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.util.*;
import java.awt.List;
import java.io.*;
import java.lang.*;
import java.lang.reflect.Array;
public class Code1 {

    
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);

        // Code starts..

        
        
        
        String s = in.nextLine();
        int n = s.length();
        int[] a = new int[n+1];
        for(int i=0; i<n; i++)
        	if(s.charAt(i)=='b')
        		a[i] = 1;
        a[n] = 1;
        int p = a[0];
        int[] ans = new int[n];
        for(int i=1; i<n; i++)
        {
        	if(a[i+1]==p)
        	{
        		ans[i] = 1;
        		p = a[i];
        	}
        }
        
        for(int i=0; i<n; i++)
        	pw.print(ans[i]+" ");
        
        // code ends...

        pw.flush();
        pw.close();
    }

    
    
    

   
    
    
    



    static class InputReader {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int snext() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

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

        public String readString() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    public static long c = 0;

    public static long mod = (long)Math.pow(10, 9)+7;
    public static int d;
    public static int p;
    public static int q;
    public static boolean flag;
    //public static long INF = Long.MAX_VALUE;

    public static void factSieve(int[] fact, long n) {

        for (int i = 2; i <= n; i += 2)
            fact[i] = 2;

        for (int i = 3; i <= n; i += 2) {
            if (fact[i] == 0) {
                fact[i] = i;

                for (int j = i; (long) j * i <= n; j++) {
                    fact[(int) ((long) i * j)] = i;
                }
            }
        }

        /*
         * int k = 1000; while(k!=1) { System.out.print(a[k]+" "); k /= a[k];
         * 
         * }
         */
    }

    public static long floorsqrt(long n) {
        long ans = 0;
        long l = 0;
        long r = n;
        long mid = 0;
        while (l <= r) {
            mid = (l + r) / 2;
            if (mid * mid == n)
                return mid;

            if (mid * mid > n) {
                r = mid - 1;
            } else {
                ans = mid;
                l = mid + 1;
            }

        }

        return ans;
    }

    public static long fun(int[] a, int[] b, int m, int n) {
        long result = 0;
        for (int i = 0; i < m; i++)
            for (int j = 0; j < m; j++) {
                long[] fib = new long[Math.max(2, n + 2)];
                fib[1] = a[i];
                fib[2] = b[j];
                for (int k = 3; k <= n; k++)
                    fib[k] = (fib[k - 1] % mod + fib[k - 2] % mod) % mod;
                result = (result % mod + fib[n] % mod) % mod;
            }

        return result;

    }

    /*
     * public static double slope(pair p1, pair p2) { double m = INF; if((p1.x -
     * p2.x)!=0) m = p1.y - p2.y/(p1.x - p2.x);
     * 
     * 
     * return Math.abs(m);
     * 
     * }
     */

    public static int count(String[] s, int f) {
        int count = 0;
        int n = s[0].length();

        if (f == 1) {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (i % 2 == 0) {
                        if (j % 2 == 0 && s[i].charAt(j) == '0')
                            count++;
                        if (j % 2 == 1 && s[i].charAt(j) == '1')
                            count++;
                    }
                    if (i % 2 == 1) {
                        if (j % 2 == 1 && s[i].charAt(j) == '0')
                            count++;
                        if (j % 2 == 0 && s[i].charAt(j) == '1')
                            count++;
                    }

                }
            }
        } else {

            count = 0;

            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (i % 2 == 1) {
                        if (j % 2 == 0 && s[i].charAt(j) == '0')
                            count++;
                        if (j % 2 == 1 && s[i].charAt(j) == '1')
                            count++;
                    }
                    if (i % 2 == 0) {
                        if (j % 2 == 1 && s[i].charAt(j) == '0')
                            count++;
                        if (j % 2 == 0 && s[i].charAt(j) == '1')
                            count++;
                    }

                }
            }

        }

        return count;

    }

    public static int gcd(int p2, int p22) {
        if (p2 == 0)
            return (int) p22;
        return gcd(p22 % p2, p2);
    }

    public static int findGCD(int arr[], int n) {
        int result = arr[0];
        for (int i = 1; i < n; i++)
            result = gcd(arr[i], result);

        return result;
    }

    public static void nextGreater(long[] a, int[] ans) {

        Stack<Integer> stk = new Stack<>();
        stk.push(0);

        for (int i = 1; i < a.length; i++) {

            if (!stk.isEmpty()) {
                int s = stk.pop();
                while (a[s] < a[i]) {
                    ans[s] = i;
                    if (!stk.isEmpty())
                        s = stk.pop();
                    else
                        break;
                }
                if (a[s] >= a[i])
                    stk.push(s);
            }

            stk.push(i);

        }
        return;

    }

    public static void nextGreaterRev(long[] a, int[] ans) {

        int n = a.length;
        int[] pans = new int[n];
        Arrays.fill(pans, -1);
        long[] arev = new long[n];
        for (int i = 0; i < n; i++)
            arev[i] = a[n - 1 - i];

        Stack<Integer> stk = new Stack<>();
        stk.push(0);

        for (int i = 1; i < n; i++) {

            if (!stk.isEmpty()) {
                int s = stk.pop();
                while (arev[s] < arev[i]) {
                    pans[s] = n - i - 1;
                    if (!stk.isEmpty())
                        s = stk.pop();
                    else
                        break;
                }
                if (arev[s] >= arev[i])
                    stk.push(s);
            }

            stk.push(i);

        }

        // for(int i=0; i<n; i++)
        // System.out.print(pans[i]+" ");

        for (int i = 0; i < n; i++)
            ans[i] = pans[n - i - 1];

        return;

    }

    public static void nextSmaller(long[] a, int[] ans) {

        Stack<Integer> stk = new Stack<>();
        stk.push(0);

        for (int i = 1; i < a.length; i++) {

            if (!stk.isEmpty()) {
                int s = stk.pop();
                while (a[s] > a[i]) {
                    ans[s] = i;
                    if (!stk.isEmpty())
                        s = stk.pop();
                    else
                        break;
                }
                if (a[s] <= a[i])
                    stk.push(s);
            }

            stk.push(i);

        }
        return;

    }

    public static long lcm(int[] numbers) {
        long lcm = 1;
        int divisor = 2;
        while (true) {
            int cnt = 0;
            boolean divisible = false;
            for (int i = 0; i < numbers.length; i++) {
                if (numbers[i] == 0) {
                    return 0;
                } else if (numbers[i] < 0) {
                    numbers[i] = numbers[i] * (-1);
                }
                if (numbers[i] == 1) {
                    cnt++;
                }
                if (numbers[i] % divisor == 0) {
                    divisible = true;
                    numbers[i] = numbers[i] / divisor;
                }
            }
            if (divisible) {
                lcm = lcm * divisor;
            } else {
                divisor++;
            }
            if (cnt == numbers.length) {
                return lcm;
            }
        }
    }

    public static long fact(long n) {

        long factorial = 1;
        for (int i = 1; i <= n; i++) {
            factorial *= i;
        }
        return factorial;
    }

    public static int lowerLimit(int[] a, int n) {
        int ans = 0;

        int ll = 0;
        int rl = a.length - 1;
        // System.out.println(a[rl]+" "+n);
        if (a[0] > n)
            return 0;
        if (a[0] == n)
            return 1;
        else if (a[rl] <= n)
            return rl + 1;

        while (ll <= rl) {

            int mid = (ll + rl) / 2;
            if (a[mid] == n) {
                ans = mid + 1;
                break;
            }

            else if (a[mid] > n) {
                rl = mid - 1;

            } else {
                ans = mid + 1;
                ll = mid + 1;
            }
        }

        return ans;
    }

    public static long choose(long total, long choose) {
        if (total < choose)
            return 0;
        if (choose == 0 || choose == total)
            return 1;
        return (choose(total - 1, choose - 1) + choose(total - 1, choose)) % mod;
    }

    public static int[] suffle(int[] a, Random gen) {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int ind = gen.nextInt(n - i) + i;
            int temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }
        return a;
    }

    public static pair[] suffle(pair[] a, Random gen) {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int ind = gen.nextInt(n - i) + i;
            pair temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }
        return a;
    }
    
    
    
    
    public static int floorSearch(int arr[], int low, int high, int x) {
        if (low > high)
            return -1;

        if (x > arr[high])
            return high;
        int mid = (low + high) / 2;

        if (mid > 0 && arr[mid - 1] < x && x < arr[mid])
            return mid - 1;

        if (x < arr[mid])
            return floorSearch(arr, low, mid - 1, x);

        return floorSearch(arr, mid + 1, high, x);
    }

    public static void swap(int a, int b) {
        int temp = a;
        a = b;
        b = temp;
    }

    public static ArrayList<Integer> primeFactorization(int n) {
        ArrayList<Integer> a = new ArrayList<Integer>();
        for (int i = 2; i * i <= n; i++) {
            while (n % i == 0) {
                a.add(i);
                n /= i;
            }
        }
        if (n != 1)
            a.add(n);
        return a;
    }
    
    
    

    public static void sieve(boolean[] isPrime, int n) {
        for (int i = 1; i < n; i++)
            isPrime[i] = true;

        isPrime[0] = false;
        isPrime[1] = false;

        for (int i = 2; i * i < n; i++) {
            if (isPrime[i] == true) {
                for (int j = (2 * i); j < n; j += i)
                    isPrime[j] = false;
            }
        }
    }

    public static int lowerbound(ArrayList<Long> net, long c2) {
        int i = Collections.binarySearch(net, c2);
        if (i < 0)
            i = -(i + 2);
        return i;

    }
    
    public static int lowerboundArray(int[] dis, int c2) {
        int i = Arrays.binarySearch(dis, c2);
        if (i < 0)
            i = -(i + 2);
        return i;

    }

    public static int uperbound(ArrayList<Integer> list, int c2) {
        int i = Collections.binarySearch(list, c2);
        if (i < 0)
            i = -(i + 1);
        return i;

    }

    public static int uperboundArray(int[] dis, int c2) {
        int i = Arrays.binarySearch(dis, c2);
        if (i < 0)
            i = -(i + 1);
        return i;

    }

    public static long[] sort(long[] a) {
        Random gen = new Random();
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int ind = gen.nextInt(n - i) + i;
            long temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }

        Arrays.sort(a);
        return a;
    }

    public static int[] sort(int[] a) {
        Random gen = new Random();
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int ind = gen.nextInt(n - i) + i;
            int temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }

        Arrays.sort(a);
        return a;
    }

    public static int GCD(int a, int b) {
        if (b == 0)
            return a;
        else
            return GCD(b, a % b);
    }

    public static long GCD(long a, long b) {
        if (b == 0)
            return a;
        else
            return GCD(b, a % b);
    }

    public static void extendedEuclid(int A, int B) {
        if (B == 0) {
            d = A;
            p = 1;
            q = 0;
        } else {
            extendedEuclid(B, A % B);
            int temp = p;
            p = q;
            q = temp - (A / B) * q;
        }
    }

    public static long LCM(long a, long b) {
        return (a * b) / GCD(a, b);
    }

    public static int LCM(int a, int b) {
        return (a * b) / GCD(a, b);
    }

    public static int binaryExponentiation(int x, int n) {
        int result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = result * x;
            x = x * x;
            n = n / 2;
        }
        return result;
    }

    public static int[] countDer(int n) {
        int der[] = new int[n + 1];

        der[0] = 1;
        der[1] = 0;
        der[2] = 1;

        for (int i = 3; i <= n; ++i)
            der[i] = (i - 1) * (der[i - 1] + der[i - 2]);

        // Return result for n
        return der;
    }

    static long binomialCoeff(int n, int k) {
        long C[][] = new long[n + 1][k + 1];
        int i, j;

        // Calculate value of Binomial Coefficient in bottom up manner
        for (i = 0; i <= n; i++) {
            for (j = 0; j <= Math.min(i, k); j++) {
                // Base Cases
                if (j == 0 || j == i)
                    C[i][j] = 1;

                // Calculate value using previosly stored values
                else
                    C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
            }
        }

        return C[n][k];
    }

    public static long binaryExponentiation(long x, long n) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = result * x;
            x = (x % mod * x % mod) % mod;
            n = n / 2;
        }
        return result;
    }

    public static int modularExponentiation(int x, int n, int M) {
        int result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = (result * x) % M;
            x = (x * x) % M;
            n = n / 2;
        }
        return result;
    }

    public static long modularExponentiation(long x, long n, long M) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = (result * x) % M;
            x = (x * x) % M;
            n = n / 2;
        }
        return result;
    }

    public static int modInverse(int A, int M) {
        return modularExponentiation(A, M - 2, M);
    }

    public static long sie(long A, long M) {
        return modularExponentiation(A, M - 2, M);
    }

    public static boolean checkYear(int year) {
        if (year % 400 == 0)
            return true;

        if (year % 100 == 0)
            return false;

        if (year % 4 == 0)
            return true;
        return false;
    }

    public static boolean isPrime(int n) {

        if (n <= 1)
            return false;
        if (n <= 3)
            return true;

        if (n % 2 == 0 || n % 3 == 0)
            return false;

        for (int i = 5; i * i <= n; i = i + 6) {
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        }

        return true;
    }

    static class pair implements Comparable<pair>

    {
        Integer x, y;

        pair(int x, int y) {
            this.x = x;
            this.y = y;
        }

        public int compareTo(pair o) {
            int result = x.compareTo(o.x);
            if (result == 0)
                result = y.compareTo(o.y);

            return result;
        }

        public String toString() {
            return x + " " + y;
        }

        public boolean equals(Object o) {
            if (o instanceof pair) {
                pair p = (pair) o;
                return p.x == x && p.y == y;
            }
            return false;
        }

        public int hashCode() {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode();
        }

    }

    static class triplet implements Comparable<triplet> {
        Integer x, y, z;

        triplet(int x, int y, int z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        public int compareTo(triplet o) {
            int result = x.compareTo(o.x);
            if (result == 0)
                result = y.compareTo(o.y);
            if (result == 0)
                result = z.compareTo(o.z);

            return result;
        }

        public boolean equlas(Object o) {
            if (o instanceof triplet) {
                triplet p = (triplet) o;
                return x == p.x && y == p.y && z == p.z;
            }
            return false;
        }

        public String toString() {
            return x + " " + y + " " + z;
        }

        public int hashCode() {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode() + new Long(z).hashCode();
        }
    }

    
    
    /*
     * static class node implements Comparable<node>
     * 
     * { Integer x, y, z; node(int x,int y, int z) { this.x=x; this.y=y; this.z=z; }
     * 
     * public int compareTo(pair o) { int result = x.compareTo(o.x); if(result==0)
     * result = y.compareTo(o.y); if(result==0) result = z.compareTo(z); return
     * result; }
     * 
     * @Override public int compareTo(node o) { // TODO Auto-generated method stub
     * return 0; } }
     */
}