2021 AMC Fall 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 is $$f(2) + f(3) + f(4) + f(5)+ f(6)?$$