| # 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. |