2021 Fall AMC 10B Problem 19

Let N be the positive integer 7777\ldots777, a 313-digit number where each digit is a 7. Let f(r) be the leading digit of the r{ }th root of N. What isf(2) + f(3) + f(4) + f(5)+ f(6)?(\textbf{A})\: 8\qquad(\textbf{B}) \: 9\qquad(\textbf{C}) \: 11\qquad(\textbf{D}) \: 22\qquad(\textbf{E}) \: 29

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.