Secret agent Roger is trying to crack a safe containing evil Syrian chemical weapons. In order to crack the safe, Roger needs to insert a key into the safe. The key consists of four digits. Roger has received a list of possible keys from his informants that he needs to try out. Trying out the whole list will take too long, so Roger needs to find a way to reduce the list.
A valid key satisfies a certain condition, which we call the 24 condition. Four digits that satisfy the 24 condition can be manipulated using addition, subtraction, multiplication, division and parentheses, in such a way, that the end result equals 24.
For example, the key (4; 7; 8; 8) satisfies the 24 condition, because (7-8/8)×4 = 24. The key (1; 1; 2; 4) does not satisfy the 24 condition, nor does (1; 1; 1; 1). These keys cannot possibly be the valid key and do not need to be tried.
Write a program that takes the list of possible keys and outputs for each key whether it satisfies the 24 condition or not.