An unbiased single $4$-sided die is thrown and its value, $T$, is noted.
$T$ unbiased $6$-sided dice are thrown and their scores are added together. The sum, $C$, is noted.
$C$ unbiased $8$-sided dice are thrown and their scores are added together. The sum, $O$, is noted.
$O$ unbiased $12$-sided dice are thrown and their scores are added together. The sum, $D$, is noted.
$D$ unbiased $20$-sided dice are thrown and their scores are added together. The sum, $I$, is noted.
Find the variance of $I$, and give your answer rounded to $4$ decimal places.