ACM

The Association of Chess Monsters (ACM) is planning its annual match against the rest of the world. The match will take place on $30$ boards: $15$ players will play with white pieces, and $15$ players will play with black pieces. ACM has many players to choose from and wants to form the strongest team. Each player's ability for playing with white pieces is measured on a scale from $1$ to $100$, and the same rule applies for playing with black pieces. In the match, a player can only play with either white or black pieces, not both. The team's total strength is the sum of the abilities of the players assigned to white and the abilities of the players assigned to black. Help ACM select a team with the highest possible total strength.