

import random






def 					__lowercase      (     _A			)     ->						bool:
						SCREAMING_SNAKE_CASE :      List[str]       =   num - 1
						SCREAMING_SNAKE_CASE :      Dict       =   0

						while s % 2 == 0:
												SCREAMING_SNAKE_CASE :      Union[str, Any]       =   s // 2
												t += 1

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






def 					__lowercase      (     _A			)     ->						bool:
						if num < 2:
												return False

						SCREAMING_SNAKE_CASE :      List[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 					__lowercase      (     _A = 1024			)     ->						int:
						while True:
												SCREAMING_SNAKE_CASE :      int       =   random.randrange(2 ** (keysize - 1)						,    2 ** (keysize)			)
												if is_prime_low_num(_A			):
																		return num


if __name__ == "__main__":
		UpperCAmelCase__ :     str				    =    generate_large_prime()
		print(("""Prime number:""", num))
		print(("""is_prime_low_num:""", is_prime_low_num(num)))







def 					__lowercase      (     _A						,    _A			)     ->						int:
      assert x is not None
      assert y is not None

      SCREAMING_SNAKE_CASE :      int       =   len(_A			)
      SCREAMING_SNAKE_CASE :      Union[str, Any]       =   len(_A			)

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

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

                  SCREAMING_SNAKE_CASE :      int       =   max(l[i - 1][j]						,    l[i][j - 1]						,    l[i - 1][j - 1] + match			)

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

            if l[i][j] == l[i - 1][j - 1] + match:
                  if match == 1:
                        SCREAMING_SNAKE_CASE :      List[Any]       =   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__ :     str				    =    """AGGTAB"""
  UpperCAmelCase__ :     Optional[int]				    =    """GXTXAYB"""
  UpperCAmelCase__ :     Tuple				    =    4
  UpperCAmelCase__ :     Dict				    =    """GTAB"""

  UpperCAmelCase__    ,   UpperCAmelCase__ :     Optional[int]				    =    longest_common_subsequence(a, b)
  print("""len =""", ln, """, sub-sequence =""", subseq)
  import doctest

  doctest.testmod()




