def all(iterable):
    for i in iterable:
        if not i:
            return False
    return True

def any(iterable):
    for i in iterable:
        if i:
            return True
    return False

def enumerate(iterable, start=0):
    n = start
    for elem in iterable:
        yield n, elem
        n += 1

def __minmax_reduce(op, args):
    if len(args) == 2:  # min(1, 2)
        return args[0] if op(args[0], args[1]) else args[1]
    if len(args) == 0:  # min()
        raise TypeError('expected 1 arguments, got 0')
    if len(args) == 1:  # min([1, 2, 3, 4]) -> min(1, 2, 3, 4)
        args = args[0]
    args = iter(args)
    try:
        res = next(args)
    except StopIteration:
        raise ValueError('args is an empty sequence')
    while True:
        try:
            i = next(args)
        except StopIteration:
            break
        if op(i, res):
            res = i
    return res

def min(*args, key=None):
    key = key or (lambda x: x)
    return __minmax_reduce(lambda x,y: key(x)<key(y), args)

def max(*args, key=None):
    key = key or (lambda x: x)
    return __minmax_reduce(lambda x,y: key(x)>key(y), args)

def sum(iterable):
    res = 0
    for i in iterable:
        res += i
    return res

def map(f, iterable):
    for i in iterable:
        yield f(i)

def filter(f, iterable):
    for i in iterable:
        if f(i):
            yield i

def zip(a, b):
    a = iter(a)
    b = iter(b)
    while True:
        try:
            ai = next(a)
            bi = next(b)
        except StopIteration:
            break
        yield ai, bi

def reversed(iterable):
    a = list(iterable)
    a.reverse()
    return a

def sorted(iterable, key=None, reverse=False):
    a = list(iterable)
    a.sort(key=key, reverse=reverse)
    return a

def dir(obj=None):
    """
    dir([object]) -> list of strings
    
    If called without an argument, return the names in the current scope.
    Else, return an alphabetized list of names comprising (some of) the attributes
    of the given object, and of attributes reachable from it.
    If the object supplies a method named __dir__, it will be used; otherwise
    the default dir() logic is used and returns:
      for a module object: the module's attributes.
      for a class object: its attributes.
      for any other object: its attributes, its class's attributes.
    """
    
    if obj is None:
        return list(globals().keys())
    
    if hasattr(obj, "__dir__"):
        return obj.__dir__
    
    attributes = set()
    # Set object attributes.
    if hasattr(obj, "__dict__"):
        attributes.update(obj.__dict__.keys())
    
    # Set type attributes.
    if not isinstance(obj, type):
        if hasattr(type(obj), "__dict__"):
            attributes.update(type(obj).__dict__.keys())
    
    return sorted(attributes)


##### str #####
def __format_string(self: str, *args, **kwargs) -> str:
    def tokenizeString(s: str):
        tokens = []
        L, R = 0,0
        
        mode = None
        curArg = 0
        # lookingForKword = False
        
        while(R<len(s)):
            curChar = s[R]
            nextChar = s[R+1] if R+1<len(s) else ''
            
            # Invalid case 1: stray '}' encountered, example: "ABCD EFGH {name} IJKL}", "Hello {vv}}", "HELLO {0} WORLD}"
            if curChar == '}' and nextChar != '}':
                raise ValueError("Single '}' encountered in format string")        
            
            # Valid Case 1: Escaping case, we escape "{{ or "}}" to be "{" or "}", example: "{{}}", "{{My Name is {0}}}"
            if (curChar == '{' and nextChar == '{') or (curChar == '}' and nextChar == '}'):
                
                if (L<R): # Valid Case 1.1: make sure we are not adding empty string
                    tokens.append(s[L:R]) # add the string before the escape
                
                
                tokens.append(curChar) # Valid Case 1.2: add the escape char
                L = R+2 # move the left pointer to the next char
                R = R+2 # move the right pointer to the next char
                continue
            
            # Valid Case 2: Regular command line arg case: example:  "ABCD EFGH {} IJKL", "{}", "HELLO {} WORLD"
            elif curChar == '{' and nextChar == '}':
                if mode is not None and mode != 'auto':
                    # Invalid case 2: mixing automatic and manual field specifications -- example: "ABCD EFGH {name} IJKL {}", "Hello {vv} {}", "HELLO {0} WORLD {}" 
                    raise ValueError("Cannot switch from manual field numbering to automatic field specification")
                
                mode = 'auto'
                if(L<R): # Valid Case 2.1: make sure we are not adding empty string
                    tokens.append(s[L:R]) # add the string before the special marker for the arg
                
                tokens.append("{"+str(curArg)+"}") # Valid Case 2.2: add the special marker for the arg
                curArg+=1 # increment the arg position, this will be used for referencing the arg later
                
                L = R+2 # move the left pointer to the next char
                R = R+2 # move the right pointer to the next char
                continue
            
            # Valid Case 3: Key-word arg case: example: "ABCD EFGH {name} IJKL", "Hello {vv}", "HELLO {name} WORLD"
            elif (curChar == '{'):
                
                if mode is not None and mode != 'manual':
                    # # Invalid case 2: mixing automatic and manual field specifications -- example: "ABCD EFGH {} IJKL {name}", "Hello {} {1}", "HELLO {} WORLD {name}"
                    raise ValueError("Cannot switch from automatic field specification to manual field numbering")
                
                mode = 'manual'
                
                if(L<R): # Valid case 3.1: make sure we are not adding empty string
                    tokens.append(s[L:R]) # add the string before the special marker for the arg
                
                # We look for the end of the keyword          
                kwL = R # Keyword left pointer
                kwR = R+1 # Keyword right pointer
                while(kwR<len(s) and s[kwR]!='}'):
                    if s[kwR] == '{': # Invalid case 3: stray '{' encountered, example: "ABCD EFGH {n{ame} IJKL {", "Hello {vv{}}", "HELLO {0} WOR{LD}"
                        raise ValueError("Unexpected '{' in field name")
                    kwR += 1
                
                # Valid case 3.2: We have successfully found the end of the keyword
                if kwR<len(s) and s[kwR] == '}':
                    tokens.append(s[kwL:kwR+1]) # add the special marker for the arg
                    L = kwR+1
                    R = kwR+1
                    
                # Invalid case 4: We didn't find the end of the keyword, throw error
                else:
                    raise ValueError("Expected '}' before end of string")
                continue
            
            R = R+1
        
        
        # Valid case 4: We have reached the end of the string, add the remaining string to the tokens 
        if L<R:
            tokens.append(s[L:R])
                
        # print(tokens)
        return tokens

    tokens = tokenizeString(self)
    argMap = {}
    for i, a in enumerate(args):
        argMap[str(i)] = a
    final_tokens = []
    for t in tokens:
        if t[0] == '{' and t[-1] == '}':
            key = t[1:-1]
            argMapVal = argMap.get(key, None)
            kwargsVal = kwargs.get(key, None)
                                    
            if argMapVal is None and kwargsVal is None:
                raise ValueError("No arg found for token: "+t)
            elif argMapVal is not None:
                final_tokens.append(str(argMapVal))
            else:
                final_tokens.append(str(kwargsVal))
        else:
            final_tokens.append(t)
    
    return ''.join(final_tokens)

str.format = __format_string
del __format_string


def help(obj):
    if hasattr(obj, '__func__'):
        obj = obj.__func__
    # print(obj.__signature__)
    if obj.__doc__:
        print(obj.__doc__)

def complex(real, imag=0):
    import cmath
    return cmath.complex(real, imag)


class set:
    def __init__(self, iterable=None):
        iterable = iterable or []
        self._a = {}
        self.update(iterable)

    def add(self, elem):
        self._a[elem] = None
        
    def discard(self, elem):
        self._a.pop(elem, None)

    def remove(self, elem):
        del self._a[elem]
        
    def clear(self):
        self._a.clear()

    def update(self, other):
        for elem in other:
            self.add(elem)

    def __len__(self):
        return len(self._a)
    
    def copy(self):
        return set(self._a.keys())
    
    def __and__(self, other):
        return {elem for elem in self if elem in other}

    def __sub__(self, other):
        return {elem for elem in self if elem not in other}
    
    def __or__(self, other):
        ret = self.copy()
        ret.update(other)
        return ret

    def __xor__(self, other): 
        _0 = self - other
        _1 = other - self
        return _0 | _1

    def union(self, other):
        return self | other

    def intersection(self, other):
        return self & other

    def difference(self, other):
        return self - other

    def symmetric_difference(self, other):      
        return self ^ other
    
    def __eq__(self, other):
        if not isinstance(other, set):
            return NotImplemented
        return len(self ^ other) == 0
    
    def __ne__(self, other):
        if not isinstance(other, set):
            return NotImplemented
        return len(self ^ other) != 0

    def isdisjoint(self, other):
        return len(self & other) == 0
    
    def issubset(self, other):
        return len(self - other) == 0
    
    def issuperset(self, other):
        return len(other - self) == 0

    def __contains__(self, elem):
        return elem in self._a
    
    def __repr__(self):
        if len(self) == 0:
            return 'set()'
        return '{'+ ', '.join([repr(i) for i in self._a.keys()]) + '}'
    
    def __iter__(self):
        return iter(self._a.keys())