24 Point Game Expression Count

The 24 Point Game is played by drawing 4 cards from a deck. The challenge is to combine the 4 given positive integers with the operators +, -, *, / and any necessary parentheses to form a valid expression that evaluates to \(24\). Two expressions are considered the same if their string representations (with full parenthesization) are identical. Given any 4 positive integers \(a, b, c, d\), count the number of distinct expressions that evaluate exactly to \(24\).

inputFormat

Four space-separated positive integers (a), (b), (c), (d).

outputFormat

An integer representing the count of distinct expressions that evaluate to (24).

sample

1 1 1 1

0