# Largest Rectangle in Background

Imagine a photo taken to be used in an advertisement. The background on the left of the motive is whitish and you want to write some text on that background. So you scan the photo with a high resolution scanner and, for each line, count the number of pixels from the left that are sufficiently white and suitable for being written on. Your job is to find the area of the largest text box you can place on those pixels.

Example:
In the figure below, the whitish background pixels of the scanned photo are represented by asterisks.

```
*********************************
*********
*******
******
******
******
**************
**************
**************
***************
*********************

``` 

If you count the pixels on each line from the left you get the list (or array, depending on which language you are using) `[33, 9, 7, 6, 6, 6, 14, 14, 14, 15, 21]`. The largest reactangle that you can place on these pixels has an area of 70, and is represented by the dots in the figure below.

```
*********************************
*********
*******
******
******
******
..............
..............
..............
..............*
..............*******
``` 

Write a function that, given a list of the number whitish pixels on each line in the background, returns the area of the largest rectangle that fits on that background.

```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 largest_rect(heights):\n        maxArea = 0\n        stack = [] # stack of pairs: (index, height)\n        \n        for i, h in enumerate(heights):\n            start = i\n            while stack and stack[-1][1] > h:\n                index, height = stack.pop()\n                maxArea = max(maxArea, height * (i - index))\n                start = index\n            stack.append((start, h))\n        \n        # remaining heights extended to the end of the histogram\n        for i, h in stack:\n            maxArea = max(maxArea, h * (len(heights) - i))\n        return maxArea'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'largest_rect'
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: 5794