Your car starts at position 0 and speed +1 on an infinite number line.  (Your car can go into negative positions.)
Your car drives automatically according to a sequence of instructions A (accelerate) and R (reverse).
When you get an instruction "A", your car does the following: position += speed, speed *= 2.
When you get an instruction "R", your car does the following: if your speed is positive then speed = -1 , otherwise speed = 1.  (Your position stays the same.)
For example, after commands "AAR", your car goes to positions 0->1->3->3, and your speed goes to 1->2->4->-1.
Now for some target position, say the length of the shortest sequence of instructions to get there.
Example 1:
Input: 
target = 3
Output: 2
Explanation: 
The shortest instruction sequence is "AA".
Your position goes from 0->1->3.

Example 2:
Input: 
target = 6
Output: 5
Explanation: 
The shortest instruction sequence is "AAARA".
Your position goes from 0->1->3->7->7->6.

 
Note: 

1 <= target <= 10000.

```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 collections import deque\nclass Solution:\n    # def racecar(self, target: int) -> int:\n    #     # position, speed\n    #     queue = deque([(0,1)])\n    #     nsteps = -1\n    #     while queue:\n    #         levelSize = len(queue)\n    #         nsteps += 1\n    #         for _ in range(levelSize):\n    #             pos, speed = queue.popleft()\n    #             if pos == target:\n    #                 return nsteps\n    #             # Always consider moving the car in the direction it is already going\n    #             queue.append( (pos+speed, speed*2) )\n    #             # Only consider changing the direction of the car if one of the following conditions is true\n    #             if (pos>target and speed>0) or \\\\\n    #                (pos<target and speed<0) or \\\\\n    #                (pos+speed>target and speed>0) or \\\\\n    #                (pos+speed<target and speed<0):\n    #                 queue.append( (pos, -1 if speed>0 else 1) )\n    #     return nsteps\n    def __init__(self):\n        self.dp = {0: 0}\n    def racecar(self, t: int) -> int:\n        if t in self.dp:\n            return self.dp[t]\n\n        n = t.bit_length()\n        if 2**n - 1 == t:\n            self.dp[t] = n\n        else:\n            # go pass the target, stop and turn back\n            self.dp[t] = self.racecar(2**n-1-t) + n + 1\n            # Go as far as possible before pass target, stop and turn back\n            for m in range(n-1):\n                self.dp[t] = min(self.dp[t], self.racecar(t - 2**(n-1) + 1 + 2**m - 1) + (n - 1) + m + 2)\n        return self.dp[t]\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'racecar'
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: 5722