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'.

Input

Input is given from Standard Input in the following format:
S

Output

Print the minimum possible unbalancedness of S'.

Constraints

• $1 \leq |S| \leq 10^6$
• Each character of S is 0, 1, or ?.

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

见题面 Input 部分

见题面 Output 部分