


'''simple docstring'''
import random


def 			a      (			__a   )  ->	bool:



					'''simple docstring'''






					UpperCamelCase__   :Optional[int]												= num - 1
					UpperCamelCase__   :Union[str, Any]												= 0

					while s % 2 == 0:
										UpperCamelCase__   :Dict												= s // 2
										t += 1

					for _ in range(5   ):
										UpperCamelCase__   :Optional[int]												= random.randrange(2 ,					num - 1   )
										UpperCamelCase__   :Union[str, Any]												= pow(a__ ,					a__ ,					a__   )
										if v != 1:
															UpperCamelCase__   :int												= 0
															while v != (num - 1):
																				if i == t - 1:
																									return False
																				else:
																									UpperCamelCase__   :Any												= i + 1
																									UpperCamelCase__   :Optional[int]												= (v**2) % num
					return True


def 			a      (			__a   )  ->	bool:



					'''simple docstring'''






					if num < 2:
										return False

					UpperCamelCase__   :str												= [
					    2,
					    3,
					    5,
					    7,
					    11,
					    13,
					    17,
					    19,
					    23,
					    29,
					    31,
					    37,
					    41,
					    43,
					    47,
					    53,
					    59,
					    61,
					    67,
					    71,
					    73,
					    79,
					    83,
					    89,
					    97,
					    101,
					    103,
					    107,
					    109,
					    113,
					    127,
					    131,
					    137,
					    139,
					    149,
					    151,
					    157,
					    163,
					    167,
					    173,
					    179,
					    181,
					    191,
					    193,
					    197,
					    199,
					    211,
					    223,
					    227,
					    229,
					    233,
					    239,
					    241,
					    251,
					    257,
					    263,
					    269,
					    271,
					    277,
					    281,
					    283,
					    293,
					    307,
					    311,
					    313,
					    317,
					    331,
					    337,
					    347,
					    349,
					    353,
					    359,
					    367,
					    373,
					    379,
					    383,
					    389,
					    397,
					    401,
					    409,
					    419,
					    421,
					    431,
					    433,
					    439,
					    443,
					    449,
					    457,
					    461,
					    463,
					    467,
					    479,
					    487,
					    491,
					    499,
					    503,
					    509,
					    521,
					    523,
					    541,
					    547,
					    557,
					    563,
					    569,
					    571,
					    577,
					    587,
					    593,
					    599,
					    601,
					    607,
					    613,
					    617,
					    619,
					    631,
					    641,
					    643,
					    647,
					    653,
					    659,
					    661,
					    673,
					    677,
					    683,
					    691,
					    701,
					    709,
					    719,
					    727,
					    733,
					    739,
					    743,
					    751,
					    757,
					    761,
					    769,
					    773,
					    787,
					    797,
					    809,
					    811,
					    821,
					    823,
					    827,
					    829,
					    839,
					    853,
					    857,
					    859,
					    863,
					    877,
					    881,
					    883,
					    887,
					    907,
					    911,
					    919,
					    929,
					    937,
					    941,
					    947,
					    953,
					    967,
					    971,
					    977,
					    983,
					    991,
					    997,
					]

					if num in low_primes:
										return True

					for prime in low_primes:
										if (num % prime) == 0:
															return False

					return rabin_miller(a__   )


def 			a      (			__a = 1024   )  ->	int:



					'''simple docstring'''






					while True:
										UpperCamelCase__   :Dict												= random.randrange(2 ** (keysize - 1) ,					2 ** (keysize)   )
										if is_prime_low_num(a__   ):
															return num


if __name__ == "__main__":
		__snake_case							      =     generate_large_prime()
		print(('''Prime number:''', num))
		print(('''is_prime_low_num:''', is_prime_low_num(num)))

def     __lowerCAmelCase			(			a__  )       ->  str:
				__a										=    []
				__a										=    set({'''(''', '''[''', '''{'''}  )
				__a										=    set({''')''', ''']''', '''}'''}  )
				__a										=    {'''{''': '''}''', '''[''': ''']''', '''(''': ''')'''}

				for i in range(len(a__  )  ):
								if s[i] in open_brackets:
												stack.append(s[i]  )

								elif s[i] in closed_brackets and (
								    len(a__  ) == 0 or (len(a__  ) > 0 and open_to_closed[stack.pop()] != s[i])
								):
												return False

				return len(a__  ) == 0


def     __lowerCAmelCase			(			)       ->  Dict:
				__a										=    input('''Enter sequence of brackets: '''  )
				if is_balanced(a__  ):
								print(a__						,    '''is balanced'''  )
				else:
								print(a__						,    '''is not balanced'''  )


if __name__ == "__main__":
					main()