_{This problem is a programming version of Problem 93 from projecteuler.net}

By using each of the digits from the set, , exactly once, and making use of the four arithmetic operations and brackets/parentheses, it is possible to form different positive integer targets.

For example,

Note that concatenations of the digits, like , are not allowed.

Using the set, , it is possible to obtain thirty-one different target numbers of which 36 is the maximum, and each of the numbers to can be obtained before encountering the first non-expressible number.

Given a set of distinct digits, , find the largest possible integer such that each integer from to is expressible using elements of and following the above rules. If is also not expressible, output instead.