Rule 30 is a one-dimensional binary cellular automaton. You can have some information here:  

* [https://en.wikipedia.org/wiki/Rule_30](https://en.wikipedia.org/wiki/Rule_30)

You have to write a function that takes as input an array of 0 and 1 and a positive integer that represents the number of iterations. This function has to performe the nth iteration of the **Rule 30** with the given input.

The rule to derive a cell from itself and its neigbour is:

Current cell  | 000 | 001 | 010 | 011 | 100 | 101 | 110 | 111
:-------------|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:
 **New cell** |  0  |  1  |  1  |  1  |  1  |  0  |  0  |  0 
 

As you can see the new state of a certain cell depends on his neighborhood. In *Current cells* you have the *nth* cell with his left and right neighbor, for example the first configuration is **000**:

* left neighbor = 0
* current cell = 0
* right neighbor = 0

The result for the current cell is **0**, as reported in **New cell** row.

You also have to pay attention to the following things:

* the borders of the list are always 0
* values different from 0 and 1 must be considered as 0
* a negative number of iteration never changes the initial sequence
* you have to return an array of 0 and 1

Here a small example step by step, starting from the list **[1]** and iterating for 5 times:

* We have only one element so first of all we have to follow the rules adding the border, so the result will be **[0, 1, 0]**
* Now we can apply the rule 30 to all the elements and the result will be **[1, 1, 1]** (first iteration)
* Then, after continuing this way for 4 times, the result will be **[1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1]**

In Python, you can also use a support function to print the sequence named printRule30. This function takes as parameters the current list of 0 and 1 to print, the max level that you can reach (number of iterations) and the length of initial array.

```python
def printRule30(list_, maxLvl, startLen):
  ...
```

The last two parameters are optional and are useful if you are printing each line of the iteration to center the result like this:

░░▓░░  -> step 1  
░▓▓▓░  -> step 2  
▓▓░░▓  -> step 3  

If you pass only the array of 0 and 1 the previous result for each line will be like this:

▓ -> step 1   
▓▓▓ -> step 2  
▓▓░░▓ -> step 3 

**Note:** the function can print only the current list that you pass to it, so you have to use it in the proper way during the interactions of the rule 30.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def rule30(a, n):\n    for _ in range(n):\n        a = [int(0 < 4*x + 2*y + z < 5) for x, y, z in\n                zip([0, 0] + a, [0] + a + [0], a + [0, 0])]\n    return a'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'rule30'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 6104