Alice and Bob take turns saying numbers. Alice starts by saying "$1$". Bob then says "$1,2$". Alice then says "$1,2,3,4$". Bob then says "$1,2,3,4,5,6,7,8$", and so on. In each turn, the number of digits said is double the number of digits said in the previous turn. What is the $60^{\text{th}}$ number said?