Ruins

An explorer finds the door of an underground treasure house in desert ruins. Two positive integers $a$ and $b$ are carved on the door, and the lock opens only after the problem posed by those two numbers is solved.

Choose positive integers $a_1, a_2, b_1, b_2$ with $a = a_1 \times a_2$ and $b = b_1 \times b_2$. The four numbers may be equal to each other. Sort the four numbers in non-decreasing order as $x_1 \le x_2 \le x_3 \le x_4$ and compute $(x_2 - x_1)^2 + (x_3 - x_2)^2 + (x_4 - x_3)^2$. Find the smallest value this expression takes over all choices.

For example, with $a = 33$ and $b = 40$, the factorizations $33 = 3 \times 11$ and $40 = 5 \times 8$ give the sequence $3, 5, 8, 11$. Its value is $(5 - 3)^2 + (8 - 5)^2 + (11 - 8)^2 = 22$, and no choice gives a smaller value.

The input consists of several data sets. Each line holds two positive integers not greater than 10,000. A line with two zeros marks the end of the input and is not processed.

For each data set, print the minimum value as a single integer on its own line. Print no extra spaces or characters.