For many sets of consecutive integers from 1 through N (1 <= N <= 39),
one can partition the set into two sets whose sums are identical.

For example, if N=3, one can partition the set {1, 2, 3} in one way so
that the sums of both subsets are identical:

• {3} and {1,2}
  

This counts as a single partitioning (i.e., reversing the order counts
as the same partitioning and thus does not increase the count of
partitions).

If N=7, there are four ways to partition the set {1, 2, 3, ... 7} so that
each partition has the same sum:

• {1,6,7} and {2,3,4,5}
  
• {2,5,7} and {1,3,4,6}
  
• {3,4,7} and {1,2,5,6}
  
• {1,2,4,7} and {3,5,6}
  

Given N, your program should print the number of ways a set containing
the integers from 1 through N can be partitioned into two sets whose
sums are identical. Print 0 if there are no such ways.

Your program must calculate the answer, not look it up from a table. TA will check your code after the deadline.