Problem: One day Nikita found the string containing letters "a" and "b" only. 

Nikita thinks that string is beautiful if it can be cut into 3 strings (possibly empty) without changing the order of the letters, where the 1-st and the 3-rd one contain only letters "a" and the 2-nd contains only letters "b".

Nikita wants to make the string beautiful by removing some (possibly none) of its characters, but without changing their order. What is the maximum length of the string he can get?

Input

The first line contains a non-empty string of length not greater than 5 000 containing only lowercase English letters "a" and "b". 

Output

Print a single integer — the maximum possible size of beautiful string Nikita can get.

Examples

Input

abba


Output

4

Input

bab


Output

2

Note

It the first sample the string is already beautiful.

In the second sample he needs to delete one of "b" to make it beautiful.

Solution (in JAVA):

Solution:

    import java.io.*;
    import java.math.BigDecimal;
    import java.util.ArrayDeque;
    import java.util.Arrays;
    import java.util.InputMismatchException;
    import java.util.Queue;
    import java.io.*;
    import java.lang.reflect.Array;
    import java.math.BigInteger;
    import java.util.*;
    import java.io.BufferedReader;
    import java.io.IOException;
    import java.util.Collections;
    import java.io.InputStreamReader;
    import java.util.logging.SimpleFormatter;


    public class Main1 {




        public static void main(String[] args) {


            FastScanner in = new FastScanner();
            PrintWriter out = new PrintWriter(System.out);


            char a[] = in.next().toCharArray() ;
            int n = a.length ;
             int l[] = new int[n] ;
             int r[] = new int[n] ;

             if (a[0] == 'a')
             l[0]++ ;
            for (int i = 1; i <n ; i++) {
                l[i] += l[i-1] ;
                if (a[i] == 'a')
                    l[i]++ ;
            }

            if (a[n-1] == 'a')
                r[n-1]++ ;
            for (int i=n-2 ; i>=0 ; i--){
                r[i] += r[i+1] ;
                if (a[i] == 'a')
                    r[i]++ ;
            }
            int len = 0 ;

            for (int i = 0; i <n ; i++) {
                if (i != n-1)
                    len = Math.max(len ,i+1 - l[i] + r[i+1]) ;

                for (int j=n-1 ; j>= i+1 ; j--){
                    int curr = j-i ;

                    int B = curr - (l[j] - l[i]) ;
                    int C = 0 ;
                    if (j != n-1){
                        C = r[j+1] ;
                        len = Math.max(len , j+1 - l[j] + r[j+1] ) ;
                    }
                    len = Math.max(len , B + C + l[i]) ;
                    len = Math.max(len , l[j-1]+ (n - j - r[j])  ) ;
                }
            }

            len = Math.max(len , l[n-1]) ;
            len = Math.max(len ,n - l[n-1]) ;

            System.out.println(len);




            out.flush();
            out.close();

        }

        static int findLCA(int a, int b, int par[][], int depth[]) {
            if (depth[a] > depth[b]) {
                a = a ^ b;
                b = a ^ b;
                a = a ^ b;
            }
            int diff = depth[b] - depth[a];
            for (int i = 19; i >= 0; i--) {
                if ((diff & (1 << i)) > 0) {
                    b = par[b][i];
                }
            }
            if (a == b)
                return a;
            for (int i = 19; i >= 0; i--) {
                if (par[b][i] != par[a][i]) {
                    b = par[b][i];
                    a = par[a][i];
                }
            }
            return par[a][0];
        }

        static void formArrayForBinaryLifting(int n, int par[][]) {
            for (int j = 1; j < 20; j++) {
                for (int i = 0; i < n; i++) {
                    if (par[i][j - 1] == -1)
                        continue;
                    par[i][j] = par[par[i][j - 1]][j - 1];
                }
            }
        }


        static void sort(int ar[]) {
            int n = ar.length;
            ArrayList<Integer> a = new ArrayList<>();
            for (int i = 0; i < n; i++)
                a.add(ar[i]);
            Collections.sort(a);
            for (int i = 0; i < n; i++)
                ar[i] = a.get(i);
        }

        static void sort1(long ar[]) {
            int n = ar.length;
            ArrayList<Long> a = new ArrayList<>();
            for (int i = 0; i < n; i++)
                a.add(ar[i]);
            Collections.sort(a);
            for (int i = 0; i < n; i++)
                ar[i] = a.get(i);
        }

        static long ncr(long n, long r, long mod) {
            if (r == 0)
                return 1;
            long val = ncr(n - 1, r - 1, mod);
            val = (n * val) % mod;
            val = (val * modInverse(r, mod)) % mod;
            return val;
        }

        static long fast_pow(long base, long n, long M) {
            if (n == 0)
                return 1;
            if (n == 1)
                return base % M;
            long halfn = fast_pow(base, n / 2, M);
            if (n % 2 == 0)
                return (halfn * halfn) % M;
            else
                return (((halfn * halfn) % M) * base) % M;
        }

        static long modInverse(long n, long M) {
            return fast_pow(n, M - 2, M);
        }


        private static int countDigits(long l) {
            if (l >= 1000000000000000000L) return 19;
            if (l >= 100000000000000000L) return 18;
            if (l >= 10000000000000000L) return 17;
            if (l >= 1000000000000000L) return 16;
            if (l >= 100000000000000L) return 15;
            if (l >= 10000000000000L) return 14;
            if (l >= 1000000000000L) return 13;
            if (l >= 100000000000L) return 12;
            if (l >= 10000000000L) return 11;
            if (l >= 1000000000L) return 10;
            if (l >= 100000000L) return 9;
            if (l >= 10000000L) return 8;
            if (l >= 1000000L) return 7;
            if (l >= 100000L) return 6;
            if (l >= 10000L) return 5;
            if (l >= 1000L) return 4;
            if (l >= 100L) return 3;
            if (l >= 10L) return 2;
            return 1;
        }


        static class FastOutput implements AutoCloseable, Closeable, Appendable {
            private static final int THRESHOLD = 32 << 10;
            private final Writer os;
            private StringBuilder cache = new StringBuilder(THRESHOLD * 2);

            public FastOutput append(CharSequence csq) {
                cache.append(csq);
                return this;
            }

            public FastOutput append(CharSequence csq, int start, int end) {
                cache.append(csq, start, end);
                return this;
            }

            private void afterWrite() {
                if (cache.length() < THRESHOLD) {
                    return;
                }
                flush();
            }

            public FastOutput(Writer os) {
                this.os = os;
            }

            public FastOutput(OutputStream os) {
                this(new OutputStreamWriter(os));
            }

            public FastOutput append(char c) {
                cache.append(c);
                afterWrite();
                return this;
            }

            public FastOutput append(long c) {
                cache.append(c);
                afterWrite();
                return this;
            }

            public FastOutput append(String c) {
                cache.append(c);
                afterWrite();
                return this;
            }

            public FastOutput println() {
                return append(System.lineSeparator());
            }

            public FastOutput flush() {
                try {
                    //            boolean success = false;
                    //            if (stringBuilderValueField != null) {
                    //                try {
                    //                    char[] value = (char[]) stringBuilderValueField.get(cache);
                    //                    os.write(value, 0, cache.length());
                    //                    success = true;
                    //                } catch (Exception e) {
                    //                }
                    //            }
                    //            if (!success) {
                    os.append(cache);
                    //            }
                    os.flush();
                    cache.setLength(0);
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
                return this;
            }

            public void close() {
                flush();
                try {
                    os.close();
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }

            public String toString() {
                return cache.toString();
            }

        }


        static class FastScanner {
            BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
            StringTokenizer st = new StringTokenizer("");

            String next() {
                while (!st.hasMoreTokens())
                    try {
                        st = new StringTokenizer(br.readLine());
                    } catch (IOException e) {
                        e.printStackTrace();
                    }
                return st.nextToken();
            }

            int nextInt() {
                return Integer.parseInt(next());
            }

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


            long nextLong() {
                return Long.parseLong(next());
            }
        }


    }