# Task

In the field, two beggars A and B found some gold at the same time. They all wanted the gold, and they decided to use simple rules to distribute gold:
```
They divided gold into n piles and be in line. 
The amount of each pile and the order of piles all are randomly.

They took turns to take away a pile of gold from the 
far left or the far right.

They always choose the bigger pile. That is to say, 
if the left is 1, the right is 2, then choose to take 2.

If the both sides are equal, take the left pile.
```

Given an integer array `golds`, and assume that A always takes first. Please calculate the final amount of gold obtained by A and B. returns a two-element array `[amount of A, amount of B]`.

# Example

For `golds = [4,2,9,5,2,7]`, the output should be `[14,15]`.
```
The pile of most left is 4, 
The pile of most right is 7, 
A choose the largest one -- > take 7

The pile of most left is 4, 
The pile of most right is 2, 
B choose the largest one -- > take 4

The pile of most left is 2, 
The pile of most left is 2, 
A choose the most left one -- > take 2

The pile of most left is 9, 
The pile of most right is 2, 
B choose the largest one -- > take 9

The pile of most left is 5, 
The pile of most left is 2, 
A choose the largest one -- > take 5

Tehn, only 1 pile left, 
B  -- > take 2

A: 7 + 2 + 5 = 14
B: 4 + 9 + 2 = 15
```

For `golds = [10,1000,2,1]`, the output should be `[12,1001]`.
```
A take 10
B take 1000
A take 2
B take 1

A: 10 + 2 = 12
B: 1000 + 1 = 1001
```

```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 = 'distribution_of=lambda g,r=[0,0],c=0: r if not len(g) else distribution_of(*([g[:-1],[r[0],r[1]+g[-1]],0] if g[-1]>g[0] else [g[1:],[r[0],r[1]+g[0]],0])) if c else distribution_of(*([g[:-1],[r[0]+g[-1],r[1]],1] if g[-1]>g[0] else [g[1:],[r[0]+g[0],r[1]],1]))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'distribution_of'
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: 7696