Although testing is a technique which does not allow us to prove the correctness of a program, it is used to assess its reliability, thus increasing our confidence in its correctness. In the literature, there are many testing methods to select test cases which are applied as an input to the program. A programmer has the intention of testing a program. With this aim in mind, he needs to know how many test cases he should obtain such that each distinct path of execution is covered with a test case. Your task is to write a program which computes the number of different paths of execution from the initial sentence to the final sentence, in a given program P . Input The first line of the input contains the number of programs. Subsequently, each program is listed. Each program consists of a set of sentences with a keyword per line. The program finishes with the keyword ENDPROGRAM There are only two types of sentences: conditional and non-conditional. A non-conditional sentence is represented by means of the keyword S. A conditional sentence is represented by the keywords IF, ELSE and END_IF. The condition of the IF sentence is omitted (i.e., only the IF keyword appears) and it is supposed that all IF sentences have a corresponding ELSE. So, for example, the shortest program with a conditional sentence would be: IF ELSE END_IF ENDPROGRAM which has 2 paths of execution. Output For every program you are to print a line containing the number N of different paths of execution. It is supposed that N is never greater than 2 ∧ 32. Sample Input 4 IF ELSE END_IF ENDPROGRAM IF S ELSE END_IF IF ELSE S END_IF ENDPROGRAM
2/2 S S S ENDPROGRAM S IF S S ELSE IF IF S ELSE S END_IF S ELSE S END_IF END_IF S ENDPROGRAM Sample Output 2 4 1 4