# Task
 Miss X has only two combs in her possession, both of which are old and miss a tooth or two. She also has many purses of different length, in which she carries the combs. The only way they fit is horizontally and without overlapping. Given teeth' positions on both combs, find the minimum length of the purse she needs to take them with her.

 It is guaranteed that there is at least one tooth at each end of the comb. 

 - Note, that the combs can not be rotated/reversed.

# Example

 For `comb1 = "*..*" and comb2 = "*.*"`, the output should be `5`

 Although it is possible to place the combs like on the first picture, the best way to do this is either picture 2 or picture 3.

 ![](https://codefightsuserpics.s3.amazonaws.com/tasks/combs/img/cbs.png?_tm=1484930552851)

# Input/Output


 - `[input]` string `comb1`

   A comb is represented as a string. If there is an asterisk ('*') in the ith position, there is a tooth there. Otherwise there is a dot ('.'), which means there is a missing tooth on the comb.

   Constraints: 1 ≤ comb1.length ≤ 10.
   
   

 - `[input]` string `comb2`

   The second comb is represented in the same way as the first one.

   Constraints: 1 ≤ comb2.length ≤ 10.
   

 - `[output]` an integer

   The minimum length of a purse Miss X needs.

```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 combs(comb1, comb2):\n    c1 = int(comb1.replace('*', '1').replace('.', '0'), 2)\n    c2 = int(comb2.replace('*', '1').replace('.', '0'), 2)\n    def r(x, y):\n        if x.__xor__(y) == x + y:\n            return max(x.bit_length(), y.bit_length())\n        return r(x<<1,y)\n    return min(r(c1,c2), r(c2,c1))"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'combs'
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: 6084