Given a positive integer `n`, return first n dgits of Thue-Morse sequence, as a string (see examples).

Thue-Morse sequence is a binary sequence with 0 as the first element. The rest of the sequece is obtained by adding the Boolean (binary) complement of a group obtained so far.

```
For example:

0
01
0110
01101001
and so on...
```

![alt](https://upload.wikimedia.org/wikipedia/commons/f/f1/Morse-Thue_sequence.gif)

Ex.:
```python
thue_morse(1);  #"0"
thue_morse(2);  #"01"
thue_morse(5);  #"01101"
thue_morse(10): #"0110100110"
```

- You don't need to test if n is valid - it will always be a positive integer.
- `n` will be between 1 and 10000

[Thue-Morse on Wikipedia](https://en.wikipedia.org/wiki/Thue%E2%80%93Morse_sequence)

[Another kata on Thue-Morse](https://www.codewars.com/kata/simple-fun-number-106-is-thue-morse) by @myjinxin2015

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

Solutions:
thue_morse = lambda n: '0110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100101101001100101101001011001101001100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010011001011001101001011010011001011010010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100101101001100101101001011001101001100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100101101001100101101001011001101001100101100110100101101001100101101001011001101001011010011001011001101001100101101001011001101001100101100110100101101001100101100110100110010110100101100110100101101001100101101001011001101001100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100101101001100101101001011001101001100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010011001011001101001011010011001011010010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010011001011001101001011010011001011010010110011010010110100110010110011010011001011010010110011010011001011001101001011010011001011001101001100101101001011001101001011010011001011010010110011010011001011001101001011010011001011010010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010011001011001101001011010011001011010010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100101101001100101101001011001101001100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010011001011001101001011010011001011010010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100101101001100101101001011001101001100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100101101001100101101001011001101001100101100110100101101001100101101001011001101001011010011001011001101001100101101001011001101001100101100110100101101001100101100110100110010110100101100110100101101001100101101001011001101001100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100101101001100101101001011001101001100101100110100101101001100101100110100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0'[:n]


def thue_morse(n):
	out = '0'
	while len(out) < n:
		out += out.replace('1', '2').replace('0', '1').replace('2', '0')
	return out[:n]


from math import log

def thue_morse(n, s='0'):
	for _ in range(int(log(n, 2)) + 1):
		s += s.translate(str.maketrans('01', '10'))
	return s[:n]


def thue_morse(n):
	k = t = 0
	while t.bit_length() < n:
		t = t << 2 ** k | ~t & (1 << 2 ** k) - 1
		k += 1
	return bin(t).replace('b', '')[:n]


def thue_morse(n):
	s = '0'
	while len(s) < n:
		s += ''.join([str(int(i) ^ 1) for i in s])
	return s[:n]


from itertools import islice

def f(tbl=str.maketrans('01', '10')):
	x = '0'
	while True:
		yield from x[len(x) // 2:]
		x += x.translate(tbl)

def thue_morse(n):
	return ''.join(islice(f(), n))


def thue_morse(n):
	code = '0'
	while len(code) < n:
		code += code.translate(code.maketrans('01', '10'))
	return code[:n]


import math

def thue_morse(n):
	return morse(2 ** (math.log2(n) // 1 + 1))[0:n]

def morse(m):
	return morse(m / 2) + ''.join([str(int(i) ^ 1) for i in morse(m / 2)]) if m > 1 else '0'


from codecs import decode
tm = b'QlpoOTFBWSZTWYSVjQkACcGIAGAAIACQEAUjUFRlVFsRLBUYVGKjKjVGJo01tbMxratRqjKjFRhU\nYJbQSyFRpCo4u5IpwoSEJKxoSA=='
for c in ('base64', 'bz2', 'utf8'):
	tm = decode(tm, c)

def thue_morse(n):
	return tm[:n]


thue_morse = m = lambda n, t='0': n > len(t) and m(n, t + t.translate({48: 49, 49: 48})) or t[:n]