor(
       lowerCAmelCase_,     dtype=torch.intaa,     device=protein['aatype'].device,     )
   __lowerCAmelCase							     =     torch.tensor(
       lowerCAmelCase_,     dtype=torch.floataa,     device=protein['aatype'].device,     )
   __lowerCAmelCase							     =     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
   __lowerCAmelCase							     =     restype_atomaa_to_atomaa[protein_aatype]
   __lowerCAmelCase							     =     restype_atomaa_mask[protein_aatype]

   __lowerCAmelCase							     =     residx_atomaa_mask
   __lowerCAmelCase							     =     residx_atomaa_to_atomaa.long()

   # create the gather indices for mapping back
   __lowerCAmelCase							     =     restype_atomaa_to_atomaa[protein_aatype]
   __lowerCAmelCase							     =     residx_atomaa_to_atomaa.long()

   # create the corresponding mask
   __lowerCAmelCase							     =     torch.zeros([21, 37],     dtype=torch.floataa,     device=protein['aatype'].device     )
   for restype, restype_letter in enumerate(rc.restypes     ):
      __lowerCAmelCase							     =     rc.restype_atoa[restype_letter]
      __lowerCAmelCase							     =     rc.residue_atoms[restype_name]
      for atom_name in atom_names:
         __lowerCAmelCase							     =     rc.atom_order[atom_name]
         __lowerCAmelCase							     =     1

   __lowerCAmelCase							     =     restype_atomaa_mask[protein_aatype]
   __lowerCAmelCase							     =     residx_atomaa_mask

   return protein




def   a_   (			lowerCAmelCase_				:      Dict[str, torch.Tensor]     ):
   __lowerCAmelCase							     =     tree_map(lambda lowerCAmelCase_     : torch.tensor(lowerCAmelCase_,     device=batch['aatype'].device     ),     lowerCAmelCase_,     np.ndarray     )
   __lowerCAmelCase							     =     tensor_tree_map(lambda lowerCAmelCase_     : np.array(lowerCAmelCase_     ),     make_atomaa_masks(lowerCAmelCase_     )     )
   return out

