CF1398B Substring Removal Game

Alice and Bob play a game. They have a binary string $ s $ (a string such that each character in it is either $ 0 $ or $ 1 $ ). Alice moves first, then Bob, then Alice again, and so on. During their move, the player can choose any number (not less than one) of consecutive equal characters in $ s $ and delete them. For example, if the string is $ 10110 $ , there are $ 6 $ possible moves (deleted characters are bold): 1. $ \textbf{1}0110 \to 0110 $ ; 2. $ 1\textbf{0}110 \to 1110 $ ; 3. $ 10\textbf{1}10 \to 1010 $ ; 4. $ 101\textbf{1}0 \to 1010 $ ; 5. $ 10\textbf{11}0 \to 100 $ ; 6. $ 1011\textbf{0} \to 1011 $ . After the characters are removed, the characters to the left and to the right of the removed block become adjacent. I. e. the following sequence of moves is valid: $ 10\textbf{11}0 \to 1\textbf{00} \to 1 $ . The game ends when the string becomes empty, and the score of each player is the number of $ 1 $ -characters deleted by them. Each player wants to maximize their score. Calculate the resulting score of Alice.

The first line contains one integer $ T $ ( $ 1 \le T \le 500 $ ) — the number of test cases. Each test case contains exactly one line containing a binary string $ s $ ( $ 1 \le |s| \le 100 $ ).

For each test case, print one integer — the resulting score of Alice (the number of $ 1 $ -characters deleted by her).

Questions about the optimal strategy will be ignored.