Singer House

2000ms

524288K

Description:

It is known that passages in Singer house are complex and intertwined. Let's define a Singer k-house as a graph built by the following process: take complete binary tree of height k and add edges from each vertex to all its successors, if they are not yet present.

$\text{[math]}$ Singer 4-house

Count the number of non-empty paths in Singer k-house which do not pass the same vertex twice. Two paths are distinct if the sets or the orders of visited vertices are different. Since the answer can be large, output it modulo 10⁹ + 7.

Input:

The only line contains single integer k (1 ≤ k ≤ 400).

Output:

Print single integer — the answer for the task modulo 10⁹ + 7.

Sample Input:

Sample Output:

Sample Input:

Sample Output:

Sample Input:

Sample Output:

550384565

Note:

There are 9 paths in the first example (the vertices are numbered on the picture below): 1, 2, 3, 1-2, 2-1, 1-3, 3-1, 2-1-3, 3-1-2.

$\text{[math]}$ Singer 2-house

Informação

Provedor Codeforces

Código CF830D