def print(*args, sep=' ', end='\n'):
    s = sep.join([str(i) for i in args])
    __sys_stdout_write(s + end)

def round(x, ndigits=0):
    assert ndigits >= 0
    if ndigits == 0:
        return x >= 0 ? int(x + 0.5) : int(x - 0.5)
    if x >= 0:
        return int(x * 10**ndigits + 0.5) / 10**ndigits
    else:
        return int(x * 10**ndigits - 0.5) / 10**ndigits

def isinstance(obj, cls):
    assert type(cls) is type
    obj_t = type(obj)
    while obj_t is not None:
        if obj_t is cls:
            return True
        obj_t = obj_t.__base__
    return False

def abs(x):
    return x < 0 ? -x : x

def max(a, b):
    return a > b ? a : b

def min(a, b):
    return a < b ? a : b

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 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):
    for i in range(min(len(a), len(b))):
        yield (a[i], b[i])

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

def sorted(iterable, reverse=False):
    a = list(iterable)
    a.sort(reverse=reverse)
    return a

##### str #####

str.__mul__ = lambda self, n: ''.join([self for _ in range(n)])

def str::split(self, sep):
    if sep == "":
        return list(self)
    res = []
    i = 0
    while i < len(self):
        if self[i:i+len(sep)] == sep:
            res.append(self[:i])
            self = self[i+len(sep):]
            i = 0
        else:
            i += 1
    res.append(self)
    return res

def str::index(self, sub):
    for i in range(len(self)):
        if self[i:i+len(sub)] == sub:
            return i
    return -1

def str::strip(self, chars=None):
    chars = chars or ' \t\n\r'
    i = 0
    while i < len(self) and self[i] in chars:
        i += 1
    j = len(self) - 1
    while j >= 0 and self[j] in chars:
        j -= 1
    return self[i:j+1]

##### list #####

list.__new__ = lambda obj: [i for i in obj]
list.__repr__ = lambda self: '[' + ', '.join([repr(i) for i in self]) + ']'
tuple.__repr__ = lambda self: '(' + ', '.join([repr(i) for i in self]) + ')'
list.__json__ = lambda self: '[' + ', '.join([i.__json__() for i in self]) + ']'
tuple.__json__ = lambda self: '[' + ', '.join([i.__json__() for i in self]) + ']'

def __qsort(a: list, L: int, R: int):
    if L >= R: return;
    mid = a[(R+L)//2];
    i, j = L, R
    while i<=j:
        while a[i]<mid: i+=1
        while a[j]>mid: j-=1
        if i<=j:
            a[i], a[j] = a[j], a[i]
            i+=1
            j-=1
    __qsort(a, L, j)
    __qsort(a, i, R)

def list::sort(self, reverse=False):
    __qsort(self, 0, len(self)-1)
    if reverse:
        self.reverse()

def list::extend(self, other):
    for i in other:
        self.append(i)

def list::remove(self, value):
    for i in range(len(self)):
        if self[i] == value:
            del self[i]
            return True
    return False

def list::index(self, value):
    for i in range(len(self)):
        if self[i] == value:
            return i
    return -1

def list::pop(self, i=-1):
    res = self[i]
    del self[i]
    return res

def list::__eq__(self, other):
    if len(self) != len(other):
        return False
    for i in range(len(self)):
        if self[i] != other[i]:
            return False
    return True
tuple.__eq__ = list.__eq__
list.__ne__ = lambda self, other: not self.__eq__(other)
tuple.__ne__ = lambda self, other: not self.__eq__(other)

def list::count(self, x):
    res = 0
    for i in self:
        if i == x:
            res += 1
    return res
tuple.count = list.count

def list::__contains__(self, item):
    for i in self:
        if i == item:
            return True
    return False
tuple.__contains__ = list.__contains__


class property:
    def __init__(self, fget):
        self.fget = fget

    def __get__(self, obj):
        return self.fget(obj)