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.util.*;
import java.io.*;
public class Main{
	static int i,j,k;
	public static void main(String[] args) throws IOException{
		String str=ns();
		char arr[]=str.toCharArray();
		int len=arr.length;
		int a[]=new int[len+2];
		int b[]=new int[len+2];
		int counta=0,countb=0;
		for(i=0;i<len;i++){
			if(arr[i]=='a')
				counta++;
			else
				countb++;
			a[i+1]=counta;
			b[i+1]=countb;
		}
		a[i+1]=counta;
		b[i+1]=countb;
		int temp=0;
		int min=Integer.MAX_VALUE;
		for(i=1;i<=len+1;i++){
			for(j=i;j<=len+1;j++){
				temp=0;
				temp += b[i-1];
				temp += (a[j-1]-a[i-1]);
				temp += (b[len+1]-b[j-1]);
				//sop(temp);
				min=Math.min(temp,min);
			}
		}
	//	sop(Arrays.toString(a));

	sop(len-min);
	}

	/*
	fuctions
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	abcdefghijklmnopqrstuvwxyz
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	*/
	static int modulo(int j,int m){
		if(j<0)
			return m+j;
		  if(j>=m)
			return j-m;

			return j;
	}
	static final int mod=1000000007;
	static final double eps=1e-8;
	static final long inf=100000000000000000L;
	static final boolean debug=true;
	static Reader in=new Reader();
	static StringBuilder ans=new StringBuilder();
	static long powm(long a,long b,long m){
		long an=1;
		long c=a;
		while(b>0){
			if(b%2==1)
				an=(an*c)%m;
			c=(c*c)%m;
			b>>=1;
		}
		return an;
	}
	static Random rn=new Random();
	static void sop(Object a){System.out.println(a);}
	static int ni(){return in.nextInt();}
	static int[] nia(int n){int a[]=new int[n];for(int i=0;i<n;i++)a[i]=ni();return a;}
	static long nl(){return in.nextLong();}
	static long[] nla(int n){long a[]=new long[n];for(int i=0; i<n; i++)a[i]=nl();return a;}
	static String ns(){return in.next();}
	static String[] nsa(int n){String a[]=new String[n];for(int i=0; i<n; i++)a[i]=ns();return a;}
	static double nd(){return in.nextDouble();}
	static double[] nda(int n){double a[]=new double[n];for(int i=0;i<n;i++)a[i]=nd();return a;}
	static class Reader{
		public BufferedReader reader;
		public StringTokenizer tokenizer;
		public Reader(){
			reader=new BufferedReader(new InputStreamReader(System.in),32768);
			tokenizer=null;
		}
		public String next(){
			while(tokenizer==null || !tokenizer.hasMoreTokens()){
				try{
					tokenizer=new StringTokenizer(reader.readLine());
				}
				catch(IOException e){
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public int nextInt(){
			return Integer.parseInt(next());
		}
		public long nextLong(){
			return Long.parseLong(next());
		}
		public double nextDouble(){
			return Double.parseDouble(next());
		}
	}
}