



from __future__ import annotations






def 					__lowerCAmelCase		(  __lowerCamelCase	:    str				,   __lowerCamelCase	:    list[str] | None = None	)  ->						list[list[str]]:
					__lowerCAmelCase	   =word_bank or []
					# create a table
					__lowerCAmelCase	   =len(__lowerCamelCase	) + 1

					__lowerCAmelCase	   =[]
					for _ in range(__lowerCamelCase	):
										table.append([]	)
					# seed value
					__lowerCAmelCase	   =[[]]  # because empty string has empty combination

					# iterate through the indices
					for i in range(__lowerCamelCase	):
										# condition
										if table[i] != []:
															for word in word_bank:
																				# slice condition
																				if target[i : i + len(__lowerCamelCase	)] == word:
																									__lowerCAmelCase	   =[
																									    [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(__lowerCamelCase	)] += new_combinations

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

					return table[len(__lowerCamelCase	)]


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'''],
				    )
				)









def 					__lowerCAmelCase		(  __lowerCamelCase	:    int	)  ->						list:
					__lowerCAmelCase	   =int(__lowerCamelCase	)
					if n_element < 1:
										__lowerCAmelCase	   =ValueError("""a should be a positive number"""	)
										raise my_error

					__lowerCAmelCase	   =[1]
					__lowerCAmelCase   ,	__lowerCAmelCase   ,	__lowerCAmelCase	   =(0, 0, 0)
					__lowerCAmelCase	   =1
					while index < n_element:
										while hamming_list[i] * 2 <= hamming_list[-1]:
															i += 1
										while hamming_list[j] * 3 <= hamming_list[-1]:
															j += 1
										while hamming_list[k] * 5 <= hamming_list[-1]:
															k += 1
										hamming_list.append(
										    min(hamming_list[i] * 2				,   hamming_list[j] * 3				,   hamming_list[k] * 5	)	)
										index += 1
					return hamming_list


if __name__ == "__main__":
				lowercase_	       =			input('''Enter the last number (nth term) of the Hamming Number Series: ''')
				print('''Formula of Hamming Number Series => 2^i * 3^j * 5^k''')
				lowercase_	       =			hamming(int(n))
				print('''-----------------------------------------------------''')
				print(F"The list with nth numbers is: {hamming_numbers}")
				print('''-----------------------------------------------------''')




