Problem:
Score : 800 points

Problem Statement

Given is a string S, where each character is 0, 1, or ?.

Consider making a string S' by replacing each occurrence of ? with 0 or 1 (we can choose the character for each ? independently).
Let us define the unbalancedness of S' as follows:

(The unbalancedness of S') = \max \{ The absolute difference between the number of occurrences of 0 and 1 between the l-th and r-th character of S (inclusive) :\ 1 \leq l \leq r \leq |S|\}

Find the minimum possible unbalancedness of S'.

Constraints

1 \leq |S| \leq 10^6

Each character of S is 0, 1, or ?.

Input

Input is given from Standard Input in the following format:

S

Output

Print the minimum possible unbalancedness of S'.

Sample Input 1

0??

Sample Output 1

1

We can make S'= 010 and achieve the minimum possible unbalancedness of 1.

Sample Input 2

0??0

Sample Output 2

2

Sample Input 3

??00????0??0????0?0??00??1???11?1?1???1?11?111???1

Sample Output 3

4

Solution in Ruby (2.7.1) (judge verdict: Runtime Error)

gets.to_i.times{
  gets
  a=gets.split.map &:to_i
  s=gets.chop.chars
  r=0
  b=[]
  a.zip(s).reverse.map{|a,f|
    b.map{a=[a,a^_1].min}
    f[?0]?b<<a:r=1 if a!=0
  }
  p r
}