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

For example,

8  =  (4   *  (1   +   3)) /   2
14 =   4   *  (3   +   1   /   2)
19 =   4   *  (2   +   3)  ?   1
36 =   3   *   4   *  (2   +   1)

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.