"""simple docstring"""


def    UpperCAmelCase       (						UpperCAmelCase = 1000   )							-> int:
     return sum(i for i in range(UpperCAmelCase   ) if i % 3 == 0 or i % 5 == 0   )


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


"""simple docstring"""


from typing import Dict, Tuple, overload

import torch
import torch.types
from torch import nn

from . import residue_constants as rc
from .rigid_utils import Rigid, Rotation
from .tensor_utils import batched_gather







@overload
def    UpperCAmelCase       (						UpperCAmelCase		,   UpperCAmelCase		,   UpperCAmelCase   )							-> torch.Tensor:
     ...







@overload
def    UpperCAmelCase       (						UpperCAmelCase		,   UpperCAmelCase		,   UpperCAmelCase   )							-> Tuple[torch.Tensor, torch.Tensor]:
     ...







def    UpperCAmelCase       (						UpperCAmelCase		,   UpperCAmelCase		,   UpperCAmelCase   )							-> Dict:
     snake_case_   			=   aatype == rc.restype_order['G']
     snake_case_   			=   rc.atom_order['CA']
     snake_case_   			=   rc.atom_order['CB']
     snake_case_   			=   torch.where(
         is_gly[..., None].expand(*((-1,) * len(is_gly.shape   ))		,   3   )		,   all_atom_positions[..., ca_idx, :]		,   all_atom_positions[..., cb_idx, :]		,   )

     if all_atom_masks is not None:
          snake_case_   			=   torch.where(
              UpperCAmelCase		,   all_atom_masks[..., ca_idx]		,   all_atom_masks[..., cb_idx]		,   )
          return pseudo_beta, pseudo_beta_mask
     else:
          return pseudo_beta







def    UpperCAmelCase       (						UpperCAmelCase		,   UpperCAmelCase   )							-> torch.Tensor:
     snake_case_   			=   batched_gather(
         UpperCAmelCase		,   batch['residx_atom37_to_atom14']		,   dim=-2		,   no_batch_dims=len(atomaa.shape[:-2]   )		,   )

     snake_case_   			=   atomaa_data * batch['atom37_atom_exists'][..., None]

     return atomaa_data







def    UpperCAmelCase       (						UpperCAmelCase   )							-> torch.Tensor:
     snake_case_   			=   template_feats['template_aatype']
     snake_case_   			=   template_feats['template_torsion_angles_sin_cos']
     snake_case_   			=   template_feats['template_alt_torsion_angles_sin_cos']
     snake_case_   			=   template_feats['template_torsion_angles_mask']
     snake_case_   			=   torch.cat(
         [
             nn.functional.one_hot(UpperCAmelCase		,   22   ),
             torsion_angles_sin_cos.reshape(*torsion_angles_sin_cos.shape[:-2]		,   14   ),
             alt_torsion_angles_sin_cos.reshape(*alt_torsion_angles_sin_cos.shape[:-2]		,   14   ),
             torsion_angles_mask,
         ]		,   dim=-1		,   )

     return template_angle_feat







def    UpperCAmelCase       (						UpperCAmelCase		,   UpperCAmelCase		,   UpperCAmelCase		,   UpperCAmelCase		,   UpperCAmelCase = False		,   UpperCAmelCase = 1e-20		,   UpperCAmelCase = 1e8		,   )							-> torch.Tensor:
     snake_case_   			=   batch['template_pseudo_beta_mask']
     snake_case_   			=   template_mask[..., None] * template_mask[..., None, :]

     # Compute distogram (this seems to differ slightly from Alg. 5)
     snake_case_   			=   batch['template_pseudo_beta']
     snake_case_   			=   torch.sum((tpb[..., None, :] - tpb[..., None, :, :]) ** 2		,   dim=-1		,   keepdim=UpperCAmelCase   )
     snake_case_   			=   torch.linspace(UpperCAmelCase		,   UpperCAmelCase		,   UpperCAmelCase		,   device=tpb.device   ) ** 2
     snake_case_   			=   torch.cat([lower[1:], lower.new_tensor([inf]   )]		,   dim=-1   )
     snake_case_   			=   ((dgram > lower) * (dgram < upper)).type(dgram.dtype   )

     snake_case_   			=   [dgram, template_mask_ad[..., None]]

     snake_case_   			=   nn.functional.one_hot(
         batch['template_aatype']		,   rc.restype_num + 2		,   )

     snake_case_   			=   batch['template_aatype'].shape[-1]
     to_concat.append(aatype_one_hot[..., None, :, :].expand(*aatype_one_hot.shape[:-2]		,   UpperCAmelCase		,   -1		,   -1   )   )
     to_concat.append(aatype_one_hot[..., None, :].expand(*aatype_one_hot.shape[:-2]		,   -1		,   UpperCAmelCase		,   -1   )   )

     snake_case_			,      snake_case_			,      snake_case_   			=   [rc.atom_order[a] for a in ['N', 'CA', 'C']]
     snake_case_   			=   Rigid.make_transform_from_reference(
         n_xyz=batch['template_all_atom_positions'][..., n, :]		,   ca_xyz=batch['template_all_atom_positions'][..., ca, :]		,   c_xyz=batch['template_all_atom_positions'][..., c, :]		,   eps=UpperCAmelCase		,   )
     snake_case_   			=   rigids.get_trans()[..., None, :, :]
     snake_case_   			=   rigids[..., None].invert_apply(UpperCAmelCase   )

     snake_case_   			=   torch.rsqrt(eps + torch.sum(rigid_vec**2		,   dim=-1   )   )

     snake_case_   			=   batch['template_all_atom_mask']
     snake_case_   			=   t_aa_masks[..., n] * t_aa_masks[..., ca] * t_aa_masks[..., c]
     snake_case_   			=   template_mask[..., None] * template_mask[..., None, :]

     snake_case_   			=   inv_distance_scalar * template_mask_ad
     snake_case_   			=   rigid_vec * inv_distance_scalar[..., None]

     if not use_unit_vector:
          snake_case_   			=   unit_vector * 0.0

     to_concat.extend(torch.unbind(unit_vector[..., None, :]		,   dim=-1   )   )
     to_concat.append(template_mask_ad[..., None]   )

     snake_case_   			=   torch.cat(UpperCAmelCase		,   dim=-1   )
     snake_case_   			=   act * template_mask_ad[..., None]

     return act







def    UpperCAmelCase       (						UpperCAmelCase   )							-> torch.Tensor:
     snake_case_   			=   nn.functional.one_hot(batch['extra_msa']		,   23   )
     snake_case_   			=   [
         msa_ahot,
         batch['extra_has_deletion'].unsqueeze(-1   ),
         batch['extra_deletion_value'].unsqueeze(-1   ),
     ]
     return torch.cat(UpperCAmelCase		,   dim=-1   )







def    UpperCAmelCase       (						UpperCAmelCase		,   UpperCAmelCase		,   UpperCAmelCase		,   UpperCAmelCase		,   )							-> Rigid:
     # [*, N, 8, 4, 4]
     snake_case_   			=   rrgdf[aatype, ...]

     # [*, N, 8] transformations, i.e.
     #   One [*, N, 8, 3, 3] rotation matrix and
     #   One [*, N, 8, 3]    translation matrix
     snake_case_   			=   r.from_tensor_axa(UpperCAmelCase   )

     snake_case_   			=   alpha.new_zeros((*((1,) * len(alpha.shape[:-1]   )), 2)   )
     snake_case_   			=   1

     # [*, N, 8, 2]
     snake_case_   			=   torch.cat([bb_rot.expand(*alpha.shape[:-2]		,   -1		,   -1   ), alpha]		,   dim=-2   )

     # [*, N, 8, 3, 3]
     # Produces rotation matrices of the form:
     # [
     #   [1, 0  , 0  ],
     #   [0, a_2,-a_1],
     #   [0, a_1, a_2]
     # ]
     # This follows the original code rather than the supplement, which uses
     # different indices.

     snake_case_   			=   alpha.new_zeros(default_r.get_rots().get_rot_mats().shape   )
     snake_case_   			=   1
     snake_case_   			=   alpha[..., 1]
     snake_case_   			=   -alpha[..., 0]
     snake_case_   			=   alpha

     snake_case_   			=   default_r.compose(Rigid(Rotation(rot_mats=UpperCAmelCase   )		,   UpperCAmelCase   )   )

     snake_case_   			=   all_frames[..., 5]
     snake_case_   			=   all_frames[..., 6]
     snake_case_   			=   all_frames[..., 7]

     snake_case_   			=   all_frames[..., 4]
     snake_case_   			=   chia_frame_to_bb.compose(UpperCAmelCase   )
     snake_case_   			=   chia_frame_to_bb.compose(UpperCAmelCase   )
     snake_case_   			=   chia_frame_to_bb.compose(UpperCAmelCase   )

     snake_case_   			=   Rigid.cat(
         [
             all_frames[..., :5],
             chia_frame_to_bb.unsqueeze(-1   ),
             chia_frame_to_bb.unsqueeze(-1   ),
             chia_frame_to_bb.unsqueeze(-1   ),
         ]		,   dim=-1		,   )

     snake_case_   			=   r[..., None].compose(UpperCAmelCase   )

     return all_frames_to_global







def    UpperCAmelCase       (						UpperCAmelCase		,   UpperCAmelCase		,   UpperCAmelCase		,   UpperCAmelCase		,   UpperCAmelCase		,   UpperCAmelCase		,   )							-> torch.Tensor:
     # [*, N, 14]
     snake_case_   			=   group_idx[aatype, ...]

     # [*, N, 14, 8]
     snake_case_   			=   nn.functional.one_hot(
         UpperCAmelCase		,   num_classes=default_frames.shape[-3]		,   )

     # [*, N, 14, 8]
     snake_case_   			=   r[..., None, :] * group_mask_one_hot

     # [*, N, 14]
     snake_case_   			=   t_atoms_to_global.map_tensor_fn(lambda UpperCAmelCase   : torch.sum(UpperCAmelCase		,   dim=-1   )   )

     # [*, N, 14, 1]
     snake_case_   			=   atom_mask[aatype, ...].unsqueeze(-1   )

     # [*, N, 14, 3]
     snake_case_   			=   lit_positions[aatype, ...]
     snake_case_   			=   t_atoms_to_global.apply(UpperCAmelCase   )
     snake_case_   			=   pred_positions * atom_mask

     return pred_positions

