





'''simple docstring'''




from __future__ import annotations






def 	_lowerCAmelCase      (  __snake_case  :			str			,							__snake_case  :			list[str] | None = None      )					->					list[list[str]]:
					__A						:			Union[str, Any]								=	word_bank or []
					# create a table
					__A						:			int								=	len(__snake_case      ) + 1

					__A						:			list[list[list[str]]]								=	[]
					for _ in range(__snake_case      ):
										table.append([]      )
					# seed value
					__A						:			Dict								=	[[]]  # because empty string has empty combination

					# iterate through the indices
					for i in range(__snake_case      ):
										# condition
										if table[i] != []:
															for word in word_bank:
																				# slice condition
																				if target[i : i + len(__snake_case      )] == word:
																									__A						:			list[list[str]]								=	[
																									    [word, *way] for way in table[i]
																									]
																									# adds the word to every combination the current position holds
																									# now,push that combination to the table[i+len(word)]
																									table[i + len(__snake_case      )] += new_combinations

    # combinations are in reverse order so reverse for better output
					for combination in table[len(__snake_case      )]:
										combination.reverse()

					return table[len(__snake_case      )]


if __name__ == "__main__":
		print(all_construct('''jwajalapa''', ['''jwa''', '''j''', '''w''', '''a''', '''la''', '''lapa''']))
		print(all_construct('''rajamati''', ['''s''', '''raj''', '''amat''', '''raja''', '''ma''', '''i''', '''t''']))
		print(
		    all_construct(
		        '''hexagonosaurus''',
		        ['''h''', '''ex''', '''hex''', '''ag''', '''ago''', '''ru''', '''auru''', '''rus''', '''go''', '''no''', '''o''', '''s'''],
		    )
		)






'''simple docstring'''




import math






def 	_lowerCAmelCase      (  __snake_case  :			int      )					->					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(__snake_case      ) + 1      )			,							6      ):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True






def 	_lowerCAmelCase      (  __snake_case  :			float = 0.1      )					->					int:
     __A						:			Dict								=	3
     __A						:			int								=	3

     while primes / (2 * j - 1) >= ratio:
          for i in range(j * j + j + 1			,							(j + 2) * (j + 2)			,							j + 1      ):
               primes += is_prime(__snake_case      )
          j += 2
     return j


if __name__ == "__main__":
  import doctest

  doctest.testmod()