code: 
  
  
  
  
  
  
  """simple docstring"""
  
  
  
  
  
  
  from typing import Dict, Optional, Tuple
  
  import torch
  
  
  
  
  def 						_UpperCamelCase			(  A			):
     UpperCamelCase_     =boundaries[1] - boundaries[0]
     UpperCamelCase_     =boundaries + step / 2
     UpperCamelCase_     =torch.cat([bin_centers, (bin_centers[-1] + step).unsqueeze(-1			)]    ,       dim=0			)
     return bin_centers
  
  
  
  
  def 						_UpperCamelCase			(  A    ,       A    ,       ):
     UpperCamelCase_     =_calculate_bin_centers(A			)
     return (
         torch.sum(aligned_distance_error_probs * bin_centers    ,       dim=-1			),
         bin_centers[-1],
     )
  
  
  
  
  def 						_UpperCamelCase			(  A    ,       A = 31    ,       A = 64    ,       **A    ,       ):
     UpperCamelCase_     =torch.linspace(0    ,       A    ,       steps=(no_bins - 1)    ,       device=logits.device			)
  
     UpperCamelCase_     =torch.nn.functional.softmax(A    ,       dim=-1			)
     UpperCamelCase_     =_calculate_expected_aligned_error(
         alignment_confidence_breaks=A    ,       aligned_distance_error_probs=A    ,       )
  
     return {
         "aligned_confidence_probs": aligned_confidence_probs,
         "predicted_aligned_error": predicted_aligned_error,
         "max_predicted_aligned_error": max_predicted_aligned_error,
     }
  
  
  
  
  def 						_UpperCamelCase			(  A    ,       A = None    ,       A = 31    ,       A = 64    ,       A = 1e-8    ,       **A    ,       ):
  
  
  
     if residue_weights is None:
        UpperCamelCase_     =logits.new_ones(logits.shape[-2]			)
  
     UpperCamelCase_     =torch.linspace(0    ,       A    ,       steps=(no_bins - 1)    ,       device=logits.device			)
  
     UpperCamelCase_     =_calculate_bin_centers(A			)
     torch.sum(A			)
     UpperCamelCase_     =logits.shape[-2]
     UpperCamelCase_     =max(A    ,       19			)
  
     UpperCamelCase_     =1.24 * (clipped_n - 15) ** (1.0 / 3) - 1.8
  
     UpperCamelCase_     =torch.nn.functional.softmax(A    ,       dim=-1			)
  
     UpperCamelCase_     =1.0 / (1 + (bin_centers**2) / (da**2))
     UpperCamelCase_     =torch.sum(probs * tm_per_bin    ,       dim=-1			)
  
     UpperCamelCase_     =residue_weights / (eps + residue_weights.sum())
     UpperCamelCase_     =torch.sum(predicted_tm_term * normed_residue_mask    ,       dim=-1			)
  
     UpperCamelCase_     =per_alignment * residue_weights
  
     UpperCamelCase_     =(weighted == torch.max(A			)).nonzero()[0]
     return per_alignment[tuple(A			)]
  
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  
  """simple docstring"""
  
  
  
  
  
  
  from collections import defaultdict
  
  
  
  
  def 						_UpperCamelCase			(  A = 5			):
     UpperCamelCase_     =defaultdict(A			)
     UpperCamelCase_     =0
  
     while True:
        UpperCamelCase_     =get_digits(A			)
        freqs[digits].append(A			)
  
        if len(freqs[digits]			) == max_base:
           UpperCamelCase_     =freqs[digits][0] ** 3
           return base
  
        num += 1
  
  
  
  
  def 						_UpperCamelCase			(  A			):
     return "".join(sorted(str(num**3			)			)			)
  
  
  if __name__ == "__main__":
      print(f'''{solution() = }''')
  