Problem: IA has so many colorful magnets on her fridge! Exactly one letter is written on each magnet, 'a' or 'b'. She loves to play with them, placing all magnets in a row. However, the girl is quickly bored and usually thinks how to make her entertainment more interesting.

Today, when IA looked at the fridge, she noticed that the word formed by magnets is really messy. "It would look much better when I'll swap some of them!" — thought the girl — "but how to do it?". After a while, she got an idea. IA will look at all prefixes with lengths from 1 to the length of the word and for each prefix she will either reverse this prefix or leave it as it is. She will consider the prefixes in the fixed order: from the shortest to the largest. She wants to get the lexicographically smallest possible word after she considers all prefixes. Can you help her, telling which prefixes should be chosen for reversing?

A string a is lexicographically smaller than a string b if and only if one of the following holds:

  * a is a prefix of b, but a ≠ b;
  * in the first position where a and b differ, the string a has a letter that appears earlier in the alphabet than the corresponding letter in b.

Input

The first and the only line contains a string s (1 ≤ |s| ≤ 1000), describing the initial string formed by magnets. The string s consists only of characters 'a' and 'b'.

Output

Output exactly |s| integers. If IA should reverse the i-th prefix (that is, the substring from 1 to i), the i-th integer should be equal to 1, and it should be equal to 0 otherwise.

If there are multiple possible sequences leading to the optimal answer, print any of them.

Examples

Input

bbab


Output

0 1 1 0


Input

aaaaa


Output

1 0 0 0 1

Note

In the first example, IA can reverse the second and the third prefix and get a string "abbb". She cannot get better result, since it is also lexicographically smallest string obtainable by permuting characters of the initial string.

In the second example, she can reverse any subset of prefixes — all letters are 'a'.

Solution (in PYTHON):

Solution:
"""
What I cannot create, I do not understand.

https://github.com/Cheran-Senthil/PyRival
Copyright (c) 2018 Cheran Senthilkumar
"""
from __future__ import division, print_function

import cmath
import itertools
import math
import operator as op
import sys
from bisect import bisect_left, bisect_right
from string import ascii_lowercase, ascii_uppercase

# import random
# from collections import Counter, MutableSequence, defaultdict, deque
# from copy import deepcopy
# from decimal import Decimal
# from difflib import SequenceMatcher
# from heapq import heappop, heappush


if sys.version_info[0] < 3:
    # from fractions import Fraction
    # from fractions import gcd
    # from cPickle import dumps
    # from Queue import PriorityQueue, Queue
    pass
else:
    # from functools import reduce
    # from fractions import Fraction
    # from math import gcd
    # from pickle import dumps
    # from queue import PriorityQueue, Queue
    pass


if sys.version_info[0] < 3:
    class dict(dict):
        def items(self):
            return dict.iteritems(self)

        def keys(self):
            return dict.iterkeys(self)

        def values(self):
            return dict.itervalues(self)

    input = raw_input
    range = xrange

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


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

    Parameters
    ----------
    sync : bool
        the new synchronization setting

    """
    global input, flush

    if sync:
        flush = sys.stdout.flush
    else:
        from atexit import register

        if sys.version_info[0] < 3:
            from io import BytesIO

            input = iter(sys.stdin.read().splitlines()).next
            sys.stdout = BytesIO()
        else:
            from io import StringIO

            input = iter(sys.stdin.read().splitlines()).__next__
            sys.stdout = StringIO()

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


def main():
    s = input()
    res = ['0']
    prev = s[0]
    for char in s[1:]:
        if char == 'a':
            if prev == 'b':
                res[-1] = '1'
            res.append('0')
            prev = 'a'
        else:
            if prev == 'a':
                res[-1] = '1'
            res.append('0')
            prev = 'b'
    if s[-1] == 'a':
        res[-1] = '1'
    print(' '.join(res))


if __name__ == '__main__':
    sys.setrecursionlimit(10000)
    sync_with_stdio()
    main()