from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch





@dataclass
class       lowercase__		:
						UpperCamelCase_  =	42  # [batch_size x 3]
						UpperCamelCase_  =	42  # [batch_size x 3]
						UpperCamelCase_  =	42  # [batch_size x 3]
						UpperCamelCase_  =	42  # [batch_size x 3]
						UpperCamelCase_  =	42
						UpperCamelCase_  =	42
						UpperCamelCase_  =	42
						UpperCamelCase_  =	42
						UpperCamelCase_  =	42


						def  __A ( self			:       List[Any]		):





												'''simple docstring'''





												assert self.x.shape[0] == self.y.shape[0] == self.z.shape[0] == self.origin.shape[0]
												assert self.x.shape[1] == self.y.shape[1] == self.z.shape[1] == self.origin.shape[1] == 3
												assert len(self.x.shape		) == len(self.y.shape		) == len(self.z.shape		) == len(self.origin.shape		) == 2


						def  __A ( self			:       str		):





												'''simple docstring'''





												return torch.from_numpy(np.array([self.width, self.height]					,	dtype=np.floataa		)		)


						def  __A ( self			:       List[Any]		):





												'''simple docstring'''





												return torch.from_numpy(np.array([self.x_fov, self.y_fov]					,	dtype=np.floataa		)		)


						def  __A ( self			:       str		):





												'''simple docstring'''





												SCREAMING_SNAKE_CASE							:					List[str]           =							torch.arange(self.height * self.width		)
												SCREAMING_SNAKE_CASE							:					List[str]           =							torch.stack(
												    [
												        pixel_indices % self.width,
												        torch.div(UpperCamelCase__					,	self.width					,	rounding_mode='''trunc'''		),
												    ]					,	axis=1					,	)
												return coords


						@property
						def  __A ( self			:       List[Any]		):





												'''simple docstring'''





												SCREAMING_SNAKE_CASE       ,						*SCREAMING_SNAKE_CASE							:					List[Any]           =							self.shape
												SCREAMING_SNAKE_CASE							:					List[str]           =							int(np.prod(UpperCamelCase__		)		)

												SCREAMING_SNAKE_CASE							:					Union[str, Any]           =							self.get_image_coords()
												SCREAMING_SNAKE_CASE							:					List[str]           =							torch.broadcast_to(coords.unsqueeze(0		)					,	[batch_size * inner_batch_size, *coords.shape]		)
												SCREAMING_SNAKE_CASE							:					List[str]           =							self.get_camera_rays(UpperCamelCase__		)

												SCREAMING_SNAKE_CASE							:					str           =							rays.view(UpperCamelCase__					,	inner_batch_size * self.height * self.width					,	2					,	3		)

												return rays


						def  __A ( self			:       Dict					,	UpperCamelCase__			:       torch.Tensor		):





												'''simple docstring'''





												SCREAMING_SNAKE_CASE       ,						*SCREAMING_SNAKE_CASE       ,						SCREAMING_SNAKE_CASE							:					Optional[Any]           =							coords.shape
												assert n_coords == 2
												assert batch_size == self.origin.shape[0]

												SCREAMING_SNAKE_CASE							:					Union[str, Any]           =							coords.view(UpperCamelCase__					,	-1					,	2		)

												SCREAMING_SNAKE_CASE							:					Any           =							self.resolution()
												SCREAMING_SNAKE_CASE							:					str           =							self.fov()

												SCREAMING_SNAKE_CASE							:					str           =							(flat.float() / (res - 1)) * 2 - 1
												SCREAMING_SNAKE_CASE							:					List[str]           =							fracs * torch.tan(fov / 2		)

												SCREAMING_SNAKE_CASE							:					int           =							fracs.view(UpperCamelCase__					,	-1					,	2		)
												SCREAMING_SNAKE_CASE							:					Optional[Any]           =							(
												    self.z.view(UpperCamelCase__					,	1					,	3		)
												    + self.x.view(UpperCamelCase__					,	1					,	3		) * fracs[:, :, :1]
												    + self.y.view(UpperCamelCase__					,	1					,	3		) * fracs[:, :, 1:]
												)
												SCREAMING_SNAKE_CASE							:					Tuple           =							directions / directions.norm(dim=-1					,	keepdim=UpperCamelCase__		)
												SCREAMING_SNAKE_CASE							:					Union[str, Any]           =							torch.stack(
												    [
												        torch.broadcast_to(self.origin.view(UpperCamelCase__					,	1					,	3		)					,	[batch_size, directions.shape[1], 3]		),
												        directions,
												    ]					,	dim=2					,	)
												return rays.view(UpperCamelCase__					,	*UpperCamelCase__					,	2					,	3		)



						def  __A ( self			:       Union[str, Any]					,	UpperCamelCase__			:       int					,	UpperCamelCase__			:       int		):





												'''simple docstring'''





												assert width * self.height == height * self.width, "The aspect ratio should not change."
												return DifferentiableProjectiveCamera(
												    origin=self.origin					,	x=self.x					,	y=self.y					,	z=self.z					,	width=UpperCamelCase__					,	height=UpperCamelCase__					,	x_fov=self.x_fov					,	y_fov=self.y_fov					,	)






def    A			(					_lowercase		):
						SCREAMING_SNAKE_CASE							:					Tuple           =							[]
						SCREAMING_SNAKE_CASE							:					Dict           =							[]
						SCREAMING_SNAKE_CASE							:					List[str]           =							[]
						SCREAMING_SNAKE_CASE							:					Tuple           =							[]
						for theta in np.linspace(0	,						2 * np.pi	,						num=20		):
												SCREAMING_SNAKE_CASE							:					int           =							np.array([np.sin(_lowercase		), np.cos(_lowercase		), -0.5]		)
												z /= np.sqrt(np.sum(z**2		)		)
												SCREAMING_SNAKE_CASE							:					Tuple           =							-z * 4
												SCREAMING_SNAKE_CASE							:					Optional[int]           =							np.array([np.cos(_lowercase		), -np.sin(_lowercase		), 0.0]		)
												SCREAMING_SNAKE_CASE							:					Tuple           =							np.cross(_lowercase	,						_lowercase		)
												origins.append(_lowercase		)
												xs.append(_lowercase		)
												ys.append(_lowercase		)
												zs.append(_lowercase		)
						return DifferentiableProjectiveCamera(
						    origin=torch.from_numpy(np.stack(_lowercase	,						axis=0		)		).float()	,						x=torch.from_numpy(np.stack(_lowercase	,						axis=0		)		).float()	,						y=torch.from_numpy(np.stack(_lowercase	,						axis=0		)		).float()	,						z=torch.from_numpy(np.stack(_lowercase	,						axis=0		)		).float()	,						width=_lowercase	,						height=_lowercase	,						x_fov=0.7	,						y_fov=0.7	,						shape=(1, len(_lowercase		))	,						)






from __future__ import annotations

import math
from collections import Counter
from string import ascii_lowercase
def    A			(					_lowercase		):
						SCREAMING_SNAKE_CASE       ,						SCREAMING_SNAKE_CASE							:					Union[str, Any]           =							analyze_text(_lowercase		)
						SCREAMING_SNAKE_CASE							:					Any           =							list(''' ''' + ascii_lowercase		)
						# what is our total sum of probabilities.
						SCREAMING_SNAKE_CASE							:					Tuple           =							sum(single_char_strings.values()		)

						# one length string
						SCREAMING_SNAKE_CASE							:					Tuple           =							0
						# for each alpha we go in our dict and if it is in it we calculate entropy
						for ch in my_alphas:
												if ch in single_char_strings:
																		SCREAMING_SNAKE_CASE							:					Tuple           =							single_char_strings[ch]
																		SCREAMING_SNAKE_CASE							:					List[str]           =							my_str / all_sum
																		my_fir_sum += prob * math.loga(_lowercase		)  # entropy formula.

    # print entropy
						print(f"""{round(-1 * my_fir_sum		):.1f}"""		)

						# two len string
						SCREAMING_SNAKE_CASE							:					Optional[Any]           =							sum(two_char_strings.values()		)
						SCREAMING_SNAKE_CASE							:					List[str]           =							0
						# for each alpha (two in size) calculate entropy.
						for cha in my_alphas:
												for cha in my_alphas:
																		SCREAMING_SNAKE_CASE							:					Union[str, Any]           =							cha + cha
																		if sequence in two_char_strings:
																								SCREAMING_SNAKE_CASE							:					Any           =							two_char_strings[sequence]
																								SCREAMING_SNAKE_CASE							:					Dict           =							int(_lowercase		) / all_sum
																								my_sec_sum += prob * math.loga(_lowercase		)

    # print second entropy
						print(f"""{round(-1 * my_sec_sum		):.1f}"""		)

						# print the difference between them
						print(f"""{round((-1 * my_sec_sum) - (-1 * my_fir_sum)		):.1f}"""		)
def    A			(					_lowercase		):
						SCREAMING_SNAKE_CASE							:					Tuple           =							Counter()  # type: ignore
						SCREAMING_SNAKE_CASE							:					Any           =							Counter()  # type: ignore
						single_char_strings[text[-1]] += 1

						# first case when we have space at start.
						two_char_strings[" " + text[0]] += 1
						for i in range(0	,						len(_lowercase		) - 1		):
												single_char_strings[text[i]] += 1
												two_char_strings[text[i : i + 2]] += 1
						return single_char_strings, two_char_strings
def    A			(					):
						import doctest

						doctest.testmod()
						# text = (
						#     "Had repulsive dashwoods suspicion sincerity but advantage now him. Remark "
						#     "easily garret nor nay. Civil those mrs enjoy shy fat merry. You greatest "
						#     "jointure saw horrible. He private he on be imagine suppose. Fertile "
						#     "beloved evident through no service elderly is. Blind there if every no so "
						#     "at. Own neglected you preferred way sincerity delivered his attempted. To "
						#     "of message cottage windows do besides against uncivil.  Delightful "
						#     "unreserved impossible few estimating men favourable see entreaties. She "
						#     "propriety immediate was improving. He or entrance humoured likewise "
						#     "moderate. Much nor game son say feel. Fat make met can must form into "
						#     "gate. Me we offending prevailed discovery. "
						# )

						# calculate_prob(text)


if __name__ == "__main__":
					main()





