




from __future__ import annotations

import math
from collections import Counter
from string import ascii_lowercase


def 					_a							(					lowerCAmelCase )->	None:
		SCREAMING_SNAKE_CASE_      ,				SCREAMING_SNAKE_CASE_					      =							analyze_text(lowerCAmelCase )
		SCREAMING_SNAKE_CASE_					      =							list(' ' + ascii_lowercase )
		# what is our total sum of probabilities.
		SCREAMING_SNAKE_CASE_					      =							sum(single_char_strings.values() )

		# one length string
		SCREAMING_SNAKE_CASE_					      =							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_					      =							single_char_strings[ch]
						SCREAMING_SNAKE_CASE_					      =							my_str / all_sum
						my_fir_sum += prob * math.loga(lowerCAmelCase )  # entropy formula.

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

		# two len string
		SCREAMING_SNAKE_CASE_					      =							sum(two_char_strings.values() )
		SCREAMING_SNAKE_CASE_					      =							0
		# for each alpha (two in size) calculate entropy.
		for cha in my_alphas:
				for cha in my_alphas:
						SCREAMING_SNAKE_CASE_					      =							cha + cha
						if sequence in two_char_strings:
								SCREAMING_SNAKE_CASE_					      =							two_char_strings[sequence]
								SCREAMING_SNAKE_CASE_					      =							int(lowerCAmelCase ) / all_sum
								my_sec_sum += prob * math.loga(lowerCAmelCase )

    # 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							(					lowerCAmelCase )->	tuple[dict, dict]:
		SCREAMING_SNAKE_CASE_					      =							Counter()  # type: ignore
		SCREAMING_SNAKE_CASE_					      =							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(lowerCAmelCase ) - 1 ):
				single_char_strings[text[i]] += 1
				two_char_strings[text[i : i + 2]] += 1
		return single_char_strings, two_char_strings


def 					_a							(					)->	str:
		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()





from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch



@dataclass
class    lowercase_		:
						lowerCAmelCase__			      =42  # [batch_size x 3]
						lowerCAmelCase__			      =42  # [batch_size x 3]
						lowerCAmelCase__			      =42  # [batch_size x 3]
						lowerCAmelCase__			      =42  # [batch_size x 3]
						lowerCAmelCase__			      =42
						lowerCAmelCase__			      =42
						lowerCAmelCase__			      =42
						lowerCAmelCase__			      =42
						lowerCAmelCase__			      =42



						def 	__a					(			self	:   Optional[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	:   Union[str, Any]  ):

								"""simple docstring"""

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



						def 	__a					(			self	:   Optional[int]  ):

								"""simple docstring"""

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



						def 	__a					(			self	:   int  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							torch.arange(self.height * self.width  )
								SCREAMING_SNAKE_CASE_					      =							torch.stack(
								    [
								        pixel_indices % self.width,
								        torch.div(snake_case__					,							self.width					,							rounding_mode='trunc'  ),
								    ]					,							axis=1					,							)
								return coords



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

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_      ,				*SCREAMING_SNAKE_CASE_					      =							self.shape
								SCREAMING_SNAKE_CASE_					      =							int(np.prod(snake_case__  )  )

								SCREAMING_SNAKE_CASE_					      =							self.get_image_coords()
								SCREAMING_SNAKE_CASE_					      =							torch.broadcast_to(coords.unsqueeze(0  )					,							[batch_size * inner_batch_size, *coords.shape]  )
								SCREAMING_SNAKE_CASE_					      =							self.get_camera_rays(snake_case__  )

								SCREAMING_SNAKE_CASE_					      =							rays.view(snake_case__					,							inner_batch_size * self.height * self.width					,							2					,							3  )

								return rays



						def 	__a					(			self	:   Optional[Any]					,							snake_case__	:   torch.Tensor  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_      ,				*SCREAMING_SNAKE_CASE_      ,				SCREAMING_SNAKE_CASE_					      =							coords.shape
								assert n_coords == 2
								assert batch_size == self.origin.shape[0]

								SCREAMING_SNAKE_CASE_					      =							coords.view(snake_case__					,							-1					,							2  )

								SCREAMING_SNAKE_CASE_					      =							self.resolution()
								SCREAMING_SNAKE_CASE_					      =							self.fov()

								SCREAMING_SNAKE_CASE_					      =							(flat.float() / (res - 1)) * 2 - 1
								SCREAMING_SNAKE_CASE_					      =							fracs * torch.tan(fov / 2  )

								SCREAMING_SNAKE_CASE_					      =							fracs.view(snake_case__					,							-1					,							2  )
								SCREAMING_SNAKE_CASE_					      =							(
								    self.z.view(snake_case__					,							1					,							3  )
								    + self.x.view(snake_case__					,							1					,							3  ) * fracs[:, :, :1]
								    + self.y.view(snake_case__					,							1					,							3  ) * fracs[:, :, 1:]
								)
								SCREAMING_SNAKE_CASE_					      =							directions / directions.norm(dim=-1					,							keepdim=snake_case__  )
								SCREAMING_SNAKE_CASE_					      =							torch.stack(
								    [
								        torch.broadcast_to(self.origin.view(snake_case__					,							1					,							3  )					,							[batch_size, directions.shape[1], 3]  ),
								        directions,
								    ]					,							dim=2					,							)
								return rays.view(snake_case__					,							*snake_case__					,							2					,							3  )






						def 	__a					(			self	:   Optional[int]					,							snake_case__	:   int					,							snake_case__	:   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=snake_case__					,							height=snake_case__					,							x_fov=self.x_fov					,							y_fov=self.y_fov					,							)


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