You have an initial power P, an initial score of 0 points, and a bag of tokens.
Each token can be used at most once, has a value token[i], and has potentially two ways to use it.

If we have at least token[i] power, we may play the token face up, losing token[i] power, and gaining 1 point.
If we have at least 1 point, we may play the token face down, gaining token[i] power, and losing 1 point.

Return the largest number of points we can have after playing any number of tokens.
 



Example 1:
Input: tokens = [100], P = 50
Output: 0


Example 2:
Input: tokens = [100,200], P = 150
Output: 1


Example 3:
Input: tokens = [100,200,300,400], P = 200
Output: 2

 
Note:

tokens.length <= 1000
0 <= tokens[i] < 10000
0 <= P < 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    # all the tokens start in a neutral position. Can either play it face up or face down.\n    def bagOfTokensScore(self, tokens: List[int], P: int) -> int:\n        tokens.sort()\n        \n        # start from front and back. greedily take all the powers from the front and spend score in back to get more to add to the front\n        def twoPointer(tokens, P):\n            i = 0\n            j = len(tokens)-1\n            score = 0\n            maxScore = 0\n            while i <= j:\n\n                flag = False\n                while i < len(tokens) and P >= tokens[i]:\n                    score += 1\n                    P -= tokens[i]\n                    i += 1\n                    flag = True\n                if flag:\n                    maxScore = max(score, maxScore)\n                    continue\n                    \n                if score > 0:\n                    score -= 1\n                    P += tokens[j]\n                    j -= 1\n                \n                elif P < tokens[i]:\n                    return score\n            return maxScore\n        \n        def helper(tokens, P, score):\n            maxVal = score\n            if score > 0 and len(tokens) > 0:\n                maxVal = max(helper(tokens[:len(tokens)-1], P + tokens[len(tokens)-1], score - 1), maxVal)\n        \n            for i in range(len(tokens)-1, -1, -1):\n                if P >= tokens[i]:\n                    maxVal = max(helper(tokens[:i] + tokens[i+1:], P - tokens[i], score + 1), maxVal)\n            return maxVal\n        \n        return twoPointer(tokens, P)\n        \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'bagOfTokensScore'
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: 5910