$7.$ A baseball league needs to track the teams and games. The requirements are the following:

$$ A league has many teams.

$$ A team has at least $12$ players and up to $16$ players with last names, first names, and SSNs$.$

$$ A team has at least one coach and up to three coaches with last names and first names, titles and their availabilities.

$$ A player may actively play for one team at a time; however, the player could have played for other team$($s$)$ before. It is necessary to track the team$($s$)$ a player has played. It is possible that a player may not play for any team.

$$ Each team plays a game with other teams in the league each year.

$$ A game consists of a home team and a visiting $($away$)$ team; it is required to know which two teams play a game.

$$ A game has a date, time and location to play.

$$ A game also includes the final scores and errors for both home and way teams.

$$ Not all the players in a team will participate in each game, you need to know who are available and whether a player in a team plays or not.

$$ A game normally consists of nine innings, but it may have extra innings if the scores are tied and require an extra inning$($s$)$ to decide which team wins the game.

$$ There is a score, number of hits, and number of errors for each team in each inning.

$$ If a player plays a game, the player$$s performance is recorded by a coach at the end of each game with a scale of $1($worst$)$ to $5($best$).$

Please design a database with ERD using IE notation. This E$/$R diagram should include entities, relationships, attributes, and constraints. You need to specify primary keys and foreign keys for all entities. You also need to specify the rationale for your design. $(25$ points$)$