



'''simple docstring'''






import string

# frequency taken from https://en.wikipedia.org/wiki/Letter_frequency
UpperCamelCase__:   str								=			{
    "E": 12.70,
    "T": 9.06,
    "A": 8.17,
    "O": 7.51,
    "I": 6.97,
    "N": 6.75,
    "S": 6.33,
    "H": 6.09,
    "R": 5.99,
    "D": 4.25,
    "L": 4.03,
    "C": 2.78,
    "U": 2.76,
    "M": 2.41,
    "W": 2.36,
    "F": 2.23,
    "G": 2.02,
    "Y": 1.97,
    "P": 1.93,
    "B": 1.29,
    "V": 0.98,
    "K": 0.77,
    "J": 0.15,
    "X": 0.15,
    "Q": 0.10,
    "Z": 0.07,
}
UpperCamelCase__:   Tuple								=			"ETAOINSHRDLCUMWFGYPBVKJXQZ"
UpperCamelCase__:   Any								=			"ABCDEFGHIJKLMNOPQRSTUVWXYZ"


def  snake_case_     (					_lowerCAmelCase  :						str  )      ->   dict[str, int]:
							UpperCAmelCase :       List[Any] 							=		{letter: 0 for letter in string.ascii_uppercase}
							for letter in message.upper():
														if letter in LETTERS:
																					letter_count[letter] += 1

							return letter_count


def  snake_case_     (					_lowerCAmelCase  :						tuple  )      ->   str:
							return x[0]


def  snake_case_     (					_lowerCAmelCase  :						str  )      ->   str:
							UpperCAmelCase :       Tuple 							=		get_letter_count(_lowerCAmelCase  )
							UpperCAmelCase :       dict[int, list[str]] 							=		{
							    freq: [] for letter, freq in letter_to_freq.items()
							}
							for letter in LETTERS:
														freq_to_letter[letter_to_freq[letter]].append(_lowerCAmelCase  )

							UpperCAmelCase :       dict[int, str] 							=		{}

							for freq in freq_to_letter:
														freq_to_letter[freq].sort(key=ETAOIN.find   ,      reverse=_lowerCAmelCase  )
														UpperCAmelCase :       Tuple 							=		''''''.join(freq_to_letter[freq]  )

							UpperCAmelCase :       Tuple 							=		list(freq_to_letter_str.items()  )
							freq_pairs.sort(key=_lowerCAmelCase   ,      reverse=_lowerCAmelCase  )

							UpperCAmelCase :       list[str] 							=		[freq_pair[1] for freq_pair in freq_pairs]

							return "".join(_lowerCAmelCase  )


def  snake_case_     (					_lowerCAmelCase  :						str  )      ->   int:
							UpperCAmelCase :       Dict 							=		get_frequency_order(_lowerCAmelCase  )
							UpperCAmelCase :       Any 							=		0
							for common_letter in ETAOIN[:6]:
														if common_letter in freq_order[:6]:
																					match_score += 1

							for uncommon_letter in ETAOIN[-6:]:
														if uncommon_letter in freq_order[-6:]:
																					match_score += 1

							return match_score


if __name__ == "__main__":
						import doctest

						doctest.testmod()










'''simple docstring'''






from __future__ import annotations

import matplotlib.pyplot as plt  # type: ignore
import numpy

# initial triangle of Koch snowflake
UpperCamelCase__:   Tuple								=			numpy.array([0, 0])
UpperCamelCase__:   Union[str, Any]								=			numpy.array([0.5, 0.8660254])
UpperCamelCase__:   Dict								=			numpy.array([1, 0])
UpperCamelCase__:   int								=			[VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]


def  snake_case_     (					_lowerCAmelCase  :						list[numpy.ndarray]   ,      _lowerCAmelCase  :						int  )      ->   list[numpy.ndarray]:
							UpperCAmelCase :       Union[str, Any] 							=		initial_vectors
							for _ in range(_lowerCAmelCase  ):
														UpperCAmelCase :       Union[str, Any] 							=		iteration_step(_lowerCAmelCase  )
							return vectors


def  snake_case_     (					_lowerCAmelCase  :						list[numpy.ndarray]  )      ->   list[numpy.ndarray]:
							UpperCAmelCase :       Tuple 							=		[]
							for i, start_vector in enumerate(vectors[:-1]  ):
														UpperCAmelCase :       List[str] 							=		vectors[i + 1]
														new_vectors.append(_lowerCAmelCase  )
														UpperCAmelCase :       Optional[Any] 							=		end_vector - start_vector
														new_vectors.append(start_vector + difference_vector / 3  )
														new_vectors.append(
														    start_vector + difference_vector / 3 + rotate(difference_vector / 3   ,      60  )  )
														new_vectors.append(start_vector + difference_vector * 2 / 3  )
							new_vectors.append(vectors[-1]  )
							return new_vectors


def  snake_case_     (					_lowerCAmelCase  :						numpy.ndarray   ,      _lowerCAmelCase  :						float  )      ->   numpy.ndarray:
							UpperCAmelCase :       List[str] 							=		numpy.radians(_lowerCAmelCase  )
							UpperCAmelCase							,		UpperCAmelCase :       Tuple 							=		numpy.cos(_lowerCAmelCase  ), numpy.sin(_lowerCAmelCase  )
							UpperCAmelCase :       Union[str, Any] 							=		numpy.array(((c, -s), (s, c))  )
							return numpy.dot(_lowerCAmelCase   ,      _lowerCAmelCase  )


def  snake_case_     (					_lowerCAmelCase  :						list[numpy.ndarray]  )      ->   None:
							UpperCAmelCase :       List[Any] 							=		plt.gca()
							axes.set_aspect('''equal'''  )

							# matplotlib.pyplot.plot takes a list of all x-coordinates and a list of all
							# y-coordinates as inputs, which are constructed from the vector-list using
							# zip()
							UpperCAmelCase							,		UpperCAmelCase :       str 							=		zip(*_lowerCAmelCase  )
							plt.plot(_lowerCAmelCase   ,      _lowerCAmelCase  )
							plt.show()


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						UpperCamelCase__:   List[Any]								=			iterate(INITIAL_VECTORS, 5)
						plot(processed_vectors)





