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 = 'def getZarr(string):\n    n = len(string)\n    z = [0] * n\n\n    # [L,R] make a window which matches \n    # with prefix of s \n    l, r, k = 0, 0, 0\n    for i in range(1, n): \n\n        # if i>R nothing matches so we will calculate. \n        # Z[i] using naive way. \n        if i > r: \n            l, r = i, 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 < n and string[r - l] == string[r]: \n                r += 1\n            z[i] = r - l \n            r -= 1\n        else: \n\n            # k = i-L so k corresponds to number which \n            # matches in [L,R] interval. \n            k = i - l \n\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                z[i] = z[k] \n\n            # For example str = "aaaaaa" and i = 2, \n            # R is 5, L is 0 \n            else: \n\n                # else start from R and check manually \n                l = i \n                while r < n and string[r - l] == string[r]: \n                    r += 1\n                z[i] = r - l \n                r -= 1\n    return z\n\ndef zfunc(str_):\n    #your code goes here\n    solution = getZarr(str_)\n    if (len(solution) > 1):\n        solution[0] = len(solution)\n    return solution'
_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: 5972