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.Scanner;
import java.util.StringTokenizer;

public class B {
	public static Scanner sc = new Scanner(System.in);
	public static StringTokenizer st;
	public static void main(String[] args) {
		String non_beaut = getLine();
		// Three DPS namely 1,2,3
		int[][] dp = new int[non_beaut.length()+1][3];
		dp[0][0] = 0;
		dp[0][1]= 0;
		dp[0][2] = 0;
		for (int index = 0;index  < non_beaut.length();index++){
			if(non_beaut.charAt(index) == 'a'){
				dp[index +1][0] = dp[index][0] + 1;
				dp[index+1][1] = Math.max(dp[index+1][0],dp[index][1]); // Either preserver from previous, or use current.
				dp[index+1][2] = Math.max(Math.max(dp[index][0]+1, dp[index][1]+1),dp[index][2]+1);
			}
			else{
				dp[index+1][0] = dp[index][0];
				dp[index+1][1] = Math.max(dp[index][0]+1, dp[index][1] + 1);
				dp[index+1][2] = Math.max(Math.max(dp[index+1][0], dp[index+1][1]),dp[index][2]);
			}
		}
		System.out.println(Math.max(Math.max(dp[non_beaut.length()][0], dp[non_beaut.length()][1]),dp[non_beaut.length()][2]));
	}
	public static int getInt(){
		if (st != null && st.hasMoreTokens()){
			return Integer.parseInt(st.nextToken());
		}
		st = new StringTokenizer(sc.nextLine());
		return Integer.parseInt(st.nextToken());
	}
	public static long getLong(){
		if (st != null && st.hasMoreTokens()){
			return Long.parseLong(st.nextToken());
		}
		st = new StringTokenizer(sc.nextLine());
		return Long.parseLong(st.nextToken());
	}
	public static double getDouble(){
		if (st != null && st.hasMoreTokens()){
			return Double.parseDouble(st.nextToken());
		}
		st = new StringTokenizer(sc.nextLine());
		return Double.parseDouble(st.nextToken());
	}
	public static String getString(){
		if(st != null && st.hasMoreTokens()){
			return st.nextToken();
		}
		st = new StringTokenizer(sc.nextLine());
		return st.nextToken();
	}
	public static String getLine(){
		return sc.nextLine();
	}
	public static int[][] readMatrix(int lines,int cols){
		int[][] matrr = new int[lines][cols];
		for (int i = 0;i < lines;i++){
			for(int j = 0;j < cols;j++){
				matrr[i][j] = getInt();
			}
		}
		return matrr;
	}
	public static int[] readArray(int lines){
		int[] ar = new int[lines];		
		for (int i = 0;i<lines;i++) ar[i] =getInt();
		return ar;
	}
	
}