.task {
  background: #fff;
  color: #333;
  padding: 25px;
  box-sizing: border-box;
  font-family: Comfortaa, sans-serif !important;
  position: relative;
}
.task code, .task_code {
  display: inline-block;
  padding: 0;
  border-radius: 2px;
  margin: 0;
  position: relative;
  top: 6px;
  background: bisque;
  border: 1px solid #f9d2a4;
  padding: 3px;
  line-height: 1em;
}
.task_code {
  top: -1px;
}
.task_header {
  color: #333 !important;
  margin-top: 0;
  font-size: 30px !important;
}
.task_inner {
  box-shadow: 0 2px 11px -3px rgba(0,0,0,.6);
  padding: 20px;
  border-radius: 3px;
}
.task_devil {
  float: right;
  margin-left: 15px;
  shape-outside: circle(150px);
}
.task_devil img {
  max-width: 150px;
}
.task_part-header { 
  font-size: 20px !important;
  font-weight: 800;
  color: #333;
  padding: 20px 0 10px;
}
.task_part-header:first-of-type {
  padding-top: 0;
}
.task_list {
  padding: 0;
  margin: 10px 0;
  padding-left: 30px;
}
.task_list ul {
  padding: 0;
  margin: 0;
}
.font-effect-canvas-print { color: black; }


Devil's Sequence

Problem



    Robodevil likes to do some mathematics between rehearsals of his orchestra. Today he invented devilish sequence No. 1729:
    

x0 = 0,
x1 = 1,
xn = (xn - 1 + xn - 2) / 2.


    For example, x10 = 0.666015625. Robodevil became interested at once how many `sixes` there were at the beginning of an arbitrary xn. In 6 nanoseconds, he had a formula. Can you do the same?
    Input
    You are given an integer n; `2 ≤ n ≤ 100000`.
    Output
    Output the number of sixes at the beginning of xn in decimal notation.
    Example



Input
Output


10
3

```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 = "from fractions import Fraction \nfrom decimal import *\n\ndef count_sixes(n):\n    a = 6 << (n - 2)\n    b = Fraction(2,3)\n    c = Fraction(1,a) \n    d = 0 \n    if n % 2 == 0:\n        d = b - c \n    else:\n        d = b + c     \n    getcontext().prec = 100000\n    e = str(Decimal(d.numerator)/Decimal(d.denominator))\n    f = 0     \n    for i in range(2,len(e)):\n        if e[i] == '6': \n            f += 1\n        else: break \n    return f\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'count_sixes'
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: 92806