





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      SCREAMING_SNAKE_CASE      (   lowerCAmelCase     ,							lowerCAmelCase     ,							lowerCAmelCase       ):
       ...


@overload
def      SCREAMING_SNAKE_CASE      (   lowerCAmelCase     ,							lowerCAmelCase     ,							lowerCAmelCase       ):
       ...


def      SCREAMING_SNAKE_CASE      (   lowerCAmelCase     ,							lowerCAmelCase     ,							lowerCAmelCase       ):
       _UpperCamelCase														=    aatype == rc.restype_order['''G''']
       _UpperCamelCase														=    rc.atom_order['''CA''']
       _UpperCamelCase														=    rc.atom_order['''CB''']
       _UpperCamelCase														=    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:
              _UpperCamelCase														=    torch.where(
                  lowerCamelCase__     ,							all_atom_masks[..., ca_idx]     ,							all_atom_masks[..., cb_idx]     ,							)
              return pseudo_beta, pseudo_beta_mask
       else:
              return pseudo_beta


def      SCREAMING_SNAKE_CASE      (   lowerCAmelCase     ,							lowerCAmelCase       ):
       _UpperCamelCase														=    batched_gather(
           lowerCamelCase__     ,							batch['''residx_atom37_to_atom14''']     ,							dim=-2     ,							no_batch_dims=len(atomaa.shape[:-2]       )     ,							)

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

       return atomaa_data


def      SCREAMING_SNAKE_CASE      (   lowerCAmelCase       ):
       _UpperCamelCase														=    template_feats['''template_aatype''']
       _UpperCamelCase														=    template_feats['''template_torsion_angles_sin_cos''']
       _UpperCamelCase														=    template_feats['''template_alt_torsion_angles_sin_cos''']
       _UpperCamelCase														=    template_feats['''template_torsion_angles_mask''']
       _UpperCamelCase														=    torch.cat(
           [
               nn.functional.one_hot(lowerCamelCase__     ,							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      SCREAMING_SNAKE_CASE      (   lowerCAmelCase     ,							lowerCAmelCase     ,							lowerCAmelCase     ,							lowerCAmelCase     ,							lowerCAmelCase = False     ,							lowerCAmelCase = 1E-20     ,							lowerCAmelCase = 1E8     ,							):
       _UpperCamelCase														=    batch['''template_pseudo_beta_mask''']
       _UpperCamelCase														=    template_mask[..., None] * template_mask[..., None, :]

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

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

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

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

       _UpperCamelCase							,		_UpperCamelCase							,		_UpperCamelCase														=    [rc.atom_order[a] for a in ['''N''', '''CA''', '''C''']]
       _UpperCamelCase														=    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=lowerCamelCase__     ,							)
       _UpperCamelCase														=    rigids.get_trans()[..., None, :, :]
       _UpperCamelCase														=    rigids[..., None].invert_apply(lowerCamelCase__       )

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

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

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

       if not use_unit_vector:
              _UpperCamelCase														=    unit_vector * 0.0

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

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

       return act


def      SCREAMING_SNAKE_CASE      (   lowerCAmelCase       ):
       _UpperCamelCase														=    nn.functional.one_hot(batch['''extra_msa''']     ,							23       )
       _UpperCamelCase														=    [
           msa_ahot,
           batch['''extra_has_deletion'''].unsqueeze(-1       ),
           batch['''extra_deletion_value'''].unsqueeze(-1       ),
       ]
       return torch.cat(lowerCamelCase__     ,							dim=-1       )


def      SCREAMING_SNAKE_CASE      (   lowerCAmelCase     ,							lowerCAmelCase     ,							lowerCAmelCase     ,							lowerCAmelCase     ,							):
       # [*, N, 8, 4, 4]
       _UpperCamelCase														=    rrgdf[aatype, ...]

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

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

       # [*, N, 8, 2]
       _UpperCamelCase														=    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.

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

       _UpperCamelCase														=    default_r.compose(Rigid(Rotation(rot_mats=lowerCamelCase__       )     ,							lowerCamelCase__       )       )

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

       _UpperCamelCase														=    all_frames[..., 4]
       _UpperCamelCase														=    chia_frame_to_bb.compose(lowerCamelCase__       )
       _UpperCamelCase														=    chia_frame_to_bb.compose(lowerCamelCase__       )
       _UpperCamelCase														=    chia_frame_to_bb.compose(lowerCamelCase__       )

       _UpperCamelCase														=    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     ,							)

       _UpperCamelCase														=    r[..., None].compose(lowerCamelCase__       )

       return all_frames_to_global


def      SCREAMING_SNAKE_CASE      (   lowerCAmelCase     ,							lowerCAmelCase     ,							lowerCAmelCase     ,							lowerCAmelCase     ,							lowerCAmelCase     ,							lowerCAmelCase     ,							):
       # [*, N, 14]
       _UpperCamelCase														=    group_idx[aatype, ...]

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

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

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

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

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

       return pred_positions











"""simple docstring"""







def 	lowerCAmelCase__      (  lowerCamelCase__      )			->				List[str]:
							A    =       [701, 301, 132, 57, 23, 10, 4, 1]
							for gap in gaps:
														for i in range(lowerCamelCase__					,   len(lowerCamelCase__      )      ):
																					A    =       collection[i]
																					A    =       i
																					while j >= gap and collection[j - gap] > insert_value:
																												A    =       collection[j - gap]
																												j -= gap
																					if j != i:
																												A    =       insert_value
							return collection


if __name__ == "__main__":
							from doctest import testmod

							testmod()
							A     =      input('Enter numbers separated by a comma:\n').strip()
							A     =      [int(item) for item in user_input.split(',')]
							print(shell_sort(unsorted))



