JMO 2000 Problem 2

Let $3n$ cards, denoted by distinct letters $a_1,a_2,\ldots ,a_{3n}$, be put in line in this order from left to right. After each shuffle, the sequence $a_1,a_2,\ldots ,a_{3n}$ is replaced by the sequence $a_3,a_6,\ldots ,a_{3n},a_2,a_5,\ldots ,a_{3n-1},a_1,a_4,\ldots ,a_{3n-2}$. Is it possible to replace the sequence of cards $1,2,\ldots ,192$ by the reverse sequence $192,191,\ldots ,1$ by a finite number of shuffles?