Nested Brackets

In this problem, we will be looking at strings that consist of brackets, '(' and ')'. You are asked to compute how many strings of brackets there are such that the brackets are properly nested. For example, there are two properly nested strings of brackets that are of length 4: "()()" and "(())". Strings "))((", "()((" and ")())" are not properly nested.

The following are all possible properly nested strings of length 6: 

1.  ()()()
2.  (()())
3.  ((()))
4.  (())()
5.  ()(())

Input Specification

Each line of the input corresponds to one test case and contains an integer n, 2 <= n <= 60 that specifies the length of the string of brackets. Input will be terminated by a line containing 0, which should not be processed.

Output Specification

Print an integer representing the number of bracket strings of length n that are properly nested. The answer to each test case should be followed by a newline character.

Sample Input

4
5
6
10
60
0

Sample Output

2
0
5
42
3814986502092304