Convert Strings by Flips 2

*This problem is similar to the problem `"STRFLIP"`. The only difference between them is the number of moves allowed — in this problem, up to $\lfloor N/2 \rfloor + 10$ moves can be made. In Div. 1 and Div. 2 this problem is worth $60$ points and `"STRFLIP"` is worth $40$. In Div. 3 this problem is non-scorable and `"STRFLIP"` is worth $100$ points.* You are given a binary string $A$ of length $N