"""simple docstring"""







from typing import Dict, Optional, Tuple

import torch


def      a__					(						UpperCAmelCase__				:	torch.Tensor	)->		Optional[Any]:
						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      a__					(						UpperCAmelCase__				:	torch.Tensor						,	UpperCAmelCase__				:	torch.Tensor						,	)->		List[Any]:
						UpperCAmelCase__    		=						_calculate_bin_centers(UpperCamelCase__	)
						return (
						    torch.sum(aligned_distance_error_probs * bin_centers						,	dim=-1	),
						    bin_centers[-1],
						)


def      a__					(						UpperCAmelCase__				:	torch.Tensor						,	UpperCAmelCase__				:	int = 3_1						,	UpperCAmelCase__				:	int = 6_4						,	**UpperCAmelCase__				:	Tuple						,	)->		Tuple:
						UpperCAmelCase__    		=						torch.linspace(0						,	UpperCamelCase__						,	steps=(no_bins - 1)						,	device=logits.device	)

						UpperCAmelCase__    		=						torch.nn.functional.softmax(UpperCamelCase__						,	dim=-1	)
						UpperCAmelCase__		,					UpperCAmelCase__    		=						_calculate_expected_aligned_error(
						    alignment_confidence_breaks=UpperCamelCase__						,	aligned_distance_error_probs=UpperCamelCase__						,	)

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







def      a__					(						UpperCAmelCase__				:	torch.Tensor						,	UpperCAmelCase__				:	Optional[torch.Tensor] = None						,	UpperCAmelCase__				:	int = 3_1						,	UpperCAmelCase__				:	int = 6_4						,	UpperCAmelCase__				:	float = 1e-8						,	**UpperCAmelCase__				:	Dict						,	)->		Optional[int]:
						if residue_weights is None:
												UpperCAmelCase__    		=						logits.new_ones(logits.shape[-2]	)

						UpperCAmelCase__    		=						torch.linspace(0						,	UpperCamelCase__						,	steps=(no_bins - 1)						,	device=logits.device	)

						UpperCAmelCase__    		=						_calculate_bin_centers(UpperCamelCase__	)
						torch.sum(UpperCamelCase__	)
						UpperCAmelCase__    		=						logits.shape[-2]
						UpperCAmelCase__    		=						max(UpperCamelCase__						,	1_9	)

						UpperCAmelCase__    		=						1.24 * (clipped_n - 1_5) ** (1.0 / 3) - 1.8

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








from __future__ import annotations

import math
import random






def  SCREAMING_SNAKE_CASE__							(				UpperCamelCase__:							int    ,      UpperCamelCase__:							int    ,      UpperCamelCase__:							int			):
		SCREAMING_SNAKE_CASE__								=					d * e - 1
		SCREAMING_SNAKE_CASE__								=					0
		SCREAMING_SNAKE_CASE__								=					0
		while p == 0:
				SCREAMING_SNAKE_CASE__								=					random.randint(2    ,      n - 1			)
				SCREAMING_SNAKE_CASE__								=					k
				while True:
						if t % 2 == 0:
								SCREAMING_SNAKE_CASE__								=					t // 2
								SCREAMING_SNAKE_CASE__								=					(g**t) % n
								SCREAMING_SNAKE_CASE__								=					math.gcd(x - 1    ,      UpperCamelCase__			)
								if x > 1 and y > 1:
										SCREAMING_SNAKE_CASE__								=					y
										SCREAMING_SNAKE_CASE__								=					n // y
										break  # find the correct factors
						else:
								break  # t is not divisible by 2, break and choose another g
		return sorted([p, q]			)


if __name__ == "__main__":
	import doctest

	doctest.testmod()