Regular expressions are a flexible way to define patterns for searching and replacing text. In this problem, we consider a subset of regular expressions that includes only:

1. Digits from 0 to 9
2. Parentheses
3. The symbol '*', which means any number of repetitions of the character or subexpression in parentheses that precedes it. For example, the expression '345*6' means that after the substring '34' there are zero or more digits '5', followed by the digit '6'. The expression '3(45)*6' means that after the digit '3' there can be zero or more repetitions of the substring '45', followed by the digit '6'.
4. The symbol '|', which means the 'OR' operation. The priority of this operation is lower than the priority of the implicit concatenation operation. For example, the expression '12|345' means the string '12' or the string '345'. The expression '(12|34)5' means that either '12' or '34' comes first, followed by the digit '5'.

One of the applications of regular expressions is to check whether a string matches a given pattern. For example, to check whether an entered non-negative integer is even, you can write the following expression (leading zeros are allowed for simplicity): (0|1|2|3|4|5|6|7|8|9)*(0|2|4|6|8)

Your task is to solve a more complex problem. You need to determine whether it is possible to rearrange the digits in a non-negative integer so that the number is divisible by 6. For example, in the number 123, the digits can be rearranged in the required way, but in the number 31, they cannot. Write a regular expression to perform this check.