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 $S'$.

0??

1

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

0??0

2

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

4