Warriors

You are a warrior and you have to fight $N$ enemy warriors (numbered $1$ through $N$) one by one, in any order you choose. You have to win as many of these fights as possible. Each warrior has some amount of power, which changes when the warrior fights. For each $i$, the $i$-th enemy warrior has power $P_i$. When you have power $x$ and you fight an enemy warrior with power $y$, the following happ