J. Count
time limit per test
1 second
memory limit per test
512 megabytes
input
standard input
output
standard output

Let $$$S(n)$$$ be the set of all trees with $$$n$$$ vertices labelled from $$$1$$$ to $$$n$$$.

For a tree $$$T \in S(n)$$$, we define $$$H(T)=\sum_{i=1}^n \sum_{j=i+1}^n dis(i,j)$$$, where $$$dis(i,j)$$$ is defined as the minimum number of edges that need to pass from vertice $$$i$$$ to vertice $$$j$$$ on the tree.

Please count how many numbers $$$x$$$ satisfying $$$\exists T \in S(n), H(T)=x$$$, and output them in order from small to large.

Input

One line, a positive integer $$$n$$$($$$1\le n \le 20$$$).

Output

The first line contains a single integer $$$cnt$$$ representing how many numbers $$$x$$$ satisfy the condition.

The second line contains $$$cnt$$$ integers from small to large, representing $$$x$$$.

Example
Input
4
Output
2
9 10