"""simple docstring"""





from __future__ import annotations

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


def  lowercase_ ( _lowerCamelCase:						NDArray[floataa]    , _lowerCamelCase:						NDArray[floataa]    , _lowerCamelCase:						list[int]    , _lowerCamelCase:						int    , )			->   Union[str, Any]:



							'''simple docstring'''

							__lowerCamelCase ,	__lowerCamelCase       :		Tuple		 =  coefficient_matrix.shape
							__lowerCamelCase ,	__lowerCamelCase       :		Any		 =  constant_matrix.shape

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

							if colsa != 1:
														__lowerCamelCase       :		List[Any]		 =  F"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
														raise ValueError(lowercase__   )

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

							if len(lowercase__   ) != rowsa:
														__lowerCamelCase       :		List[str]		 =  (
														    "Number of initial values must be equal to number of rows in coefficient "
														    F"""matrix but received {len(lowercase__   )} and {rowsa}"""
														)
														raise ValueError(lowercase__   )

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

							__lowerCamelCase       :		Union[str, Any]		 =  np.concatenate(
							    (coefficient_matrix, constant_matrix)    , axis=1   )

							__lowerCamelCase ,	__lowerCamelCase       :		List[Any]		 =  table.shape

							strictly_diagonally_dominant(lowercase__   )

							# Iterates the whole matrix for given number of times
							for _ in range(lowercase__   ):
														__lowerCamelCase       :		Union[str, Any]		 =  []
														for row in range(lowercase__   ):
																					__lowerCamelCase       :		Union[str, Any]		 =  0
																					for col in range(lowercase__   ):
																												if col == row:
																																			__lowerCamelCase       :		Union[str, Any]		 =  table[row][col]
																												elif col == cols - 1:
																																			__lowerCamelCase       :		int		 =  table[row][col]
																												else:
																																			temp += (-1) * table[row][col] * init_val[col]
																					__lowerCamelCase       :		Tuple		 =  (temp + val) / denom
																					new_val.append(lowercase__   )
														__lowerCamelCase       :		Optional[Any]		 =  new_val

							return [float(lowercase__   ) for i in new_val]


def  lowercase_ ( _lowerCamelCase:						NDArray[floataa]   )			->   str:



							'''simple docstring'''

							__lowerCamelCase ,	__lowerCamelCase       :		str		 =  table.shape

							__lowerCamelCase       :		List[Any]		 =  True

							for i in range(0    , lowercase__   ):
														__lowerCamelCase       :		Union[str, Any]		 =  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()



"""simple docstring"""




def       a_ (	lowercase__ :str     ):
			__lowerCamelCase          =      [int(lowercase__     ) for i in ip_va_address.split("""."""     ) if i.isdigit()]
			return len(lowercase__     ) == 4 and all(0 <= int(lowercase__     ) <= 254 for octet in octets     )


if __name__ == "__main__":
					__magic_name__						: Tuple    =				input().strip()
					__magic_name__						: Optional[int]    =				'valid' if is_ip_va_address_valid(ip) else 'invalid'
					print(f"""{ip} is a {valid_or_invalid} IP v4 address.""")




