


"""simple docstring"""







import sys
def 					a__			(				SCREAMING_SNAKE_CASE    :    Optional[Any]				):


  '''simple docstring'''







  lowerCAmelCase     :     Union[str, Any]								=							len(SCREAMING_SNAKE_CASE				)
  lowerCAmelCase     :     Any								=							[[0 for x in range(SCREAMING_SNAKE_CASE				)] for x in range(SCREAMING_SNAKE_CASE				)]
  lowerCAmelCase     :     Tuple								=							[[0 for x in range(SCREAMING_SNAKE_CASE				)] for x in range(SCREAMING_SNAKE_CASE				)]

  for chain_length in range(2				,      SCREAMING_SNAKE_CASE				):
    for a in range(1				,      n - chain_length + 1				):
      lowerCAmelCase     :     List[Any]								=							a + chain_length - 1

      lowerCAmelCase     :     List[Any]								=							sys.maxsize
      for c in range(SCREAMING_SNAKE_CASE				,      SCREAMING_SNAKE_CASE				):
        lowerCAmelCase     :     Union[str, Any]								=							(
            matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
        )
        if cost < matrix[a][b]:
          lowerCAmelCase     :     str								=							cost
          lowerCAmelCase     :     Optional[int]								=							c
  return matrix, sol
def 					a__			(				SCREAMING_SNAKE_CASE    :    Optional[int]				,      SCREAMING_SNAKE_CASE    :    Union[str, Any]				,      SCREAMING_SNAKE_CASE    :    str				):


  '''simple docstring'''







  if i == j:
    print("A" + str(SCREAMING_SNAKE_CASE				)				,      end=" "				)
  else:
    print("("				,      end=" "				)
    print_optiomal_solution(SCREAMING_SNAKE_CASE				,      SCREAMING_SNAKE_CASE				,      optimal_solution[i][j]				)
    print_optiomal_solution(SCREAMING_SNAKE_CASE				,      optimal_solution[i][j] + 1				,      SCREAMING_SNAKE_CASE				)
    print(")"				,      end=" "				)
def 					a__			(				):


  '''simple docstring'''







  lowerCAmelCase     :     Optional[int]								=							[3_0, 3_5, 1_5, 5, 1_0, 2_0, 2_5]
  lowerCAmelCase     :     List[Any]								=							len(SCREAMING_SNAKE_CASE				)
  # Size of matrix created from above array will be
  # 30*35 35*15 15*5 5*10 10*20 20*25
  lowerCAmelCase						,  lowerCAmelCase     :     List[Any]								=							matrix_chain_order(SCREAMING_SNAKE_CASE				)

  print("No. of Operation required: " + str(matrix[1][n - 1]				)				)
  print_optiomal_solution(SCREAMING_SNAKE_CASE				,      1				,      n - 1				)


if __name__ == "__main__":
     main()











import string

# frequency taken from https://en.wikipedia.org/wiki/Letter_frequency
__A        =    {
    "E": 1_2.7_0,
    "T": 9.0_6,
    "A": 8.1_7,
    "O": 7.5_1,
    "I": 6.9_7,
    "N": 6.7_5,
    "S": 6.3_3,
    "H": 6.0_9,
    "R": 5.9_9,
    "D": 4.2_5,
    "L": 4.0_3,
    "C": 2.7_8,
    "U": 2.7_6,
    "M": 2.4_1,
    "W": 2.3_6,
    "F": 2.2_3,
    "G": 2.0_2,
    "Y": 1.9_7,
    "P": 1.9_3,
    "B": 1.2_9,
    "V": 0.9_8,
    "K": 0.7_7,
    "J": 0.1_5,
    "X": 0.1_5,
    "Q": 0.1_0,
    "Z": 0.0_7,
}
__A        =    "ETAOINSHRDLCUMWFGYPBVKJXQZ"
__A        =    "ABCDEFGHIJKLMNOPQRSTUVWXYZ"







def 			lowerCamelCase_		(       UpperCamelCase__				:      str      )     ->       dict[str, int]:





				"""simple docstring"""


				__lowerCamelCase		       =    {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 			lowerCamelCase_		(       UpperCamelCase__				:      tuple      )     ->       str:





				"""simple docstring"""


				return x[0]







def 			lowerCamelCase_		(       UpperCamelCase__				:      str      )     ->       str:





				"""simple docstring"""


				__lowerCamelCase		       =    get_letter_count(UpperCamelCase__      )
				__lowerCamelCase		       =    {
				    freq: [] for letter, freq in letter_to_freq.items()
				}
				for letter in LETTERS:
								freq_to_letter[letter_to_freq[letter]].append(UpperCamelCase__      )

				__lowerCamelCase		       =    {}

				for freq in freq_to_letter:
								freq_to_letter[freq].sort(key=ETAOIN.find ,     reverse=UpperCamelCase__      )
								__lowerCamelCase		       =    ''.join(freq_to_letter[freq]      )

				__lowerCamelCase		       =    list(freq_to_letter_str.items()      )
				freq_pairs.sort(key=UpperCamelCase__ ,     reverse=UpperCamelCase__      )

				__lowerCamelCase		       =    [freq_pair[1] for freq_pair in freq_pairs]

				return "".join(UpperCamelCase__      )







def 			lowerCamelCase_		(       UpperCamelCase__				:      str      )     ->       int:





				"""simple docstring"""


				__lowerCamelCase		       =    get_frequency_order(UpperCamelCase__      )
				__lowerCamelCase		       =    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()


