#!/usr/bin/env python
"""
This file is part of https://github.com/Cheran-Senthil/PyRival.

Copyright 2018 <NAME> all rights reserved,
<NAME> <<EMAIL>>
Permission to use, modify, and distribute this software is given under the
terms of the MIT License.

"""
from __future__ import division, print_function

import cmath
import itertools
import math
import operator as op
# import random
import sys
from atexit import register
from bisect import bisect_left, bisect_right
# from collections import Counter, MutableSequence, defaultdict, deque
# from copy import deepcopy
# from decimal import Decimal
# from difflib import SequenceMatcher
# from fractions import Fraction
# from heapq import heappop, heappush

if sys.version_info[0] < 3:
    # from cPickle import dumps
    from io import BytesIO as stream
    # from Queue import PriorityQueue, Queue
else:
    # from functools import reduce
    from io import StringIO as stream
    from math import gcd
    # from pickle import dumps
    # from queue import PriorityQueue, Queue


if sys.version_info[0] < 3:
    class dict(dict):
        """dict() -> new empty dictionary"""
        def items(self):
            """D.items() -> a set-like object providing a view on D's items"""
            return dict.iteritems(self)

        def keys(self):
            """D.keys() -> a set-like object providing a view on D's keys"""
            return dict.iterkeys(self)

        def values(self):
            """D.values() -> an object providing a view on D's values"""
            return dict.itervalues(self)

    def gcd(x, y):
        """gcd(x, y) -> int
        greatest common divisor of x and y
        """
        while y:
            x, y = y, x % y
        return x

    input = raw_input
    range = xrange

    filter = itertools.ifilter
    map = itertools.imap
    zip = itertools.izip


def sync_with_stdio(sync=True):
    """Set whether the standard Python streams are allowed to buffer their I/O.

    Args:
        sync (bool, optional): The new synchronization setting.

    """
    global input, flush

    if sync:
        flush = sys.stdout.flush
    else:
        sys.stdin = stream(sys.stdin.read())
        input = lambda: sys.stdin.readline().rstrip('\r\n')

        sys.stdout = stream()
        register(lambda: sys.__stdout__.write(sys.stdout.getvalue()))


def main():
    pass


if __name__ == '__main__':
    sync_with_stdio(False)

    if 'PyPy' in sys.version:
        from _continuation import continulet

        def bootstrap(c):
            callable, arg = c.switch()
            while True:
                to = continulet(lambda _, f, x: f(x), callable, arg)
                callable, arg = c.switch(to=to)

        c = continulet(bootstrap)
        c.switch()

        main()

    else:
        import threading

        sys.setrecursionlimit(2097152)
        threading.stack_size(134217728)

        main_thread = threading.Thread(target=main)
        main_thread.start()
        main_thread.join()

#!/usr/bin/env python
"""
This file is part of https://github.com/Cheran-Senthil/PyRival.

Copyright 2018 <NAME> all rights reserved,
<NAME> <<EMAIL>>
Permission to use, modify, and distribute this software is given under the
terms of the MIT License.

"""
from __future__ import division, print_function

import cmath
import itertools
import math
import operator as op
# import random
import sys
from atexit import register
from bisect import bisect_left, bisect_right
# from collections import Counter, MutableSequence, defaultdict, deque
# from copy import deepcopy
# from decimal import Decimal
# from difflib import SequenceMatcher
# from fractions import Fraction
# from heapq import heappop, heappush

if sys.version_info[0] < 3:
    # from cPickle import dumps
    from io import BytesIO as stream
    # from Queue import PriorityQueue, Queue
else:
    # from functools import reduce
    from io import StringIO as stream
    from math import gcd
    # from pickle import dumps
    # from queue import PriorityQueue, Queue


if sys.version_info[0] < 3:
    class dict(dict):
        """dict() -> new empty dictionary"""
        def items(self):
            """D.items() -> a set-like object providing a view on D's items"""
            return dict.iteritems(self)

        def keys(self):
            """D.keys() -> a set-like object providing a view on D's keys"""
            return dict.iterkeys(self)

        def values(self):
            """D.values() -> an object providing a view on D's values"""
            return dict.itervalues(self)

    def gcd(x, y):
        """gcd(x, y) -> int
        greatest common divisor of x and y
        """
        while y:
            x, y = y, x % y
        return x

    input = raw_input
    range = xrange

    filter = itertools.ifilter
    map = itertools.imap
    zip = itertools.izip


def sync_with_stdio(sync=True):
    """Set whether the standard Python streams are allowed to buffer their I/O.

    Args:
        sync (bool, optional): The new synchronization setting.

    """
    global input, flush

    if sync:
        flush = sys.stdout.flush
    else:
        sys.stdin = stream(sys.stdin.read())
        input = lambda: sys.stdin.readline().rstrip('\r\n')

        sys.stdout = stream()
        register(lambda: sys.__stdout__.write(sys.stdout.getvalue()))


def main():
    pass


if __name__ == '__main__':
    sync_with_stdio(False)

    if 'PyPy' in sys.version:
        from _continuation import continulet

        def bootstrap(c):
            callable, arg = c.switch()
            while True:
                to = continulet(lambda _, f, x: f(x), callable, arg)
                callable, arg = c.switch(to=to)

        c = continulet(bootstrap)
        c.switch()

        main()

    else:
        import threading

        sys.setrecursionlimit(2097152)
        threading.stack_size(134217728)

        main_thread = threading.Thread(target=main)
        main_thread.start()
        main_thread.join()

#!/usr/bin/env python This file is part of https://github.com/Cheran-Senthil/PyRival.  Copyright 2018 <NAME> all rights reserved, <NAME> <<EMAIL>> Permission to use, modify, and distribute this software is given under the terms of the MIT License. # import random # from collections import Counter, MutableSequence, defaultdict, deque # from copy import deepcopy # from decimal import Decimal # from difflib import SequenceMatcher # from fractions import Fraction # from heapq import heappop, heappush # from cPickle import dumps # from Queue import PriorityQueue, Queue # from functools import reduce # from pickle import dumps # from queue import PriorityQueue, Queue dict() -> new empty dictionary D.items() -> a set-like object providing a view on D's items D.keys() -> a set-like object providing a view on D's keys D.values() -> an object providing a view on D's values gcd(x, y) -> int         greatest common divisor of x and y Set whether the standard Python streams are allowed to buffer their I/O.      Args:         sync (bool, optional): The new synchronization setting.