I4.4 Let $a_{1}, a_{2}, \ldots, a_{R}$ be positive integers such that $a_{1}<a_{2}<a_{3}<\ldots<a_{R-1}<a_{R}$. Given that the sum of these $R$ integers is 90 and the maximum value of $a_{1}$ is $S$, find the value of $S$.
$\begin{array}{l}a_{1}+a_{2}+\ldots+a_{12}=90 \\ a_{1}+\left(a_{1}+1\right)+\left(a_{1}+2\right)+\ldots+\left(a_{1}+11\right) \leq 90 \\ 12 a_{1}+55 \leq 90 \\ a_{1} \leq 2.9167 \\ S=\text { maximum value of } a_{1}=2\end{array}$