



from __future__ import annotations




def 	__UpperCamelCase	(  _lowerCAmelCase = 4		)       ->  list[list[int]]:



    """simple docstring"""






    A :       str          =   abs(_lowerCAmelCase		) or 4
    return [[1 + x + y * row_size for x in range(_lowerCAmelCase		)] for y in range(_lowerCAmelCase		)]




def 	__UpperCamelCase	(  _lowerCAmelCase		)       ->  list[list[int]]:



    """simple docstring"""






    return reverse_row(transpose(_lowerCAmelCase		)		)
    # OR.. transpose(reverse_column(matrix))




def 	__UpperCamelCase	(  _lowerCAmelCase		)       ->  list[list[int]]:



    """simple docstring"""






    return reverse_row(reverse_column(_lowerCAmelCase		)		)
    # OR.. reverse_column(reverse_row(matrix))




def 	__UpperCamelCase	(  _lowerCAmelCase		)       ->  list[list[int]]:



    """simple docstring"""






    return reverse_column(transpose(_lowerCAmelCase		)		)
    # OR.. transpose(reverse_row(matrix))




def 	__UpperCamelCase	(  _lowerCAmelCase		)       ->  list[list[int]]:



    """simple docstring"""






    A :       Tuple          =   [list(_lowerCAmelCase		) for x in zip(*_lowerCAmelCase		)]
    return matrix




def 	__UpperCamelCase	(  _lowerCAmelCase		)       ->  list[list[int]]:



    """simple docstring"""






    A :       List[Any]          =   matrix[::-1]
    return matrix




def 	__UpperCamelCase	(  _lowerCAmelCase		)       ->  list[list[int]]:



    """simple docstring"""






    A :       Optional[int]          =   [x[::-1] for x in matrix]
    return matrix




def 	__UpperCamelCase	(  _lowerCAmelCase		)       ->  None:



    """simple docstring"""






    for i in matrix:
        print(*_lowerCAmelCase		)


if __name__ == "__main__":
     SCREAMING_SNAKE_CASE_:int             =						make_matrix()
     print("""\norigin:\n""")
     print_matrix(matrix)
     print("""\nrotate 90 counterclockwise:\n""")
     print_matrix(rotate_aa(matrix))

     SCREAMING_SNAKE_CASE_:Tuple             =						make_matrix()
     print("""\norigin:\n""")
     print_matrix(matrix)
     print("""\nrotate 180:\n""")
     print_matrix(rotate_aaa(matrix))

     SCREAMING_SNAKE_CASE_:Dict             =						make_matrix()
     print("""\norigin:\n""")
     print_matrix(matrix)
     print("""\nrotate 270 counterclockwise:\n""")
     print_matrix(rotate_aaa(matrix))







def 	__UpperCamelCase	(  _lowerCAmelCase = 100_0000		)       ->  int:



    """simple docstring"""






    A :       str          =   limit + 1
    A :       Tuple          =   [0] * limit
    for first_term in range(1      ,     _lowerCAmelCase		):
        for n in range(_lowerCAmelCase      ,     _lowerCAmelCase      ,     _lowerCAmelCase		):
            A :       Any          =   first_term + n / first_term
            if common_difference % 4:  # d must be divisble by 4
                continue
            else:
                common_difference /= 4
                if (
                    first_term > common_difference
                    and first_term < 4 * common_difference
                ):  # since x,y,z are positive integers
                    frequency[n] += 1  # so z>0 and a>d ,also 4d<a

    A :       Optional[int]          =   sum(1 for x in frequency[1:limit] if x == 10		)

    return count


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


