For each positive integer n, let f(n) be the sum of the digits in the base-four representation of n, and let g(n) be the sum of the digits in the base-eight representation of f(n). For example, f(2020)= f\left(133210_{\text {four }}\right)=10=12_{\text {eight }}, and g(2020)= the digit sum of 12_{\text {eight }}=3. Let N be the least value of n such that the base-sixteen representation of g(n) cannot be expressed using only the digits 0 through 9. Find the remainder when N is divided by 1000 .