_{This problem is a programming version of Problem 183 from projecteuler.net}

Let be a positive integer and let be split into equal parts, , so that .

Let be the product of these parts, .

For example, if is split into five equal parts, , then .

Let for a given value of .

It turns out that the maximum for is found by splitting eleven into four equal parts which leads to ; that is, , which is a terminating decimal.

However, for the maximum is achieved by splitting it into three equal parts, so , which is a non-terminating decimal.

Let if is a non-terminating decimal and if is a terminating decimal.

For example, for is .

Find for .