A chef has collected data on the satisfaction level of his n dishes. Chef can cook any dish in 1 unit of time.
Like-time coefficient of a dish is defined as the time taken to cook that dish including previous dishes multiplied by its satisfaction level  i.e.  time[i]*satisfaction[i]
Return the maximum sum of Like-time coefficient that the chef can obtain after dishes preparation.
Dishes can be prepared in any order and the chef can discard some dishes to get this maximum value.
 
Example 1:
Input: satisfaction = [-1,-8,0,5,-9]
Output: 14
Explanation: After Removing the second and last dish, the maximum total Like-time coefficient will be equal to (-1*1 + 0*2 + 5*3 = 14). Each dish is prepared in one unit of time.
Example 2:
Input: satisfaction = [4,3,2]
Output: 20
Explanation: Dishes can be prepared in any order, (2*1 + 3*2 + 4*3 = 20)

Example 3:
Input: satisfaction = [-1,-4,-5]
Output: 0
Explanation: People don't like the dishes. No dish is prepared.

Example 4:
Input: satisfaction = [-2,5,-1,0,3,-3]
Output: 35

 
Constraints:

n == satisfaction.length
1 <= n <= 500
-10^3 <= satisfaction[i] <= 10^3

```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 = 'def merge(arr1,arr2):\n    index1,index2=0,0\n    res=[]\n    while index1 < len(arr1) or index2 < len(arr2):\n        if index1 >= len(arr1) or (index2 < len(arr2) and arr1[index1] > arr2[index2]):\n            res.append(arr2[index2])\n            index2+=1\n        else:\n            res.append(arr1[index1])\n            index1+=1\n    return res\n\ndef mergeSort(arr):\n    if len(arr) <= 1:\n        return arr\n    m = int(len(arr)/2)\n    return merge(mergeSort(arr[:m]),mergeSort(arr[m:]))\n\ndef splitAtZero(sortedArr):\n    for i in range(len(sortedArr)):\n        if sortedArr[i] >= 0:\n            return (sortedArr[:i],sortedArr[i:])\n    return (sortedArr,[])\n\ndef coefficient(arr):\n    res = 0\n    for i in range(len(arr)):\n        res += (i+1)*arr[i]\n    return res\n\nclass Solution:\n    def maxSatisfaction(self, unsortedSatisfaction: List[int]) -> int:\n        satisfaction = mergeSort(unsortedSatisfaction)\n        # negative,nonnegative = splitAtZero(satisfaction)\n        # res = nonnegative[:]\n        # for dish in reversed(negative):\n        #     attempt = [dish] + res[:]\n        #     if coefficient(attempt) > coefficient(res):\n        #         res = attempt[:]\n        #     else:\n        #         return coefficient(res)\n        runningSum = 0\n        for i in reversed(list(range(len(satisfaction)))):\n            runningSum += satisfaction[i]\n            if runningSum <= 0:\n                return coefficient(satisfaction[i+1:])\n        return coefficient(satisfaction)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'maxSatisfaction'
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: 7054