# Unflatten a list (Harder than easy)

This is the harder version of Unflatten a list (Easy)

So you have again to build a method, that creates new arrays, that can be flattened!

# Shorter: You have to unflatten a list/an array.

You get an array of integers and have to unflatten it by these rules:
```
- You have to do several runs. The depth is the number of runs, you have to do.
- In every run you have to switch the direction. First run from left, next run from right. Next left...
Every run has these rules:
- You start at the first number (from the direction).
- Take for every number x the remainder of the division by the number of still available elements (from 
  this position!) to have the number for the next decision.
- If the remainder-value is smaller than 3, take this number x (NOT the remainder-Value) direct
  for the new array and continue with the next number.
- If the remainder-value (e.g. 3) is greater than 2, take the next remainder-value-number (e.g. 3)
  elements/numbers (inclusive the number x, NOT the remainder-value) as a sub-array in the new array.
  Continue with the next number/element AFTER this taken elements/numbers.
- Every sub-array in the array is independent and is only one element for the progress on the array. 
  For every sub-array you have to follow the same rules for unflatten it.
  The direction is always the same as the actual run.
```

Sounds complicated? Yeah, thats why, this is the harder version...
Maybe an example will help.

```
 Array: [4, 5, 1, 7, 1] Depth: 2 -> [[ 4, [ 5, 1, 7 ] ], 1]
 
Steps: 
First run: (start from left side!)
1. The first number is 4. The number is smaller than the number of remaining elements, so it is the remainder-value (4 / 5 -> remainder 4).
   So 4 numbers (4, 5, 1, 7) are added as sub-array in the new array.
2. The next number is 1. It is smaller than 3, so the 1 is added direct to the new array.
Now we have --> [[4, 5, 1, 7], 1]

Second run: (start from right side!)
1. The last number (first from other side) is 1. So the 1 is added direct to the new array.
2. The next element is the sub-array. So we use the rules for this.
2a.The last number is 7. There are 4 elements in the array. So for the next decision you have to
   take the remainder from 7 / 4 -> 3. So 3 numbers (5, 1, 7) are added as sub-array in the 
   new array.
2b.Now there is the 4 and only one element last in this array. 4 / 1 -> remainder 0. It is smaller
   than 3. So the 4 is added direct to the new array.
Now we have --> [[ 4, [ 5, 1, 7 ] ], 1]
```

The given array will always contain numbers. There will only be numbers > 0.


Have fun coding it and please don't forget to vote and rank this kata! :-) 

I have created other katas. Have a look if you like coding and challenges.

```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 unflatten(flat_array, depth):\n    r=flat_array\n    direction=1\n    for d in range(depth):\n        r=_unflatten(r,direction)\n        direction*=-1\n    return r\n\ndef _unflatten(flat_array, direction):\n    q=flat_array[:]\n    r=[]\n    while(q):\n        if direction>0:\n            x=q.pop(0)\n        else:\n            x=q.pop()\n        if type(x)==list:\n            if direction>0:\n                r.append(_unflatten(x,direction))\n            else:\n                r.insert(0,_unflatten(x,direction))\n        elif x%(len(q)+1)<3:\n            if direction>0:\n                r.append(x)\n            else:\n                r.insert(0,x)\n        else:\n            t=[x]\n            for _ in range(x%(len(q)+1)-1):\n                if not q:\n                    break\n                if direction>0:\n                    t.append(q.pop(0))\n                else:\n                    t.append(q.pop())\n            if direction>0:\n                r.append(t)\n            else:\n                r.insert(0,t[::-1])\n    return r'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'unflatten'
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: 6964