By using each of the digits from the set, $\{1,2,3,4\}$, exactly once, and making use of the four arithmetic operations ($+,-,\times ,/$) and brackets/parentheses, it is possible to form different positive integer targets.

For example,

$$\begin{array}{rl}8& =(4\times (1+3))/2\\ 14& =4\times (3+1/2)\\ 19& =4\times (2+3)-1\\ 36& =3\times 4\times (2+1)\end{array}$$

Note that concatenations of the digits, like $12+34$, are not allowed.

Using the set, $\{1,2,3,4\}$, it is possible to obtain thirty-one different target numbers of which $36$ is the maximum, and each of the numbers $1$ to $28$ can be obtained before encountering the first non-expressible number.

Find the set of four distinct digits, $a<b<c<d$, for which the longest set of consecutive positive integers, $1$ to $n$, can be obtained, giving your answer as a string: abcd.