




from typing import Dict, Optional, Tuple

import torch




def        __SCREAMING_SNAKE_CASE (	lowercase_   )							->						Optional[int]:

    """simple docstring"""


    __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        __SCREAMING_SNAKE_CASE (	lowercase_       ,  lowercase_       ,  )							->						Optional[int]:

    """simple docstring"""


    __UpperCamelCase			=    _calculate_bin_centers(lowercase_   )
    return (
        torch.sum(aligned_distance_error_probs * bin_centers       ,  dim=-1   ),
        bin_centers[-1],
    )




def        __SCREAMING_SNAKE_CASE (	lowercase_       ,  lowercase_ = 31       ,  lowercase_ = 64       ,  **lowercase_       ,  )							->						Dict:

    """simple docstring"""


    __UpperCamelCase			=    torch.linspace(0       ,  lowercase_       ,  steps=(no_bins - 1)       ,  device=logits.device   )

    __UpperCamelCase			=    torch.nn.functional.softmax(lowercase_       ,  dim=-1   )
    __UpperCamelCase		,   __UpperCamelCase			=    _calculate_expected_aligned_error(
        alignment_confidence_breaks=lowercase_       ,  aligned_distance_error_probs=lowercase_       ,  )

    return {
        "aligned_confidence_probs": aligned_confidence_probs,
        "predicted_aligned_error": predicted_aligned_error,
        "max_predicted_aligned_error": max_predicted_aligned_error,
    }




def        __SCREAMING_SNAKE_CASE (	lowercase_       ,  lowercase_ = None       ,  lowercase_ = 31       ,  lowercase_ = 64       ,  lowercase_ = 1E-8       ,  **lowercase_       ,  )							->						List[str]:

    """simple docstring"""


    if residue_weights is None:
        __UpperCamelCase			=    logits.new_ones(logits.shape[-2]   )

    __UpperCamelCase			=    torch.linspace(0       ,  lowercase_       ,  steps=(no_bins - 1)       ,  device=logits.device   )

    __UpperCamelCase			=    _calculate_bin_centers(lowercase_   )
    torch.sum(lowercase_   )
    __UpperCamelCase			=    logits.shape[-2]
    __UpperCamelCase			=    max(lowercase_       ,  19   )

    __UpperCamelCase			=    1.24 * (clipped_n - 15) ** (1.0 / 3) - 1.8

    __UpperCamelCase			=    torch.nn.functional.softmax(lowercase_       ,  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(lowercase_   )).nonzero()[0]
    return per_alignment[tuple(lowercase_   )]







"""simple docstring"""






from __future__ import annotations



def     a_		(   lowerCamelCase			):
				for r in range(1   ,     lowerCamelCase			):
								UpperCAmelCase__			 =				[]
								for x in range(n - 1			):
												UpperCAmelCase__			 =				pow(lowerCamelCase   ,     lowerCamelCase   ,     lowerCamelCase			)
												if val in li:
																break
												li.append(lowerCamelCase			)
								else:
												return r
				return None


if __name__ == "__main__":
						lowerCAmelCase__    :    Any			=      int(input('Enter a prime number q: '))
						lowerCAmelCase__    :    List[str]			=      find_primitive(q)
						if a is None:
												print(F"""Cannot find the primitive for the value: {a!r}""")
						else:
												lowerCAmelCase__    :    str			=      int(input('Enter private key of A: '))
												lowerCAmelCase__    :    List[Any]			=      pow(a, a_private, q)
												lowerCAmelCase__    :    List[str]			=      int(input('Enter private key of B: '))
												lowerCAmelCase__    :    Any			=      pow(a, b_private, q)

												lowerCAmelCase__    :    Union[str, Any]			=      pow(b_public, a_private, q)
												lowerCAmelCase__    :    Tuple			=      pow(a_public, b_private, q)

												print('The key value generated by A is: ', a_secret)
												print('The key value generated by B is: ', b_secret)



