



from __future__ import annotations

a_      :      Union[str, Any]    =     []






def     __a					(		__UpperCAmelCase							,  __UpperCAmelCase							,  __UpperCAmelCase       ):
 for i in range(len(__UpperCAmelCase       )       ):
  if board[row][i] == 1:
   return False
 for i in range(len(__UpperCAmelCase       )       ):
  if board[i][column] == 1:
   return False
 for i, j in zip(range(__UpperCAmelCase							,  -1							,  -1       )							,  range(__UpperCAmelCase							,  -1							,  -1       )       ):
  if board[i][j] == 1:
   return False
 for i, j in zip(range(__UpperCAmelCase							,  -1							,  -1       )							,  range(__UpperCAmelCase							,  len(__UpperCAmelCase       )       )       ):
  if board[i][j] == 1:
   return False
 return True






def     __a					(		__UpperCAmelCase							,  __UpperCAmelCase       ):
 if row >= len(__UpperCAmelCase       ):
  solution.append(__UpperCAmelCase       )
  printboard(__UpperCAmelCase       )
  print()
  return True
 for i in range(len(__UpperCAmelCase       )       ):
  if is_safe(__UpperCAmelCase							,  __UpperCAmelCase							,  __UpperCAmelCase       ):
   a__												= 1
   solve(__UpperCAmelCase							,  row + 1       )
   a__												= 0
 return False






def     __a					(		__UpperCAmelCase       ):
 for i in range(len(__UpperCAmelCase       )       ):
  for j in range(len(__UpperCAmelCase       )       ):
   if board[i][j] == 1:
    print('''Q'''							,  end=''' '''       )
   else:
    print('''.'''							,  end=''' '''       )
  print()


# n=int(input("The no. of queens"))
a_      :      Tuple    =     8
a_      :      int    =     [[0 for i in range(n)] for j in range(n)]
solve(board, 0)

print('The total no. of solutions are :', len(solution))










import math
from collections.abc import Iterator
from itertools import takewhile






def     __a					(		__UpperCAmelCase       ):

 if 1 < number < 4:
  # 2 and 3 are primes
  return True
 elif number < 2 or number % 2 == 0 or number % 3 == 0:
  # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
  return False

 # All primes number are in format of 6k +/- 1
 for i in range(5							,  int(math.sqrt(__UpperCAmelCase       ) + 1       )							,  6       ):
  if number % i == 0 or number % (i + 2) == 0:
   return False
 return True






def     __a					(		):
 a__												= 2
 while True:
  if is_prime(__UpperCAmelCase       ):
   yield num
  num += 1






def     __a					(		__UpperCAmelCase = 200_0000       ):
 return sum(takewhile(lambda __UpperCAmelCase       : x < n							,  prime_generator()       )       )


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





