Similar setting of the [previous](https://www.codewars.com/kata/progressive-spiral-number-position/), this time you are called to identify in which "branch" of the spiral a given number will end up.

Considering a square of numbers disposed as the 25 items in [the previous kata](https://www.codewars.com/kata/progressive-spiral-number-position/), the branch are numbered as it follows:

```
17 16 15 14 13    1 1 1 1 0
18 05 04 03 12    2 1 1 0 0
19 06 01 02 11 => 2 2 0 0 0
20 07 08 09 10    2 2 3 3 0
21 22 23 24 25    2 3 3 3 3
```

Meaning that, for example, numbers in the `10-13` range will be in branch `0`, numbers in the range `14-17` are inside branch `1`, all those nice numbers in the `18-21` can call branch `2` their house and finally the `21-25` team all falls under the `3` branch.

Your function must return the number of the index of each number [`1` being a special case you might consider equivalent to being in the first branch, `0`], as per examples:

```python
branch(1) == 0 #kind of special case here
branch(5) == 1
branch(25) == 3
branch(30) == 0
branch(50) == 0
```

It might help A LOT to both solve the [previous kata](https://www.codewars.com/kata/progressive-spiral-number-position/) and to visualize the diagonals of the square. Be ready for big numbers and, as usual, inspired by [AoC](http://adventofcode.com/2017/day/3). Finally, when ready, go to compute [the distance](https://www.codewars.com/kata/progressive-spiral-number-distance/) of the series.

```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 = 'k, li = 1, [0]\n\nfor i in range(1, 1000000):\n    li.append(k)\n    k += 8 * i\n    \ndef branch(n):\n    a,b = next([i,li[i-1]+1] for i,j in enumerate(li) if j>=n)\n    step = a*2-2\n    for i in range(4):\n        if b<=n<b+step : return i\n        b += step\n    return 0'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'branch'
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: 5988