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.DataInputStream; 
import java.io.FileInputStream; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.*;
import java.math.BigDecimal;
import java.math.BigInteger;

public class JavaApplication9 { 
    
    
//***************************************************************************************    
    static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            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(); 
            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(); 
            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 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    }
//****************************************************************************************    
static boolean isp(long n)
{

   if(n==3||n==2)
   return true;
   if(n%2==0||n%3==0||n==1)
   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 int factorial(int n) 
    { 
        if (n == 0) 
          return 1; 
          
        return n*factorial(n-1); 
    } */  
    /*  public int BinaryToDecimal(int binaryNumber){
 
    int decimal = 0;
    int p = 0;
    while(true){
      if(binaryNumber == 0){
        break;
      } else {
          int temp = binaryNumber%10;
          decimal += temp*Math.pow(2, p);
          binaryNumber = binaryNumber/10;
          p++;
       }
    }
    return decimal;
   }*/
      
/*-**********************  Start   *********************************-*/
  
      
      
      
public static void main(String[] args) throws IOException
 {
//-----------------------  Code   ---------------------------------------//

Reader in=new Reader();
Scanner sc=new Scanner(System.in);
int j=0,a=1,b=0,max=0;
String s=sc.next();
if(s.length()==2)System.out.print(2);
else
    if(s.length()==1)System.out.print(1);
else
{
if(s.charAt(1)=='b')b=1;
if(s.charAt(1)=='a')j=1;
if(s.charAt(0)=='a')j++;
int dp[]=new int[s.length()];
dp[0]=1;
dp[1]=2;
for(int i=2;i<s.length();i++)
{
 if(s.charAt(i)=='a')
 {
  j++;
  dp[i]=Math.max(dp[a]+1,dp[b]+1);
  a=i;
 }
 else
 {
  dp[i]=Math.max(j+1,dp[b]+1);
  b=i;
 }
 max=Math.max(max, dp[i]);

}
System.out.print(max);
}

}
}