




def lowerCamelCase__   (							snake_case_     :  list[int]	,				snake_case_     :  list[int]	)				->    tuple[float, float]:

   # Check if the input is valid
   if not len(snake_case_	) == len(snake_case_	) == 3:
      raise ValueError('''Please enter a valid equation.'''	)
   if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
      raise ValueError('''Both a & b of two equations can\'t be zero.'''	)

   # Extract the coefficients
   __snake_case	,     __snake_case	,     __snake_case								=       equationa
   __snake_case	,     __snake_case	,     __snake_case								=       equationa

   # Calculate the determinants of the matrices
   __snake_case								=       aa * ba - aa * ba
   __snake_case								=       ca * ba - ca * ba
   __snake_case								=       aa * ca - aa * ca

   # Check if the system of linear equations has a solution (using Cramer's rule)
   if determinant == 0:
      if determinant_x == determinant_y == 0:
         raise ValueError('''Infinite solutions. (Consistent system)'''	)
      else:
         raise ValueError('''No solution. (Inconsistent system)'''	)
   else:
      if determinant_x == determinant_y == 0:
         # Trivial solution (Inconsistent system)
         return (0.0, 0.0)
      else:
         __snake_case								=       determinant_x / determinant
         __snake_case								=       determinant_y / determinant
         # Non-Trivial Solution (Consistent system)
         return (x, y)








import math






def lowerCamelCase__   (							snake_case_     :  int	)				->    list[int]:
   __snake_case								=       []
   __snake_case								=       2
   __snake_case								=       int(math.sqrt(snake_case_	)	)  # Size of every segment
   __snake_case								=       [True] * (end + 1)
   __snake_case								=       []

   while start <= end:
      if temp[start] is True:
         in_prime.append(snake_case_	)
         for i in range(start * start	,				end + 1	,				snake_case_	):
            __snake_case								=       False
      start += 1
   prime += in_prime

   __snake_case								=       end + 1
   __snake_case								=       min(2 * end	,				snake_case_	)

   while low <= n:
      __snake_case								=       [True] * (high - low + 1)
      for each in in_prime:
         __snake_case								=       math.floor(low / each	) * each
         if t < low:
            t += each

         for j in range(snake_case_	,				high + 1	,				snake_case_	):
            __snake_case								=       False

      for j in range(len(snake_case_	)	):
         if temp[j] is True:
            prime.append(j + low	)

      __snake_case								=       high + 1
      __snake_case								=       min(high + end	,				snake_case_	)

   return prime







print(sieve(10**6))

