Fibonacci numbers are generated by setting F0 = 0, F1 = 1, and then using the formula:

# Fn = Fn-1 + Fn-2

Your task is to efficiently calculate the **n**th element in the Fibonacci sequence and then count the occurrence of each digit in the number. Return a list of integer pairs sorted in **descending** order.

10 ≤ n ≤ 100000

## Examples
```
f(10) = 55  # returns [(2, 5)], as there are two occurances of digit 5

f(10000)    # returns:
  [(254, 3),
   (228, 2),
   (217, 6),
   (217, 0),
   (202, 5),
   (199, 1),
   (198, 7),
   (197, 8),
   (194, 4),
   (184, 9)]
```
If two integers have the same count, sort them in descending order.

Your algorithm must be efficient.

~~~if:javascript
Solving this Kata in Javascript requires the use of the bignumber.js library. I have included starter code to assist you with using the library. Thanks to `kazk` for assisting with the translation.
~~~

```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 fast_fib(n):\n    def pos(n):\n        if n == 0:\n            return (0, 1)\n        else:\n            a, b = pos(n // 2)\n            c = a * (b * 2 - a)\n            d = a * a + b * b\n            if n % 2 == 0:\n                return (c, d)\n            else:\n                return (d, c + d)\n    \n    def fib(n):\n        if n >= 0:\n            return pos(n)[0]\n    \n        if n < 0:\n            sign = -1 if n % 2 == 0 else 1\n            return sign*pos(abs(n))[0]\n    \n    return fib(n)\n\ndef fib_digits(n):\n    from collections import Counter\n    cnt = Counter(str(fast_fib(n)))\n    ret = [(v, int(k)) for k, v in cnt.items()]\n    ret = sorted(ret, key=lambda x: (-x[0], -x[1]))\n    \n    return ret'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'fib_digits'
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: 10801