Consider a sequence, which is formed by the following rule: next term is taken as the smallest possible non-negative integer, which is not yet in the sequence, so that `no 3` terms of sequence form an arithmetic progression.

## Example

`f(0) = 0` -- smallest non-negative  
`f(1) = 1` -- smallest non-negative, which is not yet in the sequence  
`f(2) = 3` -- since `0, 1, 2` form an arithmetic progression  
`f(3) = 4` -- neither of `0, 1, 4`, `0, 3, 4`, `1, 3, 4` form an arithmetic progression, so we can take smallest non-negative, which is larger than `3`  
`f(4) = 9` --  `5, 6, 7, 8` are not good, since `1, 3, 5`, `0, 3, 6`, `1, 4, 7`, `0, 4, 8` are all valid arithmetic progressions.  

etc...

## The task

Write a function `f(n)`, which returns the `n-th` member of sequence.

## Limitations

There are `1000` random tests with `0 <= n <= 10^9`, so you should consider algorithmic complexity of your solution.

Difficulty: EASY
Starter code: def sequence(n):
	

Solutions:
sequence = lambda n: int(format(n, 'b'), 3)


def sequence(n):
	return int(format(n, 'b'), 3)


sequence = lambda n: int(bin(n)[2:], 3)


def sequence(n):
	return n and 3 * sequence(n >> 1) + (n & 1)


from math import log2

def sequence(i):
	if i == 0:
		return 0
	e = int(log2(i))
	return 3 ** e + sequence(i - 2 ** e)


import numpy as np

def sequence(n):
	return ter2dec(dec2bin(n))

def dec2bin(n):
	bin = np.array([])
	while n > 0:
		bin = np.append(bin, [n % 2])
		n = n // 2
	return bin

def ter2dec(ter):
	dec = 0
	for i in range(len(ter)):
		dec += ter[i] * 3 ** i
	return dec


def sequence(n):
	return int(f'{n:b}', 3)


def sequence(n):
	return int(bin(n)[2:], 3)


def sequence(n):
	return 3 * sequence(n // 2) + n % 2 if n > 0 else 0