Alex has completed the game and beaten the rankth strongest player at every level. Now it's Charlie's turn to play. Whenever a player is beaten, Charlie's health decreases by the amount of strength of that player. So the initial health of Charlie must be greater than or equal to the sum of the strengths of players that are beaten throughout the game. Charlie does not want to lose to Alex, so Charlie decided to also beat the rankth strongest player at each level. What is the minimum initial health that Charlie needs to start with in order to do this?