




'''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 				SCREAMING_SNAKE_CASE_				(							__A       :				torch.Tensor ,  __A       :				torch.Tensor ,  __A       :				None						)				->				torch.Tensor:
   ...
@overload
def 				SCREAMING_SNAKE_CASE_				(							__A       :				torch.Tensor ,  __A       :				torch.Tensor ,  __A       :				torch.Tensor						)				->				Tuple[torch.Tensor, torch.Tensor]:
   ...
def 				SCREAMING_SNAKE_CASE_				(							__A       :				int ,  __A       :				Any ,  __A       :				str						)				->				Any:
   _SCREAMING_SNAKE_CASE =   aatype == rc.restype_order["G"]
   _SCREAMING_SNAKE_CASE =   rc.atom_order["CA"]
   _SCREAMING_SNAKE_CASE =   rc.atom_order["CB"]
   _SCREAMING_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:
      _SCREAMING_SNAKE_CASE =   torch.where(
          __A ,  all_atom_masks[..., ca_idx] ,  all_atom_masks[..., cb_idx] ,  )
      return pseudo_beta, pseudo_beta_mask
   else:
      return pseudo_beta
def 				SCREAMING_SNAKE_CASE_				(							__A       :				torch.Tensor ,  __A       :				Dict[str, torch.Tensor]						)				->				torch.Tensor:
   _SCREAMING_SNAKE_CASE =   batched_gather(
       __A ,  batch["residx_atom37_to_atom14"] ,  dim=-2 ,  no_batch_dims=len(atomaa.shape[:-2]						) ,  )

   _SCREAMING_SNAKE_CASE =   atomaa_data * batch["atom37_atom_exists"][..., None]

   return atomaa_data
def 				SCREAMING_SNAKE_CASE_				(							__A       :				Dict[str, torch.Tensor]						)				->				torch.Tensor:
   _SCREAMING_SNAKE_CASE =   template_feats["template_aatype"]
   _SCREAMING_SNAKE_CASE =   template_feats["template_torsion_angles_sin_cos"]
   _SCREAMING_SNAKE_CASE =   template_feats["template_alt_torsion_angles_sin_cos"]
   _SCREAMING_SNAKE_CASE =   template_feats["template_torsion_angles_mask"]
   _SCREAMING_SNAKE_CASE =   torch.cat(
       [
           nn.functional.one_hot(__A ,  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_				(							__A       :				Dict[str, torch.Tensor] ,  __A       :				torch.types.Number ,  __A       :				torch.types.Number ,  __A       :				int ,  __A       :				bool = False ,  __A       :				float = 1e-20 ,  __A       :				float = 1e8 ,  )				->				torch.Tensor:
   _SCREAMING_SNAKE_CASE =   batch["template_pseudo_beta_mask"]
   _SCREAMING_SNAKE_CASE =   template_mask[..., None] * template_mask[..., None, :]

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

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

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

   _SCREAMING_SNAKE_CASE =   batch["template_aatype"].shape[-1]
   to_concat.append(aatype_one_hot[..., None, :, :].expand(*aatype_one_hot.shape[:-2] ,  __A ,  -1 ,  -1						)						)
   to_concat.append(aatype_one_hot[..., None, :].expand(*aatype_one_hot.shape[:-2] ,  -1 ,  __A ,  -1						)						)

   _SCREAMING_SNAKE_CASE, _SCREAMING_SNAKE_CASE, _SCREAMING_SNAKE_CASE =   [rc.atom_order[a] for a in ["N", "CA", "C"]]
   _SCREAMING_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=__A ,  )
   _SCREAMING_SNAKE_CASE =   rigids.get_trans()[..., None, :, :]
   _SCREAMING_SNAKE_CASE =   rigids[..., None].invert_apply(__A						)

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

   _SCREAMING_SNAKE_CASE =   batch["template_all_atom_mask"]
   _SCREAMING_SNAKE_CASE =   t_aa_masks[..., n] * t_aa_masks[..., ca] * t_aa_masks[..., c]
   _SCREAMING_SNAKE_CASE =   template_mask[..., None] * template_mask[..., None, :]

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

   if not use_unit_vector:
      _SCREAMING_SNAKE_CASE =   unit_vector * 0.0

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

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

   return act
def 				SCREAMING_SNAKE_CASE_				(							__A       :				Dict[str, torch.Tensor]						)				->				torch.Tensor:
   _SCREAMING_SNAKE_CASE =   nn.functional.one_hot(batch["extra_msa"] ,  23						)
   _SCREAMING_SNAKE_CASE =   [
       msa_ahot,
       batch["extra_has_deletion"].unsqueeze(-1						),
       batch["extra_deletion_value"].unsqueeze(-1						),
   ]
   return torch.cat(__A ,  dim=-1						)
def 				SCREAMING_SNAKE_CASE_				(							__A       :				Rigid ,  __A       :				torch.Tensor ,  __A       :				torch.Tensor ,  __A       :				torch.Tensor ,  )				->				Rigid:
   # [*, N, 8, 4, 4]
   _SCREAMING_SNAKE_CASE =   rrgdf[aatype, ...]

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

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

   # [*, N, 8, 2]
   _SCREAMING_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.

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

   _SCREAMING_SNAKE_CASE =   default_r.compose(Rigid(Rotation(rot_mats=__A						) ,  __A						)						)

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

   _SCREAMING_SNAKE_CASE =   all_frames[..., 4]
   _SCREAMING_SNAKE_CASE =   chia_frame_to_bb.compose(__A						)
   _SCREAMING_SNAKE_CASE =   chia_frame_to_bb.compose(__A						)
   _SCREAMING_SNAKE_CASE =   chia_frame_to_bb.compose(__A						)

   _SCREAMING_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 ,  )

   _SCREAMING_SNAKE_CASE =   r[..., None].compose(__A						)

   return all_frames_to_global






def 				SCREAMING_SNAKE_CASE_				(							__A       :				Rigid ,  __A       :				torch.Tensor ,  __A       :				torch.Tensor ,  __A       :				torch.Tensor ,  __A       :				torch.Tensor ,  __A       :				torch.Tensor ,  )				->				torch.Tensor:
   # [*, N, 14]
   _SCREAMING_SNAKE_CASE =   group_idx[aatype, ...]

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

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

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

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

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

   return pred_positions







'''simple docstring'''



def 				SCREAMING_SNAKE_CASE_				(							__A       :				List[Any] ,  __A       :				Dict						)				->				Union[str, Any]:
   if n == 0:
      return 1

   elif n % 2 == 1:
      return binary_exponentiation(__A ,  n - 1						) * a

   else:
      _SCREAMING_SNAKE_CASE =   binary_exponentiation(__A ,  n / 2						)
      return b * b


if __name__ == "__main__":
 try:
  lowerCamelCase_	 =		int(input('Enter Base : ').strip())
  lowerCamelCase_	 =		int(input('Enter Power : ').strip())
 except ValueError:
  print('Invalid literal for integer')

 lowerCamelCase_	 =		binary_exponentiation(BASE, POWER)
 print(f'''{BASE}^({POWER}) : {RESULT}''')

