




from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray




def 			__magic_name__				( A		:					NDArray[floataa],  A		:					NDArray[floataa],  A		:					list[int],  A		:					int,  ):






			'''simple docstring'''







			a    ,		a    =			coefficient_matrix.shape
			a    ,		a    =			constant_matrix.shape

			if rowsa != colsa:
						a    =			F"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
						raise ValueError(A   )

			if colsa != 1:
						a    =			F"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
						raise ValueError(A   )

			if rowsa != rowsa:
						a    =			(
						    "Coefficient and constant matrices dimensions must be nxn and nx1 but "
						    F"""received {rowsa}x{colsa} and {rowsa}x{colsa}"""
						)
						raise ValueError(A   )

			if len(A   ) != rowsa:
						a    =			(
						    "Number of initial values must be equal to number of rows in coefficient "
						    F"""matrix but received {len(A   )} and {rowsa}"""
						)
						raise ValueError(A   )

			if iterations <= 0:
						raise ValueError("Iterations must be at least 1"   )

			a    =			np.concatenate(
			    (coefficient_matrix, constant_matrix),  axis=1   )

			a    ,		a    =			table.shape

			strictly_diagonally_dominant(A   )

			# Iterates the whole matrix for given number of times
			for _ in range(A   ):
						a    =			[]
						for row in range(A   ):
									a    =			0
									for col in range(A   ):
												if col == row:
															a    =			table[row][col]
												elif col == cols - 1:
															a    =			table[row][col]
												else:
															temp += (-1) * table[row][col] * init_val[col]
									a    =			(temp + val) / denom
									new_val.append(A   )
						a    =			new_val

			return [float(A   ) for i in new_val]




def 			__magic_name__				( A		:					NDArray[floataa]   ):






			'''simple docstring'''







			a    ,		a    =			table.shape

			a    =			True

			for i in range(0,  A   ):
						a    =			0
						for j in range(0,  cols - 1   ):
									if i == j:
												continue
									else:
												total += table[i][j]

						if table[i][i] <= total:
									raise ValueError("Coefficient matrix is not strictly diagonally dominant"   )

			return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
		import doctest

		doctest.testmod()










from __future__ import annotations

UpperCAmelCase_      : Tuple  					=       []







def        SCREAMING_SNAKE_CASE_						(			__A :			list[list[int]]  ,    __A :			int  ,    __A :			int				)	->		bool:

       """simple docstring"""

       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        SCREAMING_SNAKE_CASE_						(			__A :			list[list[int]]  ,    __A :			int				)	->		bool:

       """simple docstring"""

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







def        SCREAMING_SNAKE_CASE_						(			__A :			list[list[int]]				)	->		None:

       """simple docstring"""

       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"))
UpperCAmelCase_      : List[str]  					=       8
UpperCAmelCase_      : str  					=       [[0 for i in range(n)] for j in range(n)]
solve(board, 0)
print('The total no. of solutions are :', len(solution))


