Now we will confect a reagent. There are eight materials to choose from, numbered 1,2,..., 8 respectively.

We know the rules of confect:
```
material1 and material2 cannot be selected at the same time
material3 and material4 cannot be selected at the same time
material5 and material6 must be selected at the same time
material7 or  material8 must be selected(at least one, or both)
```

# Task

You are given a integer array `formula`. Array contains only digits 1-8 that represents material 1-8. Your task is to determine if the formula is valid. Returns `true` if it's valid, `false` otherwise.


# Example

For `formula = [1,3,7]`, The output should be `true`.

For `formula = [7,1,2,3]`, The output should be `false`.

For `formula = [1,3,5,7]`, The output should be `false`.

For `formula = [1,5,6,7,3]`, The output should be `true`.

For `formula = [5,6,7]`, The output should be `true`.

For `formula = [5,6,7,8]`, The output should be `true`.

For `formula = [6,7,8]`, The output should be `false`.

For `formula = [7,8]`, The output should be `true`.


# Note

- All inputs are valid. Array contains at least 1 digit. Each digit appears at most once. 

- Happy Coding `^_^`

```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 isValid(formula):\n  if len(formula) == 0:\n    return False\n  elif len(formula) == 1:\n    if 7 in formula or 8 in formula:\n      return True\n    else:\n      return False\n  elif len(formula) == 2:\n    if 7 in formula and 8 in formula:\n      return True\n    elif 7 in formula or 8 in formula:\n      if 5 in formula or 6 in formula:\n        return False\n      else:\n        return True\n    else:\n      return False\n  elif len(formula) == 3:\n    if 7 in formula and 8 in formula:\n      if 5 in formula or 6 in formula:\n        return False\n      else:\n        return True\n    elif 7 in formula or 8 in formula:\n      if 5 in formula and 6 in formula:\n        return True\n      elif (3 in formula and 4 not in formula) or (4 in formula and 3 not in formula):\n        if (1 in formula and 2 not in formula) or (2 in formula and 1 not in formula):\n          return True\n        else:\n          return False\n      else:\n        return False\n    else:\n      return False\n  elif len(formula) == 4:\n    if 7 in formula and 8 in formula:\n      if 5 in formula and 6 in formula:\n        return True\n      elif (3 in formula and 4 not in formula) or (4 in formula and 3 not in formula):\n        if (1 in formula and 2 not in formula) or (2 in formula and 1 not in formula):\n          return True\n        else:\n          return False\n      else:\n        return False\n    elif 7 in formula or 8 in formula:\n      if 5 in formula and 6 in formula:\n        return True\n      else:\n        return False\n    else:\n      return False\n  elif len(formula) == 5:\n    if 7 in formula and 8 in formula:\n      if 5 in formula and 6 in formula:\n        return True\n      else:\n        return False\n    elif 7 in formula or 8 in formula:\n      if 5 in formula and 6 in formula:\n        if (3 in formula and 4 not in formula) or (4 in formula and 3 not in formula):\n          if (1 in formula and 2 not in formula) or (2 in formula and 1 not in formula):\n            return True\n          else:\n            return False\n        else:\n          return False\n      else:\n        return False\n    else:\n      return False\n  elif len(formula) == 6:\n    if 7 in formula and 8 in formula:\n      if 5 in formula and 6 in formula:\n        if (3 in formula and 4 not in formula) or (4 in formula and 3 not in formula):\n          if (1 in formula and 2 not in formula) or (2 in formula and 1 not in formula):\n            return True\n          else:\n            return False\n        else:\n          return False\n      else:\n        return False\n    else:\n      return False\n  elif len(formula) > 6:\n    return False'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'isValid'
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: 6250