A man decides to save money by following an interesting pattern. He saves $1 on the first day, $2 on the second day, $3 on the third day, and so on, increasing his daily savings by $1 each day. After a certain number of days, he realizes that the total amount of money he has saved is exactly $2485. How many days did it take for him to save this amount? Let's think step by step and output the final answer within \boxed{}.
user