




"""simple docstring"""


def       UpperCAmelCase__ (snake_case__							:      str	,     snake_case__							:      str					):
  """simple docstring"""

  assert x is not None
  assert y is not None

  _snake_case							:	List[str]			=						len(snake_case__					)
  _snake_case							:	Any			=						len(snake_case__					)

  # declaring the array for storing the dp values
  _snake_case							:	int			=						[[0] * (n + 1) for _ in range(m + 1					)]  # noqa: E741

  for i in range(1	,     m + 1					):
    for j in range(1	,     n + 1					):
      _snake_case							:	int			=						1 if x[i - 1] == y[j - 1] else 0

      _snake_case							:	List[Any]			=						max(l[i - 1][j]	,     l[i][j - 1]	,     l[i - 1][j - 1] + match					)

  _snake_case							:	str			=						""""""
  _snake_case	,      _snake_case							:	Any			=						m, n
  while i > 0 and j > 0:
    _snake_case							:	List[Any]			=						1 if x[i - 1] == y[j - 1] else 0

    if l[i][j] == l[i - 1][j - 1] + match:
      if match == 1:
        _snake_case							:	List[str]			=						x[i - 1] + seq
      i -= 1
      j -= 1
    elif l[i][j] == l[i - 1][j]:
      i -= 1
    else:
      j -= 1

  return l[m][n], seq


if __name__ == "__main__":
     A_      			=       '''AGGTAB'''
     A_      			=       '''GXTXAYB'''
     A_      			=       4
     A_      			=       '''GTAB'''

     A_			,					A_      			=       longest_common_subsequence(a, b)
     print('''len =''', ln, ''', sub-sequence =''', subseq)
     import doctest

     doctest.testmod()








"""simple docstring"""


from __future__ import annotations

import math


def       UpperCAmelCase__ (snake_case__							:      int					):
  """simple docstring"""

  if 1 < number < 4:
    # 2 and 3 are primes
    return True
  elif number < 2 or number % 2 == 0 or number % 3 == 0:
    # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
    return False

  # All primes number are in format of 6k +/- 1
  for i in range(5	,     int(math.sqrt(snake_case__					) + 1					)	,     6					):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True


A_      			=       [num for num in range(3, 10_00_01, 2) if not is_prime(num)]


def       UpperCAmelCase__ (snake_case__							:      int					):
  """simple docstring"""

  if not isinstance(snake_case__	,     snake_case__					):
    raise ValueError("""n must be an integer"""					)
  if n <= 0:
    raise ValueError("""n must be >= 0"""					)

  _snake_case							:	Any			=						[]
  for num in range(len(snake_case__					)					):
    _snake_case							:	Optional[int]			=						0
    while 2 * i * i <= odd_composites[num]:
      _snake_case							:	Optional[int]			=						odd_composites[num] - 2 * i * i
      if is_prime(snake_case__					):
        break
      i += 1
    else:
      list_nums.append(odd_composites[num]					)
      if len(snake_case__					) == n:
        return list_nums

  return []


def       UpperCAmelCase__ ():
  """simple docstring"""

  return compute_nums(1					)[0]


if __name__ == "__main__":
     print(F'''{solution() = }''')


