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 PYTHON3):

Solution:
from sys import maxsize, stdout, stdin,stderr
mod = int(1e9+7)
import sys
def I(): return int(stdin.readline())
def lint(): return [int(x) for x in stdin.readline().split()]
def S(): return input().strip()
def grid(r, c): return [lint() for i in range(r)]
from collections import defaultdict, Counter, deque
import math
import heapq
from heapq import heappop , heappush
import bisect
from itertools import groupby
def gcd(a,b): 
    while b:
        a %= b
        tmp = a
        a = b
        b = tmp
    
    return a
 
def lcm(a,b): 
    return a  // gcd(a, b) * b
 
def check_prime(n):
    for i in range(2, int(n ** (1 / 2)) + 1):
        if not n % i:
            return False
    return True
def Bs(a, x):
    i=0
    j=0
    left = 1
    right = x
    flag=False
    while left<right:
        
        mi = (left+right)//2
        #print(smi,a[mi],x)
        
        if a[mi]<=x:
            left = mi+1
            i+=1
            
        else:
 
            right = mi
            j+=1
        #print(left,right,"----")
    #print(i-1,j)
    if left>0 and a[left-1]==x:
        return i-1, j
    else:
        return -1, -1
def nCr(n, r):
 
    return (fact(n) // (fact(r)
                * fact(n - r)))
 
# Returns factorial of n
def fact(n):
 
    res = 1
     
    for i in range(2, n+1):
        res = res * i
         
    return res
def primefactors(n):
    num=0
    
    while n % 2 == 0:
        num+=1
        n = n / 2
    
    for i in range(3,int(math.sqrt(n))+1,2):
         
    
        while n % i== 0:
            num+=1
            n = n // i
               
    
    if n > 2:
        num+=1
    return num
'''
def iter_ds(src):
    store=[src]
    while len(store):
        tmp=store.pop()
        if not vis[tmp]:
            vis[tmp]=True
            for j in ar[tmp]:
                store.append(j)
'''
def ask(a):
    print('? {}'.format(a),flush=True)
    n=I()
    
    return n


 
def dfs(i,p):
    
    a,tmp=0,0
    for j in d[i]:
        if j!=p:
            a+=1
            tmp+=dfs(j,i)
    
    if a==0:
        return 0
    
    return tmp/a + 1 
def primeFactors(n):
    l=[]
    
    while n % 2 == 0:
        l.append(2)
        n = n // 2
         

    if n > 2:
        l.append(n)
    return l
s=S()

ls=0
rs=0
n=len(s)
a,b=0,0
al,bl=[],[]
for i in range(n):
    if s[i]=='a':
        a+=1
    else:
        b+=1
    al.append(a)
    bl.append(b)
al=[0]+al+[al[-1]]
bl=[0]+bl+[bl[-1]]
#print(*al)
#print(*bl)
#print('---------------------------------------------')
ans=0
dp=[[0]*(n+2) for _ in range(n+2)]
for i in range(n+2):
    for j in range(i,n+2):
        dp[i][j]=al[-1]-al[j]+ bl[j]-bl[i]+al[i]
        #print(dp[i],dp[j])
        ans=max(ans,dp[i][j])
#for i in range(n+2):
#    print(*dp[i])

print(ans)