

from __future__ import annotations

import numpy as np





def 	__a     (      A__			:  np.ndarray       ):
    SCREAMING_SNAKE_CASE							,	SCREAMING_SNAKE_CASE										=   np.shape(A__       )
    if rows != columns:
        SCREAMING_SNAKE_CASE										=   (
            "'table' has to be of square shaped array but got a "
            F"{rows}x{columns} array:\n{table}"
        )
        raise ValueError(A__       )

    SCREAMING_SNAKE_CASE										=   np.zeros((rows, columns)       )
    SCREAMING_SNAKE_CASE										=   np.zeros((rows, columns)       )
    for i in range(A__       ):
        for j in range(A__       ):
            SCREAMING_SNAKE_CASE										=   sum(lower[i][k] * upper[k][j] for k in range(A__       )       )
            if upper[j][j] == 0:
                raise ArithmeticError("No LU decomposition exists"       )
            SCREAMING_SNAKE_CASE										=   (table[i][j] - total) / upper[j][j]
        SCREAMING_SNAKE_CASE										=   1
        for j in range(A__			,  A__       ):
            SCREAMING_SNAKE_CASE										=   sum(lower[i][k] * upper[k][j] for k in range(A__       )       )
            SCREAMING_SNAKE_CASE										=   table[i][j] - total
    return lower, upper


if __name__ == "__main__":
    import doctest

    doctest.testmod()





def 		lowerCamelCase__       (						):







	'''simple docstring'''





	for n in range(1	,      1000000				):
		yield n * (n + 1) // 2


def 		lowerCamelCase__       (						_A				):







	'''simple docstring'''





	snake_case_						       =	1
	snake_case_						       =	2
	while i * i <= n:
		snake_case_						       =	0
		while n % i == 0:
			n //= i
			multiplicity += 1
		divisors_count *= multiplicity + 1
		i += 1
	if n > 1:
		divisors_count *= 2
	return divisors_count


def 		lowerCamelCase__       (						):







	'''simple docstring'''





	return next(i for i in triangle_number_generator() if count_divisors(_A				) > 500				)


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