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 = "def green(n):\n    vec = [1, 5, 6]\n    m1 = 5\n    m2 = 6\n    tot = 3\n    h = 0\n    while tot < n:\n        s1 = str(m1)\n        s2 = str(m2)\n        m1 = morph(m1)\n        m2 = morph(m2)\n        (tot, vec, h) = recover(str(m1), s1, str(m2), s2, vec, tot, h)\n    vec.sort()\n    return vec[n - 1]\n\n\ndef recover(p, s, r, q, vec, tot, h):\n    d = len(p) - len(s)\n    d2 = len(r) - len(q)\n    for i in range(0, d):\n        if p[d - 1 - i] != '0':\n            vec.append(int(p[d - 1 - i: d] + s))\n            tot += 1\n        if r[d2 - 1 - i + h] != '0':\n            vec.append(int(r[d2 - 1 - i + h: d2 + h] + q[h:]))\n            tot += 1\n    return tot, vec, len(r) - len(p)\n\n\ndef morph(m):\n    return (3 * m * m - 2 * m * m * m) % 10 ** (2 * len(str(m)))"
_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: 5594