
def a__    (       A_					):






  '''simple docstring'''





  __magic_name__				     =       0
  __magic_name__				     =       len(A_					)

  for i in range(n - 1					):
    for j in range(i + 1,     A_					):
      if arr[i] > arr[j]:
        num_inversions += 1

  return num_inversions

def a__    (       A_					):






  '''simple docstring'''





  if len(A_					) <= 1:
    return arr, 0
  __magic_name__				     =       len(A_					) // 2
  __magic_name__				     =       arr[0:mid]
  __magic_name__				     =       arr[mid:]

  __magic_name__     ,    __magic_name__				     =       count_inversions_recursive(A_					)
  __magic_name__     ,    __magic_name__				     =       count_inversions_recursive(A_					)
  __magic_name__     ,    __magic_name__				     =       _count_cross_inversions(A_,     A_					)

  __magic_name__				     =       inversion_p + inversions_q + cross_inversions
  return c, num_inversions

def a__    (       A_,     A_					):






  '''simple docstring'''





  __magic_name__				     =       []
  __magic_name__				     =       __magic_name__				     =       __magic_name__				     =       0
  while i < len(A_					) and j < len(A_					):
    if p[i] > q[j]:
      # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
      # These are all inversions. The claim emerges from the
      # property that P is sorted.
      num_inversion += len(A_					) - i
      r.append(q[j]					)
      j += 1
    else:
      r.append(p[i]					)
      i += 1

  if i < len(A_					):
    r.extend(p[i:]					)
  else:
    r.extend(q[j:]					)

  return r, num_inversion

def a__    (       ):






  '''simple docstring'''





  __magic_name__				     =       [10, 2, 1, 5, 5, 2, 11]

  # this arr has 8 inversions:
  # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

  __magic_name__				     =       count_inversions_bf(A_					)
  __magic_name__     ,    __magic_name__				     =       count_inversions_recursive(A_					)

  assert num_inversions_bf == num_inversions_recursive == 8

  print("""number of inversions = """,     A_					)

  # testing an array with zero inversion (a sorted arr_1)

  arr_a.sort()
  __magic_name__				     =       count_inversions_bf(A_					)
  __magic_name__     ,    __magic_name__				     =       count_inversions_recursive(A_					)

  assert num_inversions_bf == num_inversions_recursive == 0
  print("""number of inversions = """,     A_					)

  # an empty list should also have zero inversions
  __magic_name__				     =       []
  __magic_name__				     =       count_inversions_bf(A_					)
  __magic_name__     ,    __magic_name__				     =       count_inversions_recursive(A_					)

  assert num_inversions_bf == num_inversions_recursive == 0
  print("""number of inversions = """,     A_					)


if __name__ == "__main__":
    main()



import string

# frequency taken from https://en.wikipedia.org/wiki/Letter_frequency
__lowerCAmelCase			:     Optional[int]           =   {
    '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,
}
__lowerCAmelCase			:     Optional[Any]           =   'ETAOINSHRDLCUMWFGYPBVKJXQZ'
__lowerCAmelCase			:     Optional[Any]           =   'ABCDEFGHIJKLMNOPQRSTUVWXYZ'

def a__    (       A_					):






  '''simple docstring'''





  __magic_name__				     =       {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 a__    (       A_					):






  '''simple docstring'''





  return x[0]

def a__    (       A_					):






  '''simple docstring'''





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

  __magic_name__				     =       {}

  for freq in freq_to_letter:
    freq_to_letter[freq].sort(key=ETAOIN.find,     reverse=A_					)
    __magic_name__				     =       """""".join(freq_to_letter[freq]					)

  __magic_name__				     =       list(freq_to_letter_str.items()					)
  freq_pairs.sort(key=A_,     reverse=A_					)

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

  return "".join(A_					)

def a__    (       A_					):






  '''simple docstring'''





  __magic_name__				     =       get_frequency_order(A_					)
  __magic_name__				     =       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()

