Bernardo and Silvia play the following game. An integer between $0$ and $1999$ inclusive is selected and given to Bernardo. Whenever Bernardo receives a number, he triples it and passes the result to Silvia. Whenever Silvia receives a number, she adds $100$ to it and passes the result to Bernardo. The winner is the last person who produces a number less than $2000$. Let $N$ be the smallest initial number that results in a win for Bernardo. What is the sum of the digits of $N$?