# p02652 AtCoder Grand Contest 045 - 01 Unbalanced

## Problem Description
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'.

Examples

Input

0??


Output

1


Input

0??0


Output

2


Input

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


Output

4

## Contest Information
- **Contest ID**: 0
- **Problem Index**: 
- **Points**: 0.0
- **Rating**: 0
- **Tags**: 
- **Time Limit**: {'seconds': 2, 'nanos': 0} seconds
- **Memory Limit**: 1073741824 bytes

## Task
Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases.