"""simple docstring"""






import random



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase )  ->  bool:
   lowercase__:   Dict					=      num - 1
   lowercase__:   Tuple					=      0

   while s % 2 == 0:
      lowercase__:   int					=      s // 2
      t += 1

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



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase )  ->  bool:
   if num < 2:
      return False

   lowercase__:   int					=      [
       2,
       3,
       5,
       7,
       1_1,
       1_3,
       1_7,
       1_9,
       2_3,
       2_9,
       3_1,
       3_7,
       4_1,
       4_3,
       4_7,
       5_3,
       5_9,
       6_1,
       6_7,
       7_1,
       7_3,
       7_9,
       8_3,
       8_9,
       9_7,
       1_0_1,
       1_0_3,
       1_0_7,
       1_0_9,
       1_1_3,
       1_2_7,
       1_3_1,
       1_3_7,
       1_3_9,
       1_4_9,
       1_5_1,
       1_5_7,
       1_6_3,
       1_6_7,
       1_7_3,
       1_7_9,
       1_8_1,
       1_9_1,
       1_9_3,
       1_9_7,
       1_9_9,
       2_1_1,
       2_2_3,
       2_2_7,
       2_2_9,
       2_3_3,
       2_3_9,
       2_4_1,
       2_5_1,
       2_5_7,
       2_6_3,
       2_6_9,
       2_7_1,
       2_7_7,
       2_8_1,
       2_8_3,
       2_9_3,
       3_0_7,
       3_1_1,
       3_1_3,
       3_1_7,
       3_3_1,
       3_3_7,
       3_4_7,
       3_4_9,
       3_5_3,
       3_5_9,
       3_6_7,
       3_7_3,
       3_7_9,
       3_8_3,
       3_8_9,
       3_9_7,
       4_0_1,
       4_0_9,
       4_1_9,
       4_2_1,
       4_3_1,
       4_3_3,
       4_3_9,
       4_4_3,
       4_4_9,
       4_5_7,
       4_6_1,
       4_6_3,
       4_6_7,
       4_7_9,
       4_8_7,
       4_9_1,
       4_9_9,
       5_0_3,
       5_0_9,
       5_2_1,
       5_2_3,
       5_4_1,
       5_4_7,
       5_5_7,
       5_6_3,
       5_6_9,
       5_7_1,
       5_7_7,
       5_8_7,
       5_9_3,
       5_9_9,
       6_0_1,
       6_0_7,
       6_1_3,
       6_1_7,
       6_1_9,
       6_3_1,
       6_4_1,
       6_4_3,
       6_4_7,
       6_5_3,
       6_5_9,
       6_6_1,
       6_7_3,
       6_7_7,
       6_8_3,
       6_9_1,
       7_0_1,
       7_0_9,
       7_1_9,
       7_2_7,
       7_3_3,
       7_3_9,
       7_4_3,
       7_5_1,
       7_5_7,
       7_6_1,
       7_6_9,
       7_7_3,
       7_8_7,
       7_9_7,
       8_0_9,
       8_1_1,
       8_2_1,
       8_2_3,
       8_2_7,
       8_2_9,
       8_3_9,
       8_5_3,
       8_5_7,
       8_5_9,
       8_6_3,
       8_7_7,
       8_8_1,
       8_8_3,
       8_8_7,
       9_0_7,
       9_1_1,
       9_1_9,
       9_2_9,
       9_3_7,
       9_4_1,
       9_4_7,
       9_5_3,
       9_6_7,
       9_7_1,
       9_7_7,
       9_8_3,
       9_9_1,
       9_9_7,
   ]

   if num in low_primes:
      return True

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

   return rabin_miller(__UpperCAmelCase )



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase = 1_0_2_4 )  ->  int:
   while True:
      lowercase__:   Optional[int]					=      random.randrange(2 ** (keysize - 1)       ,    2 ** (keysize) )
      if is_prime_low_num(__UpperCAmelCase ):
         return num


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

"""simple docstring"""






def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase )  ->  int:

   if not grid or not grid[0]:
      raise TypeError('''The grid does not contain the appropriate information''' )

   for cell_n in range(1       ,    len(grid[0] ) ):
      grid[0][cell_n] += grid[0][cell_n - 1]
   lowercase__:   Tuple					=      grid[0]

   for row_n in range(1       ,    len(__UpperCAmelCase ) ):
      lowercase__:   Tuple					=      grid[row_n]
      lowercase__:   Dict					=      fill_row(__UpperCAmelCase       ,    __UpperCAmelCase )
      lowercase__:   Union[str, Any]					=      grid[row_n]

   return grid[-1][-1]



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase )  ->  list:
   current_row[0] += row_above[0]
   for cell_n in range(1       ,    len(__UpperCAmelCase ) ):
      current_row[cell_n] += min(current_row[cell_n - 1]       ,    row_above[cell_n] )

   return current_row


if __name__ == "__main__":
       import doctest

       doctest.testmod()
