2020 AIME II Problem 14

For real number x let \lfloor x\rfloor be the greatest integer less than or equal to x, and define \{x\}=x-\lfloor x\rfloor to be the fractional part of x. For example, \{3\}=0 and \{4.56\}=0.56. Define f(x)=x\{x\}, and let N be the number of real-valued solutions to the equation f(f(f(x)))=17 for 0 \leq x \leq 2020. Find the remainder when N is divided by 1000 .