This is a very simply formulated task. Let's call an integer number `N` 'green' if `N²` ends with all of the digits of `N`. Some examples:

`5` is green, because `5² = 25` and `25` ends with `5`.

`11` is not green, because `11² = 121` and `121` does not end with `11`.

`376` is green, because `376² = 141376` and `141376` ends with `376`.

Your task is to write a function `green` that returns `n`th green number, starting with `1` - `green (1) == 1`

---

## Data range

```if:haskell
`n <= 4000` for Haskell
```
```if:java
`n <= 5000` for Java
```
```if:python
`n <= 5000` for Python
```
```if:javascript
`n <= 3000` for JavaScript

Return values should be `String`s, and should be exact. A BigNum library is recommended.
```

```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 = 'import functools\n\ndef automorphic(p):\n    t = 1\n    n = 5\n    k = 1\n    res = [1]\n    for i in range(1, p + 1):\n        size = 2 ** i\n        n = (3 * n ** 2 - 2 * n ** 3) % (10 ** size)\n        for j in range(k, size + 1):\n            m5 = n % (10 ** j)\n            m6 = 10 ** j + 1 - m5\n            # print("n = " + str(n) + "\\n[t, m5, m6] = " + str([t,m5,m6]) + " ")\n            res.append(m5)\n            res.append(m6)\n            # print("res = " + str(res))\n    return sorted(list(set(res)))\n\n@functools.lru_cache(maxsize=1)\ndef greent():\n    res = automorphic(13)\n    # print(res)\n    return res\n\ndef green(arg):\n    return greent()[arg - 1]'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'green'
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: 41427432