Question 181
A student writes the six complex roots of the equation $z^{6} + 2 = 0$ on the blackboard. At every step, he randomly chooses two numbers $a$ and $b$ from the board, erases them, and replaces them with $3ab - 3a - 3b + 4$. At the end of the fifth step, only one number is left. Find the largest possible value of this number.