# Situation
You have been hired by a company making electric garage doors. Accidents with the present product line have resulted in numerous damaged cars, broken limbs and several killed pets. Your mission is to write a safer version of their controller software.

# Specification
We always start with a closed door. The remote control has exactly one button, with the following behaviour.

+ If the door is closed, a push starts opening the door, and vice-versa
+ It takes 5 seconds for the door to open or close completely
+ While the door is moving, one push pauses movement, another push resumes movement in the same direction

In order to make the door safer, it has been equiped with resistance-based obstacle detection. When the door detects an obstacle, it must immediately reverse the direction of movement.

# Input
A string where each character represents one second, with the following possible values.

* ```'.'``` No event
* ```'P'``` Button has been pressed
* ```'O'``` Obstacle has been detected (supersedes P)

As an example, ```'..P....'``` means that nothing happens for two seconds, then the button is pressed, then no further events.

# Output
A string where each character represents one second and indicates the position of the door (0 if fully closed and 5 fully open). The door starts moving immediately, hence its position changes at the same second as the event.

# Example
```..P...O.....``` as input should yield
```001234321000``` as output

```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 State:\n    def __init__(self):\n        pass\nclass PausedIncreasing(State):\n    @classmethod\n    def handle(cls, e, val):\n        nextstate = cls\n        if e == '.':\n            pass\n        elif e == 'P':\n            val += 1\n            nextstate = MovingIncreasing\n        elif e == 'O':\n            nextstate = PausedDecreasing\n        return val, nextstate\nclass PausedDecreasing(State):\n    @classmethod\n    def handle(cls, e, val):\n        nextstate = cls\n        if e == '.':\n            pass\n        elif e == 'P':\n            val -= 1\n            nextstate = MovingDecreasing\n        elif e == 'O':\n            nextstate = PausedIncreasing\n        return val, nextstate\nclass MovingIncreasing(State):\n    @classmethod\n    def handle(cls, e, val):\n        nextstate = cls\n        if e == '.':\n            val += 1\n        elif e == 'P':\n            nextstate = PausedIncreasing\n        elif e == 'O':\n            val -= 1\n            nextstate = MovingDecreasing\n        return val, nextstate\nclass MovingDecreasing(State):\n    @classmethod\n    def handle(cls, e, val):\n        nextstate = cls\n        if e == '.':\n            val -= 1\n        elif e == 'P':\n            nextstate = PausedDecreasing\n        elif e == 'O':\n            val += 1\n            nextstate = MovingIncreasing\n        return val, nextstate\n\nclass GarageDoor:\n    def __init__(self):\n        self.val = 0\n        self.state = PausedIncreasing\n    def handle(self, e):\n        self.val, self.state = self.state.handle(e, self.val)\n        if self.val == 0:\n            self.state = PausedIncreasing\n        elif self.val == 5:\n            self.state = PausedDecreasing\n        return str(self.val)\n    def get_output(self, events):\n        return ''.join(str(self.handle(e)) for e in events)\n\ndef controller(events):\n    gd = GarageDoor()\n    return gd.get_output(events)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'controller'
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: 6266