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:
/*
    Author: @__goku__
    ssrivastava990@gmail.com

                   `\-.   `
                      \ `.  `
                       \  \ |
              __.._    |   \.       S O N - G O K U
       ..---~~     ~ . |    Y
         ~-.          `|    |
            `.               `~~--.
              \                    ~.
               \                     \__. . -- -  .
         .-~~~~~      ,    ,            ~~~~~~---...._
      .-~___        ,'/  ,'/ ,'\          __...---~~~
            ~-.    /._\_( ,(/_. 7,-.    ~~---...__
           _...>-  P""6=`_/"6"~   6)    ___...--~~~
            ~~--._ \`--') `---'   9'  _..--~~~
                  ~\ ~~/_  ~~~   /`-.--~~
                    `.  ---    .'   \_
                      `. " _.-'     | ~-.,-------._
                  ..._../~~   ./       .-'    .-~~~-.
            ,--~~~ ,'...\` _./.----~~.'/    /'       `-
        _.-(      |\    `/~ _____..-' /    /      _.-~~`.
       /   |     /. ^---~~~~       ' /    /     ,'  ~.   \
      (    /    (  .           _ ' /'    /    ,/      \   )
      (`. |     `\   - - - - ~   /'      (   /         .  |
       \.\|       \            /'        \  |`.           /
       /.'\\      `\         /'           ~-\         .  /\
      /,   (        `\     /'                `.___..-      \
     | |    \         `\_/'                  //      \.     |
     | |     |                 _Seal_      /' |       |     |
 */

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

public class C442B
{
    static PrintWriter out = new PrintWriter((System.out));
    static Kioken sc = new Kioken();

    public static void main(String args[]) throws IOException
    {
        int t = 1;
        //t = sc.nextInt();
        while (t-- > 0)
        {
            kamehameha();
        }
        out.close();
    }

    public static void kamehameha()
    {
        String s=sc.next();
        int n=s.length();
        int[] a=new int[n+1];
        int[] A=new int[n+1];
        int[] b=new int[n+1];
        int[] B=new int[n+1];
        for(int x=1;x<=n;x++)
        {
            if(s.charAt(x-1)=='a')
            {
                a[x]=a[x-1]+1;
                b[x]=b[x-1];
            }
            else
            {
                b[x]=b[x-1]+1;
                a[x]=a[x-1];
            }
        }
        if(s.charAt(n-1)=='a')
        {
            A[n]=1;
        }
        else
        {
            B[n]=1;
        }
        for(int x=n-2;x>=0;x--)
        {
            if(s.charAt(x)=='a')
            {
                A[x]=A[x+1]+1;
                B[x]=B[x+1];
            }
            else
            {
                B[x]=B[x+1]+1;
                A[x]=A[x+1];
            }
        }
        /*for(int x=0;x<=n;x++)
        {
            out.print(a[x]+" ");
        }
        out.println();
        for(int x=0;x<=n;x++)
        {
            out.print(b[x]+" ");
        }
        out.println();
        for(int x=0;x<=n;x++)
        {
            out.print(A[x]+" ");
        }
        out.println();
        for(int x=0;x<=n;x++)
        {
            out.print(B[x]+" ");
        }
        out.println();*/
        int ans=0;
        for(int x=0;x<n;x++)
        {
            for(int y=x;y<=n;y++)
            {
                int d=a[x]+(a[n]-a[y])+(b[y]-b[x]);
                //out.println(x+" "+y+" "+d);
                ans=Math.max(ans,d);
            }
        }
        out.println(ans);
    }

    public static int lower_bound(ArrayList<Integer> ar, int k)
    {
        int s = 0, e = ar.size();
        while (s != e)
        {
            int mid = s + e >> 1;
            if (ar.get(mid) <= k)
            {
                s = mid + 1;
            }
            else
            {
                e = mid;
            }
        }
        return Math.abs(s) - 1;
    }

    public static int upper_bound(ArrayList<Integer> ar, int k)
    {
        int s = 0;
        int e = ar.size();
        while (s != e)
        {
            int mid = s + e >> 1;
            if (ar.get(mid) < k)
            {
                s = mid + 1;
            }
            else
            {
                e = mid;
            }
        }
        if (s == ar.size())
        {
            return -1;
        }
        return s;
    }

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

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

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

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

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

        public String nextLine()
        {
            try
            {
                return br.readLine();
            }
            catch (Exception e)
            {
                e.printStackTrace();
            }
            return null;
        }

        public boolean hasNext()
        {
            String next = null;
            try
            {
                next = br.readLine();
            }
            catch (Exception e)
            {
            }
            if (next == null || next.length() == 0)
            {
                return false;
            }
            st = new StringTokenizer(next);
            return true;
        }
    }
}