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 JAVA):

Solution:

import java.io.*;
import java.util.*;

// CODE JAM SHIT

public class Q2 {

    public static void main(String[] args) {

        InputReader in = new InputReader(true);
        PrintWriter out = new PrintWriter(System.out);
        char arr[] = in.next().toCharArray();
        StringBuilder a = new StringBuilder();
        for (int i = 0; i < arr.length-1; i++) {
            if (arr[i]!=arr[i+1]) {
                a.append("1 ");
            }else
                a.append("0 ");
        }
        if(arr[arr.length-1]=='a')
            a.append(1);
        else
            a.append(0);
        out.println(a);
        out.close();

    }


//    public static void main(String[] args) {
//
//        InputReader in = new InputReader();
//        PrintWriter out = new PrintWriter(System.out);
//
//        int t = in.nextInt(), l = 0;
//
//        while (t-- > 0) {
//
//            out.print("Case #" + (++l) + ": ");
//
//            int N = in.nextInt(), x = in.nextInt(), max = 0;
//            HashMap<Double, Integer> map = new HashMap<>();
//            double arr[] = new double[N];
//
//            for (int i = 0; i < N; i++) {
//                arr[i] = in.nextDouble();
//                map.put(arr[i], map.getOrDefault(arr[i], 0) + 1);
//                max = Math.max(max, map.get(arr[i]));
//            }
//
//            if (max >= x)
//                out.println(0);
//            else if (x == 2)
//                out.println(1);
//            else {
//
//                int flag = 0;
//                for (int i = 0; i < N; i++) {
//                    if (arr[i] % 2 == 0) {
//                        if (map.containsKey(arr[i] / 2))
//                            flag = 1;
//                    }
//                }
//
//                if (N == 1)
//                    out.println(2);
//                else if (flag == 1)
//                    out.println(1);
//                else{
//
//                    double min = Integer.MAX_VALUE;
//                    for (int i = 0; i < N; i++) {
//                        if (map.get(arr[i]) == 2) {
//                            min = Math.min(min, arr[i]);
//                        }
//                    }
//
//                    if (min < Integer.MAX_VALUE) {
//                        for (int i = 0; i < N; i++) {
//                            if (arr[i] > min)
//                                flag = 1;
//                        }
//                    }
//
//                    if (flag == 1 && max!=1)
//                        out.println(1);
//                    else
//                        out.println(2);
//                }
//            }
//        }
//        out.close();
//
//    }


    static class InputReader {
        InputStream is;

        public InputReader(boolean onlineJudge) {
            is = System.in;
        }

        byte[] inbuf = new byte[1024];
        public int lenbuf = 0, ptrbuf = 0;

        int readByte() {
            if (lenbuf == -1)
                throw new InputMismatchException();
            if (ptrbuf >= lenbuf) {
                ptrbuf = 0;
                try {
                    lenbuf = is.read(inbuf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0)
                    return -1;
            }
            return inbuf[ptrbuf++];
        }

        boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        int skip() {
            int b;
            while ((b = readByte()) != -1 && isSpaceChar(b))
                ;
            return b;
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        char nextChar() {
            return (char) skip();
        }

        String next() {
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        String nextLine() {
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while ((!isSpaceChar(b) || b == ' ')) { // when nextLine, (isSpaceChar(b) && b != ' ')
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        char[] next(int n) {
            char[] buf = new char[n];
            int b = skip(), p = 0;
            while (p < n && !(isSpaceChar(b))) {
                buf[p++] = (char) b;
                b = readByte();
            }
            return n == p ? buf : Arrays.copyOf(buf, p);
        }

        int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
                ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = num * 10 + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        long nextLong() {
            long num = 0;
            int b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
                ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = num * 10 + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        char[][] nextMatrix(int n, int m) {
            char[][] map = new char[n][];
            for (int i = 0; i < n; i++)
                map[i] = next(m);
            return map;
        }

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }

        int[][] next2DInt(int n, int m) {
            int[][] arr = new int[n][];
            for (int i = 0; i < n; i++) {
                arr[i] = nextIntArray(m);
            }
            return arr;
        }

        long[][] next2DLong(int n, int m) {
            long[][] arr = new long[n][];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLongArray(m);
            }
            return arr;
        }

        int[] shuffle(int[] arr) {
            Random r = new Random();
            for (int i = 1, j; i < arr.length; i++) {
                j = r.nextInt(i);
                int c = arr[i];
                arr[i] = arr[j];
                arr[j] = c;
            }
            return arr;
        }

        long[] shuffle(long[] arr) {
            Random r = new Random();
            for (int i = 1, j; i < arr.length; i++) {
                j = r.nextInt(i);
                long c = arr[i];
                arr[i] = arr[j];
                arr[j] = c;
            }
            return arr;
        }

        int[] uniq(int[] arr) {
            Arrays.sort(arr);
            int[] rv = new int[arr.length];
            int pos = 0;
            rv[pos++] = arr[0];
            for (int i = 1; i < arr.length; i++) {
                if (arr[i] != arr[i - 1]) {
                    rv[pos++] = arr[i];
                }
            }
            return Arrays.copyOf(rv, pos);
        }

        long[] uniq(long[] arr) {
            Arrays.sort(arr);
            long[] rv = new long[arr.length];
            int pos = 0;
            rv[pos++] = arr[0];
            for (int i = 1; i < arr.length; i++) {
                if (arr[i] != arr[i - 1]) {
                    rv[pos++] = arr[i];
                }
            }
            return Arrays.copyOf(rv, pos);
        }

        int[] reverse(int[] arr) {
            int l = 0, r = arr.length - 1;
            while (l < r) {
                arr[l] = arr[l] ^ arr[r];
                arr[r] = arr[l] ^ arr[r];
                arr[l] = arr[l] ^ arr[r];
                l++;
                r--;
            }
            return arr;
        }

        long[] reverse(long[] arr) {
            int l = 0, r = arr.length - 1;
            while (l < r) {
                arr[l] = arr[l] ^ arr[r];
                arr[r] = arr[l] ^ arr[r];
                arr[l] = arr[l] ^ arr[r];
                l++;
                r--;
            }
            return arr;
        }

        int[] compress(int[] arr) {
            int n = arr.length;
            int[] rv = Arrays.copyOf(arr, n);
            rv = uniq(rv);
            for (int i = 0; i < n; i++) {
                arr[i] = Arrays.binarySearch(rv, arr[i]);
            }
            return arr;
        }

        long[] compress(long[] arr) {
            int n = arr.length;
            long[] rv = Arrays.copyOf(arr, n);
            rv = uniq(rv);
            for (int i = 0; i < n; i++) {
                arr[i] = Arrays.binarySearch(rv, arr[i]);
            }
            return arr;
        }

        void deepFillInt(Object array, int val) {
            if (!array.getClass().isArray()) {
                throw new IllegalArgumentException();
            }
            if (array instanceof int[]) {
                int[] intArray = (int[]) array;
                Arrays.fill(intArray, val);
            } else {
                Object[] objArray = (Object[]) array;
                for (Object obj : objArray) {
                    deepFillInt(obj, val);
                }
            }
        }

        void deepFillLong(Object array, long val) {
            if (!array.getClass().isArray()) {
                throw new IllegalArgumentException();
            }
            if (array instanceof long[]) {
                long[] intArray = (long[]) array;
                Arrays.fill(intArray, val);
            } else {
                Object[] objArray = (Object[]) array;
                for (Object obj : objArray) {
                    deepFillLong(obj, val);
                }
            }
        }

    }
}