Given a list of positive integers, the adjacent integers will perform the float division. For example, [2,3,4] -> 2 / 3 / 4.

However, you can add any number of parenthesis at any position to change the priority of operations. You should find out how to add parenthesis to get the maximum result, and return the corresponding expression in string format. Your expression should NOT contain redundant parenthesis.

Example:

Input: [1000,100,10,2]
Output: "1000/(100/10/2)"
Explanation:
1000/(100/10/2) = 1000/((100/10)/2) = 200
However, the bold parenthesis in "1000/((100/10)/2)" are redundant, since they don't influence the operation priority. So you should return "1000/(100/10/2)". 

Other cases:
1000/(100/10)/2 = 50
1000/(100/(10/2)) = 50
1000/100/10/2 = 0.5
1000/100/(10/2) = 2



Note:

The length of the input array is [1, 10].
Elements in the given array will be in range [2, 1000].
There is only one optimal division for each test case.

```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 optimalDivision(self, nums):\n         """\n         :type nums: List[int]\n         :rtype: str\n         """\n         table = [[None for i in range(len(nums))] for j in range(len(nums))]\n         for i in range(len(nums)):\n             table[i][i] = (nums[i], str(nums[i]))\n         return self.findmax(table, 0, len(nums) - 1)[1]\n \n     def findmax(self, table, i, j):\n         if table[i][j] is not None:\n             return table[i][j]\n \n         if j - i == 1:\n             a, a_s = table[i][i]\n             b, b_s = table[j][j]\n             ret = (a / b, a_s + \'/\' + b_s)\n             table[i][j] = ret\n             return ret\n         m = -1\n         ret = None\n         for d in range(i, j):\n             ma, max_rep = self.findmax(table, i, d)\n             mi, min_rep = self.findmin(table, d+1, j)\n             div = ma / mi\n             if div > m:\n                 m = div\n                 ret = (max_rep, min_rep)\n         rep = self.assemble(ret[0], ret[1])\n         print("max %d, %d: v, %f, %s" % (i, j, m, rep))\n         ret = (m, rep)\n         table[i][j] = ret\n         return ret\n \n     def findmin(self, table, i, j):\n         if table[j][i] is not None:\n             return table[j][i]\n \n         if j - i == 1:\n             a, a_s = table[i][i]\n             b, b_s = table[j][j]\n             ret = (a / b, a_s + \'/\' + b_s)\n             table[j][i] = ret\n             return ret\n \n         m = float(\'inf\')\n         ret = None\n         for d in range(i, j):\n             ma, max_rep = self.findmin(table, i, d)\n             mi, min_rep = self.findmax(table, d+1, j)\n             div = ma / mi\n             if div < m:\n                 m = div\n                 ret = (max_rep, min_rep)\n         rep = self.assemble(ret[0], ret[1])\n         print("min %d, %d: v, %f, %s" % (i, j, m, rep))\n         ret = (m, rep)\n         table[j][i] = ret\n         return ret\n \n     def assemble(self, up, down):\n         if \'/\' in down:\n             return "%s/(%s)" % (up, down)\n         else:\n             return "%s/%s" % (up, down)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'optimalDivision'
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: 9237