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.*;
import java.math.*;
public class A{
    static class Node implements Comparable<Node>{
        int x;
        int y;
        int w;
        public Node(int x,int y,int w){
            this.x=x;
            this.w=w;
            this.y=y;
        }
        public int compareTo(Node c){
            return this.w-c.w;
        }
    }
    void solve() {
        char s[]=ns().toCharArray();
        int n=s.length;
        int a[]=new int[n+1];
        int b[]=new int[n+1];
        int totala=0;
        for(int i=0;i<n;i++) if(s[i]=='a') totala++;
        for(int i=1;i<=n;i++){
            if(s[i-1]=='a') {
                a[i] = a[i - 1] + 1;
                b[i] = b[i - 1];
            }
            else {


                    a[i] = a[i - 1];
                    b[i] = b[i - 1] + 1;

            }
        }
        int ans=0;
        for(int i=0;i<=n;i++){
            for(int j=i;j<=n;j++){
                ans=Math.max(ans,a[i]+b[j]-b[i]+totala-a[j]);
            }
        }
        if(totala==0) ans=n;

        pw.println(ans);

    }






    InputStream is;
    PrintWriter pw;
    String INPUT = "";
    void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        pw = new PrintWriter(System.out);

        long s = System.currentTimeMillis();
        solve();
        pw.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }

    public static void main(String[] args) throws Exception { new A().run(); }

    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;

    private int readByte() {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }

    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }

    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }

    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }

    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }

    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }

        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }

        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private void tr(Object... o) { if(INPUT.length() > 0)System.out.println(Arrays.deepToString(o)); }
}