Bernardo and Silvia play the following game. An integer between 0 and 499, inclusive, is selected and given to Bernardo. Whenever Bernardo receives a number, he adds 25 to it and passes the result to Silvia. Whenever Silvia receives a number, she triples it and passes the result to Bernardo. The winner is the last person who produces a number less than 500. Let $N$ be the largest initial number that results in a win for Silvia. What is the sum of the digits of $N$?