





def      _lowercase					(						_UpperCAmelCase			,      _UpperCAmelCase				)						->  Optional[int]:
				assert x is not None
				assert y is not None

				lowerCamelCase	 =len(_UpperCAmelCase				)
				lowerCamelCase	 =len(_UpperCAmelCase				)

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

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

												lowerCamelCase	 =max(l[i - 1][j]			,      l[i][j - 1]			,      l[i - 1][j - 1] + match				)

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

								if l[i][j] == l[i - 1][j - 1] + match:
												if match == 1:
																lowerCamelCase	 =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__":
							UpperCAmelCase__						:			Tuple									='''AGGTAB'''
							UpperCAmelCase__						:			Dict									='''GXTXAYB'''
							UpperCAmelCase__						:			Optional[Any]									=4
							UpperCAmelCase__						:			Any									='''GTAB'''

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

							doctest.testmod()












import math
from collections.abc import Iterator
from itertools import takewhile





def      _lowercase					(						_UpperCAmelCase				)						->  bool:

				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(_UpperCAmelCase				) + 1				)			,      6				):
								if number % i == 0 or number % (i + 2) == 0:
												return False
				return True





def      _lowercase					(						)						->  Iterator[int]:
				lowerCamelCase	 =2
				while True:
								if is_prime(_UpperCAmelCase				):
												yield num
								num += 1





def      _lowercase					(						_UpperCAmelCase = 2_00_00_00				)						->  int:
				return sum(takewhile(lambda _UpperCAmelCase				: x < n			,      prime_generator()				)				)


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





