


"""simple docstring"""







import sys




def    UpperCAmelCase__       (lowerCAmelCase_   ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						   =				len(lowerCAmelCase_   )
					__SCREAMING_SNAKE_CASE						   =				[[0 for x in range(lowerCAmelCase_   )] for x in range(lowerCAmelCase_   )]
					__SCREAMING_SNAKE_CASE						   =				[[0 for x in range(lowerCAmelCase_   )] for x in range(lowerCAmelCase_   )]

					for chain_length in range(2  ,						lowerCAmelCase_   ):
										for a in range(1  ,						n - chain_length + 1   ):
															__SCREAMING_SNAKE_CASE						   =				a + chain_length - 1

															__SCREAMING_SNAKE_CASE						   =				sys.maxsize
															for c in range(lowerCAmelCase_  ,						lowerCAmelCase_   ):
																				__SCREAMING_SNAKE_CASE						   =				(
																				    matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
																				)
																				if cost < matrix[a][b]:
																									__SCREAMING_SNAKE_CASE						   =				cost
																									__SCREAMING_SNAKE_CASE						   =				c
					return matrix, sol




def    UpperCAmelCase__       (lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_   ):




					'''simple docstring'''


					if i == j:
										print("A" + str(lowerCAmelCase_   )  ,						end=" "   )
					else:
										print("("  ,						end=" "   )
										print_optiomal_solution(lowerCAmelCase_  ,						lowerCAmelCase_  ,						optimal_solution[i][j]   )
										print_optiomal_solution(lowerCAmelCase_  ,						optimal_solution[i][j] + 1  ,						lowerCAmelCase_   )
										print(")"  ,						end=" "   )




def    UpperCAmelCase__       ():




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						   =				[30, 35, 15, 5, 10, 20, 25]
					__SCREAMING_SNAKE_CASE						   =				len(lowerCAmelCase_   )
					# Size of matrix created from above array will be
					# 30*35 35*15 15*5 5*10 10*20 20*25
					__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				matrix_chain_order(lowerCAmelCase_   )

					print("No. of Operation required: " + str(matrix[1][n - 1]   )   )
					print_optiomal_solution(lowerCAmelCase_  ,						1  ,						n - 1   )


if __name__ == "__main__":
		main()




"""simple docstring"""







def    UpperCAmelCase__       (lowerCAmelCase_ = 100_0000   ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						   =				set(range(3  ,						lowerCAmelCase_  ,						2   )   )
					primes.add(2   )
					for p in range(3  ,						lowerCAmelCase_  ,						2   ):
										if p not in primes:
															continue
										primes.difference_update(set(range(p * p  ,						lowerCAmelCase_  ,						lowerCAmelCase_   )   )   )

					__SCREAMING_SNAKE_CASE						   =				[float(lowerCAmelCase_   ) for n in range(limit + 1   )]

					for p in primes:
										for n in range(lowerCAmelCase_  ,						limit + 1  ,						lowerCAmelCase_   ):
															phi[n] *= 1 - 1 / p

					return int(sum(phi[2:]   )   )


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