The goal of this Kata is to remind/show you, how Z-algorithm works and test your implementation.

For a string str[0..n-1], Z array is of same length as string. An element Z[i] of Z array stores length of the longest substring starting from str[i] which is also a prefix of str[0..n-1]. The first entry of Z array is meaning less as complete string is always prefix of itself.

Example:

Index:            0   1   2   3   4   5   6   7   8   9  10  11


Text:             "a   a   b   c   a   a   b   x   a   a   a   z"


Z values:         [11,   1,   0,   0,   3,   1,   0,   0,   2,   2,   1,   0]



Your task will be to implement Z algorithm in your code and return Z-array.

For empty string algorithm should return [].

Input: string str 

Output: Z array

For example:

print zfunc('ababcaba')

[8, 0, 2, 0, 0, 3, 0, 1]

Note, that an important part of this kata is that you have to use
efficient way to get Z-array (O(n))

```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 = '# https://www.geeksforgeeks.org/z-algorithm-linear-time-pattern-searching-algorithm/\n\n\ndef zfunc(string):\n    if not string:\n        return []\n\n    strlen = len(string)\n    Z = [0] * strlen\n\n    # [L,R] make a window which matches with prefix of s\n    L = R = 0\n    for i in range(1, strlen):\n        # if i>R nothing matches so we will calculate.\n        # Z[i] using naive way.\n        if i > R:\n            L = R = i\n\n            # R-L = 0 in starting, so it will start\n            # checking from 0\'th index. For example,\n            # for "ababab" and i = 1, the value of R\n            # remains 0 and Z[i] becomes 0. For string\n            # "aaaaaa" and i = 1, Z[i] and R become 5\n            while R < strlen and string[R - L] == string[R]:\n                R += 1\n            Z[i] = R - L\n            R -= 1\n        else:\n            # k = i-L so k corresponds to number which\n            # matches in [L,R] interval.\n            k = i - L\n            # if Z[k] is less than remaining interval\n            # then Z[i] will be equal to Z[k].\n            # For example, str = "ababab", i = 3, R = 5\n            # and L = 2\n            if Z[k] < R - i + 1:\n                # For example str = "aaaaaa" and i = 2, R is 5,\n                # L is 0\n                Z[i] = Z[k]\n            else:\n                # else start from R and check manually\n                L = i\n                while R < strlen and string[R - L] == string[R]:\n                    R += 1\n                Z[i] = R - L\n                R -= 1\n    Z[0] = strlen\n    return Z\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'zfunc'
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: 5876