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):\n        dp = [0, 1, 4] + [float(\'inf\')] * target\n        for t in range(3, target + 1):\n            k = t.bit_length()\n            if t == 2**k - 1:\n                dp[t] = k\n                continue\n            for j in range(k - 1):\n                dp[t] = min(dp[t], dp[t - 2**(k - 1) + 2**j] + k - 1 + j + 2)\n            if 2**k - 1 - t < t:\n                dp[t] = min(dp[t], dp[2**k - 1 - t] + k + 1)\n        return dp[target]\n# 比较难的一道题目，想了几天无果看了官方给的题解，还是很巧妙的。\n# 用Ak表示k次连续的A，首先结尾一定不是R，开头的RAk可以放到最后。\n# 那么最终指令应该形如Ak1RAk2R…RAkn。\n# 容易得到奇数的ki与偶数的ki都是单调递减的，且各不相同。\n# 并且到达或者超过目标位置之后继续执行A是没有意义的。\n# 因此就有了DP的做法，如果下标位置是2k−1，那么可以直接Ak达到。\n# 否则有两种情况，一是拐两次到达，正面一定有一次最大限度的2k−1，外加返回走j步（枚举j）。\n# 二是直接走刚好超过2k−1，回走到终点。\n\n#     def racecar(self, target: int) -> int:\n#         # 0 -> 1 -> 3 -> 7 - > 15\n#         # 1 -> 2 -> 4 -> 8 -> 16\n#         # 从 0 出发，每次可以 R 或 A两个方向，选择。\n#         # 可以记录每次到达的状态，\n#         # BFS\n        \n#         d = deque([(0, 0, 1)])\n#         visited = collections.defaultdict(set)\n#         visited[0].add(1)\n#         ans = float(\'inf\')\n#         flag = 0\n#         while d:\n#             flag += 1\n#             # print(\\"flag=\\", flag,\\", d=\\", d)\n#             l = len(d)\n#             while l:\n#                 l -= 1\n#                 cur = d.popleft()\n#                 # print(\\"cur=\\", cur)\n#                 pos, cost, speed = cur\n#                 if pos == target:\n#                     ans = min(ans, cost)\n#                     # continue\n#                     return cost\n#                 # use R\n#                 cost += 1\n#                 if 1:\n#                     newspeed = -1 if speed > 0 else 1\n#                     if not ((pos in visited and newspeed in visited[pos]) or (pos <= 0)):\n#                         # print(\\"past=\\", cur,\\", add=\\", (pos, cost, -1))\n#                         d.append(((pos, cost, newspeed)))\n#                         visited[pos].add(newspeed)\n#                         # 这里 if 里 break 不要瞎用，会跳出 while l 这个循环的。\n#                 # use A\n#                 if 1:\n#                     if not (( speed in visited and (cost, speed * 2) in visited[pos]) or (pos + speed > target * 2) or (pos + speed <= 0)):\n                        \n#                         # print(\\"past=\\", cur,\\", add=\\", (pos + speed, cost, speed * 2))\n#                         d.append((pos + speed, cost, speed * 2))\n#                         visited[pos].add(speed * 2)\n#         return\n                \n#   # BFS 搞了半天，终于结束了。注意要剪枝。\n# # 1. 首先 visited 加入的是 pos 和 speed。\n# # 2. 第二是 位置不能超过 target * 2 。因为 如果超过了 target * 2那么要倒车，倒车从头开始，也要 走 target。这是 不合算的。 \n# # 3. 速度不能超过 2*target。  （可以不要）\n# # 4. 不要 pos <0 的位置。\n#         # pos    0 1 3 2 3\n#         # speed  1 2 -1 1\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: 5862