4121: Singer House
内存限制：256 MB
时间限制：2 S
标准输入输出
题目类型：传统
评测方式：文本比较
上传者：
提交：2
通过：0
题目描述
D. Singer House
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output
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.
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.
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.
Examples
Input
2
Output
9
Input
3
Output
245
Input
20
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.
Singer 2-house
输入样例 复制
输出样例 复制