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\n    def racecar(self, tgt: int) -> int:\n        \n        \'\'\'\n            shortest path -> bfs\n        \n            starting from [0, 1], how to reach tgt = 5?\n            \n                [0, 1] -> [1, 2], [0, -1]\n                \n                    [1, 2] -> [3, 4], [1, -1]\n                    [0, -1] ->[-1, -2], [0, 1] ... visited\n                    \n                    \n                        [3, 4] -> [3, -1], [7, 8]\n                        [1,-1] -> [0, -2], [1, 1]\n                        [-1,-2]-> [-3,-4] ... too far, [-1,1]\n                        \n                        \n                            [3, -1] -> [2, -2], [3, 1]\n                            [7,  8] ... too far\n                            [0, -2] -> [-2, -4] ... too far, [0, 1] ... visited\n                            [1,  1] -> [2, 2], [1, -1] ...visited\n                            [-1 ,1] -> [0, 2], [-1, -1] ... too far\n                            \n                            \n                                [2, -2] -> [0, -4], [2, 1]\n                                [3,  1] -> [4,  2], [3, -1] ... visited\n                                [2,  2] -> [4,  4], [2, -1]\n                                [0,  2] -> [2,  4], [0, -1] ... visited\n                                \n                                    [0, -4] -> [-4, -8] ... too far, [0, 1] ... visited\n                                    [2,  1] -> [3,   2], [2, -1]\n                                    [4,  2] -> [6,   4], [4, -1]\n                                    [4,  4] -> [8,   8], [4, -1] ... in queue\n                                    [2, -1] -> [1,  -2], [2,  1] ... visited\n                                    [2,  4] -> [6,   8], [2, -1] ... visited\n                                    \n                                \n                                        [3, 2] -> [5 , 4]  -->> arrived\n                                        \n                                        -> 7 steps                                    \n        \'\'\'\n        \n        \'\'\'\n            1. try greedy -> can\'t pass tgt = 5\n            \n            2. list out all the step until reach the tgt -> time: O(2 ^ (num of operations) )\n            \n            3. speed up -> dont visit same nodes, dont go to \\"too far\\" nodes    \n                        \n            4. time complexity: \n                pos range: -tgt ~ tgt, spd range: 1 ~ log(tgt) -> graph node number will be 2 * tgt * log(tgt) -> O(tgt * log(tgt) )\n                                                \n        \'\'\'    \n        \n        visited = dict()        \n        q = collections.deque()        \n        \n        q.append([0, 1])        \n        visited[0] = set()\n        visited[0].add(1)\n        \n        step = 0\n        while len(q) > 0:\n            \n            curSize = len(q)           \n            \n            for i in range(0, curSize):                \n                \n                pop = q.pop()\n                pos, spd = pop[0], pop[1]\n                \n                if pos == tgt:\n                    return step\n                                                                                \n                nextSteps = [ [pos + spd, spd * 2], [pos, - 1 * spd // abs(spd)] ]\n                for nextStep in nextSteps:            \n                    \n                    nPos, nSpd = nextStep[0], nextStep[1]\n                    \n                    # check is too far node:\n                    if abs(nPos - tgt) <= tgt:                        \n                        # check visited\n                        if nPos not in visited or nSpd not in visited[nPos]:\n                            q.appendleft(nextStep)\n                            if nPos not in visited:\n                                visited[nPos] = set()\n                            \n                            visited[nPos].add(nSpd)\n                            \n            step += 1\n            \n            \n        return -1\n            \n                    \n                    \n                    \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: 7764