题目描述

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.

输入要求

There are muiltply cases;
One case contains a single line with a single integer representing N, as above.

输出要求

The Output  contains a single line with a single integer that tells how many same-sum partitions can be made from the set {1, 2, ..., N}. The output file should contain 0 if there are no ways to make a same-sum partition.

输入样例

7

输出样例

4

提示

来源

USACO