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.lang.reflect.Array;
    import java.util.*;
    import java.lang.*;
    import static java.lang.Math.*;
    public class Main implements Runnable {

        public static void main(String[] args) {
                new Thread(null, new Main(), "Check2", 1 << 28).start();// to increse stack size in java
        }
        void init(ArrayList <Integer> adj[], int n){
            for(int i=0;i<=n;i++)adj[i]=new ArrayList<>();
        }
        static long mod = (long) (1e9+7);
        public void run() {
            InputReader in = new InputReader(System.in);
            PrintWriter w = new PrintWriter(System.out);


            char c[]=in.next().toCharArray();

            char d[]=new char[3*c.length];
            for(int i=0;i<c.length;i++)d[i]='a';
            for(int i=c.length;i<2*c.length;i++)d[i]='b';
            for(int i=2*c.length;i<3*c.length;i++)d[i]='a';

            int n=c.length;
            int m=d.length;
            int dp[][]=new int[2][m+1];
            int bi=0;

            for (int i = 0; i <= n; i++)
            {
                // Compute current binary index
                bi = i & 1;

                for (int j = 0; j <= m; j++)
                {
                    if (i == 0 || j == 0)
                        dp[bi][j] = 0;

                    else if (c[i-1]== d[j-1])
                        dp[bi][j] = dp[1-bi][j-1] + 1;

                    else
                        dp[bi][j] = Math.max(dp[1-bi][j],
                                dp[bi][j-1]);
                }
            }

            w.println(dp[bi][m]);








            w.close();
        }
        class pair2  {
            int a,b;
            pair2(int a,int b){
                this.a=a;
                this.b=b;
            }
        }

        static void diji(int s, long dist[], ArrayList<pair> adj[]) {
            dist[s] = 0;
            PriorityQueue<pair> q = new PriorityQueue<>(new cmp());
            q.add(new pair(s, 0));
            while (!q.isEmpty()) {
                pair p1 = q.poll();
                for (pair ne: adj[p1.a]) {

                    if ((long) p1.b + (long) ne.b < dist[ne.a]) {
                        dist[ne.a] = (long) p1.b + (long) ne.b;
                        pair p2 = new pair(ne.a, dist[ne.a]);
                        q.add(p2);

                    }

                }
            }

        }
        static class cmp implements Comparator<pair>{

            public  int compare(pair o1,pair o2)
            {
                return o1.b<o2.b?-1:o1.b>o2.b?1:0;
            }

        }

        static class pair {
            int a;
            long b;
            pair(int a,long b){
                this.a=a;
                this.b=b;
            }
            public boolean equals(Object obj) {      //  override equals method for object to remove tem from arraylist and sets etc.......
                if (this == obj)
                    return true;
                if (obj == null)
                    return false;
                if (getClass() != obj.getClass())
                    return false;
                pair other = (pair) obj;
                if (b!= other.b||a!=other.a)
                    return false;
                return true;
            }
        }

        static long modinv(long a,long b)
        {
            long p=power(b,mod-2);

            p=a%mod*p%mod;
            p%=mod;

            return p;

        }

        static long power(long x,long y){
            if(y==0)return 1%mod;
            if(y==1)return x%mod;


            long res=1;
            x=x%mod;
            while(y>0){


                if((y%2)!=0){
                    res=(res*x)%mod;
                }


                y=y/2;
                x=(x*x)%mod;
            }


            return res;

        }
        static  long gcd(long a,long b){

            if(b==0)return a;
            return gcd(b,a%b);
        }

        static  void sev(int a[],int n){

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

                if(a[i]!=0){
                    for(int j=2*i;j<=n;){

                        a[j]=0;
                        j=j+i;
                    }
                }

            }

        }



        static class InputReader
        {
            private InputStream stream;
            private byte[] buf = new byte[1024];
            private int curChar;
            private int numChars;
            private SpaceCharFilter filter;

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

            public int read()
            {
                if (numChars==-1)
                    throw new InputMismatchException();

                if (curChar >= numChars)
                {
                    curChar = 0;
                    try
                    {
                        numChars = stream.read(buf);
                    }
                    catch (IOException e)
                    {
                        throw new InputMismatchException();
                    }

                    if(numChars <= 0)
                        return -1;
                }
                return buf[curChar++];
            }

            public String nextLine()
            {
                BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
                String str = "";
                try
                {
                    str = br.readLine();
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
                return str;
            }
            public int nextInt()
            {
                int c = read();

                while(isSpaceChar(c))
                    c = read();

                int sgn = 1;

                if (c == '-')
                {
                    sgn = -1;
                    c = read();
                }

                int res = 0;
                do
                {
                    if(c<'0'||c>'9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = read();
                }
                while (!isSpaceChar(c));

                return res * sgn;
            }

            public long nextLong()
            {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                int sgn = 1;
                if (c == '-')
                {
                    sgn = -1;
                    c = read();
                }
                long res = 0;

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

            public double nextDouble()
            {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                int sgn = 1;
                if (c == '-')
                {
                    sgn = -1;
                    c = read();
                }
                double res = 0;
                while (!isSpaceChar(c) && c != '.')
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = read();
                }
                if (c == '.')
                {
                    c = read();
                    double m = 1;
                    while (!isSpaceChar(c))
                    {
                        if (c == 'e' || c == 'E')
                            return res * Math.pow(10, nextInt());
                        if (c < '0' || c > '9')
                            throw new InputMismatchException();
                        m /= 10;
                        res += (c - '0') * m;
                        c = read();
                    }
                }
                return res * sgn;
            }

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

            public String next()
            {
                return readString();
            }

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







    }