Monsters Battle

Chef and Chefina are playing a game. Chef has $N$ monsters (numbered $1$ through $N$). For each valid $i$, the $i$-th monster has a value $V_{1,i}$ and it is either in attack mode or defense mode. The initial states of the monsters are described by a string $D_1$: for each valid $i$, the $i$-th monster is in attack mode if the $i$-th character of $D_1$ is 'A' or in defense mode if the $i$-th ch