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 = "class Solution:\n    def racecar(self, target: int) -> int:\n        f = [None] * (target + 1)\n        \n        f[0] = 0\n\n        for i in range(1, target + 1):\n            f[i] = float('inf')\n            \n            k = i.bit_length()\n            \n            if i == 2**k - 1:\n                f[i] = k\n                continue\n            \n            # underspeed\n            for j in range(k - 1):\n                f[i] = min(f[i], f[i - 2**(k - 1) + 2**j] + k - 1 + j + 2)\n            \n            # overspeed\n            if 2**k - 1 - i < i:\n                f[i] = min(f[i], f[2**k - 1 - i] + k + 1)\n        return f[target]\n    \n#         f = [None] * (target + 1)\n        \n#         f[0] = 0\n        \n#         for i in range(1, target + 1):\n#             f[i] = float('inf')\n            \n#             n = len(bin(i)[2:])\n            \n#             if 2**n - 1 == i:\n#                 f[i] = n\n#                 continue\n                \n#             # overspeed\n#             f[i] = f[2**n - 1 - i] + n + 1 # reverse once\n            \n#             # underspeed\n#             for j in range(0, n):\n#                 gap = 1 << j - 1\n#                 f[i] = min(f[i], f[i - 2**(n - 1) + gap] + n + j + 1) # reverse twice\n#         return f[target]\n            \n        \n        \n#         int[] f = new int[target + 1];\n#         for (int i = 1; i <= target; i++){\n#             int bound = (Integer.highestOneBit(i) << 1) - 1;\n#             int n = Integer.bitCount(bound);\n#             if (i == bound){\n#                 f[i] = n;\n#                 continue;\n#             }\n#             // overspeed\n#             f[i] = f[bound - i] + n + 1; // Reverse once\n#             // underspeed\n#             bound >>= 1;\n#             for (int j = 0; j < n; j++){\n#                 int gap = (1 << j) - 1;\n#                 f[i] = Math.min(f[i], f[i - bound + gap] + n + j + 1); // Reverse twice\n#             }\n#         }\n#         return f[target];\n#     }\n# }\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: 5822