bernardo and silvia play the following game. an integer between 00 and 999999 inclusive is selected and given to bernardo. whenever bernardo receives a number, he doubles it and passes the result to silvia. whenever silvia receives a number, she adds 5050 to it and passes the result to bernardo. the winner is the last person who produces a number less than 10001000. let nn be the smallest initial number that results in a win for bernardo. what is the sum of the digits of nn?