Let \(T = \{9^k : k ~ \mbox{is an integer}, 0 \le k \le 4000\}\). Given that \(9^{4000}_{}\) has \(3817\) digits and that its first (leftmost) digit is \(9\), how many elements of \(T_{}^{}\) have \(9\) as their leftmost digit?

(第八届AIME1990 第13题)