'''simple docstring'''

from __future__ import annotations

_A			:      Tuple					      =				[]







def      UpperCamelCase_						(					snake_case_       :       list[list[int]]						,		snake_case_       :       int						,		snake_case_       :       int      )					->     bool:






 '''simple docstring'''

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







def      UpperCamelCase_						(					snake_case_       :       list[list[int]]						,		snake_case_       :       int      )					->     bool:






 '''simple docstring'''

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







def      UpperCamelCase_						(					snake_case_       :       list[list[int]]      )					->     None:






 '''simple docstring'''

 for i in range(len(snake_case_      )      ):
  for j in range(len(snake_case_      )      ):
   if board[i][j] == 1:
    print("""Q"""						,		end=""" """      )
   else:
    print("""."""						,		end=""" """      )
  print()


# n=int(input("The no. of queens"))
_A			:      Any					      =				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))







'''simple docstring'''

def      UpperCamelCase_						(					snake_case_       :       Union[str, Any]=2_81_23      )					->     str:






 '''simple docstring'''

 __lowerCAmelCase											=						[1] * (limit + 1)

 for i in range(2						,		int(limit**0.5      ) + 1      ):
  sum_divs[i * i] += i
  for k in range(i + 1						,		limit // i + 1      ):
   sum_divs[k * i] += k + i

 __lowerCAmelCase											=						set()
 __lowerCAmelCase											=						0

 for n in range(1						,		limit + 1      ):
  if sum_divs[n] > n:
   abundants.add(snake_case_      )

  if not any((n - a in abundants) for a in abundants      ):
   res += n

 return res


if __name__ == "__main__":
 print(solution())






