# TODO: because _get_type turns ptn types into py types, something like this: exepcted _ptn_t_string but got _ptn_t_bool, is turned into this instead: exepcted str but got bool
class PistonRuntimeError(Exception):pass
def _raise_runtime(m):raise PistonRuntimeError(m)
def _assert(c,m):None if c else _raise_runtime(m)
def _extend(c,n=None,s=False):
    def d(f):
        fn=n if n else f.__name__
        setattr(c,fn,staticmethod(f))if s else setattr(c,fn,f)
        def w(*a,**k):return f(*a,**k)
        return w
    return d
# type util
class PistonTypeError(Exception):pass
def _get_ptn_parent_type(t):return t._t()
def _get_type(t):return _get_ptn_parent_type(t)if(isinstance(t,_ptn_type)or issubclass(t if isinstance(t,type)else type(t), _ptn_type))else t if isinstance(t,type)else type(t)
def _cmp_type(t,o):return _get_type(t)==_get_type(o)
def _ensure_iterable(o):return o if isinstance(o,(list,tuple))else[o]
def _type_of(t,o):return _get_type(t)in[_get_type(e)for e in _ensure_iterable(o)]
def _type_mismatch(t,o):raise PistonTypeError("type mismatch. expected "+("|".join([_get_type(e).__name__ for e in _ensure_iterable(o)])+" but got "+_get_type(t).__name__))
def _type_list_mismatch(i,t,o):raise PistonTypeError("type mismatch at index "+str(i)+". exepcted "+("|".join([_get_type(e).__name__ for e in _ensure_iterable(o)])+" but got "+_get_type(t).__name__))
def _type_ptn_mismatch(t):raise PistonTypeError("type mismatch. expected a piston type, but got "+_get_type(t).__name__)
def _assert_type(t,o):_type_mismatch(t,o)if not _type_of(t,o)else None
def _assert_list_type(l,t):[_type_list_mismatch(i+1,e,t)if not _type_of(e,t)else None for i,e in enumerate(l)]
def _cast_type(v,t):ns=dict(v=v,t=t);exec("try:t(v);r=False\nexcept:r=True",ns);return _type_mismatch(v,t)if(ns["r"])else t(v)
def _is_ptn_type(t):t=t if isinstance(t,type)else type(t);return issubclass(t,_ptn_type)
def _is_ptn_type_list(l):a=False;[a:=isinstance(e,_ptn_type)for e in _ensure_iterable(l)];return a;
def _assert_ptn_type(t):_type_ptn_mismatch(t)if not _is_ptn_type(t)else None
def _assert_ptn_type_list(l):[_type_ptn_mismatch(e)if not _is_ptn_type(e)else None for e in l]
def _is_types_list(l):a=False;[a:=isinstance(e,type)for e in _ensure_iterable(l)];return a
def _length_error(e,l):raise ValueError("expected length "+str(len(e))+" but got "+str(l))
def _assert_length(e,l):_length_error(e,l)if len(e)!=l else None
def _assert_min_length(e,l):_length_error(e,l)if len(e)<l else None
def _assert_max_length(e,l):_length_error(e,l)if len(e)>l else None
# match util
def _value_cb(v):return lambda:v
def _call_fn(cb,args,n):
    n_args=cb.__code__.co_argcount
    if n_args<=0:return cb()
    else:
        template="res=call({args})";str_args=[f'"{arg}"'if isinstance(arg,str)else str(arg)for arg in args];arg_dif=n_args-n
        if arg_dif<=0:str_args=str_args[:arg_dif]
        else:str_args.extend(["None"]*arg_dif)
        f_call=template.format(args=",".join(str_args));ns=dict(__name__="match");ns["call"]=cb;exec(f_call,ns);return ns["res"]
class _Matchable(object):
    def get_values(self):raise NotImplementedError
    def get_n_values(self):return len(self.get_values())
    def match(self,*cases,default):
        for case in cases:
            _assert_type(case,(tuple,list));_assert_length(case,2);comp,call=case;call=call if callable(call)else _value_cb(call)
            if self.__eq__(comp):return _call_fn(call,self.get_values(),self.get_n_values())
        if default:call=default if callable(default)else _value_cb(default);return _call_fn(call,self.get_values(),self.get_n_values())
# types
class _ptn_type(object):pass
class _ptn_t_integer(_ptn_type):
    def __init__(s,v):s.v=_cast_type(v,int)
    def __str__(s):return str(s.v)
    def __repr__(s):return str(s)
    def __len__(s):return s.v.bit_length()
    def _cast(s,t):_assert(issubclass(t,_ptn_type),"casting type must be a piston primitive type");return t(s.v)
    @staticmethod
    def _t():return int
    @staticmethod
    def _init():return _ptn_t_integer(0)
    def __lt__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return s.v<o.v
        if isinstance(o,(int,float)):return s.v<o
        else:return False
    def __gt__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return s.v>o.v
        if isinstance(o,(int,float)):return s.v>o
        else:return False
    def __le__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return s.v<=o.v
        if isinstance(o,(int,float)):return s.v<=o
        else:return False
    def __ge__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return s.v>=o.v
        if isinstance(o,(int,float)):return s.v>=o
        else:return False
    def __eq__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return s.v==o.v
        if isinstance(o,(int,float)):return s.v==o
        else:return False
    def __ne__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return s.v!=o.v
        if isinstance(o,(int,float)):return s.v!=o
        else:return False
    def __add__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v+o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v+o)
        else:_type_mismatch(o,(int,float))
    def __iadd__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v+o.v;return s
        if isinstance(o,(int,float)):s.v=s.v+o;return s
        else:_type_mismatch(o,(int,float))
    def __radd__(s,o):return s.__add__(o)
    def __sub__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v-o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v-o)
        else:_type_mismatch(o,(int,float))
    def __isub__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v-o.v;return s
        if isinstance(o,(int,float)):s.v=s.v-o;return s
        else:_type_mismatch(o,(int,float))
    def __rsub__(s,o):return s.__sub__(o)
    def __mul__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v*o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v*o)
        else:_type_mismatch(o,(int,float))
    def __imul__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v*o.v;return s
        if isinstance(o,(int,float)):s.v=s.v*o;return s
        else:_type_mismatch(o,(int,float))
    def __rmul__(s,o):return s.__mul__(o)
    def __floordiv__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v//o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v//o)
        else:_type_mismatch(o,(int,float))
    def __ifloordiv__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v//o.v;return s
        if isinstance(o,(int,float)):s.v=s.v//o;return s
        else:_type_mismatch(o,(int,float))
    def __rfloordiv__(s,o):return s.__floordiv__(o)
    def __truediv__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v/o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v/o)
        else:_type_mismatch(o,(int,float))
    def __idiv__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v/o.v;return s
        if isinstance(o,(int,float)):s.v=s.v/o;return s
        else:_type_mismatch(o,(int,float))
    def __rdiv__(s,o):return s.__truediv__(o)
    def __mod__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v%o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v%o)
        else:_type_mismatch(o,(int,float))
    def __imod__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v%o.v;return s
        if isinstance(o,(int,float)):s.v=s.v%o;return s
        else:_type_mismatch(o,(int,float))
    def __rmod__(s,o):return s.__mod__(o)
    def __pow__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v**o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v**o)
        else:_type_mismatch(o,(int,float))
    def __ipow__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v**o.v;return s
        if isinstance(o,(int,float)):s.v=s.v**o;return s
        else:_type_mismatch(o,(int,float))
    def __rpow__(s,o):return s.__pow__(o)
    def __lshift__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v<<o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v<<o)
        else:_type_mismatch(o,(int,float))
    def __ilshift__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v<<o.v;return s
        if isinstance(o,(int,float)):s.v=s.v<<o;return s
        else:_type_mismatch(o,(int,float))
    def __rlshift__(s,o):return s.__lshift__(o)
    def __rshift__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v>>o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v>>o)
        else:_type_mismatch(o,(int,float))
    def __irshift__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v>>o.v;return s
        if isinstance(o,(int,float)):s.v=s.v>>o;return s
        else:_type_mismatch(o,(int,float))
    def __rrshift__(s,o):return s.__rshift__(o)
    def __and__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v&o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v&o)
        else:_type_mismatch(o,(int,float))
    def __iand__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v&o.v;return s
        if isinstance(o,(int,float)):s.v=s.v&o;return s
        else:_type_mismatch(o,(int,float))
    def __rand__(s,o):return s.__and__(o)
    def __xor__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v^o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v^o)
        else:_type_mismatch(o,(int,float))
    def __ixor__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v^o.v;return s
        if isinstance(o,(int,float)):s.v=s.v^o;return s
        else:_type_mismatch(o,(int,float))
    def __rxor__(s,o):return s.__xor__(o)
    def __or__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v|o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v|o)
        else:_type_mismatch(o,(int,float))
    def __ior__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v|o.v;return s
        if isinstance(o,(int,float)):s.v=s.v|o;return s
        else:_type_mismatch(o,(int,float))
    def __ror__(s,o):return s.__or__(o)
    def __neg__(s):return _ptn_t_integer(-s.v)
    def __pos__(s):return _ptn_t_integer(+s.v)
    def __invert__(s):return _ptn_t_integer(~s.v)
    def __int__(s):return int(s.v)
    def __float__(s):return float(s.v)
    def __abs__(s):return _ptn_t_integer(abs(s.v))
    def __complex__(s):return _ptn_t_integer(complex(s.v))
    def __oct__(s):return _ptn_t_integer(oct(s.v))
    def __hex__(s):return _ptn_t_integer(hex(s.v))
    def __index__(s):return int(s.v)
    def __trunc__(s):return int(s.v)
    #coerce
    def __nonzero__(s):return True if s.v>0 else False
    def __sizeof__(s):return s.v.__sizeof__()
    def __bool__(s):return s.__nonzero__()
class _ptn_t_float(_ptn_type):
    def __init__(s,v):s.v=_cast_type(v,float)
    def __str__(s):return str(s.v)
    def __repr__(s):return str(s)
    def __len__(s):return s.v.__sizeof__()
    def _cast(s,t):_assert(issubclass(t,_ptn_type),"casting type must be a piston primitive type");return t(s.v)
    @staticmethod
    def _t():return float
    @staticmethod
    def _init():return _ptn_t_float(0.0)
    def __lt__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return s.v<o.v
        if isinstance(o,(int,float)):return s.v<o
        else:return False
    def __gt__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return s.v>o.v
        if isinstance(o,(int,float)):return s.v>o
        else:return False
    def __le__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return s.v<=o.v
        if isinstance(o,(int,float)):return s.v<=o
        else:return False
    def __ge__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return s.v>=o.v
        if isinstance(o,(int,float)):return s.v>=o
        else:return False
    def __eq__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return s.v==o.v
        if isinstance(o,(int,float)):return s.v==o
        else:return False
    def __ne__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return s.v!=o.v
        if isinstance(o,(int,float)):return s.v!=o
        else:return False
    def __add__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v+o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v+o)
        else:_type_mismatch(o,(int,float))
    def __iadd__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v+o.v;return s
        if isinstance(o,(int,float)):s.v=s.v+o;return s
        else:_type_mismatch(o,(int,float))
    def __radd__(s,o):return s.__add__(o)
    def __sub__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v-o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v-o)
        else:_type_mismatch(o,(int,float))
    def __isub__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v-o.v;return s
        if isinstance(o,(int,float)):s.v=s.v-o;return s
        else:_type_mismatch(o,(int,float))
    def __rsub__(s,o):return s.__sub__(o)
    def __mul__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v*o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v*o)
        else:_type_mismatch(o,(int,float))
    def __imul__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v*o.v;return s
        if isinstance(o,(int,float)):s.v=s.v*o;return s
        else:_type_mismatch(o,(int,float))
    def __rmul__(s,o):return s.__mul__(o)
    def __floordiv__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v//o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v//o)
        else:_type_mismatch(o,(int,float))
    def __ifloordiv__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v//o.v;return s
        if isinstance(o,(int,float)):s.v=s.v//o;return s
        else:_type_mismatch(o,(int,float))
    def __rfloordiv__(s,o):return s.__floordiv__(o)
    def __truediv__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v/o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v/o)
        else:_type_mismatch(o,(int,float))
    def __idiv__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v/o.v;return s
        if isinstance(o,(int,float)):s.v=s.v/o;return s
        else:_type_mismatch(o,(int,float))
    def __rdiv__(s,o):return s.__truediv__(o)
    def __mod__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v%o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v%o)
        else:_type_mismatch(o,(int,float))
    def __imod__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v%o.v;return s
        if isinstance(o,(int,float)):s.v=s.v%o;return s
        else:_type_mismatch(o,(int,float))
    def __rmod__(s,o):return s.__mod__(o)
    def __pow__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v**o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v**o)
        else:_type_mismatch(o,(int,float))
    def __ipow__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v**o.v;return s
        if isinstance(o,(int,float)):s.v=s.v**o;return s
        else:_type_mismatch(o,(int,float))
    def __rpow__(s,o):return s.__pow__(o)
    def __lshift__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v<<o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v<<o)
        else:_type_mismatch(o,(int,float))
    def __ilshift__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v<<o.v;return s
        if isinstance(o,(int,float)):s.v=s.v<<o;return s
        else:_type_mismatch(o,(int,float))
    def __rlshift__(s,o):return s.__lshift__(o)
    def __rshift__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v>>o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v>>o)
        else:_type_mismatch(o,(int,float))
    def __irshift__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v>>o.v;return s
        if isinstance(o,(int,float)):s.v=s.v>>o;return s
        else:_type_mismatch(o,(int,float))
    def __rrshift__(s,o):return s.__rshift__(o)
    def __and__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v&o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v&o)
        else:_type_mismatch(o,(int,float))
    def __iand__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v&o.v;return s
        if isinstance(o,(int,float)):s.v=s.v&o;return s
        else:_type_mismatch(o,(int,float))
    def __rand__(s,o):return s.__and__(o)
    def __xor__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v^o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v^o)
        else:_type_mismatch(o,(int,float))
    def __ixor__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v^o.v;return s
        if isinstance(o,(int,float)):s.v=s.v^o;return s
        else:_type_mismatch(o,(int,float))
    def __rxor__(s,o):return s.__xor__(o)
    def __or__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):return _ptn_t_integer(s.v|o.v)
        if isinstance(o,(int,float)):return _ptn_t_integer(s.v|o)
        else:_type_mismatch(o,(int,float))
    def __ior__(s,o):
        if isinstance(o,(_ptn_t_integer,_ptn_t_float)):s.v=s.v|o.v;return s
        if isinstance(o,(int,float)):s.v=s.v|o;return s
        else:_type_mismatch(o,(int,float))
    def __ror__(s,o):return s.__or__(o)
    def __neg__(s):return _ptn_t_integer(-s.v)
    def __pos__(s):return _ptn_t_integer(+s.v)
    def __invert__(s):return _ptn_t_integer(~s.v)
    def __int__(s):return int(s.v)
    def __float__(s):return float(s.v)
    def __abs__(s):return _ptn_t_integer(abs(s.v))
    def __complex__(s):return _ptn_t_integer(complex(s.v))
    def __oct__(s):return _ptn_t_integer(oct(s.v))
    def __hex__(s):return _ptn_t_integer(hex(s.v))
    def __index__(s):return int(s.v)
    def __trunc__(s):return int(s.v)
    #coerce
    def __nonzero__(s):return True if s.v>0 else False
    def __sizeof__(s):return s.v.__sizeof__()
    def __bool__(s):return s.__nonzero__()
class _ptn_t_string(_ptn_type):
    def __init__(s,v):s.v=_cast_type(v,str)
    def __str__(s):return str(s.v)
    def __repr__(s):return str(s)
    def __len__(s):return len(s.v)
    def _cast(s,t):_assert(issubclass(t,_ptn_type),"casting type must be a piston primitive type");return t(s.v)
    @staticmethod
    def _t():return str
    @staticmethod
    def _init():return _ptn_t_string("")
    def __eq__(s,o):
        if isinstance(o,_ptn_t_string):return s.v==o.v
        if isinstance(o,str):return s.v==o
        else:return False
    def __ne__(s,o):
        if isinstance(o,_ptn_t_string):return s.v!=o.v
        if isinstance(o,str):return s.v!=o
        else:return False
    def __contains__(s,o):return o in s.v
    def __iter__(s):
        for e in s.v:yield e
    def __int__(s):return int(s.v)
    def __float__(s):return float(s.v)
    def __bool__(s):return bool(s.v)
class _ptn_t_bool(_ptn_type):
    def __init__(s,v):s.v=_cast_type(v,bool)
    def __str__(s):return str(s.v)
    def __repr__(s):return str(s)
    def __len__(s):return s.v.bit_length()
    def _cast(s,t):_assert(issubclass(t,_ptn_type),"casting type must be a piston primitive type");return t(s.v)
    @staticmethod
    def _t():return bool
    @staticmethod
    def _init():return _ptn_t_bool(False)
    def __eq__(s,o):
        if isinstance(o,_ptn_t_bool):return s.v==o.v
        if isinstance(o,bool):return s.v==o
        else:return False
    def __ne__(s,o):
        if isinstance(o,_ptn_t_bool):return s.v!=o.v
        if isinstance(o,bool):return s.v!=o
        else:return False
    def __int__(s):return 1 if s.v else 0
    def __float__(s):return 1.0 if s.v else 0.0
class _ptn_t_array(_ptn_type):
    def __init__(s,v,l=1):
        if isinstance(v,type):s.at=v;s.ai=[s.at.init()]*l;s.al=l
        elif isinstance(v,(list,tuple)):_assert_min_length(v,1);_assert_ptn_type(v[0]);s.at=type(v[0]);_assert_list_type(v,s.at);s.ai=v;s.al=len(v)
        elif isinstance(v,_ptn_t_array):s.at=v.at;s.ai=v.ai;s.al=v.al;
        else:s.at=type(v);s.ai=[v];s.ai.extend([s.at._init()]*(l-1));s.al=l;
    def __str__(s):return str(s.ai)
    def __repr__(s):return str(s)
    def __len__(s):return s.al
    def _cast(s,t):_assert(not issubclass(t,(_ptn_t_array,_ptn_t_tuple)),"cannot cast array to array or tuple");c=[e._cast(t)for e in s.ai];return _ptn_t_array(c)
    @staticmethod
    def _t():return list
    def __getitem__(s,k):return s.ai[k]
    def __setitem__(s,k,v):_assert_type(v,s.at);s.ai[k]=v
# TODO: how do we do casting?
class _ptn_t_tuple(_ptn_type):
    def __init__(s,v):
        v=_ensure_iterable(v)
        if _is_ptn_type_list(v):s.tt=[type(e)for e in v];s.ti=v;s.tl=len(v)
        elif _is_types_list(v):_assert_ptn_type_list(v);s.tt=v;s.ti=[_raise_runtime("tuples cannot contain tuples or arrays")if issubclass(e,(_ptn_t_array,_ptn_t_tuple))else e._init()for e in v];s.tl=len(v)
        else:_raise_runtime("invalid tuple initialization "+str(v))
    def __str__(s):return str(s.ti)
    def __repr__(s):return str(s)
    def __len__(s):return s.tl
    def _cast(s,t):_assert(not issubclass(t,(_ptn_t_array,_ptn_t_tuple)),"cannot cast array to array or tuple");_raise_runtime("not implemented yet. how?")
    @staticmethod
    def _t():return tuple
    def __getitem__(s,k):return s.ti[k]
    def __setitem__(s,k,v):t=s.tt[k];_assert_type(v,t);s.ti[k]=v
def _int(v=None):return _ptn_t_integer._init()if v is None else _ptn_t_integer(v)
def _float(v=None):return _ptn_t_float._init()if v is None else _ptn_t_float(v)
def _string(v=None):return _ptn_t_string._init()if v is None else _ptn_t_string(v)
def _bool(v=None):return _ptn_t_bool._init()if v is None else _ptn_t_bool(v)
def _array(vt,l=None):return _ptn_t_array(vt)if l is None else _ptn_t_array(vt,l)
def _tuple(vt):return _ptn_t_tuple(vt)


if __name__ == '__main__':
    val = _ptn_t_integer(1.0)
    print(val.v)
    print(val.v == _ptn_t_float(1))
    print(_type_of(1,_ptn_t_integer))

    b = 1 + val
    print(b)
    b -= 5 ** val
    print(b)
    print(bool(b))
    c = b
    c /= 3.9
    print(int(int(1) / int(3)))
    print(type(c))
    print(len(c))
    z = _ptn_t_bool(b)
    print(len(z))

    print(float(b))
    d = _ptn_t_float(b)
    print(len(d))
    d += 1
    print(d)

    t = d._cast(_ptn_t_string)
    print(type(t))
    print(t)
    
    dt = t._cast(_ptn_t_float)
    print(type(dt))
    print(dt)

    arr = _ptn_t_array(dt,10)
    print(arr.ai)
    print(arr.at)
    print(arr.al)

    arr[1]=_ptn_t_float(1)
    print(arr.ai)
    print(arr.al)
    arr[2]=_ptn_t_float("6.9")
    print(arr.ai)

    carr = arr._cast(_ptn_t_string)
    print(carr.at)

    lst = [_ptn_t_string("a"), _ptn_t_string("b"), _ptn_t_string("c")]
    x = _array(lst)
    print(x.ai)

    a=_int(4);b=_int(5);print(a.v+b.v);

    mybool=_bool(True)
    myint=mybool._cast(_ptn_t_integer)
    print(myint)

    mytuple = _tuple([_ptn_t_integer(1), _ptn_t_integer(2), _ptn_t_float(3.0)])
    print(mytuple.tt)
    print(mytuple.ti)
    print(mytuple.tl)

    myothertuple = _tuple([_ptn_t_integer, _ptn_t_integer, _ptn_t_float])
    myothertuple[1]=_ptn_t_integer(2)
    print(myothertuple.tt)
    print(myothertuple.ti)
    print(myothertuple.tl)