





'''simple docstring'''






def      __A						(							a_						:  list[list[int | float]]	):
		lowerCAmelCase     :    List[str]						=   len(a_	)
		lowerCAmelCase     :    Union[str, Any]						=   len(matrix[0]	)
		lowerCAmelCase     :    Union[str, Any]						=   min(a_      ,a_	)

		for row in range(a_	):
				# Check if diagonal element is not zero
				if matrix[row][row] != 0:
						# Eliminate all the elements below the diagonal
						for col in range(row + 1      ,a_	):
								lowerCAmelCase     :    Optional[int]						=   matrix[col][row] / matrix[row][row]
								for i in range(a_      ,a_	):
										matrix[col][i] -= multiplier * matrix[row][i]
				else:
						# Find a non-zero diagonal element to swap rows
						lowerCAmelCase     :    Optional[int]						=   True
						for i in range(row + 1      ,a_	):
								if matrix[i][row] != 0:
										lowerCAmelCase	,		lowerCAmelCase     :    Optional[int]						=   matrix[i], matrix[row]
										lowerCAmelCase     :    Optional[Any]						=   False
										break
						if reduce:
								rank -= 1
								for i in range(a_	):
										lowerCAmelCase     :    Tuple						=   matrix[i][rank]

            # Reduce the row pointer by one to stay on the same row
						row -= 1

		return rank


if __name__ == "__main__":
					import doctest

					doctest.testmod()










'''simple docstring'''






from __future__ import annotations

lowerCAmelCase       		=      []






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






def      __A						(							a_						:  list[list[int]]      ,a_						:  int	):
		if row >= len(a_	):
				solution.append(a_	)
				printboard(a_	)
				print()
				return True
		for i in range(len(a_	)	):
				if is_safe(a_      ,a_      ,a_	):
						lowerCAmelCase     :    Any						=   1
						solve(a_      ,row + 1	)
						lowerCAmelCase     :    List[Any]						=   0
		return False






def      __A						(							a_						:  list[list[int]]	):
		for i in range(len(a_	)	):
				for j in range(len(a_	)	):
						if board[i][j] == 1:
								print("Q"      ,end=" "	)
						else:
								print("."      ,end=" "	)
				print()


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

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



