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.*;
public class CodeForces {
    /*****************************************WRITING CODE STARTS HERE******************************************/

    public static void solve(int test)throws IOException {
        char[] str = sc.next().toCharArray();
        int n = str.length;
        boolean firstB = false;
        boolean firstA = true;
        int[] ans = new int[n];
        for(int i=n-1;i>=0;i--){
            if(str[i] == 'a'){
                if(firstA)ans[i] = 1;
                firstA = false;
                firstB = true;
            }else{
                if(firstB)ans[i] = 1;
                firstB = false;
                firstA = true;
            }
        }
        for(int ele : ans)out.print(ele+" ");
    }


    /*****************************************WRITING CODE ENDS HERE******************************************/

    public static void main(String[] args) throws IOException{
        int testCase = 1;
//        testCase = sc.nextInt();
        for (int i = 1; i <= testCase; i++) solve(i);
        closeIO();
    }
    static FastestReader sc = new FastestReader();              // FASTEST INPUT
    static PrintWriter out = new PrintWriter(System.out);                // FAST OUTPUT


    /**************************************HELPER FUNCTION STARTS HERE ************************************/

    public static int mod = (int) 1e9 + 7;
    public static final int inf_int = (int) 1e9;
    public static final long inf_long = (long) 1e12;

    public static final String YES = "YES";
    public static final String NO = "NO";

    public static void sort(int[] a, boolean isAscending) {
        ArrayList<Integer> temp = new ArrayList<>();
        for (int j : a) temp.add(j);
        sort(temp, isAscending);
        for (int i = 0; i < a.length; i++) a[i] = temp.get(i);
    }

    public static void sort(long[] a, boolean isAscending) {
        ArrayList<Long> temp = new ArrayList<>();
        for (long ele : a) temp.add(ele);
        sort(temp, isAscending);
        for (int i = 0; i < a.length; i++) a[i] = temp.get(i);
    }
    @SuppressWarnings({"rawtypes","unchecked"})
    public static void sort(List list, boolean isAscending) {
        if (isAscending) Collections.sort(list);
        else list.sort(Collections.reverseOrder());
    }

    // count the length of a number, time O(1)
    public static int countDigitBase10(long n) {
        if (n == 0) return 0;
        return (int) (1 + Math.log10(n));
    }

    // euclidean algorithm
    public static long gcd(long a, long b) {
        // time O(max (loga ,logb))
        long x = Math.min(a, b);
        long y = Math.max(a, b);
        if (y % x == 0) return x;
        return gcd(y % x, x);
    }

    public static long lcm(long a, long b) {
        // lcm(a,b) * gcd(a,b) = a * b
        return (a / gcd(a, b)) * b;
    }
    // binary exponentiation
    public static long power(long x, long n) {
        // time O(logn)
        long ans = 1;
        while (n > 0) {
            if ((n & 1) == 1) {
                ans *= x;
                ans %= mod;
                n--;
            } else {
                x *= x;
                x %= mod;
                n >>= 1;
            }
        }
        return ans;
    }

    public static long firstDivisor(long n) {
        if (n == 1 || n == 0) return n;
        for (long i = 2; i * i <= n; i++)
            if (n % i == 0) return i;
        return -1;
    }

    public static long max3(long a, long b, long c) {
        return max2(max2(a, b), c);
    }

    public static long max2(long a, long b) {
        return Math.max(a, b);
    }

    public static long min3(long a, long b, long c) {
        return min2(min2(a, b), c);
    }

    public static long min2(long a, long b) {
        return Math.min(a, b);
    }

    public static int max3(int a, int b, int c) {
        return max2(max2(a, b), c);
    }

    public static int max2(int a, int b) {
        return Math.max(a, b);
    }

    public static int min3(int a, int b, int c) {
        return min2(min2(a, b), c);
    }

    public static int min2(int a, int b) {
        return Math.min(a, b);
    }

    /**************************************HELPER FUNCTION ENDS HERE ************************************/

    /*****************************************FAST INPUT STARTS HERE *************************************/


    public static void closeIO() throws IOException{
            out.flush();
            out.close();
            sc.close();
    }
    private static class FastestReader {
        private static final int BUFFER_SIZE = 1 << 16;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;

        public FastestReader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public FastestReader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

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

        private int skip() throws IOException {
            int b;
            //noinspection StatementWithEmptyBody
            while ((b = read()) != -1 && isSpaceChar(b)) {}
            return b;
        }

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

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            final boolean neg = c == '-';
            if (neg) { c = read(); }
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg) { return -ret; }
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ') { c = read(); }
            final boolean neg = c == '-';
            if (neg) { c = read(); }
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) { return -ret; }
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ') { c = read(); }
            final boolean neg = c == '-';
            if (neg) { c = read(); }

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg) { return -ret; }
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1) { buffer[0] = -1; }
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead) { fillBuffer(); }
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            din.close();
        }

    }
    /*****************************************FAST INPUT ENDS HERE *************************************/
}