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 racecar1(self, target: int) -> int:\n        # bfs 能够快速想起来的方法！剪枝的策略不理解！\n        q = collections.deque()\n        q.append([0, 1])\n        visited = set()\n        visited.add('0_1')\n        visited.add('0_-1')\n        steps = 0\n        while q:\n            qsize = len(q)\n            for i in range(qsize):\n                pos, speed = q.popleft()\n                \n                pos1 = pos + speed\n                speed1 = speed * 2 # 加速！注意第一个可能性的构造方法：首先是新的pos1，然后是新的速度！\n                if pos1 == target:\n                    return steps + 1\n                p1 = [pos1, speed1]\n                #key1 = '{}_{}'.format(pos1, speed1)\n                if abs(speed1) < 2*target and abs(pos1) < 2*target and not key1 in visited: #相当于说，如果>= 2*target的时候，就剪枝了！\n                    q.append(p1) #如果 < ??? # 这里没有把p1加入visited???\n                    #visited.add(key1) # this makes things slower... yet still can pass!\n                \n                speed2 = -1 if speed > 0 else 1 # 掉头！注意是维持pos位置不变，速度如果原来是》0，则变成-1，如果是《0则变成1！！\n                p2 = [pos, speed2]\n                key2 = '{}_{}'.format(pos, speed2)\n                if key2 not in visited:\n                    q.append(p2)\n                    visited.add(key2)\n            steps += 1\n        return -1\n    \n    def racecar(self, target):\n        k = target.bit_length() + 1\n        barrier = 1<<k\n        pq = [(0, target)]\n        dist = [float('inf')] * (2 * barrier + 1)\n        dist[target] = 0\n        \n        while pq:\n            steps, targ = heapq.heappop(pq)\n            if dist[targ] > steps: continue\n            \n            for k2 in range(k+1):\n                walk = (1<<k2) - 1\n                steps2, targ2 = steps + k2 + 1, walk - targ\n                if walk == targ:\n                    steps2 -= 1\n                \n                if abs(targ2) <= barrier and steps2 < dist[targ2]:\n                    heapq.heappush(pq, (steps2, targ2))\n                    dist[targ2] = steps2\n        return dist[0]"
_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: 6236